%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM926+3 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:53:37 AM UTC 2026
% Result : Theorem 228.32s 233.64s
% Output : Proof 228.44s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint,hypothesis,
is_int(one_one_int),
file('theBenchmark.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).
fof(gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint,axiom,
is_int(zero_zero_int),
file('theBenchmark.p',gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint) ).
fof(gsy_c_HOL_Oundefined_000tc__Int__Oint,axiom,
is_int(undefined_int(int)),
file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Int__Oint) ).
fof(gsy_c_Int2_OMultInv,axiom,
! [B_1_1,B_2_1] :
( ( is_int(B_2_1)
& is_int(B_1_1) )
=> is_int(multInv(B_1_1,B_2_1)) ),
file('theBenchmark.p',gsy_c_Int2_OMultInv) ).
fof(gsy_c_IntFact_Ozfact,axiom,
! [B_1_1] :
( is_int(B_1_1)
=> is_int(zfact(B_1_1)) ),
file('theBenchmark.p',gsy_c_IntFact_Ozfact) ).
fof(gsy_c_Int_OBit0,hypothesis,
! [B_1_1] :
( is_int(B_1_1)
=> is_int(bit0(B_1_1)) ),
file('theBenchmark.p',gsy_c_Int_OBit0) ).
fof(gsy_c_Int_OBit1,hypothesis,
! [B_1_1] :
( is_int(B_1_1)
=> is_int(bit1(B_1_1)) ),
file('theBenchmark.p',gsy_c_Int_OBit1) ).
fof(gsy_c_Int_OMin,axiom,
is_int(min),
file('theBenchmark.p',gsy_c_Int_OMin) ).
fof(gsy_c_Int_OPls,hypothesis,
is_int(pls),
file('theBenchmark.p',gsy_c_Int_OPls) ).
fof(gsy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint,hypothesis,
! [B_1_1] :
( is_int(B_1_1)
=> is_int(number_number_of_int(B_1_1)) ),
file('theBenchmark.p',gsy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint) ).
fof(gsy_c_Residues_OLegendre,axiom,
! [B_1_1,B_2_1] :
( ( is_int(B_2_1)
& is_int(B_1_1) )
=> is_int(legendre(B_1_1,B_2_1)) ),
file('theBenchmark.p',gsy_c_Residues_OLegendre) ).
fof(gsy_c_Residues_OStandardRes,axiom,
! [B_1_1,B_2_1] :
( ( is_int(B_2_1)
& is_int(B_1_1) )
=> is_int(standardRes(B_1_1,B_2_1)) ),
file('theBenchmark.p',gsy_c_Residues_OStandardRes) ).
fof(gsy_c_TwoSquares__Mirabelle__enbualjaop_Osum2sq,axiom,
! [B_1_1] : is_int(twoSqu1241645765sum2sq(B_1_1)),
file('theBenchmark.p',gsy_c_TwoSquares__Mirabelle__enbualjaop_Osum2sq) ).
fof(gsy_c_WilsonRuss_Oinv,axiom,
! [B_1_1,B_2_1] :
( ( is_int(B_2_1)
& is_int(B_1_1) )
=> is_int(inv(B_1_1,B_2_1)) ),
file('theBenchmark.p',gsy_c_WilsonRuss_Oinv) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_bool(hAPP_bool_bool(B_1_1,B_2_1)) ),
file('theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).
fof(gsy_c_hAPP_000tc__Int__Oint_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] :
( is_int(B_2_1)
=> is_bool(hAPP_int_bool(B_1_1,B_2_1)) ),
file('theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000tc__HOL__Obool) ).
fof(gsy_c_hAPP_000tc__Int__Oint_000tc__Int__Oint,hypothesis,
! [B_1_1,B_2_1] :
( is_int(B_2_1)
=> is_int(hAPP_int_int(B_1_1,B_2_1)) ),
file('theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000tc__Int__Oint) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_nat_bool(B_1_1,B_2_1)),
file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint,hypothesis,
! [B_1_1,B_2_1] : is_int(hAPP_nat_int(B_1_1,B_2_1)),
file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint) ).
fof(gsy_c_hAPP_000tc__RealDef__Oreal_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_real_bool(B_1_1,B_2_1)),
file('theBenchmark.p',gsy_c_hAPP_000tc__RealDef__Oreal_000tc__HOL__Obool) ).
fof(gsy_c_member_000tc__Int__Oint,axiom,
! [B_1_1,B_2_1] :
( is_int(B_1_1)
=> is_bool(member_int(B_1_1,B_2_1)) ),
file('theBenchmark.p',gsy_c_member_000tc__Int__Oint) ).
fof(gsy_v_m,hypothesis,
is_int(m),
file('theBenchmark.p',gsy_v_m) ).
fof(gsy_v_s1____,axiom,
is_int(s1),
file('theBenchmark.p',gsy_v_s1____) ).
fof(gsy_v_s____,axiom,
is_int(s),
file('theBenchmark.p',gsy_v_s____) ).
fof(gsy_v_t____,axiom,
is_int(t),
file('theBenchmark.p',gsy_v_t____) ).
fof(fact_0_tpos,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
file('theBenchmark.p',fact_0_tpos) ).
fof(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,axiom,
( t = one_one_int
=> ? [X,Y] :
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y),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(Y)
& is_int(X) ) ),
file('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(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,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
=> ? [X,Y] :
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y),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(Y)
& is_int(X) ) ),
file('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(fact_3_t__l__p,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('theBenchmark.p',fact_3_t__l__p) ).
fof(fact_4_p,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('theBenchmark.p',fact_4_p) ).
fof(fact_5_t,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('theBenchmark.p',fact_5_t) ).
fof(fact_6_qf1pt,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('theBenchmark.p',fact_6_qf1pt) ).
fof(fact_7_zadd__power2,axiom,
! [A,B] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(A),B)),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(A),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)))),A)),B))),hAPP_nat_int(power_power_int(B),number_number_of_nat(bit0(bit1(pls))))),
file('theBenchmark.p',fact_7_zadd__power2) ).
fof(fact_8_zadd__power3,axiom,
! [A,B] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(A),B)),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(A),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(A),number_number_of_nat(bit0(bit1(pls)))))),B))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit1(bit1(pls)))),A)),hAPP_nat_int(power_power_int(B),number_number_of_nat(bit0(bit1(pls))))))),hAPP_nat_int(power_power_int(B),number_number_of_nat(bit1(bit1(pls))))),
file('theBenchmark.p',fact_8_zadd__power3) ).
fof(fact_9_power2__sum,axiom,
! [X_2,Y_2] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X_2),Y_2)),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(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_2),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)))),X_2)),Y_2)),
file('theBenchmark.p',fact_9_power2__sum) ).
fof(fact_10_power2__sum,axiom,
! [X_2,Y_2] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(plus_plus_nat(X_2),Y_2)),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(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(Y_2),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)))),X_2)),Y_2)),
file('theBenchmark.p',fact_10_power2__sum) ).
fof(fact_11_power2__sum,axiom,
! [X_2,Y_2] : hAPP_nat_real(power_power_real(hAPP_real_real(plus_plus_real(X_2),Y_2)),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(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_2),number_number_of_nat(bit0(bit1(pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),X_2)),Y_2)),
file('theBenchmark.p',fact_11_power2__sum) ).
fof(fact_12_power2__eq__square__number__of,axiom,
! [W_16] : hAPP_nat_int(power_power_int(number_number_of_int(W_16)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(times_times_int(number_number_of_int(W_16)),number_number_of_int(W_16)),
file('theBenchmark.p',fact_12_power2__eq__square__number__of) ).
fof(fact_13_power2__eq__square__number__of,axiom,
! [W_16] : hAPP_nat_real(power_power_real(number267125858f_real(W_16)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_real_real(times_times_real(number267125858f_real(W_16)),number267125858f_real(W_16)),
file('theBenchmark.p',fact_13_power2__eq__square__number__of) ).
fof(fact_14_power2__eq__square__number__of,axiom,
! [W_16] : hAPP_nat_nat(power_power_nat(number_number_of_nat(W_16)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(times_times_nat(number_number_of_nat(W_16)),number_number_of_nat(W_16)),
file('theBenchmark.p',fact_14_power2__eq__square__number__of) ).
fof(fact_15_cube__square,axiom,
! [A] : hAPP_int_int(times_times_int(A),hAPP_nat_int(power_power_int(A),number_number_of_nat(bit0(bit1(pls))))) = hAPP_nat_int(power_power_int(A),number_number_of_nat(bit1(bit1(pls)))),
file('theBenchmark.p',fact_15_cube__square) ).
fof(fact_16_one__power2,axiom,
hAPP_nat_int(power_power_int(one_one_int),number_number_of_nat(bit0(bit1(pls)))) = one_one_int,
file('theBenchmark.p',fact_16_one__power2) ).
fof(fact_17_one__power2,axiom,
hAPP_nat_nat(power_power_nat(one_one_nat),number_number_of_nat(bit0(bit1(pls)))) = one_one_nat,
file('theBenchmark.p',fact_17_one__power2) ).
fof(fact_18_one__power2,axiom,
hAPP_nat_real(power_power_real(one_one_real),number_number_of_nat(bit0(bit1(pls)))) = one_one_real,
file('theBenchmark.p',fact_18_one__power2) ).
fof(fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X_26] : hAPP_int_int(times_times_int(X_26),X_26) = hAPP_nat_int(power_power_int(X_26),number_number_of_nat(bit0(bit1(pls)))),
file('theBenchmark.p',fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X_26] : hAPP_real_real(times_times_real(X_26),X_26) = hAPP_nat_real(power_power_real(X_26),number_number_of_nat(bit0(bit1(pls)))),
file('theBenchmark.p',fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X_26] : hAPP_nat_nat(times_times_nat(X_26),X_26) = hAPP_nat_nat(power_power_nat(X_26),number_number_of_nat(bit0(bit1(pls)))),
file('theBenchmark.p',fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(fact_22_power2__eq__square,axiom,
! [A_112] : hAPP_nat_int(power_power_int(A_112),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(times_times_int(A_112),A_112),
file('theBenchmark.p',fact_22_power2__eq__square) ).
fof(fact_23_power2__eq__square,axiom,
! [A_112] : hAPP_nat_real(power_power_real(A_112),number_number_of_nat(bit0(bit1(pls)))) = hAPP_real_real(times_times_real(A_112),A_112),
file('theBenchmark.p',fact_23_power2__eq__square) ).
fof(fact_24_power2__eq__square,axiom,
! [A_112] : hAPP_nat_nat(power_power_nat(A_112),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(times_times_nat(A_112),A_112),
file('theBenchmark.p',fact_24_power2__eq__square) ).
fof(fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
! [X_25,N_40] : hAPP_nat_int(power_power_int(X_25),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_40)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X_25),N_40)),hAPP_nat_int(power_power_int(X_25),N_40)),
file('theBenchmark.p',fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
fof(fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
! [X_25,N_40] : hAPP_nat_real(power_power_real(X_25),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_40)) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X_25),N_40)),hAPP_nat_real(power_power_real(X_25),N_40)),
file('theBenchmark.p',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
fof(fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
! [X_25,N_40] : hAPP_nat_nat(power_power_nat(X_25),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_40)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X_25),N_40)),hAPP_nat_nat(power_power_nat(X_25),N_40)),
file('theBenchmark.p',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
fof(fact_28_add__special_I2_J,axiom,
! [W_15] : hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(W_15)) = number_number_of_int(hAPP_int_int(plus_plus_int(bit1(pls)),W_15)),
file('theBenchmark.p',fact_28_add__special_I2_J) ).
fof(fact_29_add__special_I2_J,axiom,
! [W_15] : hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(W_15)) = number267125858f_real(hAPP_int_int(plus_plus_int(bit1(pls)),W_15)),
file('theBenchmark.p',fact_29_add__special_I2_J) ).
fof(fact_30_add__special_I3_J,axiom,
! [V_21] : hAPP_int_int(plus_plus_int(number_number_of_int(V_21)),one_one_int) = number_number_of_int(hAPP_int_int(plus_plus_int(V_21),bit1(pls))),
file('theBenchmark.p',fact_30_add__special_I3_J) ).
fof(fact_31_add__special_I3_J,axiom,
! [V_21] : hAPP_real_real(plus_plus_real(number267125858f_real(V_21)),one_one_real) = number267125858f_real(hAPP_int_int(plus_plus_int(V_21),bit1(pls))),
file('theBenchmark.p',fact_31_add__special_I3_J) ).
fof(fact_32_one__add__one__is__two,axiom,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
file('theBenchmark.p',fact_32_one__add__one__is__two) ).
fof(fact_33_one__add__one__is__two,axiom,
hAPP_real_real(plus_plus_real(one_one_real),one_one_real) = number267125858f_real(bit0(bit1(pls))),
file('theBenchmark.p',fact_33_one__add__one__is__two) ).
fof(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_,axiom,
~ ! [T_1] :
( is_int(T_1)
=> 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_1) ),
file('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(fact_35_zle__refl,axiom,
! [W] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),W)),
file('theBenchmark.p',fact_35_zle__refl) ).
fof(fact_36_zle__linear,axiom,
! [Z,W] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z),W)) ),
file('theBenchmark.p',fact_36_zle__linear) ).
fof(fact_37_zless__le,axiom,
! [Z_1,W_1] :
( ( is_int(W_1)
& is_int(Z_1) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),W_1))
<=> ( Z_1 != W_1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_1),W_1)) ) ) ),
file('theBenchmark.p',fact_37_zless__le) ).
fof(fact_38_zless__linear,axiom,
! [X_1,Y_1] :
( ( is_int(Y_1)
& is_int(X_1) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),X_1))
| X_1 = Y_1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1)) ) ),
file('theBenchmark.p',fact_38_zless__linear) ).
fof(fact_39_zle__trans,axiom,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),J_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,J_1),K_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),K_1)) ) ),
file('theBenchmark.p',fact_39_zle__trans) ).
fof(fact_40_zle__antisym,axiom,
! [Z,W] :
( ( is_int(W)
& is_int(Z) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z),W))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z))
=> Z = W ) ) ),
file('theBenchmark.p',fact_40_zle__antisym) ).
fof(fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X_24,P_7,Q_7] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X_24),P_7)),Q_7) = hAPP_nat_int(power_power_int(X_24),hAPP_nat_nat(times_times_nat(P_7),Q_7)),
file('theBenchmark.p',fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X_24,P_7,Q_7] : hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(X_24),P_7)),Q_7) = hAPP_nat_real(power_power_real(X_24),hAPP_nat_nat(times_times_nat(P_7),Q_7)),
file('theBenchmark.p',fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X_24,P_7,Q_7] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(X_24),P_7)),Q_7) = hAPP_nat_nat(power_power_nat(X_24),hAPP_nat_nat(times_times_nat(P_7),Q_7)),
file('theBenchmark.p',fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X_23] :
( is_int(X_23)
=> hAPP_nat_int(power_power_int(X_23),one_one_nat) = X_23 ),
file('theBenchmark.p',fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X_23] : hAPP_nat_real(power_power_real(X_23),one_one_nat) = X_23,
file('theBenchmark.p',fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X_23] : hAPP_nat_nat(power_power_nat(X_23),one_one_nat) = X_23,
file('theBenchmark.p',fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_47_zpower__zpower,axiom,
! [X_1,Y_1,Z] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X_1),Y_1)),Z) = hAPP_nat_int(power_power_int(X_1),hAPP_nat_nat(times_times_nat(Y_1),Z)),
file('theBenchmark.p',fact_47_zpower__zpower) ).
fof(fact_48_le__number__of__eq__not__less,axiom,
! [V_7,W_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(V_7)),number_number_of_int(W_1)))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(W_1)),number_number_of_int(V_7))) ),
file('theBenchmark.p',fact_48_le__number__of__eq__not__less) ).
fof(fact_49_le__number__of__eq__not__less,axiom,
! [V_7,W_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(V_7)),number_number_of_nat(W_1)))
<=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(W_1)),number_number_of_nat(V_7))) ),
file('theBenchmark.p',fact_49_le__number__of__eq__not__less) ).
fof(fact_50_le__number__of__eq__not__less,axiom,
! [V_7,W_1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(V_7)),number267125858f_real(W_1)))
<=> ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(W_1)),number267125858f_real(V_7))) ),
file('theBenchmark.p',fact_50_le__number__of__eq__not__less) ).
fof(fact_51_less__number__of,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X_2)),number_number_of_int(Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),Y_2)) ),
file('theBenchmark.p',fact_51_less__number__of) ).
fof(fact_52_less__number__of,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X_2)),number267125858f_real(Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),Y_2)) ),
file('theBenchmark.p',fact_52_less__number__of) ).
fof(fact_53_le__number__of,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X_2)),number_number_of_int(Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),Y_2)) ),
file('theBenchmark.p',fact_53_le__number__of) ).
fof(fact_54_le__number__of,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X_2)),number267125858f_real(Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),Y_2)) ),
file('theBenchmark.p',fact_54_le__number__of) ).
fof(fact_55_zadd__zless__mono,axiom,
! [Z_10,Z,W_14,W] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_14),W))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_10),Z))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(W_14),Z_10)),hAPP_int_int(plus_plus_int(W),Z))) ) ),
file('theBenchmark.p',fact_55_zadd__zless__mono) ).
fof(fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X_22,P_6,Q_6] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X_22),P_6)),hAPP_nat_int(power_power_int(X_22),Q_6)) = hAPP_nat_int(power_power_int(X_22),hAPP_nat_nat(plus_plus_nat(P_6),Q_6)),
file('theBenchmark.p',fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X_22,P_6,Q_6] : hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X_22),P_6)),hAPP_nat_real(power_power_real(X_22),Q_6)) = hAPP_nat_real(power_power_real(X_22),hAPP_nat_nat(plus_plus_nat(P_6),Q_6)),
file('theBenchmark.p',fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X_22,P_6,Q_6] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X_22),P_6)),hAPP_nat_nat(power_power_nat(X_22),Q_6)) = hAPP_nat_nat(power_power_nat(X_22),hAPP_nat_nat(plus_plus_nat(P_6),Q_6)),
file('theBenchmark.p',fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_59_zpower__zadd__distrib,axiom,
! [X_1,Y_1,Z] : hAPP_nat_int(power_power_int(X_1),hAPP_nat_nat(plus_plus_nat(Y_1),Z)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X_1),Y_1)),hAPP_nat_int(power_power_int(X_1),Z)),
file('theBenchmark.p',fact_59_zpower__zadd__distrib) ).
fof(fact_60_nat__mult__2,axiom,
! [Z] : hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),Z) = hAPP_nat_nat(plus_plus_nat(Z),Z),
file('theBenchmark.p',fact_60_nat__mult__2) ).
fof(fact_61_nat__mult__2__right,axiom,
! [Z] : hAPP_nat_nat(times_times_nat(Z),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(plus_plus_nat(Z),Z),
file('theBenchmark.p',fact_61_nat__mult__2__right) ).
fof(fact_62_nat__1__add__1,axiom,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
file('theBenchmark.p',fact_62_nat__1__add__1) ).
fof(fact_63_less__int__code_I16_J,axiom,
! [K1,K2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K1)),bit1(K2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2)) ),
file('theBenchmark.p',fact_63_less__int__code_I16_J) ).
fof(fact_64_rel__simps_I17_J,axiom,
! [K,L_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),bit1(L_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L_1)) ),
file('theBenchmark.p',fact_64_rel__simps_I17_J) ).
fof(fact_65_less__eq__int__code_I16_J,axiom,
! [K1,K2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K1)),bit1(K2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2)) ),
file('theBenchmark.p',fact_65_less__eq__int__code_I16_J) ).
fof(fact_66_rel__simps_I34_J,axiom,
! [K,L_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),bit1(L_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L_1)) ),
file('theBenchmark.p',fact_66_rel__simps_I34_J) ).
fof(fact_67_rel__simps_I2_J,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
file('theBenchmark.p',fact_67_rel__simps_I2_J) ).
fof(fact_68_less__int__code_I13_J,axiom,
! [K1,K2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(K1)),bit0(K2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2)) ),
file('theBenchmark.p',fact_68_less__int__code_I13_J) ).
fof(fact_69_rel__simps_I14_J,axiom,
! [K,L_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(K)),bit0(L_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L_1)) ),
file('theBenchmark.p',fact_69_rel__simps_I14_J) ).
fof(fact_70_rel__simps_I19_J,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)),
file('theBenchmark.p',fact_70_rel__simps_I19_J) ).
fof(fact_71_less__eq__int__code_I13_J,axiom,
! [K1,K2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(K1)),bit0(K2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2)) ),
file('theBenchmark.p',fact_71_less__eq__int__code_I13_J) ).
fof(fact_72_rel__simps_I31_J,axiom,
! [K,L_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(K)),bit0(L_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L_1)) ),
file('theBenchmark.p',fact_72_rel__simps_I31_J) ).
fof(fact_73_less__number__of__int__code,axiom,
! [K,L_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(K)),number_number_of_int(L_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L_1)) ),
file('theBenchmark.p',fact_73_less__number__of__int__code) ).
fof(fact_74_less__eq__number__of__int__code,axiom,
! [K,L_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(K)),number_number_of_int(L_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L_1)) ),
file('theBenchmark.p',fact_74_less__eq__number__of__int__code) ).
fof(fact_75_zadd__strict__right__mono,axiom,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),J_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(I_1),K_1)),hAPP_int_int(plus_plus_int(J_1),K_1))) ),
file('theBenchmark.p',fact_75_zadd__strict__right__mono) ).
fof(fact_76_zadd__left__mono,axiom,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),J_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(K_1),I_1)),hAPP_int_int(plus_plus_int(K_1),J_1))) ),
file('theBenchmark.p',fact_76_zadd__left__mono) ).
fof(fact_77_add__nat__number__of,axiom,
! [V_6,V] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls))
=> ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_6),pls))
=> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V)),number_number_of_nat(V_6)) = number_number_of_nat(hAPP_int_int(plus_plus_int(V),V_6)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_6),pls))
=> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V)),number_number_of_nat(V_6)) = number_number_of_nat(V) ) ) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls))
=> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V)),number_number_of_nat(V_6)) = number_number_of_nat(V_6) ) ),
file('theBenchmark.p',fact_77_add__nat__number__of) ).
fof(fact_78_nat__numeral__1__eq__1,axiom,
number_number_of_nat(bit1(pls)) = one_one_nat,
file('theBenchmark.p',fact_78_nat__numeral__1__eq__1) ).
fof(fact_79_Numeral1__eq1__nat,axiom,
one_one_nat = number_number_of_nat(bit1(pls)),
file('theBenchmark.p',fact_79_Numeral1__eq1__nat) ).
fof(fact_80_rel__simps_I29_J,axiom,
! [K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),pls))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),pls)) ),
file('theBenchmark.p',fact_80_rel__simps_I29_J) ).
fof(fact_81_rel__simps_I5_J,axiom,
! [K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(K)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K)) ),
file('theBenchmark.p',fact_81_rel__simps_I5_J) ).
fof(fact_82_less__eq__int__code_I15_J,axiom,
! [K1,K2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K1)),bit0(K2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2)) ),
file('theBenchmark.p',fact_82_less__eq__int__code_I15_J) ).
fof(fact_83_rel__simps_I33_J,axiom,
! [K,L_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),bit0(L_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L_1)) ),
file('theBenchmark.p',fact_83_rel__simps_I33_J) ).
fof(fact_84_less__int__code_I14_J,axiom,
! [K1,K2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(K1)),bit1(K2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2)) ),
file('theBenchmark.p',fact_84_less__int__code_I14_J) ).
fof(fact_85_rel__simps_I15_J,axiom,
! [K,L_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(K)),bit1(L_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L_1)) ),
file('theBenchmark.p',fact_85_rel__simps_I15_J) ).
fof(fact_86_zless__imp__add1__zle,axiom,
! [W,Z] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),Z))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(W),one_one_int)),Z)) ),
file('theBenchmark.p',fact_86_zless__imp__add1__zle) ).
fof(fact_87_add1__zle__eq,axiom,
! [W_1,Z_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(W_1),one_one_int)),Z_1))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_1)) ),
file('theBenchmark.p',fact_87_add1__zle__eq) ).
fof(fact_88_zle__add1__eq__le,axiom,
! [W_1,Z_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),hAPP_int_int(plus_plus_int(Z_1),one_one_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z_1)) ),
file('theBenchmark.p',fact_88_zle__add1__eq__le) ).
fof(fact_89_zprime__2,axiom,
hBOOL(hAPP_int_bool(zprime,number_number_of_int(bit0(bit1(pls))))),
file('theBenchmark.p',fact_89_zprime__2) ).
fof(fact_90_is__mult__sum2sq,axiom,
! [Y_1,X_1] :
( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X_1))
=> ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,Y_1))
=> hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(X_1),Y_1))) ) ),
file('theBenchmark.p',fact_90_is__mult__sum2sq) ).
fof(fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [Lx_6,Ly_4,Rx_6,Ry_4] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_6),Ly_4)),hAPP_int_int(times_times_int(Rx_6),Ry_4)) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_6),Rx_6)),hAPP_int_int(times_times_int(Ly_4),Ry_4)),
file('theBenchmark.p',fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [Lx_6,Ly_4,Rx_6,Ry_4] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_6),Ly_4)),hAPP_nat_nat(times_times_nat(Rx_6),Ry_4)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_6),Rx_6)),hAPP_nat_nat(times_times_nat(Ly_4),Ry_4)),
file('theBenchmark.p',fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [Lx_6,Ly_4,Rx_6,Ry_4] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_6),Ly_4)),hAPP_real_real(times_times_real(Rx_6),Ry_4)) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_6),Rx_6)),hAPP_real_real(times_times_real(Ly_4),Ry_4)),
file('theBenchmark.p',fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [Lx_5,Ly_3,Rx_5,Ry_3] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_5),Ly_3)),hAPP_int_int(times_times_int(Rx_5),Ry_3)) = hAPP_int_int(times_times_int(Rx_5),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_5),Ly_3)),Ry_3)),
file('theBenchmark.p',fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [Lx_5,Ly_3,Rx_5,Ry_3] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_5),Ly_3)),hAPP_nat_nat(times_times_nat(Rx_5),Ry_3)) = hAPP_nat_nat(times_times_nat(Rx_5),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_5),Ly_3)),Ry_3)),
file('theBenchmark.p',fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [Lx_5,Ly_3,Rx_5,Ry_3] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_5),Ly_3)),hAPP_real_real(times_times_real(Rx_5),Ry_3)) = hAPP_real_real(times_times_real(Rx_5),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_5),Ly_3)),Ry_3)),
file('theBenchmark.p',fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [Lx_4,Ly_2,Rx_4,Ry_2] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_4),Ly_2)),hAPP_int_int(times_times_int(Rx_4),Ry_2)) = hAPP_int_int(times_times_int(Lx_4),hAPP_int_int(times_times_int(Ly_2),hAPP_int_int(times_times_int(Rx_4),Ry_2))),
file('theBenchmark.p',fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [Lx_4,Ly_2,Rx_4,Ry_2] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_4),Ly_2)),hAPP_nat_nat(times_times_nat(Rx_4),Ry_2)) = hAPP_nat_nat(times_times_nat(Lx_4),hAPP_nat_nat(times_times_nat(Ly_2),hAPP_nat_nat(times_times_nat(Rx_4),Ry_2))),
file('theBenchmark.p',fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [Lx_4,Ly_2,Rx_4,Ry_2] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_4),Ly_2)),hAPP_real_real(times_times_real(Rx_4),Ry_2)) = hAPP_real_real(times_times_real(Lx_4),hAPP_real_real(times_times_real(Ly_2),hAPP_real_real(times_times_real(Rx_4),Ry_2))),
file('theBenchmark.p',fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [Lx_3,Ly_1,Rx_3] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_3),Ly_1)),Rx_3) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_3),Rx_3)),Ly_1),
file('theBenchmark.p',fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [Lx_3,Ly_1,Rx_3] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_3),Ly_1)),Rx_3) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_3),Rx_3)),Ly_1),
file('theBenchmark.p',fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [Lx_3,Ly_1,Rx_3] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_3),Ly_1)),Rx_3) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_3),Rx_3)),Ly_1),
file('theBenchmark.p',fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [Lx_2,Ly,Rx_2] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_2),Ly)),Rx_2) = hAPP_int_int(times_times_int(Lx_2),hAPP_int_int(times_times_int(Ly),Rx_2)),
file('theBenchmark.p',fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [Lx_2,Ly,Rx_2] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_2),Ly)),Rx_2) = hAPP_nat_nat(times_times_nat(Lx_2),hAPP_nat_nat(times_times_nat(Ly),Rx_2)),
file('theBenchmark.p',fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_105_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [Lx_2,Ly,Rx_2] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_2),Ly)),Rx_2) = hAPP_real_real(times_times_real(Lx_2),hAPP_real_real(times_times_real(Ly),Rx_2)),
file('theBenchmark.p',fact_105_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [Lx_1,Rx_1,Ry_1] : hAPP_int_int(times_times_int(Lx_1),hAPP_int_int(times_times_int(Rx_1),Ry_1)) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_1),Rx_1)),Ry_1),
file('theBenchmark.p',fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_107_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [Lx_1,Rx_1,Ry_1] : hAPP_nat_nat(times_times_nat(Lx_1),hAPP_nat_nat(times_times_nat(Rx_1),Ry_1)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_1),Rx_1)),Ry_1),
file('theBenchmark.p',fact_107_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [Lx_1,Rx_1,Ry_1] : hAPP_real_real(times_times_real(Lx_1),hAPP_real_real(times_times_real(Rx_1),Ry_1)) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_1),Rx_1)),Ry_1),
file('theBenchmark.p',fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_109_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [Lx,Rx,Ry] : hAPP_int_int(times_times_int(Lx),hAPP_int_int(times_times_int(Rx),Ry)) = hAPP_int_int(times_times_int(Rx),hAPP_int_int(times_times_int(Lx),Ry)),
file('theBenchmark.p',fact_109_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [Lx,Rx,Ry] : hAPP_nat_nat(times_times_nat(Lx),hAPP_nat_nat(times_times_nat(Rx),Ry)) = hAPP_nat_nat(times_times_nat(Rx),hAPP_nat_nat(times_times_nat(Lx),Ry)),
file('theBenchmark.p',fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [Lx,Rx,Ry] : hAPP_real_real(times_times_real(Lx),hAPP_real_real(times_times_real(Rx),Ry)) = hAPP_real_real(times_times_real(Rx),hAPP_real_real(times_times_real(Lx),Ry)),
file('theBenchmark.p',fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [A_111,B_63] : hAPP_int_int(times_times_int(A_111),B_63) = hAPP_int_int(times_times_int(B_63),A_111),
file('theBenchmark.p',fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [A_111,B_63] : hAPP_nat_nat(times_times_nat(A_111),B_63) = hAPP_nat_nat(times_times_nat(B_63),A_111),
file('theBenchmark.p',fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [A_111,B_63] : hAPP_real_real(times_times_real(A_111),B_63) = hAPP_real_real(times_times_real(B_63),A_111),
file('theBenchmark.p',fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [A_110,B_62,C_35,D_11] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(A_110),B_62)),hAPP_int_int(plus_plus_int(C_35),D_11)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(A_110),C_35)),hAPP_int_int(plus_plus_int(B_62),D_11)),
file('theBenchmark.p',fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [A_110,B_62,C_35,D_11] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(A_110),B_62)),hAPP_nat_nat(plus_plus_nat(C_35),D_11)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(A_110),C_35)),hAPP_nat_nat(plus_plus_nat(B_62),D_11)),
file('theBenchmark.p',fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [A_110,B_62,C_35,D_11] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(A_110),B_62)),hAPP_real_real(plus_plus_real(C_35),D_11)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(A_110),C_35)),hAPP_real_real(plus_plus_real(B_62),D_11)),
file('theBenchmark.p',fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_118_mem__def,axiom,
! [X_2,A_109] :
( hBOOL(member_int(X_2,A_109))
<=> hBOOL(hAPP_int_bool(A_109,X_2)) ),
file('theBenchmark.p',fact_118_mem__def) ).
fof(fact_119_Collect__def,axiom,
! [P_2] : collect_int(P_2) = P_2,
file('theBenchmark.p',fact_119_Collect__def) ).
fof(fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [A_108,B_61,C_34] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(A_108),B_61)),C_34) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(A_108),C_34)),B_61),
file('theBenchmark.p',fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [A_108,B_61,C_34] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(A_108),B_61)),C_34) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(A_108),C_34)),B_61),
file('theBenchmark.p',fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [A_108,B_61,C_34] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(A_108),B_61)),C_34) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(A_108),C_34)),B_61),
file('theBenchmark.p',fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [A_107,B_60,C_33] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(A_107),B_60)),C_33) = hAPP_int_int(plus_plus_int(A_107),hAPP_int_int(plus_plus_int(B_60),C_33)),
file('theBenchmark.p',fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [A_107,B_60,C_33] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(A_107),B_60)),C_33) = hAPP_nat_nat(plus_plus_nat(A_107),hAPP_nat_nat(plus_plus_nat(B_60),C_33)),
file('theBenchmark.p',fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [A_107,B_60,C_33] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(A_107),B_60)),C_33) = hAPP_real_real(plus_plus_real(A_107),hAPP_real_real(plus_plus_real(B_60),C_33)),
file('theBenchmark.p',fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [A_106,C_32,D_10] : hAPP_int_int(plus_plus_int(A_106),hAPP_int_int(plus_plus_int(C_32),D_10)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(A_106),C_32)),D_10),
file('theBenchmark.p',fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [A_106,C_32,D_10] : hAPP_nat_nat(plus_plus_nat(A_106),hAPP_nat_nat(plus_plus_nat(C_32),D_10)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(A_106),C_32)),D_10),
file('theBenchmark.p',fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [A_106,C_32,D_10] : hAPP_real_real(plus_plus_real(A_106),hAPP_real_real(plus_plus_real(C_32),D_10)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(A_106),C_32)),D_10),
file('theBenchmark.p',fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [A_105,C_31,D_9] : hAPP_int_int(plus_plus_int(A_105),hAPP_int_int(plus_plus_int(C_31),D_9)) = hAPP_int_int(plus_plus_int(C_31),hAPP_int_int(plus_plus_int(A_105),D_9)),
file('theBenchmark.p',fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [A_105,C_31,D_9] : hAPP_nat_nat(plus_plus_nat(A_105),hAPP_nat_nat(plus_plus_nat(C_31),D_9)) = hAPP_nat_nat(plus_plus_nat(C_31),hAPP_nat_nat(plus_plus_nat(A_105),D_9)),
file('theBenchmark.p',fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [A_105,C_31,D_9] : hAPP_real_real(plus_plus_real(A_105),hAPP_real_real(plus_plus_real(C_31),D_9)) = hAPP_real_real(plus_plus_real(C_31),hAPP_real_real(plus_plus_real(A_105),D_9)),
file('theBenchmark.p',fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [A_104,C_30] : hAPP_int_int(plus_plus_int(A_104),C_30) = hAPP_int_int(plus_plus_int(C_30),A_104),
file('theBenchmark.p',fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_133_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [A_104,C_30] : hAPP_nat_nat(plus_plus_nat(A_104),C_30) = hAPP_nat_nat(plus_plus_nat(C_30),A_104),
file('theBenchmark.p',fact_133_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_134_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [A_104,C_30] : hAPP_real_real(plus_plus_real(A_104),C_30) = hAPP_real_real(plus_plus_real(C_30),A_104),
file('theBenchmark.p',fact_134_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_135_eq__number__of,axiom,
! [X_2,Y_2] :
( ( is_int(Y_2)
& is_int(X_2) )
=> ( number_number_of_int(X_2) = number_number_of_int(Y_2)
<=> X_2 = Y_2 ) ),
file('theBenchmark.p',fact_135_eq__number__of) ).
fof(fact_136_eq__number__of,axiom,
! [X_2,Y_2] :
( ( is_int(Y_2)
& is_int(X_2) )
=> ( number267125858f_real(X_2) = number267125858f_real(Y_2)
<=> X_2 = Y_2 ) ),
file('theBenchmark.p',fact_136_eq__number__of) ).
fof(fact_137_number__of__reorient,axiom,
! [W_1,X_2] :
( number_number_of_nat(W_1) = X_2
<=> X_2 = number_number_of_nat(W_1) ),
file('theBenchmark.p',fact_137_number__of__reorient) ).
fof(fact_138_number__of__reorient,axiom,
! [W_1,X_2] :
( is_int(X_2)
=> ( number_number_of_int(W_1) = X_2
<=> X_2 = number_number_of_int(W_1) ) ),
file('theBenchmark.p',fact_138_number__of__reorient) ).
fof(fact_139_number__of__reorient,axiom,
! [W_1,X_2] :
( number267125858f_real(W_1) = X_2
<=> X_2 = number267125858f_real(W_1) ),
file('theBenchmark.p',fact_139_number__of__reorient) ).
fof(fact_140_rel__simps_I51_J,axiom,
! [K,L_1] :
( ( is_int(L_1)
& is_int(K) )
=> ( bit1(K) = bit1(L_1)
<=> K = L_1 ) ),
file('theBenchmark.p',fact_140_rel__simps_I51_J) ).
fof(fact_141_rel__simps_I48_J,axiom,
! [K,L_1] :
( ( is_int(L_1)
& is_int(K) )
=> ( bit0(K) = bit0(L_1)
<=> K = L_1 ) ),
file('theBenchmark.p',fact_141_rel__simps_I48_J) ).
fof(fact_142_zmult__assoc,axiom,
! [Z1,Z2,Z3] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Z1),Z2)),Z3) = hAPP_int_int(times_times_int(Z1),hAPP_int_int(times_times_int(Z2),Z3)),
file('theBenchmark.p',fact_142_zmult__assoc) ).
fof(fact_143_zmult__commute,axiom,
! [Z,W] : hAPP_int_int(times_times_int(Z),W) = hAPP_int_int(times_times_int(W),Z),
file('theBenchmark.p',fact_143_zmult__commute) ).
fof(fact_144_number__of__is__id,axiom,
! [K_1] :
( is_int(K_1)
=> number_number_of_int(K_1) = K_1 ),
file('theBenchmark.p',fact_144_number__of__is__id) ).
fof(fact_145_zadd__assoc,axiom,
! [Z1,Z2,Z3] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(Z1),Z2)),Z3) = hAPP_int_int(plus_plus_int(Z1),hAPP_int_int(plus_plus_int(Z2),Z3)),
file('theBenchmark.p',fact_145_zadd__assoc) ).
fof(fact_146_zadd__left__commute,axiom,
! [X_1,Y_1,Z] : hAPP_int_int(plus_plus_int(X_1),hAPP_int_int(plus_plus_int(Y_1),Z)) = hAPP_int_int(plus_plus_int(Y_1),hAPP_int_int(plus_plus_int(X_1),Z)),
file('theBenchmark.p',fact_146_zadd__left__commute) ).
fof(fact_147_zadd__commute,axiom,
! [Z,W] : hAPP_int_int(plus_plus_int(Z),W) = hAPP_int_int(plus_plus_int(W),Z),
file('theBenchmark.p',fact_147_zadd__commute) ).
fof(fact_148_rel__simps_I12_J,axiom,
! [K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),pls))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),pls)) ),
file('theBenchmark.p',fact_148_rel__simps_I12_J) ).
fof(fact_149_less__int__code_I15_J,axiom,
! [K1,K2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K1)),bit0(K2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2)) ),
file('theBenchmark.p',fact_149_less__int__code_I15_J) ).
fof(fact_150_rel__simps_I16_J,axiom,
! [K,L_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),bit0(L_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L_1)) ),
file('theBenchmark.p',fact_150_rel__simps_I16_J) ).
fof(fact_151_rel__simps_I10_J,axiom,
! [K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(K)),pls))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),pls)) ),
file('theBenchmark.p',fact_151_rel__simps_I10_J) ).
fof(fact_152_rel__simps_I4_J,axiom,
! [K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(K)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),K)) ),
file('theBenchmark.p',fact_152_rel__simps_I4_J) ).
fof(fact_153_rel__simps_I22_J,axiom,
! [K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(K)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K)) ),
file('theBenchmark.p',fact_153_rel__simps_I22_J) ).
fof(fact_154_less__eq__int__code_I14_J,axiom,
! [K1,K2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(K1)),bit1(K2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2)) ),
file('theBenchmark.p',fact_154_less__eq__int__code_I14_J) ).
fof(fact_155_rel__simps_I32_J,axiom,
! [K,L_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(K)),bit1(L_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L_1)) ),
file('theBenchmark.p',fact_155_rel__simps_I32_J) ).
fof(fact_156_rel__simps_I27_J,axiom,
! [K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(K)),pls))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),pls)) ),
file('theBenchmark.p',fact_156_rel__simps_I27_J) ).
fof(fact_157_rel__simps_I21_J,axiom,
! [K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(K)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K)) ),
file('theBenchmark.p',fact_157_rel__simps_I21_J) ).
fof(fact_158_zless__add1__eq,axiom,
! [W_1,Z_1] :
( ( is_int(Z_1)
& is_int(W_1) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),hAPP_int_int(plus_plus_int(Z_1),one_one_int)))
<=> ( W_1 = Z_1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_1)) ) ) ),
file('theBenchmark.p',fact_158_zless__add1__eq) ).
fof(fact_159_power__even__eq,axiom,
! [A_103,N_39] : hAPP_nat_int(power_power_int(A_103),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_39)) = hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(A_103),N_39)),number_number_of_nat(bit0(bit1(pls)))),
file('theBenchmark.p',fact_159_power__even__eq) ).
fof(fact_160_power__even__eq,axiom,
! [A_103,N_39] : hAPP_nat_real(power_power_real(A_103),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_39)) = hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(A_103),N_39)),number_number_of_nat(bit0(bit1(pls)))),
file('theBenchmark.p',fact_160_power__even__eq) ).
fof(fact_161_power__even__eq,axiom,
! [A_103,N_39] : hAPP_nat_nat(power_power_nat(A_103),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_39)) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(A_103),N_39)),number_number_of_nat(bit0(bit1(pls)))),
file('theBenchmark.p',fact_161_power__even__eq) ).
fof(fact_162_less__special_I4_J,axiom,
! [X_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X_2)),one_one_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),bit1(pls))) ),
file('theBenchmark.p',fact_162_less__special_I4_J) ).
fof(fact_163_less__special_I4_J,axiom,
! [X_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X_2)),one_one_real))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),bit1(pls))) ),
file('theBenchmark.p',fact_163_less__special_I4_J) ).
fof(fact_164_less__special_I2_J,axiom,
! [Y_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),Y_2)) ),
file('theBenchmark.p',fact_164_less__special_I2_J) ).
fof(fact_165_less__special_I2_J,axiom,
! [Y_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),Y_2)) ),
file('theBenchmark.p',fact_165_less__special_I2_J) ).
fof(fact_166_le__special_I4_J,axiom,
! [X_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X_2)),one_one_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),bit1(pls))) ),
file('theBenchmark.p',fact_166_le__special_I4_J) ).
fof(fact_167_le__special_I4_J,axiom,
! [X_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X_2)),one_one_real))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),bit1(pls))) ),
file('theBenchmark.p',fact_167_le__special_I4_J) ).
fof(fact_168_le__special_I2_J,axiom,
! [Y_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),Y_2)) ),
file('theBenchmark.p',fact_168_le__special_I2_J) ).
fof(fact_169_le__special_I2_J,axiom,
! [Y_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),Y_2)) ),
file('theBenchmark.p',fact_169_le__special_I2_J) ).
fof(fact_170_crossproduct__eq,axiom,
! [W_1,Y_2,X_2,Z_1] :
( ( is_int(Z_1)
& is_int(X_2)
& is_int(Y_2)
& is_int(W_1) )
=> ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(W_1),Y_2)),hAPP_int_int(times_times_int(X_2),Z_1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(W_1),Z_1)),hAPP_int_int(times_times_int(X_2),Y_2))
<=> ( Y_2 = Z_1
| W_1 = X_2 ) ) ),
file('theBenchmark.p',fact_170_crossproduct__eq) ).
fof(fact_171_crossproduct__eq,axiom,
! [W_1,Y_2,X_2,Z_1] :
( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(W_1),Y_2)),hAPP_nat_nat(times_times_nat(X_2),Z_1)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(W_1),Z_1)),hAPP_nat_nat(times_times_nat(X_2),Y_2))
<=> ( Y_2 = Z_1
| W_1 = X_2 ) ),
file('theBenchmark.p',fact_171_crossproduct__eq) ).
fof(fact_172_crossproduct__eq,axiom,
! [W_1,Y_2,X_2,Z_1] :
( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(W_1),Y_2)),hAPP_real_real(times_times_real(X_2),Z_1)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(W_1),Z_1)),hAPP_real_real(times_times_real(X_2),Y_2))
<=> ( Y_2 = Z_1
| W_1 = X_2 ) ),
file('theBenchmark.p',fact_172_crossproduct__eq) ).
fof(fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [A_102,M_13,B_59] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_102),M_13)),hAPP_int_int(times_times_int(B_59),M_13)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_102),B_59)),M_13),
file('theBenchmark.p',fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [A_102,M_13,B_59] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_102),M_13)),hAPP_nat_nat(times_times_nat(B_59),M_13)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_102),B_59)),M_13),
file('theBenchmark.p',fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [A_102,M_13,B_59] : hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_102),M_13)),hAPP_real_real(times_times_real(B_59),M_13)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_102),B_59)),M_13),
file('theBenchmark.p',fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [A_101,B_58,C_29] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_101),B_58)),C_29) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_101),C_29)),hAPP_int_int(times_times_int(B_58),C_29)),
file('theBenchmark.p',fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_177_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [A_101,B_58,C_29] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_101),B_58)),C_29) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_101),C_29)),hAPP_nat_nat(times_times_nat(B_58),C_29)),
file('theBenchmark.p',fact_177_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_178_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [A_101,B_58,C_29] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_101),B_58)),C_29) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_101),C_29)),hAPP_real_real(times_times_real(B_58),C_29)),
file('theBenchmark.p',fact_178_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_179_crossproduct__noteq,axiom,
! [C_2,D,A_2,B_2] :
( ( is_int(B_2)
& is_int(A_2)
& is_int(D)
& is_int(C_2) )
=> ( ( C_2 != D
& A_2 != B_2 )
<=> hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_2),C_2)),hAPP_int_int(times_times_int(B_2),D)) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_2),D)),hAPP_int_int(times_times_int(B_2),C_2)) ) ),
file('theBenchmark.p',fact_179_crossproduct__noteq) ).
fof(fact_180_crossproduct__noteq,axiom,
! [C_2,D,A_2,B_2] :
( ( C_2 != D
& A_2 != B_2 )
<=> hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_2),C_2)),hAPP_nat_nat(times_times_nat(B_2),D)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_2),D)),hAPP_nat_nat(times_times_nat(B_2),C_2)) ),
file('theBenchmark.p',fact_180_crossproduct__noteq) ).
fof(fact_181_crossproduct__noteq,axiom,
! [C_2,D,A_2,B_2] :
( ( C_2 != D
& A_2 != B_2 )
<=> hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_2),C_2)),hAPP_real_real(times_times_real(B_2),D)) != hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_2),D)),hAPP_real_real(times_times_real(B_2),C_2)) ),
file('theBenchmark.p',fact_181_crossproduct__noteq) ).
fof(fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [X_21,Y_18,Z_9] : hAPP_int_int(times_times_int(X_21),hAPP_int_int(plus_plus_int(Y_18),Z_9)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X_21),Y_18)),hAPP_int_int(times_times_int(X_21),Z_9)),
file('theBenchmark.p',fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [X_21,Y_18,Z_9] : hAPP_nat_nat(times_times_nat(X_21),hAPP_nat_nat(plus_plus_nat(Y_18),Z_9)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X_21),Y_18)),hAPP_nat_nat(times_times_nat(X_21),Z_9)),
file('theBenchmark.p',fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [X_21,Y_18,Z_9] : hAPP_real_real(times_times_real(X_21),hAPP_real_real(plus_plus_real(Y_18),Z_9)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X_21),Y_18)),hAPP_real_real(times_times_real(X_21),Z_9)),
file('theBenchmark.p',fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [A_100] :
( is_int(A_100)
=> hAPP_int_int(times_times_int(A_100),one_one_int) = A_100 ),
file('theBenchmark.p',fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [A_100] : hAPP_nat_nat(times_times_nat(A_100),one_one_nat) = A_100,
file('theBenchmark.p',fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [A_100] : hAPP_real_real(times_times_real(A_100),one_one_real) = A_100,
file('theBenchmark.p',fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [A_99] :
( is_int(A_99)
=> hAPP_int_int(times_times_int(one_one_int),A_99) = A_99 ),
file('theBenchmark.p',fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [A_99] : hAPP_nat_nat(times_times_nat(one_one_nat),A_99) = A_99,
file('theBenchmark.p',fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [A_99] : hAPP_real_real(times_times_real(one_one_real),A_99) = A_99,
file('theBenchmark.p',fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [X_20,Y_17,Q_5] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X_20),Y_17)),Q_5) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X_20),Q_5)),hAPP_nat_int(power_power_int(Y_17),Q_5)),
file('theBenchmark.p',fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_192_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [X_20,Y_17,Q_5] : hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(X_20),Y_17)),Q_5) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X_20),Q_5)),hAPP_nat_real(power_power_real(Y_17),Q_5)),
file('theBenchmark.p',fact_192_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [X_20,Y_17,Q_5] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X_20),Y_17)),Q_5) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X_20),Q_5)),hAPP_nat_nat(power_power_nat(Y_17),Q_5)),
file('theBenchmark.p',fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_194_rel__simps_I46_J,axiom,
! [K_1] : bit1(K_1) != pls,
file('theBenchmark.p',fact_194_rel__simps_I46_J) ).
fof(fact_195_rel__simps_I39_J,axiom,
! [L] : pls != bit1(L),
file('theBenchmark.p',fact_195_rel__simps_I39_J) ).
fof(fact_196_rel__simps_I50_J,axiom,
! [K_1,L] : bit1(K_1) != bit0(L),
file('theBenchmark.p',fact_196_rel__simps_I50_J) ).
fof(fact_197_rel__simps_I49_J,axiom,
! [K_1,L] : bit0(K_1) != bit1(L),
file('theBenchmark.p',fact_197_rel__simps_I49_J) ).
fof(fact_198_rel__simps_I44_J,axiom,
! [K] :
( is_int(K)
=> ( bit0(K) = pls
<=> K = pls ) ),
file('theBenchmark.p',fact_198_rel__simps_I44_J) ).
fof(fact_199_rel__simps_I38_J,axiom,
! [L_1] :
( is_int(L_1)
=> ( pls = bit0(L_1)
<=> pls = L_1 ) ),
file('theBenchmark.p',fact_199_rel__simps_I38_J) ).
fof(fact_200_Bit0__Pls,axiom,
bit0(pls) = pls,
file('theBenchmark.p',fact_200_Bit0__Pls) ).
fof(fact_201_mult__Pls,axiom,
! [W] : hAPP_int_int(times_times_int(pls),W) = pls,
file('theBenchmark.p',fact_201_mult__Pls) ).
fof(fact_202_mult__Bit0,axiom,
! [K_1,L] : hAPP_int_int(times_times_int(bit0(K_1)),L) = bit0(hAPP_int_int(times_times_int(K_1),L)),
file('theBenchmark.p',fact_202_mult__Bit0) ).
fof(fact_203_add__Pls__right,axiom,
! [K_1] :
( is_int(K_1)
=> hAPP_int_int(plus_plus_int(K_1),pls) = K_1 ),
file('theBenchmark.p',fact_203_add__Pls__right) ).
fof(fact_204_add__Pls,axiom,
! [K_1] :
( is_int(K_1)
=> hAPP_int_int(plus_plus_int(pls),K_1) = K_1 ),
file('theBenchmark.p',fact_204_add__Pls) ).
fof(fact_205_add__Bit0__Bit0,axiom,
! [K_1,L] : hAPP_int_int(plus_plus_int(bit0(K_1)),bit0(L)) = bit0(hAPP_int_int(plus_plus_int(K_1),L)),
file('theBenchmark.p',fact_205_add__Bit0__Bit0) ).
fof(fact_206_Bit0__def,axiom,
! [K_1] : bit0(K_1) = hAPP_int_int(plus_plus_int(K_1),K_1),
file('theBenchmark.p',fact_206_Bit0__def) ).
fof(fact_207_zmult__1__right,axiom,
! [Z] :
( is_int(Z)
=> hAPP_int_int(times_times_int(Z),one_one_int) = Z ),
file('theBenchmark.p',fact_207_zmult__1__right) ).
fof(fact_208_zmult__1,axiom,
! [Z] :
( is_int(Z)
=> hAPP_int_int(times_times_int(one_one_int),Z) = Z ),
file('theBenchmark.p',fact_208_zmult__1) ).
fof(fact_209_times__numeral__code_I5_J,axiom,
! [V,W] : hAPP_int_int(times_times_int(number_number_of_int(V)),number_number_of_int(W)) = number_number_of_int(hAPP_int_int(times_times_int(V),W)),
file('theBenchmark.p',fact_209_times__numeral__code_I5_J) ).
fof(fact_210_zadd__zmult__distrib,axiom,
! [Z1,Z2,W] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(Z1),Z2)),W) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(Z1),W)),hAPP_int_int(times_times_int(Z2),W)),
file('theBenchmark.p',fact_210_zadd__zmult__distrib) ).
fof(fact_211_zadd__zmult__distrib2,axiom,
! [W,Z1,Z2] : hAPP_int_int(times_times_int(W),hAPP_int_int(plus_plus_int(Z1),Z2)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(W),Z1)),hAPP_int_int(times_times_int(W),Z2)),
file('theBenchmark.p',fact_211_zadd__zmult__distrib2) ).
fof(fact_212_plus__numeral__code_I9_J,axiom,
! [V,W] : hAPP_int_int(plus_plus_int(number_number_of_int(V)),number_number_of_int(W)) = number_number_of_int(hAPP_int_int(plus_plus_int(V),W)),
file('theBenchmark.p',fact_212_plus__numeral__code_I9_J) ).
fof(fact_213_semiring__mult__number__of,axiom,
! [V_20,V_19] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_19))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_20))
=> hAPP_int_int(times_times_int(number_number_of_int(V_19)),number_number_of_int(V_20)) = number_number_of_int(hAPP_int_int(times_times_int(V_19),V_20)) ) ),
file('theBenchmark.p',fact_213_semiring__mult__number__of) ).
fof(fact_214_semiring__mult__number__of,axiom,
! [V_20,V_19] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_19))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_20))
=> hAPP_nat_nat(times_times_nat(number_number_of_nat(V_19)),number_number_of_nat(V_20)) = number_number_of_nat(hAPP_int_int(times_times_int(V_19),V_20)) ) ),
file('theBenchmark.p',fact_214_semiring__mult__number__of) ).
fof(fact_215_semiring__mult__number__of,axiom,
! [V_20,V_19] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_19))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_20))
=> hAPP_real_real(times_times_real(number267125858f_real(V_19)),number267125858f_real(V_20)) = number267125858f_real(hAPP_int_int(times_times_int(V_19),V_20)) ) ),
file('theBenchmark.p',fact_215_semiring__mult__number__of) ).
fof(fact_216_semiring__add__number__of,axiom,
! [V_18,V_17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_17))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_18))
=> hAPP_int_int(plus_plus_int(number_number_of_int(V_17)),number_number_of_int(V_18)) = number_number_of_int(hAPP_int_int(plus_plus_int(V_17),V_18)) ) ),
file('theBenchmark.p',fact_216_semiring__add__number__of) ).
fof(fact_217_semiring__add__number__of,axiom,
! [V_18,V_17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_17))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_18))
=> hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V_17)),number_number_of_nat(V_18)) = number_number_of_nat(hAPP_int_int(plus_plus_int(V_17),V_18)) ) ),
file('theBenchmark.p',fact_217_semiring__add__number__of) ).
fof(fact_218_semiring__add__number__of,axiom,
! [V_18,V_17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_17))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_18))
=> hAPP_real_real(plus_plus_real(number267125858f_real(V_17)),number267125858f_real(V_18)) = number267125858f_real(hAPP_int_int(plus_plus_int(V_17),V_18)) ) ),
file('theBenchmark.p',fact_218_semiring__add__number__of) ).
fof(fact_219_power2__ge__self,axiom,
! [X_1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),hAPP_nat_int(power_power_int(X_1),number_number_of_nat(bit0(bit1(pls)))))),
file('theBenchmark.p',fact_219_power2__ge__self) ).
fof(fact_220_left__distrib__number__of,axiom,
! [A_98,B_57,V_16] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_98),B_57)),number_number_of_int(V_16)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_98),number_number_of_int(V_16))),hAPP_int_int(times_times_int(B_57),number_number_of_int(V_16))),
file('theBenchmark.p',fact_220_left__distrib__number__of) ).
fof(fact_221_left__distrib__number__of,axiom,
! [A_98,B_57,V_16] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_98),B_57)),number_number_of_nat(V_16)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_98),number_number_of_nat(V_16))),hAPP_nat_nat(times_times_nat(B_57),number_number_of_nat(V_16))),
file('theBenchmark.p',fact_221_left__distrib__number__of) ).
fof(fact_222_left__distrib__number__of,axiom,
! [A_98,B_57,V_16] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_98),B_57)),number267125858f_real(V_16)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_98),number267125858f_real(V_16))),hAPP_real_real(times_times_real(B_57),number267125858f_real(V_16))),
file('theBenchmark.p',fact_222_left__distrib__number__of) ).
fof(fact_223_right__distrib__number__of,axiom,
! [V_15,B_56,C_28] : hAPP_int_int(times_times_int(number_number_of_int(V_15)),hAPP_int_int(plus_plus_int(B_56),C_28)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(V_15)),B_56)),hAPP_int_int(times_times_int(number_number_of_int(V_15)),C_28)),
file('theBenchmark.p',fact_223_right__distrib__number__of) ).
fof(fact_224_right__distrib__number__of,axiom,
! [V_15,B_56,C_28] : hAPP_nat_nat(times_times_nat(number_number_of_nat(V_15)),hAPP_nat_nat(plus_plus_nat(B_56),C_28)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(number_number_of_nat(V_15)),B_56)),hAPP_nat_nat(times_times_nat(number_number_of_nat(V_15)),C_28)),
file('theBenchmark.p',fact_224_right__distrib__number__of) ).
fof(fact_225_right__distrib__number__of,axiom,
! [V_15,B_56,C_28] : hAPP_real_real(times_times_real(number267125858f_real(V_15)),hAPP_real_real(plus_plus_real(B_56),C_28)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(number267125858f_real(V_15)),B_56)),hAPP_real_real(times_times_real(number267125858f_real(V_15)),C_28)),
file('theBenchmark.p',fact_225_right__distrib__number__of) ).
fof(fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [A_97,M_12] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_97),M_12)),M_12) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_97),one_one_int)),M_12),
file('theBenchmark.p',fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [A_97,M_12] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_97),M_12)),M_12) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_97),one_one_nat)),M_12),
file('theBenchmark.p',fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [A_97,M_12] : hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_97),M_12)),M_12) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_97),one_one_real)),M_12),
file('theBenchmark.p',fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [M_11,A_96] : hAPP_int_int(plus_plus_int(M_11),hAPP_int_int(times_times_int(A_96),M_11)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_96),one_one_int)),M_11),
file('theBenchmark.p',fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [M_11,A_96] : hAPP_nat_nat(plus_plus_nat(M_11),hAPP_nat_nat(times_times_nat(A_96),M_11)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_96),one_one_nat)),M_11),
file('theBenchmark.p',fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [M_11,A_96] : hAPP_real_real(plus_plus_real(M_11),hAPP_real_real(times_times_real(A_96),M_11)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_96),one_one_real)),M_11),
file('theBenchmark.p',fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [M_10] : hAPP_int_int(plus_plus_int(M_10),M_10) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),M_10),
file('theBenchmark.p',fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_233_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [M_10] : hAPP_nat_nat(plus_plus_nat(M_10),M_10) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),M_10),
file('theBenchmark.p',fact_233_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [M_10] : hAPP_real_real(plus_plus_real(M_10),M_10) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),M_10),
file('theBenchmark.p',fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_235_add__numeral__0,axiom,
! [A_95] :
( is_int(A_95)
=> hAPP_int_int(plus_plus_int(number_number_of_int(pls)),A_95) = A_95 ),
file('theBenchmark.p',fact_235_add__numeral__0) ).
fof(fact_236_add__numeral__0,axiom,
! [A_95] : hAPP_real_real(plus_plus_real(number267125858f_real(pls)),A_95) = A_95,
file('theBenchmark.p',fact_236_add__numeral__0) ).
fof(fact_237_add__numeral__0__right,axiom,
! [A_94] :
( is_int(A_94)
=> hAPP_int_int(plus_plus_int(A_94),number_number_of_int(pls)) = A_94 ),
file('theBenchmark.p',fact_237_add__numeral__0__right) ).
fof(fact_238_add__numeral__0__right,axiom,
! [A_94] : hAPP_real_real(plus_plus_real(A_94),number267125858f_real(pls)) = A_94,
file('theBenchmark.p',fact_238_add__numeral__0__right) ).
fof(fact_239_mult__number__of__left,axiom,
! [V_14,W_13,Z_8] : hAPP_int_int(times_times_int(number_number_of_int(V_14)),hAPP_int_int(times_times_int(number_number_of_int(W_13)),Z_8)) = hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(V_14),W_13))),Z_8),
file('theBenchmark.p',fact_239_mult__number__of__left) ).
fof(fact_240_mult__number__of__left,axiom,
! [V_14,W_13,Z_8] : hAPP_real_real(times_times_real(number267125858f_real(V_14)),hAPP_real_real(times_times_real(number267125858f_real(W_13)),Z_8)) = hAPP_real_real(times_times_real(number267125858f_real(hAPP_int_int(times_times_int(V_14),W_13))),Z_8),
file('theBenchmark.p',fact_240_mult__number__of__left) ).
fof(fact_241_arith__simps_I32_J,axiom,
! [V_13,W_12] : hAPP_int_int(times_times_int(number_number_of_int(V_13)),number_number_of_int(W_12)) = number_number_of_int(hAPP_int_int(times_times_int(V_13),W_12)),
file('theBenchmark.p',fact_241_arith__simps_I32_J) ).
fof(fact_242_arith__simps_I32_J,axiom,
! [V_13,W_12] : hAPP_real_real(times_times_real(number267125858f_real(V_13)),number267125858f_real(W_12)) = number267125858f_real(hAPP_int_int(times_times_int(V_13),W_12)),
file('theBenchmark.p',fact_242_arith__simps_I32_J) ).
fof(fact_243_number__of__mult,axiom,
! [V_12,W_11] : number_number_of_int(hAPP_int_int(times_times_int(V_12),W_11)) = hAPP_int_int(times_times_int(number_number_of_int(V_12)),number_number_of_int(W_11)),
file('theBenchmark.p',fact_243_number__of__mult) ).
fof(fact_244_number__of__mult,axiom,
! [V_12,W_11] : number267125858f_real(hAPP_int_int(times_times_int(V_12),W_11)) = hAPP_real_real(times_times_real(number267125858f_real(V_12)),number267125858f_real(W_11)),
file('theBenchmark.p',fact_244_number__of__mult) ).
fof(fact_245_add__number__of__left,axiom,
! [V_11,W_10,Z_7] : hAPP_int_int(plus_plus_int(number_number_of_int(V_11)),hAPP_int_int(plus_plus_int(number_number_of_int(W_10)),Z_7)) = hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(V_11),W_10))),Z_7),
file('theBenchmark.p',fact_245_add__number__of__left) ).
fof(fact_246_add__number__of__left,axiom,
! [V_11,W_10,Z_7] : hAPP_real_real(plus_plus_real(number267125858f_real(V_11)),hAPP_real_real(plus_plus_real(number267125858f_real(W_10)),Z_7)) = hAPP_real_real(plus_plus_real(number267125858f_real(hAPP_int_int(plus_plus_int(V_11),W_10))),Z_7),
file('theBenchmark.p',fact_246_add__number__of__left) ).
fof(fact_247_add__number__of__eq,axiom,
! [V_10,W_9] : hAPP_int_int(plus_plus_int(number_number_of_int(V_10)),number_number_of_int(W_9)) = number_number_of_int(hAPP_int_int(plus_plus_int(V_10),W_9)),
file('theBenchmark.p',fact_247_add__number__of__eq) ).
fof(fact_248_add__number__of__eq,axiom,
! [V_10,W_9] : hAPP_real_real(plus_plus_real(number267125858f_real(V_10)),number267125858f_real(W_9)) = number267125858f_real(hAPP_int_int(plus_plus_int(V_10),W_9)),
file('theBenchmark.p',fact_248_add__number__of__eq) ).
fof(fact_249_number__of__add,axiom,
! [V_9,W_8] : number_number_of_int(hAPP_int_int(plus_plus_int(V_9),W_8)) = hAPP_int_int(plus_plus_int(number_number_of_int(V_9)),number_number_of_int(W_8)),
file('theBenchmark.p',fact_249_number__of__add) ).
fof(fact_250_number__of__add,axiom,
! [V_9,W_8] : number267125858f_real(hAPP_int_int(plus_plus_int(V_9),W_8)) = hAPP_real_real(plus_plus_real(number267125858f_real(V_9)),number267125858f_real(W_8)),
file('theBenchmark.p',fact_250_number__of__add) ).
fof(fact_251_add__Bit1__Bit0,axiom,
! [K_1,L] : hAPP_int_int(plus_plus_int(bit1(K_1)),bit0(L)) = bit1(hAPP_int_int(plus_plus_int(K_1),L)),
file('theBenchmark.p',fact_251_add__Bit1__Bit0) ).
fof(fact_252_add__Bit0__Bit1,axiom,
! [K_1,L] : hAPP_int_int(plus_plus_int(bit0(K_1)),bit1(L)) = bit1(hAPP_int_int(plus_plus_int(K_1),L)),
file('theBenchmark.p',fact_252_add__Bit0__Bit1) ).
fof(fact_253_Bit1__def,axiom,
! [K_1] : bit1(K_1) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),K_1)),K_1),
file('theBenchmark.p',fact_253_Bit1__def) ).
fof(fact_254_number__of__Bit1,axiom,
! [W_7] : number_number_of_int(bit1(W_7)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(W_7))),number_number_of_int(W_7)),
file('theBenchmark.p',fact_254_number__of__Bit1) ).
fof(fact_255_number__of__Bit1,axiom,
! [W_7] : number267125858f_real(bit1(W_7)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(W_7))),number267125858f_real(W_7)),
file('theBenchmark.p',fact_255_number__of__Bit1) ).
fof(fact_256_mult__numeral__1,axiom,
! [A_93] :
( is_int(A_93)
=> hAPP_int_int(times_times_int(number_number_of_int(bit1(pls))),A_93) = A_93 ),
file('theBenchmark.p',fact_256_mult__numeral__1) ).
fof(fact_257_mult__numeral__1,axiom,
! [A_93] : hAPP_real_real(times_times_real(number267125858f_real(bit1(pls))),A_93) = A_93,
file('theBenchmark.p',fact_257_mult__numeral__1) ).
fof(fact_258_mult__numeral__1__right,axiom,
! [A_92] :
( is_int(A_92)
=> hAPP_int_int(times_times_int(A_92),number_number_of_int(bit1(pls))) = A_92 ),
file('theBenchmark.p',fact_258_mult__numeral__1__right) ).
fof(fact_259_mult__numeral__1__right,axiom,
! [A_92] : hAPP_real_real(times_times_real(A_92),number267125858f_real(bit1(pls))) = A_92,
file('theBenchmark.p',fact_259_mult__numeral__1__right) ).
fof(fact_260_semiring__numeral__1__eq__1,axiom,
number_number_of_int(bit1(pls)) = one_one_int,
file('theBenchmark.p',fact_260_semiring__numeral__1__eq__1) ).
fof(fact_261_semiring__numeral__1__eq__1,axiom,
number_number_of_nat(bit1(pls)) = one_one_nat,
file('theBenchmark.p',fact_261_semiring__numeral__1__eq__1) ).
fof(fact_262_semiring__numeral__1__eq__1,axiom,
number267125858f_real(bit1(pls)) = one_one_real,
file('theBenchmark.p',fact_262_semiring__numeral__1__eq__1) ).
fof(fact_263_numeral__1__eq__1,axiom,
number_number_of_int(bit1(pls)) = one_one_int,
file('theBenchmark.p',fact_263_numeral__1__eq__1) ).
fof(fact_264_numeral__1__eq__1,axiom,
number267125858f_real(bit1(pls)) = one_one_real,
file('theBenchmark.p',fact_264_numeral__1__eq__1) ).
fof(fact_265_semiring__norm_I110_J,axiom,
one_one_int = number_number_of_int(bit1(pls)),
file('theBenchmark.p',fact_265_semiring__norm_I110_J) ).
fof(fact_266_semiring__norm_I110_J,axiom,
one_one_real = number267125858f_real(bit1(pls)),
file('theBenchmark.p',fact_266_semiring__norm_I110_J) ).
fof(fact_267_one__is__num__one,axiom,
one_one_int = number_number_of_int(bit1(pls)),
file('theBenchmark.p',fact_267_one__is__num__one) ).
fof(fact_268_mult__Bit1,axiom,
! [K_1,L] : hAPP_int_int(times_times_int(bit1(K_1)),L) = hAPP_int_int(plus_plus_int(bit0(hAPP_int_int(times_times_int(K_1),L))),L),
file('theBenchmark.p',fact_268_mult__Bit1) ).
fof(fact_269_double__number__of__Bit0,axiom,
! [W_6] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),number_number_of_int(W_6)) = number_number_of_int(bit0(W_6)),
file('theBenchmark.p',fact_269_double__number__of__Bit0) ).
fof(fact_270_double__number__of__Bit0,axiom,
! [W_6] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(W_6)) = number267125858f_real(bit0(W_6)),
file('theBenchmark.p',fact_270_double__number__of__Bit0) ).
fof(fact_271_power3__eq__cube,axiom,
! [A_91] : hAPP_nat_int(power_power_int(A_91),number_number_of_nat(bit1(bit1(pls)))) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(A_91),A_91)),A_91),
file('theBenchmark.p',fact_271_power3__eq__cube) ).
fof(fact_272_power3__eq__cube,axiom,
! [A_91] : hAPP_nat_real(power_power_real(A_91),number_number_of_nat(bit1(bit1(pls)))) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(A_91),A_91)),A_91),
file('theBenchmark.p',fact_272_power3__eq__cube) ).
fof(fact_273_power3__eq__cube,axiom,
! [A_91] : hAPP_nat_nat(power_power_nat(A_91),number_number_of_nat(bit1(bit1(pls)))) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(A_91),A_91)),A_91),
file('theBenchmark.p',fact_273_power3__eq__cube) ).
fof(fact_274_quartic__square__square,axiom,
! [X_1] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X_1),number_number_of_nat(bit0(bit1(pls))))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(X_1),number_number_of_nat(bit0(bit0(bit1(pls))))),
file('theBenchmark.p',fact_274_quartic__square__square) ).
fof(fact_275_semiring__mult__2,axiom,
! [Z_6] : hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),Z_6) = hAPP_int_int(plus_plus_int(Z_6),Z_6),
file('theBenchmark.p',fact_275_semiring__mult__2) ).
fof(fact_276_semiring__mult__2,axiom,
! [Z_6] : hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),Z_6) = hAPP_nat_nat(plus_plus_nat(Z_6),Z_6),
file('theBenchmark.p',fact_276_semiring__mult__2) ).
fof(fact_277_semiring__mult__2,axiom,
! [Z_6] : hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),Z_6) = hAPP_real_real(plus_plus_real(Z_6),Z_6),
file('theBenchmark.p',fact_277_semiring__mult__2) ).
fof(fact_278_mult__2,axiom,
! [Z_5] : hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),Z_5) = hAPP_int_int(plus_plus_int(Z_5),Z_5),
file('theBenchmark.p',fact_278_mult__2) ).
fof(fact_279_mult__2,axiom,
! [Z_5] : hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),Z_5) = hAPP_real_real(plus_plus_real(Z_5),Z_5),
file('theBenchmark.p',fact_279_mult__2) ).
fof(fact_280_semiring__mult__2__right,axiom,
! [Z_4] : hAPP_int_int(times_times_int(Z_4),number_number_of_int(bit0(bit1(pls)))) = hAPP_int_int(plus_plus_int(Z_4),Z_4),
file('theBenchmark.p',fact_280_semiring__mult__2__right) ).
fof(fact_281_semiring__mult__2__right,axiom,
! [Z_4] : hAPP_nat_nat(times_times_nat(Z_4),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(plus_plus_nat(Z_4),Z_4),
file('theBenchmark.p',fact_281_semiring__mult__2__right) ).
fof(fact_282_semiring__mult__2__right,axiom,
! [Z_4] : hAPP_real_real(times_times_real(Z_4),number267125858f_real(bit0(bit1(pls)))) = hAPP_real_real(plus_plus_real(Z_4),Z_4),
file('theBenchmark.p',fact_282_semiring__mult__2__right) ).
fof(fact_283_mult__2__right,axiom,
! [Z_3] : hAPP_int_int(times_times_int(Z_3),number_number_of_int(bit0(bit1(pls)))) = hAPP_int_int(plus_plus_int(Z_3),Z_3),
file('theBenchmark.p',fact_283_mult__2__right) ).
fof(fact_284_mult__2__right,axiom,
! [Z_3] : hAPP_real_real(times_times_real(Z_3),number267125858f_real(bit0(bit1(pls)))) = hAPP_real_real(plus_plus_real(Z_3),Z_3),
file('theBenchmark.p',fact_284_mult__2__right) ).
fof(fact_285_semiring__one__add__one__is__two,axiom,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
file('theBenchmark.p',fact_285_semiring__one__add__one__is__two) ).
fof(fact_286_semiring__one__add__one__is__two,axiom,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
file('theBenchmark.p',fact_286_semiring__one__add__one__is__two) ).
fof(fact_287_semiring__one__add__one__is__two,axiom,
hAPP_real_real(plus_plus_real(one_one_real),one_one_real) = number267125858f_real(bit0(bit1(pls))),
file('theBenchmark.p',fact_287_semiring__one__add__one__is__two) ).
fof(fact_288_p0,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('theBenchmark.p',fact_288_p0) ).
fof(fact_289__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096,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('theBenchmark.p',fact_289__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096) ).
fof(fact_290_prime__g__5,axiom,
! [P_1] :
( is_int(P_1)
=> ( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( P_1 != number_number_of_int(bit0(bit1(pls)))
=> ( P_1 != 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))))),P_1)) ) ) ) ),
file('theBenchmark.p',fact_290_prime__g__5) ).
fof(fact_291__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096,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('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(fact_292_real__sum__squared__expand,axiom,
! [X_1,Y_1] : hAPP_nat_real(power_power_real(hAPP_real_real(plus_plus_real(X_1),Y_1)),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(X_1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_1),number_number_of_nat(bit0(bit1(pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),X_1)),Y_1)),
file('theBenchmark.p',fact_292_real__sum__squared__expand) ).
fof(fact_293_four__x__squared,axiom,
! [X_1] : hAPP_real_real(times_times_real(number267125858f_real(bit0(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X_1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),X_1)),number_number_of_nat(bit0(bit1(pls)))),
file('theBenchmark.p',fact_293_four__x__squared) ).
fof(fact_294_power__less__power__Suc,axiom,
! [N_38,A_90] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_90))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(A_90),N_38)),hAPP_int_int(times_times_int(A_90),hAPP_nat_int(power_power_int(A_90),N_38)))) ),
file('theBenchmark.p',fact_294_power__less__power__Suc) ).
fof(fact_295_power__less__power__Suc,axiom,
! [N_38,A_90] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),A_90))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(A_90),N_38)),hAPP_nat_nat(times_times_nat(A_90),hAPP_nat_nat(power_power_nat(A_90),N_38)))) ),
file('theBenchmark.p',fact_295_power__less__power__Suc) ).
fof(fact_296_power__less__power__Suc,axiom,
! [N_38,A_90] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),A_90))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(A_90),N_38)),hAPP_real_real(times_times_real(A_90),hAPP_nat_real(power_power_real(A_90),N_38)))) ),
file('theBenchmark.p',fact_296_power__less__power__Suc) ).
fof(fact_297_power__gt1__lemma,axiom,
! [N_37,A_89] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_89))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_int_int(times_times_int(A_89),hAPP_nat_int(power_power_int(A_89),N_37)))) ),
file('theBenchmark.p',fact_297_power__gt1__lemma) ).
fof(fact_298_power__gt1__lemma,axiom,
! [N_37,A_89] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),A_89))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(times_times_nat(A_89),hAPP_nat_nat(power_power_nat(A_89),N_37)))) ),
file('theBenchmark.p',fact_298_power__gt1__lemma) ).
fof(fact_299_power__gt1__lemma,axiom,
! [N_37,A_89] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),A_89))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_real_real(times_times_real(A_89),hAPP_nat_real(power_power_real(A_89),N_37)))) ),
file('theBenchmark.p',fact_299_power__gt1__lemma) ).
fof(fact_300_power__le__imp__le__exp,axiom,
! [M_9,N_36,A_88] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_88))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(A_88),M_9)),hAPP_nat_int(power_power_int(A_88),N_36)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_9),N_36)) ) ),
file('theBenchmark.p',fact_300_power__le__imp__le__exp) ).
fof(fact_301_power__le__imp__le__exp,axiom,
! [M_9,N_36,A_88] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),A_88))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(A_88),M_9)),hAPP_nat_nat(power_power_nat(A_88),N_36)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_9),N_36)) ) ),
file('theBenchmark.p',fact_301_power__le__imp__le__exp) ).
fof(fact_302_power__le__imp__le__exp,axiom,
! [M_9,N_36,A_88] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),A_88))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(A_88),M_9)),hAPP_nat_real(power_power_real(A_88),N_36)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_9),N_36)) ) ),
file('theBenchmark.p',fact_302_power__le__imp__le__exp) ).
fof(fact_303_power__increasing__iff,axiom,
! [X_2,Y_2,B_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),B_2))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(B_2),X_2)),hAPP_nat_int(power_power_int(B_2),Y_2)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) ) ),
file('theBenchmark.p',fact_303_power__increasing__iff) ).
fof(fact_304_power__increasing__iff,axiom,
! [X_2,Y_2,B_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),B_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(B_2),X_2)),hAPP_nat_nat(power_power_nat(B_2),Y_2)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) ) ),
file('theBenchmark.p',fact_304_power__increasing__iff) ).
fof(fact_305_power__increasing__iff,axiom,
! [X_2,Y_2,B_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),B_2))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(B_2),X_2)),hAPP_nat_real(power_power_real(B_2),Y_2)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) ) ),
file('theBenchmark.p',fact_305_power__increasing__iff) ).
fof(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,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('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(fact_307_s0p,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('theBenchmark.p',fact_307_s0p) ).
fof(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,axiom,
? [X] :
( ! [Y] :
( is_int(Y)
=> ( ( hBOOL(hAPP_int_bool(zcong(s1,Y),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,Y),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),Y)) )
=> Y = X ) )
& hBOOL(hAPP_int_bool(zcong(s1,X),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,X),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),X))
& is_int(X) ),
file('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(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_,axiom,
~ ! [S_1] :
( is_int(S_1)
=> ~ ( hBOOL(hAPP_int_bool(zcong(s1,S_1),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_1),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_1)) ) ),
file('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(fact_310_s1,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('theBenchmark.p',fact_310_s1) ).
fof(fact_311_power__eq__0__iff,axiom,
! [A_2,N] :
( is_int(A_2)
=> ( hAPP_nat_int(power_power_int(A_2),N) = zero_zero_int
<=> ( N != zero_zero_nat
& A_2 = zero_zero_int ) ) ),
file('theBenchmark.p',fact_311_power__eq__0__iff) ).
fof(fact_312_power__eq__0__iff,axiom,
! [A_2,N] :
( hAPP_nat_nat(power_power_nat(A_2),N) = zero_zero_nat
<=> ( N != zero_zero_nat
& A_2 = zero_zero_nat ) ),
file('theBenchmark.p',fact_312_power__eq__0__iff) ).
fof(fact_313_power__eq__0__iff,axiom,
! [A_2,N] :
( hAPP_nat_real(power_power_real(A_2),N) = zero_zero_real
<=> ( N != zero_zero_nat
& A_2 = zero_zero_real ) ),
file('theBenchmark.p',fact_313_power__eq__0__iff) ).
fof(fact_314_le__imp__power__dvd,axiom,
! [A_87,M_8,N_35] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_8),N_35))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(A_87),M_8)),hAPP_nat_real(power_power_real(A_87),N_35))) ),
file('theBenchmark.p',fact_314_le__imp__power__dvd) ).
fof(fact_315_le__imp__power__dvd,axiom,
! [A_87,M_8,N_35] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_8),N_35))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(A_87),M_8)),hAPP_nat_int(power_power_int(A_87),N_35))) ),
file('theBenchmark.p',fact_315_le__imp__power__dvd) ).
fof(fact_316_le__imp__power__dvd,axiom,
! [A_87,M_8,N_35] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_8),N_35))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(A_87),M_8)),hAPP_nat_nat(power_power_nat(A_87),N_35))) ),
file('theBenchmark.p',fact_316_le__imp__power__dvd) ).
fof(fact_317_dvd__power__le,axiom,
! [N_34,M_7,X_19,Y_16] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X_19),Y_16))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_34),M_7))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X_19),N_34)),hAPP_nat_real(power_power_real(Y_16),M_7))) ) ),
file('theBenchmark.p',fact_317_dvd__power__le) ).
fof(fact_318_dvd__power__le,axiom,
! [N_34,M_7,X_19,Y_16] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X_19),Y_16))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_34),M_7))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X_19),N_34)),hAPP_nat_int(power_power_int(Y_16),M_7))) ) ),
file('theBenchmark.p',fact_318_dvd__power__le) ).
fof(fact_319_dvd__power__le,axiom,
! [N_34,M_7,X_19,Y_16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_19),Y_16))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_34),M_7))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X_19),N_34)),hAPP_nat_nat(power_power_nat(Y_16),M_7))) ) ),
file('theBenchmark.p',fact_319_dvd__power__le) ).
fof(fact_320_power__le__dvd,axiom,
! [M_6,A_86,N_33,B_55] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(A_86),N_33)),B_55))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_6),N_33))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(A_86),M_6)),B_55)) ) ),
file('theBenchmark.p',fact_320_power__le__dvd) ).
fof(fact_321_power__le__dvd,axiom,
! [M_6,A_86,N_33,B_55] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(A_86),N_33)),B_55))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_6),N_33))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(A_86),M_6)),B_55)) ) ),
file('theBenchmark.p',fact_321_power__le__dvd) ).
fof(fact_322_power__le__dvd,axiom,
! [M_6,A_86,N_33,B_55] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(A_86),N_33)),B_55))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_6),N_33))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(A_86),M_6)),B_55)) ) ),
file('theBenchmark.p',fact_322_power__le__dvd) ).
fof(fact_323_power__eq__imp__eq__base,axiom,
! [A_85,N_32,B_54] :
( ( is_int(B_54)
& is_int(A_85) )
=> ( hAPP_nat_int(power_power_int(A_85),N_32) = hAPP_nat_int(power_power_int(B_54),N_32)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_85))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_54))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
=> A_85 = B_54 ) ) ) ) ),
file('theBenchmark.p',fact_323_power__eq__imp__eq__base) ).
fof(fact_324_power__eq__imp__eq__base,axiom,
! [A_85,N_32,B_54] :
( hAPP_nat_nat(power_power_nat(A_85),N_32) = hAPP_nat_nat(power_power_nat(B_54),N_32)
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_85))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_54))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
=> A_85 = B_54 ) ) ) ),
file('theBenchmark.p',fact_324_power__eq__imp__eq__base) ).
fof(fact_325_power__eq__imp__eq__base,axiom,
! [A_85,N_32,B_54] :
( hAPP_nat_real(power_power_real(A_85),N_32) = hAPP_nat_real(power_power_real(B_54),N_32)
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_85))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_54))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
=> A_85 = B_54 ) ) ) ),
file('theBenchmark.p',fact_325_power__eq__imp__eq__base) ).
fof(fact_326_zdvd__not__zless,axiom,
! [N_1,M] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,M),N_1))
=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,N_1),M)) ) ),
file('theBenchmark.p',fact_326_zdvd__not__zless) ).
fof(fact_327_zdvd__antisym__nonneg,axiom,
! [N_1,M] :
( ( is_int(M)
& is_int(N_1) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),M))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,M),N_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,N_1),M))
=> M = N_1 ) ) ) ) ),
file('theBenchmark.p',fact_327_zdvd__antisym__nonneg) ).
fof(fact_328_zdvd__mult__cancel,axiom,
! [K_1,M,N_1] :
( is_int(K_1)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(K_1),M)),hAPP_int_int(times_times_int(K_1),N_1)))
=> ( K_1 != zero_zero_int
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,M),N_1)) ) ) ),
file('theBenchmark.p',fact_328_zdvd__mult__cancel) ).
fof(fact_329_dvd__power__same,axiom,
! [N_31,X_18,Y_15] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X_18),Y_15))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X_18),N_31)),hAPP_nat_real(power_power_real(Y_15),N_31))) ),
file('theBenchmark.p',fact_329_dvd__power__same) ).
fof(fact_330_dvd__power__same,axiom,
! [N_31,X_18,Y_15] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X_18),Y_15))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X_18),N_31)),hAPP_nat_int(power_power_int(Y_15),N_31))) ),
file('theBenchmark.p',fact_330_dvd__power__same) ).
fof(fact_331_dvd__power__same,axiom,
! [N_31,X_18,Y_15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_18),Y_15))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X_18),N_31)),hAPP_nat_nat(power_power_nat(Y_15),N_31))) ),
file('theBenchmark.p',fact_331_dvd__power__same) ).
fof(fact_332_field__power__not__zero,axiom,
! [N_30,A_84] :
( is_int(A_84)
=> ( A_84 != zero_zero_int
=> hAPP_nat_int(power_power_int(A_84),N_30) != zero_zero_int ) ),
file('theBenchmark.p',fact_332_field__power__not__zero) ).
fof(fact_333_field__power__not__zero,axiom,
! [N_30,A_84] :
( A_84 != zero_zero_real
=> hAPP_nat_real(power_power_real(A_84),N_30) != zero_zero_real ),
file('theBenchmark.p',fact_333_field__power__not__zero) ).
fof(fact_334_power__0__left,axiom,
! [N_29] :
( ( N_29 != zero_zero_nat
=> hAPP_nat_int(power_power_int(zero_zero_int),N_29) = zero_zero_int )
& ( N_29 = zero_zero_nat
=> hAPP_nat_int(power_power_int(zero_zero_int),N_29) = one_one_int ) ),
file('theBenchmark.p',fact_334_power__0__left) ).
fof(fact_335_power__0__left,axiom,
! [N_29] :
( ( N_29 != zero_zero_nat
=> hAPP_nat_nat(power_power_nat(zero_zero_nat),N_29) = zero_zero_nat )
& ( N_29 = zero_zero_nat
=> hAPP_nat_nat(power_power_nat(zero_zero_nat),N_29) = one_one_nat ) ),
file('theBenchmark.p',fact_335_power__0__left) ).
fof(fact_336_power__0__left,axiom,
! [N_29] :
( ( N_29 != zero_zero_nat
=> hAPP_nat_real(power_power_real(zero_zero_real),N_29) = zero_zero_real )
& ( N_29 = zero_zero_nat
=> hAPP_nat_real(power_power_real(zero_zero_real),N_29) = one_one_real ) ),
file('theBenchmark.p',fact_336_power__0__left) ).
fof(fact_337_zdvd__imp__le,axiom,
! [Z,N_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Z),N_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z),N_1)) ) ),
file('theBenchmark.p',fact_337_zdvd__imp__le) ).
fof(fact_338_power__strict__mono,axiom,
! [N_28,A_83,B_53] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_83),B_53))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_28))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(A_83),N_28)),hAPP_nat_int(power_power_int(B_53),N_28))) ) ) ),
file('theBenchmark.p',fact_338_power__strict__mono) ).
fof(fact_339_power__strict__mono,axiom,
! [N_28,A_83,B_53] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_83),B_53))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_83))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_28))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(A_83),N_28)),hAPP_nat_nat(power_power_nat(B_53),N_28))) ) ) ),
file('theBenchmark.p',fact_339_power__strict__mono) ).
fof(fact_340_power__strict__mono,axiom,
! [N_28,A_83,B_53] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_83),B_53))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_83))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_28))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(A_83),N_28)),hAPP_nat_real(power_power_real(B_53),N_28))) ) ) ),
file('theBenchmark.p',fact_340_power__strict__mono) ).
fof(fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [A_82] : hAPP_int_int(times_times_int(zero_zero_int),A_82) = zero_zero_int,
file('theBenchmark.p',fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [A_82] : hAPP_nat_nat(times_times_nat(zero_zero_nat),A_82) = zero_zero_nat,
file('theBenchmark.p',fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [A_82] : hAPP_real_real(times_times_real(zero_zero_real),A_82) = zero_zero_real,
file('theBenchmark.p',fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [A_81] : hAPP_int_int(times_times_int(A_81),zero_zero_int) = zero_zero_int,
file('theBenchmark.p',fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [A_81] : hAPP_nat_nat(times_times_nat(A_81),zero_zero_nat) = zero_zero_nat,
file('theBenchmark.p',fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [A_81] : hAPP_real_real(times_times_real(A_81),zero_zero_real) = zero_zero_real,
file('theBenchmark.p',fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [A_80] :
( is_int(A_80)
=> hAPP_int_int(plus_plus_int(zero_zero_int),A_80) = A_80 ),
file('theBenchmark.p',fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [A_80] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),A_80) = A_80,
file('theBenchmark.p',fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [A_80] : hAPP_real_real(plus_plus_real(zero_zero_real),A_80) = A_80,
file('theBenchmark.p',fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [A_79] :
( is_int(A_79)
=> hAPP_int_int(plus_plus_int(A_79),zero_zero_int) = A_79 ),
file('theBenchmark.p',fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [A_79] : hAPP_nat_nat(plus_plus_nat(A_79),zero_zero_nat) = A_79,
file('theBenchmark.p',fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_352_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [A_79] : hAPP_real_real(plus_plus_real(A_79),zero_zero_real) = A_79,
file('theBenchmark.p',fact_352_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_353_add__0__iff,axiom,
! [B_2,A_2] :
( ( is_int(A_2)
& is_int(B_2) )
=> ( B_2 = hAPP_int_int(plus_plus_int(B_2),A_2)
<=> A_2 = zero_zero_int ) ),
file('theBenchmark.p',fact_353_add__0__iff) ).
fof(fact_354_add__0__iff,axiom,
! [B_2,A_2] :
( B_2 = hAPP_nat_nat(plus_plus_nat(B_2),A_2)
<=> A_2 = zero_zero_nat ),
file('theBenchmark.p',fact_354_add__0__iff) ).
fof(fact_355_add__0__iff,axiom,
! [B_2,A_2] :
( B_2 = hAPP_real_real(plus_plus_real(B_2),A_2)
<=> A_2 = zero_zero_real ),
file('theBenchmark.p',fact_355_add__0__iff) ).
fof(fact_356_double__eq__0__iff,axiom,
! [A_2] :
( is_int(A_2)
=> ( hAPP_int_int(plus_plus_int(A_2),A_2) = zero_zero_int
<=> A_2 = zero_zero_int ) ),
file('theBenchmark.p',fact_356_double__eq__0__iff) ).
fof(fact_357_double__eq__0__iff,axiom,
! [A_2] :
( hAPP_real_real(plus_plus_real(A_2),A_2) = zero_zero_real
<=> A_2 = zero_zero_real ),
file('theBenchmark.p',fact_357_double__eq__0__iff) ).
fof(fact_358_Pls__def,axiom,
pls = zero_zero_int,
file('theBenchmark.p',fact_358_Pls__def) ).
fof(fact_359_int__0__neq__1,axiom,
zero_zero_int != one_one_int,
file('theBenchmark.p',fact_359_int__0__neq__1) ).
fof(fact_360_zadd__0,axiom,
! [Z] :
( is_int(Z)
=> hAPP_int_int(plus_plus_int(zero_zero_int),Z) = Z ),
file('theBenchmark.p',fact_360_zadd__0) ).
fof(fact_361_zadd__0__right,axiom,
! [Z] :
( is_int(Z)
=> hAPP_int_int(plus_plus_int(Z),zero_zero_int) = Z ),
file('theBenchmark.p',fact_361_zadd__0__right) ).
fof(fact_362_zero__le__power,axiom,
! [N_27,A_78] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_78))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(A_78),N_27))) ),
file('theBenchmark.p',fact_362_zero__le__power) ).
fof(fact_363_zero__le__power,axiom,
! [N_27,A_78] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_78))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(A_78),N_27))) ),
file('theBenchmark.p',fact_363_zero__le__power) ).
fof(fact_364_zero__le__power,axiom,
! [N_27,A_78] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_78))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(A_78),N_27))) ),
file('theBenchmark.p',fact_364_zero__le__power) ).
fof(fact_365_power__mono,axiom,
! [N_26,A_77,B_52] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_77),B_52))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_77))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(A_77),N_26)),hAPP_nat_int(power_power_int(B_52),N_26))) ) ),
file('theBenchmark.p',fact_365_power__mono) ).
fof(fact_366_power__mono,axiom,
! [N_26,A_77,B_52] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_77),B_52))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_77))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(A_77),N_26)),hAPP_nat_nat(power_power_nat(B_52),N_26))) ) ),
file('theBenchmark.p',fact_366_power__mono) ).
fof(fact_367_power__mono,axiom,
! [N_26,A_77,B_52] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_77),B_52))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_77))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(A_77),N_26)),hAPP_nat_real(power_power_real(B_52),N_26))) ) ),
file('theBenchmark.p',fact_367_power__mono) ).
fof(fact_368_zero__less__power,axiom,
! [N_25,A_76] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_76))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_76),N_25))) ),
file('theBenchmark.p',fact_368_zero__less__power) ).
fof(fact_369_zero__less__power,axiom,
! [N_25,A_76] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_76))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(A_76),N_25))) ),
file('theBenchmark.p',fact_369_zero__less__power) ).
fof(fact_370_zero__less__power,axiom,
! [N_25,A_76] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_76))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(A_76),N_25))) ),
file('theBenchmark.p',fact_370_zero__less__power) ).
fof(fact_371_zcong__zpower__zmult,axiom,
! [Z,X_1,Y_1,P_1] :
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X_1),Y_1),one_one_int),P_1))
=> hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X_1),hAPP_nat_nat(times_times_nat(Y_1),Z)),one_one_int),P_1)) ),
file('theBenchmark.p',fact_371_zcong__zpower__zmult) ).
fof(fact_372_zdvd__reduce,axiom,
! [K,N,Ma] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K),hAPP_int_int(plus_plus_int(N),hAPP_int_int(times_times_int(K),Ma))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K),N)) ),
file('theBenchmark.p',fact_372_zdvd__reduce) ).
fof(fact_373_zdvd__period,axiom,
! [C_2,X_2,Ta,A_2,D] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_2),D))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_2),hAPP_int_int(plus_plus_int(X_2),Ta)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_2),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X_2),hAPP_int_int(times_times_int(C_2),D))),Ta))) ) ),
file('theBenchmark.p',fact_373_zdvd__period) ).
fof(fact_374_power__less__imp__less__base,axiom,
! [A_75,N_24,B_51] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(A_75),N_24)),hAPP_nat_int(power_power_int(B_51),N_24)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_51))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_75),B_51)) ) ),
file('theBenchmark.p',fact_374_power__less__imp__less__base) ).
fof(fact_375_power__less__imp__less__base,axiom,
! [A_75,N_24,B_51] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(A_75),N_24)),hAPP_nat_nat(power_power_nat(B_51),N_24)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_51))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_75),B_51)) ) ),
file('theBenchmark.p',fact_375_power__less__imp__less__base) ).
fof(fact_376_power__less__imp__less__base,axiom,
! [A_75,N_24,B_51] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(A_75),N_24)),hAPP_nat_real(power_power_real(B_51),N_24)))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_51))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_75),B_51)) ) ),
file('theBenchmark.p',fact_376_power__less__imp__less__base) ).
fof(fact_377_power__decreasing,axiom,
! [A_74,N_23,N_22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_23),N_22))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_74))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_74),one_one_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(A_74),N_22)),hAPP_nat_int(power_power_int(A_74),N_23))) ) ) ),
file('theBenchmark.p',fact_377_power__decreasing) ).
fof(fact_378_power__decreasing,axiom,
! [A_74,N_23,N_22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_23),N_22))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_74))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_74),one_one_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(A_74),N_22)),hAPP_nat_nat(power_power_nat(A_74),N_23))) ) ) ),
file('theBenchmark.p',fact_378_power__decreasing) ).
fof(fact_379_power__decreasing,axiom,
! [A_74,N_23,N_22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_23),N_22))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_74))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_74),one_one_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(A_74),N_22)),hAPP_nat_real(power_power_real(A_74),N_23))) ) ) ),
file('theBenchmark.p',fact_379_power__decreasing) ).
fof(fact_380_power__strict__decreasing,axiom,
! [A_73,N_21,N_20] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_21),N_20))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_73))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_73),one_one_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(A_73),N_20)),hAPP_nat_int(power_power_int(A_73),N_21))) ) ) ),
file('theBenchmark.p',fact_380_power__strict__decreasing) ).
fof(fact_381_power__strict__decreasing,axiom,
! [A_73,N_21,N_20] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_21),N_20))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_73))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_73),one_one_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(A_73),N_20)),hAPP_nat_nat(power_power_nat(A_73),N_21))) ) ) ),
file('theBenchmark.p',fact_381_power__strict__decreasing) ).
fof(fact_382_power__strict__decreasing,axiom,
! [A_73,N_21,N_20] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_21),N_20))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_73))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_73),one_one_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(A_73),N_20)),hAPP_nat_real(power_power_real(A_73),N_21))) ) ) ),
file('theBenchmark.p',fact_382_power__strict__decreasing) ).
fof(fact_383_even__less__0__iff,axiom,
! [A_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(A_2),A_2)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),zero_zero_int)) ),
file('theBenchmark.p',fact_383_even__less__0__iff) ).
fof(fact_384_even__less__0__iff,axiom,
! [A_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(A_2),A_2)),zero_zero_real))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),zero_zero_real)) ),
file('theBenchmark.p',fact_384_even__less__0__iff) ).
fof(fact_385_sum__squares__eq__zero__iff,axiom,
! [X_2,Y_2] :
( ( is_int(Y_2)
& is_int(X_2) )
=> ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X_2),X_2)),hAPP_int_int(times_times_int(Y_2),Y_2)) = zero_zero_int
<=> ( Y_2 = zero_zero_int
& X_2 = zero_zero_int ) ) ),
file('theBenchmark.p',fact_385_sum__squares__eq__zero__iff) ).
fof(fact_386_sum__squares__eq__zero__iff,axiom,
! [X_2,Y_2] :
( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X_2),X_2)),hAPP_real_real(times_times_real(Y_2),Y_2)) = zero_zero_real
<=> ( Y_2 = zero_zero_real
& X_2 = zero_zero_real ) ),
file('theBenchmark.p',fact_386_sum__squares__eq__zero__iff) ).
fof(fact_387_add__scale__eq__noteq,axiom,
! [C_27,D_8,A_72,B_50,R_4] :
( ( is_int(R_4)
& is_int(D_8)
& is_int(C_27) )
=> ( R_4 != zero_zero_int
=> ( ( C_27 != D_8
& A_72 = B_50 )
=> hAPP_int_int(plus_plus_int(A_72),hAPP_int_int(times_times_int(R_4),C_27)) != hAPP_int_int(plus_plus_int(B_50),hAPP_int_int(times_times_int(R_4),D_8)) ) ) ),
file('theBenchmark.p',fact_387_add__scale__eq__noteq) ).
fof(fact_388_add__scale__eq__noteq,axiom,
! [C_27,D_8,A_72,B_50,R_4] :
( R_4 != zero_zero_nat
=> ( ( C_27 != D_8
& A_72 = B_50 )
=> hAPP_nat_nat(plus_plus_nat(A_72),hAPP_nat_nat(times_times_nat(R_4),C_27)) != hAPP_nat_nat(plus_plus_nat(B_50),hAPP_nat_nat(times_times_nat(R_4),D_8)) ) ),
file('theBenchmark.p',fact_388_add__scale__eq__noteq) ).
fof(fact_389_add__scale__eq__noteq,axiom,
! [C_27,D_8,A_72,B_50,R_4] :
( R_4 != zero_zero_real
=> ( ( C_27 != D_8
& A_72 = B_50 )
=> hAPP_real_real(plus_plus_real(A_72),hAPP_real_real(times_times_real(R_4),C_27)) != hAPP_real_real(plus_plus_real(B_50),hAPP_real_real(times_times_real(R_4),D_8)) ) ),
file('theBenchmark.p',fact_389_add__scale__eq__noteq) ).
fof(fact_390_zprime__zdvd__power,axiom,
! [A,N_1,P_1] :
( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),hAPP_nat_int(power_power_int(A),N_1)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),A)) ) ),
file('theBenchmark.p',fact_390_zprime__zdvd__power) ).
fof(fact_391_semiring__norm_I112_J,axiom,
zero_zero_int = number_number_of_int(pls),
file('theBenchmark.p',fact_391_semiring__norm_I112_J) ).
fof(fact_392_semiring__norm_I112_J,axiom,
zero_zero_real = number267125858f_real(pls),
file('theBenchmark.p',fact_392_semiring__norm_I112_J) ).
fof(fact_393_number__of__Pls,axiom,
number_number_of_int(pls) = zero_zero_int,
file('theBenchmark.p',fact_393_number__of__Pls) ).
fof(fact_394_number__of__Pls,axiom,
number267125858f_real(pls) = zero_zero_real,
file('theBenchmark.p',fact_394_number__of__Pls) ).
fof(fact_395_semiring__numeral__0__eq__0,axiom,
number_number_of_int(pls) = zero_zero_int,
file('theBenchmark.p',fact_395_semiring__numeral__0__eq__0) ).
fof(fact_396_semiring__numeral__0__eq__0,axiom,
number_number_of_nat(pls) = zero_zero_nat,
file('theBenchmark.p',fact_396_semiring__numeral__0__eq__0) ).
fof(fact_397_semiring__numeral__0__eq__0,axiom,
number267125858f_real(pls) = zero_zero_real,
file('theBenchmark.p',fact_397_semiring__numeral__0__eq__0) ).
fof(fact_398_bin__less__0__simps_I4_J,axiom,
! [W_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(W_1)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),zero_zero_int)) ),
file('theBenchmark.p',fact_398_bin__less__0__simps_I4_J) ).
fof(fact_399_bin__less__0__simps_I1_J,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
file('theBenchmark.p',fact_399_bin__less__0__simps_I1_J) ).
fof(fact_400_bin__less__0__simps_I3_J,axiom,
! [W_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(W_1)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),zero_zero_int)) ),
file('theBenchmark.p',fact_400_bin__less__0__simps_I3_J) ).
fof(fact_401_zero__is__num__zero,axiom,
zero_zero_int = number_number_of_int(pls),
file('theBenchmark.p',fact_401_zero__is__num__zero) ).
fof(fact_402_int__0__less__1,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
file('theBenchmark.p',fact_402_int__0__less__1) ).
fof(fact_403_pos__zmult__pos,axiom,
! [B,A] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(A),B)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B)) ) ),
file('theBenchmark.p',fact_403_pos__zmult__pos) ).
fof(fact_404_zmult__zless__mono2,axiom,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),J_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(K_1),I_1)),hAPP_int_int(times_times_int(K_1),J_1))) ) ),
file('theBenchmark.p',fact_404_zmult__zless__mono2) ).
fof(fact_405_odd__nonzero,axiom,
! [Z] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),Z)),Z) != zero_zero_int,
file('theBenchmark.p',fact_405_odd__nonzero) ).
fof(fact_406_power__Suc__less,axiom,
! [N_19,A_71] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_71))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_71),one_one_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_71),hAPP_nat_int(power_power_int(A_71),N_19))),hAPP_nat_int(power_power_int(A_71),N_19))) ) ),
file('theBenchmark.p',fact_406_power__Suc__less) ).
fof(fact_407_power__Suc__less,axiom,
! [N_19,A_71] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_71))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_71),one_one_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(A_71),hAPP_nat_nat(power_power_nat(A_71),N_19))),hAPP_nat_nat(power_power_nat(A_71),N_19))) ) ),
file('theBenchmark.p',fact_407_power__Suc__less) ).
fof(fact_408_power__Suc__less,axiom,
! [N_19,A_71] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_71))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_71),one_one_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_71),hAPP_nat_real(power_power_real(A_71),N_19))),hAPP_nat_real(power_power_real(A_71),N_19))) ) ),
file('theBenchmark.p',fact_408_power__Suc__less) ).
fof(fact_409_zprime__power__zdvd__cancel__left,axiom,
! [N_1,B,A,P_1] :
( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),A))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(P_1),N_1)),hAPP_int_int(times_times_int(A),B)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(P_1),N_1)),B)) ) ) ),
file('theBenchmark.p',fact_409_zprime__power__zdvd__cancel__left) ).
fof(fact_410_zprime__power__zdvd__cancel__right,axiom,
! [N_1,A,B,P_1] :
( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),B))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(P_1),N_1)),hAPP_int_int(times_times_int(A),B)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(P_1),N_1)),A)) ) ) ),
file('theBenchmark.p',fact_410_zprime__power__zdvd__cancel__right) ).
fof(fact_411_sum__squares__ge__zero,axiom,
! [X_17,Y_14] : 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(X_17),X_17)),hAPP_int_int(times_times_int(Y_14),Y_14)))),
file('theBenchmark.p',fact_411_sum__squares__ge__zero) ).
fof(fact_412_sum__squares__ge__zero,axiom,
! [X_17,Y_14] : 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(X_17),X_17)),hAPP_real_real(times_times_real(Y_14),Y_14)))),
file('theBenchmark.p',fact_412_sum__squares__ge__zero) ).
fof(fact_413_sum__squares__le__zero__iff,axiom,
! [X_2,Y_2] :
( ( is_int(Y_2)
& is_int(X_2) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X_2),X_2)),hAPP_int_int(times_times_int(Y_2),Y_2))),zero_zero_int))
<=> ( Y_2 = zero_zero_int
& X_2 = zero_zero_int ) ) ),
file('theBenchmark.p',fact_413_sum__squares__le__zero__iff) ).
fof(fact_414_sum__squares__le__zero__iff,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X_2),X_2)),hAPP_real_real(times_times_real(Y_2),Y_2))),zero_zero_real))
<=> ( Y_2 = zero_zero_real
& X_2 = zero_zero_real ) ),
file('theBenchmark.p',fact_414_sum__squares__le__zero__iff) ).
fof(fact_415_less__nat__number__of,axiom,
! [V_7,V_8] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(V_7)),number_number_of_nat(V_8)))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_7),V_8))
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_7),V_8))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),V_8)) ) ) ),
file('theBenchmark.p',fact_415_less__nat__number__of) ).
fof(fact_416_not__sum__squares__lt__zero,axiom,
! [X_16,Y_13] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X_16),X_16)),hAPP_int_int(times_times_int(Y_13),Y_13))),zero_zero_int)),
file('theBenchmark.p',fact_416_not__sum__squares__lt__zero) ).
fof(fact_417_not__sum__squares__lt__zero,axiom,
! [X_16,Y_13] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X_16),X_16)),hAPP_real_real(times_times_real(Y_13),Y_13))),zero_zero_real)),
file('theBenchmark.p',fact_417_not__sum__squares__lt__zero) ).
fof(fact_418_sum__squares__gt__zero__iff,axiom,
! [X_2,Y_2] :
( ( is_int(Y_2)
& is_int(X_2) )
=> ( 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(X_2),X_2)),hAPP_int_int(times_times_int(Y_2),Y_2))))
<=> ( Y_2 != zero_zero_int
| X_2 != zero_zero_int ) ) ),
file('theBenchmark.p',fact_418_sum__squares__gt__zero__iff) ).
fof(fact_419_sum__squares__gt__zero__iff,axiom,
! [X_2,Y_2] :
( 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(X_2),X_2)),hAPP_real_real(times_times_real(Y_2),Y_2))))
<=> ( Y_2 != zero_zero_real
| X_2 != zero_zero_real ) ),
file('theBenchmark.p',fact_419_sum__squares__gt__zero__iff) ).
fof(fact_420_le__nat__number__of,axiom,
! [V_7,V_8] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(V_7)),number_number_of_nat(V_8)))
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V_7),V_8))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V_7),pls)) ) ),
file('theBenchmark.p',fact_420_le__nat__number__of) ).
fof(fact_421_number__of__Bit0,axiom,
! [W_5] : number_number_of_int(bit0(W_5)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(W_5))),number_number_of_int(W_5)),
file('theBenchmark.p',fact_421_number__of__Bit0) ).
fof(fact_422_number__of__Bit0,axiom,
! [W_5] : number267125858f_real(bit0(W_5)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(zero_zero_real),number267125858f_real(W_5))),number267125858f_real(W_5)),
file('theBenchmark.p',fact_422_number__of__Bit0) ).
fof(fact_423_power__one__right,axiom,
! [A_70] :
( is_int(A_70)
=> hAPP_nat_int(power_power_int(A_70),one_one_nat) = A_70 ),
file('theBenchmark.p',fact_423_power__one__right) ).
fof(fact_424_power__one__right,axiom,
! [A_70] : hAPP_nat_real(power_power_real(A_70),one_one_nat) = A_70,
file('theBenchmark.p',fact_424_power__one__right) ).
fof(fact_425_power__one__right,axiom,
! [A_70] : hAPP_nat_nat(power_power_nat(A_70),one_one_nat) = A_70,
file('theBenchmark.p',fact_425_power__one__right) ).
fof(fact_426_int__one__le__iff__zero__less,axiom,
! [Z_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Z_1))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_1)) ),
file('theBenchmark.p',fact_426_int__one__le__iff__zero__less) ).
fof(fact_427_pos__zmult__eq__1__iff,axiom,
! [N,Ma] :
( ( is_int(Ma)
& is_int(N) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ma))
=> ( hAPP_int_int(times_times_int(Ma),N) = one_one_int
<=> ( N = one_one_int
& Ma = one_one_int ) ) ) ),
file('theBenchmark.p',fact_427_pos__zmult__eq__1__iff) ).
fof(fact_428_odd__less__0,axiom,
! [Z_1] :
( 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),Z_1)),Z_1)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),zero_zero_int)) ),
file('theBenchmark.p',fact_428_odd__less__0) ).
fof(fact_429_less__special_I1_J,axiom,
! [Y_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),Y_2)) ),
file('theBenchmark.p',fact_429_less__special_I1_J) ).
fof(fact_430_less__special_I1_J,axiom,
! [Y_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),Y_2)) ),
file('theBenchmark.p',fact_430_less__special_I1_J) ).
fof(fact_431_less__special_I3_J,axiom,
! [X_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X_2)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),pls)) ),
file('theBenchmark.p',fact_431_less__special_I3_J) ).
fof(fact_432_less__special_I3_J,axiom,
! [X_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X_2)),zero_zero_real))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),pls)) ),
file('theBenchmark.p',fact_432_less__special_I3_J) ).
fof(fact_433_le__special_I1_J,axiom,
! [Y_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Y_2)) ),
file('theBenchmark.p',fact_433_le__special_I1_J) ).
fof(fact_434_le__special_I1_J,axiom,
! [Y_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Y_2)) ),
file('theBenchmark.p',fact_434_le__special_I1_J) ).
fof(fact_435_le__special_I3_J,axiom,
! [X_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X_2)),zero_zero_real))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),pls)) ),
file('theBenchmark.p',fact_435_le__special_I3_J) ).
fof(fact_436_le__special_I3_J,axiom,
! [X_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X_2)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),pls)) ),
file('theBenchmark.p',fact_436_le__special_I3_J) ).
fof(fact_437_le__imp__0__less,axiom,
! [Z] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),Z))) ),
file('theBenchmark.p',fact_437_le__imp__0__less) ).
fof(fact_438_zero__power2,axiom,
hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real,
file('theBenchmark.p',fact_438_zero__power2) ).
fof(fact_439_zero__power2,axiom,
hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_nat,
file('theBenchmark.p',fact_439_zero__power2) ).
fof(fact_440_zero__power2,axiom,
hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
file('theBenchmark.p',fact_440_zero__power2) ).
fof(fact_441_zero__eq__power2,axiom,
! [A_2] :
( hAPP_nat_real(power_power_real(A_2),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real
<=> A_2 = zero_zero_real ),
file('theBenchmark.p',fact_441_zero__eq__power2) ).
fof(fact_442_zero__eq__power2,axiom,
! [A_2] :
( is_int(A_2)
=> ( hAPP_nat_int(power_power_int(A_2),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int
<=> A_2 = zero_zero_int ) ),
file('theBenchmark.p',fact_442_zero__eq__power2) ).
fof(fact_443_zero__le__power2,axiom,
! [A_69] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(A_69),number_number_of_nat(bit0(bit1(pls)))))),
file('theBenchmark.p',fact_443_zero__le__power2) ).
fof(fact_444_zero__le__power2,axiom,
! [A_69] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(A_69),number_number_of_nat(bit0(bit1(pls)))))),
file('theBenchmark.p',fact_444_zero__le__power2) ).
fof(fact_445_power2__le__imp__le,axiom,
! [X_15,Y_12] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X_15),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_12),number_number_of_nat(bit0(bit1(pls))))))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y_12))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_15),Y_12)) ) ),
file('theBenchmark.p',fact_445_power2__le__imp__le) ).
fof(fact_446_power2__le__imp__le,axiom,
! [X_15,Y_12] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X_15),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(Y_12),number_number_of_nat(bit0(bit1(pls))))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),Y_12))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_15),Y_12)) ) ),
file('theBenchmark.p',fact_446_power2__le__imp__le) ).
fof(fact_447_power2__le__imp__le,axiom,
! [X_15,Y_12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X_15),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_12),number_number_of_nat(bit0(bit1(pls))))))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_12))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_15),Y_12)) ) ),
file('theBenchmark.p',fact_447_power2__le__imp__le) ).
fof(fact_448_power2__eq__imp__eq,axiom,
! [X_14,Y_11] :
( hAPP_nat_real(power_power_real(X_14),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_real(power_power_real(Y_11),number_number_of_nat(bit0(bit1(pls))))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_14))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y_11))
=> X_14 = Y_11 ) ) ),
file('theBenchmark.p',fact_448_power2__eq__imp__eq) ).
fof(fact_449_power2__eq__imp__eq,axiom,
! [X_14,Y_11] :
( hAPP_nat_nat(power_power_nat(X_14),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(power_power_nat(Y_11),number_number_of_nat(bit0(bit1(pls))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X_14))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),Y_11))
=> X_14 = Y_11 ) ) ),
file('theBenchmark.p',fact_449_power2__eq__imp__eq) ).
fof(fact_450_power2__eq__imp__eq,axiom,
! [X_14,Y_11] :
( ( is_int(Y_11)
& is_int(X_14) )
=> ( hAPP_nat_int(power_power_int(X_14),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(Y_11),number_number_of_nat(bit0(bit1(pls))))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_14))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_11))
=> X_14 = Y_11 ) ) ) ),
file('theBenchmark.p',fact_450_power2__eq__imp__eq) ).
fof(fact_451_power2__less__0,axiom,
! [A_68] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(A_68),number_number_of_nat(bit0(bit1(pls))))),zero_zero_real)),
file('theBenchmark.p',fact_451_power2__less__0) ).
fof(fact_452_power2__less__0,axiom,
! [A_68] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(A_68),number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)),
file('theBenchmark.p',fact_452_power2__less__0) ).
fof(fact_453_zero__less__power2,axiom,
! [A_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(A_2),number_number_of_nat(bit0(bit1(pls))))))
<=> A_2 != zero_zero_real ),
file('theBenchmark.p',fact_453_zero__less__power2) ).
fof(fact_454_zero__less__power2,axiom,
! [A_2] :
( is_int(A_2)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_2),number_number_of_nat(bit0(bit1(pls))))))
<=> A_2 != zero_zero_int ) ),
file('theBenchmark.p',fact_454_zero__less__power2) ).
fof(fact_455_sum__power2__eq__zero__iff,axiom,
! [X_2,Y_2] :
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
<=> ( Y_2 = zero_zero_real
& X_2 = zero_zero_real ) ),
file('theBenchmark.p',fact_455_sum__power2__eq__zero__iff) ).
fof(fact_456_sum__power2__eq__zero__iff,axiom,
! [X_2,Y_2] :
( ( is_int(Y_2)
& is_int(X_2) )
=> ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int
<=> ( Y_2 = zero_zero_int
& X_2 = zero_zero_int ) ) ),
file('theBenchmark.p',fact_456_sum__power2__eq__zero__iff) ).
fof(fact_457_power__commutes,axiom,
! [A_67,N_18] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(A_67),N_18)),A_67) = hAPP_nat_nat(times_times_nat(A_67),hAPP_nat_nat(power_power_nat(A_67),N_18)),
file('theBenchmark.p',fact_457_power__commutes) ).
fof(fact_458_power__commutes,axiom,
! [A_67,N_18] : hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(A_67),N_18)),A_67) = hAPP_real_real(times_times_real(A_67),hAPP_nat_real(power_power_real(A_67),N_18)),
file('theBenchmark.p',fact_458_power__commutes) ).
fof(fact_459_power__commutes,axiom,
! [A_67,N_18] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(A_67),N_18)),A_67) = hAPP_int_int(times_times_int(A_67),hAPP_nat_int(power_power_int(A_67),N_18)),
file('theBenchmark.p',fact_459_power__commutes) ).
fof(fact_460_power__mult__distrib,axiom,
! [A_66,B_49,N_17] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(A_66),B_49)),N_17) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(A_66),N_17)),hAPP_nat_nat(power_power_nat(B_49),N_17)),
file('theBenchmark.p',fact_460_power__mult__distrib) ).
fof(fact_461_power__mult__distrib,axiom,
! [A_66,B_49,N_17] : hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(A_66),B_49)),N_17) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(A_66),N_17)),hAPP_nat_real(power_power_real(B_49),N_17)),
file('theBenchmark.p',fact_461_power__mult__distrib) ).
fof(fact_462_power__mult__distrib,axiom,
! [A_66,B_49,N_17] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(A_66),B_49)),N_17) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(A_66),N_17)),hAPP_nat_int(power_power_int(B_49),N_17)),
file('theBenchmark.p',fact_462_power__mult__distrib) ).
fof(fact_463_power__add,axiom,
! [A_65,M_5,N_16] : hAPP_nat_nat(power_power_nat(A_65),hAPP_nat_nat(plus_plus_nat(M_5),N_16)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(A_65),M_5)),hAPP_nat_nat(power_power_nat(A_65),N_16)),
file('theBenchmark.p',fact_463_power__add) ).
fof(fact_464_power__add,axiom,
! [A_65,M_5,N_16] : hAPP_nat_real(power_power_real(A_65),hAPP_nat_nat(plus_plus_nat(M_5),N_16)) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(A_65),M_5)),hAPP_nat_real(power_power_real(A_65),N_16)),
file('theBenchmark.p',fact_464_power__add) ).
fof(fact_465_power__add,axiom,
! [A_65,M_5,N_16] : hAPP_nat_int(power_power_int(A_65),hAPP_nat_nat(plus_plus_nat(M_5),N_16)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(A_65),M_5)),hAPP_nat_int(power_power_int(A_65),N_16)),
file('theBenchmark.p',fact_465_power__add) ).
fof(fact_466_power__one,axiom,
! [N_15] : hAPP_nat_real(power_power_real(one_one_real),N_15) = one_one_real,
file('theBenchmark.p',fact_466_power__one) ).
fof(fact_467_power__one,axiom,
! [N_15] : hAPP_nat_nat(power_power_nat(one_one_nat),N_15) = one_one_nat,
file('theBenchmark.p',fact_467_power__one) ).
fof(fact_468_power__one,axiom,
! [N_15] : hAPP_nat_int(power_power_int(one_one_int),N_15) = one_one_int,
file('theBenchmark.p',fact_468_power__one) ).
fof(fact_469_power__mult,axiom,
! [A_64,M_4,N_14] : hAPP_nat_nat(power_power_nat(A_64),hAPP_nat_nat(times_times_nat(M_4),N_14)) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(A_64),M_4)),N_14),
file('theBenchmark.p',fact_469_power__mult) ).
fof(fact_470_power__mult,axiom,
! [A_64,M_4,N_14] : hAPP_nat_real(power_power_real(A_64),hAPP_nat_nat(times_times_nat(M_4),N_14)) = hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(A_64),M_4)),N_14),
file('theBenchmark.p',fact_470_power__mult) ).
fof(fact_471_power__mult,axiom,
! [A_64,M_4,N_14] : hAPP_nat_int(power_power_int(A_64),hAPP_nat_nat(times_times_nat(M_4),N_14)) = hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(A_64),M_4)),N_14),
file('theBenchmark.p',fact_471_power__mult) ).
fof(fact_472_power2__less__imp__less,axiom,
! [X_13,Y_10] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X_13),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_10),number_number_of_nat(bit0(bit1(pls))))))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y_10))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_13),Y_10)) ) ),
file('theBenchmark.p',fact_472_power2__less__imp__less) ).
fof(fact_473_power2__less__imp__less,axiom,
! [X_13,Y_10] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X_13),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(Y_10),number_number_of_nat(bit0(bit1(pls))))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),Y_10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_13),Y_10)) ) ),
file('theBenchmark.p',fact_473_power2__less__imp__less) ).
fof(fact_474_power2__less__imp__less,axiom,
! [X_13,Y_10] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X_13),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_10),number_number_of_nat(bit0(bit1(pls))))))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_10))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_13),Y_10)) ) ),
file('theBenchmark.p',fact_474_power2__less__imp__less) ).
fof(fact_475_sum__power2__ge__zero,axiom,
! [X_12,Y_9] : 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(X_12),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_9),number_number_of_nat(bit0(bit1(pls))))))),
file('theBenchmark.p',fact_475_sum__power2__ge__zero) ).
fof(fact_476_sum__power2__ge__zero,axiom,
! [X_12,Y_9] : 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(X_12),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_9),number_number_of_nat(bit0(bit1(pls))))))),
file('theBenchmark.p',fact_476_sum__power2__ge__zero) ).
fof(fact_477_sum__power2__le__zero__iff,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real))
<=> ( Y_2 = zero_zero_real
& X_2 = zero_zero_real ) ),
file('theBenchmark.p',fact_477_sum__power2__le__zero__iff) ).
fof(fact_478_sum__power2__le__zero__iff,axiom,
! [X_2,Y_2] :
( ( is_int(Y_2)
& is_int(X_2) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
<=> ( Y_2 = zero_zero_int
& X_2 = zero_zero_int ) ) ),
file('theBenchmark.p',fact_478_sum__power2__le__zero__iff) ).
fof(fact_479_not__sum__power2__lt__zero,axiom,
! [X_11,Y_8] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X_11),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_8),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)),
file('theBenchmark.p',fact_479_not__sum__power2__lt__zero) ).
fof(fact_480_not__sum__power2__lt__zero,axiom,
! [X_11,Y_8] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X_11),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_8),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)),
file('theBenchmark.p',fact_480_not__sum__power2__lt__zero) ).
fof(fact_481_sum__power2__gt__zero__iff,axiom,
! [X_2,Y_2] :
( 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(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_2),number_number_of_nat(bit0(bit1(pls)))))))
<=> ( Y_2 != zero_zero_real
| X_2 != zero_zero_real ) ),
file('theBenchmark.p',fact_481_sum__power2__gt__zero__iff) ).
fof(fact_482_sum__power2__gt__zero__iff,axiom,
! [X_2,Y_2] :
( ( is_int(Y_2)
& is_int(X_2) )
=> ( 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(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_2),number_number_of_nat(bit0(bit1(pls)))))))
<=> ( Y_2 != zero_zero_int
| X_2 != zero_zero_int ) ) ),
file('theBenchmark.p',fact_482_sum__power2__gt__zero__iff) ).
fof(fact_483_zero__le__even__power_H,axiom,
! [A_63,N_13] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(A_63),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_13)))),
file('theBenchmark.p',fact_483_zero__le__even__power_H) ).
fof(fact_484_zero__le__even__power_H,axiom,
! [A_63,N_13] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(A_63),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_13)))),
file('theBenchmark.p',fact_484_zero__le__even__power_H) ).
fof(fact_485_one__le__power,axiom,
! [N_12,A_62] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),A_62))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(A_62),N_12))) ),
file('theBenchmark.p',fact_485_one__le__power) ).
fof(fact_486_one__le__power,axiom,
! [N_12,A_62] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),A_62))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(power_power_nat(A_62),N_12))) ),
file('theBenchmark.p',fact_486_one__le__power) ).
fof(fact_487_one__le__power,axiom,
! [N_12,A_62] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),A_62))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(power_power_int(A_62),N_12))) ),
file('theBenchmark.p',fact_487_one__le__power) ).
fof(fact_488_power__increasing,axiom,
! [A_61,N_11,N_10] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_11),N_10))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),A_61))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(A_61),N_11)),hAPP_nat_real(power_power_real(A_61),N_10))) ) ),
file('theBenchmark.p',fact_488_power__increasing) ).
fof(fact_489_power__increasing,axiom,
! [A_61,N_11,N_10] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_11),N_10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),A_61))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(A_61),N_11)),hAPP_nat_nat(power_power_nat(A_61),N_10))) ) ),
file('theBenchmark.p',fact_489_power__increasing) ).
fof(fact_490_power__increasing,axiom,
! [A_61,N_11,N_10] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_11),N_10))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),A_61))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(A_61),N_11)),hAPP_nat_int(power_power_int(A_61),N_10))) ) ),
file('theBenchmark.p',fact_490_power__increasing) ).
fof(fact_491_power__inject__exp,axiom,
! [Ma,N,A_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),A_2))
=> ( hAPP_nat_real(power_power_real(A_2),Ma) = hAPP_nat_real(power_power_real(A_2),N)
<=> Ma = N ) ),
file('theBenchmark.p',fact_491_power__inject__exp) ).
fof(fact_492_power__inject__exp,axiom,
! [Ma,N,A_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),A_2))
=> ( hAPP_nat_nat(power_power_nat(A_2),Ma) = hAPP_nat_nat(power_power_nat(A_2),N)
<=> Ma = N ) ),
file('theBenchmark.p',fact_492_power__inject__exp) ).
fof(fact_493_power__inject__exp,axiom,
! [Ma,N,A_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_2))
=> ( hAPP_nat_int(power_power_int(A_2),Ma) = hAPP_nat_int(power_power_int(A_2),N)
<=> Ma = N ) ),
file('theBenchmark.p',fact_493_power__inject__exp) ).
fof(fact_494_power__strict__increasing__iff,axiom,
! [X_2,Y_2,B_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),B_2))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(B_2),X_2)),hAPP_nat_real(power_power_real(B_2),Y_2)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) ) ),
file('theBenchmark.p',fact_494_power__strict__increasing__iff) ).
fof(fact_495_power__strict__increasing__iff,axiom,
! [X_2,Y_2,B_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),B_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(B_2),X_2)),hAPP_nat_nat(power_power_nat(B_2),Y_2)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) ) ),
file('theBenchmark.p',fact_495_power__strict__increasing__iff) ).
fof(fact_496_power__strict__increasing__iff,axiom,
! [X_2,Y_2,B_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),B_2))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(B_2),X_2)),hAPP_nat_int(power_power_int(B_2),Y_2)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) ) ),
file('theBenchmark.p',fact_496_power__strict__increasing__iff) ).
fof(fact_497_power__less__imp__less__exp,axiom,
! [M_3,N_9,A_60] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),A_60))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(A_60),M_3)),hAPP_nat_real(power_power_real(A_60),N_9)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_3),N_9)) ) ),
file('theBenchmark.p',fact_497_power__less__imp__less__exp) ).
fof(fact_498_power__less__imp__less__exp,axiom,
! [M_3,N_9,A_60] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),A_60))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(A_60),M_3)),hAPP_nat_nat(power_power_nat(A_60),N_9)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_3),N_9)) ) ),
file('theBenchmark.p',fact_498_power__less__imp__less__exp) ).
fof(fact_499_power__less__imp__less__exp,axiom,
! [M_3,N_9,A_60] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_60))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(A_60),M_3)),hAPP_nat_int(power_power_int(A_60),N_9)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_3),N_9)) ) ),
file('theBenchmark.p',fact_499_power__less__imp__less__exp) ).
fof(fact_500_power__strict__increasing,axiom,
! [A_59,N_8,N_7] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_8),N_7))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),A_59))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(A_59),N_8)),hAPP_nat_real(power_power_real(A_59),N_7))) ) ),
file('theBenchmark.p',fact_500_power__strict__increasing) ).
fof(fact_501_power__strict__increasing,axiom,
! [A_59,N_8,N_7] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_8),N_7))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),A_59))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(A_59),N_8)),hAPP_nat_nat(power_power_nat(A_59),N_7))) ) ),
file('theBenchmark.p',fact_501_power__strict__increasing) ).
fof(fact_502_power__strict__increasing,axiom,
! [A_59,N_8,N_7] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_8),N_7))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_59))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(A_59),N_8)),hAPP_nat_int(power_power_int(A_59),N_7))) ) ),
file('theBenchmark.p',fact_502_power__strict__increasing) ).
fof(fact_503_s,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('theBenchmark.p',fact_503_s) ).
fof(fact_504_Euler_Oaux____1,axiom,
! [Y_1,X_1,P_1] :
( ~ hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),P_1))
=> ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(Y_1),number_number_of_nat(bit0(bit1(pls)))),X_1),P_1))
=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),Y_1)) ) ),
file('theBenchmark.p',fact_504_Euler_Oaux____1) ).
fof(fact_505_int__pos__lt__two__imp__zero__or__one,axiom,
! [X_1] :
( is_int(X_1)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),number_number_of_int(bit0(bit1(pls)))))
=> ( X_1 = one_one_int
| X_1 = zero_zero_int ) ) ) ),
file('theBenchmark.p',fact_505_int__pos__lt__two__imp__zero__or__one) ).
fof(fact_506_even__power__le__0__imp__0,axiom,
! [A_58,K_4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(A_58),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),K_4))),zero_zero_real))
=> A_58 = zero_zero_real ),
file('theBenchmark.p',fact_506_even__power__le__0__imp__0) ).
fof(fact_507_even__power__le__0__imp__0,axiom,
! [A_58,K_4] :
( is_int(A_58)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(A_58),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),K_4))),zero_zero_int))
=> A_58 = zero_zero_int ) ),
file('theBenchmark.p',fact_507_even__power__le__0__imp__0) ).
fof(fact_508_zprime__def,axiom,
! [P_3] :
( is_int(P_3)
=> ( hBOOL(hAPP_int_bool(zprime,P_3))
<=> ( ! [M_2] :
( is_int(M_2)
=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,M_2),P_3))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),M_2)) )
=> ( M_2 = P_3
| M_2 = one_one_int ) ) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),P_3)) ) ) ),
file('theBenchmark.p',fact_508_zprime__def) ).
fof(fact_509_self__quotient__aux2,axiom,
! [R_1,Q_1,A] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A))
=> ( A = hAPP_int_int(plus_plus_int(R_1),hAPP_int_int(times_times_int(A),Q_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),one_one_int)) ) ) ),
file('theBenchmark.p',fact_509_self__quotient__aux2) ).
fof(fact_510_self__quotient__aux1,axiom,
! [R_1,Q_1,A] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A))
=> ( A = hAPP_int_int(plus_plus_int(R_1),hAPP_int_int(times_times_int(A),Q_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),A))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Q_1)) ) ) ),
file('theBenchmark.p',fact_510_self__quotient__aux1) ).
fof(fact_511_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(bit1(pls))))),
file('theBenchmark.p',fact_511_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
fof(fact_512__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_,axiom,
~ ! [S1] :
( is_int(S1)
=> ~ 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('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(fact_513__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096,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('theBenchmark.p',fact_513__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096) ).
fof(fact_514_nat__zero__less__power__iff,axiom,
! [X_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X_2),N)))
<=> ( N = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X_2)) ) ),
file('theBenchmark.p',fact_514_nat__zero__less__power__iff) ).
fof(fact_515_zero__less__power__nat__eq,axiom,
! [X_2,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X_2),N)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X_2))
| N = zero_zero_nat ) ),
file('theBenchmark.p',fact_515_zero__less__power__nat__eq) ).
fof(fact_516_zero__less__power__nat__eq__number__of,axiom,
! [X_2,W_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X_2),number_number_of_nat(W_1))))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X_2))
| number_number_of_nat(W_1) = zero_zero_nat ) ),
file('theBenchmark.p',fact_516_zero__less__power__nat__eq__number__of) ).
fof(fact_517_nat__power__less__imp__less,axiom,
! [M,N_1,I_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),I_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(I_1),M)),hAPP_nat_nat(power_power_nat(I_1),N_1)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ) ),
file('theBenchmark.p',fact_517_nat__power__less__imp__less) ).
fof(fact_518_rel__simps_I47_J,axiom,
! [K] :
( is_int(K)
=> ( bit1(K) = min
<=> K = min ) ),
file('theBenchmark.p',fact_518_rel__simps_I47_J) ).
fof(fact_519_rel__simps_I43_J,axiom,
! [L_1] :
( is_int(L_1)
=> ( min = bit1(L_1)
<=> min = L_1 ) ),
file('theBenchmark.p',fact_519_rel__simps_I43_J) ).
fof(fact_520_Bit1__Min,axiom,
bit1(min) = min,
file('theBenchmark.p',fact_520_Bit1__Min) ).
fof(fact_521_rel__simps_I37_J,axiom,
pls != min,
file('theBenchmark.p',fact_521_rel__simps_I37_J) ).
fof(fact_522_rel__simps_I40_J,axiom,
min != pls,
file('theBenchmark.p',fact_522_rel__simps_I40_J) ).
fof(fact_523_rel__simps_I45_J,axiom,
! [K_1] : bit0(K_1) != min,
file('theBenchmark.p',fact_523_rel__simps_I45_J) ).
fof(fact_524_rel__simps_I42_J,axiom,
! [L] : min != bit0(L),
file('theBenchmark.p',fact_524_rel__simps_I42_J) ).
fof(fact_525_rel__simps_I7_J,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),min)),
file('theBenchmark.p',fact_525_rel__simps_I7_J) ).
fof(fact_526_rel__simps_I24_J,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),min)),
file('theBenchmark.p',fact_526_rel__simps_I24_J) ).
fof(fact_527_not__real__square__gt__zero,axiom,
! [X_2] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X_2),X_2)))
<=> X_2 = zero_zero_real ),
file('theBenchmark.p',fact_527_not__real__square__gt__zero) ).
fof(fact_528_rel__simps_I13_J,axiom,
! [K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),min))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),min)) ),
file('theBenchmark.p',fact_528_rel__simps_I13_J) ).
fof(fact_529_rel__simps_I9_J,axiom,
! [K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit1(K)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),K)) ),
file('theBenchmark.p',fact_529_rel__simps_I9_J) ).
fof(fact_530_rel__simps_I3_J,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),min)),
file('theBenchmark.p',fact_530_rel__simps_I3_J) ).
fof(fact_531_rel__simps_I6_J,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),pls)),
file('theBenchmark.p',fact_531_rel__simps_I6_J) ).
fof(fact_532_rel__simps_I8_J,axiom,
! [K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit0(K)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),K)) ),
file('theBenchmark.p',fact_532_rel__simps_I8_J) ).
fof(fact_533_bin__less__0__simps_I2_J,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),zero_zero_int)),
file('theBenchmark.p',fact_533_bin__less__0__simps_I2_J) ).
fof(fact_534_rel__simps_I30_J,axiom,
! [K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),min))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),min)) ),
file('theBenchmark.p',fact_534_rel__simps_I30_J) ).
fof(fact_535_rel__simps_I26_J,axiom,
! [K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit1(K)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),K)) ),
file('theBenchmark.p',fact_535_rel__simps_I26_J) ).
fof(fact_536_rel__simps_I20_J,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),min)),
file('theBenchmark.p',fact_536_rel__simps_I20_J) ).
fof(fact_537_rel__simps_I23_J,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),pls)),
file('theBenchmark.p',fact_537_rel__simps_I23_J) ).
fof(fact_538_rel__simps_I28_J,axiom,
! [K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(K)),min))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),min)) ),
file('theBenchmark.p',fact_538_rel__simps_I28_J) ).
fof(fact_539_eq__number__of__Pls__Min,axiom,
number_number_of_int(pls) != number_number_of_int(min),
file('theBenchmark.p',fact_539_eq__number__of__Pls__Min) ).
fof(fact_540_power__dvd__imp__le,axiom,
! [I_1,M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(I_1),M)),hAPP_nat_nat(power_power_nat(I_1),N_1)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),I_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) ) ),
file('theBenchmark.p',fact_540_power__dvd__imp__le) ).
fof(fact_541_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [X_10] : hAPP_nat_real(power_power_real(X_10),zero_zero_nat) = one_one_real,
file('theBenchmark.p',fact_541_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_542_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [X_10] : hAPP_nat_nat(power_power_nat(X_10),zero_zero_nat) = one_one_nat,
file('theBenchmark.p',fact_542_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_543_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [X_10] : hAPP_nat_int(power_power_int(X_10),zero_zero_nat) = one_one_int,
file('theBenchmark.p',fact_543_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_544_power__0,axiom,
! [A_57] : hAPP_nat_real(power_power_real(A_57),zero_zero_nat) = one_one_real,
file('theBenchmark.p',fact_544_power__0) ).
fof(fact_545_power__0,axiom,
! [A_57] : hAPP_nat_nat(power_power_nat(A_57),zero_zero_nat) = one_one_nat,
file('theBenchmark.p',fact_545_power__0) ).
fof(fact_546_power__0,axiom,
! [A_57] : hAPP_nat_int(power_power_int(A_57),zero_zero_nat) = one_one_int,
file('theBenchmark.p',fact_546_power__0) ).
fof(fact_547_nat__number__of__Pls,axiom,
number_number_of_nat(pls) = zero_zero_nat,
file('theBenchmark.p',fact_547_nat__number__of__Pls) ).
fof(fact_548_semiring__norm_I113_J,axiom,
zero_zero_nat = number_number_of_nat(pls),
file('theBenchmark.p',fact_548_semiring__norm_I113_J) ).
fof(fact_549_rel__simps_I25_J,axiom,
! [K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit0(K)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),K)) ),
file('theBenchmark.p',fact_549_rel__simps_I25_J) ).
fof(fact_550_rel__simps_I11_J,axiom,
! [K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(K)),min))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),min)) ),
file('theBenchmark.p',fact_550_rel__simps_I11_J) ).
fof(fact_551_pos__zmult__eq__1__iff__lemma,axiom,
! [M,N_1] :
( is_int(M)
=> ( hAPP_int_int(times_times_int(M),N_1) = one_one_int
=> ( M = number_number_of_int(min)
| M = one_one_int ) ) ),
file('theBenchmark.p',fact_551_pos__zmult__eq__1__iff__lemma) ).
fof(fact_552_zmult__eq__1__iff,axiom,
! [Ma,N] :
( ( is_int(N)
& is_int(Ma) )
=> ( hAPP_int_int(times_times_int(Ma),N) = one_one_int
<=> ( ( N = number_number_of_int(min)
& Ma = number_number_of_int(min) )
| ( N = one_one_int
& Ma = one_one_int ) ) ) ),
file('theBenchmark.p',fact_552_zmult__eq__1__iff) ).
fof(fact_553_one__less__power,axiom,
! [N_6,A_56] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),A_56))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_6))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_nat_real(power_power_real(A_56),N_6))) ) ),
file('theBenchmark.p',fact_553_one__less__power) ).
fof(fact_554_one__less__power,axiom,
! [N_6,A_56] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),A_56))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_6))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(power_power_nat(A_56),N_6))) ) ),
file('theBenchmark.p',fact_554_one__less__power) ).
fof(fact_555_one__less__power,axiom,
! [N_6,A_56] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_56))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_6))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_nat_int(power_power_int(A_56),N_6))) ) ),
file('theBenchmark.p',fact_555_one__less__power) ).
fof(fact_556_dvd__power,axiom,
! [X_9,N_5] :
( ( X_9 = one_one_real
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_5)) )
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X_9),hAPP_nat_real(power_power_real(X_9),N_5))) ),
file('theBenchmark.p',fact_556_dvd__power) ).
fof(fact_557_dvd__power,axiom,
! [X_9,N_5] :
( ( X_9 = one_one_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_5)) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_9),hAPP_nat_nat(power_power_nat(X_9),N_5))) ),
file('theBenchmark.p',fact_557_dvd__power) ).
fof(fact_558_dvd__power,axiom,
! [X_9,N_5] :
( ( X_9 = one_one_int
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_5)) )
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X_9),hAPP_nat_int(power_power_int(X_9),N_5))) ),
file('theBenchmark.p',fact_558_dvd__power) ).
fof(fact_559_less__0__number__of,axiom,
! [V_7] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(V_7)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),V_7)) ),
file('theBenchmark.p',fact_559_less__0__number__of) ).
fof(fact_560_eq__number__of__0,axiom,
! [V_7] :
( number_number_of_nat(V_7) = zero_zero_nat
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V_7),pls)) ),
file('theBenchmark.p',fact_560_eq__number__of__0) ).
fof(fact_561_eq__0__number__of,axiom,
! [V_7] :
( zero_zero_nat = number_number_of_nat(V_7)
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V_7),pls)) ),
file('theBenchmark.p',fact_561_eq__0__number__of) ).
fof(fact_562_zcong__sym,axiom,
! [A_2,B_2,Ma] :
( hBOOL(hAPP_int_bool(zcong(A_2,B_2),Ma))
<=> hBOOL(hAPP_int_bool(zcong(B_2,A_2),Ma)) ),
file('theBenchmark.p',fact_562_zcong__sym) ).
fof(fact_563_zcong__refl,axiom,
! [K_1,M] : hBOOL(hAPP_int_bool(zcong(K_1,K_1),M)),
file('theBenchmark.p',fact_563_zcong__refl) ).
fof(fact_564_zcong__trans,axiom,
! [C,A,B,M] :
( hBOOL(hAPP_int_bool(zcong(A,B),M))
=> ( hBOOL(hAPP_int_bool(zcong(B,C),M))
=> hBOOL(hAPP_int_bool(zcong(A,C),M)) ) ),
file('theBenchmark.p',fact_564_zcong__trans) ).
fof(fact_565_pos2,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(bit0(bit1(pls))))),
file('theBenchmark.p',fact_565_pos2) ).
fof(fact_566_nat__number__of__mult__left,axiom,
! [V_6,K_1,V] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls))
=> hAPP_nat_nat(times_times_nat(number_number_of_nat(V)),hAPP_nat_nat(times_times_nat(number_number_of_nat(V_6)),K_1)) = hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(times_times_int(V),V_6))),K_1) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls))
=> hAPP_nat_nat(times_times_nat(number_number_of_nat(V)),hAPP_nat_nat(times_times_nat(number_number_of_nat(V_6)),K_1)) = zero_zero_nat ) ),
file('theBenchmark.p',fact_566_nat__number__of__mult__left) ).
fof(fact_567_mult__nat__number__of,axiom,
! [V_6,V] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls))
=> hAPP_nat_nat(times_times_nat(number_number_of_nat(V)),number_number_of_nat(V_6)) = number_number_of_nat(hAPP_int_int(times_times_int(V),V_6)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls))
=> hAPP_nat_nat(times_times_nat(number_number_of_nat(V)),number_number_of_nat(V_6)) = zero_zero_nat ) ),
file('theBenchmark.p',fact_567_mult__nat__number__of) ).
fof(fact_568_order__le__neq__implies__less,axiom,
! [X_8,Y_7] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_8),Y_7))
=> ( X_8 != Y_7
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_8),Y_7)) ) ),
file('theBenchmark.p',fact_568_order__le__neq__implies__less) ).
fof(fact_569_order__le__neq__implies__less,axiom,
! [X_8,Y_7] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_8),Y_7))
=> ( X_8 != Y_7
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_8),Y_7)) ) ),
file('theBenchmark.p',fact_569_order__le__neq__implies__less) ).
fof(fact_570_order__le__neq__implies__less,axiom,
! [X_8,Y_7] :
( ( is_int(Y_7)
& is_int(X_8) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_8),Y_7))
=> ( X_8 != Y_7
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_8),Y_7)) ) ) ),
file('theBenchmark.p',fact_570_order__le__neq__implies__less) ).
fof(fact_571_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
file('theBenchmark.p',fact_571_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
fof(fact_572_Euler_Oaux2,axiom,
! [B,A,C] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),C))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),C))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B),A))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A),B)) ) ) ),
file('theBenchmark.p',fact_572_Euler_Oaux2) ).
fof(fact_573_IntPrimes_Ozcong__zero,axiom,
! [A_2,B_2] :
( ( is_int(B_2)
& is_int(A_2) )
=> ( hBOOL(hAPP_int_bool(zcong(A_2,B_2),zero_zero_int))
<=> A_2 = B_2 ) ),
file('theBenchmark.p',fact_573_IntPrimes_Ozcong__zero) ).
fof(fact_574_zcong__1,axiom,
! [A,B] : hBOOL(hAPP_int_bool(zcong(A,B),one_one_int)),
file('theBenchmark.p',fact_574_zcong__1) ).
fof(fact_575_zcong__zmult,axiom,
! [C,D_5,A,B,M] :
( hBOOL(hAPP_int_bool(zcong(A,B),M))
=> ( hBOOL(hAPP_int_bool(zcong(C,D_5),M))
=> hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),C),hAPP_int_int(times_times_int(B),D_5)),M)) ) ),
file('theBenchmark.p',fact_575_zcong__zmult) ).
fof(fact_576_zcong__scalar2,axiom,
! [K_1,A,B,M] :
( hBOOL(hAPP_int_bool(zcong(A,B),M))
=> hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(K_1),A),hAPP_int_int(times_times_int(K_1),B)),M)) ),
file('theBenchmark.p',fact_576_zcong__scalar2) ).
fof(fact_577_zcong__scalar,axiom,
! [K_1,A,B,M] :
( hBOOL(hAPP_int_bool(zcong(A,B),M))
=> hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),K_1),hAPP_int_int(times_times_int(B),K_1)),M)) ),
file('theBenchmark.p',fact_577_zcong__scalar) ).
fof(fact_578_zcong__zmult__self,axiom,
! [A,M,B] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),M),hAPP_int_int(times_times_int(B),M)),M)),
file('theBenchmark.p',fact_578_zcong__zmult__self) ).
fof(fact_579_zcong__zadd,axiom,
! [C,D_5,A,B,M] :
( hBOOL(hAPP_int_bool(zcong(A,B),M))
=> ( hBOOL(hAPP_int_bool(zcong(C,D_5),M))
=> hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(A),C),hAPP_int_int(plus_plus_int(B),D_5)),M)) ) ),
file('theBenchmark.p',fact_579_zcong__zadd) ).
fof(fact_580_power__m1__even,axiom,
! [N_4] : hAPP_nat_real(power_power_real(number267125858f_real(min)),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_4)) = one_one_real,
file('theBenchmark.p',fact_580_power__m1__even) ).
fof(fact_581_power__m1__even,axiom,
! [N_4] : hAPP_nat_int(power_power_int(number_number_of_int(min)),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_4)) = one_one_int,
file('theBenchmark.p',fact_581_power__m1__even) ).
fof(fact_582_power__eq__0__iff__number__of,axiom,
! [A_2,W_1] :
( hAPP_nat_real(power_power_real(A_2),number_number_of_nat(W_1)) = zero_zero_real
<=> ( number_number_of_nat(W_1) != zero_zero_nat
& A_2 = zero_zero_real ) ),
file('theBenchmark.p',fact_582_power__eq__0__iff__number__of) ).
fof(fact_583_power__eq__0__iff__number__of,axiom,
! [A_2,W_1] :
( hAPP_nat_nat(power_power_nat(A_2),number_number_of_nat(W_1)) = zero_zero_nat
<=> ( number_number_of_nat(W_1) != zero_zero_nat
& A_2 = zero_zero_nat ) ),
file('theBenchmark.p',fact_583_power__eq__0__iff__number__of) ).
fof(fact_584_power__eq__0__iff__number__of,axiom,
! [A_2,W_1] :
( is_int(A_2)
=> ( hAPP_nat_int(power_power_int(A_2),number_number_of_nat(W_1)) = zero_zero_int
<=> ( number_number_of_nat(W_1) != zero_zero_nat
& A_2 = zero_zero_int ) ) ),
file('theBenchmark.p',fact_584_power__eq__0__iff__number__of) ).
fof(fact_585_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
file('theBenchmark.p',fact_585_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(fact_586_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
! [Y_1,X_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(X_1),Y_1))) ) ),
file('theBenchmark.p',fact_586_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_587_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
! [Y_1,X_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X_1),Y_1))) ) ),
file('theBenchmark.p',fact_587_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_588_zcong__not,axiom,
! [B,M,A] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),M))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),A))
=> ~ hBOOL(hAPP_int_bool(zcong(A,B),M)) ) ) ) ),
file('theBenchmark.p',fact_588_zcong__not) ).
fof(fact_589_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [N_1,X_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X_1),N_1))) ),
file('theBenchmark.p',fact_589_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(fact_590_zcong__iff__lin,axiom,
! [A_2,B_2,Ma] :
( is_int(B_2)
=> ( hBOOL(hAPP_int_bool(zcong(A_2,B_2),Ma))
<=> ? [K_2] :
( B_2 = hAPP_int_int(plus_plus_int(A_2),hAPP_int_int(times_times_int(Ma),K_2))
& is_int(K_2) ) ) ),
file('theBenchmark.p',fact_590_zcong__iff__lin) ).
fof(fact_591_power__0__left__number__of,axiom,
! [W_4] :
( ( number_number_of_nat(W_4) != zero_zero_nat
=> hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(W_4)) = zero_zero_real )
& ( number_number_of_nat(W_4) = zero_zero_nat
=> hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(W_4)) = one_one_real ) ),
file('theBenchmark.p',fact_591_power__0__left__number__of) ).
fof(fact_592_power__0__left__number__of,axiom,
! [W_4] :
( ( number_number_of_nat(W_4) != zero_zero_nat
=> hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(W_4)) = zero_zero_nat )
& ( number_number_of_nat(W_4) = zero_zero_nat
=> hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(W_4)) = one_one_nat ) ),
file('theBenchmark.p',fact_592_power__0__left__number__of) ).
fof(fact_593_power__0__left__number__of,axiom,
! [W_4] :
( ( number_number_of_nat(W_4) != zero_zero_nat
=> hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(W_4)) = zero_zero_int )
& ( number_number_of_nat(W_4) = zero_zero_nat
=> hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(W_4)) = one_one_int ) ),
file('theBenchmark.p',fact_593_power__0__left__number__of) ).
fof(fact_594_zcong__zless__imp__eq,axiom,
! [B,M,A] :
( ( is_int(A)
& is_int(B) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),M))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),M))
=> ( hBOOL(hAPP_int_bool(zcong(A,B),M))
=> A = B ) ) ) ) ) ),
file('theBenchmark.p',fact_594_zcong__zless__imp__eq) ).
fof(fact_595_zcong__zless__0,axiom,
! [M,A] :
( is_int(A)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),M))
=> ( hBOOL(hAPP_int_bool(zcong(A,zero_zero_int),M))
=> A = zero_zero_int ) ) ) ),
file('theBenchmark.p',fact_595_zcong__zless__0) ).
fof(fact_596_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(bit1(pls))))),
file('theBenchmark.p',fact_596_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
fof(fact_597_zdiv__mono2__neg__lemma,axiom,
! [B,Q_1,R_1,B_48,Q_4,R_3] :
( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),Q_1)),R_1) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B_48),Q_4)),R_3)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B_48),Q_4)),R_3)),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_3))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_48))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_48),B))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_4),Q_1)) ) ) ) ) ) ),
file('theBenchmark.p',fact_597_zdiv__mono2__neg__lemma) ).
fof(fact_598_unique__quotient__lemma__neg,axiom,
! [B,Q_4,R_3,Q_1,R_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),Q_4)),R_3)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),Q_1)),R_1)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_1),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),R_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),R_3))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q_4)) ) ) ) ),
file('theBenchmark.p',fact_598_unique__quotient__lemma__neg) ).
fof(fact_599_zdiv__mono2__lemma,axiom,
! [B,Q_1,R_1,B_48,Q_4,R_3] :
( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),Q_1)),R_1) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B_48),Q_4)),R_3)
=> ( 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(B_48),Q_4)),R_3)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_3),B_48))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_48))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_48),B))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q_4)) ) ) ) ) ) ),
file('theBenchmark.p',fact_599_zdiv__mono2__lemma) ).
fof(fact_600_unique__quotient__lemma,axiom,
! [B,Q_4,R_3,Q_1,R_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),Q_4)),R_3)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),Q_1)),R_1)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_3))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_3),B))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_4),Q_1)) ) ) ) ),
file('theBenchmark.p',fact_600_unique__quotient__lemma) ).
fof(fact_601_q__neg__lemma,axiom,
! [B_48,Q_4,R_3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B_48),Q_4)),R_3)),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_3))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_48))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_4),zero_zero_int)) ) ) ),
file('theBenchmark.p',fact_601_q__neg__lemma) ).
fof(fact_602_q__pos__lemma,axiom,
! [B_48,Q_4,R_3] :
( 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(B_48),Q_4)),R_3)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_3),B_48))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_48))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Q_4)) ) ) ),
file('theBenchmark.p',fact_602_q__pos__lemma) ).
fof(fact_603_zprime__zdvd__zmult,axiom,
! [N_1,P_1,M] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),M))
=> ( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),hAPP_int_int(times_times_int(M),N_1)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),N_1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),M)) ) ) ) ),
file('theBenchmark.p',fact_603_zprime__zdvd__zmult) ).
fof(fact_604__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096,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('theBenchmark.p',fact_604__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096) ).
fof(fact_605__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096,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(minus_minus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),number_number_of_int(min)))),
file('theBenchmark.p',fact_605__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096) ).
fof(fact_606_neg__one__power__eq__mod__m,axiom,
! [J_1,K_1,M] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),M))
=> ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(number_number_of_int(min)),J_1),hAPP_nat_int(power_power_int(number_number_of_int(min)),K_1)),M))
=> hAPP_nat_int(power_power_int(number_number_of_int(min)),J_1) = hAPP_nat_int(power_power_int(number_number_of_int(min)),K_1) ) ),
file('theBenchmark.p',fact_606_neg__one__power__eq__mod__m) ).
fof(fact_607_zcong__neg__1__impl__ne__1,axiom,
! [X_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1))
=> ( hBOOL(hAPP_int_bool(zcong(X_1,number_number_of_int(min)),P_1))
=> ~ hBOOL(hAPP_int_bool(zcong(X_1,one_one_int),P_1)) ) ),
file('theBenchmark.p',fact_607_zcong__neg__1__impl__ne__1) ).
fof(fact_608_one__not__neg__one__mod__m,axiom,
! [M] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),M))
=> ~ hBOOL(hAPP_int_bool(zcong(one_one_int,number_number_of_int(min)),M)) ),
file('theBenchmark.p',fact_608_one__not__neg__one__mod__m) ).
fof(fact_609__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096,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('theBenchmark.p',fact_609__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
fof(fact_610__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N,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('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(fact_611_Int2_Oaux1,axiom,
! [A,B,C] :
( is_int(A)
=> ( hAPP_int_int(minus_minus_int(A),B) = C
=> A = hAPP_int_int(plus_plus_int(C),B) ) ),
file('theBenchmark.p',fact_611_Int2_Oaux1) ).
fof(fact_612_number__of__diff,axiom,
! [V_5,W_3] : number267125858f_real(hAPP_int_int(minus_minus_int(V_5),W_3)) = hAPP_real_real(minus_minus_real(number267125858f_real(V_5)),number267125858f_real(W_3)),
file('theBenchmark.p',fact_612_number__of__diff) ).
fof(fact_613_number__of__diff,axiom,
! [V_5,W_3] : number_number_of_int(hAPP_int_int(minus_minus_int(V_5),W_3)) = hAPP_int_int(minus_minus_int(number_number_of_int(V_5)),number_number_of_int(W_3)),
file('theBenchmark.p',fact_613_number__of__diff) ).
fof(fact_614_diff__bin__simps_I1_J,axiom,
! [K_1] :
( is_int(K_1)
=> hAPP_int_int(minus_minus_int(K_1),pls) = K_1 ),
file('theBenchmark.p',fact_614_diff__bin__simps_I1_J) ).
fof(fact_615_diff__bin__simps_I7_J,axiom,
! [K_1,L] : hAPP_int_int(minus_minus_int(bit0(K_1)),bit0(L)) = bit0(hAPP_int_int(minus_minus_int(K_1),L)),
file('theBenchmark.p',fact_615_diff__bin__simps_I7_J) ).
fof(fact_616_zdiff__zmult__distrib2,axiom,
! [W,Z1,Z2] : hAPP_int_int(times_times_int(W),hAPP_int_int(minus_minus_int(Z1),Z2)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(W),Z1)),hAPP_int_int(times_times_int(W),Z2)),
file('theBenchmark.p',fact_616_zdiff__zmult__distrib2) ).
fof(fact_617_zdiff__zmult__distrib,axiom,
! [Z1,Z2,W] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(Z1),Z2)),W) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(Z1),W)),hAPP_int_int(times_times_int(Z2),W)),
file('theBenchmark.p',fact_617_zdiff__zmult__distrib) ).
fof(fact_618_zcong__zdiff,axiom,
! [C,D_5,A,B,M] :
( hBOOL(hAPP_int_bool(zcong(A,B),M))
=> ( hBOOL(hAPP_int_bool(zcong(C,D_5),M))
=> hBOOL(hAPP_int_bool(zcong(hAPP_int_int(minus_minus_int(A),C),hAPP_int_int(minus_minus_int(B),D_5)),M)) ) ),
file('theBenchmark.p',fact_618_zcong__zdiff) ).
fof(fact_619_zdvd__zdiffD,axiom,
! [K_1,M,N_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),hAPP_int_int(minus_minus_int(M),N_1)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),N_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),M)) ) ),
file('theBenchmark.p',fact_619_zdvd__zdiffD) ).
fof(fact_620_right__diff__distrib__number__of,axiom,
! [V_4,B_47,C_26] : hAPP_real_real(times_times_real(number267125858f_real(V_4)),hAPP_real_real(minus_minus_real(B_47),C_26)) = hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(number267125858f_real(V_4)),B_47)),hAPP_real_real(times_times_real(number267125858f_real(V_4)),C_26)),
file('theBenchmark.p',fact_620_right__diff__distrib__number__of) ).
fof(fact_621_right__diff__distrib__number__of,axiom,
! [V_4,B_47,C_26] : hAPP_int_int(times_times_int(number_number_of_int(V_4)),hAPP_int_int(minus_minus_int(B_47),C_26)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(V_4)),B_47)),hAPP_int_int(times_times_int(number_number_of_int(V_4)),C_26)),
file('theBenchmark.p',fact_621_right__diff__distrib__number__of) ).
fof(fact_622_left__diff__distrib__number__of,axiom,
! [A_55,B_46,V_3] : hAPP_real_real(times_times_real(hAPP_real_real(minus_minus_real(A_55),B_46)),number267125858f_real(V_3)) = hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(A_55),number267125858f_real(V_3))),hAPP_real_real(times_times_real(B_46),number267125858f_real(V_3))),
file('theBenchmark.p',fact_622_left__diff__distrib__number__of) ).
fof(fact_623_left__diff__distrib__number__of,axiom,
! [A_55,B_46,V_3] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(A_55),B_46)),number_number_of_int(V_3)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(A_55),number_number_of_int(V_3))),hAPP_int_int(times_times_int(B_46),number_number_of_int(V_3))),
file('theBenchmark.p',fact_623_left__diff__distrib__number__of) ).
fof(fact_624_diff__bin__simps_I9_J,axiom,
! [K_1,L] : hAPP_int_int(minus_minus_int(bit1(K_1)),bit0(L)) = bit1(hAPP_int_int(minus_minus_int(K_1),L)),
file('theBenchmark.p',fact_624_diff__bin__simps_I9_J) ).
fof(fact_625_diff__bin__simps_I10_J,axiom,
! [K_1,L] : hAPP_int_int(minus_minus_int(bit1(K_1)),bit1(L)) = bit0(hAPP_int_int(minus_minus_int(K_1),L)),
file('theBenchmark.p',fact_625_diff__bin__simps_I10_J) ).
fof(fact_626_diff__bin__simps_I3_J,axiom,
! [L] : hAPP_int_int(minus_minus_int(pls),bit0(L)) = bit0(hAPP_int_int(minus_minus_int(pls),L)),
file('theBenchmark.p',fact_626_diff__bin__simps_I3_J) ).
fof(fact_627_less__bin__lemma,axiom,
! [K,L_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L_1))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(K),L_1)),zero_zero_int)) ),
file('theBenchmark.p',fact_627_less__bin__lemma) ).
fof(fact_628_xzgcda__linear__aux1,axiom,
! [A,R_1,B,M,C,D_5,N_1] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(A),hAPP_int_int(times_times_int(R_1),B))),M)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(C),hAPP_int_int(times_times_int(R_1),D_5))),N_1)) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A),M)),hAPP_int_int(times_times_int(C),N_1))),hAPP_int_int(times_times_int(R_1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),M)),hAPP_int_int(times_times_int(D_5),N_1)))),
file('theBenchmark.p',fact_628_xzgcda__linear__aux1) ).
fof(fact_629_zcong__def,axiom,
! [A_2,B_2,Ma] :
( hBOOL(hAPP_int_bool(zcong(A_2,B_2),Ma))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Ma),hAPP_int_int(minus_minus_int(A_2),B_2))) ),
file('theBenchmark.p',fact_629_zcong__def) ).
fof(fact_630_add__number__of__diff1,axiom,
! [V_2,W_2,C_25] : hAPP_real_real(plus_plus_real(number267125858f_real(V_2)),hAPP_real_real(minus_minus_real(number267125858f_real(W_2)),C_25)) = hAPP_real_real(minus_minus_real(number267125858f_real(hAPP_int_int(plus_plus_int(V_2),W_2))),C_25),
file('theBenchmark.p',fact_630_add__number__of__diff1) ).
fof(fact_631_add__number__of__diff1,axiom,
! [V_2,W_2,C_25] : hAPP_int_int(plus_plus_int(number_number_of_int(V_2)),hAPP_int_int(minus_minus_int(number_number_of_int(W_2)),C_25)) = hAPP_int_int(minus_minus_int(number_number_of_int(hAPP_int_int(plus_plus_int(V_2),W_2))),C_25),
file('theBenchmark.p',fact_631_add__number__of__diff1) ).
fof(fact_632_Euler_Oaux1,axiom,
! [A,X_1] :
( is_int(X_1)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),A))
=> ( X_1 != hAPP_int_int(minus_minus_int(A),one_one_int)
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),hAPP_int_int(minus_minus_int(A),one_one_int))) ) ) ) ),
file('theBenchmark.p',fact_632_Euler_Oaux1) ).
fof(fact_633_zle__diff1__eq,axiom,
! [W_1,Z_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),hAPP_int_int(minus_minus_int(Z_1),one_one_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_1)) ),
file('theBenchmark.p',fact_633_zle__diff1__eq) ).
fof(fact_634_diff__bin__simps_I4_J,axiom,
! [L] : hAPP_int_int(minus_minus_int(pls),bit1(L)) = bit1(hAPP_int_int(minus_minus_int(min),L)),
file('theBenchmark.p',fact_634_diff__bin__simps_I4_J) ).
fof(fact_635_diff__bin__simps_I5_J,axiom,
! [L] : hAPP_int_int(minus_minus_int(min),bit0(L)) = bit1(hAPP_int_int(minus_minus_int(min),L)),
file('theBenchmark.p',fact_635_diff__bin__simps_I5_J) ).
fof(fact_636_diff__bin__simps_I6_J,axiom,
! [L] : hAPP_int_int(minus_minus_int(min),bit1(L)) = bit0(hAPP_int_int(minus_minus_int(min),L)),
file('theBenchmark.p',fact_636_diff__bin__simps_I6_J) ).
fof(fact_637_inv__not__p__minus__1__aux,axiom,
! [A_2,P_3] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A_2),hAPP_int_int(minus_minus_int(P_3),one_one_int)),one_one_int),P_3))
<=> hBOOL(hAPP_int_bool(zcong(A_2,hAPP_int_int(minus_minus_int(P_3),one_one_int)),P_3)) ),
file('theBenchmark.p',fact_637_inv__not__p__minus__1__aux) ).
fof(fact_638_zcong__eq__trans,axiom,
! [D_5,C,A,B,M] :
( hBOOL(hAPP_int_bool(zcong(A,B),M))
=> ( B = C
=> ( hBOOL(hAPP_int_bool(zcong(C,D_5),M))
=> hBOOL(hAPP_int_bool(zcong(A,D_5),M)) ) ) ),
file('theBenchmark.p',fact_638_zcong__eq__trans) ).
fof(fact_639_mult__sum2sq,axiom,
! [A,B,P_1,Q_1] : hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(product_Pair_int_int(A,B))),twoSqu1241645765sum2sq(product_Pair_int_int(P_1,Q_1))) = twoSqu1241645765sum2sq(product_Pair_int_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A),P_1)),hAPP_int_int(times_times_int(B),Q_1)),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(A),Q_1)),hAPP_int_int(times_times_int(B),P_1)))),
file('theBenchmark.p',fact_639_mult__sum2sq) ).
fof(fact_640_zcong__square,axiom,
! [A,P_1] :
( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A))
=> ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),A),one_one_int),P_1))
=> ( hBOOL(hAPP_int_bool(zcong(A,hAPP_int_int(minus_minus_int(P_1),one_one_int)),P_1))
| hBOOL(hAPP_int_bool(zcong(A,one_one_int),P_1)) ) ) ) ),
file('theBenchmark.p',fact_640_zcong__square) ).
fof(fact_641_zcong__square__zless,axiom,
! [A,P_1] :
( is_int(A)
=> ( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),P_1))
=> ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),A),one_one_int),P_1))
=> ( A = hAPP_int_int(minus_minus_int(P_1),one_one_int)
| A = one_one_int ) ) ) ) ) ),
file('theBenchmark.p',fact_641_zcong__square__zless) ).
fof(fact_642_zspecial__product,axiom,
! [A,B] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A),B)),hAPP_int_int(minus_minus_int(A),B)) = hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(A),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(B),number_number_of_nat(bit0(bit1(pls))))),
file('theBenchmark.p',fact_642_zspecial__product) ).
fof(fact_643_zcong__id,axiom,
! [M] : hBOOL(hAPP_int_bool(zcong(M,zero_zero_int),M)),
file('theBenchmark.p',fact_643_zcong__id) ).
fof(fact_644_zcong__zmult__prop1,axiom,
! [C_2,D,A_2,B_2,Ma] :
( hBOOL(hAPP_int_bool(zcong(A_2,B_2),Ma))
=> ( hBOOL(hAPP_int_bool(zcong(C_2,hAPP_int_int(times_times_int(A_2),D)),Ma))
<=> hBOOL(hAPP_int_bool(zcong(C_2,hAPP_int_int(times_times_int(B_2),D)),Ma)) ) ),
file('theBenchmark.p',fact_644_zcong__zmult__prop1) ).
fof(fact_645_zcong__zmult__prop2,axiom,
! [C_2,D,A_2,B_2,Ma] :
( hBOOL(hAPP_int_bool(zcong(A_2,B_2),Ma))
=> ( hBOOL(hAPP_int_bool(zcong(C_2,hAPP_int_int(times_times_int(D),A_2)),Ma))
<=> hBOOL(hAPP_int_bool(zcong(C_2,hAPP_int_int(times_times_int(D),B_2)),Ma)) ) ),
file('theBenchmark.p',fact_645_zcong__zmult__prop2) ).
fof(fact_646_zcong__shift,axiom,
! [C,A,B,M] :
( hBOOL(hAPP_int_bool(zcong(A,B),M))
=> hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(A),C),hAPP_int_int(plus_plus_int(B),C)),M)) ),
file('theBenchmark.p',fact_646_zcong__shift) ).
fof(fact_647_zcong__zpower,axiom,
! [Z,X_1,Y_1,M] :
( hBOOL(hAPP_int_bool(zcong(X_1,Y_1),M))
=> hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X_1),Z),hAPP_nat_int(power_power_int(Y_1),Z)),M)) ),
file('theBenchmark.p',fact_647_zcong__zpower) ).
fof(fact_648_power2__diff,axiom,
! [X_7,Y_6] : hAPP_nat_real(power_power_real(hAPP_real_real(minus_minus_real(X_7),Y_6)),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(X_7),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_6),number_number_of_nat(bit0(bit1(pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),X_7)),Y_6)),
file('theBenchmark.p',fact_648_power2__diff) ).
fof(fact_649_power2__diff,axiom,
! [X_7,Y_6] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(X_7),Y_6)),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(X_7),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_6),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)))),X_7)),Y_6)),
file('theBenchmark.p',fact_649_power2__diff) ).
fof(fact_650_zdiff__power2,axiom,
! [A,B] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(A),B)),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(A),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)))),A)),B))),hAPP_nat_int(power_power_int(B),number_number_of_nat(bit0(bit1(pls))))),
file('theBenchmark.p',fact_650_zdiff__power2) ).
fof(fact_651_zdiff__power3,axiom,
! [A,B] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(A),B)),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(A),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(A),number_number_of_nat(bit0(bit1(pls)))))),B))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit1(bit1(pls)))),A)),hAPP_nat_int(power_power_int(B),number_number_of_nat(bit0(bit1(pls))))))),hAPP_nat_int(power_power_int(B),number_number_of_nat(bit1(bit1(pls))))),
file('theBenchmark.p',fact_651_zdiff__power3) ).
fof(fact_652_zcong__less__eq,axiom,
! [M,Y_1,X_1] :
( ( is_int(X_1)
& is_int(Y_1) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Y_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M))
=> ( hBOOL(hAPP_int_bool(zcong(X_1,Y_1),M))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),M))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),M))
=> X_1 = Y_1 ) ) ) ) ) ) ),
file('theBenchmark.p',fact_652_zcong__less__eq) ).
fof(fact_653_zcong__not__zero,axiom,
! [M,X_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),M))
=> ~ hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),M)) ) ),
file('theBenchmark.p',fact_653_zcong__not__zero) ).
fof(fact_654_zdvd__bounds,axiom,
! [N_1,M] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,N_1),M))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,N_1),M))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,M),zero_zero_int)) ) ),
file('theBenchmark.p',fact_654_zdvd__bounds) ).
fof(fact_655_zcong__eq__zdvd__prop,axiom,
! [X_2,P_3] :
( hBOOL(hAPP_int_bool(zcong(X_2,zero_zero_int),P_3))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),X_2)) ),
file('theBenchmark.p',fact_655_zcong__eq__zdvd__prop) ).
fof(fact_656_zcong__zero__equiv__div,axiom,
! [A_2,Ma] :
( hBOOL(hAPP_int_bool(zcong(A_2,zero_zero_int),Ma))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Ma),A_2)) ),
file('theBenchmark.p',fact_656_zcong__zero__equiv__div) ).
fof(fact_657_zprime__zdvd__zmult__better,axiom,
! [M,N_1,P_1] :
( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),hAPP_int_int(times_times_int(M),N_1)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),N_1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),M)) ) ) ),
file('theBenchmark.p',fact_657_zprime__zdvd__zmult__better) ).
fof(fact_658_Int2_Ozcong__zero,axiom,
! [M,X_1] :
( is_int(X_1)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),M))
=> ( hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),M))
=> X_1 = zero_zero_int ) ) ) ),
file('theBenchmark.p',fact_658_Int2_Ozcong__zero) ).
fof(fact_659_zpower__zdvd__prop1,axiom,
! [P_1,Y_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),Y_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),hAPP_nat_int(power_power_int(Y_1),N_1))) ) ),
file('theBenchmark.p',fact_659_zpower__zdvd__prop1) ).
fof(fact_660_neg__one__power,axiom,
! [N_1] :
( hAPP_nat_int(power_power_int(number_number_of_int(min)),N_1) = number_number_of_int(min)
| hAPP_nat_int(power_power_int(number_number_of_int(min)),N_1) = one_one_int ),
file('theBenchmark.p',fact_660_neg__one__power) ).
fof(fact_661_zcong__zmult__prop3,axiom,
! [Y_1,X_1,P_1] :
( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( ~ hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),P_1))
=> ( ~ hBOOL(hAPP_int_bool(zcong(Y_1,zero_zero_int),P_1))
=> ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X_1),Y_1),zero_zero_int),P_1)) ) ) ),
file('theBenchmark.p',fact_661_zcong__zmult__prop3) ).
fof(fact_662_zcong__zprime__prod__zero,axiom,
! [B,A,P_1] :
( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A))
=> ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),B),zero_zero_int),P_1))
=> ( hBOOL(hAPP_int_bool(zcong(B,zero_zero_int),P_1))
| hBOOL(hAPP_int_bool(zcong(A,zero_zero_int),P_1)) ) ) ) ),
file('theBenchmark.p',fact_662_zcong__zprime__prod__zero) ).
fof(fact_663_zcong__zprime__prod__zero__contra,axiom,
! [B,A,P_1] :
( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A))
=> ( ( ~ hBOOL(hAPP_int_bool(zcong(B,zero_zero_int),P_1))
& ~ hBOOL(hAPP_int_bool(zcong(A,zero_zero_int),P_1)) )
=> ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),B),zero_zero_int),P_1)) ) ) ),
file('theBenchmark.p',fact_663_zcong__zprime__prod__zero__contra) ).
fof(fact_664_zpower__zdvd__prop2,axiom,
! [Y_1,N_1,P_1] :
( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),hAPP_nat_int(power_power_int(Y_1),N_1)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),Y_1)) ) ) ),
file('theBenchmark.p',fact_664_zpower__zdvd__prop2) ).
fof(fact_665_Legendre__1mod4,axiom,
! [M] :
( 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)))
=> 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('theBenchmark.p',fact_665_Legendre__1mod4) ).
fof(fact_666_Legendre__def,axiom,
! [A,P_1] :
( ( ~ hBOOL(hAPP_int_bool(zcong(A,zero_zero_int),P_1))
=> ( ( ~ hBOOL(hAPP_int_bool(quadRes(P_1),A))
=> legendre(A,P_1) = number_number_of_int(min) )
& ( hBOOL(hAPP_int_bool(quadRes(P_1),A))
=> legendre(A,P_1) = one_one_int ) ) )
& ( hBOOL(hAPP_int_bool(zcong(A,zero_zero_int),P_1))
=> legendre(A,P_1) = zero_zero_int ) ),
file('theBenchmark.p',fact_666_Legendre__def) ).
fof(fact_667_divides__cases,axiom,
! [N_1,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,N_1),M))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_1)),M))
| M = N_1
| M = zero_zero_nat ) ),
file('theBenchmark.p',fact_667_divides__cases) ).
fof(fact_668_QuadRes__def,axiom,
! [Ma,X_2] :
( hBOOL(hAPP_int_bool(quadRes(Ma),X_2))
<=> ? [Y] :
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(Y),number_number_of_nat(bit0(bit1(pls)))),X_2),Ma))
& is_int(Y) ) ),
file('theBenchmark.p',fact_668_QuadRes__def) ).
fof(fact_669_realpow__two__sum__zero__iff,axiom,
! [X_2,Y_2] :
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
<=> ( Y_2 = zero_zero_real
& X_2 = zero_zero_real ) ),
file('theBenchmark.p',fact_669_realpow__two__sum__zero__iff) ).
fof(fact_670_convex__bound__lt,axiom,
! [V_1,U_2,Y_5,X_6,A_54] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_6),A_54))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_5),A_54))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),V_1))
=> ( hAPP_real_real(plus_plus_real(U_2),V_1) = 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(U_2),X_6)),hAPP_real_real(times_times_real(V_1),Y_5))),A_54)) ) ) ) ) ),
file('theBenchmark.p',fact_670_convex__bound__lt) ).
fof(fact_671_convex__bound__lt,axiom,
! [V_1,U_2,Y_5,X_6,A_54] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_6),A_54))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_5),A_54))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),V_1))
=> ( hAPP_int_int(plus_plus_int(U_2),V_1) = 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(U_2),X_6)),hAPP_int_int(times_times_int(V_1),Y_5))),A_54)) ) ) ) ) ),
file('theBenchmark.p',fact_671_convex__bound__lt) ).
fof(fact_672_dvd__0__right,axiom,
! [A_53] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_53),zero_zero_real)),
file('theBenchmark.p',fact_672_dvd__0__right) ).
fof(fact_673_dvd__0__right,axiom,
! [A_53] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_53),zero_zero_nat)),
file('theBenchmark.p',fact_673_dvd__0__right) ).
fof(fact_674_dvd__0__right,axiom,
! [A_53] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_53),zero_zero_int)),
file('theBenchmark.p',fact_674_dvd__0__right) ).
fof(fact_675_real__le__eq__diff,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Y_2))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(minus_minus_real(X_2),Y_2)),zero_zero_real)) ),
file('theBenchmark.p',fact_675_real__le__eq__diff) ).
fof(fact_676_linorder__neqE__linordered__idom,axiom,
! [X_5,Y_4] :
( X_5 != Y_4
=> ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_5),Y_4))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_4),X_5)) ) ),
file('theBenchmark.p',fact_676_linorder__neqE__linordered__idom) ).
fof(fact_677_linorder__neqE__linordered__idom,axiom,
! [X_5,Y_4] :
( ( is_int(Y_4)
& is_int(X_5) )
=> ( X_5 != Y_4
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_5),Y_4))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_4),X_5)) ) ) ),
file('theBenchmark.p',fact_677_linorder__neqE__linordered__idom) ).
fof(fact_678_dvd__refl,axiom,
! [A_52] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_52),A_52)),
file('theBenchmark.p',fact_678_dvd__refl) ).
fof(fact_679_dvd__refl,axiom,
! [A_52] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_52),A_52)),
file('theBenchmark.p',fact_679_dvd__refl) ).
fof(fact_680_dvd__refl,axiom,
! [A_52] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_52),A_52)),
file('theBenchmark.p',fact_680_dvd__refl) ).
fof(fact_681_dvd__trans,axiom,
! [C_24,A_51,B_45] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_51),B_45))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,B_45),C_24))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_51),C_24)) ) ),
file('theBenchmark.p',fact_681_dvd__trans) ).
fof(fact_682_dvd__trans,axiom,
! [C_24,A_51,B_45] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_51),B_45))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B_45),C_24))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_51),C_24)) ) ),
file('theBenchmark.p',fact_682_dvd__trans) ).
fof(fact_683_dvd__trans,axiom,
! [C_24,A_51,B_45] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_51),B_45))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,B_45),C_24))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_51),C_24)) ) ),
file('theBenchmark.p',fact_683_dvd__trans) ).
fof(fact_684_real__zero__not__eq__one,axiom,
zero_zero_real != one_one_real,
file('theBenchmark.p',fact_684_real__zero__not__eq__one) ).
fof(fact_685_less__eq__real__def,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Y_2))
<=> ( X_2 = Y_2
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),Y_2)) ) ),
file('theBenchmark.p',fact_685_less__eq__real__def) ).
fof(fact_686_real__less__def,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),Y_2))
<=> ( X_2 != Y_2
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Y_2)) ) ),
file('theBenchmark.p',fact_686_real__less__def) ).
fof(fact_687_divides__antisym,axiom,
! [X_2,Y_2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) )
<=> X_2 = Y_2 ),
file('theBenchmark.p',fact_687_divides__antisym) ).
fof(fact_688_real__mult__assoc,axiom,
! [Z1,Z2,Z3] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Z1),Z2)),Z3) = hAPP_real_real(times_times_real(Z1),hAPP_real_real(times_times_real(Z2),Z3)),
file('theBenchmark.p',fact_688_real__mult__assoc) ).
fof(fact_689_real__mult__commute,axiom,
! [Z,W] : hAPP_real_real(times_times_real(Z),W) = hAPP_real_real(times_times_real(W),Z),
file('theBenchmark.p',fact_689_real__mult__commute) ).
fof(fact_690_real__mult__1,axiom,
! [Z] : hAPP_real_real(times_times_real(one_one_real),Z) = Z,
file('theBenchmark.p',fact_690_real__mult__1) ).
fof(fact_691_real__add__left__mono,axiom,
! [Z,X_1,Y_1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_1))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(Z),X_1)),hAPP_real_real(plus_plus_real(Z),Y_1))) ),
file('theBenchmark.p',fact_691_real__add__left__mono) ).
fof(fact_692_realpow__minus__mult,axiom,
! [X_4,N_3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_3))
=> hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X_4),hAPP_nat_nat(minus_minus_nat(N_3),one_one_nat))),X_4) = hAPP_nat_nat(power_power_nat(X_4),N_3) ),
file('theBenchmark.p',fact_692_realpow__minus__mult) ).
fof(fact_693_realpow__minus__mult,axiom,
! [X_4,N_3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_3))
=> hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X_4),hAPP_nat_nat(minus_minus_nat(N_3),one_one_nat))),X_4) = hAPP_nat_real(power_power_real(X_4),N_3) ),
file('theBenchmark.p',fact_693_realpow__minus__mult) ).
fof(fact_694_realpow__minus__mult,axiom,
! [X_4,N_3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_3))
=> hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X_4),hAPP_nat_nat(minus_minus_nat(N_3),one_one_nat))),X_4) = hAPP_nat_int(power_power_int(X_4),N_3) ),
file('theBenchmark.p',fact_694_realpow__minus__mult) ).
fof(fact_695_mult__eq__if,axiom,
! [N_1,M] :
( ( M != zero_zero_nat
=> hAPP_nat_nat(times_times_nat(M),N_1) = hAPP_nat_nat(plus_plus_nat(N_1),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(M),one_one_nat)),N_1)) )
& ( M = zero_zero_nat
=> hAPP_nat_nat(times_times_nat(M),N_1) = zero_zero_nat ) ),
file('theBenchmark.p',fact_695_mult__eq__if) ).
fof(fact_696_power__eq__if,axiom,
! [P_1,M] :
( ( M != zero_zero_nat
=> hAPP_nat_nat(power_power_nat(P_1),M) = hAPP_nat_nat(times_times_nat(P_1),hAPP_nat_nat(power_power_nat(P_1),hAPP_nat_nat(minus_minus_nat(M),one_one_nat))) )
& ( M = zero_zero_nat
=> hAPP_nat_nat(power_power_nat(P_1),M) = one_one_nat ) ),
file('theBenchmark.p',fact_696_power__eq__if) ).
fof(fact_697_diff__square,axiom,
! [X_1,Y_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(power_power_nat(X_1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(Y_1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X_1),Y_1)),hAPP_nat_nat(minus_minus_nat(X_1),Y_1)),
file('theBenchmark.p',fact_697_diff__square) ).
fof(fact_698_divisors__zero,axiom,
! [A_50,B_44] :
( hAPP_real_real(times_times_real(A_50),B_44) = zero_zero_real
=> ( B_44 = zero_zero_real
| A_50 = zero_zero_real ) ),
file('theBenchmark.p',fact_698_divisors__zero) ).
fof(fact_699_divisors__zero,axiom,
! [A_50,B_44] :
( hAPP_nat_nat(times_times_nat(A_50),B_44) = zero_zero_nat
=> ( B_44 = zero_zero_nat
| A_50 = zero_zero_nat ) ),
file('theBenchmark.p',fact_699_divisors__zero) ).
fof(fact_700_divisors__zero,axiom,
! [A_50,B_44] :
( ( is_int(B_44)
& is_int(A_50) )
=> ( hAPP_int_int(times_times_int(A_50),B_44) = zero_zero_int
=> ( B_44 = zero_zero_int
| A_50 = zero_zero_int ) ) ),
file('theBenchmark.p',fact_700_divisors__zero) ).
fof(fact_701_no__zero__divisors,axiom,
! [B_43,A_49] :
( A_49 != zero_zero_real
=> ( B_43 != zero_zero_real
=> hAPP_real_real(times_times_real(A_49),B_43) != zero_zero_real ) ),
file('theBenchmark.p',fact_701_no__zero__divisors) ).
fof(fact_702_no__zero__divisors,axiom,
! [B_43,A_49] :
( A_49 != zero_zero_nat
=> ( B_43 != zero_zero_nat
=> hAPP_nat_nat(times_times_nat(A_49),B_43) != zero_zero_nat ) ),
file('theBenchmark.p',fact_702_no__zero__divisors) ).
fof(fact_703_no__zero__divisors,axiom,
! [B_43,A_49] :
( ( is_int(A_49)
& is_int(B_43) )
=> ( A_49 != zero_zero_int
=> ( B_43 != zero_zero_int
=> hAPP_int_int(times_times_int(A_49),B_43) != zero_zero_int ) ) ),
file('theBenchmark.p',fact_703_no__zero__divisors) ).
fof(fact_704_mult__eq__0__iff,axiom,
! [A_2,B_2] :
( hAPP_real_real(times_times_real(A_2),B_2) = zero_zero_real
<=> ( B_2 = zero_zero_real
| A_2 = zero_zero_real ) ),
file('theBenchmark.p',fact_704_mult__eq__0__iff) ).
fof(fact_705_mult__eq__0__iff,axiom,
! [A_2,B_2] :
( ( is_int(B_2)
& is_int(A_2) )
=> ( hAPP_int_int(times_times_int(A_2),B_2) = zero_zero_int
<=> ( B_2 = zero_zero_int
| A_2 = zero_zero_int ) ) ),
file('theBenchmark.p',fact_705_mult__eq__0__iff) ).
fof(fact_706_mult__zero__right,axiom,
! [A_48] : hAPP_real_real(times_times_real(A_48),zero_zero_real) = zero_zero_real,
file('theBenchmark.p',fact_706_mult__zero__right) ).
fof(fact_707_mult__zero__right,axiom,
! [A_48] : hAPP_nat_nat(times_times_nat(A_48),zero_zero_nat) = zero_zero_nat,
file('theBenchmark.p',fact_707_mult__zero__right) ).
fof(fact_708_mult__zero__right,axiom,
! [A_48] : hAPP_int_int(times_times_int(A_48),zero_zero_int) = zero_zero_int,
file('theBenchmark.p',fact_708_mult__zero__right) ).
fof(fact_709_mult__zero__left,axiom,
! [A_47] : hAPP_real_real(times_times_real(zero_zero_real),A_47) = zero_zero_real,
file('theBenchmark.p',fact_709_mult__zero__left) ).
fof(fact_710_mult__zero__left,axiom,
! [A_47] : hAPP_nat_nat(times_times_nat(zero_zero_nat),A_47) = zero_zero_nat,
file('theBenchmark.p',fact_710_mult__zero__left) ).
fof(fact_711_mult__zero__left,axiom,
! [A_47] : hAPP_int_int(times_times_int(zero_zero_int),A_47) = zero_zero_int,
file('theBenchmark.p',fact_711_mult__zero__left) ).
fof(fact_712_zero__neq__one,axiom,
zero_zero_real != one_one_real,
file('theBenchmark.p',fact_712_zero__neq__one) ).
fof(fact_713_zero__neq__one,axiom,
zero_zero_nat != one_one_nat,
file('theBenchmark.p',fact_713_zero__neq__one) ).
fof(fact_714_zero__neq__one,axiom,
zero_zero_int != one_one_int,
file('theBenchmark.p',fact_714_zero__neq__one) ).
fof(fact_715_one__neq__zero,axiom,
one_one_real != zero_zero_real,
file('theBenchmark.p',fact_715_one__neq__zero) ).
fof(fact_716_one__neq__zero,axiom,
one_one_nat != zero_zero_nat,
file('theBenchmark.p',fact_716_one__neq__zero) ).
fof(fact_717_one__neq__zero,axiom,
one_one_int != zero_zero_int,
file('theBenchmark.p',fact_717_one__neq__zero) ).
fof(fact_718_combine__common__factor,axiom,
! [A_46,E,B_42,C_23] : hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_46),E)),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(B_42),E)),C_23)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_46),B_42)),E)),C_23),
file('theBenchmark.p',fact_718_combine__common__factor) ).
fof(fact_719_combine__common__factor,axiom,
! [A_46,E,B_42,C_23] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_46),E)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(B_42),E)),C_23)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_46),B_42)),E)),C_23),
file('theBenchmark.p',fact_719_combine__common__factor) ).
fof(fact_720_combine__common__factor,axiom,
! [A_46,E,B_42,C_23] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_46),E)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B_42),E)),C_23)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_46),B_42)),E)),C_23),
file('theBenchmark.p',fact_720_combine__common__factor) ).
fof(fact_721_comm__semiring__class_Odistrib,axiom,
! [A_45,B_41,C_22] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_45),B_41)),C_22) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_45),C_22)),hAPP_real_real(times_times_real(B_41),C_22)),
file('theBenchmark.p',fact_721_comm__semiring__class_Odistrib) ).
fof(fact_722_comm__semiring__class_Odistrib,axiom,
! [A_45,B_41,C_22] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_45),B_41)),C_22) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_45),C_22)),hAPP_nat_nat(times_times_nat(B_41),C_22)),
file('theBenchmark.p',fact_722_comm__semiring__class_Odistrib) ).
fof(fact_723_comm__semiring__class_Odistrib,axiom,
! [A_45,B_41,C_22] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_45),B_41)),C_22) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_45),C_22)),hAPP_int_int(times_times_int(B_41),C_22)),
file('theBenchmark.p',fact_723_comm__semiring__class_Odistrib) ).
fof(fact_724_dvd__0__left,axiom,
! [A_44] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,zero_zero_real),A_44))
=> A_44 = zero_zero_real ),
file('theBenchmark.p',fact_724_dvd__0__left) ).
fof(fact_725_dvd__0__left,axiom,
! [A_44] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),A_44))
=> A_44 = zero_zero_nat ),
file('theBenchmark.p',fact_725_dvd__0__left) ).
fof(fact_726_dvd__0__left,axiom,
! [A_44] :
( is_int(A_44)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,zero_zero_int),A_44))
=> A_44 = zero_zero_int ) ),
file('theBenchmark.p',fact_726_dvd__0__left) ).
fof(fact_727_add__diff__add,axiom,
! [A_43,C_21,B_40,D_7] : hAPP_real_real(minus_minus_real(hAPP_real_real(plus_plus_real(A_43),C_21)),hAPP_real_real(plus_plus_real(B_40),D_7)) = hAPP_real_real(plus_plus_real(hAPP_real_real(minus_minus_real(A_43),B_40)),hAPP_real_real(minus_minus_real(C_21),D_7)),
file('theBenchmark.p',fact_727_add__diff__add) ).
fof(fact_728_add__diff__add,axiom,
! [A_43,C_21,B_40,D_7] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(A_43),C_21)),hAPP_int_int(plus_plus_int(B_40),D_7)) = hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(A_43),B_40)),hAPP_int_int(minus_minus_int(C_21),D_7)),
file('theBenchmark.p',fact_728_add__diff__add) ).
fof(fact_729_dvd__mult__right,axiom,
! [A_42,B_39,C_20] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(A_42),B_39)),C_20))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,B_39),C_20)) ),
file('theBenchmark.p',fact_729_dvd__mult__right) ).
fof(fact_730_dvd__mult__right,axiom,
! [A_42,B_39,C_20] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(A_42),B_39)),C_20))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B_39),C_20)) ),
file('theBenchmark.p',fact_730_dvd__mult__right) ).
fof(fact_731_dvd__mult__right,axiom,
! [A_42,B_39,C_20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(A_42),B_39)),C_20))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,B_39),C_20)) ),
file('theBenchmark.p',fact_731_dvd__mult__right) ).
fof(fact_732_dvd__mult__left,axiom,
! [A_41,B_38,C_19] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(A_41),B_38)),C_19))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_41),C_19)) ),
file('theBenchmark.p',fact_732_dvd__mult__left) ).
fof(fact_733_dvd__mult__left,axiom,
! [A_41,B_38,C_19] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(A_41),B_38)),C_19))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_41),C_19)) ),
file('theBenchmark.p',fact_733_dvd__mult__left) ).
fof(fact_734_dvd__mult__left,axiom,
! [A_41,B_38,C_19] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(A_41),B_38)),C_19))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_41),C_19)) ),
file('theBenchmark.p',fact_734_dvd__mult__left) ).
fof(fact_735_dvdI,axiom,
! [A_40,B_37,K_3] :
( A_40 = hAPP_real_real(times_times_real(B_37),K_3)
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,B_37),A_40)) ),
file('theBenchmark.p',fact_735_dvdI) ).
fof(fact_736_dvdI,axiom,
! [A_40,B_37,K_3] :
( A_40 = hAPP_nat_nat(times_times_nat(B_37),K_3)
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B_37),A_40)) ),
file('theBenchmark.p',fact_736_dvdI) ).
fof(fact_737_dvdI,axiom,
! [A_40,B_37,K_3] :
( A_40 = hAPP_int_int(times_times_int(B_37),K_3)
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,B_37),A_40)) ),
file('theBenchmark.p',fact_737_dvdI) ).
fof(fact_738_mult__dvd__mono,axiom,
! [C_18,D_6,A_39,B_36] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_39),B_36))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,C_18),D_6))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(A_39),C_18)),hAPP_real_real(times_times_real(B_36),D_6))) ) ),
file('theBenchmark.p',fact_738_mult__dvd__mono) ).
fof(fact_739_mult__dvd__mono,axiom,
! [C_18,D_6,A_39,B_36] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_39),B_36))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,C_18),D_6))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(A_39),C_18)),hAPP_nat_nat(times_times_nat(B_36),D_6))) ) ),
file('theBenchmark.p',fact_739_mult__dvd__mono) ).
fof(fact_740_mult__dvd__mono,axiom,
! [C_18,D_6,A_39,B_36] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_39),B_36))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,C_18),D_6))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(A_39),C_18)),hAPP_int_int(times_times_int(B_36),D_6))) ) ),
file('theBenchmark.p',fact_740_mult__dvd__mono) ).
fof(fact_741_dvd__mult,axiom,
! [B_35,A_38,C_17] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_38),C_17))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_38),hAPP_real_real(times_times_real(B_35),C_17))) ),
file('theBenchmark.p',fact_741_dvd__mult) ).
fof(fact_742_dvd__mult,axiom,
! [B_35,A_38,C_17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_38),C_17))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_38),hAPP_nat_nat(times_times_nat(B_35),C_17))) ),
file('theBenchmark.p',fact_742_dvd__mult) ).
fof(fact_743_dvd__mult,axiom,
! [B_35,A_38,C_17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_38),C_17))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_38),hAPP_int_int(times_times_int(B_35),C_17))) ),
file('theBenchmark.p',fact_743_dvd__mult) ).
fof(fact_744_dvd__mult2,axiom,
! [C_16,A_37,B_34] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_37),B_34))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_37),hAPP_real_real(times_times_real(B_34),C_16))) ),
file('theBenchmark.p',fact_744_dvd__mult2) ).
fof(fact_745_dvd__mult2,axiom,
! [C_16,A_37,B_34] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_37),B_34))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_37),hAPP_nat_nat(times_times_nat(B_34),C_16))) ),
file('theBenchmark.p',fact_745_dvd__mult2) ).
fof(fact_746_dvd__mult2,axiom,
! [C_16,A_37,B_34] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_37),B_34))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_37),hAPP_int_int(times_times_int(B_34),C_16))) ),
file('theBenchmark.p',fact_746_dvd__mult2) ).
fof(fact_747_dvd__triv__right,axiom,
! [A_36,B_33] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_36),hAPP_real_real(times_times_real(B_33),A_36))),
file('theBenchmark.p',fact_747_dvd__triv__right) ).
fof(fact_748_dvd__triv__right,axiom,
! [A_36,B_33] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_36),hAPP_nat_nat(times_times_nat(B_33),A_36))),
file('theBenchmark.p',fact_748_dvd__triv__right) ).
fof(fact_749_dvd__triv__right,axiom,
! [A_36,B_33] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_36),hAPP_int_int(times_times_int(B_33),A_36))),
file('theBenchmark.p',fact_749_dvd__triv__right) ).
fof(fact_750_dvd__triv__left,axiom,
! [A_35,B_32] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_35),hAPP_real_real(times_times_real(A_35),B_32))),
file('theBenchmark.p',fact_750_dvd__triv__left) ).
fof(fact_751_dvd__triv__left,axiom,
! [A_35,B_32] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_35),hAPP_nat_nat(times_times_nat(A_35),B_32))),
file('theBenchmark.p',fact_751_dvd__triv__left) ).
fof(fact_752_dvd__triv__left,axiom,
! [A_35,B_32] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_35),hAPP_int_int(times_times_int(A_35),B_32))),
file('theBenchmark.p',fact_752_dvd__triv__left) ).
fof(fact_753_dvd__add,axiom,
! [C_15,A_34,B_31] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_34),B_31))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_34),C_15))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_34),hAPP_real_real(plus_plus_real(B_31),C_15))) ) ),
file('theBenchmark.p',fact_753_dvd__add) ).
fof(fact_754_dvd__add,axiom,
! [C_15,A_34,B_31] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_34),B_31))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_34),C_15))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_34),hAPP_nat_nat(plus_plus_nat(B_31),C_15))) ) ),
file('theBenchmark.p',fact_754_dvd__add) ).
fof(fact_755_dvd__add,axiom,
! [C_15,A_34,B_31] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_34),B_31))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_34),C_15))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_34),hAPP_int_int(plus_plus_int(B_31),C_15))) ) ),
file('theBenchmark.p',fact_755_dvd__add) ).
fof(fact_756_one__dvd,axiom,
! [A_33] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,one_one_real),A_33)),
file('theBenchmark.p',fact_756_one__dvd) ).
fof(fact_757_one__dvd,axiom,
! [A_33] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),A_33)),
file('theBenchmark.p',fact_757_one__dvd) ).
fof(fact_758_one__dvd,axiom,
! [A_33] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),A_33)),
file('theBenchmark.p',fact_758_one__dvd) ).
fof(fact_759_dvd__diff,axiom,
! [Z_2,X_3,Y_3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X_3),Y_3))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X_3),Z_2))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X_3),hAPP_real_real(minus_minus_real(Y_3),Z_2))) ) ),
file('theBenchmark.p',fact_759_dvd__diff) ).
fof(fact_760_dvd__diff,axiom,
! [Z_2,X_3,Y_3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X_3),Y_3))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X_3),Z_2))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X_3),hAPP_int_int(minus_minus_int(Y_3),Z_2))) ) ),
file('theBenchmark.p',fact_760_dvd__diff) ).
fof(fact_761_real__mult__right__cancel,axiom,
! [A_2,B_2,C_2] :
( C_2 != zero_zero_real
=> ( hAPP_real_real(times_times_real(A_2),C_2) = hAPP_real_real(times_times_real(B_2),C_2)
<=> A_2 = B_2 ) ),
file('theBenchmark.p',fact_761_real__mult__right__cancel) ).
fof(fact_762_real__mult__left__cancel,axiom,
! [A_2,B_2,C_2] :
( C_2 != zero_zero_real
=> ( hAPP_real_real(times_times_real(C_2),A_2) = hAPP_real_real(times_times_real(C_2),B_2)
<=> A_2 = B_2 ) ),
file('theBenchmark.p',fact_762_real__mult__left__cancel) ).
fof(fact_763_divides__add__revr,axiom,
! [B,D_5,A] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D_5),A))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D_5),hAPP_nat_nat(plus_plus_nat(A),B)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D_5),B)) ) ),
file('theBenchmark.p',fact_763_divides__add__revr) ).
fof(fact_764_divides__mul__l,axiom,
! [C,A,B] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(C),A)),hAPP_nat_nat(times_times_nat(C),B))) ),
file('theBenchmark.p',fact_764_divides__mul__l) ).
fof(fact_765_divides__mul__r,axiom,
! [C,A,B] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(A),C)),hAPP_nat_nat(times_times_nat(B),C))) ),
file('theBenchmark.p',fact_765_divides__mul__r) ).
fof(fact_766_nat__mult__eq__one,axiom,
! [N,Ma] :
( hAPP_nat_nat(times_times_nat(N),Ma) = one_one_nat
<=> ( Ma = one_one_nat
& N = one_one_nat ) ),
file('theBenchmark.p',fact_766_nat__mult__eq__one) ).
fof(fact_767_real__add__mult__distrib,axiom,
! [Z1,Z2,W] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(Z1),Z2)),W) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(Z1),W)),hAPP_real_real(times_times_real(Z2),W)),
file('theBenchmark.p',fact_767_real__add__mult__distrib) ).
fof(fact_768_nat__power__eq__0__iff,axiom,
! [Ma,N] :
( hAPP_nat_nat(power_power_nat(Ma),N) = zero_zero_nat
<=> ( Ma = zero_zero_nat
& N != zero_zero_nat ) ),
file('theBenchmark.p',fact_768_nat__power__eq__0__iff) ).
fof(fact_769_divides__exp,axiom,
! [N_1,X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X_1),N_1)),hAPP_nat_nat(power_power_nat(Y_1),N_1))) ),
file('theBenchmark.p',fact_769_divides__exp) ).
fof(fact_770_split__mult__neg__le,axiom,
! [B_30,A_32] :
( ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_30))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_32),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_30),zero_zero_real))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_32)) ) )
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_32),B_30)),zero_zero_real)) ),
file('theBenchmark.p',fact_770_split__mult__neg__le) ).
fof(fact_771_split__mult__neg__le,axiom,
! [B_30,A_32] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_30))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_32),zero_zero_nat)) )
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_30),zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_32)) ) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(A_32),B_30)),zero_zero_nat)) ),
file('theBenchmark.p',fact_771_split__mult__neg__le) ).
fof(fact_772_split__mult__neg__le,axiom,
! [B_30,A_32] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_30))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_32),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_30),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_32)) ) )
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_32),B_30)),zero_zero_int)) ),
file('theBenchmark.p',fact_772_split__mult__neg__le) ).
fof(fact_773_split__mult__pos__le,axiom,
! [B_29,A_31] :
( ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_29),zero_zero_real))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_31),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_29))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_31)) ) )
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(A_31),B_29))) ),
file('theBenchmark.p',fact_773_split__mult__pos__le) ).
fof(fact_774_split__mult__pos__le,axiom,
! [B_29,A_31] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_29),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_31),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_29))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_31)) ) )
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(A_31),B_29))) ),
file('theBenchmark.p',fact_774_split__mult__pos__le) ).
fof(fact_775_mult__mono,axiom,
! [C_14,D_4,A_30,B_28] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_30),B_28))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_14),D_4))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_28))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_14))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_30),C_14)),hAPP_real_real(times_times_real(B_28),D_4))) ) ) ) ),
file('theBenchmark.p',fact_775_mult__mono) ).
fof(fact_776_mult__mono,axiom,
! [C_14,D_4,A_30,B_28] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_30),B_28))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_14),D_4))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_28))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(A_30),C_14)),hAPP_nat_nat(times_times_nat(B_28),D_4))) ) ) ) ),
file('theBenchmark.p',fact_776_mult__mono) ).
fof(fact_777_mult__mono,axiom,
! [C_14,D_4,A_30,B_28] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_30),B_28))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_14),D_4))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_28))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_14))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_30),C_14)),hAPP_int_int(times_times_int(B_28),D_4))) ) ) ) ),
file('theBenchmark.p',fact_777_mult__mono) ).
fof(fact_778_mult__mono_H,axiom,
! [C_13,D_3,A_29,B_27] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_29),B_27))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_13),D_3))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_29))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_13))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_29),C_13)),hAPP_real_real(times_times_real(B_27),D_3))) ) ) ) ),
file('theBenchmark.p',fact_778_mult__mono_H) ).
fof(fact_779_mult__mono_H,axiom,
! [C_13,D_3,A_29,B_27] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_29),B_27))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_13),D_3))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_29))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_13))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(A_29),C_13)),hAPP_nat_nat(times_times_nat(B_27),D_3))) ) ) ) ),
file('theBenchmark.p',fact_779_mult__mono_H) ).
fof(fact_780_mult__mono_H,axiom,
! [C_13,D_3,A_29,B_27] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_29),B_27))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_13),D_3))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_29))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_13))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_29),C_13)),hAPP_int_int(times_times_int(B_27),D_3))) ) ) ) ),
file('theBenchmark.p',fact_780_mult__mono_H) ).
fof(fact_781_mult__left__mono__neg,axiom,
! [C_12,B_26,A_28] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_26),A_28))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_12),zero_zero_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(C_12),A_28)),hAPP_real_real(times_times_real(C_12),B_26))) ) ),
file('theBenchmark.p',fact_781_mult__left__mono__neg) ).
fof(fact_782_mult__left__mono__neg,axiom,
! [C_12,B_26,A_28] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_26),A_28))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_12),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(C_12),A_28)),hAPP_int_int(times_times_int(C_12),B_26))) ) ),
file('theBenchmark.p',fact_782_mult__left__mono__neg) ).
fof(fact_783_mult__right__mono__neg,axiom,
! [C_11,B_25,A_27] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_25),A_27))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_11),zero_zero_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_27),C_11)),hAPP_real_real(times_times_real(B_25),C_11))) ) ),
file('theBenchmark.p',fact_783_mult__right__mono__neg) ).
fof(fact_784_mult__right__mono__neg,axiom,
! [C_11,B_25,A_27] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_25),A_27))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_11),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_27),C_11)),hAPP_int_int(times_times_int(B_25),C_11))) ) ),
file('theBenchmark.p',fact_784_mult__right__mono__neg) ).
fof(fact_785_comm__mult__left__mono,axiom,
! [C_10,A_26,B_24] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_26),B_24))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_10))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(C_10),A_26)),hAPP_real_real(times_times_real(C_10),B_24))) ) ),
file('theBenchmark.p',fact_785_comm__mult__left__mono) ).
fof(fact_786_comm__mult__left__mono,axiom,
! [C_10,A_26,B_24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_26),B_24))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(C_10),A_26)),hAPP_nat_nat(times_times_nat(C_10),B_24))) ) ),
file('theBenchmark.p',fact_786_comm__mult__left__mono) ).
fof(fact_787_comm__mult__left__mono,axiom,
! [C_10,A_26,B_24] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_26),B_24))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_10))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(C_10),A_26)),hAPP_int_int(times_times_int(C_10),B_24))) ) ),
file('theBenchmark.p',fact_787_comm__mult__left__mono) ).
fof(fact_788_mult__left__mono,axiom,
! [C_9,A_25,B_23] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_25),B_23))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_9))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(C_9),A_25)),hAPP_real_real(times_times_real(C_9),B_23))) ) ),
file('theBenchmark.p',fact_788_mult__left__mono) ).
fof(fact_789_mult__left__mono,axiom,
! [C_9,A_25,B_23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_25),B_23))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_9))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(C_9),A_25)),hAPP_nat_nat(times_times_nat(C_9),B_23))) ) ),
file('theBenchmark.p',fact_789_mult__left__mono) ).
fof(fact_790_mult__left__mono,axiom,
! [C_9,A_25,B_23] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_25),B_23))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_9))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(C_9),A_25)),hAPP_int_int(times_times_int(C_9),B_23))) ) ),
file('theBenchmark.p',fact_790_mult__left__mono) ).
fof(fact_791_mult__right__mono,axiom,
! [C_8,A_24,B_22] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_24),B_22))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_8))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_24),C_8)),hAPP_real_real(times_times_real(B_22),C_8))) ) ),
file('theBenchmark.p',fact_791_mult__right__mono) ).
fof(fact_792_mult__right__mono,axiom,
! [C_8,A_24,B_22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_24),B_22))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_8))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(A_24),C_8)),hAPP_nat_nat(times_times_nat(B_22),C_8))) ) ),
file('theBenchmark.p',fact_792_mult__right__mono) ).
fof(fact_793_mult__right__mono,axiom,
! [C_8,A_24,B_22] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_24),B_22))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_8))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_24),C_8)),hAPP_int_int(times_times_int(B_22),C_8))) ) ),
file('theBenchmark.p',fact_793_mult__right__mono) ).
fof(fact_794_mult__nonpos__nonpos,axiom,
! [B_21,A_23] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_23),zero_zero_real))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_21),zero_zero_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(A_23),B_21))) ) ),
file('theBenchmark.p',fact_794_mult__nonpos__nonpos) ).
fof(fact_795_mult__nonpos__nonpos,axiom,
! [B_21,A_23] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_23),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_21),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(A_23),B_21))) ) ),
file('theBenchmark.p',fact_795_mult__nonpos__nonpos) ).
fof(fact_796_mult__nonpos__nonneg,axiom,
! [B_20,A_22] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_22),zero_zero_real))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_20))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_22),B_20)),zero_zero_real)) ) ),
file('theBenchmark.p',fact_796_mult__nonpos__nonneg) ).
fof(fact_797_mult__nonpos__nonneg,axiom,
! [B_20,A_22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_22),zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_20))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(A_22),B_20)),zero_zero_nat)) ) ),
file('theBenchmark.p',fact_797_mult__nonpos__nonneg) ).
fof(fact_798_mult__nonpos__nonneg,axiom,
! [B_20,A_22] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_22),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_20))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_22),B_20)),zero_zero_int)) ) ),
file('theBenchmark.p',fact_798_mult__nonpos__nonneg) ).
fof(fact_799_mult__nonneg__nonpos2,axiom,
! [B_19,A_21] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_21))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_19),zero_zero_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(B_19),A_21)),zero_zero_real)) ) ),
file('theBenchmark.p',fact_799_mult__nonneg__nonpos2) ).
fof(fact_800_mult__nonneg__nonpos2,axiom,
! [B_19,A_21] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_21))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_19),zero_zero_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(B_19),A_21)),zero_zero_nat)) ) ),
file('theBenchmark.p',fact_800_mult__nonneg__nonpos2) ).
fof(fact_801_mult__nonneg__nonpos2,axiom,
! [B_19,A_21] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_21))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_19),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(B_19),A_21)),zero_zero_int)) ) ),
file('theBenchmark.p',fact_801_mult__nonneg__nonpos2) ).
fof(fact_802_mult__nonneg__nonpos,axiom,
! [B_18,A_20] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_20))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_18),zero_zero_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_20),B_18)),zero_zero_real)) ) ),
file('theBenchmark.p',fact_802_mult__nonneg__nonpos) ).
fof(fact_803_mult__nonneg__nonpos,axiom,
! [B_18,A_20] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_20))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_18),zero_zero_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(A_20),B_18)),zero_zero_nat)) ) ),
file('theBenchmark.p',fact_803_mult__nonneg__nonpos) ).
fof(fact_804_mult__nonneg__nonpos,axiom,
! [B_18,A_20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_20))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_18),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_20),B_18)),zero_zero_int)) ) ),
file('theBenchmark.p',fact_804_mult__nonneg__nonpos) ).
fof(fact_805_mult__nonneg__nonneg,axiom,
! [B_17,A_19] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_19))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_17))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(A_19),B_17))) ) ),
file('theBenchmark.p',fact_805_mult__nonneg__nonneg) ).
fof(fact_806_mult__nonneg__nonneg,axiom,
! [B_17,A_19] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_19))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_17))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(A_19),B_17))) ) ),
file('theBenchmark.p',fact_806_mult__nonneg__nonneg) ).
fof(fact_807_mult__nonneg__nonneg,axiom,
! [B_17,A_19] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_19))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_17))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(A_19),B_17))) ) ),
file('theBenchmark.p',fact_807_mult__nonneg__nonneg) ).
fof(fact_808_mult__le__0__iff,axiom,
! [A_2,B_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_2),B_2)),zero_zero_real))
<=> ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_2))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_2),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_2),zero_zero_real))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_2)) ) ) ),
file('theBenchmark.p',fact_808_mult__le__0__iff) ).
fof(fact_809_mult__le__0__iff,axiom,
! [A_2,B_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_2),B_2)),zero_zero_int))
<=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_2)) ) ) ),
file('theBenchmark.p',fact_809_mult__le__0__iff) ).
fof(fact_810_zero__le__mult__iff,axiom,
! [A_2,B_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(A_2),B_2)))
<=> ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_2),zero_zero_real))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_2),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_2))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_2)) ) ) ),
file('theBenchmark.p',fact_810_zero__le__mult__iff) ).
fof(fact_811_zero__le__mult__iff,axiom,
! [A_2,B_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(A_2),B_2)))
<=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_2)) ) ) ),
file('theBenchmark.p',fact_811_zero__le__mult__iff) ).
fof(fact_812_zero__le__square,axiom,
! [A_18] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(A_18),A_18))),
file('theBenchmark.p',fact_812_zero__le__square) ).
fof(fact_813_zero__le__square,axiom,
! [A_18] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(A_18),A_18))),
file('theBenchmark.p',fact_813_zero__le__square) ).
fof(fact_814_mult__strict__left__mono__neg,axiom,
! [C_7,B_16,A_17] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_16),A_17))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_7),zero_zero_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_7),A_17)),hAPP_real_real(times_times_real(C_7),B_16))) ) ),
file('theBenchmark.p',fact_814_mult__strict__left__mono__neg) ).
fof(fact_815_mult__strict__left__mono__neg,axiom,
! [C_7,B_16,A_17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_16),A_17))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_7),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_7),A_17)),hAPP_int_int(times_times_int(C_7),B_16))) ) ),
file('theBenchmark.p',fact_815_mult__strict__left__mono__neg) ).
fof(fact_816_mult__strict__right__mono__neg,axiom,
! [C_6,B_15,A_16] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_15),A_16))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_6),zero_zero_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_16),C_6)),hAPP_real_real(times_times_real(B_15),C_6))) ) ),
file('theBenchmark.p',fact_816_mult__strict__right__mono__neg) ).
fof(fact_817_mult__strict__right__mono__neg,axiom,
! [C_6,B_15,A_16] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_15),A_16))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_6),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_16),C_6)),hAPP_int_int(times_times_int(B_15),C_6))) ) ),
file('theBenchmark.p',fact_817_mult__strict__right__mono__neg) ).
fof(fact_818_comm__mult__strict__left__mono,axiom,
! [C_5,A_15,B_14] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_15),B_14))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_5))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_5),A_15)),hAPP_real_real(times_times_real(C_5),B_14))) ) ),
file('theBenchmark.p',fact_818_comm__mult__strict__left__mono) ).
fof(fact_819_comm__mult__strict__left__mono,axiom,
! [C_5,A_15,B_14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_15),B_14))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(C_5),A_15)),hAPP_nat_nat(times_times_nat(C_5),B_14))) ) ),
file('theBenchmark.p',fact_819_comm__mult__strict__left__mono) ).
fof(fact_820_comm__mult__strict__left__mono,axiom,
! [C_5,A_15,B_14] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_15),B_14))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_5))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_5),A_15)),hAPP_int_int(times_times_int(C_5),B_14))) ) ),
file('theBenchmark.p',fact_820_comm__mult__strict__left__mono) ).
fof(fact_821_mult__strict__left__mono,axiom,
! [C_4,A_14,B_13] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_14),B_13))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_4))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_4),A_14)),hAPP_real_real(times_times_real(C_4),B_13))) ) ),
file('theBenchmark.p',fact_821_mult__strict__left__mono) ).
fof(fact_822_mult__strict__left__mono,axiom,
! [C_4,A_14,B_13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_14),B_13))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(C_4),A_14)),hAPP_nat_nat(times_times_nat(C_4),B_13))) ) ),
file('theBenchmark.p',fact_822_mult__strict__left__mono) ).
fof(fact_823_mult__strict__left__mono,axiom,
! [C_4,A_14,B_13] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_14),B_13))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_4))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_4),A_14)),hAPP_int_int(times_times_int(C_4),B_13))) ) ),
file('theBenchmark.p',fact_823_mult__strict__left__mono) ).
fof(fact_824_mult__strict__right__mono,axiom,
! [C_3,A_13,B_12] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_13),B_12))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_3))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_13),C_3)),hAPP_real_real(times_times_real(B_12),C_3))) ) ),
file('theBenchmark.p',fact_824_mult__strict__right__mono) ).
fof(fact_825_mult__strict__right__mono,axiom,
! [C_3,A_13,B_12] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_13),B_12))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_3))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(A_13),C_3)),hAPP_nat_nat(times_times_nat(B_12),C_3))) ) ),
file('theBenchmark.p',fact_825_mult__strict__right__mono) ).
fof(fact_826_mult__strict__right__mono,axiom,
! [C_3,A_13,B_12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_13),B_12))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_3))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_13),C_3)),hAPP_int_int(times_times_int(B_12),C_3))) ) ),
file('theBenchmark.p',fact_826_mult__strict__right__mono) ).
fof(fact_827_mult__neg__neg,axiom,
! [B_11,A_12] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_12),zero_zero_real))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_11),zero_zero_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(A_12),B_11))) ) ),
file('theBenchmark.p',fact_827_mult__neg__neg) ).
fof(fact_828_mult__neg__neg,axiom,
! [B_11,A_12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_12),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_11),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(A_12),B_11))) ) ),
file('theBenchmark.p',fact_828_mult__neg__neg) ).
fof(fact_829_mult__neg__pos,axiom,
! [B_10,A_11] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_11),zero_zero_real))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_10))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_11),B_10)),zero_zero_real)) ) ),
file('theBenchmark.p',fact_829_mult__neg__pos) ).
fof(fact_830_mult__neg__pos,axiom,
! [B_10,A_11] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_11),zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(A_11),B_10)),zero_zero_nat)) ) ),
file('theBenchmark.p',fact_830_mult__neg__pos) ).
fof(fact_831_mult__neg__pos,axiom,
! [B_10,A_11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_11),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_10))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_11),B_10)),zero_zero_int)) ) ),
file('theBenchmark.p',fact_831_mult__neg__pos) ).
fof(fact_832_mult__less__cancel__left__neg,axiom,
! [A_2,B_2,C_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_2),zero_zero_real))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_2),A_2)),hAPP_real_real(times_times_real(C_2),B_2)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_2),A_2)) ) ),
file('theBenchmark.p',fact_832_mult__less__cancel__left__neg) ).
fof(fact_833_mult__less__cancel__left__neg,axiom,
! [A_2,B_2,C_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_2),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_2),A_2)),hAPP_int_int(times_times_int(C_2),B_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_2),A_2)) ) ),
file('theBenchmark.p',fact_833_mult__less__cancel__left__neg) ).
fof(fact_834_zero__less__mult__pos2,axiom,
! [B_9,A_10] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(B_9),A_10)))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_10))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_9)) ) ),
file('theBenchmark.p',fact_834_zero__less__mult__pos2) ).
fof(fact_835_zero__less__mult__pos2,axiom,
! [B_9,A_10] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(B_9),A_10)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_9)) ) ),
file('theBenchmark.p',fact_835_zero__less__mult__pos2) ).
fof(fact_836_zero__less__mult__pos2,axiom,
! [B_9,A_10] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(B_9),A_10)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_10))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_9)) ) ),
file('theBenchmark.p',fact_836_zero__less__mult__pos2) ).
fof(fact_837_zero__less__mult__pos,axiom,
! [A_9,B_8] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(A_9),B_8)))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_9))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_8)) ) ),
file('theBenchmark.p',fact_837_zero__less__mult__pos) ).
fof(fact_838_zero__less__mult__pos,axiom,
! [A_9,B_8] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(A_9),B_8)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_9))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_8)) ) ),
file('theBenchmark.p',fact_838_zero__less__mult__pos) ).
fof(fact_839_zero__less__mult__pos,axiom,
! [A_9,B_8] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(A_9),B_8)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_9))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_8)) ) ),
file('theBenchmark.p',fact_839_zero__less__mult__pos) ).
fof(fact_840_mult__pos__neg2,axiom,
! [B_7,A_8] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_8))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_7),zero_zero_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(B_7),A_8)),zero_zero_real)) ) ),
file('theBenchmark.p',fact_840_mult__pos__neg2) ).
fof(fact_841_mult__pos__neg2,axiom,
! [B_7,A_8] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_8))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_7),zero_zero_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(B_7),A_8)),zero_zero_nat)) ) ),
file('theBenchmark.p',fact_841_mult__pos__neg2) ).
fof(fact_842_mult__pos__neg2,axiom,
! [B_7,A_8] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_8))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_7),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(B_7),A_8)),zero_zero_int)) ) ),
file('theBenchmark.p',fact_842_mult__pos__neg2) ).
fof(fact_843_mult__pos__neg,axiom,
! [B_6,A_7] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_7))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_6),zero_zero_real))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_7),B_6)),zero_zero_real)) ) ),
file('theBenchmark.p',fact_843_mult__pos__neg) ).
fof(fact_844_mult__pos__neg,axiom,
! [B_6,A_7] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_7))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_6),zero_zero_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(A_7),B_6)),zero_zero_nat)) ) ),
file('theBenchmark.p',fact_844_mult__pos__neg) ).
fof(fact_845_mult__pos__neg,axiom,
! [B_6,A_7] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_7))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_6),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_7),B_6)),zero_zero_int)) ) ),
file('theBenchmark.p',fact_845_mult__pos__neg) ).
fof(fact_846_mult__pos__pos,axiom,
! [B_5,A_6] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_6))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_5))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(A_6),B_5))) ) ),
file('theBenchmark.p',fact_846_mult__pos__pos) ).
fof(fact_847_mult__pos__pos,axiom,
! [B_5,A_6] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_6))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(A_6),B_5))) ) ),
file('theBenchmark.p',fact_847_mult__pos__pos) ).
fof(fact_848_mult__pos__pos,axiom,
! [B_5,A_6] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_6))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_5))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(A_6),B_5))) ) ),
file('theBenchmark.p',fact_848_mult__pos__pos) ).
fof(fact_849_mult__less__cancel__left__pos,axiom,
! [A_2,B_2,C_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_2))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_2),A_2)),hAPP_real_real(times_times_real(C_2),B_2)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),B_2)) ) ),
file('theBenchmark.p',fact_849_mult__less__cancel__left__pos) ).
fof(fact_850_mult__less__cancel__left__pos,axiom,
! [A_2,B_2,C_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_2))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_2),A_2)),hAPP_int_int(times_times_int(C_2),B_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),B_2)) ) ),
file('theBenchmark.p',fact_850_mult__less__cancel__left__pos) ).
fof(fact_851_mult__less__cancel__left__disj,axiom,
! [C_2,A_2,B_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_2),A_2)),hAPP_real_real(times_times_real(C_2),B_2)))
<=> ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_2),A_2))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_2),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),B_2))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_2)) ) ) ),
file('theBenchmark.p',fact_851_mult__less__cancel__left__disj) ).
fof(fact_852_mult__less__cancel__left__disj,axiom,
! [C_2,A_2,B_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_2),A_2)),hAPP_int_int(times_times_int(C_2),B_2)))
<=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_2),A_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_2),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),B_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_2)) ) ) ),
file('theBenchmark.p',fact_852_mult__less__cancel__left__disj) ).
fof(fact_853_mult__less__cancel__right__disj,axiom,
! [A_2,C_2,B_2] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_2),C_2)),hAPP_real_real(times_times_real(B_2),C_2)))
<=> ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_2),A_2))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_2),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),B_2))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_2)) ) ) ),
file('theBenchmark.p',fact_853_mult__less__cancel__right__disj) ).
fof(fact_854_mult__less__cancel__right__disj,axiom,
! [A_2,C_2,B_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_2),C_2)),hAPP_int_int(times_times_int(B_2),C_2)))
<=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_2),A_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_2),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),B_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_2)) ) ) ),
file('theBenchmark.p',fact_854_mult__less__cancel__right__disj) ).
fof(fact_855_not__square__less__zero,axiom,
! [A_5] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_5),A_5)),zero_zero_real)),
file('theBenchmark.p',fact_855_not__square__less__zero) ).
fof(fact_856_not__square__less__zero,axiom,
! [A_5] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_5),A_5)),zero_zero_int)),
file('theBenchmark.p',fact_856_not__square__less__zero) ).
fof(fact_857_pos__add__strict,axiom,
! [B_4,C_1,A_4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_4))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_4),C_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_4),hAPP_nat_nat(plus_plus_nat(A_4),C_1))) ) ),
file('theBenchmark.p',fact_857_pos__add__strict) ).
fof(fact_858_pos__add__strict,axiom,
! [B_4,C_1,A_4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_4))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_4),C_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_4),hAPP_int_int(plus_plus_int(A_4),C_1))) ) ),
file('theBenchmark.p',fact_858_pos__add__strict) ).
fof(fact_859_divides__ge,axiom,
! [A,B] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A),B))
| B = zero_zero_nat ) ),
file('theBenchmark.p',fact_859_divides__ge) ).
fof(fact_860_nat__mult__dvd__cancel__disj_H,axiom,
! [Ma,K,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(Ma),K)),hAPP_nat_nat(times_times_nat(N),K)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Ma),N))
| K = zero_zero_nat ) ),
file('theBenchmark.p',fact_860_nat__mult__dvd__cancel__disj_H) ).
fof(fact_861_real__mult__less__iff1,axiom,
! [X_2,Y_2,Z_1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Z_1))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X_2),Z_1)),hAPP_real_real(times_times_real(Y_2),Z_1)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),Y_2)) ) ),
file('theBenchmark.p',fact_861_real__mult__less__iff1) ).
fof(fact_862_real__mult__le__cancel__iff1,axiom,
! [X_2,Y_2,Z_1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Z_1))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X_2),Z_1)),hAPP_real_real(times_times_real(Y_2),Z_1)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Y_2)) ) ),
file('theBenchmark.p',fact_862_real__mult__le__cancel__iff1) ).
fof(fact_863_real__mult__le__cancel__iff2,axiom,
! [X_2,Y_2,Z_1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Z_1))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(Z_1),X_2)),hAPP_real_real(times_times_real(Z_1),Y_2)))
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Y_2)) ) ),
file('theBenchmark.p',fact_863_real__mult__le__cancel__iff2) ).
fof(fact_864_real__mult__order,axiom,
! [Y_1,X_1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y_1))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X_1),Y_1))) ) ),
file('theBenchmark.p',fact_864_real__mult__order) ).
fof(fact_865_real__mult__less__mono2,axiom,
! [X_1,Y_1,Z] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Z))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_1))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(Z),X_1)),hAPP_real_real(times_times_real(Z),Y_1))) ) ),
file('theBenchmark.p',fact_865_real__mult__less__mono2) ).
fof(fact_866_real__two__squares__add__zero__iff,axiom,
! [X_2,Y_2] :
( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X_2),X_2)),hAPP_real_real(times_times_real(Y_2),Y_2)) = zero_zero_real
<=> ( Y_2 = zero_zero_real
& X_2 = zero_zero_real ) ),
file('theBenchmark.p',fact_866_real__two__squares__add__zero__iff) ).
fof(fact_867_divides__exp2,axiom,
! [X_1,Y_1,N_1] :
( N_1 != zero_zero_nat
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X_1),N_1)),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) ) ),
file('theBenchmark.p',fact_867_divides__exp2) ).
fof(fact_868_divides__rev,axiom,
! [A,N_1,B] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(A),N_1)),hAPP_nat_nat(power_power_nat(B),N_1)))
=> ( N_1 != zero_zero_nat
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B)) ) ),
file('theBenchmark.p',fact_868_divides__rev) ).
fof(fact_869_exp__eq__1,axiom,
! [X_2,N] :
( hAPP_nat_nat(power_power_nat(X_2),N) = one_one_nat
<=> ( N = zero_zero_nat
| X_2 = one_one_nat ) ),
file('theBenchmark.p',fact_869_exp__eq__1) ).
fof(fact_870_divides__div__not,axiom,
! [X_1,Q_1,N_1,R_1] :
( X_1 = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(Q_1),N_1)),R_1)
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),R_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,R_1),N_1))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,N_1),X_1)) ) ) ),
file('theBenchmark.p',fact_870_divides__div__not) ).
fof(fact_871_two__realpow__ge__one,axiom,
! [N_1] : 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)))),N_1))),
file('theBenchmark.p',fact_871_two__realpow__ge__one) ).
fof(fact_872_realpow__pos__nth,axiom,
! [A,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A))
=> ? [R_2] :
( hAPP_nat_real(power_power_real(R_2),N_1) = A
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),R_2)) ) ) ),
file('theBenchmark.p',fact_872_realpow__pos__nth) ).
fof(fact_873_realpow__pos__nth__unique,axiom,
! [A,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A))
=> ? [X] :
( ! [Y] :
( ( hAPP_nat_real(power_power_real(Y),N_1) = A
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y)) )
=> Y = X )
& hAPP_nat_real(power_power_real(X),N_1) = A
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) ) ) ),
file('theBenchmark.p',fact_873_realpow__pos__nth__unique) ).
fof(fact_874_dvd__mult__cancel2,axiom,
! [N,Ma] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Ma))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(N),Ma)),Ma))
<=> N = one_one_nat ) ),
file('theBenchmark.p',fact_874_dvd__mult__cancel2) ).
fof(fact_875_dvd__mult__cancel1,axiom,
! [N,Ma] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Ma))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(Ma),N)),Ma))
<=> N = one_one_nat ) ),
file('theBenchmark.p',fact_875_dvd__mult__cancel1) ).
fof(fact_876_le0,axiom,
! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1)),
file('theBenchmark.p',fact_876_le0) ).
fof(fact_877_dvd_Oorder__refl,axiom,
! [X_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),X_1)),
file('theBenchmark.p',fact_877_dvd_Oorder__refl) ).
fof(fact_878_less__zeroE,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)),
file('theBenchmark.p',fact_878_less__zeroE) ).
fof(fact_879_diff__commute,axiom,
! [I_1,J_1,K_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_1),J_1)),K_1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_1),K_1)),J_1),
file('theBenchmark.p',fact_879_diff__commute) ).
fof(fact_880_real__le__refl,axiom,
! [W] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,W),W)),
file('theBenchmark.p',fact_880_real__le__refl) ).
fof(fact_881_real__le__linear,axiom,
! [Z,W] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,W),Z))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Z),W)) ),
file('theBenchmark.p',fact_881_real__le__linear) ).
fof(fact_882_real__le__trans,axiom,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,I_1),J_1))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,J_1),K_1))
=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,I_1),K_1)) ) ),
file('theBenchmark.p',fact_882_real__le__trans) ).
fof(fact_883_real__le__antisym,axiom,
! [Z,W] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Z),W))
=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,W),Z))
=> Z = W ) ),
file('theBenchmark.p',fact_883_real__le__antisym) ).
fof(fact_884_diff__0__eq__0,axiom,
! [N_1] : hAPP_nat_nat(minus_minus_nat(zero_zero_nat),N_1) = zero_zero_nat,
file('theBenchmark.p',fact_884_diff__0__eq__0) ).
fof(fact_885_minus__nat_Odiff__0,axiom,
! [M] : hAPP_nat_nat(minus_minus_nat(M),zero_zero_nat) = M,
file('theBenchmark.p',fact_885_minus__nat_Odiff__0) ).
fof(fact_886_diff__self__eq__0,axiom,
! [M] : hAPP_nat_nat(minus_minus_nat(M),M) = zero_zero_nat,
file('theBenchmark.p',fact_886_diff__self__eq__0) ).
fof(fact_887_diffs0__imp__equal,axiom,
! [M,N_1] :
( hAPP_nat_nat(minus_minus_nat(M),N_1) = zero_zero_nat
=> ( hAPP_nat_nat(minus_minus_nat(N_1),M) = zero_zero_nat
=> M = N_1 ) ),
file('theBenchmark.p',fact_887_diffs0__imp__equal) ).
fof(fact_888_nat__less__cases,axiom,
! [P_2,Ma,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_2,N),Ma)) )
=> ( ( Ma = N
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_2,N),Ma)) )
=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),Ma))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_2,N),Ma)) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_2,N),Ma)) ) ) ),
file('theBenchmark.p',fact_888_nat__less__cases) ).
fof(fact_889_less__not__refl3,axiom,
! [S,T] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T))
=> S != T ),
file('theBenchmark.p',fact_889_less__not__refl3) ).
fof(fact_890_less__not__refl2,axiom,
! [N_1,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M))
=> M != N_1 ),
file('theBenchmark.p',fact_890_less__not__refl2) ).
fof(fact_891_less__irrefl__nat,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1)),
file('theBenchmark.p',fact_891_less__irrefl__nat) ).
fof(fact_892_linorder__neqE__nat,axiom,
! [X_1,Y_1] :
( X_1 != Y_1
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1)) ) ),
file('theBenchmark.p',fact_892_linorder__neqE__nat) ).
fof(fact_893_nat__neq__iff,axiom,
! [Ma,N] :
( Ma != N
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),Ma))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N)) ) ),
file('theBenchmark.p',fact_893_nat__neq__iff) ).
fof(fact_894_less__not__refl,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1)),
file('theBenchmark.p',fact_894_less__not__refl) ).
fof(fact_895_diff__less__mono2,axiom,
! [L,M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),L))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(L),N_1)),hAPP_nat_nat(minus_minus_nat(L),M))) ) ),
file('theBenchmark.p',fact_895_diff__less__mono2) ).
fof(fact_896_less__imp__diff__less,axiom,
! [N_1,J_1,K_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),K_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(J_1),N_1)),K_1)) ),
file('theBenchmark.p',fact_896_less__imp__diff__less) ).
fof(fact_897_dvd_Oless__asym,axiom,
! [X_1,Y_1] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) )
=> ~ ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1)) ) ),
file('theBenchmark.p',fact_897_dvd_Oless__asym) ).
fof(fact_898_dvd_Oless__trans,axiom,
! [Z,X_1,Y_1] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) )
=> ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Z),Y_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),Z)) )
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Z),X_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Z)) ) ) ),
file('theBenchmark.p',fact_898_dvd_Oless__trans) ).
fof(fact_899_dvd_Oless__asym_H,axiom,
! [A,B] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B),A))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B)) )
=> ~ ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B),A)) ) ),
file('theBenchmark.p',fact_899_dvd_Oless__asym_H) ).
fof(fact_900_dvd_Oless__le__trans,axiom,
! [Z,X_1,Y_1] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) )
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),Z))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Z),X_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Z)) ) ) ),
file('theBenchmark.p',fact_900_dvd_Oless__le__trans) ).
fof(fact_901_dvd_Oord__less__eq__trans,axiom,
! [C,A,B] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B),A))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B)) )
=> ( B = C
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,C),A))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),C)) ) ) ),
file('theBenchmark.p',fact_901_dvd_Oord__less__eq__trans) ).
fof(fact_902_dvd_Oless__imp__triv,axiom,
! [P_2,X_2,Y_2] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) )
=> ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2)) )
=> hBOOL(P_2) ) ),
file('theBenchmark.p',fact_902_dvd_Oless__imp__triv) ).
fof(fact_903_dvd_Oless__imp__not__eq2,axiom,
! [X_1,Y_1] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) )
=> Y_1 != X_1 ),
file('theBenchmark.p',fact_903_dvd_Oless__imp__not__eq2) ).
fof(fact_904_dvd_Oless__imp__not__eq,axiom,
! [X_1,Y_1] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) )
=> X_1 != Y_1 ),
file('theBenchmark.p',fact_904_dvd_Oless__imp__not__eq) ).
fof(fact_905_dvd_Oless__imp__not__less,axiom,
! [X_1,Y_1] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) )
=> ~ ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1)) ) ),
file('theBenchmark.p',fact_905_dvd_Oless__imp__not__less) ).
fof(fact_906_dvd_Oless__imp__le,axiom,
! [X_1,Y_1] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) ),
file('theBenchmark.p',fact_906_dvd_Oless__imp__le) ).
fof(fact_907_dvd_Oless__not__sym,axiom,
! [X_1,Y_1] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) )
=> ~ ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1)) ) ),
file('theBenchmark.p',fact_907_dvd_Oless__not__sym) ).
fof(fact_908_dvd_Oless__imp__neq,axiom,
! [X_1,Y_1] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) )
=> X_1 != Y_1 ),
file('theBenchmark.p',fact_908_dvd_Oless__imp__neq) ).
fof(fact_909_dvd_Ole__less__trans,axiom,
! [Z,X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1))
=> ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Z),Y_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),Z)) )
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Z),X_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Z)) ) ) ),
file('theBenchmark.p',fact_909_dvd_Ole__less__trans) ).
fof(fact_910_dvd_Oord__eq__less__trans,axiom,
! [C,A,B] :
( A = B
=> ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,C),B))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B),C)) )
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,C),A))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),C)) ) ) ),
file('theBenchmark.p',fact_910_dvd_Oord__eq__less__trans) ).
fof(fact_911_dvd_Oorder__trans,axiom,
! [Z,X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),Z))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Z)) ) ),
file('theBenchmark.p',fact_911_dvd_Oorder__trans) ).
fof(fact_912_dvd_Oantisym,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
=> X_1 = Y_1 ) ),
file('theBenchmark.p',fact_912_dvd_Oantisym) ).
fof(fact_913_dvd__antisym,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M),N_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,N_1),M))
=> M = N_1 ) ),
file('theBenchmark.p',fact_913_dvd__antisym) ).
fof(fact_914_dvd_Oord__le__eq__trans,axiom,
! [C,A,B] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B))
=> ( B = C
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),C)) ) ),
file('theBenchmark.p',fact_914_dvd_Oord__le__eq__trans) ).
fof(fact_915_dvd_Oord__eq__le__trans,axiom,
! [C,A,B] :
( A = B
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B),C))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),C)) ) ),
file('theBenchmark.p',fact_915_dvd_Oord__eq__le__trans) ).
fof(fact_916_dvd_Ole__neq__trans,axiom,
! [A,B] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B))
=> ( A != B
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B),A))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B)) ) ) ),
file('theBenchmark.p',fact_916_dvd_Ole__neq__trans) ).
fof(fact_917_dvd_Ole__imp__less__or__eq,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1))
=> ( X_1 = Y_1
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) ) ) ),
file('theBenchmark.p',fact_917_dvd_Ole__imp__less__or__eq) ).
fof(fact_918_dvd_Oantisym__conv,axiom,
! [Y_2,X_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2))
<=> X_2 = Y_2 ) ),
file('theBenchmark.p',fact_918_dvd_Oantisym__conv) ).
fof(fact_919_dvd_Oeq__refl,axiom,
! [X_1,Y_1] :
( X_1 = Y_1
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) ),
file('theBenchmark.p',fact_919_dvd_Oeq__refl) ).
fof(fact_920_dvd_Oneq__le__trans,axiom,
! [A,B] :
( A != B
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B),A))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B)) ) ) ),
file('theBenchmark.p',fact_920_dvd_Oneq__le__trans) ).
fof(fact_921_dvd_Oless__le__not__le,axiom,
! [X_2,Y_2] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) )
<=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) ) ),
file('theBenchmark.p',fact_921_dvd_Oless__le__not__le) ).
fof(fact_922_dvd_Oless__le,axiom,
! [X_2,Y_2] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) )
<=> ( X_2 != Y_2
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) ) ),
file('theBenchmark.p',fact_922_dvd_Oless__le) ).
fof(fact_923_dvd_Ole__less,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2))
<=> ( X_2 = Y_2
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) ) ) ),
file('theBenchmark.p',fact_923_dvd_Ole__less) ).
fof(fact_924_dvd_Oeq__iff,axiom,
! [X_2,Y_2] :
( X_2 = Y_2
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) ) ),
file('theBenchmark.p',fact_924_dvd_Oeq__iff) ).
fof(fact_925_dvd_Oless__irrefl,axiom,
! [X_1] :
~ ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),X_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),X_1)) ),
file('theBenchmark.p',fact_925_dvd_Oless__irrefl) ).
fof(fact_926_dvd__diff__nat,axiom,
! [N_1,K_1,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),M))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),hAPP_nat_nat(minus_minus_nat(M),N_1))) ) ),
file('theBenchmark.p',fact_926_dvd__diff__nat) ).
fof(fact_927_nat__add__commute,axiom,
! [M,N_1] : hAPP_nat_nat(plus_plus_nat(M),N_1) = hAPP_nat_nat(plus_plus_nat(N_1),M),
file('theBenchmark.p',fact_927_nat__add__commute) ).
fof(fact_928_nat__add__left__commute,axiom,
! [X_1,Y_1,Z] : hAPP_nat_nat(plus_plus_nat(X_1),hAPP_nat_nat(plus_plus_nat(Y_1),Z)) = hAPP_nat_nat(plus_plus_nat(Y_1),hAPP_nat_nat(plus_plus_nat(X_1),Z)),
file('theBenchmark.p',fact_928_nat__add__left__commute) ).
fof(fact_929_nat__add__assoc,axiom,
! [M,N_1,K_1] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(M),N_1)),K_1) = hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(plus_plus_nat(N_1),K_1)),
file('theBenchmark.p',fact_929_nat__add__assoc) ).
fof(fact_930_nat__add__left__cancel,axiom,
! [K,Ma,N] :
( hAPP_nat_nat(plus_plus_nat(K),Ma) = hAPP_nat_nat(plus_plus_nat(K),N)
<=> Ma = N ),
file('theBenchmark.p',fact_930_nat__add__left__cancel) ).
fof(fact_931_nat__add__right__cancel,axiom,
! [Ma,K,N] :
( hAPP_nat_nat(plus_plus_nat(Ma),K) = hAPP_nat_nat(plus_plus_nat(N),K)
<=> Ma = N ),
file('theBenchmark.p',fact_931_nat__add__right__cancel) ).
fof(fact_932_diff__add__inverse2,axiom,
! [M,N_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),N_1)),N_1) = M,
file('theBenchmark.p',fact_932_diff__add__inverse2) ).
fof(fact_933_diff__add__inverse,axiom,
! [N_1,M] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(N_1),M)),N_1) = M,
file('theBenchmark.p',fact_933_diff__add__inverse) ).
fof(fact_934_diff__diff__left,axiom,
! [I_1,J_1,K_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_1),J_1)),K_1) = hAPP_nat_nat(minus_minus_nat(I_1),hAPP_nat_nat(plus_plus_nat(J_1),K_1)),
file('theBenchmark.p',fact_934_diff__diff__left) ).
fof(fact_935_Nat_Odiff__cancel,axiom,
! [K_1,M,N_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(K_1),M)),hAPP_nat_nat(plus_plus_nat(K_1),N_1)) = hAPP_nat_nat(minus_minus_nat(M),N_1),
file('theBenchmark.p',fact_935_Nat_Odiff__cancel) ).
fof(fact_936_diff__cancel2,axiom,
! [M,K_1,N_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),K_1)),hAPP_nat_nat(plus_plus_nat(N_1),K_1)) = hAPP_nat_nat(minus_minus_nat(M),N_1),
file('theBenchmark.p',fact_936_diff__cancel2) ).
fof(fact_937_le__refl,axiom,
! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),N_1)),
file('theBenchmark.p',fact_937_le__refl) ).
fof(fact_938_nat__le__linear,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) ),
file('theBenchmark.p',fact_938_nat__le__linear) ).
fof(fact_939_eq__imp__le,axiom,
! [M,N_1] :
( M = N_1
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) ),
file('theBenchmark.p',fact_939_eq__imp__le) ).
fof(fact_940_le__trans,axiom,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),K_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),K_1)) ) ),
file('theBenchmark.p',fact_940_le__trans) ).
fof(fact_941_le__antisym,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M))
=> M = N_1 ) ),
file('theBenchmark.p',fact_941_le__antisym) ).
fof(fact_942_Nat_Odiff__le__self,axiom,
! [M,N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M),N_1)),M)),
file('theBenchmark.p',fact_942_Nat_Odiff__le__self) ).
fof(fact_943_diff__le__mono2,axiom,
! [L,M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(L),N_1)),hAPP_nat_nat(minus_minus_nat(L),M))) ),
file('theBenchmark.p',fact_943_diff__le__mono2) ).
fof(fact_944_diff__le__mono,axiom,
! [L,M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M),L)),hAPP_nat_nat(minus_minus_nat(N_1),L))) ),
file('theBenchmark.p',fact_944_diff__le__mono) ).
fof(fact_945_diff__diff__cancel,axiom,
! [I_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),N_1))
=> hAPP_nat_nat(minus_minus_nat(N_1),hAPP_nat_nat(minus_minus_nat(N_1),I_1)) = I_1 ),
file('theBenchmark.p',fact_945_diff__diff__cancel) ).
fof(fact_946_eq__diff__iff,axiom,
! [N,K,Ma] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),Ma))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N))
=> ( hAPP_nat_nat(minus_minus_nat(Ma),K) = hAPP_nat_nat(minus_minus_nat(N),K)
<=> Ma = N ) ) ),
file('theBenchmark.p',fact_946_eq__diff__iff) ).
fof(fact_947_Nat_Odiff__diff__eq,axiom,
! [N_1,K_1,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1))
=> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),K_1)),hAPP_nat_nat(minus_minus_nat(N_1),K_1)) = hAPP_nat_nat(minus_minus_nat(M),N_1) ) ),
file('theBenchmark.p',fact_947_Nat_Odiff__diff__eq) ).
fof(fact_948_le__diff__iff,axiom,
! [N,K,Ma] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),Ma))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(Ma),K)),hAPP_nat_nat(minus_minus_nat(N),K)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N)) ) ) ),
file('theBenchmark.p',fact_948_le__diff__iff) ).
fof(fact_949_nat__mult__assoc,axiom,
! [M,N_1,K_1] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(M),N_1)),K_1) = hAPP_nat_nat(times_times_nat(M),hAPP_nat_nat(times_times_nat(N_1),K_1)),
file('theBenchmark.p',fact_949_nat__mult__assoc) ).
fof(fact_950_nat__mult__commute,axiom,
! [M,N_1] : hAPP_nat_nat(times_times_nat(M),N_1) = hAPP_nat_nat(times_times_nat(N_1),M),
file('theBenchmark.p',fact_950_nat__mult__commute) ).
fof(fact_951_diff__mult__distrib,axiom,
! [M,N_1,K_1] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(M),N_1)),K_1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(M),K_1)),hAPP_nat_nat(times_times_nat(N_1),K_1)),
file('theBenchmark.p',fact_951_diff__mult__distrib) ).
fof(fact_952_diff__mult__distrib2,axiom,
! [K_1,M,N_1] : hAPP_nat_nat(times_times_nat(K_1),hAPP_nat_nat(minus_minus_nat(M),N_1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(K_1),M)),hAPP_nat_nat(times_times_nat(K_1),N_1)),
file('theBenchmark.p',fact_952_diff__mult__distrib2) ).
fof(fact_953_gr0I,axiom,
! [N_1] :
( N_1 != zero_zero_nat
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) ),
file('theBenchmark.p',fact_953_gr0I) ).
fof(fact_954_gr__implies__not0,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
=> N_1 != zero_zero_nat ),
file('theBenchmark.p',fact_954_gr__implies__not0) ).
fof(fact_955_less__nat__zero__code,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)),
file('theBenchmark.p',fact_955_less__nat__zero__code) ).
fof(fact_956_neq0__conv,axiom,
! [N] :
( N != zero_zero_nat
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) ),
file('theBenchmark.p',fact_956_neq0__conv) ).
fof(fact_957_not__less0,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)),
file('theBenchmark.p',fact_957_not__less0) ).
fof(fact_958_diff__less,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M),N_1)),M)) ) ),
file('theBenchmark.p',fact_958_diff__less) ).
fof(fact_959_zero__less__diff,axiom,
! [N,Ma] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(N),Ma)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N)) ),
file('theBenchmark.p',fact_959_zero__less__diff) ).
fof(fact_960_add__eq__self__zero,axiom,
! [M,N_1] :
( hAPP_nat_nat(plus_plus_nat(M),N_1) = M
=> N_1 = zero_zero_nat ),
file('theBenchmark.p',fact_960_add__eq__self__zero) ).
fof(fact_961_add__is__0,axiom,
! [Ma,N] :
( hAPP_nat_nat(plus_plus_nat(Ma),N) = zero_zero_nat
<=> ( N = zero_zero_nat
& Ma = zero_zero_nat ) ),
file('theBenchmark.p',fact_961_add__is__0) ).
fof(fact_962_Nat_Oadd__0__right,axiom,
! [M] : hAPP_nat_nat(plus_plus_nat(M),zero_zero_nat) = M,
file('theBenchmark.p',fact_962_Nat_Oadd__0__right) ).
fof(fact_963_plus__nat_Oadd__0,axiom,
! [N_1] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),N_1) = N_1,
file('theBenchmark.p',fact_963_plus__nat_Oadd__0) ).
fof(fact_964_diff__add__0,axiom,
! [N_1,M] : hAPP_nat_nat(minus_minus_nat(N_1),hAPP_nat_nat(plus_plus_nat(N_1),M)) = zero_zero_nat,
file('theBenchmark.p',fact_964_diff__add__0) ).
fof(fact_965_le__0__eq,axiom,
! [N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),zero_zero_nat))
<=> N = zero_zero_nat ),
file('theBenchmark.p',fact_965_le__0__eq) ).
fof(fact_966_less__eq__nat_Osimps_I1_J,axiom,
! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1)),
file('theBenchmark.p',fact_966_less__eq__nat_Osimps_I1_J) ).
fof(fact_967_diff__is__0__eq_H,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
=> hAPP_nat_nat(minus_minus_nat(M),N_1) = zero_zero_nat ),
file('theBenchmark.p',fact_967_diff__is__0__eq_H) ).
fof(fact_968_diff__is__0__eq,axiom,
! [Ma,N] :
( hAPP_nat_nat(minus_minus_nat(Ma),N) = zero_zero_nat
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N)) ),
file('theBenchmark.p',fact_968_diff__is__0__eq) ).
fof(fact_969_mult__0,axiom,
! [N_1] : hAPP_nat_nat(times_times_nat(zero_zero_nat),N_1) = zero_zero_nat,
file('theBenchmark.p',fact_969_mult__0) ).
fof(fact_970_mult__0__right,axiom,
! [M] : hAPP_nat_nat(times_times_nat(M),zero_zero_nat) = zero_zero_nat,
file('theBenchmark.p',fact_970_mult__0__right) ).
fof(fact_971_mult__is__0,axiom,
! [Ma,N] :
( hAPP_nat_nat(times_times_nat(Ma),N) = zero_zero_nat
<=> ( N = zero_zero_nat
| Ma = zero_zero_nat ) ),
file('theBenchmark.p',fact_971_mult__is__0) ).
fof(fact_972_mult__cancel1,axiom,
! [K,Ma,N] :
( hAPP_nat_nat(times_times_nat(K),Ma) = hAPP_nat_nat(times_times_nat(K),N)
<=> ( K = zero_zero_nat
| Ma = N ) ),
file('theBenchmark.p',fact_972_mult__cancel1) ).
fof(fact_973_mult__cancel2,axiom,
! [Ma,K,N] :
( hAPP_nat_nat(times_times_nat(Ma),K) = hAPP_nat_nat(times_times_nat(N),K)
<=> ( K = zero_zero_nat
| Ma = N ) ),
file('theBenchmark.p',fact_973_mult__cancel2) ).
fof(fact_974_not__add__less1,axiom,
! [I_1,J_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_1),J_1)),I_1)),
file('theBenchmark.p',fact_974_not__add__less1) ).
fof(fact_975_not__add__less2,axiom,
! [J_1,I_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(J_1),I_1)),I_1)),
file('theBenchmark.p',fact_975_not__add__less2) ).
fof(fact_976_nat__add__left__cancel__less,axiom,
! [K,Ma,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(K),Ma)),hAPP_nat_nat(plus_plus_nat(K),N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N)) ),
file('theBenchmark.p',fact_976_nat__add__left__cancel__less) ).
fof(fact_977_trans__less__add1,axiom,
! [M,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(plus_plus_nat(J_1),M))) ),
file('theBenchmark.p',fact_977_trans__less__add1) ).
fof(fact_978_trans__less__add2,axiom,
! [M,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(plus_plus_nat(M),J_1))) ),
file('theBenchmark.p',fact_978_trans__less__add2) ).
fof(fact_979_add__less__mono1,axiom,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_1)),hAPP_nat_nat(plus_plus_nat(J_1),K_1))) ),
file('theBenchmark.p',fact_979_add__less__mono1) ).
fof(fact_980_add__less__mono,axiom,
! [K_1,L,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_1)),hAPP_nat_nat(plus_plus_nat(J_1),L))) ) ),
file('theBenchmark.p',fact_980_add__less__mono) ).
fof(fact_981_less__add__eq__less,axiom,
! [M,N_1,K_1,L] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L))
=> ( hAPP_nat_nat(plus_plus_nat(M),L) = hAPP_nat_nat(plus_plus_nat(K_1),N_1)
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ) ),
file('theBenchmark.p',fact_981_less__add__eq__less) ).
fof(fact_982_add__lessD1,axiom,
! [I_1,J_1,K_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_1),J_1)),K_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),K_1)) ),
file('theBenchmark.p',fact_982_add__lessD1) ).
fof(fact_983_add__diff__inverse,axiom,
! [M,N_1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
=> hAPP_nat_nat(plus_plus_nat(N_1),hAPP_nat_nat(minus_minus_nat(M),N_1)) = M ),
file('theBenchmark.p',fact_983_add__diff__inverse) ).
fof(fact_984_less__diff__conv,axiom,
! [I_2,J_2,K] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(minus_minus_nat(J_2),K)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_2),K)),J_2)) ),
file('theBenchmark.p',fact_984_less__diff__conv) ).
fof(fact_985_nat__less__le,axiom,
! [Ma,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N))
<=> ( Ma != N
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N)) ) ),
file('theBenchmark.p',fact_985_nat__less__le) ).
fof(fact_986_le__eq__less__or__eq,axiom,
! [Ma,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N))
<=> ( Ma = N
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N)) ) ),
file('theBenchmark.p',fact_986_le__eq__less__or__eq) ).
fof(fact_987_less__imp__le__nat,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) ),
file('theBenchmark.p',fact_987_less__imp__le__nat) ).
fof(fact_988_le__neq__implies__less,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
=> ( M != N_1
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ) ),
file('theBenchmark.p',fact_988_le__neq__implies__less) ).
fof(fact_989_less__or__eq__imp__le,axiom,
! [M,N_1] :
( ( M = N_1
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) ),
file('theBenchmark.p',fact_989_less__or__eq__imp__le) ).
fof(fact_990_less__diff__iff,axiom,
! [N,K,Ma] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),Ma))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(Ma),K)),hAPP_nat_nat(minus_minus_nat(N),K)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N)) ) ) ),
file('theBenchmark.p',fact_990_less__diff__iff) ).
fof(fact_991_diff__less__mono,axiom,
! [C,A,B] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A),B))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C),A))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(A),C)),hAPP_nat_nat(minus_minus_nat(B),C))) ) ),
file('theBenchmark.p',fact_991_diff__less__mono) ).
fof(fact_992_dvd__reduce,axiom,
! [K,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K),hAPP_nat_nat(plus_plus_nat(N),K)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K),N)) ),
file('theBenchmark.p',fact_992_dvd__reduce) ).
fof(fact_993_dvd__diffD1,axiom,
! [K_1,M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),hAPP_nat_nat(minus_minus_nat(M),N_1)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),M))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),N_1)) ) ) ),
file('theBenchmark.p',fact_993_dvd__diffD1) ).
fof(fact_994_dvd__diffD,axiom,
! [K_1,M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),hAPP_nat_nat(minus_minus_nat(M),N_1)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),N_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),M)) ) ) ),
file('theBenchmark.p',fact_994_dvd__diffD) ).
fof(fact_995_le__add2,axiom,
! [N_1,M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(plus_plus_nat(M),N_1))),
file('theBenchmark.p',fact_995_le__add2) ).
fof(fact_996_le__add1,axiom,
! [N_1,M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(plus_plus_nat(N_1),M))),
file('theBenchmark.p',fact_996_le__add1) ).
fof(fact_997_le__iff__add,axiom,
! [Ma,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N))
<=> ? [K_2] : N = hAPP_nat_nat(plus_plus_nat(Ma),K_2) ),
file('theBenchmark.p',fact_997_le__iff__add) ).
fof(fact_998_nat__add__left__cancel__le,axiom,
! [K,Ma,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(K),Ma)),hAPP_nat_nat(plus_plus_nat(K),N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N)) ),
file('theBenchmark.p',fact_998_nat__add__left__cancel__le) ).
fof(fact_999_trans__le__add1,axiom,
! [M,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(plus_plus_nat(J_1),M))) ),
file('theBenchmark.p',fact_999_trans__le__add1) ).
fof(fact_1000_trans__le__add2,axiom,
! [M,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(plus_plus_nat(M),J_1))) ),
file('theBenchmark.p',fact_1000_trans__le__add2) ).
fof(fact_1001_add__le__mono1,axiom,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_1)),hAPP_nat_nat(plus_plus_nat(J_1),K_1))) ),
file('theBenchmark.p',fact_1001_add__le__mono1) ).
fof(fact_1002_add__le__mono,axiom,
! [K_1,L,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),L))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_1)),hAPP_nat_nat(plus_plus_nat(J_1),L))) ) ),
file('theBenchmark.p',fact_1002_add__le__mono) ).
fof(fact_1003_add__leD2,axiom,
! [M,K_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K_1)),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) ),
file('theBenchmark.p',fact_1003_add__leD2) ).
fof(fact_1004_add__leD1,axiom,
! [M,K_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K_1)),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) ),
file('theBenchmark.p',fact_1004_add__leD1) ).
fof(fact_1005_add__leE,axiom,
! [M,K_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K_1)),N_1))
=> ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) ) ),
file('theBenchmark.p',fact_1005_add__leE) ).
fof(fact_1006_diff__diff__right,axiom,
! [I_1,K_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J_1))
=> hAPP_nat_nat(minus_minus_nat(I_1),hAPP_nat_nat(minus_minus_nat(J_1),K_1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I_1),K_1)),J_1) ),
file('theBenchmark.p',fact_1006_diff__diff__right) ).
fof(fact_1007_le__diff__conv,axiom,
! [J_2,K,I_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(J_2),K)),I_2))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),hAPP_nat_nat(plus_plus_nat(I_2),K))) ),
file('theBenchmark.p',fact_1007_le__diff__conv) ).
fof(fact_1008_le__add__diff,axiom,
! [M,K_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(N_1),M)),K_1))) ),
file('theBenchmark.p',fact_1008_le__add__diff) ).
fof(fact_1009_le__add__diff__inverse,axiom,
! [N_1,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M))
=> hAPP_nat_nat(plus_plus_nat(N_1),hAPP_nat_nat(minus_minus_nat(M),N_1)) = M ),
file('theBenchmark.p',fact_1009_le__add__diff__inverse) ).
fof(fact_1010_add__diff__assoc,axiom,
! [I_1,K_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J_1))
=> hAPP_nat_nat(plus_plus_nat(I_1),hAPP_nat_nat(minus_minus_nat(J_1),K_1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I_1),J_1)),K_1) ),
file('theBenchmark.p',fact_1010_add__diff__assoc) ).
fof(fact_1011_le__diff__conv2,axiom,
! [I_2,K,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(minus_minus_nat(J_2),K)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I_2),K)),J_2)) ) ),
file('theBenchmark.p',fact_1011_le__diff__conv2) ).
fof(fact_1012_le__add__diff__inverse2,axiom,
! [N_1,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M))
=> hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(M),N_1)),N_1) = M ),
file('theBenchmark.p',fact_1012_le__add__diff__inverse2) ).
fof(fact_1013_le__imp__diff__is__add,axiom,
! [K,I_2,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2))
=> ( hAPP_nat_nat(minus_minus_nat(J_2),I_2) = K
<=> J_2 = hAPP_nat_nat(plus_plus_nat(K),I_2) ) ),
file('theBenchmark.p',fact_1013_le__imp__diff__is__add) ).
fof(fact_1014_diff__add__assoc,axiom,
! [I_1,K_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J_1))
=> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I_1),J_1)),K_1) = hAPP_nat_nat(plus_plus_nat(I_1),hAPP_nat_nat(minus_minus_nat(J_1),K_1)) ),
file('theBenchmark.p',fact_1014_diff__add__assoc) ).
fof(fact_1015_add__diff__assoc2,axiom,
! [I_1,K_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J_1))
=> hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(J_1),K_1)),I_1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(J_1),I_1)),K_1) ),
file('theBenchmark.p',fact_1015_add__diff__assoc2) ).
fof(fact_1016_diff__add__assoc2,axiom,
! [I_1,K_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J_1))
=> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(J_1),I_1)),K_1) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(J_1),K_1)),I_1) ),
file('theBenchmark.p',fact_1016_diff__add__assoc2) ).
fof(fact_1017_add__mult__distrib,axiom,
! [M,N_1,K_1] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(M),N_1)),K_1) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(M),K_1)),hAPP_nat_nat(times_times_nat(N_1),K_1)),
file('theBenchmark.p',fact_1017_add__mult__distrib) ).
fof(fact_1018_add__mult__distrib2,axiom,
! [K_1,M,N_1] : hAPP_nat_nat(times_times_nat(K_1),hAPP_nat_nat(plus_plus_nat(M),N_1)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(K_1),M)),hAPP_nat_nat(times_times_nat(K_1),N_1)),
file('theBenchmark.p',fact_1018_add__mult__distrib2) ).
fof(fact_1019_nat__dvd__1__iff__1,axiom,
! [Ma] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Ma),one_one_nat))
<=> Ma = one_one_nat ),
file('theBenchmark.p',fact_1019_nat__dvd__1__iff__1) ).
fof(fact_1020_mult__le__mono,axiom,
! [K_1,L,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),L))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(I_1),K_1)),hAPP_nat_nat(times_times_nat(J_1),L))) ) ),
file('theBenchmark.p',fact_1020_mult__le__mono) ).
fof(fact_1021_mult__le__mono2,axiom,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K_1),I_1)),hAPP_nat_nat(times_times_nat(K_1),J_1))) ),
file('theBenchmark.p',fact_1021_mult__le__mono2) ).
fof(fact_1022_mult__le__mono1,axiom,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(I_1),K_1)),hAPP_nat_nat(times_times_nat(J_1),K_1))) ),
file('theBenchmark.p',fact_1022_mult__le__mono1) ).
fof(fact_1023_le__cube,axiom,
! [M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(times_times_nat(M),hAPP_nat_nat(times_times_nat(M),M)))),
file('theBenchmark.p',fact_1023_le__cube) ).
fof(fact_1024_le__square,axiom,
! [M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(times_times_nat(M),M))),
file('theBenchmark.p',fact_1024_le__square) ).
fof(fact_1025_nat__mult__eq__1__iff,axiom,
! [Ma,N] :
( hAPP_nat_nat(times_times_nat(Ma),N) = one_one_nat
<=> ( N = one_one_nat
& Ma = one_one_nat ) ),
file('theBenchmark.p',fact_1025_nat__mult__eq__1__iff) ).
fof(fact_1026_nat__mult__1__right,axiom,
! [N_1] : hAPP_nat_nat(times_times_nat(N_1),one_one_nat) = N_1,
file('theBenchmark.p',fact_1026_nat__mult__1__right) ).
fof(fact_1027_nat__1__eq__mult__iff,axiom,
! [Ma,N] :
( one_one_nat = hAPP_nat_nat(times_times_nat(Ma),N)
<=> ( N = one_one_nat
& Ma = one_one_nat ) ),
file('theBenchmark.p',fact_1027_nat__1__eq__mult__iff) ).
fof(fact_1028_nat__mult__1,axiom,
! [N_1] : hAPP_nat_nat(times_times_nat(one_one_nat),N_1) = N_1,
file('theBenchmark.p',fact_1028_nat__mult__1) ).
fof(fact_1029_nat__dvd__not__less,axiom,
! [N_1,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,N_1),M)) ) ),
file('theBenchmark.p',fact_1029_nat__dvd__not__less) ).
fof(fact_1030_add__gr__0,axiom,
! [Ma,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(Ma),N)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Ma)) ) ),
file('theBenchmark.p',fact_1030_add__gr__0) ).
fof(fact_1031_nat__diff__split,axiom,
! [P_2,A_2,B_2] :
( hBOOL(hAPP_nat_bool(P_2,hAPP_nat_nat(minus_minus_nat(A_2),B_2)))
<=> ( ! [D_2] :
( A_2 = hAPP_nat_nat(plus_plus_nat(B_2),D_2)
=> hBOOL(hAPP_nat_bool(P_2,D_2)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_2))
=> hBOOL(hAPP_nat_bool(P_2,zero_zero_nat)) ) ) ),
file('theBenchmark.p',fact_1031_nat__diff__split) ).
fof(fact_1032_nat__diff__split__asm,axiom,
! [P_2,A_2,B_2] :
( hBOOL(hAPP_nat_bool(P_2,hAPP_nat_nat(minus_minus_nat(A_2),B_2)))
<=> ~ ( ? [D_2] :
( ~ hBOOL(hAPP_nat_bool(P_2,D_2))
& A_2 = hAPP_nat_nat(plus_plus_nat(B_2),D_2) )
| ( ~ hBOOL(hAPP_nat_bool(P_2,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_2)) ) ) ),
file('theBenchmark.p',fact_1032_nat__diff__split__asm) ).
fof(fact_1033_mult__less__mono2,axiom,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K_1),I_1)),hAPP_nat_nat(times_times_nat(K_1),J_1))) ) ),
file('theBenchmark.p',fact_1033_mult__less__mono2) ).
fof(fact_1034_mult__less__mono1,axiom,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(I_1),K_1)),hAPP_nat_nat(times_times_nat(J_1),K_1))) ) ),
file('theBenchmark.p',fact_1034_mult__less__mono1) ).
fof(fact_1035_mult__less__cancel2,axiom,
! [Ma,K,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(Ma),K)),hAPP_nat_nat(times_times_nat(N),K)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ) ),
file('theBenchmark.p',fact_1035_mult__less__cancel2) ).
fof(fact_1036_mult__less__cancel1,axiom,
! [K,Ma,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K),Ma)),hAPP_nat_nat(times_times_nat(K),N)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ) ),
file('theBenchmark.p',fact_1036_mult__less__cancel1) ).
fof(fact_1037_nat__0__less__mult__iff,axiom,
! [Ma,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(Ma),N)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Ma)) ) ),
file('theBenchmark.p',fact_1037_nat__0__less__mult__iff) ).
fof(fact_1038_mult__eq__self__implies__10,axiom,
! [M,N_1] :
( M = hAPP_nat_nat(times_times_nat(M),N_1)
=> ( M = zero_zero_nat
| N_1 = one_one_nat ) ),
file('theBenchmark.p',fact_1038_mult__eq__self__implies__10) ).
fof(fact_1039_dvd__imp__le,axiom,
! [K_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),N_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) ) ),
file('theBenchmark.p',fact_1039_dvd__imp__le) ).
fof(fact_1040_dvd__mult__cancel,axiom,
! [K_1,M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(K_1),M)),hAPP_nat_nat(times_times_nat(K_1),N_1)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M),N_1)) ) ),
file('theBenchmark.p',fact_1040_dvd__mult__cancel) ).
fof(fact_1041_mult__le__cancel1,axiom,
! [K,Ma,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K),Ma)),hAPP_nat_nat(times_times_nat(K),N)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N)) ) ),
file('theBenchmark.p',fact_1041_mult__le__cancel1) ).
fof(fact_1042_mult__le__cancel2,axiom,
! [Ma,K,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(Ma),K)),hAPP_nat_nat(times_times_nat(N),K)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N)) ) ),
file('theBenchmark.p',fact_1042_mult__le__cancel2) ).
fof(fact_1043_ex__least__nat__less,axiom,
! [N,P_2] :
( ~ hBOOL(hAPP_nat_bool(P_2,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(P_2,N))
=> ? [K_2] :
( hBOOL(hAPP_nat_bool(P_2,hAPP_nat_nat(plus_plus_nat(K_2),one_one_nat)))
& ! [I] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K_2))
=> ~ hBOOL(hAPP_nat_bool(P_2,I)) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),N)) ) ) ),
file('theBenchmark.p',fact_1043_ex__least__nat__less) ).
fof(fact_1044_nat__less__add__iff2,axiom,
! [U,Ma,N,I_2,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_2),U)),Ma)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(J_2),I_2)),U)),N))) ) ),
file('theBenchmark.p',fact_1044_nat__less__add__iff2) ).
fof(fact_1045_nat__mult__eq__cancel__disj,axiom,
! [K,Ma,N] :
( hAPP_nat_nat(times_times_nat(K),Ma) = hAPP_nat_nat(times_times_nat(K),N)
<=> ( Ma = N
| K = zero_zero_nat ) ),
file('theBenchmark.p',fact_1045_nat__mult__eq__cancel__disj) ).
fof(fact_1046_left__add__mult__distrib,axiom,
! [I_1,U_1,J_1,K_1] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_1),U_1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_1),U_1)),K_1)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(I_1),J_1)),U_1)),K_1),
file('theBenchmark.p',fact_1046_left__add__mult__distrib) ).
fof(fact_1047_nat__mult__eq__cancel1,axiom,
! [Ma,N,K] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
=> ( hAPP_nat_nat(times_times_nat(K),Ma) = hAPP_nat_nat(times_times_nat(K),N)
<=> Ma = N ) ),
file('theBenchmark.p',fact_1047_nat__mult__eq__cancel1) ).
fof(fact_1048_nat__mult__less__cancel1,axiom,
! [Ma,N,K] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K),Ma)),hAPP_nat_nat(times_times_nat(K),N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N)) ) ),
file('theBenchmark.p',fact_1048_nat__mult__less__cancel1) ).
fof(fact_1049_nat__mult__dvd__cancel__disj,axiom,
! [K,Ma,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(K),Ma)),hAPP_nat_nat(times_times_nat(K),N)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Ma),N))
| K = zero_zero_nat ) ),
file('theBenchmark.p',fact_1049_nat__mult__dvd__cancel__disj) ).
fof(fact_1050_nat__mult__dvd__cancel1,axiom,
! [Ma,N,K] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(K),Ma)),hAPP_nat_nat(times_times_nat(K),N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Ma),N)) ) ),
file('theBenchmark.p',fact_1050_nat__mult__dvd__cancel1) ).
fof(fact_1051_nat__mult__le__cancel1,axiom,
! [Ma,N,K] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K),Ma)),hAPP_nat_nat(times_times_nat(K),N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N)) ) ),
file('theBenchmark.p',fact_1051_nat__mult__le__cancel1) ).
fof(fact_1052_nat__le__add__iff1,axiom,
! [U,Ma,N,J_2,I_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_2),U)),Ma)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N)))
<=> 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(I_2),J_2)),U)),Ma)),N)) ) ),
file('theBenchmark.p',fact_1052_nat__le__add__iff1) ).
fof(fact_1053_nat__diff__add__eq1,axiom,
! [U_1,M,N_1,J_1,I_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),I_1))
=> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_1),U_1)),M)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_1),U_1)),N_1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(I_1),J_1)),U_1)),M)),N_1) ),
file('theBenchmark.p',fact_1053_nat__diff__add__eq1) ).
fof(fact_1054_nat__eq__add__iff1,axiom,
! [U,Ma,N,J_2,I_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I_2))
=> ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_2),U)),Ma) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N)
<=> hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(I_2),J_2)),U)),Ma) = N ) ),
file('theBenchmark.p',fact_1054_nat__eq__add__iff1) ).
fof(fact_1055_nat__le__add__iff2,axiom,
! [U,Ma,N,I_2,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_2),U)),Ma)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(J_2),I_2)),U)),N))) ) ),
file('theBenchmark.p',fact_1055_nat__le__add__iff2) ).
fof(fact_1056_nat__diff__add__eq2,axiom,
! [U_1,M,N_1,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
=> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_1),U_1)),M)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_1),U_1)),N_1)) = hAPP_nat_nat(minus_minus_nat(M),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(J_1),I_1)),U_1)),N_1)) ),
file('theBenchmark.p',fact_1056_nat__diff__add__eq2) ).
fof(fact_1057_nat__eq__add__iff2,axiom,
! [U,Ma,N,I_2,J_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2))
=> ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_2),U)),Ma) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N)
<=> Ma = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(J_2),I_2)),U)),N) ) ),
file('theBenchmark.p',fact_1057_nat__eq__add__iff2) ).
fof(fact_1058_nat__less__add__iff1,axiom,
! [U,Ma,N,J_2,I_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I_2))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_2),U)),Ma)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N)))
<=> 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(I_2),J_2)),U)),Ma)),N)) ) ),
file('theBenchmark.p',fact_1058_nat__less__add__iff1) ).
fof(fact_1059_number__of1,axiom,
! [N_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(N_1)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(N_1))))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(N_1)))) ) ),
file('theBenchmark.p',fact_1059_number__of1) ).
fof(fact_1060_is__sum2sq__def,axiom,
! [X_2] :
( is_int(X_2)
=> ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X_2))
<=> ? [A_3,B_3] :
( twoSqu1241645765sum2sq(product_Pair_int_int(A_3,B_3)) = X_2
& is_int(B_3)
& is_int(A_3) ) ) ),
file('theBenchmark.p',fact_1060_is__sum2sq__def) ).
fof(fact_1061_imp__le__cong,axiom,
! [P_5,P_2,X_2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2))
=> ( hBOOL(P_2)
<=> hBOOL(P_5) ) )
=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2))
=> hBOOL(P_2) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2))
=> hBOOL(P_5) ) ) ),
file('theBenchmark.p',fact_1061_imp__le__cong) ).
fof(fact_1062_conj__le__cong,axiom,
! [P_5,P_2,X_2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2))
=> ( hBOOL(P_2)
<=> hBOOL(P_5) ) )
=> ( ( hBOOL(P_2)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) )
<=> ( hBOOL(P_5)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) ) ) ),
file('theBenchmark.p',fact_1062_conj__le__cong) ).
fof(fact_1063_zdvd__mono,axiom,
! [Ma,Ta,K] :
( is_int(K)
=> ( K != zero_zero_int
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Ma),Ta))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(K),Ma)),hAPP_int_int(times_times_int(K),Ta))) ) ) ),
file('theBenchmark.p',fact_1063_zdvd__mono) ).
fof(fact_1064_number__of2,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(pls))),
file('theBenchmark.p',fact_1064_number__of2) ).
fof(fact_1065_decr__mult__lemma,axiom,
! [K,P_2,D] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D))
=> ( ! [X] :
( is_int(X)
=> ( hBOOL(hAPP_int_bool(P_2,X))
=> hBOOL(hAPP_int_bool(P_2,hAPP_int_int(minus_minus_int(X),D))) ) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K))
=> ! [X] :
( hBOOL(hAPP_int_bool(P_2,X))
=> hBOOL(hAPP_int_bool(P_2,hAPP_int_int(minus_minus_int(X),hAPP_int_int(times_times_int(K),D)))) ) ) ) ),
file('theBenchmark.p',fact_1065_decr__mult__lemma) ).
fof(fact_1066_incr__mult__lemma,axiom,
! [K,P_2,D] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D))
=> ( ! [X] :
( is_int(X)
=> ( hBOOL(hAPP_int_bool(P_2,X))
=> hBOOL(hAPP_int_bool(P_2,hAPP_int_int(plus_plus_int(X),D))) ) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K))
=> ! [X] :
( hBOOL(hAPP_int_bool(P_2,X))
=> hBOOL(hAPP_int_bool(P_2,hAPP_int_int(plus_plus_int(X),hAPP_int_int(times_times_int(K),D)))) ) ) ) ),
file('theBenchmark.p',fact_1066_incr__mult__lemma) ).
fof(fact_1067_zprime__factor__exists,axiom,
! [A] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A))
=> ? [P_4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_4),A))
& hBOOL(hAPP_int_bool(zprime,P_4))
& is_int(P_4) ) ),
file('theBenchmark.p',fact_1067_zprime__factor__exists) ).
fof(fact_1068_zcong__zless__unique,axiom,
! [A,M] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M))
=> ? [X] :
( ! [Y] :
( is_int(Y)
=> ( ( hBOOL(hAPP_int_bool(zcong(A,Y),M))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y),M))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y)) )
=> Y = X ) )
& hBOOL(hAPP_int_bool(zcong(A,X),M))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X),M))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X))
& is_int(X) ) ),
file('theBenchmark.p',fact_1068_zcong__zless__unique) ).
fof(fact_1069_norR__mem__unique__aux,axiom,
! [A,B] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A),hAPP_int_int(minus_minus_int(B),one_one_int)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),B)) ),
file('theBenchmark.p',fact_1069_norR__mem__unique__aux) ).
fof(fact_1070_Wilson__Russ,axiom,
! [P_1] :
( hBOOL(hAPP_int_bool(zprime,P_1))
=> hBOOL(hAPP_int_bool(zcong(zfact(hAPP_int_int(minus_minus_int(P_1),one_one_int)),number_number_of_int(min)),P_1)) ),
file('theBenchmark.p',fact_1070_Wilson__Russ) ).
fof(fact_1071_zfact_Osimps,axiom,
! [N_1] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,N_1),zero_zero_int))
=> zfact(N_1) = hAPP_int_int(times_times_int(N_1),zfact(hAPP_int_int(minus_minus_int(N_1),one_one_int))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,N_1),zero_zero_int))
=> zfact(N_1) = one_one_int ) ),
file('theBenchmark.p',fact_1071_zfact_Osimps) ).
fof(fact_1072_inv__inv,axiom,
! [A,P_1] :
( is_int(A)
=> ( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),P_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),P_1))
=> inv(P_1,inv(P_1,A)) = A ) ) ) ) ),
file('theBenchmark.p',fact_1072_inv__inv) ).
fof(fact_1073_MultInvPair__distinct,axiom,
! [J_1,A,P_1] :
( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1))
=> ( ~ hBOOL(hAPP_int_bool(zcong(A,zero_zero_int),P_1))
=> ( ~ hBOOL(hAPP_int_bool(zcong(J_1,zero_zero_int),P_1))
=> ( ~ hBOOL(hAPP_int_bool(quadRes(P_1),A))
=> ~ hBOOL(hAPP_int_bool(zcong(J_1,hAPP_int_int(times_times_int(A),multInv(P_1,J_1))),P_1)) ) ) ) ) ),
file('theBenchmark.p',fact_1073_MultInvPair__distinct) ).
fof(fact_1074_aux______3,axiom,
! [J_1,K_1,A,P_1] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(J_1),K_1),A),P_1))
=> hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(multInv(P_1,J_1)),J_1)),K_1),hAPP_int_int(times_times_int(multInv(P_1,J_1)),A)),P_1)) ),
file('theBenchmark.p',fact_1074_aux______3) ).
fof(fact_1075_aux______1,axiom,
! [J_1,A,P_1,K_1] :
( hBOOL(hAPP_int_bool(zcong(J_1,hAPP_int_int(times_times_int(A),multInv(P_1,K_1))),P_1))
=> hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(J_1),K_1),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(A),multInv(P_1,K_1))),K_1)),P_1)) ),
file('theBenchmark.p',fact_1075_aux______1) ).
fof(fact_1076_inv__distinct,axiom,
! [A,P_1] :
( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),hAPP_int_int(minus_minus_int(P_1),one_one_int)))
=> A != inv(P_1,A) ) ) ),
file('theBenchmark.p',fact_1076_inv__distinct) ).
fof(fact_1077_inv__not__1,axiom,
! [A,P_1] :
( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),hAPP_int_int(minus_minus_int(P_1),one_one_int)))
=> inv(P_1,A) != one_one_int ) ) ),
file('theBenchmark.p',fact_1077_inv__not__1) ).
fof(fact_1078_inv__not__p__minus__1,axiom,
! [A,P_1] :
( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),hAPP_int_int(minus_minus_int(P_1),one_one_int)))
=> inv(P_1,A) != hAPP_int_int(minus_minus_int(P_1),one_one_int) ) ) ),
file('theBenchmark.p',fact_1078_inv__not__p__minus__1) ).
fof(fact_1079_inv__g__1,axiom,
! [A,P_1] :
( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),hAPP_int_int(minus_minus_int(P_1),one_one_int)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),inv(P_1,A))) ) ) ),
file('theBenchmark.p',fact_1079_inv__g__1) ).
fof(fact_1080_inv__less__p__minus__1,axiom,
! [A,P_1] :
( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),hAPP_int_int(minus_minus_int(P_1),one_one_int)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,inv(P_1,A)),hAPP_int_int(minus_minus_int(P_1),one_one_int))) ) ) ),
file('theBenchmark.p',fact_1080_inv__less__p__minus__1) ).
fof(fact_1081_MultInv__prop1,axiom,
! [X_1,Y_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1))
=> ( hBOOL(hAPP_int_bool(zcong(X_1,Y_1),P_1))
=> hBOOL(hAPP_int_bool(zcong(multInv(P_1,X_1),multInv(P_1,Y_1)),P_1)) ) ),
file('theBenchmark.p',fact_1081_MultInv__prop1) ).
fof(fact_1082_inv__not__0,axiom,
! [A,P_1] :
( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),hAPP_int_int(minus_minus_int(P_1),one_one_int)))
=> inv(P_1,A) != zero_zero_int ) ) ),
file('theBenchmark.p',fact_1082_inv__not__0) ).
fof(fact_1083_MultInv__zcong__prop1,axiom,
! [A,J_1,K_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1))
=> ( hBOOL(hAPP_int_bool(zcong(J_1,K_1),P_1))
=> hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),multInv(P_1,J_1)),hAPP_int_int(times_times_int(A),multInv(P_1,K_1))),P_1)) ) ),
file('theBenchmark.p',fact_1083_MultInv__zcong__prop1) ).
fof(fact_1084_MultInv__prop5,axiom,
! [Y_1,X_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1))
=> ( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( ~ hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),P_1))
=> ( ~ hBOOL(hAPP_int_bool(zcong(Y_1,zero_zero_int),P_1))
=> ( hBOOL(hAPP_int_bool(zcong(multInv(P_1,X_1),multInv(P_1,Y_1)),P_1))
=> hBOOL(hAPP_int_bool(zcong(X_1,Y_1),P_1)) ) ) ) ) ),
file('theBenchmark.p',fact_1084_MultInv__prop5) ).
fof(fact_1085_MultInv__prop4,axiom,
! [X_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1))
=> ( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( ~ hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),P_1))
=> hBOOL(hAPP_int_bool(zcong(multInv(P_1,multInv(P_1,X_1)),X_1),P_1)) ) ) ),
file('theBenchmark.p',fact_1085_MultInv__prop4) ).
fof(fact_1086_MultInv__prop3,axiom,
! [X_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1))
=> ( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( ~ hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),P_1))
=> ~ hBOOL(hAPP_int_bool(zcong(multInv(P_1,X_1),zero_zero_int),P_1)) ) ) ),
file('theBenchmark.p',fact_1086_MultInv__prop3) ).
fof(fact_1087_inv__is__inv,axiom,
! [A,P_1] :
( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),P_1))
=> hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),inv(P_1,A)),one_one_int),P_1)) ) ) ),
file('theBenchmark.p',fact_1087_inv__is__inv) ).
fof(fact_1088_aux______4,axiom,
! [K_1,A,J_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1))
=> ( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( ~ hBOOL(hAPP_int_bool(zcong(J_1,zero_zero_int),P_1))
=> ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(multInv(P_1,J_1)),J_1)),K_1),hAPP_int_int(times_times_int(multInv(P_1,J_1)),A)),P_1))
=> hBOOL(hAPP_int_bool(zcong(K_1,hAPP_int_int(times_times_int(A),multInv(P_1,J_1))),P_1)) ) ) ) ),
file('theBenchmark.p',fact_1088_aux______4) ).
fof(fact_1089_aux______2,axiom,
! [J_1,A,K_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1))
=> ( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( ~ hBOOL(hAPP_int_bool(zcong(K_1,zero_zero_int),P_1))
=> ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(J_1),K_1),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(A),multInv(P_1,K_1))),K_1)),P_1))
=> hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(J_1),K_1),A),P_1)) ) ) ) ),
file('theBenchmark.p',fact_1089_aux______2) ).
fof(fact_1090_MultInv__zcong__prop2,axiom,
! [A,J_1,K_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1))
=> ( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( ~ hBOOL(hAPP_int_bool(zcong(K_1,zero_zero_int),P_1))
=> ( ~ hBOOL(hAPP_int_bool(zcong(J_1,zero_zero_int),P_1))
=> ( hBOOL(hAPP_int_bool(zcong(J_1,hAPP_int_int(times_times_int(A),multInv(P_1,K_1))),P_1))
=> hBOOL(hAPP_int_bool(zcong(K_1,hAPP_int_int(times_times_int(A),multInv(P_1,J_1))),P_1)) ) ) ) ) ),
file('theBenchmark.p',fact_1090_MultInv__zcong__prop2) ).
fof(fact_1091_MultInv__zcong__prop3,axiom,
! [J_1,K_1,A,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1))
=> ( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( ~ hBOOL(hAPP_int_bool(zcong(A,zero_zero_int),P_1))
=> ( ~ hBOOL(hAPP_int_bool(zcong(K_1,zero_zero_int),P_1))
=> ( ~ hBOOL(hAPP_int_bool(zcong(J_1,zero_zero_int),P_1))
=> ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),multInv(P_1,J_1)),hAPP_int_int(times_times_int(A),multInv(P_1,K_1))),P_1))
=> hBOOL(hAPP_int_bool(zcong(J_1,K_1),P_1)) ) ) ) ) ) ),
file('theBenchmark.p',fact_1091_MultInv__zcong__prop3) ).
fof(fact_1092_Int2_Oaux____2,axiom,
! [X_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1))
=> ( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( ~ hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),P_1))
=> hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X_1),multInv(P_1,X_1))),multInv(P_1,multInv(P_1,X_1))),X_1),P_1)) ) ) ),
file('theBenchmark.p',fact_1092_Int2_Oaux____2) ).
fof(fact_1093_Int2_Oaux____1,axiom,
! [X_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1))
=> ( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( ~ hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),P_1))
=> hBOOL(hAPP_int_bool(zcong(multInv(P_1,multInv(P_1,X_1)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X_1),multInv(P_1,X_1))),multInv(P_1,multInv(P_1,X_1)))),P_1)) ) ) ),
file('theBenchmark.p',fact_1093_Int2_Oaux____1) ).
fof(fact_1094_MultInv__prop2a,axiom,
! [X_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1))
=> ( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( ~ hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),P_1))
=> hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(multInv(P_1,X_1)),X_1),one_one_int),P_1)) ) ) ),
file('theBenchmark.p',fact_1094_MultInv__prop2a) ).
fof(fact_1095_MultInv__prop2,axiom,
! [X_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1))
=> ( hBOOL(hAPP_int_bool(zprime,P_1))
=> ( ~ hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),P_1))
=> hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X_1),multInv(P_1,X_1)),one_one_int),P_1)) ) ) ),
file('theBenchmark.p',fact_1095_MultInv__prop2) ).
fof(fact_1096_wset__mem__inv__mem,axiom,
! [B_2,A_2,P_3] :
( hBOOL(hAPP_int_bool(zprime,P_3))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),P_3))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),hAPP_int_int(minus_minus_int(P_3),one_one_int)))
=> ( hBOOL(member_int(B_2,wset(A_2,P_3)))
=> hBOOL(member_int(inv(P_3,B_2),wset(A_2,P_3))) ) ) ) ),
file('theBenchmark.p',fact_1096_wset__mem__inv__mem) ).
fof(fact_1097_wset__inv__mem__mem,axiom,
! [B_2,A_2,P_3] :
( hBOOL(hAPP_int_bool(zprime,P_3))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),P_3))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),hAPP_int_int(minus_minus_int(P_3),one_one_int)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),B_2))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_2),hAPP_int_int(minus_minus_int(P_3),one_one_int)))
=> ( hBOOL(member_int(inv(P_3,B_2),wset(A_2,P_3)))
=> hBOOL(member_int(B_2,wset(A_2,P_3))) ) ) ) ) ) ),
file('theBenchmark.p',fact_1097_wset__inv__mem__mem) ).
fof(fact_1098_wset__mem__mem,axiom,
! [P_3,A_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_2))
=> hBOOL(member_int(A_2,wset(A_2,P_3))) ),
file('theBenchmark.p',fact_1098_wset__mem__mem) ).
fof(fact_1099_wset__subset,axiom,
! [B_2,P_3,A_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_2))
=> ( hBOOL(member_int(B_2,wset(hAPP_int_int(minus_minus_int(A_2),one_one_int),P_3)))
=> hBOOL(member_int(B_2,wset(A_2,P_3))) ) ),
file('theBenchmark.p',fact_1099_wset__subset) ).
fof(fact_1100_wset__less,axiom,
! [B_2,A_2,P_3] :
( hBOOL(hAPP_int_bool(zprime,P_3))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),hAPP_int_int(minus_minus_int(P_3),one_one_int)))
=> ( hBOOL(member_int(B_2,wset(A_2,P_3)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_2),hAPP_int_int(minus_minus_int(P_3),one_one_int))) ) ) ),
file('theBenchmark.p',fact_1100_wset__less) ).
fof(fact_1101_wset__g__1,axiom,
! [B_2,A_2,P_3] :
( hBOOL(hAPP_int_bool(zprime,P_3))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),hAPP_int_int(minus_minus_int(P_3),one_one_int)))
=> ( hBOOL(member_int(B_2,wset(A_2,P_3)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),B_2)) ) ) ),
file('theBenchmark.p',fact_1101_wset__g__1) ).
fof(fact_1102_wset__mem__imp__or,axiom,
! [B_2,P_3,A_2] :
( ( is_int(A_2)
& is_int(B_2) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_2))
=> ( ~ hBOOL(member_int(B_2,wset(hAPP_int_int(minus_minus_int(A_2),one_one_int),P_3)))
=> ( hBOOL(member_int(B_2,wset(A_2,P_3)))
=> ( B_2 = inv(P_3,A_2)
| B_2 = A_2 ) ) ) ) ),
file('theBenchmark.p',fact_1102_wset__mem__imp__or) ).
fof(fact_1103_wset__mem,axiom,
! [B_2,A_2,P_3] :
( hBOOL(hAPP_int_bool(zprime,P_3))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),hAPP_int_int(minus_minus_int(P_3),one_one_int)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),B_2))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),A_2))
=> hBOOL(member_int(B_2,wset(A_2,P_3))) ) ) ) ),
file('theBenchmark.p',fact_1103_wset__mem) ).
fof(fact_1104_int__le__induct,axiom,
! [P_2,I_2,K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_2),K))
=> ( hBOOL(hAPP_int_bool(P_2,K))
=> ( ! [I] :
( is_int(I)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I),K))
=> ( hBOOL(hAPP_int_bool(P_2,I))
=> hBOOL(hAPP_int_bool(P_2,hAPP_int_int(minus_minus_int(I),one_one_int))) ) ) )
=> hBOOL(hAPP_int_bool(P_2,I_2)) ) ) ),
file('theBenchmark.p',fact_1104_int__le__induct) ).
fof(fact_1105_int__less__induct,axiom,
! [P_2,I_2,K] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_2),K))
=> ( hBOOL(hAPP_int_bool(P_2,hAPP_int_int(minus_minus_int(K),one_one_int)))
=> ( ! [I] :
( is_int(I)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I),K))
=> ( hBOOL(hAPP_int_bool(P_2,I))
=> hBOOL(hAPP_int_bool(P_2,hAPP_int_int(minus_minus_int(I),one_one_int))) ) ) )
=> hBOOL(hAPP_int_bool(P_2,I_2)) ) ) ),
file('theBenchmark.p',fact_1105_int__less__induct) ).
fof(fact_1106_d22set__induct__old,axiom,
! [X_2,P_2] :
( ! [A_3] :
( is_int(A_3)
=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_3))
=> hBOOL(hAPP_int_bool(P_2,hAPP_int_int(minus_minus_int(A_3),one_one_int))) )
=> hBOOL(hAPP_int_bool(P_2,A_3)) ) )
=> hBOOL(hAPP_int_bool(P_2,X_2)) ),
file('theBenchmark.p',fact_1106_d22set__induct__old) ).
fof(fact_1107_int__ge__induct,axiom,
! [P_2,K,I_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),I_2))
=> ( hBOOL(hAPP_int_bool(P_2,K))
=> ( ! [I] :
( is_int(I)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),I))
=> ( hBOOL(hAPP_int_bool(P_2,I))
=> hBOOL(hAPP_int_bool(P_2,hAPP_int_int(plus_plus_int(I),one_one_int))) ) ) )
=> hBOOL(hAPP_int_bool(P_2,I_2)) ) ) ),
file('theBenchmark.p',fact_1107_int__ge__induct) ).
fof(fact_1108_int__gr__induct,axiom,
! [P_2,K,I_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),I_2))
=> ( hBOOL(hAPP_int_bool(P_2,hAPP_int_int(plus_plus_int(K),one_one_int)))
=> ( ! [I] :
( is_int(I)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),I))
=> ( hBOOL(hAPP_int_bool(P_2,I))
=> hBOOL(hAPP_int_bool(P_2,hAPP_int_int(plus_plus_int(I),one_one_int))) ) ) )
=> hBOOL(hAPP_int_bool(P_2,I_2)) ) ) ),
file('theBenchmark.p',fact_1108_int__gr__induct) ).
fof(fact_1109_mono__nat__linear__lb,axiom,
! [Ma,K,F_1] :
( ! [M_2,N_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F_1,M_2)),hAPP_nat_nat(F_1,N_2))) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(F_1,Ma)),K)),hAPP_nat_nat(F_1,hAPP_nat_nat(plus_plus_nat(Ma),K)))) ),
file('theBenchmark.p',fact_1109_mono__nat__linear__lb) ).
fof(fact_1110_d22set__eq__wset,axiom,
! [P_3] :
( hBOOL(hAPP_int_bool(zprime,P_3))
=> d22set(hAPP_int_int(minus_minus_int(P_3),number_number_of_int(bit0(bit1(pls))))) = wset(hAPP_int_int(minus_minus_int(P_3),number_number_of_int(bit0(bit1(pls)))),P_3) ),
file('theBenchmark.p',fact_1110_d22set__eq__wset) ).
fof(fact_1111_ex__least__nat__le,axiom,
! [N,P_2] :
( ~ hBOOL(hAPP_nat_bool(P_2,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(P_2,N))
=> ? [K_2] :
( hBOOL(hAPP_nat_bool(P_2,K_2))
& ! [I] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_2))
=> ~ hBOOL(hAPP_nat_bool(P_2,I)) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N)) ) ) ),
file('theBenchmark.p',fact_1111_ex__least__nat__le) ).
fof(fact_1112_d22set__le,axiom,
! [B_2,A_2] :
( hBOOL(member_int(B_2,d22set(A_2)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),A_2)) ),
file('theBenchmark.p',fact_1112_d22set__le) ).
fof(fact_1113_d22set__le__swap,axiom,
! [A_2,B_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),B_2))
=> ~ hBOOL(member_int(B_2,d22set(A_2))) ),
file('theBenchmark.p',fact_1113_d22set__le__swap) ).
fof(fact_1114_d22set__g__1,axiom,
! [B_2,A_2] :
( hBOOL(member_int(B_2,d22set(A_2)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),B_2)) ),
file('theBenchmark.p',fact_1114_d22set__g__1) ).
fof(fact_1115_d22set__mem,axiom,
! [A_2,B_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),B_2))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),A_2))
=> hBOOL(member_int(B_2,d22set(A_2))) ) ),
file('theBenchmark.p',fact_1115_d22set__mem) ).
fof(fact_1116_less__imp__add__positive,axiom,
! [I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_1))
=> ? [K_2] :
( hAPP_nat_nat(plus_plus_nat(I_1),K_2) = J_1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) ) ),
file('theBenchmark.p',fact_1116_less__imp__add__positive) ).
fof(fact_1117_pow__divides__eq__int,axiom,
! [A_2,B_2,N] :
( N != zero_zero_nat
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(A_2),N)),hAPP_nat_int(power_power_int(B_2),N)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_2),B_2)) ) ),
file('theBenchmark.p',fact_1117_pow__divides__eq__int) ).
fof(fact_1118_gcd__lcm__complete__lattice__nat_Otop__le,axiom,
! [A] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),A))
=> A = zero_zero_nat ),
file('theBenchmark.p',fact_1118_gcd__lcm__complete__lattice__nat_Otop__le) ).
fof(fact_1119_gcd__lcm__complete__lattice__nat_Otop__unique,axiom,
! [A_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),A_2))
<=> A_2 = zero_zero_nat ),
file('theBenchmark.p',fact_1119_gcd__lcm__complete__lattice__nat_Otop__unique) ).
fof(fact_1120_gcd__lcm__complete__lattice__nat_Oless__top,axiom,
! [A_2] :
( A_2 != zero_zero_nat
<=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),A_2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),zero_zero_nat)) ) ),
file('theBenchmark.p',fact_1120_gcd__lcm__complete__lattice__nat_Oless__top) ).
fof(fact_1121_gcd__lcm__complete__lattice__nat_Otop__greatest,axiom,
! [A] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),zero_zero_nat)),
file('theBenchmark.p',fact_1121_gcd__lcm__complete__lattice__nat_Otop__greatest) ).
fof(fact_1122_gcd__lcm__complete__lattice__nat_Onot__top__less,axiom,
! [A] :
~ ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),A)) ),
file('theBenchmark.p',fact_1122_gcd__lcm__complete__lattice__nat_Onot__top__less) ).
fof(fact_1123_gcd__lcm__complete__lattice__nat_Onot__less__bot,axiom,
! [A] :
~ ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),A))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),one_one_nat)) ),
file('theBenchmark.p',fact_1123_gcd__lcm__complete__lattice__nat_Onot__less__bot) ).
fof(fact_1124_gcd__lcm__complete__lattice__nat_Obot__least,axiom,
! [A] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),A)),
file('theBenchmark.p',fact_1124_gcd__lcm__complete__lattice__nat_Obot__least) ).
fof(fact_1125_gcd__lcm__complete__lattice__nat_Obot__less,axiom,
! [A_2] :
( A_2 != one_one_nat
<=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),one_one_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),A_2)) ) ),
file('theBenchmark.p',fact_1125_gcd__lcm__complete__lattice__nat_Obot__less) ).
fof(fact_1126_gcd__lcm__complete__lattice__nat_Obot__unique,axiom,
! [A_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),one_one_nat))
<=> A_2 = one_one_nat ),
file('theBenchmark.p',fact_1126_gcd__lcm__complete__lattice__nat_Obot__unique) ).
fof(fact_1127_gcd__lcm__complete__lattice__nat_Ole__bot,axiom,
! [A] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),one_one_nat))
=> A = one_one_nat ),
file('theBenchmark.p',fact_1127_gcd__lcm__complete__lattice__nat_Ole__bot) ).
fof(fact_1128_dvd__pos__nat,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) ) ),
file('theBenchmark.p',fact_1128_dvd__pos__nat) ).
fof(fact_1129_pow__divides__eq__nat,axiom,
! [A_2,B_2,N] :
( N != zero_zero_nat
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(A_2),N)),hAPP_nat_nat(power_power_nat(B_2),N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),B_2)) ) ),
file('theBenchmark.p',fact_1129_pow__divides__eq__nat) ).
fof(fact_1130_pow__divides__pow__int,axiom,
! [A,N_1,B] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(A),N_1)),hAPP_nat_int(power_power_int(B),N_1)))
=> ( N_1 != zero_zero_nat
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A),B)) ) ),
file('theBenchmark.p',fact_1130_pow__divides__pow__int) ).
fof(fact_1131_divides__le,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M),N_1))
=> ( N_1 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) ) ),
file('theBenchmark.p',fact_1131_divides__le) ).
fof(fact_1132_mult__left__cancel,axiom,
! [N_1,M,K_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
=> ( hAPP_nat_nat(times_times_nat(K_1),N_1) = hAPP_nat_nat(times_times_nat(K_1),M)
=> N_1 = M ) ),
file('theBenchmark.p',fact_1132_mult__left__cancel) ).
fof(fact_1133_SR__def,axiom,
! [P_3] : sr(P_3) = 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,P_3))),
file('theBenchmark.p',fact_1133_SR__def) ).
fof(fact_1134_neg__zmod__mult__2,axiom,
! [B,A] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A),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)))),B))),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),A)) = 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(B),one_one_int)),A))),one_one_int) ),
file('theBenchmark.p',fact_1134_neg__zmod__mult__2) ).
fof(fact_1135_zmod__number__of__Bit1,axiom,
! [V,W] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(W)))
=> hAPP_int_int(div_mod_int(number_number_of_int(bit1(V))),number_number_of_int(bit0(W))) = 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(V)),one_one_int)),number_number_of_int(W)))),one_one_int) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(W)))
=> hAPP_int_int(div_mod_int(number_number_of_int(bit1(V))),number_number_of_int(bit0(W))) = 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(V)),number_number_of_int(W)))),one_one_int) ) ),
file('theBenchmark.p',fact_1135_zmod__number__of__Bit1) ).
fof(fact_1136_zdvd__iff__zmod__eq__0__number__of,axiom,
! [X_2,Y_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X_2)),number_number_of_int(Y_2)))
<=> hAPP_int_int(div_mod_int(number_number_of_int(Y_2)),number_number_of_int(X_2)) = zero_zero_int ),
file('theBenchmark.p',fact_1136_zdvd__iff__zmod__eq__0__number__of) ).
fof(fact_1137_neg__mod__bound,axiom,
! [A,B] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),hAPP_int_int(div_mod_int(A),B))) ),
file('theBenchmark.p',fact_1137_neg__mod__bound) ).
fof(fact_1138_pos__mod__bound,axiom,
! [A,B] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(div_mod_int(A),B)),B)) ),
file('theBenchmark.p',fact_1138_pos__mod__bound) ).
fof(fact_1139_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
! [Y_1,X_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(div_mod_int(X_1),Y_1))) ) ),
file('theBenchmark.p',fact_1139_Divides_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_1140_zmod__le__nonneg__dividend,axiom,
! [K_1,M] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),M))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(M),K_1)),M)) ),
file('theBenchmark.p',fact_1140_zmod__le__nonneg__dividend) ).
fof(fact_1141_zmod__eq__0__iff,axiom,
! [Ma,D] :
( is_int(Ma)
=> ( hAPP_int_int(div_mod_int(Ma),D) = zero_zero_int
<=> ? [Q_2] :
( Ma = hAPP_int_int(times_times_int(D),Q_2)
& is_int(Q_2) ) ) ),
file('theBenchmark.p',fact_1141_zmod__eq__0__iff) ).
fof(fact_1142_zmod__eq__dvd__iff,axiom,
! [X_2,N,Y_2] :
( hAPP_int_int(div_mod_int(X_2),N) = hAPP_int_int(div_mod_int(Y_2),N)
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,N),hAPP_int_int(minus_minus_int(X_2),Y_2))) ),
file('theBenchmark.p',fact_1142_zmod__eq__dvd__iff) ).
fof(fact_1143_Residues_Oaux,axiom,
! [X_1,M,Y_1] :
( hAPP_int_int(div_mod_int(X_1),M) = hAPP_int_int(div_mod_int(Y_1),M)
=> hBOOL(hAPP_int_bool(zcong(X_1,Y_1),M)) ),
file('theBenchmark.p',fact_1143_Residues_Oaux) ).
fof(fact_1144_mod__mod__is__mod,axiom,
! [X_1,M] : hBOOL(hAPP_int_bool(zcong(X_1,hAPP_int_int(div_mod_int(X_1),M)),M)),
file('theBenchmark.p',fact_1144_mod__mod__is__mod) ).
fof(fact_1145_zcong__zmod,axiom,
! [A_2,B_2,Ma] :
( hBOOL(hAPP_int_bool(zcong(A_2,B_2),Ma))
<=> hBOOL(hAPP_int_bool(zcong(hAPP_int_int(div_mod_int(A_2),Ma),hAPP_int_int(div_mod_int(B_2),Ma)),Ma)) ),
file('theBenchmark.p',fact_1145_zcong__zmod) ).
fof(fact_1146_zdvd__zmod__imp__zdvd,axiom,
! [K_1,M,N_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),hAPP_int_int(div_mod_int(M),N_1)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),N_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),M)) ) ),
file('theBenchmark.p',fact_1146_zdvd__zmod__imp__zdvd) ).
fof(fact_1147_zdvd__zmod,axiom,
! [N_1,F,M] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,F),M))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,F),N_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,F),hAPP_int_int(div_mod_int(M),N_1))) ) ),
file('theBenchmark.p',fact_1147_zdvd__zmod) ).
fof(fact_1148_zpower__zmod,axiom,
! [X_1,M,Y_1] : hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(hAPP_int_int(div_mod_int(X_1),M)),Y_1)),M) = hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(X_1),Y_1)),M),
file('theBenchmark.p',fact_1148_zpower__zmod) ).
fof(fact_1149_zmod__zmult1__eq,axiom,
! [A,B,C] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(A),B)),C) = hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(A),hAPP_int_int(div_mod_int(B),C))),C),
file('theBenchmark.p',fact_1149_zmod__zmult1__eq) ).
fof(fact_1150_zmod__simps_I3_J,axiom,
! [A,B,C] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(A),hAPP_int_int(div_mod_int(B),C))),C) = hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(A),B)),C),
file('theBenchmark.p',fact_1150_zmod__simps_I3_J) ).
fof(fact_1151_zmod__self,axiom,
! [A] : hAPP_int_int(div_mod_int(A),A) = zero_zero_int,
file('theBenchmark.p',fact_1151_zmod__self) ).
fof(fact_1152_zmod__zero,axiom,
! [B] : hAPP_int_int(div_mod_int(zero_zero_int),B) = zero_zero_int,
file('theBenchmark.p',fact_1152_zmod__zero) ).
fof(fact_1153_zdiff__zmod__right,axiom,
! [X_1,Y_1,M] : hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(X_1),hAPP_int_int(div_mod_int(Y_1),M))),M) = hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(X_1),Y_1)),M),
file('theBenchmark.p',fact_1153_zdiff__zmod__right) ).
fof(fact_1154_zdiff__zmod__left,axiom,
! [X_1,M,Y_1] : hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(hAPP_int_int(div_mod_int(X_1),M)),Y_1)),M) = hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(X_1),Y_1)),M),
file('theBenchmark.p',fact_1154_zdiff__zmod__left) ).
fof(fact_1155_zmod__minus1__right,axiom,
! [A] : hAPP_int_int(div_mod_int(A),number_number_of_int(min)) = zero_zero_int,
file('theBenchmark.p',fact_1155_zmod__minus1__right) ).
fof(fact_1156_zmod__zdvd__zmod,axiom,
! [A,B,M] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,M),B))
=> hAPP_int_int(div_mod_int(hAPP_int_int(div_mod_int(A),B)),M) = hAPP_int_int(div_mod_int(A),M) ) ),
file('theBenchmark.p',fact_1156_zmod__zdvd__zmod) ).
fof(fact_1157_zcong__zmod__eq,axiom,
! [A_2,B_2,Ma] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ma))
=> ( hBOOL(hAPP_int_bool(zcong(A_2,B_2),Ma))
<=> hAPP_int_int(div_mod_int(A_2),Ma) = hAPP_int_int(div_mod_int(B_2),Ma) ) ),
file('theBenchmark.p',fact_1157_zcong__zmod__eq) ).
fof(fact_1158_pos__mod__sign,axiom,
! [A,B] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(div_mod_int(A),B))) ),
file('theBenchmark.p',fact_1158_pos__mod__sign) ).
fof(fact_1159_pos__mod__conj,axiom,
! [A,B] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(div_mod_int(A),B)),B))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(div_mod_int(A),B))) ) ),
file('theBenchmark.p',fact_1159_pos__mod__conj) ).
fof(fact_1160_mod__pos__pos__trivial,axiom,
! [B,A] :
( is_int(A)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),B))
=> hAPP_int_int(div_mod_int(A),B) = A ) ) ),
file('theBenchmark.p',fact_1160_mod__pos__pos__trivial) ).
fof(fact_1161_neg__mod__sign,axiom,
! [A,B] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(A),B)),zero_zero_int)) ),
file('theBenchmark.p',fact_1161_neg__mod__sign) ).
fof(fact_1162_neg__mod__conj,axiom,
! [A,B] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),hAPP_int_int(div_mod_int(A),B)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(A),B)),zero_zero_int)) ) ),
file('theBenchmark.p',fact_1162_neg__mod__conj) ).
fof(fact_1163_mod__neg__neg__trivial,axiom,
! [B,A] :
( is_int(A)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),A))
=> hAPP_int_int(div_mod_int(A),B) = A ) ) ),
file('theBenchmark.p',fact_1163_mod__neg__neg__trivial) ).
fof(fact_1164_mod__pos__neg__trivial,axiom,
! [B,A] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(A),B)),zero_zero_int))
=> hAPP_int_int(div_mod_int(A),B) = hAPP_int_int(plus_plus_int(A),B) ) ),
file('theBenchmark.p',fact_1164_mod__pos__neg__trivial) ).
fof(fact_1165_zmod__number__of__Bit0,axiom,
! [V,W] : hAPP_int_int(div_mod_int(number_number_of_int(bit0(V))),number_number_of_int(bit0(W))) = hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),hAPP_int_int(div_mod_int(number_number_of_int(V)),number_number_of_int(W))),
file('theBenchmark.p',fact_1165_zmod__number__of__Bit0) ).
fof(fact_1166_split__zmod,axiom,
! [P_2,N,K] :
( ( is_int(K)
& is_int(N) )
=> ( hBOOL(hAPP_int_bool(P_2,hAPP_int_int(div_mod_int(N),K)))
<=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),zero_zero_int))
=> ! [I,J] :
( ( is_int(J)
& is_int(I) )
=> ( ( N = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(K),I)),J)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,J),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),J)) )
=> hBOOL(hAPP_int_bool(P_2,J)) ) ) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K))
=> ! [I,J] :
( ( is_int(J)
& is_int(I) )
=> ( ( N = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(K),I)),J)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,J),K))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),J)) )
=> hBOOL(hAPP_int_bool(P_2,J)) ) ) )
& ( K = zero_zero_int
=> hBOOL(hAPP_int_bool(P_2,N)) ) ) ) ),
file('theBenchmark.p',fact_1166_split__zmod) ).
fof(fact_1167_zmult2__lemma__aux3,axiom,
! [Q_1,B,R_1,C] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B))
=> 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(B),hAPP_int_int(div_mod_int(Q_1),C))),R_1))) ) ) ),
file('theBenchmark.p',fact_1167_zmult2__lemma__aux3) ).
fof(fact_1168_zmult2__lemma__aux4,axiom,
! [Q_1,B,R_1,C] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),hAPP_int_int(div_mod_int(Q_1),C))),R_1)),hAPP_int_int(times_times_int(B),C))) ) ) ),
file('theBenchmark.p',fact_1168_zmult2__lemma__aux4) ).
fof(fact_1169_zmult2__lemma__aux1,axiom,
! [Q_1,B,R_1,C] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),R_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_1),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(B),C)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),hAPP_int_int(div_mod_int(Q_1),C))),R_1))) ) ) ),
file('theBenchmark.p',fact_1169_zmult2__lemma__aux1) ).
fof(fact_1170_zmult2__lemma__aux2,axiom,
! [Q_1,B,R_1,C] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),R_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_1),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(B),hAPP_int_int(div_mod_int(Q_1),C))),R_1)),zero_zero_int)) ) ) ),
file('theBenchmark.p',fact_1170_zmult2__lemma__aux2) ).
fof(fact_1171_divmod__int__rel__mod__eq,axiom,
! [A_1,B_1,Q_3,Y_1] :
( ( is_int(Y_1)
& is_int(B_1) )
=> ( A_1 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B_1),Q_3)),Y_1)
=> ( ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),Y_1)) ) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),B_1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_1)) ) ) )
=> ( B_1 != zero_zero_int
=> hAPP_int_int(div_mod_int(A_1),B_1) = Y_1 ) ) ) ),
file('theBenchmark.p',fact_1171_divmod__int__rel__mod__eq) ).
fof(fact_1172_neq__one__mod__two,axiom,
! [X_2] :
( hAPP_int_int(div_mod_int(X_2),number_number_of_int(bit0(bit1(pls)))) != zero_zero_int
<=> hAPP_int_int(div_mod_int(X_2),number_number_of_int(bit0(bit1(pls)))) = one_one_int ),
file('theBenchmark.p',fact_1172_neq__one__mod__two) ).
fof(fact_1173_zmod__minus1,axiom,
! [B] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B))
=> hAPP_int_int(div_mod_int(number_number_of_int(min)),B) = hAPP_int_int(minus_minus_int(B),one_one_int) ),
file('theBenchmark.p',fact_1173_zmod__minus1) ).
fof(fact_1174_pos__zmod__mult__2,axiom,
! [B,A] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A))
=> 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)))),B))),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),A)) = 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(B),A))) ),
file('theBenchmark.p',fact_1174_pos__zmod__mult__2) ).
fof(fact_1175_zmod__eq__0D,axiom,
! [M_1,D_1] :
( is_int(M_1)
=> ( hAPP_int_int(div_mod_int(M_1),D_1) = zero_zero_int
=> ? [Q_2] :
( M_1 = hAPP_int_int(times_times_int(D_1),Q_2)
& is_int(Q_2) ) ) ),
file('theBenchmark.p',fact_1175_zmod__eq__0D) ).
fof(fact_1176_StandardRes__prop4,axiom,
! [X_1,Y_1,M] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),M))
=> hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(standardRes(M,X_1)),standardRes(M,Y_1)),hAPP_int_int(times_times_int(X_1),Y_1)),M)) ),
file('theBenchmark.p',fact_1176_StandardRes__prop4) ).
fof(fact_1177_mod__le__divisor,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(M),N_1)),N_1)) ),
file('theBenchmark.p',fact_1177_mod__le__divisor) ).
fof(fact_1178_mod__less__divisor,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(div_mod_nat(M),N_1)),N_1)) ),
file('theBenchmark.p',fact_1178_mod__less__divisor) ).
fof(fact_1179_mod__eq__0__iff,axiom,
! [Ma,D] :
( hAPP_nat_nat(div_mod_nat(Ma),D) = zero_zero_nat
<=> ? [Q_2] : Ma = hAPP_nat_nat(times_times_nat(D),Q_2) ),
file('theBenchmark.p',fact_1179_mod__eq__0__iff) ).
fof(fact_1180_mod__geq,axiom,
! [M,N_1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
=> hAPP_nat_nat(div_mod_nat(M),N_1) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(M),N_1)),N_1) ),
file('theBenchmark.p',fact_1180_mod__geq) ).
fof(fact_1181_mod__if,axiom,
! [M,N_1] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
=> hAPP_nat_nat(div_mod_nat(M),N_1) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(M),N_1)),N_1) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
=> hAPP_nat_nat(div_mod_nat(M),N_1) = M ) ),
file('theBenchmark.p',fact_1181_mod__if) ).
fof(fact_1182_mod__mult__self3,axiom,
! [K_1,N_1,M] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(K_1),N_1)),M)),N_1) = hAPP_nat_nat(div_mod_nat(M),N_1),
file('theBenchmark.p',fact_1182_mod__mult__self3) ).
fof(fact_1183_le__mod__geq,axiom,
! [N_1,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M))
=> hAPP_nat_nat(div_mod_nat(M),N_1) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(M),N_1)),N_1) ),
file('theBenchmark.p',fact_1183_le__mod__geq) ).
fof(fact_1184_StandardRes__def,axiom,
! [M,X_1] : standardRes(M,X_1) = hAPP_int_int(div_mod_int(X_1),M),
file('theBenchmark.p',fact_1184_StandardRes__def) ).
fof(fact_1185_mod__mult__distrib,axiom,
! [M,N_1,K_1] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(div_mod_nat(M),N_1)),K_1) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(M),K_1)),hAPP_nat_nat(times_times_nat(N_1),K_1)),
file('theBenchmark.p',fact_1185_mod__mult__distrib) ).
fof(fact_1186_mod__mult__distrib2,axiom,
! [K_1,M,N_1] : hAPP_nat_nat(times_times_nat(K_1),hAPP_nat_nat(div_mod_nat(M),N_1)) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(K_1),M)),hAPP_nat_nat(times_times_nat(K_1),N_1)),
file('theBenchmark.p',fact_1186_mod__mult__distrib2) ).
fof(fact_1187_mod__less,axiom,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
=> hAPP_nat_nat(div_mod_nat(M),N_1) = M ),
file('theBenchmark.p',fact_1187_mod__less) ).
fof(fact_1188_mod__less__eq__dividend,axiom,
! [M,N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(M),N_1)),M)),
file('theBenchmark.p',fact_1188_mod__less__eq__dividend) ).
fof(fact_1189_StandardRes__eq__zcong,axiom,
! [Ma,X_2] :
( standardRes(Ma,X_2) = zero_zero_int
<=> hBOOL(hAPP_int_bool(zcong(X_2,zero_zero_int),Ma)) ),
file('theBenchmark.p',fact_1189_StandardRes__eq__zcong) ).
fof(fact_1190_StandardRes__prop3,axiom,
! [X_2,P_3] :
( ~ hBOOL(hAPP_int_bool(zcong(X_2,zero_zero_int),P_3))
<=> standardRes(P_3,X_2) != zero_zero_int ),
file('theBenchmark.p',fact_1190_StandardRes__prop3) ).
fof(fact_1191_StandardRes__prop1,axiom,
! [X_1,M] : hBOOL(hAPP_int_bool(zcong(X_1,standardRes(M,X_1)),M)),
file('theBenchmark.p',fact_1191_StandardRes__prop1) ).
fof(fact_1192_StandardRes__ubound,axiom,
! [X_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),P_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,standardRes(P_1,X_1)),P_1)) ),
file('theBenchmark.p',fact_1192_StandardRes__ubound) ).
fof(fact_1193_StandardRes__SR__prop,axiom,
! [X_2,P_3] :
( is_int(X_2)
=> ( hBOOL(member_int(X_2,sr(P_3)))
=> standardRes(P_3,X_2) = X_2 ) ),
file('theBenchmark.p',fact_1193_StandardRes__SR__prop) ).
fof(fact_1194_split__mod,axiom,
! [P_2,N,K] :
( hBOOL(hAPP_nat_bool(P_2,hAPP_nat_nat(div_mod_nat(N),K)))
<=> ( ( K != zero_zero_nat
=> ! [I,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K))
=> ( N = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(K),I)),J)
=> hBOOL(hAPP_nat_bool(P_2,J)) ) ) )
& ( K = zero_zero_nat
=> hBOOL(hAPP_nat_bool(P_2,N)) ) ) ),
file('theBenchmark.p',fact_1194_split__mod) ).
fof(fact_1195_mod__lemma,axiom,
! [Q_1,R_1,B,C] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,R_1),B))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(B),hAPP_nat_nat(div_mod_nat(Q_1),C))),R_1)),hAPP_nat_nat(times_times_nat(B),C))) ) ),
file('theBenchmark.p',fact_1195_mod__lemma) ).
fof(fact_1196_StandardRes__lbound,axiom,
! [X_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),P_1))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),standardRes(P_1,X_1))) ),
file('theBenchmark.p',fact_1196_StandardRes__lbound) ).
fof(fact_1197_StandardRes__prop2,axiom,
! [X1,X2,Ma] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ma))
=> ( standardRes(Ma,X1) = standardRes(Ma,X2)
<=> hBOOL(hAPP_int_bool(zcong(X1,X2),Ma)) ) ),
file('theBenchmark.p',fact_1197_StandardRes__prop2) ).
fof(help_fconj_1_1_U,axiom,
! [Q,P] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
| ~ hBOOL(Q)
| ~ hBOOL(P) ),
file('theBenchmark.p',help_fconj_1_1_U) ).
fof(help_fconj_2_1_U,axiom,
! [P,Q] :
( hBOOL(P)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ),
file('theBenchmark.p',help_fconj_2_1_U) ).
fof(help_fconj_3_1_U,axiom,
! [P,Q] :
( hBOOL(Q)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ),
file('theBenchmark.p',help_fconj_3_1_U) ).
fof(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_int_bool(cOMBC_int_int_bool(P,Q),R) = hAPP_int_bool(hAPP_i1948725293t_bool(P,R),Q),
file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U) ).
fof(help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_int_bool(cOMBS_int_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_i68813070l_bool(P,R),hAPP_int_bool(Q,R)),
file('theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
! [P,Q,R] : hAPP_i68813070l_bool(cOMBB_1652995168ol_int(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_int_bool(Q,R)),
file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).
fof(conj_0,conjecture,
? [X,Y] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y),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('theBenchmark.p',conj_0) ).
fof(f_1_1,plain,
is_int(one_one_int),
inference(fof_nnf,[status(thm)],[gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint]) ).
cnf(f_1_2,plain,
is_int(one_one_int),
inference(clausify,[status(thm)],[f_1_1]) ).
fof(f_2_1,plain,
is_int(zero_zero_int),
inference(fof_nnf,[status(thm)],[gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint]) ).
cnf(f_2_2,plain,
is_int(zero_zero_int),
inference(clausify,[status(thm)],[f_2_1]) ).
fof(f_3_1,plain,
is_int(undefined_int(int)),
inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__Int__Oint]) ).
cnf(f_3_2,plain,
is_int(undefined_int(int)),
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
! [B_1_1,B_2_1] :
( is_int(multInv(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) ),
inference(fof_nnf,[status(thm)],[gsy_c_Int2_OMultInv]) ).
fof(f_4_2,plain,
! [U_1,U_0] :
( is_int(multInv(U_1,U_0))
| ~ is_int(U_0)
| ~ is_int(U_1) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( is_int(multInv(U_1,U_0))
| ~ is_int(U_0)
| ~ is_int(U_1) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [B_1_1] :
( is_int(zfact(B_1_1))
| ~ is_int(B_1_1) ),
inference(fof_nnf,[status(thm)],[gsy_c_IntFact_Ozfact]) ).
fof(f_5_2,plain,
! [U_2] :
( is_int(zfact(U_2))
| ~ is_int(U_2) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( is_int(zfact(U_2))
| ~ is_int(U_2) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [B_1_1] :
( is_int(bit0(B_1_1))
| ~ is_int(B_1_1) ),
inference(fof_nnf,[status(thm)],[gsy_c_Int_OBit0]) ).
fof(f_6_2,plain,
! [U_3] :
( is_int(bit0(U_3))
| ~ is_int(U_3) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( is_int(bit0(U_3))
| ~ is_int(U_3) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [B_1_1] :
( is_int(bit1(B_1_1))
| ~ is_int(B_1_1) ),
inference(fof_nnf,[status(thm)],[gsy_c_Int_OBit1]) ).
fof(f_7_2,plain,
! [U_4] :
( is_int(bit1(U_4))
| ~ is_int(U_4) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( is_int(bit1(U_4))
| ~ is_int(U_4) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
is_int(min),
inference(fof_nnf,[status(thm)],[gsy_c_Int_OMin]) ).
cnf(f_8_2,plain,
is_int(min),
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
is_int(pls),
inference(fof_nnf,[status(thm)],[gsy_c_Int_OPls]) ).
cnf(f_9_2,plain,
is_int(pls),
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_1,plain,
! [B_1_1] :
( is_int(number_number_of_int(B_1_1))
| ~ is_int(B_1_1) ),
inference(fof_nnf,[status(thm)],[gsy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint]) ).
fof(f_10_2,plain,
! [U_5] :
( is_int(number_number_of_int(U_5))
| ~ is_int(U_5) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( is_int(number_number_of_int(U_5))
| ~ is_int(U_5) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [B_1_1,B_2_1] :
( is_int(legendre(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) ),
inference(fof_nnf,[status(thm)],[gsy_c_Residues_OLegendre]) ).
fof(f_11_2,plain,
! [U_7,U_6] :
( is_int(legendre(U_7,U_6))
| ~ is_int(U_6)
| ~ is_int(U_7) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( is_int(legendre(U_7,U_6))
| ~ is_int(U_6)
| ~ is_int(U_7) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [B_1_1,B_2_1] :
( is_int(standardRes(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) ),
inference(fof_nnf,[status(thm)],[gsy_c_Residues_OStandardRes]) ).
fof(f_12_2,plain,
! [U_9,U_8] :
( is_int(standardRes(U_9,U_8))
| ~ is_int(U_8)
| ~ is_int(U_9) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( is_int(standardRes(U_9,U_8))
| ~ is_int(U_8)
| ~ is_int(U_9) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [B_1_1] : is_int(twoSqu1241645765sum2sq(B_1_1)),
inference(fof_nnf,[status(thm)],[gsy_c_TwoSquares__Mirabelle__enbualjaop_Osum2sq]) ).
fof(f_13_2,plain,
! [U_10] : is_int(twoSqu1241645765sum2sq(U_10)),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
is_int(twoSqu1241645765sum2sq(U_10)),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [B_1_1,B_2_1] :
( is_int(inv(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) ),
inference(fof_nnf,[status(thm)],[gsy_c_WilsonRuss_Oinv]) ).
fof(f_14_2,plain,
! [U_12,U_11] :
( is_int(inv(U_12,U_11))
| ~ is_int(U_11)
| ~ is_int(U_12) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( is_int(inv(U_12,U_11))
| ~ is_int(U_11)
| ~ is_int(U_12) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [B_1_1,B_2_1] :
( is_bool(hAPP_bool_bool(B_1_1,B_2_1))
| ~ is_bool(B_2_1) ),
inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool]) ).
fof(f_15_2,plain,
! [U_14,U_13] :
( is_bool(hAPP_bool_bool(U_14,U_13))
| ~ is_bool(U_13) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( is_bool(hAPP_bool_bool(U_14,U_13))
| ~ is_bool(U_13) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [B_1_1,B_2_1] :
( is_bool(hAPP_int_bool(B_1_1,B_2_1))
| ~ is_int(B_2_1) ),
inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Int__Oint_000tc__HOL__Obool]) ).
fof(f_16_2,plain,
! [U_16,U_15] :
( is_bool(hAPP_int_bool(U_16,U_15))
| ~ is_int(U_15) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( is_bool(hAPP_int_bool(U_16,U_15))
| ~ is_int(U_15) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [B_1_1,B_2_1] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) ),
inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Int__Oint_000tc__Int__Oint]) ).
fof(f_17_2,plain,
! [U_18,U_17] :
( is_int(hAPP_int_int(U_18,U_17))
| ~ is_int(U_17) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( is_int(hAPP_int_int(U_18,U_17))
| ~ is_int(U_17) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [B_1_1,B_2_1] : is_bool(hAPP_nat_bool(B_1_1,B_2_1)),
inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool]) ).
fof(f_18_2,plain,
! [U_20,U_19] : is_bool(hAPP_nat_bool(U_20,U_19)),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
is_bool(hAPP_nat_bool(U_20,U_19)),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [B_1_1,B_2_1] : is_int(hAPP_nat_int(B_1_1,B_2_1)),
inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint]) ).
fof(f_19_2,plain,
! [U_22,U_21] : is_int(hAPP_nat_int(U_22,U_21)),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
is_int(hAPP_nat_int(U_22,U_21)),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [B_1_1,B_2_1] : is_bool(hAPP_real_bool(B_1_1,B_2_1)),
inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__RealDef__Oreal_000tc__HOL__Obool]) ).
fof(f_20_2,plain,
! [U_24,U_23] : is_bool(hAPP_real_bool(U_24,U_23)),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
is_bool(hAPP_real_bool(U_24,U_23)),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [B_1_1,B_2_1] :
( is_bool(member_int(B_1_1,B_2_1))
| ~ is_int(B_1_1) ),
inference(fof_nnf,[status(thm)],[gsy_c_member_000tc__Int__Oint]) ).
fof(f_21_2,plain,
! [U_26,U_25] :
( is_bool(member_int(U_26,U_25))
| ~ is_int(U_26) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_26] :
( ! [U_25] : is_bool(member_int(U_26,U_25))
| ~ is_int(U_26) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( is_bool(member_int(U_26,U_25))
| ~ is_int(U_26) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
is_int(m),
inference(fof_nnf,[status(thm)],[gsy_v_m]) ).
cnf(f_22_2,plain,
is_int(m),
inference(clausify,[status(thm)],[f_22_1]) ).
fof(f_23_1,plain,
is_int(s1),
inference(fof_nnf,[status(thm)],[gsy_v_s1____]) ).
cnf(f_23_2,plain,
is_int(s1),
inference(clausify,[status(thm)],[f_23_1]) ).
fof(f_24_1,plain,
is_int(s),
inference(fof_nnf,[status(thm)],[gsy_v_s____]) ).
cnf(f_24_2,plain,
is_int(s),
inference(clausify,[status(thm)],[f_24_1]) ).
fof(f_25_1,plain,
is_int(t),
inference(fof_nnf,[status(thm)],[gsy_v_t____]) ).
cnf(f_25_2,plain,
is_int(t),
inference(clausify,[status(thm)],[f_25_1]) ).
fof(f_26_1,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
inference(fof_nnf,[status(thm)],[fact_0_tpos]) ).
cnf(f_26_2,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
inference(clausify,[status(thm)],[f_26_1]) ).
fof(f_27_1,plain,
( ? [X,Y] :
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y),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(Y)
& is_int(X) )
| t != one_one_int ),
inference(fof_nnf,[status(thm)],[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(f_27_2,plain,
( ? [U_28,U_27] :
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(U_28),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_27),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(U_27)
& is_int(U_28) )
| t != one_one_int ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ? [U_28] :
( ? [U_27] :
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(U_28),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_27),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(U_27) )
& is_int(U_28) )
| t != one_one_int ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
( ( ? [U_27] :
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_27),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(U_27) )
& is_int(sK1) )
| t != one_one_int ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_28,sK1)],[f_27_3]) ).
fof(f_27_5,plain,
( ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK2),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(sK2)
& is_int(sK1) )
| t != one_one_int ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_27,sK2)],[f_27_4]) ).
cnf(f_27_6,plain,
( is_int(sK1)
| t != one_one_int ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_7,plain,
( is_int(sK2)
| t != one_one_int ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_8,plain,
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK2),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)
| t != one_one_int ),
inference(clausify,[status(thm)],[f_27_5]) ).
fof(f_28_1,plain,
( ? [X,Y] :
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y),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(Y)
& is_int(X) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(fof_nnf,[status(thm)],[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(f_28_2,plain,
( ? [U_30,U_29] :
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(U_30),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_29),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(U_29)
& is_int(U_30) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ? [U_30] :
( ? [U_29] :
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(U_30),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_29),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(U_29) )
& is_int(U_30) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
( ( ? [U_29] :
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK3),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_29),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(U_29) )
& is_int(sK3) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_30,sK3)],[f_28_3]) ).
fof(f_28_5,plain,
( ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK3),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK4),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(sK4)
& is_int(sK3) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_29,sK4)],[f_28_4]) ).
cnf(f_28_6,plain,
( is_int(sK3)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_7,plain,
( is_int(sK4)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_8,plain,
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK3),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK4),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)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(clausify,[status(thm)],[f_28_5]) ).
fof(f_29_1,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(fof_nnf,[status(thm)],[fact_3_t__l__p]) ).
cnf(f_29_2,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(clausify,[status(thm)],[f_29_1]) ).
fof(f_30_1,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(fof_nnf,[status(thm)],[fact_4_p]) ).
cnf(f_30_2,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(clausify,[status(thm)],[f_30_1]) ).
fof(f_31_1,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(fof_nnf,[status(thm)],[fact_5_t]) ).
cnf(f_31_2,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(clausify,[status(thm)],[f_31_1]) ).
fof(f_32_1,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(fof_nnf,[status(thm)],[fact_6_qf1pt]) ).
cnf(f_32_2,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(clausify,[status(thm)],[f_32_1]) ).
fof(f_33_1,plain,
! [A,B] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(A),B)),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(A),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)))),A)),B))),hAPP_nat_int(power_power_int(B),number_number_of_nat(bit0(bit1(pls))))),
inference(fof_nnf,[status(thm)],[fact_7_zadd__power2]) ).
fof(f_33_2,plain,
! [U_32,U_31] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(U_32),U_31)),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(U_32),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)))),U_32)),U_31))),hAPP_nat_int(power_power_int(U_31),number_number_of_nat(bit0(bit1(pls))))),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(U_32),U_31)),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(U_32),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)))),U_32)),U_31))),hAPP_nat_int(power_power_int(U_31),number_number_of_nat(bit0(bit1(pls))))),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [A,B] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(A),B)),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(A),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(A),number_number_of_nat(bit0(bit1(pls)))))),B))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit1(bit1(pls)))),A)),hAPP_nat_int(power_power_int(B),number_number_of_nat(bit0(bit1(pls))))))),hAPP_nat_int(power_power_int(B),number_number_of_nat(bit1(bit1(pls))))),
inference(fof_nnf,[status(thm)],[fact_8_zadd__power3]) ).
fof(f_34_2,plain,
! [U_34,U_33] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(U_34),U_33)),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(U_34),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(U_34),number_number_of_nat(bit0(bit1(pls)))))),U_33))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit1(bit1(pls)))),U_34)),hAPP_nat_int(power_power_int(U_33),number_number_of_nat(bit0(bit1(pls))))))),hAPP_nat_int(power_power_int(U_33),number_number_of_nat(bit1(bit1(pls))))),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(U_34),U_33)),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(U_34),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(U_34),number_number_of_nat(bit0(bit1(pls)))))),U_33))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit1(bit1(pls)))),U_34)),hAPP_nat_int(power_power_int(U_33),number_number_of_nat(bit0(bit1(pls))))))),hAPP_nat_int(power_power_int(U_33),number_number_of_nat(bit1(bit1(pls))))),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [X_2,Y_2] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(X_2),Y_2)),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(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_2),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)))),X_2)),Y_2)),
inference(fof_nnf,[status(thm)],[fact_9_power2__sum]) ).
fof(f_35_2,plain,
! [U_36,U_35] : hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(U_36),U_35)),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(U_36),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_35),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)))),U_36)),U_35)),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(U_36),U_35)),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(U_36),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_35),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)))),U_36)),U_35)),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [X_2,Y_2] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(plus_plus_nat(X_2),Y_2)),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(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(Y_2),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)))),X_2)),Y_2)),
inference(fof_nnf,[status(thm)],[fact_10_power2__sum]) ).
fof(f_36_2,plain,
! [U_38,U_37] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(plus_plus_nat(U_38),U_37)),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(U_38),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(U_37),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)))),U_38)),U_37)),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
hAPP_nat_nat(power_power_nat(hAPP_nat_nat(plus_plus_nat(U_38),U_37)),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(U_38),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(U_37),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)))),U_38)),U_37)),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [X_2,Y_2] : hAPP_nat_real(power_power_real(hAPP_real_real(plus_plus_real(X_2),Y_2)),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(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_2),number_number_of_nat(bit0(bit1(pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),X_2)),Y_2)),
inference(fof_nnf,[status(thm)],[fact_11_power2__sum]) ).
fof(f_37_2,plain,
! [U_40,U_39] : hAPP_nat_real(power_power_real(hAPP_real_real(plus_plus_real(U_40),U_39)),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(U_40),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_39),number_number_of_nat(bit0(bit1(pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),U_40)),U_39)),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
hAPP_nat_real(power_power_real(hAPP_real_real(plus_plus_real(U_40),U_39)),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(U_40),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_39),number_number_of_nat(bit0(bit1(pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),U_40)),U_39)),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [W_16] : hAPP_nat_int(power_power_int(number_number_of_int(W_16)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(times_times_int(number_number_of_int(W_16)),number_number_of_int(W_16)),
inference(fof_nnf,[status(thm)],[fact_12_power2__eq__square__number__of]) ).
fof(f_38_2,plain,
! [U_41] : hAPP_nat_int(power_power_int(number_number_of_int(U_41)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(times_times_int(number_number_of_int(U_41)),number_number_of_int(U_41)),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
hAPP_nat_int(power_power_int(number_number_of_int(U_41)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(times_times_int(number_number_of_int(U_41)),number_number_of_int(U_41)),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
! [W_16] : hAPP_nat_real(power_power_real(number267125858f_real(W_16)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_real_real(times_times_real(number267125858f_real(W_16)),number267125858f_real(W_16)),
inference(fof_nnf,[status(thm)],[fact_13_power2__eq__square__number__of]) ).
fof(f_39_2,plain,
! [U_42] : hAPP_nat_real(power_power_real(number267125858f_real(U_42)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_real_real(times_times_real(number267125858f_real(U_42)),number267125858f_real(U_42)),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
hAPP_nat_real(power_power_real(number267125858f_real(U_42)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_real_real(times_times_real(number267125858f_real(U_42)),number267125858f_real(U_42)),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
! [W_16] : hAPP_nat_nat(power_power_nat(number_number_of_nat(W_16)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(times_times_nat(number_number_of_nat(W_16)),number_number_of_nat(W_16)),
inference(fof_nnf,[status(thm)],[fact_14_power2__eq__square__number__of]) ).
fof(f_40_2,plain,
! [U_43] : hAPP_nat_nat(power_power_nat(number_number_of_nat(U_43)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(times_times_nat(number_number_of_nat(U_43)),number_number_of_nat(U_43)),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
hAPP_nat_nat(power_power_nat(number_number_of_nat(U_43)),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(times_times_nat(number_number_of_nat(U_43)),number_number_of_nat(U_43)),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [A] : hAPP_int_int(times_times_int(A),hAPP_nat_int(power_power_int(A),number_number_of_nat(bit0(bit1(pls))))) = hAPP_nat_int(power_power_int(A),number_number_of_nat(bit1(bit1(pls)))),
inference(fof_nnf,[status(thm)],[fact_15_cube__square]) ).
fof(f_41_2,plain,
! [U_44] : hAPP_int_int(times_times_int(U_44),hAPP_nat_int(power_power_int(U_44),number_number_of_nat(bit0(bit1(pls))))) = hAPP_nat_int(power_power_int(U_44),number_number_of_nat(bit1(bit1(pls)))),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
hAPP_int_int(times_times_int(U_44),hAPP_nat_int(power_power_int(U_44),number_number_of_nat(bit0(bit1(pls))))) = hAPP_nat_int(power_power_int(U_44),number_number_of_nat(bit1(bit1(pls)))),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
hAPP_nat_int(power_power_int(one_one_int),number_number_of_nat(bit0(bit1(pls)))) = one_one_int,
inference(fof_nnf,[status(thm)],[fact_16_one__power2]) ).
cnf(f_42_2,plain,
hAPP_nat_int(power_power_int(one_one_int),number_number_of_nat(bit0(bit1(pls)))) = one_one_int,
inference(clausify,[status(thm)],[f_42_1]) ).
fof(f_43_1,plain,
hAPP_nat_nat(power_power_nat(one_one_nat),number_number_of_nat(bit0(bit1(pls)))) = one_one_nat,
inference(fof_nnf,[status(thm)],[fact_17_one__power2]) ).
cnf(f_43_2,plain,
hAPP_nat_nat(power_power_nat(one_one_nat),number_number_of_nat(bit0(bit1(pls)))) = one_one_nat,
inference(clausify,[status(thm)],[f_43_1]) ).
fof(f_44_1,plain,
hAPP_nat_real(power_power_real(one_one_real),number_number_of_nat(bit0(bit1(pls)))) = one_one_real,
inference(fof_nnf,[status(thm)],[fact_18_one__power2]) ).
cnf(f_44_2,plain,
hAPP_nat_real(power_power_real(one_one_real),number_number_of_nat(bit0(bit1(pls)))) = one_one_real,
inference(clausify,[status(thm)],[f_44_1]) ).
fof(f_45_1,plain,
! [X_26] : hAPP_int_int(times_times_int(X_26),X_26) = hAPP_nat_int(power_power_int(X_26),number_number_of_nat(bit0(bit1(pls)))),
inference(fof_nnf,[status(thm)],[fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
fof(f_45_2,plain,
! [U_45] : hAPP_int_int(times_times_int(U_45),U_45) = hAPP_nat_int(power_power_int(U_45),number_number_of_nat(bit0(bit1(pls)))),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
hAPP_int_int(times_times_int(U_45),U_45) = hAPP_nat_int(power_power_int(U_45),number_number_of_nat(bit0(bit1(pls)))),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
! [X_26] : hAPP_real_real(times_times_real(X_26),X_26) = hAPP_nat_real(power_power_real(X_26),number_number_of_nat(bit0(bit1(pls)))),
inference(fof_nnf,[status(thm)],[fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
fof(f_46_2,plain,
! [U_46] : hAPP_real_real(times_times_real(U_46),U_46) = hAPP_nat_real(power_power_real(U_46),number_number_of_nat(bit0(bit1(pls)))),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
hAPP_real_real(times_times_real(U_46),U_46) = hAPP_nat_real(power_power_real(U_46),number_number_of_nat(bit0(bit1(pls)))),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
! [X_26] : hAPP_nat_nat(times_times_nat(X_26),X_26) = hAPP_nat_nat(power_power_nat(X_26),number_number_of_nat(bit0(bit1(pls)))),
inference(fof_nnf,[status(thm)],[fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
fof(f_47_2,plain,
! [U_47] : hAPP_nat_nat(times_times_nat(U_47),U_47) = hAPP_nat_nat(power_power_nat(U_47),number_number_of_nat(bit0(bit1(pls)))),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
hAPP_nat_nat(times_times_nat(U_47),U_47) = hAPP_nat_nat(power_power_nat(U_47),number_number_of_nat(bit0(bit1(pls)))),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_1,plain,
! [A_112] : hAPP_nat_int(power_power_int(A_112),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(times_times_int(A_112),A_112),
inference(fof_nnf,[status(thm)],[fact_22_power2__eq__square]) ).
fof(f_48_2,plain,
! [U_48] : hAPP_nat_int(power_power_int(U_48),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(times_times_int(U_48),U_48),
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
hAPP_nat_int(power_power_int(U_48),number_number_of_nat(bit0(bit1(pls)))) = hAPP_int_int(times_times_int(U_48),U_48),
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_1,plain,
! [A_112] : hAPP_nat_real(power_power_real(A_112),number_number_of_nat(bit0(bit1(pls)))) = hAPP_real_real(times_times_real(A_112),A_112),
inference(fof_nnf,[status(thm)],[fact_23_power2__eq__square]) ).
fof(f_49_2,plain,
! [U_49] : hAPP_nat_real(power_power_real(U_49),number_number_of_nat(bit0(bit1(pls)))) = hAPP_real_real(times_times_real(U_49),U_49),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
hAPP_nat_real(power_power_real(U_49),number_number_of_nat(bit0(bit1(pls)))) = hAPP_real_real(times_times_real(U_49),U_49),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_1,plain,
! [A_112] : hAPP_nat_nat(power_power_nat(A_112),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(times_times_nat(A_112),A_112),
inference(fof_nnf,[status(thm)],[fact_24_power2__eq__square]) ).
fof(f_50_2,plain,
! [U_50] : hAPP_nat_nat(power_power_nat(U_50),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(times_times_nat(U_50),U_50),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
hAPP_nat_nat(power_power_nat(U_50),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(times_times_nat(U_50),U_50),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,plain,
! [X_25,N_40] : hAPP_nat_int(power_power_int(X_25),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_40)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X_25),N_40)),hAPP_nat_int(power_power_int(X_25),N_40)),
inference(fof_nnf,[status(thm)],[fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J]) ).
fof(f_51_2,plain,
! [U_52,U_51] : hAPP_nat_int(power_power_int(U_52),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_51)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(U_52),U_51)),hAPP_nat_int(power_power_int(U_52),U_51)),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
hAPP_nat_int(power_power_int(U_52),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_51)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(U_52),U_51)),hAPP_nat_int(power_power_int(U_52),U_51)),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_1,plain,
! [X_25,N_40] : hAPP_nat_real(power_power_real(X_25),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_40)) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X_25),N_40)),hAPP_nat_real(power_power_real(X_25),N_40)),
inference(fof_nnf,[status(thm)],[fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J]) ).
fof(f_52_2,plain,
! [U_54,U_53] : hAPP_nat_real(power_power_real(U_54),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_53)) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(U_54),U_53)),hAPP_nat_real(power_power_real(U_54),U_53)),
inference(variable_rename,[status(thm)],[f_52_1]) ).
cnf(f_52_3,plain,
hAPP_nat_real(power_power_real(U_54),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_53)) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(U_54),U_53)),hAPP_nat_real(power_power_real(U_54),U_53)),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_1,plain,
! [X_25,N_40] : hAPP_nat_nat(power_power_nat(X_25),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_40)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X_25),N_40)),hAPP_nat_nat(power_power_nat(X_25),N_40)),
inference(fof_nnf,[status(thm)],[fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J]) ).
fof(f_53_2,plain,
! [U_56,U_55] : hAPP_nat_nat(power_power_nat(U_56),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_55)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(U_56),U_55)),hAPP_nat_nat(power_power_nat(U_56),U_55)),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
hAPP_nat_nat(power_power_nat(U_56),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_55)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(U_56),U_55)),hAPP_nat_nat(power_power_nat(U_56),U_55)),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
! [W_15] : hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(W_15)) = number_number_of_int(hAPP_int_int(plus_plus_int(bit1(pls)),W_15)),
inference(fof_nnf,[status(thm)],[fact_28_add__special_I2_J]) ).
fof(f_54_2,plain,
! [U_57] : hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(U_57)) = number_number_of_int(hAPP_int_int(plus_plus_int(bit1(pls)),U_57)),
inference(variable_rename,[status(thm)],[f_54_1]) ).
cnf(f_54_3,plain,
hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(U_57)) = number_number_of_int(hAPP_int_int(plus_plus_int(bit1(pls)),U_57)),
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_55_1,plain,
! [W_15] : hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(W_15)) = number267125858f_real(hAPP_int_int(plus_plus_int(bit1(pls)),W_15)),
inference(fof_nnf,[status(thm)],[fact_29_add__special_I2_J]) ).
fof(f_55_2,plain,
! [U_58] : hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(U_58)) = number267125858f_real(hAPP_int_int(plus_plus_int(bit1(pls)),U_58)),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(U_58)) = number267125858f_real(hAPP_int_int(plus_plus_int(bit1(pls)),U_58)),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_1,plain,
! [V_21] : hAPP_int_int(plus_plus_int(number_number_of_int(V_21)),one_one_int) = number_number_of_int(hAPP_int_int(plus_plus_int(V_21),bit1(pls))),
inference(fof_nnf,[status(thm)],[fact_30_add__special_I3_J]) ).
fof(f_56_2,plain,
! [U_59] : hAPP_int_int(plus_plus_int(number_number_of_int(U_59)),one_one_int) = number_number_of_int(hAPP_int_int(plus_plus_int(U_59),bit1(pls))),
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
hAPP_int_int(plus_plus_int(number_number_of_int(U_59)),one_one_int) = number_number_of_int(hAPP_int_int(plus_plus_int(U_59),bit1(pls))),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_1,plain,
! [V_21] : hAPP_real_real(plus_plus_real(number267125858f_real(V_21)),one_one_real) = number267125858f_real(hAPP_int_int(plus_plus_int(V_21),bit1(pls))),
inference(fof_nnf,[status(thm)],[fact_31_add__special_I3_J]) ).
fof(f_57_2,plain,
! [U_60] : hAPP_real_real(plus_plus_real(number267125858f_real(U_60)),one_one_real) = number267125858f_real(hAPP_int_int(plus_plus_int(U_60),bit1(pls))),
inference(variable_rename,[status(thm)],[f_57_1]) ).
cnf(f_57_3,plain,
hAPP_real_real(plus_plus_real(number267125858f_real(U_60)),one_one_real) = number267125858f_real(hAPP_int_int(plus_plus_int(U_60),bit1(pls))),
inference(clausify,[status(thm)],[f_57_2]) ).
fof(f_58_1,plain,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
inference(fof_nnf,[status(thm)],[fact_32_one__add__one__is__two]) ).
cnf(f_58_2,plain,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
inference(clausify,[status(thm)],[f_58_1]) ).
fof(f_59_1,plain,
hAPP_real_real(plus_plus_real(one_one_real),one_one_real) = number267125858f_real(bit0(bit1(pls))),
inference(fof_nnf,[status(thm)],[fact_33_one__add__one__is__two]) ).
cnf(f_59_2,plain,
hAPP_real_real(plus_plus_real(one_one_real),one_one_real) = number267125858f_real(bit0(bit1(pls))),
inference(clausify,[status(thm)],[f_59_1]) ).
fof(f_60_1,plain,
? [T_1] :
( 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_1)
& is_int(T_1) ),
inference(fof_nnf,[status(thm)],[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(f_60_2,plain,
? [U_61] :
( 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)),U_61)
& is_int(U_61) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,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)),sK5)
& is_int(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_61,sK5)],[f_60_2]) ).
cnf(f_60_4,plain,
is_int(sK5),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_5,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)),sK5),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
! [W] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),W)),
inference(fof_nnf,[status(thm)],[fact_35_zle__refl]) ).
fof(f_61_2,plain,
! [U_62] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_62),U_62)),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_62),U_62)),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_1,plain,
! [Z,W] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z),W)) ),
inference(fof_nnf,[status(thm)],[fact_36_zle__linear]) ).
fof(f_62_2,plain,
! [U_64,U_63] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_63),U_64))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_64),U_63)) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
cnf(f_62_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_63),U_64))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_64),U_63)) ),
inference(clausify,[status(thm)],[f_62_2]) ).
fof(f_63_1,plain,
! [Z_1,W_1] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),W_1))
| Z_1 = W_1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_1),W_1)) )
& ( ( Z_1 != W_1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_1),W_1)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),W_1)) ) )
| ~ is_int(W_1)
| ~ is_int(Z_1) ),
inference(fof_nnf,[status(thm)],[fact_37_zless__le]) ).
fof(f_63_2,plain,
! [U_66,U_65] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_66),U_65))
| U_66 = U_65
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_66),U_65)) )
& ( ( U_66 != U_65
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_66),U_65)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_66),U_65)) ) )
| ~ is_int(U_65)
| ~ is_int(U_66) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
cnf(f_63_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_66),U_65))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_66),U_65))
| ~ is_int(U_65)
| ~ is_int(U_66) ),
inference(clausify,[status(thm)],[f_63_2]) ).
cnf(f_63_4,plain,
( U_66 != U_65
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_66),U_65))
| ~ is_int(U_65)
| ~ is_int(U_66) ),
inference(clausify,[status(thm)],[f_63_2]) ).
cnf(f_63_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_66),U_65))
| U_66 = U_65
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_66),U_65))
| ~ is_int(U_65)
| ~ is_int(U_66) ),
inference(clausify,[status(thm)],[f_63_2]) ).
fof(f_64_1,plain,
! [X_1,Y_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),X_1))
| X_1 = Y_1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_1))
| ~ is_int(Y_1)
| ~ is_int(X_1) ),
inference(fof_nnf,[status(thm)],[fact_38_zless__linear]) ).
fof(f_64_2,plain,
! [U_68,U_67] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_67),U_68))
| U_68 = U_67
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_68),U_67))
| ~ is_int(U_67)
| ~ is_int(U_68) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
cnf(f_64_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_67),U_68))
| U_68 = U_67
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_68),U_67))
| ~ is_int(U_67)
| ~ is_int(U_68) ),
inference(clausify,[status(thm)],[f_64_2]) ).
fof(f_65_1,plain,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),K_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,J_1),K_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_39_zle__trans]) ).
fof(f_65_2,plain,
! [U_71,U_70,U_69] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_70),U_71))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_69),U_71))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_70),U_69)) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
cnf(f_65_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_70),U_71))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_69),U_71))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_70),U_69)) ),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_1,plain,
! [Z,W] :
( Z = W
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z),W))
| ~ is_int(W)
| ~ is_int(Z) ),
inference(fof_nnf,[status(thm)],[fact_40_zle__antisym]) ).
fof(f_66_2,plain,
! [U_73,U_72] :
( U_73 = U_72
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_72),U_73))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_73),U_72))
| ~ is_int(U_72)
| ~ is_int(U_73) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
cnf(f_66_3,plain,
( U_73 = U_72
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_72),U_73))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_73),U_72))
| ~ is_int(U_72)
| ~ is_int(U_73) ),
inference(clausify,[status(thm)],[f_66_2]) ).
fof(f_67_1,plain,
! [X_24,P_7,Q_7] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X_24),P_7)),Q_7) = hAPP_nat_int(power_power_int(X_24),hAPP_nat_nat(times_times_nat(P_7),Q_7)),
inference(fof_nnf,[status(thm)],[fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J]) ).
fof(f_67_2,plain,
! [U_76,U_75,U_74] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(U_76),U_75)),U_74) = hAPP_nat_int(power_power_int(U_76),hAPP_nat_nat(times_times_nat(U_75),U_74)),
inference(variable_rename,[status(thm)],[f_67_1]) ).
cnf(f_67_3,plain,
hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(U_76),U_75)),U_74) = hAPP_nat_int(power_power_int(U_76),hAPP_nat_nat(times_times_nat(U_75),U_74)),
inference(clausify,[status(thm)],[f_67_2]) ).
fof(f_68_1,plain,
! [X_24,P_7,Q_7] : hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(X_24),P_7)),Q_7) = hAPP_nat_real(power_power_real(X_24),hAPP_nat_nat(times_times_nat(P_7),Q_7)),
inference(fof_nnf,[status(thm)],[fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J]) ).
fof(f_68_2,plain,
! [U_79,U_78,U_77] : hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(U_79),U_78)),U_77) = hAPP_nat_real(power_power_real(U_79),hAPP_nat_nat(times_times_nat(U_78),U_77)),
inference(variable_rename,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(U_79),U_78)),U_77) = hAPP_nat_real(power_power_real(U_79),hAPP_nat_nat(times_times_nat(U_78),U_77)),
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_1,plain,
! [X_24,P_7,Q_7] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(X_24),P_7)),Q_7) = hAPP_nat_nat(power_power_nat(X_24),hAPP_nat_nat(times_times_nat(P_7),Q_7)),
inference(fof_nnf,[status(thm)],[fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J]) ).
fof(f_69_2,plain,
! [U_82,U_81,U_80] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(U_82),U_81)),U_80) = hAPP_nat_nat(power_power_nat(U_82),hAPP_nat_nat(times_times_nat(U_81),U_80)),
inference(variable_rename,[status(thm)],[f_69_1]) ).
cnf(f_69_3,plain,
hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(U_82),U_81)),U_80) = hAPP_nat_nat(power_power_nat(U_82),hAPP_nat_nat(times_times_nat(U_81),U_80)),
inference(clausify,[status(thm)],[f_69_2]) ).
fof(f_70_1,plain,
! [X_23] :
( hAPP_nat_int(power_power_int(X_23),one_one_nat) = X_23
| ~ is_int(X_23) ),
inference(fof_nnf,[status(thm)],[fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J]) ).
fof(f_70_2,plain,
! [U_83] :
( hAPP_nat_int(power_power_int(U_83),one_one_nat) = U_83
| ~ is_int(U_83) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
cnf(f_70_3,plain,
( hAPP_nat_int(power_power_int(U_83),one_one_nat) = U_83
| ~ is_int(U_83) ),
inference(clausify,[status(thm)],[f_70_2]) ).
fof(f_71_1,plain,
! [X_23] : hAPP_nat_real(power_power_real(X_23),one_one_nat) = X_23,
inference(fof_nnf,[status(thm)],[fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J]) ).
fof(f_71_2,plain,
! [U_84] : hAPP_nat_real(power_power_real(U_84),one_one_nat) = U_84,
inference(variable_rename,[status(thm)],[f_71_1]) ).
cnf(f_71_3,plain,
hAPP_nat_real(power_power_real(U_84),one_one_nat) = U_84,
inference(clausify,[status(thm)],[f_71_2]) ).
fof(f_72_1,plain,
! [X_23] : hAPP_nat_nat(power_power_nat(X_23),one_one_nat) = X_23,
inference(fof_nnf,[status(thm)],[fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J]) ).
fof(f_72_2,plain,
! [U_85] : hAPP_nat_nat(power_power_nat(U_85),one_one_nat) = U_85,
inference(variable_rename,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
hAPP_nat_nat(power_power_nat(U_85),one_one_nat) = U_85,
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_1,plain,
! [X_1,Y_1,Z] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X_1),Y_1)),Z) = hAPP_nat_int(power_power_int(X_1),hAPP_nat_nat(times_times_nat(Y_1),Z)),
inference(fof_nnf,[status(thm)],[fact_47_zpower__zpower]) ).
fof(f_73_2,plain,
! [U_88,U_87,U_86] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(U_88),U_87)),U_86) = hAPP_nat_int(power_power_int(U_88),hAPP_nat_nat(times_times_nat(U_87),U_86)),
inference(variable_rename,[status(thm)],[f_73_1]) ).
cnf(f_73_3,plain,
hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(U_88),U_87)),U_86) = hAPP_nat_int(power_power_int(U_88),hAPP_nat_nat(times_times_nat(U_87),U_86)),
inference(clausify,[status(thm)],[f_73_2]) ).
fof(f_74_1,plain,
! [V_7,W_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(V_7)),number_number_of_int(W_1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(W_1)),number_number_of_int(V_7))) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(W_1)),number_number_of_int(V_7)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(V_7)),number_number_of_int(W_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_48_le__number__of__eq__not__less]) ).
fof(f_74_2,plain,
! [U_90,U_89] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_90)),number_number_of_int(U_89)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_89)),number_number_of_int(U_90))) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_89)),number_number_of_int(U_90)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_90)),number_number_of_int(U_89))) ) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
( ! [U_94,U_92] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_94)),number_number_of_int(U_92)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_92)),number_number_of_int(U_94))) )
& ! [U_93,U_91] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_91)),number_number_of_int(U_93)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_93)),number_number_of_int(U_91))) ) ),
inference(miniscope,[status(thm)],[f_74_2]) ).
cnf(f_74_4,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_91)),number_number_of_int(U_93)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_93)),number_number_of_int(U_91))) ),
inference(clausify,[status(thm)],[f_74_3]) ).
cnf(f_74_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_94)),number_number_of_int(U_92)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_92)),number_number_of_int(U_94))) ),
inference(clausify,[status(thm)],[f_74_3]) ).
fof(f_75_1,plain,
! [V_7,W_1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(V_7)),number_number_of_nat(W_1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(W_1)),number_number_of_nat(V_7))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(W_1)),number_number_of_nat(V_7)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(V_7)),number_number_of_nat(W_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_49_le__number__of__eq__not__less]) ).
fof(f_75_2,plain,
! [U_96,U_95] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(U_96)),number_number_of_nat(U_95)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(U_95)),number_number_of_nat(U_96))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(U_95)),number_number_of_nat(U_96)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(U_96)),number_number_of_nat(U_95))) ) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
( ! [U_100,U_98] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(U_100)),number_number_of_nat(U_98)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(U_98)),number_number_of_nat(U_100))) )
& ! [U_99,U_97] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(U_97)),number_number_of_nat(U_99)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(U_99)),number_number_of_nat(U_97))) ) ),
inference(miniscope,[status(thm)],[f_75_2]) ).
cnf(f_75_4,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(U_97)),number_number_of_nat(U_99)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(U_99)),number_number_of_nat(U_97))) ),
inference(clausify,[status(thm)],[f_75_3]) ).
cnf(f_75_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(U_100)),number_number_of_nat(U_98)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(U_98)),number_number_of_nat(U_100))) ),
inference(clausify,[status(thm)],[f_75_3]) ).
fof(f_76_1,plain,
! [V_7,W_1] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(V_7)),number267125858f_real(W_1)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(W_1)),number267125858f_real(V_7))) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(W_1)),number267125858f_real(V_7)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(V_7)),number267125858f_real(W_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_50_le__number__of__eq__not__less]) ).
fof(f_76_2,plain,
! [U_102,U_101] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_102)),number267125858f_real(U_101)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_101)),number267125858f_real(U_102))) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_101)),number267125858f_real(U_102)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_102)),number267125858f_real(U_101))) ) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
( ! [U_106,U_104] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_106)),number267125858f_real(U_104)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_104)),number267125858f_real(U_106))) )
& ! [U_105,U_103] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_103)),number267125858f_real(U_105)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_105)),number267125858f_real(U_103))) ) ),
inference(miniscope,[status(thm)],[f_76_2]) ).
cnf(f_76_4,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_103)),number267125858f_real(U_105)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_105)),number267125858f_real(U_103))) ),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_5,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_106)),number267125858f_real(U_104)))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_104)),number267125858f_real(U_106))) ),
inference(clausify,[status(thm)],[f_76_3]) ).
fof(f_77_1,plain,
! [X_2,Y_2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X_2)),number_number_of_int(Y_2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),Y_2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),Y_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X_2)),number_number_of_int(Y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_51_less__number__of]) ).
fof(f_77_2,plain,
! [U_108,U_107] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_108)),number_number_of_int(U_107)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_108),U_107)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_108),U_107))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_108)),number_number_of_int(U_107))) ) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
( ! [U_112,U_110] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_112)),number_number_of_int(U_110)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_112),U_110)) )
& ! [U_111,U_109] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_111),U_109))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_111)),number_number_of_int(U_109))) ) ),
inference(miniscope,[status(thm)],[f_77_2]) ).
cnf(f_77_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_111),U_109))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_111)),number_number_of_int(U_109))) ),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_112)),number_number_of_int(U_110)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_112),U_110)) ),
inference(clausify,[status(thm)],[f_77_3]) ).
fof(f_78_1,plain,
! [X_2,Y_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X_2)),number267125858f_real(Y_2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),Y_2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),Y_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X_2)),number267125858f_real(Y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_52_less__number__of]) ).
fof(f_78_2,plain,
! [U_114,U_113] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_114)),number267125858f_real(U_113)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_114),U_113)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_114),U_113))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_114)),number267125858f_real(U_113))) ) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
( ! [U_118,U_116] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_118)),number267125858f_real(U_116)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_118),U_116)) )
& ! [U_117,U_115] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_117),U_115))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_117)),number267125858f_real(U_115))) ) ),
inference(miniscope,[status(thm)],[f_78_2]) ).
cnf(f_78_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_117),U_115))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_117)),number267125858f_real(U_115))) ),
inference(clausify,[status(thm)],[f_78_3]) ).
cnf(f_78_5,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_118)),number267125858f_real(U_116)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_118),U_116)) ),
inference(clausify,[status(thm)],[f_78_3]) ).
fof(f_79_1,plain,
! [X_2,Y_2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X_2)),number_number_of_int(Y_2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),Y_2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),Y_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X_2)),number_number_of_int(Y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_53_le__number__of]) ).
fof(f_79_2,plain,
! [U_120,U_119] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_120)),number_number_of_int(U_119)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_120),U_119)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_120),U_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_120)),number_number_of_int(U_119))) ) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
( ! [U_124,U_122] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_124)),number_number_of_int(U_122)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_124),U_122)) )
& ! [U_123,U_121] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_123),U_121))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_123)),number_number_of_int(U_121))) ) ),
inference(miniscope,[status(thm)],[f_79_2]) ).
cnf(f_79_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_123),U_121))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_123)),number_number_of_int(U_121))) ),
inference(clausify,[status(thm)],[f_79_3]) ).
cnf(f_79_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_124)),number_number_of_int(U_122)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_124),U_122)) ),
inference(clausify,[status(thm)],[f_79_3]) ).
fof(f_80_1,plain,
! [X_2,Y_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X_2)),number267125858f_real(Y_2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),Y_2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),Y_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X_2)),number267125858f_real(Y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_54_le__number__of]) ).
fof(f_80_2,plain,
! [U_126,U_125] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_126)),number267125858f_real(U_125)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_126),U_125)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_126),U_125))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_126)),number267125858f_real(U_125))) ) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
( ! [U_130,U_128] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_130)),number267125858f_real(U_128)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_130),U_128)) )
& ! [U_129,U_127] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_129),U_127))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_129)),number267125858f_real(U_127))) ) ),
inference(miniscope,[status(thm)],[f_80_2]) ).
cnf(f_80_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_129),U_127))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_129)),number267125858f_real(U_127))) ),
inference(clausify,[status(thm)],[f_80_3]) ).
cnf(f_80_5,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_130)),number267125858f_real(U_128)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_130),U_128)) ),
inference(clausify,[status(thm)],[f_80_3]) ).
fof(f_81_1,plain,
! [Z_10,Z,W_14,W] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(W_14),Z_10)),hAPP_int_int(plus_plus_int(W),Z)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_10),Z))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_14),W)) ),
inference(fof_nnf,[status(thm)],[fact_55_zadd__zless__mono]) ).
fof(f_81_2,plain,
! [U_134,U_133,U_132,U_131] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(U_132),U_134)),hAPP_int_int(plus_plus_int(U_131),U_133)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_134),U_133))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_132),U_131)) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
cnf(f_81_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(U_132),U_134)),hAPP_int_int(plus_plus_int(U_131),U_133)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_134),U_133))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_132),U_131)) ),
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_1,plain,
! [X_22,P_6,Q_6] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X_22),P_6)),hAPP_nat_int(power_power_int(X_22),Q_6)) = hAPP_nat_int(power_power_int(X_22),hAPP_nat_nat(plus_plus_nat(P_6),Q_6)),
inference(fof_nnf,[status(thm)],[fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J]) ).
fof(f_82_2,plain,
! [U_137,U_136,U_135] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(U_137),U_136)),hAPP_nat_int(power_power_int(U_137),U_135)) = hAPP_nat_int(power_power_int(U_137),hAPP_nat_nat(plus_plus_nat(U_136),U_135)),
inference(variable_rename,[status(thm)],[f_82_1]) ).
cnf(f_82_3,plain,
hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(U_137),U_136)),hAPP_nat_int(power_power_int(U_137),U_135)) = hAPP_nat_int(power_power_int(U_137),hAPP_nat_nat(plus_plus_nat(U_136),U_135)),
inference(clausify,[status(thm)],[f_82_2]) ).
fof(f_83_1,plain,
! [X_22,P_6,Q_6] : hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X_22),P_6)),hAPP_nat_real(power_power_real(X_22),Q_6)) = hAPP_nat_real(power_power_real(X_22),hAPP_nat_nat(plus_plus_nat(P_6),Q_6)),
inference(fof_nnf,[status(thm)],[fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J]) ).
fof(f_83_2,plain,
! [U_140,U_139,U_138] : hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(U_140),U_139)),hAPP_nat_real(power_power_real(U_140),U_138)) = hAPP_nat_real(power_power_real(U_140),hAPP_nat_nat(plus_plus_nat(U_139),U_138)),
inference(variable_rename,[status(thm)],[f_83_1]) ).
cnf(f_83_3,plain,
hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(U_140),U_139)),hAPP_nat_real(power_power_real(U_140),U_138)) = hAPP_nat_real(power_power_real(U_140),hAPP_nat_nat(plus_plus_nat(U_139),U_138)),
inference(clausify,[status(thm)],[f_83_2]) ).
fof(f_84_1,plain,
! [X_22,P_6,Q_6] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X_22),P_6)),hAPP_nat_nat(power_power_nat(X_22),Q_6)) = hAPP_nat_nat(power_power_nat(X_22),hAPP_nat_nat(plus_plus_nat(P_6),Q_6)),
inference(fof_nnf,[status(thm)],[fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J]) ).
fof(f_84_2,plain,
! [U_143,U_142,U_141] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(U_143),U_142)),hAPP_nat_nat(power_power_nat(U_143),U_141)) = hAPP_nat_nat(power_power_nat(U_143),hAPP_nat_nat(plus_plus_nat(U_142),U_141)),
inference(variable_rename,[status(thm)],[f_84_1]) ).
cnf(f_84_3,plain,
hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(U_143),U_142)),hAPP_nat_nat(power_power_nat(U_143),U_141)) = hAPP_nat_nat(power_power_nat(U_143),hAPP_nat_nat(plus_plus_nat(U_142),U_141)),
inference(clausify,[status(thm)],[f_84_2]) ).
fof(f_85_1,plain,
! [X_1,Y_1,Z] : hAPP_nat_int(power_power_int(X_1),hAPP_nat_nat(plus_plus_nat(Y_1),Z)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X_1),Y_1)),hAPP_nat_int(power_power_int(X_1),Z)),
inference(fof_nnf,[status(thm)],[fact_59_zpower__zadd__distrib]) ).
fof(f_85_2,plain,
! [U_146,U_145,U_144] : hAPP_nat_int(power_power_int(U_146),hAPP_nat_nat(plus_plus_nat(U_145),U_144)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(U_146),U_145)),hAPP_nat_int(power_power_int(U_146),U_144)),
inference(variable_rename,[status(thm)],[f_85_1]) ).
cnf(f_85_3,plain,
hAPP_nat_int(power_power_int(U_146),hAPP_nat_nat(plus_plus_nat(U_145),U_144)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(U_146),U_145)),hAPP_nat_int(power_power_int(U_146),U_144)),
inference(clausify,[status(thm)],[f_85_2]) ).
fof(f_86_1,plain,
! [Z] : hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),Z) = hAPP_nat_nat(plus_plus_nat(Z),Z),
inference(fof_nnf,[status(thm)],[fact_60_nat__mult__2]) ).
fof(f_86_2,plain,
! [U_147] : hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_147) = hAPP_nat_nat(plus_plus_nat(U_147),U_147),
inference(variable_rename,[status(thm)],[f_86_1]) ).
cnf(f_86_3,plain,
hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_147) = hAPP_nat_nat(plus_plus_nat(U_147),U_147),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_1,plain,
! [Z] : hAPP_nat_nat(times_times_nat(Z),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(plus_plus_nat(Z),Z),
inference(fof_nnf,[status(thm)],[fact_61_nat__mult__2__right]) ).
fof(f_87_2,plain,
! [U_148] : hAPP_nat_nat(times_times_nat(U_148),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(plus_plus_nat(U_148),U_148),
inference(variable_rename,[status(thm)],[f_87_1]) ).
cnf(f_87_3,plain,
hAPP_nat_nat(times_times_nat(U_148),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(plus_plus_nat(U_148),U_148),
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_1,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(fof_nnf,[status(thm)],[fact_62_nat__1__add__1]) ).
cnf(f_88_2,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(clausify,[status(thm)],[f_88_1]) ).
fof(f_89_1,plain,
! [K1,K2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K1)),bit1(K2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K1)),bit1(K2))) ) ),
inference(fof_nnf,[status(thm)],[fact_63_less__int__code_I16_J]) ).
fof(f_89_2,plain,
! [U_150,U_149] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_150)),bit1(U_149)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_150),U_149)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_150),U_149))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_150)),bit1(U_149))) ) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
fof(f_89_3,plain,
( ! [U_154,U_152] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_154)),bit1(U_152)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_154),U_152)) )
& ! [U_153,U_151] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_153),U_151))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_153)),bit1(U_151))) ) ),
inference(miniscope,[status(thm)],[f_89_2]) ).
cnf(f_89_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_153),U_151))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_153)),bit1(U_151))) ),
inference(clausify,[status(thm)],[f_89_3]) ).
cnf(f_89_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_154)),bit1(U_152)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_154),U_152)) ),
inference(clausify,[status(thm)],[f_89_3]) ).
fof(f_90_1,plain,
! [K,L_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),bit1(L_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L_1)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),bit1(L_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_64_rel__simps_I17_J]) ).
fof(f_90_2,plain,
! [U_156,U_155] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_156)),bit1(U_155)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_156),U_155)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_156),U_155))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_156)),bit1(U_155))) ) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
( ! [U_160,U_158] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_160)),bit1(U_158)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_160),U_158)) )
& ! [U_159,U_157] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_159),U_157))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_159)),bit1(U_157))) ) ),
inference(miniscope,[status(thm)],[f_90_2]) ).
cnf(f_90_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_159),U_157))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_159)),bit1(U_157))) ),
inference(clausify,[status(thm)],[f_90_3]) ).
cnf(f_90_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_160)),bit1(U_158)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_160),U_158)) ),
inference(clausify,[status(thm)],[f_90_3]) ).
fof(f_91_1,plain,
! [K1,K2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K1)),bit1(K2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K1)),bit1(K2))) ) ),
inference(fof_nnf,[status(thm)],[fact_65_less__eq__int__code_I16_J]) ).
fof(f_91_2,plain,
! [U_162,U_161] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_162)),bit1(U_161)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_162),U_161)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_162),U_161))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_162)),bit1(U_161))) ) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
( ! [U_166,U_164] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_166)),bit1(U_164)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_166),U_164)) )
& ! [U_165,U_163] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_165),U_163))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_165)),bit1(U_163))) ) ),
inference(miniscope,[status(thm)],[f_91_2]) ).
cnf(f_91_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_165),U_163))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_165)),bit1(U_163))) ),
inference(clausify,[status(thm)],[f_91_3]) ).
cnf(f_91_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_166)),bit1(U_164)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_166),U_164)) ),
inference(clausify,[status(thm)],[f_91_3]) ).
fof(f_92_1,plain,
! [K,L_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),bit1(L_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L_1)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),bit1(L_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_66_rel__simps_I34_J]) ).
fof(f_92_2,plain,
! [U_168,U_167] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_168)),bit1(U_167)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_168),U_167)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_168),U_167))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_168)),bit1(U_167))) ) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
( ! [U_172,U_170] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_172)),bit1(U_170)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_172),U_170)) )
& ! [U_171,U_169] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_171),U_169))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_171)),bit1(U_169))) ) ),
inference(miniscope,[status(thm)],[f_92_2]) ).
cnf(f_92_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_171),U_169))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_171)),bit1(U_169))) ),
inference(clausify,[status(thm)],[f_92_3]) ).
cnf(f_92_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_172)),bit1(U_170)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_172),U_170)) ),
inference(clausify,[status(thm)],[f_92_3]) ).
fof(f_93_1,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(fof_nnf,[status(thm)],[fact_67_rel__simps_I2_J]) ).
cnf(f_93_2,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(clausify,[status(thm)],[f_93_1]) ).
fof(f_94_1,plain,
! [K1,K2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(K1)),bit0(K2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(K1)),bit0(K2))) ) ),
inference(fof_nnf,[status(thm)],[fact_68_less__int__code_I13_J]) ).
fof(f_94_2,plain,
! [U_174,U_173] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_174)),bit0(U_173)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_174),U_173)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_174),U_173))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_174)),bit0(U_173))) ) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
( ! [U_178,U_176] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_178)),bit0(U_176)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_178),U_176)) )
& ! [U_177,U_175] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_177),U_175))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_177)),bit0(U_175))) ) ),
inference(miniscope,[status(thm)],[f_94_2]) ).
cnf(f_94_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_177),U_175))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_177)),bit0(U_175))) ),
inference(clausify,[status(thm)],[f_94_3]) ).
cnf(f_94_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_178)),bit0(U_176)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_178),U_176)) ),
inference(clausify,[status(thm)],[f_94_3]) ).
fof(f_95_1,plain,
! [K,L_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(K)),bit0(L_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L_1)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(K)),bit0(L_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_69_rel__simps_I14_J]) ).
fof(f_95_2,plain,
! [U_180,U_179] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_180)),bit0(U_179)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_180),U_179)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_180),U_179))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_180)),bit0(U_179))) ) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
( ! [U_184,U_182] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_184)),bit0(U_182)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_184),U_182)) )
& ! [U_183,U_181] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_183),U_181))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_183)),bit0(U_181))) ) ),
inference(miniscope,[status(thm)],[f_95_2]) ).
cnf(f_95_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_183),U_181))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_183)),bit0(U_181))) ),
inference(clausify,[status(thm)],[f_95_3]) ).
cnf(f_95_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_184)),bit0(U_182)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_184),U_182)) ),
inference(clausify,[status(thm)],[f_95_3]) ).
fof(f_96_1,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)),
inference(fof_nnf,[status(thm)],[fact_70_rel__simps_I19_J]) ).
cnf(f_96_2,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)),
inference(clausify,[status(thm)],[f_96_1]) ).
fof(f_97_1,plain,
! [K1,K2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(K1)),bit0(K2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(K1)),bit0(K2))) ) ),
inference(fof_nnf,[status(thm)],[fact_71_less__eq__int__code_I13_J]) ).
fof(f_97_2,plain,
! [U_186,U_185] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_186)),bit0(U_185)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_186),U_185)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_186),U_185))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_186)),bit0(U_185))) ) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
( ! [U_190,U_188] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_190)),bit0(U_188)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_190),U_188)) )
& ! [U_189,U_187] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_189),U_187))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_189)),bit0(U_187))) ) ),
inference(miniscope,[status(thm)],[f_97_2]) ).
cnf(f_97_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_189),U_187))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_189)),bit0(U_187))) ),
inference(clausify,[status(thm)],[f_97_3]) ).
cnf(f_97_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_190)),bit0(U_188)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_190),U_188)) ),
inference(clausify,[status(thm)],[f_97_3]) ).
fof(f_98_1,plain,
! [K,L_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(K)),bit0(L_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L_1)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(K)),bit0(L_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_72_rel__simps_I31_J]) ).
fof(f_98_2,plain,
! [U_192,U_191] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_192)),bit0(U_191)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_192),U_191)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_192),U_191))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_192)),bit0(U_191))) ) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
( ! [U_196,U_194] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_196)),bit0(U_194)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_196),U_194)) )
& ! [U_195,U_193] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_195),U_193))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_195)),bit0(U_193))) ) ),
inference(miniscope,[status(thm)],[f_98_2]) ).
cnf(f_98_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_195),U_193))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_195)),bit0(U_193))) ),
inference(clausify,[status(thm)],[f_98_3]) ).
cnf(f_98_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_196)),bit0(U_194)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_196),U_194)) ),
inference(clausify,[status(thm)],[f_98_3]) ).
fof(f_99_1,plain,
! [K,L_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(K)),number_number_of_int(L_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L_1)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(K)),number_number_of_int(L_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_73_less__number__of__int__code]) ).
fof(f_99_2,plain,
! [U_198,U_197] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_198)),number_number_of_int(U_197)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_198),U_197)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_198),U_197))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_198)),number_number_of_int(U_197))) ) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
( ! [U_202,U_200] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_202)),number_number_of_int(U_200)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_202),U_200)) )
& ! [U_201,U_199] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_201),U_199))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_201)),number_number_of_int(U_199))) ) ),
inference(miniscope,[status(thm)],[f_99_2]) ).
cnf(f_99_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_201),U_199))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_201)),number_number_of_int(U_199))) ),
inference(clausify,[status(thm)],[f_99_3]) ).
cnf(f_99_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_202)),number_number_of_int(U_200)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_202),U_200)) ),
inference(clausify,[status(thm)],[f_99_3]) ).
fof(f_100_1,plain,
! [K,L_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(K)),number_number_of_int(L_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L_1)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(K)),number_number_of_int(L_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_74_less__eq__number__of__int__code]) ).
fof(f_100_2,plain,
! [U_204,U_203] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_204)),number_number_of_int(U_203)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_204),U_203)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_204),U_203))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_204)),number_number_of_int(U_203))) ) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
( ! [U_208,U_206] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_208)),number_number_of_int(U_206)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_208),U_206)) )
& ! [U_207,U_205] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_207),U_205))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_207)),number_number_of_int(U_205))) ) ),
inference(miniscope,[status(thm)],[f_100_2]) ).
cnf(f_100_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_207),U_205))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_207)),number_number_of_int(U_205))) ),
inference(clausify,[status(thm)],[f_100_3]) ).
cnf(f_100_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_208)),number_number_of_int(U_206)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_208),U_206)) ),
inference(clausify,[status(thm)],[f_100_3]) ).
fof(f_101_1,plain,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(I_1),K_1)),hAPP_int_int(plus_plus_int(J_1),K_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_75_zadd__strict__right__mono]) ).
fof(f_101_2,plain,
! [U_211,U_210,U_209] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(U_210),U_211)),hAPP_int_int(plus_plus_int(U_209),U_211)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_210),U_209)) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
cnf(f_101_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(U_210),U_211)),hAPP_int_int(plus_plus_int(U_209),U_211)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_210),U_209)) ),
inference(clausify,[status(thm)],[f_101_2]) ).
fof(f_102_1,plain,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(K_1),I_1)),hAPP_int_int(plus_plus_int(K_1),J_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_76_zadd__left__mono]) ).
fof(f_102_2,plain,
! [U_214,U_213,U_212] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(U_214),U_213)),hAPP_int_int(plus_plus_int(U_214),U_212)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_213),U_212)) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
cnf(f_102_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(U_214),U_213)),hAPP_int_int(plus_plus_int(U_214),U_212)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_213),U_212)) ),
inference(clausify,[status(thm)],[f_102_2]) ).
fof(f_103_1,plain,
! [V_6,V] :
( ( ( ( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V)),number_number_of_nat(V_6)) = number_number_of_nat(hAPP_int_int(plus_plus_int(V),V_6))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_6),pls)) )
& ( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V)),number_number_of_nat(V_6)) = number_number_of_nat(V)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_6),pls)) ) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) )
& ( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V)),number_number_of_nat(V_6)) = number_number_of_nat(V_6)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) ) ),
inference(fof_nnf,[status(thm)],[fact_77_add__nat__number__of]) ).
fof(f_103_2,plain,
! [U_216,U_215] :
( ( ( ( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(U_215)),number_number_of_nat(U_216)) = number_number_of_nat(hAPP_int_int(plus_plus_int(U_215),U_216))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_216),pls)) )
& ( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(U_215)),number_number_of_nat(U_216)) = number_number_of_nat(U_215)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_216),pls)) ) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_215),pls)) )
& ( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(U_215)),number_number_of_nat(U_216)) = number_number_of_nat(U_216)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_215),pls)) ) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
( ! [U_220,U_218] :
( ( ( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(U_218)),number_number_of_nat(U_220)) = number_number_of_nat(hAPP_int_int(plus_plus_int(U_218),U_220))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_220),pls)) )
& ( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(U_218)),number_number_of_nat(U_220)) = number_number_of_nat(U_218)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_220),pls)) ) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_218),pls)) )
& ! [U_219,U_217] :
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(U_217)),number_number_of_nat(U_219)) = number_number_of_nat(U_219)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_217),pls)) ) ),
inference(miniscope,[status(thm)],[f_103_2]) ).
cnf(f_103_4,plain,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(U_217)),number_number_of_nat(U_219)) = number_number_of_nat(U_219)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_217),pls)) ),
inference(clausify,[status(thm)],[f_103_3]) ).
cnf(f_103_5,plain,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(U_218)),number_number_of_nat(U_220)) = number_number_of_nat(U_218)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_220),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_218),pls)) ),
inference(clausify,[status(thm)],[f_103_3]) ).
cnf(f_103_6,plain,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(U_218)),number_number_of_nat(U_220)) = number_number_of_nat(hAPP_int_int(plus_plus_int(U_218),U_220))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_220),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_218),pls)) ),
inference(clausify,[status(thm)],[f_103_3]) ).
fof(f_104_1,plain,
number_number_of_nat(bit1(pls)) = one_one_nat,
inference(fof_nnf,[status(thm)],[fact_78_nat__numeral__1__eq__1]) ).
cnf(f_104_2,plain,
number_number_of_nat(bit1(pls)) = one_one_nat,
inference(clausify,[status(thm)],[f_104_1]) ).
fof(f_105_1,plain,
one_one_nat = number_number_of_nat(bit1(pls)),
inference(fof_nnf,[status(thm)],[fact_79_Numeral1__eq1__nat]) ).
cnf(f_105_2,plain,
one_one_nat = number_number_of_nat(bit1(pls)),
inference(clausify,[status(thm)],[f_105_1]) ).
fof(f_106_1,plain,
! [K] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),pls)) ) ),
inference(fof_nnf,[status(thm)],[fact_80_rel__simps_I29_J]) ).
fof(f_106_2,plain,
! [U_221] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_221)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_221),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_221),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_221)),pls)) ) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
( ! [U_223] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_223)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_223),pls)) )
& ! [U_222] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_222),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_222)),pls)) ) ),
inference(miniscope,[status(thm)],[f_106_2]) ).
cnf(f_106_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_222),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_222)),pls)) ),
inference(clausify,[status(thm)],[f_106_3]) ).
cnf(f_106_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_223)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_223),pls)) ),
inference(clausify,[status(thm)],[f_106_3]) ).
fof(f_107_1,plain,
! [K] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(K)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(K))) ) ),
inference(fof_nnf,[status(thm)],[fact_81_rel__simps_I5_J]) ).
fof(f_107_2,plain,
! [U_224] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(U_224)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_224)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_224))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(U_224))) ) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
( ! [U_226] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(U_226)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_226)) )
& ! [U_225] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_225))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(U_225))) ) ),
inference(miniscope,[status(thm)],[f_107_2]) ).
cnf(f_107_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_225))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(U_225))) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(U_226)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_226)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
fof(f_108_1,plain,
! [K1,K2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K1)),bit0(K2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K1)),bit0(K2))) ) ),
inference(fof_nnf,[status(thm)],[fact_82_less__eq__int__code_I15_J]) ).
fof(f_108_2,plain,
! [U_228,U_227] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_228)),bit0(U_227)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_228),U_227)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_228),U_227))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_228)),bit0(U_227))) ) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
fof(f_108_3,plain,
( ! [U_232,U_230] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_232)),bit0(U_230)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_232),U_230)) )
& ! [U_231,U_229] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_231),U_229))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_231)),bit0(U_229))) ) ),
inference(miniscope,[status(thm)],[f_108_2]) ).
cnf(f_108_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_231),U_229))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_231)),bit0(U_229))) ),
inference(clausify,[status(thm)],[f_108_3]) ).
cnf(f_108_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_232)),bit0(U_230)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_232),U_230)) ),
inference(clausify,[status(thm)],[f_108_3]) ).
fof(f_109_1,plain,
! [K,L_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),bit0(L_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L_1)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),bit0(L_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_83_rel__simps_I33_J]) ).
fof(f_109_2,plain,
! [U_234,U_233] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_234)),bit0(U_233)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_234),U_233)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_234),U_233))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_234)),bit0(U_233))) ) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
( ! [U_238,U_236] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_238)),bit0(U_236)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_238),U_236)) )
& ! [U_237,U_235] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_237),U_235))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_237)),bit0(U_235))) ) ),
inference(miniscope,[status(thm)],[f_109_2]) ).
cnf(f_109_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_237),U_235))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_237)),bit0(U_235))) ),
inference(clausify,[status(thm)],[f_109_3]) ).
cnf(f_109_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_238)),bit0(U_236)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_238),U_236)) ),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_1,plain,
! [K1,K2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(K1)),bit1(K2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(K1)),bit1(K2))) ) ),
inference(fof_nnf,[status(thm)],[fact_84_less__int__code_I14_J]) ).
fof(f_110_2,plain,
! [U_240,U_239] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_240)),bit1(U_239)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_240),U_239)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_240),U_239))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_240)),bit1(U_239))) ) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
( ! [U_244,U_242] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_244)),bit1(U_242)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_244),U_242)) )
& ! [U_243,U_241] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_243),U_241))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_243)),bit1(U_241))) ) ),
inference(miniscope,[status(thm)],[f_110_2]) ).
cnf(f_110_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_243),U_241))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_243)),bit1(U_241))) ),
inference(clausify,[status(thm)],[f_110_3]) ).
cnf(f_110_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_244)),bit1(U_242)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_244),U_242)) ),
inference(clausify,[status(thm)],[f_110_3]) ).
fof(f_111_1,plain,
! [K,L_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(K)),bit1(L_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L_1)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(K)),bit1(L_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_85_rel__simps_I15_J]) ).
fof(f_111_2,plain,
! [U_246,U_245] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_246)),bit1(U_245)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_246),U_245)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_246),U_245))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_246)),bit1(U_245))) ) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
( ! [U_250,U_248] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_250)),bit1(U_248)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_250),U_248)) )
& ! [U_249,U_247] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_249),U_247))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_249)),bit1(U_247))) ) ),
inference(miniscope,[status(thm)],[f_111_2]) ).
cnf(f_111_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_249),U_247))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_249)),bit1(U_247))) ),
inference(clausify,[status(thm)],[f_111_3]) ).
cnf(f_111_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_250)),bit1(U_248)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_250),U_248)) ),
inference(clausify,[status(thm)],[f_111_3]) ).
fof(f_112_1,plain,
! [W,Z] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(W),one_one_int)),Z))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),Z)) ),
inference(fof_nnf,[status(thm)],[fact_86_zless__imp__add1__zle]) ).
fof(f_112_2,plain,
! [U_252,U_251] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(U_252),one_one_int)),U_251))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_252),U_251)) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
cnf(f_112_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(U_252),one_one_int)),U_251))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_252),U_251)) ),
inference(clausify,[status(thm)],[f_112_2]) ).
fof(f_113_1,plain,
! [W_1,Z_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(W_1),one_one_int)),Z_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_1)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(W_1),one_one_int)),Z_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_87_add1__zle__eq]) ).
fof(f_113_2,plain,
! [U_254,U_253] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(U_254),one_one_int)),U_253))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_254),U_253)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_254),U_253))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(U_254),one_one_int)),U_253)) ) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
( ! [U_258,U_256] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(U_258),one_one_int)),U_256))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_258),U_256)) )
& ! [U_257,U_255] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_257),U_255))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(U_257),one_one_int)),U_255)) ) ),
inference(miniscope,[status(thm)],[f_113_2]) ).
cnf(f_113_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_257),U_255))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(U_257),one_one_int)),U_255)) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(U_258),one_one_int)),U_256))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_258),U_256)) ),
inference(clausify,[status(thm)],[f_113_3]) ).
fof(f_114_1,plain,
! [W_1,Z_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),hAPP_int_int(plus_plus_int(Z_1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z_1)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),hAPP_int_int(plus_plus_int(Z_1),one_one_int))) ) ),
inference(fof_nnf,[status(thm)],[fact_88_zle__add1__eq__le]) ).
fof(f_114_2,plain,
! [U_260,U_259] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_260),hAPP_int_int(plus_plus_int(U_259),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_260),U_259)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_260),U_259))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_260),hAPP_int_int(plus_plus_int(U_259),one_one_int))) ) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
( ! [U_264,U_262] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_264),hAPP_int_int(plus_plus_int(U_262),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_264),U_262)) )
& ! [U_263,U_261] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_263),U_261))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_263),hAPP_int_int(plus_plus_int(U_261),one_one_int))) ) ),
inference(miniscope,[status(thm)],[f_114_2]) ).
cnf(f_114_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_263),U_261))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_263),hAPP_int_int(plus_plus_int(U_261),one_one_int))) ),
inference(clausify,[status(thm)],[f_114_3]) ).
cnf(f_114_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_264),hAPP_int_int(plus_plus_int(U_262),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_264),U_262)) ),
inference(clausify,[status(thm)],[f_114_3]) ).
fof(f_115_1,plain,
hBOOL(hAPP_int_bool(zprime,number_number_of_int(bit0(bit1(pls))))),
inference(fof_nnf,[status(thm)],[fact_89_zprime__2]) ).
cnf(f_115_2,plain,
hBOOL(hAPP_int_bool(zprime,number_number_of_int(bit0(bit1(pls))))),
inference(clausify,[status(thm)],[f_115_1]) ).
fof(f_116_1,plain,
! [Y_1,X_1] :
( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(X_1),Y_1)))
| ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,Y_1))
| ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X_1)) ),
inference(fof_nnf,[status(thm)],[fact_90_is__mult__sum2sq]) ).
fof(f_116_2,plain,
! [U_266,U_265] :
( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(U_265),U_266)))
| ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,U_266))
| ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,U_265)) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
cnf(f_116_3,plain,
( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,hAPP_int_int(times_times_int(U_265),U_266)))
| ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,U_266))
| ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,U_265)) ),
inference(clausify,[status(thm)],[f_116_2]) ).
fof(f_117_1,plain,
! [Lx_6,Ly_4,Rx_6,Ry_4] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_6),Ly_4)),hAPP_int_int(times_times_int(Rx_6),Ry_4)) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_6),Rx_6)),hAPP_int_int(times_times_int(Ly_4),Ry_4)),
inference(fof_nnf,[status(thm)],[fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J]) ).
fof(f_117_2,plain,
! [U_270,U_269,U_268,U_267] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_270),U_269)),hAPP_int_int(times_times_int(U_268),U_267)) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_270),U_268)),hAPP_int_int(times_times_int(U_269),U_267)),
inference(variable_rename,[status(thm)],[f_117_1]) ).
cnf(f_117_3,plain,
hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_270),U_269)),hAPP_int_int(times_times_int(U_268),U_267)) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_270),U_268)),hAPP_int_int(times_times_int(U_269),U_267)),
inference(clausify,[status(thm)],[f_117_2]) ).
fof(f_118_1,plain,
! [Lx_6,Ly_4,Rx_6,Ry_4] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_6),Ly_4)),hAPP_nat_nat(times_times_nat(Rx_6),Ry_4)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_6),Rx_6)),hAPP_nat_nat(times_times_nat(Ly_4),Ry_4)),
inference(fof_nnf,[status(thm)],[fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J]) ).
fof(f_118_2,plain,
! [U_274,U_273,U_272,U_271] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_274),U_273)),hAPP_nat_nat(times_times_nat(U_272),U_271)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_274),U_272)),hAPP_nat_nat(times_times_nat(U_273),U_271)),
inference(variable_rename,[status(thm)],[f_118_1]) ).
cnf(f_118_3,plain,
hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_274),U_273)),hAPP_nat_nat(times_times_nat(U_272),U_271)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_274),U_272)),hAPP_nat_nat(times_times_nat(U_273),U_271)),
inference(clausify,[status(thm)],[f_118_2]) ).
fof(f_119_1,plain,
! [Lx_6,Ly_4,Rx_6,Ry_4] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_6),Ly_4)),hAPP_real_real(times_times_real(Rx_6),Ry_4)) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_6),Rx_6)),hAPP_real_real(times_times_real(Ly_4),Ry_4)),
inference(fof_nnf,[status(thm)],[fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J]) ).
fof(f_119_2,plain,
! [U_278,U_277,U_276,U_275] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_278),U_277)),hAPP_real_real(times_times_real(U_276),U_275)) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_278),U_276)),hAPP_real_real(times_times_real(U_277),U_275)),
inference(variable_rename,[status(thm)],[f_119_1]) ).
cnf(f_119_3,plain,
hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_278),U_277)),hAPP_real_real(times_times_real(U_276),U_275)) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_278),U_276)),hAPP_real_real(times_times_real(U_277),U_275)),
inference(clausify,[status(thm)],[f_119_2]) ).
fof(f_120_1,plain,
! [Lx_5,Ly_3,Rx_5,Ry_3] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_5),Ly_3)),hAPP_int_int(times_times_int(Rx_5),Ry_3)) = hAPP_int_int(times_times_int(Rx_5),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_5),Ly_3)),Ry_3)),
inference(fof_nnf,[status(thm)],[fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J]) ).
fof(f_120_2,plain,
! [U_282,U_281,U_280,U_279] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_282),U_281)),hAPP_int_int(times_times_int(U_280),U_279)) = hAPP_int_int(times_times_int(U_280),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_282),U_281)),U_279)),
inference(variable_rename,[status(thm)],[f_120_1]) ).
cnf(f_120_3,plain,
hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_282),U_281)),hAPP_int_int(times_times_int(U_280),U_279)) = hAPP_int_int(times_times_int(U_280),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_282),U_281)),U_279)),
inference(clausify,[status(thm)],[f_120_2]) ).
fof(f_121_1,plain,
! [Lx_5,Ly_3,Rx_5,Ry_3] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_5),Ly_3)),hAPP_nat_nat(times_times_nat(Rx_5),Ry_3)) = hAPP_nat_nat(times_times_nat(Rx_5),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_5),Ly_3)),Ry_3)),
inference(fof_nnf,[status(thm)],[fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J]) ).
fof(f_121_2,plain,
! [U_286,U_285,U_284,U_283] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_286),U_285)),hAPP_nat_nat(times_times_nat(U_284),U_283)) = hAPP_nat_nat(times_times_nat(U_284),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_286),U_285)),U_283)),
inference(variable_rename,[status(thm)],[f_121_1]) ).
cnf(f_121_3,plain,
hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_286),U_285)),hAPP_nat_nat(times_times_nat(U_284),U_283)) = hAPP_nat_nat(times_times_nat(U_284),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_286),U_285)),U_283)),
inference(clausify,[status(thm)],[f_121_2]) ).
fof(f_122_1,plain,
! [Lx_5,Ly_3,Rx_5,Ry_3] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_5),Ly_3)),hAPP_real_real(times_times_real(Rx_5),Ry_3)) = hAPP_real_real(times_times_real(Rx_5),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_5),Ly_3)),Ry_3)),
inference(fof_nnf,[status(thm)],[fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J]) ).
fof(f_122_2,plain,
! [U_290,U_289,U_288,U_287] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_290),U_289)),hAPP_real_real(times_times_real(U_288),U_287)) = hAPP_real_real(times_times_real(U_288),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_290),U_289)),U_287)),
inference(variable_rename,[status(thm)],[f_122_1]) ).
cnf(f_122_3,plain,
hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_290),U_289)),hAPP_real_real(times_times_real(U_288),U_287)) = hAPP_real_real(times_times_real(U_288),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_290),U_289)),U_287)),
inference(clausify,[status(thm)],[f_122_2]) ).
fof(f_123_1,plain,
! [Lx_4,Ly_2,Rx_4,Ry_2] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_4),Ly_2)),hAPP_int_int(times_times_int(Rx_4),Ry_2)) = hAPP_int_int(times_times_int(Lx_4),hAPP_int_int(times_times_int(Ly_2),hAPP_int_int(times_times_int(Rx_4),Ry_2))),
inference(fof_nnf,[status(thm)],[fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J]) ).
fof(f_123_2,plain,
! [U_294,U_293,U_292,U_291] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_294),U_293)),hAPP_int_int(times_times_int(U_292),U_291)) = hAPP_int_int(times_times_int(U_294),hAPP_int_int(times_times_int(U_293),hAPP_int_int(times_times_int(U_292),U_291))),
inference(variable_rename,[status(thm)],[f_123_1]) ).
cnf(f_123_3,plain,
hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_294),U_293)),hAPP_int_int(times_times_int(U_292),U_291)) = hAPP_int_int(times_times_int(U_294),hAPP_int_int(times_times_int(U_293),hAPP_int_int(times_times_int(U_292),U_291))),
inference(clausify,[status(thm)],[f_123_2]) ).
fof(f_124_1,plain,
! [Lx_4,Ly_2,Rx_4,Ry_2] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_4),Ly_2)),hAPP_nat_nat(times_times_nat(Rx_4),Ry_2)) = hAPP_nat_nat(times_times_nat(Lx_4),hAPP_nat_nat(times_times_nat(Ly_2),hAPP_nat_nat(times_times_nat(Rx_4),Ry_2))),
inference(fof_nnf,[status(thm)],[fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J]) ).
fof(f_124_2,plain,
! [U_298,U_297,U_296,U_295] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_298),U_297)),hAPP_nat_nat(times_times_nat(U_296),U_295)) = hAPP_nat_nat(times_times_nat(U_298),hAPP_nat_nat(times_times_nat(U_297),hAPP_nat_nat(times_times_nat(U_296),U_295))),
inference(variable_rename,[status(thm)],[f_124_1]) ).
cnf(f_124_3,plain,
hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_298),U_297)),hAPP_nat_nat(times_times_nat(U_296),U_295)) = hAPP_nat_nat(times_times_nat(U_298),hAPP_nat_nat(times_times_nat(U_297),hAPP_nat_nat(times_times_nat(U_296),U_295))),
inference(clausify,[status(thm)],[f_124_2]) ).
fof(f_125_1,plain,
! [Lx_4,Ly_2,Rx_4,Ry_2] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_4),Ly_2)),hAPP_real_real(times_times_real(Rx_4),Ry_2)) = hAPP_real_real(times_times_real(Lx_4),hAPP_real_real(times_times_real(Ly_2),hAPP_real_real(times_times_real(Rx_4),Ry_2))),
inference(fof_nnf,[status(thm)],[fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J]) ).
fof(f_125_2,plain,
! [U_302,U_301,U_300,U_299] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_302),U_301)),hAPP_real_real(times_times_real(U_300),U_299)) = hAPP_real_real(times_times_real(U_302),hAPP_real_real(times_times_real(U_301),hAPP_real_real(times_times_real(U_300),U_299))),
inference(variable_rename,[status(thm)],[f_125_1]) ).
cnf(f_125_3,plain,
hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_302),U_301)),hAPP_real_real(times_times_real(U_300),U_299)) = hAPP_real_real(times_times_real(U_302),hAPP_real_real(times_times_real(U_301),hAPP_real_real(times_times_real(U_300),U_299))),
inference(clausify,[status(thm)],[f_125_2]) ).
fof(f_126_1,plain,
! [Lx_3,Ly_1,Rx_3] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_3),Ly_1)),Rx_3) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_3),Rx_3)),Ly_1),
inference(fof_nnf,[status(thm)],[fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J]) ).
fof(f_126_2,plain,
! [U_305,U_304,U_303] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_305),U_304)),U_303) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_305),U_303)),U_304),
inference(variable_rename,[status(thm)],[f_126_1]) ).
cnf(f_126_3,plain,
hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_305),U_304)),U_303) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_305),U_303)),U_304),
inference(clausify,[status(thm)],[f_126_2]) ).
fof(f_127_1,plain,
! [Lx_3,Ly_1,Rx_3] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_3),Ly_1)),Rx_3) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_3),Rx_3)),Ly_1),
inference(fof_nnf,[status(thm)],[fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J]) ).
fof(f_127_2,plain,
! [U_308,U_307,U_306] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_308),U_307)),U_306) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_308),U_306)),U_307),
inference(variable_rename,[status(thm)],[f_127_1]) ).
cnf(f_127_3,plain,
hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_308),U_307)),U_306) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_308),U_306)),U_307),
inference(clausify,[status(thm)],[f_127_2]) ).
fof(f_128_1,plain,
! [Lx_3,Ly_1,Rx_3] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_3),Ly_1)),Rx_3) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_3),Rx_3)),Ly_1),
inference(fof_nnf,[status(thm)],[fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J]) ).
fof(f_128_2,plain,
! [U_311,U_310,U_309] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_311),U_310)),U_309) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_311),U_309)),U_310),
inference(variable_rename,[status(thm)],[f_128_1]) ).
cnf(f_128_3,plain,
hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_311),U_310)),U_309) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_311),U_309)),U_310),
inference(clausify,[status(thm)],[f_128_2]) ).
fof(f_129_1,plain,
! [Lx_2,Ly,Rx_2] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_2),Ly)),Rx_2) = hAPP_int_int(times_times_int(Lx_2),hAPP_int_int(times_times_int(Ly),Rx_2)),
inference(fof_nnf,[status(thm)],[fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J]) ).
fof(f_129_2,plain,
! [U_314,U_313,U_312] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_314),U_313)),U_312) = hAPP_int_int(times_times_int(U_314),hAPP_int_int(times_times_int(U_313),U_312)),
inference(variable_rename,[status(thm)],[f_129_1]) ).
cnf(f_129_3,plain,
hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_314),U_313)),U_312) = hAPP_int_int(times_times_int(U_314),hAPP_int_int(times_times_int(U_313),U_312)),
inference(clausify,[status(thm)],[f_129_2]) ).
fof(f_130_1,plain,
! [Lx_2,Ly,Rx_2] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_2),Ly)),Rx_2) = hAPP_nat_nat(times_times_nat(Lx_2),hAPP_nat_nat(times_times_nat(Ly),Rx_2)),
inference(fof_nnf,[status(thm)],[fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J]) ).
fof(f_130_2,plain,
! [U_317,U_316,U_315] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_317),U_316)),U_315) = hAPP_nat_nat(times_times_nat(U_317),hAPP_nat_nat(times_times_nat(U_316),U_315)),
inference(variable_rename,[status(thm)],[f_130_1]) ).
cnf(f_130_3,plain,
hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_317),U_316)),U_315) = hAPP_nat_nat(times_times_nat(U_317),hAPP_nat_nat(times_times_nat(U_316),U_315)),
inference(clausify,[status(thm)],[f_130_2]) ).
fof(f_131_1,plain,
! [Lx_2,Ly,Rx_2] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_2),Ly)),Rx_2) = hAPP_real_real(times_times_real(Lx_2),hAPP_real_real(times_times_real(Ly),Rx_2)),
inference(fof_nnf,[status(thm)],[fact_105_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J]) ).
fof(f_131_2,plain,
! [U_320,U_319,U_318] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_320),U_319)),U_318) = hAPP_real_real(times_times_real(U_320),hAPP_real_real(times_times_real(U_319),U_318)),
inference(variable_rename,[status(thm)],[f_131_1]) ).
cnf(f_131_3,plain,
hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_320),U_319)),U_318) = hAPP_real_real(times_times_real(U_320),hAPP_real_real(times_times_real(U_319),U_318)),
inference(clausify,[status(thm)],[f_131_2]) ).
fof(f_132_1,plain,
! [Lx_1,Rx_1,Ry_1] : hAPP_int_int(times_times_int(Lx_1),hAPP_int_int(times_times_int(Rx_1),Ry_1)) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Lx_1),Rx_1)),Ry_1),
inference(fof_nnf,[status(thm)],[fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J]) ).
fof(f_132_2,plain,
! [U_323,U_322,U_321] : hAPP_int_int(times_times_int(U_323),hAPP_int_int(times_times_int(U_322),U_321)) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_323),U_322)),U_321),
inference(variable_rename,[status(thm)],[f_132_1]) ).
cnf(f_132_3,plain,
hAPP_int_int(times_times_int(U_323),hAPP_int_int(times_times_int(U_322),U_321)) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_323),U_322)),U_321),
inference(clausify,[status(thm)],[f_132_2]) ).
fof(f_133_1,plain,
! [Lx_1,Rx_1,Ry_1] : hAPP_nat_nat(times_times_nat(Lx_1),hAPP_nat_nat(times_times_nat(Rx_1),Ry_1)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(Lx_1),Rx_1)),Ry_1),
inference(fof_nnf,[status(thm)],[fact_107_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J]) ).
fof(f_133_2,plain,
! [U_326,U_325,U_324] : hAPP_nat_nat(times_times_nat(U_326),hAPP_nat_nat(times_times_nat(U_325),U_324)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_326),U_325)),U_324),
inference(variable_rename,[status(thm)],[f_133_1]) ).
cnf(f_133_3,plain,
hAPP_nat_nat(times_times_nat(U_326),hAPP_nat_nat(times_times_nat(U_325),U_324)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_326),U_325)),U_324),
inference(clausify,[status(thm)],[f_133_2]) ).
fof(f_134_1,plain,
! [Lx_1,Rx_1,Ry_1] : hAPP_real_real(times_times_real(Lx_1),hAPP_real_real(times_times_real(Rx_1),Ry_1)) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Lx_1),Rx_1)),Ry_1),
inference(fof_nnf,[status(thm)],[fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J]) ).
fof(f_134_2,plain,
! [U_329,U_328,U_327] : hAPP_real_real(times_times_real(U_329),hAPP_real_real(times_times_real(U_328),U_327)) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_329),U_328)),U_327),
inference(variable_rename,[status(thm)],[f_134_1]) ).
cnf(f_134_3,plain,
hAPP_real_real(times_times_real(U_329),hAPP_real_real(times_times_real(U_328),U_327)) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_329),U_328)),U_327),
inference(clausify,[status(thm)],[f_134_2]) ).
fof(f_135_1,plain,
! [Lx,Rx,Ry] : hAPP_int_int(times_times_int(Lx),hAPP_int_int(times_times_int(Rx),Ry)) = hAPP_int_int(times_times_int(Rx),hAPP_int_int(times_times_int(Lx),Ry)),
inference(fof_nnf,[status(thm)],[fact_109_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J]) ).
fof(f_135_2,plain,
! [U_332,U_331,U_330] : hAPP_int_int(times_times_int(U_332),hAPP_int_int(times_times_int(U_331),U_330)) = hAPP_int_int(times_times_int(U_331),hAPP_int_int(times_times_int(U_332),U_330)),
inference(variable_rename,[status(thm)],[f_135_1]) ).
cnf(f_135_3,plain,
hAPP_int_int(times_times_int(U_332),hAPP_int_int(times_times_int(U_331),U_330)) = hAPP_int_int(times_times_int(U_331),hAPP_int_int(times_times_int(U_332),U_330)),
inference(clausify,[status(thm)],[f_135_2]) ).
fof(f_136_1,plain,
! [Lx,Rx,Ry] : hAPP_nat_nat(times_times_nat(Lx),hAPP_nat_nat(times_times_nat(Rx),Ry)) = hAPP_nat_nat(times_times_nat(Rx),hAPP_nat_nat(times_times_nat(Lx),Ry)),
inference(fof_nnf,[status(thm)],[fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J]) ).
fof(f_136_2,plain,
! [U_335,U_334,U_333] : hAPP_nat_nat(times_times_nat(U_335),hAPP_nat_nat(times_times_nat(U_334),U_333)) = hAPP_nat_nat(times_times_nat(U_334),hAPP_nat_nat(times_times_nat(U_335),U_333)),
inference(variable_rename,[status(thm)],[f_136_1]) ).
cnf(f_136_3,plain,
hAPP_nat_nat(times_times_nat(U_335),hAPP_nat_nat(times_times_nat(U_334),U_333)) = hAPP_nat_nat(times_times_nat(U_334),hAPP_nat_nat(times_times_nat(U_335),U_333)),
inference(clausify,[status(thm)],[f_136_2]) ).
fof(f_137_1,plain,
! [Lx,Rx,Ry] : hAPP_real_real(times_times_real(Lx),hAPP_real_real(times_times_real(Rx),Ry)) = hAPP_real_real(times_times_real(Rx),hAPP_real_real(times_times_real(Lx),Ry)),
inference(fof_nnf,[status(thm)],[fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J]) ).
fof(f_137_2,plain,
! [U_338,U_337,U_336] : hAPP_real_real(times_times_real(U_338),hAPP_real_real(times_times_real(U_337),U_336)) = hAPP_real_real(times_times_real(U_337),hAPP_real_real(times_times_real(U_338),U_336)),
inference(variable_rename,[status(thm)],[f_137_1]) ).
cnf(f_137_3,plain,
hAPP_real_real(times_times_real(U_338),hAPP_real_real(times_times_real(U_337),U_336)) = hAPP_real_real(times_times_real(U_337),hAPP_real_real(times_times_real(U_338),U_336)),
inference(clausify,[status(thm)],[f_137_2]) ).
fof(f_138_1,plain,
! [A_111,B_63] : hAPP_int_int(times_times_int(A_111),B_63) = hAPP_int_int(times_times_int(B_63),A_111),
inference(fof_nnf,[status(thm)],[fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).
fof(f_138_2,plain,
! [U_340,U_339] : hAPP_int_int(times_times_int(U_340),U_339) = hAPP_int_int(times_times_int(U_339),U_340),
inference(variable_rename,[status(thm)],[f_138_1]) ).
cnf(f_138_3,plain,
hAPP_int_int(times_times_int(U_340),U_339) = hAPP_int_int(times_times_int(U_339),U_340),
inference(clausify,[status(thm)],[f_138_2]) ).
fof(f_139_1,plain,
! [A_111,B_63] : hAPP_nat_nat(times_times_nat(A_111),B_63) = hAPP_nat_nat(times_times_nat(B_63),A_111),
inference(fof_nnf,[status(thm)],[fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).
fof(f_139_2,plain,
! [U_342,U_341] : hAPP_nat_nat(times_times_nat(U_342),U_341) = hAPP_nat_nat(times_times_nat(U_341),U_342),
inference(variable_rename,[status(thm)],[f_139_1]) ).
cnf(f_139_3,plain,
hAPP_nat_nat(times_times_nat(U_342),U_341) = hAPP_nat_nat(times_times_nat(U_341),U_342),
inference(clausify,[status(thm)],[f_139_2]) ).
fof(f_140_1,plain,
! [A_111,B_63] : hAPP_real_real(times_times_real(A_111),B_63) = hAPP_real_real(times_times_real(B_63),A_111),
inference(fof_nnf,[status(thm)],[fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).
fof(f_140_2,plain,
! [U_344,U_343] : hAPP_real_real(times_times_real(U_344),U_343) = hAPP_real_real(times_times_real(U_343),U_344),
inference(variable_rename,[status(thm)],[f_140_1]) ).
cnf(f_140_3,plain,
hAPP_real_real(times_times_real(U_344),U_343) = hAPP_real_real(times_times_real(U_343),U_344),
inference(clausify,[status(thm)],[f_140_2]) ).
fof(f_141_1,plain,
! [A_110,B_62,C_35,D_11] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(A_110),B_62)),hAPP_int_int(plus_plus_int(C_35),D_11)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(A_110),C_35)),hAPP_int_int(plus_plus_int(B_62),D_11)),
inference(fof_nnf,[status(thm)],[fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).
fof(f_141_2,plain,
! [U_348,U_347,U_346,U_345] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(U_348),U_347)),hAPP_int_int(plus_plus_int(U_346),U_345)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(U_348),U_346)),hAPP_int_int(plus_plus_int(U_347),U_345)),
inference(variable_rename,[status(thm)],[f_141_1]) ).
cnf(f_141_3,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(U_348),U_347)),hAPP_int_int(plus_plus_int(U_346),U_345)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(U_348),U_346)),hAPP_int_int(plus_plus_int(U_347),U_345)),
inference(clausify,[status(thm)],[f_141_2]) ).
fof(f_142_1,plain,
! [A_110,B_62,C_35,D_11] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(A_110),B_62)),hAPP_nat_nat(plus_plus_nat(C_35),D_11)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(A_110),C_35)),hAPP_nat_nat(plus_plus_nat(B_62),D_11)),
inference(fof_nnf,[status(thm)],[fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).
fof(f_142_2,plain,
! [U_352,U_351,U_350,U_349] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(U_352),U_351)),hAPP_nat_nat(plus_plus_nat(U_350),U_349)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(U_352),U_350)),hAPP_nat_nat(plus_plus_nat(U_351),U_349)),
inference(variable_rename,[status(thm)],[f_142_1]) ).
cnf(f_142_3,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(U_352),U_351)),hAPP_nat_nat(plus_plus_nat(U_350),U_349)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(U_352),U_350)),hAPP_nat_nat(plus_plus_nat(U_351),U_349)),
inference(clausify,[status(thm)],[f_142_2]) ).
fof(f_143_1,plain,
! [A_110,B_62,C_35,D_11] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(A_110),B_62)),hAPP_real_real(plus_plus_real(C_35),D_11)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(A_110),C_35)),hAPP_real_real(plus_plus_real(B_62),D_11)),
inference(fof_nnf,[status(thm)],[fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).
fof(f_143_2,plain,
! [U_356,U_355,U_354,U_353] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(U_356),U_355)),hAPP_real_real(plus_plus_real(U_354),U_353)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(U_356),U_354)),hAPP_real_real(plus_plus_real(U_355),U_353)),
inference(variable_rename,[status(thm)],[f_143_1]) ).
cnf(f_143_3,plain,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(U_356),U_355)),hAPP_real_real(plus_plus_real(U_354),U_353)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(U_356),U_354)),hAPP_real_real(plus_plus_real(U_355),U_353)),
inference(clausify,[status(thm)],[f_143_2]) ).
fof(f_144_1,plain,
! [X_2,A_109] :
( ( hBOOL(member_int(X_2,A_109))
| ~ hBOOL(hAPP_int_bool(A_109,X_2)) )
& ( hBOOL(hAPP_int_bool(A_109,X_2))
| ~ hBOOL(member_int(X_2,A_109)) ) ),
inference(fof_nnf,[status(thm)],[fact_118_mem__def]) ).
fof(f_144_2,plain,
! [U_358,U_357] :
( ( hBOOL(member_int(U_358,U_357))
| ~ hBOOL(hAPP_int_bool(U_357,U_358)) )
& ( hBOOL(hAPP_int_bool(U_357,U_358))
| ~ hBOOL(member_int(U_358,U_357)) ) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
( ! [U_362,U_360] :
( hBOOL(member_int(U_362,U_360))
| ~ hBOOL(hAPP_int_bool(U_360,U_362)) )
& ! [U_361,U_359] :
( hBOOL(hAPP_int_bool(U_359,U_361))
| ~ hBOOL(member_int(U_361,U_359)) ) ),
inference(miniscope,[status(thm)],[f_144_2]) ).
cnf(f_144_4,plain,
( hBOOL(hAPP_int_bool(U_359,U_361))
| ~ hBOOL(member_int(U_361,U_359)) ),
inference(clausify,[status(thm)],[f_144_3]) ).
cnf(f_144_5,plain,
( hBOOL(member_int(U_362,U_360))
| ~ hBOOL(hAPP_int_bool(U_360,U_362)) ),
inference(clausify,[status(thm)],[f_144_3]) ).
fof(f_145_1,plain,
! [P_2] : collect_int(P_2) = P_2,
inference(fof_nnf,[status(thm)],[fact_119_Collect__def]) ).
fof(f_145_2,plain,
! [U_363] : collect_int(U_363) = U_363,
inference(variable_rename,[status(thm)],[f_145_1]) ).
cnf(f_145_3,plain,
collect_int(U_363) = U_363,
inference(clausify,[status(thm)],[f_145_2]) ).
fof(f_146_1,plain,
! [A_108,B_61,C_34] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(A_108),B_61)),C_34) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(A_108),C_34)),B_61),
inference(fof_nnf,[status(thm)],[fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).
fof(f_146_2,plain,
! [U_366,U_365,U_364] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(U_366),U_365)),U_364) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(U_366),U_364)),U_365),
inference(variable_rename,[status(thm)],[f_146_1]) ).
cnf(f_146_3,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(U_366),U_365)),U_364) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(U_366),U_364)),U_365),
inference(clausify,[status(thm)],[f_146_2]) ).
fof(f_147_1,plain,
! [A_108,B_61,C_34] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(A_108),B_61)),C_34) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(A_108),C_34)),B_61),
inference(fof_nnf,[status(thm)],[fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).
fof(f_147_2,plain,
! [U_369,U_368,U_367] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(U_369),U_368)),U_367) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(U_369),U_367)),U_368),
inference(variable_rename,[status(thm)],[f_147_1]) ).
cnf(f_147_3,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(U_369),U_368)),U_367) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(U_369),U_367)),U_368),
inference(clausify,[status(thm)],[f_147_2]) ).
fof(f_148_1,plain,
! [A_108,B_61,C_34] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(A_108),B_61)),C_34) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(A_108),C_34)),B_61),
inference(fof_nnf,[status(thm)],[fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).
fof(f_148_2,plain,
! [U_372,U_371,U_370] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(U_372),U_371)),U_370) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(U_372),U_370)),U_371),
inference(variable_rename,[status(thm)],[f_148_1]) ).
cnf(f_148_3,plain,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(U_372),U_371)),U_370) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(U_372),U_370)),U_371),
inference(clausify,[status(thm)],[f_148_2]) ).
fof(f_149_1,plain,
! [A_107,B_60,C_33] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(A_107),B_60)),C_33) = hAPP_int_int(plus_plus_int(A_107),hAPP_int_int(plus_plus_int(B_60),C_33)),
inference(fof_nnf,[status(thm)],[fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).
fof(f_149_2,plain,
! [U_375,U_374,U_373] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(U_375),U_374)),U_373) = hAPP_int_int(plus_plus_int(U_375),hAPP_int_int(plus_plus_int(U_374),U_373)),
inference(variable_rename,[status(thm)],[f_149_1]) ).
cnf(f_149_3,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(U_375),U_374)),U_373) = hAPP_int_int(plus_plus_int(U_375),hAPP_int_int(plus_plus_int(U_374),U_373)),
inference(clausify,[status(thm)],[f_149_2]) ).
fof(f_150_1,plain,
! [A_107,B_60,C_33] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(A_107),B_60)),C_33) = hAPP_nat_nat(plus_plus_nat(A_107),hAPP_nat_nat(plus_plus_nat(B_60),C_33)),
inference(fof_nnf,[status(thm)],[fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).
fof(f_150_2,plain,
! [U_378,U_377,U_376] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(U_378),U_377)),U_376) = hAPP_nat_nat(plus_plus_nat(U_378),hAPP_nat_nat(plus_plus_nat(U_377),U_376)),
inference(variable_rename,[status(thm)],[f_150_1]) ).
cnf(f_150_3,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(U_378),U_377)),U_376) = hAPP_nat_nat(plus_plus_nat(U_378),hAPP_nat_nat(plus_plus_nat(U_377),U_376)),
inference(clausify,[status(thm)],[f_150_2]) ).
fof(f_151_1,plain,
! [A_107,B_60,C_33] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(A_107),B_60)),C_33) = hAPP_real_real(plus_plus_real(A_107),hAPP_real_real(plus_plus_real(B_60),C_33)),
inference(fof_nnf,[status(thm)],[fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).
fof(f_151_2,plain,
! [U_381,U_380,U_379] : hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(U_381),U_380)),U_379) = hAPP_real_real(plus_plus_real(U_381),hAPP_real_real(plus_plus_real(U_380),U_379)),
inference(variable_rename,[status(thm)],[f_151_1]) ).
cnf(f_151_3,plain,
hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(U_381),U_380)),U_379) = hAPP_real_real(plus_plus_real(U_381),hAPP_real_real(plus_plus_real(U_380),U_379)),
inference(clausify,[status(thm)],[f_151_2]) ).
fof(f_152_1,plain,
! [A_106,C_32,D_10] : hAPP_int_int(plus_plus_int(A_106),hAPP_int_int(plus_plus_int(C_32),D_10)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(A_106),C_32)),D_10),
inference(fof_nnf,[status(thm)],[fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).
fof(f_152_2,plain,
! [U_384,U_383,U_382] : hAPP_int_int(plus_plus_int(U_384),hAPP_int_int(plus_plus_int(U_383),U_382)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(U_384),U_383)),U_382),
inference(variable_rename,[status(thm)],[f_152_1]) ).
cnf(f_152_3,plain,
hAPP_int_int(plus_plus_int(U_384),hAPP_int_int(plus_plus_int(U_383),U_382)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(U_384),U_383)),U_382),
inference(clausify,[status(thm)],[f_152_2]) ).
fof(f_153_1,plain,
! [A_106,C_32,D_10] : hAPP_nat_nat(plus_plus_nat(A_106),hAPP_nat_nat(plus_plus_nat(C_32),D_10)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(A_106),C_32)),D_10),
inference(fof_nnf,[status(thm)],[fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).
fof(f_153_2,plain,
! [U_387,U_386,U_385] : hAPP_nat_nat(plus_plus_nat(U_387),hAPP_nat_nat(plus_plus_nat(U_386),U_385)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(U_387),U_386)),U_385),
inference(variable_rename,[status(thm)],[f_153_1]) ).
cnf(f_153_3,plain,
hAPP_nat_nat(plus_plus_nat(U_387),hAPP_nat_nat(plus_plus_nat(U_386),U_385)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(U_387),U_386)),U_385),
inference(clausify,[status(thm)],[f_153_2]) ).
fof(f_154_1,plain,
! [A_106,C_32,D_10] : hAPP_real_real(plus_plus_real(A_106),hAPP_real_real(plus_plus_real(C_32),D_10)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(A_106),C_32)),D_10),
inference(fof_nnf,[status(thm)],[fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).
fof(f_154_2,plain,
! [U_390,U_389,U_388] : hAPP_real_real(plus_plus_real(U_390),hAPP_real_real(plus_plus_real(U_389),U_388)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(U_390),U_389)),U_388),
inference(variable_rename,[status(thm)],[f_154_1]) ).
cnf(f_154_3,plain,
hAPP_real_real(plus_plus_real(U_390),hAPP_real_real(plus_plus_real(U_389),U_388)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(U_390),U_389)),U_388),
inference(clausify,[status(thm)],[f_154_2]) ).
fof(f_155_1,plain,
! [A_105,C_31,D_9] : hAPP_int_int(plus_plus_int(A_105),hAPP_int_int(plus_plus_int(C_31),D_9)) = hAPP_int_int(plus_plus_int(C_31),hAPP_int_int(plus_plus_int(A_105),D_9)),
inference(fof_nnf,[status(thm)],[fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).
fof(f_155_2,plain,
! [U_393,U_392,U_391] : hAPP_int_int(plus_plus_int(U_393),hAPP_int_int(plus_plus_int(U_392),U_391)) = hAPP_int_int(plus_plus_int(U_392),hAPP_int_int(plus_plus_int(U_393),U_391)),
inference(variable_rename,[status(thm)],[f_155_1]) ).
cnf(f_155_3,plain,
hAPP_int_int(plus_plus_int(U_393),hAPP_int_int(plus_plus_int(U_392),U_391)) = hAPP_int_int(plus_plus_int(U_392),hAPP_int_int(plus_plus_int(U_393),U_391)),
inference(clausify,[status(thm)],[f_155_2]) ).
fof(f_156_1,plain,
! [A_105,C_31,D_9] : hAPP_nat_nat(plus_plus_nat(A_105),hAPP_nat_nat(plus_plus_nat(C_31),D_9)) = hAPP_nat_nat(plus_plus_nat(C_31),hAPP_nat_nat(plus_plus_nat(A_105),D_9)),
inference(fof_nnf,[status(thm)],[fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).
fof(f_156_2,plain,
! [U_396,U_395,U_394] : hAPP_nat_nat(plus_plus_nat(U_396),hAPP_nat_nat(plus_plus_nat(U_395),U_394)) = hAPP_nat_nat(plus_plus_nat(U_395),hAPP_nat_nat(plus_plus_nat(U_396),U_394)),
inference(variable_rename,[status(thm)],[f_156_1]) ).
cnf(f_156_3,plain,
hAPP_nat_nat(plus_plus_nat(U_396),hAPP_nat_nat(plus_plus_nat(U_395),U_394)) = hAPP_nat_nat(plus_plus_nat(U_395),hAPP_nat_nat(plus_plus_nat(U_396),U_394)),
inference(clausify,[status(thm)],[f_156_2]) ).
fof(f_157_1,plain,
! [A_105,C_31,D_9] : hAPP_real_real(plus_plus_real(A_105),hAPP_real_real(plus_plus_real(C_31),D_9)) = hAPP_real_real(plus_plus_real(C_31),hAPP_real_real(plus_plus_real(A_105),D_9)),
inference(fof_nnf,[status(thm)],[fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).
fof(f_157_2,plain,
! [U_399,U_398,U_397] : hAPP_real_real(plus_plus_real(U_399),hAPP_real_real(plus_plus_real(U_398),U_397)) = hAPP_real_real(plus_plus_real(U_398),hAPP_real_real(plus_plus_real(U_399),U_397)),
inference(variable_rename,[status(thm)],[f_157_1]) ).
cnf(f_157_3,plain,
hAPP_real_real(plus_plus_real(U_399),hAPP_real_real(plus_plus_real(U_398),U_397)) = hAPP_real_real(plus_plus_real(U_398),hAPP_real_real(plus_plus_real(U_399),U_397)),
inference(clausify,[status(thm)],[f_157_2]) ).
fof(f_158_1,plain,
! [A_104,C_30] : hAPP_int_int(plus_plus_int(A_104),C_30) = hAPP_int_int(plus_plus_int(C_30),A_104),
inference(fof_nnf,[status(thm)],[fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
fof(f_158_2,plain,
! [U_401,U_400] : hAPP_int_int(plus_plus_int(U_401),U_400) = hAPP_int_int(plus_plus_int(U_400),U_401),
inference(variable_rename,[status(thm)],[f_158_1]) ).
cnf(f_158_3,plain,
hAPP_int_int(plus_plus_int(U_401),U_400) = hAPP_int_int(plus_plus_int(U_400),U_401),
inference(clausify,[status(thm)],[f_158_2]) ).
fof(f_159_1,plain,
! [A_104,C_30] : hAPP_nat_nat(plus_plus_nat(A_104),C_30) = hAPP_nat_nat(plus_plus_nat(C_30),A_104),
inference(fof_nnf,[status(thm)],[fact_133_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
fof(f_159_2,plain,
! [U_403,U_402] : hAPP_nat_nat(plus_plus_nat(U_403),U_402) = hAPP_nat_nat(plus_plus_nat(U_402),U_403),
inference(variable_rename,[status(thm)],[f_159_1]) ).
cnf(f_159_3,plain,
hAPP_nat_nat(plus_plus_nat(U_403),U_402) = hAPP_nat_nat(plus_plus_nat(U_402),U_403),
inference(clausify,[status(thm)],[f_159_2]) ).
fof(f_160_1,plain,
! [A_104,C_30] : hAPP_real_real(plus_plus_real(A_104),C_30) = hAPP_real_real(plus_plus_real(C_30),A_104),
inference(fof_nnf,[status(thm)],[fact_134_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
fof(f_160_2,plain,
! [U_405,U_404] : hAPP_real_real(plus_plus_real(U_405),U_404) = hAPP_real_real(plus_plus_real(U_404),U_405),
inference(variable_rename,[status(thm)],[f_160_1]) ).
cnf(f_160_3,plain,
hAPP_real_real(plus_plus_real(U_405),U_404) = hAPP_real_real(plus_plus_real(U_404),U_405),
inference(clausify,[status(thm)],[f_160_2]) ).
fof(f_161_1,plain,
! [X_2,Y_2] :
( ( ( number_number_of_int(X_2) = number_number_of_int(Y_2)
| X_2 != Y_2 )
& ( X_2 = Y_2
| number_number_of_int(X_2) != number_number_of_int(Y_2) ) )
| ~ is_int(Y_2)
| ~ is_int(X_2) ),
inference(fof_nnf,[status(thm)],[fact_135_eq__number__of]) ).
fof(f_161_2,plain,
! [U_407,U_406] :
( ( ( number_number_of_int(U_407) = number_number_of_int(U_406)
| U_407 != U_406 )
& ( U_407 = U_406
| number_number_of_int(U_407) != number_number_of_int(U_406) ) )
| ~ is_int(U_406)
| ~ is_int(U_407) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
cnf(f_161_3,plain,
( U_407 = U_406
| number_number_of_int(U_407) != number_number_of_int(U_406)
| ~ is_int(U_406)
| ~ is_int(U_407) ),
inference(clausify,[status(thm)],[f_161_2]) ).
cnf(f_161_4,plain,
( number_number_of_int(U_407) = number_number_of_int(U_406)
| U_407 != U_406
| ~ is_int(U_406)
| ~ is_int(U_407) ),
inference(clausify,[status(thm)],[f_161_2]) ).
fof(f_162_1,plain,
! [X_2,Y_2] :
( ( ( number267125858f_real(X_2) = number267125858f_real(Y_2)
| X_2 != Y_2 )
& ( X_2 = Y_2
| number267125858f_real(X_2) != number267125858f_real(Y_2) ) )
| ~ is_int(Y_2)
| ~ is_int(X_2) ),
inference(fof_nnf,[status(thm)],[fact_136_eq__number__of]) ).
fof(f_162_2,plain,
! [U_409,U_408] :
( ( ( number267125858f_real(U_409) = number267125858f_real(U_408)
| U_409 != U_408 )
& ( U_409 = U_408
| number267125858f_real(U_409) != number267125858f_real(U_408) ) )
| ~ is_int(U_408)
| ~ is_int(U_409) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
cnf(f_162_3,plain,
( U_409 = U_408
| number267125858f_real(U_409) != number267125858f_real(U_408)
| ~ is_int(U_408)
| ~ is_int(U_409) ),
inference(clausify,[status(thm)],[f_162_2]) ).
cnf(f_162_4,plain,
( number267125858f_real(U_409) = number267125858f_real(U_408)
| U_409 != U_408
| ~ is_int(U_408)
| ~ is_int(U_409) ),
inference(clausify,[status(thm)],[f_162_2]) ).
fof(f_163_1,plain,
! [W_1,X_2] :
( ( number_number_of_nat(W_1) = X_2
| X_2 != number_number_of_nat(W_1) )
& ( X_2 = number_number_of_nat(W_1)
| number_number_of_nat(W_1) != X_2 ) ),
inference(fof_nnf,[status(thm)],[fact_137_number__of__reorient]) ).
fof(f_163_2,plain,
! [U_411,U_410] :
( ( number_number_of_nat(U_411) = U_410
| U_410 != number_number_of_nat(U_411) )
& ( U_410 = number_number_of_nat(U_411)
| number_number_of_nat(U_411) != U_410 ) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
( ! [U_415,U_413] :
( number_number_of_nat(U_415) = U_413
| U_413 != number_number_of_nat(U_415) )
& ! [U_414,U_412] :
( U_412 = number_number_of_nat(U_414)
| number_number_of_nat(U_414) != U_412 ) ),
inference(miniscope,[status(thm)],[f_163_2]) ).
cnf(f_163_4,plain,
( U_412 = number_number_of_nat(U_414)
| number_number_of_nat(U_414) != U_412 ),
inference(clausify,[status(thm)],[f_163_3]) ).
cnf(f_163_5,plain,
( number_number_of_nat(U_415) = U_413
| U_413 != number_number_of_nat(U_415) ),
inference(clausify,[status(thm)],[f_163_3]) ).
fof(f_164_1,plain,
! [W_1,X_2] :
( ( ( number_number_of_int(W_1) = X_2
| X_2 != number_number_of_int(W_1) )
& ( X_2 = number_number_of_int(W_1)
| number_number_of_int(W_1) != X_2 ) )
| ~ is_int(X_2) ),
inference(fof_nnf,[status(thm)],[fact_138_number__of__reorient]) ).
fof(f_164_2,plain,
! [U_417,U_416] :
( ( ( number_number_of_int(U_417) = U_416
| U_416 != number_number_of_int(U_417) )
& ( U_416 = number_number_of_int(U_417)
| number_number_of_int(U_417) != U_416 ) )
| ~ is_int(U_416) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
cnf(f_164_3,plain,
( U_416 = number_number_of_int(U_417)
| number_number_of_int(U_417) != U_416
| ~ is_int(U_416) ),
inference(clausify,[status(thm)],[f_164_2]) ).
cnf(f_164_4,plain,
( number_number_of_int(U_417) = U_416
| U_416 != number_number_of_int(U_417)
| ~ is_int(U_416) ),
inference(clausify,[status(thm)],[f_164_2]) ).
fof(f_165_1,plain,
! [W_1,X_2] :
( ( number267125858f_real(W_1) = X_2
| X_2 != number267125858f_real(W_1) )
& ( X_2 = number267125858f_real(W_1)
| number267125858f_real(W_1) != X_2 ) ),
inference(fof_nnf,[status(thm)],[fact_139_number__of__reorient]) ).
fof(f_165_2,plain,
! [U_419,U_418] :
( ( number267125858f_real(U_419) = U_418
| U_418 != number267125858f_real(U_419) )
& ( U_418 = number267125858f_real(U_419)
| number267125858f_real(U_419) != U_418 ) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
fof(f_165_3,plain,
( ! [U_423,U_421] :
( number267125858f_real(U_423) = U_421
| U_421 != number267125858f_real(U_423) )
& ! [U_422,U_420] :
( U_420 = number267125858f_real(U_422)
| number267125858f_real(U_422) != U_420 ) ),
inference(miniscope,[status(thm)],[f_165_2]) ).
cnf(f_165_4,plain,
( U_420 = number267125858f_real(U_422)
| number267125858f_real(U_422) != U_420 ),
inference(clausify,[status(thm)],[f_165_3]) ).
cnf(f_165_5,plain,
( number267125858f_real(U_423) = U_421
| U_421 != number267125858f_real(U_423) ),
inference(clausify,[status(thm)],[f_165_3]) ).
fof(f_166_1,plain,
! [K,L_1] :
( ( ( bit1(K) = bit1(L_1)
| K != L_1 )
& ( K = L_1
| bit1(K) != bit1(L_1) ) )
| ~ is_int(L_1)
| ~ is_int(K) ),
inference(fof_nnf,[status(thm)],[fact_140_rel__simps_I51_J]) ).
fof(f_166_2,plain,
! [U_425,U_424] :
( ( ( bit1(U_425) = bit1(U_424)
| U_425 != U_424 )
& ( U_425 = U_424
| bit1(U_425) != bit1(U_424) ) )
| ~ is_int(U_424)
| ~ is_int(U_425) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
cnf(f_166_3,plain,
( U_425 = U_424
| bit1(U_425) != bit1(U_424)
| ~ is_int(U_424)
| ~ is_int(U_425) ),
inference(clausify,[status(thm)],[f_166_2]) ).
cnf(f_166_4,plain,
( bit1(U_425) = bit1(U_424)
| U_425 != U_424
| ~ is_int(U_424)
| ~ is_int(U_425) ),
inference(clausify,[status(thm)],[f_166_2]) ).
fof(f_167_1,plain,
! [K,L_1] :
( ( ( bit0(K) = bit0(L_1)
| K != L_1 )
& ( K = L_1
| bit0(K) != bit0(L_1) ) )
| ~ is_int(L_1)
| ~ is_int(K) ),
inference(fof_nnf,[status(thm)],[fact_141_rel__simps_I48_J]) ).
fof(f_167_2,plain,
! [U_427,U_426] :
( ( ( bit0(U_427) = bit0(U_426)
| U_427 != U_426 )
& ( U_427 = U_426
| bit0(U_427) != bit0(U_426) ) )
| ~ is_int(U_426)
| ~ is_int(U_427) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
cnf(f_167_3,plain,
( U_427 = U_426
| bit0(U_427) != bit0(U_426)
| ~ is_int(U_426)
| ~ is_int(U_427) ),
inference(clausify,[status(thm)],[f_167_2]) ).
cnf(f_167_4,plain,
( bit0(U_427) = bit0(U_426)
| U_427 != U_426
| ~ is_int(U_426)
| ~ is_int(U_427) ),
inference(clausify,[status(thm)],[f_167_2]) ).
fof(f_168_1,plain,
! [Z1,Z2,Z3] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(Z1),Z2)),Z3) = hAPP_int_int(times_times_int(Z1),hAPP_int_int(times_times_int(Z2),Z3)),
inference(fof_nnf,[status(thm)],[fact_142_zmult__assoc]) ).
fof(f_168_2,plain,
! [U_430,U_429,U_428] : hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_430),U_429)),U_428) = hAPP_int_int(times_times_int(U_430),hAPP_int_int(times_times_int(U_429),U_428)),
inference(variable_rename,[status(thm)],[f_168_1]) ).
cnf(f_168_3,plain,
hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_430),U_429)),U_428) = hAPP_int_int(times_times_int(U_430),hAPP_int_int(times_times_int(U_429),U_428)),
inference(clausify,[status(thm)],[f_168_2]) ).
fof(f_169_1,plain,
! [Z,W] : hAPP_int_int(times_times_int(Z),W) = hAPP_int_int(times_times_int(W),Z),
inference(fof_nnf,[status(thm)],[fact_143_zmult__commute]) ).
fof(f_169_2,plain,
! [U_432,U_431] : hAPP_int_int(times_times_int(U_432),U_431) = hAPP_int_int(times_times_int(U_431),U_432),
inference(variable_rename,[status(thm)],[f_169_1]) ).
cnf(f_169_3,plain,
hAPP_int_int(times_times_int(U_432),U_431) = hAPP_int_int(times_times_int(U_431),U_432),
inference(clausify,[status(thm)],[f_169_2]) ).
fof(f_170_1,plain,
! [K_1] :
( number_number_of_int(K_1) = K_1
| ~ is_int(K_1) ),
inference(fof_nnf,[status(thm)],[fact_144_number__of__is__id]) ).
fof(f_170_2,plain,
! [U_433] :
( number_number_of_int(U_433) = U_433
| ~ is_int(U_433) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
cnf(f_170_3,plain,
( number_number_of_int(U_433) = U_433
| ~ is_int(U_433) ),
inference(clausify,[status(thm)],[f_170_2]) ).
fof(f_171_1,plain,
! [Z1,Z2,Z3] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(Z1),Z2)),Z3) = hAPP_int_int(plus_plus_int(Z1),hAPP_int_int(plus_plus_int(Z2),Z3)),
inference(fof_nnf,[status(thm)],[fact_145_zadd__assoc]) ).
fof(f_171_2,plain,
! [U_436,U_435,U_434] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(U_436),U_435)),U_434) = hAPP_int_int(plus_plus_int(U_436),hAPP_int_int(plus_plus_int(U_435),U_434)),
inference(variable_rename,[status(thm)],[f_171_1]) ).
cnf(f_171_3,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(U_436),U_435)),U_434) = hAPP_int_int(plus_plus_int(U_436),hAPP_int_int(plus_plus_int(U_435),U_434)),
inference(clausify,[status(thm)],[f_171_2]) ).
fof(f_172_1,plain,
! [X_1,Y_1,Z] : hAPP_int_int(plus_plus_int(X_1),hAPP_int_int(plus_plus_int(Y_1),Z)) = hAPP_int_int(plus_plus_int(Y_1),hAPP_int_int(plus_plus_int(X_1),Z)),
inference(fof_nnf,[status(thm)],[fact_146_zadd__left__commute]) ).
fof(f_172_2,plain,
! [U_439,U_438,U_437] : hAPP_int_int(plus_plus_int(U_439),hAPP_int_int(plus_plus_int(U_438),U_437)) = hAPP_int_int(plus_plus_int(U_438),hAPP_int_int(plus_plus_int(U_439),U_437)),
inference(variable_rename,[status(thm)],[f_172_1]) ).
cnf(f_172_3,plain,
hAPP_int_int(plus_plus_int(U_439),hAPP_int_int(plus_plus_int(U_438),U_437)) = hAPP_int_int(plus_plus_int(U_438),hAPP_int_int(plus_plus_int(U_439),U_437)),
inference(clausify,[status(thm)],[f_172_2]) ).
fof(f_173_1,plain,
! [Z,W] : hAPP_int_int(plus_plus_int(Z),W) = hAPP_int_int(plus_plus_int(W),Z),
inference(fof_nnf,[status(thm)],[fact_147_zadd__commute]) ).
fof(f_173_2,plain,
! [U_441,U_440] : hAPP_int_int(plus_plus_int(U_441),U_440) = hAPP_int_int(plus_plus_int(U_440),U_441),
inference(variable_rename,[status(thm)],[f_173_1]) ).
cnf(f_173_3,plain,
hAPP_int_int(plus_plus_int(U_441),U_440) = hAPP_int_int(plus_plus_int(U_440),U_441),
inference(clausify,[status(thm)],[f_173_2]) ).
fof(f_174_1,plain,
! [K] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),pls)) ) ),
inference(fof_nnf,[status(thm)],[fact_148_rel__simps_I12_J]) ).
fof(f_174_2,plain,
! [U_442] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_442)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_442),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_442),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_442)),pls)) ) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
fof(f_174_3,plain,
( ! [U_444] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_444)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_444),pls)) )
& ! [U_443] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_443),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_443)),pls)) ) ),
inference(miniscope,[status(thm)],[f_174_2]) ).
cnf(f_174_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_443),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_443)),pls)) ),
inference(clausify,[status(thm)],[f_174_3]) ).
cnf(f_174_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_444)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_444),pls)) ),
inference(clausify,[status(thm)],[f_174_3]) ).
fof(f_175_1,plain,
! [K1,K2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K1)),bit0(K2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K1)),bit0(K2))) ) ),
inference(fof_nnf,[status(thm)],[fact_149_less__int__code_I15_J]) ).
fof(f_175_2,plain,
! [U_446,U_445] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_446)),bit0(U_445)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_446),U_445)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_446),U_445))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_446)),bit0(U_445))) ) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
fof(f_175_3,plain,
( ! [U_450,U_448] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_450)),bit0(U_448)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_450),U_448)) )
& ! [U_449,U_447] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_449),U_447))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_449)),bit0(U_447))) ) ),
inference(miniscope,[status(thm)],[f_175_2]) ).
cnf(f_175_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_449),U_447))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_449)),bit0(U_447))) ),
inference(clausify,[status(thm)],[f_175_3]) ).
cnf(f_175_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_450)),bit0(U_448)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_450),U_448)) ),
inference(clausify,[status(thm)],[f_175_3]) ).
fof(f_176_1,plain,
! [K,L_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),bit0(L_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L_1)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),bit0(L_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_150_rel__simps_I16_J]) ).
fof(f_176_2,plain,
! [U_452,U_451] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_452)),bit0(U_451)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_452),U_451)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_452),U_451))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_452)),bit0(U_451))) ) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
fof(f_176_3,plain,
( ! [U_456,U_454] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_456)),bit0(U_454)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_456),U_454)) )
& ! [U_455,U_453] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_455),U_453))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_455)),bit0(U_453))) ) ),
inference(miniscope,[status(thm)],[f_176_2]) ).
cnf(f_176_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_455),U_453))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_455)),bit0(U_453))) ),
inference(clausify,[status(thm)],[f_176_3]) ).
cnf(f_176_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_456)),bit0(U_454)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_456),U_454)) ),
inference(clausify,[status(thm)],[f_176_3]) ).
fof(f_177_1,plain,
! [K] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(K)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(K)),pls)) ) ),
inference(fof_nnf,[status(thm)],[fact_151_rel__simps_I10_J]) ).
fof(f_177_2,plain,
! [U_457] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_457)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_457),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_457),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_457)),pls)) ) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
fof(f_177_3,plain,
( ! [U_459] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_459)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_459),pls)) )
& ! [U_458] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_458),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_458)),pls)) ) ),
inference(miniscope,[status(thm)],[f_177_2]) ).
cnf(f_177_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_458),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_458)),pls)) ),
inference(clausify,[status(thm)],[f_177_3]) ).
cnf(f_177_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_459)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_459),pls)) ),
inference(clausify,[status(thm)],[f_177_3]) ).
fof(f_178_1,plain,
! [K] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(K)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),K)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),K))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(K))) ) ),
inference(fof_nnf,[status(thm)],[fact_152_rel__simps_I4_J]) ).
fof(f_178_2,plain,
! [U_460] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(U_460)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_460)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_460))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(U_460))) ) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
( ! [U_462] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(U_462)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_462)) )
& ! [U_461] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_461))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(U_461))) ) ),
inference(miniscope,[status(thm)],[f_178_2]) ).
cnf(f_178_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_461))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(U_461))) ),
inference(clausify,[status(thm)],[f_178_3]) ).
cnf(f_178_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit0(U_462)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_462)) ),
inference(clausify,[status(thm)],[f_178_3]) ).
fof(f_179_1,plain,
! [K] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(K)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(K))) ) ),
inference(fof_nnf,[status(thm)],[fact_153_rel__simps_I22_J]) ).
fof(f_179_2,plain,
! [U_463] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(U_463)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_463)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_463))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(U_463))) ) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
fof(f_179_3,plain,
( ! [U_465] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(U_465)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_465)) )
& ! [U_464] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_464))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(U_464))) ) ),
inference(miniscope,[status(thm)],[f_179_2]) ).
cnf(f_179_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_464))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(U_464))) ),
inference(clausify,[status(thm)],[f_179_3]) ).
cnf(f_179_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(U_465)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_465)) ),
inference(clausify,[status(thm)],[f_179_3]) ).
fof(f_180_1,plain,
! [K1,K2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(K1)),bit1(K2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(K1)),bit1(K2))) ) ),
inference(fof_nnf,[status(thm)],[fact_154_less__eq__int__code_I14_J]) ).
fof(f_180_2,plain,
! [U_467,U_466] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_467)),bit1(U_466)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_467),U_466)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_467),U_466))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_467)),bit1(U_466))) ) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
fof(f_180_3,plain,
( ! [U_471,U_469] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_471)),bit1(U_469)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_471),U_469)) )
& ! [U_470,U_468] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_470),U_468))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_470)),bit1(U_468))) ) ),
inference(miniscope,[status(thm)],[f_180_2]) ).
cnf(f_180_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_470),U_468))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_470)),bit1(U_468))) ),
inference(clausify,[status(thm)],[f_180_3]) ).
cnf(f_180_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_471)),bit1(U_469)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_471),U_469)) ),
inference(clausify,[status(thm)],[f_180_3]) ).
fof(f_181_1,plain,
! [K,L_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(K)),bit1(L_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L_1)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(K)),bit1(L_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_155_rel__simps_I32_J]) ).
fof(f_181_2,plain,
! [U_473,U_472] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_473)),bit1(U_472)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_473),U_472)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_473),U_472))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_473)),bit1(U_472))) ) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
( ! [U_477,U_475] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_477)),bit1(U_475)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_477),U_475)) )
& ! [U_476,U_474] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_476),U_474))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_476)),bit1(U_474))) ) ),
inference(miniscope,[status(thm)],[f_181_2]) ).
cnf(f_181_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_476),U_474))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_476)),bit1(U_474))) ),
inference(clausify,[status(thm)],[f_181_3]) ).
cnf(f_181_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_477)),bit1(U_475)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_477),U_475)) ),
inference(clausify,[status(thm)],[f_181_3]) ).
fof(f_182_1,plain,
! [K] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(K)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(K)),pls)) ) ),
inference(fof_nnf,[status(thm)],[fact_156_rel__simps_I27_J]) ).
fof(f_182_2,plain,
! [U_478] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_478)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_478),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_478),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_478)),pls)) ) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
fof(f_182_3,plain,
( ! [U_480] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_480)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_480),pls)) )
& ! [U_479] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_479),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_479)),pls)) ) ),
inference(miniscope,[status(thm)],[f_182_2]) ).
cnf(f_182_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_479),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_479)),pls)) ),
inference(clausify,[status(thm)],[f_182_3]) ).
cnf(f_182_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_480)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_480),pls)) ),
inference(clausify,[status(thm)],[f_182_3]) ).
fof(f_183_1,plain,
! [K] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(K)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(K))) ) ),
inference(fof_nnf,[status(thm)],[fact_157_rel__simps_I21_J]) ).
fof(f_183_2,plain,
! [U_481] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(U_481)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_481)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_481))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(U_481))) ) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
( ! [U_483] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(U_483)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_483)) )
& ! [U_482] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_482))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(U_482))) ) ),
inference(miniscope,[status(thm)],[f_183_2]) ).
cnf(f_183_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_482))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(U_482))) ),
inference(clausify,[status(thm)],[f_183_3]) ).
cnf(f_183_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit0(U_483)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_483)) ),
inference(clausify,[status(thm)],[f_183_3]) ).
fof(f_184_1,plain,
! [W_1,Z_1] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),hAPP_int_int(plus_plus_int(Z_1),one_one_int)))
| ( W_1 != Z_1
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_1)) ) )
& ( W_1 = Z_1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),hAPP_int_int(plus_plus_int(Z_1),one_one_int))) ) )
| ~ is_int(Z_1)
| ~ is_int(W_1) ),
inference(fof_nnf,[status(thm)],[fact_158_zless__add1__eq]) ).
fof(f_184_2,plain,
! [U_485,U_484] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_485),hAPP_int_int(plus_plus_int(U_484),one_one_int)))
| ( U_485 != U_484
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_485),U_484)) ) )
& ( U_485 = U_484
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_485),U_484))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_485),hAPP_int_int(plus_plus_int(U_484),one_one_int))) ) )
| ~ is_int(U_484)
| ~ is_int(U_485) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
cnf(f_184_3,plain,
( U_485 = U_484
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_485),U_484))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_485),hAPP_int_int(plus_plus_int(U_484),one_one_int)))
| ~ is_int(U_484)
| ~ is_int(U_485) ),
inference(clausify,[status(thm)],[f_184_2]) ).
cnf(f_184_4,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_485),U_484))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_485),hAPP_int_int(plus_plus_int(U_484),one_one_int)))
| ~ is_int(U_484)
| ~ is_int(U_485) ),
inference(clausify,[status(thm)],[f_184_2]) ).
cnf(f_184_5,plain,
( U_485 != U_484
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_485),hAPP_int_int(plus_plus_int(U_484),one_one_int)))
| ~ is_int(U_484)
| ~ is_int(U_485) ),
inference(clausify,[status(thm)],[f_184_2]) ).
fof(f_185_1,plain,
! [A_103,N_39] : hAPP_nat_int(power_power_int(A_103),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_39)) = hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(A_103),N_39)),number_number_of_nat(bit0(bit1(pls)))),
inference(fof_nnf,[status(thm)],[fact_159_power__even__eq]) ).
fof(f_185_2,plain,
! [U_487,U_486] : hAPP_nat_int(power_power_int(U_487),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_486)) = hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(U_487),U_486)),number_number_of_nat(bit0(bit1(pls)))),
inference(variable_rename,[status(thm)],[f_185_1]) ).
cnf(f_185_3,plain,
hAPP_nat_int(power_power_int(U_487),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_486)) = hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(U_487),U_486)),number_number_of_nat(bit0(bit1(pls)))),
inference(clausify,[status(thm)],[f_185_2]) ).
fof(f_186_1,plain,
! [A_103,N_39] : hAPP_nat_real(power_power_real(A_103),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_39)) = hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(A_103),N_39)),number_number_of_nat(bit0(bit1(pls)))),
inference(fof_nnf,[status(thm)],[fact_160_power__even__eq]) ).
fof(f_186_2,plain,
! [U_489,U_488] : hAPP_nat_real(power_power_real(U_489),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_488)) = hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(U_489),U_488)),number_number_of_nat(bit0(bit1(pls)))),
inference(variable_rename,[status(thm)],[f_186_1]) ).
cnf(f_186_3,plain,
hAPP_nat_real(power_power_real(U_489),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_488)) = hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(U_489),U_488)),number_number_of_nat(bit0(bit1(pls)))),
inference(clausify,[status(thm)],[f_186_2]) ).
fof(f_187_1,plain,
! [A_103,N_39] : hAPP_nat_nat(power_power_nat(A_103),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_39)) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(A_103),N_39)),number_number_of_nat(bit0(bit1(pls)))),
inference(fof_nnf,[status(thm)],[fact_161_power__even__eq]) ).
fof(f_187_2,plain,
! [U_491,U_490] : hAPP_nat_nat(power_power_nat(U_491),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_490)) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(U_491),U_490)),number_number_of_nat(bit0(bit1(pls)))),
inference(variable_rename,[status(thm)],[f_187_1]) ).
cnf(f_187_3,plain,
hAPP_nat_nat(power_power_nat(U_491),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_490)) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(U_491),U_490)),number_number_of_nat(bit0(bit1(pls)))),
inference(clausify,[status(thm)],[f_187_2]) ).
fof(f_188_1,plain,
! [X_2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X_2)),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),bit1(pls))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),bit1(pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X_2)),one_one_int)) ) ),
inference(fof_nnf,[status(thm)],[fact_162_less__special_I4_J]) ).
fof(f_188_2,plain,
! [U_492] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_492)),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_492),bit1(pls))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_492),bit1(pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_492)),one_one_int)) ) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
fof(f_188_3,plain,
( ! [U_494] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_494)),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_494),bit1(pls))) )
& ! [U_493] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_493),bit1(pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_493)),one_one_int)) ) ),
inference(miniscope,[status(thm)],[f_188_2]) ).
cnf(f_188_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_493),bit1(pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_493)),one_one_int)) ),
inference(clausify,[status(thm)],[f_188_3]) ).
cnf(f_188_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_494)),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_494),bit1(pls))) ),
inference(clausify,[status(thm)],[f_188_3]) ).
fof(f_189_1,plain,
! [X_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X_2)),one_one_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),bit1(pls))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),bit1(pls)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X_2)),one_one_real)) ) ),
inference(fof_nnf,[status(thm)],[fact_163_less__special_I4_J]) ).
fof(f_189_2,plain,
! [U_495] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_495)),one_one_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_495),bit1(pls))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_495),bit1(pls)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_495)),one_one_real)) ) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
fof(f_189_3,plain,
( ! [U_497] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_497)),one_one_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_497),bit1(pls))) )
& ! [U_496] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_496),bit1(pls)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_496)),one_one_real)) ) ),
inference(miniscope,[status(thm)],[f_189_2]) ).
cnf(f_189_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_496),bit1(pls)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_496)),one_one_real)) ),
inference(clausify,[status(thm)],[f_189_3]) ).
cnf(f_189_5,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_497)),one_one_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_497),bit1(pls))) ),
inference(clausify,[status(thm)],[f_189_3]) ).
fof(f_190_1,plain,
! [Y_2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(Y_2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),Y_2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),Y_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(Y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_164_less__special_I2_J]) ).
fof(f_190_2,plain,
! [U_498] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(U_498)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),U_498)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),U_498))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(U_498))) ) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
fof(f_190_3,plain,
( ! [U_500] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(U_500)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),U_500)) )
& ! [U_499] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),U_499))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(U_499))) ) ),
inference(miniscope,[status(thm)],[f_190_2]) ).
cnf(f_190_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),U_499))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(U_499))) ),
inference(clausify,[status(thm)],[f_190_3]) ).
cnf(f_190_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),number_number_of_int(U_500)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),U_500)) ),
inference(clausify,[status(thm)],[f_190_3]) ).
fof(f_191_1,plain,
! [Y_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(Y_2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),Y_2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),Y_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(Y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_165_less__special_I2_J]) ).
fof(f_191_2,plain,
! [U_501] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(U_501)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),U_501)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),U_501))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(U_501))) ) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
fof(f_191_3,plain,
( ! [U_503] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(U_503)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),U_503)) )
& ! [U_502] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),U_502))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(U_502))) ) ),
inference(miniscope,[status(thm)],[f_191_2]) ).
cnf(f_191_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),U_502))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(U_502))) ),
inference(clausify,[status(thm)],[f_191_3]) ).
cnf(f_191_5,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),number267125858f_real(U_503)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(pls)),U_503)) ),
inference(clausify,[status(thm)],[f_191_3]) ).
fof(f_192_1,plain,
! [X_2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X_2)),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),bit1(pls))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),bit1(pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X_2)),one_one_int)) ) ),
inference(fof_nnf,[status(thm)],[fact_166_le__special_I4_J]) ).
fof(f_192_2,plain,
! [U_504] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_504)),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_504),bit1(pls))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_504),bit1(pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_504)),one_one_int)) ) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
fof(f_192_3,plain,
( ! [U_506] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_506)),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_506),bit1(pls))) )
& ! [U_505] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_505),bit1(pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_505)),one_one_int)) ) ),
inference(miniscope,[status(thm)],[f_192_2]) ).
cnf(f_192_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_505),bit1(pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_505)),one_one_int)) ),
inference(clausify,[status(thm)],[f_192_3]) ).
cnf(f_192_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_506)),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_506),bit1(pls))) ),
inference(clausify,[status(thm)],[f_192_3]) ).
fof(f_193_1,plain,
! [X_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X_2)),one_one_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),bit1(pls))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),bit1(pls)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X_2)),one_one_real)) ) ),
inference(fof_nnf,[status(thm)],[fact_167_le__special_I4_J]) ).
fof(f_193_2,plain,
! [U_507] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_507)),one_one_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_507),bit1(pls))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_507),bit1(pls)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_507)),one_one_real)) ) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
fof(f_193_3,plain,
( ! [U_509] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_509)),one_one_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_509),bit1(pls))) )
& ! [U_508] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_508),bit1(pls)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_508)),one_one_real)) ) ),
inference(miniscope,[status(thm)],[f_193_2]) ).
cnf(f_193_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_508),bit1(pls)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_508)),one_one_real)) ),
inference(clausify,[status(thm)],[f_193_3]) ).
cnf(f_193_5,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_509)),one_one_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_509),bit1(pls))) ),
inference(clausify,[status(thm)],[f_193_3]) ).
fof(f_194_1,plain,
! [Y_2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(Y_2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),Y_2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),Y_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(Y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_168_le__special_I2_J]) ).
fof(f_194_2,plain,
! [U_510] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(U_510)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),U_510)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),U_510))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(U_510))) ) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
fof(f_194_3,plain,
( ! [U_512] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(U_512)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),U_512)) )
& ! [U_511] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),U_511))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(U_511))) ) ),
inference(miniscope,[status(thm)],[f_194_2]) ).
cnf(f_194_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),U_511))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(U_511))) ),
inference(clausify,[status(thm)],[f_194_3]) ).
cnf(f_194_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),number_number_of_int(U_512)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),U_512)) ),
inference(clausify,[status(thm)],[f_194_3]) ).
fof(f_195_1,plain,
! [Y_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(Y_2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),Y_2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),Y_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(Y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_169_le__special_I2_J]) ).
fof(f_195_2,plain,
! [U_513] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(U_513)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),U_513)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),U_513))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(U_513))) ) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
fof(f_195_3,plain,
( ! [U_515] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(U_515)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),U_515)) )
& ! [U_514] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),U_514))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(U_514))) ) ),
inference(miniscope,[status(thm)],[f_195_2]) ).
cnf(f_195_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),U_514))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(U_514))) ),
inference(clausify,[status(thm)],[f_195_3]) ).
cnf(f_195_5,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),number267125858f_real(U_515)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(pls)),U_515)) ),
inference(clausify,[status(thm)],[f_195_3]) ).
fof(f_196_1,plain,
! [W_1,Y_2,X_2,Z_1] :
( ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(W_1),Y_2)),hAPP_int_int(times_times_int(X_2),Z_1)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(W_1),Z_1)),hAPP_int_int(times_times_int(X_2),Y_2))
| ( Y_2 != Z_1
& W_1 != X_2 ) )
& ( Y_2 = Z_1
| W_1 = X_2
| hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(W_1),Y_2)),hAPP_int_int(times_times_int(X_2),Z_1)) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(W_1),Z_1)),hAPP_int_int(times_times_int(X_2),Y_2)) ) )
| ~ is_int(Z_1)
| ~ is_int(X_2)
| ~ is_int(Y_2)
| ~ is_int(W_1) ),
inference(fof_nnf,[status(thm)],[fact_170_crossproduct__eq]) ).
fof(f_196_2,plain,
! [U_519,U_518,U_517,U_516] :
( ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_519),U_518)),hAPP_int_int(times_times_int(U_517),U_516)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_519),U_516)),hAPP_int_int(times_times_int(U_517),U_518))
| ( U_518 != U_516
& U_519 != U_517 ) )
& ( U_518 = U_516
| U_519 = U_517
| hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_519),U_518)),hAPP_int_int(times_times_int(U_517),U_516)) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_519),U_516)),hAPP_int_int(times_times_int(U_517),U_518)) ) )
| ~ is_int(U_516)
| ~ is_int(U_517)
| ~ is_int(U_518)
| ~ is_int(U_519) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
cnf(f_196_3,plain,
( U_518 = U_516
| U_519 = U_517
| hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_519),U_518)),hAPP_int_int(times_times_int(U_517),U_516)) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_519),U_516)),hAPP_int_int(times_times_int(U_517),U_518))
| ~ is_int(U_516)
| ~ is_int(U_517)
| ~ is_int(U_518)
| ~ is_int(U_519) ),
inference(clausify,[status(thm)],[f_196_2]) ).
cnf(f_196_4,plain,
( U_519 != U_517
| hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_519),U_518)),hAPP_int_int(times_times_int(U_517),U_516)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_519),U_516)),hAPP_int_int(times_times_int(U_517),U_518))
| ~ is_int(U_516)
| ~ is_int(U_517)
| ~ is_int(U_518)
| ~ is_int(U_519) ),
inference(clausify,[status(thm)],[f_196_2]) ).
cnf(f_196_5,plain,
( U_518 != U_516
| hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_519),U_518)),hAPP_int_int(times_times_int(U_517),U_516)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_519),U_516)),hAPP_int_int(times_times_int(U_517),U_518))
| ~ is_int(U_516)
| ~ is_int(U_517)
| ~ is_int(U_518)
| ~ is_int(U_519) ),
inference(clausify,[status(thm)],[f_196_2]) ).
fof(f_197_1,plain,
! [W_1,Y_2,X_2,Z_1] :
( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(W_1),Y_2)),hAPP_nat_nat(times_times_nat(X_2),Z_1)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(W_1),Z_1)),hAPP_nat_nat(times_times_nat(X_2),Y_2))
| ( Y_2 != Z_1
& W_1 != X_2 ) )
& ( Y_2 = Z_1
| W_1 = X_2
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(W_1),Y_2)),hAPP_nat_nat(times_times_nat(X_2),Z_1)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(W_1),Z_1)),hAPP_nat_nat(times_times_nat(X_2),Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_171_crossproduct__eq]) ).
fof(f_197_2,plain,
! [U_523,U_522,U_521,U_520] :
( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_523),U_522)),hAPP_nat_nat(times_times_nat(U_521),U_520)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_523),U_520)),hAPP_nat_nat(times_times_nat(U_521),U_522))
| ( U_522 != U_520
& U_523 != U_521 ) )
& ( U_522 = U_520
| U_523 = U_521
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_523),U_522)),hAPP_nat_nat(times_times_nat(U_521),U_520)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_523),U_520)),hAPP_nat_nat(times_times_nat(U_521),U_522)) ) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
fof(f_197_3,plain,
( ! [U_531,U_529,U_527,U_525] :
( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_531),U_529)),hAPP_nat_nat(times_times_nat(U_527),U_525)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_531),U_525)),hAPP_nat_nat(times_times_nat(U_527),U_529))
| ( U_529 != U_525
& U_531 != U_527 ) )
& ! [U_530,U_528,U_526,U_524] :
( U_528 = U_524
| U_530 = U_526
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_530),U_528)),hAPP_nat_nat(times_times_nat(U_526),U_524)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_530),U_524)),hAPP_nat_nat(times_times_nat(U_526),U_528)) ) ),
inference(miniscope,[status(thm)],[f_197_2]) ).
cnf(f_197_4,plain,
( U_528 = U_524
| U_530 = U_526
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_530),U_528)),hAPP_nat_nat(times_times_nat(U_526),U_524)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_530),U_524)),hAPP_nat_nat(times_times_nat(U_526),U_528)) ),
inference(clausify,[status(thm)],[f_197_3]) ).
cnf(f_197_5,plain,
( U_531 != U_527
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_531),U_529)),hAPP_nat_nat(times_times_nat(U_527),U_525)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_531),U_525)),hAPP_nat_nat(times_times_nat(U_527),U_529)) ),
inference(clausify,[status(thm)],[f_197_3]) ).
cnf(f_197_6,plain,
( U_529 != U_525
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_531),U_529)),hAPP_nat_nat(times_times_nat(U_527),U_525)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_531),U_525)),hAPP_nat_nat(times_times_nat(U_527),U_529)) ),
inference(clausify,[status(thm)],[f_197_3]) ).
fof(f_198_1,plain,
! [W_1,Y_2,X_2,Z_1] :
( ( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(W_1),Y_2)),hAPP_real_real(times_times_real(X_2),Z_1)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(W_1),Z_1)),hAPP_real_real(times_times_real(X_2),Y_2))
| ( Y_2 != Z_1
& W_1 != X_2 ) )
& ( Y_2 = Z_1
| W_1 = X_2
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(W_1),Y_2)),hAPP_real_real(times_times_real(X_2),Z_1)) != hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(W_1),Z_1)),hAPP_real_real(times_times_real(X_2),Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_172_crossproduct__eq]) ).
fof(f_198_2,plain,
! [U_535,U_534,U_533,U_532] :
( ( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_535),U_534)),hAPP_real_real(times_times_real(U_533),U_532)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_535),U_532)),hAPP_real_real(times_times_real(U_533),U_534))
| ( U_534 != U_532
& U_535 != U_533 ) )
& ( U_534 = U_532
| U_535 = U_533
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_535),U_534)),hAPP_real_real(times_times_real(U_533),U_532)) != hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_535),U_532)),hAPP_real_real(times_times_real(U_533),U_534)) ) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
fof(f_198_3,plain,
( ! [U_543,U_541,U_539,U_537] :
( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_543),U_541)),hAPP_real_real(times_times_real(U_539),U_537)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_543),U_537)),hAPP_real_real(times_times_real(U_539),U_541))
| ( U_541 != U_537
& U_543 != U_539 ) )
& ! [U_542,U_540,U_538,U_536] :
( U_540 = U_536
| U_542 = U_538
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_542),U_540)),hAPP_real_real(times_times_real(U_538),U_536)) != hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_542),U_536)),hAPP_real_real(times_times_real(U_538),U_540)) ) ),
inference(miniscope,[status(thm)],[f_198_2]) ).
cnf(f_198_4,plain,
( U_540 = U_536
| U_542 = U_538
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_542),U_540)),hAPP_real_real(times_times_real(U_538),U_536)) != hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_542),U_536)),hAPP_real_real(times_times_real(U_538),U_540)) ),
inference(clausify,[status(thm)],[f_198_3]) ).
cnf(f_198_5,plain,
( U_543 != U_539
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_543),U_541)),hAPP_real_real(times_times_real(U_539),U_537)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_543),U_537)),hAPP_real_real(times_times_real(U_539),U_541)) ),
inference(clausify,[status(thm)],[f_198_3]) ).
cnf(f_198_6,plain,
( U_541 != U_537
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_543),U_541)),hAPP_real_real(times_times_real(U_539),U_537)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_543),U_537)),hAPP_real_real(times_times_real(U_539),U_541)) ),
inference(clausify,[status(thm)],[f_198_3]) ).
fof(f_199_1,plain,
! [A_102,M_13,B_59] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_102),M_13)),hAPP_int_int(times_times_int(B_59),M_13)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_102),B_59)),M_13),
inference(fof_nnf,[status(thm)],[fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J]) ).
fof(f_199_2,plain,
! [U_546,U_545,U_544] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_546),U_545)),hAPP_int_int(times_times_int(U_544),U_545)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(U_546),U_544)),U_545),
inference(variable_rename,[status(thm)],[f_199_1]) ).
cnf(f_199_3,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_546),U_545)),hAPP_int_int(times_times_int(U_544),U_545)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(U_546),U_544)),U_545),
inference(clausify,[status(thm)],[f_199_2]) ).
fof(f_200_1,plain,
! [A_102,M_13,B_59] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_102),M_13)),hAPP_nat_nat(times_times_nat(B_59),M_13)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_102),B_59)),M_13),
inference(fof_nnf,[status(thm)],[fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J]) ).
fof(f_200_2,plain,
! [U_549,U_548,U_547] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_549),U_548)),hAPP_nat_nat(times_times_nat(U_547),U_548)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_549),U_547)),U_548),
inference(variable_rename,[status(thm)],[f_200_1]) ).
cnf(f_200_3,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_549),U_548)),hAPP_nat_nat(times_times_nat(U_547),U_548)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_549),U_547)),U_548),
inference(clausify,[status(thm)],[f_200_2]) ).
fof(f_201_1,plain,
! [A_102,M_13,B_59] : hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_102),M_13)),hAPP_real_real(times_times_real(B_59),M_13)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_102),B_59)),M_13),
inference(fof_nnf,[status(thm)],[fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J]) ).
fof(f_201_2,plain,
! [U_552,U_551,U_550] : hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_552),U_551)),hAPP_real_real(times_times_real(U_550),U_551)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(U_552),U_550)),U_551),
inference(variable_rename,[status(thm)],[f_201_1]) ).
cnf(f_201_3,plain,
hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_552),U_551)),hAPP_real_real(times_times_real(U_550),U_551)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(U_552),U_550)),U_551),
inference(clausify,[status(thm)],[f_201_2]) ).
fof(f_202_1,plain,
! [A_101,B_58,C_29] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_101),B_58)),C_29) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_101),C_29)),hAPP_int_int(times_times_int(B_58),C_29)),
inference(fof_nnf,[status(thm)],[fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J]) ).
fof(f_202_2,plain,
! [U_555,U_554,U_553] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(U_555),U_554)),U_553) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_555),U_553)),hAPP_int_int(times_times_int(U_554),U_553)),
inference(variable_rename,[status(thm)],[f_202_1]) ).
cnf(f_202_3,plain,
hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(U_555),U_554)),U_553) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_555),U_553)),hAPP_int_int(times_times_int(U_554),U_553)),
inference(clausify,[status(thm)],[f_202_2]) ).
fof(f_203_1,plain,
! [A_101,B_58,C_29] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_101),B_58)),C_29) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_101),C_29)),hAPP_nat_nat(times_times_nat(B_58),C_29)),
inference(fof_nnf,[status(thm)],[fact_177_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J]) ).
fof(f_203_2,plain,
! [U_558,U_557,U_556] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_558),U_557)),U_556) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_558),U_556)),hAPP_nat_nat(times_times_nat(U_557),U_556)),
inference(variable_rename,[status(thm)],[f_203_1]) ).
cnf(f_203_3,plain,
hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_558),U_557)),U_556) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_558),U_556)),hAPP_nat_nat(times_times_nat(U_557),U_556)),
inference(clausify,[status(thm)],[f_203_2]) ).
fof(f_204_1,plain,
! [A_101,B_58,C_29] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_101),B_58)),C_29) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_101),C_29)),hAPP_real_real(times_times_real(B_58),C_29)),
inference(fof_nnf,[status(thm)],[fact_178_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J]) ).
fof(f_204_2,plain,
! [U_561,U_560,U_559] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(U_561),U_560)),U_559) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_561),U_559)),hAPP_real_real(times_times_real(U_560),U_559)),
inference(variable_rename,[status(thm)],[f_204_1]) ).
cnf(f_204_3,plain,
hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(U_561),U_560)),U_559) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_561),U_559)),hAPP_real_real(times_times_real(U_560),U_559)),
inference(clausify,[status(thm)],[f_204_2]) ).
fof(f_205_1,plain,
! [C_2,D,A_2,B_2] :
( ( ( ( C_2 != D
& A_2 != B_2 )
| hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_2),C_2)),hAPP_int_int(times_times_int(B_2),D)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_2),D)),hAPP_int_int(times_times_int(B_2),C_2)) )
& ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_2),C_2)),hAPP_int_int(times_times_int(B_2),D)) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_2),D)),hAPP_int_int(times_times_int(B_2),C_2))
| C_2 = D
| A_2 = B_2 ) )
| ~ is_int(B_2)
| ~ is_int(A_2)
| ~ is_int(D)
| ~ is_int(C_2) ),
inference(fof_nnf,[status(thm)],[fact_179_crossproduct__noteq]) ).
fof(f_205_2,plain,
! [U_565,U_564,U_563,U_562] :
( ( ( ( U_565 != U_564
& U_563 != U_562 )
| hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_563),U_565)),hAPP_int_int(times_times_int(U_562),U_564)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_563),U_564)),hAPP_int_int(times_times_int(U_562),U_565)) )
& ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_563),U_565)),hAPP_int_int(times_times_int(U_562),U_564)) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_563),U_564)),hAPP_int_int(times_times_int(U_562),U_565))
| U_565 = U_564
| U_563 = U_562 ) )
| ~ is_int(U_562)
| ~ is_int(U_563)
| ~ is_int(U_564)
| ~ is_int(U_565) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
cnf(f_205_3,plain,
( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_563),U_565)),hAPP_int_int(times_times_int(U_562),U_564)) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_563),U_564)),hAPP_int_int(times_times_int(U_562),U_565))
| U_565 = U_564
| U_563 = U_562
| ~ is_int(U_562)
| ~ is_int(U_563)
| ~ is_int(U_564)
| ~ is_int(U_565) ),
inference(clausify,[status(thm)],[f_205_2]) ).
cnf(f_205_4,plain,
( U_563 != U_562
| hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_563),U_565)),hAPP_int_int(times_times_int(U_562),U_564)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_563),U_564)),hAPP_int_int(times_times_int(U_562),U_565))
| ~ is_int(U_562)
| ~ is_int(U_563)
| ~ is_int(U_564)
| ~ is_int(U_565) ),
inference(clausify,[status(thm)],[f_205_2]) ).
cnf(f_205_5,plain,
( U_565 != U_564
| hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_563),U_565)),hAPP_int_int(times_times_int(U_562),U_564)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_563),U_564)),hAPP_int_int(times_times_int(U_562),U_565))
| ~ is_int(U_562)
| ~ is_int(U_563)
| ~ is_int(U_564)
| ~ is_int(U_565) ),
inference(clausify,[status(thm)],[f_205_2]) ).
fof(f_206_1,plain,
! [C_2,D,A_2,B_2] :
( ( ( C_2 != D
& A_2 != B_2 )
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_2),C_2)),hAPP_nat_nat(times_times_nat(B_2),D)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_2),D)),hAPP_nat_nat(times_times_nat(B_2),C_2)) )
& ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_2),C_2)),hAPP_nat_nat(times_times_nat(B_2),D)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_2),D)),hAPP_nat_nat(times_times_nat(B_2),C_2))
| C_2 = D
| A_2 = B_2 ) ),
inference(fof_nnf,[status(thm)],[fact_180_crossproduct__noteq]) ).
fof(f_206_2,plain,
! [U_569,U_568,U_567,U_566] :
( ( ( U_569 != U_568
& U_567 != U_566 )
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_567),U_569)),hAPP_nat_nat(times_times_nat(U_566),U_568)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_567),U_568)),hAPP_nat_nat(times_times_nat(U_566),U_569)) )
& ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_567),U_569)),hAPP_nat_nat(times_times_nat(U_566),U_568)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_567),U_568)),hAPP_nat_nat(times_times_nat(U_566),U_569))
| U_569 = U_568
| U_567 = U_566 ) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
fof(f_206_3,plain,
( ! [U_577,U_575,U_573,U_571] :
( ( U_577 != U_575
& U_573 != U_571 )
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_573),U_577)),hAPP_nat_nat(times_times_nat(U_571),U_575)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_573),U_575)),hAPP_nat_nat(times_times_nat(U_571),U_577)) )
& ! [U_576,U_574,U_572,U_570] :
( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_572),U_576)),hAPP_nat_nat(times_times_nat(U_570),U_574)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_572),U_574)),hAPP_nat_nat(times_times_nat(U_570),U_576))
| U_576 = U_574
| U_572 = U_570 ) ),
inference(miniscope,[status(thm)],[f_206_2]) ).
cnf(f_206_4,plain,
( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_572),U_576)),hAPP_nat_nat(times_times_nat(U_570),U_574)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_572),U_574)),hAPP_nat_nat(times_times_nat(U_570),U_576))
| U_576 = U_574
| U_572 = U_570 ),
inference(clausify,[status(thm)],[f_206_3]) ).
cnf(f_206_5,plain,
( U_573 != U_571
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_573),U_577)),hAPP_nat_nat(times_times_nat(U_571),U_575)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_573),U_575)),hAPP_nat_nat(times_times_nat(U_571),U_577)) ),
inference(clausify,[status(thm)],[f_206_3]) ).
cnf(f_206_6,plain,
( U_577 != U_575
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_573),U_577)),hAPP_nat_nat(times_times_nat(U_571),U_575)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_573),U_575)),hAPP_nat_nat(times_times_nat(U_571),U_577)) ),
inference(clausify,[status(thm)],[f_206_3]) ).
fof(f_207_1,plain,
! [C_2,D,A_2,B_2] :
( ( ( C_2 != D
& A_2 != B_2 )
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_2),C_2)),hAPP_real_real(times_times_real(B_2),D)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_2),D)),hAPP_real_real(times_times_real(B_2),C_2)) )
& ( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_2),C_2)),hAPP_real_real(times_times_real(B_2),D)) != hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_2),D)),hAPP_real_real(times_times_real(B_2),C_2))
| C_2 = D
| A_2 = B_2 ) ),
inference(fof_nnf,[status(thm)],[fact_181_crossproduct__noteq]) ).
fof(f_207_2,plain,
! [U_581,U_580,U_579,U_578] :
( ( ( U_581 != U_580
& U_579 != U_578 )
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_579),U_581)),hAPP_real_real(times_times_real(U_578),U_580)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_579),U_580)),hAPP_real_real(times_times_real(U_578),U_581)) )
& ( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_579),U_581)),hAPP_real_real(times_times_real(U_578),U_580)) != hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_579),U_580)),hAPP_real_real(times_times_real(U_578),U_581))
| U_581 = U_580
| U_579 = U_578 ) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
fof(f_207_3,plain,
( ! [U_589,U_587,U_585,U_583] :
( ( U_589 != U_587
& U_585 != U_583 )
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_585),U_589)),hAPP_real_real(times_times_real(U_583),U_587)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_585),U_587)),hAPP_real_real(times_times_real(U_583),U_589)) )
& ! [U_588,U_586,U_584,U_582] :
( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_584),U_588)),hAPP_real_real(times_times_real(U_582),U_586)) != hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_584),U_586)),hAPP_real_real(times_times_real(U_582),U_588))
| U_588 = U_586
| U_584 = U_582 ) ),
inference(miniscope,[status(thm)],[f_207_2]) ).
cnf(f_207_4,plain,
( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_584),U_588)),hAPP_real_real(times_times_real(U_582),U_586)) != hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_584),U_586)),hAPP_real_real(times_times_real(U_582),U_588))
| U_588 = U_586
| U_584 = U_582 ),
inference(clausify,[status(thm)],[f_207_3]) ).
cnf(f_207_5,plain,
( U_585 != U_583
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_585),U_589)),hAPP_real_real(times_times_real(U_583),U_587)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_585),U_587)),hAPP_real_real(times_times_real(U_583),U_589)) ),
inference(clausify,[status(thm)],[f_207_3]) ).
cnf(f_207_6,plain,
( U_589 != U_587
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_585),U_589)),hAPP_real_real(times_times_real(U_583),U_587)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_585),U_587)),hAPP_real_real(times_times_real(U_583),U_589)) ),
inference(clausify,[status(thm)],[f_207_3]) ).
fof(f_208_1,plain,
! [X_21,Y_18,Z_9] : hAPP_int_int(times_times_int(X_21),hAPP_int_int(plus_plus_int(Y_18),Z_9)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X_21),Y_18)),hAPP_int_int(times_times_int(X_21),Z_9)),
inference(fof_nnf,[status(thm)],[fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J]) ).
fof(f_208_2,plain,
! [U_592,U_591,U_590] : hAPP_int_int(times_times_int(U_592),hAPP_int_int(plus_plus_int(U_591),U_590)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_592),U_591)),hAPP_int_int(times_times_int(U_592),U_590)),
inference(variable_rename,[status(thm)],[f_208_1]) ).
cnf(f_208_3,plain,
hAPP_int_int(times_times_int(U_592),hAPP_int_int(plus_plus_int(U_591),U_590)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_592),U_591)),hAPP_int_int(times_times_int(U_592),U_590)),
inference(clausify,[status(thm)],[f_208_2]) ).
fof(f_209_1,plain,
! [X_21,Y_18,Z_9] : hAPP_nat_nat(times_times_nat(X_21),hAPP_nat_nat(plus_plus_nat(Y_18),Z_9)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(X_21),Y_18)),hAPP_nat_nat(times_times_nat(X_21),Z_9)),
inference(fof_nnf,[status(thm)],[fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J]) ).
fof(f_209_2,plain,
! [U_595,U_594,U_593] : hAPP_nat_nat(times_times_nat(U_595),hAPP_nat_nat(plus_plus_nat(U_594),U_593)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_595),U_594)),hAPP_nat_nat(times_times_nat(U_595),U_593)),
inference(variable_rename,[status(thm)],[f_209_1]) ).
cnf(f_209_3,plain,
hAPP_nat_nat(times_times_nat(U_595),hAPP_nat_nat(plus_plus_nat(U_594),U_593)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_595),U_594)),hAPP_nat_nat(times_times_nat(U_595),U_593)),
inference(clausify,[status(thm)],[f_209_2]) ).
fof(f_210_1,plain,
! [X_21,Y_18,Z_9] : hAPP_real_real(times_times_real(X_21),hAPP_real_real(plus_plus_real(Y_18),Z_9)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X_21),Y_18)),hAPP_real_real(times_times_real(X_21),Z_9)),
inference(fof_nnf,[status(thm)],[fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J]) ).
fof(f_210_2,plain,
! [U_598,U_597,U_596] : hAPP_real_real(times_times_real(U_598),hAPP_real_real(plus_plus_real(U_597),U_596)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_598),U_597)),hAPP_real_real(times_times_real(U_598),U_596)),
inference(variable_rename,[status(thm)],[f_210_1]) ).
cnf(f_210_3,plain,
hAPP_real_real(times_times_real(U_598),hAPP_real_real(plus_plus_real(U_597),U_596)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_598),U_597)),hAPP_real_real(times_times_real(U_598),U_596)),
inference(clausify,[status(thm)],[f_210_2]) ).
fof(f_211_1,plain,
! [A_100] :
( hAPP_int_int(times_times_int(A_100),one_one_int) = A_100
| ~ is_int(A_100) ),
inference(fof_nnf,[status(thm)],[fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J]) ).
fof(f_211_2,plain,
! [U_599] :
( hAPP_int_int(times_times_int(U_599),one_one_int) = U_599
| ~ is_int(U_599) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
cnf(f_211_3,plain,
( hAPP_int_int(times_times_int(U_599),one_one_int) = U_599
| ~ is_int(U_599) ),
inference(clausify,[status(thm)],[f_211_2]) ).
fof(f_212_1,plain,
! [A_100] : hAPP_nat_nat(times_times_nat(A_100),one_one_nat) = A_100,
inference(fof_nnf,[status(thm)],[fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J]) ).
fof(f_212_2,plain,
! [U_600] : hAPP_nat_nat(times_times_nat(U_600),one_one_nat) = U_600,
inference(variable_rename,[status(thm)],[f_212_1]) ).
cnf(f_212_3,plain,
hAPP_nat_nat(times_times_nat(U_600),one_one_nat) = U_600,
inference(clausify,[status(thm)],[f_212_2]) ).
fof(f_213_1,plain,
! [A_100] : hAPP_real_real(times_times_real(A_100),one_one_real) = A_100,
inference(fof_nnf,[status(thm)],[fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J]) ).
fof(f_213_2,plain,
! [U_601] : hAPP_real_real(times_times_real(U_601),one_one_real) = U_601,
inference(variable_rename,[status(thm)],[f_213_1]) ).
cnf(f_213_3,plain,
hAPP_real_real(times_times_real(U_601),one_one_real) = U_601,
inference(clausify,[status(thm)],[f_213_2]) ).
fof(f_214_1,plain,
! [A_99] :
( hAPP_int_int(times_times_int(one_one_int),A_99) = A_99
| ~ is_int(A_99) ),
inference(fof_nnf,[status(thm)],[fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J]) ).
fof(f_214_2,plain,
! [U_602] :
( hAPP_int_int(times_times_int(one_one_int),U_602) = U_602
| ~ is_int(U_602) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
cnf(f_214_3,plain,
( hAPP_int_int(times_times_int(one_one_int),U_602) = U_602
| ~ is_int(U_602) ),
inference(clausify,[status(thm)],[f_214_2]) ).
fof(f_215_1,plain,
! [A_99] : hAPP_nat_nat(times_times_nat(one_one_nat),A_99) = A_99,
inference(fof_nnf,[status(thm)],[fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J]) ).
fof(f_215_2,plain,
! [U_603] : hAPP_nat_nat(times_times_nat(one_one_nat),U_603) = U_603,
inference(variable_rename,[status(thm)],[f_215_1]) ).
cnf(f_215_3,plain,
hAPP_nat_nat(times_times_nat(one_one_nat),U_603) = U_603,
inference(clausify,[status(thm)],[f_215_2]) ).
fof(f_216_1,plain,
! [A_99] : hAPP_real_real(times_times_real(one_one_real),A_99) = A_99,
inference(fof_nnf,[status(thm)],[fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J]) ).
fof(f_216_2,plain,
! [U_604] : hAPP_real_real(times_times_real(one_one_real),U_604) = U_604,
inference(variable_rename,[status(thm)],[f_216_1]) ).
cnf(f_216_3,plain,
hAPP_real_real(times_times_real(one_one_real),U_604) = U_604,
inference(clausify,[status(thm)],[f_216_2]) ).
fof(f_217_1,plain,
! [X_20,Y_17,Q_5] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(X_20),Y_17)),Q_5) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X_20),Q_5)),hAPP_nat_int(power_power_int(Y_17),Q_5)),
inference(fof_nnf,[status(thm)],[fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J]) ).
fof(f_217_2,plain,
! [U_607,U_606,U_605] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(U_607),U_606)),U_605) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(U_607),U_605)),hAPP_nat_int(power_power_int(U_606),U_605)),
inference(variable_rename,[status(thm)],[f_217_1]) ).
cnf(f_217_3,plain,
hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(U_607),U_606)),U_605) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(U_607),U_605)),hAPP_nat_int(power_power_int(U_606),U_605)),
inference(clausify,[status(thm)],[f_217_2]) ).
fof(f_218_1,plain,
! [X_20,Y_17,Q_5] : hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(X_20),Y_17)),Q_5) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X_20),Q_5)),hAPP_nat_real(power_power_real(Y_17),Q_5)),
inference(fof_nnf,[status(thm)],[fact_192_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J]) ).
fof(f_218_2,plain,
! [U_610,U_609,U_608] : hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(U_610),U_609)),U_608) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(U_610),U_608)),hAPP_nat_real(power_power_real(U_609),U_608)),
inference(variable_rename,[status(thm)],[f_218_1]) ).
cnf(f_218_3,plain,
hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(U_610),U_609)),U_608) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(U_610),U_608)),hAPP_nat_real(power_power_real(U_609),U_608)),
inference(clausify,[status(thm)],[f_218_2]) ).
fof(f_219_1,plain,
! [X_20,Y_17,Q_5] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(X_20),Y_17)),Q_5) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X_20),Q_5)),hAPP_nat_nat(power_power_nat(Y_17),Q_5)),
inference(fof_nnf,[status(thm)],[fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J]) ).
fof(f_219_2,plain,
! [U_613,U_612,U_611] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(U_613),U_612)),U_611) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(U_613),U_611)),hAPP_nat_nat(power_power_nat(U_612),U_611)),
inference(variable_rename,[status(thm)],[f_219_1]) ).
cnf(f_219_3,plain,
hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(U_613),U_612)),U_611) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(U_613),U_611)),hAPP_nat_nat(power_power_nat(U_612),U_611)),
inference(clausify,[status(thm)],[f_219_2]) ).
fof(f_220_1,plain,
! [K_1] : bit1(K_1) != pls,
inference(fof_nnf,[status(thm)],[fact_194_rel__simps_I46_J]) ).
fof(f_220_2,plain,
! [U_614] : bit1(U_614) != pls,
inference(variable_rename,[status(thm)],[f_220_1]) ).
cnf(f_220_3,plain,
bit1(U_614) != pls,
inference(clausify,[status(thm)],[f_220_2]) ).
fof(f_221_1,plain,
! [L] : pls != bit1(L),
inference(fof_nnf,[status(thm)],[fact_195_rel__simps_I39_J]) ).
fof(f_221_2,plain,
! [U_615] : pls != bit1(U_615),
inference(variable_rename,[status(thm)],[f_221_1]) ).
cnf(f_221_3,plain,
pls != bit1(U_615),
inference(clausify,[status(thm)],[f_221_2]) ).
fof(f_222_1,plain,
! [K_1,L] : bit1(K_1) != bit0(L),
inference(fof_nnf,[status(thm)],[fact_196_rel__simps_I50_J]) ).
fof(f_222_2,plain,
! [U_617,U_616] : bit1(U_617) != bit0(U_616),
inference(variable_rename,[status(thm)],[f_222_1]) ).
cnf(f_222_3,plain,
bit1(U_617) != bit0(U_616),
inference(clausify,[status(thm)],[f_222_2]) ).
fof(f_223_1,plain,
! [K_1,L] : bit0(K_1) != bit1(L),
inference(fof_nnf,[status(thm)],[fact_197_rel__simps_I49_J]) ).
fof(f_223_2,plain,
! [U_619,U_618] : bit0(U_619) != bit1(U_618),
inference(variable_rename,[status(thm)],[f_223_1]) ).
cnf(f_223_3,plain,
bit0(U_619) != bit1(U_618),
inference(clausify,[status(thm)],[f_223_2]) ).
fof(f_224_1,plain,
! [K] :
( ( ( bit0(K) = pls
| K != pls )
& ( K = pls
| bit0(K) != pls ) )
| ~ is_int(K) ),
inference(fof_nnf,[status(thm)],[fact_198_rel__simps_I44_J]) ).
fof(f_224_2,plain,
! [U_620] :
( ( ( bit0(U_620) = pls
| U_620 != pls )
& ( U_620 = pls
| bit0(U_620) != pls ) )
| ~ is_int(U_620) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
cnf(f_224_3,plain,
( U_620 = pls
| bit0(U_620) != pls
| ~ is_int(U_620) ),
inference(clausify,[status(thm)],[f_224_2]) ).
cnf(f_224_4,plain,
( bit0(U_620) = pls
| U_620 != pls
| ~ is_int(U_620) ),
inference(clausify,[status(thm)],[f_224_2]) ).
fof(f_225_1,plain,
! [L_1] :
( ( ( pls = bit0(L_1)
| pls != L_1 )
& ( pls = L_1
| pls != bit0(L_1) ) )
| ~ is_int(L_1) ),
inference(fof_nnf,[status(thm)],[fact_199_rel__simps_I38_J]) ).
fof(f_225_2,plain,
! [U_621] :
( ( ( pls = bit0(U_621)
| pls != U_621 )
& ( pls = U_621
| pls != bit0(U_621) ) )
| ~ is_int(U_621) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
cnf(f_225_3,plain,
( pls = U_621
| pls != bit0(U_621)
| ~ is_int(U_621) ),
inference(clausify,[status(thm)],[f_225_2]) ).
cnf(f_225_4,plain,
( pls = bit0(U_621)
| pls != U_621
| ~ is_int(U_621) ),
inference(clausify,[status(thm)],[f_225_2]) ).
fof(f_226_1,plain,
bit0(pls) = pls,
inference(fof_nnf,[status(thm)],[fact_200_Bit0__Pls]) ).
cnf(f_226_2,plain,
bit0(pls) = pls,
inference(clausify,[status(thm)],[f_226_1]) ).
fof(f_227_1,plain,
! [W] : hAPP_int_int(times_times_int(pls),W) = pls,
inference(fof_nnf,[status(thm)],[fact_201_mult__Pls]) ).
fof(f_227_2,plain,
! [U_622] : hAPP_int_int(times_times_int(pls),U_622) = pls,
inference(variable_rename,[status(thm)],[f_227_1]) ).
cnf(f_227_3,plain,
hAPP_int_int(times_times_int(pls),U_622) = pls,
inference(clausify,[status(thm)],[f_227_2]) ).
fof(f_228_1,plain,
! [K_1,L] : hAPP_int_int(times_times_int(bit0(K_1)),L) = bit0(hAPP_int_int(times_times_int(K_1),L)),
inference(fof_nnf,[status(thm)],[fact_202_mult__Bit0]) ).
fof(f_228_2,plain,
! [U_624,U_623] : hAPP_int_int(times_times_int(bit0(U_624)),U_623) = bit0(hAPP_int_int(times_times_int(U_624),U_623)),
inference(variable_rename,[status(thm)],[f_228_1]) ).
cnf(f_228_3,plain,
hAPP_int_int(times_times_int(bit0(U_624)),U_623) = bit0(hAPP_int_int(times_times_int(U_624),U_623)),
inference(clausify,[status(thm)],[f_228_2]) ).
fof(f_229_1,plain,
! [K_1] :
( hAPP_int_int(plus_plus_int(K_1),pls) = K_1
| ~ is_int(K_1) ),
inference(fof_nnf,[status(thm)],[fact_203_add__Pls__right]) ).
fof(f_229_2,plain,
! [U_625] :
( hAPP_int_int(plus_plus_int(U_625),pls) = U_625
| ~ is_int(U_625) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
cnf(f_229_3,plain,
( hAPP_int_int(plus_plus_int(U_625),pls) = U_625
| ~ is_int(U_625) ),
inference(clausify,[status(thm)],[f_229_2]) ).
fof(f_230_1,plain,
! [K_1] :
( hAPP_int_int(plus_plus_int(pls),K_1) = K_1
| ~ is_int(K_1) ),
inference(fof_nnf,[status(thm)],[fact_204_add__Pls]) ).
fof(f_230_2,plain,
! [U_626] :
( hAPP_int_int(plus_plus_int(pls),U_626) = U_626
| ~ is_int(U_626) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
cnf(f_230_3,plain,
( hAPP_int_int(plus_plus_int(pls),U_626) = U_626
| ~ is_int(U_626) ),
inference(clausify,[status(thm)],[f_230_2]) ).
fof(f_231_1,plain,
! [K_1,L] : hAPP_int_int(plus_plus_int(bit0(K_1)),bit0(L)) = bit0(hAPP_int_int(plus_plus_int(K_1),L)),
inference(fof_nnf,[status(thm)],[fact_205_add__Bit0__Bit0]) ).
fof(f_231_2,plain,
! [U_628,U_627] : hAPP_int_int(plus_plus_int(bit0(U_628)),bit0(U_627)) = bit0(hAPP_int_int(plus_plus_int(U_628),U_627)),
inference(variable_rename,[status(thm)],[f_231_1]) ).
cnf(f_231_3,plain,
hAPP_int_int(plus_plus_int(bit0(U_628)),bit0(U_627)) = bit0(hAPP_int_int(plus_plus_int(U_628),U_627)),
inference(clausify,[status(thm)],[f_231_2]) ).
fof(f_232_1,plain,
! [K_1] : bit0(K_1) = hAPP_int_int(plus_plus_int(K_1),K_1),
inference(fof_nnf,[status(thm)],[fact_206_Bit0__def]) ).
fof(f_232_2,plain,
! [U_629] : bit0(U_629) = hAPP_int_int(plus_plus_int(U_629),U_629),
inference(variable_rename,[status(thm)],[f_232_1]) ).
cnf(f_232_3,plain,
bit0(U_629) = hAPP_int_int(plus_plus_int(U_629),U_629),
inference(clausify,[status(thm)],[f_232_2]) ).
fof(f_233_1,plain,
! [Z] :
( hAPP_int_int(times_times_int(Z),one_one_int) = Z
| ~ is_int(Z) ),
inference(fof_nnf,[status(thm)],[fact_207_zmult__1__right]) ).
fof(f_233_2,plain,
! [U_630] :
( hAPP_int_int(times_times_int(U_630),one_one_int) = U_630
| ~ is_int(U_630) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
cnf(f_233_3,plain,
( hAPP_int_int(times_times_int(U_630),one_one_int) = U_630
| ~ is_int(U_630) ),
inference(clausify,[status(thm)],[f_233_2]) ).
fof(f_234_1,plain,
! [Z] :
( hAPP_int_int(times_times_int(one_one_int),Z) = Z
| ~ is_int(Z) ),
inference(fof_nnf,[status(thm)],[fact_208_zmult__1]) ).
fof(f_234_2,plain,
! [U_631] :
( hAPP_int_int(times_times_int(one_one_int),U_631) = U_631
| ~ is_int(U_631) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
cnf(f_234_3,plain,
( hAPP_int_int(times_times_int(one_one_int),U_631) = U_631
| ~ is_int(U_631) ),
inference(clausify,[status(thm)],[f_234_2]) ).
fof(f_235_1,plain,
! [V,W] : hAPP_int_int(times_times_int(number_number_of_int(V)),number_number_of_int(W)) = number_number_of_int(hAPP_int_int(times_times_int(V),W)),
inference(fof_nnf,[status(thm)],[fact_209_times__numeral__code_I5_J]) ).
fof(f_235_2,plain,
! [U_633,U_632] : hAPP_int_int(times_times_int(number_number_of_int(U_633)),number_number_of_int(U_632)) = number_number_of_int(hAPP_int_int(times_times_int(U_633),U_632)),
inference(variable_rename,[status(thm)],[f_235_1]) ).
cnf(f_235_3,plain,
hAPP_int_int(times_times_int(number_number_of_int(U_633)),number_number_of_int(U_632)) = number_number_of_int(hAPP_int_int(times_times_int(U_633),U_632)),
inference(clausify,[status(thm)],[f_235_2]) ).
fof(f_236_1,plain,
! [Z1,Z2,W] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(Z1),Z2)),W) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(Z1),W)),hAPP_int_int(times_times_int(Z2),W)),
inference(fof_nnf,[status(thm)],[fact_210_zadd__zmult__distrib]) ).
fof(f_236_2,plain,
! [U_636,U_635,U_634] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(U_636),U_635)),U_634) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_636),U_634)),hAPP_int_int(times_times_int(U_635),U_634)),
inference(variable_rename,[status(thm)],[f_236_1]) ).
cnf(f_236_3,plain,
hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(U_636),U_635)),U_634) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_636),U_634)),hAPP_int_int(times_times_int(U_635),U_634)),
inference(clausify,[status(thm)],[f_236_2]) ).
fof(f_237_1,plain,
! [W,Z1,Z2] : hAPP_int_int(times_times_int(W),hAPP_int_int(plus_plus_int(Z1),Z2)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(W),Z1)),hAPP_int_int(times_times_int(W),Z2)),
inference(fof_nnf,[status(thm)],[fact_211_zadd__zmult__distrib2]) ).
fof(f_237_2,plain,
! [U_639,U_638,U_637] : hAPP_int_int(times_times_int(U_639),hAPP_int_int(plus_plus_int(U_638),U_637)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_639),U_638)),hAPP_int_int(times_times_int(U_639),U_637)),
inference(variable_rename,[status(thm)],[f_237_1]) ).
cnf(f_237_3,plain,
hAPP_int_int(times_times_int(U_639),hAPP_int_int(plus_plus_int(U_638),U_637)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_639),U_638)),hAPP_int_int(times_times_int(U_639),U_637)),
inference(clausify,[status(thm)],[f_237_2]) ).
fof(f_238_1,plain,
! [V,W] : hAPP_int_int(plus_plus_int(number_number_of_int(V)),number_number_of_int(W)) = number_number_of_int(hAPP_int_int(plus_plus_int(V),W)),
inference(fof_nnf,[status(thm)],[fact_212_plus__numeral__code_I9_J]) ).
fof(f_238_2,plain,
! [U_641,U_640] : hAPP_int_int(plus_plus_int(number_number_of_int(U_641)),number_number_of_int(U_640)) = number_number_of_int(hAPP_int_int(plus_plus_int(U_641),U_640)),
inference(variable_rename,[status(thm)],[f_238_1]) ).
cnf(f_238_3,plain,
hAPP_int_int(plus_plus_int(number_number_of_int(U_641)),number_number_of_int(U_640)) = number_number_of_int(hAPP_int_int(plus_plus_int(U_641),U_640)),
inference(clausify,[status(thm)],[f_238_2]) ).
fof(f_239_1,plain,
! [V_20,V_19] :
( hAPP_int_int(times_times_int(number_number_of_int(V_19)),number_number_of_int(V_20)) = number_number_of_int(hAPP_int_int(times_times_int(V_19),V_20))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_20))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_19)) ),
inference(fof_nnf,[status(thm)],[fact_213_semiring__mult__number__of]) ).
fof(f_239_2,plain,
! [U_643,U_642] :
( hAPP_int_int(times_times_int(number_number_of_int(U_642)),number_number_of_int(U_643)) = number_number_of_int(hAPP_int_int(times_times_int(U_642),U_643))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_643))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_642)) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
cnf(f_239_3,plain,
( hAPP_int_int(times_times_int(number_number_of_int(U_642)),number_number_of_int(U_643)) = number_number_of_int(hAPP_int_int(times_times_int(U_642),U_643))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_643))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_642)) ),
inference(clausify,[status(thm)],[f_239_2]) ).
fof(f_240_1,plain,
! [V_20,V_19] :
( hAPP_nat_nat(times_times_nat(number_number_of_nat(V_19)),number_number_of_nat(V_20)) = number_number_of_nat(hAPP_int_int(times_times_int(V_19),V_20))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_20))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_19)) ),
inference(fof_nnf,[status(thm)],[fact_214_semiring__mult__number__of]) ).
fof(f_240_2,plain,
! [U_645,U_644] :
( hAPP_nat_nat(times_times_nat(number_number_of_nat(U_644)),number_number_of_nat(U_645)) = number_number_of_nat(hAPP_int_int(times_times_int(U_644),U_645))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_645))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_644)) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
cnf(f_240_3,plain,
( hAPP_nat_nat(times_times_nat(number_number_of_nat(U_644)),number_number_of_nat(U_645)) = number_number_of_nat(hAPP_int_int(times_times_int(U_644),U_645))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_645))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_644)) ),
inference(clausify,[status(thm)],[f_240_2]) ).
fof(f_241_1,plain,
! [V_20,V_19] :
( hAPP_real_real(times_times_real(number267125858f_real(V_19)),number267125858f_real(V_20)) = number267125858f_real(hAPP_int_int(times_times_int(V_19),V_20))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_20))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_19)) ),
inference(fof_nnf,[status(thm)],[fact_215_semiring__mult__number__of]) ).
fof(f_241_2,plain,
! [U_647,U_646] :
( hAPP_real_real(times_times_real(number267125858f_real(U_646)),number267125858f_real(U_647)) = number267125858f_real(hAPP_int_int(times_times_int(U_646),U_647))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_647))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_646)) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
cnf(f_241_3,plain,
( hAPP_real_real(times_times_real(number267125858f_real(U_646)),number267125858f_real(U_647)) = number267125858f_real(hAPP_int_int(times_times_int(U_646),U_647))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_647))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_646)) ),
inference(clausify,[status(thm)],[f_241_2]) ).
fof(f_242_1,plain,
! [V_18,V_17] :
( hAPP_int_int(plus_plus_int(number_number_of_int(V_17)),number_number_of_int(V_18)) = number_number_of_int(hAPP_int_int(plus_plus_int(V_17),V_18))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_18))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_17)) ),
inference(fof_nnf,[status(thm)],[fact_216_semiring__add__number__of]) ).
fof(f_242_2,plain,
! [U_649,U_648] :
( hAPP_int_int(plus_plus_int(number_number_of_int(U_648)),number_number_of_int(U_649)) = number_number_of_int(hAPP_int_int(plus_plus_int(U_648),U_649))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_649))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_648)) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
cnf(f_242_3,plain,
( hAPP_int_int(plus_plus_int(number_number_of_int(U_648)),number_number_of_int(U_649)) = number_number_of_int(hAPP_int_int(plus_plus_int(U_648),U_649))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_649))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_648)) ),
inference(clausify,[status(thm)],[f_242_2]) ).
fof(f_243_1,plain,
! [V_18,V_17] :
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(V_17)),number_number_of_nat(V_18)) = number_number_of_nat(hAPP_int_int(plus_plus_int(V_17),V_18))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_18))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_17)) ),
inference(fof_nnf,[status(thm)],[fact_217_semiring__add__number__of]) ).
fof(f_243_2,plain,
! [U_651,U_650] :
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(U_650)),number_number_of_nat(U_651)) = number_number_of_nat(hAPP_int_int(plus_plus_int(U_650),U_651))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_651))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_650)) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
cnf(f_243_3,plain,
( hAPP_nat_nat(plus_plus_nat(number_number_of_nat(U_650)),number_number_of_nat(U_651)) = number_number_of_nat(hAPP_int_int(plus_plus_int(U_650),U_651))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_651))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_650)) ),
inference(clausify,[status(thm)],[f_243_2]) ).
fof(f_244_1,plain,
! [V_18,V_17] :
( hAPP_real_real(plus_plus_real(number267125858f_real(V_17)),number267125858f_real(V_18)) = number267125858f_real(hAPP_int_int(plus_plus_int(V_17),V_18))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_18))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),V_17)) ),
inference(fof_nnf,[status(thm)],[fact_218_semiring__add__number__of]) ).
fof(f_244_2,plain,
! [U_653,U_652] :
( hAPP_real_real(plus_plus_real(number267125858f_real(U_652)),number267125858f_real(U_653)) = number267125858f_real(hAPP_int_int(plus_plus_int(U_652),U_653))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_653))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_652)) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
cnf(f_244_3,plain,
( hAPP_real_real(plus_plus_real(number267125858f_real(U_652)),number267125858f_real(U_653)) = number267125858f_real(hAPP_int_int(plus_plus_int(U_652),U_653))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_653))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_652)) ),
inference(clausify,[status(thm)],[f_244_2]) ).
fof(f_245_1,plain,
! [X_1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),hAPP_nat_int(power_power_int(X_1),number_number_of_nat(bit0(bit1(pls)))))),
inference(fof_nnf,[status(thm)],[fact_219_power2__ge__self]) ).
fof(f_245_2,plain,
! [U_654] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_654),hAPP_nat_int(power_power_int(U_654),number_number_of_nat(bit0(bit1(pls)))))),
inference(variable_rename,[status(thm)],[f_245_1]) ).
cnf(f_245_3,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_654),hAPP_nat_int(power_power_int(U_654),number_number_of_nat(bit0(bit1(pls)))))),
inference(clausify,[status(thm)],[f_245_2]) ).
fof(f_246_1,plain,
! [A_98,B_57,V_16] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_98),B_57)),number_number_of_int(V_16)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_98),number_number_of_int(V_16))),hAPP_int_int(times_times_int(B_57),number_number_of_int(V_16))),
inference(fof_nnf,[status(thm)],[fact_220_left__distrib__number__of]) ).
fof(f_246_2,plain,
! [U_657,U_656,U_655] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(U_657),U_656)),number_number_of_int(U_655)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_657),number_number_of_int(U_655))),hAPP_int_int(times_times_int(U_656),number_number_of_int(U_655))),
inference(variable_rename,[status(thm)],[f_246_1]) ).
cnf(f_246_3,plain,
hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(U_657),U_656)),number_number_of_int(U_655)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_657),number_number_of_int(U_655))),hAPP_int_int(times_times_int(U_656),number_number_of_int(U_655))),
inference(clausify,[status(thm)],[f_246_2]) ).
fof(f_247_1,plain,
! [A_98,B_57,V_16] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_98),B_57)),number_number_of_nat(V_16)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_98),number_number_of_nat(V_16))),hAPP_nat_nat(times_times_nat(B_57),number_number_of_nat(V_16))),
inference(fof_nnf,[status(thm)],[fact_221_left__distrib__number__of]) ).
fof(f_247_2,plain,
! [U_660,U_659,U_658] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_660),U_659)),number_number_of_nat(U_658)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_660),number_number_of_nat(U_658))),hAPP_nat_nat(times_times_nat(U_659),number_number_of_nat(U_658))),
inference(variable_rename,[status(thm)],[f_247_1]) ).
cnf(f_247_3,plain,
hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_660),U_659)),number_number_of_nat(U_658)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_660),number_number_of_nat(U_658))),hAPP_nat_nat(times_times_nat(U_659),number_number_of_nat(U_658))),
inference(clausify,[status(thm)],[f_247_2]) ).
fof(f_248_1,plain,
! [A_98,B_57,V_16] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_98),B_57)),number267125858f_real(V_16)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_98),number267125858f_real(V_16))),hAPP_real_real(times_times_real(B_57),number267125858f_real(V_16))),
inference(fof_nnf,[status(thm)],[fact_222_left__distrib__number__of]) ).
fof(f_248_2,plain,
! [U_663,U_662,U_661] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(U_663),U_662)),number267125858f_real(U_661)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_663),number267125858f_real(U_661))),hAPP_real_real(times_times_real(U_662),number267125858f_real(U_661))),
inference(variable_rename,[status(thm)],[f_248_1]) ).
cnf(f_248_3,plain,
hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(U_663),U_662)),number267125858f_real(U_661)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_663),number267125858f_real(U_661))),hAPP_real_real(times_times_real(U_662),number267125858f_real(U_661))),
inference(clausify,[status(thm)],[f_248_2]) ).
fof(f_249_1,plain,
! [V_15,B_56,C_28] : hAPP_int_int(times_times_int(number_number_of_int(V_15)),hAPP_int_int(plus_plus_int(B_56),C_28)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(V_15)),B_56)),hAPP_int_int(times_times_int(number_number_of_int(V_15)),C_28)),
inference(fof_nnf,[status(thm)],[fact_223_right__distrib__number__of]) ).
fof(f_249_2,plain,
! [U_666,U_665,U_664] : hAPP_int_int(times_times_int(number_number_of_int(U_666)),hAPP_int_int(plus_plus_int(U_665),U_664)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(U_666)),U_665)),hAPP_int_int(times_times_int(number_number_of_int(U_666)),U_664)),
inference(variable_rename,[status(thm)],[f_249_1]) ).
cnf(f_249_3,plain,
hAPP_int_int(times_times_int(number_number_of_int(U_666)),hAPP_int_int(plus_plus_int(U_665),U_664)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(U_666)),U_665)),hAPP_int_int(times_times_int(number_number_of_int(U_666)),U_664)),
inference(clausify,[status(thm)],[f_249_2]) ).
fof(f_250_1,plain,
! [V_15,B_56,C_28] : hAPP_nat_nat(times_times_nat(number_number_of_nat(V_15)),hAPP_nat_nat(plus_plus_nat(B_56),C_28)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(number_number_of_nat(V_15)),B_56)),hAPP_nat_nat(times_times_nat(number_number_of_nat(V_15)),C_28)),
inference(fof_nnf,[status(thm)],[fact_224_right__distrib__number__of]) ).
fof(f_250_2,plain,
! [U_669,U_668,U_667] : hAPP_nat_nat(times_times_nat(number_number_of_nat(U_669)),hAPP_nat_nat(plus_plus_nat(U_668),U_667)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(number_number_of_nat(U_669)),U_668)),hAPP_nat_nat(times_times_nat(number_number_of_nat(U_669)),U_667)),
inference(variable_rename,[status(thm)],[f_250_1]) ).
cnf(f_250_3,plain,
hAPP_nat_nat(times_times_nat(number_number_of_nat(U_669)),hAPP_nat_nat(plus_plus_nat(U_668),U_667)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(number_number_of_nat(U_669)),U_668)),hAPP_nat_nat(times_times_nat(number_number_of_nat(U_669)),U_667)),
inference(clausify,[status(thm)],[f_250_2]) ).
fof(f_251_1,plain,
! [V_15,B_56,C_28] : hAPP_real_real(times_times_real(number267125858f_real(V_15)),hAPP_real_real(plus_plus_real(B_56),C_28)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(number267125858f_real(V_15)),B_56)),hAPP_real_real(times_times_real(number267125858f_real(V_15)),C_28)),
inference(fof_nnf,[status(thm)],[fact_225_right__distrib__number__of]) ).
fof(f_251_2,plain,
! [U_672,U_671,U_670] : hAPP_real_real(times_times_real(number267125858f_real(U_672)),hAPP_real_real(plus_plus_real(U_671),U_670)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(number267125858f_real(U_672)),U_671)),hAPP_real_real(times_times_real(number267125858f_real(U_672)),U_670)),
inference(variable_rename,[status(thm)],[f_251_1]) ).
cnf(f_251_3,plain,
hAPP_real_real(times_times_real(number267125858f_real(U_672)),hAPP_real_real(plus_plus_real(U_671),U_670)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(number267125858f_real(U_672)),U_671)),hAPP_real_real(times_times_real(number267125858f_real(U_672)),U_670)),
inference(clausify,[status(thm)],[f_251_2]) ).
fof(f_252_1,plain,
! [A_97,M_12] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_97),M_12)),M_12) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_97),one_one_int)),M_12),
inference(fof_nnf,[status(thm)],[fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J]) ).
fof(f_252_2,plain,
! [U_674,U_673] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_674),U_673)),U_673) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(U_674),one_one_int)),U_673),
inference(variable_rename,[status(thm)],[f_252_1]) ).
cnf(f_252_3,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_674),U_673)),U_673) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(U_674),one_one_int)),U_673),
inference(clausify,[status(thm)],[f_252_2]) ).
fof(f_253_1,plain,
! [A_97,M_12] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_97),M_12)),M_12) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_97),one_one_nat)),M_12),
inference(fof_nnf,[status(thm)],[fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J]) ).
fof(f_253_2,plain,
! [U_676,U_675] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_676),U_675)),U_675) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_676),one_one_nat)),U_675),
inference(variable_rename,[status(thm)],[f_253_1]) ).
cnf(f_253_3,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_676),U_675)),U_675) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_676),one_one_nat)),U_675),
inference(clausify,[status(thm)],[f_253_2]) ).
fof(f_254_1,plain,
! [A_97,M_12] : hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_97),M_12)),M_12) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_97),one_one_real)),M_12),
inference(fof_nnf,[status(thm)],[fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J]) ).
fof(f_254_2,plain,
! [U_678,U_677] : hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_678),U_677)),U_677) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(U_678),one_one_real)),U_677),
inference(variable_rename,[status(thm)],[f_254_1]) ).
cnf(f_254_3,plain,
hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_678),U_677)),U_677) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(U_678),one_one_real)),U_677),
inference(clausify,[status(thm)],[f_254_2]) ).
fof(f_255_1,plain,
! [M_11,A_96] : hAPP_int_int(plus_plus_int(M_11),hAPP_int_int(times_times_int(A_96),M_11)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_96),one_one_int)),M_11),
inference(fof_nnf,[status(thm)],[fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J]) ).
fof(f_255_2,plain,
! [U_680,U_679] : hAPP_int_int(plus_plus_int(U_680),hAPP_int_int(times_times_int(U_679),U_680)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(U_679),one_one_int)),U_680),
inference(variable_rename,[status(thm)],[f_255_1]) ).
cnf(f_255_3,plain,
hAPP_int_int(plus_plus_int(U_680),hAPP_int_int(times_times_int(U_679),U_680)) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(U_679),one_one_int)),U_680),
inference(clausify,[status(thm)],[f_255_2]) ).
fof(f_256_1,plain,
! [M_11,A_96] : hAPP_nat_nat(plus_plus_nat(M_11),hAPP_nat_nat(times_times_nat(A_96),M_11)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_96),one_one_nat)),M_11),
inference(fof_nnf,[status(thm)],[fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J]) ).
fof(f_256_2,plain,
! [U_682,U_681] : hAPP_nat_nat(plus_plus_nat(U_682),hAPP_nat_nat(times_times_nat(U_681),U_682)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_681),one_one_nat)),U_682),
inference(variable_rename,[status(thm)],[f_256_1]) ).
cnf(f_256_3,plain,
hAPP_nat_nat(plus_plus_nat(U_682),hAPP_nat_nat(times_times_nat(U_681),U_682)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_681),one_one_nat)),U_682),
inference(clausify,[status(thm)],[f_256_2]) ).
fof(f_257_1,plain,
! [M_11,A_96] : hAPP_real_real(plus_plus_real(M_11),hAPP_real_real(times_times_real(A_96),M_11)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_96),one_one_real)),M_11),
inference(fof_nnf,[status(thm)],[fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J]) ).
fof(f_257_2,plain,
! [U_684,U_683] : hAPP_real_real(plus_plus_real(U_684),hAPP_real_real(times_times_real(U_683),U_684)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(U_683),one_one_real)),U_684),
inference(variable_rename,[status(thm)],[f_257_1]) ).
cnf(f_257_3,plain,
hAPP_real_real(plus_plus_real(U_684),hAPP_real_real(times_times_real(U_683),U_684)) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(U_683),one_one_real)),U_684),
inference(clausify,[status(thm)],[f_257_2]) ).
fof(f_258_1,plain,
! [M_10] : hAPP_int_int(plus_plus_int(M_10),M_10) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),M_10),
inference(fof_nnf,[status(thm)],[fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).
fof(f_258_2,plain,
! [U_685] : hAPP_int_int(plus_plus_int(U_685),U_685) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),U_685),
inference(variable_rename,[status(thm)],[f_258_1]) ).
cnf(f_258_3,plain,
hAPP_int_int(plus_plus_int(U_685),U_685) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),U_685),
inference(clausify,[status(thm)],[f_258_2]) ).
fof(f_259_1,plain,
! [M_10] : hAPP_nat_nat(plus_plus_nat(M_10),M_10) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),M_10),
inference(fof_nnf,[status(thm)],[fact_233_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).
fof(f_259_2,plain,
! [U_686] : hAPP_nat_nat(plus_plus_nat(U_686),U_686) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),U_686),
inference(variable_rename,[status(thm)],[f_259_1]) ).
cnf(f_259_3,plain,
hAPP_nat_nat(plus_plus_nat(U_686),U_686) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),U_686),
inference(clausify,[status(thm)],[f_259_2]) ).
fof(f_260_1,plain,
! [M_10] : hAPP_real_real(plus_plus_real(M_10),M_10) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),M_10),
inference(fof_nnf,[status(thm)],[fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).
fof(f_260_2,plain,
! [U_687] : hAPP_real_real(plus_plus_real(U_687),U_687) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),U_687),
inference(variable_rename,[status(thm)],[f_260_1]) ).
cnf(f_260_3,plain,
hAPP_real_real(plus_plus_real(U_687),U_687) = hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),U_687),
inference(clausify,[status(thm)],[f_260_2]) ).
fof(f_261_1,plain,
! [A_95] :
( hAPP_int_int(plus_plus_int(number_number_of_int(pls)),A_95) = A_95
| ~ is_int(A_95) ),
inference(fof_nnf,[status(thm)],[fact_235_add__numeral__0]) ).
fof(f_261_2,plain,
! [U_688] :
( hAPP_int_int(plus_plus_int(number_number_of_int(pls)),U_688) = U_688
| ~ is_int(U_688) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
cnf(f_261_3,plain,
( hAPP_int_int(plus_plus_int(number_number_of_int(pls)),U_688) = U_688
| ~ is_int(U_688) ),
inference(clausify,[status(thm)],[f_261_2]) ).
fof(f_262_1,plain,
! [A_95] : hAPP_real_real(plus_plus_real(number267125858f_real(pls)),A_95) = A_95,
inference(fof_nnf,[status(thm)],[fact_236_add__numeral__0]) ).
fof(f_262_2,plain,
! [U_689] : hAPP_real_real(plus_plus_real(number267125858f_real(pls)),U_689) = U_689,
inference(variable_rename,[status(thm)],[f_262_1]) ).
cnf(f_262_3,plain,
hAPP_real_real(plus_plus_real(number267125858f_real(pls)),U_689) = U_689,
inference(clausify,[status(thm)],[f_262_2]) ).
fof(f_263_1,plain,
! [A_94] :
( hAPP_int_int(plus_plus_int(A_94),number_number_of_int(pls)) = A_94
| ~ is_int(A_94) ),
inference(fof_nnf,[status(thm)],[fact_237_add__numeral__0__right]) ).
fof(f_263_2,plain,
! [U_690] :
( hAPP_int_int(plus_plus_int(U_690),number_number_of_int(pls)) = U_690
| ~ is_int(U_690) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
cnf(f_263_3,plain,
( hAPP_int_int(plus_plus_int(U_690),number_number_of_int(pls)) = U_690
| ~ is_int(U_690) ),
inference(clausify,[status(thm)],[f_263_2]) ).
fof(f_264_1,plain,
! [A_94] : hAPP_real_real(plus_plus_real(A_94),number267125858f_real(pls)) = A_94,
inference(fof_nnf,[status(thm)],[fact_238_add__numeral__0__right]) ).
fof(f_264_2,plain,
! [U_691] : hAPP_real_real(plus_plus_real(U_691),number267125858f_real(pls)) = U_691,
inference(variable_rename,[status(thm)],[f_264_1]) ).
cnf(f_264_3,plain,
hAPP_real_real(plus_plus_real(U_691),number267125858f_real(pls)) = U_691,
inference(clausify,[status(thm)],[f_264_2]) ).
fof(f_265_1,plain,
! [V_14,W_13,Z_8] : hAPP_int_int(times_times_int(number_number_of_int(V_14)),hAPP_int_int(times_times_int(number_number_of_int(W_13)),Z_8)) = hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(V_14),W_13))),Z_8),
inference(fof_nnf,[status(thm)],[fact_239_mult__number__of__left]) ).
fof(f_265_2,plain,
! [U_694,U_693,U_692] : hAPP_int_int(times_times_int(number_number_of_int(U_694)),hAPP_int_int(times_times_int(number_number_of_int(U_693)),U_692)) = hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(U_694),U_693))),U_692),
inference(variable_rename,[status(thm)],[f_265_1]) ).
cnf(f_265_3,plain,
hAPP_int_int(times_times_int(number_number_of_int(U_694)),hAPP_int_int(times_times_int(number_number_of_int(U_693)),U_692)) = hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(times_times_int(U_694),U_693))),U_692),
inference(clausify,[status(thm)],[f_265_2]) ).
fof(f_266_1,plain,
! [V_14,W_13,Z_8] : hAPP_real_real(times_times_real(number267125858f_real(V_14)),hAPP_real_real(times_times_real(number267125858f_real(W_13)),Z_8)) = hAPP_real_real(times_times_real(number267125858f_real(hAPP_int_int(times_times_int(V_14),W_13))),Z_8),
inference(fof_nnf,[status(thm)],[fact_240_mult__number__of__left]) ).
fof(f_266_2,plain,
! [U_697,U_696,U_695] : hAPP_real_real(times_times_real(number267125858f_real(U_697)),hAPP_real_real(times_times_real(number267125858f_real(U_696)),U_695)) = hAPP_real_real(times_times_real(number267125858f_real(hAPP_int_int(times_times_int(U_697),U_696))),U_695),
inference(variable_rename,[status(thm)],[f_266_1]) ).
cnf(f_266_3,plain,
hAPP_real_real(times_times_real(number267125858f_real(U_697)),hAPP_real_real(times_times_real(number267125858f_real(U_696)),U_695)) = hAPP_real_real(times_times_real(number267125858f_real(hAPP_int_int(times_times_int(U_697),U_696))),U_695),
inference(clausify,[status(thm)],[f_266_2]) ).
fof(f_267_1,plain,
! [V_13,W_12] : hAPP_int_int(times_times_int(number_number_of_int(V_13)),number_number_of_int(W_12)) = number_number_of_int(hAPP_int_int(times_times_int(V_13),W_12)),
inference(fof_nnf,[status(thm)],[fact_241_arith__simps_I32_J]) ).
fof(f_267_2,plain,
! [U_699,U_698] : hAPP_int_int(times_times_int(number_number_of_int(U_699)),number_number_of_int(U_698)) = number_number_of_int(hAPP_int_int(times_times_int(U_699),U_698)),
inference(variable_rename,[status(thm)],[f_267_1]) ).
cnf(f_267_3,plain,
hAPP_int_int(times_times_int(number_number_of_int(U_699)),number_number_of_int(U_698)) = number_number_of_int(hAPP_int_int(times_times_int(U_699),U_698)),
inference(clausify,[status(thm)],[f_267_2]) ).
fof(f_268_1,plain,
! [V_13,W_12] : hAPP_real_real(times_times_real(number267125858f_real(V_13)),number267125858f_real(W_12)) = number267125858f_real(hAPP_int_int(times_times_int(V_13),W_12)),
inference(fof_nnf,[status(thm)],[fact_242_arith__simps_I32_J]) ).
fof(f_268_2,plain,
! [U_701,U_700] : hAPP_real_real(times_times_real(number267125858f_real(U_701)),number267125858f_real(U_700)) = number267125858f_real(hAPP_int_int(times_times_int(U_701),U_700)),
inference(variable_rename,[status(thm)],[f_268_1]) ).
cnf(f_268_3,plain,
hAPP_real_real(times_times_real(number267125858f_real(U_701)),number267125858f_real(U_700)) = number267125858f_real(hAPP_int_int(times_times_int(U_701),U_700)),
inference(clausify,[status(thm)],[f_268_2]) ).
fof(f_269_1,plain,
! [V_12,W_11] : number_number_of_int(hAPP_int_int(times_times_int(V_12),W_11)) = hAPP_int_int(times_times_int(number_number_of_int(V_12)),number_number_of_int(W_11)),
inference(fof_nnf,[status(thm)],[fact_243_number__of__mult]) ).
fof(f_269_2,plain,
! [U_703,U_702] : number_number_of_int(hAPP_int_int(times_times_int(U_703),U_702)) = hAPP_int_int(times_times_int(number_number_of_int(U_703)),number_number_of_int(U_702)),
inference(variable_rename,[status(thm)],[f_269_1]) ).
cnf(f_269_3,plain,
number_number_of_int(hAPP_int_int(times_times_int(U_703),U_702)) = hAPP_int_int(times_times_int(number_number_of_int(U_703)),number_number_of_int(U_702)),
inference(clausify,[status(thm)],[f_269_2]) ).
fof(f_270_1,plain,
! [V_12,W_11] : number267125858f_real(hAPP_int_int(times_times_int(V_12),W_11)) = hAPP_real_real(times_times_real(number267125858f_real(V_12)),number267125858f_real(W_11)),
inference(fof_nnf,[status(thm)],[fact_244_number__of__mult]) ).
fof(f_270_2,plain,
! [U_705,U_704] : number267125858f_real(hAPP_int_int(times_times_int(U_705),U_704)) = hAPP_real_real(times_times_real(number267125858f_real(U_705)),number267125858f_real(U_704)),
inference(variable_rename,[status(thm)],[f_270_1]) ).
cnf(f_270_3,plain,
number267125858f_real(hAPP_int_int(times_times_int(U_705),U_704)) = hAPP_real_real(times_times_real(number267125858f_real(U_705)),number267125858f_real(U_704)),
inference(clausify,[status(thm)],[f_270_2]) ).
fof(f_271_1,plain,
! [V_11,W_10,Z_7] : hAPP_int_int(plus_plus_int(number_number_of_int(V_11)),hAPP_int_int(plus_plus_int(number_number_of_int(W_10)),Z_7)) = hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(V_11),W_10))),Z_7),
inference(fof_nnf,[status(thm)],[fact_245_add__number__of__left]) ).
fof(f_271_2,plain,
! [U_708,U_707,U_706] : hAPP_int_int(plus_plus_int(number_number_of_int(U_708)),hAPP_int_int(plus_plus_int(number_number_of_int(U_707)),U_706)) = hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(U_708),U_707))),U_706),
inference(variable_rename,[status(thm)],[f_271_1]) ).
cnf(f_271_3,plain,
hAPP_int_int(plus_plus_int(number_number_of_int(U_708)),hAPP_int_int(plus_plus_int(number_number_of_int(U_707)),U_706)) = hAPP_int_int(plus_plus_int(number_number_of_int(hAPP_int_int(plus_plus_int(U_708),U_707))),U_706),
inference(clausify,[status(thm)],[f_271_2]) ).
fof(f_272_1,plain,
! [V_11,W_10,Z_7] : hAPP_real_real(plus_plus_real(number267125858f_real(V_11)),hAPP_real_real(plus_plus_real(number267125858f_real(W_10)),Z_7)) = hAPP_real_real(plus_plus_real(number267125858f_real(hAPP_int_int(plus_plus_int(V_11),W_10))),Z_7),
inference(fof_nnf,[status(thm)],[fact_246_add__number__of__left]) ).
fof(f_272_2,plain,
! [U_711,U_710,U_709] : hAPP_real_real(plus_plus_real(number267125858f_real(U_711)),hAPP_real_real(plus_plus_real(number267125858f_real(U_710)),U_709)) = hAPP_real_real(plus_plus_real(number267125858f_real(hAPP_int_int(plus_plus_int(U_711),U_710))),U_709),
inference(variable_rename,[status(thm)],[f_272_1]) ).
cnf(f_272_3,plain,
hAPP_real_real(plus_plus_real(number267125858f_real(U_711)),hAPP_real_real(plus_plus_real(number267125858f_real(U_710)),U_709)) = hAPP_real_real(plus_plus_real(number267125858f_real(hAPP_int_int(plus_plus_int(U_711),U_710))),U_709),
inference(clausify,[status(thm)],[f_272_2]) ).
fof(f_273_1,plain,
! [V_10,W_9] : hAPP_int_int(plus_plus_int(number_number_of_int(V_10)),number_number_of_int(W_9)) = number_number_of_int(hAPP_int_int(plus_plus_int(V_10),W_9)),
inference(fof_nnf,[status(thm)],[fact_247_add__number__of__eq]) ).
fof(f_273_2,plain,
! [U_713,U_712] : hAPP_int_int(plus_plus_int(number_number_of_int(U_713)),number_number_of_int(U_712)) = number_number_of_int(hAPP_int_int(plus_plus_int(U_713),U_712)),
inference(variable_rename,[status(thm)],[f_273_1]) ).
cnf(f_273_3,plain,
hAPP_int_int(plus_plus_int(number_number_of_int(U_713)),number_number_of_int(U_712)) = number_number_of_int(hAPP_int_int(plus_plus_int(U_713),U_712)),
inference(clausify,[status(thm)],[f_273_2]) ).
fof(f_274_1,plain,
! [V_10,W_9] : hAPP_real_real(plus_plus_real(number267125858f_real(V_10)),number267125858f_real(W_9)) = number267125858f_real(hAPP_int_int(plus_plus_int(V_10),W_9)),
inference(fof_nnf,[status(thm)],[fact_248_add__number__of__eq]) ).
fof(f_274_2,plain,
! [U_715,U_714] : hAPP_real_real(plus_plus_real(number267125858f_real(U_715)),number267125858f_real(U_714)) = number267125858f_real(hAPP_int_int(plus_plus_int(U_715),U_714)),
inference(variable_rename,[status(thm)],[f_274_1]) ).
cnf(f_274_3,plain,
hAPP_real_real(plus_plus_real(number267125858f_real(U_715)),number267125858f_real(U_714)) = number267125858f_real(hAPP_int_int(plus_plus_int(U_715),U_714)),
inference(clausify,[status(thm)],[f_274_2]) ).
fof(f_275_1,plain,
! [V_9,W_8] : number_number_of_int(hAPP_int_int(plus_plus_int(V_9),W_8)) = hAPP_int_int(plus_plus_int(number_number_of_int(V_9)),number_number_of_int(W_8)),
inference(fof_nnf,[status(thm)],[fact_249_number__of__add]) ).
fof(f_275_2,plain,
! [U_717,U_716] : number_number_of_int(hAPP_int_int(plus_plus_int(U_717),U_716)) = hAPP_int_int(plus_plus_int(number_number_of_int(U_717)),number_number_of_int(U_716)),
inference(variable_rename,[status(thm)],[f_275_1]) ).
cnf(f_275_3,plain,
number_number_of_int(hAPP_int_int(plus_plus_int(U_717),U_716)) = hAPP_int_int(plus_plus_int(number_number_of_int(U_717)),number_number_of_int(U_716)),
inference(clausify,[status(thm)],[f_275_2]) ).
fof(f_276_1,plain,
! [V_9,W_8] : number267125858f_real(hAPP_int_int(plus_plus_int(V_9),W_8)) = hAPP_real_real(plus_plus_real(number267125858f_real(V_9)),number267125858f_real(W_8)),
inference(fof_nnf,[status(thm)],[fact_250_number__of__add]) ).
fof(f_276_2,plain,
! [U_719,U_718] : number267125858f_real(hAPP_int_int(plus_plus_int(U_719),U_718)) = hAPP_real_real(plus_plus_real(number267125858f_real(U_719)),number267125858f_real(U_718)),
inference(variable_rename,[status(thm)],[f_276_1]) ).
cnf(f_276_3,plain,
number267125858f_real(hAPP_int_int(plus_plus_int(U_719),U_718)) = hAPP_real_real(plus_plus_real(number267125858f_real(U_719)),number267125858f_real(U_718)),
inference(clausify,[status(thm)],[f_276_2]) ).
fof(f_277_1,plain,
! [K_1,L] : hAPP_int_int(plus_plus_int(bit1(K_1)),bit0(L)) = bit1(hAPP_int_int(plus_plus_int(K_1),L)),
inference(fof_nnf,[status(thm)],[fact_251_add__Bit1__Bit0]) ).
fof(f_277_2,plain,
! [U_721,U_720] : hAPP_int_int(plus_plus_int(bit1(U_721)),bit0(U_720)) = bit1(hAPP_int_int(plus_plus_int(U_721),U_720)),
inference(variable_rename,[status(thm)],[f_277_1]) ).
cnf(f_277_3,plain,
hAPP_int_int(plus_plus_int(bit1(U_721)),bit0(U_720)) = bit1(hAPP_int_int(plus_plus_int(U_721),U_720)),
inference(clausify,[status(thm)],[f_277_2]) ).
fof(f_278_1,plain,
! [K_1,L] : hAPP_int_int(plus_plus_int(bit0(K_1)),bit1(L)) = bit1(hAPP_int_int(plus_plus_int(K_1),L)),
inference(fof_nnf,[status(thm)],[fact_252_add__Bit0__Bit1]) ).
fof(f_278_2,plain,
! [U_723,U_722] : hAPP_int_int(plus_plus_int(bit0(U_723)),bit1(U_722)) = bit1(hAPP_int_int(plus_plus_int(U_723),U_722)),
inference(variable_rename,[status(thm)],[f_278_1]) ).
cnf(f_278_3,plain,
hAPP_int_int(plus_plus_int(bit0(U_723)),bit1(U_722)) = bit1(hAPP_int_int(plus_plus_int(U_723),U_722)),
inference(clausify,[status(thm)],[f_278_2]) ).
fof(f_279_1,plain,
! [K_1] : bit1(K_1) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),K_1)),K_1),
inference(fof_nnf,[status(thm)],[fact_253_Bit1__def]) ).
fof(f_279_2,plain,
! [U_724] : bit1(U_724) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),U_724)),U_724),
inference(variable_rename,[status(thm)],[f_279_1]) ).
cnf(f_279_3,plain,
bit1(U_724) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),U_724)),U_724),
inference(clausify,[status(thm)],[f_279_2]) ).
fof(f_280_1,plain,
! [W_7] : number_number_of_int(bit1(W_7)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(W_7))),number_number_of_int(W_7)),
inference(fof_nnf,[status(thm)],[fact_254_number__of__Bit1]) ).
fof(f_280_2,plain,
! [U_725] : number_number_of_int(bit1(U_725)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(U_725))),number_number_of_int(U_725)),
inference(variable_rename,[status(thm)],[f_280_1]) ).
cnf(f_280_3,plain,
number_number_of_int(bit1(U_725)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(U_725))),number_number_of_int(U_725)),
inference(clausify,[status(thm)],[f_280_2]) ).
fof(f_281_1,plain,
! [W_7] : number267125858f_real(bit1(W_7)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(W_7))),number267125858f_real(W_7)),
inference(fof_nnf,[status(thm)],[fact_255_number__of__Bit1]) ).
fof(f_281_2,plain,
! [U_726] : number267125858f_real(bit1(U_726)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(U_726))),number267125858f_real(U_726)),
inference(variable_rename,[status(thm)],[f_281_1]) ).
cnf(f_281_3,plain,
number267125858f_real(bit1(U_726)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(one_one_real),number267125858f_real(U_726))),number267125858f_real(U_726)),
inference(clausify,[status(thm)],[f_281_2]) ).
fof(f_282_1,plain,
! [A_93] :
( hAPP_int_int(times_times_int(number_number_of_int(bit1(pls))),A_93) = A_93
| ~ is_int(A_93) ),
inference(fof_nnf,[status(thm)],[fact_256_mult__numeral__1]) ).
fof(f_282_2,plain,
! [U_727] :
( hAPP_int_int(times_times_int(number_number_of_int(bit1(pls))),U_727) = U_727
| ~ is_int(U_727) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
cnf(f_282_3,plain,
( hAPP_int_int(times_times_int(number_number_of_int(bit1(pls))),U_727) = U_727
| ~ is_int(U_727) ),
inference(clausify,[status(thm)],[f_282_2]) ).
fof(f_283_1,plain,
! [A_93] : hAPP_real_real(times_times_real(number267125858f_real(bit1(pls))),A_93) = A_93,
inference(fof_nnf,[status(thm)],[fact_257_mult__numeral__1]) ).
fof(f_283_2,plain,
! [U_728] : hAPP_real_real(times_times_real(number267125858f_real(bit1(pls))),U_728) = U_728,
inference(variable_rename,[status(thm)],[f_283_1]) ).
cnf(f_283_3,plain,
hAPP_real_real(times_times_real(number267125858f_real(bit1(pls))),U_728) = U_728,
inference(clausify,[status(thm)],[f_283_2]) ).
fof(f_284_1,plain,
! [A_92] :
( hAPP_int_int(times_times_int(A_92),number_number_of_int(bit1(pls))) = A_92
| ~ is_int(A_92) ),
inference(fof_nnf,[status(thm)],[fact_258_mult__numeral__1__right]) ).
fof(f_284_2,plain,
! [U_729] :
( hAPP_int_int(times_times_int(U_729),number_number_of_int(bit1(pls))) = U_729
| ~ is_int(U_729) ),
inference(variable_rename,[status(thm)],[f_284_1]) ).
cnf(f_284_3,plain,
( hAPP_int_int(times_times_int(U_729),number_number_of_int(bit1(pls))) = U_729
| ~ is_int(U_729) ),
inference(clausify,[status(thm)],[f_284_2]) ).
fof(f_285_1,plain,
! [A_92] : hAPP_real_real(times_times_real(A_92),number267125858f_real(bit1(pls))) = A_92,
inference(fof_nnf,[status(thm)],[fact_259_mult__numeral__1__right]) ).
fof(f_285_2,plain,
! [U_730] : hAPP_real_real(times_times_real(U_730),number267125858f_real(bit1(pls))) = U_730,
inference(variable_rename,[status(thm)],[f_285_1]) ).
cnf(f_285_3,plain,
hAPP_real_real(times_times_real(U_730),number267125858f_real(bit1(pls))) = U_730,
inference(clausify,[status(thm)],[f_285_2]) ).
fof(f_286_1,plain,
number_number_of_int(bit1(pls)) = one_one_int,
inference(fof_nnf,[status(thm)],[fact_260_semiring__numeral__1__eq__1]) ).
cnf(f_286_2,plain,
number_number_of_int(bit1(pls)) = one_one_int,
inference(clausify,[status(thm)],[f_286_1]) ).
fof(f_287_1,plain,
number_number_of_nat(bit1(pls)) = one_one_nat,
inference(fof_nnf,[status(thm)],[fact_261_semiring__numeral__1__eq__1]) ).
cnf(f_287_2,plain,
number_number_of_nat(bit1(pls)) = one_one_nat,
inference(clausify,[status(thm)],[f_287_1]) ).
fof(f_288_1,plain,
number267125858f_real(bit1(pls)) = one_one_real,
inference(fof_nnf,[status(thm)],[fact_262_semiring__numeral__1__eq__1]) ).
cnf(f_288_2,plain,
number267125858f_real(bit1(pls)) = one_one_real,
inference(clausify,[status(thm)],[f_288_1]) ).
fof(f_289_1,plain,
number_number_of_int(bit1(pls)) = one_one_int,
inference(fof_nnf,[status(thm)],[fact_263_numeral__1__eq__1]) ).
cnf(f_289_2,plain,
number_number_of_int(bit1(pls)) = one_one_int,
inference(clausify,[status(thm)],[f_289_1]) ).
fof(f_290_1,plain,
number267125858f_real(bit1(pls)) = one_one_real,
inference(fof_nnf,[status(thm)],[fact_264_numeral__1__eq__1]) ).
cnf(f_290_2,plain,
number267125858f_real(bit1(pls)) = one_one_real,
inference(clausify,[status(thm)],[f_290_1]) ).
fof(f_291_1,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(fof_nnf,[status(thm)],[fact_265_semiring__norm_I110_J]) ).
cnf(f_291_2,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(clausify,[status(thm)],[f_291_1]) ).
fof(f_292_1,plain,
one_one_real = number267125858f_real(bit1(pls)),
inference(fof_nnf,[status(thm)],[fact_266_semiring__norm_I110_J]) ).
cnf(f_292_2,plain,
one_one_real = number267125858f_real(bit1(pls)),
inference(clausify,[status(thm)],[f_292_1]) ).
fof(f_293_1,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(fof_nnf,[status(thm)],[fact_267_one__is__num__one]) ).
cnf(f_293_2,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(clausify,[status(thm)],[f_293_1]) ).
fof(f_294_1,plain,
! [K_1,L] : hAPP_int_int(times_times_int(bit1(K_1)),L) = hAPP_int_int(plus_plus_int(bit0(hAPP_int_int(times_times_int(K_1),L))),L),
inference(fof_nnf,[status(thm)],[fact_268_mult__Bit1]) ).
fof(f_294_2,plain,
! [U_732,U_731] : hAPP_int_int(times_times_int(bit1(U_732)),U_731) = hAPP_int_int(plus_plus_int(bit0(hAPP_int_int(times_times_int(U_732),U_731))),U_731),
inference(variable_rename,[status(thm)],[f_294_1]) ).
cnf(f_294_3,plain,
hAPP_int_int(times_times_int(bit1(U_732)),U_731) = hAPP_int_int(plus_plus_int(bit0(hAPP_int_int(times_times_int(U_732),U_731))),U_731),
inference(clausify,[status(thm)],[f_294_2]) ).
fof(f_295_1,plain,
! [W_6] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),number_number_of_int(W_6)) = number_number_of_int(bit0(W_6)),
inference(fof_nnf,[status(thm)],[fact_269_double__number__of__Bit0]) ).
fof(f_295_2,plain,
! [U_733] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),number_number_of_int(U_733)) = number_number_of_int(bit0(U_733)),
inference(variable_rename,[status(thm)],[f_295_1]) ).
cnf(f_295_3,plain,
hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)),number_number_of_int(U_733)) = number_number_of_int(bit0(U_733)),
inference(clausify,[status(thm)],[f_295_2]) ).
fof(f_296_1,plain,
! [W_6] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(W_6)) = number267125858f_real(bit0(W_6)),
inference(fof_nnf,[status(thm)],[fact_270_double__number__of__Bit0]) ).
fof(f_296_2,plain,
! [U_734] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(U_734)) = number267125858f_real(bit0(U_734)),
inference(variable_rename,[status(thm)],[f_296_1]) ).
cnf(f_296_3,plain,
hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(one_one_real),one_one_real)),number267125858f_real(U_734)) = number267125858f_real(bit0(U_734)),
inference(clausify,[status(thm)],[f_296_2]) ).
fof(f_297_1,plain,
! [A_91] : hAPP_nat_int(power_power_int(A_91),number_number_of_nat(bit1(bit1(pls)))) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(A_91),A_91)),A_91),
inference(fof_nnf,[status(thm)],[fact_271_power3__eq__cube]) ).
fof(f_297_2,plain,
! [U_735] : hAPP_nat_int(power_power_int(U_735),number_number_of_nat(bit1(bit1(pls)))) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_735),U_735)),U_735),
inference(variable_rename,[status(thm)],[f_297_1]) ).
cnf(f_297_3,plain,
hAPP_nat_int(power_power_int(U_735),number_number_of_nat(bit1(bit1(pls)))) = hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_735),U_735)),U_735),
inference(clausify,[status(thm)],[f_297_2]) ).
fof(f_298_1,plain,
! [A_91] : hAPP_nat_real(power_power_real(A_91),number_number_of_nat(bit1(bit1(pls)))) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(A_91),A_91)),A_91),
inference(fof_nnf,[status(thm)],[fact_272_power3__eq__cube]) ).
fof(f_298_2,plain,
! [U_736] : hAPP_nat_real(power_power_real(U_736),number_number_of_nat(bit1(bit1(pls)))) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_736),U_736)),U_736),
inference(variable_rename,[status(thm)],[f_298_1]) ).
cnf(f_298_3,plain,
hAPP_nat_real(power_power_real(U_736),number_number_of_nat(bit1(bit1(pls)))) = hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_736),U_736)),U_736),
inference(clausify,[status(thm)],[f_298_2]) ).
fof(f_299_1,plain,
! [A_91] : hAPP_nat_nat(power_power_nat(A_91),number_number_of_nat(bit1(bit1(pls)))) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(A_91),A_91)),A_91),
inference(fof_nnf,[status(thm)],[fact_273_power3__eq__cube]) ).
fof(f_299_2,plain,
! [U_737] : hAPP_nat_nat(power_power_nat(U_737),number_number_of_nat(bit1(bit1(pls)))) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_737),U_737)),U_737),
inference(variable_rename,[status(thm)],[f_299_1]) ).
cnf(f_299_3,plain,
hAPP_nat_nat(power_power_nat(U_737),number_number_of_nat(bit1(bit1(pls)))) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_737),U_737)),U_737),
inference(clausify,[status(thm)],[f_299_2]) ).
fof(f_300_1,plain,
! [X_1] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(X_1),number_number_of_nat(bit0(bit1(pls))))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(X_1),number_number_of_nat(bit0(bit0(bit1(pls))))),
inference(fof_nnf,[status(thm)],[fact_274_quartic__square__square]) ).
fof(f_300_2,plain,
! [U_738] : hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(U_738),number_number_of_nat(bit0(bit1(pls))))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(U_738),number_number_of_nat(bit0(bit0(bit1(pls))))),
inference(variable_rename,[status(thm)],[f_300_1]) ).
cnf(f_300_3,plain,
hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(U_738),number_number_of_nat(bit0(bit1(pls))))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(U_738),number_number_of_nat(bit0(bit0(bit1(pls))))),
inference(clausify,[status(thm)],[f_300_2]) ).
fof(f_301_1,plain,
! [Z_6] : hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),Z_6) = hAPP_int_int(plus_plus_int(Z_6),Z_6),
inference(fof_nnf,[status(thm)],[fact_275_semiring__mult__2]) ).
fof(f_301_2,plain,
! [U_739] : hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),U_739) = hAPP_int_int(plus_plus_int(U_739),U_739),
inference(variable_rename,[status(thm)],[f_301_1]) ).
cnf(f_301_3,plain,
hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),U_739) = hAPP_int_int(plus_plus_int(U_739),U_739),
inference(clausify,[status(thm)],[f_301_2]) ).
fof(f_302_1,plain,
! [Z_6] : hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),Z_6) = hAPP_nat_nat(plus_plus_nat(Z_6),Z_6),
inference(fof_nnf,[status(thm)],[fact_276_semiring__mult__2]) ).
fof(f_302_2,plain,
! [U_740] : hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_740) = hAPP_nat_nat(plus_plus_nat(U_740),U_740),
inference(variable_rename,[status(thm)],[f_302_1]) ).
cnf(f_302_3,plain,
hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_740) = hAPP_nat_nat(plus_plus_nat(U_740),U_740),
inference(clausify,[status(thm)],[f_302_2]) ).
fof(f_303_1,plain,
! [Z_6] : hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),Z_6) = hAPP_real_real(plus_plus_real(Z_6),Z_6),
inference(fof_nnf,[status(thm)],[fact_277_semiring__mult__2]) ).
fof(f_303_2,plain,
! [U_741] : hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),U_741) = hAPP_real_real(plus_plus_real(U_741),U_741),
inference(variable_rename,[status(thm)],[f_303_1]) ).
cnf(f_303_3,plain,
hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),U_741) = hAPP_real_real(plus_plus_real(U_741),U_741),
inference(clausify,[status(thm)],[f_303_2]) ).
fof(f_304_1,plain,
! [Z_5] : hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),Z_5) = hAPP_int_int(plus_plus_int(Z_5),Z_5),
inference(fof_nnf,[status(thm)],[fact_278_mult__2]) ).
fof(f_304_2,plain,
! [U_742] : hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),U_742) = hAPP_int_int(plus_plus_int(U_742),U_742),
inference(variable_rename,[status(thm)],[f_304_1]) ).
cnf(f_304_3,plain,
hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),U_742) = hAPP_int_int(plus_plus_int(U_742),U_742),
inference(clausify,[status(thm)],[f_304_2]) ).
fof(f_305_1,plain,
! [Z_5] : hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),Z_5) = hAPP_real_real(plus_plus_real(Z_5),Z_5),
inference(fof_nnf,[status(thm)],[fact_279_mult__2]) ).
fof(f_305_2,plain,
! [U_743] : hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),U_743) = hAPP_real_real(plus_plus_real(U_743),U_743),
inference(variable_rename,[status(thm)],[f_305_1]) ).
cnf(f_305_3,plain,
hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),U_743) = hAPP_real_real(plus_plus_real(U_743),U_743),
inference(clausify,[status(thm)],[f_305_2]) ).
fof(f_306_1,plain,
! [Z_4] : hAPP_int_int(times_times_int(Z_4),number_number_of_int(bit0(bit1(pls)))) = hAPP_int_int(plus_plus_int(Z_4),Z_4),
inference(fof_nnf,[status(thm)],[fact_280_semiring__mult__2__right]) ).
fof(f_306_2,plain,
! [U_744] : hAPP_int_int(times_times_int(U_744),number_number_of_int(bit0(bit1(pls)))) = hAPP_int_int(plus_plus_int(U_744),U_744),
inference(variable_rename,[status(thm)],[f_306_1]) ).
cnf(f_306_3,plain,
hAPP_int_int(times_times_int(U_744),number_number_of_int(bit0(bit1(pls)))) = hAPP_int_int(plus_plus_int(U_744),U_744),
inference(clausify,[status(thm)],[f_306_2]) ).
fof(f_307_1,plain,
! [Z_4] : hAPP_nat_nat(times_times_nat(Z_4),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(plus_plus_nat(Z_4),Z_4),
inference(fof_nnf,[status(thm)],[fact_281_semiring__mult__2__right]) ).
fof(f_307_2,plain,
! [U_745] : hAPP_nat_nat(times_times_nat(U_745),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(plus_plus_nat(U_745),U_745),
inference(variable_rename,[status(thm)],[f_307_1]) ).
cnf(f_307_3,plain,
hAPP_nat_nat(times_times_nat(U_745),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_nat(plus_plus_nat(U_745),U_745),
inference(clausify,[status(thm)],[f_307_2]) ).
fof(f_308_1,plain,
! [Z_4] : hAPP_real_real(times_times_real(Z_4),number267125858f_real(bit0(bit1(pls)))) = hAPP_real_real(plus_plus_real(Z_4),Z_4),
inference(fof_nnf,[status(thm)],[fact_282_semiring__mult__2__right]) ).
fof(f_308_2,plain,
! [U_746] : hAPP_real_real(times_times_real(U_746),number267125858f_real(bit0(bit1(pls)))) = hAPP_real_real(plus_plus_real(U_746),U_746),
inference(variable_rename,[status(thm)],[f_308_1]) ).
cnf(f_308_3,plain,
hAPP_real_real(times_times_real(U_746),number267125858f_real(bit0(bit1(pls)))) = hAPP_real_real(plus_plus_real(U_746),U_746),
inference(clausify,[status(thm)],[f_308_2]) ).
fof(f_309_1,plain,
! [Z_3] : hAPP_int_int(times_times_int(Z_3),number_number_of_int(bit0(bit1(pls)))) = hAPP_int_int(plus_plus_int(Z_3),Z_3),
inference(fof_nnf,[status(thm)],[fact_283_mult__2__right]) ).
fof(f_309_2,plain,
! [U_747] : hAPP_int_int(times_times_int(U_747),number_number_of_int(bit0(bit1(pls)))) = hAPP_int_int(plus_plus_int(U_747),U_747),
inference(variable_rename,[status(thm)],[f_309_1]) ).
cnf(f_309_3,plain,
hAPP_int_int(times_times_int(U_747),number_number_of_int(bit0(bit1(pls)))) = hAPP_int_int(plus_plus_int(U_747),U_747),
inference(clausify,[status(thm)],[f_309_2]) ).
fof(f_310_1,plain,
! [Z_3] : hAPP_real_real(times_times_real(Z_3),number267125858f_real(bit0(bit1(pls)))) = hAPP_real_real(plus_plus_real(Z_3),Z_3),
inference(fof_nnf,[status(thm)],[fact_284_mult__2__right]) ).
fof(f_310_2,plain,
! [U_748] : hAPP_real_real(times_times_real(U_748),number267125858f_real(bit0(bit1(pls)))) = hAPP_real_real(plus_plus_real(U_748),U_748),
inference(variable_rename,[status(thm)],[f_310_1]) ).
cnf(f_310_3,plain,
hAPP_real_real(times_times_real(U_748),number267125858f_real(bit0(bit1(pls)))) = hAPP_real_real(plus_plus_real(U_748),U_748),
inference(clausify,[status(thm)],[f_310_2]) ).
fof(f_311_1,plain,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
inference(fof_nnf,[status(thm)],[fact_285_semiring__one__add__one__is__two]) ).
cnf(f_311_2,plain,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
inference(clausify,[status(thm)],[f_311_1]) ).
fof(f_312_1,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(fof_nnf,[status(thm)],[fact_286_semiring__one__add__one__is__two]) ).
cnf(f_312_2,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(clausify,[status(thm)],[f_312_1]) ).
fof(f_313_1,plain,
hAPP_real_real(plus_plus_real(one_one_real),one_one_real) = number267125858f_real(bit0(bit1(pls))),
inference(fof_nnf,[status(thm)],[fact_287_semiring__one__add__one__is__two]) ).
cnf(f_313_2,plain,
hAPP_real_real(plus_plus_real(one_one_real),one_one_real) = number267125858f_real(bit0(bit1(pls))),
inference(clausify,[status(thm)],[f_313_1]) ).
fof(f_314_1,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(fof_nnf,[status(thm)],[fact_288_p0]) ).
cnf(f_314_2,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(clausify,[status(thm)],[f_314_1]) ).
fof(f_315_1,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(fof_nnf,[status(thm)],[fact_289__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096]) ).
cnf(f_315_2,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(clausify,[status(thm)],[f_315_1]) ).
fof(f_316_1,plain,
! [P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),P_1))
| P_1 = number_number_of_int(bit1(bit1(pls)))
| P_1 = number_number_of_int(bit0(bit1(pls)))
| ~ hBOOL(hAPP_int_bool(zprime,P_1))
| ~ is_int(P_1) ),
inference(fof_nnf,[status(thm)],[fact_290_prime__g__5]) ).
fof(f_316_2,plain,
! [U_749] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),U_749))
| U_749 = number_number_of_int(bit1(bit1(pls)))
| U_749 = number_number_of_int(bit0(bit1(pls)))
| ~ hBOOL(hAPP_int_bool(zprime,U_749))
| ~ is_int(U_749) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
cnf(f_316_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),U_749))
| U_749 = number_number_of_int(bit1(bit1(pls)))
| U_749 = number_number_of_int(bit0(bit1(pls)))
| ~ hBOOL(hAPP_int_bool(zprime,U_749))
| ~ is_int(U_749) ),
inference(clausify,[status(thm)],[f_316_2]) ).
fof(f_317_1,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(bit0(bit0(bit1(pls))))),m)),one_one_int)),t),
inference(fof_nnf,[status(thm)],[fact_291__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096]) ).
cnf(f_317_2,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(bit0(bit0(bit1(pls))))),m)),one_one_int)),t),
inference(clausify,[status(thm)],[f_317_1]) ).
fof(f_318_1,plain,
! [X_1,Y_1] : hAPP_nat_real(power_power_real(hAPP_real_real(plus_plus_real(X_1),Y_1)),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(X_1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_1),number_number_of_nat(bit0(bit1(pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),X_1)),Y_1)),
inference(fof_nnf,[status(thm)],[fact_292_real__sum__squared__expand]) ).
fof(f_318_2,plain,
! [U_751,U_750] : hAPP_nat_real(power_power_real(hAPP_real_real(plus_plus_real(U_751),U_750)),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(U_751),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_750),number_number_of_nat(bit0(bit1(pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),U_751)),U_750)),
inference(variable_rename,[status(thm)],[f_318_1]) ).
cnf(f_318_3,plain,
hAPP_nat_real(power_power_real(hAPP_real_real(plus_plus_real(U_751),U_750)),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(U_751),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_750),number_number_of_nat(bit0(bit1(pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),U_751)),U_750)),
inference(clausify,[status(thm)],[f_318_2]) ).
fof(f_319_1,plain,
! [X_1] : hAPP_real_real(times_times_real(number267125858f_real(bit0(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(X_1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),X_1)),number_number_of_nat(bit0(bit1(pls)))),
inference(fof_nnf,[status(thm)],[fact_293_four__x__squared]) ).
fof(f_319_2,plain,
! [U_752] : hAPP_real_real(times_times_real(number267125858f_real(bit0(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_752),number_number_of_nat(bit0(bit1(pls))))) = hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),U_752)),number_number_of_nat(bit0(bit1(pls)))),
inference(variable_rename,[status(thm)],[f_319_1]) ).
cnf(f_319_3,plain,
hAPP_real_real(times_times_real(number267125858f_real(bit0(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_752),number_number_of_nat(bit0(bit1(pls))))) = hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),U_752)),number_number_of_nat(bit0(bit1(pls)))),
inference(clausify,[status(thm)],[f_319_2]) ).
fof(f_320_1,plain,
! [N_38,A_90] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(A_90),N_38)),hAPP_int_int(times_times_int(A_90),hAPP_nat_int(power_power_int(A_90),N_38))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_90)) ),
inference(fof_nnf,[status(thm)],[fact_294_power__less__power__Suc]) ).
fof(f_320_2,plain,
! [U_754,U_753] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_753),U_754)),hAPP_int_int(times_times_int(U_753),hAPP_nat_int(power_power_int(U_753),U_754))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_753)) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
cnf(f_320_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_753),U_754)),hAPP_int_int(times_times_int(U_753),hAPP_nat_int(power_power_int(U_753),U_754))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_753)) ),
inference(clausify,[status(thm)],[f_320_2]) ).
fof(f_321_1,plain,
! [N_38,A_90] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(A_90),N_38)),hAPP_nat_nat(times_times_nat(A_90),hAPP_nat_nat(power_power_nat(A_90),N_38))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),A_90)) ),
inference(fof_nnf,[status(thm)],[fact_295_power__less__power__Suc]) ).
fof(f_321_2,plain,
! [U_756,U_755] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_755),U_756)),hAPP_nat_nat(times_times_nat(U_755),hAPP_nat_nat(power_power_nat(U_755),U_756))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_755)) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
cnf(f_321_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_755),U_756)),hAPP_nat_nat(times_times_nat(U_755),hAPP_nat_nat(power_power_nat(U_755),U_756))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_755)) ),
inference(clausify,[status(thm)],[f_321_2]) ).
fof(f_322_1,plain,
! [N_38,A_90] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(A_90),N_38)),hAPP_real_real(times_times_real(A_90),hAPP_nat_real(power_power_real(A_90),N_38))))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),A_90)) ),
inference(fof_nnf,[status(thm)],[fact_296_power__less__power__Suc]) ).
fof(f_322_2,plain,
! [U_758,U_757] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_757),U_758)),hAPP_real_real(times_times_real(U_757),hAPP_nat_real(power_power_real(U_757),U_758))))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_757)) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
cnf(f_322_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_757),U_758)),hAPP_real_real(times_times_real(U_757),hAPP_nat_real(power_power_real(U_757),U_758))))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_757)) ),
inference(clausify,[status(thm)],[f_322_2]) ).
fof(f_323_1,plain,
! [N_37,A_89] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_int_int(times_times_int(A_89),hAPP_nat_int(power_power_int(A_89),N_37))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_89)) ),
inference(fof_nnf,[status(thm)],[fact_297_power__gt1__lemma]) ).
fof(f_323_2,plain,
! [U_760,U_759] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_int_int(times_times_int(U_759),hAPP_nat_int(power_power_int(U_759),U_760))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_759)) ),
inference(variable_rename,[status(thm)],[f_323_1]) ).
cnf(f_323_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_int_int(times_times_int(U_759),hAPP_nat_int(power_power_int(U_759),U_760))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_759)) ),
inference(clausify,[status(thm)],[f_323_2]) ).
fof(f_324_1,plain,
! [N_37,A_89] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(times_times_nat(A_89),hAPP_nat_nat(power_power_nat(A_89),N_37))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),A_89)) ),
inference(fof_nnf,[status(thm)],[fact_298_power__gt1__lemma]) ).
fof(f_324_2,plain,
! [U_762,U_761] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(times_times_nat(U_761),hAPP_nat_nat(power_power_nat(U_761),U_762))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_761)) ),
inference(variable_rename,[status(thm)],[f_324_1]) ).
cnf(f_324_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(times_times_nat(U_761),hAPP_nat_nat(power_power_nat(U_761),U_762))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_761)) ),
inference(clausify,[status(thm)],[f_324_2]) ).
fof(f_325_1,plain,
! [N_37,A_89] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_real_real(times_times_real(A_89),hAPP_nat_real(power_power_real(A_89),N_37))))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),A_89)) ),
inference(fof_nnf,[status(thm)],[fact_299_power__gt1__lemma]) ).
fof(f_325_2,plain,
! [U_764,U_763] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_real_real(times_times_real(U_763),hAPP_nat_real(power_power_real(U_763),U_764))))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_763)) ),
inference(variable_rename,[status(thm)],[f_325_1]) ).
cnf(f_325_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_real_real(times_times_real(U_763),hAPP_nat_real(power_power_real(U_763),U_764))))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_763)) ),
inference(clausify,[status(thm)],[f_325_2]) ).
fof(f_326_1,plain,
! [M_9,N_36,A_88] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_9),N_36))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(A_88),M_9)),hAPP_nat_int(power_power_int(A_88),N_36)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_88)) ),
inference(fof_nnf,[status(thm)],[fact_300_power__le__imp__le__exp]) ).
fof(f_326_2,plain,
! [U_767,U_766,U_765] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_767),U_766))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(U_765),U_767)),hAPP_nat_int(power_power_int(U_765),U_766)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_765)) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
cnf(f_326_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_767),U_766))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(U_765),U_767)),hAPP_nat_int(power_power_int(U_765),U_766)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_765)) ),
inference(clausify,[status(thm)],[f_326_2]) ).
fof(f_327_1,plain,
! [M_9,N_36,A_88] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_9),N_36))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(A_88),M_9)),hAPP_nat_nat(power_power_nat(A_88),N_36)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),A_88)) ),
inference(fof_nnf,[status(thm)],[fact_301_power__le__imp__le__exp]) ).
fof(f_327_2,plain,
! [U_770,U_769,U_768] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_770),U_769))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(U_768),U_770)),hAPP_nat_nat(power_power_nat(U_768),U_769)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_768)) ),
inference(variable_rename,[status(thm)],[f_327_1]) ).
cnf(f_327_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_770),U_769))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(U_768),U_770)),hAPP_nat_nat(power_power_nat(U_768),U_769)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_768)) ),
inference(clausify,[status(thm)],[f_327_2]) ).
fof(f_328_1,plain,
! [M_9,N_36,A_88] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_9),N_36))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(A_88),M_9)),hAPP_nat_real(power_power_real(A_88),N_36)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),A_88)) ),
inference(fof_nnf,[status(thm)],[fact_302_power__le__imp__le__exp]) ).
fof(f_328_2,plain,
! [U_773,U_772,U_771] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_773),U_772))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(U_771),U_773)),hAPP_nat_real(power_power_real(U_771),U_772)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_771)) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
cnf(f_328_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_773),U_772))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(U_771),U_773)),hAPP_nat_real(power_power_real(U_771),U_772)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_771)) ),
inference(clausify,[status(thm)],[f_328_2]) ).
fof(f_329_1,plain,
! [X_2,Y_2,B_2] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(B_2),X_2)),hAPP_nat_int(power_power_int(B_2),Y_2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(B_2),X_2)),hAPP_nat_int(power_power_int(B_2),Y_2))) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),B_2)) ),
inference(fof_nnf,[status(thm)],[fact_303_power__increasing__iff]) ).
fof(f_329_2,plain,
! [U_776,U_775,U_774] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(U_774),U_776)),hAPP_nat_int(power_power_int(U_774),U_775)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_776),U_775)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_776),U_775))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(U_774),U_776)),hAPP_nat_int(power_power_int(U_774),U_775))) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_774)) ),
inference(variable_rename,[status(thm)],[f_329_1]) ).
cnf(f_329_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_776),U_775))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(U_774),U_776)),hAPP_nat_int(power_power_int(U_774),U_775)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_774)) ),
inference(clausify,[status(thm)],[f_329_2]) ).
cnf(f_329_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(U_774),U_776)),hAPP_nat_int(power_power_int(U_774),U_775)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_776),U_775))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_774)) ),
inference(clausify,[status(thm)],[f_329_2]) ).
fof(f_330_1,plain,
! [X_2,Y_2,B_2] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(B_2),X_2)),hAPP_nat_nat(power_power_nat(B_2),Y_2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(B_2),X_2)),hAPP_nat_nat(power_power_nat(B_2),Y_2))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),B_2)) ),
inference(fof_nnf,[status(thm)],[fact_304_power__increasing__iff]) ).
fof(f_330_2,plain,
! [U_779,U_778,U_777] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(U_777),U_779)),hAPP_nat_nat(power_power_nat(U_777),U_778)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_779),U_778)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_779),U_778))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(U_777),U_779)),hAPP_nat_nat(power_power_nat(U_777),U_778))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_777)) ),
inference(variable_rename,[status(thm)],[f_330_1]) ).
cnf(f_330_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_779),U_778))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(U_777),U_779)),hAPP_nat_nat(power_power_nat(U_777),U_778)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_777)) ),
inference(clausify,[status(thm)],[f_330_2]) ).
cnf(f_330_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(U_777),U_779)),hAPP_nat_nat(power_power_nat(U_777),U_778)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_779),U_778))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_777)) ),
inference(clausify,[status(thm)],[f_330_2]) ).
fof(f_331_1,plain,
! [X_2,Y_2,B_2] :
( ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(B_2),X_2)),hAPP_nat_real(power_power_real(B_2),Y_2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(B_2),X_2)),hAPP_nat_real(power_power_real(B_2),Y_2))) ) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),B_2)) ),
inference(fof_nnf,[status(thm)],[fact_305_power__increasing__iff]) ).
fof(f_331_2,plain,
! [U_782,U_781,U_780] :
( ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(U_780),U_782)),hAPP_nat_real(power_power_real(U_780),U_781)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_782),U_781)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_782),U_781))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(U_780),U_782)),hAPP_nat_real(power_power_real(U_780),U_781))) ) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_780)) ),
inference(variable_rename,[status(thm)],[f_331_1]) ).
cnf(f_331_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_782),U_781))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(U_780),U_782)),hAPP_nat_real(power_power_real(U_780),U_781)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_780)) ),
inference(clausify,[status(thm)],[f_331_2]) ).
cnf(f_331_4,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(U_780),U_782)),hAPP_nat_real(power_power_real(U_780),U_781)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_782),U_781))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_780)) ),
inference(clausify,[status(thm)],[f_331_2]) ).
fof(f_332_1,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(fof_nnf,[status(thm)],[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]) ).
cnf(f_332_2,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(clausify,[status(thm)],[f_332_1]) ).
fof(f_333_1,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)))
& 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)) ),
inference(fof_nnf,[status(thm)],[fact_307_s0p]) ).
cnf(f_333_2,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),s)),
inference(clausify,[status(thm)],[f_333_1]) ).
cnf(f_333_3,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(clausify,[status(thm)],[f_333_1]) ).
cnf(f_333_4,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(clausify,[status(thm)],[f_333_1]) ).
fof(f_334_1,plain,
? [X] :
( ! [Y] :
( Y = X
| ~ hBOOL(hAPP_int_bool(zcong(s1,Y),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,Y),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),Y))
| ~ is_int(Y) )
& hBOOL(hAPP_int_bool(zcong(s1,X),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,X),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),X))
& is_int(X) ),
inference(fof_nnf,[status(thm)],[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(f_334_2,plain,
? [U_784] :
( ! [U_783] :
( U_783 = U_784
| ~ hBOOL(hAPP_int_bool(zcong(s1,U_783),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,U_783),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),U_783))
| ~ is_int(U_783) )
& hBOOL(hAPP_int_bool(zcong(s1,U_784),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,U_784),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),U_784))
& is_int(U_784) ),
inference(variable_rename,[status(thm)],[f_334_1]) ).
fof(f_334_3,plain,
( ! [U_783] :
( U_783 = sK6
| ~ hBOOL(hAPP_int_bool(zcong(s1,U_783),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,U_783),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),U_783))
| ~ is_int(U_783) )
& hBOOL(hAPP_int_bool(zcong(s1,sK6),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,sK6),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),sK6))
& is_int(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_784,sK6)],[f_334_2]) ).
cnf(f_334_4,plain,
is_int(sK6),
inference(clausify,[status(thm)],[f_334_3]) ).
cnf(f_334_5,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK6)),
inference(clausify,[status(thm)],[f_334_3]) ).
cnf(f_334_6,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK6),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(clausify,[status(thm)],[f_334_3]) ).
cnf(f_334_7,plain,
hBOOL(hAPP_int_bool(zcong(s1,sK6),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(clausify,[status(thm)],[f_334_3]) ).
cnf(f_334_8,plain,
( U_783 = sK6
| ~ hBOOL(hAPP_int_bool(zcong(s1,U_783),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,U_783),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),U_783))
| ~ is_int(U_783) ),
inference(clausify,[status(thm)],[f_334_3]) ).
fof(f_335_1,plain,
? [S_1] :
( hBOOL(hAPP_int_bool(zcong(s1,S_1),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_1),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_1))
& is_int(S_1) ),
inference(fof_nnf,[status(thm)],[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(f_335_2,plain,
? [U_785] :
( hBOOL(hAPP_int_bool(zcong(s1,U_785),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,U_785),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),U_785))
& is_int(U_785) ),
inference(variable_rename,[status(thm)],[f_335_1]) ).
fof(f_335_3,plain,
( hBOOL(hAPP_int_bool(zcong(s1,sK7),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,sK7),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),sK7))
& is_int(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_785,sK7)],[f_335_2]) ).
cnf(f_335_4,plain,
is_int(sK7),
inference(clausify,[status(thm)],[f_335_3]) ).
cnf(f_335_5,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK7)),
inference(clausify,[status(thm)],[f_335_3]) ).
cnf(f_335_6,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK7),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(clausify,[status(thm)],[f_335_3]) ).
cnf(f_335_7,plain,
hBOOL(hAPP_int_bool(zcong(s1,sK7),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(clausify,[status(thm)],[f_335_3]) ).
fof(f_336_1,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(fof_nnf,[status(thm)],[fact_310_s1]) ).
cnf(f_336_2,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(clausify,[status(thm)],[f_336_1]) ).
fof(f_337_1,plain,
! [A_2,N] :
( ( ( hAPP_nat_int(power_power_int(A_2),N) = zero_zero_int
| N = zero_zero_nat
| A_2 != zero_zero_int )
& ( ( N != zero_zero_nat
& A_2 = zero_zero_int )
| hAPP_nat_int(power_power_int(A_2),N) != zero_zero_int ) )
| ~ is_int(A_2) ),
inference(fof_nnf,[status(thm)],[fact_311_power__eq__0__iff]) ).
fof(f_337_2,plain,
! [U_787,U_786] :
( ( ( hAPP_nat_int(power_power_int(U_787),U_786) = zero_zero_int
| U_786 = zero_zero_nat
| U_787 != zero_zero_int )
& ( ( U_786 != zero_zero_nat
& U_787 = zero_zero_int )
| hAPP_nat_int(power_power_int(U_787),U_786) != zero_zero_int ) )
| ~ is_int(U_787) ),
inference(variable_rename,[status(thm)],[f_337_1]) ).
fof(f_337_3,plain,
! [U_787] :
( ( ! [U_789] :
( hAPP_nat_int(power_power_int(U_787),U_789) = zero_zero_int
| U_789 = zero_zero_nat
| U_787 != zero_zero_int )
& ! [U_788] :
( ( U_788 != zero_zero_nat
& U_787 = zero_zero_int )
| hAPP_nat_int(power_power_int(U_787),U_788) != zero_zero_int ) )
| ~ is_int(U_787) ),
inference(miniscope,[status(thm)],[f_337_2]) ).
cnf(f_337_4,plain,
( U_787 = zero_zero_int
| hAPP_nat_int(power_power_int(U_787),U_788) != zero_zero_int
| ~ is_int(U_787) ),
inference(clausify,[status(thm)],[f_337_3]) ).
cnf(f_337_5,plain,
( U_788 != zero_zero_nat
| hAPP_nat_int(power_power_int(U_787),U_788) != zero_zero_int
| ~ is_int(U_787) ),
inference(clausify,[status(thm)],[f_337_3]) ).
cnf(f_337_6,plain,
( hAPP_nat_int(power_power_int(U_787),U_789) = zero_zero_int
| U_789 = zero_zero_nat
| U_787 != zero_zero_int
| ~ is_int(U_787) ),
inference(clausify,[status(thm)],[f_337_3]) ).
fof(f_338_1,plain,
! [A_2,N] :
( ( hAPP_nat_nat(power_power_nat(A_2),N) = zero_zero_nat
| N = zero_zero_nat
| A_2 != zero_zero_nat )
& ( ( N != zero_zero_nat
& A_2 = zero_zero_nat )
| hAPP_nat_nat(power_power_nat(A_2),N) != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_312_power__eq__0__iff]) ).
fof(f_338_2,plain,
! [U_791,U_790] :
( ( hAPP_nat_nat(power_power_nat(U_791),U_790) = zero_zero_nat
| U_790 = zero_zero_nat
| U_791 != zero_zero_nat )
& ( ( U_790 != zero_zero_nat
& U_791 = zero_zero_nat )
| hAPP_nat_nat(power_power_nat(U_791),U_790) != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_338_1]) ).
fof(f_338_3,plain,
( ! [U_795,U_793] :
( hAPP_nat_nat(power_power_nat(U_795),U_793) = zero_zero_nat
| U_793 = zero_zero_nat
| U_795 != zero_zero_nat )
& ! [U_794,U_792] :
( ( U_792 != zero_zero_nat
& U_794 = zero_zero_nat )
| hAPP_nat_nat(power_power_nat(U_794),U_792) != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_338_2]) ).
cnf(f_338_4,plain,
( U_794 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(U_794),U_792) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_338_3]) ).
cnf(f_338_5,plain,
( U_792 != zero_zero_nat
| hAPP_nat_nat(power_power_nat(U_794),U_792) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_338_3]) ).
cnf(f_338_6,plain,
( hAPP_nat_nat(power_power_nat(U_795),U_793) = zero_zero_nat
| U_793 = zero_zero_nat
| U_795 != zero_zero_nat ),
inference(clausify,[status(thm)],[f_338_3]) ).
fof(f_339_1,plain,
! [A_2,N] :
( ( hAPP_nat_real(power_power_real(A_2),N) = zero_zero_real
| N = zero_zero_nat
| A_2 != zero_zero_real )
& ( ( N != zero_zero_nat
& A_2 = zero_zero_real )
| hAPP_nat_real(power_power_real(A_2),N) != zero_zero_real ) ),
inference(fof_nnf,[status(thm)],[fact_313_power__eq__0__iff]) ).
fof(f_339_2,plain,
! [U_797,U_796] :
( ( hAPP_nat_real(power_power_real(U_797),U_796) = zero_zero_real
| U_796 = zero_zero_nat
| U_797 != zero_zero_real )
& ( ( U_796 != zero_zero_nat
& U_797 = zero_zero_real )
| hAPP_nat_real(power_power_real(U_797),U_796) != zero_zero_real ) ),
inference(variable_rename,[status(thm)],[f_339_1]) ).
fof(f_339_3,plain,
( ! [U_801,U_799] :
( hAPP_nat_real(power_power_real(U_801),U_799) = zero_zero_real
| U_799 = zero_zero_nat
| U_801 != zero_zero_real )
& ! [U_800,U_798] :
( ( U_798 != zero_zero_nat
& U_800 = zero_zero_real )
| hAPP_nat_real(power_power_real(U_800),U_798) != zero_zero_real ) ),
inference(miniscope,[status(thm)],[f_339_2]) ).
cnf(f_339_4,plain,
( U_800 = zero_zero_real
| hAPP_nat_real(power_power_real(U_800),U_798) != zero_zero_real ),
inference(clausify,[status(thm)],[f_339_3]) ).
cnf(f_339_5,plain,
( U_798 != zero_zero_nat
| hAPP_nat_real(power_power_real(U_800),U_798) != zero_zero_real ),
inference(clausify,[status(thm)],[f_339_3]) ).
cnf(f_339_6,plain,
( hAPP_nat_real(power_power_real(U_801),U_799) = zero_zero_real
| U_799 = zero_zero_nat
| U_801 != zero_zero_real ),
inference(clausify,[status(thm)],[f_339_3]) ).
fof(f_340_1,plain,
! [A_87,M_8,N_35] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(A_87),M_8)),hAPP_nat_real(power_power_real(A_87),N_35)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_8),N_35)) ),
inference(fof_nnf,[status(thm)],[fact_314_le__imp__power__dvd]) ).
fof(f_340_2,plain,
! [U_804,U_803,U_802] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(U_804),U_803)),hAPP_nat_real(power_power_real(U_804),U_802)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_803),U_802)) ),
inference(variable_rename,[status(thm)],[f_340_1]) ).
cnf(f_340_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(U_804),U_803)),hAPP_nat_real(power_power_real(U_804),U_802)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_803),U_802)) ),
inference(clausify,[status(thm)],[f_340_2]) ).
fof(f_341_1,plain,
! [A_87,M_8,N_35] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(A_87),M_8)),hAPP_nat_int(power_power_int(A_87),N_35)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_8),N_35)) ),
inference(fof_nnf,[status(thm)],[fact_315_le__imp__power__dvd]) ).
fof(f_341_2,plain,
! [U_807,U_806,U_805] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_807),U_806)),hAPP_nat_int(power_power_int(U_807),U_805)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_806),U_805)) ),
inference(variable_rename,[status(thm)],[f_341_1]) ).
cnf(f_341_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_807),U_806)),hAPP_nat_int(power_power_int(U_807),U_805)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_806),U_805)) ),
inference(clausify,[status(thm)],[f_341_2]) ).
fof(f_342_1,plain,
! [A_87,M_8,N_35] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(A_87),M_8)),hAPP_nat_nat(power_power_nat(A_87),N_35)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_8),N_35)) ),
inference(fof_nnf,[status(thm)],[fact_316_le__imp__power__dvd]) ).
fof(f_342_2,plain,
! [U_810,U_809,U_808] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_810),U_809)),hAPP_nat_nat(power_power_nat(U_810),U_808)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_809),U_808)) ),
inference(variable_rename,[status(thm)],[f_342_1]) ).
cnf(f_342_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_810),U_809)),hAPP_nat_nat(power_power_nat(U_810),U_808)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_809),U_808)) ),
inference(clausify,[status(thm)],[f_342_2]) ).
fof(f_343_1,plain,
! [N_34,M_7,X_19,Y_16] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X_19),N_34)),hAPP_nat_real(power_power_real(Y_16),M_7)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_34),M_7))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X_19),Y_16)) ),
inference(fof_nnf,[status(thm)],[fact_317_dvd__power__le]) ).
fof(f_343_2,plain,
! [U_814,U_813,U_812,U_811] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(U_812),U_814)),hAPP_nat_real(power_power_real(U_811),U_813)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_814),U_813))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_812),U_811)) ),
inference(variable_rename,[status(thm)],[f_343_1]) ).
cnf(f_343_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(U_812),U_814)),hAPP_nat_real(power_power_real(U_811),U_813)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_814),U_813))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_812),U_811)) ),
inference(clausify,[status(thm)],[f_343_2]) ).
fof(f_344_1,plain,
! [N_34,M_7,X_19,Y_16] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X_19),N_34)),hAPP_nat_int(power_power_int(Y_16),M_7)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_34),M_7))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X_19),Y_16)) ),
inference(fof_nnf,[status(thm)],[fact_318_dvd__power__le]) ).
fof(f_344_2,plain,
! [U_818,U_817,U_816,U_815] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_816),U_818)),hAPP_nat_int(power_power_int(U_815),U_817)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_818),U_817))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_816),U_815)) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
cnf(f_344_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_816),U_818)),hAPP_nat_int(power_power_int(U_815),U_817)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_818),U_817))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_816),U_815)) ),
inference(clausify,[status(thm)],[f_344_2]) ).
fof(f_345_1,plain,
! [N_34,M_7,X_19,Y_16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X_19),N_34)),hAPP_nat_nat(power_power_nat(Y_16),M_7)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_34),M_7))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_19),Y_16)) ),
inference(fof_nnf,[status(thm)],[fact_319_dvd__power__le]) ).
fof(f_345_2,plain,
! [U_822,U_821,U_820,U_819] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_820),U_822)),hAPP_nat_nat(power_power_nat(U_819),U_821)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_822),U_821))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_820),U_819)) ),
inference(variable_rename,[status(thm)],[f_345_1]) ).
cnf(f_345_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_820),U_822)),hAPP_nat_nat(power_power_nat(U_819),U_821)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_822),U_821))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_820),U_819)) ),
inference(clausify,[status(thm)],[f_345_2]) ).
fof(f_346_1,plain,
! [M_6,A_86,N_33,B_55] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(A_86),M_6)),B_55))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_6),N_33))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(A_86),N_33)),B_55)) ),
inference(fof_nnf,[status(thm)],[fact_320_power__le__dvd]) ).
fof(f_346_2,plain,
! [U_826,U_825,U_824,U_823] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(U_825),U_826)),U_823))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_826),U_824))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(U_825),U_824)),U_823)) ),
inference(variable_rename,[status(thm)],[f_346_1]) ).
cnf(f_346_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(U_825),U_826)),U_823))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_826),U_824))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(U_825),U_824)),U_823)) ),
inference(clausify,[status(thm)],[f_346_2]) ).
fof(f_347_1,plain,
! [M_6,A_86,N_33,B_55] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(A_86),M_6)),B_55))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_6),N_33))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(A_86),N_33)),B_55)) ),
inference(fof_nnf,[status(thm)],[fact_321_power__le__dvd]) ).
fof(f_347_2,plain,
! [U_830,U_829,U_828,U_827] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_829),U_830)),U_827))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_830),U_828))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_829),U_828)),U_827)) ),
inference(variable_rename,[status(thm)],[f_347_1]) ).
cnf(f_347_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_829),U_830)),U_827))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_830),U_828))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_829),U_828)),U_827)) ),
inference(clausify,[status(thm)],[f_347_2]) ).
fof(f_348_1,plain,
! [M_6,A_86,N_33,B_55] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(A_86),M_6)),B_55))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_6),N_33))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(A_86),N_33)),B_55)) ),
inference(fof_nnf,[status(thm)],[fact_322_power__le__dvd]) ).
fof(f_348_2,plain,
! [U_834,U_833,U_832,U_831] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_833),U_834)),U_831))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_834),U_832))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_833),U_832)),U_831)) ),
inference(variable_rename,[status(thm)],[f_348_1]) ).
cnf(f_348_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_833),U_834)),U_831))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_834),U_832))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_833),U_832)),U_831)) ),
inference(clausify,[status(thm)],[f_348_2]) ).
fof(f_349_1,plain,
! [A_85,N_32,B_54] :
( A_85 = B_54
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_54))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_85))
| hAPP_nat_int(power_power_int(A_85),N_32) != hAPP_nat_int(power_power_int(B_54),N_32)
| ~ is_int(B_54)
| ~ is_int(A_85) ),
inference(fof_nnf,[status(thm)],[fact_323_power__eq__imp__eq__base]) ).
fof(f_349_2,plain,
! [U_837,U_836,U_835] :
( U_837 = U_835
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_836))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_835))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_837))
| hAPP_nat_int(power_power_int(U_837),U_836) != hAPP_nat_int(power_power_int(U_835),U_836)
| ~ is_int(U_835)
| ~ is_int(U_837) ),
inference(variable_rename,[status(thm)],[f_349_1]) ).
cnf(f_349_3,plain,
( U_837 = U_835
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_836))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_835))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_837))
| hAPP_nat_int(power_power_int(U_837),U_836) != hAPP_nat_int(power_power_int(U_835),U_836)
| ~ is_int(U_835)
| ~ is_int(U_837) ),
inference(clausify,[status(thm)],[f_349_2]) ).
fof(f_350_1,plain,
! [A_85,N_32,B_54] :
( A_85 = B_54
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_54))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_85))
| hAPP_nat_nat(power_power_nat(A_85),N_32) != hAPP_nat_nat(power_power_nat(B_54),N_32) ),
inference(fof_nnf,[status(thm)],[fact_324_power__eq__imp__eq__base]) ).
fof(f_350_2,plain,
! [U_840,U_839,U_838] :
( U_840 = U_838
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_839))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_838))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_840))
| hAPP_nat_nat(power_power_nat(U_840),U_839) != hAPP_nat_nat(power_power_nat(U_838),U_839) ),
inference(variable_rename,[status(thm)],[f_350_1]) ).
cnf(f_350_3,plain,
( U_840 = U_838
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_839))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_838))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_840))
| hAPP_nat_nat(power_power_nat(U_840),U_839) != hAPP_nat_nat(power_power_nat(U_838),U_839) ),
inference(clausify,[status(thm)],[f_350_2]) ).
fof(f_351_1,plain,
! [A_85,N_32,B_54] :
( A_85 = B_54
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_32))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_54))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_85))
| hAPP_nat_real(power_power_real(A_85),N_32) != hAPP_nat_real(power_power_real(B_54),N_32) ),
inference(fof_nnf,[status(thm)],[fact_325_power__eq__imp__eq__base]) ).
fof(f_351_2,plain,
! [U_843,U_842,U_841] :
( U_843 = U_841
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_842))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_841))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_843))
| hAPP_nat_real(power_power_real(U_843),U_842) != hAPP_nat_real(power_power_real(U_841),U_842) ),
inference(variable_rename,[status(thm)],[f_351_1]) ).
cnf(f_351_3,plain,
( U_843 = U_841
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_842))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_841))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_843))
| hAPP_nat_real(power_power_real(U_843),U_842) != hAPP_nat_real(power_power_real(U_841),U_842) ),
inference(clausify,[status(thm)],[f_351_2]) ).
fof(f_352_1,plain,
! [N_1,M] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,N_1),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,M),N_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M)) ),
inference(fof_nnf,[status(thm)],[fact_326_zdvd__not__zless]) ).
fof(f_352_2,plain,
! [U_845,U_844] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_845),U_844))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_844),U_845))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_844)) ),
inference(variable_rename,[status(thm)],[f_352_1]) ).
cnf(f_352_3,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_845),U_844))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_844),U_845))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_844)) ),
inference(clausify,[status(thm)],[f_352_2]) ).
fof(f_353_1,plain,
! [N_1,M] :
( M = N_1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,N_1),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,M),N_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),M))
| ~ is_int(M)
| ~ is_int(N_1) ),
inference(fof_nnf,[status(thm)],[fact_327_zdvd__antisym__nonneg]) ).
fof(f_353_2,plain,
! [U_847,U_846] :
( U_846 = U_847
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_847),U_846))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_846),U_847))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_847))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_846))
| ~ is_int(U_846)
| ~ is_int(U_847) ),
inference(variable_rename,[status(thm)],[f_353_1]) ).
cnf(f_353_3,plain,
( U_846 = U_847
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_847),U_846))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_846),U_847))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_847))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_846))
| ~ is_int(U_846)
| ~ is_int(U_847) ),
inference(clausify,[status(thm)],[f_353_2]) ).
fof(f_354_1,plain,
! [K_1,M,N_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,M),N_1))
| K_1 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(K_1),M)),hAPP_int_int(times_times_int(K_1),N_1)))
| ~ is_int(K_1) ),
inference(fof_nnf,[status(thm)],[fact_328_zdvd__mult__cancel]) ).
fof(f_354_2,plain,
! [U_850,U_849,U_848] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_849),U_848))
| U_850 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(U_850),U_849)),hAPP_int_int(times_times_int(U_850),U_848)))
| ~ is_int(U_850) ),
inference(variable_rename,[status(thm)],[f_354_1]) ).
fof(f_354_3,plain,
! [U_850] :
( ! [U_849,U_848] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_849),U_848))
| U_850 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(U_850),U_849)),hAPP_int_int(times_times_int(U_850),U_848))) )
| ~ is_int(U_850) ),
inference(miniscope,[status(thm)],[f_354_2]) ).
cnf(f_354_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_849),U_848))
| U_850 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(U_850),U_849)),hAPP_int_int(times_times_int(U_850),U_848)))
| ~ is_int(U_850) ),
inference(clausify,[status(thm)],[f_354_3]) ).
fof(f_355_1,plain,
! [N_31,X_18,Y_15] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(X_18),N_31)),hAPP_nat_real(power_power_real(Y_15),N_31)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X_18),Y_15)) ),
inference(fof_nnf,[status(thm)],[fact_329_dvd__power__same]) ).
fof(f_355_2,plain,
! [U_853,U_852,U_851] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(U_852),U_853)),hAPP_nat_real(power_power_real(U_851),U_853)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_852),U_851)) ),
inference(variable_rename,[status(thm)],[f_355_1]) ).
cnf(f_355_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_nat_real(power_power_real(U_852),U_853)),hAPP_nat_real(power_power_real(U_851),U_853)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_852),U_851)) ),
inference(clausify,[status(thm)],[f_355_2]) ).
fof(f_356_1,plain,
! [N_31,X_18,Y_15] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(X_18),N_31)),hAPP_nat_int(power_power_int(Y_15),N_31)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X_18),Y_15)) ),
inference(fof_nnf,[status(thm)],[fact_330_dvd__power__same]) ).
fof(f_356_2,plain,
! [U_856,U_855,U_854] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_855),U_856)),hAPP_nat_int(power_power_int(U_854),U_856)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_855),U_854)) ),
inference(variable_rename,[status(thm)],[f_356_1]) ).
cnf(f_356_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_855),U_856)),hAPP_nat_int(power_power_int(U_854),U_856)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_855),U_854)) ),
inference(clausify,[status(thm)],[f_356_2]) ).
fof(f_357_1,plain,
! [N_31,X_18,Y_15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X_18),N_31)),hAPP_nat_nat(power_power_nat(Y_15),N_31)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_18),Y_15)) ),
inference(fof_nnf,[status(thm)],[fact_331_dvd__power__same]) ).
fof(f_357_2,plain,
! [U_859,U_858,U_857] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_858),U_859)),hAPP_nat_nat(power_power_nat(U_857),U_859)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_858),U_857)) ),
inference(variable_rename,[status(thm)],[f_357_1]) ).
cnf(f_357_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_858),U_859)),hAPP_nat_nat(power_power_nat(U_857),U_859)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_858),U_857)) ),
inference(clausify,[status(thm)],[f_357_2]) ).
fof(f_358_1,plain,
! [N_30,A_84] :
( hAPP_nat_int(power_power_int(A_84),N_30) != zero_zero_int
| A_84 = zero_zero_int
| ~ is_int(A_84) ),
inference(fof_nnf,[status(thm)],[fact_332_field__power__not__zero]) ).
fof(f_358_2,plain,
! [U_861,U_860] :
( hAPP_nat_int(power_power_int(U_860),U_861) != zero_zero_int
| U_860 = zero_zero_int
| ~ is_int(U_860) ),
inference(variable_rename,[status(thm)],[f_358_1]) ).
cnf(f_358_3,plain,
( hAPP_nat_int(power_power_int(U_860),U_861) != zero_zero_int
| U_860 = zero_zero_int
| ~ is_int(U_860) ),
inference(clausify,[status(thm)],[f_358_2]) ).
fof(f_359_1,plain,
! [N_30,A_84] :
( hAPP_nat_real(power_power_real(A_84),N_30) != zero_zero_real
| A_84 = zero_zero_real ),
inference(fof_nnf,[status(thm)],[fact_333_field__power__not__zero]) ).
fof(f_359_2,plain,
! [U_863,U_862] :
( hAPP_nat_real(power_power_real(U_862),U_863) != zero_zero_real
| U_862 = zero_zero_real ),
inference(variable_rename,[status(thm)],[f_359_1]) ).
cnf(f_359_3,plain,
( hAPP_nat_real(power_power_real(U_862),U_863) != zero_zero_real
| U_862 = zero_zero_real ),
inference(clausify,[status(thm)],[f_359_2]) ).
fof(f_360_1,plain,
! [N_29] :
( ( hAPP_nat_int(power_power_int(zero_zero_int),N_29) = zero_zero_int
| N_29 = zero_zero_nat )
& ( hAPP_nat_int(power_power_int(zero_zero_int),N_29) = one_one_int
| N_29 != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_334_power__0__left]) ).
fof(f_360_2,plain,
! [U_864] :
( ( hAPP_nat_int(power_power_int(zero_zero_int),U_864) = zero_zero_int
| U_864 = zero_zero_nat )
& ( hAPP_nat_int(power_power_int(zero_zero_int),U_864) = one_one_int
| U_864 != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_360_1]) ).
fof(f_360_3,plain,
( ! [U_866] :
( hAPP_nat_int(power_power_int(zero_zero_int),U_866) = zero_zero_int
| U_866 = zero_zero_nat )
& ! [U_865] :
( hAPP_nat_int(power_power_int(zero_zero_int),U_865) = one_one_int
| U_865 != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_360_2]) ).
cnf(f_360_4,plain,
( hAPP_nat_int(power_power_int(zero_zero_int),U_865) = one_one_int
| U_865 != zero_zero_nat ),
inference(clausify,[status(thm)],[f_360_3]) ).
cnf(f_360_5,plain,
( hAPP_nat_int(power_power_int(zero_zero_int),U_866) = zero_zero_int
| U_866 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_360_3]) ).
fof(f_361_1,plain,
! [N_29] :
( ( hAPP_nat_nat(power_power_nat(zero_zero_nat),N_29) = zero_zero_nat
| N_29 = zero_zero_nat )
& ( hAPP_nat_nat(power_power_nat(zero_zero_nat),N_29) = one_one_nat
| N_29 != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_335_power__0__left]) ).
fof(f_361_2,plain,
! [U_867] :
( ( hAPP_nat_nat(power_power_nat(zero_zero_nat),U_867) = zero_zero_nat
| U_867 = zero_zero_nat )
& ( hAPP_nat_nat(power_power_nat(zero_zero_nat),U_867) = one_one_nat
| U_867 != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_361_1]) ).
fof(f_361_3,plain,
( ! [U_869] :
( hAPP_nat_nat(power_power_nat(zero_zero_nat),U_869) = zero_zero_nat
| U_869 = zero_zero_nat )
& ! [U_868] :
( hAPP_nat_nat(power_power_nat(zero_zero_nat),U_868) = one_one_nat
| U_868 != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_361_2]) ).
cnf(f_361_4,plain,
( hAPP_nat_nat(power_power_nat(zero_zero_nat),U_868) = one_one_nat
| U_868 != zero_zero_nat ),
inference(clausify,[status(thm)],[f_361_3]) ).
cnf(f_361_5,plain,
( hAPP_nat_nat(power_power_nat(zero_zero_nat),U_869) = zero_zero_nat
| U_869 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_361_3]) ).
fof(f_362_1,plain,
! [N_29] :
( ( hAPP_nat_real(power_power_real(zero_zero_real),N_29) = zero_zero_real
| N_29 = zero_zero_nat )
& ( hAPP_nat_real(power_power_real(zero_zero_real),N_29) = one_one_real
| N_29 != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_336_power__0__left]) ).
fof(f_362_2,plain,
! [U_870] :
( ( hAPP_nat_real(power_power_real(zero_zero_real),U_870) = zero_zero_real
| U_870 = zero_zero_nat )
& ( hAPP_nat_real(power_power_real(zero_zero_real),U_870) = one_one_real
| U_870 != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_362_1]) ).
fof(f_362_3,plain,
( ! [U_872] :
( hAPP_nat_real(power_power_real(zero_zero_real),U_872) = zero_zero_real
| U_872 = zero_zero_nat )
& ! [U_871] :
( hAPP_nat_real(power_power_real(zero_zero_real),U_871) = one_one_real
| U_871 != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_362_2]) ).
cnf(f_362_4,plain,
( hAPP_nat_real(power_power_real(zero_zero_real),U_871) = one_one_real
| U_871 != zero_zero_nat ),
inference(clausify,[status(thm)],[f_362_3]) ).
cnf(f_362_5,plain,
( hAPP_nat_real(power_power_real(zero_zero_real),U_872) = zero_zero_real
| U_872 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_362_3]) ).
fof(f_363_1,plain,
! [Z,N_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z),N_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Z),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_337_zdvd__imp__le]) ).
fof(f_363_2,plain,
! [U_874,U_873] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_874),U_873))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_873))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_874),U_873)) ),
inference(variable_rename,[status(thm)],[f_363_1]) ).
cnf(f_363_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_874),U_873))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_873))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_874),U_873)) ),
inference(clausify,[status(thm)],[f_363_2]) ).
fof(f_364_1,plain,
! [N_28,A_83,B_53] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(A_83),N_28)),hAPP_nat_int(power_power_int(B_53),N_28)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_28))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_83),B_53)) ),
inference(fof_nnf,[status(thm)],[fact_338_power__strict__mono]) ).
fof(f_364_2,plain,
! [U_877,U_876,U_875] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_876),U_877)),hAPP_nat_int(power_power_int(U_875),U_877)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_877))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_876))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_876),U_875)) ),
inference(variable_rename,[status(thm)],[f_364_1]) ).
cnf(f_364_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_876),U_877)),hAPP_nat_int(power_power_int(U_875),U_877)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_877))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_876))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_876),U_875)) ),
inference(clausify,[status(thm)],[f_364_2]) ).
fof(f_365_1,plain,
! [N_28,A_83,B_53] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(A_83),N_28)),hAPP_nat_nat(power_power_nat(B_53),N_28)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_28))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_83))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_83),B_53)) ),
inference(fof_nnf,[status(thm)],[fact_339_power__strict__mono]) ).
fof(f_365_2,plain,
! [U_880,U_879,U_878] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_879),U_880)),hAPP_nat_nat(power_power_nat(U_878),U_880)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_880))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_879))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_879),U_878)) ),
inference(variable_rename,[status(thm)],[f_365_1]) ).
cnf(f_365_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_879),U_880)),hAPP_nat_nat(power_power_nat(U_878),U_880)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_880))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_879))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_879),U_878)) ),
inference(clausify,[status(thm)],[f_365_2]) ).
fof(f_366_1,plain,
! [N_28,A_83,B_53] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(A_83),N_28)),hAPP_nat_real(power_power_real(B_53),N_28)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_28))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_83))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_83),B_53)) ),
inference(fof_nnf,[status(thm)],[fact_340_power__strict__mono]) ).
fof(f_366_2,plain,
! [U_883,U_882,U_881] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_882),U_883)),hAPP_nat_real(power_power_real(U_881),U_883)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_883))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_882))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_882),U_881)) ),
inference(variable_rename,[status(thm)],[f_366_1]) ).
cnf(f_366_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_882),U_883)),hAPP_nat_real(power_power_real(U_881),U_883)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_883))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_882))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_882),U_881)) ),
inference(clausify,[status(thm)],[f_366_2]) ).
fof(f_367_1,plain,
! [A_82] : hAPP_int_int(times_times_int(zero_zero_int),A_82) = zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J]) ).
fof(f_367_2,plain,
! [U_884] : hAPP_int_int(times_times_int(zero_zero_int),U_884) = zero_zero_int,
inference(variable_rename,[status(thm)],[f_367_1]) ).
cnf(f_367_3,plain,
hAPP_int_int(times_times_int(zero_zero_int),U_884) = zero_zero_int,
inference(clausify,[status(thm)],[f_367_2]) ).
fof(f_368_1,plain,
! [A_82] : hAPP_nat_nat(times_times_nat(zero_zero_nat),A_82) = zero_zero_nat,
inference(fof_nnf,[status(thm)],[fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J]) ).
fof(f_368_2,plain,
! [U_885] : hAPP_nat_nat(times_times_nat(zero_zero_nat),U_885) = zero_zero_nat,
inference(variable_rename,[status(thm)],[f_368_1]) ).
cnf(f_368_3,plain,
hAPP_nat_nat(times_times_nat(zero_zero_nat),U_885) = zero_zero_nat,
inference(clausify,[status(thm)],[f_368_2]) ).
fof(f_369_1,plain,
! [A_82] : hAPP_real_real(times_times_real(zero_zero_real),A_82) = zero_zero_real,
inference(fof_nnf,[status(thm)],[fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J]) ).
fof(f_369_2,plain,
! [U_886] : hAPP_real_real(times_times_real(zero_zero_real),U_886) = zero_zero_real,
inference(variable_rename,[status(thm)],[f_369_1]) ).
cnf(f_369_3,plain,
hAPP_real_real(times_times_real(zero_zero_real),U_886) = zero_zero_real,
inference(clausify,[status(thm)],[f_369_2]) ).
fof(f_370_1,plain,
! [A_81] : hAPP_int_int(times_times_int(A_81),zero_zero_int) = zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).
fof(f_370_2,plain,
! [U_887] : hAPP_int_int(times_times_int(U_887),zero_zero_int) = zero_zero_int,
inference(variable_rename,[status(thm)],[f_370_1]) ).
cnf(f_370_3,plain,
hAPP_int_int(times_times_int(U_887),zero_zero_int) = zero_zero_int,
inference(clausify,[status(thm)],[f_370_2]) ).
fof(f_371_1,plain,
! [A_81] : hAPP_nat_nat(times_times_nat(A_81),zero_zero_nat) = zero_zero_nat,
inference(fof_nnf,[status(thm)],[fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).
fof(f_371_2,plain,
! [U_888] : hAPP_nat_nat(times_times_nat(U_888),zero_zero_nat) = zero_zero_nat,
inference(variable_rename,[status(thm)],[f_371_1]) ).
cnf(f_371_3,plain,
hAPP_nat_nat(times_times_nat(U_888),zero_zero_nat) = zero_zero_nat,
inference(clausify,[status(thm)],[f_371_2]) ).
fof(f_372_1,plain,
! [A_81] : hAPP_real_real(times_times_real(A_81),zero_zero_real) = zero_zero_real,
inference(fof_nnf,[status(thm)],[fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).
fof(f_372_2,plain,
! [U_889] : hAPP_real_real(times_times_real(U_889),zero_zero_real) = zero_zero_real,
inference(variable_rename,[status(thm)],[f_372_1]) ).
cnf(f_372_3,plain,
hAPP_real_real(times_times_real(U_889),zero_zero_real) = zero_zero_real,
inference(clausify,[status(thm)],[f_372_2]) ).
fof(f_373_1,plain,
! [A_80] :
( hAPP_int_int(plus_plus_int(zero_zero_int),A_80) = A_80
| ~ is_int(A_80) ),
inference(fof_nnf,[status(thm)],[fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J]) ).
fof(f_373_2,plain,
! [U_890] :
( hAPP_int_int(plus_plus_int(zero_zero_int),U_890) = U_890
| ~ is_int(U_890) ),
inference(variable_rename,[status(thm)],[f_373_1]) ).
cnf(f_373_3,plain,
( hAPP_int_int(plus_plus_int(zero_zero_int),U_890) = U_890
| ~ is_int(U_890) ),
inference(clausify,[status(thm)],[f_373_2]) ).
fof(f_374_1,plain,
! [A_80] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),A_80) = A_80,
inference(fof_nnf,[status(thm)],[fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J]) ).
fof(f_374_2,plain,
! [U_891] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),U_891) = U_891,
inference(variable_rename,[status(thm)],[f_374_1]) ).
cnf(f_374_3,plain,
hAPP_nat_nat(plus_plus_nat(zero_zero_nat),U_891) = U_891,
inference(clausify,[status(thm)],[f_374_2]) ).
fof(f_375_1,plain,
! [A_80] : hAPP_real_real(plus_plus_real(zero_zero_real),A_80) = A_80,
inference(fof_nnf,[status(thm)],[fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J]) ).
fof(f_375_2,plain,
! [U_892] : hAPP_real_real(plus_plus_real(zero_zero_real),U_892) = U_892,
inference(variable_rename,[status(thm)],[f_375_1]) ).
cnf(f_375_3,plain,
hAPP_real_real(plus_plus_real(zero_zero_real),U_892) = U_892,
inference(clausify,[status(thm)],[f_375_2]) ).
fof(f_376_1,plain,
! [A_79] :
( hAPP_int_int(plus_plus_int(A_79),zero_zero_int) = A_79
| ~ is_int(A_79) ),
inference(fof_nnf,[status(thm)],[fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J]) ).
fof(f_376_2,plain,
! [U_893] :
( hAPP_int_int(plus_plus_int(U_893),zero_zero_int) = U_893
| ~ is_int(U_893) ),
inference(variable_rename,[status(thm)],[f_376_1]) ).
cnf(f_376_3,plain,
( hAPP_int_int(plus_plus_int(U_893),zero_zero_int) = U_893
| ~ is_int(U_893) ),
inference(clausify,[status(thm)],[f_376_2]) ).
fof(f_377_1,plain,
! [A_79] : hAPP_nat_nat(plus_plus_nat(A_79),zero_zero_nat) = A_79,
inference(fof_nnf,[status(thm)],[fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J]) ).
fof(f_377_2,plain,
! [U_894] : hAPP_nat_nat(plus_plus_nat(U_894),zero_zero_nat) = U_894,
inference(variable_rename,[status(thm)],[f_377_1]) ).
cnf(f_377_3,plain,
hAPP_nat_nat(plus_plus_nat(U_894),zero_zero_nat) = U_894,
inference(clausify,[status(thm)],[f_377_2]) ).
fof(f_378_1,plain,
! [A_79] : hAPP_real_real(plus_plus_real(A_79),zero_zero_real) = A_79,
inference(fof_nnf,[status(thm)],[fact_352_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J]) ).
fof(f_378_2,plain,
! [U_895] : hAPP_real_real(plus_plus_real(U_895),zero_zero_real) = U_895,
inference(variable_rename,[status(thm)],[f_378_1]) ).
cnf(f_378_3,plain,
hAPP_real_real(plus_plus_real(U_895),zero_zero_real) = U_895,
inference(clausify,[status(thm)],[f_378_2]) ).
fof(f_379_1,plain,
! [B_2,A_2] :
( ( ( B_2 = hAPP_int_int(plus_plus_int(B_2),A_2)
| A_2 != zero_zero_int )
& ( A_2 = zero_zero_int
| B_2 != hAPP_int_int(plus_plus_int(B_2),A_2) ) )
| ~ is_int(A_2)
| ~ is_int(B_2) ),
inference(fof_nnf,[status(thm)],[fact_353_add__0__iff]) ).
fof(f_379_2,plain,
! [U_897,U_896] :
( ( ( U_897 = hAPP_int_int(plus_plus_int(U_897),U_896)
| U_896 != zero_zero_int )
& ( U_896 = zero_zero_int
| U_897 != hAPP_int_int(plus_plus_int(U_897),U_896) ) )
| ~ is_int(U_896)
| ~ is_int(U_897) ),
inference(variable_rename,[status(thm)],[f_379_1]) ).
cnf(f_379_3,plain,
( U_896 = zero_zero_int
| U_897 != hAPP_int_int(plus_plus_int(U_897),U_896)
| ~ is_int(U_896)
| ~ is_int(U_897) ),
inference(clausify,[status(thm)],[f_379_2]) ).
cnf(f_379_4,plain,
( U_897 = hAPP_int_int(plus_plus_int(U_897),U_896)
| U_896 != zero_zero_int
| ~ is_int(U_896)
| ~ is_int(U_897) ),
inference(clausify,[status(thm)],[f_379_2]) ).
fof(f_380_1,plain,
! [B_2,A_2] :
( ( B_2 = hAPP_nat_nat(plus_plus_nat(B_2),A_2)
| A_2 != zero_zero_nat )
& ( A_2 = zero_zero_nat
| B_2 != hAPP_nat_nat(plus_plus_nat(B_2),A_2) ) ),
inference(fof_nnf,[status(thm)],[fact_354_add__0__iff]) ).
fof(f_380_2,plain,
! [U_899,U_898] :
( ( U_899 = hAPP_nat_nat(plus_plus_nat(U_899),U_898)
| U_898 != zero_zero_nat )
& ( U_898 = zero_zero_nat
| U_899 != hAPP_nat_nat(plus_plus_nat(U_899),U_898) ) ),
inference(variable_rename,[status(thm)],[f_380_1]) ).
fof(f_380_3,plain,
( ! [U_903,U_901] :
( U_903 = hAPP_nat_nat(plus_plus_nat(U_903),U_901)
| U_901 != zero_zero_nat )
& ! [U_902,U_900] :
( U_900 = zero_zero_nat
| U_902 != hAPP_nat_nat(plus_plus_nat(U_902),U_900) ) ),
inference(miniscope,[status(thm)],[f_380_2]) ).
cnf(f_380_4,plain,
( U_900 = zero_zero_nat
| U_902 != hAPP_nat_nat(plus_plus_nat(U_902),U_900) ),
inference(clausify,[status(thm)],[f_380_3]) ).
cnf(f_380_5,plain,
( U_903 = hAPP_nat_nat(plus_plus_nat(U_903),U_901)
| U_901 != zero_zero_nat ),
inference(clausify,[status(thm)],[f_380_3]) ).
fof(f_381_1,plain,
! [B_2,A_2] :
( ( B_2 = hAPP_real_real(plus_plus_real(B_2),A_2)
| A_2 != zero_zero_real )
& ( A_2 = zero_zero_real
| B_2 != hAPP_real_real(plus_plus_real(B_2),A_2) ) ),
inference(fof_nnf,[status(thm)],[fact_355_add__0__iff]) ).
fof(f_381_2,plain,
! [U_905,U_904] :
( ( U_905 = hAPP_real_real(plus_plus_real(U_905),U_904)
| U_904 != zero_zero_real )
& ( U_904 = zero_zero_real
| U_905 != hAPP_real_real(plus_plus_real(U_905),U_904) ) ),
inference(variable_rename,[status(thm)],[f_381_1]) ).
fof(f_381_3,plain,
( ! [U_909,U_907] :
( U_909 = hAPP_real_real(plus_plus_real(U_909),U_907)
| U_907 != zero_zero_real )
& ! [U_908,U_906] :
( U_906 = zero_zero_real
| U_908 != hAPP_real_real(plus_plus_real(U_908),U_906) ) ),
inference(miniscope,[status(thm)],[f_381_2]) ).
cnf(f_381_4,plain,
( U_906 = zero_zero_real
| U_908 != hAPP_real_real(plus_plus_real(U_908),U_906) ),
inference(clausify,[status(thm)],[f_381_3]) ).
cnf(f_381_5,plain,
( U_909 = hAPP_real_real(plus_plus_real(U_909),U_907)
| U_907 != zero_zero_real ),
inference(clausify,[status(thm)],[f_381_3]) ).
fof(f_382_1,plain,
! [A_2] :
( ( ( hAPP_int_int(plus_plus_int(A_2),A_2) = zero_zero_int
| A_2 != zero_zero_int )
& ( A_2 = zero_zero_int
| hAPP_int_int(plus_plus_int(A_2),A_2) != zero_zero_int ) )
| ~ is_int(A_2) ),
inference(fof_nnf,[status(thm)],[fact_356_double__eq__0__iff]) ).
fof(f_382_2,plain,
! [U_910] :
( ( ( hAPP_int_int(plus_plus_int(U_910),U_910) = zero_zero_int
| U_910 != zero_zero_int )
& ( U_910 = zero_zero_int
| hAPP_int_int(plus_plus_int(U_910),U_910) != zero_zero_int ) )
| ~ is_int(U_910) ),
inference(variable_rename,[status(thm)],[f_382_1]) ).
cnf(f_382_3,plain,
( U_910 = zero_zero_int
| hAPP_int_int(plus_plus_int(U_910),U_910) != zero_zero_int
| ~ is_int(U_910) ),
inference(clausify,[status(thm)],[f_382_2]) ).
cnf(f_382_4,plain,
( hAPP_int_int(plus_plus_int(U_910),U_910) = zero_zero_int
| U_910 != zero_zero_int
| ~ is_int(U_910) ),
inference(clausify,[status(thm)],[f_382_2]) ).
fof(f_383_1,plain,
! [A_2] :
( ( hAPP_real_real(plus_plus_real(A_2),A_2) = zero_zero_real
| A_2 != zero_zero_real )
& ( A_2 = zero_zero_real
| hAPP_real_real(plus_plus_real(A_2),A_2) != zero_zero_real ) ),
inference(fof_nnf,[status(thm)],[fact_357_double__eq__0__iff]) ).
fof(f_383_2,plain,
! [U_911] :
( ( hAPP_real_real(plus_plus_real(U_911),U_911) = zero_zero_real
| U_911 != zero_zero_real )
& ( U_911 = zero_zero_real
| hAPP_real_real(plus_plus_real(U_911),U_911) != zero_zero_real ) ),
inference(variable_rename,[status(thm)],[f_383_1]) ).
fof(f_383_3,plain,
( ! [U_913] :
( hAPP_real_real(plus_plus_real(U_913),U_913) = zero_zero_real
| U_913 != zero_zero_real )
& ! [U_912] :
( U_912 = zero_zero_real
| hAPP_real_real(plus_plus_real(U_912),U_912) != zero_zero_real ) ),
inference(miniscope,[status(thm)],[f_383_2]) ).
cnf(f_383_4,plain,
( U_912 = zero_zero_real
| hAPP_real_real(plus_plus_real(U_912),U_912) != zero_zero_real ),
inference(clausify,[status(thm)],[f_383_3]) ).
cnf(f_383_5,plain,
( hAPP_real_real(plus_plus_real(U_913),U_913) = zero_zero_real
| U_913 != zero_zero_real ),
inference(clausify,[status(thm)],[f_383_3]) ).
fof(f_384_1,plain,
pls = zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_358_Pls__def]) ).
cnf(f_384_2,plain,
pls = zero_zero_int,
inference(clausify,[status(thm)],[f_384_1]) ).
fof(f_385_1,plain,
zero_zero_int != one_one_int,
inference(fof_nnf,[status(thm)],[fact_359_int__0__neq__1]) ).
cnf(f_385_2,plain,
zero_zero_int != one_one_int,
inference(clausify,[status(thm)],[f_385_1]) ).
fof(f_386_1,plain,
! [Z] :
( hAPP_int_int(plus_plus_int(zero_zero_int),Z) = Z
| ~ is_int(Z) ),
inference(fof_nnf,[status(thm)],[fact_360_zadd__0]) ).
fof(f_386_2,plain,
! [U_914] :
( hAPP_int_int(plus_plus_int(zero_zero_int),U_914) = U_914
| ~ is_int(U_914) ),
inference(variable_rename,[status(thm)],[f_386_1]) ).
cnf(f_386_3,plain,
( hAPP_int_int(plus_plus_int(zero_zero_int),U_914) = U_914
| ~ is_int(U_914) ),
inference(clausify,[status(thm)],[f_386_2]) ).
fof(f_387_1,plain,
! [Z] :
( hAPP_int_int(plus_plus_int(Z),zero_zero_int) = Z
| ~ is_int(Z) ),
inference(fof_nnf,[status(thm)],[fact_361_zadd__0__right]) ).
fof(f_387_2,plain,
! [U_915] :
( hAPP_int_int(plus_plus_int(U_915),zero_zero_int) = U_915
| ~ is_int(U_915) ),
inference(variable_rename,[status(thm)],[f_387_1]) ).
cnf(f_387_3,plain,
( hAPP_int_int(plus_plus_int(U_915),zero_zero_int) = U_915
| ~ is_int(U_915) ),
inference(clausify,[status(thm)],[f_387_2]) ).
fof(f_388_1,plain,
! [N_27,A_78] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(A_78),N_27)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_78)) ),
inference(fof_nnf,[status(thm)],[fact_362_zero__le__power]) ).
fof(f_388_2,plain,
! [U_917,U_916] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(U_916),U_917)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_916)) ),
inference(variable_rename,[status(thm)],[f_388_1]) ).
cnf(f_388_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(U_916),U_917)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_916)) ),
inference(clausify,[status(thm)],[f_388_2]) ).
fof(f_389_1,plain,
! [N_27,A_78] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(A_78),N_27)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_78)) ),
inference(fof_nnf,[status(thm)],[fact_363_zero__le__power]) ).
fof(f_389_2,plain,
! [U_919,U_918] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_918),U_919)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_918)) ),
inference(variable_rename,[status(thm)],[f_389_1]) ).
cnf(f_389_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_918),U_919)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_918)) ),
inference(clausify,[status(thm)],[f_389_2]) ).
fof(f_390_1,plain,
! [N_27,A_78] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(A_78),N_27)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_78)) ),
inference(fof_nnf,[status(thm)],[fact_364_zero__le__power]) ).
fof(f_390_2,plain,
! [U_921,U_920] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(U_920),U_921)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_920)) ),
inference(variable_rename,[status(thm)],[f_390_1]) ).
cnf(f_390_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(U_920),U_921)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_920)) ),
inference(clausify,[status(thm)],[f_390_2]) ).
fof(f_391_1,plain,
! [N_26,A_77,B_52] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(A_77),N_26)),hAPP_nat_int(power_power_int(B_52),N_26)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_77))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_77),B_52)) ),
inference(fof_nnf,[status(thm)],[fact_365_power__mono]) ).
fof(f_391_2,plain,
! [U_924,U_923,U_922] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(U_923),U_924)),hAPP_nat_int(power_power_int(U_922),U_924)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_923))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_923),U_922)) ),
inference(variable_rename,[status(thm)],[f_391_1]) ).
cnf(f_391_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(U_923),U_924)),hAPP_nat_int(power_power_int(U_922),U_924)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_923))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_923),U_922)) ),
inference(clausify,[status(thm)],[f_391_2]) ).
fof(f_392_1,plain,
! [N_26,A_77,B_52] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(A_77),N_26)),hAPP_nat_nat(power_power_nat(B_52),N_26)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_77))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_77),B_52)) ),
inference(fof_nnf,[status(thm)],[fact_366_power__mono]) ).
fof(f_392_2,plain,
! [U_927,U_926,U_925] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(U_926),U_927)),hAPP_nat_nat(power_power_nat(U_925),U_927)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_926))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_926),U_925)) ),
inference(variable_rename,[status(thm)],[f_392_1]) ).
cnf(f_392_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(U_926),U_927)),hAPP_nat_nat(power_power_nat(U_925),U_927)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_926))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_926),U_925)) ),
inference(clausify,[status(thm)],[f_392_2]) ).
fof(f_393_1,plain,
! [N_26,A_77,B_52] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(A_77),N_26)),hAPP_nat_real(power_power_real(B_52),N_26)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_77))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_77),B_52)) ),
inference(fof_nnf,[status(thm)],[fact_367_power__mono]) ).
fof(f_393_2,plain,
! [U_930,U_929,U_928] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(U_929),U_930)),hAPP_nat_real(power_power_real(U_928),U_930)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_929))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_929),U_928)) ),
inference(variable_rename,[status(thm)],[f_393_1]) ).
cnf(f_393_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(U_929),U_930)),hAPP_nat_real(power_power_real(U_928),U_930)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_929))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_929),U_928)) ),
inference(clausify,[status(thm)],[f_393_2]) ).
fof(f_394_1,plain,
! [N_25,A_76] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_76),N_25)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_76)) ),
inference(fof_nnf,[status(thm)],[fact_368_zero__less__power]) ).
fof(f_394_2,plain,
! [U_932,U_931] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(U_931),U_932)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_931)) ),
inference(variable_rename,[status(thm)],[f_394_1]) ).
cnf(f_394_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(U_931),U_932)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_931)) ),
inference(clausify,[status(thm)],[f_394_2]) ).
fof(f_395_1,plain,
! [N_25,A_76] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(A_76),N_25)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_76)) ),
inference(fof_nnf,[status(thm)],[fact_369_zero__less__power]) ).
fof(f_395_2,plain,
! [U_934,U_933] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_933),U_934)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_933)) ),
inference(variable_rename,[status(thm)],[f_395_1]) ).
cnf(f_395_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_933),U_934)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_933)) ),
inference(clausify,[status(thm)],[f_395_2]) ).
fof(f_396_1,plain,
! [N_25,A_76] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(A_76),N_25)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_76)) ),
inference(fof_nnf,[status(thm)],[fact_370_zero__less__power]) ).
fof(f_396_2,plain,
! [U_936,U_935] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(U_935),U_936)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_935)) ),
inference(variable_rename,[status(thm)],[f_396_1]) ).
cnf(f_396_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(U_935),U_936)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_935)) ),
inference(clausify,[status(thm)],[f_396_2]) ).
fof(f_397_1,plain,
! [Z,X_1,Y_1,P_1] :
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X_1),hAPP_nat_nat(times_times_nat(Y_1),Z)),one_one_int),P_1))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X_1),Y_1),one_one_int),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_371_zcong__zpower__zmult]) ).
fof(f_397_2,plain,
! [U_940,U_939,U_938,U_937] :
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(U_939),hAPP_nat_nat(times_times_nat(U_938),U_940)),one_one_int),U_937))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(U_939),U_938),one_one_int),U_937)) ),
inference(variable_rename,[status(thm)],[f_397_1]) ).
cnf(f_397_3,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(U_939),hAPP_nat_nat(times_times_nat(U_938),U_940)),one_one_int),U_937))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(U_939),U_938),one_one_int),U_937)) ),
inference(clausify,[status(thm)],[f_397_2]) ).
fof(f_398_1,plain,
! [K,N,Ma] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K),hAPP_int_int(plus_plus_int(N),hAPP_int_int(times_times_int(K),Ma))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K),N)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K),N))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K),hAPP_int_int(plus_plus_int(N),hAPP_int_int(times_times_int(K),Ma)))) ) ),
inference(fof_nnf,[status(thm)],[fact_372_zdvd__reduce]) ).
fof(f_398_2,plain,
! [U_943,U_942,U_941] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_943),hAPP_int_int(plus_plus_int(U_942),hAPP_int_int(times_times_int(U_943),U_941))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_943),U_942)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_943),U_942))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_943),hAPP_int_int(plus_plus_int(U_942),hAPP_int_int(times_times_int(U_943),U_941)))) ) ),
inference(variable_rename,[status(thm)],[f_398_1]) ).
fof(f_398_3,plain,
( ! [U_949,U_947] :
( ! [U_945] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_949),hAPP_int_int(plus_plus_int(U_947),hAPP_int_int(times_times_int(U_949),U_945))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_949),U_947)) )
& ! [U_948,U_946] :
( ! [U_944] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_948),hAPP_int_int(plus_plus_int(U_946),hAPP_int_int(times_times_int(U_948),U_944))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_948),U_946)) ) ),
inference(miniscope,[status(thm)],[f_398_2]) ).
cnf(f_398_4,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_948),hAPP_int_int(plus_plus_int(U_946),hAPP_int_int(times_times_int(U_948),U_944))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_948),U_946)) ),
inference(clausify,[status(thm)],[f_398_3]) ).
cnf(f_398_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_949),hAPP_int_int(plus_plus_int(U_947),hAPP_int_int(times_times_int(U_949),U_945))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_949),U_947)) ),
inference(clausify,[status(thm)],[f_398_3]) ).
fof(f_399_1,plain,
! [C_2,X_2,Ta,A_2,D] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_2),hAPP_int_int(plus_plus_int(X_2),Ta)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_2),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X_2),hAPP_int_int(times_times_int(C_2),D))),Ta))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_2),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X_2),hAPP_int_int(times_times_int(C_2),D))),Ta)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_2),hAPP_int_int(plus_plus_int(X_2),Ta))) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_2),D)) ),
inference(fof_nnf,[status(thm)],[fact_373_zdvd__period]) ).
fof(f_399_2,plain,
! [U_954,U_953,U_952,U_951,U_950] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_951),hAPP_int_int(plus_plus_int(U_953),U_952)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_951),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(U_953),hAPP_int_int(times_times_int(U_954),U_950))),U_952))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_951),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(U_953),hAPP_int_int(times_times_int(U_954),U_950))),U_952)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_951),hAPP_int_int(plus_plus_int(U_953),U_952))) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_951),U_950)) ),
inference(variable_rename,[status(thm)],[f_399_1]) ).
cnf(f_399_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_951),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(U_953),hAPP_int_int(times_times_int(U_954),U_950))),U_952)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_951),hAPP_int_int(plus_plus_int(U_953),U_952)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_951),U_950)) ),
inference(clausify,[status(thm)],[f_399_2]) ).
cnf(f_399_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_951),hAPP_int_int(plus_plus_int(U_953),U_952)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_951),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(U_953),hAPP_int_int(times_times_int(U_954),U_950))),U_952)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_951),U_950)) ),
inference(clausify,[status(thm)],[f_399_2]) ).
fof(f_400_1,plain,
! [A_75,N_24,B_51] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_75),B_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(A_75),N_24)),hAPP_nat_int(power_power_int(B_51),N_24))) ),
inference(fof_nnf,[status(thm)],[fact_374_power__less__imp__less__base]) ).
fof(f_400_2,plain,
! [U_957,U_956,U_955] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_957),U_955))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_955))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_957),U_956)),hAPP_nat_int(power_power_int(U_955),U_956))) ),
inference(variable_rename,[status(thm)],[f_400_1]) ).
cnf(f_400_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_957),U_955))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_955))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_957),U_956)),hAPP_nat_int(power_power_int(U_955),U_956))) ),
inference(clausify,[status(thm)],[f_400_2]) ).
fof(f_401_1,plain,
! [A_75,N_24,B_51] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_75),B_51))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_51))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(A_75),N_24)),hAPP_nat_nat(power_power_nat(B_51),N_24))) ),
inference(fof_nnf,[status(thm)],[fact_375_power__less__imp__less__base]) ).
fof(f_401_2,plain,
! [U_960,U_959,U_958] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_960),U_958))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_958))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_960),U_959)),hAPP_nat_nat(power_power_nat(U_958),U_959))) ),
inference(variable_rename,[status(thm)],[f_401_1]) ).
cnf(f_401_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_960),U_958))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_958))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_960),U_959)),hAPP_nat_nat(power_power_nat(U_958),U_959))) ),
inference(clausify,[status(thm)],[f_401_2]) ).
fof(f_402_1,plain,
! [A_75,N_24,B_51] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_75),B_51))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_51))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(A_75),N_24)),hAPP_nat_real(power_power_real(B_51),N_24))) ),
inference(fof_nnf,[status(thm)],[fact_376_power__less__imp__less__base]) ).
fof(f_402_2,plain,
! [U_963,U_962,U_961] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_963),U_961))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_961))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_963),U_962)),hAPP_nat_real(power_power_real(U_961),U_962))) ),
inference(variable_rename,[status(thm)],[f_402_1]) ).
cnf(f_402_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_963),U_961))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_961))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_963),U_962)),hAPP_nat_real(power_power_real(U_961),U_962))) ),
inference(clausify,[status(thm)],[f_402_2]) ).
fof(f_403_1,plain,
! [A_74,N_23,N_22] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(A_74),N_22)),hAPP_nat_int(power_power_int(A_74),N_23)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_74),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_74))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_23),N_22)) ),
inference(fof_nnf,[status(thm)],[fact_377_power__decreasing]) ).
fof(f_403_2,plain,
! [U_966,U_965,U_964] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(U_966),U_964)),hAPP_nat_int(power_power_int(U_966),U_965)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_966),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_966))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_965),U_964)) ),
inference(variable_rename,[status(thm)],[f_403_1]) ).
cnf(f_403_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(U_966),U_964)),hAPP_nat_int(power_power_int(U_966),U_965)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_966),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_966))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_965),U_964)) ),
inference(clausify,[status(thm)],[f_403_2]) ).
fof(f_404_1,plain,
! [A_74,N_23,N_22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(A_74),N_22)),hAPP_nat_nat(power_power_nat(A_74),N_23)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_74),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_74))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_23),N_22)) ),
inference(fof_nnf,[status(thm)],[fact_378_power__decreasing]) ).
fof(f_404_2,plain,
! [U_969,U_968,U_967] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(U_969),U_967)),hAPP_nat_nat(power_power_nat(U_969),U_968)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_969),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_969))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_968),U_967)) ),
inference(variable_rename,[status(thm)],[f_404_1]) ).
cnf(f_404_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(U_969),U_967)),hAPP_nat_nat(power_power_nat(U_969),U_968)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_969),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_969))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_968),U_967)) ),
inference(clausify,[status(thm)],[f_404_2]) ).
fof(f_405_1,plain,
! [A_74,N_23,N_22] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(A_74),N_22)),hAPP_nat_real(power_power_real(A_74),N_23)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_74),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_74))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_23),N_22)) ),
inference(fof_nnf,[status(thm)],[fact_379_power__decreasing]) ).
fof(f_405_2,plain,
! [U_972,U_971,U_970] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(U_972),U_970)),hAPP_nat_real(power_power_real(U_972),U_971)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_972),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_972))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_971),U_970)) ),
inference(variable_rename,[status(thm)],[f_405_1]) ).
cnf(f_405_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(U_972),U_970)),hAPP_nat_real(power_power_real(U_972),U_971)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_972),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_972))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_971),U_970)) ),
inference(clausify,[status(thm)],[f_405_2]) ).
fof(f_406_1,plain,
! [A_73,N_21,N_20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(A_73),N_20)),hAPP_nat_int(power_power_int(A_73),N_21)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_73),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_73))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_21),N_20)) ),
inference(fof_nnf,[status(thm)],[fact_380_power__strict__decreasing]) ).
fof(f_406_2,plain,
! [U_975,U_974,U_973] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_975),U_973)),hAPP_nat_int(power_power_int(U_975),U_974)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_975),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_975))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_974),U_973)) ),
inference(variable_rename,[status(thm)],[f_406_1]) ).
cnf(f_406_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_975),U_973)),hAPP_nat_int(power_power_int(U_975),U_974)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_975),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_975))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_974),U_973)) ),
inference(clausify,[status(thm)],[f_406_2]) ).
fof(f_407_1,plain,
! [A_73,N_21,N_20] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(A_73),N_20)),hAPP_nat_nat(power_power_nat(A_73),N_21)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_73),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_73))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_21),N_20)) ),
inference(fof_nnf,[status(thm)],[fact_381_power__strict__decreasing]) ).
fof(f_407_2,plain,
! [U_978,U_977,U_976] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_978),U_976)),hAPP_nat_nat(power_power_nat(U_978),U_977)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_978),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_978))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_977),U_976)) ),
inference(variable_rename,[status(thm)],[f_407_1]) ).
cnf(f_407_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_978),U_976)),hAPP_nat_nat(power_power_nat(U_978),U_977)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_978),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_978))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_977),U_976)) ),
inference(clausify,[status(thm)],[f_407_2]) ).
fof(f_408_1,plain,
! [A_73,N_21,N_20] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(A_73),N_20)),hAPP_nat_real(power_power_real(A_73),N_21)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_73),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_73))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_21),N_20)) ),
inference(fof_nnf,[status(thm)],[fact_382_power__strict__decreasing]) ).
fof(f_408_2,plain,
! [U_981,U_980,U_979] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_981),U_979)),hAPP_nat_real(power_power_real(U_981),U_980)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_981),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_981))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_980),U_979)) ),
inference(variable_rename,[status(thm)],[f_408_1]) ).
cnf(f_408_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_981),U_979)),hAPP_nat_real(power_power_real(U_981),U_980)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_981),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_981))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_980),U_979)) ),
inference(clausify,[status(thm)],[f_408_2]) ).
fof(f_409_1,plain,
! [A_2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(A_2),A_2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),zero_zero_int)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(A_2),A_2)),zero_zero_int)) ) ),
inference(fof_nnf,[status(thm)],[fact_383_even__less__0__iff]) ).
fof(f_409_2,plain,
! [U_982] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(U_982),U_982)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_982),zero_zero_int)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_982),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(U_982),U_982)),zero_zero_int)) ) ),
inference(variable_rename,[status(thm)],[f_409_1]) ).
fof(f_409_3,plain,
( ! [U_984] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(U_984),U_984)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_984),zero_zero_int)) )
& ! [U_983] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_983),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(U_983),U_983)),zero_zero_int)) ) ),
inference(miniscope,[status(thm)],[f_409_2]) ).
cnf(f_409_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_983),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(U_983),U_983)),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_409_3]) ).
cnf(f_409_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(U_984),U_984)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_984),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_409_3]) ).
fof(f_410_1,plain,
! [A_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(A_2),A_2)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),zero_zero_real)) )
& ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(A_2),A_2)),zero_zero_real)) ) ),
inference(fof_nnf,[status(thm)],[fact_384_even__less__0__iff]) ).
fof(f_410_2,plain,
! [U_985] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(U_985),U_985)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_985),zero_zero_real)) )
& ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_985),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(U_985),U_985)),zero_zero_real)) ) ),
inference(variable_rename,[status(thm)],[f_410_1]) ).
fof(f_410_3,plain,
( ! [U_987] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(U_987),U_987)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_987),zero_zero_real)) )
& ! [U_986] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_986),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(U_986),U_986)),zero_zero_real)) ) ),
inference(miniscope,[status(thm)],[f_410_2]) ).
cnf(f_410_4,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_986),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(U_986),U_986)),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_410_3]) ).
cnf(f_410_5,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(U_987),U_987)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_987),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_410_3]) ).
fof(f_411_1,plain,
! [X_2,Y_2] :
( ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X_2),X_2)),hAPP_int_int(times_times_int(Y_2),Y_2)) = zero_zero_int
| Y_2 != zero_zero_int
| X_2 != zero_zero_int )
& ( ( Y_2 = zero_zero_int
& X_2 = zero_zero_int )
| hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X_2),X_2)),hAPP_int_int(times_times_int(Y_2),Y_2)) != zero_zero_int ) )
| ~ is_int(Y_2)
| ~ is_int(X_2) ),
inference(fof_nnf,[status(thm)],[fact_385_sum__squares__eq__zero__iff]) ).
fof(f_411_2,plain,
! [U_989,U_988] :
( ( ( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_989),U_989)),hAPP_int_int(times_times_int(U_988),U_988)) = zero_zero_int
| U_988 != zero_zero_int
| U_989 != zero_zero_int )
& ( ( U_988 = zero_zero_int
& U_989 = zero_zero_int )
| hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_989),U_989)),hAPP_int_int(times_times_int(U_988),U_988)) != zero_zero_int ) )
| ~ is_int(U_988)
| ~ is_int(U_989) ),
inference(variable_rename,[status(thm)],[f_411_1]) ).
cnf(f_411_3,plain,
( U_989 = zero_zero_int
| hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_989),U_989)),hAPP_int_int(times_times_int(U_988),U_988)) != zero_zero_int
| ~ is_int(U_988)
| ~ is_int(U_989) ),
inference(clausify,[status(thm)],[f_411_2]) ).
cnf(f_411_4,plain,
( U_988 = zero_zero_int
| hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_989),U_989)),hAPP_int_int(times_times_int(U_988),U_988)) != zero_zero_int
| ~ is_int(U_988)
| ~ is_int(U_989) ),
inference(clausify,[status(thm)],[f_411_2]) ).
cnf(f_411_5,plain,
( hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_989),U_989)),hAPP_int_int(times_times_int(U_988),U_988)) = zero_zero_int
| U_988 != zero_zero_int
| U_989 != zero_zero_int
| ~ is_int(U_988)
| ~ is_int(U_989) ),
inference(clausify,[status(thm)],[f_411_2]) ).
fof(f_412_1,plain,
! [X_2,Y_2] :
( ( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X_2),X_2)),hAPP_real_real(times_times_real(Y_2),Y_2)) = zero_zero_real
| Y_2 != zero_zero_real
| X_2 != zero_zero_real )
& ( ( Y_2 = zero_zero_real
& X_2 = zero_zero_real )
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X_2),X_2)),hAPP_real_real(times_times_real(Y_2),Y_2)) != zero_zero_real ) ),
inference(fof_nnf,[status(thm)],[fact_386_sum__squares__eq__zero__iff]) ).
fof(f_412_2,plain,
! [U_991,U_990] :
( ( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_991),U_991)),hAPP_real_real(times_times_real(U_990),U_990)) = zero_zero_real
| U_990 != zero_zero_real
| U_991 != zero_zero_real )
& ( ( U_990 = zero_zero_real
& U_991 = zero_zero_real )
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_991),U_991)),hAPP_real_real(times_times_real(U_990),U_990)) != zero_zero_real ) ),
inference(variable_rename,[status(thm)],[f_412_1]) ).
fof(f_412_3,plain,
( ! [U_995,U_993] :
( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_995),U_995)),hAPP_real_real(times_times_real(U_993),U_993)) = zero_zero_real
| U_993 != zero_zero_real
| U_995 != zero_zero_real )
& ! [U_994,U_992] :
( ( U_992 = zero_zero_real
& U_994 = zero_zero_real )
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_994),U_994)),hAPP_real_real(times_times_real(U_992),U_992)) != zero_zero_real ) ),
inference(miniscope,[status(thm)],[f_412_2]) ).
cnf(f_412_4,plain,
( U_994 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_994),U_994)),hAPP_real_real(times_times_real(U_992),U_992)) != zero_zero_real ),
inference(clausify,[status(thm)],[f_412_3]) ).
cnf(f_412_5,plain,
( U_992 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_994),U_994)),hAPP_real_real(times_times_real(U_992),U_992)) != zero_zero_real ),
inference(clausify,[status(thm)],[f_412_3]) ).
cnf(f_412_6,plain,
( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_995),U_995)),hAPP_real_real(times_times_real(U_993),U_993)) = zero_zero_real
| U_993 != zero_zero_real
| U_995 != zero_zero_real ),
inference(clausify,[status(thm)],[f_412_3]) ).
fof(f_413_1,plain,
! [C_27,D_8,A_72,B_50,R_4] :
( hAPP_int_int(plus_plus_int(A_72),hAPP_int_int(times_times_int(R_4),C_27)) != hAPP_int_int(plus_plus_int(B_50),hAPP_int_int(times_times_int(R_4),D_8))
| C_27 = D_8
| A_72 != B_50
| R_4 = zero_zero_int
| ~ is_int(R_4)
| ~ is_int(D_8)
| ~ is_int(C_27) ),
inference(fof_nnf,[status(thm)],[fact_387_add__scale__eq__noteq]) ).
fof(f_413_2,plain,
! [U_1000,U_999,U_998,U_997,U_996] :
( hAPP_int_int(plus_plus_int(U_998),hAPP_int_int(times_times_int(U_996),U_1000)) != hAPP_int_int(plus_plus_int(U_997),hAPP_int_int(times_times_int(U_996),U_999))
| U_1000 = U_999
| U_998 != U_997
| U_996 = zero_zero_int
| ~ is_int(U_996)
| ~ is_int(U_999)
| ~ is_int(U_1000) ),
inference(variable_rename,[status(thm)],[f_413_1]) ).
cnf(f_413_3,plain,
( hAPP_int_int(plus_plus_int(U_998),hAPP_int_int(times_times_int(U_996),U_1000)) != hAPP_int_int(plus_plus_int(U_997),hAPP_int_int(times_times_int(U_996),U_999))
| U_1000 = U_999
| U_998 != U_997
| U_996 = zero_zero_int
| ~ is_int(U_996)
| ~ is_int(U_999)
| ~ is_int(U_1000) ),
inference(clausify,[status(thm)],[f_413_2]) ).
fof(f_414_1,plain,
! [C_27,D_8,A_72,B_50,R_4] :
( hAPP_nat_nat(plus_plus_nat(A_72),hAPP_nat_nat(times_times_nat(R_4),C_27)) != hAPP_nat_nat(plus_plus_nat(B_50),hAPP_nat_nat(times_times_nat(R_4),D_8))
| C_27 = D_8
| A_72 != B_50
| R_4 = zero_zero_nat ),
inference(fof_nnf,[status(thm)],[fact_388_add__scale__eq__noteq]) ).
fof(f_414_2,plain,
! [U_1005,U_1004,U_1003,U_1002,U_1001] :
( hAPP_nat_nat(plus_plus_nat(U_1003),hAPP_nat_nat(times_times_nat(U_1001),U_1005)) != hAPP_nat_nat(plus_plus_nat(U_1002),hAPP_nat_nat(times_times_nat(U_1001),U_1004))
| U_1005 = U_1004
| U_1003 != U_1002
| U_1001 = zero_zero_nat ),
inference(variable_rename,[status(thm)],[f_414_1]) ).
cnf(f_414_3,plain,
( hAPP_nat_nat(plus_plus_nat(U_1003),hAPP_nat_nat(times_times_nat(U_1001),U_1005)) != hAPP_nat_nat(plus_plus_nat(U_1002),hAPP_nat_nat(times_times_nat(U_1001),U_1004))
| U_1005 = U_1004
| U_1003 != U_1002
| U_1001 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_414_2]) ).
fof(f_415_1,plain,
! [C_27,D_8,A_72,B_50,R_4] :
( hAPP_real_real(plus_plus_real(A_72),hAPP_real_real(times_times_real(R_4),C_27)) != hAPP_real_real(plus_plus_real(B_50),hAPP_real_real(times_times_real(R_4),D_8))
| C_27 = D_8
| A_72 != B_50
| R_4 = zero_zero_real ),
inference(fof_nnf,[status(thm)],[fact_389_add__scale__eq__noteq]) ).
fof(f_415_2,plain,
! [U_1010,U_1009,U_1008,U_1007,U_1006] :
( hAPP_real_real(plus_plus_real(U_1008),hAPP_real_real(times_times_real(U_1006),U_1010)) != hAPP_real_real(plus_plus_real(U_1007),hAPP_real_real(times_times_real(U_1006),U_1009))
| U_1010 = U_1009
| U_1008 != U_1007
| U_1006 = zero_zero_real ),
inference(variable_rename,[status(thm)],[f_415_1]) ).
cnf(f_415_3,plain,
( hAPP_real_real(plus_plus_real(U_1008),hAPP_real_real(times_times_real(U_1006),U_1010)) != hAPP_real_real(plus_plus_real(U_1007),hAPP_real_real(times_times_real(U_1006),U_1009))
| U_1010 = U_1009
| U_1008 != U_1007
| U_1006 = zero_zero_real ),
inference(clausify,[status(thm)],[f_415_2]) ).
fof(f_416_1,plain,
! [A,N_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),A))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),hAPP_nat_int(power_power_int(A),N_1)))
| ~ hBOOL(hAPP_int_bool(zprime,P_1)) ),
inference(fof_nnf,[status(thm)],[fact_390_zprime__zdvd__power]) ).
fof(f_416_2,plain,
! [U_1013,U_1012,U_1011] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1011),U_1013))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1011),hAPP_nat_int(power_power_int(U_1013),U_1012)))
| ~ hBOOL(hAPP_int_bool(zprime,U_1011)) ),
inference(variable_rename,[status(thm)],[f_416_1]) ).
cnf(f_416_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1011),U_1013))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1011),hAPP_nat_int(power_power_int(U_1013),U_1012)))
| ~ hBOOL(hAPP_int_bool(zprime,U_1011)) ),
inference(clausify,[status(thm)],[f_416_2]) ).
fof(f_417_1,plain,
zero_zero_int = number_number_of_int(pls),
inference(fof_nnf,[status(thm)],[fact_391_semiring__norm_I112_J]) ).
cnf(f_417_2,plain,
zero_zero_int = number_number_of_int(pls),
inference(clausify,[status(thm)],[f_417_1]) ).
fof(f_418_1,plain,
zero_zero_real = number267125858f_real(pls),
inference(fof_nnf,[status(thm)],[fact_392_semiring__norm_I112_J]) ).
cnf(f_418_2,plain,
zero_zero_real = number267125858f_real(pls),
inference(clausify,[status(thm)],[f_418_1]) ).
fof(f_419_1,plain,
number_number_of_int(pls) = zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_393_number__of__Pls]) ).
cnf(f_419_2,plain,
number_number_of_int(pls) = zero_zero_int,
inference(clausify,[status(thm)],[f_419_1]) ).
fof(f_420_1,plain,
number267125858f_real(pls) = zero_zero_real,
inference(fof_nnf,[status(thm)],[fact_394_number__of__Pls]) ).
cnf(f_420_2,plain,
number267125858f_real(pls) = zero_zero_real,
inference(clausify,[status(thm)],[f_420_1]) ).
fof(f_421_1,plain,
number_number_of_int(pls) = zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_395_semiring__numeral__0__eq__0]) ).
cnf(f_421_2,plain,
number_number_of_int(pls) = zero_zero_int,
inference(clausify,[status(thm)],[f_421_1]) ).
fof(f_422_1,plain,
number_number_of_nat(pls) = zero_zero_nat,
inference(fof_nnf,[status(thm)],[fact_396_semiring__numeral__0__eq__0]) ).
cnf(f_422_2,plain,
number_number_of_nat(pls) = zero_zero_nat,
inference(clausify,[status(thm)],[f_422_1]) ).
fof(f_423_1,plain,
number267125858f_real(pls) = zero_zero_real,
inference(fof_nnf,[status(thm)],[fact_397_semiring__numeral__0__eq__0]) ).
cnf(f_423_2,plain,
number267125858f_real(pls) = zero_zero_real,
inference(clausify,[status(thm)],[f_423_1]) ).
fof(f_424_1,plain,
! [W_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(W_1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),zero_zero_int)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(W_1)),zero_zero_int)) ) ),
inference(fof_nnf,[status(thm)],[fact_398_bin__less__0__simps_I4_J]) ).
fof(f_424_2,plain,
! [U_1014] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_1014)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1014),zero_zero_int)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1014),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_1014)),zero_zero_int)) ) ),
inference(variable_rename,[status(thm)],[f_424_1]) ).
fof(f_424_3,plain,
( ! [U_1016] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_1016)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1016),zero_zero_int)) )
& ! [U_1015] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1015),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_1015)),zero_zero_int)) ) ),
inference(miniscope,[status(thm)],[f_424_2]) ).
cnf(f_424_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1015),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_1015)),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_424_3]) ).
cnf(f_424_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_1016)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1016),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_424_3]) ).
fof(f_425_1,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
inference(fof_nnf,[status(thm)],[fact_399_bin__less__0__simps_I1_J]) ).
cnf(f_425_2,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
inference(clausify,[status(thm)],[f_425_1]) ).
fof(f_426_1,plain,
! [W_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(W_1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),zero_zero_int)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(W_1)),zero_zero_int)) ) ),
inference(fof_nnf,[status(thm)],[fact_400_bin__less__0__simps_I3_J]) ).
fof(f_426_2,plain,
! [U_1017] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_1017)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1017),zero_zero_int)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1017),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_1017)),zero_zero_int)) ) ),
inference(variable_rename,[status(thm)],[f_426_1]) ).
fof(f_426_3,plain,
( ! [U_1019] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_1019)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1019),zero_zero_int)) )
& ! [U_1018] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1018),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_1018)),zero_zero_int)) ) ),
inference(miniscope,[status(thm)],[f_426_2]) ).
cnf(f_426_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1018),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_1018)),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_426_3]) ).
cnf(f_426_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_1019)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1019),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_426_3]) ).
fof(f_427_1,plain,
zero_zero_int = number_number_of_int(pls),
inference(fof_nnf,[status(thm)],[fact_401_zero__is__num__zero]) ).
cnf(f_427_2,plain,
zero_zero_int = number_number_of_int(pls),
inference(clausify,[status(thm)],[f_427_1]) ).
fof(f_428_1,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
inference(fof_nnf,[status(thm)],[fact_402_int__0__less__1]) ).
cnf(f_428_2,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
inference(clausify,[status(thm)],[f_428_1]) ).
fof(f_429_1,plain,
! [B,A] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(A),B)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A)) ),
inference(fof_nnf,[status(thm)],[fact_403_pos__zmult__pos]) ).
fof(f_429_2,plain,
! [U_1021,U_1020] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1021))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(U_1020),U_1021)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1020)) ),
inference(variable_rename,[status(thm)],[f_429_1]) ).
cnf(f_429_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1021))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(U_1020),U_1021)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1020)) ),
inference(clausify,[status(thm)],[f_429_2]) ).
fof(f_430_1,plain,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(K_1),I_1)),hAPP_int_int(times_times_int(K_1),J_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_404_zmult__zless__mono2]) ).
fof(f_430_2,plain,
! [U_1024,U_1023,U_1022] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_1024),U_1023)),hAPP_int_int(times_times_int(U_1024),U_1022)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1024))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1023),U_1022)) ),
inference(variable_rename,[status(thm)],[f_430_1]) ).
cnf(f_430_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_1024),U_1023)),hAPP_int_int(times_times_int(U_1024),U_1022)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1024))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1023),U_1022)) ),
inference(clausify,[status(thm)],[f_430_2]) ).
fof(f_431_1,plain,
! [Z] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),Z)),Z) != zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_405_odd__nonzero]) ).
fof(f_431_2,plain,
! [U_1025] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),U_1025)),U_1025) != zero_zero_int,
inference(variable_rename,[status(thm)],[f_431_1]) ).
cnf(f_431_3,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),U_1025)),U_1025) != zero_zero_int,
inference(clausify,[status(thm)],[f_431_2]) ).
fof(f_432_1,plain,
! [N_19,A_71] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_71),hAPP_nat_int(power_power_int(A_71),N_19))),hAPP_nat_int(power_power_int(A_71),N_19)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_71),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_71)) ),
inference(fof_nnf,[status(thm)],[fact_406_power__Suc__less]) ).
fof(f_432_2,plain,
! [U_1027,U_1026] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_1026),hAPP_nat_int(power_power_int(U_1026),U_1027))),hAPP_nat_int(power_power_int(U_1026),U_1027)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1026),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1026)) ),
inference(variable_rename,[status(thm)],[f_432_1]) ).
cnf(f_432_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_1026),hAPP_nat_int(power_power_int(U_1026),U_1027))),hAPP_nat_int(power_power_int(U_1026),U_1027)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1026),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1026)) ),
inference(clausify,[status(thm)],[f_432_2]) ).
fof(f_433_1,plain,
! [N_19,A_71] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(A_71),hAPP_nat_nat(power_power_nat(A_71),N_19))),hAPP_nat_nat(power_power_nat(A_71),N_19)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_71),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_71)) ),
inference(fof_nnf,[status(thm)],[fact_407_power__Suc__less]) ).
fof(f_433_2,plain,
! [U_1029,U_1028] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_1028),hAPP_nat_nat(power_power_nat(U_1028),U_1029))),hAPP_nat_nat(power_power_nat(U_1028),U_1029)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1028),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1028)) ),
inference(variable_rename,[status(thm)],[f_433_1]) ).
cnf(f_433_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_1028),hAPP_nat_nat(power_power_nat(U_1028),U_1029))),hAPP_nat_nat(power_power_nat(U_1028),U_1029)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1028),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1028)) ),
inference(clausify,[status(thm)],[f_433_2]) ).
fof(f_434_1,plain,
! [N_19,A_71] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_71),hAPP_nat_real(power_power_real(A_71),N_19))),hAPP_nat_real(power_power_real(A_71),N_19)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_71),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_71)) ),
inference(fof_nnf,[status(thm)],[fact_408_power__Suc__less]) ).
fof(f_434_2,plain,
! [U_1031,U_1030] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_1030),hAPP_nat_real(power_power_real(U_1030),U_1031))),hAPP_nat_real(power_power_real(U_1030),U_1031)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1030),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_1030)) ),
inference(variable_rename,[status(thm)],[f_434_1]) ).
cnf(f_434_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_1030),hAPP_nat_real(power_power_real(U_1030),U_1031))),hAPP_nat_real(power_power_real(U_1030),U_1031)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1030),one_one_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_1030)) ),
inference(clausify,[status(thm)],[f_434_2]) ).
fof(f_435_1,plain,
! [N_1,B,A,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(P_1),N_1)),B))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(P_1),N_1)),hAPP_int_int(times_times_int(A),B)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),A))
| ~ hBOOL(hAPP_int_bool(zprime,P_1)) ),
inference(fof_nnf,[status(thm)],[fact_409_zprime__power__zdvd__cancel__left]) ).
fof(f_435_2,plain,
! [U_1035,U_1034,U_1033,U_1032] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_1032),U_1035)),U_1034))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_1032),U_1035)),hAPP_int_int(times_times_int(U_1033),U_1034)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1032),U_1033))
| ~ hBOOL(hAPP_int_bool(zprime,U_1032)) ),
inference(variable_rename,[status(thm)],[f_435_1]) ).
cnf(f_435_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_1032),U_1035)),U_1034))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_1032),U_1035)),hAPP_int_int(times_times_int(U_1033),U_1034)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1032),U_1033))
| ~ hBOOL(hAPP_int_bool(zprime,U_1032)) ),
inference(clausify,[status(thm)],[f_435_2]) ).
fof(f_436_1,plain,
! [N_1,A,B,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(P_1),N_1)),A))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(P_1),N_1)),hAPP_int_int(times_times_int(A),B)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),B))
| ~ hBOOL(hAPP_int_bool(zprime,P_1)) ),
inference(fof_nnf,[status(thm)],[fact_410_zprime__power__zdvd__cancel__right]) ).
fof(f_436_2,plain,
! [U_1039,U_1038,U_1037,U_1036] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_1036),U_1039)),U_1038))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_1036),U_1039)),hAPP_int_int(times_times_int(U_1038),U_1037)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1036),U_1037))
| ~ hBOOL(hAPP_int_bool(zprime,U_1036)) ),
inference(variable_rename,[status(thm)],[f_436_1]) ).
cnf(f_436_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_1036),U_1039)),U_1038))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_1036),U_1039)),hAPP_int_int(times_times_int(U_1038),U_1037)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1036),U_1037))
| ~ hBOOL(hAPP_int_bool(zprime,U_1036)) ),
inference(clausify,[status(thm)],[f_436_2]) ).
fof(f_437_1,plain,
! [X_17,Y_14] : 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(X_17),X_17)),hAPP_int_int(times_times_int(Y_14),Y_14)))),
inference(fof_nnf,[status(thm)],[fact_411_sum__squares__ge__zero]) ).
fof(f_437_2,plain,
! [U_1041,U_1040] : 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(U_1041),U_1041)),hAPP_int_int(times_times_int(U_1040),U_1040)))),
inference(variable_rename,[status(thm)],[f_437_1]) ).
cnf(f_437_3,plain,
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(U_1041),U_1041)),hAPP_int_int(times_times_int(U_1040),U_1040)))),
inference(clausify,[status(thm)],[f_437_2]) ).
fof(f_438_1,plain,
! [X_17,Y_14] : 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(X_17),X_17)),hAPP_real_real(times_times_real(Y_14),Y_14)))),
inference(fof_nnf,[status(thm)],[fact_412_sum__squares__ge__zero]) ).
fof(f_438_2,plain,
! [U_1043,U_1042] : 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(U_1043),U_1043)),hAPP_real_real(times_times_real(U_1042),U_1042)))),
inference(variable_rename,[status(thm)],[f_438_1]) ).
cnf(f_438_3,plain,
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(U_1043),U_1043)),hAPP_real_real(times_times_real(U_1042),U_1042)))),
inference(clausify,[status(thm)],[f_438_2]) ).
fof(f_439_1,plain,
! [X_2,Y_2] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X_2),X_2)),hAPP_int_int(times_times_int(Y_2),Y_2))),zero_zero_int))
| Y_2 != zero_zero_int
| X_2 != zero_zero_int )
& ( ( Y_2 = zero_zero_int
& X_2 = 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(X_2),X_2)),hAPP_int_int(times_times_int(Y_2),Y_2))),zero_zero_int)) ) )
| ~ is_int(Y_2)
| ~ is_int(X_2) ),
inference(fof_nnf,[status(thm)],[fact_413_sum__squares__le__zero__iff]) ).
fof(f_439_2,plain,
! [U_1045,U_1044] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1045),U_1045)),hAPP_int_int(times_times_int(U_1044),U_1044))),zero_zero_int))
| U_1044 != zero_zero_int
| U_1045 != zero_zero_int )
& ( ( U_1044 = zero_zero_int
& U_1045 = 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(U_1045),U_1045)),hAPP_int_int(times_times_int(U_1044),U_1044))),zero_zero_int)) ) )
| ~ is_int(U_1044)
| ~ is_int(U_1045) ),
inference(variable_rename,[status(thm)],[f_439_1]) ).
cnf(f_439_3,plain,
( U_1045 = 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(U_1045),U_1045)),hAPP_int_int(times_times_int(U_1044),U_1044))),zero_zero_int))
| ~ is_int(U_1044)
| ~ is_int(U_1045) ),
inference(clausify,[status(thm)],[f_439_2]) ).
cnf(f_439_4,plain,
( U_1044 = 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(U_1045),U_1045)),hAPP_int_int(times_times_int(U_1044),U_1044))),zero_zero_int))
| ~ is_int(U_1044)
| ~ is_int(U_1045) ),
inference(clausify,[status(thm)],[f_439_2]) ).
cnf(f_439_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1045),U_1045)),hAPP_int_int(times_times_int(U_1044),U_1044))),zero_zero_int))
| U_1044 != zero_zero_int
| U_1045 != zero_zero_int
| ~ is_int(U_1044)
| ~ is_int(U_1045) ),
inference(clausify,[status(thm)],[f_439_2]) ).
fof(f_440_1,plain,
! [X_2,Y_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X_2),X_2)),hAPP_real_real(times_times_real(Y_2),Y_2))),zero_zero_real))
| Y_2 != zero_zero_real
| X_2 != zero_zero_real )
& ( ( Y_2 = zero_zero_real
& X_2 = 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(X_2),X_2)),hAPP_real_real(times_times_real(Y_2),Y_2))),zero_zero_real)) ) ),
inference(fof_nnf,[status(thm)],[fact_414_sum__squares__le__zero__iff]) ).
fof(f_440_2,plain,
! [U_1047,U_1046] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_1047),U_1047)),hAPP_real_real(times_times_real(U_1046),U_1046))),zero_zero_real))
| U_1046 != zero_zero_real
| U_1047 != zero_zero_real )
& ( ( U_1046 = zero_zero_real
& U_1047 = 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(U_1047),U_1047)),hAPP_real_real(times_times_real(U_1046),U_1046))),zero_zero_real)) ) ),
inference(variable_rename,[status(thm)],[f_440_1]) ).
fof(f_440_3,plain,
( ! [U_1051,U_1049] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_1051),U_1051)),hAPP_real_real(times_times_real(U_1049),U_1049))),zero_zero_real))
| U_1049 != zero_zero_real
| U_1051 != zero_zero_real )
& ! [U_1050,U_1048] :
( ( U_1048 = zero_zero_real
& U_1050 = 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(U_1050),U_1050)),hAPP_real_real(times_times_real(U_1048),U_1048))),zero_zero_real)) ) ),
inference(miniscope,[status(thm)],[f_440_2]) ).
cnf(f_440_4,plain,
( U_1050 = 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(U_1050),U_1050)),hAPP_real_real(times_times_real(U_1048),U_1048))),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_440_3]) ).
cnf(f_440_5,plain,
( U_1048 = 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(U_1050),U_1050)),hAPP_real_real(times_times_real(U_1048),U_1048))),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_440_3]) ).
cnf(f_440_6,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_1051),U_1051)),hAPP_real_real(times_times_real(U_1049),U_1049))),zero_zero_real))
| U_1049 != zero_zero_real
| U_1051 != zero_zero_real ),
inference(clausify,[status(thm)],[f_440_3]) ).
fof(f_441_1,plain,
! [V_7,V_8] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(V_7)),number_number_of_nat(V_8)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_7),V_8))
| ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),V_8))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_7),V_8)) ) )
& ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_7),V_8))
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),V_8))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V_7),V_8)) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(V_7)),number_number_of_nat(V_8))) ) ),
inference(fof_nnf,[status(thm)],[fact_415_less__nat__number__of]) ).
fof(f_441_2,plain,
! [U_1053,U_1052] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(U_1053)),number_number_of_nat(U_1052)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1053),U_1052))
| ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1052))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1053),U_1052)) ) )
& ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1053),U_1052))
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1052))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1053),U_1052)) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(U_1053)),number_number_of_nat(U_1052))) ) ),
inference(variable_rename,[status(thm)],[f_441_1]) ).
fof(f_441_3,plain,
( ! [U_1057,U_1055] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(U_1057)),number_number_of_nat(U_1055)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1057),U_1055))
| ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1055))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1057),U_1055)) ) )
& ! [U_1056,U_1054] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1056),U_1054))
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1054))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1056),U_1054)) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(U_1056)),number_number_of_nat(U_1054))) ) ),
inference(miniscope,[status(thm)],[f_441_2]) ).
cnf(f_441_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1054))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1056),U_1054))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(U_1056)),number_number_of_nat(U_1054))) ),
inference(clausify,[status(thm)],[f_441_3]) ).
cnf(f_441_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1056),U_1054))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(U_1056)),number_number_of_nat(U_1054))) ),
inference(clausify,[status(thm)],[f_441_3]) ).
cnf(f_441_6,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1057),U_1055))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1057),U_1055))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(U_1057)),number_number_of_nat(U_1055))) ),
inference(clausify,[status(thm)],[f_441_3]) ).
cnf(f_441_7,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1055))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1057),U_1055))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,number_number_of_nat(U_1057)),number_number_of_nat(U_1055))) ),
inference(clausify,[status(thm)],[f_441_3]) ).
fof(f_442_1,plain,
! [X_16,Y_13] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(X_16),X_16)),hAPP_int_int(times_times_int(Y_13),Y_13))),zero_zero_int)),
inference(fof_nnf,[status(thm)],[fact_416_not__sum__squares__lt__zero]) ).
fof(f_442_2,plain,
! [U_1059,U_1058] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1059),U_1059)),hAPP_int_int(times_times_int(U_1058),U_1058))),zero_zero_int)),
inference(variable_rename,[status(thm)],[f_442_1]) ).
cnf(f_442_3,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1059),U_1059)),hAPP_int_int(times_times_int(U_1058),U_1058))),zero_zero_int)),
inference(clausify,[status(thm)],[f_442_2]) ).
fof(f_443_1,plain,
! [X_16,Y_13] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X_16),X_16)),hAPP_real_real(times_times_real(Y_13),Y_13))),zero_zero_real)),
inference(fof_nnf,[status(thm)],[fact_417_not__sum__squares__lt__zero]) ).
fof(f_443_2,plain,
! [U_1061,U_1060] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_1061),U_1061)),hAPP_real_real(times_times_real(U_1060),U_1060))),zero_zero_real)),
inference(variable_rename,[status(thm)],[f_443_1]) ).
cnf(f_443_3,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_1061),U_1061)),hAPP_real_real(times_times_real(U_1060),U_1060))),zero_zero_real)),
inference(clausify,[status(thm)],[f_443_2]) ).
fof(f_444_1,plain,
! [X_2,Y_2] :
( ( ( 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(X_2),X_2)),hAPP_int_int(times_times_int(Y_2),Y_2))))
| ( Y_2 = zero_zero_int
& X_2 = zero_zero_int ) )
& ( Y_2 != zero_zero_int
| X_2 != zero_zero_int
| ~ 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(X_2),X_2)),hAPP_int_int(times_times_int(Y_2),Y_2)))) ) )
| ~ is_int(Y_2)
| ~ is_int(X_2) ),
inference(fof_nnf,[status(thm)],[fact_418_sum__squares__gt__zero__iff]) ).
fof(f_444_2,plain,
! [U_1063,U_1062] :
( ( ( 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(U_1063),U_1063)),hAPP_int_int(times_times_int(U_1062),U_1062))))
| ( U_1062 = zero_zero_int
& U_1063 = zero_zero_int ) )
& ( U_1062 != zero_zero_int
| U_1063 != zero_zero_int
| ~ 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(U_1063),U_1063)),hAPP_int_int(times_times_int(U_1062),U_1062)))) ) )
| ~ is_int(U_1062)
| ~ is_int(U_1063) ),
inference(variable_rename,[status(thm)],[f_444_1]) ).
cnf(f_444_3,plain,
( U_1062 != zero_zero_int
| U_1063 != zero_zero_int
| ~ 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(U_1063),U_1063)),hAPP_int_int(times_times_int(U_1062),U_1062))))
| ~ is_int(U_1062)
| ~ is_int(U_1063) ),
inference(clausify,[status(thm)],[f_444_2]) ).
cnf(f_444_4,plain,
( U_1063 = zero_zero_int
| 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(U_1063),U_1063)),hAPP_int_int(times_times_int(U_1062),U_1062))))
| ~ is_int(U_1062)
| ~ is_int(U_1063) ),
inference(clausify,[status(thm)],[f_444_2]) ).
cnf(f_444_5,plain,
( U_1062 = zero_zero_int
| 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(U_1063),U_1063)),hAPP_int_int(times_times_int(U_1062),U_1062))))
| ~ is_int(U_1062)
| ~ is_int(U_1063) ),
inference(clausify,[status(thm)],[f_444_2]) ).
fof(f_445_1,plain,
! [X_2,Y_2] :
( ( 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(X_2),X_2)),hAPP_real_real(times_times_real(Y_2),Y_2))))
| ( Y_2 = zero_zero_real
& X_2 = zero_zero_real ) )
& ( Y_2 != zero_zero_real
| X_2 != zero_zero_real
| ~ 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(X_2),X_2)),hAPP_real_real(times_times_real(Y_2),Y_2)))) ) ),
inference(fof_nnf,[status(thm)],[fact_419_sum__squares__gt__zero__iff]) ).
fof(f_445_2,plain,
! [U_1065,U_1064] :
( ( 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(U_1065),U_1065)),hAPP_real_real(times_times_real(U_1064),U_1064))))
| ( U_1064 = zero_zero_real
& U_1065 = zero_zero_real ) )
& ( U_1064 != zero_zero_real
| U_1065 != zero_zero_real
| ~ 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(U_1065),U_1065)),hAPP_real_real(times_times_real(U_1064),U_1064)))) ) ),
inference(variable_rename,[status(thm)],[f_445_1]) ).
fof(f_445_3,plain,
( ! [U_1069,U_1067] :
( 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(U_1069),U_1069)),hAPP_real_real(times_times_real(U_1067),U_1067))))
| ( U_1067 = zero_zero_real
& U_1069 = zero_zero_real ) )
& ! [U_1068,U_1066] :
( U_1066 != zero_zero_real
| U_1068 != zero_zero_real
| ~ 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(U_1068),U_1068)),hAPP_real_real(times_times_real(U_1066),U_1066)))) ) ),
inference(miniscope,[status(thm)],[f_445_2]) ).
cnf(f_445_4,plain,
( U_1066 != zero_zero_real
| U_1068 != zero_zero_real
| ~ 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(U_1068),U_1068)),hAPP_real_real(times_times_real(U_1066),U_1066)))) ),
inference(clausify,[status(thm)],[f_445_3]) ).
cnf(f_445_5,plain,
( U_1069 = zero_zero_real
| 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(U_1069),U_1069)),hAPP_real_real(times_times_real(U_1067),U_1067)))) ),
inference(clausify,[status(thm)],[f_445_3]) ).
cnf(f_445_6,plain,
( U_1067 = zero_zero_real
| 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(U_1069),U_1069)),hAPP_real_real(times_times_real(U_1067),U_1067)))) ),
inference(clausify,[status(thm)],[f_445_3]) ).
fof(f_446_1,plain,
! [V_7,V_8] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(V_7)),number_number_of_nat(V_8)))
| ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V_7),pls))
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V_7),V_8)) ) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V_7),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V_7),V_8))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(V_7)),number_number_of_nat(V_8))) ) ),
inference(fof_nnf,[status(thm)],[fact_420_le__nat__number__of]) ).
fof(f_446_2,plain,
! [U_1071,U_1070] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(U_1071)),number_number_of_nat(U_1070)))
| ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1071),pls))
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1071),U_1070)) ) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1071),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1071),U_1070))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(U_1071)),number_number_of_nat(U_1070))) ) ),
inference(variable_rename,[status(thm)],[f_446_1]) ).
fof(f_446_3,plain,
( ! [U_1075,U_1073] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(U_1075)),number_number_of_nat(U_1073)))
| ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1075),pls))
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1075),U_1073)) ) )
& ! [U_1074,U_1072] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1074),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1074),U_1072))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(U_1074)),number_number_of_nat(U_1072))) ) ),
inference(miniscope,[status(thm)],[f_446_2]) ).
cnf(f_446_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1074),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1074),U_1072))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(U_1074)),number_number_of_nat(U_1072))) ),
inference(clausify,[status(thm)],[f_446_3]) ).
cnf(f_446_5,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1075),U_1073))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(U_1075)),number_number_of_nat(U_1073))) ),
inference(clausify,[status(thm)],[f_446_3]) ).
cnf(f_446_6,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1075),pls))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,number_number_of_nat(U_1075)),number_number_of_nat(U_1073))) ),
inference(clausify,[status(thm)],[f_446_3]) ).
fof(f_447_1,plain,
! [W_5] : number_number_of_int(bit0(W_5)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(W_5))),number_number_of_int(W_5)),
inference(fof_nnf,[status(thm)],[fact_421_number__of__Bit0]) ).
fof(f_447_2,plain,
! [U_1076] : number_number_of_int(bit0(U_1076)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(U_1076))),number_number_of_int(U_1076)),
inference(variable_rename,[status(thm)],[f_447_1]) ).
cnf(f_447_3,plain,
number_number_of_int(bit0(U_1076)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(U_1076))),number_number_of_int(U_1076)),
inference(clausify,[status(thm)],[f_447_2]) ).
fof(f_448_1,plain,
! [W_5] : number267125858f_real(bit0(W_5)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(zero_zero_real),number267125858f_real(W_5))),number267125858f_real(W_5)),
inference(fof_nnf,[status(thm)],[fact_422_number__of__Bit0]) ).
fof(f_448_2,plain,
! [U_1077] : number267125858f_real(bit0(U_1077)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(zero_zero_real),number267125858f_real(U_1077))),number267125858f_real(U_1077)),
inference(variable_rename,[status(thm)],[f_448_1]) ).
cnf(f_448_3,plain,
number267125858f_real(bit0(U_1077)) = hAPP_real_real(plus_plus_real(hAPP_real_real(plus_plus_real(zero_zero_real),number267125858f_real(U_1077))),number267125858f_real(U_1077)),
inference(clausify,[status(thm)],[f_448_2]) ).
fof(f_449_1,plain,
! [A_70] :
( hAPP_nat_int(power_power_int(A_70),one_one_nat) = A_70
| ~ is_int(A_70) ),
inference(fof_nnf,[status(thm)],[fact_423_power__one__right]) ).
fof(f_449_2,plain,
! [U_1078] :
( hAPP_nat_int(power_power_int(U_1078),one_one_nat) = U_1078
| ~ is_int(U_1078) ),
inference(variable_rename,[status(thm)],[f_449_1]) ).
cnf(f_449_3,plain,
( hAPP_nat_int(power_power_int(U_1078),one_one_nat) = U_1078
| ~ is_int(U_1078) ),
inference(clausify,[status(thm)],[f_449_2]) ).
fof(f_450_1,plain,
! [A_70] : hAPP_nat_real(power_power_real(A_70),one_one_nat) = A_70,
inference(fof_nnf,[status(thm)],[fact_424_power__one__right]) ).
fof(f_450_2,plain,
! [U_1079] : hAPP_nat_real(power_power_real(U_1079),one_one_nat) = U_1079,
inference(variable_rename,[status(thm)],[f_450_1]) ).
cnf(f_450_3,plain,
hAPP_nat_real(power_power_real(U_1079),one_one_nat) = U_1079,
inference(clausify,[status(thm)],[f_450_2]) ).
fof(f_451_1,plain,
! [A_70] : hAPP_nat_nat(power_power_nat(A_70),one_one_nat) = A_70,
inference(fof_nnf,[status(thm)],[fact_425_power__one__right]) ).
fof(f_451_2,plain,
! [U_1080] : hAPP_nat_nat(power_power_nat(U_1080),one_one_nat) = U_1080,
inference(variable_rename,[status(thm)],[f_451_1]) ).
cnf(f_451_3,plain,
hAPP_nat_nat(power_power_nat(U_1080),one_one_nat) = U_1080,
inference(clausify,[status(thm)],[f_451_2]) ).
fof(f_452_1,plain,
! [Z_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Z_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_1)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Z_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_426_int__one__le__iff__zero__less]) ).
fof(f_452_2,plain,
! [U_1081] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_1081))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1081)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1081))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_1081)) ) ),
inference(variable_rename,[status(thm)],[f_452_1]) ).
fof(f_452_3,plain,
( ! [U_1083] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_1083))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1083)) )
& ! [U_1082] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1082))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_1082)) ) ),
inference(miniscope,[status(thm)],[f_452_2]) ).
cnf(f_452_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1082))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_1082)) ),
inference(clausify,[status(thm)],[f_452_3]) ).
cnf(f_452_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_1083))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1083)) ),
inference(clausify,[status(thm)],[f_452_3]) ).
fof(f_453_1,plain,
! [N,Ma] :
( ( ( hAPP_int_int(times_times_int(Ma),N) = one_one_int
| N != one_one_int
| Ma != one_one_int )
& ( ( N = one_one_int
& Ma = one_one_int )
| hAPP_int_int(times_times_int(Ma),N) != one_one_int ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ma))
| ~ is_int(Ma)
| ~ is_int(N) ),
inference(fof_nnf,[status(thm)],[fact_427_pos__zmult__eq__1__iff]) ).
fof(f_453_2,plain,
! [U_1085,U_1084] :
( ( ( hAPP_int_int(times_times_int(U_1084),U_1085) = one_one_int
| U_1085 != one_one_int
| U_1084 != one_one_int )
& ( ( U_1085 = one_one_int
& U_1084 = one_one_int )
| hAPP_int_int(times_times_int(U_1084),U_1085) != one_one_int ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1084))
| ~ is_int(U_1084)
| ~ is_int(U_1085) ),
inference(variable_rename,[status(thm)],[f_453_1]) ).
cnf(f_453_3,plain,
( U_1084 = one_one_int
| hAPP_int_int(times_times_int(U_1084),U_1085) != one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1084))
| ~ is_int(U_1084)
| ~ is_int(U_1085) ),
inference(clausify,[status(thm)],[f_453_2]) ).
cnf(f_453_4,plain,
( U_1085 = one_one_int
| hAPP_int_int(times_times_int(U_1084),U_1085) != one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1084))
| ~ is_int(U_1084)
| ~ is_int(U_1085) ),
inference(clausify,[status(thm)],[f_453_2]) ).
cnf(f_453_5,plain,
( hAPP_int_int(times_times_int(U_1084),U_1085) = one_one_int
| U_1085 != one_one_int
| U_1084 != one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1084))
| ~ is_int(U_1084)
| ~ is_int(U_1085) ),
inference(clausify,[status(thm)],[f_453_2]) ).
fof(f_454_1,plain,
! [Z_1] :
( ( 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),Z_1)),Z_1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),zero_zero_int)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),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),Z_1)),Z_1)),zero_zero_int)) ) ),
inference(fof_nnf,[status(thm)],[fact_428_odd__less__0]) ).
fof(f_454_2,plain,
! [U_1086] :
( ( 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),U_1086)),U_1086)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1086),zero_zero_int)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1086),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),U_1086)),U_1086)),zero_zero_int)) ) ),
inference(variable_rename,[status(thm)],[f_454_1]) ).
fof(f_454_3,plain,
( ! [U_1088] :
( 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),U_1088)),U_1088)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1088),zero_zero_int)) )
& ! [U_1087] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1087),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),U_1087)),U_1087)),zero_zero_int)) ) ),
inference(miniscope,[status(thm)],[f_454_2]) ).
cnf(f_454_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1087),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),U_1087)),U_1087)),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_454_3]) ).
cnf(f_454_5,plain,
( 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),U_1088)),U_1088)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1088),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_454_3]) ).
fof(f_455_1,plain,
! [Y_2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(Y_2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),Y_2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),Y_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(Y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_429_less__special_I1_J]) ).
fof(f_455_2,plain,
! [U_1089] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(U_1089)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1089)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1089))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(U_1089))) ) ),
inference(variable_rename,[status(thm)],[f_455_1]) ).
fof(f_455_3,plain,
( ! [U_1091] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(U_1091)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1091)) )
& ! [U_1090] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1090))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(U_1090))) ) ),
inference(miniscope,[status(thm)],[f_455_2]) ).
cnf(f_455_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1090))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(U_1090))) ),
inference(clausify,[status(thm)],[f_455_3]) ).
cnf(f_455_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(U_1091)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1091)) ),
inference(clausify,[status(thm)],[f_455_3]) ).
fof(f_456_1,plain,
! [Y_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(Y_2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),Y_2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),Y_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(Y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_430_less__special_I1_J]) ).
fof(f_456_2,plain,
! [U_1092] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(U_1092)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1092)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1092))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(U_1092))) ) ),
inference(variable_rename,[status(thm)],[f_456_1]) ).
fof(f_456_3,plain,
( ! [U_1094] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(U_1094)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1094)) )
& ! [U_1093] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1093))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(U_1093))) ) ),
inference(miniscope,[status(thm)],[f_456_2]) ).
cnf(f_456_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1093))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(U_1093))) ),
inference(clausify,[status(thm)],[f_456_3]) ).
cnf(f_456_5,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(U_1094)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1094)) ),
inference(clausify,[status(thm)],[f_456_3]) ).
fof(f_457_1,plain,
! [X_2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X_2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X_2)),zero_zero_int)) ) ),
inference(fof_nnf,[status(thm)],[fact_431_less__special_I3_J]) ).
fof(f_457_2,plain,
! [U_1095] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_1095)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1095),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1095),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_1095)),zero_zero_int)) ) ),
inference(variable_rename,[status(thm)],[f_457_1]) ).
fof(f_457_3,plain,
( ! [U_1097] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_1097)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1097),pls)) )
& ! [U_1096] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1096),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_1096)),zero_zero_int)) ) ),
inference(miniscope,[status(thm)],[f_457_2]) ).
cnf(f_457_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1096),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_1096)),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_457_3]) ).
cnf(f_457_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_1097)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1097),pls)) ),
inference(clausify,[status(thm)],[f_457_3]) ).
fof(f_458_1,plain,
! [X_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X_2)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X_2)),zero_zero_real)) ) ),
inference(fof_nnf,[status(thm)],[fact_432_less__special_I3_J]) ).
fof(f_458_2,plain,
! [U_1098] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_1098)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1098),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1098),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_1098)),zero_zero_real)) ) ),
inference(variable_rename,[status(thm)],[f_458_1]) ).
fof(f_458_3,plain,
( ! [U_1100] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_1100)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1100),pls)) )
& ! [U_1099] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1099),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_1099)),zero_zero_real)) ) ),
inference(miniscope,[status(thm)],[f_458_2]) ).
cnf(f_458_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1099),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_1099)),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_458_3]) ).
cnf(f_458_5,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(U_1100)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1100),pls)) ),
inference(clausify,[status(thm)],[f_458_3]) ).
fof(f_459_1,plain,
! [Y_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(Y_2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Y_2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Y_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(Y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_433_le__special_I1_J]) ).
fof(f_459_2,plain,
! [U_1101] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(U_1101)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_1101)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_1101))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(U_1101))) ) ),
inference(variable_rename,[status(thm)],[f_459_1]) ).
fof(f_459_3,plain,
( ! [U_1103] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(U_1103)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_1103)) )
& ! [U_1102] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_1102))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(U_1102))) ) ),
inference(miniscope,[status(thm)],[f_459_2]) ).
cnf(f_459_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_1102))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(U_1102))) ),
inference(clausify,[status(thm)],[f_459_3]) ).
cnf(f_459_5,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(U_1103)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_1103)) ),
inference(clausify,[status(thm)],[f_459_3]) ).
fof(f_460_1,plain,
! [Y_2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(Y_2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Y_2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Y_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(Y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_434_le__special_I1_J]) ).
fof(f_460_2,plain,
! [U_1104] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(U_1104)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_1104)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_1104))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(U_1104))) ) ),
inference(variable_rename,[status(thm)],[f_460_1]) ).
fof(f_460_3,plain,
( ! [U_1106] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(U_1106)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_1106)) )
& ! [U_1105] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_1105))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(U_1105))) ) ),
inference(miniscope,[status(thm)],[f_460_2]) ).
cnf(f_460_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_1105))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(U_1105))) ),
inference(clausify,[status(thm)],[f_460_3]) ).
cnf(f_460_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(U_1106)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_1106)) ),
inference(clausify,[status(thm)],[f_460_3]) ).
fof(f_461_1,plain,
! [X_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X_2)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X_2)),zero_zero_real)) ) ),
inference(fof_nnf,[status(thm)],[fact_435_le__special_I3_J]) ).
fof(f_461_2,plain,
! [U_1107] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_1107)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1107),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1107),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_1107)),zero_zero_real)) ) ),
inference(variable_rename,[status(thm)],[f_461_1]) ).
fof(f_461_3,plain,
( ! [U_1109] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_1109)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1109),pls)) )
& ! [U_1108] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1108),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_1108)),zero_zero_real)) ) ),
inference(miniscope,[status(thm)],[f_461_2]) ).
cnf(f_461_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1108),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_1108)),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_461_3]) ).
cnf(f_461_5,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(U_1109)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1109),pls)) ),
inference(clausify,[status(thm)],[f_461_3]) ).
fof(f_462_1,plain,
! [X_2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X_2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_2),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X_2)),zero_zero_int)) ) ),
inference(fof_nnf,[status(thm)],[fact_436_le__special_I3_J]) ).
fof(f_462_2,plain,
! [U_1110] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_1110)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1110),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1110),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_1110)),zero_zero_int)) ) ),
inference(variable_rename,[status(thm)],[f_462_1]) ).
fof(f_462_3,plain,
( ! [U_1112] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_1112)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1112),pls)) )
& ! [U_1111] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1111),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_1111)),zero_zero_int)) ) ),
inference(miniscope,[status(thm)],[f_462_2]) ).
cnf(f_462_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1111),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_1111)),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_462_3]) ).
cnf(f_462_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_1112)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1112),pls)) ),
inference(clausify,[status(thm)],[f_462_3]) ).
fof(f_463_1,plain,
! [Z] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),Z)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z)) ),
inference(fof_nnf,[status(thm)],[fact_437_le__imp__0__less]) ).
fof(f_463_2,plain,
! [U_1113] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),U_1113)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1113)) ),
inference(variable_rename,[status(thm)],[f_463_1]) ).
cnf(f_463_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),U_1113)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1113)) ),
inference(clausify,[status(thm)],[f_463_2]) ).
fof(f_464_1,plain,
hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real,
inference(fof_nnf,[status(thm)],[fact_438_zero__power2]) ).
cnf(f_464_2,plain,
hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real,
inference(clausify,[status(thm)],[f_464_1]) ).
fof(f_465_1,plain,
hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_nat,
inference(fof_nnf,[status(thm)],[fact_439_zero__power2]) ).
cnf(f_465_2,plain,
hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_nat,
inference(clausify,[status(thm)],[f_465_1]) ).
fof(f_466_1,plain,
hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_440_zero__power2]) ).
cnf(f_466_2,plain,
hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(clausify,[status(thm)],[f_466_1]) ).
fof(f_467_1,plain,
! [A_2] :
( ( hAPP_nat_real(power_power_real(A_2),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real
| A_2 != zero_zero_real )
& ( A_2 = zero_zero_real
| hAPP_nat_real(power_power_real(A_2),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_real ) ),
inference(fof_nnf,[status(thm)],[fact_441_zero__eq__power2]) ).
fof(f_467_2,plain,
! [U_1114] :
( ( hAPP_nat_real(power_power_real(U_1114),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real
| U_1114 != zero_zero_real )
& ( U_1114 = zero_zero_real
| hAPP_nat_real(power_power_real(U_1114),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_real ) ),
inference(variable_rename,[status(thm)],[f_467_1]) ).
fof(f_467_3,plain,
( ! [U_1116] :
( hAPP_nat_real(power_power_real(U_1116),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real
| U_1116 != zero_zero_real )
& ! [U_1115] :
( U_1115 = zero_zero_real
| hAPP_nat_real(power_power_real(U_1115),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_real ) ),
inference(miniscope,[status(thm)],[f_467_2]) ).
cnf(f_467_4,plain,
( U_1115 = zero_zero_real
| hAPP_nat_real(power_power_real(U_1115),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_real ),
inference(clausify,[status(thm)],[f_467_3]) ).
cnf(f_467_5,plain,
( hAPP_nat_real(power_power_real(U_1116),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real
| U_1116 != zero_zero_real ),
inference(clausify,[status(thm)],[f_467_3]) ).
fof(f_468_1,plain,
! [A_2] :
( ( ( hAPP_nat_int(power_power_int(A_2),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int
| A_2 != zero_zero_int )
& ( A_2 = zero_zero_int
| hAPP_nat_int(power_power_int(A_2),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ) )
| ~ is_int(A_2) ),
inference(fof_nnf,[status(thm)],[fact_442_zero__eq__power2]) ).
fof(f_468_2,plain,
! [U_1117] :
( ( ( hAPP_nat_int(power_power_int(U_1117),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int
| U_1117 != zero_zero_int )
& ( U_1117 = zero_zero_int
| hAPP_nat_int(power_power_int(U_1117),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ) )
| ~ is_int(U_1117) ),
inference(variable_rename,[status(thm)],[f_468_1]) ).
cnf(f_468_3,plain,
( U_1117 = zero_zero_int
| hAPP_nat_int(power_power_int(U_1117),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int
| ~ is_int(U_1117) ),
inference(clausify,[status(thm)],[f_468_2]) ).
cnf(f_468_4,plain,
( hAPP_nat_int(power_power_int(U_1117),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int
| U_1117 != zero_zero_int
| ~ is_int(U_1117) ),
inference(clausify,[status(thm)],[f_468_2]) ).
fof(f_469_1,plain,
! [A_69] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(A_69),number_number_of_nat(bit0(bit1(pls)))))),
inference(fof_nnf,[status(thm)],[fact_443_zero__le__power2]) ).
fof(f_469_2,plain,
! [U_1118] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(U_1118),number_number_of_nat(bit0(bit1(pls)))))),
inference(variable_rename,[status(thm)],[f_469_1]) ).
cnf(f_469_3,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(U_1118),number_number_of_nat(bit0(bit1(pls)))))),
inference(clausify,[status(thm)],[f_469_2]) ).
fof(f_470_1,plain,
! [A_69] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(A_69),number_number_of_nat(bit0(bit1(pls)))))),
inference(fof_nnf,[status(thm)],[fact_444_zero__le__power2]) ).
fof(f_470_2,plain,
! [U_1119] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(U_1119),number_number_of_nat(bit0(bit1(pls)))))),
inference(variable_rename,[status(thm)],[f_470_1]) ).
cnf(f_470_3,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(U_1119),number_number_of_nat(bit0(bit1(pls)))))),
inference(clausify,[status(thm)],[f_470_2]) ).
fof(f_471_1,plain,
! [X_15,Y_12] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_15),Y_12))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y_12))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(X_15),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_12),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(fof_nnf,[status(thm)],[fact_445_power2__le__imp__le]) ).
fof(f_471_2,plain,
! [U_1121,U_1120] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1121),U_1120))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1120))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(U_1121),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1120),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(variable_rename,[status(thm)],[f_471_1]) ).
cnf(f_471_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1121),U_1120))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1120))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(U_1121),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1120),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(clausify,[status(thm)],[f_471_2]) ).
fof(f_472_1,plain,
! [X_15,Y_12] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_15),Y_12))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),Y_12))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(X_15),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(Y_12),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(fof_nnf,[status(thm)],[fact_446_power2__le__imp__le]) ).
fof(f_472_2,plain,
! [U_1123,U_1122] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1123),U_1122))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1122))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(U_1123),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(U_1122),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(variable_rename,[status(thm)],[f_472_1]) ).
cnf(f_472_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1123),U_1122))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1122))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(U_1123),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(U_1122),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(clausify,[status(thm)],[f_472_2]) ).
fof(f_473_1,plain,
! [X_15,Y_12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_15),Y_12))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_12))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(X_15),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_12),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(fof_nnf,[status(thm)],[fact_447_power2__le__imp__le]) ).
fof(f_473_2,plain,
! [U_1125,U_1124] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1125),U_1124))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1124))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(U_1125),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1124),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(variable_rename,[status(thm)],[f_473_1]) ).
cnf(f_473_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1125),U_1124))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1124))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(U_1125),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1124),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(clausify,[status(thm)],[f_473_2]) ).
fof(f_474_1,plain,
! [X_14,Y_11] :
( X_14 = Y_11
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y_11))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X_14))
| hAPP_nat_real(power_power_real(X_14),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_real(power_power_real(Y_11),number_number_of_nat(bit0(bit1(pls)))) ),
inference(fof_nnf,[status(thm)],[fact_448_power2__eq__imp__eq]) ).
fof(f_474_2,plain,
! [U_1127,U_1126] :
( U_1127 = U_1126
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1126))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1127))
| hAPP_nat_real(power_power_real(U_1127),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_real(power_power_real(U_1126),number_number_of_nat(bit0(bit1(pls)))) ),
inference(variable_rename,[status(thm)],[f_474_1]) ).
cnf(f_474_3,plain,
( U_1127 = U_1126
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1126))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1127))
| hAPP_nat_real(power_power_real(U_1127),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_real(power_power_real(U_1126),number_number_of_nat(bit0(bit1(pls)))) ),
inference(clausify,[status(thm)],[f_474_2]) ).
fof(f_475_1,plain,
! [X_14,Y_11] :
( X_14 = Y_11
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),Y_11))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X_14))
| hAPP_nat_nat(power_power_nat(X_14),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_nat(power_power_nat(Y_11),number_number_of_nat(bit0(bit1(pls)))) ),
inference(fof_nnf,[status(thm)],[fact_449_power2__eq__imp__eq]) ).
fof(f_475_2,plain,
! [U_1129,U_1128] :
( U_1129 = U_1128
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1128))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1129))
| hAPP_nat_nat(power_power_nat(U_1129),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_nat(power_power_nat(U_1128),number_number_of_nat(bit0(bit1(pls)))) ),
inference(variable_rename,[status(thm)],[f_475_1]) ).
cnf(f_475_3,plain,
( U_1129 = U_1128
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1128))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1129))
| hAPP_nat_nat(power_power_nat(U_1129),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_nat(power_power_nat(U_1128),number_number_of_nat(bit0(bit1(pls)))) ),
inference(clausify,[status(thm)],[f_475_2]) ).
fof(f_476_1,plain,
! [X_14,Y_11] :
( X_14 = Y_11
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_11))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_14))
| hAPP_nat_int(power_power_int(X_14),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(Y_11),number_number_of_nat(bit0(bit1(pls))))
| ~ is_int(Y_11)
| ~ is_int(X_14) ),
inference(fof_nnf,[status(thm)],[fact_450_power2__eq__imp__eq]) ).
fof(f_476_2,plain,
! [U_1131,U_1130] :
( U_1131 = U_1130
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1130))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1131))
| hAPP_nat_int(power_power_int(U_1131),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(U_1130),number_number_of_nat(bit0(bit1(pls))))
| ~ is_int(U_1130)
| ~ is_int(U_1131) ),
inference(variable_rename,[status(thm)],[f_476_1]) ).
cnf(f_476_3,plain,
( U_1131 = U_1130
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1130))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1131))
| hAPP_nat_int(power_power_int(U_1131),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(U_1130),number_number_of_nat(bit0(bit1(pls))))
| ~ is_int(U_1130)
| ~ is_int(U_1131) ),
inference(clausify,[status(thm)],[f_476_2]) ).
fof(f_477_1,plain,
! [A_68] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(A_68),number_number_of_nat(bit0(bit1(pls))))),zero_zero_real)),
inference(fof_nnf,[status(thm)],[fact_451_power2__less__0]) ).
fof(f_477_2,plain,
! [U_1132] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_1132),number_number_of_nat(bit0(bit1(pls))))),zero_zero_real)),
inference(variable_rename,[status(thm)],[f_477_1]) ).
cnf(f_477_3,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_1132),number_number_of_nat(bit0(bit1(pls))))),zero_zero_real)),
inference(clausify,[status(thm)],[f_477_2]) ).
fof(f_478_1,plain,
! [A_68] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(A_68),number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)),
inference(fof_nnf,[status(thm)],[fact_452_power2__less__0]) ).
fof(f_478_2,plain,
! [U_1133] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_1133),number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)),
inference(variable_rename,[status(thm)],[f_478_1]) ).
cnf(f_478_3,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_1133),number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)),
inference(clausify,[status(thm)],[f_478_2]) ).
fof(f_479_1,plain,
! [A_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(A_2),number_number_of_nat(bit0(bit1(pls))))))
| A_2 = zero_zero_real )
& ( A_2 != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(A_2),number_number_of_nat(bit0(bit1(pls)))))) ) ),
inference(fof_nnf,[status(thm)],[fact_453_zero__less__power2]) ).
fof(f_479_2,plain,
! [U_1134] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(U_1134),number_number_of_nat(bit0(bit1(pls))))))
| U_1134 = zero_zero_real )
& ( U_1134 != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(U_1134),number_number_of_nat(bit0(bit1(pls)))))) ) ),
inference(variable_rename,[status(thm)],[f_479_1]) ).
fof(f_479_3,plain,
( ! [U_1136] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(U_1136),number_number_of_nat(bit0(bit1(pls))))))
| U_1136 = zero_zero_real )
& ! [U_1135] :
( U_1135 != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(U_1135),number_number_of_nat(bit0(bit1(pls)))))) ) ),
inference(miniscope,[status(thm)],[f_479_2]) ).
cnf(f_479_4,plain,
( U_1135 != zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(U_1135),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(clausify,[status(thm)],[f_479_3]) ).
cnf(f_479_5,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_nat_real(power_power_real(U_1136),number_number_of_nat(bit0(bit1(pls))))))
| U_1136 = zero_zero_real ),
inference(clausify,[status(thm)],[f_479_3]) ).
fof(f_480_1,plain,
! [A_2] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_2),number_number_of_nat(bit0(bit1(pls))))))
| A_2 = zero_zero_int )
& ( A_2 != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_2),number_number_of_nat(bit0(bit1(pls)))))) ) )
| ~ is_int(A_2) ),
inference(fof_nnf,[status(thm)],[fact_454_zero__less__power2]) ).
fof(f_480_2,plain,
! [U_1137] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(U_1137),number_number_of_nat(bit0(bit1(pls))))))
| U_1137 = zero_zero_int )
& ( U_1137 != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(U_1137),number_number_of_nat(bit0(bit1(pls)))))) ) )
| ~ is_int(U_1137) ),
inference(variable_rename,[status(thm)],[f_480_1]) ).
cnf(f_480_3,plain,
( U_1137 != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(U_1137),number_number_of_nat(bit0(bit1(pls))))))
| ~ is_int(U_1137) ),
inference(clausify,[status(thm)],[f_480_2]) ).
cnf(f_480_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(U_1137),number_number_of_nat(bit0(bit1(pls))))))
| U_1137 = zero_zero_int
| ~ is_int(U_1137) ),
inference(clausify,[status(thm)],[f_480_2]) ).
fof(f_481_1,plain,
! [X_2,Y_2] :
( ( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| Y_2 != zero_zero_real
| X_2 != zero_zero_real )
& ( ( Y_2 = zero_zero_real
& X_2 = zero_zero_real )
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ) ),
inference(fof_nnf,[status(thm)],[fact_455_sum__power2__eq__zero__iff]) ).
fof(f_481_2,plain,
! [U_1139,U_1138] :
( ( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(U_1139),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1138),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| U_1138 != zero_zero_real
| U_1139 != zero_zero_real )
& ( ( U_1138 = zero_zero_real
& U_1139 = zero_zero_real )
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(U_1139),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1138),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ) ),
inference(variable_rename,[status(thm)],[f_481_1]) ).
fof(f_481_3,plain,
( ! [U_1143,U_1141] :
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(U_1143),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1141),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| U_1141 != zero_zero_real
| U_1143 != zero_zero_real )
& ! [U_1142,U_1140] :
( ( U_1140 = zero_zero_real
& U_1142 = zero_zero_real )
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(U_1142),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1140),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ) ),
inference(miniscope,[status(thm)],[f_481_2]) ).
cnf(f_481_4,plain,
( U_1142 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(U_1142),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1140),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ),
inference(clausify,[status(thm)],[f_481_3]) ).
cnf(f_481_5,plain,
( U_1140 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(U_1142),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1140),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ),
inference(clausify,[status(thm)],[f_481_3]) ).
cnf(f_481_6,plain,
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(U_1143),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1141),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| U_1141 != zero_zero_real
| U_1143 != zero_zero_real ),
inference(clausify,[status(thm)],[f_481_3]) ).
fof(f_482_1,plain,
! [X_2,Y_2] :
( ( ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int
| Y_2 != zero_zero_int
| X_2 != zero_zero_int )
& ( ( Y_2 = zero_zero_int
& X_2 = zero_zero_int )
| hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int ) )
| ~ is_int(Y_2)
| ~ is_int(X_2) ),
inference(fof_nnf,[status(thm)],[fact_456_sum__power2__eq__zero__iff]) ).
fof(f_482_2,plain,
! [U_1145,U_1144] :
( ( ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(U_1145),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1144),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int
| U_1144 != zero_zero_int
| U_1145 != zero_zero_int )
& ( ( U_1144 = zero_zero_int
& U_1145 = zero_zero_int )
| hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(U_1145),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1144),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int ) )
| ~ is_int(U_1144)
| ~ is_int(U_1145) ),
inference(variable_rename,[status(thm)],[f_482_1]) ).
cnf(f_482_3,plain,
( U_1145 = zero_zero_int
| hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(U_1145),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1144),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int
| ~ is_int(U_1144)
| ~ is_int(U_1145) ),
inference(clausify,[status(thm)],[f_482_2]) ).
cnf(f_482_4,plain,
( U_1144 = zero_zero_int
| hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(U_1145),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1144),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int
| ~ is_int(U_1144)
| ~ is_int(U_1145) ),
inference(clausify,[status(thm)],[f_482_2]) ).
cnf(f_482_5,plain,
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(U_1145),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1144),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int
| U_1144 != zero_zero_int
| U_1145 != zero_zero_int
| ~ is_int(U_1144)
| ~ is_int(U_1145) ),
inference(clausify,[status(thm)],[f_482_2]) ).
fof(f_483_1,plain,
! [A_67,N_18] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(A_67),N_18)),A_67) = hAPP_nat_nat(times_times_nat(A_67),hAPP_nat_nat(power_power_nat(A_67),N_18)),
inference(fof_nnf,[status(thm)],[fact_457_power__commutes]) ).
fof(f_483_2,plain,
! [U_1147,U_1146] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(U_1147),U_1146)),U_1147) = hAPP_nat_nat(times_times_nat(U_1147),hAPP_nat_nat(power_power_nat(U_1147),U_1146)),
inference(variable_rename,[status(thm)],[f_483_1]) ).
cnf(f_483_3,plain,
hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(U_1147),U_1146)),U_1147) = hAPP_nat_nat(times_times_nat(U_1147),hAPP_nat_nat(power_power_nat(U_1147),U_1146)),
inference(clausify,[status(thm)],[f_483_2]) ).
fof(f_484_1,plain,
! [A_67,N_18] : hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(A_67),N_18)),A_67) = hAPP_real_real(times_times_real(A_67),hAPP_nat_real(power_power_real(A_67),N_18)),
inference(fof_nnf,[status(thm)],[fact_458_power__commutes]) ).
fof(f_484_2,plain,
! [U_1149,U_1148] : hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(U_1149),U_1148)),U_1149) = hAPP_real_real(times_times_real(U_1149),hAPP_nat_real(power_power_real(U_1149),U_1148)),
inference(variable_rename,[status(thm)],[f_484_1]) ).
cnf(f_484_3,plain,
hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(U_1149),U_1148)),U_1149) = hAPP_real_real(times_times_real(U_1149),hAPP_nat_real(power_power_real(U_1149),U_1148)),
inference(clausify,[status(thm)],[f_484_2]) ).
fof(f_485_1,plain,
! [A_67,N_18] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(A_67),N_18)),A_67) = hAPP_int_int(times_times_int(A_67),hAPP_nat_int(power_power_int(A_67),N_18)),
inference(fof_nnf,[status(thm)],[fact_459_power__commutes]) ).
fof(f_485_2,plain,
! [U_1151,U_1150] : hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(U_1151),U_1150)),U_1151) = hAPP_int_int(times_times_int(U_1151),hAPP_nat_int(power_power_int(U_1151),U_1150)),
inference(variable_rename,[status(thm)],[f_485_1]) ).
cnf(f_485_3,plain,
hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(U_1151),U_1150)),U_1151) = hAPP_int_int(times_times_int(U_1151),hAPP_nat_int(power_power_int(U_1151),U_1150)),
inference(clausify,[status(thm)],[f_485_2]) ).
fof(f_486_1,plain,
! [A_66,B_49,N_17] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(A_66),B_49)),N_17) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(A_66),N_17)),hAPP_nat_nat(power_power_nat(B_49),N_17)),
inference(fof_nnf,[status(thm)],[fact_460_power__mult__distrib]) ).
fof(f_486_2,plain,
! [U_1154,U_1153,U_1152] : hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(U_1154),U_1153)),U_1152) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(U_1154),U_1152)),hAPP_nat_nat(power_power_nat(U_1153),U_1152)),
inference(variable_rename,[status(thm)],[f_486_1]) ).
cnf(f_486_3,plain,
hAPP_nat_nat(power_power_nat(hAPP_nat_nat(times_times_nat(U_1154),U_1153)),U_1152) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(U_1154),U_1152)),hAPP_nat_nat(power_power_nat(U_1153),U_1152)),
inference(clausify,[status(thm)],[f_486_2]) ).
fof(f_487_1,plain,
! [A_66,B_49,N_17] : hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(A_66),B_49)),N_17) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(A_66),N_17)),hAPP_nat_real(power_power_real(B_49),N_17)),
inference(fof_nnf,[status(thm)],[fact_461_power__mult__distrib]) ).
fof(f_487_2,plain,
! [U_1157,U_1156,U_1155] : hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(U_1157),U_1156)),U_1155) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(U_1157),U_1155)),hAPP_nat_real(power_power_real(U_1156),U_1155)),
inference(variable_rename,[status(thm)],[f_487_1]) ).
cnf(f_487_3,plain,
hAPP_nat_real(power_power_real(hAPP_real_real(times_times_real(U_1157),U_1156)),U_1155) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(U_1157),U_1155)),hAPP_nat_real(power_power_real(U_1156),U_1155)),
inference(clausify,[status(thm)],[f_487_2]) ).
fof(f_488_1,plain,
! [A_66,B_49,N_17] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(A_66),B_49)),N_17) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(A_66),N_17)),hAPP_nat_int(power_power_int(B_49),N_17)),
inference(fof_nnf,[status(thm)],[fact_462_power__mult__distrib]) ).
fof(f_488_2,plain,
! [U_1160,U_1159,U_1158] : hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(U_1160),U_1159)),U_1158) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(U_1160),U_1158)),hAPP_nat_int(power_power_int(U_1159),U_1158)),
inference(variable_rename,[status(thm)],[f_488_1]) ).
cnf(f_488_3,plain,
hAPP_nat_int(power_power_int(hAPP_int_int(times_times_int(U_1160),U_1159)),U_1158) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(U_1160),U_1158)),hAPP_nat_int(power_power_int(U_1159),U_1158)),
inference(clausify,[status(thm)],[f_488_2]) ).
fof(f_489_1,plain,
! [A_65,M_5,N_16] : hAPP_nat_nat(power_power_nat(A_65),hAPP_nat_nat(plus_plus_nat(M_5),N_16)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(A_65),M_5)),hAPP_nat_nat(power_power_nat(A_65),N_16)),
inference(fof_nnf,[status(thm)],[fact_463_power__add]) ).
fof(f_489_2,plain,
! [U_1163,U_1162,U_1161] : hAPP_nat_nat(power_power_nat(U_1163),hAPP_nat_nat(plus_plus_nat(U_1162),U_1161)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(U_1163),U_1162)),hAPP_nat_nat(power_power_nat(U_1163),U_1161)),
inference(variable_rename,[status(thm)],[f_489_1]) ).
cnf(f_489_3,plain,
hAPP_nat_nat(power_power_nat(U_1163),hAPP_nat_nat(plus_plus_nat(U_1162),U_1161)) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(U_1163),U_1162)),hAPP_nat_nat(power_power_nat(U_1163),U_1161)),
inference(clausify,[status(thm)],[f_489_2]) ).
fof(f_490_1,plain,
! [A_65,M_5,N_16] : hAPP_nat_real(power_power_real(A_65),hAPP_nat_nat(plus_plus_nat(M_5),N_16)) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(A_65),M_5)),hAPP_nat_real(power_power_real(A_65),N_16)),
inference(fof_nnf,[status(thm)],[fact_464_power__add]) ).
fof(f_490_2,plain,
! [U_1166,U_1165,U_1164] : hAPP_nat_real(power_power_real(U_1166),hAPP_nat_nat(plus_plus_nat(U_1165),U_1164)) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(U_1166),U_1165)),hAPP_nat_real(power_power_real(U_1166),U_1164)),
inference(variable_rename,[status(thm)],[f_490_1]) ).
cnf(f_490_3,plain,
hAPP_nat_real(power_power_real(U_1166),hAPP_nat_nat(plus_plus_nat(U_1165),U_1164)) = hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(U_1166),U_1165)),hAPP_nat_real(power_power_real(U_1166),U_1164)),
inference(clausify,[status(thm)],[f_490_2]) ).
fof(f_491_1,plain,
! [A_65,M_5,N_16] : hAPP_nat_int(power_power_int(A_65),hAPP_nat_nat(plus_plus_nat(M_5),N_16)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(A_65),M_5)),hAPP_nat_int(power_power_int(A_65),N_16)),
inference(fof_nnf,[status(thm)],[fact_465_power__add]) ).
fof(f_491_2,plain,
! [U_1169,U_1168,U_1167] : hAPP_nat_int(power_power_int(U_1169),hAPP_nat_nat(plus_plus_nat(U_1168),U_1167)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(U_1169),U_1168)),hAPP_nat_int(power_power_int(U_1169),U_1167)),
inference(variable_rename,[status(thm)],[f_491_1]) ).
cnf(f_491_3,plain,
hAPP_nat_int(power_power_int(U_1169),hAPP_nat_nat(plus_plus_nat(U_1168),U_1167)) = hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(U_1169),U_1168)),hAPP_nat_int(power_power_int(U_1169),U_1167)),
inference(clausify,[status(thm)],[f_491_2]) ).
fof(f_492_1,plain,
! [N_15] : hAPP_nat_real(power_power_real(one_one_real),N_15) = one_one_real,
inference(fof_nnf,[status(thm)],[fact_466_power__one]) ).
fof(f_492_2,plain,
! [U_1170] : hAPP_nat_real(power_power_real(one_one_real),U_1170) = one_one_real,
inference(variable_rename,[status(thm)],[f_492_1]) ).
cnf(f_492_3,plain,
hAPP_nat_real(power_power_real(one_one_real),U_1170) = one_one_real,
inference(clausify,[status(thm)],[f_492_2]) ).
fof(f_493_1,plain,
! [N_15] : hAPP_nat_nat(power_power_nat(one_one_nat),N_15) = one_one_nat,
inference(fof_nnf,[status(thm)],[fact_467_power__one]) ).
fof(f_493_2,plain,
! [U_1171] : hAPP_nat_nat(power_power_nat(one_one_nat),U_1171) = one_one_nat,
inference(variable_rename,[status(thm)],[f_493_1]) ).
cnf(f_493_3,plain,
hAPP_nat_nat(power_power_nat(one_one_nat),U_1171) = one_one_nat,
inference(clausify,[status(thm)],[f_493_2]) ).
fof(f_494_1,plain,
! [N_15] : hAPP_nat_int(power_power_int(one_one_int),N_15) = one_one_int,
inference(fof_nnf,[status(thm)],[fact_468_power__one]) ).
fof(f_494_2,plain,
! [U_1172] : hAPP_nat_int(power_power_int(one_one_int),U_1172) = one_one_int,
inference(variable_rename,[status(thm)],[f_494_1]) ).
cnf(f_494_3,plain,
hAPP_nat_int(power_power_int(one_one_int),U_1172) = one_one_int,
inference(clausify,[status(thm)],[f_494_2]) ).
fof(f_495_1,plain,
! [A_64,M_4,N_14] : hAPP_nat_nat(power_power_nat(A_64),hAPP_nat_nat(times_times_nat(M_4),N_14)) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(A_64),M_4)),N_14),
inference(fof_nnf,[status(thm)],[fact_469_power__mult]) ).
fof(f_495_2,plain,
! [U_1175,U_1174,U_1173] : hAPP_nat_nat(power_power_nat(U_1175),hAPP_nat_nat(times_times_nat(U_1174),U_1173)) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(U_1175),U_1174)),U_1173),
inference(variable_rename,[status(thm)],[f_495_1]) ).
cnf(f_495_3,plain,
hAPP_nat_nat(power_power_nat(U_1175),hAPP_nat_nat(times_times_nat(U_1174),U_1173)) = hAPP_nat_nat(power_power_nat(hAPP_nat_nat(power_power_nat(U_1175),U_1174)),U_1173),
inference(clausify,[status(thm)],[f_495_2]) ).
fof(f_496_1,plain,
! [A_64,M_4,N_14] : hAPP_nat_real(power_power_real(A_64),hAPP_nat_nat(times_times_nat(M_4),N_14)) = hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(A_64),M_4)),N_14),
inference(fof_nnf,[status(thm)],[fact_470_power__mult]) ).
fof(f_496_2,plain,
! [U_1178,U_1177,U_1176] : hAPP_nat_real(power_power_real(U_1178),hAPP_nat_nat(times_times_nat(U_1177),U_1176)) = hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(U_1178),U_1177)),U_1176),
inference(variable_rename,[status(thm)],[f_496_1]) ).
cnf(f_496_3,plain,
hAPP_nat_real(power_power_real(U_1178),hAPP_nat_nat(times_times_nat(U_1177),U_1176)) = hAPP_nat_real(power_power_real(hAPP_nat_real(power_power_real(U_1178),U_1177)),U_1176),
inference(clausify,[status(thm)],[f_496_2]) ).
fof(f_497_1,plain,
! [A_64,M_4,N_14] : hAPP_nat_int(power_power_int(A_64),hAPP_nat_nat(times_times_nat(M_4),N_14)) = hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(A_64),M_4)),N_14),
inference(fof_nnf,[status(thm)],[fact_471_power__mult]) ).
fof(f_497_2,plain,
! [U_1181,U_1180,U_1179] : hAPP_nat_int(power_power_int(U_1181),hAPP_nat_nat(times_times_nat(U_1180),U_1179)) = hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(U_1181),U_1180)),U_1179),
inference(variable_rename,[status(thm)],[f_497_1]) ).
cnf(f_497_3,plain,
hAPP_nat_int(power_power_int(U_1181),hAPP_nat_nat(times_times_nat(U_1180),U_1179)) = hAPP_nat_int(power_power_int(hAPP_nat_int(power_power_int(U_1181),U_1180)),U_1179),
inference(clausify,[status(thm)],[f_497_2]) ).
fof(f_498_1,plain,
! [X_13,Y_10] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_13),Y_10))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),Y_10))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(X_13),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_10),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(fof_nnf,[status(thm)],[fact_472_power2__less__imp__less]) ).
fof(f_498_2,plain,
! [U_1183,U_1182] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1183),U_1182))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1182))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_1183),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1182),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(variable_rename,[status(thm)],[f_498_1]) ).
cnf(f_498_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1183),U_1182))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1182))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_1183),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1182),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(clausify,[status(thm)],[f_498_2]) ).
fof(f_499_1,plain,
! [X_13,Y_10] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_13),Y_10))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),Y_10))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(X_13),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(Y_10),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(fof_nnf,[status(thm)],[fact_473_power2__less__imp__less]) ).
fof(f_499_2,plain,
! [U_1185,U_1184] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1185),U_1184))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1184))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_1185),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(U_1184),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(variable_rename,[status(thm)],[f_499_1]) ).
cnf(f_499_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1185),U_1184))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1184))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_1185),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(U_1184),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(clausify,[status(thm)],[f_499_2]) ).
fof(f_500_1,plain,
! [X_13,Y_10] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_13),Y_10))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_10))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(X_13),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_10),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(fof_nnf,[status(thm)],[fact_474_power2__less__imp__less]) ).
fof(f_500_2,plain,
! [U_1187,U_1186] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1187),U_1186))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1186))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_1187),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1186),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(variable_rename,[status(thm)],[f_500_1]) ).
cnf(f_500_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1187),U_1186))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1186))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_1187),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1186),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(clausify,[status(thm)],[f_500_2]) ).
fof(f_501_1,plain,
! [X_12,Y_9] : 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(X_12),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_9),number_number_of_nat(bit0(bit1(pls))))))),
inference(fof_nnf,[status(thm)],[fact_475_sum__power2__ge__zero]) ).
fof(f_501_2,plain,
! [U_1189,U_1188] : 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(U_1189),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1188),number_number_of_nat(bit0(bit1(pls))))))),
inference(variable_rename,[status(thm)],[f_501_1]) ).
cnf(f_501_3,plain,
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(U_1189),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1188),number_number_of_nat(bit0(bit1(pls))))))),
inference(clausify,[status(thm)],[f_501_2]) ).
fof(f_502_1,plain,
! [X_12,Y_9] : 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(X_12),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_9),number_number_of_nat(bit0(bit1(pls))))))),
inference(fof_nnf,[status(thm)],[fact_476_sum__power2__ge__zero]) ).
fof(f_502_2,plain,
! [U_1191,U_1190] : 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(U_1191),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1190),number_number_of_nat(bit0(bit1(pls))))))),
inference(variable_rename,[status(thm)],[f_502_1]) ).
cnf(f_502_3,plain,
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(U_1191),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1190),number_number_of_nat(bit0(bit1(pls))))))),
inference(clausify,[status(thm)],[f_502_2]) ).
fof(f_503_1,plain,
! [X_2,Y_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real))
| Y_2 != zero_zero_real
| X_2 != zero_zero_real )
& ( ( Y_2 = zero_zero_real
& X_2 = 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(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)) ) ),
inference(fof_nnf,[status(thm)],[fact_477_sum__power2__le__zero__iff]) ).
fof(f_503_2,plain,
! [U_1193,U_1192] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(U_1193),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1192),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real))
| U_1192 != zero_zero_real
| U_1193 != zero_zero_real )
& ( ( U_1192 = zero_zero_real
& U_1193 = 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(U_1193),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1192),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)) ) ),
inference(variable_rename,[status(thm)],[f_503_1]) ).
fof(f_503_3,plain,
( ! [U_1197,U_1195] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(U_1197),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1195),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real))
| U_1195 != zero_zero_real
| U_1197 != zero_zero_real )
& ! [U_1196,U_1194] :
( ( U_1194 = zero_zero_real
& U_1196 = 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(U_1196),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1194),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)) ) ),
inference(miniscope,[status(thm)],[f_503_2]) ).
cnf(f_503_4,plain,
( U_1196 = 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(U_1196),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1194),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_503_3]) ).
cnf(f_503_5,plain,
( U_1194 = 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(U_1196),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1194),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_503_3]) ).
cnf(f_503_6,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(U_1197),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1195),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real))
| U_1195 != zero_zero_real
| U_1197 != zero_zero_real ),
inference(clausify,[status(thm)],[f_503_3]) ).
fof(f_504_1,plain,
! [X_2,Y_2] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
| Y_2 != zero_zero_int
| X_2 != zero_zero_int )
& ( ( Y_2 = zero_zero_int
& X_2 = zero_zero_int )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_2),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)) ) )
| ~ is_int(Y_2)
| ~ is_int(X_2) ),
inference(fof_nnf,[status(thm)],[fact_478_sum__power2__le__zero__iff]) ).
fof(f_504_2,plain,
! [U_1199,U_1198] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(U_1199),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1198),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
| U_1198 != zero_zero_int
| U_1199 != zero_zero_int )
& ( ( U_1198 = zero_zero_int
& U_1199 = zero_zero_int )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(U_1199),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1198),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)) ) )
| ~ is_int(U_1198)
| ~ is_int(U_1199) ),
inference(variable_rename,[status(thm)],[f_504_1]) ).
cnf(f_504_3,plain,
( U_1199 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(U_1199),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1198),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
| ~ is_int(U_1198)
| ~ is_int(U_1199) ),
inference(clausify,[status(thm)],[f_504_2]) ).
cnf(f_504_4,plain,
( U_1198 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(U_1199),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1198),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
| ~ is_int(U_1198)
| ~ is_int(U_1199) ),
inference(clausify,[status(thm)],[f_504_2]) ).
cnf(f_504_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(U_1199),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1198),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int))
| U_1198 != zero_zero_int
| U_1199 != zero_zero_int
| ~ is_int(U_1198)
| ~ is_int(U_1199) ),
inference(clausify,[status(thm)],[f_504_2]) ).
fof(f_505_1,plain,
! [X_11,Y_8] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X_11),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_8),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)),
inference(fof_nnf,[status(thm)],[fact_479_not__sum__power2__lt__zero]) ).
fof(f_505_2,plain,
! [U_1201,U_1200] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(U_1201),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1200),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)),
inference(variable_rename,[status(thm)],[f_505_1]) ).
cnf(f_505_3,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(U_1201),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1200),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_real)),
inference(clausify,[status(thm)],[f_505_2]) ).
fof(f_506_1,plain,
! [X_11,Y_8] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X_11),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_8),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)),
inference(fof_nnf,[status(thm)],[fact_480_not__sum__power2__lt__zero]) ).
fof(f_506_2,plain,
! [U_1203,U_1202] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(U_1203),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1202),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)),
inference(variable_rename,[status(thm)],[f_506_1]) ).
cnf(f_506_3,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(U_1203),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1202),number_number_of_nat(bit0(bit1(pls)))))),zero_zero_int)),
inference(clausify,[status(thm)],[f_506_2]) ).
fof(f_507_1,plain,
! [X_2,Y_2] :
( ( 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(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_2),number_number_of_nat(bit0(bit1(pls)))))))
| ( Y_2 = zero_zero_real
& X_2 = zero_zero_real ) )
& ( Y_2 != zero_zero_real
| X_2 != zero_zero_real
| ~ 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(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_2),number_number_of_nat(bit0(bit1(pls))))))) ) ),
inference(fof_nnf,[status(thm)],[fact_481_sum__power2__gt__zero__iff]) ).
fof(f_507_2,plain,
! [U_1205,U_1204] :
( ( 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(U_1205),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1204),number_number_of_nat(bit0(bit1(pls)))))))
| ( U_1204 = zero_zero_real
& U_1205 = zero_zero_real ) )
& ( U_1204 != zero_zero_real
| U_1205 != zero_zero_real
| ~ 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(U_1205),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1204),number_number_of_nat(bit0(bit1(pls))))))) ) ),
inference(variable_rename,[status(thm)],[f_507_1]) ).
fof(f_507_3,plain,
( ! [U_1209,U_1207] :
( 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(U_1209),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1207),number_number_of_nat(bit0(bit1(pls)))))))
| ( U_1207 = zero_zero_real
& U_1209 = zero_zero_real ) )
& ! [U_1208,U_1206] :
( U_1206 != zero_zero_real
| U_1208 != zero_zero_real
| ~ 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(U_1208),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1206),number_number_of_nat(bit0(bit1(pls))))))) ) ),
inference(miniscope,[status(thm)],[f_507_2]) ).
cnf(f_507_4,plain,
( U_1206 != zero_zero_real
| U_1208 != zero_zero_real
| ~ 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(U_1208),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1206),number_number_of_nat(bit0(bit1(pls))))))) ),
inference(clausify,[status(thm)],[f_507_3]) ).
cnf(f_507_5,plain,
( U_1209 = zero_zero_real
| 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(U_1209),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1207),number_number_of_nat(bit0(bit1(pls))))))) ),
inference(clausify,[status(thm)],[f_507_3]) ).
cnf(f_507_6,plain,
( U_1207 = zero_zero_real
| 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(U_1209),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1207),number_number_of_nat(bit0(bit1(pls))))))) ),
inference(clausify,[status(thm)],[f_507_3]) ).
fof(f_508_1,plain,
! [X_2,Y_2] :
( ( ( 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(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_2),number_number_of_nat(bit0(bit1(pls)))))))
| ( Y_2 = zero_zero_int
& X_2 = zero_zero_int ) )
& ( Y_2 != zero_zero_int
| X_2 != zero_zero_int
| ~ 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(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_2),number_number_of_nat(bit0(bit1(pls))))))) ) )
| ~ is_int(Y_2)
| ~ is_int(X_2) ),
inference(fof_nnf,[status(thm)],[fact_482_sum__power2__gt__zero__iff]) ).
fof(f_508_2,plain,
! [U_1211,U_1210] :
( ( ( 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(U_1211),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1210),number_number_of_nat(bit0(bit1(pls)))))))
| ( U_1210 = zero_zero_int
& U_1211 = zero_zero_int ) )
& ( U_1210 != zero_zero_int
| U_1211 != zero_zero_int
| ~ 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(U_1211),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1210),number_number_of_nat(bit0(bit1(pls))))))) ) )
| ~ is_int(U_1210)
| ~ is_int(U_1211) ),
inference(variable_rename,[status(thm)],[f_508_1]) ).
cnf(f_508_3,plain,
( U_1210 != zero_zero_int
| U_1211 != zero_zero_int
| ~ 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(U_1211),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1210),number_number_of_nat(bit0(bit1(pls)))))))
| ~ is_int(U_1210)
| ~ is_int(U_1211) ),
inference(clausify,[status(thm)],[f_508_2]) ).
cnf(f_508_4,plain,
( U_1211 = zero_zero_int
| 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(U_1211),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1210),number_number_of_nat(bit0(bit1(pls)))))))
| ~ is_int(U_1210)
| ~ is_int(U_1211) ),
inference(clausify,[status(thm)],[f_508_2]) ).
cnf(f_508_5,plain,
( U_1210 = zero_zero_int
| 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(U_1211),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1210),number_number_of_nat(bit0(bit1(pls)))))))
| ~ is_int(U_1210)
| ~ is_int(U_1211) ),
inference(clausify,[status(thm)],[f_508_2]) ).
fof(f_509_1,plain,
! [A_63,N_13] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(A_63),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_13)))),
inference(fof_nnf,[status(thm)],[fact_483_zero__le__even__power_H]) ).
fof(f_509_2,plain,
! [U_1213,U_1212] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(U_1213),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_1212)))),
inference(variable_rename,[status(thm)],[f_509_1]) ).
cnf(f_509_3,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_nat_real(power_power_real(U_1213),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_1212)))),
inference(clausify,[status(thm)],[f_509_2]) ).
fof(f_510_1,plain,
! [A_63,N_13] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(A_63),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_13)))),
inference(fof_nnf,[status(thm)],[fact_484_zero__le__even__power_H]) ).
fof(f_510_2,plain,
! [U_1215,U_1214] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(U_1215),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_1214)))),
inference(variable_rename,[status(thm)],[f_510_1]) ).
cnf(f_510_3,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(U_1215),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_1214)))),
inference(clausify,[status(thm)],[f_510_2]) ).
fof(f_511_1,plain,
! [N_12,A_62] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(A_62),N_12)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),A_62)) ),
inference(fof_nnf,[status(thm)],[fact_485_one__le__power]) ).
fof(f_511_2,plain,
! [U_1217,U_1216] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(U_1216),U_1217)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),U_1216)) ),
inference(variable_rename,[status(thm)],[f_511_1]) ).
cnf(f_511_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),hAPP_nat_real(power_power_real(U_1216),U_1217)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),U_1216)) ),
inference(clausify,[status(thm)],[f_511_2]) ).
fof(f_512_1,plain,
! [N_12,A_62] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(power_power_nat(A_62),N_12)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),A_62)) ),
inference(fof_nnf,[status(thm)],[fact_486_one__le__power]) ).
fof(f_512_2,plain,
! [U_1219,U_1218] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(power_power_nat(U_1218),U_1219)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),U_1218)) ),
inference(variable_rename,[status(thm)],[f_512_1]) ).
cnf(f_512_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(power_power_nat(U_1218),U_1219)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),U_1218)) ),
inference(clausify,[status(thm)],[f_512_2]) ).
fof(f_513_1,plain,
! [N_12,A_62] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(power_power_int(A_62),N_12)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),A_62)) ),
inference(fof_nnf,[status(thm)],[fact_487_one__le__power]) ).
fof(f_513_2,plain,
! [U_1221,U_1220] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(power_power_int(U_1220),U_1221)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_1220)) ),
inference(variable_rename,[status(thm)],[f_513_1]) ).
cnf(f_513_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_nat_int(power_power_int(U_1220),U_1221)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_1220)) ),
inference(clausify,[status(thm)],[f_513_2]) ).
fof(f_514_1,plain,
! [A_61,N_11,N_10] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(A_61),N_11)),hAPP_nat_real(power_power_real(A_61),N_10)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),A_61))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_11),N_10)) ),
inference(fof_nnf,[status(thm)],[fact_488_power__increasing]) ).
fof(f_514_2,plain,
! [U_1224,U_1223,U_1222] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(U_1224),U_1223)),hAPP_nat_real(power_power_real(U_1224),U_1222)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),U_1224))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1223),U_1222)) ),
inference(variable_rename,[status(thm)],[f_514_1]) ).
cnf(f_514_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(U_1224),U_1223)),hAPP_nat_real(power_power_real(U_1224),U_1222)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,one_one_real),U_1224))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1223),U_1222)) ),
inference(clausify,[status(thm)],[f_514_2]) ).
fof(f_515_1,plain,
! [A_61,N_11,N_10] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(A_61),N_11)),hAPP_nat_nat(power_power_nat(A_61),N_10)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),A_61))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_11),N_10)) ),
inference(fof_nnf,[status(thm)],[fact_489_power__increasing]) ).
fof(f_515_2,plain,
! [U_1227,U_1226,U_1225] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(U_1227),U_1226)),hAPP_nat_nat(power_power_nat(U_1227),U_1225)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),U_1227))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1226),U_1225)) ),
inference(variable_rename,[status(thm)],[f_515_1]) ).
cnf(f_515_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(power_power_nat(U_1227),U_1226)),hAPP_nat_nat(power_power_nat(U_1227),U_1225)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),U_1227))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1226),U_1225)) ),
inference(clausify,[status(thm)],[f_515_2]) ).
fof(f_516_1,plain,
! [A_61,N_11,N_10] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(A_61),N_11)),hAPP_nat_int(power_power_int(A_61),N_10)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),A_61))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_11),N_10)) ),
inference(fof_nnf,[status(thm)],[fact_490_power__increasing]) ).
fof(f_516_2,plain,
! [U_1230,U_1229,U_1228] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(U_1230),U_1229)),hAPP_nat_int(power_power_int(U_1230),U_1228)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_1230))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1229),U_1228)) ),
inference(variable_rename,[status(thm)],[f_516_1]) ).
cnf(f_516_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(U_1230),U_1229)),hAPP_nat_int(power_power_int(U_1230),U_1228)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_1230))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1229),U_1228)) ),
inference(clausify,[status(thm)],[f_516_2]) ).
fof(f_517_1,plain,
! [Ma,N,A_2] :
( ( ( hAPP_nat_real(power_power_real(A_2),Ma) = hAPP_nat_real(power_power_real(A_2),N)
| Ma != N )
& ( Ma = N
| hAPP_nat_real(power_power_real(A_2),Ma) != hAPP_nat_real(power_power_real(A_2),N) ) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),A_2)) ),
inference(fof_nnf,[status(thm)],[fact_491_power__inject__exp]) ).
fof(f_517_2,plain,
! [U_1233,U_1232,U_1231] :
( ( ( hAPP_nat_real(power_power_real(U_1231),U_1233) = hAPP_nat_real(power_power_real(U_1231),U_1232)
| U_1233 != U_1232 )
& ( U_1233 = U_1232
| hAPP_nat_real(power_power_real(U_1231),U_1233) != hAPP_nat_real(power_power_real(U_1231),U_1232) ) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_1231)) ),
inference(variable_rename,[status(thm)],[f_517_1]) ).
cnf(f_517_3,plain,
( U_1233 = U_1232
| hAPP_nat_real(power_power_real(U_1231),U_1233) != hAPP_nat_real(power_power_real(U_1231),U_1232)
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_1231)) ),
inference(clausify,[status(thm)],[f_517_2]) ).
cnf(f_517_4,plain,
( hAPP_nat_real(power_power_real(U_1231),U_1233) = hAPP_nat_real(power_power_real(U_1231),U_1232)
| U_1233 != U_1232
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_1231)) ),
inference(clausify,[status(thm)],[f_517_2]) ).
fof(f_518_1,plain,
! [Ma,N,A_2] :
( ( ( hAPP_nat_nat(power_power_nat(A_2),Ma) = hAPP_nat_nat(power_power_nat(A_2),N)
| Ma != N )
& ( Ma = N
| hAPP_nat_nat(power_power_nat(A_2),Ma) != hAPP_nat_nat(power_power_nat(A_2),N) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),A_2)) ),
inference(fof_nnf,[status(thm)],[fact_492_power__inject__exp]) ).
fof(f_518_2,plain,
! [U_1236,U_1235,U_1234] :
( ( ( hAPP_nat_nat(power_power_nat(U_1234),U_1236) = hAPP_nat_nat(power_power_nat(U_1234),U_1235)
| U_1236 != U_1235 )
& ( U_1236 = U_1235
| hAPP_nat_nat(power_power_nat(U_1234),U_1236) != hAPP_nat_nat(power_power_nat(U_1234),U_1235) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_1234)) ),
inference(variable_rename,[status(thm)],[f_518_1]) ).
cnf(f_518_3,plain,
( U_1236 = U_1235
| hAPP_nat_nat(power_power_nat(U_1234),U_1236) != hAPP_nat_nat(power_power_nat(U_1234),U_1235)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_1234)) ),
inference(clausify,[status(thm)],[f_518_2]) ).
cnf(f_518_4,plain,
( hAPP_nat_nat(power_power_nat(U_1234),U_1236) = hAPP_nat_nat(power_power_nat(U_1234),U_1235)
| U_1236 != U_1235
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_1234)) ),
inference(clausify,[status(thm)],[f_518_2]) ).
fof(f_519_1,plain,
! [Ma,N,A_2] :
( ( ( hAPP_nat_int(power_power_int(A_2),Ma) = hAPP_nat_int(power_power_int(A_2),N)
| Ma != N )
& ( Ma = N
| hAPP_nat_int(power_power_int(A_2),Ma) != hAPP_nat_int(power_power_int(A_2),N) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_2)) ),
inference(fof_nnf,[status(thm)],[fact_493_power__inject__exp]) ).
fof(f_519_2,plain,
! [U_1239,U_1238,U_1237] :
( ( ( hAPP_nat_int(power_power_int(U_1237),U_1239) = hAPP_nat_int(power_power_int(U_1237),U_1238)
| U_1239 != U_1238 )
& ( U_1239 = U_1238
| hAPP_nat_int(power_power_int(U_1237),U_1239) != hAPP_nat_int(power_power_int(U_1237),U_1238) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1237)) ),
inference(variable_rename,[status(thm)],[f_519_1]) ).
cnf(f_519_3,plain,
( U_1239 = U_1238
| hAPP_nat_int(power_power_int(U_1237),U_1239) != hAPP_nat_int(power_power_int(U_1237),U_1238)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1237)) ),
inference(clausify,[status(thm)],[f_519_2]) ).
cnf(f_519_4,plain,
( hAPP_nat_int(power_power_int(U_1237),U_1239) = hAPP_nat_int(power_power_int(U_1237),U_1238)
| U_1239 != U_1238
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1237)) ),
inference(clausify,[status(thm)],[f_519_2]) ).
fof(f_520_1,plain,
! [X_2,Y_2,B_2] :
( ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(B_2),X_2)),hAPP_nat_real(power_power_real(B_2),Y_2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(B_2),X_2)),hAPP_nat_real(power_power_real(B_2),Y_2))) ) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),B_2)) ),
inference(fof_nnf,[status(thm)],[fact_494_power__strict__increasing__iff]) ).
fof(f_520_2,plain,
! [U_1242,U_1241,U_1240] :
( ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_1240),U_1242)),hAPP_nat_real(power_power_real(U_1240),U_1241)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1242),U_1241)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1242),U_1241))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_1240),U_1242)),hAPP_nat_real(power_power_real(U_1240),U_1241))) ) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_1240)) ),
inference(variable_rename,[status(thm)],[f_520_1]) ).
cnf(f_520_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1242),U_1241))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_1240),U_1242)),hAPP_nat_real(power_power_real(U_1240),U_1241)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_1240)) ),
inference(clausify,[status(thm)],[f_520_2]) ).
cnf(f_520_4,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_1240),U_1242)),hAPP_nat_real(power_power_real(U_1240),U_1241)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1242),U_1241))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_1240)) ),
inference(clausify,[status(thm)],[f_520_2]) ).
fof(f_521_1,plain,
! [X_2,Y_2,B_2] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(B_2),X_2)),hAPP_nat_nat(power_power_nat(B_2),Y_2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(B_2),X_2)),hAPP_nat_nat(power_power_nat(B_2),Y_2))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),B_2)) ),
inference(fof_nnf,[status(thm)],[fact_495_power__strict__increasing__iff]) ).
fof(f_521_2,plain,
! [U_1245,U_1244,U_1243] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_1243),U_1245)),hAPP_nat_nat(power_power_nat(U_1243),U_1244)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1245),U_1244)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1245),U_1244))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_1243),U_1245)),hAPP_nat_nat(power_power_nat(U_1243),U_1244))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_1243)) ),
inference(variable_rename,[status(thm)],[f_521_1]) ).
cnf(f_521_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1245),U_1244))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_1243),U_1245)),hAPP_nat_nat(power_power_nat(U_1243),U_1244)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_1243)) ),
inference(clausify,[status(thm)],[f_521_2]) ).
cnf(f_521_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_1243),U_1245)),hAPP_nat_nat(power_power_nat(U_1243),U_1244)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1245),U_1244))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_1243)) ),
inference(clausify,[status(thm)],[f_521_2]) ).
fof(f_522_1,plain,
! [X_2,Y_2,B_2] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(B_2),X_2)),hAPP_nat_int(power_power_int(B_2),Y_2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(B_2),X_2)),hAPP_nat_int(power_power_int(B_2),Y_2))) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),B_2)) ),
inference(fof_nnf,[status(thm)],[fact_496_power__strict__increasing__iff]) ).
fof(f_522_2,plain,
! [U_1248,U_1247,U_1246] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_1246),U_1248)),hAPP_nat_int(power_power_int(U_1246),U_1247)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1248),U_1247)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1248),U_1247))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_1246),U_1248)),hAPP_nat_int(power_power_int(U_1246),U_1247))) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1246)) ),
inference(variable_rename,[status(thm)],[f_522_1]) ).
cnf(f_522_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1248),U_1247))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_1246),U_1248)),hAPP_nat_int(power_power_int(U_1246),U_1247)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1246)) ),
inference(clausify,[status(thm)],[f_522_2]) ).
cnf(f_522_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_1246),U_1248)),hAPP_nat_int(power_power_int(U_1246),U_1247)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1248),U_1247))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1246)) ),
inference(clausify,[status(thm)],[f_522_2]) ).
fof(f_523_1,plain,
! [M_3,N_9,A_60] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_3),N_9))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(A_60),M_3)),hAPP_nat_real(power_power_real(A_60),N_9)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),A_60)) ),
inference(fof_nnf,[status(thm)],[fact_497_power__less__imp__less__exp]) ).
fof(f_523_2,plain,
! [U_1251,U_1250,U_1249] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1251),U_1250))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_1249),U_1251)),hAPP_nat_real(power_power_real(U_1249),U_1250)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_1249)) ),
inference(variable_rename,[status(thm)],[f_523_1]) ).
cnf(f_523_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1251),U_1250))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_1249),U_1251)),hAPP_nat_real(power_power_real(U_1249),U_1250)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_1249)) ),
inference(clausify,[status(thm)],[f_523_2]) ).
fof(f_524_1,plain,
! [M_3,N_9,A_60] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_3),N_9))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(A_60),M_3)),hAPP_nat_nat(power_power_nat(A_60),N_9)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),A_60)) ),
inference(fof_nnf,[status(thm)],[fact_498_power__less__imp__less__exp]) ).
fof(f_524_2,plain,
! [U_1254,U_1253,U_1252] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1254),U_1253))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_1252),U_1254)),hAPP_nat_nat(power_power_nat(U_1252),U_1253)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_1252)) ),
inference(variable_rename,[status(thm)],[f_524_1]) ).
cnf(f_524_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1254),U_1253))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_1252),U_1254)),hAPP_nat_nat(power_power_nat(U_1252),U_1253)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_1252)) ),
inference(clausify,[status(thm)],[f_524_2]) ).
fof(f_525_1,plain,
! [M_3,N_9,A_60] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_3),N_9))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(A_60),M_3)),hAPP_nat_int(power_power_int(A_60),N_9)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_60)) ),
inference(fof_nnf,[status(thm)],[fact_499_power__less__imp__less__exp]) ).
fof(f_525_2,plain,
! [U_1257,U_1256,U_1255] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1257),U_1256))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_1255),U_1257)),hAPP_nat_int(power_power_int(U_1255),U_1256)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1255)) ),
inference(variable_rename,[status(thm)],[f_525_1]) ).
cnf(f_525_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1257),U_1256))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_1255),U_1257)),hAPP_nat_int(power_power_int(U_1255),U_1256)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1255)) ),
inference(clausify,[status(thm)],[f_525_2]) ).
fof(f_526_1,plain,
! [A_59,N_8,N_7] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(A_59),N_8)),hAPP_nat_real(power_power_real(A_59),N_7)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),A_59))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_8),N_7)) ),
inference(fof_nnf,[status(thm)],[fact_500_power__strict__increasing]) ).
fof(f_526_2,plain,
! [U_1260,U_1259,U_1258] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_1260),U_1259)),hAPP_nat_real(power_power_real(U_1260),U_1258)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_1260))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1259),U_1258)) ),
inference(variable_rename,[status(thm)],[f_526_1]) ).
cnf(f_526_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(power_power_real(U_1260),U_1259)),hAPP_nat_real(power_power_real(U_1260),U_1258)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_1260))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1259),U_1258)) ),
inference(clausify,[status(thm)],[f_526_2]) ).
fof(f_527_1,plain,
! [A_59,N_8,N_7] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(A_59),N_8)),hAPP_nat_nat(power_power_nat(A_59),N_7)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),A_59))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_8),N_7)) ),
inference(fof_nnf,[status(thm)],[fact_501_power__strict__increasing]) ).
fof(f_527_2,plain,
! [U_1263,U_1262,U_1261] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_1263),U_1262)),hAPP_nat_nat(power_power_nat(U_1263),U_1261)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_1263))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1262),U_1261)) ),
inference(variable_rename,[status(thm)],[f_527_1]) ).
cnf(f_527_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_1263),U_1262)),hAPP_nat_nat(power_power_nat(U_1263),U_1261)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_1263))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1262),U_1261)) ),
inference(clausify,[status(thm)],[f_527_2]) ).
fof(f_528_1,plain,
! [A_59,N_8,N_7] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(A_59),N_8)),hAPP_nat_int(power_power_int(A_59),N_7)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_59))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_8),N_7)) ),
inference(fof_nnf,[status(thm)],[fact_502_power__strict__increasing]) ).
fof(f_528_2,plain,
! [U_1266,U_1265,U_1264] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_1266),U_1265)),hAPP_nat_int(power_power_int(U_1266),U_1264)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1266))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1265),U_1264)) ),
inference(variable_rename,[status(thm)],[f_528_1]) ).
cnf(f_528_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(power_power_int(U_1266),U_1265)),hAPP_nat_int(power_power_int(U_1266),U_1264)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1266))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1265),U_1264)) ),
inference(clausify,[status(thm)],[f_528_2]) ).
fof(f_529_1,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(fof_nnf,[status(thm)],[fact_503_s]) ).
cnf(f_529_2,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(clausify,[status(thm)],[f_529_1]) ).
fof(f_530_1,plain,
! [Y_1,X_1,P_1] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),Y_1))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(Y_1),number_number_of_nat(bit0(bit1(pls)))),X_1),P_1))
| hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_504_Euler_Oaux____1]) ).
fof(f_530_2,plain,
! [U_1269,U_1268,U_1267] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1267),U_1269))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(U_1269),number_number_of_nat(bit0(bit1(pls)))),U_1268),U_1267))
| hBOOL(hAPP_int_bool(zcong(U_1268,zero_zero_int),U_1267)) ),
inference(variable_rename,[status(thm)],[f_530_1]) ).
cnf(f_530_3,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1267),U_1269))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(U_1269),number_number_of_nat(bit0(bit1(pls)))),U_1268),U_1267))
| hBOOL(hAPP_int_bool(zcong(U_1268,zero_zero_int),U_1267)) ),
inference(clausify,[status(thm)],[f_530_2]) ).
fof(f_531_1,plain,
! [X_1] :
( X_1 = one_one_int
| X_1 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),number_number_of_int(bit0(bit1(pls)))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
| ~ is_int(X_1) ),
inference(fof_nnf,[status(thm)],[fact_505_int__pos__lt__two__imp__zero__or__one]) ).
fof(f_531_2,plain,
! [U_1270] :
( U_1270 = one_one_int
| U_1270 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1270),number_number_of_int(bit0(bit1(pls)))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1270))
| ~ is_int(U_1270) ),
inference(variable_rename,[status(thm)],[f_531_1]) ).
cnf(f_531_3,plain,
( U_1270 = one_one_int
| U_1270 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1270),number_number_of_int(bit0(bit1(pls)))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1270))
| ~ is_int(U_1270) ),
inference(clausify,[status(thm)],[f_531_2]) ).
fof(f_532_1,plain,
! [A_58,K_4] :
( A_58 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(A_58),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),K_4))),zero_zero_real)) ),
inference(fof_nnf,[status(thm)],[fact_506_even__power__le__0__imp__0]) ).
fof(f_532_2,plain,
! [U_1272,U_1271] :
( U_1272 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(U_1272),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_1271))),zero_zero_real)) ),
inference(variable_rename,[status(thm)],[f_532_1]) ).
fof(f_532_3,plain,
! [U_1272] :
( ! [U_1271] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(U_1272),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_1271))),zero_zero_real))
| U_1272 = zero_zero_real ),
inference(miniscope,[status(thm)],[f_532_2]) ).
cnf(f_532_4,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_nat_real(power_power_real(U_1272),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_1271))),zero_zero_real))
| U_1272 = zero_zero_real ),
inference(clausify,[status(thm)],[f_532_3]) ).
fof(f_533_1,plain,
! [A_58,K_4] :
( A_58 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(A_58),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),K_4))),zero_zero_int))
| ~ is_int(A_58) ),
inference(fof_nnf,[status(thm)],[fact_507_even__power__le__0__imp__0]) ).
fof(f_533_2,plain,
! [U_1274,U_1273] :
( U_1274 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(U_1274),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_1273))),zero_zero_int))
| ~ is_int(U_1274) ),
inference(variable_rename,[status(thm)],[f_533_1]) ).
fof(f_533_3,plain,
! [U_1274] :
( ! [U_1273] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(U_1274),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_1273))),zero_zero_int))
| U_1274 = zero_zero_int
| ~ is_int(U_1274) ),
inference(miniscope,[status(thm)],[f_533_2]) ).
cnf(f_533_4,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(power_power_int(U_1274),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_1273))),zero_zero_int))
| U_1274 = zero_zero_int
| ~ is_int(U_1274) ),
inference(clausify,[status(thm)],[f_533_3]) ).
fof(f_534_1,plain,
! [P_3] :
( ( ( hBOOL(hAPP_int_bool(zprime,P_3))
| ? [M_2] :
( M_2 != P_3
& M_2 != one_one_int
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,M_2),P_3))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),M_2))
& is_int(M_2) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),P_3)) )
& ( ( ! [M_2] :
( M_2 = P_3
| M_2 = one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,M_2),P_3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),M_2))
| ~ is_int(M_2) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),P_3)) )
| ~ hBOOL(hAPP_int_bool(zprime,P_3)) ) )
| ~ is_int(P_3) ),
inference(fof_nnf,[status(thm)],[fact_508_zprime__def]) ).
fof(f_534_2,plain,
! [U_1277] :
( ( ( hBOOL(hAPP_int_bool(zprime,U_1277))
| ? [U_1276] :
( U_1276 != U_1277
& U_1276 != one_one_int
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1276),U_1277))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1276))
& is_int(U_1276) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1277)) )
& ( ( ! [U_1275] :
( U_1275 = U_1277
| U_1275 = one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1275),U_1277))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1275))
| ~ is_int(U_1275) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1277)) )
| ~ hBOOL(hAPP_int_bool(zprime,U_1277)) ) )
| ~ is_int(U_1277) ),
inference(variable_rename,[status(thm)],[f_534_1]) ).
fof(f_534_3,plain,
! [U_1277] :
( ( ( hBOOL(hAPP_int_bool(zprime,U_1277))
| ( sK8(U_1277) != U_1277
& sK8(U_1277) != one_one_int
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK8(U_1277)),U_1277))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK8(U_1277)))
& is_int(sK8(U_1277)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1277)) )
& ( ( ! [U_1275] :
( U_1275 = U_1277
| U_1275 = one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1275),U_1277))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1275))
| ~ is_int(U_1275) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1277)) )
| ~ hBOOL(hAPP_int_bool(zprime,U_1277)) ) )
| ~ is_int(U_1277) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_1276,sK8(U_1277))],[f_534_2]) ).
cnf(f_534_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1277))
| ~ hBOOL(hAPP_int_bool(zprime,U_1277))
| ~ is_int(U_1277) ),
inference(clausify,[status(thm)],[f_534_3]) ).
cnf(f_534_5,plain,
( U_1275 = U_1277
| U_1275 = one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1275),U_1277))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1275))
| ~ is_int(U_1275)
| ~ hBOOL(hAPP_int_bool(zprime,U_1277))
| ~ is_int(U_1277) ),
inference(clausify,[status(thm)],[f_534_3]) ).
cnf(f_534_6,plain,
( is_int(sK8(U_1277))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1277))
| hBOOL(hAPP_int_bool(zprime,U_1277))
| ~ is_int(U_1277) ),
inference(clausify,[status(thm)],[f_534_3]) ).
cnf(f_534_7,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK8(U_1277)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1277))
| hBOOL(hAPP_int_bool(zprime,U_1277))
| ~ is_int(U_1277) ),
inference(clausify,[status(thm)],[f_534_3]) ).
cnf(f_534_8,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK8(U_1277)),U_1277))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1277))
| hBOOL(hAPP_int_bool(zprime,U_1277))
| ~ is_int(U_1277) ),
inference(clausify,[status(thm)],[f_534_3]) ).
cnf(f_534_9,plain,
( sK8(U_1277) != one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1277))
| hBOOL(hAPP_int_bool(zprime,U_1277))
| ~ is_int(U_1277) ),
inference(clausify,[status(thm)],[f_534_3]) ).
cnf(f_534_10,plain,
( sK8(U_1277) != U_1277
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1277))
| hBOOL(hAPP_int_bool(zprime,U_1277))
| ~ is_int(U_1277) ),
inference(clausify,[status(thm)],[f_534_3]) ).
fof(f_535_1,plain,
! [R_1,Q_1,A] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1))
| A != hAPP_int_int(plus_plus_int(R_1),hAPP_int_int(times_times_int(A),Q_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A)) ),
inference(fof_nnf,[status(thm)],[fact_509_self__quotient__aux2]) ).
fof(f_535_2,plain,
! [U_1280,U_1279,U_1278] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1279),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1280))
| U_1278 != hAPP_int_int(plus_plus_int(U_1280),hAPP_int_int(times_times_int(U_1278),U_1279))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1278)) ),
inference(variable_rename,[status(thm)],[f_535_1]) ).
cnf(f_535_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1279),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1280))
| U_1278 != hAPP_int_int(plus_plus_int(U_1280),hAPP_int_int(times_times_int(U_1278),U_1279))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1278)) ),
inference(clausify,[status(thm)],[f_535_2]) ).
fof(f_536_1,plain,
! [R_1,Q_1,A] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Q_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),A))
| A != hAPP_int_int(plus_plus_int(R_1),hAPP_int_int(times_times_int(A),Q_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A)) ),
inference(fof_nnf,[status(thm)],[fact_510_self__quotient__aux1]) ).
fof(f_536_2,plain,
! [U_1283,U_1282,U_1281] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_1282))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1283),U_1281))
| U_1281 != hAPP_int_int(plus_plus_int(U_1283),hAPP_int_int(times_times_int(U_1281),U_1282))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1281)) ),
inference(variable_rename,[status(thm)],[f_536_1]) ).
cnf(f_536_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_1282))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1283),U_1281))
| U_1281 != hAPP_int_int(plus_plus_int(U_1283),hAPP_int_int(times_times_int(U_1281),U_1282))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1281)) ),
inference(clausify,[status(thm)],[f_536_2]) ).
fof(f_537_1,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(bit1(pls))))),
inference(fof_nnf,[status(thm)],[fact_511_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J]) ).
cnf(f_537_2,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(bit1(pls))))),
inference(clausify,[status(thm)],[f_537_1]) ).
fof(f_538_1,plain,
? [S1] :
( 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)))
& is_int(S1) ),
inference(fof_nnf,[status(thm)],[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(f_538_2,plain,
? [U_1284] :
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(U_1284),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)))
& is_int(U_1284) ),
inference(variable_rename,[status(thm)],[f_538_1]) ).
fof(f_538_3,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK9),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)))
& is_int(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_1284,sK9)],[f_538_2]) ).
cnf(f_538_4,plain,
is_int(sK9),
inference(clausify,[status(thm)],[f_538_3]) ).
cnf(f_538_5,plain,
hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK9),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(clausify,[status(thm)],[f_538_3]) ).
fof(f_539_1,plain,
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(fof_nnf,[status(thm)],[fact_513__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096]) ).
cnf(f_539_2,plain,
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(clausify,[status(thm)],[f_539_1]) ).
fof(f_540_1,plain,
! [X_2,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X_2),N)))
| ( N != zero_zero_nat
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X_2)) ) )
& ( N = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X_2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X_2),N))) ) ),
inference(fof_nnf,[status(thm)],[fact_514_nat__zero__less__power__iff]) ).
fof(f_540_2,plain,
! [U_1286,U_1285] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1286),U_1285)))
| ( U_1285 != zero_zero_nat
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1286)) ) )
& ( U_1285 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1286))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1286),U_1285))) ) ),
inference(variable_rename,[status(thm)],[f_540_1]) ).
fof(f_540_3,plain,
( ! [U_1290,U_1288] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1290),U_1288)))
| ( U_1288 != zero_zero_nat
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1290)) ) )
& ! [U_1289,U_1287] :
( U_1287 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1289))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1289),U_1287))) ) ),
inference(miniscope,[status(thm)],[f_540_2]) ).
cnf(f_540_4,plain,
( U_1287 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1289))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1289),U_1287))) ),
inference(clausify,[status(thm)],[f_540_3]) ).
cnf(f_540_5,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1290))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1290),U_1288))) ),
inference(clausify,[status(thm)],[f_540_3]) ).
cnf(f_540_6,plain,
( U_1288 != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1290),U_1288))) ),
inference(clausify,[status(thm)],[f_540_3]) ).
fof(f_541_1,plain,
! [X_2,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X_2),N)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X_2))
& N != zero_zero_nat ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X_2))
| N = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X_2),N))) ) ),
inference(fof_nnf,[status(thm)],[fact_515_zero__less__power__nat__eq]) ).
fof(f_541_2,plain,
! [U_1292,U_1291] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1292),U_1291)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1292))
& U_1291 != zero_zero_nat ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1292))
| U_1291 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1292),U_1291))) ) ),
inference(variable_rename,[status(thm)],[f_541_1]) ).
fof(f_541_3,plain,
( ! [U_1296,U_1294] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1296),U_1294)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1296))
& U_1294 != zero_zero_nat ) )
& ! [U_1295,U_1293] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1295))
| U_1293 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1295),U_1293))) ) ),
inference(miniscope,[status(thm)],[f_541_2]) ).
cnf(f_541_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1295))
| U_1293 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1295),U_1293))) ),
inference(clausify,[status(thm)],[f_541_3]) ).
cnf(f_541_5,plain,
( U_1294 != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1296),U_1294))) ),
inference(clausify,[status(thm)],[f_541_3]) ).
cnf(f_541_6,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1296))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1296),U_1294))) ),
inference(clausify,[status(thm)],[f_541_3]) ).
fof(f_542_1,plain,
! [X_2,W_1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X_2),number_number_of_nat(W_1))))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X_2))
& number_number_of_nat(W_1) != zero_zero_nat ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X_2))
| number_number_of_nat(W_1) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(X_2),number_number_of_nat(W_1)))) ) ),
inference(fof_nnf,[status(thm)],[fact_516_zero__less__power__nat__eq__number__of]) ).
fof(f_542_2,plain,
! [U_1298,U_1297] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1298),number_number_of_nat(U_1297))))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1298))
& number_number_of_nat(U_1297) != zero_zero_nat ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1298))
| number_number_of_nat(U_1297) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1298),number_number_of_nat(U_1297)))) ) ),
inference(variable_rename,[status(thm)],[f_542_1]) ).
fof(f_542_3,plain,
( ! [U_1302,U_1300] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1302),number_number_of_nat(U_1300))))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1302))
& number_number_of_nat(U_1300) != zero_zero_nat ) )
& ! [U_1301,U_1299] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1301))
| number_number_of_nat(U_1299) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1301),number_number_of_nat(U_1299)))) ) ),
inference(miniscope,[status(thm)],[f_542_2]) ).
cnf(f_542_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1301))
| number_number_of_nat(U_1299) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1301),number_number_of_nat(U_1299)))) ),
inference(clausify,[status(thm)],[f_542_3]) ).
cnf(f_542_5,plain,
( number_number_of_nat(U_1300) != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1302),number_number_of_nat(U_1300)))) ),
inference(clausify,[status(thm)],[f_542_3]) ).
cnf(f_542_6,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1302))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(power_power_nat(U_1302),number_number_of_nat(U_1300)))) ),
inference(clausify,[status(thm)],[f_542_3]) ).
fof(f_543_1,plain,
! [M,N_1,I_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(I_1),M)),hAPP_nat_nat(power_power_nat(I_1),N_1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),I_1)) ),
inference(fof_nnf,[status(thm)],[fact_517_nat__power__less__imp__less]) ).
fof(f_543_2,plain,
! [U_1305,U_1304,U_1303] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1305),U_1304))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_1303),U_1305)),hAPP_nat_nat(power_power_nat(U_1303),U_1304)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1303)) ),
inference(variable_rename,[status(thm)],[f_543_1]) ).
cnf(f_543_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1305),U_1304))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(power_power_nat(U_1303),U_1305)),hAPP_nat_nat(power_power_nat(U_1303),U_1304)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1303)) ),
inference(clausify,[status(thm)],[f_543_2]) ).
fof(f_544_1,plain,
! [K] :
( ( ( bit1(K) = min
| K != min )
& ( K = min
| bit1(K) != min ) )
| ~ is_int(K) ),
inference(fof_nnf,[status(thm)],[fact_518_rel__simps_I47_J]) ).
fof(f_544_2,plain,
! [U_1306] :
( ( ( bit1(U_1306) = min
| U_1306 != min )
& ( U_1306 = min
| bit1(U_1306) != min ) )
| ~ is_int(U_1306) ),
inference(variable_rename,[status(thm)],[f_544_1]) ).
cnf(f_544_3,plain,
( U_1306 = min
| bit1(U_1306) != min
| ~ is_int(U_1306) ),
inference(clausify,[status(thm)],[f_544_2]) ).
cnf(f_544_4,plain,
( bit1(U_1306) = min
| U_1306 != min
| ~ is_int(U_1306) ),
inference(clausify,[status(thm)],[f_544_2]) ).
fof(f_545_1,plain,
! [L_1] :
( ( ( min = bit1(L_1)
| min != L_1 )
& ( min = L_1
| min != bit1(L_1) ) )
| ~ is_int(L_1) ),
inference(fof_nnf,[status(thm)],[fact_519_rel__simps_I43_J]) ).
fof(f_545_2,plain,
! [U_1307] :
( ( ( min = bit1(U_1307)
| min != U_1307 )
& ( min = U_1307
| min != bit1(U_1307) ) )
| ~ is_int(U_1307) ),
inference(variable_rename,[status(thm)],[f_545_1]) ).
cnf(f_545_3,plain,
( min = U_1307
| min != bit1(U_1307)
| ~ is_int(U_1307) ),
inference(clausify,[status(thm)],[f_545_2]) ).
cnf(f_545_4,plain,
( min = bit1(U_1307)
| min != U_1307
| ~ is_int(U_1307) ),
inference(clausify,[status(thm)],[f_545_2]) ).
fof(f_546_1,plain,
bit1(min) = min,
inference(fof_nnf,[status(thm)],[fact_520_Bit1__Min]) ).
cnf(f_546_2,plain,
bit1(min) = min,
inference(clausify,[status(thm)],[f_546_1]) ).
fof(f_547_1,plain,
pls != min,
inference(fof_nnf,[status(thm)],[fact_521_rel__simps_I37_J]) ).
cnf(f_547_2,plain,
pls != min,
inference(clausify,[status(thm)],[f_547_1]) ).
fof(f_548_1,plain,
min != pls,
inference(fof_nnf,[status(thm)],[fact_522_rel__simps_I40_J]) ).
cnf(f_548_2,plain,
min != pls,
inference(clausify,[status(thm)],[f_548_1]) ).
fof(f_549_1,plain,
! [K_1] : bit0(K_1) != min,
inference(fof_nnf,[status(thm)],[fact_523_rel__simps_I45_J]) ).
fof(f_549_2,plain,
! [U_1308] : bit0(U_1308) != min,
inference(variable_rename,[status(thm)],[f_549_1]) ).
cnf(f_549_3,plain,
bit0(U_1308) != min,
inference(clausify,[status(thm)],[f_549_2]) ).
fof(f_550_1,plain,
! [L] : min != bit0(L),
inference(fof_nnf,[status(thm)],[fact_524_rel__simps_I42_J]) ).
fof(f_550_2,plain,
! [U_1309] : min != bit0(U_1309),
inference(variable_rename,[status(thm)],[f_550_1]) ).
cnf(f_550_3,plain,
min != bit0(U_1309),
inference(clausify,[status(thm)],[f_550_2]) ).
fof(f_551_1,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),min)),
inference(fof_nnf,[status(thm)],[fact_525_rel__simps_I7_J]) ).
cnf(f_551_2,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),min)),
inference(clausify,[status(thm)],[f_551_1]) ).
fof(f_552_1,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),min)),
inference(fof_nnf,[status(thm)],[fact_526_rel__simps_I24_J]) ).
cnf(f_552_2,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),min)),
inference(clausify,[status(thm)],[f_552_1]) ).
fof(f_553_1,plain,
! [X_2] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X_2),X_2)))
| X_2 != zero_zero_real )
& ( X_2 = zero_zero_real
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X_2),X_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_527_not__real__square__gt__zero]) ).
fof(f_553_2,plain,
! [U_1310] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(U_1310),U_1310)))
| U_1310 != zero_zero_real )
& ( U_1310 = zero_zero_real
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(U_1310),U_1310))) ) ),
inference(variable_rename,[status(thm)],[f_553_1]) ).
fof(f_553_3,plain,
( ! [U_1312] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(U_1312),U_1312)))
| U_1312 != zero_zero_real )
& ! [U_1311] :
( U_1311 = zero_zero_real
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(U_1311),U_1311))) ) ),
inference(miniscope,[status(thm)],[f_553_2]) ).
cnf(f_553_4,plain,
( U_1311 = zero_zero_real
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(U_1311),U_1311))) ),
inference(clausify,[status(thm)],[f_553_3]) ).
cnf(f_553_5,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(U_1312),U_1312)))
| U_1312 != zero_zero_real ),
inference(clausify,[status(thm)],[f_553_3]) ).
fof(f_554_1,plain,
! [K] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),min)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),min)) ) ),
inference(fof_nnf,[status(thm)],[fact_528_rel__simps_I13_J]) ).
fof(f_554_2,plain,
! [U_1313] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_1313)),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1313),min)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1313),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_1313)),min)) ) ),
inference(variable_rename,[status(thm)],[f_554_1]) ).
fof(f_554_3,plain,
( ! [U_1315] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_1315)),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1315),min)) )
& ! [U_1314] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1314),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_1314)),min)) ) ),
inference(miniscope,[status(thm)],[f_554_2]) ).
cnf(f_554_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1314),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_1314)),min)) ),
inference(clausify,[status(thm)],[f_554_3]) ).
cnf(f_554_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_1315)),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1315),min)) ),
inference(clausify,[status(thm)],[f_554_3]) ).
fof(f_555_1,plain,
! [K] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit1(K)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),K)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),K))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit1(K))) ) ),
inference(fof_nnf,[status(thm)],[fact_529_rel__simps_I9_J]) ).
fof(f_555_2,plain,
! [U_1316] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit1(U_1316)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),U_1316)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),U_1316))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit1(U_1316))) ) ),
inference(variable_rename,[status(thm)],[f_555_1]) ).
fof(f_555_3,plain,
( ! [U_1318] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit1(U_1318)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),U_1318)) )
& ! [U_1317] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),U_1317))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit1(U_1317))) ) ),
inference(miniscope,[status(thm)],[f_555_2]) ).
cnf(f_555_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),U_1317))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit1(U_1317))) ),
inference(clausify,[status(thm)],[f_555_3]) ).
cnf(f_555_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit1(U_1318)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),U_1318)) ),
inference(clausify,[status(thm)],[f_555_3]) ).
fof(f_556_1,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),min)),
inference(fof_nnf,[status(thm)],[fact_530_rel__simps_I3_J]) ).
cnf(f_556_2,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),min)),
inference(clausify,[status(thm)],[f_556_1]) ).
fof(f_557_1,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),pls)),
inference(fof_nnf,[status(thm)],[fact_531_rel__simps_I6_J]) ).
cnf(f_557_2,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),pls)),
inference(clausify,[status(thm)],[f_557_1]) ).
fof(f_558_1,plain,
! [K] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit0(K)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),K)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),K))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit0(K))) ) ),
inference(fof_nnf,[status(thm)],[fact_532_rel__simps_I8_J]) ).
fof(f_558_2,plain,
! [U_1319] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit0(U_1319)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),U_1319)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),U_1319))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit0(U_1319))) ) ),
inference(variable_rename,[status(thm)],[f_558_1]) ).
fof(f_558_3,plain,
( ! [U_1321] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit0(U_1321)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),U_1321)) )
& ! [U_1320] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),U_1320))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit0(U_1320))) ) ),
inference(miniscope,[status(thm)],[f_558_2]) ).
cnf(f_558_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),U_1320))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit0(U_1320))) ),
inference(clausify,[status(thm)],[f_558_3]) ).
cnf(f_558_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),bit0(U_1321)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),U_1321)) ),
inference(clausify,[status(thm)],[f_558_3]) ).
fof(f_559_1,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),zero_zero_int)),
inference(fof_nnf,[status(thm)],[fact_533_bin__less__0__simps_I2_J]) ).
cnf(f_559_2,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),zero_zero_int)),
inference(clausify,[status(thm)],[f_559_1]) ).
fof(f_560_1,plain,
! [K] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),min)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),min)) ) ),
inference(fof_nnf,[status(thm)],[fact_534_rel__simps_I30_J]) ).
fof(f_560_2,plain,
! [U_1322] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_1322)),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1322),min)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1322),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_1322)),min)) ) ),
inference(variable_rename,[status(thm)],[f_560_1]) ).
fof(f_560_3,plain,
( ! [U_1324] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_1324)),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1324),min)) )
& ! [U_1323] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1323),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_1323)),min)) ) ),
inference(miniscope,[status(thm)],[f_560_2]) ).
cnf(f_560_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1323),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_1323)),min)) ),
inference(clausify,[status(thm)],[f_560_3]) ).
cnf(f_560_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_1324)),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1324),min)) ),
inference(clausify,[status(thm)],[f_560_3]) ).
fof(f_561_1,plain,
! [K] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit1(K)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),K)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),K))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit1(K))) ) ),
inference(fof_nnf,[status(thm)],[fact_535_rel__simps_I26_J]) ).
fof(f_561_2,plain,
! [U_1325] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit1(U_1325)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),U_1325)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),U_1325))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit1(U_1325))) ) ),
inference(variable_rename,[status(thm)],[f_561_1]) ).
fof(f_561_3,plain,
( ! [U_1327] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit1(U_1327)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),U_1327)) )
& ! [U_1326] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),U_1326))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit1(U_1326))) ) ),
inference(miniscope,[status(thm)],[f_561_2]) ).
cnf(f_561_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),U_1326))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit1(U_1326))) ),
inference(clausify,[status(thm)],[f_561_3]) ).
cnf(f_561_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit1(U_1327)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),U_1327)) ),
inference(clausify,[status(thm)],[f_561_3]) ).
fof(f_562_1,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),min)),
inference(fof_nnf,[status(thm)],[fact_536_rel__simps_I20_J]) ).
cnf(f_562_2,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),min)),
inference(clausify,[status(thm)],[f_562_1]) ).
fof(f_563_1,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),pls)),
inference(fof_nnf,[status(thm)],[fact_537_rel__simps_I23_J]) ).
cnf(f_563_2,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),pls)),
inference(clausify,[status(thm)],[f_563_1]) ).
fof(f_564_1,plain,
! [K] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(K)),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),min)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(K)),min)) ) ),
inference(fof_nnf,[status(thm)],[fact_538_rel__simps_I28_J]) ).
fof(f_564_2,plain,
! [U_1328] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_1328)),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1328),min)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1328),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_1328)),min)) ) ),
inference(variable_rename,[status(thm)],[f_564_1]) ).
fof(f_564_3,plain,
( ! [U_1330] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_1330)),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1330),min)) )
& ! [U_1329] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1329),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_1329)),min)) ) ),
inference(miniscope,[status(thm)],[f_564_2]) ).
cnf(f_564_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1329),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_1329)),min)) ),
inference(clausify,[status(thm)],[f_564_3]) ).
cnf(f_564_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit0(U_1330)),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1330),min)) ),
inference(clausify,[status(thm)],[f_564_3]) ).
fof(f_565_1,plain,
number_number_of_int(pls) != number_number_of_int(min),
inference(fof_nnf,[status(thm)],[fact_539_eq__number__of__Pls__Min]) ).
cnf(f_565_2,plain,
number_number_of_int(pls) != number_number_of_int(min),
inference(clausify,[status(thm)],[f_565_1]) ).
fof(f_566_1,plain,
! [I_1,M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),I_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(I_1),M)),hAPP_nat_nat(power_power_nat(I_1),N_1))) ),
inference(fof_nnf,[status(thm)],[fact_540_power__dvd__imp__le]) ).
fof(f_566_2,plain,
! [U_1333,U_1332,U_1331] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1332),U_1331))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_1333))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_1333),U_1332)),hAPP_nat_nat(power_power_nat(U_1333),U_1331))) ),
inference(variable_rename,[status(thm)],[f_566_1]) ).
cnf(f_566_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1332),U_1331))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_1333))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_1333),U_1332)),hAPP_nat_nat(power_power_nat(U_1333),U_1331))) ),
inference(clausify,[status(thm)],[f_566_2]) ).
fof(f_567_1,plain,
! [X_10] : hAPP_nat_real(power_power_real(X_10),zero_zero_nat) = one_one_real,
inference(fof_nnf,[status(thm)],[fact_541_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J]) ).
fof(f_567_2,plain,
! [U_1334] : hAPP_nat_real(power_power_real(U_1334),zero_zero_nat) = one_one_real,
inference(variable_rename,[status(thm)],[f_567_1]) ).
cnf(f_567_3,plain,
hAPP_nat_real(power_power_real(U_1334),zero_zero_nat) = one_one_real,
inference(clausify,[status(thm)],[f_567_2]) ).
fof(f_568_1,plain,
! [X_10] : hAPP_nat_nat(power_power_nat(X_10),zero_zero_nat) = one_one_nat,
inference(fof_nnf,[status(thm)],[fact_542_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J]) ).
fof(f_568_2,plain,
! [U_1335] : hAPP_nat_nat(power_power_nat(U_1335),zero_zero_nat) = one_one_nat,
inference(variable_rename,[status(thm)],[f_568_1]) ).
cnf(f_568_3,plain,
hAPP_nat_nat(power_power_nat(U_1335),zero_zero_nat) = one_one_nat,
inference(clausify,[status(thm)],[f_568_2]) ).
fof(f_569_1,plain,
! [X_10] : hAPP_nat_int(power_power_int(X_10),zero_zero_nat) = one_one_int,
inference(fof_nnf,[status(thm)],[fact_543_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J]) ).
fof(f_569_2,plain,
! [U_1336] : hAPP_nat_int(power_power_int(U_1336),zero_zero_nat) = one_one_int,
inference(variable_rename,[status(thm)],[f_569_1]) ).
cnf(f_569_3,plain,
hAPP_nat_int(power_power_int(U_1336),zero_zero_nat) = one_one_int,
inference(clausify,[status(thm)],[f_569_2]) ).
fof(f_570_1,plain,
! [A_57] : hAPP_nat_real(power_power_real(A_57),zero_zero_nat) = one_one_real,
inference(fof_nnf,[status(thm)],[fact_544_power__0]) ).
fof(f_570_2,plain,
! [U_1337] : hAPP_nat_real(power_power_real(U_1337),zero_zero_nat) = one_one_real,
inference(variable_rename,[status(thm)],[f_570_1]) ).
cnf(f_570_3,plain,
hAPP_nat_real(power_power_real(U_1337),zero_zero_nat) = one_one_real,
inference(clausify,[status(thm)],[f_570_2]) ).
fof(f_571_1,plain,
! [A_57] : hAPP_nat_nat(power_power_nat(A_57),zero_zero_nat) = one_one_nat,
inference(fof_nnf,[status(thm)],[fact_545_power__0]) ).
fof(f_571_2,plain,
! [U_1338] : hAPP_nat_nat(power_power_nat(U_1338),zero_zero_nat) = one_one_nat,
inference(variable_rename,[status(thm)],[f_571_1]) ).
cnf(f_571_3,plain,
hAPP_nat_nat(power_power_nat(U_1338),zero_zero_nat) = one_one_nat,
inference(clausify,[status(thm)],[f_571_2]) ).
fof(f_572_1,plain,
! [A_57] : hAPP_nat_int(power_power_int(A_57),zero_zero_nat) = one_one_int,
inference(fof_nnf,[status(thm)],[fact_546_power__0]) ).
fof(f_572_2,plain,
! [U_1339] : hAPP_nat_int(power_power_int(U_1339),zero_zero_nat) = one_one_int,
inference(variable_rename,[status(thm)],[f_572_1]) ).
cnf(f_572_3,plain,
hAPP_nat_int(power_power_int(U_1339),zero_zero_nat) = one_one_int,
inference(clausify,[status(thm)],[f_572_2]) ).
fof(f_573_1,plain,
number_number_of_nat(pls) = zero_zero_nat,
inference(fof_nnf,[status(thm)],[fact_547_nat__number__of__Pls]) ).
cnf(f_573_2,plain,
number_number_of_nat(pls) = zero_zero_nat,
inference(clausify,[status(thm)],[f_573_1]) ).
fof(f_574_1,plain,
zero_zero_nat = number_number_of_nat(pls),
inference(fof_nnf,[status(thm)],[fact_548_semiring__norm_I113_J]) ).
cnf(f_574_2,plain,
zero_zero_nat = number_number_of_nat(pls),
inference(clausify,[status(thm)],[f_574_1]) ).
fof(f_575_1,plain,
! [K] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit0(K)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),K)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),K))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit0(K))) ) ),
inference(fof_nnf,[status(thm)],[fact_549_rel__simps_I25_J]) ).
fof(f_575_2,plain,
! [U_1340] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit0(U_1340)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),U_1340)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),U_1340))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit0(U_1340))) ) ),
inference(variable_rename,[status(thm)],[f_575_1]) ).
fof(f_575_3,plain,
( ! [U_1342] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit0(U_1342)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),U_1342)) )
& ! [U_1341] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),U_1341))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit0(U_1341))) ) ),
inference(miniscope,[status(thm)],[f_575_2]) ).
cnf(f_575_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),U_1341))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit0(U_1341))) ),
inference(clausify,[status(thm)],[f_575_3]) ).
cnf(f_575_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),bit0(U_1342)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),U_1342)) ),
inference(clausify,[status(thm)],[f_575_3]) ).
fof(f_576_1,plain,
! [K] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(K)),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),min)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(K)),min)) ) ),
inference(fof_nnf,[status(thm)],[fact_550_rel__simps_I11_J]) ).
fof(f_576_2,plain,
! [U_1343] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_1343)),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1343),min)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1343),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_1343)),min)) ) ),
inference(variable_rename,[status(thm)],[f_576_1]) ).
fof(f_576_3,plain,
( ! [U_1345] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_1345)),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1345),min)) )
& ! [U_1344] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1344),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_1344)),min)) ) ),
inference(miniscope,[status(thm)],[f_576_2]) ).
cnf(f_576_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1344),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_1344)),min)) ),
inference(clausify,[status(thm)],[f_576_3]) ).
cnf(f_576_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit0(U_1345)),min))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1345),min)) ),
inference(clausify,[status(thm)],[f_576_3]) ).
fof(f_577_1,plain,
! [M,N_1] :
( M = number_number_of_int(min)
| M = one_one_int
| hAPP_int_int(times_times_int(M),N_1) != one_one_int
| ~ is_int(M) ),
inference(fof_nnf,[status(thm)],[fact_551_pos__zmult__eq__1__iff__lemma]) ).
fof(f_577_2,plain,
! [U_1347,U_1346] :
( U_1347 = number_number_of_int(min)
| U_1347 = one_one_int
| hAPP_int_int(times_times_int(U_1347),U_1346) != one_one_int
| ~ is_int(U_1347) ),
inference(variable_rename,[status(thm)],[f_577_1]) ).
fof(f_577_3,plain,
! [U_1347] :
( ! [U_1346] : hAPP_int_int(times_times_int(U_1347),U_1346) != one_one_int
| U_1347 = number_number_of_int(min)
| U_1347 = one_one_int
| ~ is_int(U_1347) ),
inference(miniscope,[status(thm)],[f_577_2]) ).
cnf(f_577_4,plain,
( hAPP_int_int(times_times_int(U_1347),U_1346) != one_one_int
| U_1347 = number_number_of_int(min)
| U_1347 = one_one_int
| ~ is_int(U_1347) ),
inference(clausify,[status(thm)],[f_577_3]) ).
fof(f_578_1,plain,
! [Ma,N] :
( ( ( hAPP_int_int(times_times_int(Ma),N) = one_one_int
| ( ( N != number_number_of_int(min)
| Ma != number_number_of_int(min) )
& ( N != one_one_int
| Ma != one_one_int ) ) )
& ( ( N = number_number_of_int(min)
& Ma = number_number_of_int(min) )
| ( N = one_one_int
& Ma = one_one_int )
| hAPP_int_int(times_times_int(Ma),N) != one_one_int ) )
| ~ is_int(N)
| ~ is_int(Ma) ),
inference(fof_nnf,[status(thm)],[fact_552_zmult__eq__1__iff]) ).
fof(f_578_2,plain,
! [U_1349,U_1348] :
( ( ( hAPP_int_int(times_times_int(U_1349),U_1348) = one_one_int
| ( ( U_1348 != number_number_of_int(min)
| U_1349 != number_number_of_int(min) )
& ( U_1348 != one_one_int
| U_1349 != one_one_int ) ) )
& ( ( U_1348 = number_number_of_int(min)
& U_1349 = number_number_of_int(min) )
| ( U_1348 = one_one_int
& U_1349 = one_one_int )
| hAPP_int_int(times_times_int(U_1349),U_1348) != one_one_int ) )
| ~ is_int(U_1348)
| ~ is_int(U_1349) ),
inference(variable_rename,[status(thm)],[f_578_1]) ).
cnf(f_578_3,plain,
( U_1349 = number_number_of_int(min)
| U_1349 = one_one_int
| hAPP_int_int(times_times_int(U_1349),U_1348) != one_one_int
| ~ is_int(U_1348)
| ~ is_int(U_1349) ),
inference(clausify,[status(thm)],[f_578_2]) ).
cnf(f_578_4,plain,
( U_1348 = number_number_of_int(min)
| U_1349 = one_one_int
| hAPP_int_int(times_times_int(U_1349),U_1348) != one_one_int
| ~ is_int(U_1348)
| ~ is_int(U_1349) ),
inference(clausify,[status(thm)],[f_578_2]) ).
cnf(f_578_5,plain,
( U_1349 = number_number_of_int(min)
| U_1348 = one_one_int
| hAPP_int_int(times_times_int(U_1349),U_1348) != one_one_int
| ~ is_int(U_1348)
| ~ is_int(U_1349) ),
inference(clausify,[status(thm)],[f_578_2]) ).
cnf(f_578_6,plain,
( U_1348 = number_number_of_int(min)
| U_1348 = one_one_int
| hAPP_int_int(times_times_int(U_1349),U_1348) != one_one_int
| ~ is_int(U_1348)
| ~ is_int(U_1349) ),
inference(clausify,[status(thm)],[f_578_2]) ).
cnf(f_578_7,plain,
( U_1348 != one_one_int
| U_1349 != one_one_int
| hAPP_int_int(times_times_int(U_1349),U_1348) = one_one_int
| ~ is_int(U_1348)
| ~ is_int(U_1349) ),
inference(clausify,[status(thm)],[f_578_2]) ).
cnf(f_578_8,plain,
( U_1348 != number_number_of_int(min)
| U_1349 != number_number_of_int(min)
| hAPP_int_int(times_times_int(U_1349),U_1348) = one_one_int
| ~ is_int(U_1348)
| ~ is_int(U_1349) ),
inference(clausify,[status(thm)],[f_578_2]) ).
fof(f_579_1,plain,
! [N_6,A_56] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_nat_real(power_power_real(A_56),N_6)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_6))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),A_56)) ),
inference(fof_nnf,[status(thm)],[fact_553_one__less__power]) ).
fof(f_579_2,plain,
! [U_1351,U_1350] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_nat_real(power_power_real(U_1350),U_1351)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1351))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_1350)) ),
inference(variable_rename,[status(thm)],[f_579_1]) ).
cnf(f_579_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),hAPP_nat_real(power_power_real(U_1350),U_1351)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1351))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),U_1350)) ),
inference(clausify,[status(thm)],[f_579_2]) ).
fof(f_580_1,plain,
! [N_6,A_56] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(power_power_nat(A_56),N_6)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_6))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),A_56)) ),
inference(fof_nnf,[status(thm)],[fact_554_one__less__power]) ).
fof(f_580_2,plain,
! [U_1353,U_1352] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(power_power_nat(U_1352),U_1353)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1353))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_1352)) ),
inference(variable_rename,[status(thm)],[f_580_1]) ).
cnf(f_580_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),hAPP_nat_nat(power_power_nat(U_1352),U_1353)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1353))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),U_1352)) ),
inference(clausify,[status(thm)],[f_580_2]) ).
fof(f_581_1,plain,
! [N_6,A_56] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_nat_int(power_power_int(A_56),N_6)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_6))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_56)) ),
inference(fof_nnf,[status(thm)],[fact_555_one__less__power]) ).
fof(f_581_2,plain,
! [U_1355,U_1354] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_nat_int(power_power_int(U_1354),U_1355)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1355))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1354)) ),
inference(variable_rename,[status(thm)],[f_581_1]) ).
cnf(f_581_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),hAPP_nat_int(power_power_int(U_1354),U_1355)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1355))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_1354)) ),
inference(clausify,[status(thm)],[f_581_2]) ).
fof(f_582_1,plain,
! [X_9,N_5] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X_9),hAPP_nat_real(power_power_real(X_9),N_5)))
| ( X_9 != one_one_real
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_5)) ) ),
inference(fof_nnf,[status(thm)],[fact_556_dvd__power]) ).
fof(f_582_2,plain,
! [U_1357,U_1356] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1357),hAPP_nat_real(power_power_real(U_1357),U_1356)))
| ( U_1357 != one_one_real
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1356)) ) ),
inference(variable_rename,[status(thm)],[f_582_1]) ).
cnf(f_582_3,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1356))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1357),hAPP_nat_real(power_power_real(U_1357),U_1356))) ),
inference(clausify,[status(thm)],[f_582_2]) ).
cnf(f_582_4,plain,
( U_1357 != one_one_real
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1357),hAPP_nat_real(power_power_real(U_1357),U_1356))) ),
inference(clausify,[status(thm)],[f_582_2]) ).
fof(f_583_1,plain,
! [X_9,N_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_9),hAPP_nat_nat(power_power_nat(X_9),N_5)))
| ( X_9 != one_one_nat
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_5)) ) ),
inference(fof_nnf,[status(thm)],[fact_557_dvd__power]) ).
fof(f_583_2,plain,
! [U_1359,U_1358] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1359),hAPP_nat_nat(power_power_nat(U_1359),U_1358)))
| ( U_1359 != one_one_nat
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1358)) ) ),
inference(variable_rename,[status(thm)],[f_583_1]) ).
cnf(f_583_3,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1358))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1359),hAPP_nat_nat(power_power_nat(U_1359),U_1358))) ),
inference(clausify,[status(thm)],[f_583_2]) ).
cnf(f_583_4,plain,
( U_1359 != one_one_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1359),hAPP_nat_nat(power_power_nat(U_1359),U_1358))) ),
inference(clausify,[status(thm)],[f_583_2]) ).
fof(f_584_1,plain,
! [X_9,N_5] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X_9),hAPP_nat_int(power_power_int(X_9),N_5)))
| ( X_9 != one_one_int
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_5)) ) ),
inference(fof_nnf,[status(thm)],[fact_558_dvd__power]) ).
fof(f_584_2,plain,
! [U_1361,U_1360] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1361),hAPP_nat_int(power_power_int(U_1361),U_1360)))
| ( U_1361 != one_one_int
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1360)) ) ),
inference(variable_rename,[status(thm)],[f_584_1]) ).
cnf(f_584_3,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1360))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1361),hAPP_nat_int(power_power_int(U_1361),U_1360))) ),
inference(clausify,[status(thm)],[f_584_2]) ).
cnf(f_584_4,plain,
( U_1361 != one_one_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1361),hAPP_nat_int(power_power_int(U_1361),U_1360))) ),
inference(clausify,[status(thm)],[f_584_2]) ).
fof(f_585_1,plain,
! [V_7] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(V_7)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),V_7)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),V_7))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(V_7))) ) ),
inference(fof_nnf,[status(thm)],[fact_559_less__0__number__of]) ).
fof(f_585_2,plain,
! [U_1362] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(U_1362)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1362)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1362))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(U_1362))) ) ),
inference(variable_rename,[status(thm)],[f_585_1]) ).
fof(f_585_3,plain,
( ! [U_1364] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(U_1364)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1364)) )
& ! [U_1363] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1363))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(U_1363))) ) ),
inference(miniscope,[status(thm)],[f_585_2]) ).
cnf(f_585_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1363))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(U_1363))) ),
inference(clausify,[status(thm)],[f_585_3]) ).
cnf(f_585_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(U_1364)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),U_1364)) ),
inference(clausify,[status(thm)],[f_585_3]) ).
fof(f_586_1,plain,
! [V_7] :
( ( number_number_of_nat(V_7) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V_7),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V_7),pls))
| number_number_of_nat(V_7) != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_560_eq__number__of__0]) ).
fof(f_586_2,plain,
! [U_1365] :
( ( number_number_of_nat(U_1365) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1365),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1365),pls))
| number_number_of_nat(U_1365) != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_586_1]) ).
fof(f_586_3,plain,
( ! [U_1367] :
( number_number_of_nat(U_1367) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1367),pls)) )
& ! [U_1366] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1366),pls))
| number_number_of_nat(U_1366) != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_586_2]) ).
cnf(f_586_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1366),pls))
| number_number_of_nat(U_1366) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_586_3]) ).
cnf(f_586_5,plain,
( number_number_of_nat(U_1367) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1367),pls)) ),
inference(clausify,[status(thm)],[f_586_3]) ).
fof(f_587_1,plain,
! [V_7] :
( ( zero_zero_nat = number_number_of_nat(V_7)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V_7),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,V_7),pls))
| zero_zero_nat != number_number_of_nat(V_7) ) ),
inference(fof_nnf,[status(thm)],[fact_561_eq__0__number__of]) ).
fof(f_587_2,plain,
! [U_1368] :
( ( zero_zero_nat = number_number_of_nat(U_1368)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1368),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1368),pls))
| zero_zero_nat != number_number_of_nat(U_1368) ) ),
inference(variable_rename,[status(thm)],[f_587_1]) ).
fof(f_587_3,plain,
( ! [U_1370] :
( zero_zero_nat = number_number_of_nat(U_1370)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1370),pls)) )
& ! [U_1369] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1369),pls))
| zero_zero_nat != number_number_of_nat(U_1369) ) ),
inference(miniscope,[status(thm)],[f_587_2]) ).
cnf(f_587_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1369),pls))
| zero_zero_nat != number_number_of_nat(U_1369) ),
inference(clausify,[status(thm)],[f_587_3]) ).
cnf(f_587_5,plain,
( zero_zero_nat = number_number_of_nat(U_1370)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1370),pls)) ),
inference(clausify,[status(thm)],[f_587_3]) ).
fof(f_588_1,plain,
! [A_2,B_2,Ma] :
( ( hBOOL(hAPP_int_bool(zcong(A_2,B_2),Ma))
| ~ hBOOL(hAPP_int_bool(zcong(B_2,A_2),Ma)) )
& ( hBOOL(hAPP_int_bool(zcong(B_2,A_2),Ma))
| ~ hBOOL(hAPP_int_bool(zcong(A_2,B_2),Ma)) ) ),
inference(fof_nnf,[status(thm)],[fact_562_zcong__sym]) ).
fof(f_588_2,plain,
! [U_1373,U_1372,U_1371] :
( ( hBOOL(hAPP_int_bool(zcong(U_1373,U_1372),U_1371))
| ~ hBOOL(hAPP_int_bool(zcong(U_1372,U_1373),U_1371)) )
& ( hBOOL(hAPP_int_bool(zcong(U_1372,U_1373),U_1371))
| ~ hBOOL(hAPP_int_bool(zcong(U_1373,U_1372),U_1371)) ) ),
inference(variable_rename,[status(thm)],[f_588_1]) ).
fof(f_588_3,plain,
( ! [U_1379,U_1377,U_1375] :
( hBOOL(hAPP_int_bool(zcong(U_1379,U_1377),U_1375))
| ~ hBOOL(hAPP_int_bool(zcong(U_1377,U_1379),U_1375)) )
& ! [U_1378,U_1376,U_1374] :
( hBOOL(hAPP_int_bool(zcong(U_1376,U_1378),U_1374))
| ~ hBOOL(hAPP_int_bool(zcong(U_1378,U_1376),U_1374)) ) ),
inference(miniscope,[status(thm)],[f_588_2]) ).
cnf(f_588_4,plain,
( hBOOL(hAPP_int_bool(zcong(U_1376,U_1378),U_1374))
| ~ hBOOL(hAPP_int_bool(zcong(U_1378,U_1376),U_1374)) ),
inference(clausify,[status(thm)],[f_588_3]) ).
cnf(f_588_5,plain,
( hBOOL(hAPP_int_bool(zcong(U_1379,U_1377),U_1375))
| ~ hBOOL(hAPP_int_bool(zcong(U_1377,U_1379),U_1375)) ),
inference(clausify,[status(thm)],[f_588_3]) ).
fof(f_589_1,plain,
! [K_1,M] : hBOOL(hAPP_int_bool(zcong(K_1,K_1),M)),
inference(fof_nnf,[status(thm)],[fact_563_zcong__refl]) ).
fof(f_589_2,plain,
! [U_1381,U_1380] : hBOOL(hAPP_int_bool(zcong(U_1381,U_1381),U_1380)),
inference(variable_rename,[status(thm)],[f_589_1]) ).
cnf(f_589_3,plain,
hBOOL(hAPP_int_bool(zcong(U_1381,U_1381),U_1380)),
inference(clausify,[status(thm)],[f_589_2]) ).
fof(f_590_1,plain,
! [C,A,B,M] :
( hBOOL(hAPP_int_bool(zcong(A,C),M))
| ~ hBOOL(hAPP_int_bool(zcong(B,C),M))
| ~ hBOOL(hAPP_int_bool(zcong(A,B),M)) ),
inference(fof_nnf,[status(thm)],[fact_564_zcong__trans]) ).
fof(f_590_2,plain,
! [U_1385,U_1384,U_1383,U_1382] :
( hBOOL(hAPP_int_bool(zcong(U_1384,U_1385),U_1382))
| ~ hBOOL(hAPP_int_bool(zcong(U_1383,U_1385),U_1382))
| ~ hBOOL(hAPP_int_bool(zcong(U_1384,U_1383),U_1382)) ),
inference(variable_rename,[status(thm)],[f_590_1]) ).
cnf(f_590_3,plain,
( hBOOL(hAPP_int_bool(zcong(U_1384,U_1385),U_1382))
| ~ hBOOL(hAPP_int_bool(zcong(U_1383,U_1385),U_1382))
| ~ hBOOL(hAPP_int_bool(zcong(U_1384,U_1383),U_1382)) ),
inference(clausify,[status(thm)],[f_590_2]) ).
fof(f_591_1,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(bit0(bit1(pls))))),
inference(fof_nnf,[status(thm)],[fact_565_pos2]) ).
cnf(f_591_2,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(bit0(bit1(pls))))),
inference(clausify,[status(thm)],[f_591_1]) ).
fof(f_592_1,plain,
! [V_6,K_1,V] :
( ( hAPP_nat_nat(times_times_nat(number_number_of_nat(V)),hAPP_nat_nat(times_times_nat(number_number_of_nat(V_6)),K_1)) = hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(times_times_int(V),V_6))),K_1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) )
& ( hAPP_nat_nat(times_times_nat(number_number_of_nat(V)),hAPP_nat_nat(times_times_nat(number_number_of_nat(V_6)),K_1)) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) ) ),
inference(fof_nnf,[status(thm)],[fact_566_nat__number__of__mult__left]) ).
fof(f_592_2,plain,
! [U_1388,U_1387,U_1386] :
( ( hAPP_nat_nat(times_times_nat(number_number_of_nat(U_1386)),hAPP_nat_nat(times_times_nat(number_number_of_nat(U_1388)),U_1387)) = hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(times_times_int(U_1386),U_1388))),U_1387)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1386),pls)) )
& ( hAPP_nat_nat(times_times_nat(number_number_of_nat(U_1386)),hAPP_nat_nat(times_times_nat(number_number_of_nat(U_1388)),U_1387)) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1386),pls)) ) ),
inference(variable_rename,[status(thm)],[f_592_1]) ).
fof(f_592_3,plain,
( ! [U_1394,U_1392,U_1390] :
( hAPP_nat_nat(times_times_nat(number_number_of_nat(U_1390)),hAPP_nat_nat(times_times_nat(number_number_of_nat(U_1394)),U_1392)) = hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(times_times_int(U_1390),U_1394))),U_1392)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1390),pls)) )
& ! [U_1393,U_1391,U_1389] :
( hAPP_nat_nat(times_times_nat(number_number_of_nat(U_1389)),hAPP_nat_nat(times_times_nat(number_number_of_nat(U_1393)),U_1391)) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1389),pls)) ) ),
inference(miniscope,[status(thm)],[f_592_2]) ).
cnf(f_592_4,plain,
( hAPP_nat_nat(times_times_nat(number_number_of_nat(U_1389)),hAPP_nat_nat(times_times_nat(number_number_of_nat(U_1393)),U_1391)) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1389),pls)) ),
inference(clausify,[status(thm)],[f_592_3]) ).
cnf(f_592_5,plain,
( hAPP_nat_nat(times_times_nat(number_number_of_nat(U_1390)),hAPP_nat_nat(times_times_nat(number_number_of_nat(U_1394)),U_1392)) = hAPP_nat_nat(times_times_nat(number_number_of_nat(hAPP_int_int(times_times_int(U_1390),U_1394))),U_1392)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1390),pls)) ),
inference(clausify,[status(thm)],[f_592_3]) ).
fof(f_593_1,plain,
! [V_6,V] :
( ( hAPP_nat_nat(times_times_nat(number_number_of_nat(V)),number_number_of_nat(V_6)) = number_number_of_nat(hAPP_int_int(times_times_int(V),V_6))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) )
& ( hAPP_nat_nat(times_times_nat(number_number_of_nat(V)),number_number_of_nat(V_6)) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) ) ),
inference(fof_nnf,[status(thm)],[fact_567_mult__nat__number__of]) ).
fof(f_593_2,plain,
! [U_1396,U_1395] :
( ( hAPP_nat_nat(times_times_nat(number_number_of_nat(U_1395)),number_number_of_nat(U_1396)) = number_number_of_nat(hAPP_int_int(times_times_int(U_1395),U_1396))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1395),pls)) )
& ( hAPP_nat_nat(times_times_nat(number_number_of_nat(U_1395)),number_number_of_nat(U_1396)) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1395),pls)) ) ),
inference(variable_rename,[status(thm)],[f_593_1]) ).
fof(f_593_3,plain,
( ! [U_1400,U_1398] :
( hAPP_nat_nat(times_times_nat(number_number_of_nat(U_1398)),number_number_of_nat(U_1400)) = number_number_of_nat(hAPP_int_int(times_times_int(U_1398),U_1400))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1398),pls)) )
& ! [U_1399,U_1397] :
( hAPP_nat_nat(times_times_nat(number_number_of_nat(U_1397)),number_number_of_nat(U_1399)) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1397),pls)) ) ),
inference(miniscope,[status(thm)],[f_593_2]) ).
cnf(f_593_4,plain,
( hAPP_nat_nat(times_times_nat(number_number_of_nat(U_1397)),number_number_of_nat(U_1399)) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1397),pls)) ),
inference(clausify,[status(thm)],[f_593_3]) ).
cnf(f_593_5,plain,
( hAPP_nat_nat(times_times_nat(number_number_of_nat(U_1398)),number_number_of_nat(U_1400)) = number_number_of_nat(hAPP_int_int(times_times_int(U_1398),U_1400))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1398),pls)) ),
inference(clausify,[status(thm)],[f_593_3]) ).
fof(f_594_1,plain,
! [X_8,Y_7] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_8),Y_7))
| X_8 = Y_7
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_8),Y_7)) ),
inference(fof_nnf,[status(thm)],[fact_568_order__le__neq__implies__less]) ).
fof(f_594_2,plain,
! [U_1402,U_1401] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1402),U_1401))
| U_1402 = U_1401
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1402),U_1401)) ),
inference(variable_rename,[status(thm)],[f_594_1]) ).
cnf(f_594_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1402),U_1401))
| U_1402 = U_1401
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1402),U_1401)) ),
inference(clausify,[status(thm)],[f_594_2]) ).
fof(f_595_1,plain,
! [X_8,Y_7] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_8),Y_7))
| X_8 = Y_7
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_8),Y_7)) ),
inference(fof_nnf,[status(thm)],[fact_569_order__le__neq__implies__less]) ).
fof(f_595_2,plain,
! [U_1404,U_1403] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1404),U_1403))
| U_1404 = U_1403
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1404),U_1403)) ),
inference(variable_rename,[status(thm)],[f_595_1]) ).
cnf(f_595_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_1404),U_1403))
| U_1404 = U_1403
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1404),U_1403)) ),
inference(clausify,[status(thm)],[f_595_2]) ).
fof(f_596_1,plain,
! [X_8,Y_7] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_8),Y_7))
| X_8 = Y_7
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_8),Y_7))
| ~ is_int(Y_7)
| ~ is_int(X_8) ),
inference(fof_nnf,[status(thm)],[fact_570_order__le__neq__implies__less]) ).
fof(f_596_2,plain,
! [U_1406,U_1405] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1406),U_1405))
| U_1406 = U_1405
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1406),U_1405))
| ~ is_int(U_1405)
| ~ is_int(U_1406) ),
inference(variable_rename,[status(thm)],[f_596_1]) ).
cnf(f_596_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1406),U_1405))
| U_1406 = U_1405
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1406),U_1405))
| ~ is_int(U_1405)
| ~ is_int(U_1406) ),
inference(clausify,[status(thm)],[f_596_2]) ).
fof(f_597_1,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
inference(fof_nnf,[status(thm)],[fact_571_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]) ).
cnf(f_597_2,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
inference(clausify,[status(thm)],[f_597_1]) ).
fof(f_598_1,plain,
! [B,A,C] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B),A))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A),B))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),C))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),C)) ),
inference(fof_nnf,[status(thm)],[fact_572_Euler_Oaux2]) ).
fof(f_598_2,plain,
! [U_1409,U_1408,U_1407] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1409),U_1408))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1408),U_1409))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1409),U_1407))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1408),U_1407)) ),
inference(variable_rename,[status(thm)],[f_598_1]) ).
cnf(f_598_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1409),U_1408))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1408),U_1409))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1409),U_1407))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1408),U_1407)) ),
inference(clausify,[status(thm)],[f_598_2]) ).
fof(f_599_1,plain,
! [A_2,B_2] :
( ( ( hBOOL(hAPP_int_bool(zcong(A_2,B_2),zero_zero_int))
| A_2 != B_2 )
& ( A_2 = B_2
| ~ hBOOL(hAPP_int_bool(zcong(A_2,B_2),zero_zero_int)) ) )
| ~ is_int(B_2)
| ~ is_int(A_2) ),
inference(fof_nnf,[status(thm)],[fact_573_IntPrimes_Ozcong__zero]) ).
fof(f_599_2,plain,
! [U_1411,U_1410] :
( ( ( hBOOL(hAPP_int_bool(zcong(U_1411,U_1410),zero_zero_int))
| U_1411 != U_1410 )
& ( U_1411 = U_1410
| ~ hBOOL(hAPP_int_bool(zcong(U_1411,U_1410),zero_zero_int)) ) )
| ~ is_int(U_1410)
| ~ is_int(U_1411) ),
inference(variable_rename,[status(thm)],[f_599_1]) ).
cnf(f_599_3,plain,
( U_1411 = U_1410
| ~ hBOOL(hAPP_int_bool(zcong(U_1411,U_1410),zero_zero_int))
| ~ is_int(U_1410)
| ~ is_int(U_1411) ),
inference(clausify,[status(thm)],[f_599_2]) ).
cnf(f_599_4,plain,
( hBOOL(hAPP_int_bool(zcong(U_1411,U_1410),zero_zero_int))
| U_1411 != U_1410
| ~ is_int(U_1410)
| ~ is_int(U_1411) ),
inference(clausify,[status(thm)],[f_599_2]) ).
fof(f_600_1,plain,
! [A,B] : hBOOL(hAPP_int_bool(zcong(A,B),one_one_int)),
inference(fof_nnf,[status(thm)],[fact_574_zcong__1]) ).
fof(f_600_2,plain,
! [U_1413,U_1412] : hBOOL(hAPP_int_bool(zcong(U_1413,U_1412),one_one_int)),
inference(variable_rename,[status(thm)],[f_600_1]) ).
cnf(f_600_3,plain,
hBOOL(hAPP_int_bool(zcong(U_1413,U_1412),one_one_int)),
inference(clausify,[status(thm)],[f_600_2]) ).
fof(f_601_1,plain,
! [C,D_5,A,B,M] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),C),hAPP_int_int(times_times_int(B),D_5)),M))
| ~ hBOOL(hAPP_int_bool(zcong(C,D_5),M))
| ~ hBOOL(hAPP_int_bool(zcong(A,B),M)) ),
inference(fof_nnf,[status(thm)],[fact_575_zcong__zmult]) ).
fof(f_601_2,plain,
! [U_1418,U_1417,U_1416,U_1415,U_1414] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1416),U_1418),hAPP_int_int(times_times_int(U_1415),U_1417)),U_1414))
| ~ hBOOL(hAPP_int_bool(zcong(U_1418,U_1417),U_1414))
| ~ hBOOL(hAPP_int_bool(zcong(U_1416,U_1415),U_1414)) ),
inference(variable_rename,[status(thm)],[f_601_1]) ).
cnf(f_601_3,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1416),U_1418),hAPP_int_int(times_times_int(U_1415),U_1417)),U_1414))
| ~ hBOOL(hAPP_int_bool(zcong(U_1418,U_1417),U_1414))
| ~ hBOOL(hAPP_int_bool(zcong(U_1416,U_1415),U_1414)) ),
inference(clausify,[status(thm)],[f_601_2]) ).
fof(f_602_1,plain,
! [K_1,A,B,M] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(K_1),A),hAPP_int_int(times_times_int(K_1),B)),M))
| ~ hBOOL(hAPP_int_bool(zcong(A,B),M)) ),
inference(fof_nnf,[status(thm)],[fact_576_zcong__scalar2]) ).
fof(f_602_2,plain,
! [U_1422,U_1421,U_1420,U_1419] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1422),U_1421),hAPP_int_int(times_times_int(U_1422),U_1420)),U_1419))
| ~ hBOOL(hAPP_int_bool(zcong(U_1421,U_1420),U_1419)) ),
inference(variable_rename,[status(thm)],[f_602_1]) ).
cnf(f_602_3,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1422),U_1421),hAPP_int_int(times_times_int(U_1422),U_1420)),U_1419))
| ~ hBOOL(hAPP_int_bool(zcong(U_1421,U_1420),U_1419)) ),
inference(clausify,[status(thm)],[f_602_2]) ).
fof(f_603_1,plain,
! [K_1,A,B,M] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),K_1),hAPP_int_int(times_times_int(B),K_1)),M))
| ~ hBOOL(hAPP_int_bool(zcong(A,B),M)) ),
inference(fof_nnf,[status(thm)],[fact_577_zcong__scalar]) ).
fof(f_603_2,plain,
! [U_1426,U_1425,U_1424,U_1423] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1425),U_1426),hAPP_int_int(times_times_int(U_1424),U_1426)),U_1423))
| ~ hBOOL(hAPP_int_bool(zcong(U_1425,U_1424),U_1423)) ),
inference(variable_rename,[status(thm)],[f_603_1]) ).
cnf(f_603_3,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1425),U_1426),hAPP_int_int(times_times_int(U_1424),U_1426)),U_1423))
| ~ hBOOL(hAPP_int_bool(zcong(U_1425,U_1424),U_1423)) ),
inference(clausify,[status(thm)],[f_603_2]) ).
fof(f_604_1,plain,
! [A,M,B] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),M),hAPP_int_int(times_times_int(B),M)),M)),
inference(fof_nnf,[status(thm)],[fact_578_zcong__zmult__self]) ).
fof(f_604_2,plain,
! [U_1429,U_1428,U_1427] : hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1429),U_1428),hAPP_int_int(times_times_int(U_1427),U_1428)),U_1428)),
inference(variable_rename,[status(thm)],[f_604_1]) ).
cnf(f_604_3,plain,
hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1429),U_1428),hAPP_int_int(times_times_int(U_1427),U_1428)),U_1428)),
inference(clausify,[status(thm)],[f_604_2]) ).
fof(f_605_1,plain,
! [C,D_5,A,B,M] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(A),C),hAPP_int_int(plus_plus_int(B),D_5)),M))
| ~ hBOOL(hAPP_int_bool(zcong(C,D_5),M))
| ~ hBOOL(hAPP_int_bool(zcong(A,B),M)) ),
inference(fof_nnf,[status(thm)],[fact_579_zcong__zadd]) ).
fof(f_605_2,plain,
! [U_1434,U_1433,U_1432,U_1431,U_1430] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(U_1432),U_1434),hAPP_int_int(plus_plus_int(U_1431),U_1433)),U_1430))
| ~ hBOOL(hAPP_int_bool(zcong(U_1434,U_1433),U_1430))
| ~ hBOOL(hAPP_int_bool(zcong(U_1432,U_1431),U_1430)) ),
inference(variable_rename,[status(thm)],[f_605_1]) ).
cnf(f_605_3,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(U_1432),U_1434),hAPP_int_int(plus_plus_int(U_1431),U_1433)),U_1430))
| ~ hBOOL(hAPP_int_bool(zcong(U_1434,U_1433),U_1430))
| ~ hBOOL(hAPP_int_bool(zcong(U_1432,U_1431),U_1430)) ),
inference(clausify,[status(thm)],[f_605_2]) ).
fof(f_606_1,plain,
! [N_4] : hAPP_nat_real(power_power_real(number267125858f_real(min)),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_4)) = one_one_real,
inference(fof_nnf,[status(thm)],[fact_580_power__m1__even]) ).
fof(f_606_2,plain,
! [U_1435] : hAPP_nat_real(power_power_real(number267125858f_real(min)),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_1435)) = one_one_real,
inference(variable_rename,[status(thm)],[f_606_1]) ).
cnf(f_606_3,plain,
hAPP_nat_real(power_power_real(number267125858f_real(min)),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_1435)) = one_one_real,
inference(clausify,[status(thm)],[f_606_2]) ).
fof(f_607_1,plain,
! [N_4] : hAPP_nat_int(power_power_int(number_number_of_int(min)),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_4)) = one_one_int,
inference(fof_nnf,[status(thm)],[fact_581_power__m1__even]) ).
fof(f_607_2,plain,
! [U_1436] : hAPP_nat_int(power_power_int(number_number_of_int(min)),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_1436)) = one_one_int,
inference(variable_rename,[status(thm)],[f_607_1]) ).
cnf(f_607_3,plain,
hAPP_nat_int(power_power_int(number_number_of_int(min)),hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_1436)) = one_one_int,
inference(clausify,[status(thm)],[f_607_2]) ).
fof(f_608_1,plain,
! [A_2,W_1] :
( ( hAPP_nat_real(power_power_real(A_2),number_number_of_nat(W_1)) = zero_zero_real
| number_number_of_nat(W_1) = zero_zero_nat
| A_2 != zero_zero_real )
& ( ( number_number_of_nat(W_1) != zero_zero_nat
& A_2 = zero_zero_real )
| hAPP_nat_real(power_power_real(A_2),number_number_of_nat(W_1)) != zero_zero_real ) ),
inference(fof_nnf,[status(thm)],[fact_582_power__eq__0__iff__number__of]) ).
fof(f_608_2,plain,
! [U_1438,U_1437] :
( ( hAPP_nat_real(power_power_real(U_1438),number_number_of_nat(U_1437)) = zero_zero_real
| number_number_of_nat(U_1437) = zero_zero_nat
| U_1438 != zero_zero_real )
& ( ( number_number_of_nat(U_1437) != zero_zero_nat
& U_1438 = zero_zero_real )
| hAPP_nat_real(power_power_real(U_1438),number_number_of_nat(U_1437)) != zero_zero_real ) ),
inference(variable_rename,[status(thm)],[f_608_1]) ).
fof(f_608_3,plain,
( ! [U_1442,U_1440] :
( hAPP_nat_real(power_power_real(U_1442),number_number_of_nat(U_1440)) = zero_zero_real
| number_number_of_nat(U_1440) = zero_zero_nat
| U_1442 != zero_zero_real )
& ! [U_1441,U_1439] :
( ( number_number_of_nat(U_1439) != zero_zero_nat
& U_1441 = zero_zero_real )
| hAPP_nat_real(power_power_real(U_1441),number_number_of_nat(U_1439)) != zero_zero_real ) ),
inference(miniscope,[status(thm)],[f_608_2]) ).
cnf(f_608_4,plain,
( U_1441 = zero_zero_real
| hAPP_nat_real(power_power_real(U_1441),number_number_of_nat(U_1439)) != zero_zero_real ),
inference(clausify,[status(thm)],[f_608_3]) ).
cnf(f_608_5,plain,
( number_number_of_nat(U_1439) != zero_zero_nat
| hAPP_nat_real(power_power_real(U_1441),number_number_of_nat(U_1439)) != zero_zero_real ),
inference(clausify,[status(thm)],[f_608_3]) ).
cnf(f_608_6,plain,
( hAPP_nat_real(power_power_real(U_1442),number_number_of_nat(U_1440)) = zero_zero_real
| number_number_of_nat(U_1440) = zero_zero_nat
| U_1442 != zero_zero_real ),
inference(clausify,[status(thm)],[f_608_3]) ).
fof(f_609_1,plain,
! [A_2,W_1] :
( ( hAPP_nat_nat(power_power_nat(A_2),number_number_of_nat(W_1)) = zero_zero_nat
| number_number_of_nat(W_1) = zero_zero_nat
| A_2 != zero_zero_nat )
& ( ( number_number_of_nat(W_1) != zero_zero_nat
& A_2 = zero_zero_nat )
| hAPP_nat_nat(power_power_nat(A_2),number_number_of_nat(W_1)) != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_583_power__eq__0__iff__number__of]) ).
fof(f_609_2,plain,
! [U_1444,U_1443] :
( ( hAPP_nat_nat(power_power_nat(U_1444),number_number_of_nat(U_1443)) = zero_zero_nat
| number_number_of_nat(U_1443) = zero_zero_nat
| U_1444 != zero_zero_nat )
& ( ( number_number_of_nat(U_1443) != zero_zero_nat
& U_1444 = zero_zero_nat )
| hAPP_nat_nat(power_power_nat(U_1444),number_number_of_nat(U_1443)) != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_609_1]) ).
fof(f_609_3,plain,
( ! [U_1448,U_1446] :
( hAPP_nat_nat(power_power_nat(U_1448),number_number_of_nat(U_1446)) = zero_zero_nat
| number_number_of_nat(U_1446) = zero_zero_nat
| U_1448 != zero_zero_nat )
& ! [U_1447,U_1445] :
( ( number_number_of_nat(U_1445) != zero_zero_nat
& U_1447 = zero_zero_nat )
| hAPP_nat_nat(power_power_nat(U_1447),number_number_of_nat(U_1445)) != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_609_2]) ).
cnf(f_609_4,plain,
( U_1447 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(U_1447),number_number_of_nat(U_1445)) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_609_3]) ).
cnf(f_609_5,plain,
( number_number_of_nat(U_1445) != zero_zero_nat
| hAPP_nat_nat(power_power_nat(U_1447),number_number_of_nat(U_1445)) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_609_3]) ).
cnf(f_609_6,plain,
( hAPP_nat_nat(power_power_nat(U_1448),number_number_of_nat(U_1446)) = zero_zero_nat
| number_number_of_nat(U_1446) = zero_zero_nat
| U_1448 != zero_zero_nat ),
inference(clausify,[status(thm)],[f_609_3]) ).
fof(f_610_1,plain,
! [A_2,W_1] :
( ( ( hAPP_nat_int(power_power_int(A_2),number_number_of_nat(W_1)) = zero_zero_int
| number_number_of_nat(W_1) = zero_zero_nat
| A_2 != zero_zero_int )
& ( ( number_number_of_nat(W_1) != zero_zero_nat
& A_2 = zero_zero_int )
| hAPP_nat_int(power_power_int(A_2),number_number_of_nat(W_1)) != zero_zero_int ) )
| ~ is_int(A_2) ),
inference(fof_nnf,[status(thm)],[fact_584_power__eq__0__iff__number__of]) ).
fof(f_610_2,plain,
! [U_1450,U_1449] :
( ( ( hAPP_nat_int(power_power_int(U_1450),number_number_of_nat(U_1449)) = zero_zero_int
| number_number_of_nat(U_1449) = zero_zero_nat
| U_1450 != zero_zero_int )
& ( ( number_number_of_nat(U_1449) != zero_zero_nat
& U_1450 = zero_zero_int )
| hAPP_nat_int(power_power_int(U_1450),number_number_of_nat(U_1449)) != zero_zero_int ) )
| ~ is_int(U_1450) ),
inference(variable_rename,[status(thm)],[f_610_1]) ).
fof(f_610_3,plain,
! [U_1450] :
( ( ! [U_1452] :
( hAPP_nat_int(power_power_int(U_1450),number_number_of_nat(U_1452)) = zero_zero_int
| number_number_of_nat(U_1452) = zero_zero_nat
| U_1450 != zero_zero_int )
& ! [U_1451] :
( ( number_number_of_nat(U_1451) != zero_zero_nat
& U_1450 = zero_zero_int )
| hAPP_nat_int(power_power_int(U_1450),number_number_of_nat(U_1451)) != zero_zero_int ) )
| ~ is_int(U_1450) ),
inference(miniscope,[status(thm)],[f_610_2]) ).
cnf(f_610_4,plain,
( U_1450 = zero_zero_int
| hAPP_nat_int(power_power_int(U_1450),number_number_of_nat(U_1451)) != zero_zero_int
| ~ is_int(U_1450) ),
inference(clausify,[status(thm)],[f_610_3]) ).
cnf(f_610_5,plain,
( number_number_of_nat(U_1451) != zero_zero_nat
| hAPP_nat_int(power_power_int(U_1450),number_number_of_nat(U_1451)) != zero_zero_int
| ~ is_int(U_1450) ),
inference(clausify,[status(thm)],[f_610_3]) ).
cnf(f_610_6,plain,
( hAPP_nat_int(power_power_int(U_1450),number_number_of_nat(U_1452)) = zero_zero_int
| number_number_of_nat(U_1452) = zero_zero_nat
| U_1450 != zero_zero_int
| ~ is_int(U_1450) ),
inference(clausify,[status(thm)],[f_610_3]) ).
fof(f_611_1,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
inference(fof_nnf,[status(thm)],[fact_585_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]) ).
cnf(f_611_2,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
inference(clausify,[status(thm)],[f_611_1]) ).
fof(f_612_1,plain,
! [Y_1,X_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(X_1),Y_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) ),
inference(fof_nnf,[status(thm)],[fact_586_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J]) ).
fof(f_612_2,plain,
! [U_1454,U_1453] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_1453),U_1454)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1454))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1453)) ),
inference(variable_rename,[status(thm)],[f_612_1]) ).
cnf(f_612_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_1453),U_1454)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1454))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1453)) ),
inference(clausify,[status(thm)],[f_612_2]) ).
fof(f_613_1,plain,
! [Y_1,X_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(X_1),Y_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) ),
inference(fof_nnf,[status(thm)],[fact_587_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J]) ).
fof(f_613_2,plain,
! [U_1456,U_1455] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(U_1455),U_1456)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1456))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1455)) ),
inference(variable_rename,[status(thm)],[f_613_1]) ).
cnf(f_613_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(plus_plus_int(U_1455),U_1456)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1456))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1455)) ),
inference(clausify,[status(thm)],[f_613_2]) ).
fof(f_614_1,plain,
! [B,M,A] :
( ~ hBOOL(hAPP_int_bool(zcong(A,B),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),A))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A)) ),
inference(fof_nnf,[status(thm)],[fact_588_zcong__not]) ).
fof(f_614_2,plain,
! [U_1459,U_1458,U_1457] :
( ~ hBOOL(hAPP_int_bool(zcong(U_1457,U_1459),U_1458))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1459),U_1457))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1459))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1457),U_1458))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1457)) ),
inference(variable_rename,[status(thm)],[f_614_1]) ).
cnf(f_614_3,plain,
( ~ hBOOL(hAPP_int_bool(zcong(U_1457,U_1459),U_1458))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1459),U_1457))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1459))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1457),U_1458))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1457)) ),
inference(clausify,[status(thm)],[f_614_2]) ).
fof(f_615_1,plain,
! [N_1,X_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(X_1),N_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) ),
inference(fof_nnf,[status(thm)],[fact_589_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J]) ).
fof(f_615_2,plain,
! [U_1461,U_1460] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(U_1460),U_1461)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1460)) ),
inference(variable_rename,[status(thm)],[f_615_1]) ).
cnf(f_615_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(U_1460),U_1461)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1460)) ),
inference(clausify,[status(thm)],[f_615_2]) ).
fof(f_616_1,plain,
! [A_2,B_2,Ma] :
( ( ( hBOOL(hAPP_int_bool(zcong(A_2,B_2),Ma))
| ! [K_2] :
( B_2 != hAPP_int_int(plus_plus_int(A_2),hAPP_int_int(times_times_int(Ma),K_2))
| ~ is_int(K_2) ) )
& ( ? [K_2] :
( B_2 = hAPP_int_int(plus_plus_int(A_2),hAPP_int_int(times_times_int(Ma),K_2))
& is_int(K_2) )
| ~ hBOOL(hAPP_int_bool(zcong(A_2,B_2),Ma)) ) )
| ~ is_int(B_2) ),
inference(fof_nnf,[status(thm)],[fact_590_zcong__iff__lin]) ).
fof(f_616_2,plain,
! [U_1466,U_1465,U_1464] :
( ( ( hBOOL(hAPP_int_bool(zcong(U_1466,U_1465),U_1464))
| ! [U_1463] :
( U_1465 != hAPP_int_int(plus_plus_int(U_1466),hAPP_int_int(times_times_int(U_1464),U_1463))
| ~ is_int(U_1463) ) )
& ( ? [U_1462] :
( U_1465 = hAPP_int_int(plus_plus_int(U_1466),hAPP_int_int(times_times_int(U_1464),U_1462))
& is_int(U_1462) )
| ~ hBOOL(hAPP_int_bool(zcong(U_1466,U_1465),U_1464)) ) )
| ~ is_int(U_1465) ),
inference(variable_rename,[status(thm)],[f_616_1]) ).
fof(f_616_3,plain,
! [U_1466,U_1465] :
( ( ! [U_1468] :
( hBOOL(hAPP_int_bool(zcong(U_1466,U_1465),U_1468))
| ! [U_1463] :
( U_1465 != hAPP_int_int(plus_plus_int(U_1466),hAPP_int_int(times_times_int(U_1468),U_1463))
| ~ is_int(U_1463) ) )
& ! [U_1467] :
( ? [U_1462] :
( U_1465 = hAPP_int_int(plus_plus_int(U_1466),hAPP_int_int(times_times_int(U_1467),U_1462))
& is_int(U_1462) )
| ~ hBOOL(hAPP_int_bool(zcong(U_1466,U_1465),U_1467)) ) )
| ~ is_int(U_1465) ),
inference(miniscope,[status(thm)],[f_616_2]) ).
fof(f_616_4,plain,
! [U_1466,U_1465] :
( ( ! [U_1468] :
( hBOOL(hAPP_int_bool(zcong(U_1466,U_1465),U_1468))
| ! [U_1463] :
( U_1465 != hAPP_int_int(plus_plus_int(U_1466),hAPP_int_int(times_times_int(U_1468),U_1463))
| ~ is_int(U_1463) ) )
& ! [U_1467] :
( ( U_1465 = hAPP_int_int(plus_plus_int(U_1466),hAPP_int_int(times_times_int(U_1467),sK10(U_1466,U_1465,U_1467)))
& is_int(sK10(U_1466,U_1465,U_1467)) )
| ~ hBOOL(hAPP_int_bool(zcong(U_1466,U_1465),U_1467)) ) )
| ~ is_int(U_1465) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_1462,sK10(U_1466,U_1465,U_1467))],[f_616_3]) ).
cnf(f_616_5,plain,
( is_int(sK10(U_1466,U_1465,U_1467))
| ~ hBOOL(hAPP_int_bool(zcong(U_1466,U_1465),U_1467))
| ~ is_int(U_1465) ),
inference(clausify,[status(thm)],[f_616_4]) ).
cnf(f_616_6,plain,
( U_1465 = hAPP_int_int(plus_plus_int(U_1466),hAPP_int_int(times_times_int(U_1467),sK10(U_1466,U_1465,U_1467)))
| ~ hBOOL(hAPP_int_bool(zcong(U_1466,U_1465),U_1467))
| ~ is_int(U_1465) ),
inference(clausify,[status(thm)],[f_616_4]) ).
cnf(f_616_7,plain,
( hBOOL(hAPP_int_bool(zcong(U_1466,U_1465),U_1468))
| U_1465 != hAPP_int_int(plus_plus_int(U_1466),hAPP_int_int(times_times_int(U_1468),U_1463))
| ~ is_int(U_1463)
| ~ is_int(U_1465) ),
inference(clausify,[status(thm)],[f_616_4]) ).
fof(f_617_1,plain,
! [W_4] :
( ( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(W_4)) = zero_zero_real
| number_number_of_nat(W_4) = zero_zero_nat )
& ( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(W_4)) = one_one_real
| number_number_of_nat(W_4) != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_591_power__0__left__number__of]) ).
fof(f_617_2,plain,
! [U_1469] :
( ( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(U_1469)) = zero_zero_real
| number_number_of_nat(U_1469) = zero_zero_nat )
& ( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(U_1469)) = one_one_real
| number_number_of_nat(U_1469) != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_617_1]) ).
fof(f_617_3,plain,
( ! [U_1471] :
( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(U_1471)) = zero_zero_real
| number_number_of_nat(U_1471) = zero_zero_nat )
& ! [U_1470] :
( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(U_1470)) = one_one_real
| number_number_of_nat(U_1470) != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_617_2]) ).
cnf(f_617_4,plain,
( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(U_1470)) = one_one_real
| number_number_of_nat(U_1470) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_617_3]) ).
cnf(f_617_5,plain,
( hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(U_1471)) = zero_zero_real
| number_number_of_nat(U_1471) = zero_zero_nat ),
inference(clausify,[status(thm)],[f_617_3]) ).
fof(f_618_1,plain,
! [W_4] :
( ( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(W_4)) = zero_zero_nat
| number_number_of_nat(W_4) = zero_zero_nat )
& ( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(W_4)) = one_one_nat
| number_number_of_nat(W_4) != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_592_power__0__left__number__of]) ).
fof(f_618_2,plain,
! [U_1472] :
( ( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(U_1472)) = zero_zero_nat
| number_number_of_nat(U_1472) = zero_zero_nat )
& ( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(U_1472)) = one_one_nat
| number_number_of_nat(U_1472) != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_618_1]) ).
fof(f_618_3,plain,
( ! [U_1474] :
( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(U_1474)) = zero_zero_nat
| number_number_of_nat(U_1474) = zero_zero_nat )
& ! [U_1473] :
( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(U_1473)) = one_one_nat
| number_number_of_nat(U_1473) != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_618_2]) ).
cnf(f_618_4,plain,
( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(U_1473)) = one_one_nat
| number_number_of_nat(U_1473) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_618_3]) ).
cnf(f_618_5,plain,
( hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(U_1474)) = zero_zero_nat
| number_number_of_nat(U_1474) = zero_zero_nat ),
inference(clausify,[status(thm)],[f_618_3]) ).
fof(f_619_1,plain,
! [W_4] :
( ( hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(W_4)) = zero_zero_int
| number_number_of_nat(W_4) = zero_zero_nat )
& ( hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(W_4)) = one_one_int
| number_number_of_nat(W_4) != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_593_power__0__left__number__of]) ).
fof(f_619_2,plain,
! [U_1475] :
( ( hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(U_1475)) = zero_zero_int
| number_number_of_nat(U_1475) = zero_zero_nat )
& ( hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(U_1475)) = one_one_int
| number_number_of_nat(U_1475) != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_619_1]) ).
fof(f_619_3,plain,
( ! [U_1477] :
( hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(U_1477)) = zero_zero_int
| number_number_of_nat(U_1477) = zero_zero_nat )
& ! [U_1476] :
( hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(U_1476)) = one_one_int
| number_number_of_nat(U_1476) != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_619_2]) ).
cnf(f_619_4,plain,
( hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(U_1476)) = one_one_int
| number_number_of_nat(U_1476) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_619_3]) ).
cnf(f_619_5,plain,
( hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(U_1477)) = zero_zero_int
| number_number_of_nat(U_1477) = zero_zero_nat ),
inference(clausify,[status(thm)],[f_619_3]) ).
fof(f_620_1,plain,
! [B,M,A] :
( A = B
| ~ hBOOL(hAPP_int_bool(zcong(A,B),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A))
| ~ is_int(A)
| ~ is_int(B) ),
inference(fof_nnf,[status(thm)],[fact_594_zcong__zless__imp__eq]) ).
fof(f_620_2,plain,
! [U_1480,U_1479,U_1478] :
( U_1478 = U_1480
| ~ hBOOL(hAPP_int_bool(zcong(U_1478,U_1480),U_1479))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1480),U_1479))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1480))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1478),U_1479))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1478))
| ~ is_int(U_1478)
| ~ is_int(U_1480) ),
inference(variable_rename,[status(thm)],[f_620_1]) ).
cnf(f_620_3,plain,
( U_1478 = U_1480
| ~ hBOOL(hAPP_int_bool(zcong(U_1478,U_1480),U_1479))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1480),U_1479))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1480))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1478),U_1479))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1478))
| ~ is_int(U_1478)
| ~ is_int(U_1480) ),
inference(clausify,[status(thm)],[f_620_2]) ).
fof(f_621_1,plain,
! [M,A] :
( A = zero_zero_int
| ~ hBOOL(hAPP_int_bool(zcong(A,zero_zero_int),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A))
| ~ is_int(A) ),
inference(fof_nnf,[status(thm)],[fact_595_zcong__zless__0]) ).
fof(f_621_2,plain,
! [U_1482,U_1481] :
( U_1481 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(zcong(U_1481,zero_zero_int),U_1482))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1481),U_1482))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1481))
| ~ is_int(U_1481) ),
inference(variable_rename,[status(thm)],[f_621_1]) ).
cnf(f_621_3,plain,
( U_1481 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(zcong(U_1481,zero_zero_int),U_1482))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1481),U_1482))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1481))
| ~ is_int(U_1481) ),
inference(clausify,[status(thm)],[f_621_2]) ).
fof(f_622_1,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(bit1(pls))))),
inference(fof_nnf,[status(thm)],[fact_596_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J]) ).
cnf(f_622_2,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(bit1(pls))))),
inference(clausify,[status(thm)],[f_622_1]) ).
fof(f_623_1,plain,
! [B,Q_1,R_1,B_48,Q_4,R_3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_4),Q_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_48),B))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_48))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B_48),Q_4)),R_3)),zero_zero_int))
| hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),Q_1)),R_1) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B_48),Q_4)),R_3) ),
inference(fof_nnf,[status(thm)],[fact_597_zdiv__mono2__neg__lemma]) ).
fof(f_623_2,plain,
! [U_1488,U_1487,U_1486,U_1485,U_1484,U_1483] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1484),U_1487))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1485),U_1488))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1485))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1483))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1486),U_1488))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1485),U_1484)),U_1483)),zero_zero_int))
| hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1488),U_1487)),U_1486) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1485),U_1484)),U_1483) ),
inference(variable_rename,[status(thm)],[f_623_1]) ).
cnf(f_623_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1484),U_1487))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1485),U_1488))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1485))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1483))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1486),U_1488))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1485),U_1484)),U_1483)),zero_zero_int))
| hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1488),U_1487)),U_1486) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1485),U_1484)),U_1483) ),
inference(clausify,[status(thm)],[f_623_2]) ).
fof(f_624_1,plain,
! [B,Q_4,R_3,Q_1,R_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q_4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),R_3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),R_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_1),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(B),Q_4)),R_3)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),Q_1)),R_1))) ),
inference(fof_nnf,[status(thm)],[fact_598_unique__quotient__lemma__neg]) ).
fof(f_624_2,plain,
! [U_1493,U_1492,U_1491,U_1490,U_1489] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1490),U_1492))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1493),U_1491))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1493),U_1489))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1489),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(U_1493),U_1492)),U_1491)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1493),U_1490)),U_1489))) ),
inference(variable_rename,[status(thm)],[f_624_1]) ).
cnf(f_624_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1490),U_1492))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1493),U_1491))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1493),U_1489))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1489),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(U_1493),U_1492)),U_1491)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1493),U_1490)),U_1489))) ),
inference(clausify,[status(thm)],[f_624_2]) ).
fof(f_625_1,plain,
! [B,Q_1,R_1,B_48,Q_4,R_3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q_4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_48),B))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_48))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_3),B_48))
| ~ 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(B_48),Q_4)),R_3)))
| hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),Q_1)),R_1) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B_48),Q_4)),R_3) ),
inference(fof_nnf,[status(thm)],[fact_599_zdiv__mono2__lemma]) ).
fof(f_625_2,plain,
! [U_1499,U_1498,U_1497,U_1496,U_1495,U_1494] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1498),U_1495))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1496),U_1499))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1496))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1497))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1494),U_1496))
| ~ 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(U_1496),U_1495)),U_1494)))
| hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1499),U_1498)),U_1497) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1496),U_1495)),U_1494) ),
inference(variable_rename,[status(thm)],[f_625_1]) ).
cnf(f_625_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1498),U_1495))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1496),U_1499))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1496))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1497))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1494),U_1496))
| ~ 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(U_1496),U_1495)),U_1494)))
| hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1499),U_1498)),U_1497) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1496),U_1495)),U_1494) ),
inference(clausify,[status(thm)],[f_625_2]) ).
fof(f_626_1,plain,
! [B,Q_4,R_3,Q_1,R_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_4),Q_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_3),B))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),Q_4)),R_3)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),Q_1)),R_1))) ),
inference(fof_nnf,[status(thm)],[fact_600_unique__quotient__lemma]) ).
fof(f_626_2,plain,
! [U_1504,U_1503,U_1502,U_1501,U_1500] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1503),U_1501))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1500),U_1504))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1502),U_1504))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1502))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1504),U_1503)),U_1502)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1504),U_1501)),U_1500))) ),
inference(variable_rename,[status(thm)],[f_626_1]) ).
cnf(f_626_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1503),U_1501))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1500),U_1504))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1502),U_1504))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1502))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1504),U_1503)),U_1502)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1504),U_1501)),U_1500))) ),
inference(clausify,[status(thm)],[f_626_2]) ).
fof(f_627_1,plain,
! [B_48,Q_4,R_3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_4),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_48))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B_48),Q_4)),R_3)),zero_zero_int)) ),
inference(fof_nnf,[status(thm)],[fact_601_q__neg__lemma]) ).
fof(f_627_2,plain,
! [U_1507,U_1506,U_1505] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1506),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1507))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1505))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1507),U_1506)),U_1505)),zero_zero_int)) ),
inference(variable_rename,[status(thm)],[f_627_1]) ).
cnf(f_627_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1506),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1507))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1505))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1507),U_1506)),U_1505)),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_627_2]) ).
fof(f_628_1,plain,
! [B_48,Q_4,R_3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Q_4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_48))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_3),B_48))
| ~ 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(B_48),Q_4)),R_3))) ),
inference(fof_nnf,[status(thm)],[fact_602_q__pos__lemma]) ).
fof(f_628_2,plain,
! [U_1510,U_1509,U_1508] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1509))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1510))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1508),U_1510))
| ~ 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(U_1510),U_1509)),U_1508))) ),
inference(variable_rename,[status(thm)],[f_628_1]) ).
cnf(f_628_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1509))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1510))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1508),U_1510))
| ~ 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(U_1510),U_1509)),U_1508))) ),
inference(clausify,[status(thm)],[f_628_2]) ).
fof(f_629_1,plain,
! [N_1,P_1,M] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),N_1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),hAPP_int_int(times_times_int(M),N_1)))
| ~ hBOOL(hAPP_int_bool(zprime,P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),M)) ),
inference(fof_nnf,[status(thm)],[fact_603_zprime__zdvd__zmult]) ).
fof(f_629_2,plain,
! [U_1513,U_1512,U_1511] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1512),U_1513))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1512),U_1511))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1512),hAPP_int_int(times_times_int(U_1511),U_1513)))
| ~ hBOOL(hAPP_int_bool(zprime,U_1512))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1511)) ),
inference(variable_rename,[status(thm)],[f_629_1]) ).
cnf(f_629_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1512),U_1513))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1512),U_1511))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1512),hAPP_int_int(times_times_int(U_1511),U_1513)))
| ~ hBOOL(hAPP_int_bool(zprime,U_1512))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1511)) ),
inference(clausify,[status(thm)],[f_629_2]) ).
fof(f_630_1,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(fof_nnf,[status(thm)],[fact_604__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096]) ).
cnf(f_630_2,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(clausify,[status(thm)],[f_630_1]) ).
fof(f_631_1,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(minus_minus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),number_number_of_int(min)))),
inference(fof_nnf,[status(thm)],[fact_605__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096]) ).
cnf(f_631_2,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(minus_minus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),number_number_of_int(min)))),
inference(clausify,[status(thm)],[f_631_1]) ).
fof(f_632_1,plain,
! [J_1,K_1,M] :
( hAPP_nat_int(power_power_int(number_number_of_int(min)),J_1) = hAPP_nat_int(power_power_int(number_number_of_int(min)),K_1)
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(number_number_of_int(min)),J_1),hAPP_nat_int(power_power_int(number_number_of_int(min)),K_1)),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),M)) ),
inference(fof_nnf,[status(thm)],[fact_606_neg__one__power__eq__mod__m]) ).
fof(f_632_2,plain,
! [U_1516,U_1515,U_1514] :
( hAPP_nat_int(power_power_int(number_number_of_int(min)),U_1516) = hAPP_nat_int(power_power_int(number_number_of_int(min)),U_1515)
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(number_number_of_int(min)),U_1516),hAPP_nat_int(power_power_int(number_number_of_int(min)),U_1515)),U_1514))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_1514)) ),
inference(variable_rename,[status(thm)],[f_632_1]) ).
cnf(f_632_3,plain,
( hAPP_nat_int(power_power_int(number_number_of_int(min)),U_1516) = hAPP_nat_int(power_power_int(number_number_of_int(min)),U_1515)
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(number_number_of_int(min)),U_1516),hAPP_nat_int(power_power_int(number_number_of_int(min)),U_1515)),U_1514))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_1514)) ),
inference(clausify,[status(thm)],[f_632_2]) ).
fof(f_633_1,plain,
! [X_1,P_1] :
( ~ hBOOL(hAPP_int_bool(zcong(X_1,one_one_int),P_1))
| ~ hBOOL(hAPP_int_bool(zcong(X_1,number_number_of_int(min)),P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_607_zcong__neg__1__impl__ne__1]) ).
fof(f_633_2,plain,
! [U_1518,U_1517] :
( ~ hBOOL(hAPP_int_bool(zcong(U_1518,one_one_int),U_1517))
| ~ hBOOL(hAPP_int_bool(zcong(U_1518,number_number_of_int(min)),U_1517))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_1517)) ),
inference(variable_rename,[status(thm)],[f_633_1]) ).
cnf(f_633_3,plain,
( ~ hBOOL(hAPP_int_bool(zcong(U_1518,one_one_int),U_1517))
| ~ hBOOL(hAPP_int_bool(zcong(U_1518,number_number_of_int(min)),U_1517))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_1517)) ),
inference(clausify,[status(thm)],[f_633_2]) ).
fof(f_634_1,plain,
! [M] :
( ~ hBOOL(hAPP_int_bool(zcong(one_one_int,number_number_of_int(min)),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),M)) ),
inference(fof_nnf,[status(thm)],[fact_608_one__not__neg__one__mod__m]) ).
fof(f_634_2,plain,
! [U_1519] :
( ~ hBOOL(hAPP_int_bool(zcong(one_one_int,number_number_of_int(min)),U_1519))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_1519)) ),
inference(variable_rename,[status(thm)],[f_634_1]) ).
cnf(f_634_3,plain,
( ~ hBOOL(hAPP_int_bool(zcong(one_one_int,number_number_of_int(min)),U_1519))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_1519)) ),
inference(clausify,[status(thm)],[f_634_2]) ).
fof(f_635_1,plain,
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),
inference(fof_nnf,[status(thm)],[fact_609__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096]) ).
cnf(f_635_2,plain,
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),
inference(clausify,[status(thm)],[f_635_1]) ).
fof(f_636_1,plain,
( 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
| 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(fof_nnf,[status(thm)],[fact_610__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N]) ).
cnf(f_636_2,plain,
( 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
| 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(clausify,[status(thm)],[f_636_1]) ).
fof(f_637_1,plain,
! [A,B,C] :
( A = hAPP_int_int(plus_plus_int(C),B)
| hAPP_int_int(minus_minus_int(A),B) != C
| ~ is_int(A) ),
inference(fof_nnf,[status(thm)],[fact_611_Int2_Oaux1]) ).
fof(f_637_2,plain,
! [U_1522,U_1521,U_1520] :
( U_1522 = hAPP_int_int(plus_plus_int(U_1520),U_1521)
| hAPP_int_int(minus_minus_int(U_1522),U_1521) != U_1520
| ~ is_int(U_1522) ),
inference(variable_rename,[status(thm)],[f_637_1]) ).
fof(f_637_3,plain,
! [U_1522] :
( ! [U_1521,U_1520] :
( U_1522 = hAPP_int_int(plus_plus_int(U_1520),U_1521)
| hAPP_int_int(minus_minus_int(U_1522),U_1521) != U_1520 )
| ~ is_int(U_1522) ),
inference(miniscope,[status(thm)],[f_637_2]) ).
cnf(f_637_4,plain,
( U_1522 = hAPP_int_int(plus_plus_int(U_1520),U_1521)
| hAPP_int_int(minus_minus_int(U_1522),U_1521) != U_1520
| ~ is_int(U_1522) ),
inference(clausify,[status(thm)],[f_637_3]) ).
fof(f_638_1,plain,
! [V_5,W_3] : number267125858f_real(hAPP_int_int(minus_minus_int(V_5),W_3)) = hAPP_real_real(minus_minus_real(number267125858f_real(V_5)),number267125858f_real(W_3)),
inference(fof_nnf,[status(thm)],[fact_612_number__of__diff]) ).
fof(f_638_2,plain,
! [U_1524,U_1523] : number267125858f_real(hAPP_int_int(minus_minus_int(U_1524),U_1523)) = hAPP_real_real(minus_minus_real(number267125858f_real(U_1524)),number267125858f_real(U_1523)),
inference(variable_rename,[status(thm)],[f_638_1]) ).
cnf(f_638_3,plain,
number267125858f_real(hAPP_int_int(minus_minus_int(U_1524),U_1523)) = hAPP_real_real(minus_minus_real(number267125858f_real(U_1524)),number267125858f_real(U_1523)),
inference(clausify,[status(thm)],[f_638_2]) ).
fof(f_639_1,plain,
! [V_5,W_3] : number_number_of_int(hAPP_int_int(minus_minus_int(V_5),W_3)) = hAPP_int_int(minus_minus_int(number_number_of_int(V_5)),number_number_of_int(W_3)),
inference(fof_nnf,[status(thm)],[fact_613_number__of__diff]) ).
fof(f_639_2,plain,
! [U_1526,U_1525] : number_number_of_int(hAPP_int_int(minus_minus_int(U_1526),U_1525)) = hAPP_int_int(minus_minus_int(number_number_of_int(U_1526)),number_number_of_int(U_1525)),
inference(variable_rename,[status(thm)],[f_639_1]) ).
cnf(f_639_3,plain,
number_number_of_int(hAPP_int_int(minus_minus_int(U_1526),U_1525)) = hAPP_int_int(minus_minus_int(number_number_of_int(U_1526)),number_number_of_int(U_1525)),
inference(clausify,[status(thm)],[f_639_2]) ).
fof(f_640_1,plain,
! [K_1] :
( hAPP_int_int(minus_minus_int(K_1),pls) = K_1
| ~ is_int(K_1) ),
inference(fof_nnf,[status(thm)],[fact_614_diff__bin__simps_I1_J]) ).
fof(f_640_2,plain,
! [U_1527] :
( hAPP_int_int(minus_minus_int(U_1527),pls) = U_1527
| ~ is_int(U_1527) ),
inference(variable_rename,[status(thm)],[f_640_1]) ).
cnf(f_640_3,plain,
( hAPP_int_int(minus_minus_int(U_1527),pls) = U_1527
| ~ is_int(U_1527) ),
inference(clausify,[status(thm)],[f_640_2]) ).
fof(f_641_1,plain,
! [K_1,L] : hAPP_int_int(minus_minus_int(bit0(K_1)),bit0(L)) = bit0(hAPP_int_int(minus_minus_int(K_1),L)),
inference(fof_nnf,[status(thm)],[fact_615_diff__bin__simps_I7_J]) ).
fof(f_641_2,plain,
! [U_1529,U_1528] : hAPP_int_int(minus_minus_int(bit0(U_1529)),bit0(U_1528)) = bit0(hAPP_int_int(minus_minus_int(U_1529),U_1528)),
inference(variable_rename,[status(thm)],[f_641_1]) ).
cnf(f_641_3,plain,
hAPP_int_int(minus_minus_int(bit0(U_1529)),bit0(U_1528)) = bit0(hAPP_int_int(minus_minus_int(U_1529),U_1528)),
inference(clausify,[status(thm)],[f_641_2]) ).
fof(f_642_1,plain,
! [W,Z1,Z2] : hAPP_int_int(times_times_int(W),hAPP_int_int(minus_minus_int(Z1),Z2)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(W),Z1)),hAPP_int_int(times_times_int(W),Z2)),
inference(fof_nnf,[status(thm)],[fact_616_zdiff__zmult__distrib2]) ).
fof(f_642_2,plain,
! [U_1532,U_1531,U_1530] : hAPP_int_int(times_times_int(U_1532),hAPP_int_int(minus_minus_int(U_1531),U_1530)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(U_1532),U_1531)),hAPP_int_int(times_times_int(U_1532),U_1530)),
inference(variable_rename,[status(thm)],[f_642_1]) ).
cnf(f_642_3,plain,
hAPP_int_int(times_times_int(U_1532),hAPP_int_int(minus_minus_int(U_1531),U_1530)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(U_1532),U_1531)),hAPP_int_int(times_times_int(U_1532),U_1530)),
inference(clausify,[status(thm)],[f_642_2]) ).
fof(f_643_1,plain,
! [Z1,Z2,W] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(Z1),Z2)),W) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(Z1),W)),hAPP_int_int(times_times_int(Z2),W)),
inference(fof_nnf,[status(thm)],[fact_617_zdiff__zmult__distrib]) ).
fof(f_643_2,plain,
! [U_1535,U_1534,U_1533] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(U_1535),U_1534)),U_1533) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(U_1535),U_1533)),hAPP_int_int(times_times_int(U_1534),U_1533)),
inference(variable_rename,[status(thm)],[f_643_1]) ).
cnf(f_643_3,plain,
hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(U_1535),U_1534)),U_1533) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(U_1535),U_1533)),hAPP_int_int(times_times_int(U_1534),U_1533)),
inference(clausify,[status(thm)],[f_643_2]) ).
fof(f_644_1,plain,
! [C,D_5,A,B,M] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(minus_minus_int(A),C),hAPP_int_int(minus_minus_int(B),D_5)),M))
| ~ hBOOL(hAPP_int_bool(zcong(C,D_5),M))
| ~ hBOOL(hAPP_int_bool(zcong(A,B),M)) ),
inference(fof_nnf,[status(thm)],[fact_618_zcong__zdiff]) ).
fof(f_644_2,plain,
! [U_1540,U_1539,U_1538,U_1537,U_1536] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(minus_minus_int(U_1538),U_1540),hAPP_int_int(minus_minus_int(U_1537),U_1539)),U_1536))
| ~ hBOOL(hAPP_int_bool(zcong(U_1540,U_1539),U_1536))
| ~ hBOOL(hAPP_int_bool(zcong(U_1538,U_1537),U_1536)) ),
inference(variable_rename,[status(thm)],[f_644_1]) ).
cnf(f_644_3,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(minus_minus_int(U_1538),U_1540),hAPP_int_int(minus_minus_int(U_1537),U_1539)),U_1536))
| ~ hBOOL(hAPP_int_bool(zcong(U_1540,U_1539),U_1536))
| ~ hBOOL(hAPP_int_bool(zcong(U_1538,U_1537),U_1536)) ),
inference(clausify,[status(thm)],[f_644_2]) ).
fof(f_645_1,plain,
! [K_1,M,N_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),N_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),hAPP_int_int(minus_minus_int(M),N_1))) ),
inference(fof_nnf,[status(thm)],[fact_619_zdvd__zdiffD]) ).
fof(f_645_2,plain,
! [U_1543,U_1542,U_1541] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1543),U_1542))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1543),U_1541))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1543),hAPP_int_int(minus_minus_int(U_1542),U_1541))) ),
inference(variable_rename,[status(thm)],[f_645_1]) ).
cnf(f_645_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1543),U_1542))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1543),U_1541))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1543),hAPP_int_int(minus_minus_int(U_1542),U_1541))) ),
inference(clausify,[status(thm)],[f_645_2]) ).
fof(f_646_1,plain,
! [V_4,B_47,C_26] : hAPP_real_real(times_times_real(number267125858f_real(V_4)),hAPP_real_real(minus_minus_real(B_47),C_26)) = hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(number267125858f_real(V_4)),B_47)),hAPP_real_real(times_times_real(number267125858f_real(V_4)),C_26)),
inference(fof_nnf,[status(thm)],[fact_620_right__diff__distrib__number__of]) ).
fof(f_646_2,plain,
! [U_1546,U_1545,U_1544] : hAPP_real_real(times_times_real(number267125858f_real(U_1546)),hAPP_real_real(minus_minus_real(U_1545),U_1544)) = hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(number267125858f_real(U_1546)),U_1545)),hAPP_real_real(times_times_real(number267125858f_real(U_1546)),U_1544)),
inference(variable_rename,[status(thm)],[f_646_1]) ).
cnf(f_646_3,plain,
hAPP_real_real(times_times_real(number267125858f_real(U_1546)),hAPP_real_real(minus_minus_real(U_1545),U_1544)) = hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(number267125858f_real(U_1546)),U_1545)),hAPP_real_real(times_times_real(number267125858f_real(U_1546)),U_1544)),
inference(clausify,[status(thm)],[f_646_2]) ).
fof(f_647_1,plain,
! [V_4,B_47,C_26] : hAPP_int_int(times_times_int(number_number_of_int(V_4)),hAPP_int_int(minus_minus_int(B_47),C_26)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(V_4)),B_47)),hAPP_int_int(times_times_int(number_number_of_int(V_4)),C_26)),
inference(fof_nnf,[status(thm)],[fact_621_right__diff__distrib__number__of]) ).
fof(f_647_2,plain,
! [U_1549,U_1548,U_1547] : hAPP_int_int(times_times_int(number_number_of_int(U_1549)),hAPP_int_int(minus_minus_int(U_1548),U_1547)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(U_1549)),U_1548)),hAPP_int_int(times_times_int(number_number_of_int(U_1549)),U_1547)),
inference(variable_rename,[status(thm)],[f_647_1]) ).
cnf(f_647_3,plain,
hAPP_int_int(times_times_int(number_number_of_int(U_1549)),hAPP_int_int(minus_minus_int(U_1548),U_1547)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(number_number_of_int(U_1549)),U_1548)),hAPP_int_int(times_times_int(number_number_of_int(U_1549)),U_1547)),
inference(clausify,[status(thm)],[f_647_2]) ).
fof(f_648_1,plain,
! [A_55,B_46,V_3] : hAPP_real_real(times_times_real(hAPP_real_real(minus_minus_real(A_55),B_46)),number267125858f_real(V_3)) = hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(A_55),number267125858f_real(V_3))),hAPP_real_real(times_times_real(B_46),number267125858f_real(V_3))),
inference(fof_nnf,[status(thm)],[fact_622_left__diff__distrib__number__of]) ).
fof(f_648_2,plain,
! [U_1552,U_1551,U_1550] : hAPP_real_real(times_times_real(hAPP_real_real(minus_minus_real(U_1552),U_1551)),number267125858f_real(U_1550)) = hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(U_1552),number267125858f_real(U_1550))),hAPP_real_real(times_times_real(U_1551),number267125858f_real(U_1550))),
inference(variable_rename,[status(thm)],[f_648_1]) ).
cnf(f_648_3,plain,
hAPP_real_real(times_times_real(hAPP_real_real(minus_minus_real(U_1552),U_1551)),number267125858f_real(U_1550)) = hAPP_real_real(minus_minus_real(hAPP_real_real(times_times_real(U_1552),number267125858f_real(U_1550))),hAPP_real_real(times_times_real(U_1551),number267125858f_real(U_1550))),
inference(clausify,[status(thm)],[f_648_2]) ).
fof(f_649_1,plain,
! [A_55,B_46,V_3] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(A_55),B_46)),number_number_of_int(V_3)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(A_55),number_number_of_int(V_3))),hAPP_int_int(times_times_int(B_46),number_number_of_int(V_3))),
inference(fof_nnf,[status(thm)],[fact_623_left__diff__distrib__number__of]) ).
fof(f_649_2,plain,
! [U_1555,U_1554,U_1553] : hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(U_1555),U_1554)),number_number_of_int(U_1553)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(U_1555),number_number_of_int(U_1553))),hAPP_int_int(times_times_int(U_1554),number_number_of_int(U_1553))),
inference(variable_rename,[status(thm)],[f_649_1]) ).
cnf(f_649_3,plain,
hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(U_1555),U_1554)),number_number_of_int(U_1553)) = hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(U_1555),number_number_of_int(U_1553))),hAPP_int_int(times_times_int(U_1554),number_number_of_int(U_1553))),
inference(clausify,[status(thm)],[f_649_2]) ).
fof(f_650_1,plain,
! [K_1,L] : hAPP_int_int(minus_minus_int(bit1(K_1)),bit0(L)) = bit1(hAPP_int_int(minus_minus_int(K_1),L)),
inference(fof_nnf,[status(thm)],[fact_624_diff__bin__simps_I9_J]) ).
fof(f_650_2,plain,
! [U_1557,U_1556] : hAPP_int_int(minus_minus_int(bit1(U_1557)),bit0(U_1556)) = bit1(hAPP_int_int(minus_minus_int(U_1557),U_1556)),
inference(variable_rename,[status(thm)],[f_650_1]) ).
cnf(f_650_3,plain,
hAPP_int_int(minus_minus_int(bit1(U_1557)),bit0(U_1556)) = bit1(hAPP_int_int(minus_minus_int(U_1557),U_1556)),
inference(clausify,[status(thm)],[f_650_2]) ).
fof(f_651_1,plain,
! [K_1,L] : hAPP_int_int(minus_minus_int(bit1(K_1)),bit1(L)) = bit0(hAPP_int_int(minus_minus_int(K_1),L)),
inference(fof_nnf,[status(thm)],[fact_625_diff__bin__simps_I10_J]) ).
fof(f_651_2,plain,
! [U_1559,U_1558] : hAPP_int_int(minus_minus_int(bit1(U_1559)),bit1(U_1558)) = bit0(hAPP_int_int(minus_minus_int(U_1559),U_1558)),
inference(variable_rename,[status(thm)],[f_651_1]) ).
cnf(f_651_3,plain,
hAPP_int_int(minus_minus_int(bit1(U_1559)),bit1(U_1558)) = bit0(hAPP_int_int(minus_minus_int(U_1559),U_1558)),
inference(clausify,[status(thm)],[f_651_2]) ).
fof(f_652_1,plain,
! [L] : hAPP_int_int(minus_minus_int(pls),bit0(L)) = bit0(hAPP_int_int(minus_minus_int(pls),L)),
inference(fof_nnf,[status(thm)],[fact_626_diff__bin__simps_I3_J]) ).
fof(f_652_2,plain,
! [U_1560] : hAPP_int_int(minus_minus_int(pls),bit0(U_1560)) = bit0(hAPP_int_int(minus_minus_int(pls),U_1560)),
inference(variable_rename,[status(thm)],[f_652_1]) ).
cnf(f_652_3,plain,
hAPP_int_int(minus_minus_int(pls),bit0(U_1560)) = bit0(hAPP_int_int(minus_minus_int(pls),U_1560)),
inference(clausify,[status(thm)],[f_652_2]) ).
fof(f_653_1,plain,
! [K,L_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(K),L_1)),zero_zero_int)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(K),L_1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_627_less__bin__lemma]) ).
fof(f_653_2,plain,
! [U_1562,U_1561] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1562),U_1561))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(U_1562),U_1561)),zero_zero_int)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(U_1562),U_1561)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1562),U_1561)) ) ),
inference(variable_rename,[status(thm)],[f_653_1]) ).
fof(f_653_3,plain,
( ! [U_1566,U_1564] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1566),U_1564))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(U_1566),U_1564)),zero_zero_int)) )
& ! [U_1565,U_1563] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(U_1565),U_1563)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1565),U_1563)) ) ),
inference(miniscope,[status(thm)],[f_653_2]) ).
cnf(f_653_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(U_1565),U_1563)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1565),U_1563)) ),
inference(clausify,[status(thm)],[f_653_3]) ).
cnf(f_653_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1566),U_1564))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(minus_minus_int(U_1566),U_1564)),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_653_3]) ).
fof(f_654_1,plain,
! [A,R_1,B,M,C,D_5,N_1] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(A),hAPP_int_int(times_times_int(R_1),B))),M)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(C),hAPP_int_int(times_times_int(R_1),D_5))),N_1)) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A),M)),hAPP_int_int(times_times_int(C),N_1))),hAPP_int_int(times_times_int(R_1),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),M)),hAPP_int_int(times_times_int(D_5),N_1)))),
inference(fof_nnf,[status(thm)],[fact_628_xzgcda__linear__aux1]) ).
fof(f_654_2,plain,
! [U_1573,U_1572,U_1571,U_1570,U_1569,U_1568,U_1567] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(U_1573),hAPP_int_int(times_times_int(U_1572),U_1571))),U_1570)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(U_1569),hAPP_int_int(times_times_int(U_1572),U_1568))),U_1567)) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1573),U_1570)),hAPP_int_int(times_times_int(U_1569),U_1567))),hAPP_int_int(times_times_int(U_1572),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1571),U_1570)),hAPP_int_int(times_times_int(U_1568),U_1567)))),
inference(variable_rename,[status(thm)],[f_654_1]) ).
cnf(f_654_3,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(U_1573),hAPP_int_int(times_times_int(U_1572),U_1571))),U_1570)),hAPP_int_int(times_times_int(hAPP_int_int(minus_minus_int(U_1569),hAPP_int_int(times_times_int(U_1572),U_1568))),U_1567)) = hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1573),U_1570)),hAPP_int_int(times_times_int(U_1569),U_1567))),hAPP_int_int(times_times_int(U_1572),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1571),U_1570)),hAPP_int_int(times_times_int(U_1568),U_1567)))),
inference(clausify,[status(thm)],[f_654_2]) ).
fof(f_655_1,plain,
! [A_2,B_2,Ma] :
( ( hBOOL(hAPP_int_bool(zcong(A_2,B_2),Ma))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Ma),hAPP_int_int(minus_minus_int(A_2),B_2))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Ma),hAPP_int_int(minus_minus_int(A_2),B_2)))
| ~ hBOOL(hAPP_int_bool(zcong(A_2,B_2),Ma)) ) ),
inference(fof_nnf,[status(thm)],[fact_629_zcong__def]) ).
fof(f_655_2,plain,
! [U_1576,U_1575,U_1574] :
( ( hBOOL(hAPP_int_bool(zcong(U_1576,U_1575),U_1574))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1574),hAPP_int_int(minus_minus_int(U_1576),U_1575))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1574),hAPP_int_int(minus_minus_int(U_1576),U_1575)))
| ~ hBOOL(hAPP_int_bool(zcong(U_1576,U_1575),U_1574)) ) ),
inference(variable_rename,[status(thm)],[f_655_1]) ).
fof(f_655_3,plain,
( ! [U_1582,U_1580,U_1578] :
( hBOOL(hAPP_int_bool(zcong(U_1582,U_1580),U_1578))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1578),hAPP_int_int(minus_minus_int(U_1582),U_1580))) )
& ! [U_1581,U_1579,U_1577] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1577),hAPP_int_int(minus_minus_int(U_1581),U_1579)))
| ~ hBOOL(hAPP_int_bool(zcong(U_1581,U_1579),U_1577)) ) ),
inference(miniscope,[status(thm)],[f_655_2]) ).
cnf(f_655_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1577),hAPP_int_int(minus_minus_int(U_1581),U_1579)))
| ~ hBOOL(hAPP_int_bool(zcong(U_1581,U_1579),U_1577)) ),
inference(clausify,[status(thm)],[f_655_3]) ).
cnf(f_655_5,plain,
( hBOOL(hAPP_int_bool(zcong(U_1582,U_1580),U_1578))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1578),hAPP_int_int(minus_minus_int(U_1582),U_1580))) ),
inference(clausify,[status(thm)],[f_655_3]) ).
fof(f_656_1,plain,
! [V_2,W_2,C_25] : hAPP_real_real(plus_plus_real(number267125858f_real(V_2)),hAPP_real_real(minus_minus_real(number267125858f_real(W_2)),C_25)) = hAPP_real_real(minus_minus_real(number267125858f_real(hAPP_int_int(plus_plus_int(V_2),W_2))),C_25),
inference(fof_nnf,[status(thm)],[fact_630_add__number__of__diff1]) ).
fof(f_656_2,plain,
! [U_1585,U_1584,U_1583] : hAPP_real_real(plus_plus_real(number267125858f_real(U_1585)),hAPP_real_real(minus_minus_real(number267125858f_real(U_1584)),U_1583)) = hAPP_real_real(minus_minus_real(number267125858f_real(hAPP_int_int(plus_plus_int(U_1585),U_1584))),U_1583),
inference(variable_rename,[status(thm)],[f_656_1]) ).
cnf(f_656_3,plain,
hAPP_real_real(plus_plus_real(number267125858f_real(U_1585)),hAPP_real_real(minus_minus_real(number267125858f_real(U_1584)),U_1583)) = hAPP_real_real(minus_minus_real(number267125858f_real(hAPP_int_int(plus_plus_int(U_1585),U_1584))),U_1583),
inference(clausify,[status(thm)],[f_656_2]) ).
fof(f_657_1,plain,
! [V_2,W_2,C_25] : hAPP_int_int(plus_plus_int(number_number_of_int(V_2)),hAPP_int_int(minus_minus_int(number_number_of_int(W_2)),C_25)) = hAPP_int_int(minus_minus_int(number_number_of_int(hAPP_int_int(plus_plus_int(V_2),W_2))),C_25),
inference(fof_nnf,[status(thm)],[fact_631_add__number__of__diff1]) ).
fof(f_657_2,plain,
! [U_1588,U_1587,U_1586] : hAPP_int_int(plus_plus_int(number_number_of_int(U_1588)),hAPP_int_int(minus_minus_int(number_number_of_int(U_1587)),U_1586)) = hAPP_int_int(minus_minus_int(number_number_of_int(hAPP_int_int(plus_plus_int(U_1588),U_1587))),U_1586),
inference(variable_rename,[status(thm)],[f_657_1]) ).
cnf(f_657_3,plain,
hAPP_int_int(plus_plus_int(number_number_of_int(U_1588)),hAPP_int_int(minus_minus_int(number_number_of_int(U_1587)),U_1586)) = hAPP_int_int(minus_minus_int(number_number_of_int(hAPP_int_int(plus_plus_int(U_1588),U_1587))),U_1586),
inference(clausify,[status(thm)],[f_657_2]) ).
fof(f_658_1,plain,
! [A,X_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),hAPP_int_int(minus_minus_int(A),one_one_int)))
| X_1 = hAPP_int_int(minus_minus_int(A),one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),A))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X_1))
| ~ is_int(X_1) ),
inference(fof_nnf,[status(thm)],[fact_632_Euler_Oaux1]) ).
fof(f_658_2,plain,
! [U_1590,U_1589] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1589),hAPP_int_int(minus_minus_int(U_1590),one_one_int)))
| U_1589 = hAPP_int_int(minus_minus_int(U_1590),one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1589),U_1590))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1589))
| ~ is_int(U_1589) ),
inference(variable_rename,[status(thm)],[f_658_1]) ).
cnf(f_658_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1589),hAPP_int_int(minus_minus_int(U_1590),one_one_int)))
| U_1589 = hAPP_int_int(minus_minus_int(U_1590),one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1589),U_1590))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1589))
| ~ is_int(U_1589) ),
inference(clausify,[status(thm)],[f_658_2]) ).
fof(f_659_1,plain,
! [W_1,Z_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),hAPP_int_int(minus_minus_int(Z_1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_1)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),hAPP_int_int(minus_minus_int(Z_1),one_one_int))) ) ),
inference(fof_nnf,[status(thm)],[fact_633_zle__diff1__eq]) ).
fof(f_659_2,plain,
! [U_1592,U_1591] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1592),hAPP_int_int(minus_minus_int(U_1591),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1592),U_1591)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1592),U_1591))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1592),hAPP_int_int(minus_minus_int(U_1591),one_one_int))) ) ),
inference(variable_rename,[status(thm)],[f_659_1]) ).
fof(f_659_3,plain,
( ! [U_1596,U_1594] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1596),hAPP_int_int(minus_minus_int(U_1594),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1596),U_1594)) )
& ! [U_1595,U_1593] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1595),U_1593))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1595),hAPP_int_int(minus_minus_int(U_1593),one_one_int))) ) ),
inference(miniscope,[status(thm)],[f_659_2]) ).
cnf(f_659_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1595),U_1593))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1595),hAPP_int_int(minus_minus_int(U_1593),one_one_int))) ),
inference(clausify,[status(thm)],[f_659_3]) ).
cnf(f_659_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1596),hAPP_int_int(minus_minus_int(U_1594),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1596),U_1594)) ),
inference(clausify,[status(thm)],[f_659_3]) ).
fof(f_660_1,plain,
! [L] : hAPP_int_int(minus_minus_int(pls),bit1(L)) = bit1(hAPP_int_int(minus_minus_int(min),L)),
inference(fof_nnf,[status(thm)],[fact_634_diff__bin__simps_I4_J]) ).
fof(f_660_2,plain,
! [U_1597] : hAPP_int_int(minus_minus_int(pls),bit1(U_1597)) = bit1(hAPP_int_int(minus_minus_int(min),U_1597)),
inference(variable_rename,[status(thm)],[f_660_1]) ).
cnf(f_660_3,plain,
hAPP_int_int(minus_minus_int(pls),bit1(U_1597)) = bit1(hAPP_int_int(minus_minus_int(min),U_1597)),
inference(clausify,[status(thm)],[f_660_2]) ).
fof(f_661_1,plain,
! [L] : hAPP_int_int(minus_minus_int(min),bit0(L)) = bit1(hAPP_int_int(minus_minus_int(min),L)),
inference(fof_nnf,[status(thm)],[fact_635_diff__bin__simps_I5_J]) ).
fof(f_661_2,plain,
! [U_1598] : hAPP_int_int(minus_minus_int(min),bit0(U_1598)) = bit1(hAPP_int_int(minus_minus_int(min),U_1598)),
inference(variable_rename,[status(thm)],[f_661_1]) ).
cnf(f_661_3,plain,
hAPP_int_int(minus_minus_int(min),bit0(U_1598)) = bit1(hAPP_int_int(minus_minus_int(min),U_1598)),
inference(clausify,[status(thm)],[f_661_2]) ).
fof(f_662_1,plain,
! [L] : hAPP_int_int(minus_minus_int(min),bit1(L)) = bit0(hAPP_int_int(minus_minus_int(min),L)),
inference(fof_nnf,[status(thm)],[fact_636_diff__bin__simps_I6_J]) ).
fof(f_662_2,plain,
! [U_1599] : hAPP_int_int(minus_minus_int(min),bit1(U_1599)) = bit0(hAPP_int_int(minus_minus_int(min),U_1599)),
inference(variable_rename,[status(thm)],[f_662_1]) ).
cnf(f_662_3,plain,
hAPP_int_int(minus_minus_int(min),bit1(U_1599)) = bit0(hAPP_int_int(minus_minus_int(min),U_1599)),
inference(clausify,[status(thm)],[f_662_2]) ).
fof(f_663_1,plain,
! [A_2,P_3] :
( ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A_2),hAPP_int_int(minus_minus_int(P_3),one_one_int)),one_one_int),P_3))
| ~ hBOOL(hAPP_int_bool(zcong(A_2,hAPP_int_int(minus_minus_int(P_3),one_one_int)),P_3)) )
& ( hBOOL(hAPP_int_bool(zcong(A_2,hAPP_int_int(minus_minus_int(P_3),one_one_int)),P_3))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A_2),hAPP_int_int(minus_minus_int(P_3),one_one_int)),one_one_int),P_3)) ) ),
inference(fof_nnf,[status(thm)],[fact_637_inv__not__p__minus__1__aux]) ).
fof(f_663_2,plain,
! [U_1601,U_1600] :
( ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1601),hAPP_int_int(minus_minus_int(U_1600),one_one_int)),one_one_int),U_1600))
| ~ hBOOL(hAPP_int_bool(zcong(U_1601,hAPP_int_int(minus_minus_int(U_1600),one_one_int)),U_1600)) )
& ( hBOOL(hAPP_int_bool(zcong(U_1601,hAPP_int_int(minus_minus_int(U_1600),one_one_int)),U_1600))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1601),hAPP_int_int(minus_minus_int(U_1600),one_one_int)),one_one_int),U_1600)) ) ),
inference(variable_rename,[status(thm)],[f_663_1]) ).
fof(f_663_3,plain,
( ! [U_1605,U_1603] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1605),hAPP_int_int(minus_minus_int(U_1603),one_one_int)),one_one_int),U_1603))
| ~ hBOOL(hAPP_int_bool(zcong(U_1605,hAPP_int_int(minus_minus_int(U_1603),one_one_int)),U_1603)) )
& ! [U_1604,U_1602] :
( hBOOL(hAPP_int_bool(zcong(U_1604,hAPP_int_int(minus_minus_int(U_1602),one_one_int)),U_1602))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1604),hAPP_int_int(minus_minus_int(U_1602),one_one_int)),one_one_int),U_1602)) ) ),
inference(miniscope,[status(thm)],[f_663_2]) ).
cnf(f_663_4,plain,
( hBOOL(hAPP_int_bool(zcong(U_1604,hAPP_int_int(minus_minus_int(U_1602),one_one_int)),U_1602))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1604),hAPP_int_int(minus_minus_int(U_1602),one_one_int)),one_one_int),U_1602)) ),
inference(clausify,[status(thm)],[f_663_3]) ).
cnf(f_663_5,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1605),hAPP_int_int(minus_minus_int(U_1603),one_one_int)),one_one_int),U_1603))
| ~ hBOOL(hAPP_int_bool(zcong(U_1605,hAPP_int_int(minus_minus_int(U_1603),one_one_int)),U_1603)) ),
inference(clausify,[status(thm)],[f_663_3]) ).
fof(f_664_1,plain,
! [D_5,C,A,B,M] :
( hBOOL(hAPP_int_bool(zcong(A,D_5),M))
| ~ hBOOL(hAPP_int_bool(zcong(C,D_5),M))
| B != C
| ~ hBOOL(hAPP_int_bool(zcong(A,B),M)) ),
inference(fof_nnf,[status(thm)],[fact_638_zcong__eq__trans]) ).
fof(f_664_2,plain,
! [U_1610,U_1609,U_1608,U_1607,U_1606] :
( hBOOL(hAPP_int_bool(zcong(U_1608,U_1610),U_1606))
| ~ hBOOL(hAPP_int_bool(zcong(U_1609,U_1610),U_1606))
| U_1607 != U_1609
| ~ hBOOL(hAPP_int_bool(zcong(U_1608,U_1607),U_1606)) ),
inference(variable_rename,[status(thm)],[f_664_1]) ).
cnf(f_664_3,plain,
( hBOOL(hAPP_int_bool(zcong(U_1608,U_1610),U_1606))
| ~ hBOOL(hAPP_int_bool(zcong(U_1609,U_1610),U_1606))
| U_1607 != U_1609
| ~ hBOOL(hAPP_int_bool(zcong(U_1608,U_1607),U_1606)) ),
inference(clausify,[status(thm)],[f_664_2]) ).
fof(f_665_1,plain,
! [A,B,P_1,Q_1] : hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(product_Pair_int_int(A,B))),twoSqu1241645765sum2sq(product_Pair_int_int(P_1,Q_1))) = twoSqu1241645765sum2sq(product_Pair_int_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A),P_1)),hAPP_int_int(times_times_int(B),Q_1)),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(A),Q_1)),hAPP_int_int(times_times_int(B),P_1)))),
inference(fof_nnf,[status(thm)],[fact_639_mult__sum2sq]) ).
fof(f_665_2,plain,
! [U_1614,U_1613,U_1612,U_1611] : hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(product_Pair_int_int(U_1614,U_1613))),twoSqu1241645765sum2sq(product_Pair_int_int(U_1612,U_1611))) = twoSqu1241645765sum2sq(product_Pair_int_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1614),U_1612)),hAPP_int_int(times_times_int(U_1613),U_1611)),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(U_1614),U_1611)),hAPP_int_int(times_times_int(U_1613),U_1612)))),
inference(variable_rename,[status(thm)],[f_665_1]) ).
cnf(f_665_3,plain,
hAPP_int_int(times_times_int(twoSqu1241645765sum2sq(product_Pair_int_int(U_1614,U_1613))),twoSqu1241645765sum2sq(product_Pair_int_int(U_1612,U_1611))) = twoSqu1241645765sum2sq(product_Pair_int_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1614),U_1612)),hAPP_int_int(times_times_int(U_1613),U_1611)),hAPP_int_int(minus_minus_int(hAPP_int_int(times_times_int(U_1614),U_1611)),hAPP_int_int(times_times_int(U_1613),U_1612)))),
inference(clausify,[status(thm)],[f_665_2]) ).
fof(f_666_1,plain,
! [A,P_1] :
( hBOOL(hAPP_int_bool(zcong(A,hAPP_int_int(minus_minus_int(P_1),one_one_int)),P_1))
| hBOOL(hAPP_int_bool(zcong(A,one_one_int),P_1))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),A),one_one_int),P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A))
| ~ hBOOL(hAPP_int_bool(zprime,P_1)) ),
inference(fof_nnf,[status(thm)],[fact_640_zcong__square]) ).
fof(f_666_2,plain,
! [U_1616,U_1615] :
( hBOOL(hAPP_int_bool(zcong(U_1616,hAPP_int_int(minus_minus_int(U_1615),one_one_int)),U_1615))
| hBOOL(hAPP_int_bool(zcong(U_1616,one_one_int),U_1615))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1616),U_1616),one_one_int),U_1615))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1616))
| ~ hBOOL(hAPP_int_bool(zprime,U_1615)) ),
inference(variable_rename,[status(thm)],[f_666_1]) ).
cnf(f_666_3,plain,
( hBOOL(hAPP_int_bool(zcong(U_1616,hAPP_int_int(minus_minus_int(U_1615),one_one_int)),U_1615))
| hBOOL(hAPP_int_bool(zcong(U_1616,one_one_int),U_1615))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1616),U_1616),one_one_int),U_1615))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1616))
| ~ hBOOL(hAPP_int_bool(zprime,U_1615)) ),
inference(clausify,[status(thm)],[f_666_2]) ).
fof(f_667_1,plain,
! [A,P_1] :
( A = hAPP_int_int(minus_minus_int(P_1),one_one_int)
| A = one_one_int
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),A),one_one_int),P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A))
| ~ hBOOL(hAPP_int_bool(zprime,P_1))
| ~ is_int(A) ),
inference(fof_nnf,[status(thm)],[fact_641_zcong__square__zless]) ).
fof(f_667_2,plain,
! [U_1618,U_1617] :
( U_1618 = hAPP_int_int(minus_minus_int(U_1617),one_one_int)
| U_1618 = one_one_int
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1618),U_1618),one_one_int),U_1617))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1618),U_1617))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1618))
| ~ hBOOL(hAPP_int_bool(zprime,U_1617))
| ~ is_int(U_1618) ),
inference(variable_rename,[status(thm)],[f_667_1]) ).
fof(f_667_3,plain,
! [U_1618] :
( ! [U_1617] :
( U_1618 = hAPP_int_int(minus_minus_int(U_1617),one_one_int)
| U_1618 = one_one_int
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1618),U_1618),one_one_int),U_1617))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1618),U_1617))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1618))
| ~ hBOOL(hAPP_int_bool(zprime,U_1617)) )
| ~ is_int(U_1618) ),
inference(miniscope,[status(thm)],[f_667_2]) ).
cnf(f_667_4,plain,
( U_1618 = hAPP_int_int(minus_minus_int(U_1617),one_one_int)
| U_1618 = one_one_int
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1618),U_1618),one_one_int),U_1617))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1618),U_1617))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1618))
| ~ hBOOL(hAPP_int_bool(zprime,U_1617))
| ~ is_int(U_1618) ),
inference(clausify,[status(thm)],[f_667_3]) ).
fof(f_668_1,plain,
! [A,B] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A),B)),hAPP_int_int(minus_minus_int(A),B)) = hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(A),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(B),number_number_of_nat(bit0(bit1(pls))))),
inference(fof_nnf,[status(thm)],[fact_642_zspecial__product]) ).
fof(f_668_2,plain,
! [U_1620,U_1619] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(U_1620),U_1619)),hAPP_int_int(minus_minus_int(U_1620),U_1619)) = hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(U_1620),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1619),number_number_of_nat(bit0(bit1(pls))))),
inference(variable_rename,[status(thm)],[f_668_1]) ).
cnf(f_668_3,plain,
hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(U_1620),U_1619)),hAPP_int_int(minus_minus_int(U_1620),U_1619)) = hAPP_int_int(minus_minus_int(hAPP_nat_int(power_power_int(U_1620),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1619),number_number_of_nat(bit0(bit1(pls))))),
inference(clausify,[status(thm)],[f_668_2]) ).
fof(f_669_1,plain,
! [M] : hBOOL(hAPP_int_bool(zcong(M,zero_zero_int),M)),
inference(fof_nnf,[status(thm)],[fact_643_zcong__id]) ).
fof(f_669_2,plain,
! [U_1621] : hBOOL(hAPP_int_bool(zcong(U_1621,zero_zero_int),U_1621)),
inference(variable_rename,[status(thm)],[f_669_1]) ).
cnf(f_669_3,plain,
hBOOL(hAPP_int_bool(zcong(U_1621,zero_zero_int),U_1621)),
inference(clausify,[status(thm)],[f_669_2]) ).
fof(f_670_1,plain,
! [C_2,D,A_2,B_2,Ma] :
( ( ( hBOOL(hAPP_int_bool(zcong(C_2,hAPP_int_int(times_times_int(A_2),D)),Ma))
| ~ hBOOL(hAPP_int_bool(zcong(C_2,hAPP_int_int(times_times_int(B_2),D)),Ma)) )
& ( hBOOL(hAPP_int_bool(zcong(C_2,hAPP_int_int(times_times_int(B_2),D)),Ma))
| ~ hBOOL(hAPP_int_bool(zcong(C_2,hAPP_int_int(times_times_int(A_2),D)),Ma)) ) )
| ~ hBOOL(hAPP_int_bool(zcong(A_2,B_2),Ma)) ),
inference(fof_nnf,[status(thm)],[fact_644_zcong__zmult__prop1]) ).
fof(f_670_2,plain,
! [U_1626,U_1625,U_1624,U_1623,U_1622] :
( ( ( hBOOL(hAPP_int_bool(zcong(U_1626,hAPP_int_int(times_times_int(U_1624),U_1625)),U_1622))
| ~ hBOOL(hAPP_int_bool(zcong(U_1626,hAPP_int_int(times_times_int(U_1623),U_1625)),U_1622)) )
& ( hBOOL(hAPP_int_bool(zcong(U_1626,hAPP_int_int(times_times_int(U_1623),U_1625)),U_1622))
| ~ hBOOL(hAPP_int_bool(zcong(U_1626,hAPP_int_int(times_times_int(U_1624),U_1625)),U_1622)) ) )
| ~ hBOOL(hAPP_int_bool(zcong(U_1624,U_1623),U_1622)) ),
inference(variable_rename,[status(thm)],[f_670_1]) ).
cnf(f_670_3,plain,
( hBOOL(hAPP_int_bool(zcong(U_1626,hAPP_int_int(times_times_int(U_1623),U_1625)),U_1622))
| ~ hBOOL(hAPP_int_bool(zcong(U_1626,hAPP_int_int(times_times_int(U_1624),U_1625)),U_1622))
| ~ hBOOL(hAPP_int_bool(zcong(U_1624,U_1623),U_1622)) ),
inference(clausify,[status(thm)],[f_670_2]) ).
cnf(f_670_4,plain,
( hBOOL(hAPP_int_bool(zcong(U_1626,hAPP_int_int(times_times_int(U_1624),U_1625)),U_1622))
| ~ hBOOL(hAPP_int_bool(zcong(U_1626,hAPP_int_int(times_times_int(U_1623),U_1625)),U_1622))
| ~ hBOOL(hAPP_int_bool(zcong(U_1624,U_1623),U_1622)) ),
inference(clausify,[status(thm)],[f_670_2]) ).
fof(f_671_1,plain,
! [C_2,D,A_2,B_2,Ma] :
( ( ( hBOOL(hAPP_int_bool(zcong(C_2,hAPP_int_int(times_times_int(D),A_2)),Ma))
| ~ hBOOL(hAPP_int_bool(zcong(C_2,hAPP_int_int(times_times_int(D),B_2)),Ma)) )
& ( hBOOL(hAPP_int_bool(zcong(C_2,hAPP_int_int(times_times_int(D),B_2)),Ma))
| ~ hBOOL(hAPP_int_bool(zcong(C_2,hAPP_int_int(times_times_int(D),A_2)),Ma)) ) )
| ~ hBOOL(hAPP_int_bool(zcong(A_2,B_2),Ma)) ),
inference(fof_nnf,[status(thm)],[fact_645_zcong__zmult__prop2]) ).
fof(f_671_2,plain,
! [U_1631,U_1630,U_1629,U_1628,U_1627] :
( ( ( hBOOL(hAPP_int_bool(zcong(U_1631,hAPP_int_int(times_times_int(U_1630),U_1629)),U_1627))
| ~ hBOOL(hAPP_int_bool(zcong(U_1631,hAPP_int_int(times_times_int(U_1630),U_1628)),U_1627)) )
& ( hBOOL(hAPP_int_bool(zcong(U_1631,hAPP_int_int(times_times_int(U_1630),U_1628)),U_1627))
| ~ hBOOL(hAPP_int_bool(zcong(U_1631,hAPP_int_int(times_times_int(U_1630),U_1629)),U_1627)) ) )
| ~ hBOOL(hAPP_int_bool(zcong(U_1629,U_1628),U_1627)) ),
inference(variable_rename,[status(thm)],[f_671_1]) ).
cnf(f_671_3,plain,
( hBOOL(hAPP_int_bool(zcong(U_1631,hAPP_int_int(times_times_int(U_1630),U_1628)),U_1627))
| ~ hBOOL(hAPP_int_bool(zcong(U_1631,hAPP_int_int(times_times_int(U_1630),U_1629)),U_1627))
| ~ hBOOL(hAPP_int_bool(zcong(U_1629,U_1628),U_1627)) ),
inference(clausify,[status(thm)],[f_671_2]) ).
cnf(f_671_4,plain,
( hBOOL(hAPP_int_bool(zcong(U_1631,hAPP_int_int(times_times_int(U_1630),U_1629)),U_1627))
| ~ hBOOL(hAPP_int_bool(zcong(U_1631,hAPP_int_int(times_times_int(U_1630),U_1628)),U_1627))
| ~ hBOOL(hAPP_int_bool(zcong(U_1629,U_1628),U_1627)) ),
inference(clausify,[status(thm)],[f_671_2]) ).
fof(f_672_1,plain,
! [C,A,B,M] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(A),C),hAPP_int_int(plus_plus_int(B),C)),M))
| ~ hBOOL(hAPP_int_bool(zcong(A,B),M)) ),
inference(fof_nnf,[status(thm)],[fact_646_zcong__shift]) ).
fof(f_672_2,plain,
! [U_1635,U_1634,U_1633,U_1632] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(U_1634),U_1635),hAPP_int_int(plus_plus_int(U_1633),U_1635)),U_1632))
| ~ hBOOL(hAPP_int_bool(zcong(U_1634,U_1633),U_1632)) ),
inference(variable_rename,[status(thm)],[f_672_1]) ).
cnf(f_672_3,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(plus_plus_int(U_1634),U_1635),hAPP_int_int(plus_plus_int(U_1633),U_1635)),U_1632))
| ~ hBOOL(hAPP_int_bool(zcong(U_1634,U_1633),U_1632)) ),
inference(clausify,[status(thm)],[f_672_2]) ).
fof(f_673_1,plain,
! [Z,X_1,Y_1,M] :
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X_1),Z),hAPP_nat_int(power_power_int(Y_1),Z)),M))
| ~ hBOOL(hAPP_int_bool(zcong(X_1,Y_1),M)) ),
inference(fof_nnf,[status(thm)],[fact_647_zcong__zpower]) ).
fof(f_673_2,plain,
! [U_1639,U_1638,U_1637,U_1636] :
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(U_1638),U_1639),hAPP_nat_int(power_power_int(U_1637),U_1639)),U_1636))
| ~ hBOOL(hAPP_int_bool(zcong(U_1638,U_1637),U_1636)) ),
inference(variable_rename,[status(thm)],[f_673_1]) ).
cnf(f_673_3,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(U_1638),U_1639),hAPP_nat_int(power_power_int(U_1637),U_1639)),U_1636))
| ~ hBOOL(hAPP_int_bool(zcong(U_1638,U_1637),U_1636)) ),
inference(clausify,[status(thm)],[f_673_2]) ).
fof(f_674_1,plain,
! [X_7,Y_6] : hAPP_nat_real(power_power_real(hAPP_real_real(minus_minus_real(X_7),Y_6)),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(X_7),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_6),number_number_of_nat(bit0(bit1(pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),X_7)),Y_6)),
inference(fof_nnf,[status(thm)],[fact_648_power2__diff]) ).
fof(f_674_2,plain,
! [U_1641,U_1640] : hAPP_nat_real(power_power_real(hAPP_real_real(minus_minus_real(U_1641),U_1640)),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(U_1641),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1640),number_number_of_nat(bit0(bit1(pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),U_1641)),U_1640)),
inference(variable_rename,[status(thm)],[f_674_1]) ).
cnf(f_674_3,plain,
hAPP_nat_real(power_power_real(hAPP_real_real(minus_minus_real(U_1641),U_1640)),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(U_1641),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1640),number_number_of_nat(bit0(bit1(pls)))))),hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(number267125858f_real(bit0(bit1(pls)))),U_1641)),U_1640)),
inference(clausify,[status(thm)],[f_674_2]) ).
fof(f_675_1,plain,
! [X_7,Y_6] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(X_7),Y_6)),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(X_7),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y_6),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)))),X_7)),Y_6)),
inference(fof_nnf,[status(thm)],[fact_649_power2__diff]) ).
fof(f_675_2,plain,
! [U_1643,U_1642] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(U_1643),U_1642)),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(U_1643),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1642),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)))),U_1643)),U_1642)),
inference(variable_rename,[status(thm)],[f_675_1]) ).
cnf(f_675_3,plain,
hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(U_1643),U_1642)),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(U_1643),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_1642),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)))),U_1643)),U_1642)),
inference(clausify,[status(thm)],[f_675_2]) ).
fof(f_676_1,plain,
! [A,B] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(A),B)),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(A),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)))),A)),B))),hAPP_nat_int(power_power_int(B),number_number_of_nat(bit0(bit1(pls))))),
inference(fof_nnf,[status(thm)],[fact_650_zdiff__power2]) ).
fof(f_676_2,plain,
! [U_1645,U_1644] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(U_1645),U_1644)),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(U_1645),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)))),U_1645)),U_1644))),hAPP_nat_int(power_power_int(U_1644),number_number_of_nat(bit0(bit1(pls))))),
inference(variable_rename,[status(thm)],[f_676_1]) ).
cnf(f_676_3,plain,
hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(U_1645),U_1644)),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(U_1645),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)))),U_1645)),U_1644))),hAPP_nat_int(power_power_int(U_1644),number_number_of_nat(bit0(bit1(pls))))),
inference(clausify,[status(thm)],[f_676_2]) ).
fof(f_677_1,plain,
! [A,B] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(A),B)),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(A),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(A),number_number_of_nat(bit0(bit1(pls)))))),B))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit1(bit1(pls)))),A)),hAPP_nat_int(power_power_int(B),number_number_of_nat(bit0(bit1(pls))))))),hAPP_nat_int(power_power_int(B),number_number_of_nat(bit1(bit1(pls))))),
inference(fof_nnf,[status(thm)],[fact_651_zdiff__power3]) ).
fof(f_677_2,plain,
! [U_1647,U_1646] : hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(U_1647),U_1646)),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(U_1647),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(U_1647),number_number_of_nat(bit0(bit1(pls)))))),U_1646))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit1(bit1(pls)))),U_1647)),hAPP_nat_int(power_power_int(U_1646),number_number_of_nat(bit0(bit1(pls))))))),hAPP_nat_int(power_power_int(U_1646),number_number_of_nat(bit1(bit1(pls))))),
inference(variable_rename,[status(thm)],[f_677_1]) ).
cnf(f_677_3,plain,
hAPP_nat_int(power_power_int(hAPP_int_int(minus_minus_int(U_1647),U_1646)),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(U_1647),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(U_1647),number_number_of_nat(bit0(bit1(pls)))))),U_1646))),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(number_number_of_int(bit1(bit1(pls)))),U_1647)),hAPP_nat_int(power_power_int(U_1646),number_number_of_nat(bit0(bit1(pls))))))),hAPP_nat_int(power_power_int(U_1646),number_number_of_nat(bit1(bit1(pls))))),
inference(clausify,[status(thm)],[f_677_2]) ).
fof(f_678_1,plain,
! [M,Y_1,X_1] :
( X_1 = Y_1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),M))
| ~ hBOOL(hAPP_int_bool(zcong(X_1,Y_1),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Y_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X_1))
| ~ is_int(X_1)
| ~ is_int(Y_1) ),
inference(fof_nnf,[status(thm)],[fact_652_zcong__less__eq]) ).
fof(f_678_2,plain,
! [U_1650,U_1649,U_1648] :
( U_1648 = U_1649
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1649),U_1650))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1648),U_1650))
| ~ hBOOL(hAPP_int_bool(zcong(U_1648,U_1649),U_1650))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1650))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1649))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1648))
| ~ is_int(U_1648)
| ~ is_int(U_1649) ),
inference(variable_rename,[status(thm)],[f_678_1]) ).
cnf(f_678_3,plain,
( U_1648 = U_1649
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1649),U_1650))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1648),U_1650))
| ~ hBOOL(hAPP_int_bool(zcong(U_1648,U_1649),U_1650))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1650))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1649))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1648))
| ~ is_int(U_1648)
| ~ is_int(U_1649) ),
inference(clausify,[status(thm)],[f_678_2]) ).
fof(f_679_1,plain,
! [M,X_1] :
( ~ hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X_1)) ),
inference(fof_nnf,[status(thm)],[fact_653_zcong__not__zero]) ).
fof(f_679_2,plain,
! [U_1652,U_1651] :
( ~ hBOOL(hAPP_int_bool(zcong(U_1651,zero_zero_int),U_1652))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1651),U_1652))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1651)) ),
inference(variable_rename,[status(thm)],[f_679_1]) ).
cnf(f_679_3,plain,
( ~ hBOOL(hAPP_int_bool(zcong(U_1651,zero_zero_int),U_1652))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1651),U_1652))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1651)) ),
inference(clausify,[status(thm)],[f_679_2]) ).
fof(f_680_1,plain,
! [N_1,M] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,N_1),M))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,M),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,N_1),M)) ),
inference(fof_nnf,[status(thm)],[fact_654_zdvd__bounds]) ).
fof(f_680_2,plain,
! [U_1654,U_1653] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1654),U_1653))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1653),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1654),U_1653)) ),
inference(variable_rename,[status(thm)],[f_680_1]) ).
cnf(f_680_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1654),U_1653))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1653),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1654),U_1653)) ),
inference(clausify,[status(thm)],[f_680_2]) ).
fof(f_681_1,plain,
! [X_2,P_3] :
( ( hBOOL(hAPP_int_bool(zcong(X_2,zero_zero_int),P_3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),X_2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_3),X_2))
| ~ hBOOL(hAPP_int_bool(zcong(X_2,zero_zero_int),P_3)) ) ),
inference(fof_nnf,[status(thm)],[fact_655_zcong__eq__zdvd__prop]) ).
fof(f_681_2,plain,
! [U_1656,U_1655] :
( ( hBOOL(hAPP_int_bool(zcong(U_1656,zero_zero_int),U_1655))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1655),U_1656)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1655),U_1656))
| ~ hBOOL(hAPP_int_bool(zcong(U_1656,zero_zero_int),U_1655)) ) ),
inference(variable_rename,[status(thm)],[f_681_1]) ).
fof(f_681_3,plain,
( ! [U_1660,U_1658] :
( hBOOL(hAPP_int_bool(zcong(U_1660,zero_zero_int),U_1658))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1658),U_1660)) )
& ! [U_1659,U_1657] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1657),U_1659))
| ~ hBOOL(hAPP_int_bool(zcong(U_1659,zero_zero_int),U_1657)) ) ),
inference(miniscope,[status(thm)],[f_681_2]) ).
cnf(f_681_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1657),U_1659))
| ~ hBOOL(hAPP_int_bool(zcong(U_1659,zero_zero_int),U_1657)) ),
inference(clausify,[status(thm)],[f_681_3]) ).
cnf(f_681_5,plain,
( hBOOL(hAPP_int_bool(zcong(U_1660,zero_zero_int),U_1658))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1658),U_1660)) ),
inference(clausify,[status(thm)],[f_681_3]) ).
fof(f_682_1,plain,
! [A_2,Ma] :
( ( hBOOL(hAPP_int_bool(zcong(A_2,zero_zero_int),Ma))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Ma),A_2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Ma),A_2))
| ~ hBOOL(hAPP_int_bool(zcong(A_2,zero_zero_int),Ma)) ) ),
inference(fof_nnf,[status(thm)],[fact_656_zcong__zero__equiv__div]) ).
fof(f_682_2,plain,
! [U_1662,U_1661] :
( ( hBOOL(hAPP_int_bool(zcong(U_1662,zero_zero_int),U_1661))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1661),U_1662)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1661),U_1662))
| ~ hBOOL(hAPP_int_bool(zcong(U_1662,zero_zero_int),U_1661)) ) ),
inference(variable_rename,[status(thm)],[f_682_1]) ).
fof(f_682_3,plain,
( ! [U_1666,U_1664] :
( hBOOL(hAPP_int_bool(zcong(U_1666,zero_zero_int),U_1664))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1664),U_1666)) )
& ! [U_1665,U_1663] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1663),U_1665))
| ~ hBOOL(hAPP_int_bool(zcong(U_1665,zero_zero_int),U_1663)) ) ),
inference(miniscope,[status(thm)],[f_682_2]) ).
cnf(f_682_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1663),U_1665))
| ~ hBOOL(hAPP_int_bool(zcong(U_1665,zero_zero_int),U_1663)) ),
inference(clausify,[status(thm)],[f_682_3]) ).
cnf(f_682_5,plain,
( hBOOL(hAPP_int_bool(zcong(U_1666,zero_zero_int),U_1664))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1664),U_1666)) ),
inference(clausify,[status(thm)],[f_682_3]) ).
fof(f_683_1,plain,
! [M,N_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),N_1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),hAPP_int_int(times_times_int(M),N_1)))
| ~ hBOOL(hAPP_int_bool(zprime,P_1)) ),
inference(fof_nnf,[status(thm)],[fact_657_zprime__zdvd__zmult__better]) ).
fof(f_683_2,plain,
! [U_1669,U_1668,U_1667] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1667),U_1668))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1667),U_1669))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1667),hAPP_int_int(times_times_int(U_1669),U_1668)))
| ~ hBOOL(hAPP_int_bool(zprime,U_1667)) ),
inference(variable_rename,[status(thm)],[f_683_1]) ).
cnf(f_683_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1667),U_1668))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1667),U_1669))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1667),hAPP_int_int(times_times_int(U_1669),U_1668)))
| ~ hBOOL(hAPP_int_bool(zprime,U_1667)) ),
inference(clausify,[status(thm)],[f_683_2]) ).
fof(f_684_1,plain,
! [M,X_1] :
( X_1 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
| ~ is_int(X_1) ),
inference(fof_nnf,[status(thm)],[fact_658_Int2_Ozcong__zero]) ).
fof(f_684_2,plain,
! [U_1671,U_1670] :
( U_1670 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(zcong(U_1670,zero_zero_int),U_1671))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1670),U_1671))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1670))
| ~ is_int(U_1670) ),
inference(variable_rename,[status(thm)],[f_684_1]) ).
cnf(f_684_3,plain,
( U_1670 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(zcong(U_1670,zero_zero_int),U_1671))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1670),U_1671))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1670))
| ~ is_int(U_1670) ),
inference(clausify,[status(thm)],[f_684_2]) ).
fof(f_685_1,plain,
! [P_1,Y_1,N_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),hAPP_nat_int(power_power_int(Y_1),N_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),Y_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_659_zpower__zdvd__prop1]) ).
fof(f_685_2,plain,
! [U_1674,U_1673,U_1672] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1674),hAPP_nat_int(power_power_int(U_1673),U_1672)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1674),U_1673))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1672)) ),
inference(variable_rename,[status(thm)],[f_685_1]) ).
cnf(f_685_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1674),hAPP_nat_int(power_power_int(U_1673),U_1672)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1674),U_1673))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1672)) ),
inference(clausify,[status(thm)],[f_685_2]) ).
fof(f_686_1,plain,
! [N_1] :
( hAPP_nat_int(power_power_int(number_number_of_int(min)),N_1) = number_number_of_int(min)
| hAPP_nat_int(power_power_int(number_number_of_int(min)),N_1) = one_one_int ),
inference(fof_nnf,[status(thm)],[fact_660_neg__one__power]) ).
fof(f_686_2,plain,
! [U_1675] :
( hAPP_nat_int(power_power_int(number_number_of_int(min)),U_1675) = number_number_of_int(min)
| hAPP_nat_int(power_power_int(number_number_of_int(min)),U_1675) = one_one_int ),
inference(variable_rename,[status(thm)],[f_686_1]) ).
cnf(f_686_3,plain,
( hAPP_nat_int(power_power_int(number_number_of_int(min)),U_1675) = number_number_of_int(min)
| hAPP_nat_int(power_power_int(number_number_of_int(min)),U_1675) = one_one_int ),
inference(clausify,[status(thm)],[f_686_2]) ).
fof(f_687_1,plain,
! [Y_1,X_1,P_1] :
( ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X_1),Y_1),zero_zero_int),P_1))
| hBOOL(hAPP_int_bool(zcong(Y_1,zero_zero_int),P_1))
| hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),P_1))
| ~ hBOOL(hAPP_int_bool(zprime,P_1)) ),
inference(fof_nnf,[status(thm)],[fact_661_zcong__zmult__prop3]) ).
fof(f_687_2,plain,
! [U_1678,U_1677,U_1676] :
( ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1677),U_1678),zero_zero_int),U_1676))
| hBOOL(hAPP_int_bool(zcong(U_1678,zero_zero_int),U_1676))
| hBOOL(hAPP_int_bool(zcong(U_1677,zero_zero_int),U_1676))
| ~ hBOOL(hAPP_int_bool(zprime,U_1676)) ),
inference(variable_rename,[status(thm)],[f_687_1]) ).
cnf(f_687_3,plain,
( ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1677),U_1678),zero_zero_int),U_1676))
| hBOOL(hAPP_int_bool(zcong(U_1678,zero_zero_int),U_1676))
| hBOOL(hAPP_int_bool(zcong(U_1677,zero_zero_int),U_1676))
| ~ hBOOL(hAPP_int_bool(zprime,U_1676)) ),
inference(clausify,[status(thm)],[f_687_2]) ).
fof(f_688_1,plain,
! [B,A,P_1] :
( hBOOL(hAPP_int_bool(zcong(B,zero_zero_int),P_1))
| hBOOL(hAPP_int_bool(zcong(A,zero_zero_int),P_1))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),B),zero_zero_int),P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A))
| ~ hBOOL(hAPP_int_bool(zprime,P_1)) ),
inference(fof_nnf,[status(thm)],[fact_662_zcong__zprime__prod__zero]) ).
fof(f_688_2,plain,
! [U_1681,U_1680,U_1679] :
( hBOOL(hAPP_int_bool(zcong(U_1681,zero_zero_int),U_1679))
| hBOOL(hAPP_int_bool(zcong(U_1680,zero_zero_int),U_1679))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1680),U_1681),zero_zero_int),U_1679))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1680))
| ~ hBOOL(hAPP_int_bool(zprime,U_1679)) ),
inference(variable_rename,[status(thm)],[f_688_1]) ).
cnf(f_688_3,plain,
( hBOOL(hAPP_int_bool(zcong(U_1681,zero_zero_int),U_1679))
| hBOOL(hAPP_int_bool(zcong(U_1680,zero_zero_int),U_1679))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1680),U_1681),zero_zero_int),U_1679))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1680))
| ~ hBOOL(hAPP_int_bool(zprime,U_1679)) ),
inference(clausify,[status(thm)],[f_688_2]) ).
fof(f_689_1,plain,
! [B,A,P_1] :
( ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),B),zero_zero_int),P_1))
| hBOOL(hAPP_int_bool(zcong(B,zero_zero_int),P_1))
| hBOOL(hAPP_int_bool(zcong(A,zero_zero_int),P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A))
| ~ hBOOL(hAPP_int_bool(zprime,P_1)) ),
inference(fof_nnf,[status(thm)],[fact_663_zcong__zprime__prod__zero__contra]) ).
fof(f_689_2,plain,
! [U_1684,U_1683,U_1682] :
( ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1683),U_1684),zero_zero_int),U_1682))
| hBOOL(hAPP_int_bool(zcong(U_1684,zero_zero_int),U_1682))
| hBOOL(hAPP_int_bool(zcong(U_1683,zero_zero_int),U_1682))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1683))
| ~ hBOOL(hAPP_int_bool(zprime,U_1682)) ),
inference(variable_rename,[status(thm)],[f_689_1]) ).
cnf(f_689_3,plain,
( ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_1683),U_1684),zero_zero_int),U_1682))
| hBOOL(hAPP_int_bool(zcong(U_1684,zero_zero_int),U_1682))
| hBOOL(hAPP_int_bool(zcong(U_1683,zero_zero_int),U_1682))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_1683))
| ~ hBOOL(hAPP_int_bool(zprime,U_1682)) ),
inference(clausify,[status(thm)],[f_689_2]) ).
fof(f_690_1,plain,
! [Y_1,N_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),Y_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_1),hAPP_nat_int(power_power_int(Y_1),N_1)))
| ~ hBOOL(hAPP_int_bool(zprime,P_1)) ),
inference(fof_nnf,[status(thm)],[fact_664_zpower__zdvd__prop2]) ).
fof(f_690_2,plain,
! [U_1687,U_1686,U_1685] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1685),U_1687))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1686))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1685),hAPP_nat_int(power_power_int(U_1687),U_1686)))
| ~ hBOOL(hAPP_int_bool(zprime,U_1685)) ),
inference(variable_rename,[status(thm)],[f_690_1]) ).
cnf(f_690_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1685),U_1687))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1686))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1685),hAPP_nat_int(power_power_int(U_1687),U_1686)))
| ~ hBOOL(hAPP_int_bool(zprime,U_1685)) ),
inference(clausify,[status(thm)],[f_690_2]) ).
fof(f_691_1,plain,
! [M] :
( 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
| ~ 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(fof_nnf,[status(thm)],[fact_665_Legendre__1mod4]) ).
fof(f_691_2,plain,
! [U_1688] :
( 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))))),U_1688)),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(bit0(bit0(bit1(pls))))),U_1688)),one_one_int))) ),
inference(variable_rename,[status(thm)],[f_691_1]) ).
cnf(f_691_3,plain,
( 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))))),U_1688)),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(bit0(bit0(bit1(pls))))),U_1688)),one_one_int))) ),
inference(clausify,[status(thm)],[f_691_2]) ).
fof(f_692_1,plain,
! [A,P_1] :
( ( ( ( legendre(A,P_1) = number_number_of_int(min)
| hBOOL(hAPP_int_bool(quadRes(P_1),A)) )
& ( legendre(A,P_1) = one_one_int
| ~ hBOOL(hAPP_int_bool(quadRes(P_1),A)) ) )
| hBOOL(hAPP_int_bool(zcong(A,zero_zero_int),P_1)) )
& ( legendre(A,P_1) = zero_zero_int
| ~ hBOOL(hAPP_int_bool(zcong(A,zero_zero_int),P_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_666_Legendre__def]) ).
fof(f_692_2,plain,
! [U_1690,U_1689] :
( ( ( ( legendre(U_1690,U_1689) = number_number_of_int(min)
| hBOOL(hAPP_int_bool(quadRes(U_1689),U_1690)) )
& ( legendre(U_1690,U_1689) = one_one_int
| ~ hBOOL(hAPP_int_bool(quadRes(U_1689),U_1690)) ) )
| hBOOL(hAPP_int_bool(zcong(U_1690,zero_zero_int),U_1689)) )
& ( legendre(U_1690,U_1689) = zero_zero_int
| ~ hBOOL(hAPP_int_bool(zcong(U_1690,zero_zero_int),U_1689)) ) ),
inference(variable_rename,[status(thm)],[f_692_1]) ).
fof(f_692_3,plain,
( ! [U_1694,U_1692] :
( ( ( legendre(U_1694,U_1692) = number_number_of_int(min)
| hBOOL(hAPP_int_bool(quadRes(U_1692),U_1694)) )
& ( legendre(U_1694,U_1692) = one_one_int
| ~ hBOOL(hAPP_int_bool(quadRes(U_1692),U_1694)) ) )
| hBOOL(hAPP_int_bool(zcong(U_1694,zero_zero_int),U_1692)) )
& ! [U_1693,U_1691] :
( legendre(U_1693,U_1691) = zero_zero_int
| ~ hBOOL(hAPP_int_bool(zcong(U_1693,zero_zero_int),U_1691)) ) ),
inference(miniscope,[status(thm)],[f_692_2]) ).
cnf(f_692_4,plain,
( legendre(U_1693,U_1691) = zero_zero_int
| ~ hBOOL(hAPP_int_bool(zcong(U_1693,zero_zero_int),U_1691)) ),
inference(clausify,[status(thm)],[f_692_3]) ).
cnf(f_692_5,plain,
( legendre(U_1694,U_1692) = one_one_int
| ~ hBOOL(hAPP_int_bool(quadRes(U_1692),U_1694))
| hBOOL(hAPP_int_bool(zcong(U_1694,zero_zero_int),U_1692)) ),
inference(clausify,[status(thm)],[f_692_3]) ).
cnf(f_692_6,plain,
( legendre(U_1694,U_1692) = number_number_of_int(min)
| hBOOL(hAPP_int_bool(quadRes(U_1692),U_1694))
| hBOOL(hAPP_int_bool(zcong(U_1694,zero_zero_int),U_1692)) ),
inference(clausify,[status(thm)],[f_692_3]) ).
fof(f_693_1,plain,
! [N_1,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),N_1)),M))
| M = N_1
| M = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,N_1),M)) ),
inference(fof_nnf,[status(thm)],[fact_667_divides__cases]) ).
fof(f_693_2,plain,
! [U_1696,U_1695] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_1696)),U_1695))
| U_1695 = U_1696
| U_1695 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1696),U_1695)) ),
inference(variable_rename,[status(thm)],[f_693_1]) ).
cnf(f_693_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls)))),U_1696)),U_1695))
| U_1695 = U_1696
| U_1695 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1696),U_1695)) ),
inference(clausify,[status(thm)],[f_693_2]) ).
fof(f_694_1,plain,
! [Ma,X_2] :
( ( hBOOL(hAPP_int_bool(quadRes(Ma),X_2))
| ! [Y] :
( ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(Y),number_number_of_nat(bit0(bit1(pls)))),X_2),Ma))
| ~ is_int(Y) ) )
& ( ? [Y] :
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(Y),number_number_of_nat(bit0(bit1(pls)))),X_2),Ma))
& is_int(Y) )
| ~ hBOOL(hAPP_int_bool(quadRes(Ma),X_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_668_QuadRes__def]) ).
fof(f_694_2,plain,
! [U_1700,U_1699] :
( ( hBOOL(hAPP_int_bool(quadRes(U_1700),U_1699))
| ! [U_1698] :
( ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(U_1698),number_number_of_nat(bit0(bit1(pls)))),U_1699),U_1700))
| ~ is_int(U_1698) ) )
& ( ? [U_1697] :
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(U_1697),number_number_of_nat(bit0(bit1(pls)))),U_1699),U_1700))
& is_int(U_1697) )
| ~ hBOOL(hAPP_int_bool(quadRes(U_1700),U_1699)) ) ),
inference(variable_rename,[status(thm)],[f_694_1]) ).
fof(f_694_3,plain,
( ! [U_1704,U_1702] :
( hBOOL(hAPP_int_bool(quadRes(U_1704),U_1702))
| ! [U_1698] :
( ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(U_1698),number_number_of_nat(bit0(bit1(pls)))),U_1702),U_1704))
| ~ is_int(U_1698) ) )
& ! [U_1703,U_1701] :
( ? [U_1697] :
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(U_1697),number_number_of_nat(bit0(bit1(pls)))),U_1701),U_1703))
& is_int(U_1697) )
| ~ hBOOL(hAPP_int_bool(quadRes(U_1703),U_1701)) ) ),
inference(miniscope,[status(thm)],[f_694_2]) ).
fof(f_694_4,plain,
( ! [U_1704,U_1702] :
( hBOOL(hAPP_int_bool(quadRes(U_1704),U_1702))
| ! [U_1698] :
( ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(U_1698),number_number_of_nat(bit0(bit1(pls)))),U_1702),U_1704))
| ~ is_int(U_1698) ) )
& ! [U_1703,U_1701] :
( ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK11(U_1703,U_1701)),number_number_of_nat(bit0(bit1(pls)))),U_1701),U_1703))
& is_int(sK11(U_1703,U_1701)) )
| ~ hBOOL(hAPP_int_bool(quadRes(U_1703),U_1701)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_1697,sK11(U_1703,U_1701))],[f_694_3]) ).
cnf(f_694_5,plain,
( is_int(sK11(U_1703,U_1701))
| ~ hBOOL(hAPP_int_bool(quadRes(U_1703),U_1701)) ),
inference(clausify,[status(thm)],[f_694_4]) ).
cnf(f_694_6,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK11(U_1703,U_1701)),number_number_of_nat(bit0(bit1(pls)))),U_1701),U_1703))
| ~ hBOOL(hAPP_int_bool(quadRes(U_1703),U_1701)) ),
inference(clausify,[status(thm)],[f_694_4]) ).
cnf(f_694_7,plain,
( hBOOL(hAPP_int_bool(quadRes(U_1704),U_1702))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(U_1698),number_number_of_nat(bit0(bit1(pls)))),U_1702),U_1704))
| ~ is_int(U_1698) ),
inference(clausify,[status(thm)],[f_694_4]) ).
fof(f_695_1,plain,
! [X_2,Y_2] :
( ( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_2),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| Y_2 != zero_zero_real
| X_2 != zero_zero_real )
& ( ( Y_2 = zero_zero_real
& X_2 = zero_zero_real )
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(X_2),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(Y_2),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ) ),
inference(fof_nnf,[status(thm)],[fact_669_realpow__two__sum__zero__iff]) ).
fof(f_695_2,plain,
! [U_1706,U_1705] :
( ( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(U_1706),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1705),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| U_1705 != zero_zero_real
| U_1706 != zero_zero_real )
& ( ( U_1705 = zero_zero_real
& U_1706 = zero_zero_real )
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(U_1706),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1705),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ) ),
inference(variable_rename,[status(thm)],[f_695_1]) ).
fof(f_695_3,plain,
( ! [U_1710,U_1708] :
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(U_1710),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1708),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| U_1708 != zero_zero_real
| U_1710 != zero_zero_real )
& ! [U_1709,U_1707] :
( ( U_1707 = zero_zero_real
& U_1709 = zero_zero_real )
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(U_1709),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1707),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ) ),
inference(miniscope,[status(thm)],[f_695_2]) ).
cnf(f_695_4,plain,
( U_1709 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(U_1709),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1707),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ),
inference(clausify,[status(thm)],[f_695_3]) ).
cnf(f_695_5,plain,
( U_1707 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(U_1709),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1707),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ),
inference(clausify,[status(thm)],[f_695_3]) ).
cnf(f_695_6,plain,
( hAPP_real_real(plus_plus_real(hAPP_nat_real(power_power_real(U_1710),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_real(power_power_real(U_1708),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| U_1708 != zero_zero_real
| U_1710 != zero_zero_real ),
inference(clausify,[status(thm)],[f_695_3]) ).
fof(f_696_1,plain,
! [V_1,U_2,Y_5,X_6,A_54] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_2),X_6)),hAPP_real_real(times_times_real(V_1),Y_5))),A_54))
| hAPP_real_real(plus_plus_real(U_2),V_1) != one_one_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),V_1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_5),A_54))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_6),A_54)) ),
inference(fof_nnf,[status(thm)],[fact_670_convex__bound__lt]) ).
fof(f_696_2,plain,
! [U_1715,U_1714,U_1713,U_1712,U_1711] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_1714),U_1712)),hAPP_real_real(times_times_real(U_1715),U_1713))),U_1711))
| hAPP_real_real(plus_plus_real(U_1714),U_1715) != one_one_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1715))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1714))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1713),U_1711))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1712),U_1711)) ),
inference(variable_rename,[status(thm)],[f_696_1]) ).
cnf(f_696_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_1714),U_1712)),hAPP_real_real(times_times_real(U_1715),U_1713))),U_1711))
| hAPP_real_real(plus_plus_real(U_1714),U_1715) != one_one_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1715))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1714))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1713),U_1711))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1712),U_1711)) ),
inference(clausify,[status(thm)],[f_696_2]) ).
fof(f_697_1,plain,
! [V_1,U_2,Y_5,X_6,A_54] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_2),X_6)),hAPP_int_int(times_times_int(V_1),Y_5))),A_54))
| hAPP_int_int(plus_plus_int(U_2),V_1) != one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),V_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_5),A_54))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_6),A_54)) ),
inference(fof_nnf,[status(thm)],[fact_671_convex__bound__lt]) ).
fof(f_697_2,plain,
! [U_1720,U_1719,U_1718,U_1717,U_1716] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1719),U_1717)),hAPP_int_int(times_times_int(U_1720),U_1718))),U_1716))
| hAPP_int_int(plus_plus_int(U_1719),U_1720) != one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1720))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1719))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1718),U_1716))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1717),U_1716)) ),
inference(variable_rename,[status(thm)],[f_697_1]) ).
cnf(f_697_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1719),U_1717)),hAPP_int_int(times_times_int(U_1720),U_1718))),U_1716))
| hAPP_int_int(plus_plus_int(U_1719),U_1720) != one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1720))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1719))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1718),U_1716))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1717),U_1716)) ),
inference(clausify,[status(thm)],[f_697_2]) ).
fof(f_698_1,plain,
! [A_53] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_53),zero_zero_real)),
inference(fof_nnf,[status(thm)],[fact_672_dvd__0__right]) ).
fof(f_698_2,plain,
! [U_1721] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1721),zero_zero_real)),
inference(variable_rename,[status(thm)],[f_698_1]) ).
cnf(f_698_3,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1721),zero_zero_real)),
inference(clausify,[status(thm)],[f_698_2]) ).
fof(f_699_1,plain,
! [A_53] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_53),zero_zero_nat)),
inference(fof_nnf,[status(thm)],[fact_673_dvd__0__right]) ).
fof(f_699_2,plain,
! [U_1722] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1722),zero_zero_nat)),
inference(variable_rename,[status(thm)],[f_699_1]) ).
cnf(f_699_3,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1722),zero_zero_nat)),
inference(clausify,[status(thm)],[f_699_2]) ).
fof(f_700_1,plain,
! [A_53] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_53),zero_zero_int)),
inference(fof_nnf,[status(thm)],[fact_674_dvd__0__right]) ).
fof(f_700_2,plain,
! [U_1723] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1723),zero_zero_int)),
inference(variable_rename,[status(thm)],[f_700_1]) ).
cnf(f_700_3,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1723),zero_zero_int)),
inference(clausify,[status(thm)],[f_700_2]) ).
fof(f_701_1,plain,
! [X_2,Y_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Y_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(minus_minus_real(X_2),Y_2)),zero_zero_real)) )
& ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(minus_minus_real(X_2),Y_2)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_675_real__le__eq__diff]) ).
fof(f_701_2,plain,
! [U_1725,U_1724] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1725),U_1724))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(minus_minus_real(U_1725),U_1724)),zero_zero_real)) )
& ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(minus_minus_real(U_1725),U_1724)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1725),U_1724)) ) ),
inference(variable_rename,[status(thm)],[f_701_1]) ).
fof(f_701_3,plain,
( ! [U_1729,U_1727] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1729),U_1727))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(minus_minus_real(U_1729),U_1727)),zero_zero_real)) )
& ! [U_1728,U_1726] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(minus_minus_real(U_1728),U_1726)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1728),U_1726)) ) ),
inference(miniscope,[status(thm)],[f_701_2]) ).
cnf(f_701_4,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(minus_minus_real(U_1728),U_1726)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1728),U_1726)) ),
inference(clausify,[status(thm)],[f_701_3]) ).
cnf(f_701_5,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1729),U_1727))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(minus_minus_real(U_1729),U_1727)),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_701_3]) ).
fof(f_702_1,plain,
! [X_5,Y_4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,Y_4),X_5))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_5),Y_4))
| X_5 = Y_4 ),
inference(fof_nnf,[status(thm)],[fact_676_linorder__neqE__linordered__idom]) ).
fof(f_702_2,plain,
! [U_1731,U_1730] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1730),U_1731))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1731),U_1730))
| U_1731 = U_1730 ),
inference(variable_rename,[status(thm)],[f_702_1]) ).
cnf(f_702_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1730),U_1731))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1731),U_1730))
| U_1731 = U_1730 ),
inference(clausify,[status(thm)],[f_702_2]) ).
fof(f_703_1,plain,
! [X_5,Y_4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_4),X_5))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_5),Y_4))
| X_5 = Y_4
| ~ is_int(Y_4)
| ~ is_int(X_5) ),
inference(fof_nnf,[status(thm)],[fact_677_linorder__neqE__linordered__idom]) ).
fof(f_703_2,plain,
! [U_1733,U_1732] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1732),U_1733))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1733),U_1732))
| U_1733 = U_1732
| ~ is_int(U_1732)
| ~ is_int(U_1733) ),
inference(variable_rename,[status(thm)],[f_703_1]) ).
cnf(f_703_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1732),U_1733))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_1733),U_1732))
| U_1733 = U_1732
| ~ is_int(U_1732)
| ~ is_int(U_1733) ),
inference(clausify,[status(thm)],[f_703_2]) ).
fof(f_704_1,plain,
! [A_52] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_52),A_52)),
inference(fof_nnf,[status(thm)],[fact_678_dvd__refl]) ).
fof(f_704_2,plain,
! [U_1734] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1734),U_1734)),
inference(variable_rename,[status(thm)],[f_704_1]) ).
cnf(f_704_3,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1734),U_1734)),
inference(clausify,[status(thm)],[f_704_2]) ).
fof(f_705_1,plain,
! [A_52] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_52),A_52)),
inference(fof_nnf,[status(thm)],[fact_679_dvd__refl]) ).
fof(f_705_2,plain,
! [U_1735] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1735),U_1735)),
inference(variable_rename,[status(thm)],[f_705_1]) ).
cnf(f_705_3,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1735),U_1735)),
inference(clausify,[status(thm)],[f_705_2]) ).
fof(f_706_1,plain,
! [A_52] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_52),A_52)),
inference(fof_nnf,[status(thm)],[fact_680_dvd__refl]) ).
fof(f_706_2,plain,
! [U_1736] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1736),U_1736)),
inference(variable_rename,[status(thm)],[f_706_1]) ).
cnf(f_706_3,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1736),U_1736)),
inference(clausify,[status(thm)],[f_706_2]) ).
fof(f_707_1,plain,
! [C_24,A_51,B_45] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_51),C_24))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,B_45),C_24))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_51),B_45)) ),
inference(fof_nnf,[status(thm)],[fact_681_dvd__trans]) ).
fof(f_707_2,plain,
! [U_1739,U_1738,U_1737] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1738),U_1739))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1737),U_1739))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1738),U_1737)) ),
inference(variable_rename,[status(thm)],[f_707_1]) ).
cnf(f_707_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1738),U_1739))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1737),U_1739))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1738),U_1737)) ),
inference(clausify,[status(thm)],[f_707_2]) ).
fof(f_708_1,plain,
! [C_24,A_51,B_45] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_51),C_24))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B_45),C_24))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_51),B_45)) ),
inference(fof_nnf,[status(thm)],[fact_682_dvd__trans]) ).
fof(f_708_2,plain,
! [U_1742,U_1741,U_1740] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1741),U_1742))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1740),U_1742))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1741),U_1740)) ),
inference(variable_rename,[status(thm)],[f_708_1]) ).
cnf(f_708_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1741),U_1742))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1740),U_1742))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1741),U_1740)) ),
inference(clausify,[status(thm)],[f_708_2]) ).
fof(f_709_1,plain,
! [C_24,A_51,B_45] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_51),C_24))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,B_45),C_24))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_51),B_45)) ),
inference(fof_nnf,[status(thm)],[fact_683_dvd__trans]) ).
fof(f_709_2,plain,
! [U_1745,U_1744,U_1743] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1744),U_1745))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1743),U_1745))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1744),U_1743)) ),
inference(variable_rename,[status(thm)],[f_709_1]) ).
cnf(f_709_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1744),U_1745))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1743),U_1745))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1744),U_1743)) ),
inference(clausify,[status(thm)],[f_709_2]) ).
fof(f_710_1,plain,
zero_zero_real != one_one_real,
inference(fof_nnf,[status(thm)],[fact_684_real__zero__not__eq__one]) ).
cnf(f_710_2,plain,
zero_zero_real != one_one_real,
inference(clausify,[status(thm)],[f_710_1]) ).
fof(f_711_1,plain,
! [X_2,Y_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Y_2))
| ( X_2 != Y_2
& ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),Y_2)) ) )
& ( X_2 = Y_2
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),Y_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_685_less__eq__real__def]) ).
fof(f_711_2,plain,
! [U_1747,U_1746] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1747),U_1746))
| ( U_1747 != U_1746
& ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1747),U_1746)) ) )
& ( U_1747 = U_1746
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1747),U_1746))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1747),U_1746)) ) ),
inference(variable_rename,[status(thm)],[f_711_1]) ).
fof(f_711_3,plain,
( ! [U_1751,U_1749] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1751),U_1749))
| ( U_1751 != U_1749
& ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1751),U_1749)) ) )
& ! [U_1750,U_1748] :
( U_1750 = U_1748
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1750),U_1748))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1750),U_1748)) ) ),
inference(miniscope,[status(thm)],[f_711_2]) ).
cnf(f_711_4,plain,
( U_1750 = U_1748
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1750),U_1748))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1750),U_1748)) ),
inference(clausify,[status(thm)],[f_711_3]) ).
cnf(f_711_5,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1751),U_1749))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1751),U_1749)) ),
inference(clausify,[status(thm)],[f_711_3]) ).
cnf(f_711_6,plain,
( U_1751 != U_1749
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1751),U_1749)) ),
inference(clausify,[status(thm)],[f_711_3]) ).
fof(f_712_1,plain,
! [X_2,Y_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),Y_2))
| X_2 = Y_2
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Y_2)) )
& ( ( X_2 != Y_2
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Y_2)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_686_real__less__def]) ).
fof(f_712_2,plain,
! [U_1753,U_1752] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1753),U_1752))
| U_1753 = U_1752
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1753),U_1752)) )
& ( ( U_1753 != U_1752
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1753),U_1752)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1753),U_1752)) ) ),
inference(variable_rename,[status(thm)],[f_712_1]) ).
fof(f_712_3,plain,
( ! [U_1757,U_1755] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1757),U_1755))
| U_1757 = U_1755
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1757),U_1755)) )
& ! [U_1756,U_1754] :
( ( U_1756 != U_1754
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1756),U_1754)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1756),U_1754)) ) ),
inference(miniscope,[status(thm)],[f_712_2]) ).
cnf(f_712_4,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1756),U_1754))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1756),U_1754)) ),
inference(clausify,[status(thm)],[f_712_3]) ).
cnf(f_712_5,plain,
( U_1756 != U_1754
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1756),U_1754)) ),
inference(clausify,[status(thm)],[f_712_3]) ).
cnf(f_712_6,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_1757),U_1755))
| U_1757 = U_1755
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1757),U_1755)) ),
inference(clausify,[status(thm)],[f_712_3]) ).
fof(f_713_1,plain,
! [X_2,Y_2] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) )
| X_2 != Y_2 )
& ( X_2 = Y_2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_687_divides__antisym]) ).
fof(f_713_2,plain,
! [U_1759,U_1758] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1758),U_1759))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1759),U_1758)) )
| U_1759 != U_1758 )
& ( U_1759 = U_1758
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1758),U_1759))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1759),U_1758)) ) ),
inference(variable_rename,[status(thm)],[f_713_1]) ).
fof(f_713_3,plain,
( ! [U_1763,U_1761] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1761),U_1763))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1763),U_1761)) )
| U_1763 != U_1761 )
& ! [U_1762,U_1760] :
( U_1762 = U_1760
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1760),U_1762))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1762),U_1760)) ) ),
inference(miniscope,[status(thm)],[f_713_2]) ).
cnf(f_713_4,plain,
( U_1762 = U_1760
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1760),U_1762))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1762),U_1760)) ),
inference(clausify,[status(thm)],[f_713_3]) ).
cnf(f_713_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1763),U_1761))
| U_1763 != U_1761 ),
inference(clausify,[status(thm)],[f_713_3]) ).
cnf(f_713_6,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1761),U_1763))
| U_1763 != U_1761 ),
inference(clausify,[status(thm)],[f_713_3]) ).
fof(f_714_1,plain,
! [Z1,Z2,Z3] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(Z1),Z2)),Z3) = hAPP_real_real(times_times_real(Z1),hAPP_real_real(times_times_real(Z2),Z3)),
inference(fof_nnf,[status(thm)],[fact_688_real__mult__assoc]) ).
fof(f_714_2,plain,
! [U_1766,U_1765,U_1764] : hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_1766),U_1765)),U_1764) = hAPP_real_real(times_times_real(U_1766),hAPP_real_real(times_times_real(U_1765),U_1764)),
inference(variable_rename,[status(thm)],[f_714_1]) ).
cnf(f_714_3,plain,
hAPP_real_real(times_times_real(hAPP_real_real(times_times_real(U_1766),U_1765)),U_1764) = hAPP_real_real(times_times_real(U_1766),hAPP_real_real(times_times_real(U_1765),U_1764)),
inference(clausify,[status(thm)],[f_714_2]) ).
fof(f_715_1,plain,
! [Z,W] : hAPP_real_real(times_times_real(Z),W) = hAPP_real_real(times_times_real(W),Z),
inference(fof_nnf,[status(thm)],[fact_689_real__mult__commute]) ).
fof(f_715_2,plain,
! [U_1768,U_1767] : hAPP_real_real(times_times_real(U_1768),U_1767) = hAPP_real_real(times_times_real(U_1767),U_1768),
inference(variable_rename,[status(thm)],[f_715_1]) ).
cnf(f_715_3,plain,
hAPP_real_real(times_times_real(U_1768),U_1767) = hAPP_real_real(times_times_real(U_1767),U_1768),
inference(clausify,[status(thm)],[f_715_2]) ).
fof(f_716_1,plain,
! [Z] : hAPP_real_real(times_times_real(one_one_real),Z) = Z,
inference(fof_nnf,[status(thm)],[fact_690_real__mult__1]) ).
fof(f_716_2,plain,
! [U_1769] : hAPP_real_real(times_times_real(one_one_real),U_1769) = U_1769,
inference(variable_rename,[status(thm)],[f_716_1]) ).
cnf(f_716_3,plain,
hAPP_real_real(times_times_real(one_one_real),U_1769) = U_1769,
inference(clausify,[status(thm)],[f_716_2]) ).
fof(f_717_1,plain,
! [Z,X_1,Y_1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(Z),X_1)),hAPP_real_real(plus_plus_real(Z),Y_1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_1),Y_1)) ),
inference(fof_nnf,[status(thm)],[fact_691_real__add__left__mono]) ).
fof(f_717_2,plain,
! [U_1772,U_1771,U_1770] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(U_1772),U_1771)),hAPP_real_real(plus_plus_real(U_1772),U_1770)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1771),U_1770)) ),
inference(variable_rename,[status(thm)],[f_717_1]) ).
cnf(f_717_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(plus_plus_real(U_1772),U_1771)),hAPP_real_real(plus_plus_real(U_1772),U_1770)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1771),U_1770)) ),
inference(clausify,[status(thm)],[f_717_2]) ).
fof(f_718_1,plain,
! [X_4,N_3] :
( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(X_4),hAPP_nat_nat(minus_minus_nat(N_3),one_one_nat))),X_4) = hAPP_nat_nat(power_power_nat(X_4),N_3)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_3)) ),
inference(fof_nnf,[status(thm)],[fact_692_realpow__minus__mult]) ).
fof(f_718_2,plain,
! [U_1774,U_1773] :
( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(U_1774),hAPP_nat_nat(minus_minus_nat(U_1773),one_one_nat))),U_1774) = hAPP_nat_nat(power_power_nat(U_1774),U_1773)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1773)) ),
inference(variable_rename,[status(thm)],[f_718_1]) ).
cnf(f_718_3,plain,
( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(power_power_nat(U_1774),hAPP_nat_nat(minus_minus_nat(U_1773),one_one_nat))),U_1774) = hAPP_nat_nat(power_power_nat(U_1774),U_1773)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1773)) ),
inference(clausify,[status(thm)],[f_718_2]) ).
fof(f_719_1,plain,
! [X_4,N_3] :
( hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(X_4),hAPP_nat_nat(minus_minus_nat(N_3),one_one_nat))),X_4) = hAPP_nat_real(power_power_real(X_4),N_3)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_3)) ),
inference(fof_nnf,[status(thm)],[fact_693_realpow__minus__mult]) ).
fof(f_719_2,plain,
! [U_1776,U_1775] :
( hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(U_1776),hAPP_nat_nat(minus_minus_nat(U_1775),one_one_nat))),U_1776) = hAPP_nat_real(power_power_real(U_1776),U_1775)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1775)) ),
inference(variable_rename,[status(thm)],[f_719_1]) ).
cnf(f_719_3,plain,
( hAPP_real_real(times_times_real(hAPP_nat_real(power_power_real(U_1776),hAPP_nat_nat(minus_minus_nat(U_1775),one_one_nat))),U_1776) = hAPP_nat_real(power_power_real(U_1776),U_1775)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1775)) ),
inference(clausify,[status(thm)],[f_719_2]) ).
fof(f_720_1,plain,
! [X_4,N_3] :
( hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(X_4),hAPP_nat_nat(minus_minus_nat(N_3),one_one_nat))),X_4) = hAPP_nat_int(power_power_int(X_4),N_3)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_3)) ),
inference(fof_nnf,[status(thm)],[fact_694_realpow__minus__mult]) ).
fof(f_720_2,plain,
! [U_1778,U_1777] :
( hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(U_1778),hAPP_nat_nat(minus_minus_nat(U_1777),one_one_nat))),U_1778) = hAPP_nat_int(power_power_int(U_1778),U_1777)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1777)) ),
inference(variable_rename,[status(thm)],[f_720_1]) ).
cnf(f_720_3,plain,
( hAPP_int_int(times_times_int(hAPP_nat_int(power_power_int(U_1778),hAPP_nat_nat(minus_minus_nat(U_1777),one_one_nat))),U_1778) = hAPP_nat_int(power_power_int(U_1778),U_1777)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_1777)) ),
inference(clausify,[status(thm)],[f_720_2]) ).
fof(f_721_1,plain,
! [N_1,M] :
( ( hAPP_nat_nat(times_times_nat(M),N_1) = hAPP_nat_nat(plus_plus_nat(N_1),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(M),one_one_nat)),N_1))
| M = zero_zero_nat )
& ( hAPP_nat_nat(times_times_nat(M),N_1) = zero_zero_nat
| M != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_695_mult__eq__if]) ).
fof(f_721_2,plain,
! [U_1780,U_1779] :
( ( hAPP_nat_nat(times_times_nat(U_1779),U_1780) = hAPP_nat_nat(plus_plus_nat(U_1780),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_1779),one_one_nat)),U_1780))
| U_1779 = zero_zero_nat )
& ( hAPP_nat_nat(times_times_nat(U_1779),U_1780) = zero_zero_nat
| U_1779 != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_721_1]) ).
fof(f_721_3,plain,
( ! [U_1784,U_1782] :
( hAPP_nat_nat(times_times_nat(U_1782),U_1784) = hAPP_nat_nat(plus_plus_nat(U_1784),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_1782),one_one_nat)),U_1784))
| U_1782 = zero_zero_nat )
& ! [U_1783,U_1781] :
( hAPP_nat_nat(times_times_nat(U_1781),U_1783) = zero_zero_nat
| U_1781 != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_721_2]) ).
cnf(f_721_4,plain,
( hAPP_nat_nat(times_times_nat(U_1781),U_1783) = zero_zero_nat
| U_1781 != zero_zero_nat ),
inference(clausify,[status(thm)],[f_721_3]) ).
cnf(f_721_5,plain,
( hAPP_nat_nat(times_times_nat(U_1782),U_1784) = hAPP_nat_nat(plus_plus_nat(U_1784),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_1782),one_one_nat)),U_1784))
| U_1782 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_721_3]) ).
fof(f_722_1,plain,
! [P_1,M] :
( ( hAPP_nat_nat(power_power_nat(P_1),M) = hAPP_nat_nat(times_times_nat(P_1),hAPP_nat_nat(power_power_nat(P_1),hAPP_nat_nat(minus_minus_nat(M),one_one_nat)))
| M = zero_zero_nat )
& ( hAPP_nat_nat(power_power_nat(P_1),M) = one_one_nat
| M != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_696_power__eq__if]) ).
fof(f_722_2,plain,
! [U_1786,U_1785] :
( ( hAPP_nat_nat(power_power_nat(U_1786),U_1785) = hAPP_nat_nat(times_times_nat(U_1786),hAPP_nat_nat(power_power_nat(U_1786),hAPP_nat_nat(minus_minus_nat(U_1785),one_one_nat)))
| U_1785 = zero_zero_nat )
& ( hAPP_nat_nat(power_power_nat(U_1786),U_1785) = one_one_nat
| U_1785 != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_722_1]) ).
fof(f_722_3,plain,
( ! [U_1790,U_1788] :
( hAPP_nat_nat(power_power_nat(U_1790),U_1788) = hAPP_nat_nat(times_times_nat(U_1790),hAPP_nat_nat(power_power_nat(U_1790),hAPP_nat_nat(minus_minus_nat(U_1788),one_one_nat)))
| U_1788 = zero_zero_nat )
& ! [U_1789,U_1787] :
( hAPP_nat_nat(power_power_nat(U_1789),U_1787) = one_one_nat
| U_1787 != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_722_2]) ).
cnf(f_722_4,plain,
( hAPP_nat_nat(power_power_nat(U_1789),U_1787) = one_one_nat
| U_1787 != zero_zero_nat ),
inference(clausify,[status(thm)],[f_722_3]) ).
cnf(f_722_5,plain,
( hAPP_nat_nat(power_power_nat(U_1790),U_1788) = hAPP_nat_nat(times_times_nat(U_1790),hAPP_nat_nat(power_power_nat(U_1790),hAPP_nat_nat(minus_minus_nat(U_1788),one_one_nat)))
| U_1788 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_722_3]) ).
fof(f_723_1,plain,
! [X_1,Y_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(power_power_nat(X_1),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(Y_1),number_number_of_nat(bit0(bit1(pls))))) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(X_1),Y_1)),hAPP_nat_nat(minus_minus_nat(X_1),Y_1)),
inference(fof_nnf,[status(thm)],[fact_697_diff__square]) ).
fof(f_723_2,plain,
! [U_1792,U_1791] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(power_power_nat(U_1792),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(U_1791),number_number_of_nat(bit0(bit1(pls))))) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_1792),U_1791)),hAPP_nat_nat(minus_minus_nat(U_1792),U_1791)),
inference(variable_rename,[status(thm)],[f_723_1]) ).
cnf(f_723_3,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(power_power_nat(U_1792),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_nat(power_power_nat(U_1791),number_number_of_nat(bit0(bit1(pls))))) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_1792),U_1791)),hAPP_nat_nat(minus_minus_nat(U_1792),U_1791)),
inference(clausify,[status(thm)],[f_723_2]) ).
fof(f_724_1,plain,
! [A_50,B_44] :
( B_44 = zero_zero_real
| A_50 = zero_zero_real
| hAPP_real_real(times_times_real(A_50),B_44) != zero_zero_real ),
inference(fof_nnf,[status(thm)],[fact_698_divisors__zero]) ).
fof(f_724_2,plain,
! [U_1794,U_1793] :
( U_1793 = zero_zero_real
| U_1794 = zero_zero_real
| hAPP_real_real(times_times_real(U_1794),U_1793) != zero_zero_real ),
inference(variable_rename,[status(thm)],[f_724_1]) ).
cnf(f_724_3,plain,
( U_1793 = zero_zero_real
| U_1794 = zero_zero_real
| hAPP_real_real(times_times_real(U_1794),U_1793) != zero_zero_real ),
inference(clausify,[status(thm)],[f_724_2]) ).
fof(f_725_1,plain,
! [A_50,B_44] :
( B_44 = zero_zero_nat
| A_50 = zero_zero_nat
| hAPP_nat_nat(times_times_nat(A_50),B_44) != zero_zero_nat ),
inference(fof_nnf,[status(thm)],[fact_699_divisors__zero]) ).
fof(f_725_2,plain,
! [U_1796,U_1795] :
( U_1795 = zero_zero_nat
| U_1796 = zero_zero_nat
| hAPP_nat_nat(times_times_nat(U_1796),U_1795) != zero_zero_nat ),
inference(variable_rename,[status(thm)],[f_725_1]) ).
cnf(f_725_3,plain,
( U_1795 = zero_zero_nat
| U_1796 = zero_zero_nat
| hAPP_nat_nat(times_times_nat(U_1796),U_1795) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_725_2]) ).
fof(f_726_1,plain,
! [A_50,B_44] :
( B_44 = zero_zero_int
| A_50 = zero_zero_int
| hAPP_int_int(times_times_int(A_50),B_44) != zero_zero_int
| ~ is_int(B_44)
| ~ is_int(A_50) ),
inference(fof_nnf,[status(thm)],[fact_700_divisors__zero]) ).
fof(f_726_2,plain,
! [U_1798,U_1797] :
( U_1797 = zero_zero_int
| U_1798 = zero_zero_int
| hAPP_int_int(times_times_int(U_1798),U_1797) != zero_zero_int
| ~ is_int(U_1797)
| ~ is_int(U_1798) ),
inference(variable_rename,[status(thm)],[f_726_1]) ).
cnf(f_726_3,plain,
( U_1797 = zero_zero_int
| U_1798 = zero_zero_int
| hAPP_int_int(times_times_int(U_1798),U_1797) != zero_zero_int
| ~ is_int(U_1797)
| ~ is_int(U_1798) ),
inference(clausify,[status(thm)],[f_726_2]) ).
fof(f_727_1,plain,
! [B_43,A_49] :
( hAPP_real_real(times_times_real(A_49),B_43) != zero_zero_real
| B_43 = zero_zero_real
| A_49 = zero_zero_real ),
inference(fof_nnf,[status(thm)],[fact_701_no__zero__divisors]) ).
fof(f_727_2,plain,
! [U_1800,U_1799] :
( hAPP_real_real(times_times_real(U_1799),U_1800) != zero_zero_real
| U_1800 = zero_zero_real
| U_1799 = zero_zero_real ),
inference(variable_rename,[status(thm)],[f_727_1]) ).
cnf(f_727_3,plain,
( hAPP_real_real(times_times_real(U_1799),U_1800) != zero_zero_real
| U_1800 = zero_zero_real
| U_1799 = zero_zero_real ),
inference(clausify,[status(thm)],[f_727_2]) ).
fof(f_728_1,plain,
! [B_43,A_49] :
( hAPP_nat_nat(times_times_nat(A_49),B_43) != zero_zero_nat
| B_43 = zero_zero_nat
| A_49 = zero_zero_nat ),
inference(fof_nnf,[status(thm)],[fact_702_no__zero__divisors]) ).
fof(f_728_2,plain,
! [U_1802,U_1801] :
( hAPP_nat_nat(times_times_nat(U_1801),U_1802) != zero_zero_nat
| U_1802 = zero_zero_nat
| U_1801 = zero_zero_nat ),
inference(variable_rename,[status(thm)],[f_728_1]) ).
cnf(f_728_3,plain,
( hAPP_nat_nat(times_times_nat(U_1801),U_1802) != zero_zero_nat
| U_1802 = zero_zero_nat
| U_1801 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_728_2]) ).
fof(f_729_1,plain,
! [B_43,A_49] :
( hAPP_int_int(times_times_int(A_49),B_43) != zero_zero_int
| B_43 = zero_zero_int
| A_49 = zero_zero_int
| ~ is_int(A_49)
| ~ is_int(B_43) ),
inference(fof_nnf,[status(thm)],[fact_703_no__zero__divisors]) ).
fof(f_729_2,plain,
! [U_1804,U_1803] :
( hAPP_int_int(times_times_int(U_1803),U_1804) != zero_zero_int
| U_1804 = zero_zero_int
| U_1803 = zero_zero_int
| ~ is_int(U_1803)
| ~ is_int(U_1804) ),
inference(variable_rename,[status(thm)],[f_729_1]) ).
cnf(f_729_3,plain,
( hAPP_int_int(times_times_int(U_1803),U_1804) != zero_zero_int
| U_1804 = zero_zero_int
| U_1803 = zero_zero_int
| ~ is_int(U_1803)
| ~ is_int(U_1804) ),
inference(clausify,[status(thm)],[f_729_2]) ).
fof(f_730_1,plain,
! [A_2,B_2] :
( ( hAPP_real_real(times_times_real(A_2),B_2) = zero_zero_real
| ( B_2 != zero_zero_real
& A_2 != zero_zero_real ) )
& ( B_2 = zero_zero_real
| A_2 = zero_zero_real
| hAPP_real_real(times_times_real(A_2),B_2) != zero_zero_real ) ),
inference(fof_nnf,[status(thm)],[fact_704_mult__eq__0__iff]) ).
fof(f_730_2,plain,
! [U_1806,U_1805] :
( ( hAPP_real_real(times_times_real(U_1806),U_1805) = zero_zero_real
| ( U_1805 != zero_zero_real
& U_1806 != zero_zero_real ) )
& ( U_1805 = zero_zero_real
| U_1806 = zero_zero_real
| hAPP_real_real(times_times_real(U_1806),U_1805) != zero_zero_real ) ),
inference(variable_rename,[status(thm)],[f_730_1]) ).
fof(f_730_3,plain,
( ! [U_1810,U_1808] :
( hAPP_real_real(times_times_real(U_1810),U_1808) = zero_zero_real
| ( U_1808 != zero_zero_real
& U_1810 != zero_zero_real ) )
& ! [U_1809,U_1807] :
( U_1807 = zero_zero_real
| U_1809 = zero_zero_real
| hAPP_real_real(times_times_real(U_1809),U_1807) != zero_zero_real ) ),
inference(miniscope,[status(thm)],[f_730_2]) ).
cnf(f_730_4,plain,
( U_1807 = zero_zero_real
| U_1809 = zero_zero_real
| hAPP_real_real(times_times_real(U_1809),U_1807) != zero_zero_real ),
inference(clausify,[status(thm)],[f_730_3]) ).
cnf(f_730_5,plain,
( U_1810 != zero_zero_real
| hAPP_real_real(times_times_real(U_1810),U_1808) = zero_zero_real ),
inference(clausify,[status(thm)],[f_730_3]) ).
cnf(f_730_6,plain,
( U_1808 != zero_zero_real
| hAPP_real_real(times_times_real(U_1810),U_1808) = zero_zero_real ),
inference(clausify,[status(thm)],[f_730_3]) ).
fof(f_731_1,plain,
! [A_2,B_2] :
( ( ( hAPP_int_int(times_times_int(A_2),B_2) = zero_zero_int
| ( B_2 != zero_zero_int
& A_2 != zero_zero_int ) )
& ( B_2 = zero_zero_int
| A_2 = zero_zero_int
| hAPP_int_int(times_times_int(A_2),B_2) != zero_zero_int ) )
| ~ is_int(B_2)
| ~ is_int(A_2) ),
inference(fof_nnf,[status(thm)],[fact_705_mult__eq__0__iff]) ).
fof(f_731_2,plain,
! [U_1812,U_1811] :
( ( ( hAPP_int_int(times_times_int(U_1812),U_1811) = zero_zero_int
| ( U_1811 != zero_zero_int
& U_1812 != zero_zero_int ) )
& ( U_1811 = zero_zero_int
| U_1812 = zero_zero_int
| hAPP_int_int(times_times_int(U_1812),U_1811) != zero_zero_int ) )
| ~ is_int(U_1811)
| ~ is_int(U_1812) ),
inference(variable_rename,[status(thm)],[f_731_1]) ).
cnf(f_731_3,plain,
( U_1811 = zero_zero_int
| U_1812 = zero_zero_int
| hAPP_int_int(times_times_int(U_1812),U_1811) != zero_zero_int
| ~ is_int(U_1811)
| ~ is_int(U_1812) ),
inference(clausify,[status(thm)],[f_731_2]) ).
cnf(f_731_4,plain,
( U_1812 != zero_zero_int
| hAPP_int_int(times_times_int(U_1812),U_1811) = zero_zero_int
| ~ is_int(U_1811)
| ~ is_int(U_1812) ),
inference(clausify,[status(thm)],[f_731_2]) ).
cnf(f_731_5,plain,
( U_1811 != zero_zero_int
| hAPP_int_int(times_times_int(U_1812),U_1811) = zero_zero_int
| ~ is_int(U_1811)
| ~ is_int(U_1812) ),
inference(clausify,[status(thm)],[f_731_2]) ).
fof(f_732_1,plain,
! [A_48] : hAPP_real_real(times_times_real(A_48),zero_zero_real) = zero_zero_real,
inference(fof_nnf,[status(thm)],[fact_706_mult__zero__right]) ).
fof(f_732_2,plain,
! [U_1813] : hAPP_real_real(times_times_real(U_1813),zero_zero_real) = zero_zero_real,
inference(variable_rename,[status(thm)],[f_732_1]) ).
cnf(f_732_3,plain,
hAPP_real_real(times_times_real(U_1813),zero_zero_real) = zero_zero_real,
inference(clausify,[status(thm)],[f_732_2]) ).
fof(f_733_1,plain,
! [A_48] : hAPP_nat_nat(times_times_nat(A_48),zero_zero_nat) = zero_zero_nat,
inference(fof_nnf,[status(thm)],[fact_707_mult__zero__right]) ).
fof(f_733_2,plain,
! [U_1814] : hAPP_nat_nat(times_times_nat(U_1814),zero_zero_nat) = zero_zero_nat,
inference(variable_rename,[status(thm)],[f_733_1]) ).
cnf(f_733_3,plain,
hAPP_nat_nat(times_times_nat(U_1814),zero_zero_nat) = zero_zero_nat,
inference(clausify,[status(thm)],[f_733_2]) ).
fof(f_734_1,plain,
! [A_48] : hAPP_int_int(times_times_int(A_48),zero_zero_int) = zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_708_mult__zero__right]) ).
fof(f_734_2,plain,
! [U_1815] : hAPP_int_int(times_times_int(U_1815),zero_zero_int) = zero_zero_int,
inference(variable_rename,[status(thm)],[f_734_1]) ).
cnf(f_734_3,plain,
hAPP_int_int(times_times_int(U_1815),zero_zero_int) = zero_zero_int,
inference(clausify,[status(thm)],[f_734_2]) ).
fof(f_735_1,plain,
! [A_47] : hAPP_real_real(times_times_real(zero_zero_real),A_47) = zero_zero_real,
inference(fof_nnf,[status(thm)],[fact_709_mult__zero__left]) ).
fof(f_735_2,plain,
! [U_1816] : hAPP_real_real(times_times_real(zero_zero_real),U_1816) = zero_zero_real,
inference(variable_rename,[status(thm)],[f_735_1]) ).
cnf(f_735_3,plain,
hAPP_real_real(times_times_real(zero_zero_real),U_1816) = zero_zero_real,
inference(clausify,[status(thm)],[f_735_2]) ).
fof(f_736_1,plain,
! [A_47] : hAPP_nat_nat(times_times_nat(zero_zero_nat),A_47) = zero_zero_nat,
inference(fof_nnf,[status(thm)],[fact_710_mult__zero__left]) ).
fof(f_736_2,plain,
! [U_1817] : hAPP_nat_nat(times_times_nat(zero_zero_nat),U_1817) = zero_zero_nat,
inference(variable_rename,[status(thm)],[f_736_1]) ).
cnf(f_736_3,plain,
hAPP_nat_nat(times_times_nat(zero_zero_nat),U_1817) = zero_zero_nat,
inference(clausify,[status(thm)],[f_736_2]) ).
fof(f_737_1,plain,
! [A_47] : hAPP_int_int(times_times_int(zero_zero_int),A_47) = zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_711_mult__zero__left]) ).
fof(f_737_2,plain,
! [U_1818] : hAPP_int_int(times_times_int(zero_zero_int),U_1818) = zero_zero_int,
inference(variable_rename,[status(thm)],[f_737_1]) ).
cnf(f_737_3,plain,
hAPP_int_int(times_times_int(zero_zero_int),U_1818) = zero_zero_int,
inference(clausify,[status(thm)],[f_737_2]) ).
fof(f_738_1,plain,
zero_zero_real != one_one_real,
inference(fof_nnf,[status(thm)],[fact_712_zero__neq__one]) ).
cnf(f_738_2,plain,
zero_zero_real != one_one_real,
inference(clausify,[status(thm)],[f_738_1]) ).
fof(f_739_1,plain,
zero_zero_nat != one_one_nat,
inference(fof_nnf,[status(thm)],[fact_713_zero__neq__one]) ).
cnf(f_739_2,plain,
zero_zero_nat != one_one_nat,
inference(clausify,[status(thm)],[f_739_1]) ).
fof(f_740_1,plain,
zero_zero_int != one_one_int,
inference(fof_nnf,[status(thm)],[fact_714_zero__neq__one]) ).
cnf(f_740_2,plain,
zero_zero_int != one_one_int,
inference(clausify,[status(thm)],[f_740_1]) ).
fof(f_741_1,plain,
one_one_real != zero_zero_real,
inference(fof_nnf,[status(thm)],[fact_715_one__neq__zero]) ).
cnf(f_741_2,plain,
one_one_real != zero_zero_real,
inference(clausify,[status(thm)],[f_741_1]) ).
fof(f_742_1,plain,
one_one_nat != zero_zero_nat,
inference(fof_nnf,[status(thm)],[fact_716_one__neq__zero]) ).
cnf(f_742_2,plain,
one_one_nat != zero_zero_nat,
inference(clausify,[status(thm)],[f_742_1]) ).
fof(f_743_1,plain,
one_one_int != zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_717_one__neq__zero]) ).
cnf(f_743_2,plain,
one_one_int != zero_zero_int,
inference(clausify,[status(thm)],[f_743_1]) ).
fof(f_744_1,plain,
! [A_46,E,B_42,C_23] : hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_46),E)),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(B_42),E)),C_23)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_46),B_42)),E)),C_23),
inference(fof_nnf,[status(thm)],[fact_718_combine__common__factor]) ).
fof(f_744_2,plain,
! [U_1822,U_1821,U_1820,U_1819] : hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_1822),U_1821)),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_1820),U_1821)),U_1819)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(U_1822),U_1820)),U_1821)),U_1819),
inference(variable_rename,[status(thm)],[f_744_1]) ).
cnf(f_744_3,plain,
hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_1822),U_1821)),hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_1820),U_1821)),U_1819)) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(U_1822),U_1820)),U_1821)),U_1819),
inference(clausify,[status(thm)],[f_744_2]) ).
fof(f_745_1,plain,
! [A_46,E,B_42,C_23] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_46),E)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(B_42),E)),C_23)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_46),B_42)),E)),C_23),
inference(fof_nnf,[status(thm)],[fact_719_combine__common__factor]) ).
fof(f_745_2,plain,
! [U_1826,U_1825,U_1824,U_1823] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_1826),U_1825)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_1824),U_1825)),U_1823)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_1826),U_1824)),U_1825)),U_1823),
inference(variable_rename,[status(thm)],[f_745_1]) ).
cnf(f_745_3,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_1826),U_1825)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_1824),U_1825)),U_1823)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_1826),U_1824)),U_1825)),U_1823),
inference(clausify,[status(thm)],[f_745_2]) ).
fof(f_746_1,plain,
! [A_46,E,B_42,C_23] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_46),E)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B_42),E)),C_23)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_46),B_42)),E)),C_23),
inference(fof_nnf,[status(thm)],[fact_720_combine__common__factor]) ).
fof(f_746_2,plain,
! [U_1830,U_1829,U_1828,U_1827] : hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1830),U_1829)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1828),U_1829)),U_1827)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(U_1830),U_1828)),U_1829)),U_1827),
inference(variable_rename,[status(thm)],[f_746_1]) ).
cnf(f_746_3,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1830),U_1829)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1828),U_1829)),U_1827)) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(U_1830),U_1828)),U_1829)),U_1827),
inference(clausify,[status(thm)],[f_746_2]) ).
fof(f_747_1,plain,
! [A_45,B_41,C_22] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(A_45),B_41)),C_22) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(A_45),C_22)),hAPP_real_real(times_times_real(B_41),C_22)),
inference(fof_nnf,[status(thm)],[fact_721_comm__semiring__class_Odistrib]) ).
fof(f_747_2,plain,
! [U_1833,U_1832,U_1831] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(U_1833),U_1832)),U_1831) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_1833),U_1831)),hAPP_real_real(times_times_real(U_1832),U_1831)),
inference(variable_rename,[status(thm)],[f_747_1]) ).
cnf(f_747_3,plain,
hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(U_1833),U_1832)),U_1831) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_1833),U_1831)),hAPP_real_real(times_times_real(U_1832),U_1831)),
inference(clausify,[status(thm)],[f_747_2]) ).
fof(f_748_1,plain,
! [A_45,B_41,C_22] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(A_45),B_41)),C_22) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(A_45),C_22)),hAPP_nat_nat(times_times_nat(B_41),C_22)),
inference(fof_nnf,[status(thm)],[fact_722_comm__semiring__class_Odistrib]) ).
fof(f_748_2,plain,
! [U_1836,U_1835,U_1834] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_1836),U_1835)),U_1834) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_1836),U_1834)),hAPP_nat_nat(times_times_nat(U_1835),U_1834)),
inference(variable_rename,[status(thm)],[f_748_1]) ).
cnf(f_748_3,plain,
hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_1836),U_1835)),U_1834) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_1836),U_1834)),hAPP_nat_nat(times_times_nat(U_1835),U_1834)),
inference(clausify,[status(thm)],[f_748_2]) ).
fof(f_749_1,plain,
! [A_45,B_41,C_22] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(A_45),B_41)),C_22) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(A_45),C_22)),hAPP_int_int(times_times_int(B_41),C_22)),
inference(fof_nnf,[status(thm)],[fact_723_comm__semiring__class_Odistrib]) ).
fof(f_749_2,plain,
! [U_1839,U_1838,U_1837] : hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(U_1839),U_1838)),U_1837) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1839),U_1837)),hAPP_int_int(times_times_int(U_1838),U_1837)),
inference(variable_rename,[status(thm)],[f_749_1]) ).
cnf(f_749_3,plain,
hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(U_1839),U_1838)),U_1837) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_1839),U_1837)),hAPP_int_int(times_times_int(U_1838),U_1837)),
inference(clausify,[status(thm)],[f_749_2]) ).
fof(f_750_1,plain,
! [A_44] :
( A_44 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,zero_zero_real),A_44)) ),
inference(fof_nnf,[status(thm)],[fact_724_dvd__0__left]) ).
fof(f_750_2,plain,
! [U_1840] :
( U_1840 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,zero_zero_real),U_1840)) ),
inference(variable_rename,[status(thm)],[f_750_1]) ).
cnf(f_750_3,plain,
( U_1840 = zero_zero_real
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,zero_zero_real),U_1840)) ),
inference(clausify,[status(thm)],[f_750_2]) ).
fof(f_751_1,plain,
! [A_44] :
( A_44 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),A_44)) ),
inference(fof_nnf,[status(thm)],[fact_725_dvd__0__left]) ).
fof(f_751_2,plain,
! [U_1841] :
( U_1841 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),U_1841)) ),
inference(variable_rename,[status(thm)],[f_751_1]) ).
cnf(f_751_3,plain,
( U_1841 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),U_1841)) ),
inference(clausify,[status(thm)],[f_751_2]) ).
fof(f_752_1,plain,
! [A_44] :
( A_44 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,zero_zero_int),A_44))
| ~ is_int(A_44) ),
inference(fof_nnf,[status(thm)],[fact_726_dvd__0__left]) ).
fof(f_752_2,plain,
! [U_1842] :
( U_1842 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,zero_zero_int),U_1842))
| ~ is_int(U_1842) ),
inference(variable_rename,[status(thm)],[f_752_1]) ).
cnf(f_752_3,plain,
( U_1842 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,zero_zero_int),U_1842))
| ~ is_int(U_1842) ),
inference(clausify,[status(thm)],[f_752_2]) ).
fof(f_753_1,plain,
! [A_43,C_21,B_40,D_7] : hAPP_real_real(minus_minus_real(hAPP_real_real(plus_plus_real(A_43),C_21)),hAPP_real_real(plus_plus_real(B_40),D_7)) = hAPP_real_real(plus_plus_real(hAPP_real_real(minus_minus_real(A_43),B_40)),hAPP_real_real(minus_minus_real(C_21),D_7)),
inference(fof_nnf,[status(thm)],[fact_727_add__diff__add]) ).
fof(f_753_2,plain,
! [U_1846,U_1845,U_1844,U_1843] : hAPP_real_real(minus_minus_real(hAPP_real_real(plus_plus_real(U_1846),U_1845)),hAPP_real_real(plus_plus_real(U_1844),U_1843)) = hAPP_real_real(plus_plus_real(hAPP_real_real(minus_minus_real(U_1846),U_1844)),hAPP_real_real(minus_minus_real(U_1845),U_1843)),
inference(variable_rename,[status(thm)],[f_753_1]) ).
cnf(f_753_3,plain,
hAPP_real_real(minus_minus_real(hAPP_real_real(plus_plus_real(U_1846),U_1845)),hAPP_real_real(plus_plus_real(U_1844),U_1843)) = hAPP_real_real(plus_plus_real(hAPP_real_real(minus_minus_real(U_1846),U_1844)),hAPP_real_real(minus_minus_real(U_1845),U_1843)),
inference(clausify,[status(thm)],[f_753_2]) ).
fof(f_754_1,plain,
! [A_43,C_21,B_40,D_7] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(A_43),C_21)),hAPP_int_int(plus_plus_int(B_40),D_7)) = hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(A_43),B_40)),hAPP_int_int(minus_minus_int(C_21),D_7)),
inference(fof_nnf,[status(thm)],[fact_728_add__diff__add]) ).
fof(f_754_2,plain,
! [U_1850,U_1849,U_1848,U_1847] : hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(U_1850),U_1849)),hAPP_int_int(plus_plus_int(U_1848),U_1847)) = hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(U_1850),U_1848)),hAPP_int_int(minus_minus_int(U_1849),U_1847)),
inference(variable_rename,[status(thm)],[f_754_1]) ).
cnf(f_754_3,plain,
hAPP_int_int(minus_minus_int(hAPP_int_int(plus_plus_int(U_1850),U_1849)),hAPP_int_int(plus_plus_int(U_1848),U_1847)) = hAPP_int_int(plus_plus_int(hAPP_int_int(minus_minus_int(U_1850),U_1848)),hAPP_int_int(minus_minus_int(U_1849),U_1847)),
inference(clausify,[status(thm)],[f_754_2]) ).
fof(f_755_1,plain,
! [A_42,B_39,C_20] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,B_39),C_20))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(A_42),B_39)),C_20)) ),
inference(fof_nnf,[status(thm)],[fact_729_dvd__mult__right]) ).
fof(f_755_2,plain,
! [U_1853,U_1852,U_1851] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1852),U_1851))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(U_1853),U_1852)),U_1851)) ),
inference(variable_rename,[status(thm)],[f_755_1]) ).
cnf(f_755_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1852),U_1851))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(U_1853),U_1852)),U_1851)) ),
inference(clausify,[status(thm)],[f_755_2]) ).
fof(f_756_1,plain,
! [A_42,B_39,C_20] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B_39),C_20))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(A_42),B_39)),C_20)) ),
inference(fof_nnf,[status(thm)],[fact_730_dvd__mult__right]) ).
fof(f_756_2,plain,
! [U_1856,U_1855,U_1854] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1855),U_1854))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_1856),U_1855)),U_1854)) ),
inference(variable_rename,[status(thm)],[f_756_1]) ).
cnf(f_756_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1855),U_1854))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_1856),U_1855)),U_1854)) ),
inference(clausify,[status(thm)],[f_756_2]) ).
fof(f_757_1,plain,
! [A_42,B_39,C_20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,B_39),C_20))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(A_42),B_39)),C_20)) ),
inference(fof_nnf,[status(thm)],[fact_731_dvd__mult__right]) ).
fof(f_757_2,plain,
! [U_1859,U_1858,U_1857] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1858),U_1857))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(U_1859),U_1858)),U_1857)) ),
inference(variable_rename,[status(thm)],[f_757_1]) ).
cnf(f_757_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1858),U_1857))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(U_1859),U_1858)),U_1857)) ),
inference(clausify,[status(thm)],[f_757_2]) ).
fof(f_758_1,plain,
! [A_41,B_38,C_19] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_41),C_19))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(A_41),B_38)),C_19)) ),
inference(fof_nnf,[status(thm)],[fact_732_dvd__mult__left]) ).
fof(f_758_2,plain,
! [U_1862,U_1861,U_1860] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1862),U_1860))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(U_1862),U_1861)),U_1860)) ),
inference(variable_rename,[status(thm)],[f_758_1]) ).
cnf(f_758_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1862),U_1860))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(U_1862),U_1861)),U_1860)) ),
inference(clausify,[status(thm)],[f_758_2]) ).
fof(f_759_1,plain,
! [A_41,B_38,C_19] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_41),C_19))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(A_41),B_38)),C_19)) ),
inference(fof_nnf,[status(thm)],[fact_733_dvd__mult__left]) ).
fof(f_759_2,plain,
! [U_1865,U_1864,U_1863] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1865),U_1863))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_1865),U_1864)),U_1863)) ),
inference(variable_rename,[status(thm)],[f_759_1]) ).
cnf(f_759_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1865),U_1863))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_1865),U_1864)),U_1863)) ),
inference(clausify,[status(thm)],[f_759_2]) ).
fof(f_760_1,plain,
! [A_41,B_38,C_19] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_41),C_19))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(A_41),B_38)),C_19)) ),
inference(fof_nnf,[status(thm)],[fact_734_dvd__mult__left]) ).
fof(f_760_2,plain,
! [U_1868,U_1867,U_1866] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1868),U_1866))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(U_1868),U_1867)),U_1866)) ),
inference(variable_rename,[status(thm)],[f_760_1]) ).
cnf(f_760_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1868),U_1866))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(U_1868),U_1867)),U_1866)) ),
inference(clausify,[status(thm)],[f_760_2]) ).
fof(f_761_1,plain,
! [A_40,B_37,K_3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,B_37),A_40))
| A_40 != hAPP_real_real(times_times_real(B_37),K_3) ),
inference(fof_nnf,[status(thm)],[fact_735_dvdI]) ).
fof(f_761_2,plain,
! [U_1871,U_1870,U_1869] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1870),U_1871))
| U_1871 != hAPP_real_real(times_times_real(U_1870),U_1869) ),
inference(variable_rename,[status(thm)],[f_761_1]) ).
fof(f_761_3,plain,
! [U_1871,U_1870] :
( ! [U_1869] : U_1871 != hAPP_real_real(times_times_real(U_1870),U_1869)
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1870),U_1871)) ),
inference(miniscope,[status(thm)],[f_761_2]) ).
cnf(f_761_4,plain,
( U_1871 != hAPP_real_real(times_times_real(U_1870),U_1869)
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1870),U_1871)) ),
inference(clausify,[status(thm)],[f_761_3]) ).
fof(f_762_1,plain,
! [A_40,B_37,K_3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B_37),A_40))
| A_40 != hAPP_nat_nat(times_times_nat(B_37),K_3) ),
inference(fof_nnf,[status(thm)],[fact_736_dvdI]) ).
fof(f_762_2,plain,
! [U_1874,U_1873,U_1872] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1873),U_1874))
| U_1874 != hAPP_nat_nat(times_times_nat(U_1873),U_1872) ),
inference(variable_rename,[status(thm)],[f_762_1]) ).
fof(f_762_3,plain,
! [U_1874,U_1873] :
( ! [U_1872] : U_1874 != hAPP_nat_nat(times_times_nat(U_1873),U_1872)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1873),U_1874)) ),
inference(miniscope,[status(thm)],[f_762_2]) ).
cnf(f_762_4,plain,
( U_1874 != hAPP_nat_nat(times_times_nat(U_1873),U_1872)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1873),U_1874)) ),
inference(clausify,[status(thm)],[f_762_3]) ).
fof(f_763_1,plain,
! [A_40,B_37,K_3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,B_37),A_40))
| A_40 != hAPP_int_int(times_times_int(B_37),K_3) ),
inference(fof_nnf,[status(thm)],[fact_737_dvdI]) ).
fof(f_763_2,plain,
! [U_1877,U_1876,U_1875] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1876),U_1877))
| U_1877 != hAPP_int_int(times_times_int(U_1876),U_1875) ),
inference(variable_rename,[status(thm)],[f_763_1]) ).
fof(f_763_3,plain,
! [U_1877,U_1876] :
( ! [U_1875] : U_1877 != hAPP_int_int(times_times_int(U_1876),U_1875)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1876),U_1877)) ),
inference(miniscope,[status(thm)],[f_763_2]) ).
cnf(f_763_4,plain,
( U_1877 != hAPP_int_int(times_times_int(U_1876),U_1875)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1876),U_1877)) ),
inference(clausify,[status(thm)],[f_763_3]) ).
fof(f_764_1,plain,
! [C_18,D_6,A_39,B_36] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(A_39),C_18)),hAPP_real_real(times_times_real(B_36),D_6)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,C_18),D_6))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_39),B_36)) ),
inference(fof_nnf,[status(thm)],[fact_738_mult__dvd__mono]) ).
fof(f_764_2,plain,
! [U_1881,U_1880,U_1879,U_1878] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(U_1879),U_1881)),hAPP_real_real(times_times_real(U_1878),U_1880)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1881),U_1880))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1879),U_1878)) ),
inference(variable_rename,[status(thm)],[f_764_1]) ).
cnf(f_764_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,hAPP_real_real(times_times_real(U_1879),U_1881)),hAPP_real_real(times_times_real(U_1878),U_1880)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1881),U_1880))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1879),U_1878)) ),
inference(clausify,[status(thm)],[f_764_2]) ).
fof(f_765_1,plain,
! [C_18,D_6,A_39,B_36] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(A_39),C_18)),hAPP_nat_nat(times_times_nat(B_36),D_6)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,C_18),D_6))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_39),B_36)) ),
inference(fof_nnf,[status(thm)],[fact_739_mult__dvd__mono]) ).
fof(f_765_2,plain,
! [U_1885,U_1884,U_1883,U_1882] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_1883),U_1885)),hAPP_nat_nat(times_times_nat(U_1882),U_1884)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1885),U_1884))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1883),U_1882)) ),
inference(variable_rename,[status(thm)],[f_765_1]) ).
cnf(f_765_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_1883),U_1885)),hAPP_nat_nat(times_times_nat(U_1882),U_1884)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1885),U_1884))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1883),U_1882)) ),
inference(clausify,[status(thm)],[f_765_2]) ).
fof(f_766_1,plain,
! [C_18,D_6,A_39,B_36] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(A_39),C_18)),hAPP_int_int(times_times_int(B_36),D_6)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,C_18),D_6))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_39),B_36)) ),
inference(fof_nnf,[status(thm)],[fact_740_mult__dvd__mono]) ).
fof(f_766_2,plain,
! [U_1889,U_1888,U_1887,U_1886] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(U_1887),U_1889)),hAPP_int_int(times_times_int(U_1886),U_1888)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1889),U_1888))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1887),U_1886)) ),
inference(variable_rename,[status(thm)],[f_766_1]) ).
cnf(f_766_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(U_1887),U_1889)),hAPP_int_int(times_times_int(U_1886),U_1888)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1889),U_1888))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1887),U_1886)) ),
inference(clausify,[status(thm)],[f_766_2]) ).
fof(f_767_1,plain,
! [B_35,A_38,C_17] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_38),hAPP_real_real(times_times_real(B_35),C_17)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_38),C_17)) ),
inference(fof_nnf,[status(thm)],[fact_741_dvd__mult]) ).
fof(f_767_2,plain,
! [U_1892,U_1891,U_1890] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1891),hAPP_real_real(times_times_real(U_1892),U_1890)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1891),U_1890)) ),
inference(variable_rename,[status(thm)],[f_767_1]) ).
cnf(f_767_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1891),hAPP_real_real(times_times_real(U_1892),U_1890)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1891),U_1890)) ),
inference(clausify,[status(thm)],[f_767_2]) ).
fof(f_768_1,plain,
! [B_35,A_38,C_17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_38),hAPP_nat_nat(times_times_nat(B_35),C_17)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_38),C_17)) ),
inference(fof_nnf,[status(thm)],[fact_742_dvd__mult]) ).
fof(f_768_2,plain,
! [U_1895,U_1894,U_1893] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1894),hAPP_nat_nat(times_times_nat(U_1895),U_1893)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1894),U_1893)) ),
inference(variable_rename,[status(thm)],[f_768_1]) ).
cnf(f_768_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1894),hAPP_nat_nat(times_times_nat(U_1895),U_1893)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1894),U_1893)) ),
inference(clausify,[status(thm)],[f_768_2]) ).
fof(f_769_1,plain,
! [B_35,A_38,C_17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_38),hAPP_int_int(times_times_int(B_35),C_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_38),C_17)) ),
inference(fof_nnf,[status(thm)],[fact_743_dvd__mult]) ).
fof(f_769_2,plain,
! [U_1898,U_1897,U_1896] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1897),hAPP_int_int(times_times_int(U_1898),U_1896)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1897),U_1896)) ),
inference(variable_rename,[status(thm)],[f_769_1]) ).
cnf(f_769_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1897),hAPP_int_int(times_times_int(U_1898),U_1896)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1897),U_1896)) ),
inference(clausify,[status(thm)],[f_769_2]) ).
fof(f_770_1,plain,
! [C_16,A_37,B_34] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_37),hAPP_real_real(times_times_real(B_34),C_16)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_37),B_34)) ),
inference(fof_nnf,[status(thm)],[fact_744_dvd__mult2]) ).
fof(f_770_2,plain,
! [U_1901,U_1900,U_1899] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1900),hAPP_real_real(times_times_real(U_1899),U_1901)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1900),U_1899)) ),
inference(variable_rename,[status(thm)],[f_770_1]) ).
cnf(f_770_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1900),hAPP_real_real(times_times_real(U_1899),U_1901)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1900),U_1899)) ),
inference(clausify,[status(thm)],[f_770_2]) ).
fof(f_771_1,plain,
! [C_16,A_37,B_34] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_37),hAPP_nat_nat(times_times_nat(B_34),C_16)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_37),B_34)) ),
inference(fof_nnf,[status(thm)],[fact_745_dvd__mult2]) ).
fof(f_771_2,plain,
! [U_1904,U_1903,U_1902] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1903),hAPP_nat_nat(times_times_nat(U_1902),U_1904)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1903),U_1902)) ),
inference(variable_rename,[status(thm)],[f_771_1]) ).
cnf(f_771_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1903),hAPP_nat_nat(times_times_nat(U_1902),U_1904)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1903),U_1902)) ),
inference(clausify,[status(thm)],[f_771_2]) ).
fof(f_772_1,plain,
! [C_16,A_37,B_34] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_37),hAPP_int_int(times_times_int(B_34),C_16)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_37),B_34)) ),
inference(fof_nnf,[status(thm)],[fact_746_dvd__mult2]) ).
fof(f_772_2,plain,
! [U_1907,U_1906,U_1905] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1906),hAPP_int_int(times_times_int(U_1905),U_1907)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1906),U_1905)) ),
inference(variable_rename,[status(thm)],[f_772_1]) ).
cnf(f_772_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1906),hAPP_int_int(times_times_int(U_1905),U_1907)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1906),U_1905)) ),
inference(clausify,[status(thm)],[f_772_2]) ).
fof(f_773_1,plain,
! [A_36,B_33] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_36),hAPP_real_real(times_times_real(B_33),A_36))),
inference(fof_nnf,[status(thm)],[fact_747_dvd__triv__right]) ).
fof(f_773_2,plain,
! [U_1909,U_1908] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1909),hAPP_real_real(times_times_real(U_1908),U_1909))),
inference(variable_rename,[status(thm)],[f_773_1]) ).
cnf(f_773_3,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1909),hAPP_real_real(times_times_real(U_1908),U_1909))),
inference(clausify,[status(thm)],[f_773_2]) ).
fof(f_774_1,plain,
! [A_36,B_33] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_36),hAPP_nat_nat(times_times_nat(B_33),A_36))),
inference(fof_nnf,[status(thm)],[fact_748_dvd__triv__right]) ).
fof(f_774_2,plain,
! [U_1911,U_1910] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1911),hAPP_nat_nat(times_times_nat(U_1910),U_1911))),
inference(variable_rename,[status(thm)],[f_774_1]) ).
cnf(f_774_3,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1911),hAPP_nat_nat(times_times_nat(U_1910),U_1911))),
inference(clausify,[status(thm)],[f_774_2]) ).
fof(f_775_1,plain,
! [A_36,B_33] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_36),hAPP_int_int(times_times_int(B_33),A_36))),
inference(fof_nnf,[status(thm)],[fact_749_dvd__triv__right]) ).
fof(f_775_2,plain,
! [U_1913,U_1912] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1913),hAPP_int_int(times_times_int(U_1912),U_1913))),
inference(variable_rename,[status(thm)],[f_775_1]) ).
cnf(f_775_3,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1913),hAPP_int_int(times_times_int(U_1912),U_1913))),
inference(clausify,[status(thm)],[f_775_2]) ).
fof(f_776_1,plain,
! [A_35,B_32] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_35),hAPP_real_real(times_times_real(A_35),B_32))),
inference(fof_nnf,[status(thm)],[fact_750_dvd__triv__left]) ).
fof(f_776_2,plain,
! [U_1915,U_1914] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1915),hAPP_real_real(times_times_real(U_1915),U_1914))),
inference(variable_rename,[status(thm)],[f_776_1]) ).
cnf(f_776_3,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1915),hAPP_real_real(times_times_real(U_1915),U_1914))),
inference(clausify,[status(thm)],[f_776_2]) ).
fof(f_777_1,plain,
! [A_35,B_32] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_35),hAPP_nat_nat(times_times_nat(A_35),B_32))),
inference(fof_nnf,[status(thm)],[fact_751_dvd__triv__left]) ).
fof(f_777_2,plain,
! [U_1917,U_1916] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1917),hAPP_nat_nat(times_times_nat(U_1917),U_1916))),
inference(variable_rename,[status(thm)],[f_777_1]) ).
cnf(f_777_3,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1917),hAPP_nat_nat(times_times_nat(U_1917),U_1916))),
inference(clausify,[status(thm)],[f_777_2]) ).
fof(f_778_1,plain,
! [A_35,B_32] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_35),hAPP_int_int(times_times_int(A_35),B_32))),
inference(fof_nnf,[status(thm)],[fact_752_dvd__triv__left]) ).
fof(f_778_2,plain,
! [U_1919,U_1918] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1919),hAPP_int_int(times_times_int(U_1919),U_1918))),
inference(variable_rename,[status(thm)],[f_778_1]) ).
cnf(f_778_3,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1919),hAPP_int_int(times_times_int(U_1919),U_1918))),
inference(clausify,[status(thm)],[f_778_2]) ).
fof(f_779_1,plain,
! [C_15,A_34,B_31] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_34),hAPP_real_real(plus_plus_real(B_31),C_15)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_34),C_15))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,A_34),B_31)) ),
inference(fof_nnf,[status(thm)],[fact_753_dvd__add]) ).
fof(f_779_2,plain,
! [U_1922,U_1921,U_1920] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1921),hAPP_real_real(plus_plus_real(U_1920),U_1922)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1921),U_1922))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1921),U_1920)) ),
inference(variable_rename,[status(thm)],[f_779_1]) ).
cnf(f_779_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1921),hAPP_real_real(plus_plus_real(U_1920),U_1922)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1921),U_1922))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1921),U_1920)) ),
inference(clausify,[status(thm)],[f_779_2]) ).
fof(f_780_1,plain,
! [C_15,A_34,B_31] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_34),hAPP_nat_nat(plus_plus_nat(B_31),C_15)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_34),C_15))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_34),B_31)) ),
inference(fof_nnf,[status(thm)],[fact_754_dvd__add]) ).
fof(f_780_2,plain,
! [U_1925,U_1924,U_1923] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1924),hAPP_nat_nat(plus_plus_nat(U_1923),U_1925)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1924),U_1925))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1924),U_1923)) ),
inference(variable_rename,[status(thm)],[f_780_1]) ).
cnf(f_780_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1924),hAPP_nat_nat(plus_plus_nat(U_1923),U_1925)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1924),U_1925))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1924),U_1923)) ),
inference(clausify,[status(thm)],[f_780_2]) ).
fof(f_781_1,plain,
! [C_15,A_34,B_31] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_34),hAPP_int_int(plus_plus_int(B_31),C_15)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_34),C_15))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_34),B_31)) ),
inference(fof_nnf,[status(thm)],[fact_755_dvd__add]) ).
fof(f_781_2,plain,
! [U_1928,U_1927,U_1926] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1927),hAPP_int_int(plus_plus_int(U_1926),U_1928)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1927),U_1928))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1927),U_1926)) ),
inference(variable_rename,[status(thm)],[f_781_1]) ).
cnf(f_781_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1927),hAPP_int_int(plus_plus_int(U_1926),U_1928)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1927),U_1928))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1927),U_1926)) ),
inference(clausify,[status(thm)],[f_781_2]) ).
fof(f_782_1,plain,
! [A_33] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,one_one_real),A_33)),
inference(fof_nnf,[status(thm)],[fact_756_one__dvd]) ).
fof(f_782_2,plain,
! [U_1929] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,one_one_real),U_1929)),
inference(variable_rename,[status(thm)],[f_782_1]) ).
cnf(f_782_3,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,one_one_real),U_1929)),
inference(clausify,[status(thm)],[f_782_2]) ).
fof(f_783_1,plain,
! [A_33] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),A_33)),
inference(fof_nnf,[status(thm)],[fact_757_one__dvd]) ).
fof(f_783_2,plain,
! [U_1930] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),U_1930)),
inference(variable_rename,[status(thm)],[f_783_1]) ).
cnf(f_783_3,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),U_1930)),
inference(clausify,[status(thm)],[f_783_2]) ).
fof(f_784_1,plain,
! [A_33] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),A_33)),
inference(fof_nnf,[status(thm)],[fact_758_one__dvd]) ).
fof(f_784_2,plain,
! [U_1931] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),U_1931)),
inference(variable_rename,[status(thm)],[f_784_1]) ).
cnf(f_784_3,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,one_one_int),U_1931)),
inference(clausify,[status(thm)],[f_784_2]) ).
fof(f_785_1,plain,
! [Z_2,X_3,Y_3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X_3),hAPP_real_real(minus_minus_real(Y_3),Z_2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X_3),Z_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,X_3),Y_3)) ),
inference(fof_nnf,[status(thm)],[fact_759_dvd__diff]) ).
fof(f_785_2,plain,
! [U_1934,U_1933,U_1932] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1933),hAPP_real_real(minus_minus_real(U_1932),U_1934)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1933),U_1934))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1933),U_1932)) ),
inference(variable_rename,[status(thm)],[f_785_1]) ).
cnf(f_785_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1933),hAPP_real_real(minus_minus_real(U_1932),U_1934)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1933),U_1934))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(dvd_dvd_real,U_1933),U_1932)) ),
inference(clausify,[status(thm)],[f_785_2]) ).
fof(f_786_1,plain,
! [Z_2,X_3,Y_3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X_3),hAPP_int_int(minus_minus_int(Y_3),Z_2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X_3),Z_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X_3),Y_3)) ),
inference(fof_nnf,[status(thm)],[fact_760_dvd__diff]) ).
fof(f_786_2,plain,
! [U_1937,U_1936,U_1935] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1936),hAPP_int_int(minus_minus_int(U_1935),U_1937)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1936),U_1937))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1936),U_1935)) ),
inference(variable_rename,[status(thm)],[f_786_1]) ).
cnf(f_786_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1936),hAPP_int_int(minus_minus_int(U_1935),U_1937)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1936),U_1937))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_1936),U_1935)) ),
inference(clausify,[status(thm)],[f_786_2]) ).
fof(f_787_1,plain,
! [A_2,B_2,C_2] :
( ( ( hAPP_real_real(times_times_real(A_2),C_2) = hAPP_real_real(times_times_real(B_2),C_2)
| A_2 != B_2 )
& ( A_2 = B_2
| hAPP_real_real(times_times_real(A_2),C_2) != hAPP_real_real(times_times_real(B_2),C_2) ) )
| C_2 = zero_zero_real ),
inference(fof_nnf,[status(thm)],[fact_761_real__mult__right__cancel]) ).
fof(f_787_2,plain,
! [U_1940,U_1939,U_1938] :
( ( ( hAPP_real_real(times_times_real(U_1940),U_1938) = hAPP_real_real(times_times_real(U_1939),U_1938)
| U_1940 != U_1939 )
& ( U_1940 = U_1939
| hAPP_real_real(times_times_real(U_1940),U_1938) != hAPP_real_real(times_times_real(U_1939),U_1938) ) )
| U_1938 = zero_zero_real ),
inference(variable_rename,[status(thm)],[f_787_1]) ).
cnf(f_787_3,plain,
( U_1940 = U_1939
| hAPP_real_real(times_times_real(U_1940),U_1938) != hAPP_real_real(times_times_real(U_1939),U_1938)
| U_1938 = zero_zero_real ),
inference(clausify,[status(thm)],[f_787_2]) ).
cnf(f_787_4,plain,
( hAPP_real_real(times_times_real(U_1940),U_1938) = hAPP_real_real(times_times_real(U_1939),U_1938)
| U_1940 != U_1939
| U_1938 = zero_zero_real ),
inference(clausify,[status(thm)],[f_787_2]) ).
fof(f_788_1,plain,
! [A_2,B_2,C_2] :
( ( ( hAPP_real_real(times_times_real(C_2),A_2) = hAPP_real_real(times_times_real(C_2),B_2)
| A_2 != B_2 )
& ( A_2 = B_2
| hAPP_real_real(times_times_real(C_2),A_2) != hAPP_real_real(times_times_real(C_2),B_2) ) )
| C_2 = zero_zero_real ),
inference(fof_nnf,[status(thm)],[fact_762_real__mult__left__cancel]) ).
fof(f_788_2,plain,
! [U_1943,U_1942,U_1941] :
( ( ( hAPP_real_real(times_times_real(U_1941),U_1943) = hAPP_real_real(times_times_real(U_1941),U_1942)
| U_1943 != U_1942 )
& ( U_1943 = U_1942
| hAPP_real_real(times_times_real(U_1941),U_1943) != hAPP_real_real(times_times_real(U_1941),U_1942) ) )
| U_1941 = zero_zero_real ),
inference(variable_rename,[status(thm)],[f_788_1]) ).
cnf(f_788_3,plain,
( U_1943 = U_1942
| hAPP_real_real(times_times_real(U_1941),U_1943) != hAPP_real_real(times_times_real(U_1941),U_1942)
| U_1941 = zero_zero_real ),
inference(clausify,[status(thm)],[f_788_2]) ).
cnf(f_788_4,plain,
( hAPP_real_real(times_times_real(U_1941),U_1943) = hAPP_real_real(times_times_real(U_1941),U_1942)
| U_1943 != U_1942
| U_1941 = zero_zero_real ),
inference(clausify,[status(thm)],[f_788_2]) ).
fof(f_789_1,plain,
! [B,D_5,A] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D_5),B))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D_5),hAPP_nat_nat(plus_plus_nat(A),B)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,D_5),A)) ),
inference(fof_nnf,[status(thm)],[fact_763_divides__add__revr]) ).
fof(f_789_2,plain,
! [U_1946,U_1945,U_1944] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1945),U_1946))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1945),hAPP_nat_nat(plus_plus_nat(U_1944),U_1946)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1945),U_1944)) ),
inference(variable_rename,[status(thm)],[f_789_1]) ).
cnf(f_789_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1945),U_1946))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1945),hAPP_nat_nat(plus_plus_nat(U_1944),U_1946)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1945),U_1944)) ),
inference(clausify,[status(thm)],[f_789_2]) ).
fof(f_790_1,plain,
! [C,A,B] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(C),A)),hAPP_nat_nat(times_times_nat(C),B)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B)) ),
inference(fof_nnf,[status(thm)],[fact_764_divides__mul__l]) ).
fof(f_790_2,plain,
! [U_1949,U_1948,U_1947] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_1949),U_1948)),hAPP_nat_nat(times_times_nat(U_1949),U_1947)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1948),U_1947)) ),
inference(variable_rename,[status(thm)],[f_790_1]) ).
cnf(f_790_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_1949),U_1948)),hAPP_nat_nat(times_times_nat(U_1949),U_1947)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1948),U_1947)) ),
inference(clausify,[status(thm)],[f_790_2]) ).
fof(f_791_1,plain,
! [C,A,B] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(A),C)),hAPP_nat_nat(times_times_nat(B),C)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B)) ),
inference(fof_nnf,[status(thm)],[fact_765_divides__mul__r]) ).
fof(f_791_2,plain,
! [U_1952,U_1951,U_1950] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_1951),U_1952)),hAPP_nat_nat(times_times_nat(U_1950),U_1952)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1951),U_1950)) ),
inference(variable_rename,[status(thm)],[f_791_1]) ).
cnf(f_791_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_1951),U_1952)),hAPP_nat_nat(times_times_nat(U_1950),U_1952)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1951),U_1950)) ),
inference(clausify,[status(thm)],[f_791_2]) ).
fof(f_792_1,plain,
! [N,Ma] :
( ( hAPP_nat_nat(times_times_nat(N),Ma) = one_one_nat
| Ma != one_one_nat
| N != one_one_nat )
& ( ( Ma = one_one_nat
& N = one_one_nat )
| hAPP_nat_nat(times_times_nat(N),Ma) != one_one_nat ) ),
inference(fof_nnf,[status(thm)],[fact_766_nat__mult__eq__one]) ).
fof(f_792_2,plain,
! [U_1954,U_1953] :
( ( hAPP_nat_nat(times_times_nat(U_1954),U_1953) = one_one_nat
| U_1953 != one_one_nat
| U_1954 != one_one_nat )
& ( ( U_1953 = one_one_nat
& U_1954 = one_one_nat )
| hAPP_nat_nat(times_times_nat(U_1954),U_1953) != one_one_nat ) ),
inference(variable_rename,[status(thm)],[f_792_1]) ).
fof(f_792_3,plain,
( ! [U_1958,U_1956] :
( hAPP_nat_nat(times_times_nat(U_1958),U_1956) = one_one_nat
| U_1956 != one_one_nat
| U_1958 != one_one_nat )
& ! [U_1957,U_1955] :
( ( U_1955 = one_one_nat
& U_1957 = one_one_nat )
| hAPP_nat_nat(times_times_nat(U_1957),U_1955) != one_one_nat ) ),
inference(miniscope,[status(thm)],[f_792_2]) ).
cnf(f_792_4,plain,
( U_1957 = one_one_nat
| hAPP_nat_nat(times_times_nat(U_1957),U_1955) != one_one_nat ),
inference(clausify,[status(thm)],[f_792_3]) ).
cnf(f_792_5,plain,
( U_1955 = one_one_nat
| hAPP_nat_nat(times_times_nat(U_1957),U_1955) != one_one_nat ),
inference(clausify,[status(thm)],[f_792_3]) ).
cnf(f_792_6,plain,
( hAPP_nat_nat(times_times_nat(U_1958),U_1956) = one_one_nat
| U_1956 != one_one_nat
| U_1958 != one_one_nat ),
inference(clausify,[status(thm)],[f_792_3]) ).
fof(f_793_1,plain,
! [Z1,Z2,W] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(Z1),Z2)),W) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(Z1),W)),hAPP_real_real(times_times_real(Z2),W)),
inference(fof_nnf,[status(thm)],[fact_767_real__add__mult__distrib]) ).
fof(f_793_2,plain,
! [U_1961,U_1960,U_1959] : hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(U_1961),U_1960)),U_1959) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_1961),U_1959)),hAPP_real_real(times_times_real(U_1960),U_1959)),
inference(variable_rename,[status(thm)],[f_793_1]) ).
cnf(f_793_3,plain,
hAPP_real_real(times_times_real(hAPP_real_real(plus_plus_real(U_1961),U_1960)),U_1959) = hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_1961),U_1959)),hAPP_real_real(times_times_real(U_1960),U_1959)),
inference(clausify,[status(thm)],[f_793_2]) ).
fof(f_794_1,plain,
! [Ma,N] :
( ( hAPP_nat_nat(power_power_nat(Ma),N) = zero_zero_nat
| Ma != zero_zero_nat
| N = zero_zero_nat )
& ( ( Ma = zero_zero_nat
& N != zero_zero_nat )
| hAPP_nat_nat(power_power_nat(Ma),N) != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_768_nat__power__eq__0__iff]) ).
fof(f_794_2,plain,
! [U_1963,U_1962] :
( ( hAPP_nat_nat(power_power_nat(U_1963),U_1962) = zero_zero_nat
| U_1963 != zero_zero_nat
| U_1962 = zero_zero_nat )
& ( ( U_1963 = zero_zero_nat
& U_1962 != zero_zero_nat )
| hAPP_nat_nat(power_power_nat(U_1963),U_1962) != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_794_1]) ).
fof(f_794_3,plain,
( ! [U_1967,U_1965] :
( hAPP_nat_nat(power_power_nat(U_1967),U_1965) = zero_zero_nat
| U_1967 != zero_zero_nat
| U_1965 = zero_zero_nat )
& ! [U_1966,U_1964] :
( ( U_1966 = zero_zero_nat
& U_1964 != zero_zero_nat )
| hAPP_nat_nat(power_power_nat(U_1966),U_1964) != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_794_2]) ).
cnf(f_794_4,plain,
( U_1964 != zero_zero_nat
| hAPP_nat_nat(power_power_nat(U_1966),U_1964) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_794_3]) ).
cnf(f_794_5,plain,
( U_1966 = zero_zero_nat
| hAPP_nat_nat(power_power_nat(U_1966),U_1964) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_794_3]) ).
cnf(f_794_6,plain,
( hAPP_nat_nat(power_power_nat(U_1967),U_1965) = zero_zero_nat
| U_1967 != zero_zero_nat
| U_1965 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_794_3]) ).
fof(f_795_1,plain,
! [N_1,X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X_1),N_1)),hAPP_nat_nat(power_power_nat(Y_1),N_1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) ),
inference(fof_nnf,[status(thm)],[fact_769_divides__exp]) ).
fof(f_795_2,plain,
! [U_1970,U_1969,U_1968] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_1969),U_1970)),hAPP_nat_nat(power_power_nat(U_1968),U_1970)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1969),U_1968)) ),
inference(variable_rename,[status(thm)],[f_795_1]) ).
cnf(f_795_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_1969),U_1970)),hAPP_nat_nat(power_power_nat(U_1968),U_1970)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_1969),U_1968)) ),
inference(clausify,[status(thm)],[f_795_2]) ).
fof(f_796_1,plain,
! [B_30,A_32] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_32),B_30)),zero_zero_real))
| ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_30))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_32),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_30),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_32)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_770_split__mult__neg__le]) ).
fof(f_796_2,plain,
! [U_1972,U_1971] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_1971),U_1972)),zero_zero_real))
| ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1972))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1971),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1972),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1971)) ) ) ),
inference(variable_rename,[status(thm)],[f_796_1]) ).
cnf(f_796_3,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1972),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1971))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_1971),U_1972)),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_796_2]) ).
cnf(f_796_4,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1972))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1971),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_1971),U_1972)),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_796_2]) ).
fof(f_797_1,plain,
! [B_30,A_32] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(A_32),B_30)),zero_zero_nat))
| ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_30))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_32),zero_zero_nat)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_30),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_32)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_771_split__mult__neg__le]) ).
fof(f_797_2,plain,
! [U_1974,U_1973] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_1973),U_1974)),zero_zero_nat))
| ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1974))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1973),zero_zero_nat)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1974),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1973)) ) ) ),
inference(variable_rename,[status(thm)],[f_797_1]) ).
cnf(f_797_3,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1974),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1973))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_1973),U_1974)),zero_zero_nat)) ),
inference(clausify,[status(thm)],[f_797_2]) ).
cnf(f_797_4,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1974))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1973),zero_zero_nat))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_1973),U_1974)),zero_zero_nat)) ),
inference(clausify,[status(thm)],[f_797_2]) ).
fof(f_798_1,plain,
! [B_30,A_32] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_32),B_30)),zero_zero_int))
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_30))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_32),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_30),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_32)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_772_split__mult__neg__le]) ).
fof(f_798_2,plain,
! [U_1976,U_1975] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_1975),U_1976)),zero_zero_int))
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1976))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1975),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1976),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1975)) ) ) ),
inference(variable_rename,[status(thm)],[f_798_1]) ).
cnf(f_798_3,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1976),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1975))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_1975),U_1976)),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_798_2]) ).
cnf(f_798_4,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1976))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1975),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_1975),U_1976)),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_798_2]) ).
fof(f_799_1,plain,
! [B_29,A_31] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(A_31),B_29)))
| ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_29),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_31),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_29))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_31)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_773_split__mult__pos__le]) ).
fof(f_799_2,plain,
! [U_1978,U_1977] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(U_1977),U_1978)))
| ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1978),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1977),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1978))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1977)) ) ) ),
inference(variable_rename,[status(thm)],[f_799_1]) ).
cnf(f_799_3,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1978))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1977))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(U_1977),U_1978))) ),
inference(clausify,[status(thm)],[f_799_2]) ).
cnf(f_799_4,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1978),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1977),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(U_1977),U_1978))) ),
inference(clausify,[status(thm)],[f_799_2]) ).
fof(f_800_1,plain,
! [B_29,A_31] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(A_31),B_29)))
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_29),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_31),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_29))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_31)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_774_split__mult__pos__le]) ).
fof(f_800_2,plain,
! [U_1980,U_1979] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_1979),U_1980)))
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1980),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1979),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1980))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1979)) ) ) ),
inference(variable_rename,[status(thm)],[f_800_1]) ).
cnf(f_800_3,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1980))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1979))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_1979),U_1980))) ),
inference(clausify,[status(thm)],[f_800_2]) ).
cnf(f_800_4,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1980),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1979),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_1979),U_1980))) ),
inference(clausify,[status(thm)],[f_800_2]) ).
fof(f_801_1,plain,
! [C_14,D_4,A_30,B_28] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_30),C_14)),hAPP_real_real(times_times_real(B_28),D_4)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_14))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_28))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_14),D_4))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_30),B_28)) ),
inference(fof_nnf,[status(thm)],[fact_775_mult__mono]) ).
fof(f_801_2,plain,
! [U_1984,U_1983,U_1982,U_1981] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_1982),U_1984)),hAPP_real_real(times_times_real(U_1981),U_1983)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1984))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1981))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1984),U_1983))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1982),U_1981)) ),
inference(variable_rename,[status(thm)],[f_801_1]) ).
cnf(f_801_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_1982),U_1984)),hAPP_real_real(times_times_real(U_1981),U_1983)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1984))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1981))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1984),U_1983))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1982),U_1981)) ),
inference(clausify,[status(thm)],[f_801_2]) ).
fof(f_802_1,plain,
! [C_14,D_4,A_30,B_28] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(A_30),C_14)),hAPP_nat_nat(times_times_nat(B_28),D_4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_14))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_28))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_14),D_4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_30),B_28)) ),
inference(fof_nnf,[status(thm)],[fact_776_mult__mono]) ).
fof(f_802_2,plain,
! [U_1988,U_1987,U_1986,U_1985] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_1986),U_1988)),hAPP_nat_nat(times_times_nat(U_1985),U_1987)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1988))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1985))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1988),U_1987))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1986),U_1985)) ),
inference(variable_rename,[status(thm)],[f_802_1]) ).
cnf(f_802_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_1986),U_1988)),hAPP_nat_nat(times_times_nat(U_1985),U_1987)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1988))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1985))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1988),U_1987))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1986),U_1985)) ),
inference(clausify,[status(thm)],[f_802_2]) ).
fof(f_803_1,plain,
! [C_14,D_4,A_30,B_28] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_30),C_14)),hAPP_int_int(times_times_int(B_28),D_4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_14))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_28))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_14),D_4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_30),B_28)) ),
inference(fof_nnf,[status(thm)],[fact_777_mult__mono]) ).
fof(f_803_2,plain,
! [U_1992,U_1991,U_1990,U_1989] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_1990),U_1992)),hAPP_int_int(times_times_int(U_1989),U_1991)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1992))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1989))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1992),U_1991))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1990),U_1989)) ),
inference(variable_rename,[status(thm)],[f_803_1]) ).
cnf(f_803_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_1990),U_1992)),hAPP_int_int(times_times_int(U_1989),U_1991)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1992))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_1989))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1992),U_1991))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1990),U_1989)) ),
inference(clausify,[status(thm)],[f_803_2]) ).
fof(f_804_1,plain,
! [C_13,D_3,A_29,B_27] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_29),C_13)),hAPP_real_real(times_times_real(B_27),D_3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_13))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_29))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_13),D_3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_29),B_27)) ),
inference(fof_nnf,[status(thm)],[fact_778_mult__mono_H]) ).
fof(f_804_2,plain,
! [U_1996,U_1995,U_1994,U_1993] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_1994),U_1996)),hAPP_real_real(times_times_real(U_1993),U_1995)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1996))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1994))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1996),U_1995))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1994),U_1993)) ),
inference(variable_rename,[status(thm)],[f_804_1]) ).
cnf(f_804_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_1994),U_1996)),hAPP_real_real(times_times_real(U_1993),U_1995)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1996))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_1994))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1996),U_1995))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_1994),U_1993)) ),
inference(clausify,[status(thm)],[f_804_2]) ).
fof(f_805_1,plain,
! [C_13,D_3,A_29,B_27] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(A_29),C_13)),hAPP_nat_nat(times_times_nat(B_27),D_3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_13))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_29))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_13),D_3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_29),B_27)) ),
inference(fof_nnf,[status(thm)],[fact_779_mult__mono_H]) ).
fof(f_805_2,plain,
! [U_2000,U_1999,U_1998,U_1997] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_1998),U_2000)),hAPP_nat_nat(times_times_nat(U_1997),U_1999)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2000))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1998))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2000),U_1999))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1998),U_1997)) ),
inference(variable_rename,[status(thm)],[f_805_1]) ).
cnf(f_805_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_1998),U_2000)),hAPP_nat_nat(times_times_nat(U_1997),U_1999)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2000))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_1998))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2000),U_1999))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1998),U_1997)) ),
inference(clausify,[status(thm)],[f_805_2]) ).
fof(f_806_1,plain,
! [C_13,D_3,A_29,B_27] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_29),C_13)),hAPP_int_int(times_times_int(B_27),D_3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_13))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_29))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_13),D_3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_29),B_27)) ),
inference(fof_nnf,[status(thm)],[fact_780_mult__mono_H]) ).
fof(f_806_2,plain,
! [U_2004,U_2003,U_2002,U_2001] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2002),U_2004)),hAPP_int_int(times_times_int(U_2001),U_2003)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2004))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2002))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2004),U_2003))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2002),U_2001)) ),
inference(variable_rename,[status(thm)],[f_806_1]) ).
cnf(f_806_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2002),U_2004)),hAPP_int_int(times_times_int(U_2001),U_2003)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2004))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2002))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2004),U_2003))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2002),U_2001)) ),
inference(clausify,[status(thm)],[f_806_2]) ).
fof(f_807_1,plain,
! [C_12,B_26,A_28] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(C_12),A_28)),hAPP_real_real(times_times_real(C_12),B_26)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_12),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_26),A_28)) ),
inference(fof_nnf,[status(thm)],[fact_781_mult__left__mono__neg]) ).
fof(f_807_2,plain,
! [U_2007,U_2006,U_2005] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2007),U_2005)),hAPP_real_real(times_times_real(U_2007),U_2006)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2007),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2006),U_2005)) ),
inference(variable_rename,[status(thm)],[f_807_1]) ).
cnf(f_807_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2007),U_2005)),hAPP_real_real(times_times_real(U_2007),U_2006)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2007),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2006),U_2005)) ),
inference(clausify,[status(thm)],[f_807_2]) ).
fof(f_808_1,plain,
! [C_12,B_26,A_28] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(C_12),A_28)),hAPP_int_int(times_times_int(C_12),B_26)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_12),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_26),A_28)) ),
inference(fof_nnf,[status(thm)],[fact_782_mult__left__mono__neg]) ).
fof(f_808_2,plain,
! [U_2010,U_2009,U_2008] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2010),U_2008)),hAPP_int_int(times_times_int(U_2010),U_2009)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2010),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2009),U_2008)) ),
inference(variable_rename,[status(thm)],[f_808_1]) ).
cnf(f_808_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2010),U_2008)),hAPP_int_int(times_times_int(U_2010),U_2009)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2010),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2009),U_2008)) ),
inference(clausify,[status(thm)],[f_808_2]) ).
fof(f_809_1,plain,
! [C_11,B_25,A_27] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_27),C_11)),hAPP_real_real(times_times_real(B_25),C_11)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,C_11),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_25),A_27)) ),
inference(fof_nnf,[status(thm)],[fact_783_mult__right__mono__neg]) ).
fof(f_809_2,plain,
! [U_2013,U_2012,U_2011] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2011),U_2013)),hAPP_real_real(times_times_real(U_2012),U_2013)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2013),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2012),U_2011)) ),
inference(variable_rename,[status(thm)],[f_809_1]) ).
cnf(f_809_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2011),U_2013)),hAPP_real_real(times_times_real(U_2012),U_2013)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2013),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2012),U_2011)) ),
inference(clausify,[status(thm)],[f_809_2]) ).
fof(f_810_1,plain,
! [C_11,B_25,A_27] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_27),C_11)),hAPP_int_int(times_times_int(B_25),C_11)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_11),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_25),A_27)) ),
inference(fof_nnf,[status(thm)],[fact_784_mult__right__mono__neg]) ).
fof(f_810_2,plain,
! [U_2016,U_2015,U_2014] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2014),U_2016)),hAPP_int_int(times_times_int(U_2015),U_2016)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2016),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2015),U_2014)) ),
inference(variable_rename,[status(thm)],[f_810_1]) ).
cnf(f_810_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2014),U_2016)),hAPP_int_int(times_times_int(U_2015),U_2016)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2016),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2015),U_2014)) ),
inference(clausify,[status(thm)],[f_810_2]) ).
fof(f_811_1,plain,
! [C_10,A_26,B_24] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(C_10),A_26)),hAPP_real_real(times_times_real(C_10),B_24)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_10))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_26),B_24)) ),
inference(fof_nnf,[status(thm)],[fact_785_comm__mult__left__mono]) ).
fof(f_811_2,plain,
! [U_2019,U_2018,U_2017] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2019),U_2018)),hAPP_real_real(times_times_real(U_2019),U_2017)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2019))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2018),U_2017)) ),
inference(variable_rename,[status(thm)],[f_811_1]) ).
cnf(f_811_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2019),U_2018)),hAPP_real_real(times_times_real(U_2019),U_2017)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2019))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2018),U_2017)) ),
inference(clausify,[status(thm)],[f_811_2]) ).
fof(f_812_1,plain,
! [C_10,A_26,B_24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(C_10),A_26)),hAPP_nat_nat(times_times_nat(C_10),B_24)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_10))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_26),B_24)) ),
inference(fof_nnf,[status(thm)],[fact_786_comm__mult__left__mono]) ).
fof(f_812_2,plain,
! [U_2022,U_2021,U_2020] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2022),U_2021)),hAPP_nat_nat(times_times_nat(U_2022),U_2020)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2022))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2021),U_2020)) ),
inference(variable_rename,[status(thm)],[f_812_1]) ).
cnf(f_812_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2022),U_2021)),hAPP_nat_nat(times_times_nat(U_2022),U_2020)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2022))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2021),U_2020)) ),
inference(clausify,[status(thm)],[f_812_2]) ).
fof(f_813_1,plain,
! [C_10,A_26,B_24] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(C_10),A_26)),hAPP_int_int(times_times_int(C_10),B_24)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_10))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_26),B_24)) ),
inference(fof_nnf,[status(thm)],[fact_787_comm__mult__left__mono]) ).
fof(f_813_2,plain,
! [U_2025,U_2024,U_2023] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2025),U_2024)),hAPP_int_int(times_times_int(U_2025),U_2023)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2025))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2024),U_2023)) ),
inference(variable_rename,[status(thm)],[f_813_1]) ).
cnf(f_813_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2025),U_2024)),hAPP_int_int(times_times_int(U_2025),U_2023)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2025))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2024),U_2023)) ),
inference(clausify,[status(thm)],[f_813_2]) ).
fof(f_814_1,plain,
! [C_9,A_25,B_23] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(C_9),A_25)),hAPP_real_real(times_times_real(C_9),B_23)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_9))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_25),B_23)) ),
inference(fof_nnf,[status(thm)],[fact_788_mult__left__mono]) ).
fof(f_814_2,plain,
! [U_2028,U_2027,U_2026] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2028),U_2027)),hAPP_real_real(times_times_real(U_2028),U_2026)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2028))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2027),U_2026)) ),
inference(variable_rename,[status(thm)],[f_814_1]) ).
cnf(f_814_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2028),U_2027)),hAPP_real_real(times_times_real(U_2028),U_2026)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2028))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2027),U_2026)) ),
inference(clausify,[status(thm)],[f_814_2]) ).
fof(f_815_1,plain,
! [C_9,A_25,B_23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(C_9),A_25)),hAPP_nat_nat(times_times_nat(C_9),B_23)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_9))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_25),B_23)) ),
inference(fof_nnf,[status(thm)],[fact_789_mult__left__mono]) ).
fof(f_815_2,plain,
! [U_2031,U_2030,U_2029] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2031),U_2030)),hAPP_nat_nat(times_times_nat(U_2031),U_2029)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2031))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2030),U_2029)) ),
inference(variable_rename,[status(thm)],[f_815_1]) ).
cnf(f_815_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2031),U_2030)),hAPP_nat_nat(times_times_nat(U_2031),U_2029)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2031))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2030),U_2029)) ),
inference(clausify,[status(thm)],[f_815_2]) ).
fof(f_816_1,plain,
! [C_9,A_25,B_23] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(C_9),A_25)),hAPP_int_int(times_times_int(C_9),B_23)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_9))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_25),B_23)) ),
inference(fof_nnf,[status(thm)],[fact_790_mult__left__mono]) ).
fof(f_816_2,plain,
! [U_2034,U_2033,U_2032] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2034),U_2033)),hAPP_int_int(times_times_int(U_2034),U_2032)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2034))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2033),U_2032)) ),
inference(variable_rename,[status(thm)],[f_816_1]) ).
cnf(f_816_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2034),U_2033)),hAPP_int_int(times_times_int(U_2034),U_2032)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2034))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2033),U_2032)) ),
inference(clausify,[status(thm)],[f_816_2]) ).
fof(f_817_1,plain,
! [C_8,A_24,B_22] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_24),C_8)),hAPP_real_real(times_times_real(B_22),C_8)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),C_8))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_24),B_22)) ),
inference(fof_nnf,[status(thm)],[fact_791_mult__right__mono]) ).
fof(f_817_2,plain,
! [U_2037,U_2036,U_2035] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2036),U_2037)),hAPP_real_real(times_times_real(U_2035),U_2037)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2037))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2036),U_2035)) ),
inference(variable_rename,[status(thm)],[f_817_1]) ).
cnf(f_817_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2036),U_2037)),hAPP_real_real(times_times_real(U_2035),U_2037)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2037))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2036),U_2035)) ),
inference(clausify,[status(thm)],[f_817_2]) ).
fof(f_818_1,plain,
! [C_8,A_24,B_22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(A_24),C_8)),hAPP_nat_nat(times_times_nat(B_22),C_8)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_8))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_24),B_22)) ),
inference(fof_nnf,[status(thm)],[fact_792_mult__right__mono]) ).
fof(f_818_2,plain,
! [U_2040,U_2039,U_2038] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2039),U_2040)),hAPP_nat_nat(times_times_nat(U_2038),U_2040)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2040))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2039),U_2038)) ),
inference(variable_rename,[status(thm)],[f_818_1]) ).
cnf(f_818_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2039),U_2040)),hAPP_nat_nat(times_times_nat(U_2038),U_2040)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2040))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2039),U_2038)) ),
inference(clausify,[status(thm)],[f_818_2]) ).
fof(f_819_1,plain,
! [C_8,A_24,B_22] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_24),C_8)),hAPP_int_int(times_times_int(B_22),C_8)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),C_8))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_24),B_22)) ),
inference(fof_nnf,[status(thm)],[fact_793_mult__right__mono]) ).
fof(f_819_2,plain,
! [U_2043,U_2042,U_2041] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2042),U_2043)),hAPP_int_int(times_times_int(U_2041),U_2043)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2043))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2042),U_2041)) ),
inference(variable_rename,[status(thm)],[f_819_1]) ).
cnf(f_819_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2042),U_2043)),hAPP_int_int(times_times_int(U_2041),U_2043)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2043))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2042),U_2041)) ),
inference(clausify,[status(thm)],[f_819_2]) ).
fof(f_820_1,plain,
! [B_21,A_23] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(A_23),B_21)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_21),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_23),zero_zero_real)) ),
inference(fof_nnf,[status(thm)],[fact_794_mult__nonpos__nonpos]) ).
fof(f_820_2,plain,
! [U_2045,U_2044] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(U_2044),U_2045)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2045),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2044),zero_zero_real)) ),
inference(variable_rename,[status(thm)],[f_820_1]) ).
cnf(f_820_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(U_2044),U_2045)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2045),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2044),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_820_2]) ).
fof(f_821_1,plain,
! [B_21,A_23] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(A_23),B_21)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_21),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_23),zero_zero_int)) ),
inference(fof_nnf,[status(thm)],[fact_795_mult__nonpos__nonpos]) ).
fof(f_821_2,plain,
! [U_2047,U_2046] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_2046),U_2047)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2047),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2046),zero_zero_int)) ),
inference(variable_rename,[status(thm)],[f_821_1]) ).
cnf(f_821_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_2046),U_2047)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2047),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2046),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_821_2]) ).
fof(f_822_1,plain,
! [B_20,A_22] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_22),B_20)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_20))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_22),zero_zero_real)) ),
inference(fof_nnf,[status(thm)],[fact_796_mult__nonpos__nonneg]) ).
fof(f_822_2,plain,
! [U_2049,U_2048] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2048),U_2049)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2049))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2048),zero_zero_real)) ),
inference(variable_rename,[status(thm)],[f_822_1]) ).
cnf(f_822_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2048),U_2049)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2049))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2048),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_822_2]) ).
fof(f_823_1,plain,
! [B_20,A_22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(A_22),B_20)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_20))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_22),zero_zero_nat)) ),
inference(fof_nnf,[status(thm)],[fact_797_mult__nonpos__nonneg]) ).
fof(f_823_2,plain,
! [U_2051,U_2050] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2050),U_2051)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2051))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2050),zero_zero_nat)) ),
inference(variable_rename,[status(thm)],[f_823_1]) ).
cnf(f_823_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2050),U_2051)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2051))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2050),zero_zero_nat)) ),
inference(clausify,[status(thm)],[f_823_2]) ).
fof(f_824_1,plain,
! [B_20,A_22] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_22),B_20)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_20))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_22),zero_zero_int)) ),
inference(fof_nnf,[status(thm)],[fact_798_mult__nonpos__nonneg]) ).
fof(f_824_2,plain,
! [U_2053,U_2052] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2052),U_2053)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2053))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2052),zero_zero_int)) ),
inference(variable_rename,[status(thm)],[f_824_1]) ).
cnf(f_824_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2052),U_2053)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2053))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2052),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_824_2]) ).
fof(f_825_1,plain,
! [B_19,A_21] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(B_19),A_21)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_19),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_21)) ),
inference(fof_nnf,[status(thm)],[fact_799_mult__nonneg__nonpos2]) ).
fof(f_825_2,plain,
! [U_2055,U_2054] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2055),U_2054)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2055),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2054)) ),
inference(variable_rename,[status(thm)],[f_825_1]) ).
cnf(f_825_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2055),U_2054)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2055),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2054)) ),
inference(clausify,[status(thm)],[f_825_2]) ).
fof(f_826_1,plain,
! [B_19,A_21] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(B_19),A_21)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_19),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_21)) ),
inference(fof_nnf,[status(thm)],[fact_800_mult__nonneg__nonpos2]) ).
fof(f_826_2,plain,
! [U_2057,U_2056] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2057),U_2056)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2057),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2056)) ),
inference(variable_rename,[status(thm)],[f_826_1]) ).
cnf(f_826_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2057),U_2056)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2057),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2056)) ),
inference(clausify,[status(thm)],[f_826_2]) ).
fof(f_827_1,plain,
! [B_19,A_21] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(B_19),A_21)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_19),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_21)) ),
inference(fof_nnf,[status(thm)],[fact_801_mult__nonneg__nonpos2]) ).
fof(f_827_2,plain,
! [U_2059,U_2058] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2059),U_2058)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2059),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2058)) ),
inference(variable_rename,[status(thm)],[f_827_1]) ).
cnf(f_827_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2059),U_2058)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2059),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2058)) ),
inference(clausify,[status(thm)],[f_827_2]) ).
fof(f_828_1,plain,
! [B_18,A_20] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_20),B_18)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_18),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_20)) ),
inference(fof_nnf,[status(thm)],[fact_802_mult__nonneg__nonpos]) ).
fof(f_828_2,plain,
! [U_2061,U_2060] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2060),U_2061)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2061),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2060)) ),
inference(variable_rename,[status(thm)],[f_828_1]) ).
cnf(f_828_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2060),U_2061)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2061),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2060)) ),
inference(clausify,[status(thm)],[f_828_2]) ).
fof(f_829_1,plain,
! [B_18,A_20] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(A_20),B_18)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_18),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_20)) ),
inference(fof_nnf,[status(thm)],[fact_803_mult__nonneg__nonpos]) ).
fof(f_829_2,plain,
! [U_2063,U_2062] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2062),U_2063)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2063),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2062)) ),
inference(variable_rename,[status(thm)],[f_829_1]) ).
cnf(f_829_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2062),U_2063)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2063),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2062)) ),
inference(clausify,[status(thm)],[f_829_2]) ).
fof(f_830_1,plain,
! [B_18,A_20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_20),B_18)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_18),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_20)) ),
inference(fof_nnf,[status(thm)],[fact_804_mult__nonneg__nonpos]) ).
fof(f_830_2,plain,
! [U_2065,U_2064] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2064),U_2065)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2065),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2064)) ),
inference(variable_rename,[status(thm)],[f_830_1]) ).
cnf(f_830_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2064),U_2065)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2065),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2064)) ),
inference(clausify,[status(thm)],[f_830_2]) ).
fof(f_831_1,plain,
! [B_17,A_19] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(A_19),B_17)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_17))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_19)) ),
inference(fof_nnf,[status(thm)],[fact_805_mult__nonneg__nonneg]) ).
fof(f_831_2,plain,
! [U_2067,U_2066] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(U_2066),U_2067)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2067))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2066)) ),
inference(variable_rename,[status(thm)],[f_831_1]) ).
cnf(f_831_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(U_2066),U_2067)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2067))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2066)) ),
inference(clausify,[status(thm)],[f_831_2]) ).
fof(f_832_1,plain,
! [B_17,A_19] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(A_19),B_17)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_17))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_19)) ),
inference(fof_nnf,[status(thm)],[fact_806_mult__nonneg__nonneg]) ).
fof(f_832_2,plain,
! [U_2069,U_2068] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_2068),U_2069)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2069))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2068)) ),
inference(variable_rename,[status(thm)],[f_832_1]) ).
cnf(f_832_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_2068),U_2069)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2069))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2068)) ),
inference(clausify,[status(thm)],[f_832_2]) ).
fof(f_833_1,plain,
! [B_17,A_19] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(A_19),B_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_17))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_19)) ),
inference(fof_nnf,[status(thm)],[fact_807_mult__nonneg__nonneg]) ).
fof(f_833_2,plain,
! [U_2071,U_2070] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_2070),U_2071)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2071))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2070)) ),
inference(variable_rename,[status(thm)],[f_833_1]) ).
cnf(f_833_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_2070),U_2071)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2071))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2070)) ),
inference(clausify,[status(thm)],[f_833_2]) ).
fof(f_834_1,plain,
! [A_2,B_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_2),B_2)),zero_zero_real))
| ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_2),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_2),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_2)) ) ) )
& ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_2))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_2),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_2),zero_zero_real))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_2)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(A_2),B_2)),zero_zero_real)) ) ),
inference(fof_nnf,[status(thm)],[fact_808_mult__le__0__iff]) ).
fof(f_834_2,plain,
! [U_2073,U_2072] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2073),U_2072)),zero_zero_real))
| ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2072))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2073),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2072),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2073)) ) ) )
& ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2072))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2073),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2072),zero_zero_real))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2073)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2073),U_2072)),zero_zero_real)) ) ),
inference(variable_rename,[status(thm)],[f_834_1]) ).
fof(f_834_3,plain,
( ! [U_2077,U_2075] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2077),U_2075)),zero_zero_real))
| ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2075))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2077),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2075),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2077)) ) ) )
& ! [U_2076,U_2074] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2074))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2076),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2074),zero_zero_real))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2076)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2076),U_2074)),zero_zero_real)) ) ),
inference(miniscope,[status(thm)],[f_834_2]) ).
cnf(f_834_4,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2076),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2076))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2076),U_2074)),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_834_3]) ).
cnf(f_834_5,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2074))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2076))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2076),U_2074)),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_834_3]) ).
cnf(f_834_6,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2076),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2074),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2076),U_2074)),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_834_3]) ).
cnf(f_834_7,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2074))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2074),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2076),U_2074)),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_834_3]) ).
cnf(f_834_8,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2075),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2077))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2077),U_2075)),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_834_3]) ).
cnf(f_834_9,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2075))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2077),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2077),U_2075)),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_834_3]) ).
fof(f_835_1,plain,
! [A_2,B_2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_2),B_2)),zero_zero_int))
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_2)) ) ) )
& ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_2)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(A_2),B_2)),zero_zero_int)) ) ),
inference(fof_nnf,[status(thm)],[fact_809_mult__le__0__iff]) ).
fof(f_835_2,plain,
! [U_2079,U_2078] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2079),U_2078)),zero_zero_int))
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2078))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2079),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2078),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2079)) ) ) )
& ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2078))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2079),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2078),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2079)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2079),U_2078)),zero_zero_int)) ) ),
inference(variable_rename,[status(thm)],[f_835_1]) ).
fof(f_835_3,plain,
( ! [U_2083,U_2081] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2083),U_2081)),zero_zero_int))
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2081))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2083),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2081),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2083)) ) ) )
& ! [U_2082,U_2080] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2080))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2082),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2080),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2082)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2082),U_2080)),zero_zero_int)) ) ),
inference(miniscope,[status(thm)],[f_835_2]) ).
cnf(f_835_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2082),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2082))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2082),U_2080)),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_835_3]) ).
cnf(f_835_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2080))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2082))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2082),U_2080)),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_835_3]) ).
cnf(f_835_6,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2082),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2080),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2082),U_2080)),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_835_3]) ).
cnf(f_835_7,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2080))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2080),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2082),U_2080)),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_835_3]) ).
cnf(f_835_8,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2081),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2083))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2083),U_2081)),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_835_3]) ).
cnf(f_835_9,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2081))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2083),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(times_times_int(U_2083),U_2081)),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_835_3]) ).
fof(f_836_1,plain,
! [A_2,B_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(A_2),B_2)))
| ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_2),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_2),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_2)) ) ) )
& ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,B_2),zero_zero_real))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,A_2),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),B_2))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),A_2)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(A_2),B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_810_zero__le__mult__iff]) ).
fof(f_836_2,plain,
! [U_2085,U_2084] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(U_2085),U_2084)))
| ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2084),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2085),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2084))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2085)) ) ) )
& ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2084),zero_zero_real))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2085),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2084))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2085)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(U_2085),U_2084))) ) ),
inference(variable_rename,[status(thm)],[f_836_1]) ).
fof(f_836_3,plain,
( ! [U_2089,U_2087] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(U_2089),U_2087)))
| ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2087),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2089),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2087))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2089)) ) ) )
& ! [U_2088,U_2086] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2086),zero_zero_real))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2088),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2086))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2088)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(U_2088),U_2086))) ) ),
inference(miniscope,[status(thm)],[f_836_2]) ).
cnf(f_836_4,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2088),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2088))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(U_2088),U_2086))) ),
inference(clausify,[status(thm)],[f_836_3]) ).
cnf(f_836_5,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2086),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2088))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(U_2088),U_2086))) ),
inference(clausify,[status(thm)],[f_836_3]) ).
cnf(f_836_6,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2088),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2086))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(U_2088),U_2086))) ),
inference(clausify,[status(thm)],[f_836_3]) ).
cnf(f_836_7,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2086),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2086))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(U_2088),U_2086))) ),
inference(clausify,[status(thm)],[f_836_3]) ).
cnf(f_836_8,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2087))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),U_2089))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(U_2089),U_2087))) ),
inference(clausify,[status(thm)],[f_836_3]) ).
cnf(f_836_9,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2087),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2089),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(U_2089),U_2087))) ),
inference(clausify,[status(thm)],[f_836_3]) ).
fof(f_837_1,plain,
! [A_2,B_2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(A_2),B_2)))
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_2)) ) ) )
& ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_2)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(A_2),B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_811_zero__le__mult__iff]) ).
fof(f_837_2,plain,
! [U_2091,U_2090] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_2091),U_2090)))
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2090),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2091),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2090))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2091)) ) ) )
& ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2090),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2091),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2090))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2091)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_2091),U_2090))) ) ),
inference(variable_rename,[status(thm)],[f_837_1]) ).
fof(f_837_3,plain,
( ! [U_2095,U_2093] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_2095),U_2093)))
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2093),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2095),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2093))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2095)) ) ) )
& ! [U_2094,U_2092] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2092),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2094),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2092))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2094)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_2094),U_2092))) ) ),
inference(miniscope,[status(thm)],[f_837_2]) ).
cnf(f_837_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2094),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2094))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_2094),U_2092))) ),
inference(clausify,[status(thm)],[f_837_3]) ).
cnf(f_837_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2092),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2094))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_2094),U_2092))) ),
inference(clausify,[status(thm)],[f_837_3]) ).
cnf(f_837_6,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2094),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2092))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_2094),U_2092))) ),
inference(clausify,[status(thm)],[f_837_3]) ).
cnf(f_837_7,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2092),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2092))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_2094),U_2092))) ),
inference(clausify,[status(thm)],[f_837_3]) ).
cnf(f_837_8,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2093))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2095))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_2095),U_2093))) ),
inference(clausify,[status(thm)],[f_837_3]) ).
cnf(f_837_9,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2093),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2095),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_2095),U_2093))) ),
inference(clausify,[status(thm)],[f_837_3]) ).
fof(f_838_1,plain,
! [A_18] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(A_18),A_18))),
inference(fof_nnf,[status(thm)],[fact_812_zero__le__square]) ).
fof(f_838_2,plain,
! [U_2096] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(U_2096),U_2096))),
inference(variable_rename,[status(thm)],[f_838_1]) ).
cnf(f_838_3,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),hAPP_real_real(times_times_real(U_2096),U_2096))),
inference(clausify,[status(thm)],[f_838_2]) ).
fof(f_839_1,plain,
! [A_18] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(A_18),A_18))),
inference(fof_nnf,[status(thm)],[fact_813_zero__le__square]) ).
fof(f_839_2,plain,
! [U_2097] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_2097),U_2097))),
inference(variable_rename,[status(thm)],[f_839_1]) ).
cnf(f_839_3,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(times_times_int(U_2097),U_2097))),
inference(clausify,[status(thm)],[f_839_2]) ).
fof(f_840_1,plain,
! [C_7,B_16,A_17] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_7),A_17)),hAPP_real_real(times_times_real(C_7),B_16)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_7),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_16),A_17)) ),
inference(fof_nnf,[status(thm)],[fact_814_mult__strict__left__mono__neg]) ).
fof(f_840_2,plain,
! [U_2100,U_2099,U_2098] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2100),U_2098)),hAPP_real_real(times_times_real(U_2100),U_2099)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2100),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2099),U_2098)) ),
inference(variable_rename,[status(thm)],[f_840_1]) ).
cnf(f_840_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2100),U_2098)),hAPP_real_real(times_times_real(U_2100),U_2099)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2100),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2099),U_2098)) ),
inference(clausify,[status(thm)],[f_840_2]) ).
fof(f_841_1,plain,
! [C_7,B_16,A_17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_7),A_17)),hAPP_int_int(times_times_int(C_7),B_16)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_7),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_16),A_17)) ),
inference(fof_nnf,[status(thm)],[fact_815_mult__strict__left__mono__neg]) ).
fof(f_841_2,plain,
! [U_2103,U_2102,U_2101] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2103),U_2101)),hAPP_int_int(times_times_int(U_2103),U_2102)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2103),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2102),U_2101)) ),
inference(variable_rename,[status(thm)],[f_841_1]) ).
cnf(f_841_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2103),U_2101)),hAPP_int_int(times_times_int(U_2103),U_2102)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2103),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2102),U_2101)) ),
inference(clausify,[status(thm)],[f_841_2]) ).
fof(f_842_1,plain,
! [C_6,B_15,A_16] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_16),C_6)),hAPP_real_real(times_times_real(B_15),C_6)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_6),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_15),A_16)) ),
inference(fof_nnf,[status(thm)],[fact_816_mult__strict__right__mono__neg]) ).
fof(f_842_2,plain,
! [U_2106,U_2105,U_2104] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2104),U_2106)),hAPP_real_real(times_times_real(U_2105),U_2106)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2106),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2105),U_2104)) ),
inference(variable_rename,[status(thm)],[f_842_1]) ).
cnf(f_842_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2104),U_2106)),hAPP_real_real(times_times_real(U_2105),U_2106)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2106),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2105),U_2104)) ),
inference(clausify,[status(thm)],[f_842_2]) ).
fof(f_843_1,plain,
! [C_6,B_15,A_16] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_16),C_6)),hAPP_int_int(times_times_int(B_15),C_6)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_6),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_15),A_16)) ),
inference(fof_nnf,[status(thm)],[fact_817_mult__strict__right__mono__neg]) ).
fof(f_843_2,plain,
! [U_2109,U_2108,U_2107] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2107),U_2109)),hAPP_int_int(times_times_int(U_2108),U_2109)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2109),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2108),U_2107)) ),
inference(variable_rename,[status(thm)],[f_843_1]) ).
cnf(f_843_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2107),U_2109)),hAPP_int_int(times_times_int(U_2108),U_2109)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2109),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2108),U_2107)) ),
inference(clausify,[status(thm)],[f_843_2]) ).
fof(f_844_1,plain,
! [C_5,A_15,B_14] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_5),A_15)),hAPP_real_real(times_times_real(C_5),B_14)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_5))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_15),B_14)) ),
inference(fof_nnf,[status(thm)],[fact_818_comm__mult__strict__left__mono]) ).
fof(f_844_2,plain,
! [U_2112,U_2111,U_2110] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2112),U_2111)),hAPP_real_real(times_times_real(U_2112),U_2110)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2112))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2111),U_2110)) ),
inference(variable_rename,[status(thm)],[f_844_1]) ).
cnf(f_844_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2112),U_2111)),hAPP_real_real(times_times_real(U_2112),U_2110)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2112))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2111),U_2110)) ),
inference(clausify,[status(thm)],[f_844_2]) ).
fof(f_845_1,plain,
! [C_5,A_15,B_14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(C_5),A_15)),hAPP_nat_nat(times_times_nat(C_5),B_14)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_5))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_15),B_14)) ),
inference(fof_nnf,[status(thm)],[fact_819_comm__mult__strict__left__mono]) ).
fof(f_845_2,plain,
! [U_2115,U_2114,U_2113] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2115),U_2114)),hAPP_nat_nat(times_times_nat(U_2115),U_2113)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2115))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2114),U_2113)) ),
inference(variable_rename,[status(thm)],[f_845_1]) ).
cnf(f_845_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2115),U_2114)),hAPP_nat_nat(times_times_nat(U_2115),U_2113)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2115))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2114),U_2113)) ),
inference(clausify,[status(thm)],[f_845_2]) ).
fof(f_846_1,plain,
! [C_5,A_15,B_14] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_5),A_15)),hAPP_int_int(times_times_int(C_5),B_14)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_5))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_15),B_14)) ),
inference(fof_nnf,[status(thm)],[fact_820_comm__mult__strict__left__mono]) ).
fof(f_846_2,plain,
! [U_2118,U_2117,U_2116] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2118),U_2117)),hAPP_int_int(times_times_int(U_2118),U_2116)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2117),U_2116)) ),
inference(variable_rename,[status(thm)],[f_846_1]) ).
cnf(f_846_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2118),U_2117)),hAPP_int_int(times_times_int(U_2118),U_2116)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2117),U_2116)) ),
inference(clausify,[status(thm)],[f_846_2]) ).
fof(f_847_1,plain,
! [C_4,A_14,B_13] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_4),A_14)),hAPP_real_real(times_times_real(C_4),B_13)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_4))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_14),B_13)) ),
inference(fof_nnf,[status(thm)],[fact_821_mult__strict__left__mono]) ).
fof(f_847_2,plain,
! [U_2121,U_2120,U_2119] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2121),U_2120)),hAPP_real_real(times_times_real(U_2121),U_2119)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2121))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2120),U_2119)) ),
inference(variable_rename,[status(thm)],[f_847_1]) ).
cnf(f_847_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2121),U_2120)),hAPP_real_real(times_times_real(U_2121),U_2119)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2121))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2120),U_2119)) ),
inference(clausify,[status(thm)],[f_847_2]) ).
fof(f_848_1,plain,
! [C_4,A_14,B_13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(C_4),A_14)),hAPP_nat_nat(times_times_nat(C_4),B_13)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_14),B_13)) ),
inference(fof_nnf,[status(thm)],[fact_822_mult__strict__left__mono]) ).
fof(f_848_2,plain,
! [U_2124,U_2123,U_2122] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2124),U_2123)),hAPP_nat_nat(times_times_nat(U_2124),U_2122)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2124))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2123),U_2122)) ),
inference(variable_rename,[status(thm)],[f_848_1]) ).
cnf(f_848_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2124),U_2123)),hAPP_nat_nat(times_times_nat(U_2124),U_2122)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2124))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2123),U_2122)) ),
inference(clausify,[status(thm)],[f_848_2]) ).
fof(f_849_1,plain,
! [C_4,A_14,B_13] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_4),A_14)),hAPP_int_int(times_times_int(C_4),B_13)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_14),B_13)) ),
inference(fof_nnf,[status(thm)],[fact_823_mult__strict__left__mono]) ).
fof(f_849_2,plain,
! [U_2127,U_2126,U_2125] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2127),U_2126)),hAPP_int_int(times_times_int(U_2127),U_2125)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2127))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2126),U_2125)) ),
inference(variable_rename,[status(thm)],[f_849_1]) ).
cnf(f_849_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2127),U_2126)),hAPP_int_int(times_times_int(U_2127),U_2125)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2127))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2126),U_2125)) ),
inference(clausify,[status(thm)],[f_849_2]) ).
fof(f_850_1,plain,
! [C_3,A_13,B_12] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_13),C_3)),hAPP_real_real(times_times_real(B_12),C_3)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_3))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_13),B_12)) ),
inference(fof_nnf,[status(thm)],[fact_824_mult__strict__right__mono]) ).
fof(f_850_2,plain,
! [U_2130,U_2129,U_2128] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2129),U_2130)),hAPP_real_real(times_times_real(U_2128),U_2130)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2130))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2129),U_2128)) ),
inference(variable_rename,[status(thm)],[f_850_1]) ).
cnf(f_850_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2129),U_2130)),hAPP_real_real(times_times_real(U_2128),U_2130)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2130))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2129),U_2128)) ),
inference(clausify,[status(thm)],[f_850_2]) ).
fof(f_851_1,plain,
! [C_3,A_13,B_12] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(A_13),C_3)),hAPP_nat_nat(times_times_nat(B_12),C_3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C_3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_13),B_12)) ),
inference(fof_nnf,[status(thm)],[fact_825_mult__strict__right__mono]) ).
fof(f_851_2,plain,
! [U_2133,U_2132,U_2131] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2132),U_2133)),hAPP_nat_nat(times_times_nat(U_2131),U_2133)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2133))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2132),U_2131)) ),
inference(variable_rename,[status(thm)],[f_851_1]) ).
cnf(f_851_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2132),U_2133)),hAPP_nat_nat(times_times_nat(U_2131),U_2133)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2133))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2132),U_2131)) ),
inference(clausify,[status(thm)],[f_851_2]) ).
fof(f_852_1,plain,
! [C_3,A_13,B_12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_13),C_3)),hAPP_int_int(times_times_int(B_12),C_3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_13),B_12)) ),
inference(fof_nnf,[status(thm)],[fact_826_mult__strict__right__mono]) ).
fof(f_852_2,plain,
! [U_2136,U_2135,U_2134] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2135),U_2136)),hAPP_int_int(times_times_int(U_2134),U_2136)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2136))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2135),U_2134)) ),
inference(variable_rename,[status(thm)],[f_852_1]) ).
cnf(f_852_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2135),U_2136)),hAPP_int_int(times_times_int(U_2134),U_2136)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2136))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2135),U_2134)) ),
inference(clausify,[status(thm)],[f_852_2]) ).
fof(f_853_1,plain,
! [B_11,A_12] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(A_12),B_11)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_11),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_12),zero_zero_real)) ),
inference(fof_nnf,[status(thm)],[fact_827_mult__neg__neg]) ).
fof(f_853_2,plain,
! [U_2138,U_2137] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(U_2137),U_2138)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2138),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2137),zero_zero_real)) ),
inference(variable_rename,[status(thm)],[f_853_1]) ).
cnf(f_853_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(U_2137),U_2138)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2138),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2137),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_853_2]) ).
fof(f_854_1,plain,
! [B_11,A_12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(A_12),B_11)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_11),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_12),zero_zero_int)) ),
inference(fof_nnf,[status(thm)],[fact_828_mult__neg__neg]) ).
fof(f_854_2,plain,
! [U_2140,U_2139] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(U_2139),U_2140)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2140),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2139),zero_zero_int)) ),
inference(variable_rename,[status(thm)],[f_854_1]) ).
cnf(f_854_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(U_2139),U_2140)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2140),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2139),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_854_2]) ).
fof(f_855_1,plain,
! [B_10,A_11] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_11),B_10)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_10))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_11),zero_zero_real)) ),
inference(fof_nnf,[status(thm)],[fact_829_mult__neg__pos]) ).
fof(f_855_2,plain,
! [U_2142,U_2141] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2141),U_2142)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2142))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2141),zero_zero_real)) ),
inference(variable_rename,[status(thm)],[f_855_1]) ).
cnf(f_855_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2141),U_2142)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2142))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2141),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_855_2]) ).
fof(f_856_1,plain,
! [B_10,A_11] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(A_11),B_10)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_10))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_11),zero_zero_nat)) ),
inference(fof_nnf,[status(thm)],[fact_830_mult__neg__pos]) ).
fof(f_856_2,plain,
! [U_2144,U_2143] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2143),U_2144)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2144))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2143),zero_zero_nat)) ),
inference(variable_rename,[status(thm)],[f_856_1]) ).
cnf(f_856_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2143),U_2144)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2144))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2143),zero_zero_nat)) ),
inference(clausify,[status(thm)],[f_856_2]) ).
fof(f_857_1,plain,
! [B_10,A_11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_11),B_10)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_10))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_11),zero_zero_int)) ),
inference(fof_nnf,[status(thm)],[fact_831_mult__neg__pos]) ).
fof(f_857_2,plain,
! [U_2146,U_2145] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2145),U_2146)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2146))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2145),zero_zero_int)) ),
inference(variable_rename,[status(thm)],[f_857_1]) ).
cnf(f_857_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2145),U_2146)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2146))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2145),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_857_2]) ).
fof(f_858_1,plain,
! [A_2,B_2,C_2] :
( ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_2),A_2)),hAPP_real_real(times_times_real(C_2),B_2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_2),A_2)) )
& ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_2),A_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_2),A_2)),hAPP_real_real(times_times_real(C_2),B_2))) ) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_2),zero_zero_real)) ),
inference(fof_nnf,[status(thm)],[fact_832_mult__less__cancel__left__neg]) ).
fof(f_858_2,plain,
! [U_2149,U_2148,U_2147] :
( ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2147),U_2149)),hAPP_real_real(times_times_real(U_2147),U_2148)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2148),U_2149)) )
& ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2148),U_2149))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2147),U_2149)),hAPP_real_real(times_times_real(U_2147),U_2148))) ) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2147),zero_zero_real)) ),
inference(variable_rename,[status(thm)],[f_858_1]) ).
cnf(f_858_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2148),U_2149))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2147),U_2149)),hAPP_real_real(times_times_real(U_2147),U_2148)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2147),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_858_2]) ).
cnf(f_858_4,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2147),U_2149)),hAPP_real_real(times_times_real(U_2147),U_2148)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2148),U_2149))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2147),zero_zero_real)) ),
inference(clausify,[status(thm)],[f_858_2]) ).
fof(f_859_1,plain,
! [A_2,B_2,C_2] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_2),A_2)),hAPP_int_int(times_times_int(C_2),B_2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_2),A_2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_2),A_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_2),A_2)),hAPP_int_int(times_times_int(C_2),B_2))) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_2),zero_zero_int)) ),
inference(fof_nnf,[status(thm)],[fact_833_mult__less__cancel__left__neg]) ).
fof(f_859_2,plain,
! [U_2152,U_2151,U_2150] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2150),U_2152)),hAPP_int_int(times_times_int(U_2150),U_2151)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2151),U_2152)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2151),U_2152))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2150),U_2152)),hAPP_int_int(times_times_int(U_2150),U_2151))) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2150),zero_zero_int)) ),
inference(variable_rename,[status(thm)],[f_859_1]) ).
cnf(f_859_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2151),U_2152))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2150),U_2152)),hAPP_int_int(times_times_int(U_2150),U_2151)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2150),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_859_2]) ).
cnf(f_859_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2150),U_2152)),hAPP_int_int(times_times_int(U_2150),U_2151)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2151),U_2152))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2150),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_859_2]) ).
fof(f_860_1,plain,
! [B_9,A_10] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_9))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_10))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(B_9),A_10))) ),
inference(fof_nnf,[status(thm)],[fact_834_zero__less__mult__pos2]) ).
fof(f_860_2,plain,
! [U_2154,U_2153] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2154))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2153))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(U_2154),U_2153))) ),
inference(variable_rename,[status(thm)],[f_860_1]) ).
cnf(f_860_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2154))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2153))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(U_2154),U_2153))) ),
inference(clausify,[status(thm)],[f_860_2]) ).
fof(f_861_1,plain,
! [B_9,A_10] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_9))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_10))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(B_9),A_10))) ),
inference(fof_nnf,[status(thm)],[fact_835_zero__less__mult__pos2]) ).
fof(f_861_2,plain,
! [U_2156,U_2155] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2156))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2155))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_2156),U_2155))) ),
inference(variable_rename,[status(thm)],[f_861_1]) ).
cnf(f_861_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2156))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2155))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_2156),U_2155))) ),
inference(clausify,[status(thm)],[f_861_2]) ).
fof(f_862_1,plain,
! [B_9,A_10] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_9))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_10))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(B_9),A_10))) ),
inference(fof_nnf,[status(thm)],[fact_836_zero__less__mult__pos2]) ).
fof(f_862_2,plain,
! [U_2158,U_2157] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2157))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(U_2158),U_2157))) ),
inference(variable_rename,[status(thm)],[f_862_1]) ).
cnf(f_862_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2157))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(U_2158),U_2157))) ),
inference(clausify,[status(thm)],[f_862_2]) ).
fof(f_863_1,plain,
! [A_9,B_8] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_8))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_9))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(A_9),B_8))) ),
inference(fof_nnf,[status(thm)],[fact_837_zero__less__mult__pos]) ).
fof(f_863_2,plain,
! [U_2160,U_2159] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2159))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2160))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(U_2160),U_2159))) ),
inference(variable_rename,[status(thm)],[f_863_1]) ).
cnf(f_863_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2159))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2160))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(U_2160),U_2159))) ),
inference(clausify,[status(thm)],[f_863_2]) ).
fof(f_864_1,plain,
! [A_9,B_8] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_8))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_9))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(A_9),B_8))) ),
inference(fof_nnf,[status(thm)],[fact_838_zero__less__mult__pos]) ).
fof(f_864_2,plain,
! [U_2162,U_2161] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2161))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2162))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_2162),U_2161))) ),
inference(variable_rename,[status(thm)],[f_864_1]) ).
cnf(f_864_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2161))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2162))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_2162),U_2161))) ),
inference(clausify,[status(thm)],[f_864_2]) ).
fof(f_865_1,plain,
! [A_9,B_8] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_8))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_9))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(A_9),B_8))) ),
inference(fof_nnf,[status(thm)],[fact_839_zero__less__mult__pos]) ).
fof(f_865_2,plain,
! [U_2164,U_2163] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2163))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2164))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(U_2164),U_2163))) ),
inference(variable_rename,[status(thm)],[f_865_1]) ).
cnf(f_865_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2163))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2164))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(U_2164),U_2163))) ),
inference(clausify,[status(thm)],[f_865_2]) ).
fof(f_866_1,plain,
! [B_7,A_8] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(B_7),A_8)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_7),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_8)) ),
inference(fof_nnf,[status(thm)],[fact_840_mult__pos__neg2]) ).
fof(f_866_2,plain,
! [U_2166,U_2165] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2166),U_2165)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2166),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2165)) ),
inference(variable_rename,[status(thm)],[f_866_1]) ).
cnf(f_866_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2166),U_2165)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2166),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2165)) ),
inference(clausify,[status(thm)],[f_866_2]) ).
fof(f_867_1,plain,
! [B_7,A_8] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(B_7),A_8)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_7),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_8)) ),
inference(fof_nnf,[status(thm)],[fact_841_mult__pos__neg2]) ).
fof(f_867_2,plain,
! [U_2168,U_2167] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2168),U_2167)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2168),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2167)) ),
inference(variable_rename,[status(thm)],[f_867_1]) ).
cnf(f_867_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2168),U_2167)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2168),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2167)) ),
inference(clausify,[status(thm)],[f_867_2]) ).
fof(f_868_1,plain,
! [B_7,A_8] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(B_7),A_8)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_7),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_8)) ),
inference(fof_nnf,[status(thm)],[fact_842_mult__pos__neg2]) ).
fof(f_868_2,plain,
! [U_2170,U_2169] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2170),U_2169)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2170),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2169)) ),
inference(variable_rename,[status(thm)],[f_868_1]) ).
cnf(f_868_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2170),U_2169)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2170),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2169)) ),
inference(clausify,[status(thm)],[f_868_2]) ).
fof(f_869_1,plain,
! [B_6,A_7] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_7),B_6)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_6),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_7)) ),
inference(fof_nnf,[status(thm)],[fact_843_mult__pos__neg]) ).
fof(f_869_2,plain,
! [U_2172,U_2171] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2171),U_2172)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2172),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2171)) ),
inference(variable_rename,[status(thm)],[f_869_1]) ).
cnf(f_869_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2171),U_2172)),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2172),zero_zero_real))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2171)) ),
inference(clausify,[status(thm)],[f_869_2]) ).
fof(f_870_1,plain,
! [B_6,A_7] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(A_7),B_6)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_6),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_7)) ),
inference(fof_nnf,[status(thm)],[fact_844_mult__pos__neg]) ).
fof(f_870_2,plain,
! [U_2174,U_2173] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2173),U_2174)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2174),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2173)) ),
inference(variable_rename,[status(thm)],[f_870_1]) ).
cnf(f_870_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2173),U_2174)),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2174),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2173)) ),
inference(clausify,[status(thm)],[f_870_2]) ).
fof(f_871_1,plain,
! [B_6,A_7] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_7),B_6)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_6),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_7)) ),
inference(fof_nnf,[status(thm)],[fact_845_mult__pos__neg]) ).
fof(f_871_2,plain,
! [U_2176,U_2175] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2175),U_2176)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2176),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2175)) ),
inference(variable_rename,[status(thm)],[f_871_1]) ).
cnf(f_871_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2175),U_2176)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2176),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2175)) ),
inference(clausify,[status(thm)],[f_871_2]) ).
fof(f_872_1,plain,
! [B_5,A_6] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(A_6),B_5)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),B_5))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A_6)) ),
inference(fof_nnf,[status(thm)],[fact_846_mult__pos__pos]) ).
fof(f_872_2,plain,
! [U_2178,U_2177] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(U_2177),U_2178)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2178))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2177)) ),
inference(variable_rename,[status(thm)],[f_872_1]) ).
cnf(f_872_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(U_2177),U_2178)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2178))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2177)) ),
inference(clausify,[status(thm)],[f_872_2]) ).
fof(f_873_1,plain,
! [B_5,A_6] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(A_6),B_5)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_5))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_6)) ),
inference(fof_nnf,[status(thm)],[fact_847_mult__pos__pos]) ).
fof(f_873_2,plain,
! [U_2180,U_2179] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_2179),U_2180)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2180))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2179)) ),
inference(variable_rename,[status(thm)],[f_873_1]) ).
cnf(f_873_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_2179),U_2180)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2180))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2179)) ),
inference(clausify,[status(thm)],[f_873_2]) ).
fof(f_874_1,plain,
! [B_5,A_6] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(A_6),B_5)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_5))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_6)) ),
inference(fof_nnf,[status(thm)],[fact_848_mult__pos__pos]) ).
fof(f_874_2,plain,
! [U_2182,U_2181] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(U_2181),U_2182)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2182))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2181)) ),
inference(variable_rename,[status(thm)],[f_874_1]) ).
cnf(f_874_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(times_times_int(U_2181),U_2182)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2182))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2181)) ),
inference(clausify,[status(thm)],[f_874_2]) ).
fof(f_875_1,plain,
! [A_2,B_2,C_2] :
( ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_2),A_2)),hAPP_real_real(times_times_real(C_2),B_2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),B_2)) )
& ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),B_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_2),A_2)),hAPP_real_real(times_times_real(C_2),B_2))) ) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_2)) ),
inference(fof_nnf,[status(thm)],[fact_849_mult__less__cancel__left__pos]) ).
fof(f_875_2,plain,
! [U_2185,U_2184,U_2183] :
( ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2183),U_2185)),hAPP_real_real(times_times_real(U_2183),U_2184)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2185),U_2184)) )
& ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2185),U_2184))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2183),U_2185)),hAPP_real_real(times_times_real(U_2183),U_2184))) ) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2183)) ),
inference(variable_rename,[status(thm)],[f_875_1]) ).
cnf(f_875_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2185),U_2184))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2183),U_2185)),hAPP_real_real(times_times_real(U_2183),U_2184)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2183)) ),
inference(clausify,[status(thm)],[f_875_2]) ).
cnf(f_875_4,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2183),U_2185)),hAPP_real_real(times_times_real(U_2183),U_2184)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2185),U_2184))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2183)) ),
inference(clausify,[status(thm)],[f_875_2]) ).
fof(f_876_1,plain,
! [A_2,B_2,C_2] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_2),A_2)),hAPP_int_int(times_times_int(C_2),B_2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),B_2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),B_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_2),A_2)),hAPP_int_int(times_times_int(C_2),B_2))) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_2)) ),
inference(fof_nnf,[status(thm)],[fact_850_mult__less__cancel__left__pos]) ).
fof(f_876_2,plain,
! [U_2188,U_2187,U_2186] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2186),U_2188)),hAPP_int_int(times_times_int(U_2186),U_2187)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2188),U_2187)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2188),U_2187))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2186),U_2188)),hAPP_int_int(times_times_int(U_2186),U_2187))) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2186)) ),
inference(variable_rename,[status(thm)],[f_876_1]) ).
cnf(f_876_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2188),U_2187))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2186),U_2188)),hAPP_int_int(times_times_int(U_2186),U_2187)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2186)) ),
inference(clausify,[status(thm)],[f_876_2]) ).
cnf(f_876_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2186),U_2188)),hAPP_int_int(times_times_int(U_2186),U_2187)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2188),U_2187))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2186)) ),
inference(clausify,[status(thm)],[f_876_2]) ).
fof(f_877_1,plain,
! [C_2,A_2,B_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_2),A_2)),hAPP_real_real(times_times_real(C_2),B_2)))
| ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_2),A_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_2),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),B_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_2)) ) ) )
& ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_2),A_2))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_2),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),B_2))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_2)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(C_2),A_2)),hAPP_real_real(times_times_real(C_2),B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_851_mult__less__cancel__left__disj]) ).
fof(f_877_2,plain,
! [U_2191,U_2190,U_2189] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2191),U_2190)),hAPP_real_real(times_times_real(U_2191),U_2189)))
| ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2189),U_2190))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2191),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2190),U_2189))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2191)) ) ) )
& ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2189),U_2190))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2191),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2190),U_2189))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2191)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2191),U_2190)),hAPP_real_real(times_times_real(U_2191),U_2189))) ) ),
inference(variable_rename,[status(thm)],[f_877_1]) ).
fof(f_877_3,plain,
( ! [U_2197,U_2195,U_2193] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2197),U_2195)),hAPP_real_real(times_times_real(U_2197),U_2193)))
| ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2193),U_2195))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2197),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2195),U_2193))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2197)) ) ) )
& ! [U_2196,U_2194,U_2192] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2192),U_2194))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2196),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2194),U_2192))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2196)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2196),U_2194)),hAPP_real_real(times_times_real(U_2196),U_2192))) ) ),
inference(miniscope,[status(thm)],[f_877_2]) ).
cnf(f_877_4,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2196),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2196))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2196),U_2194)),hAPP_real_real(times_times_real(U_2196),U_2192))) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_5,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2192),U_2194))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2196))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2196),U_2194)),hAPP_real_real(times_times_real(U_2196),U_2192))) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_6,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2196),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2194),U_2192))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2196),U_2194)),hAPP_real_real(times_times_real(U_2196),U_2192))) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_7,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2192),U_2194))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2194),U_2192))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2196),U_2194)),hAPP_real_real(times_times_real(U_2196),U_2192))) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_8,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2195),U_2193))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2197))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2197),U_2195)),hAPP_real_real(times_times_real(U_2197),U_2193))) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_9,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2193),U_2195))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2197),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2197),U_2195)),hAPP_real_real(times_times_real(U_2197),U_2193))) ),
inference(clausify,[status(thm)],[f_877_3]) ).
fof(f_878_1,plain,
! [C_2,A_2,B_2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_2),A_2)),hAPP_int_int(times_times_int(C_2),B_2)))
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_2),A_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_2),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),B_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_2)) ) ) )
& ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_2),A_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_2),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),B_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_2)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(C_2),A_2)),hAPP_int_int(times_times_int(C_2),B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_852_mult__less__cancel__left__disj]) ).
fof(f_878_2,plain,
! [U_2200,U_2199,U_2198] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2200),U_2199)),hAPP_int_int(times_times_int(U_2200),U_2198)))
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2198),U_2199))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2200),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2199),U_2198))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2200)) ) ) )
& ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2198),U_2199))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2200),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2199),U_2198))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2200)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2200),U_2199)),hAPP_int_int(times_times_int(U_2200),U_2198))) ) ),
inference(variable_rename,[status(thm)],[f_878_1]) ).
fof(f_878_3,plain,
( ! [U_2206,U_2204,U_2202] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2206),U_2204)),hAPP_int_int(times_times_int(U_2206),U_2202)))
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2202),U_2204))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2206),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2204),U_2202))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2206)) ) ) )
& ! [U_2205,U_2203,U_2201] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2201),U_2203))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2205),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2203),U_2201))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2205)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2205),U_2203)),hAPP_int_int(times_times_int(U_2205),U_2201))) ) ),
inference(miniscope,[status(thm)],[f_878_2]) ).
cnf(f_878_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2205),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2205))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2205),U_2203)),hAPP_int_int(times_times_int(U_2205),U_2201))) ),
inference(clausify,[status(thm)],[f_878_3]) ).
cnf(f_878_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2201),U_2203))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2205))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2205),U_2203)),hAPP_int_int(times_times_int(U_2205),U_2201))) ),
inference(clausify,[status(thm)],[f_878_3]) ).
cnf(f_878_6,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2205),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2203),U_2201))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2205),U_2203)),hAPP_int_int(times_times_int(U_2205),U_2201))) ),
inference(clausify,[status(thm)],[f_878_3]) ).
cnf(f_878_7,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2201),U_2203))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2203),U_2201))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2205),U_2203)),hAPP_int_int(times_times_int(U_2205),U_2201))) ),
inference(clausify,[status(thm)],[f_878_3]) ).
cnf(f_878_8,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2204),U_2202))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2206))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2206),U_2204)),hAPP_int_int(times_times_int(U_2206),U_2202))) ),
inference(clausify,[status(thm)],[f_878_3]) ).
cnf(f_878_9,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2202),U_2204))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2206),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2206),U_2204)),hAPP_int_int(times_times_int(U_2206),U_2202))) ),
inference(clausify,[status(thm)],[f_878_3]) ).
fof(f_879_1,plain,
! [A_2,C_2,B_2] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_2),C_2)),hAPP_real_real(times_times_real(B_2),C_2)))
| ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_2),A_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_2),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),B_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_2)) ) ) )
& ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,B_2),A_2))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,C_2),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,A_2),B_2))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),C_2)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_2),C_2)),hAPP_real_real(times_times_real(B_2),C_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_853_mult__less__cancel__right__disj]) ).
fof(f_879_2,plain,
! [U_2209,U_2208,U_2207] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2209),U_2208)),hAPP_real_real(times_times_real(U_2207),U_2208)))
| ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2207),U_2209))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2208),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2209),U_2207))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2208)) ) ) )
& ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2207),U_2209))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2208),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2209),U_2207))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2208)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2209),U_2208)),hAPP_real_real(times_times_real(U_2207),U_2208))) ) ),
inference(variable_rename,[status(thm)],[f_879_1]) ).
fof(f_879_3,plain,
( ! [U_2215,U_2213,U_2211] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2215),U_2213)),hAPP_real_real(times_times_real(U_2211),U_2213)))
| ( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2211),U_2215))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2213),zero_zero_real)) )
& ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2215),U_2211))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2213)) ) ) )
& ! [U_2214,U_2212,U_2210] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2210),U_2214))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2212),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2214),U_2210))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2212)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2214),U_2212)),hAPP_real_real(times_times_real(U_2210),U_2212))) ) ),
inference(miniscope,[status(thm)],[f_879_2]) ).
cnf(f_879_4,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2212),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2212))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2214),U_2212)),hAPP_real_real(times_times_real(U_2210),U_2212))) ),
inference(clausify,[status(thm)],[f_879_3]) ).
cnf(f_879_5,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2210),U_2214))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2212))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2214),U_2212)),hAPP_real_real(times_times_real(U_2210),U_2212))) ),
inference(clausify,[status(thm)],[f_879_3]) ).
cnf(f_879_6,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2212),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2214),U_2210))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2214),U_2212)),hAPP_real_real(times_times_real(U_2210),U_2212))) ),
inference(clausify,[status(thm)],[f_879_3]) ).
cnf(f_879_7,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2210),U_2214))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2214),U_2210))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2214),U_2212)),hAPP_real_real(times_times_real(U_2210),U_2212))) ),
inference(clausify,[status(thm)],[f_879_3]) ).
cnf(f_879_8,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2215),U_2211))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2213))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2215),U_2213)),hAPP_real_real(times_times_real(U_2211),U_2213))) ),
inference(clausify,[status(thm)],[f_879_3]) ).
cnf(f_879_9,plain,
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2211),U_2215))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2213),zero_zero_real))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2215),U_2213)),hAPP_real_real(times_times_real(U_2211),U_2213))) ),
inference(clausify,[status(thm)],[f_879_3]) ).
fof(f_880_1,plain,
! [A_2,C_2,B_2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_2),C_2)),hAPP_int_int(times_times_int(B_2),C_2)))
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_2),A_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_2),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),B_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_2)) ) ) )
& ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_2),A_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_2),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),B_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C_2)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_2),C_2)),hAPP_int_int(times_times_int(B_2),C_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_854_mult__less__cancel__right__disj]) ).
fof(f_880_2,plain,
! [U_2218,U_2217,U_2216] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2218),U_2217)),hAPP_int_int(times_times_int(U_2216),U_2217)))
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2216),U_2218))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2217),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2218),U_2216))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2217)) ) ) )
& ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2216),U_2218))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2217),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2218),U_2216))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2217)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2218),U_2217)),hAPP_int_int(times_times_int(U_2216),U_2217))) ) ),
inference(variable_rename,[status(thm)],[f_880_1]) ).
fof(f_880_3,plain,
( ! [U_2224,U_2222,U_2220] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2224),U_2222)),hAPP_int_int(times_times_int(U_2220),U_2222)))
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2220),U_2224))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2222),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2224),U_2220))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2222)) ) ) )
& ! [U_2223,U_2221,U_2219] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2219),U_2223))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2221),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2223),U_2219))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2221)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2223),U_2221)),hAPP_int_int(times_times_int(U_2219),U_2221))) ) ),
inference(miniscope,[status(thm)],[f_880_2]) ).
cnf(f_880_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2221),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2221))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2223),U_2221)),hAPP_int_int(times_times_int(U_2219),U_2221))) ),
inference(clausify,[status(thm)],[f_880_3]) ).
cnf(f_880_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2219),U_2223))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2221))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2223),U_2221)),hAPP_int_int(times_times_int(U_2219),U_2221))) ),
inference(clausify,[status(thm)],[f_880_3]) ).
cnf(f_880_6,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2221),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2223),U_2219))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2223),U_2221)),hAPP_int_int(times_times_int(U_2219),U_2221))) ),
inference(clausify,[status(thm)],[f_880_3]) ).
cnf(f_880_7,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2219),U_2223))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2223),U_2219))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2223),U_2221)),hAPP_int_int(times_times_int(U_2219),U_2221))) ),
inference(clausify,[status(thm)],[f_880_3]) ).
cnf(f_880_8,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2224),U_2220))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2222))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2224),U_2222)),hAPP_int_int(times_times_int(U_2220),U_2222))) ),
inference(clausify,[status(thm)],[f_880_3]) ).
cnf(f_880_9,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2220),U_2224))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2222),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2224),U_2222)),hAPP_int_int(times_times_int(U_2220),U_2222))) ),
inference(clausify,[status(thm)],[f_880_3]) ).
fof(f_881_1,plain,
! [A_5] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(A_5),A_5)),zero_zero_real)),
inference(fof_nnf,[status(thm)],[fact_855_not__square__less__zero]) ).
fof(f_881_2,plain,
! [U_2225] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2225),U_2225)),zero_zero_real)),
inference(variable_rename,[status(thm)],[f_881_1]) ).
cnf(f_881_3,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2225),U_2225)),zero_zero_real)),
inference(clausify,[status(thm)],[f_881_2]) ).
fof(f_882_1,plain,
! [A_5] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(A_5),A_5)),zero_zero_int)),
inference(fof_nnf,[status(thm)],[fact_856_not__square__less__zero]) ).
fof(f_882_2,plain,
! [U_2226] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2226),U_2226)),zero_zero_int)),
inference(variable_rename,[status(thm)],[f_882_1]) ).
cnf(f_882_3,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_2226),U_2226)),zero_zero_int)),
inference(clausify,[status(thm)],[f_882_2]) ).
fof(f_883_1,plain,
! [B_4,C_1,A_4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_4),hAPP_nat_nat(plus_plus_nat(A_4),C_1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_4),C_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_4)) ),
inference(fof_nnf,[status(thm)],[fact_857_pos__add__strict]) ).
fof(f_883_2,plain,
! [U_2229,U_2228,U_2227] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2229),hAPP_nat_nat(plus_plus_nat(U_2227),U_2228)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2229),U_2228))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2227)) ),
inference(variable_rename,[status(thm)],[f_883_1]) ).
cnf(f_883_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2229),hAPP_nat_nat(plus_plus_nat(U_2227),U_2228)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2229),U_2228))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2227)) ),
inference(clausify,[status(thm)],[f_883_2]) ).
fof(f_884_1,plain,
! [B_4,C_1,A_4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_4),hAPP_int_int(plus_plus_int(A_4),C_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_4),C_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_4)) ),
inference(fof_nnf,[status(thm)],[fact_858_pos__add__strict]) ).
fof(f_884_2,plain,
! [U_2232,U_2231,U_2230] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2232),hAPP_int_int(plus_plus_int(U_2230),U_2231)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2232),U_2231))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2230)) ),
inference(variable_rename,[status(thm)],[f_884_1]) ).
cnf(f_884_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2232),hAPP_int_int(plus_plus_int(U_2230),U_2231)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2232),U_2231))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2230)) ),
inference(clausify,[status(thm)],[f_884_2]) ).
fof(f_885_1,plain,
! [A,B] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A),B))
| B = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B)) ),
inference(fof_nnf,[status(thm)],[fact_859_divides__ge]) ).
fof(f_885_2,plain,
! [U_2234,U_2233] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2234),U_2233))
| U_2233 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2234),U_2233)) ),
inference(variable_rename,[status(thm)],[f_885_1]) ).
cnf(f_885_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2234),U_2233))
| U_2233 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2234),U_2233)) ),
inference(clausify,[status(thm)],[f_885_2]) ).
fof(f_886_1,plain,
! [Ma,K,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(Ma),K)),hAPP_nat_nat(times_times_nat(N),K)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Ma),N))
& K != zero_zero_nat ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Ma),N))
| K = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(Ma),K)),hAPP_nat_nat(times_times_nat(N),K))) ) ),
inference(fof_nnf,[status(thm)],[fact_860_nat__mult__dvd__cancel__disj_H]) ).
fof(f_886_2,plain,
! [U_2237,U_2236,U_2235] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2237),U_2236)),hAPP_nat_nat(times_times_nat(U_2235),U_2236)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2237),U_2235))
& U_2236 != zero_zero_nat ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2237),U_2235))
| U_2236 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2237),U_2236)),hAPP_nat_nat(times_times_nat(U_2235),U_2236))) ) ),
inference(variable_rename,[status(thm)],[f_886_1]) ).
fof(f_886_3,plain,
( ! [U_2243,U_2241,U_2239] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2243),U_2241)),hAPP_nat_nat(times_times_nat(U_2239),U_2241)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2243),U_2239))
& U_2241 != zero_zero_nat ) )
& ! [U_2242,U_2240,U_2238] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2242),U_2238))
| U_2240 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2242),U_2240)),hAPP_nat_nat(times_times_nat(U_2238),U_2240))) ) ),
inference(miniscope,[status(thm)],[f_886_2]) ).
cnf(f_886_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2242),U_2238))
| U_2240 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2242),U_2240)),hAPP_nat_nat(times_times_nat(U_2238),U_2240))) ),
inference(clausify,[status(thm)],[f_886_3]) ).
cnf(f_886_5,plain,
( U_2241 != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2243),U_2241)),hAPP_nat_nat(times_times_nat(U_2239),U_2241))) ),
inference(clausify,[status(thm)],[f_886_3]) ).
cnf(f_886_6,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2243),U_2239))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2243),U_2241)),hAPP_nat_nat(times_times_nat(U_2239),U_2241))) ),
inference(clausify,[status(thm)],[f_886_3]) ).
fof(f_887_1,plain,
! [X_2,Y_2,Z_1] :
( ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X_2),Z_1)),hAPP_real_real(times_times_real(Y_2),Z_1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),Y_2)) )
& ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_2),Y_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(X_2),Z_1)),hAPP_real_real(times_times_real(Y_2),Z_1))) ) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Z_1)) ),
inference(fof_nnf,[status(thm)],[fact_861_real__mult__less__iff1]) ).
fof(f_887_2,plain,
! [U_2246,U_2245,U_2244] :
( ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2246),U_2244)),hAPP_real_real(times_times_real(U_2245),U_2244)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2246),U_2245)) )
& ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2246),U_2245))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2246),U_2244)),hAPP_real_real(times_times_real(U_2245),U_2244))) ) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2244)) ),
inference(variable_rename,[status(thm)],[f_887_1]) ).
cnf(f_887_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2246),U_2245))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2246),U_2244)),hAPP_real_real(times_times_real(U_2245),U_2244)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2244)) ),
inference(clausify,[status(thm)],[f_887_2]) ).
cnf(f_887_4,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2246),U_2244)),hAPP_real_real(times_times_real(U_2245),U_2244)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2246),U_2245))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2244)) ),
inference(clausify,[status(thm)],[f_887_2]) ).
fof(f_888_1,plain,
! [X_2,Y_2,Z_1] :
( ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X_2),Z_1)),hAPP_real_real(times_times_real(Y_2),Z_1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Y_2)) )
& ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Y_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(X_2),Z_1)),hAPP_real_real(times_times_real(Y_2),Z_1))) ) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Z_1)) ),
inference(fof_nnf,[status(thm)],[fact_862_real__mult__le__cancel__iff1]) ).
fof(f_888_2,plain,
! [U_2249,U_2248,U_2247] :
( ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2249),U_2247)),hAPP_real_real(times_times_real(U_2248),U_2247)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2249),U_2248)) )
& ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2249),U_2248))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2249),U_2247)),hAPP_real_real(times_times_real(U_2248),U_2247))) ) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2247)) ),
inference(variable_rename,[status(thm)],[f_888_1]) ).
cnf(f_888_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2249),U_2248))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2249),U_2247)),hAPP_real_real(times_times_real(U_2248),U_2247)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2247)) ),
inference(clausify,[status(thm)],[f_888_2]) ).
cnf(f_888_4,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2249),U_2247)),hAPP_real_real(times_times_real(U_2248),U_2247)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2249),U_2248))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2247)) ),
inference(clausify,[status(thm)],[f_888_2]) ).
fof(f_889_1,plain,
! [X_2,Y_2,Z_1] :
( ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(Z_1),X_2)),hAPP_real_real(times_times_real(Z_1),Y_2)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Y_2)) )
& ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X_2),Y_2))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(Z_1),X_2)),hAPP_real_real(times_times_real(Z_1),Y_2))) ) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Z_1)) ),
inference(fof_nnf,[status(thm)],[fact_863_real__mult__le__cancel__iff2]) ).
fof(f_889_2,plain,
! [U_2252,U_2251,U_2250] :
( ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2250),U_2252)),hAPP_real_real(times_times_real(U_2250),U_2251)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2252),U_2251)) )
& ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2252),U_2251))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2250),U_2252)),hAPP_real_real(times_times_real(U_2250),U_2251))) ) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2250)) ),
inference(variable_rename,[status(thm)],[f_889_1]) ).
cnf(f_889_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2252),U_2251))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2250),U_2252)),hAPP_real_real(times_times_real(U_2250),U_2251)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2250)) ),
inference(clausify,[status(thm)],[f_889_2]) ).
cnf(f_889_4,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,hAPP_real_real(times_times_real(U_2250),U_2252)),hAPP_real_real(times_times_real(U_2250),U_2251)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2252),U_2251))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2250)) ),
inference(clausify,[status(thm)],[f_889_2]) ).
fof(f_890_1,plain,
! [Y_1,X_1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(X_1),Y_1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y_1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X_1)) ),
inference(fof_nnf,[status(thm)],[fact_864_real__mult__order]) ).
fof(f_890_2,plain,
! [U_2254,U_2253] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(U_2253),U_2254)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2254))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2253)) ),
inference(variable_rename,[status(thm)],[f_890_1]) ).
cnf(f_890_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_real_real(times_times_real(U_2253),U_2254)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2254))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2253)) ),
inference(clausify,[status(thm)],[f_890_2]) ).
fof(f_891_1,plain,
! [X_1,Y_1,Z] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(Z),X_1)),hAPP_real_real(times_times_real(Z),Y_1)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X_1),Y_1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Z)) ),
inference(fof_nnf,[status(thm)],[fact_865_real__mult__less__mono2]) ).
fof(f_891_2,plain,
! [U_2257,U_2256,U_2255] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2255),U_2257)),hAPP_real_real(times_times_real(U_2255),U_2256)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2257),U_2256))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2255)) ),
inference(variable_rename,[status(thm)],[f_891_1]) ).
cnf(f_891_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_real_real(times_times_real(U_2255),U_2257)),hAPP_real_real(times_times_real(U_2255),U_2256)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,U_2257),U_2256))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2255)) ),
inference(clausify,[status(thm)],[f_891_2]) ).
fof(f_892_1,plain,
! [X_2,Y_2] :
( ( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X_2),X_2)),hAPP_real_real(times_times_real(Y_2),Y_2)) = zero_zero_real
| Y_2 != zero_zero_real
| X_2 != zero_zero_real )
& ( ( Y_2 = zero_zero_real
& X_2 = zero_zero_real )
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(X_2),X_2)),hAPP_real_real(times_times_real(Y_2),Y_2)) != zero_zero_real ) ),
inference(fof_nnf,[status(thm)],[fact_866_real__two__squares__add__zero__iff]) ).
fof(f_892_2,plain,
! [U_2259,U_2258] :
( ( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_2259),U_2259)),hAPP_real_real(times_times_real(U_2258),U_2258)) = zero_zero_real
| U_2258 != zero_zero_real
| U_2259 != zero_zero_real )
& ( ( U_2258 = zero_zero_real
& U_2259 = zero_zero_real )
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_2259),U_2259)),hAPP_real_real(times_times_real(U_2258),U_2258)) != zero_zero_real ) ),
inference(variable_rename,[status(thm)],[f_892_1]) ).
fof(f_892_3,plain,
( ! [U_2263,U_2261] :
( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_2263),U_2263)),hAPP_real_real(times_times_real(U_2261),U_2261)) = zero_zero_real
| U_2261 != zero_zero_real
| U_2263 != zero_zero_real )
& ! [U_2262,U_2260] :
( ( U_2260 = zero_zero_real
& U_2262 = zero_zero_real )
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_2262),U_2262)),hAPP_real_real(times_times_real(U_2260),U_2260)) != zero_zero_real ) ),
inference(miniscope,[status(thm)],[f_892_2]) ).
cnf(f_892_4,plain,
( U_2262 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_2262),U_2262)),hAPP_real_real(times_times_real(U_2260),U_2260)) != zero_zero_real ),
inference(clausify,[status(thm)],[f_892_3]) ).
cnf(f_892_5,plain,
( U_2260 = zero_zero_real
| hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_2262),U_2262)),hAPP_real_real(times_times_real(U_2260),U_2260)) != zero_zero_real ),
inference(clausify,[status(thm)],[f_892_3]) ).
cnf(f_892_6,plain,
( hAPP_real_real(plus_plus_real(hAPP_real_real(times_times_real(U_2263),U_2263)),hAPP_real_real(times_times_real(U_2261),U_2261)) = zero_zero_real
| U_2261 != zero_zero_real
| U_2263 != zero_zero_real ),
inference(clausify,[status(thm)],[f_892_3]) ).
fof(f_893_1,plain,
! [X_1,Y_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(X_1),N_1)),Y_1))
| N_1 = zero_zero_nat ),
inference(fof_nnf,[status(thm)],[fact_867_divides__exp2]) ).
fof(f_893_2,plain,
! [U_2266,U_2265,U_2264] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2266),U_2265))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_2266),U_2264)),U_2265))
| U_2264 = zero_zero_nat ),
inference(variable_rename,[status(thm)],[f_893_1]) ).
cnf(f_893_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2266),U_2265))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_2266),U_2264)),U_2265))
| U_2264 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_893_2]) ).
fof(f_894_1,plain,
! [A,N_1,B] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B))
| N_1 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(A),N_1)),hAPP_nat_nat(power_power_nat(B),N_1))) ),
inference(fof_nnf,[status(thm)],[fact_868_divides__rev]) ).
fof(f_894_2,plain,
! [U_2269,U_2268,U_2267] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2269),U_2267))
| U_2268 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_2269),U_2268)),hAPP_nat_nat(power_power_nat(U_2267),U_2268))) ),
inference(variable_rename,[status(thm)],[f_894_1]) ).
cnf(f_894_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2269),U_2267))
| U_2268 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_2269),U_2268)),hAPP_nat_nat(power_power_nat(U_2267),U_2268))) ),
inference(clausify,[status(thm)],[f_894_2]) ).
fof(f_895_1,plain,
! [X_2,N] :
( ( hAPP_nat_nat(power_power_nat(X_2),N) = one_one_nat
| ( N != zero_zero_nat
& X_2 != one_one_nat ) )
& ( N = zero_zero_nat
| X_2 = one_one_nat
| hAPP_nat_nat(power_power_nat(X_2),N) != one_one_nat ) ),
inference(fof_nnf,[status(thm)],[fact_869_exp__eq__1]) ).
fof(f_895_2,plain,
! [U_2271,U_2270] :
( ( hAPP_nat_nat(power_power_nat(U_2271),U_2270) = one_one_nat
| ( U_2270 != zero_zero_nat
& U_2271 != one_one_nat ) )
& ( U_2270 = zero_zero_nat
| U_2271 = one_one_nat
| hAPP_nat_nat(power_power_nat(U_2271),U_2270) != one_one_nat ) ),
inference(variable_rename,[status(thm)],[f_895_1]) ).
fof(f_895_3,plain,
( ! [U_2275,U_2273] :
( hAPP_nat_nat(power_power_nat(U_2275),U_2273) = one_one_nat
| ( U_2273 != zero_zero_nat
& U_2275 != one_one_nat ) )
& ! [U_2274,U_2272] :
( U_2272 = zero_zero_nat
| U_2274 = one_one_nat
| hAPP_nat_nat(power_power_nat(U_2274),U_2272) != one_one_nat ) ),
inference(miniscope,[status(thm)],[f_895_2]) ).
cnf(f_895_4,plain,
( U_2272 = zero_zero_nat
| U_2274 = one_one_nat
| hAPP_nat_nat(power_power_nat(U_2274),U_2272) != one_one_nat ),
inference(clausify,[status(thm)],[f_895_3]) ).
cnf(f_895_5,plain,
( U_2275 != one_one_nat
| hAPP_nat_nat(power_power_nat(U_2275),U_2273) = one_one_nat ),
inference(clausify,[status(thm)],[f_895_3]) ).
cnf(f_895_6,plain,
( U_2273 != zero_zero_nat
| hAPP_nat_nat(power_power_nat(U_2275),U_2273) = one_one_nat ),
inference(clausify,[status(thm)],[f_895_3]) ).
fof(f_896_1,plain,
! [X_1,Q_1,N_1,R_1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,N_1),X_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,R_1),N_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),R_1))
| X_1 != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(Q_1),N_1)),R_1) ),
inference(fof_nnf,[status(thm)],[fact_870_divides__div__not]) ).
fof(f_896_2,plain,
! [U_2279,U_2278,U_2277,U_2276] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2277),U_2279))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2276),U_2277))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2276))
| U_2279 != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2278),U_2277)),U_2276) ),
inference(variable_rename,[status(thm)],[f_896_1]) ).
cnf(f_896_3,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2277),U_2279))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2276),U_2277))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2276))
| U_2279 != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2278),U_2277)),U_2276) ),
inference(clausify,[status(thm)],[f_896_2]) ).
fof(f_897_1,plain,
! [N_1] : 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)))),N_1))),
inference(fof_nnf,[status(thm)],[fact_871_two__realpow__ge__one]) ).
fof(f_897_2,plain,
! [U_2280] : 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)))),U_2280))),
inference(variable_rename,[status(thm)],[f_897_1]) ).
cnf(f_897_3,plain,
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)))),U_2280))),
inference(clausify,[status(thm)],[f_897_2]) ).
fof(f_898_1,plain,
! [A,N_1] :
( ? [R_2] :
( hAPP_nat_real(power_power_real(R_2),N_1) = A
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),R_2)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_872_realpow__pos__nth]) ).
fof(f_898_2,plain,
! [U_2283,U_2282] :
( ? [U_2281] :
( hAPP_nat_real(power_power_real(U_2281),U_2282) = U_2283
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2281)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2283))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2282)) ),
inference(variable_rename,[status(thm)],[f_898_1]) ).
fof(f_898_3,plain,
! [U_2283,U_2282] :
( ( hAPP_nat_real(power_power_real(sK12(U_2283,U_2282)),U_2282) = U_2283
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sK12(U_2283,U_2282))) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2283))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2282)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_2281,sK12(U_2283,U_2282))],[f_898_2]) ).
cnf(f_898_4,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sK12(U_2283,U_2282)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2283))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2282)) ),
inference(clausify,[status(thm)],[f_898_3]) ).
cnf(f_898_5,plain,
( hAPP_nat_real(power_power_real(sK12(U_2283,U_2282)),U_2282) = U_2283
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2283))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2282)) ),
inference(clausify,[status(thm)],[f_898_3]) ).
fof(f_899_1,plain,
! [A,N_1] :
( ? [X] :
( ! [Y] :
( Y = X
| hAPP_nat_real(power_power_real(Y),N_1) != A
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),Y)) )
& hAPP_nat_real(power_power_real(X),N_1) = A
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),X)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),A))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_873_realpow__pos__nth__unique]) ).
fof(f_899_2,plain,
! [U_2287,U_2286] :
( ? [U_2285] :
( ! [U_2284] :
( U_2284 = U_2285
| hAPP_nat_real(power_power_real(U_2284),U_2286) != U_2287
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2284)) )
& hAPP_nat_real(power_power_real(U_2285),U_2286) = U_2287
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2285)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2287))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2286)) ),
inference(variable_rename,[status(thm)],[f_899_1]) ).
fof(f_899_3,plain,
! [U_2287,U_2286] :
( ( ! [U_2284] :
( U_2284 = sK13(U_2287,U_2286)
| hAPP_nat_real(power_power_real(U_2284),U_2286) != U_2287
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2284)) )
& hAPP_nat_real(power_power_real(sK13(U_2287,U_2286)),U_2286) = U_2287
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sK13(U_2287,U_2286))) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2287))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2286)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_2285,sK13(U_2287,U_2286))],[f_899_2]) ).
cnf(f_899_4,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),sK13(U_2287,U_2286)))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2287))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2286)) ),
inference(clausify,[status(thm)],[f_899_3]) ).
cnf(f_899_5,plain,
( hAPP_nat_real(power_power_real(sK13(U_2287,U_2286)),U_2286) = U_2287
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2287))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2286)) ),
inference(clausify,[status(thm)],[f_899_3]) ).
cnf(f_899_6,plain,
( U_2284 = sK13(U_2287,U_2286)
| hAPP_nat_real(power_power_real(U_2284),U_2286) != U_2287
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2284))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),U_2287))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2286)) ),
inference(clausify,[status(thm)],[f_899_3]) ).
fof(f_900_1,plain,
! [N,Ma] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(N),Ma)),Ma))
| N != one_one_nat )
& ( N = one_one_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(N),Ma)),Ma)) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Ma)) ),
inference(fof_nnf,[status(thm)],[fact_874_dvd__mult__cancel2]) ).
fof(f_900_2,plain,
! [U_2289,U_2288] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2289),U_2288)),U_2288))
| U_2289 != one_one_nat )
& ( U_2289 = one_one_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2289),U_2288)),U_2288)) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2288)) ),
inference(variable_rename,[status(thm)],[f_900_1]) ).
cnf(f_900_3,plain,
( U_2289 = one_one_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2289),U_2288)),U_2288))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2288)) ),
inference(clausify,[status(thm)],[f_900_2]) ).
cnf(f_900_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2289),U_2288)),U_2288))
| U_2289 != one_one_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2288)) ),
inference(clausify,[status(thm)],[f_900_2]) ).
fof(f_901_1,plain,
! [N,Ma] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(Ma),N)),Ma))
| N != one_one_nat )
& ( N = one_one_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(Ma),N)),Ma)) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Ma)) ),
inference(fof_nnf,[status(thm)],[fact_875_dvd__mult__cancel1]) ).
fof(f_901_2,plain,
! [U_2291,U_2290] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2290),U_2291)),U_2290))
| U_2291 != one_one_nat )
& ( U_2291 = one_one_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2290),U_2291)),U_2290)) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2290)) ),
inference(variable_rename,[status(thm)],[f_901_1]) ).
cnf(f_901_3,plain,
( U_2291 = one_one_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2290),U_2291)),U_2290))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2290)) ),
inference(clausify,[status(thm)],[f_901_2]) ).
cnf(f_901_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2290),U_2291)),U_2290))
| U_2291 != one_one_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2290)) ),
inference(clausify,[status(thm)],[f_901_2]) ).
fof(f_902_1,plain,
! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1)),
inference(fof_nnf,[status(thm)],[fact_876_le0]) ).
fof(f_902_2,plain,
! [U_2292] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2292)),
inference(variable_rename,[status(thm)],[f_902_1]) ).
cnf(f_902_3,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2292)),
inference(clausify,[status(thm)],[f_902_2]) ).
fof(f_903_1,plain,
! [X_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),X_1)),
inference(fof_nnf,[status(thm)],[fact_877_dvd_Oorder__refl]) ).
fof(f_903_2,plain,
! [U_2293] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2293),U_2293)),
inference(variable_rename,[status(thm)],[f_903_1]) ).
cnf(f_903_3,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2293),U_2293)),
inference(clausify,[status(thm)],[f_903_2]) ).
fof(f_904_1,plain,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)),
inference(fof_nnf,[status(thm)],[fact_878_less__zeroE]) ).
fof(f_904_2,plain,
! [U_2294] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2294),zero_zero_nat)),
inference(variable_rename,[status(thm)],[f_904_1]) ).
cnf(f_904_3,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2294),zero_zero_nat)),
inference(clausify,[status(thm)],[f_904_2]) ).
fof(f_905_1,plain,
! [I_1,J_1,K_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_1),J_1)),K_1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_1),K_1)),J_1),
inference(fof_nnf,[status(thm)],[fact_879_diff__commute]) ).
fof(f_905_2,plain,
! [U_2297,U_2296,U_2295] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_2297),U_2296)),U_2295) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_2297),U_2295)),U_2296),
inference(variable_rename,[status(thm)],[f_905_1]) ).
cnf(f_905_3,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_2297),U_2296)),U_2295) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_2297),U_2295)),U_2296),
inference(clausify,[status(thm)],[f_905_2]) ).
fof(f_906_1,plain,
! [W] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,W),W)),
inference(fof_nnf,[status(thm)],[fact_880_real__le__refl]) ).
fof(f_906_2,plain,
! [U_2298] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2298),U_2298)),
inference(variable_rename,[status(thm)],[f_906_1]) ).
cnf(f_906_3,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2298),U_2298)),
inference(clausify,[status(thm)],[f_906_2]) ).
fof(f_907_1,plain,
! [Z,W] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,W),Z))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Z),W)) ),
inference(fof_nnf,[status(thm)],[fact_881_real__le__linear]) ).
fof(f_907_2,plain,
! [U_2300,U_2299] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2299),U_2300))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2300),U_2299)) ),
inference(variable_rename,[status(thm)],[f_907_1]) ).
cnf(f_907_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2299),U_2300))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2300),U_2299)) ),
inference(clausify,[status(thm)],[f_907_2]) ).
fof(f_908_1,plain,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,I_1),K_1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,J_1),K_1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_882_real__le__trans]) ).
fof(f_908_2,plain,
! [U_2303,U_2302,U_2301] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2302),U_2303))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2301),U_2303))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2302),U_2301)) ),
inference(variable_rename,[status(thm)],[f_908_1]) ).
cnf(f_908_3,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2302),U_2303))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2301),U_2303))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2302),U_2301)) ),
inference(clausify,[status(thm)],[f_908_2]) ).
fof(f_909_1,plain,
! [Z,W] :
( Z = W
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,W),Z))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,Z),W)) ),
inference(fof_nnf,[status(thm)],[fact_883_real__le__antisym]) ).
fof(f_909_2,plain,
! [U_2305,U_2304] :
( U_2305 = U_2304
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2304),U_2305))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2305),U_2304)) ),
inference(variable_rename,[status(thm)],[f_909_1]) ).
cnf(f_909_3,plain,
( U_2305 = U_2304
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2304),U_2305))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,U_2305),U_2304)) ),
inference(clausify,[status(thm)],[f_909_2]) ).
fof(f_910_1,plain,
! [N_1] : hAPP_nat_nat(minus_minus_nat(zero_zero_nat),N_1) = zero_zero_nat,
inference(fof_nnf,[status(thm)],[fact_884_diff__0__eq__0]) ).
fof(f_910_2,plain,
! [U_2306] : hAPP_nat_nat(minus_minus_nat(zero_zero_nat),U_2306) = zero_zero_nat,
inference(variable_rename,[status(thm)],[f_910_1]) ).
cnf(f_910_3,plain,
hAPP_nat_nat(minus_minus_nat(zero_zero_nat),U_2306) = zero_zero_nat,
inference(clausify,[status(thm)],[f_910_2]) ).
fof(f_911_1,plain,
! [M] : hAPP_nat_nat(minus_minus_nat(M),zero_zero_nat) = M,
inference(fof_nnf,[status(thm)],[fact_885_minus__nat_Odiff__0]) ).
fof(f_911_2,plain,
! [U_2307] : hAPP_nat_nat(minus_minus_nat(U_2307),zero_zero_nat) = U_2307,
inference(variable_rename,[status(thm)],[f_911_1]) ).
cnf(f_911_3,plain,
hAPP_nat_nat(minus_minus_nat(U_2307),zero_zero_nat) = U_2307,
inference(clausify,[status(thm)],[f_911_2]) ).
fof(f_912_1,plain,
! [M] : hAPP_nat_nat(minus_minus_nat(M),M) = zero_zero_nat,
inference(fof_nnf,[status(thm)],[fact_886_diff__self__eq__0]) ).
fof(f_912_2,plain,
! [U_2308] : hAPP_nat_nat(minus_minus_nat(U_2308),U_2308) = zero_zero_nat,
inference(variable_rename,[status(thm)],[f_912_1]) ).
cnf(f_912_3,plain,
hAPP_nat_nat(minus_minus_nat(U_2308),U_2308) = zero_zero_nat,
inference(clausify,[status(thm)],[f_912_2]) ).
fof(f_913_1,plain,
! [M,N_1] :
( M = N_1
| hAPP_nat_nat(minus_minus_nat(N_1),M) != zero_zero_nat
| hAPP_nat_nat(minus_minus_nat(M),N_1) != zero_zero_nat ),
inference(fof_nnf,[status(thm)],[fact_887_diffs0__imp__equal]) ).
fof(f_913_2,plain,
! [U_2310,U_2309] :
( U_2310 = U_2309
| hAPP_nat_nat(minus_minus_nat(U_2309),U_2310) != zero_zero_nat
| hAPP_nat_nat(minus_minus_nat(U_2310),U_2309) != zero_zero_nat ),
inference(variable_rename,[status(thm)],[f_913_1]) ).
cnf(f_913_3,plain,
( U_2310 = U_2309
| hAPP_nat_nat(minus_minus_nat(U_2309),U_2310) != zero_zero_nat
| hAPP_nat_nat(minus_minus_nat(U_2310),U_2309) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_913_2]) ).
fof(f_914_1,plain,
! [P_2,Ma,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_2,N),Ma))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_2,N),Ma))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),Ma)) )
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_2,N),Ma))
& Ma = N )
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_2,N),Ma))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N)) ) ),
inference(fof_nnf,[status(thm)],[fact_888_nat__less__cases]) ).
fof(f_914_2,plain,
! [U_2313,U_2312,U_2311] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2311),U_2312)) )
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
& U_2312 = U_2311 )
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2312),U_2311)) ) ),
inference(variable_rename,[status(thm)],[f_914_1]) ).
cnf(f_914_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2311),U_2312))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
| U_2312 = U_2311
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2312),U_2311)) ),
inference(clausify,[status(thm)],[f_914_2]) ).
cnf(f_914_4,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
| U_2312 = U_2311
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2312),U_2311)) ),
inference(clausify,[status(thm)],[f_914_2]) ).
cnf(f_914_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2311),U_2312))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2312),U_2311)) ),
inference(clausify,[status(thm)],[f_914_2]) ).
cnf(f_914_6,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2312),U_2311)) ),
inference(clausify,[status(thm)],[f_914_2]) ).
cnf(f_914_7,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2311),U_2312))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
| U_2312 = U_2311
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312)) ),
inference(clausify,[status(thm)],[f_914_2]) ).
cnf(f_914_8,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
| U_2312 = U_2311
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312)) ),
inference(clausify,[status(thm)],[f_914_2]) ).
cnf(f_914_9,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2311),U_2312))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312)) ),
inference(clausify,[status(thm)],[f_914_2]) ).
cnf(f_914_10,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2313,U_2311),U_2312)) ),
inference(clausify,[status(thm)],[f_914_2]) ).
fof(f_915_1,plain,
! [S,T] :
( S != T
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T)) ),
inference(fof_nnf,[status(thm)],[fact_889_less__not__refl3]) ).
fof(f_915_2,plain,
! [U_2315,U_2314] :
( U_2315 != U_2314
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2315),U_2314)) ),
inference(variable_rename,[status(thm)],[f_915_1]) ).
cnf(f_915_3,plain,
( U_2315 != U_2314
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2315),U_2314)) ),
inference(clausify,[status(thm)],[f_915_2]) ).
fof(f_916_1,plain,
! [N_1,M] :
( M != N_1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M)) ),
inference(fof_nnf,[status(thm)],[fact_890_less__not__refl2]) ).
fof(f_916_2,plain,
! [U_2317,U_2316] :
( U_2316 != U_2317
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2317),U_2316)) ),
inference(variable_rename,[status(thm)],[f_916_1]) ).
cnf(f_916_3,plain,
( U_2316 != U_2317
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2317),U_2316)) ),
inference(clausify,[status(thm)],[f_916_2]) ).
fof(f_917_1,plain,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1)),
inference(fof_nnf,[status(thm)],[fact_891_less__irrefl__nat]) ).
fof(f_917_2,plain,
! [U_2318] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2318),U_2318)),
inference(variable_rename,[status(thm)],[f_917_1]) ).
cnf(f_917_3,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2318),U_2318)),
inference(clausify,[status(thm)],[f_917_2]) ).
fof(f_918_1,plain,
! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
| X_1 = Y_1 ),
inference(fof_nnf,[status(thm)],[fact_892_linorder__neqE__nat]) ).
fof(f_918_2,plain,
! [U_2320,U_2319] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2319),U_2320))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2320),U_2319))
| U_2320 = U_2319 ),
inference(variable_rename,[status(thm)],[f_918_1]) ).
cnf(f_918_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2319),U_2320))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2320),U_2319))
| U_2320 = U_2319 ),
inference(clausify,[status(thm)],[f_918_2]) ).
fof(f_919_1,plain,
! [Ma,N] :
( ( Ma != N
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),Ma))
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N)) ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),Ma))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N))
| Ma = N ) ),
inference(fof_nnf,[status(thm)],[fact_893_nat__neq__iff]) ).
fof(f_919_2,plain,
! [U_2322,U_2321] :
( ( U_2322 != U_2321
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2321),U_2322))
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2322),U_2321)) ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2321),U_2322))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2322),U_2321))
| U_2322 = U_2321 ) ),
inference(variable_rename,[status(thm)],[f_919_1]) ).
fof(f_919_3,plain,
( ! [U_2326,U_2324] :
( U_2326 != U_2324
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2324),U_2326))
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2326),U_2324)) ) )
& ! [U_2325,U_2323] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2323),U_2325))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2325),U_2323))
| U_2325 = U_2323 ) ),
inference(miniscope,[status(thm)],[f_919_2]) ).
cnf(f_919_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2323),U_2325))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2325),U_2323))
| U_2325 = U_2323 ),
inference(clausify,[status(thm)],[f_919_3]) ).
cnf(f_919_5,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2326),U_2324))
| U_2326 != U_2324 ),
inference(clausify,[status(thm)],[f_919_3]) ).
cnf(f_919_6,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2324),U_2326))
| U_2326 != U_2324 ),
inference(clausify,[status(thm)],[f_919_3]) ).
fof(f_920_1,plain,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1)),
inference(fof_nnf,[status(thm)],[fact_894_less__not__refl]) ).
fof(f_920_2,plain,
! [U_2327] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2327),U_2327)),
inference(variable_rename,[status(thm)],[f_920_1]) ).
cnf(f_920_3,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2327),U_2327)),
inference(clausify,[status(thm)],[f_920_2]) ).
fof(f_921_1,plain,
! [L,M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(L),N_1)),hAPP_nat_nat(minus_minus_nat(L),M)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),L))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_895_diff__less__mono2]) ).
fof(f_921_2,plain,
! [U_2330,U_2329,U_2328] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2330),U_2328)),hAPP_nat_nat(minus_minus_nat(U_2330),U_2329)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2329),U_2330))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2329),U_2328)) ),
inference(variable_rename,[status(thm)],[f_921_1]) ).
cnf(f_921_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2330),U_2328)),hAPP_nat_nat(minus_minus_nat(U_2330),U_2329)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2329),U_2330))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2329),U_2328)) ),
inference(clausify,[status(thm)],[f_921_2]) ).
fof(f_922_1,plain,
! [N_1,J_1,K_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(J_1),N_1)),K_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),K_1)) ),
inference(fof_nnf,[status(thm)],[fact_896_less__imp__diff__less]) ).
fof(f_922_2,plain,
! [U_2333,U_2332,U_2331] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2332),U_2333)),U_2331))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2332),U_2331)) ),
inference(variable_rename,[status(thm)],[f_922_1]) ).
cnf(f_922_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2332),U_2333)),U_2331))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2332),U_2331)) ),
inference(clausify,[status(thm)],[f_922_2]) ).
fof(f_923_1,plain,
! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) ),
inference(fof_nnf,[status(thm)],[fact_897_dvd_Oless__asym]) ).
fof(f_923_2,plain,
! [U_2335,U_2334] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2335),U_2334))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2334),U_2335))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2334),U_2335))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2335),U_2334)) ),
inference(variable_rename,[status(thm)],[f_923_1]) ).
cnf(f_923_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2335),U_2334))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2334),U_2335))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2334),U_2335))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2335),U_2334)) ),
inference(clausify,[status(thm)],[f_923_2]) ).
fof(f_924_1,plain,
! [Z,X_1,Y_1] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Z),X_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Z)) )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Z),Y_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),Z))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) ),
inference(fof_nnf,[status(thm)],[fact_898_dvd_Oless__trans]) ).
fof(f_924_2,plain,
! [U_2338,U_2337,U_2336] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2338),U_2337))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2337),U_2338)) )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2338),U_2336))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2336),U_2338))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2336),U_2337))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2337),U_2336)) ),
inference(variable_rename,[status(thm)],[f_924_1]) ).
cnf(f_924_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2337),U_2338))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2338),U_2336))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2336),U_2338))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2336),U_2337))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2337),U_2336)) ),
inference(clausify,[status(thm)],[f_924_2]) ).
cnf(f_924_4,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2338),U_2337))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2338),U_2336))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2336),U_2338))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2336),U_2337))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2337),U_2336)) ),
inference(clausify,[status(thm)],[f_924_2]) ).
fof(f_925_1,plain,
! [A,B] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B),A))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B),A))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B)) ),
inference(fof_nnf,[status(thm)],[fact_899_dvd_Oless__asym_H]) ).
fof(f_925_2,plain,
! [U_2340,U_2339] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2340),U_2339))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2339),U_2340))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2339),U_2340))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2340),U_2339)) ),
inference(variable_rename,[status(thm)],[f_925_1]) ).
cnf(f_925_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2340),U_2339))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2339),U_2340))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2339),U_2340))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2340),U_2339)) ),
inference(clausify,[status(thm)],[f_925_2]) ).
fof(f_926_1,plain,
! [Z,X_1,Y_1] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Z),X_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Z)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),Z))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) ),
inference(fof_nnf,[status(thm)],[fact_900_dvd_Oless__le__trans]) ).
fof(f_926_2,plain,
! [U_2343,U_2342,U_2341] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2343),U_2342))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2342),U_2343)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2341),U_2343))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2341),U_2342))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2342),U_2341)) ),
inference(variable_rename,[status(thm)],[f_926_1]) ).
cnf(f_926_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2342),U_2343))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2341),U_2343))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2341),U_2342))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2342),U_2341)) ),
inference(clausify,[status(thm)],[f_926_2]) ).
cnf(f_926_4,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2343),U_2342))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2341),U_2343))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2341),U_2342))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2342),U_2341)) ),
inference(clausify,[status(thm)],[f_926_2]) ).
fof(f_927_1,plain,
! [C,A,B] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,C),A))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),C)) )
| B != C
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B),A))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B)) ),
inference(fof_nnf,[status(thm)],[fact_901_dvd_Oord__less__eq__trans]) ).
fof(f_927_2,plain,
! [U_2346,U_2345,U_2344] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2346),U_2345))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2345),U_2346)) )
| U_2344 != U_2346
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2344),U_2345))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2345),U_2344)) ),
inference(variable_rename,[status(thm)],[f_927_1]) ).
cnf(f_927_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2345),U_2346))
| U_2344 != U_2346
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2344),U_2345))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2345),U_2344)) ),
inference(clausify,[status(thm)],[f_927_2]) ).
cnf(f_927_4,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2346),U_2345))
| U_2344 != U_2346
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2344),U_2345))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2345),U_2344)) ),
inference(clausify,[status(thm)],[f_927_2]) ).
fof(f_928_1,plain,
! [P_2,X_2,Y_2] :
( hBOOL(P_2)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) ),
inference(fof_nnf,[status(thm)],[fact_902_dvd_Oless__imp__triv]) ).
fof(f_928_2,plain,
! [U_2349,U_2348,U_2347] :
( hBOOL(U_2349)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2348),U_2347))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2347),U_2348))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2347),U_2348))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2348),U_2347)) ),
inference(variable_rename,[status(thm)],[f_928_1]) ).
cnf(f_928_3,plain,
( hBOOL(U_2349)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2348),U_2347))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2347),U_2348))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2347),U_2348))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2348),U_2347)) ),
inference(clausify,[status(thm)],[f_928_2]) ).
fof(f_929_1,plain,
! [X_1,Y_1] :
( Y_1 != X_1
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) ),
inference(fof_nnf,[status(thm)],[fact_903_dvd_Oless__imp__not__eq2]) ).
fof(f_929_2,plain,
! [U_2351,U_2350] :
( U_2350 != U_2351
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2350),U_2351))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2351),U_2350)) ),
inference(variable_rename,[status(thm)],[f_929_1]) ).
cnf(f_929_3,plain,
( U_2350 != U_2351
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2350),U_2351))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2351),U_2350)) ),
inference(clausify,[status(thm)],[f_929_2]) ).
fof(f_930_1,plain,
! [X_1,Y_1] :
( X_1 != Y_1
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) ),
inference(fof_nnf,[status(thm)],[fact_904_dvd_Oless__imp__not__eq]) ).
fof(f_930_2,plain,
! [U_2353,U_2352] :
( U_2353 != U_2352
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2352),U_2353))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2353),U_2352)) ),
inference(variable_rename,[status(thm)],[f_930_1]) ).
cnf(f_930_3,plain,
( U_2353 != U_2352
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2352),U_2353))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2353),U_2352)) ),
inference(clausify,[status(thm)],[f_930_2]) ).
fof(f_931_1,plain,
! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) ),
inference(fof_nnf,[status(thm)],[fact_905_dvd_Oless__imp__not__less]) ).
fof(f_931_2,plain,
! [U_2355,U_2354] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2355),U_2354))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2354),U_2355))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2354),U_2355))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2355),U_2354)) ),
inference(variable_rename,[status(thm)],[f_931_1]) ).
cnf(f_931_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2355),U_2354))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2354),U_2355))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2354),U_2355))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2355),U_2354)) ),
inference(clausify,[status(thm)],[f_931_2]) ).
fof(f_932_1,plain,
! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) ),
inference(fof_nnf,[status(thm)],[fact_906_dvd_Oless__imp__le]) ).
fof(f_932_2,plain,
! [U_2357,U_2356] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2357),U_2356))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2356),U_2357))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2357),U_2356)) ),
inference(variable_rename,[status(thm)],[f_932_1]) ).
cnf(f_932_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2357),U_2356))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2356),U_2357))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2357),U_2356)) ),
inference(clausify,[status(thm)],[f_932_2]) ).
fof(f_933_1,plain,
! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) ),
inference(fof_nnf,[status(thm)],[fact_907_dvd_Oless__not__sym]) ).
fof(f_933_2,plain,
! [U_2359,U_2358] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2359),U_2358))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2358),U_2359))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2358),U_2359))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2359),U_2358)) ),
inference(variable_rename,[status(thm)],[f_933_1]) ).
cnf(f_933_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2359),U_2358))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2358),U_2359))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2358),U_2359))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2359),U_2358)) ),
inference(clausify,[status(thm)],[f_933_2]) ).
fof(f_934_1,plain,
! [X_1,Y_1] :
( X_1 != Y_1
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) ),
inference(fof_nnf,[status(thm)],[fact_908_dvd_Oless__imp__neq]) ).
fof(f_934_2,plain,
! [U_2361,U_2360] :
( U_2361 != U_2360
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2360),U_2361))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2361),U_2360)) ),
inference(variable_rename,[status(thm)],[f_934_1]) ).
cnf(f_934_3,plain,
( U_2361 != U_2360
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2360),U_2361))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2361),U_2360)) ),
inference(clausify,[status(thm)],[f_934_2]) ).
fof(f_935_1,plain,
! [Z,X_1,Y_1] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Z),X_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Z)) )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Z),Y_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),Z))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) ),
inference(fof_nnf,[status(thm)],[fact_909_dvd_Ole__less__trans]) ).
fof(f_935_2,plain,
! [U_2364,U_2363,U_2362] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2364),U_2363))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2363),U_2364)) )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2364),U_2362))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2362),U_2364))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2363),U_2362)) ),
inference(variable_rename,[status(thm)],[f_935_1]) ).
cnf(f_935_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2363),U_2364))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2364),U_2362))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2362),U_2364))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2363),U_2362)) ),
inference(clausify,[status(thm)],[f_935_2]) ).
cnf(f_935_4,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2364),U_2363))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2364),U_2362))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2362),U_2364))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2363),U_2362)) ),
inference(clausify,[status(thm)],[f_935_2]) ).
fof(f_936_1,plain,
! [C,A,B] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,C),A))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),C)) )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,C),B))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B),C))
| A != B ),
inference(fof_nnf,[status(thm)],[fact_910_dvd_Oord__eq__less__trans]) ).
fof(f_936_2,plain,
! [U_2367,U_2366,U_2365] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2367),U_2366))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2366),U_2367)) )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2367),U_2365))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2365),U_2367))
| U_2366 != U_2365 ),
inference(variable_rename,[status(thm)],[f_936_1]) ).
cnf(f_936_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2366),U_2367))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2367),U_2365))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2365),U_2367))
| U_2366 != U_2365 ),
inference(clausify,[status(thm)],[f_936_2]) ).
cnf(f_936_4,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2367),U_2366))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2367),U_2365))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2365),U_2367))
| U_2366 != U_2365 ),
inference(clausify,[status(thm)],[f_936_2]) ).
fof(f_937_1,plain,
! [Z,X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Z))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),Z))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) ),
inference(fof_nnf,[status(thm)],[fact_911_dvd_Oorder__trans]) ).
fof(f_937_2,plain,
! [U_2370,U_2369,U_2368] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2369),U_2370))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2368),U_2370))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2369),U_2368)) ),
inference(variable_rename,[status(thm)],[f_937_1]) ).
cnf(f_937_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2369),U_2370))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2368),U_2370))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2369),U_2368)) ),
inference(clausify,[status(thm)],[f_937_2]) ).
fof(f_938_1,plain,
! [X_1,Y_1] :
( X_1 = Y_1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) ),
inference(fof_nnf,[status(thm)],[fact_912_dvd_Oantisym]) ).
fof(f_938_2,plain,
! [U_2372,U_2371] :
( U_2372 = U_2371
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2371),U_2372))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2372),U_2371)) ),
inference(variable_rename,[status(thm)],[f_938_1]) ).
cnf(f_938_3,plain,
( U_2372 = U_2371
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2371),U_2372))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2372),U_2371)) ),
inference(clausify,[status(thm)],[f_938_2]) ).
fof(f_939_1,plain,
! [M,N_1] :
( M = N_1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,N_1),M))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_913_dvd__antisym]) ).
fof(f_939_2,plain,
! [U_2374,U_2373] :
( U_2374 = U_2373
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2373),U_2374))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2374),U_2373)) ),
inference(variable_rename,[status(thm)],[f_939_1]) ).
cnf(f_939_3,plain,
( U_2374 = U_2373
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2373),U_2374))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2374),U_2373)) ),
inference(clausify,[status(thm)],[f_939_2]) ).
fof(f_940_1,plain,
! [C,A,B] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),C))
| B != C
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B)) ),
inference(fof_nnf,[status(thm)],[fact_914_dvd_Oord__le__eq__trans]) ).
fof(f_940_2,plain,
! [U_2377,U_2376,U_2375] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2376),U_2377))
| U_2375 != U_2377
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2376),U_2375)) ),
inference(variable_rename,[status(thm)],[f_940_1]) ).
cnf(f_940_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2376),U_2377))
| U_2375 != U_2377
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2376),U_2375)) ),
inference(clausify,[status(thm)],[f_940_2]) ).
fof(f_941_1,plain,
! [C,A,B] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),C))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B),C))
| A != B ),
inference(fof_nnf,[status(thm)],[fact_915_dvd_Oord__eq__le__trans]) ).
fof(f_941_2,plain,
! [U_2380,U_2379,U_2378] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2379),U_2380))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2378),U_2380))
| U_2379 != U_2378 ),
inference(variable_rename,[status(thm)],[f_941_1]) ).
cnf(f_941_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2379),U_2380))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2378),U_2380))
| U_2379 != U_2378 ),
inference(clausify,[status(thm)],[f_941_2]) ).
fof(f_942_1,plain,
! [A,B] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B),A))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B)) )
| A = B
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B)) ),
inference(fof_nnf,[status(thm)],[fact_916_dvd_Ole__neq__trans]) ).
fof(f_942_2,plain,
! [U_2382,U_2381] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2381),U_2382))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2382),U_2381)) )
| U_2382 = U_2381
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2382),U_2381)) ),
inference(variable_rename,[status(thm)],[f_942_1]) ).
cnf(f_942_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2382),U_2381))
| U_2382 = U_2381
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2382),U_2381)) ),
inference(clausify,[status(thm)],[f_942_2]) ).
cnf(f_942_4,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2381),U_2382))
| U_2382 = U_2381
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2382),U_2381)) ),
inference(clausify,[status(thm)],[f_942_2]) ).
fof(f_943_1,plain,
! [X_1,Y_1] :
( X_1 = Y_1
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_1),X_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1)) ),
inference(fof_nnf,[status(thm)],[fact_917_dvd_Ole__imp__less__or__eq]) ).
fof(f_943_2,plain,
! [U_2384,U_2383] :
( U_2384 = U_2383
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2383),U_2384))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2384),U_2383)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2384),U_2383)) ),
inference(variable_rename,[status(thm)],[f_943_1]) ).
cnf(f_943_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2384),U_2383))
| U_2384 = U_2383
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2384),U_2383)) ),
inference(clausify,[status(thm)],[f_943_2]) ).
cnf(f_943_4,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2383),U_2384))
| U_2384 = U_2383
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2384),U_2383)) ),
inference(clausify,[status(thm)],[f_943_2]) ).
fof(f_944_1,plain,
! [Y_2,X_2] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2))
| X_2 != Y_2 )
& ( X_2 = Y_2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2)) ),
inference(fof_nnf,[status(thm)],[fact_918_dvd_Oantisym__conv]) ).
fof(f_944_2,plain,
! [U_2386,U_2385] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2385),U_2386))
| U_2385 != U_2386 )
& ( U_2385 = U_2386
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2385),U_2386)) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2386),U_2385)) ),
inference(variable_rename,[status(thm)],[f_944_1]) ).
cnf(f_944_3,plain,
( U_2385 = U_2386
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2385),U_2386))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2386),U_2385)) ),
inference(clausify,[status(thm)],[f_944_2]) ).
cnf(f_944_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2385),U_2386))
| U_2385 != U_2386
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2386),U_2385)) ),
inference(clausify,[status(thm)],[f_944_2]) ).
fof(f_945_1,plain,
! [X_1,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),Y_1))
| X_1 != Y_1 ),
inference(fof_nnf,[status(thm)],[fact_919_dvd_Oeq__refl]) ).
fof(f_945_2,plain,
! [U_2388,U_2387] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2388),U_2387))
| U_2388 != U_2387 ),
inference(variable_rename,[status(thm)],[f_945_1]) ).
cnf(f_945_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2388),U_2387))
| U_2388 != U_2387 ),
inference(clausify,[status(thm)],[f_945_2]) ).
fof(f_946_1,plain,
! [A,B] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,B),A))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),B))
| A = B ),
inference(fof_nnf,[status(thm)],[fact_920_dvd_Oneq__le__trans]) ).
fof(f_946_2,plain,
! [U_2390,U_2389] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2389),U_2390))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2390),U_2389)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2390),U_2389))
| U_2390 = U_2389 ),
inference(variable_rename,[status(thm)],[f_946_1]) ).
cnf(f_946_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2390),U_2389))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2390),U_2389))
| U_2390 = U_2389 ),
inference(clausify,[status(thm)],[f_946_2]) ).
cnf(f_946_4,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2389),U_2390))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2390),U_2389))
| U_2390 = U_2389 ),
inference(clausify,[status(thm)],[f_946_2]) ).
fof(f_947_1,plain,
! [X_2,Y_2] :
( ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) )
& ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_921_dvd_Oless__le__not__le]) ).
fof(f_947_2,plain,
! [U_2392,U_2391] :
( ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2391),U_2392))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2392),U_2391)) )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2391),U_2392))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2392),U_2391)) )
& ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2391),U_2392))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2392),U_2391)) )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2391),U_2392))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2392),U_2391)) ) ),
inference(variable_rename,[status(thm)],[f_947_1]) ).
fof(f_947_3,plain,
( ! [U_2396,U_2394] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2394),U_2396))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2396),U_2394)) )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2394),U_2396))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2396),U_2394)) )
& ! [U_2395,U_2393] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2393),U_2395))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2395),U_2393)) )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2393),U_2395))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2395),U_2393)) ) ),
inference(miniscope,[status(thm)],[f_947_2]) ).
cnf(f_947_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2395),U_2393))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2393),U_2395))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2395),U_2393)) ),
inference(clausify,[status(thm)],[f_947_3]) ).
cnf(f_947_5,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2393),U_2395))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2393),U_2395))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2395),U_2393)) ),
inference(clausify,[status(thm)],[f_947_3]) ).
cnf(f_947_6,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2396),U_2394))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2394),U_2396))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2396),U_2394)) ),
inference(clausify,[status(thm)],[f_947_3]) ).
cnf(f_947_7,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2394),U_2396))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2394),U_2396))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2396),U_2394)) ),
inference(clausify,[status(thm)],[f_947_3]) ).
fof(f_948_1,plain,
! [X_2,Y_2] :
( ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) )
| X_2 = Y_2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) )
& ( ( X_2 != Y_2
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_922_dvd_Oless__le]) ).
fof(f_948_2,plain,
! [U_2398,U_2397] :
( ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2397),U_2398))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2398),U_2397)) )
| U_2398 = U_2397
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2398),U_2397)) )
& ( ( U_2398 != U_2397
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2398),U_2397)) )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2397),U_2398))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2398),U_2397)) ) ),
inference(variable_rename,[status(thm)],[f_948_1]) ).
fof(f_948_3,plain,
( ! [U_2402,U_2400] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2400),U_2402))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2402),U_2400)) )
| U_2402 = U_2400
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2402),U_2400)) )
& ! [U_2401,U_2399] :
( ( U_2401 != U_2399
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2401),U_2399)) )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2399),U_2401))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2401),U_2399)) ) ),
inference(miniscope,[status(thm)],[f_948_2]) ).
cnf(f_948_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2401),U_2399))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2399),U_2401))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2401),U_2399)) ),
inference(clausify,[status(thm)],[f_948_3]) ).
cnf(f_948_5,plain,
( U_2401 != U_2399
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2399),U_2401))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2401),U_2399)) ),
inference(clausify,[status(thm)],[f_948_3]) ).
cnf(f_948_6,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2402),U_2400))
| U_2402 = U_2400
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2402),U_2400)) ),
inference(clausify,[status(thm)],[f_948_3]) ).
cnf(f_948_7,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2400),U_2402))
| U_2402 = U_2400
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2402),U_2400)) ),
inference(clausify,[status(thm)],[f_948_3]) ).
fof(f_949_1,plain,
! [X_2,Y_2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2))
| ( X_2 != Y_2
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) ) ) )
& ( X_2 = Y_2
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_923_dvd_Ole__less]) ).
fof(f_949_2,plain,
! [U_2404,U_2403] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2404),U_2403))
| ( U_2404 != U_2403
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2403),U_2404))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2404),U_2403)) ) ) )
& ( U_2404 = U_2403
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2403),U_2404))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2404),U_2403)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2404),U_2403)) ) ),
inference(variable_rename,[status(thm)],[f_949_1]) ).
fof(f_949_3,plain,
( ! [U_2408,U_2406] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2408),U_2406))
| ( U_2408 != U_2406
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2406),U_2408))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2408),U_2406)) ) ) )
& ! [U_2407,U_2405] :
( U_2407 = U_2405
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2405),U_2407))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2407),U_2405)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2407),U_2405)) ) ),
inference(miniscope,[status(thm)],[f_949_2]) ).
cnf(f_949_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2407),U_2405))
| U_2407 = U_2405
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2407),U_2405)) ),
inference(clausify,[status(thm)],[f_949_3]) ).
cnf(f_949_5,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2405),U_2407))
| U_2407 = U_2405
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2407),U_2405)) ),
inference(clausify,[status(thm)],[f_949_3]) ).
cnf(f_949_6,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2406),U_2408))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2408),U_2406))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2408),U_2406)) ),
inference(clausify,[status(thm)],[f_949_3]) ).
cnf(f_949_7,plain,
( U_2408 != U_2406
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2408),U_2406)) ),
inference(clausify,[status(thm)],[f_949_3]) ).
fof(f_950_1,plain,
! [X_2,Y_2] :
( ( X_2 = Y_2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) )
& ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Y_2),X_2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_2),Y_2)) )
| X_2 != Y_2 ) ),
inference(fof_nnf,[status(thm)],[fact_924_dvd_Oeq__iff]) ).
fof(f_950_2,plain,
! [U_2410,U_2409] :
( ( U_2410 = U_2409
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2409),U_2410))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2410),U_2409)) )
& ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2409),U_2410))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2410),U_2409)) )
| U_2410 != U_2409 ) ),
inference(variable_rename,[status(thm)],[f_950_1]) ).
fof(f_950_3,plain,
( ! [U_2414,U_2412] :
( U_2414 = U_2412
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2412),U_2414))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2414),U_2412)) )
& ! [U_2413,U_2411] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2411),U_2413))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2413),U_2411)) )
| U_2413 != U_2411 ) ),
inference(miniscope,[status(thm)],[f_950_2]) ).
cnf(f_950_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2413),U_2411))
| U_2413 != U_2411 ),
inference(clausify,[status(thm)],[f_950_3]) ).
cnf(f_950_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2411),U_2413))
| U_2413 != U_2411 ),
inference(clausify,[status(thm)],[f_950_3]) ).
cnf(f_950_6,plain,
( U_2414 = U_2412
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2412),U_2414))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2414),U_2412)) ),
inference(clausify,[status(thm)],[f_950_3]) ).
fof(f_951_1,plain,
! [X_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),X_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X_1),X_1)) ),
inference(fof_nnf,[status(thm)],[fact_925_dvd_Oless__irrefl]) ).
fof(f_951_2,plain,
! [U_2415] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2415),U_2415))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2415),U_2415)) ),
inference(variable_rename,[status(thm)],[f_951_1]) ).
cnf(f_951_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2415),U_2415))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2415),U_2415)) ),
inference(clausify,[status(thm)],[f_951_2]) ).
fof(f_952_1,plain,
! [N_1,K_1,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),hAPP_nat_nat(minus_minus_nat(M),N_1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),N_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),M)) ),
inference(fof_nnf,[status(thm)],[fact_926_dvd__diff__nat]) ).
fof(f_952_2,plain,
! [U_2418,U_2417,U_2416] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2417),hAPP_nat_nat(minus_minus_nat(U_2416),U_2418)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2417),U_2418))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2417),U_2416)) ),
inference(variable_rename,[status(thm)],[f_952_1]) ).
cnf(f_952_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2417),hAPP_nat_nat(minus_minus_nat(U_2416),U_2418)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2417),U_2418))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2417),U_2416)) ),
inference(clausify,[status(thm)],[f_952_2]) ).
fof(f_953_1,plain,
! [M,N_1] : hAPP_nat_nat(plus_plus_nat(M),N_1) = hAPP_nat_nat(plus_plus_nat(N_1),M),
inference(fof_nnf,[status(thm)],[fact_927_nat__add__commute]) ).
fof(f_953_2,plain,
! [U_2420,U_2419] : hAPP_nat_nat(plus_plus_nat(U_2420),U_2419) = hAPP_nat_nat(plus_plus_nat(U_2419),U_2420),
inference(variable_rename,[status(thm)],[f_953_1]) ).
cnf(f_953_3,plain,
hAPP_nat_nat(plus_plus_nat(U_2420),U_2419) = hAPP_nat_nat(plus_plus_nat(U_2419),U_2420),
inference(clausify,[status(thm)],[f_953_2]) ).
fof(f_954_1,plain,
! [X_1,Y_1,Z] : hAPP_nat_nat(plus_plus_nat(X_1),hAPP_nat_nat(plus_plus_nat(Y_1),Z)) = hAPP_nat_nat(plus_plus_nat(Y_1),hAPP_nat_nat(plus_plus_nat(X_1),Z)),
inference(fof_nnf,[status(thm)],[fact_928_nat__add__left__commute]) ).
fof(f_954_2,plain,
! [U_2423,U_2422,U_2421] : hAPP_nat_nat(plus_plus_nat(U_2423),hAPP_nat_nat(plus_plus_nat(U_2422),U_2421)) = hAPP_nat_nat(plus_plus_nat(U_2422),hAPP_nat_nat(plus_plus_nat(U_2423),U_2421)),
inference(variable_rename,[status(thm)],[f_954_1]) ).
cnf(f_954_3,plain,
hAPP_nat_nat(plus_plus_nat(U_2423),hAPP_nat_nat(plus_plus_nat(U_2422),U_2421)) = hAPP_nat_nat(plus_plus_nat(U_2422),hAPP_nat_nat(plus_plus_nat(U_2423),U_2421)),
inference(clausify,[status(thm)],[f_954_2]) ).
fof(f_955_1,plain,
! [M,N_1,K_1] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(M),N_1)),K_1) = hAPP_nat_nat(plus_plus_nat(M),hAPP_nat_nat(plus_plus_nat(N_1),K_1)),
inference(fof_nnf,[status(thm)],[fact_929_nat__add__assoc]) ).
fof(f_955_2,plain,
! [U_2426,U_2425,U_2424] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(U_2426),U_2425)),U_2424) = hAPP_nat_nat(plus_plus_nat(U_2426),hAPP_nat_nat(plus_plus_nat(U_2425),U_2424)),
inference(variable_rename,[status(thm)],[f_955_1]) ).
cnf(f_955_3,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(U_2426),U_2425)),U_2424) = hAPP_nat_nat(plus_plus_nat(U_2426),hAPP_nat_nat(plus_plus_nat(U_2425),U_2424)),
inference(clausify,[status(thm)],[f_955_2]) ).
fof(f_956_1,plain,
! [K,Ma,N] :
( ( hAPP_nat_nat(plus_plus_nat(K),Ma) = hAPP_nat_nat(plus_plus_nat(K),N)
| Ma != N )
& ( Ma = N
| hAPP_nat_nat(plus_plus_nat(K),Ma) != hAPP_nat_nat(plus_plus_nat(K),N) ) ),
inference(fof_nnf,[status(thm)],[fact_930_nat__add__left__cancel]) ).
fof(f_956_2,plain,
! [U_2429,U_2428,U_2427] :
( ( hAPP_nat_nat(plus_plus_nat(U_2429),U_2428) = hAPP_nat_nat(plus_plus_nat(U_2429),U_2427)
| U_2428 != U_2427 )
& ( U_2428 = U_2427
| hAPP_nat_nat(plus_plus_nat(U_2429),U_2428) != hAPP_nat_nat(plus_plus_nat(U_2429),U_2427) ) ),
inference(variable_rename,[status(thm)],[f_956_1]) ).
fof(f_956_3,plain,
( ! [U_2435,U_2433,U_2431] :
( hAPP_nat_nat(plus_plus_nat(U_2435),U_2433) = hAPP_nat_nat(plus_plus_nat(U_2435),U_2431)
| U_2433 != U_2431 )
& ! [U_2434,U_2432,U_2430] :
( U_2432 = U_2430
| hAPP_nat_nat(plus_plus_nat(U_2434),U_2432) != hAPP_nat_nat(plus_plus_nat(U_2434),U_2430) ) ),
inference(miniscope,[status(thm)],[f_956_2]) ).
cnf(f_956_4,plain,
( U_2432 = U_2430
| hAPP_nat_nat(plus_plus_nat(U_2434),U_2432) != hAPP_nat_nat(plus_plus_nat(U_2434),U_2430) ),
inference(clausify,[status(thm)],[f_956_3]) ).
cnf(f_956_5,plain,
( hAPP_nat_nat(plus_plus_nat(U_2435),U_2433) = hAPP_nat_nat(plus_plus_nat(U_2435),U_2431)
| U_2433 != U_2431 ),
inference(clausify,[status(thm)],[f_956_3]) ).
fof(f_957_1,plain,
! [Ma,K,N] :
( ( hAPP_nat_nat(plus_plus_nat(Ma),K) = hAPP_nat_nat(plus_plus_nat(N),K)
| Ma != N )
& ( Ma = N
| hAPP_nat_nat(plus_plus_nat(Ma),K) != hAPP_nat_nat(plus_plus_nat(N),K) ) ),
inference(fof_nnf,[status(thm)],[fact_931_nat__add__right__cancel]) ).
fof(f_957_2,plain,
! [U_2438,U_2437,U_2436] :
( ( hAPP_nat_nat(plus_plus_nat(U_2438),U_2437) = hAPP_nat_nat(plus_plus_nat(U_2436),U_2437)
| U_2438 != U_2436 )
& ( U_2438 = U_2436
| hAPP_nat_nat(plus_plus_nat(U_2438),U_2437) != hAPP_nat_nat(plus_plus_nat(U_2436),U_2437) ) ),
inference(variable_rename,[status(thm)],[f_957_1]) ).
fof(f_957_3,plain,
( ! [U_2444,U_2442,U_2440] :
( hAPP_nat_nat(plus_plus_nat(U_2444),U_2442) = hAPP_nat_nat(plus_plus_nat(U_2440),U_2442)
| U_2444 != U_2440 )
& ! [U_2443,U_2441,U_2439] :
( U_2443 = U_2439
| hAPP_nat_nat(plus_plus_nat(U_2443),U_2441) != hAPP_nat_nat(plus_plus_nat(U_2439),U_2441) ) ),
inference(miniscope,[status(thm)],[f_957_2]) ).
cnf(f_957_4,plain,
( U_2443 = U_2439
| hAPP_nat_nat(plus_plus_nat(U_2443),U_2441) != hAPP_nat_nat(plus_plus_nat(U_2439),U_2441) ),
inference(clausify,[status(thm)],[f_957_3]) ).
cnf(f_957_5,plain,
( hAPP_nat_nat(plus_plus_nat(U_2444),U_2442) = hAPP_nat_nat(plus_plus_nat(U_2440),U_2442)
| U_2444 != U_2440 ),
inference(clausify,[status(thm)],[f_957_3]) ).
fof(f_958_1,plain,
! [M,N_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),N_1)),N_1) = M,
inference(fof_nnf,[status(thm)],[fact_932_diff__add__inverse2]) ).
fof(f_958_2,plain,
! [U_2446,U_2445] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2446),U_2445)),U_2445) = U_2446,
inference(variable_rename,[status(thm)],[f_958_1]) ).
cnf(f_958_3,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2446),U_2445)),U_2445) = U_2446,
inference(clausify,[status(thm)],[f_958_2]) ).
fof(f_959_1,plain,
! [N_1,M] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(N_1),M)),N_1) = M,
inference(fof_nnf,[status(thm)],[fact_933_diff__add__inverse]) ).
fof(f_959_2,plain,
! [U_2448,U_2447] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2448),U_2447)),U_2448) = U_2447,
inference(variable_rename,[status(thm)],[f_959_1]) ).
cnf(f_959_3,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2448),U_2447)),U_2448) = U_2447,
inference(clausify,[status(thm)],[f_959_2]) ).
fof(f_960_1,plain,
! [I_1,J_1,K_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_1),J_1)),K_1) = hAPP_nat_nat(minus_minus_nat(I_1),hAPP_nat_nat(plus_plus_nat(J_1),K_1)),
inference(fof_nnf,[status(thm)],[fact_934_diff__diff__left]) ).
fof(f_960_2,plain,
! [U_2451,U_2450,U_2449] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_2451),U_2450)),U_2449) = hAPP_nat_nat(minus_minus_nat(U_2451),hAPP_nat_nat(plus_plus_nat(U_2450),U_2449)),
inference(variable_rename,[status(thm)],[f_960_1]) ).
cnf(f_960_3,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_2451),U_2450)),U_2449) = hAPP_nat_nat(minus_minus_nat(U_2451),hAPP_nat_nat(plus_plus_nat(U_2450),U_2449)),
inference(clausify,[status(thm)],[f_960_2]) ).
fof(f_961_1,plain,
! [K_1,M,N_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(K_1),M)),hAPP_nat_nat(plus_plus_nat(K_1),N_1)) = hAPP_nat_nat(minus_minus_nat(M),N_1),
inference(fof_nnf,[status(thm)],[fact_935_Nat_Odiff__cancel]) ).
fof(f_961_2,plain,
! [U_2454,U_2453,U_2452] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2454),U_2453)),hAPP_nat_nat(plus_plus_nat(U_2454),U_2452)) = hAPP_nat_nat(minus_minus_nat(U_2453),U_2452),
inference(variable_rename,[status(thm)],[f_961_1]) ).
cnf(f_961_3,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2454),U_2453)),hAPP_nat_nat(plus_plus_nat(U_2454),U_2452)) = hAPP_nat_nat(minus_minus_nat(U_2453),U_2452),
inference(clausify,[status(thm)],[f_961_2]) ).
fof(f_962_1,plain,
! [M,K_1,N_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(M),K_1)),hAPP_nat_nat(plus_plus_nat(N_1),K_1)) = hAPP_nat_nat(minus_minus_nat(M),N_1),
inference(fof_nnf,[status(thm)],[fact_936_diff__cancel2]) ).
fof(f_962_2,plain,
! [U_2457,U_2456,U_2455] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2457),U_2456)),hAPP_nat_nat(plus_plus_nat(U_2455),U_2456)) = hAPP_nat_nat(minus_minus_nat(U_2457),U_2455),
inference(variable_rename,[status(thm)],[f_962_1]) ).
cnf(f_962_3,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2457),U_2456)),hAPP_nat_nat(plus_plus_nat(U_2455),U_2456)) = hAPP_nat_nat(minus_minus_nat(U_2457),U_2455),
inference(clausify,[status(thm)],[f_962_2]) ).
fof(f_963_1,plain,
! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),N_1)),
inference(fof_nnf,[status(thm)],[fact_937_le__refl]) ).
fof(f_963_2,plain,
! [U_2458] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2458),U_2458)),
inference(variable_rename,[status(thm)],[f_963_1]) ).
cnf(f_963_3,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2458),U_2458)),
inference(clausify,[status(thm)],[f_963_2]) ).
fof(f_964_1,plain,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_938_nat__le__linear]) ).
fof(f_964_2,plain,
! [U_2460,U_2459] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2459),U_2460))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2460),U_2459)) ),
inference(variable_rename,[status(thm)],[f_964_1]) ).
cnf(f_964_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2459),U_2460))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2460),U_2459)) ),
inference(clausify,[status(thm)],[f_964_2]) ).
fof(f_965_1,plain,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
| M != N_1 ),
inference(fof_nnf,[status(thm)],[fact_939_eq__imp__le]) ).
fof(f_965_2,plain,
! [U_2462,U_2461] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2462),U_2461))
| U_2462 != U_2461 ),
inference(variable_rename,[status(thm)],[f_965_1]) ).
cnf(f_965_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2462),U_2461))
| U_2462 != U_2461 ),
inference(clausify,[status(thm)],[f_965_2]) ).
fof(f_966_1,plain,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),K_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),K_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_940_le__trans]) ).
fof(f_966_2,plain,
! [U_2465,U_2464,U_2463] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2464),U_2465))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2463),U_2465))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2464),U_2463)) ),
inference(variable_rename,[status(thm)],[f_966_1]) ).
cnf(f_966_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2464),U_2465))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2463),U_2465))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2464),U_2463)) ),
inference(clausify,[status(thm)],[f_966_2]) ).
fof(f_967_1,plain,
! [M,N_1] :
( M = N_1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_941_le__antisym]) ).
fof(f_967_2,plain,
! [U_2467,U_2466] :
( U_2467 = U_2466
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2466),U_2467))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2467),U_2466)) ),
inference(variable_rename,[status(thm)],[f_967_1]) ).
cnf(f_967_3,plain,
( U_2467 = U_2466
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2466),U_2467))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2467),U_2466)) ),
inference(clausify,[status(thm)],[f_967_2]) ).
fof(f_968_1,plain,
! [M,N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M),N_1)),M)),
inference(fof_nnf,[status(thm)],[fact_942_Nat_Odiff__le__self]) ).
fof(f_968_2,plain,
! [U_2469,U_2468] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_2469),U_2468)),U_2469)),
inference(variable_rename,[status(thm)],[f_968_1]) ).
cnf(f_968_3,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_2469),U_2468)),U_2469)),
inference(clausify,[status(thm)],[f_968_2]) ).
fof(f_969_1,plain,
! [L,M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(L),N_1)),hAPP_nat_nat(minus_minus_nat(L),M)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_943_diff__le__mono2]) ).
fof(f_969_2,plain,
! [U_2472,U_2471,U_2470] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_2472),U_2470)),hAPP_nat_nat(minus_minus_nat(U_2472),U_2471)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2471),U_2470)) ),
inference(variable_rename,[status(thm)],[f_969_1]) ).
cnf(f_969_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_2472),U_2470)),hAPP_nat_nat(minus_minus_nat(U_2472),U_2471)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2471),U_2470)) ),
inference(clausify,[status(thm)],[f_969_2]) ).
fof(f_970_1,plain,
! [L,M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M),L)),hAPP_nat_nat(minus_minus_nat(N_1),L)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_944_diff__le__mono]) ).
fof(f_970_2,plain,
! [U_2475,U_2474,U_2473] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_2474),U_2475)),hAPP_nat_nat(minus_minus_nat(U_2473),U_2475)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2474),U_2473)) ),
inference(variable_rename,[status(thm)],[f_970_1]) ).
cnf(f_970_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_2474),U_2475)),hAPP_nat_nat(minus_minus_nat(U_2473),U_2475)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2474),U_2473)) ),
inference(clausify,[status(thm)],[f_970_2]) ).
fof(f_971_1,plain,
! [I_1,N_1] :
( hAPP_nat_nat(minus_minus_nat(N_1),hAPP_nat_nat(minus_minus_nat(N_1),I_1)) = I_1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_945_diff__diff__cancel]) ).
fof(f_971_2,plain,
! [U_2477,U_2476] :
( hAPP_nat_nat(minus_minus_nat(U_2476),hAPP_nat_nat(minus_minus_nat(U_2476),U_2477)) = U_2477
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2477),U_2476)) ),
inference(variable_rename,[status(thm)],[f_971_1]) ).
cnf(f_971_3,plain,
( hAPP_nat_nat(minus_minus_nat(U_2476),hAPP_nat_nat(minus_minus_nat(U_2476),U_2477)) = U_2477
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2477),U_2476)) ),
inference(clausify,[status(thm)],[f_971_2]) ).
fof(f_972_1,plain,
! [N,K,Ma] :
( ( ( hAPP_nat_nat(minus_minus_nat(Ma),K) = hAPP_nat_nat(minus_minus_nat(N),K)
| Ma != N )
& ( Ma = N
| hAPP_nat_nat(minus_minus_nat(Ma),K) != hAPP_nat_nat(minus_minus_nat(N),K) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),Ma)) ),
inference(fof_nnf,[status(thm)],[fact_946_eq__diff__iff]) ).
fof(f_972_2,plain,
! [U_2480,U_2479,U_2478] :
( ( ( hAPP_nat_nat(minus_minus_nat(U_2478),U_2479) = hAPP_nat_nat(minus_minus_nat(U_2480),U_2479)
| U_2478 != U_2480 )
& ( U_2478 = U_2480
| hAPP_nat_nat(minus_minus_nat(U_2478),U_2479) != hAPP_nat_nat(minus_minus_nat(U_2480),U_2479) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2479),U_2480))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2479),U_2478)) ),
inference(variable_rename,[status(thm)],[f_972_1]) ).
cnf(f_972_3,plain,
( U_2478 = U_2480
| hAPP_nat_nat(minus_minus_nat(U_2478),U_2479) != hAPP_nat_nat(minus_minus_nat(U_2480),U_2479)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2479),U_2480))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2479),U_2478)) ),
inference(clausify,[status(thm)],[f_972_2]) ).
cnf(f_972_4,plain,
( hAPP_nat_nat(minus_minus_nat(U_2478),U_2479) = hAPP_nat_nat(minus_minus_nat(U_2480),U_2479)
| U_2478 != U_2480
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2479),U_2480))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2479),U_2478)) ),
inference(clausify,[status(thm)],[f_972_2]) ).
fof(f_973_1,plain,
! [N_1,K_1,M] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M),K_1)),hAPP_nat_nat(minus_minus_nat(N_1),K_1)) = hAPP_nat_nat(minus_minus_nat(M),N_1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M)) ),
inference(fof_nnf,[status(thm)],[fact_947_Nat_Odiff__diff__eq]) ).
fof(f_973_2,plain,
! [U_2483,U_2482,U_2481] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_2481),U_2482)),hAPP_nat_nat(minus_minus_nat(U_2483),U_2482)) = hAPP_nat_nat(minus_minus_nat(U_2481),U_2483)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2482),U_2483))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2482),U_2481)) ),
inference(variable_rename,[status(thm)],[f_973_1]) ).
cnf(f_973_3,plain,
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_2481),U_2482)),hAPP_nat_nat(minus_minus_nat(U_2483),U_2482)) = hAPP_nat_nat(minus_minus_nat(U_2481),U_2483)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2482),U_2483))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2482),U_2481)) ),
inference(clausify,[status(thm)],[f_973_2]) ).
fof(f_974_1,plain,
! [N,K,Ma] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(Ma),K)),hAPP_nat_nat(minus_minus_nat(N),K)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(Ma),K)),hAPP_nat_nat(minus_minus_nat(N),K))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),Ma)) ),
inference(fof_nnf,[status(thm)],[fact_948_le__diff__iff]) ).
fof(f_974_2,plain,
! [U_2486,U_2485,U_2484] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_2484),U_2485)),hAPP_nat_nat(minus_minus_nat(U_2486),U_2485)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2484),U_2486)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2484),U_2486))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_2484),U_2485)),hAPP_nat_nat(minus_minus_nat(U_2486),U_2485))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2485),U_2486))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2485),U_2484)) ),
inference(variable_rename,[status(thm)],[f_974_1]) ).
cnf(f_974_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2484),U_2486))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_2484),U_2485)),hAPP_nat_nat(minus_minus_nat(U_2486),U_2485)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2485),U_2486))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2485),U_2484)) ),
inference(clausify,[status(thm)],[f_974_2]) ).
cnf(f_974_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_2484),U_2485)),hAPP_nat_nat(minus_minus_nat(U_2486),U_2485)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2484),U_2486))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2485),U_2486))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2485),U_2484)) ),
inference(clausify,[status(thm)],[f_974_2]) ).
fof(f_975_1,plain,
! [M,N_1,K_1] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(M),N_1)),K_1) = hAPP_nat_nat(times_times_nat(M),hAPP_nat_nat(times_times_nat(N_1),K_1)),
inference(fof_nnf,[status(thm)],[fact_949_nat__mult__assoc]) ).
fof(f_975_2,plain,
! [U_2489,U_2488,U_2487] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_2489),U_2488)),U_2487) = hAPP_nat_nat(times_times_nat(U_2489),hAPP_nat_nat(times_times_nat(U_2488),U_2487)),
inference(variable_rename,[status(thm)],[f_975_1]) ).
cnf(f_975_3,plain,
hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(U_2489),U_2488)),U_2487) = hAPP_nat_nat(times_times_nat(U_2489),hAPP_nat_nat(times_times_nat(U_2488),U_2487)),
inference(clausify,[status(thm)],[f_975_2]) ).
fof(f_976_1,plain,
! [M,N_1] : hAPP_nat_nat(times_times_nat(M),N_1) = hAPP_nat_nat(times_times_nat(N_1),M),
inference(fof_nnf,[status(thm)],[fact_950_nat__mult__commute]) ).
fof(f_976_2,plain,
! [U_2491,U_2490] : hAPP_nat_nat(times_times_nat(U_2491),U_2490) = hAPP_nat_nat(times_times_nat(U_2490),U_2491),
inference(variable_rename,[status(thm)],[f_976_1]) ).
cnf(f_976_3,plain,
hAPP_nat_nat(times_times_nat(U_2491),U_2490) = hAPP_nat_nat(times_times_nat(U_2490),U_2491),
inference(clausify,[status(thm)],[f_976_2]) ).
fof(f_977_1,plain,
! [M,N_1,K_1] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(M),N_1)),K_1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(M),K_1)),hAPP_nat_nat(times_times_nat(N_1),K_1)),
inference(fof_nnf,[status(thm)],[fact_951_diff__mult__distrib]) ).
fof(f_977_2,plain,
! [U_2494,U_2493,U_2492] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2494),U_2493)),U_2492) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(U_2494),U_2492)),hAPP_nat_nat(times_times_nat(U_2493),U_2492)),
inference(variable_rename,[status(thm)],[f_977_1]) ).
cnf(f_977_3,plain,
hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2494),U_2493)),U_2492) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(U_2494),U_2492)),hAPP_nat_nat(times_times_nat(U_2493),U_2492)),
inference(clausify,[status(thm)],[f_977_2]) ).
fof(f_978_1,plain,
! [K_1,M,N_1] : hAPP_nat_nat(times_times_nat(K_1),hAPP_nat_nat(minus_minus_nat(M),N_1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(K_1),M)),hAPP_nat_nat(times_times_nat(K_1),N_1)),
inference(fof_nnf,[status(thm)],[fact_952_diff__mult__distrib2]) ).
fof(f_978_2,plain,
! [U_2497,U_2496,U_2495] : hAPP_nat_nat(times_times_nat(U_2497),hAPP_nat_nat(minus_minus_nat(U_2496),U_2495)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(U_2497),U_2496)),hAPP_nat_nat(times_times_nat(U_2497),U_2495)),
inference(variable_rename,[status(thm)],[f_978_1]) ).
cnf(f_978_3,plain,
hAPP_nat_nat(times_times_nat(U_2497),hAPP_nat_nat(minus_minus_nat(U_2496),U_2495)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(times_times_nat(U_2497),U_2496)),hAPP_nat_nat(times_times_nat(U_2497),U_2495)),
inference(clausify,[status(thm)],[f_978_2]) ).
fof(f_979_1,plain,
! [N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
| N_1 = zero_zero_nat ),
inference(fof_nnf,[status(thm)],[fact_953_gr0I]) ).
fof(f_979_2,plain,
! [U_2498] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2498))
| U_2498 = zero_zero_nat ),
inference(variable_rename,[status(thm)],[f_979_1]) ).
cnf(f_979_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2498))
| U_2498 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_979_2]) ).
fof(f_980_1,plain,
! [M,N_1] :
( N_1 != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_954_gr__implies__not0]) ).
fof(f_980_2,plain,
! [U_2500,U_2499] :
( U_2499 != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2500),U_2499)) ),
inference(variable_rename,[status(thm)],[f_980_1]) ).
cnf(f_980_3,plain,
( U_2499 != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2500),U_2499)) ),
inference(clausify,[status(thm)],[f_980_2]) ).
fof(f_981_1,plain,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)),
inference(fof_nnf,[status(thm)],[fact_955_less__nat__zero__code]) ).
fof(f_981_2,plain,
! [U_2501] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2501),zero_zero_nat)),
inference(variable_rename,[status(thm)],[f_981_1]) ).
cnf(f_981_3,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2501),zero_zero_nat)),
inference(clausify,[status(thm)],[f_981_2]) ).
fof(f_982_1,plain,
! [N] :
( ( N != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
| N = zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_956_neq0__conv]) ).
fof(f_982_2,plain,
! [U_2502] :
( ( U_2502 != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2502)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2502))
| U_2502 = zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_982_1]) ).
fof(f_982_3,plain,
( ! [U_2504] :
( U_2504 != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2504)) )
& ! [U_2503] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2503))
| U_2503 = zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_982_2]) ).
cnf(f_982_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2503))
| U_2503 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_982_3]) ).
cnf(f_982_5,plain,
( U_2504 != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2504)) ),
inference(clausify,[status(thm)],[f_982_3]) ).
fof(f_983_1,plain,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)),
inference(fof_nnf,[status(thm)],[fact_957_not__less0]) ).
fof(f_983_2,plain,
! [U_2505] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2505),zero_zero_nat)),
inference(variable_rename,[status(thm)],[f_983_1]) ).
cnf(f_983_3,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2505),zero_zero_nat)),
inference(clausify,[status(thm)],[f_983_2]) ).
fof(f_984_1,plain,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(M),N_1)),M))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_958_diff__less]) ).
fof(f_984_2,plain,
! [U_2507,U_2506] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2507),U_2506)),U_2507))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2507))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2506)) ),
inference(variable_rename,[status(thm)],[f_984_1]) ).
cnf(f_984_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2507),U_2506)),U_2507))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2507))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2506)) ),
inference(clausify,[status(thm)],[f_984_2]) ).
fof(f_985_1,plain,
! [N,Ma] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(N),Ma)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(N),Ma))) ) ),
inference(fof_nnf,[status(thm)],[fact_959_zero__less__diff]) ).
fof(f_985_2,plain,
! [U_2509,U_2508] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(U_2509),U_2508)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2508),U_2509)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2508),U_2509))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(U_2509),U_2508))) ) ),
inference(variable_rename,[status(thm)],[f_985_1]) ).
fof(f_985_3,plain,
( ! [U_2513,U_2511] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(U_2513),U_2511)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2511),U_2513)) )
& ! [U_2512,U_2510] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2510),U_2512))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(U_2512),U_2510))) ) ),
inference(miniscope,[status(thm)],[f_985_2]) ).
cnf(f_985_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2510),U_2512))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(U_2512),U_2510))) ),
inference(clausify,[status(thm)],[f_985_3]) ).
cnf(f_985_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(minus_minus_nat(U_2513),U_2511)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2511),U_2513)) ),
inference(clausify,[status(thm)],[f_985_3]) ).
fof(f_986_1,plain,
! [M,N_1] :
( N_1 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(M),N_1) != M ),
inference(fof_nnf,[status(thm)],[fact_960_add__eq__self__zero]) ).
fof(f_986_2,plain,
! [U_2515,U_2514] :
( U_2514 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(U_2515),U_2514) != U_2515 ),
inference(variable_rename,[status(thm)],[f_986_1]) ).
cnf(f_986_3,plain,
( U_2514 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(U_2515),U_2514) != U_2515 ),
inference(clausify,[status(thm)],[f_986_2]) ).
fof(f_987_1,plain,
! [Ma,N] :
( ( hAPP_nat_nat(plus_plus_nat(Ma),N) = zero_zero_nat
| N != zero_zero_nat
| Ma != zero_zero_nat )
& ( ( N = zero_zero_nat
& Ma = zero_zero_nat )
| hAPP_nat_nat(plus_plus_nat(Ma),N) != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_961_add__is__0]) ).
fof(f_987_2,plain,
! [U_2517,U_2516] :
( ( hAPP_nat_nat(plus_plus_nat(U_2517),U_2516) = zero_zero_nat
| U_2516 != zero_zero_nat
| U_2517 != zero_zero_nat )
& ( ( U_2516 = zero_zero_nat
& U_2517 = zero_zero_nat )
| hAPP_nat_nat(plus_plus_nat(U_2517),U_2516) != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_987_1]) ).
fof(f_987_3,plain,
( ! [U_2521,U_2519] :
( hAPP_nat_nat(plus_plus_nat(U_2521),U_2519) = zero_zero_nat
| U_2519 != zero_zero_nat
| U_2521 != zero_zero_nat )
& ! [U_2520,U_2518] :
( ( U_2518 = zero_zero_nat
& U_2520 = zero_zero_nat )
| hAPP_nat_nat(plus_plus_nat(U_2520),U_2518) != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_987_2]) ).
cnf(f_987_4,plain,
( U_2520 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(U_2520),U_2518) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_987_3]) ).
cnf(f_987_5,plain,
( U_2518 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(U_2520),U_2518) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_987_3]) ).
cnf(f_987_6,plain,
( hAPP_nat_nat(plus_plus_nat(U_2521),U_2519) = zero_zero_nat
| U_2519 != zero_zero_nat
| U_2521 != zero_zero_nat ),
inference(clausify,[status(thm)],[f_987_3]) ).
fof(f_988_1,plain,
! [M] : hAPP_nat_nat(plus_plus_nat(M),zero_zero_nat) = M,
inference(fof_nnf,[status(thm)],[fact_962_Nat_Oadd__0__right]) ).
fof(f_988_2,plain,
! [U_2522] : hAPP_nat_nat(plus_plus_nat(U_2522),zero_zero_nat) = U_2522,
inference(variable_rename,[status(thm)],[f_988_1]) ).
cnf(f_988_3,plain,
hAPP_nat_nat(plus_plus_nat(U_2522),zero_zero_nat) = U_2522,
inference(clausify,[status(thm)],[f_988_2]) ).
fof(f_989_1,plain,
! [N_1] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),N_1) = N_1,
inference(fof_nnf,[status(thm)],[fact_963_plus__nat_Oadd__0]) ).
fof(f_989_2,plain,
! [U_2523] : hAPP_nat_nat(plus_plus_nat(zero_zero_nat),U_2523) = U_2523,
inference(variable_rename,[status(thm)],[f_989_1]) ).
cnf(f_989_3,plain,
hAPP_nat_nat(plus_plus_nat(zero_zero_nat),U_2523) = U_2523,
inference(clausify,[status(thm)],[f_989_2]) ).
fof(f_990_1,plain,
! [N_1,M] : hAPP_nat_nat(minus_minus_nat(N_1),hAPP_nat_nat(plus_plus_nat(N_1),M)) = zero_zero_nat,
inference(fof_nnf,[status(thm)],[fact_964_diff__add__0]) ).
fof(f_990_2,plain,
! [U_2525,U_2524] : hAPP_nat_nat(minus_minus_nat(U_2525),hAPP_nat_nat(plus_plus_nat(U_2525),U_2524)) = zero_zero_nat,
inference(variable_rename,[status(thm)],[f_990_1]) ).
cnf(f_990_3,plain,
hAPP_nat_nat(minus_minus_nat(U_2525),hAPP_nat_nat(plus_plus_nat(U_2525),U_2524)) = zero_zero_nat,
inference(clausify,[status(thm)],[f_990_2]) ).
fof(f_991_1,plain,
! [N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),zero_zero_nat))
| N != zero_zero_nat )
& ( N = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),zero_zero_nat)) ) ),
inference(fof_nnf,[status(thm)],[fact_965_le__0__eq]) ).
fof(f_991_2,plain,
! [U_2526] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2526),zero_zero_nat))
| U_2526 != zero_zero_nat )
& ( U_2526 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2526),zero_zero_nat)) ) ),
inference(variable_rename,[status(thm)],[f_991_1]) ).
fof(f_991_3,plain,
( ! [U_2528] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2528),zero_zero_nat))
| U_2528 != zero_zero_nat )
& ! [U_2527] :
( U_2527 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2527),zero_zero_nat)) ) ),
inference(miniscope,[status(thm)],[f_991_2]) ).
cnf(f_991_4,plain,
( U_2527 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2527),zero_zero_nat)) ),
inference(clausify,[status(thm)],[f_991_3]) ).
cnf(f_991_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2528),zero_zero_nat))
| U_2528 != zero_zero_nat ),
inference(clausify,[status(thm)],[f_991_3]) ).
fof(f_992_1,plain,
! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1)),
inference(fof_nnf,[status(thm)],[fact_966_less__eq__nat_Osimps_I1_J]) ).
fof(f_992_2,plain,
! [U_2529] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2529)),
inference(variable_rename,[status(thm)],[f_992_1]) ).
cnf(f_992_3,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_2529)),
inference(clausify,[status(thm)],[f_992_2]) ).
fof(f_993_1,plain,
! [M,N_1] :
( hAPP_nat_nat(minus_minus_nat(M),N_1) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_967_diff__is__0__eq_H]) ).
fof(f_993_2,plain,
! [U_2531,U_2530] :
( hAPP_nat_nat(minus_minus_nat(U_2531),U_2530) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2531),U_2530)) ),
inference(variable_rename,[status(thm)],[f_993_1]) ).
cnf(f_993_3,plain,
( hAPP_nat_nat(minus_minus_nat(U_2531),U_2530) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2531),U_2530)) ),
inference(clausify,[status(thm)],[f_993_2]) ).
fof(f_994_1,plain,
! [Ma,N] :
( ( hAPP_nat_nat(minus_minus_nat(Ma),N) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N))
| hAPP_nat_nat(minus_minus_nat(Ma),N) != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_968_diff__is__0__eq]) ).
fof(f_994_2,plain,
! [U_2533,U_2532] :
( ( hAPP_nat_nat(minus_minus_nat(U_2533),U_2532) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2533),U_2532)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2533),U_2532))
| hAPP_nat_nat(minus_minus_nat(U_2533),U_2532) != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_994_1]) ).
fof(f_994_3,plain,
( ! [U_2537,U_2535] :
( hAPP_nat_nat(minus_minus_nat(U_2537),U_2535) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2537),U_2535)) )
& ! [U_2536,U_2534] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2536),U_2534))
| hAPP_nat_nat(minus_minus_nat(U_2536),U_2534) != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_994_2]) ).
cnf(f_994_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2536),U_2534))
| hAPP_nat_nat(minus_minus_nat(U_2536),U_2534) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_994_3]) ).
cnf(f_994_5,plain,
( hAPP_nat_nat(minus_minus_nat(U_2537),U_2535) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2537),U_2535)) ),
inference(clausify,[status(thm)],[f_994_3]) ).
fof(f_995_1,plain,
! [N_1] : hAPP_nat_nat(times_times_nat(zero_zero_nat),N_1) = zero_zero_nat,
inference(fof_nnf,[status(thm)],[fact_969_mult__0]) ).
fof(f_995_2,plain,
! [U_2538] : hAPP_nat_nat(times_times_nat(zero_zero_nat),U_2538) = zero_zero_nat,
inference(variable_rename,[status(thm)],[f_995_1]) ).
cnf(f_995_3,plain,
hAPP_nat_nat(times_times_nat(zero_zero_nat),U_2538) = zero_zero_nat,
inference(clausify,[status(thm)],[f_995_2]) ).
fof(f_996_1,plain,
! [M] : hAPP_nat_nat(times_times_nat(M),zero_zero_nat) = zero_zero_nat,
inference(fof_nnf,[status(thm)],[fact_970_mult__0__right]) ).
fof(f_996_2,plain,
! [U_2539] : hAPP_nat_nat(times_times_nat(U_2539),zero_zero_nat) = zero_zero_nat,
inference(variable_rename,[status(thm)],[f_996_1]) ).
cnf(f_996_3,plain,
hAPP_nat_nat(times_times_nat(U_2539),zero_zero_nat) = zero_zero_nat,
inference(clausify,[status(thm)],[f_996_2]) ).
fof(f_997_1,plain,
! [Ma,N] :
( ( hAPP_nat_nat(times_times_nat(Ma),N) = zero_zero_nat
| ( N != zero_zero_nat
& Ma != zero_zero_nat ) )
& ( N = zero_zero_nat
| Ma = zero_zero_nat
| hAPP_nat_nat(times_times_nat(Ma),N) != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_971_mult__is__0]) ).
fof(f_997_2,plain,
! [U_2541,U_2540] :
( ( hAPP_nat_nat(times_times_nat(U_2541),U_2540) = zero_zero_nat
| ( U_2540 != zero_zero_nat
& U_2541 != zero_zero_nat ) )
& ( U_2540 = zero_zero_nat
| U_2541 = zero_zero_nat
| hAPP_nat_nat(times_times_nat(U_2541),U_2540) != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_997_1]) ).
fof(f_997_3,plain,
( ! [U_2545,U_2543] :
( hAPP_nat_nat(times_times_nat(U_2545),U_2543) = zero_zero_nat
| ( U_2543 != zero_zero_nat
& U_2545 != zero_zero_nat ) )
& ! [U_2544,U_2542] :
( U_2542 = zero_zero_nat
| U_2544 = zero_zero_nat
| hAPP_nat_nat(times_times_nat(U_2544),U_2542) != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_997_2]) ).
cnf(f_997_4,plain,
( U_2542 = zero_zero_nat
| U_2544 = zero_zero_nat
| hAPP_nat_nat(times_times_nat(U_2544),U_2542) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_997_3]) ).
cnf(f_997_5,plain,
( U_2545 != zero_zero_nat
| hAPP_nat_nat(times_times_nat(U_2545),U_2543) = zero_zero_nat ),
inference(clausify,[status(thm)],[f_997_3]) ).
cnf(f_997_6,plain,
( U_2543 != zero_zero_nat
| hAPP_nat_nat(times_times_nat(U_2545),U_2543) = zero_zero_nat ),
inference(clausify,[status(thm)],[f_997_3]) ).
fof(f_998_1,plain,
! [K,Ma,N] :
( ( hAPP_nat_nat(times_times_nat(K),Ma) = hAPP_nat_nat(times_times_nat(K),N)
| ( K != zero_zero_nat
& Ma != N ) )
& ( K = zero_zero_nat
| Ma = N
| hAPP_nat_nat(times_times_nat(K),Ma) != hAPP_nat_nat(times_times_nat(K),N) ) ),
inference(fof_nnf,[status(thm)],[fact_972_mult__cancel1]) ).
fof(f_998_2,plain,
! [U_2548,U_2547,U_2546] :
( ( hAPP_nat_nat(times_times_nat(U_2548),U_2547) = hAPP_nat_nat(times_times_nat(U_2548),U_2546)
| ( U_2548 != zero_zero_nat
& U_2547 != U_2546 ) )
& ( U_2548 = zero_zero_nat
| U_2547 = U_2546
| hAPP_nat_nat(times_times_nat(U_2548),U_2547) != hAPP_nat_nat(times_times_nat(U_2548),U_2546) ) ),
inference(variable_rename,[status(thm)],[f_998_1]) ).
fof(f_998_3,plain,
( ! [U_2554,U_2552,U_2550] :
( hAPP_nat_nat(times_times_nat(U_2554),U_2552) = hAPP_nat_nat(times_times_nat(U_2554),U_2550)
| ( U_2554 != zero_zero_nat
& U_2552 != U_2550 ) )
& ! [U_2553,U_2551,U_2549] :
( U_2553 = zero_zero_nat
| U_2551 = U_2549
| hAPP_nat_nat(times_times_nat(U_2553),U_2551) != hAPP_nat_nat(times_times_nat(U_2553),U_2549) ) ),
inference(miniscope,[status(thm)],[f_998_2]) ).
cnf(f_998_4,plain,
( U_2553 = zero_zero_nat
| U_2551 = U_2549
| hAPP_nat_nat(times_times_nat(U_2553),U_2551) != hAPP_nat_nat(times_times_nat(U_2553),U_2549) ),
inference(clausify,[status(thm)],[f_998_3]) ).
cnf(f_998_5,plain,
( U_2552 != U_2550
| hAPP_nat_nat(times_times_nat(U_2554),U_2552) = hAPP_nat_nat(times_times_nat(U_2554),U_2550) ),
inference(clausify,[status(thm)],[f_998_3]) ).
cnf(f_998_6,plain,
( U_2554 != zero_zero_nat
| hAPP_nat_nat(times_times_nat(U_2554),U_2552) = hAPP_nat_nat(times_times_nat(U_2554),U_2550) ),
inference(clausify,[status(thm)],[f_998_3]) ).
fof(f_999_1,plain,
! [Ma,K,N] :
( ( hAPP_nat_nat(times_times_nat(Ma),K) = hAPP_nat_nat(times_times_nat(N),K)
| ( K != zero_zero_nat
& Ma != N ) )
& ( K = zero_zero_nat
| Ma = N
| hAPP_nat_nat(times_times_nat(Ma),K) != hAPP_nat_nat(times_times_nat(N),K) ) ),
inference(fof_nnf,[status(thm)],[fact_973_mult__cancel2]) ).
fof(f_999_2,plain,
! [U_2557,U_2556,U_2555] :
( ( hAPP_nat_nat(times_times_nat(U_2557),U_2556) = hAPP_nat_nat(times_times_nat(U_2555),U_2556)
| ( U_2556 != zero_zero_nat
& U_2557 != U_2555 ) )
& ( U_2556 = zero_zero_nat
| U_2557 = U_2555
| hAPP_nat_nat(times_times_nat(U_2557),U_2556) != hAPP_nat_nat(times_times_nat(U_2555),U_2556) ) ),
inference(variable_rename,[status(thm)],[f_999_1]) ).
fof(f_999_3,plain,
( ! [U_2563,U_2561,U_2559] :
( hAPP_nat_nat(times_times_nat(U_2563),U_2561) = hAPP_nat_nat(times_times_nat(U_2559),U_2561)
| ( U_2561 != zero_zero_nat
& U_2563 != U_2559 ) )
& ! [U_2562,U_2560,U_2558] :
( U_2560 = zero_zero_nat
| U_2562 = U_2558
| hAPP_nat_nat(times_times_nat(U_2562),U_2560) != hAPP_nat_nat(times_times_nat(U_2558),U_2560) ) ),
inference(miniscope,[status(thm)],[f_999_2]) ).
cnf(f_999_4,plain,
( U_2560 = zero_zero_nat
| U_2562 = U_2558
| hAPP_nat_nat(times_times_nat(U_2562),U_2560) != hAPP_nat_nat(times_times_nat(U_2558),U_2560) ),
inference(clausify,[status(thm)],[f_999_3]) ).
cnf(f_999_5,plain,
( U_2563 != U_2559
| hAPP_nat_nat(times_times_nat(U_2563),U_2561) = hAPP_nat_nat(times_times_nat(U_2559),U_2561) ),
inference(clausify,[status(thm)],[f_999_3]) ).
cnf(f_999_6,plain,
( U_2561 != zero_zero_nat
| hAPP_nat_nat(times_times_nat(U_2563),U_2561) = hAPP_nat_nat(times_times_nat(U_2559),U_2561) ),
inference(clausify,[status(thm)],[f_999_3]) ).
fof(f_1000_1,plain,
! [I_1,J_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_1),J_1)),I_1)),
inference(fof_nnf,[status(thm)],[fact_974_not__add__less1]) ).
fof(f_1000_2,plain,
! [U_2565,U_2564] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2565),U_2564)),U_2565)),
inference(variable_rename,[status(thm)],[f_1000_1]) ).
cnf(f_1000_3,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2565),U_2564)),U_2565)),
inference(clausify,[status(thm)],[f_1000_2]) ).
fof(f_1001_1,plain,
! [J_1,I_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(J_1),I_1)),I_1)),
inference(fof_nnf,[status(thm)],[fact_975_not__add__less2]) ).
fof(f_1001_2,plain,
! [U_2567,U_2566] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2567),U_2566)),U_2566)),
inference(variable_rename,[status(thm)],[f_1001_1]) ).
cnf(f_1001_3,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2567),U_2566)),U_2566)),
inference(clausify,[status(thm)],[f_1001_2]) ).
fof(f_1002_1,plain,
! [K,Ma,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(K),Ma)),hAPP_nat_nat(plus_plus_nat(K),N)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(K),Ma)),hAPP_nat_nat(plus_plus_nat(K),N))) ) ),
inference(fof_nnf,[status(thm)],[fact_976_nat__add__left__cancel__less]) ).
fof(f_1002_2,plain,
! [U_2570,U_2569,U_2568] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2570),U_2569)),hAPP_nat_nat(plus_plus_nat(U_2570),U_2568)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2569),U_2568)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2569),U_2568))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2570),U_2569)),hAPP_nat_nat(plus_plus_nat(U_2570),U_2568))) ) ),
inference(variable_rename,[status(thm)],[f_1002_1]) ).
fof(f_1002_3,plain,
( ! [U_2576,U_2574,U_2572] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2576),U_2574)),hAPP_nat_nat(plus_plus_nat(U_2576),U_2572)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2574),U_2572)) )
& ! [U_2575,U_2573,U_2571] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2573),U_2571))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2575),U_2573)),hAPP_nat_nat(plus_plus_nat(U_2575),U_2571))) ) ),
inference(miniscope,[status(thm)],[f_1002_2]) ).
cnf(f_1002_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2573),U_2571))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2575),U_2573)),hAPP_nat_nat(plus_plus_nat(U_2575),U_2571))) ),
inference(clausify,[status(thm)],[f_1002_3]) ).
cnf(f_1002_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2576),U_2574)),hAPP_nat_nat(plus_plus_nat(U_2576),U_2572)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2574),U_2572)) ),
inference(clausify,[status(thm)],[f_1002_3]) ).
fof(f_1003_1,plain,
! [M,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(plus_plus_nat(J_1),M)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_977_trans__less__add1]) ).
fof(f_1003_2,plain,
! [U_2579,U_2578,U_2577] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2578),hAPP_nat_nat(plus_plus_nat(U_2577),U_2579)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2578),U_2577)) ),
inference(variable_rename,[status(thm)],[f_1003_1]) ).
cnf(f_1003_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2578),hAPP_nat_nat(plus_plus_nat(U_2577),U_2579)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2578),U_2577)) ),
inference(clausify,[status(thm)],[f_1003_2]) ).
fof(f_1004_1,plain,
! [M,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(plus_plus_nat(M),J_1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_978_trans__less__add2]) ).
fof(f_1004_2,plain,
! [U_2582,U_2581,U_2580] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2581),hAPP_nat_nat(plus_plus_nat(U_2582),U_2580)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2581),U_2580)) ),
inference(variable_rename,[status(thm)],[f_1004_1]) ).
cnf(f_1004_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2581),hAPP_nat_nat(plus_plus_nat(U_2582),U_2580)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2581),U_2580)) ),
inference(clausify,[status(thm)],[f_1004_2]) ).
fof(f_1005_1,plain,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_1)),hAPP_nat_nat(plus_plus_nat(J_1),K_1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_979_add__less__mono1]) ).
fof(f_1005_2,plain,
! [U_2585,U_2584,U_2583] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2584),U_2585)),hAPP_nat_nat(plus_plus_nat(U_2583),U_2585)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2584),U_2583)) ),
inference(variable_rename,[status(thm)],[f_1005_1]) ).
cnf(f_1005_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2584),U_2585)),hAPP_nat_nat(plus_plus_nat(U_2583),U_2585)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2584),U_2583)) ),
inference(clausify,[status(thm)],[f_1005_2]) ).
fof(f_1006_1,plain,
! [K_1,L,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_1)),hAPP_nat_nat(plus_plus_nat(J_1),L)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_980_add__less__mono]) ).
fof(f_1006_2,plain,
! [U_2589,U_2588,U_2587,U_2586] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2587),U_2589)),hAPP_nat_nat(plus_plus_nat(U_2586),U_2588)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2589),U_2588))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2587),U_2586)) ),
inference(variable_rename,[status(thm)],[f_1006_1]) ).
cnf(f_1006_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2587),U_2589)),hAPP_nat_nat(plus_plus_nat(U_2586),U_2588)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2589),U_2588))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2587),U_2586)) ),
inference(clausify,[status(thm)],[f_1006_2]) ).
fof(f_1007_1,plain,
! [M,N_1,K_1,L] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
| hAPP_nat_nat(plus_plus_nat(M),L) != hAPP_nat_nat(plus_plus_nat(K_1),N_1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L)) ),
inference(fof_nnf,[status(thm)],[fact_981_less__add__eq__less]) ).
fof(f_1007_2,plain,
! [U_2593,U_2592,U_2591,U_2590] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2593),U_2592))
| hAPP_nat_nat(plus_plus_nat(U_2593),U_2590) != hAPP_nat_nat(plus_plus_nat(U_2591),U_2592)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2591),U_2590)) ),
inference(variable_rename,[status(thm)],[f_1007_1]) ).
cnf(f_1007_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2593),U_2592))
| hAPP_nat_nat(plus_plus_nat(U_2593),U_2590) != hAPP_nat_nat(plus_plus_nat(U_2591),U_2592)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2591),U_2590)) ),
inference(clausify,[status(thm)],[f_1007_2]) ).
fof(f_1008_1,plain,
! [I_1,J_1,K_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),K_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_1),J_1)),K_1)) ),
inference(fof_nnf,[status(thm)],[fact_982_add__lessD1]) ).
fof(f_1008_2,plain,
! [U_2596,U_2595,U_2594] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2596),U_2594))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2596),U_2595)),U_2594)) ),
inference(variable_rename,[status(thm)],[f_1008_1]) ).
cnf(f_1008_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2596),U_2594))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2596),U_2595)),U_2594)) ),
inference(clausify,[status(thm)],[f_1008_2]) ).
fof(f_1009_1,plain,
! [M,N_1] :
( hAPP_nat_nat(plus_plus_nat(N_1),hAPP_nat_nat(minus_minus_nat(M),N_1)) = M
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_983_add__diff__inverse]) ).
fof(f_1009_2,plain,
! [U_2598,U_2597] :
( hAPP_nat_nat(plus_plus_nat(U_2597),hAPP_nat_nat(minus_minus_nat(U_2598),U_2597)) = U_2598
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2598),U_2597)) ),
inference(variable_rename,[status(thm)],[f_1009_1]) ).
cnf(f_1009_3,plain,
( hAPP_nat_nat(plus_plus_nat(U_2597),hAPP_nat_nat(minus_minus_nat(U_2598),U_2597)) = U_2598
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2598),U_2597)) ),
inference(clausify,[status(thm)],[f_1009_2]) ).
fof(f_1010_1,plain,
! [I_2,J_2,K] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(minus_minus_nat(J_2),K)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_2),K)),J_2)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(I_2),K)),J_2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(minus_minus_nat(J_2),K))) ) ),
inference(fof_nnf,[status(thm)],[fact_984_less__diff__conv]) ).
fof(f_1010_2,plain,
! [U_2601,U_2600,U_2599] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2601),hAPP_nat_nat(minus_minus_nat(U_2600),U_2599)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2601),U_2599)),U_2600)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2601),U_2599)),U_2600))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2601),hAPP_nat_nat(minus_minus_nat(U_2600),U_2599))) ) ),
inference(variable_rename,[status(thm)],[f_1010_1]) ).
fof(f_1010_3,plain,
( ! [U_2607,U_2605,U_2603] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2607),hAPP_nat_nat(minus_minus_nat(U_2605),U_2603)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2607),U_2603)),U_2605)) )
& ! [U_2606,U_2604,U_2602] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2606),U_2602)),U_2604))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2606),hAPP_nat_nat(minus_minus_nat(U_2604),U_2602))) ) ),
inference(miniscope,[status(thm)],[f_1010_2]) ).
cnf(f_1010_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2606),U_2602)),U_2604))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2606),hAPP_nat_nat(minus_minus_nat(U_2604),U_2602))) ),
inference(clausify,[status(thm)],[f_1010_3]) ).
cnf(f_1010_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2607),hAPP_nat_nat(minus_minus_nat(U_2605),U_2603)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(U_2607),U_2603)),U_2605)) ),
inference(clausify,[status(thm)],[f_1010_3]) ).
fof(f_1011_1,plain,
! [Ma,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N))
| Ma = N
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N)) )
& ( ( Ma != N
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N)) ) ),
inference(fof_nnf,[status(thm)],[fact_985_nat__less__le]) ).
fof(f_1011_2,plain,
! [U_2609,U_2608] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2609),U_2608))
| U_2609 = U_2608
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2609),U_2608)) )
& ( ( U_2609 != U_2608
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2609),U_2608)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2609),U_2608)) ) ),
inference(variable_rename,[status(thm)],[f_1011_1]) ).
fof(f_1011_3,plain,
( ! [U_2613,U_2611] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2613),U_2611))
| U_2613 = U_2611
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2613),U_2611)) )
& ! [U_2612,U_2610] :
( ( U_2612 != U_2610
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2612),U_2610)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2612),U_2610)) ) ),
inference(miniscope,[status(thm)],[f_1011_2]) ).
cnf(f_1011_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2612),U_2610))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2612),U_2610)) ),
inference(clausify,[status(thm)],[f_1011_3]) ).
cnf(f_1011_5,plain,
( U_2612 != U_2610
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2612),U_2610)) ),
inference(clausify,[status(thm)],[f_1011_3]) ).
cnf(f_1011_6,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2613),U_2611))
| U_2613 = U_2611
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2613),U_2611)) ),
inference(clausify,[status(thm)],[f_1011_3]) ).
fof(f_1012_1,plain,
! [Ma,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N))
| ( Ma != N
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N)) ) )
& ( Ma = N
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N)) ) ),
inference(fof_nnf,[status(thm)],[fact_986_le__eq__less__or__eq]) ).
fof(f_1012_2,plain,
! [U_2615,U_2614] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2615),U_2614))
| ( U_2615 != U_2614
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2615),U_2614)) ) )
& ( U_2615 = U_2614
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2615),U_2614))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2615),U_2614)) ) ),
inference(variable_rename,[status(thm)],[f_1012_1]) ).
fof(f_1012_3,plain,
( ! [U_2619,U_2617] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2619),U_2617))
| ( U_2619 != U_2617
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2619),U_2617)) ) )
& ! [U_2618,U_2616] :
( U_2618 = U_2616
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2618),U_2616))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2618),U_2616)) ) ),
inference(miniscope,[status(thm)],[f_1012_2]) ).
cnf(f_1012_4,plain,
( U_2618 = U_2616
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2618),U_2616))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2618),U_2616)) ),
inference(clausify,[status(thm)],[f_1012_3]) ).
cnf(f_1012_5,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2619),U_2617))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2619),U_2617)) ),
inference(clausify,[status(thm)],[f_1012_3]) ).
cnf(f_1012_6,plain,
( U_2619 != U_2617
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2619),U_2617)) ),
inference(clausify,[status(thm)],[f_1012_3]) ).
fof(f_1013_1,plain,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_987_less__imp__le__nat]) ).
fof(f_1013_2,plain,
! [U_2621,U_2620] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2621),U_2620))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2621),U_2620)) ),
inference(variable_rename,[status(thm)],[f_1013_1]) ).
cnf(f_1013_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2621),U_2620))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2621),U_2620)) ),
inference(clausify,[status(thm)],[f_1013_2]) ).
fof(f_1014_1,plain,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
| M = N_1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_988_le__neq__implies__less]) ).
fof(f_1014_2,plain,
! [U_2623,U_2622] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2623),U_2622))
| U_2623 = U_2622
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2623),U_2622)) ),
inference(variable_rename,[status(thm)],[f_1014_1]) ).
cnf(f_1014_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2623),U_2622))
| U_2623 = U_2622
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2623),U_2622)) ),
inference(clausify,[status(thm)],[f_1014_2]) ).
fof(f_1015_1,plain,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
| ( M != N_1
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_989_less__or__eq__imp__le]) ).
fof(f_1015_2,plain,
! [U_2625,U_2624] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2625),U_2624))
| ( U_2625 != U_2624
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2625),U_2624)) ) ),
inference(variable_rename,[status(thm)],[f_1015_1]) ).
cnf(f_1015_3,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2625),U_2624))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2625),U_2624)) ),
inference(clausify,[status(thm)],[f_1015_2]) ).
cnf(f_1015_4,plain,
( U_2625 != U_2624
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2625),U_2624)) ),
inference(clausify,[status(thm)],[f_1015_2]) ).
fof(f_1016_1,plain,
! [N,K,Ma] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(Ma),K)),hAPP_nat_nat(minus_minus_nat(N),K)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(Ma),K)),hAPP_nat_nat(minus_minus_nat(N),K))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),Ma)) ),
inference(fof_nnf,[status(thm)],[fact_990_less__diff__iff]) ).
fof(f_1016_2,plain,
! [U_2628,U_2627,U_2626] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2626),U_2627)),hAPP_nat_nat(minus_minus_nat(U_2628),U_2627)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2626),U_2628)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2626),U_2628))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2626),U_2627)),hAPP_nat_nat(minus_minus_nat(U_2628),U_2627))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2627),U_2628))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2627),U_2626)) ),
inference(variable_rename,[status(thm)],[f_1016_1]) ).
cnf(f_1016_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2626),U_2628))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2626),U_2627)),hAPP_nat_nat(minus_minus_nat(U_2628),U_2627)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2627),U_2628))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2627),U_2626)) ),
inference(clausify,[status(thm)],[f_1016_2]) ).
cnf(f_1016_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2626),U_2627)),hAPP_nat_nat(minus_minus_nat(U_2628),U_2627)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2626),U_2628))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2627),U_2628))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2627),U_2626)) ),
inference(clausify,[status(thm)],[f_1016_2]) ).
fof(f_1017_1,plain,
! [C,A,B] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(A),C)),hAPP_nat_nat(minus_minus_nat(B),C)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C),A))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A),B)) ),
inference(fof_nnf,[status(thm)],[fact_991_diff__less__mono]) ).
fof(f_1017_2,plain,
! [U_2631,U_2630,U_2629] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2630),U_2631)),hAPP_nat_nat(minus_minus_nat(U_2629),U_2631)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2631),U_2630))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2630),U_2629)) ),
inference(variable_rename,[status(thm)],[f_1017_1]) ).
cnf(f_1017_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(U_2630),U_2631)),hAPP_nat_nat(minus_minus_nat(U_2629),U_2631)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2631),U_2630))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2630),U_2629)) ),
inference(clausify,[status(thm)],[f_1017_2]) ).
fof(f_1018_1,plain,
! [K,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K),hAPP_nat_nat(plus_plus_nat(N),K)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K),N)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K),hAPP_nat_nat(plus_plus_nat(N),K))) ) ),
inference(fof_nnf,[status(thm)],[fact_992_dvd__reduce]) ).
fof(f_1018_2,plain,
! [U_2633,U_2632] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2633),hAPP_nat_nat(plus_plus_nat(U_2632),U_2633)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2633),U_2632)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2633),U_2632))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2633),hAPP_nat_nat(plus_plus_nat(U_2632),U_2633))) ) ),
inference(variable_rename,[status(thm)],[f_1018_1]) ).
fof(f_1018_3,plain,
( ! [U_2637,U_2635] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2637),hAPP_nat_nat(plus_plus_nat(U_2635),U_2637)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2637),U_2635)) )
& ! [U_2636,U_2634] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2636),U_2634))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2636),hAPP_nat_nat(plus_plus_nat(U_2634),U_2636))) ) ),
inference(miniscope,[status(thm)],[f_1018_2]) ).
cnf(f_1018_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2636),U_2634))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2636),hAPP_nat_nat(plus_plus_nat(U_2634),U_2636))) ),
inference(clausify,[status(thm)],[f_1018_3]) ).
cnf(f_1018_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2637),hAPP_nat_nat(plus_plus_nat(U_2635),U_2637)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2637),U_2635)) ),
inference(clausify,[status(thm)],[f_1018_3]) ).
fof(f_1019_1,plain,
! [K_1,M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),N_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),M))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),hAPP_nat_nat(minus_minus_nat(M),N_1))) ),
inference(fof_nnf,[status(thm)],[fact_993_dvd__diffD1]) ).
fof(f_1019_2,plain,
! [U_2640,U_2639,U_2638] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2640),U_2638))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2638),U_2639))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2640),U_2639))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2640),hAPP_nat_nat(minus_minus_nat(U_2639),U_2638))) ),
inference(variable_rename,[status(thm)],[f_1019_1]) ).
cnf(f_1019_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2640),U_2638))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2638),U_2639))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2640),U_2639))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2640),hAPP_nat_nat(minus_minus_nat(U_2639),U_2638))) ),
inference(clausify,[status(thm)],[f_1019_2]) ).
fof(f_1020_1,plain,
! [K_1,M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),M))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),N_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),hAPP_nat_nat(minus_minus_nat(M),N_1))) ),
inference(fof_nnf,[status(thm)],[fact_994_dvd__diffD]) ).
fof(f_1020_2,plain,
! [U_2643,U_2642,U_2641] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2643),U_2642))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2641),U_2642))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2643),U_2641))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2643),hAPP_nat_nat(minus_minus_nat(U_2642),U_2641))) ),
inference(variable_rename,[status(thm)],[f_1020_1]) ).
cnf(f_1020_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2643),U_2642))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2641),U_2642))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2643),U_2641))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2643),hAPP_nat_nat(minus_minus_nat(U_2642),U_2641))) ),
inference(clausify,[status(thm)],[f_1020_2]) ).
fof(f_1021_1,plain,
! [N_1,M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(plus_plus_nat(M),N_1))),
inference(fof_nnf,[status(thm)],[fact_995_le__add2]) ).
fof(f_1021_2,plain,
! [U_2645,U_2644] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2645),hAPP_nat_nat(plus_plus_nat(U_2644),U_2645))),
inference(variable_rename,[status(thm)],[f_1021_1]) ).
cnf(f_1021_3,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2645),hAPP_nat_nat(plus_plus_nat(U_2644),U_2645))),
inference(clausify,[status(thm)],[f_1021_2]) ).
fof(f_1022_1,plain,
! [N_1,M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(plus_plus_nat(N_1),M))),
inference(fof_nnf,[status(thm)],[fact_996_le__add1]) ).
fof(f_1022_2,plain,
! [U_2647,U_2646] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2647),hAPP_nat_nat(plus_plus_nat(U_2647),U_2646))),
inference(variable_rename,[status(thm)],[f_1022_1]) ).
cnf(f_1022_3,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2647),hAPP_nat_nat(plus_plus_nat(U_2647),U_2646))),
inference(clausify,[status(thm)],[f_1022_2]) ).
fof(f_1023_1,plain,
! [Ma,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N))
| ! [K_2] : N != hAPP_nat_nat(plus_plus_nat(Ma),K_2) )
& ( ? [K_2] : N = hAPP_nat_nat(plus_plus_nat(Ma),K_2)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N)) ) ),
inference(fof_nnf,[status(thm)],[fact_997_le__iff__add]) ).
fof(f_1023_2,plain,
! [U_2651,U_2650] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2651),U_2650))
| ! [U_2649] : U_2650 != hAPP_nat_nat(plus_plus_nat(U_2651),U_2649) )
& ( ? [U_2648] : U_2650 = hAPP_nat_nat(plus_plus_nat(U_2651),U_2648)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2651),U_2650)) ) ),
inference(variable_rename,[status(thm)],[f_1023_1]) ).
fof(f_1023_3,plain,
( ! [U_2655,U_2653] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2655),U_2653))
| ! [U_2649] : U_2653 != hAPP_nat_nat(plus_plus_nat(U_2655),U_2649) )
& ! [U_2654,U_2652] :
( ? [U_2648] : U_2652 = hAPP_nat_nat(plus_plus_nat(U_2654),U_2648)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2654),U_2652)) ) ),
inference(miniscope,[status(thm)],[f_1023_2]) ).
fof(f_1023_4,plain,
( ! [U_2655,U_2653] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2655),U_2653))
| ! [U_2649] : U_2653 != hAPP_nat_nat(plus_plus_nat(U_2655),U_2649) )
& ! [U_2654,U_2652] :
( U_2652 = hAPP_nat_nat(plus_plus_nat(U_2654),sK14(U_2654,U_2652))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2654),U_2652)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_2648,sK14(U_2654,U_2652))],[f_1023_3]) ).
cnf(f_1023_5,plain,
( U_2652 = hAPP_nat_nat(plus_plus_nat(U_2654),sK14(U_2654,U_2652))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2654),U_2652)) ),
inference(clausify,[status(thm)],[f_1023_4]) ).
cnf(f_1023_6,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2655),U_2653))
| U_2653 != hAPP_nat_nat(plus_plus_nat(U_2655),U_2649) ),
inference(clausify,[status(thm)],[f_1023_4]) ).
fof(f_1024_1,plain,
! [K,Ma,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(K),Ma)),hAPP_nat_nat(plus_plus_nat(K),N)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(K),Ma)),hAPP_nat_nat(plus_plus_nat(K),N))) ) ),
inference(fof_nnf,[status(thm)],[fact_998_nat__add__left__cancel__le]) ).
fof(f_1024_2,plain,
! [U_2658,U_2657,U_2656] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2658),U_2657)),hAPP_nat_nat(plus_plus_nat(U_2658),U_2656)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2657),U_2656)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2657),U_2656))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2658),U_2657)),hAPP_nat_nat(plus_plus_nat(U_2658),U_2656))) ) ),
inference(variable_rename,[status(thm)],[f_1024_1]) ).
fof(f_1024_3,plain,
( ! [U_2664,U_2662,U_2660] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2664),U_2662)),hAPP_nat_nat(plus_plus_nat(U_2664),U_2660)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2662),U_2660)) )
& ! [U_2663,U_2661,U_2659] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2661),U_2659))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2663),U_2661)),hAPP_nat_nat(plus_plus_nat(U_2663),U_2659))) ) ),
inference(miniscope,[status(thm)],[f_1024_2]) ).
cnf(f_1024_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2661),U_2659))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2663),U_2661)),hAPP_nat_nat(plus_plus_nat(U_2663),U_2659))) ),
inference(clausify,[status(thm)],[f_1024_3]) ).
cnf(f_1024_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2664),U_2662)),hAPP_nat_nat(plus_plus_nat(U_2664),U_2660)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2662),U_2660)) ),
inference(clausify,[status(thm)],[f_1024_3]) ).
fof(f_1025_1,plain,
! [M,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(plus_plus_nat(J_1),M)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_999_trans__le__add1]) ).
fof(f_1025_2,plain,
! [U_2667,U_2666,U_2665] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2666),hAPP_nat_nat(plus_plus_nat(U_2665),U_2667)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2666),U_2665)) ),
inference(variable_rename,[status(thm)],[f_1025_1]) ).
cnf(f_1025_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2666),hAPP_nat_nat(plus_plus_nat(U_2665),U_2667)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2666),U_2665)) ),
inference(clausify,[status(thm)],[f_1025_2]) ).
fof(f_1026_1,plain,
! [M,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(plus_plus_nat(M),J_1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_1000_trans__le__add2]) ).
fof(f_1026_2,plain,
! [U_2670,U_2669,U_2668] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2669),hAPP_nat_nat(plus_plus_nat(U_2670),U_2668)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2669),U_2668)) ),
inference(variable_rename,[status(thm)],[f_1026_1]) ).
cnf(f_1026_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2669),hAPP_nat_nat(plus_plus_nat(U_2670),U_2668)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2669),U_2668)) ),
inference(clausify,[status(thm)],[f_1026_2]) ).
fof(f_1027_1,plain,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_1)),hAPP_nat_nat(plus_plus_nat(J_1),K_1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_1001_add__le__mono1]) ).
fof(f_1027_2,plain,
! [U_2673,U_2672,U_2671] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2672),U_2673)),hAPP_nat_nat(plus_plus_nat(U_2671),U_2673)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2672),U_2671)) ),
inference(variable_rename,[status(thm)],[f_1027_1]) ).
cnf(f_1027_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2672),U_2673)),hAPP_nat_nat(plus_plus_nat(U_2671),U_2673)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2672),U_2671)) ),
inference(clausify,[status(thm)],[f_1027_2]) ).
fof(f_1028_1,plain,
! [K_1,L,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I_1),K_1)),hAPP_nat_nat(plus_plus_nat(J_1),L)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),L))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_1002_add__le__mono]) ).
fof(f_1028_2,plain,
! [U_2677,U_2676,U_2675,U_2674] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2675),U_2677)),hAPP_nat_nat(plus_plus_nat(U_2674),U_2676)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2677),U_2676))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2675),U_2674)) ),
inference(variable_rename,[status(thm)],[f_1028_1]) ).
cnf(f_1028_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2675),U_2677)),hAPP_nat_nat(plus_plus_nat(U_2674),U_2676)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2677),U_2676))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2675),U_2674)) ),
inference(clausify,[status(thm)],[f_1028_2]) ).
fof(f_1029_1,plain,
! [M,K_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K_1)),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_1003_add__leD2]) ).
fof(f_1029_2,plain,
! [U_2680,U_2679,U_2678] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2679),U_2678))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2680),U_2679)),U_2678)) ),
inference(variable_rename,[status(thm)],[f_1029_1]) ).
cnf(f_1029_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2679),U_2678))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2680),U_2679)),U_2678)) ),
inference(clausify,[status(thm)],[f_1029_2]) ).
fof(f_1030_1,plain,
! [M,K_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K_1)),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_1004_add__leD1]) ).
fof(f_1030_2,plain,
! [U_2683,U_2682,U_2681] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2683),U_2681))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2683),U_2682)),U_2681)) ),
inference(variable_rename,[status(thm)],[f_1030_1]) ).
cnf(f_1030_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2683),U_2681))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2683),U_2682)),U_2681)) ),
inference(clausify,[status(thm)],[f_1030_2]) ).
fof(f_1031_1,plain,
! [M,K_1,N_1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(M),K_1)),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_1005_add__leE]) ).
fof(f_1031_2,plain,
! [U_2686,U_2685,U_2684] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2685),U_2684))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2686),U_2684)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2686),U_2685)),U_2684)) ),
inference(variable_rename,[status(thm)],[f_1031_1]) ).
cnf(f_1031_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2686),U_2684))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2686),U_2685)),U_2684)) ),
inference(clausify,[status(thm)],[f_1031_2]) ).
cnf(f_1031_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2685),U_2684))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2686),U_2685)),U_2684)) ),
inference(clausify,[status(thm)],[f_1031_2]) ).
fof(f_1032_1,plain,
! [I_1,K_1,J_1] :
( hAPP_nat_nat(minus_minus_nat(I_1),hAPP_nat_nat(minus_minus_nat(J_1),K_1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I_1),K_1)),J_1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_1006_diff__diff__right]) ).
fof(f_1032_2,plain,
! [U_2689,U_2688,U_2687] :
( hAPP_nat_nat(minus_minus_nat(U_2689),hAPP_nat_nat(minus_minus_nat(U_2687),U_2688)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2689),U_2688)),U_2687)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2688),U_2687)) ),
inference(variable_rename,[status(thm)],[f_1032_1]) ).
cnf(f_1032_3,plain,
( hAPP_nat_nat(minus_minus_nat(U_2689),hAPP_nat_nat(minus_minus_nat(U_2687),U_2688)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2689),U_2688)),U_2687)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2688),U_2687)) ),
inference(clausify,[status(thm)],[f_1032_2]) ).
fof(f_1033_1,plain,
! [J_2,K,I_2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(J_2),K)),I_2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),hAPP_nat_nat(plus_plus_nat(I_2),K))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),hAPP_nat_nat(plus_plus_nat(I_2),K)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(J_2),K)),I_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_1007_le__diff__conv]) ).
fof(f_1033_2,plain,
! [U_2692,U_2691,U_2690] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_2692),U_2691)),U_2690))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2692),hAPP_nat_nat(plus_plus_nat(U_2690),U_2691))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2692),hAPP_nat_nat(plus_plus_nat(U_2690),U_2691)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_2692),U_2691)),U_2690)) ) ),
inference(variable_rename,[status(thm)],[f_1033_1]) ).
fof(f_1033_3,plain,
( ! [U_2698,U_2696,U_2694] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_2698),U_2696)),U_2694))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2698),hAPP_nat_nat(plus_plus_nat(U_2694),U_2696))) )
& ! [U_2697,U_2695,U_2693] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2697),hAPP_nat_nat(plus_plus_nat(U_2693),U_2695)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_2697),U_2695)),U_2693)) ) ),
inference(miniscope,[status(thm)],[f_1033_2]) ).
cnf(f_1033_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2697),hAPP_nat_nat(plus_plus_nat(U_2693),U_2695)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_2697),U_2695)),U_2693)) ),
inference(clausify,[status(thm)],[f_1033_3]) ).
cnf(f_1033_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_2698),U_2696)),U_2694))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2698),hAPP_nat_nat(plus_plus_nat(U_2694),U_2696))) ),
inference(clausify,[status(thm)],[f_1033_3]) ).
fof(f_1034_1,plain,
! [M,K_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(N_1),M)),K_1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_1008_le__add__diff]) ).
fof(f_1034_2,plain,
! [U_2701,U_2700,U_2699] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2701),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2699),U_2701)),U_2700)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2700),U_2699)) ),
inference(variable_rename,[status(thm)],[f_1034_1]) ).
cnf(f_1034_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2701),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2699),U_2701)),U_2700)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2700),U_2699)) ),
inference(clausify,[status(thm)],[f_1034_2]) ).
fof(f_1035_1,plain,
! [N_1,M] :
( hAPP_nat_nat(plus_plus_nat(N_1),hAPP_nat_nat(minus_minus_nat(M),N_1)) = M
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M)) ),
inference(fof_nnf,[status(thm)],[fact_1009_le__add__diff__inverse]) ).
fof(f_1035_2,plain,
! [U_2703,U_2702] :
( hAPP_nat_nat(plus_plus_nat(U_2703),hAPP_nat_nat(minus_minus_nat(U_2702),U_2703)) = U_2702
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2703),U_2702)) ),
inference(variable_rename,[status(thm)],[f_1035_1]) ).
cnf(f_1035_3,plain,
( hAPP_nat_nat(plus_plus_nat(U_2703),hAPP_nat_nat(minus_minus_nat(U_2702),U_2703)) = U_2702
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2703),U_2702)) ),
inference(clausify,[status(thm)],[f_1035_2]) ).
fof(f_1036_1,plain,
! [I_1,K_1,J_1] :
( hAPP_nat_nat(plus_plus_nat(I_1),hAPP_nat_nat(minus_minus_nat(J_1),K_1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I_1),J_1)),K_1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_1010_add__diff__assoc]) ).
fof(f_1036_2,plain,
! [U_2706,U_2705,U_2704] :
( hAPP_nat_nat(plus_plus_nat(U_2706),hAPP_nat_nat(minus_minus_nat(U_2704),U_2705)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2706),U_2704)),U_2705)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2705),U_2704)) ),
inference(variable_rename,[status(thm)],[f_1036_1]) ).
cnf(f_1036_3,plain,
( hAPP_nat_nat(plus_plus_nat(U_2706),hAPP_nat_nat(minus_minus_nat(U_2704),U_2705)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2706),U_2704)),U_2705)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2705),U_2704)) ),
inference(clausify,[status(thm)],[f_1036_2]) ).
fof(f_1037_1,plain,
! [I_2,K,J_2] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(minus_minus_nat(J_2),K)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I_2),K)),J_2)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(I_2),K)),J_2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(minus_minus_nat(J_2),K))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_2)) ),
inference(fof_nnf,[status(thm)],[fact_1011_le__diff__conv2]) ).
fof(f_1037_2,plain,
! [U_2709,U_2708,U_2707] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2709),hAPP_nat_nat(minus_minus_nat(U_2707),U_2708)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2709),U_2708)),U_2707)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2709),U_2708)),U_2707))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2709),hAPP_nat_nat(minus_minus_nat(U_2707),U_2708))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2708),U_2707)) ),
inference(variable_rename,[status(thm)],[f_1037_1]) ).
cnf(f_1037_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2709),U_2708)),U_2707))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2709),hAPP_nat_nat(minus_minus_nat(U_2707),U_2708)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2708),U_2707)) ),
inference(clausify,[status(thm)],[f_1037_2]) ).
cnf(f_1037_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2709),hAPP_nat_nat(minus_minus_nat(U_2707),U_2708)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(U_2709),U_2708)),U_2707))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2708),U_2707)) ),
inference(clausify,[status(thm)],[f_1037_2]) ).
fof(f_1038_1,plain,
! [N_1,M] :
( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(M),N_1)),N_1) = M
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M)) ),
inference(fof_nnf,[status(thm)],[fact_1012_le__add__diff__inverse2]) ).
fof(f_1038_2,plain,
! [U_2711,U_2710] :
( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(U_2710),U_2711)),U_2711) = U_2710
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2711),U_2710)) ),
inference(variable_rename,[status(thm)],[f_1038_1]) ).
cnf(f_1038_3,plain,
( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(U_2710),U_2711)),U_2711) = U_2710
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2711),U_2710)) ),
inference(clausify,[status(thm)],[f_1038_2]) ).
fof(f_1039_1,plain,
! [K,I_2,J_2] :
( ( ( hAPP_nat_nat(minus_minus_nat(J_2),I_2) = K
| J_2 != hAPP_nat_nat(plus_plus_nat(K),I_2) )
& ( J_2 = hAPP_nat_nat(plus_plus_nat(K),I_2)
| hAPP_nat_nat(minus_minus_nat(J_2),I_2) != K ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2)) ),
inference(fof_nnf,[status(thm)],[fact_1013_le__imp__diff__is__add]) ).
fof(f_1039_2,plain,
! [U_2714,U_2713,U_2712] :
( ( ( hAPP_nat_nat(minus_minus_nat(U_2712),U_2713) = U_2714
| U_2712 != hAPP_nat_nat(plus_plus_nat(U_2714),U_2713) )
& ( U_2712 = hAPP_nat_nat(plus_plus_nat(U_2714),U_2713)
| hAPP_nat_nat(minus_minus_nat(U_2712),U_2713) != U_2714 ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2713),U_2712)) ),
inference(variable_rename,[status(thm)],[f_1039_1]) ).
cnf(f_1039_3,plain,
( U_2712 = hAPP_nat_nat(plus_plus_nat(U_2714),U_2713)
| hAPP_nat_nat(minus_minus_nat(U_2712),U_2713) != U_2714
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2713),U_2712)) ),
inference(clausify,[status(thm)],[f_1039_2]) ).
cnf(f_1039_4,plain,
( hAPP_nat_nat(minus_minus_nat(U_2712),U_2713) = U_2714
| U_2712 != hAPP_nat_nat(plus_plus_nat(U_2714),U_2713)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2713),U_2712)) ),
inference(clausify,[status(thm)],[f_1039_2]) ).
fof(f_1040_1,plain,
! [I_1,K_1,J_1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(I_1),J_1)),K_1) = hAPP_nat_nat(plus_plus_nat(I_1),hAPP_nat_nat(minus_minus_nat(J_1),K_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_1014_diff__add__assoc]) ).
fof(f_1040_2,plain,
! [U_2717,U_2716,U_2715] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2717),U_2715)),U_2716) = hAPP_nat_nat(plus_plus_nat(U_2717),hAPP_nat_nat(minus_minus_nat(U_2715),U_2716))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2716),U_2715)) ),
inference(variable_rename,[status(thm)],[f_1040_1]) ).
cnf(f_1040_3,plain,
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2717),U_2715)),U_2716) = hAPP_nat_nat(plus_plus_nat(U_2717),hAPP_nat_nat(minus_minus_nat(U_2715),U_2716))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2716),U_2715)) ),
inference(clausify,[status(thm)],[f_1040_2]) ).
fof(f_1041_1,plain,
! [I_1,K_1,J_1] :
( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(J_1),K_1)),I_1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(J_1),I_1)),K_1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_1015_add__diff__assoc2]) ).
fof(f_1041_2,plain,
! [U_2720,U_2719,U_2718] :
( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(U_2718),U_2719)),U_2720) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2718),U_2720)),U_2719)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2719),U_2718)) ),
inference(variable_rename,[status(thm)],[f_1041_1]) ).
cnf(f_1041_3,plain,
( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(U_2718),U_2719)),U_2720) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2718),U_2720)),U_2719)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2719),U_2718)) ),
inference(clausify,[status(thm)],[f_1041_2]) ).
fof(f_1042_1,plain,
! [I_1,K_1,J_1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(J_1),I_1)),K_1) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(J_1),K_1)),I_1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_1016_diff__add__assoc2]) ).
fof(f_1042_2,plain,
! [U_2723,U_2722,U_2721] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2721),U_2723)),U_2722) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(U_2721),U_2722)),U_2723)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2722),U_2721)) ),
inference(variable_rename,[status(thm)],[f_1042_1]) ).
cnf(f_1042_3,plain,
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(U_2721),U_2723)),U_2722) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(U_2721),U_2722)),U_2723)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2722),U_2721)) ),
inference(clausify,[status(thm)],[f_1042_2]) ).
fof(f_1043_1,plain,
! [M,N_1,K_1] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(M),N_1)),K_1) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(M),K_1)),hAPP_nat_nat(times_times_nat(N_1),K_1)),
inference(fof_nnf,[status(thm)],[fact_1017_add__mult__distrib]) ).
fof(f_1043_2,plain,
! [U_2726,U_2725,U_2724] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_2726),U_2725)),U_2724) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2726),U_2724)),hAPP_nat_nat(times_times_nat(U_2725),U_2724)),
inference(variable_rename,[status(thm)],[f_1043_1]) ).
cnf(f_1043_3,plain,
hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_2726),U_2725)),U_2724) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2726),U_2724)),hAPP_nat_nat(times_times_nat(U_2725),U_2724)),
inference(clausify,[status(thm)],[f_1043_2]) ).
fof(f_1044_1,plain,
! [K_1,M,N_1] : hAPP_nat_nat(times_times_nat(K_1),hAPP_nat_nat(plus_plus_nat(M),N_1)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(K_1),M)),hAPP_nat_nat(times_times_nat(K_1),N_1)),
inference(fof_nnf,[status(thm)],[fact_1018_add__mult__distrib2]) ).
fof(f_1044_2,plain,
! [U_2729,U_2728,U_2727] : hAPP_nat_nat(times_times_nat(U_2729),hAPP_nat_nat(plus_plus_nat(U_2728),U_2727)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2729),U_2728)),hAPP_nat_nat(times_times_nat(U_2729),U_2727)),
inference(variable_rename,[status(thm)],[f_1044_1]) ).
cnf(f_1044_3,plain,
hAPP_nat_nat(times_times_nat(U_2729),hAPP_nat_nat(plus_plus_nat(U_2728),U_2727)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2729),U_2728)),hAPP_nat_nat(times_times_nat(U_2729),U_2727)),
inference(clausify,[status(thm)],[f_1044_2]) ).
fof(f_1045_1,plain,
! [Ma] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Ma),one_one_nat))
| Ma != one_one_nat )
& ( Ma = one_one_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Ma),one_one_nat)) ) ),
inference(fof_nnf,[status(thm)],[fact_1019_nat__dvd__1__iff__1]) ).
fof(f_1045_2,plain,
! [U_2730] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2730),one_one_nat))
| U_2730 != one_one_nat )
& ( U_2730 = one_one_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2730),one_one_nat)) ) ),
inference(variable_rename,[status(thm)],[f_1045_1]) ).
fof(f_1045_3,plain,
( ! [U_2732] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2732),one_one_nat))
| U_2732 != one_one_nat )
& ! [U_2731] :
( U_2731 = one_one_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2731),one_one_nat)) ) ),
inference(miniscope,[status(thm)],[f_1045_2]) ).
cnf(f_1045_4,plain,
( U_2731 = one_one_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2731),one_one_nat)) ),
inference(clausify,[status(thm)],[f_1045_3]) ).
cnf(f_1045_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2732),one_one_nat))
| U_2732 != one_one_nat ),
inference(clausify,[status(thm)],[f_1045_3]) ).
fof(f_1046_1,plain,
! [K_1,L,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(I_1),K_1)),hAPP_nat_nat(times_times_nat(J_1),L)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),L))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_1020_mult__le__mono]) ).
fof(f_1046_2,plain,
! [U_2736,U_2735,U_2734,U_2733] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2734),U_2736)),hAPP_nat_nat(times_times_nat(U_2733),U_2735)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2736),U_2735))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2734),U_2733)) ),
inference(variable_rename,[status(thm)],[f_1046_1]) ).
cnf(f_1046_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2734),U_2736)),hAPP_nat_nat(times_times_nat(U_2733),U_2735)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2736),U_2735))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2734),U_2733)) ),
inference(clausify,[status(thm)],[f_1046_2]) ).
fof(f_1047_1,plain,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K_1),I_1)),hAPP_nat_nat(times_times_nat(K_1),J_1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_1021_mult__le__mono2]) ).
fof(f_1047_2,plain,
! [U_2739,U_2738,U_2737] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2739),U_2738)),hAPP_nat_nat(times_times_nat(U_2739),U_2737)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2738),U_2737)) ),
inference(variable_rename,[status(thm)],[f_1047_1]) ).
cnf(f_1047_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2739),U_2738)),hAPP_nat_nat(times_times_nat(U_2739),U_2737)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2738),U_2737)) ),
inference(clausify,[status(thm)],[f_1047_2]) ).
fof(f_1048_1,plain,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(I_1),K_1)),hAPP_nat_nat(times_times_nat(J_1),K_1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_1022_mult__le__mono1]) ).
fof(f_1048_2,plain,
! [U_2742,U_2741,U_2740] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2741),U_2742)),hAPP_nat_nat(times_times_nat(U_2740),U_2742)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2741),U_2740)) ),
inference(variable_rename,[status(thm)],[f_1048_1]) ).
cnf(f_1048_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2741),U_2742)),hAPP_nat_nat(times_times_nat(U_2740),U_2742)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2741),U_2740)) ),
inference(clausify,[status(thm)],[f_1048_2]) ).
fof(f_1049_1,plain,
! [M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(times_times_nat(M),hAPP_nat_nat(times_times_nat(M),M)))),
inference(fof_nnf,[status(thm)],[fact_1023_le__cube]) ).
fof(f_1049_2,plain,
! [U_2743] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2743),hAPP_nat_nat(times_times_nat(U_2743),hAPP_nat_nat(times_times_nat(U_2743),U_2743)))),
inference(variable_rename,[status(thm)],[f_1049_1]) ).
cnf(f_1049_3,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2743),hAPP_nat_nat(times_times_nat(U_2743),hAPP_nat_nat(times_times_nat(U_2743),U_2743)))),
inference(clausify,[status(thm)],[f_1049_2]) ).
fof(f_1050_1,plain,
! [M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(times_times_nat(M),M))),
inference(fof_nnf,[status(thm)],[fact_1024_le__square]) ).
fof(f_1050_2,plain,
! [U_2744] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2744),hAPP_nat_nat(times_times_nat(U_2744),U_2744))),
inference(variable_rename,[status(thm)],[f_1050_1]) ).
cnf(f_1050_3,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2744),hAPP_nat_nat(times_times_nat(U_2744),U_2744))),
inference(clausify,[status(thm)],[f_1050_2]) ).
fof(f_1051_1,plain,
! [Ma,N] :
( ( hAPP_nat_nat(times_times_nat(Ma),N) = one_one_nat
| N != one_one_nat
| Ma != one_one_nat )
& ( ( N = one_one_nat
& Ma = one_one_nat )
| hAPP_nat_nat(times_times_nat(Ma),N) != one_one_nat ) ),
inference(fof_nnf,[status(thm)],[fact_1025_nat__mult__eq__1__iff]) ).
fof(f_1051_2,plain,
! [U_2746,U_2745] :
( ( hAPP_nat_nat(times_times_nat(U_2746),U_2745) = one_one_nat
| U_2745 != one_one_nat
| U_2746 != one_one_nat )
& ( ( U_2745 = one_one_nat
& U_2746 = one_one_nat )
| hAPP_nat_nat(times_times_nat(U_2746),U_2745) != one_one_nat ) ),
inference(variable_rename,[status(thm)],[f_1051_1]) ).
fof(f_1051_3,plain,
( ! [U_2750,U_2748] :
( hAPP_nat_nat(times_times_nat(U_2750),U_2748) = one_one_nat
| U_2748 != one_one_nat
| U_2750 != one_one_nat )
& ! [U_2749,U_2747] :
( ( U_2747 = one_one_nat
& U_2749 = one_one_nat )
| hAPP_nat_nat(times_times_nat(U_2749),U_2747) != one_one_nat ) ),
inference(miniscope,[status(thm)],[f_1051_2]) ).
cnf(f_1051_4,plain,
( U_2749 = one_one_nat
| hAPP_nat_nat(times_times_nat(U_2749),U_2747) != one_one_nat ),
inference(clausify,[status(thm)],[f_1051_3]) ).
cnf(f_1051_5,plain,
( U_2747 = one_one_nat
| hAPP_nat_nat(times_times_nat(U_2749),U_2747) != one_one_nat ),
inference(clausify,[status(thm)],[f_1051_3]) ).
cnf(f_1051_6,plain,
( hAPP_nat_nat(times_times_nat(U_2750),U_2748) = one_one_nat
| U_2748 != one_one_nat
| U_2750 != one_one_nat ),
inference(clausify,[status(thm)],[f_1051_3]) ).
fof(f_1052_1,plain,
! [N_1] : hAPP_nat_nat(times_times_nat(N_1),one_one_nat) = N_1,
inference(fof_nnf,[status(thm)],[fact_1026_nat__mult__1__right]) ).
fof(f_1052_2,plain,
! [U_2751] : hAPP_nat_nat(times_times_nat(U_2751),one_one_nat) = U_2751,
inference(variable_rename,[status(thm)],[f_1052_1]) ).
cnf(f_1052_3,plain,
hAPP_nat_nat(times_times_nat(U_2751),one_one_nat) = U_2751,
inference(clausify,[status(thm)],[f_1052_2]) ).
fof(f_1053_1,plain,
! [Ma,N] :
( ( one_one_nat = hAPP_nat_nat(times_times_nat(Ma),N)
| N != one_one_nat
| Ma != one_one_nat )
& ( ( N = one_one_nat
& Ma = one_one_nat )
| one_one_nat != hAPP_nat_nat(times_times_nat(Ma),N) ) ),
inference(fof_nnf,[status(thm)],[fact_1027_nat__1__eq__mult__iff]) ).
fof(f_1053_2,plain,
! [U_2753,U_2752] :
( ( one_one_nat = hAPP_nat_nat(times_times_nat(U_2753),U_2752)
| U_2752 != one_one_nat
| U_2753 != one_one_nat )
& ( ( U_2752 = one_one_nat
& U_2753 = one_one_nat )
| one_one_nat != hAPP_nat_nat(times_times_nat(U_2753),U_2752) ) ),
inference(variable_rename,[status(thm)],[f_1053_1]) ).
fof(f_1053_3,plain,
( ! [U_2757,U_2755] :
( one_one_nat = hAPP_nat_nat(times_times_nat(U_2757),U_2755)
| U_2755 != one_one_nat
| U_2757 != one_one_nat )
& ! [U_2756,U_2754] :
( ( U_2754 = one_one_nat
& U_2756 = one_one_nat )
| one_one_nat != hAPP_nat_nat(times_times_nat(U_2756),U_2754) ) ),
inference(miniscope,[status(thm)],[f_1053_2]) ).
cnf(f_1053_4,plain,
( U_2756 = one_one_nat
| one_one_nat != hAPP_nat_nat(times_times_nat(U_2756),U_2754) ),
inference(clausify,[status(thm)],[f_1053_3]) ).
cnf(f_1053_5,plain,
( U_2754 = one_one_nat
| one_one_nat != hAPP_nat_nat(times_times_nat(U_2756),U_2754) ),
inference(clausify,[status(thm)],[f_1053_3]) ).
cnf(f_1053_6,plain,
( one_one_nat = hAPP_nat_nat(times_times_nat(U_2757),U_2755)
| U_2755 != one_one_nat
| U_2757 != one_one_nat ),
inference(clausify,[status(thm)],[f_1053_3]) ).
fof(f_1054_1,plain,
! [N_1] : hAPP_nat_nat(times_times_nat(one_one_nat),N_1) = N_1,
inference(fof_nnf,[status(thm)],[fact_1028_nat__mult__1]) ).
fof(f_1054_2,plain,
! [U_2758] : hAPP_nat_nat(times_times_nat(one_one_nat),U_2758) = U_2758,
inference(variable_rename,[status(thm)],[f_1054_1]) ).
cnf(f_1054_3,plain,
hAPP_nat_nat(times_times_nat(one_one_nat),U_2758) = U_2758,
inference(clausify,[status(thm)],[f_1054_2]) ).
fof(f_1055_1,plain,
! [N_1,M] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,N_1),M))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) ),
inference(fof_nnf,[status(thm)],[fact_1029_nat__dvd__not__less]) ).
fof(f_1055_2,plain,
! [U_2760,U_2759] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2760),U_2759))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2759),U_2760))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2759)) ),
inference(variable_rename,[status(thm)],[f_1055_1]) ).
cnf(f_1055_3,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2760),U_2759))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2759),U_2760))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2759)) ),
inference(clausify,[status(thm)],[f_1055_2]) ).
fof(f_1056_1,plain,
! [Ma,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(Ma),N)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Ma)) ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Ma))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(Ma),N))) ) ),
inference(fof_nnf,[status(thm)],[fact_1030_add__gr__0]) ).
fof(f_1056_2,plain,
! [U_2762,U_2761] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(U_2762),U_2761)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2761))
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2762)) ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2761))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2762))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(U_2762),U_2761))) ) ),
inference(variable_rename,[status(thm)],[f_1056_1]) ).
fof(f_1056_3,plain,
( ! [U_2766,U_2764] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(U_2766),U_2764)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2764))
& ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2766)) ) )
& ! [U_2765,U_2763] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2763))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2765))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(U_2765),U_2763))) ) ),
inference(miniscope,[status(thm)],[f_1056_2]) ).
cnf(f_1056_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2763))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2765))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(U_2765),U_2763))) ),
inference(clausify,[status(thm)],[f_1056_3]) ).
cnf(f_1056_5,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2766))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(U_2766),U_2764))) ),
inference(clausify,[status(thm)],[f_1056_3]) ).
cnf(f_1056_6,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2764))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(plus_plus_nat(U_2766),U_2764))) ),
inference(clausify,[status(thm)],[f_1056_3]) ).
fof(f_1057_1,plain,
! [P_2,A_2,B_2] :
( ( hBOOL(hAPP_nat_bool(P_2,hAPP_nat_nat(minus_minus_nat(A_2),B_2)))
| ? [D_2] :
( ~ hBOOL(hAPP_nat_bool(P_2,D_2))
& A_2 = hAPP_nat_nat(plus_plus_nat(B_2),D_2) )
| ( ~ hBOOL(hAPP_nat_bool(P_2,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_2)) ) )
& ( ( ! [D_2] :
( hBOOL(hAPP_nat_bool(P_2,D_2))
| A_2 != hAPP_nat_nat(plus_plus_nat(B_2),D_2) )
& ( hBOOL(hAPP_nat_bool(P_2,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_2)) ) )
| ~ hBOOL(hAPP_nat_bool(P_2,hAPP_nat_nat(minus_minus_nat(A_2),B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_1031_nat__diff__split]) ).
fof(f_1057_2,plain,
! [U_2771,U_2770,U_2769] :
( ( hBOOL(hAPP_nat_bool(U_2771,hAPP_nat_nat(minus_minus_nat(U_2770),U_2769)))
| ? [U_2768] :
( ~ hBOOL(hAPP_nat_bool(U_2771,U_2768))
& U_2770 = hAPP_nat_nat(plus_plus_nat(U_2769),U_2768) )
| ( ~ hBOOL(hAPP_nat_bool(U_2771,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2770),U_2769)) ) )
& ( ( ! [U_2767] :
( hBOOL(hAPP_nat_bool(U_2771,U_2767))
| U_2770 != hAPP_nat_nat(plus_plus_nat(U_2769),U_2767) )
& ( hBOOL(hAPP_nat_bool(U_2771,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2770),U_2769)) ) )
| ~ hBOOL(hAPP_nat_bool(U_2771,hAPP_nat_nat(minus_minus_nat(U_2770),U_2769))) ) ),
inference(variable_rename,[status(thm)],[f_1057_1]) ).
fof(f_1057_3,plain,
( ! [U_2777,U_2775,U_2773] :
( hBOOL(hAPP_nat_bool(U_2777,hAPP_nat_nat(minus_minus_nat(U_2775),U_2773)))
| ? [U_2768] :
( ~ hBOOL(hAPP_nat_bool(U_2777,U_2768))
& U_2775 = hAPP_nat_nat(plus_plus_nat(U_2773),U_2768) )
| ( ~ hBOOL(hAPP_nat_bool(U_2777,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2775),U_2773)) ) )
& ! [U_2776,U_2774,U_2772] :
( ( ! [U_2767] :
( hBOOL(hAPP_nat_bool(U_2776,U_2767))
| U_2774 != hAPP_nat_nat(plus_plus_nat(U_2772),U_2767) )
& ( hBOOL(hAPP_nat_bool(U_2776,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2774),U_2772)) ) )
| ~ hBOOL(hAPP_nat_bool(U_2776,hAPP_nat_nat(minus_minus_nat(U_2774),U_2772))) ) ),
inference(miniscope,[status(thm)],[f_1057_2]) ).
fof(f_1057_4,plain,
( ! [U_2777,U_2775,U_2773] :
( hBOOL(hAPP_nat_bool(U_2777,hAPP_nat_nat(minus_minus_nat(U_2775),U_2773)))
| ( ~ hBOOL(hAPP_nat_bool(U_2777,sK15(U_2777,U_2775,U_2773)))
& U_2775 = hAPP_nat_nat(plus_plus_nat(U_2773),sK15(U_2777,U_2775,U_2773)) )
| ( ~ hBOOL(hAPP_nat_bool(U_2777,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2775),U_2773)) ) )
& ! [U_2776,U_2774,U_2772] :
( ( ! [U_2767] :
( hBOOL(hAPP_nat_bool(U_2776,U_2767))
| U_2774 != hAPP_nat_nat(plus_plus_nat(U_2772),U_2767) )
& ( hBOOL(hAPP_nat_bool(U_2776,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2774),U_2772)) ) )
| ~ hBOOL(hAPP_nat_bool(U_2776,hAPP_nat_nat(minus_minus_nat(U_2774),U_2772))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_2768,sK15(U_2777,U_2775,U_2773))],[f_1057_3]) ).
cnf(f_1057_5,plain,
( hBOOL(hAPP_nat_bool(U_2776,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2774),U_2772))
| ~ hBOOL(hAPP_nat_bool(U_2776,hAPP_nat_nat(minus_minus_nat(U_2774),U_2772))) ),
inference(clausify,[status(thm)],[f_1057_4]) ).
cnf(f_1057_6,plain,
( hBOOL(hAPP_nat_bool(U_2776,U_2767))
| U_2774 != hAPP_nat_nat(plus_plus_nat(U_2772),U_2767)
| ~ hBOOL(hAPP_nat_bool(U_2776,hAPP_nat_nat(minus_minus_nat(U_2774),U_2772))) ),
inference(clausify,[status(thm)],[f_1057_4]) ).
cnf(f_1057_7,plain,
( U_2775 = hAPP_nat_nat(plus_plus_nat(U_2773),sK15(U_2777,U_2775,U_2773))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2775),U_2773))
| hBOOL(hAPP_nat_bool(U_2777,hAPP_nat_nat(minus_minus_nat(U_2775),U_2773))) ),
inference(clausify,[status(thm)],[f_1057_4]) ).
cnf(f_1057_8,plain,
( ~ hBOOL(hAPP_nat_bool(U_2777,sK15(U_2777,U_2775,U_2773)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2775),U_2773))
| hBOOL(hAPP_nat_bool(U_2777,hAPP_nat_nat(minus_minus_nat(U_2775),U_2773))) ),
inference(clausify,[status(thm)],[f_1057_4]) ).
cnf(f_1057_9,plain,
( U_2775 = hAPP_nat_nat(plus_plus_nat(U_2773),sK15(U_2777,U_2775,U_2773))
| ~ hBOOL(hAPP_nat_bool(U_2777,zero_zero_nat))
| hBOOL(hAPP_nat_bool(U_2777,hAPP_nat_nat(minus_minus_nat(U_2775),U_2773))) ),
inference(clausify,[status(thm)],[f_1057_4]) ).
cnf(f_1057_10,plain,
( ~ hBOOL(hAPP_nat_bool(U_2777,sK15(U_2777,U_2775,U_2773)))
| ~ hBOOL(hAPP_nat_bool(U_2777,zero_zero_nat))
| hBOOL(hAPP_nat_bool(U_2777,hAPP_nat_nat(minus_minus_nat(U_2775),U_2773))) ),
inference(clausify,[status(thm)],[f_1057_4]) ).
fof(f_1058_1,plain,
! [P_2,A_2,B_2] :
( ( hBOOL(hAPP_nat_bool(P_2,hAPP_nat_nat(minus_minus_nat(A_2),B_2)))
| ? [D_2] :
( ~ hBOOL(hAPP_nat_bool(P_2,D_2))
& A_2 = hAPP_nat_nat(plus_plus_nat(B_2),D_2) )
| ( ~ hBOOL(hAPP_nat_bool(P_2,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_2)) ) )
& ( ( ! [D_2] :
( hBOOL(hAPP_nat_bool(P_2,D_2))
| A_2 != hAPP_nat_nat(plus_plus_nat(B_2),D_2) )
& ( hBOOL(hAPP_nat_bool(P_2,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_2)) ) )
| ~ hBOOL(hAPP_nat_bool(P_2,hAPP_nat_nat(minus_minus_nat(A_2),B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_1032_nat__diff__split__asm]) ).
fof(f_1058_2,plain,
! [U_2782,U_2781,U_2780] :
( ( hBOOL(hAPP_nat_bool(U_2782,hAPP_nat_nat(minus_minus_nat(U_2781),U_2780)))
| ? [U_2779] :
( ~ hBOOL(hAPP_nat_bool(U_2782,U_2779))
& U_2781 = hAPP_nat_nat(plus_plus_nat(U_2780),U_2779) )
| ( ~ hBOOL(hAPP_nat_bool(U_2782,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2781),U_2780)) ) )
& ( ( ! [U_2778] :
( hBOOL(hAPP_nat_bool(U_2782,U_2778))
| U_2781 != hAPP_nat_nat(plus_plus_nat(U_2780),U_2778) )
& ( hBOOL(hAPP_nat_bool(U_2782,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2781),U_2780)) ) )
| ~ hBOOL(hAPP_nat_bool(U_2782,hAPP_nat_nat(minus_minus_nat(U_2781),U_2780))) ) ),
inference(variable_rename,[status(thm)],[f_1058_1]) ).
fof(f_1058_3,plain,
( ! [U_2788,U_2786,U_2784] :
( hBOOL(hAPP_nat_bool(U_2788,hAPP_nat_nat(minus_minus_nat(U_2786),U_2784)))
| ? [U_2779] :
( ~ hBOOL(hAPP_nat_bool(U_2788,U_2779))
& U_2786 = hAPP_nat_nat(plus_plus_nat(U_2784),U_2779) )
| ( ~ hBOOL(hAPP_nat_bool(U_2788,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2786),U_2784)) ) )
& ! [U_2787,U_2785,U_2783] :
( ( ! [U_2778] :
( hBOOL(hAPP_nat_bool(U_2787,U_2778))
| U_2785 != hAPP_nat_nat(plus_plus_nat(U_2783),U_2778) )
& ( hBOOL(hAPP_nat_bool(U_2787,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2785),U_2783)) ) )
| ~ hBOOL(hAPP_nat_bool(U_2787,hAPP_nat_nat(minus_minus_nat(U_2785),U_2783))) ) ),
inference(miniscope,[status(thm)],[f_1058_2]) ).
fof(f_1058_4,plain,
( ! [U_2788,U_2786,U_2784] :
( hBOOL(hAPP_nat_bool(U_2788,hAPP_nat_nat(minus_minus_nat(U_2786),U_2784)))
| ( ~ hBOOL(hAPP_nat_bool(U_2788,sK16(U_2788,U_2786,U_2784)))
& U_2786 = hAPP_nat_nat(plus_plus_nat(U_2784),sK16(U_2788,U_2786,U_2784)) )
| ( ~ hBOOL(hAPP_nat_bool(U_2788,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2786),U_2784)) ) )
& ! [U_2787,U_2785,U_2783] :
( ( ! [U_2778] :
( hBOOL(hAPP_nat_bool(U_2787,U_2778))
| U_2785 != hAPP_nat_nat(plus_plus_nat(U_2783),U_2778) )
& ( hBOOL(hAPP_nat_bool(U_2787,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2785),U_2783)) ) )
| ~ hBOOL(hAPP_nat_bool(U_2787,hAPP_nat_nat(minus_minus_nat(U_2785),U_2783))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_2779,sK16(U_2788,U_2786,U_2784))],[f_1058_3]) ).
cnf(f_1058_5,plain,
( hBOOL(hAPP_nat_bool(U_2787,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2785),U_2783))
| ~ hBOOL(hAPP_nat_bool(U_2787,hAPP_nat_nat(minus_minus_nat(U_2785),U_2783))) ),
inference(clausify,[status(thm)],[f_1058_4]) ).
cnf(f_1058_6,plain,
( hBOOL(hAPP_nat_bool(U_2787,U_2778))
| U_2785 != hAPP_nat_nat(plus_plus_nat(U_2783),U_2778)
| ~ hBOOL(hAPP_nat_bool(U_2787,hAPP_nat_nat(minus_minus_nat(U_2785),U_2783))) ),
inference(clausify,[status(thm)],[f_1058_4]) ).
cnf(f_1058_7,plain,
( U_2786 = hAPP_nat_nat(plus_plus_nat(U_2784),sK16(U_2788,U_2786,U_2784))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2786),U_2784))
| hBOOL(hAPP_nat_bool(U_2788,hAPP_nat_nat(minus_minus_nat(U_2786),U_2784))) ),
inference(clausify,[status(thm)],[f_1058_4]) ).
cnf(f_1058_8,plain,
( ~ hBOOL(hAPP_nat_bool(U_2788,sK16(U_2788,U_2786,U_2784)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2786),U_2784))
| hBOOL(hAPP_nat_bool(U_2788,hAPP_nat_nat(minus_minus_nat(U_2786),U_2784))) ),
inference(clausify,[status(thm)],[f_1058_4]) ).
cnf(f_1058_9,plain,
( U_2786 = hAPP_nat_nat(plus_plus_nat(U_2784),sK16(U_2788,U_2786,U_2784))
| ~ hBOOL(hAPP_nat_bool(U_2788,zero_zero_nat))
| hBOOL(hAPP_nat_bool(U_2788,hAPP_nat_nat(minus_minus_nat(U_2786),U_2784))) ),
inference(clausify,[status(thm)],[f_1058_4]) ).
cnf(f_1058_10,plain,
( ~ hBOOL(hAPP_nat_bool(U_2788,sK16(U_2788,U_2786,U_2784)))
| ~ hBOOL(hAPP_nat_bool(U_2788,zero_zero_nat))
| hBOOL(hAPP_nat_bool(U_2788,hAPP_nat_nat(minus_minus_nat(U_2786),U_2784))) ),
inference(clausify,[status(thm)],[f_1058_4]) ).
fof(f_1059_1,plain,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K_1),I_1)),hAPP_nat_nat(times_times_nat(K_1),J_1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_1033_mult__less__mono2]) ).
fof(f_1059_2,plain,
! [U_2791,U_2790,U_2789] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2791),U_2790)),hAPP_nat_nat(times_times_nat(U_2791),U_2789)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2791))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2790),U_2789)) ),
inference(variable_rename,[status(thm)],[f_1059_1]) ).
cnf(f_1059_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2791),U_2790)),hAPP_nat_nat(times_times_nat(U_2791),U_2789)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2791))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2790),U_2789)) ),
inference(clausify,[status(thm)],[f_1059_2]) ).
fof(f_1060_1,plain,
! [K_1,I_1,J_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(I_1),K_1)),hAPP_nat_nat(times_times_nat(J_1),K_1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_1034_mult__less__mono1]) ).
fof(f_1060_2,plain,
! [U_2794,U_2793,U_2792] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2793),U_2794)),hAPP_nat_nat(times_times_nat(U_2792),U_2794)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2794))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2793),U_2792)) ),
inference(variable_rename,[status(thm)],[f_1060_1]) ).
cnf(f_1060_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2793),U_2794)),hAPP_nat_nat(times_times_nat(U_2792),U_2794)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2794))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2793),U_2792)) ),
inference(clausify,[status(thm)],[f_1060_2]) ).
fof(f_1061_1,plain,
! [Ma,K,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(Ma),K)),hAPP_nat_nat(times_times_nat(N),K)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) )
& ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(Ma),K)),hAPP_nat_nat(times_times_nat(N),K))) ) ),
inference(fof_nnf,[status(thm)],[fact_1035_mult__less__cancel2]) ).
fof(f_1061_2,plain,
! [U_2797,U_2796,U_2795] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2797),U_2796)),hAPP_nat_nat(times_times_nat(U_2795),U_2796)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2797),U_2795))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2796)) )
& ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2797),U_2795))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2796)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2797),U_2796)),hAPP_nat_nat(times_times_nat(U_2795),U_2796))) ) ),
inference(variable_rename,[status(thm)],[f_1061_1]) ).
fof(f_1061_3,plain,
( ! [U_2803,U_2801,U_2799] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2803),U_2801)),hAPP_nat_nat(times_times_nat(U_2799),U_2801)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2803),U_2799))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2801)) )
& ! [U_2802,U_2800,U_2798] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2802),U_2798))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2800)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2802),U_2800)),hAPP_nat_nat(times_times_nat(U_2798),U_2800))) ) ),
inference(miniscope,[status(thm)],[f_1061_2]) ).
cnf(f_1061_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2800))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2802),U_2800)),hAPP_nat_nat(times_times_nat(U_2798),U_2800))) ),
inference(clausify,[status(thm)],[f_1061_3]) ).
cnf(f_1061_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2802),U_2798))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2802),U_2800)),hAPP_nat_nat(times_times_nat(U_2798),U_2800))) ),
inference(clausify,[status(thm)],[f_1061_3]) ).
cnf(f_1061_6,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2803),U_2801)),hAPP_nat_nat(times_times_nat(U_2799),U_2801)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2803),U_2799))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2801)) ),
inference(clausify,[status(thm)],[f_1061_3]) ).
fof(f_1062_1,plain,
! [K,Ma,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K),Ma)),hAPP_nat_nat(times_times_nat(K),N)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) )
& ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K),Ma)),hAPP_nat_nat(times_times_nat(K),N))) ) ),
inference(fof_nnf,[status(thm)],[fact_1036_mult__less__cancel1]) ).
fof(f_1062_2,plain,
! [U_2806,U_2805,U_2804] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2806),U_2805)),hAPP_nat_nat(times_times_nat(U_2806),U_2804)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2805),U_2804))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2806)) )
& ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2805),U_2804))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2806)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2806),U_2805)),hAPP_nat_nat(times_times_nat(U_2806),U_2804))) ) ),
inference(variable_rename,[status(thm)],[f_1062_1]) ).
fof(f_1062_3,plain,
( ! [U_2812,U_2810,U_2808] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2812),U_2810)),hAPP_nat_nat(times_times_nat(U_2812),U_2808)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2810),U_2808))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2812)) )
& ! [U_2811,U_2809,U_2807] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2809),U_2807))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2811)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2811),U_2809)),hAPP_nat_nat(times_times_nat(U_2811),U_2807))) ) ),
inference(miniscope,[status(thm)],[f_1062_2]) ).
cnf(f_1062_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2811))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2811),U_2809)),hAPP_nat_nat(times_times_nat(U_2811),U_2807))) ),
inference(clausify,[status(thm)],[f_1062_3]) ).
cnf(f_1062_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2809),U_2807))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2811),U_2809)),hAPP_nat_nat(times_times_nat(U_2811),U_2807))) ),
inference(clausify,[status(thm)],[f_1062_3]) ).
cnf(f_1062_6,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2812),U_2810)),hAPP_nat_nat(times_times_nat(U_2812),U_2808)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2810),U_2808))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2812)) ),
inference(clausify,[status(thm)],[f_1062_3]) ).
fof(f_1063_1,plain,
! [Ma,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(Ma),N)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Ma)) )
& ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Ma)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(Ma),N))) ) ),
inference(fof_nnf,[status(thm)],[fact_1037_nat__0__less__mult__iff]) ).
fof(f_1063_2,plain,
! [U_2814,U_2813] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_2814),U_2813)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2813))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2814)) )
& ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2813))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2814)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_2814),U_2813))) ) ),
inference(variable_rename,[status(thm)],[f_1063_1]) ).
fof(f_1063_3,plain,
( ! [U_2818,U_2816] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_2818),U_2816)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2816))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2818)) )
& ! [U_2817,U_2815] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2815))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2817)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_2817),U_2815))) ) ),
inference(miniscope,[status(thm)],[f_1063_2]) ).
cnf(f_1063_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2817))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_2817),U_2815))) ),
inference(clausify,[status(thm)],[f_1063_3]) ).
cnf(f_1063_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2815))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_2817),U_2815))) ),
inference(clausify,[status(thm)],[f_1063_3]) ).
cnf(f_1063_6,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(U_2818),U_2816)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2816))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2818)) ),
inference(clausify,[status(thm)],[f_1063_3]) ).
fof(f_1064_1,plain,
! [M,N_1] :
( M = zero_zero_nat
| N_1 = one_one_nat
| M != hAPP_nat_nat(times_times_nat(M),N_1) ),
inference(fof_nnf,[status(thm)],[fact_1038_mult__eq__self__implies__10]) ).
fof(f_1064_2,plain,
! [U_2820,U_2819] :
( U_2820 = zero_zero_nat
| U_2819 = one_one_nat
| U_2820 != hAPP_nat_nat(times_times_nat(U_2820),U_2819) ),
inference(variable_rename,[status(thm)],[f_1064_1]) ).
cnf(f_1064_3,plain,
( U_2820 = zero_zero_nat
| U_2819 = one_one_nat
| U_2820 != hAPP_nat_nat(times_times_nat(U_2820),U_2819) ),
inference(clausify,[status(thm)],[f_1064_2]) ).
fof(f_1065_1,plain,
! [K_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,K_1),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_1039_dvd__imp__le]) ).
fof(f_1065_2,plain,
! [U_2822,U_2821] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2822),U_2821))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2821))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2822),U_2821)) ),
inference(variable_rename,[status(thm)],[f_1065_1]) ).
cnf(f_1065_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2822),U_2821))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2821))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2822),U_2821)) ),
inference(clausify,[status(thm)],[f_1065_2]) ).
fof(f_1066_1,plain,
! [K_1,M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M),N_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(K_1),M)),hAPP_nat_nat(times_times_nat(K_1),N_1))) ),
inference(fof_nnf,[status(thm)],[fact_1040_dvd__mult__cancel]) ).
fof(f_1066_2,plain,
! [U_2825,U_2824,U_2823] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2824),U_2823))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2825))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2825),U_2824)),hAPP_nat_nat(times_times_nat(U_2825),U_2823))) ),
inference(variable_rename,[status(thm)],[f_1066_1]) ).
cnf(f_1066_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2824),U_2823))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2825))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2825),U_2824)),hAPP_nat_nat(times_times_nat(U_2825),U_2823))) ),
inference(clausify,[status(thm)],[f_1066_2]) ).
fof(f_1067_1,plain,
! [K,Ma,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K),Ma)),hAPP_nat_nat(times_times_nat(K),N)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K),Ma)),hAPP_nat_nat(times_times_nat(K),N))) ) ),
inference(fof_nnf,[status(thm)],[fact_1041_mult__le__cancel1]) ).
fof(f_1067_2,plain,
! [U_2828,U_2827,U_2826] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2828),U_2827)),hAPP_nat_nat(times_times_nat(U_2828),U_2826)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2827),U_2826))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2828)) ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2827),U_2826))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2828))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2828),U_2827)),hAPP_nat_nat(times_times_nat(U_2828),U_2826))) ) ),
inference(variable_rename,[status(thm)],[f_1067_1]) ).
fof(f_1067_3,plain,
( ! [U_2834,U_2832,U_2830] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2834),U_2832)),hAPP_nat_nat(times_times_nat(U_2834),U_2830)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2832),U_2830))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2834)) ) )
& ! [U_2833,U_2831,U_2829] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2831),U_2829))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2833))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2833),U_2831)),hAPP_nat_nat(times_times_nat(U_2833),U_2829))) ) ),
inference(miniscope,[status(thm)],[f_1067_2]) ).
cnf(f_1067_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2831),U_2829))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2833))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2833),U_2831)),hAPP_nat_nat(times_times_nat(U_2833),U_2829))) ),
inference(clausify,[status(thm)],[f_1067_3]) ).
cnf(f_1067_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2834))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2834),U_2832)),hAPP_nat_nat(times_times_nat(U_2834),U_2830))) ),
inference(clausify,[status(thm)],[f_1067_3]) ).
cnf(f_1067_6,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2832),U_2830))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2834),U_2832)),hAPP_nat_nat(times_times_nat(U_2834),U_2830))) ),
inference(clausify,[status(thm)],[f_1067_3]) ).
fof(f_1068_1,plain,
! [Ma,K,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(Ma),K)),hAPP_nat_nat(times_times_nat(N),K)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(Ma),K)),hAPP_nat_nat(times_times_nat(N),K))) ) ),
inference(fof_nnf,[status(thm)],[fact_1042_mult__le__cancel2]) ).
fof(f_1068_2,plain,
! [U_2837,U_2836,U_2835] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2837),U_2836)),hAPP_nat_nat(times_times_nat(U_2835),U_2836)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2837),U_2835))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2836)) ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2837),U_2835))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2836))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2837),U_2836)),hAPP_nat_nat(times_times_nat(U_2835),U_2836))) ) ),
inference(variable_rename,[status(thm)],[f_1068_1]) ).
fof(f_1068_3,plain,
( ! [U_2843,U_2841,U_2839] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2843),U_2841)),hAPP_nat_nat(times_times_nat(U_2839),U_2841)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2843),U_2839))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2841)) ) )
& ! [U_2842,U_2840,U_2838] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2842),U_2838))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2840))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2842),U_2840)),hAPP_nat_nat(times_times_nat(U_2838),U_2840))) ) ),
inference(miniscope,[status(thm)],[f_1068_2]) ).
cnf(f_1068_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2842),U_2838))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2840))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2842),U_2840)),hAPP_nat_nat(times_times_nat(U_2838),U_2840))) ),
inference(clausify,[status(thm)],[f_1068_3]) ).
cnf(f_1068_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2841))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2843),U_2841)),hAPP_nat_nat(times_times_nat(U_2839),U_2841))) ),
inference(clausify,[status(thm)],[f_1068_3]) ).
cnf(f_1068_6,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2843),U_2839))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2843),U_2841)),hAPP_nat_nat(times_times_nat(U_2839),U_2841))) ),
inference(clausify,[status(thm)],[f_1068_3]) ).
fof(f_1069_1,plain,
! [N,P_2] :
( ? [K_2] :
( hBOOL(hAPP_nat_bool(P_2,hAPP_nat_nat(plus_plus_nat(K_2),one_one_nat)))
& ! [I] :
( ~ hBOOL(hAPP_nat_bool(P_2,I))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K_2)) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),N)) )
| ~ hBOOL(hAPP_nat_bool(P_2,N))
| hBOOL(hAPP_nat_bool(P_2,zero_zero_nat)) ),
inference(fof_nnf,[status(thm)],[fact_1043_ex__least__nat__less]) ).
fof(f_1069_2,plain,
! [U_2847,U_2846] :
( ? [U_2845] :
( hBOOL(hAPP_nat_bool(U_2846,hAPP_nat_nat(plus_plus_nat(U_2845),one_one_nat)))
& ! [U_2844] :
( ~ hBOOL(hAPP_nat_bool(U_2846,U_2844))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2844),U_2845)) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2845),U_2847)) )
| ~ hBOOL(hAPP_nat_bool(U_2846,U_2847))
| hBOOL(hAPP_nat_bool(U_2846,zero_zero_nat)) ),
inference(variable_rename,[status(thm)],[f_1069_1]) ).
fof(f_1069_3,plain,
! [U_2847,U_2846] :
( ( hBOOL(hAPP_nat_bool(U_2846,hAPP_nat_nat(plus_plus_nat(sK17(U_2847,U_2846)),one_one_nat)))
& ! [U_2844] :
( ~ hBOOL(hAPP_nat_bool(U_2846,U_2844))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2844),sK17(U_2847,U_2846))) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK17(U_2847,U_2846)),U_2847)) )
| ~ hBOOL(hAPP_nat_bool(U_2846,U_2847))
| hBOOL(hAPP_nat_bool(U_2846,zero_zero_nat)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_2845,sK17(U_2847,U_2846))],[f_1069_2]) ).
cnf(f_1069_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK17(U_2847,U_2846)),U_2847))
| ~ hBOOL(hAPP_nat_bool(U_2846,U_2847))
| hBOOL(hAPP_nat_bool(U_2846,zero_zero_nat)) ),
inference(clausify,[status(thm)],[f_1069_3]) ).
cnf(f_1069_5,plain,
( ~ hBOOL(hAPP_nat_bool(U_2846,U_2844))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2844),sK17(U_2847,U_2846)))
| ~ hBOOL(hAPP_nat_bool(U_2846,U_2847))
| hBOOL(hAPP_nat_bool(U_2846,zero_zero_nat)) ),
inference(clausify,[status(thm)],[f_1069_3]) ).
cnf(f_1069_6,plain,
( hBOOL(hAPP_nat_bool(U_2846,hAPP_nat_nat(plus_plus_nat(sK17(U_2847,U_2846)),one_one_nat)))
| ~ hBOOL(hAPP_nat_bool(U_2846,U_2847))
| hBOOL(hAPP_nat_bool(U_2846,zero_zero_nat)) ),
inference(clausify,[status(thm)],[f_1069_3]) ).
fof(f_1070_1,plain,
! [U,Ma,N,I_2,J_2] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_2),U)),Ma)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(J_2),I_2)),U)),N))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(J_2),I_2)),U)),N)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_2),U)),Ma)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2)) ),
inference(fof_nnf,[status(thm)],[fact_1044_nat__less__add__iff2]) ).
fof(f_1070_2,plain,
! [U_2852,U_2851,U_2850,U_2849,U_2848] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2849),U_2852)),U_2851)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2848),U_2852)),U_2850)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2851),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2848),U_2849)),U_2852)),U_2850))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2851),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2848),U_2849)),U_2852)),U_2850)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2849),U_2852)),U_2851)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2848),U_2852)),U_2850))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2849),U_2848)) ),
inference(variable_rename,[status(thm)],[f_1070_1]) ).
cnf(f_1070_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2851),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2848),U_2849)),U_2852)),U_2850)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2849),U_2852)),U_2851)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2848),U_2852)),U_2850)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2849),U_2848)) ),
inference(clausify,[status(thm)],[f_1070_2]) ).
cnf(f_1070_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2849),U_2852)),U_2851)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2848),U_2852)),U_2850)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2851),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2848),U_2849)),U_2852)),U_2850)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2849),U_2848)) ),
inference(clausify,[status(thm)],[f_1070_2]) ).
fof(f_1071_1,plain,
! [K,Ma,N] :
( ( hAPP_nat_nat(times_times_nat(K),Ma) = hAPP_nat_nat(times_times_nat(K),N)
| ( Ma != N
& K != zero_zero_nat ) )
& ( Ma = N
| K = zero_zero_nat
| hAPP_nat_nat(times_times_nat(K),Ma) != hAPP_nat_nat(times_times_nat(K),N) ) ),
inference(fof_nnf,[status(thm)],[fact_1045_nat__mult__eq__cancel__disj]) ).
fof(f_1071_2,plain,
! [U_2855,U_2854,U_2853] :
( ( hAPP_nat_nat(times_times_nat(U_2855),U_2854) = hAPP_nat_nat(times_times_nat(U_2855),U_2853)
| ( U_2854 != U_2853
& U_2855 != zero_zero_nat ) )
& ( U_2854 = U_2853
| U_2855 = zero_zero_nat
| hAPP_nat_nat(times_times_nat(U_2855),U_2854) != hAPP_nat_nat(times_times_nat(U_2855),U_2853) ) ),
inference(variable_rename,[status(thm)],[f_1071_1]) ).
fof(f_1071_3,plain,
( ! [U_2861,U_2859,U_2857] :
( hAPP_nat_nat(times_times_nat(U_2861),U_2859) = hAPP_nat_nat(times_times_nat(U_2861),U_2857)
| ( U_2859 != U_2857
& U_2861 != zero_zero_nat ) )
& ! [U_2860,U_2858,U_2856] :
( U_2858 = U_2856
| U_2860 = zero_zero_nat
| hAPP_nat_nat(times_times_nat(U_2860),U_2858) != hAPP_nat_nat(times_times_nat(U_2860),U_2856) ) ),
inference(miniscope,[status(thm)],[f_1071_2]) ).
cnf(f_1071_4,plain,
( U_2858 = U_2856
| U_2860 = zero_zero_nat
| hAPP_nat_nat(times_times_nat(U_2860),U_2858) != hAPP_nat_nat(times_times_nat(U_2860),U_2856) ),
inference(clausify,[status(thm)],[f_1071_3]) ).
cnf(f_1071_5,plain,
( U_2861 != zero_zero_nat
| hAPP_nat_nat(times_times_nat(U_2861),U_2859) = hAPP_nat_nat(times_times_nat(U_2861),U_2857) ),
inference(clausify,[status(thm)],[f_1071_3]) ).
cnf(f_1071_6,plain,
( U_2859 != U_2857
| hAPP_nat_nat(times_times_nat(U_2861),U_2859) = hAPP_nat_nat(times_times_nat(U_2861),U_2857) ),
inference(clausify,[status(thm)],[f_1071_3]) ).
fof(f_1072_1,plain,
! [I_1,U_1,J_1,K_1] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_1),U_1)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_1),U_1)),K_1)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(I_1),J_1)),U_1)),K_1),
inference(fof_nnf,[status(thm)],[fact_1046_left__add__mult__distrib]) ).
fof(f_1072_2,plain,
! [U_2865,U_2864,U_2863,U_2862] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2865),U_2864)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2863),U_2864)),U_2862)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_2865),U_2863)),U_2864)),U_2862),
inference(variable_rename,[status(thm)],[f_1072_1]) ).
cnf(f_1072_3,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2865),U_2864)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2863),U_2864)),U_2862)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(plus_plus_nat(U_2865),U_2863)),U_2864)),U_2862),
inference(clausify,[status(thm)],[f_1072_2]) ).
fof(f_1073_1,plain,
! [Ma,N,K] :
( ( ( hAPP_nat_nat(times_times_nat(K),Ma) = hAPP_nat_nat(times_times_nat(K),N)
| Ma != N )
& ( Ma = N
| hAPP_nat_nat(times_times_nat(K),Ma) != hAPP_nat_nat(times_times_nat(K),N) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ),
inference(fof_nnf,[status(thm)],[fact_1047_nat__mult__eq__cancel1]) ).
fof(f_1073_2,plain,
! [U_2868,U_2867,U_2866] :
( ( ( hAPP_nat_nat(times_times_nat(U_2866),U_2868) = hAPP_nat_nat(times_times_nat(U_2866),U_2867)
| U_2868 != U_2867 )
& ( U_2868 = U_2867
| hAPP_nat_nat(times_times_nat(U_2866),U_2868) != hAPP_nat_nat(times_times_nat(U_2866),U_2867) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2866)) ),
inference(variable_rename,[status(thm)],[f_1073_1]) ).
cnf(f_1073_3,plain,
( U_2868 = U_2867
| hAPP_nat_nat(times_times_nat(U_2866),U_2868) != hAPP_nat_nat(times_times_nat(U_2866),U_2867)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2866)) ),
inference(clausify,[status(thm)],[f_1073_2]) ).
cnf(f_1073_4,plain,
( hAPP_nat_nat(times_times_nat(U_2866),U_2868) = hAPP_nat_nat(times_times_nat(U_2866),U_2867)
| U_2868 != U_2867
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2866)) ),
inference(clausify,[status(thm)],[f_1073_2]) ).
fof(f_1074_1,plain,
! [Ma,N,K] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K),Ma)),hAPP_nat_nat(times_times_nat(K),N)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ma),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K),Ma)),hAPP_nat_nat(times_times_nat(K),N))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ),
inference(fof_nnf,[status(thm)],[fact_1048_nat__mult__less__cancel1]) ).
fof(f_1074_2,plain,
! [U_2871,U_2870,U_2869] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2869),U_2871)),hAPP_nat_nat(times_times_nat(U_2869),U_2870)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2871),U_2870)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2871),U_2870))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2869),U_2871)),hAPP_nat_nat(times_times_nat(U_2869),U_2870))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2869)) ),
inference(variable_rename,[status(thm)],[f_1074_1]) ).
cnf(f_1074_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2871),U_2870))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2869),U_2871)),hAPP_nat_nat(times_times_nat(U_2869),U_2870)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2869)) ),
inference(clausify,[status(thm)],[f_1074_2]) ).
cnf(f_1074_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(U_2869),U_2871)),hAPP_nat_nat(times_times_nat(U_2869),U_2870)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2871),U_2870))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2869)) ),
inference(clausify,[status(thm)],[f_1074_2]) ).
fof(f_1075_1,plain,
! [K,Ma,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(K),Ma)),hAPP_nat_nat(times_times_nat(K),N)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Ma),N))
& K != zero_zero_nat ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Ma),N))
| K = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(K),Ma)),hAPP_nat_nat(times_times_nat(K),N))) ) ),
inference(fof_nnf,[status(thm)],[fact_1049_nat__mult__dvd__cancel__disj]) ).
fof(f_1075_2,plain,
! [U_2874,U_2873,U_2872] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2874),U_2873)),hAPP_nat_nat(times_times_nat(U_2874),U_2872)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2873),U_2872))
& U_2874 != zero_zero_nat ) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2873),U_2872))
| U_2874 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2874),U_2873)),hAPP_nat_nat(times_times_nat(U_2874),U_2872))) ) ),
inference(variable_rename,[status(thm)],[f_1075_1]) ).
fof(f_1075_3,plain,
( ! [U_2880,U_2878,U_2876] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2880),U_2878)),hAPP_nat_nat(times_times_nat(U_2880),U_2876)))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2878),U_2876))
& U_2880 != zero_zero_nat ) )
& ! [U_2879,U_2877,U_2875] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2877),U_2875))
| U_2879 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2879),U_2877)),hAPP_nat_nat(times_times_nat(U_2879),U_2875))) ) ),
inference(miniscope,[status(thm)],[f_1075_2]) ).
cnf(f_1075_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2877),U_2875))
| U_2879 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2879),U_2877)),hAPP_nat_nat(times_times_nat(U_2879),U_2875))) ),
inference(clausify,[status(thm)],[f_1075_3]) ).
cnf(f_1075_5,plain,
( U_2880 != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2880),U_2878)),hAPP_nat_nat(times_times_nat(U_2880),U_2876))) ),
inference(clausify,[status(thm)],[f_1075_3]) ).
cnf(f_1075_6,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2878),U_2876))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2880),U_2878)),hAPP_nat_nat(times_times_nat(U_2880),U_2876))) ),
inference(clausify,[status(thm)],[f_1075_3]) ).
fof(f_1076_1,plain,
! [Ma,N,K] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(K),Ma)),hAPP_nat_nat(times_times_nat(K),N)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Ma),N)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,Ma),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(K),Ma)),hAPP_nat_nat(times_times_nat(K),N))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ),
inference(fof_nnf,[status(thm)],[fact_1050_nat__mult__dvd__cancel1]) ).
fof(f_1076_2,plain,
! [U_2883,U_2882,U_2881] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2881),U_2883)),hAPP_nat_nat(times_times_nat(U_2881),U_2882)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2883),U_2882)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2883),U_2882))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2881),U_2883)),hAPP_nat_nat(times_times_nat(U_2881),U_2882))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2881)) ),
inference(variable_rename,[status(thm)],[f_1076_1]) ).
cnf(f_1076_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2883),U_2882))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2881),U_2883)),hAPP_nat_nat(times_times_nat(U_2881),U_2882)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2881)) ),
inference(clausify,[status(thm)],[f_1076_2]) ).
cnf(f_1076_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(times_times_nat(U_2881),U_2883)),hAPP_nat_nat(times_times_nat(U_2881),U_2882)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_2883),U_2882))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2881)) ),
inference(clausify,[status(thm)],[f_1076_2]) ).
fof(f_1077_1,plain,
! [Ma,N,K] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K),Ma)),hAPP_nat_nat(times_times_nat(K),N)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K),Ma)),hAPP_nat_nat(times_times_nat(K),N))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ),
inference(fof_nnf,[status(thm)],[fact_1051_nat__mult__le__cancel1]) ).
fof(f_1077_2,plain,
! [U_2886,U_2885,U_2884] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2884),U_2886)),hAPP_nat_nat(times_times_nat(U_2884),U_2885)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2886),U_2885)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2886),U_2885))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2884),U_2886)),hAPP_nat_nat(times_times_nat(U_2884),U_2885))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2884)) ),
inference(variable_rename,[status(thm)],[f_1077_1]) ).
cnf(f_1077_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2886),U_2885))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2884),U_2886)),hAPP_nat_nat(times_times_nat(U_2884),U_2885)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2884)) ),
inference(clausify,[status(thm)],[f_1077_2]) ).
cnf(f_1077_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(U_2884),U_2886)),hAPP_nat_nat(times_times_nat(U_2884),U_2885)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2886),U_2885))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_2884)) ),
inference(clausify,[status(thm)],[f_1077_2]) ).
fof(f_1078_1,plain,
! [U,Ma,N,J_2,I_2] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_2),U)),Ma)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N)))
| ~ 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(I_2),J_2)),U)),Ma)),N)) )
& ( 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(I_2),J_2)),U)),Ma)),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_2),U)),Ma)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I_2)) ),
inference(fof_nnf,[status(thm)],[fact_1052_nat__le__add__iff1]) ).
fof(f_1078_2,plain,
! [U_2891,U_2890,U_2889,U_2888,U_2887] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2887),U_2891)),U_2890)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2888),U_2891)),U_2889)))
| ~ 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(U_2887),U_2888)),U_2891)),U_2890)),U_2889)) )
& ( 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(U_2887),U_2888)),U_2891)),U_2890)),U_2889))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2887),U_2891)),U_2890)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2888),U_2891)),U_2889))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2888),U_2887)) ),
inference(variable_rename,[status(thm)],[f_1078_1]) ).
cnf(f_1078_3,plain,
( 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(U_2887),U_2888)),U_2891)),U_2890)),U_2889))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2887),U_2891)),U_2890)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2888),U_2891)),U_2889)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2888),U_2887)) ),
inference(clausify,[status(thm)],[f_1078_2]) ).
cnf(f_1078_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2887),U_2891)),U_2890)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2888),U_2891)),U_2889)))
| ~ 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(U_2887),U_2888)),U_2891)),U_2890)),U_2889))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2888),U_2887)) ),
inference(clausify,[status(thm)],[f_1078_2]) ).
fof(f_1079_1,plain,
! [U_1,M,N_1,J_1,I_1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_1),U_1)),M)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_1),U_1)),N_1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(I_1),J_1)),U_1)),M)),N_1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),I_1)) ),
inference(fof_nnf,[status(thm)],[fact_1053_nat__diff__add__eq1]) ).
fof(f_1079_2,plain,
! [U_2896,U_2895,U_2894,U_2893,U_2892] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2892),U_2896)),U_2895)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2893),U_2896)),U_2894)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2892),U_2893)),U_2896)),U_2895)),U_2894)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2893),U_2892)) ),
inference(variable_rename,[status(thm)],[f_1079_1]) ).
cnf(f_1079_3,plain,
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2892),U_2896)),U_2895)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2893),U_2896)),U_2894)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2892),U_2893)),U_2896)),U_2895)),U_2894)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2893),U_2892)) ),
inference(clausify,[status(thm)],[f_1079_2]) ).
fof(f_1080_1,plain,
! [U,Ma,N,J_2,I_2] :
( ( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_2),U)),Ma) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N)
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(I_2),J_2)),U)),Ma) != N )
& ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(I_2),J_2)),U)),Ma) = N
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_2),U)),Ma) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I_2)) ),
inference(fof_nnf,[status(thm)],[fact_1054_nat__eq__add__iff1]) ).
fof(f_1080_2,plain,
! [U_2901,U_2900,U_2899,U_2898,U_2897] :
( ( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2897),U_2901)),U_2900) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2898),U_2901)),U_2899)
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2897),U_2898)),U_2901)),U_2900) != U_2899 )
& ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2897),U_2898)),U_2901)),U_2900) = U_2899
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2897),U_2901)),U_2900) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2898),U_2901)),U_2899) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2898),U_2897)) ),
inference(variable_rename,[status(thm)],[f_1080_1]) ).
cnf(f_1080_3,plain,
( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2897),U_2898)),U_2901)),U_2900) = U_2899
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2897),U_2901)),U_2900) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2898),U_2901)),U_2899)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2898),U_2897)) ),
inference(clausify,[status(thm)],[f_1080_2]) ).
cnf(f_1080_4,plain,
( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2897),U_2901)),U_2900) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2898),U_2901)),U_2899)
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2897),U_2898)),U_2901)),U_2900) != U_2899
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2898),U_2897)) ),
inference(clausify,[status(thm)],[f_1080_2]) ).
fof(f_1081_1,plain,
! [U,Ma,N,I_2,J_2] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_2),U)),Ma)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(J_2),I_2)),U)),N))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ma),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(J_2),I_2)),U)),N)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_2),U)),Ma)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2)) ),
inference(fof_nnf,[status(thm)],[fact_1055_nat__le__add__iff2]) ).
fof(f_1081_2,plain,
! [U_2906,U_2905,U_2904,U_2903,U_2902] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2903),U_2906)),U_2905)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2902),U_2906)),U_2904)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2905),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2902),U_2903)),U_2906)),U_2904))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2905),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2902),U_2903)),U_2906)),U_2904)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2903),U_2906)),U_2905)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2902),U_2906)),U_2904))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2903),U_2902)) ),
inference(variable_rename,[status(thm)],[f_1081_1]) ).
cnf(f_1081_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2905),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2902),U_2903)),U_2906)),U_2904)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2903),U_2906)),U_2905)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2902),U_2906)),U_2904)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2903),U_2902)) ),
inference(clausify,[status(thm)],[f_1081_2]) ).
cnf(f_1081_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2903),U_2906)),U_2905)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2902),U_2906)),U_2904)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2905),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2902),U_2903)),U_2906)),U_2904)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2903),U_2902)) ),
inference(clausify,[status(thm)],[f_1081_2]) ).
fof(f_1082_1,plain,
! [U_1,M,N_1,I_1,J_1] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_1),U_1)),M)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_1),U_1)),N_1)) = hAPP_nat_nat(minus_minus_nat(M),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(J_1),I_1)),U_1)),N_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_1056_nat__diff__add__eq2]) ).
fof(f_1082_2,plain,
! [U_2911,U_2910,U_2909,U_2908,U_2907] :
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2908),U_2911)),U_2910)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2907),U_2911)),U_2909)) = hAPP_nat_nat(minus_minus_nat(U_2910),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2907),U_2908)),U_2911)),U_2909))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2908),U_2907)) ),
inference(variable_rename,[status(thm)],[f_1082_1]) ).
cnf(f_1082_3,plain,
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2908),U_2911)),U_2910)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2907),U_2911)),U_2909)) = hAPP_nat_nat(minus_minus_nat(U_2910),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2907),U_2908)),U_2911)),U_2909))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2908),U_2907)) ),
inference(clausify,[status(thm)],[f_1082_2]) ).
fof(f_1083_1,plain,
! [U,Ma,N,I_2,J_2] :
( ( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_2),U)),Ma) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N)
| Ma != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(J_2),I_2)),U)),N) )
& ( Ma = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(J_2),I_2)),U)),N)
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_2),U)),Ma) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_2)) ),
inference(fof_nnf,[status(thm)],[fact_1057_nat__eq__add__iff2]) ).
fof(f_1083_2,plain,
! [U_2916,U_2915,U_2914,U_2913,U_2912] :
( ( ( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2913),U_2916)),U_2915) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2912),U_2916)),U_2914)
| U_2915 != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2912),U_2913)),U_2916)),U_2914) )
& ( U_2915 = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2912),U_2913)),U_2916)),U_2914)
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2913),U_2916)),U_2915) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2912),U_2916)),U_2914) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2913),U_2912)) ),
inference(variable_rename,[status(thm)],[f_1083_1]) ).
cnf(f_1083_3,plain,
( U_2915 = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2912),U_2913)),U_2916)),U_2914)
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2913),U_2916)),U_2915) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2912),U_2916)),U_2914)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2913),U_2912)) ),
inference(clausify,[status(thm)],[f_1083_2]) ).
cnf(f_1083_4,plain,
( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2913),U_2916)),U_2915) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2912),U_2916)),U_2914)
| U_2915 != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(hAPP_nat_nat(minus_minus_nat(U_2912),U_2913)),U_2916)),U_2914)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2913),U_2912)) ),
inference(clausify,[status(thm)],[f_1083_2]) ).
fof(f_1084_1,plain,
! [U,Ma,N,J_2,I_2] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_2),U)),Ma)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N)))
| ~ 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(I_2),J_2)),U)),Ma)),N)) )
& ( 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(I_2),J_2)),U)),Ma)),N))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(I_2),U)),Ma)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(J_2),U)),N))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),I_2)) ),
inference(fof_nnf,[status(thm)],[fact_1058_nat__less__add__iff1]) ).
fof(f_1084_2,plain,
! [U_2921,U_2920,U_2919,U_2918,U_2917] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2917),U_2921)),U_2920)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2918),U_2921)),U_2919)))
| ~ 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(U_2917),U_2918)),U_2921)),U_2920)),U_2919)) )
& ( 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(U_2917),U_2918)),U_2921)),U_2920)),U_2919))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2917),U_2921)),U_2920)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2918),U_2921)),U_2919))) ) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2918),U_2917)) ),
inference(variable_rename,[status(thm)],[f_1084_1]) ).
cnf(f_1084_3,plain,
( 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(U_2917),U_2918)),U_2921)),U_2920)),U_2919))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2917),U_2921)),U_2920)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2918),U_2921)),U_2919)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2918),U_2917)) ),
inference(clausify,[status(thm)],[f_1084_2]) ).
cnf(f_1084_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2917),U_2921)),U_2920)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_2918),U_2921)),U_2919)))
| ~ 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(U_2917),U_2918)),U_2921)),U_2920)),U_2919))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2918),U_2917)) ),
inference(clausify,[status(thm)],[f_1084_2]) ).
fof(f_1085_1,plain,
! [N_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(N_1))))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(N_1)))) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(N_1))) ),
inference(fof_nnf,[status(thm)],[fact_1059_number__of1]) ).
fof(f_1085_2,plain,
! [U_2922] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(U_2922))))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(U_2922)))) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(U_2922))) ),
inference(variable_rename,[status(thm)],[f_1085_1]) ).
cnf(f_1085_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(U_2922))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(U_2922))) ),
inference(clausify,[status(thm)],[f_1085_2]) ).
cnf(f_1085_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(U_2922))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(U_2922))) ),
inference(clausify,[status(thm)],[f_1085_2]) ).
fof(f_1086_1,plain,
! [X_2] :
( ( ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X_2))
| ! [A_3,B_3] :
( twoSqu1241645765sum2sq(product_Pair_int_int(A_3,B_3)) != X_2
| ~ is_int(B_3)
| ~ is_int(A_3) ) )
& ( ? [A_3,B_3] :
( twoSqu1241645765sum2sq(product_Pair_int_int(A_3,B_3)) = X_2
& is_int(B_3)
& is_int(A_3) )
| ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,X_2)) ) )
| ~ is_int(X_2) ),
inference(fof_nnf,[status(thm)],[fact_1060_is__sum2sq__def]) ).
fof(f_1086_2,plain,
! [U_2927] :
( ( ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,U_2927))
| ! [U_2926,U_2925] :
( twoSqu1241645765sum2sq(product_Pair_int_int(U_2926,U_2925)) != U_2927
| ~ is_int(U_2925)
| ~ is_int(U_2926) ) )
& ( ? [U_2924,U_2923] :
( twoSqu1241645765sum2sq(product_Pair_int_int(U_2924,U_2923)) = U_2927
& is_int(U_2923)
& is_int(U_2924) )
| ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,U_2927)) ) )
| ~ is_int(U_2927) ),
inference(variable_rename,[status(thm)],[f_1086_1]) ).
fof(f_1086_3,plain,
! [U_2927] :
( ( ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,U_2927))
| ! [U_2926] :
( ! [U_2925] :
( twoSqu1241645765sum2sq(product_Pair_int_int(U_2926,U_2925)) != U_2927
| ~ is_int(U_2925) )
| ~ is_int(U_2926) ) )
& ( ? [U_2924] :
( ? [U_2923] :
( twoSqu1241645765sum2sq(product_Pair_int_int(U_2924,U_2923)) = U_2927
& is_int(U_2923) )
& is_int(U_2924) )
| ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,U_2927)) ) )
| ~ is_int(U_2927) ),
inference(miniscope,[status(thm)],[f_1086_2]) ).
fof(f_1086_4,plain,
! [U_2927] :
( ( ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,U_2927))
| ! [U_2926] :
( ! [U_2925] :
( twoSqu1241645765sum2sq(product_Pair_int_int(U_2926,U_2925)) != U_2927
| ~ is_int(U_2925) )
| ~ is_int(U_2926) ) )
& ( ( ? [U_2923] :
( twoSqu1241645765sum2sq(product_Pair_int_int(sK18(U_2927),U_2923)) = U_2927
& is_int(U_2923) )
& is_int(sK18(U_2927)) )
| ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,U_2927)) ) )
| ~ is_int(U_2927) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_2924,sK18(U_2927))],[f_1086_3]) ).
fof(f_1086_5,plain,
! [U_2927] :
( ( ( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,U_2927))
| ! [U_2926] :
( ! [U_2925] :
( twoSqu1241645765sum2sq(product_Pair_int_int(U_2926,U_2925)) != U_2927
| ~ is_int(U_2925) )
| ~ is_int(U_2926) ) )
& ( ( twoSqu1241645765sum2sq(product_Pair_int_int(sK18(U_2927),sK19(U_2927))) = U_2927
& is_int(sK19(U_2927))
& is_int(sK18(U_2927)) )
| ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,U_2927)) ) )
| ~ is_int(U_2927) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_2923,sK19(U_2927))],[f_1086_4]) ).
cnf(f_1086_6,plain,
( is_int(sK18(U_2927))
| ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,U_2927))
| ~ is_int(U_2927) ),
inference(clausify,[status(thm)],[f_1086_5]) ).
cnf(f_1086_7,plain,
( is_int(sK19(U_2927))
| ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,U_2927))
| ~ is_int(U_2927) ),
inference(clausify,[status(thm)],[f_1086_5]) ).
cnf(f_1086_8,plain,
( twoSqu1241645765sum2sq(product_Pair_int_int(sK18(U_2927),sK19(U_2927))) = U_2927
| ~ hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,U_2927))
| ~ is_int(U_2927) ),
inference(clausify,[status(thm)],[f_1086_5]) ).
cnf(f_1086_9,plain,
( hBOOL(hAPP_int_bool(twoSqu1154269391sum2sq,U_2927))
| twoSqu1241645765sum2sq(product_Pair_int_int(U_2926,U_2925)) != U_2927
| ~ is_int(U_2925)
| ~ is_int(U_2926)
| ~ is_int(U_2927) ),
inference(clausify,[status(thm)],[f_1086_5]) ).
fof(f_1087_1,plain,
! [P_5,P_2,X_2] :
( ( ( hBOOL(P_2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2))
| ( ~ hBOOL(P_5)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) ) )
& ( hBOOL(P_5)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2))
| ( ~ hBOOL(P_2)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) ) ) )
| ( ( ( ~ hBOOL(P_2)
& hBOOL(P_5) )
| ( ~ hBOOL(P_5)
& hBOOL(P_2) ) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_1061_imp__le__cong]) ).
fof(f_1087_2,plain,
! [U_2930,U_2929,U_2928] :
( ( ( hBOOL(U_2929)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928))
| ( ~ hBOOL(U_2930)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ) )
& ( hBOOL(U_2930)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928))
| ( ~ hBOOL(U_2929)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ) ) )
| ( ( ( ~ hBOOL(U_2929)
& hBOOL(U_2930) )
| ( ~ hBOOL(U_2930)
& hBOOL(U_2929) ) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ) ),
inference(variable_rename,[status(thm)],[f_1087_1]) ).
cnf(f_1087_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928))
| hBOOL(U_2930)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
cnf(f_1087_4,plain,
( ~ hBOOL(U_2929)
| hBOOL(U_2930)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
cnf(f_1087_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928))
| hBOOL(U_2929)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
cnf(f_1087_6,plain,
( ~ hBOOL(U_2930)
| hBOOL(U_2929)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
cnf(f_1087_7,plain,
( hBOOL(U_2930)
| hBOOL(U_2929)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928))
| hBOOL(U_2930)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
cnf(f_1087_8,plain,
( ~ hBOOL(U_2929)
| hBOOL(U_2929)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928))
| hBOOL(U_2930)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
cnf(f_1087_9,plain,
( hBOOL(U_2930)
| hBOOL(U_2929)
| ~ hBOOL(U_2929)
| hBOOL(U_2930)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
cnf(f_1087_10,plain,
( ~ hBOOL(U_2929)
| hBOOL(U_2929)
| ~ hBOOL(U_2929)
| hBOOL(U_2930)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
cnf(f_1087_11,plain,
( hBOOL(U_2930)
| ~ hBOOL(U_2930)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928))
| hBOOL(U_2930)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
cnf(f_1087_12,plain,
( ~ hBOOL(U_2929)
| ~ hBOOL(U_2930)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928))
| hBOOL(U_2930)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
cnf(f_1087_13,plain,
( hBOOL(U_2930)
| ~ hBOOL(U_2930)
| ~ hBOOL(U_2929)
| hBOOL(U_2930)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
cnf(f_1087_14,plain,
( ~ hBOOL(U_2929)
| ~ hBOOL(U_2930)
| ~ hBOOL(U_2929)
| hBOOL(U_2930)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
cnf(f_1087_15,plain,
( hBOOL(U_2930)
| hBOOL(U_2929)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928))
| hBOOL(U_2929)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
cnf(f_1087_16,plain,
( ~ hBOOL(U_2929)
| hBOOL(U_2929)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928))
| hBOOL(U_2929)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
cnf(f_1087_17,plain,
( hBOOL(U_2930)
| hBOOL(U_2929)
| ~ hBOOL(U_2930)
| hBOOL(U_2929)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
cnf(f_1087_18,plain,
( ~ hBOOL(U_2929)
| hBOOL(U_2929)
| ~ hBOOL(U_2930)
| hBOOL(U_2929)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
cnf(f_1087_19,plain,
( hBOOL(U_2930)
| ~ hBOOL(U_2930)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928))
| hBOOL(U_2929)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
cnf(f_1087_20,plain,
( ~ hBOOL(U_2929)
| ~ hBOOL(U_2930)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928))
| hBOOL(U_2929)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
cnf(f_1087_21,plain,
( hBOOL(U_2930)
| ~ hBOOL(U_2930)
| ~ hBOOL(U_2930)
| hBOOL(U_2929)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
cnf(f_1087_22,plain,
( ~ hBOOL(U_2929)
| ~ hBOOL(U_2930)
| ~ hBOOL(U_2930)
| hBOOL(U_2929)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2928)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
fof(f_1088_1,plain,
! [P_5,P_2,X_2] :
( ( ( ( hBOOL(P_2)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) )
| ~ hBOOL(P_5)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) )
& ( ( hBOOL(P_5)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) )
| ~ hBOOL(P_2)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) ) )
| ( ( ( ~ hBOOL(P_2)
& hBOOL(P_5) )
| ( ~ hBOOL(P_5)
& hBOOL(P_2) ) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_1062_conj__le__cong]) ).
fof(f_1088_2,plain,
! [U_2933,U_2932,U_2931] :
( ( ( ( hBOOL(U_2932)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) )
| ~ hBOOL(U_2933)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) )
& ( ( hBOOL(U_2933)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) )
| ~ hBOOL(U_2932)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ) )
| ( ( ( ~ hBOOL(U_2932)
& hBOOL(U_2933) )
| ( ~ hBOOL(U_2933)
& hBOOL(U_2932) ) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ) ),
inference(variable_rename,[status(thm)],[f_1088_1]) ).
cnf(f_1088_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931))
| ~ hBOOL(U_2932)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
cnf(f_1088_4,plain,
( hBOOL(U_2933)
| ~ hBOOL(U_2932)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
cnf(f_1088_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931))
| ~ hBOOL(U_2933)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
cnf(f_1088_6,plain,
( hBOOL(U_2932)
| ~ hBOOL(U_2933)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
cnf(f_1088_7,plain,
( hBOOL(U_2933)
| hBOOL(U_2932)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931))
| ~ hBOOL(U_2932)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
cnf(f_1088_8,plain,
( ~ hBOOL(U_2932)
| hBOOL(U_2932)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931))
| ~ hBOOL(U_2932)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
cnf(f_1088_9,plain,
( hBOOL(U_2933)
| hBOOL(U_2932)
| hBOOL(U_2933)
| ~ hBOOL(U_2932)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
cnf(f_1088_10,plain,
( ~ hBOOL(U_2932)
| hBOOL(U_2932)
| hBOOL(U_2933)
| ~ hBOOL(U_2932)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
cnf(f_1088_11,plain,
( hBOOL(U_2933)
| ~ hBOOL(U_2933)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931))
| ~ hBOOL(U_2932)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
cnf(f_1088_12,plain,
( ~ hBOOL(U_2932)
| ~ hBOOL(U_2933)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931))
| ~ hBOOL(U_2932)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
cnf(f_1088_13,plain,
( hBOOL(U_2933)
| ~ hBOOL(U_2933)
| hBOOL(U_2933)
| ~ hBOOL(U_2932)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
cnf(f_1088_14,plain,
( ~ hBOOL(U_2932)
| ~ hBOOL(U_2933)
| hBOOL(U_2933)
| ~ hBOOL(U_2932)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
cnf(f_1088_15,plain,
( hBOOL(U_2933)
| hBOOL(U_2932)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931))
| ~ hBOOL(U_2933)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
cnf(f_1088_16,plain,
( ~ hBOOL(U_2932)
| hBOOL(U_2932)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931))
| ~ hBOOL(U_2933)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
cnf(f_1088_17,plain,
( hBOOL(U_2933)
| hBOOL(U_2932)
| hBOOL(U_2932)
| ~ hBOOL(U_2933)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
cnf(f_1088_18,plain,
( ~ hBOOL(U_2932)
| hBOOL(U_2932)
| hBOOL(U_2932)
| ~ hBOOL(U_2933)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
cnf(f_1088_19,plain,
( hBOOL(U_2933)
| ~ hBOOL(U_2933)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931))
| ~ hBOOL(U_2933)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
cnf(f_1088_20,plain,
( ~ hBOOL(U_2932)
| ~ hBOOL(U_2933)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931))
| ~ hBOOL(U_2933)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
cnf(f_1088_21,plain,
( hBOOL(U_2933)
| ~ hBOOL(U_2933)
| hBOOL(U_2932)
| ~ hBOOL(U_2933)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
cnf(f_1088_22,plain,
( ~ hBOOL(U_2932)
| ~ hBOOL(U_2933)
| hBOOL(U_2932)
| ~ hBOOL(U_2933)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2931)) ),
inference(clausify,[status(thm)],[f_1088_2]) ).
fof(f_1089_1,plain,
! [Ma,Ta,K] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Ma),Ta))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(K),Ma)),hAPP_int_int(times_times_int(K),Ta))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(K),Ma)),hAPP_int_int(times_times_int(K),Ta)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,Ma),Ta)) ) )
| K = zero_zero_int
| ~ is_int(K) ),
inference(fof_nnf,[status(thm)],[fact_1063_zdvd__mono]) ).
fof(f_1089_2,plain,
! [U_2936,U_2935,U_2934] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_2936),U_2935))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(U_2934),U_2936)),hAPP_int_int(times_times_int(U_2934),U_2935))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(U_2934),U_2936)),hAPP_int_int(times_times_int(U_2934),U_2935)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_2936),U_2935)) ) )
| U_2934 = zero_zero_int
| ~ is_int(U_2934) ),
inference(variable_rename,[status(thm)],[f_1089_1]) ).
cnf(f_1089_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(U_2934),U_2936)),hAPP_int_int(times_times_int(U_2934),U_2935)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_2936),U_2935))
| U_2934 = zero_zero_int
| ~ is_int(U_2934) ),
inference(clausify,[status(thm)],[f_1089_2]) ).
cnf(f_1089_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_2936),U_2935))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_int_int(times_times_int(U_2934),U_2936)),hAPP_int_int(times_times_int(U_2934),U_2935)))
| U_2934 = zero_zero_int
| ~ is_int(U_2934) ),
inference(clausify,[status(thm)],[f_1089_2]) ).
fof(f_1090_1,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(pls))),
inference(fof_nnf,[status(thm)],[fact_1064_number__of2]) ).
cnf(f_1090_2,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(pls))),
inference(clausify,[status(thm)],[f_1090_1]) ).
fof(f_1091_1,plain,
! [K,P_2,D] :
( ! [X] :
( hBOOL(hAPP_int_bool(P_2,hAPP_int_int(minus_minus_int(X),hAPP_int_int(times_times_int(K),D))))
| ~ hBOOL(hAPP_int_bool(P_2,X)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K))
| ? [X] :
( ~ hBOOL(hAPP_int_bool(P_2,hAPP_int_int(minus_minus_int(X),D)))
& hBOOL(hAPP_int_bool(P_2,X))
& is_int(X) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D)) ),
inference(fof_nnf,[status(thm)],[fact_1065_decr__mult__lemma]) ).
fof(f_1091_2,plain,
! [U_2941,U_2940,U_2939] :
( ! [U_2938] :
( hBOOL(hAPP_int_bool(U_2940,hAPP_int_int(minus_minus_int(U_2938),hAPP_int_int(times_times_int(U_2941),U_2939))))
| ~ hBOOL(hAPP_int_bool(U_2940,U_2938)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2941))
| ? [U_2937] :
( ~ hBOOL(hAPP_int_bool(U_2940,hAPP_int_int(minus_minus_int(U_2937),U_2939)))
& hBOOL(hAPP_int_bool(U_2940,U_2937))
& is_int(U_2937) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2939)) ),
inference(variable_rename,[status(thm)],[f_1091_1]) ).
fof(f_1091_3,plain,
! [U_2941,U_2940,U_2939] :
( ! [U_2938] :
( hBOOL(hAPP_int_bool(U_2940,hAPP_int_int(minus_minus_int(U_2938),hAPP_int_int(times_times_int(U_2941),U_2939))))
| ~ hBOOL(hAPP_int_bool(U_2940,U_2938)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2941))
| ( ~ hBOOL(hAPP_int_bool(U_2940,hAPP_int_int(minus_minus_int(sK20(U_2941,U_2940,U_2939)),U_2939)))
& hBOOL(hAPP_int_bool(U_2940,sK20(U_2941,U_2940,U_2939)))
& is_int(sK20(U_2941,U_2940,U_2939)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2939)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_2937,sK20(U_2941,U_2940,U_2939))],[f_1091_2]) ).
cnf(f_1091_4,plain,
( is_int(sK20(U_2941,U_2940,U_2939))
| hBOOL(hAPP_int_bool(U_2940,hAPP_int_int(minus_minus_int(U_2938),hAPP_int_int(times_times_int(U_2941),U_2939))))
| ~ hBOOL(hAPP_int_bool(U_2940,U_2938))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2941))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2939)) ),
inference(clausify,[status(thm)],[f_1091_3]) ).
cnf(f_1091_5,plain,
( hBOOL(hAPP_int_bool(U_2940,sK20(U_2941,U_2940,U_2939)))
| hBOOL(hAPP_int_bool(U_2940,hAPP_int_int(minus_minus_int(U_2938),hAPP_int_int(times_times_int(U_2941),U_2939))))
| ~ hBOOL(hAPP_int_bool(U_2940,U_2938))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2941))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2939)) ),
inference(clausify,[status(thm)],[f_1091_3]) ).
cnf(f_1091_6,plain,
( ~ hBOOL(hAPP_int_bool(U_2940,hAPP_int_int(minus_minus_int(sK20(U_2941,U_2940,U_2939)),U_2939)))
| hBOOL(hAPP_int_bool(U_2940,hAPP_int_int(minus_minus_int(U_2938),hAPP_int_int(times_times_int(U_2941),U_2939))))
| ~ hBOOL(hAPP_int_bool(U_2940,U_2938))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2941))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2939)) ),
inference(clausify,[status(thm)],[f_1091_3]) ).
fof(f_1092_1,plain,
! [K,P_2,D] :
( ! [X] :
( hBOOL(hAPP_int_bool(P_2,hAPP_int_int(plus_plus_int(X),hAPP_int_int(times_times_int(K),D))))
| ~ hBOOL(hAPP_int_bool(P_2,X)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K))
| ? [X] :
( ~ hBOOL(hAPP_int_bool(P_2,hAPP_int_int(plus_plus_int(X),D)))
& hBOOL(hAPP_int_bool(P_2,X))
& is_int(X) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D)) ),
inference(fof_nnf,[status(thm)],[fact_1066_incr__mult__lemma]) ).
fof(f_1092_2,plain,
! [U_2946,U_2945,U_2944] :
( ! [U_2943] :
( hBOOL(hAPP_int_bool(U_2945,hAPP_int_int(plus_plus_int(U_2943),hAPP_int_int(times_times_int(U_2946),U_2944))))
| ~ hBOOL(hAPP_int_bool(U_2945,U_2943)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2946))
| ? [U_2942] :
( ~ hBOOL(hAPP_int_bool(U_2945,hAPP_int_int(plus_plus_int(U_2942),U_2944)))
& hBOOL(hAPP_int_bool(U_2945,U_2942))
& is_int(U_2942) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2944)) ),
inference(variable_rename,[status(thm)],[f_1092_1]) ).
fof(f_1092_3,plain,
! [U_2946,U_2945,U_2944] :
( ! [U_2943] :
( hBOOL(hAPP_int_bool(U_2945,hAPP_int_int(plus_plus_int(U_2943),hAPP_int_int(times_times_int(U_2946),U_2944))))
| ~ hBOOL(hAPP_int_bool(U_2945,U_2943)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2946))
| ( ~ hBOOL(hAPP_int_bool(U_2945,hAPP_int_int(plus_plus_int(sK21(U_2946,U_2945,U_2944)),U_2944)))
& hBOOL(hAPP_int_bool(U_2945,sK21(U_2946,U_2945,U_2944)))
& is_int(sK21(U_2946,U_2945,U_2944)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2944)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_2942,sK21(U_2946,U_2945,U_2944))],[f_1092_2]) ).
cnf(f_1092_4,plain,
( is_int(sK21(U_2946,U_2945,U_2944))
| hBOOL(hAPP_int_bool(U_2945,hAPP_int_int(plus_plus_int(U_2943),hAPP_int_int(times_times_int(U_2946),U_2944))))
| ~ hBOOL(hAPP_int_bool(U_2945,U_2943))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2946))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2944)) ),
inference(clausify,[status(thm)],[f_1092_3]) ).
cnf(f_1092_5,plain,
( hBOOL(hAPP_int_bool(U_2945,sK21(U_2946,U_2945,U_2944)))
| hBOOL(hAPP_int_bool(U_2945,hAPP_int_int(plus_plus_int(U_2943),hAPP_int_int(times_times_int(U_2946),U_2944))))
| ~ hBOOL(hAPP_int_bool(U_2945,U_2943))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2946))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2944)) ),
inference(clausify,[status(thm)],[f_1092_3]) ).
cnf(f_1092_6,plain,
( ~ hBOOL(hAPP_int_bool(U_2945,hAPP_int_int(plus_plus_int(sK21(U_2946,U_2945,U_2944)),U_2944)))
| hBOOL(hAPP_int_bool(U_2945,hAPP_int_int(plus_plus_int(U_2943),hAPP_int_int(times_times_int(U_2946),U_2944))))
| ~ hBOOL(hAPP_int_bool(U_2945,U_2943))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2946))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2944)) ),
inference(clausify,[status(thm)],[f_1092_3]) ).
fof(f_1093_1,plain,
! [A] :
( ? [P_4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,P_4),A))
& hBOOL(hAPP_int_bool(zprime,P_4))
& is_int(P_4) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A)) ),
inference(fof_nnf,[status(thm)],[fact_1067_zprime__factor__exists]) ).
fof(f_1093_2,plain,
! [U_2948] :
( ? [U_2947] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_2947),U_2948))
& hBOOL(hAPP_int_bool(zprime,U_2947))
& is_int(U_2947) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_2948)) ),
inference(variable_rename,[status(thm)],[f_1093_1]) ).
fof(f_1093_3,plain,
! [U_2948] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK22(U_2948)),U_2948))
& hBOOL(hAPP_int_bool(zprime,sK22(U_2948)))
& is_int(sK22(U_2948)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_2948)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_2947,sK22(U_2948))],[f_1093_2]) ).
cnf(f_1093_4,plain,
( is_int(sK22(U_2948))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_2948)) ),
inference(clausify,[status(thm)],[f_1093_3]) ).
cnf(f_1093_5,plain,
( hBOOL(hAPP_int_bool(zprime,sK22(U_2948)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_2948)) ),
inference(clausify,[status(thm)],[f_1093_3]) ).
cnf(f_1093_6,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK22(U_2948)),U_2948))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_2948)) ),
inference(clausify,[status(thm)],[f_1093_3]) ).
fof(f_1094_1,plain,
! [A,M] :
( ? [X] :
( ! [Y] :
( Y = X
| ~ hBOOL(hAPP_int_bool(zcong(A,Y),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y))
| ~ is_int(Y) )
& hBOOL(hAPP_int_bool(zcong(A,X),M))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X),M))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X))
& is_int(X) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M)) ),
inference(fof_nnf,[status(thm)],[fact_1068_zcong__zless__unique]) ).
fof(f_1094_2,plain,
! [U_2952,U_2951] :
( ? [U_2950] :
( ! [U_2949] :
( U_2949 = U_2950
| ~ hBOOL(hAPP_int_bool(zcong(U_2952,U_2949),U_2951))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2949),U_2951))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2949))
| ~ is_int(U_2949) )
& hBOOL(hAPP_int_bool(zcong(U_2952,U_2950),U_2951))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2950),U_2951))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2950))
& is_int(U_2950) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2951)) ),
inference(variable_rename,[status(thm)],[f_1094_1]) ).
fof(f_1094_3,plain,
! [U_2952,U_2951] :
( ( ! [U_2949] :
( U_2949 = sK23(U_2952,U_2951)
| ~ hBOOL(hAPP_int_bool(zcong(U_2952,U_2949),U_2951))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2949),U_2951))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2949))
| ~ is_int(U_2949) )
& hBOOL(hAPP_int_bool(zcong(U_2952,sK23(U_2952,U_2951)),U_2951))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK23(U_2952,U_2951)),U_2951))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK23(U_2952,U_2951)))
& is_int(sK23(U_2952,U_2951)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2951)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_2950,sK23(U_2952,U_2951))],[f_1094_2]) ).
cnf(f_1094_4,plain,
( is_int(sK23(U_2952,U_2951))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2951)) ),
inference(clausify,[status(thm)],[f_1094_3]) ).
cnf(f_1094_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK23(U_2952,U_2951)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2951)) ),
inference(clausify,[status(thm)],[f_1094_3]) ).
cnf(f_1094_6,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK23(U_2952,U_2951)),U_2951))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2951)) ),
inference(clausify,[status(thm)],[f_1094_3]) ).
cnf(f_1094_7,plain,
( hBOOL(hAPP_int_bool(zcong(U_2952,sK23(U_2952,U_2951)),U_2951))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2951)) ),
inference(clausify,[status(thm)],[f_1094_3]) ).
cnf(f_1094_8,plain,
( U_2949 = sK23(U_2952,U_2951)
| ~ hBOOL(hAPP_int_bool(zcong(U_2952,U_2949),U_2951))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2949),U_2951))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_2949))
| ~ is_int(U_2949)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2951)) ),
inference(clausify,[status(thm)],[f_1094_3]) ).
fof(f_1095_1,plain,
! [A,B] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),B))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A),hAPP_int_int(minus_minus_int(B),one_one_int))) ),
inference(fof_nnf,[status(thm)],[fact_1069_norR__mem__unique__aux]) ).
fof(f_1095_2,plain,
! [U_2954,U_2953] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2954),U_2953))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2954),hAPP_int_int(minus_minus_int(U_2953),one_one_int))) ),
inference(variable_rename,[status(thm)],[f_1095_1]) ).
cnf(f_1095_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2954),U_2953))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2954),hAPP_int_int(minus_minus_int(U_2953),one_one_int))) ),
inference(clausify,[status(thm)],[f_1095_2]) ).
fof(f_1096_1,plain,
! [P_1] :
( hBOOL(hAPP_int_bool(zcong(zfact(hAPP_int_int(minus_minus_int(P_1),one_one_int)),number_number_of_int(min)),P_1))
| ~ hBOOL(hAPP_int_bool(zprime,P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1070_Wilson__Russ]) ).
fof(f_1096_2,plain,
! [U_2955] :
( hBOOL(hAPP_int_bool(zcong(zfact(hAPP_int_int(minus_minus_int(U_2955),one_one_int)),number_number_of_int(min)),U_2955))
| ~ hBOOL(hAPP_int_bool(zprime,U_2955)) ),
inference(variable_rename,[status(thm)],[f_1096_1]) ).
cnf(f_1096_3,plain,
( hBOOL(hAPP_int_bool(zcong(zfact(hAPP_int_int(minus_minus_int(U_2955),one_one_int)),number_number_of_int(min)),U_2955))
| ~ hBOOL(hAPP_int_bool(zprime,U_2955)) ),
inference(clausify,[status(thm)],[f_1096_2]) ).
fof(f_1097_1,plain,
! [N_1] :
( ( zfact(N_1) = hAPP_int_int(times_times_int(N_1),zfact(hAPP_int_int(minus_minus_int(N_1),one_one_int)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,N_1),zero_zero_int)) )
& ( zfact(N_1) = one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,N_1),zero_zero_int)) ) ),
inference(fof_nnf,[status(thm)],[fact_1071_zfact_Osimps]) ).
fof(f_1097_2,plain,
! [U_2956] :
( ( zfact(U_2956) = hAPP_int_int(times_times_int(U_2956),zfact(hAPP_int_int(minus_minus_int(U_2956),one_one_int)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2956),zero_zero_int)) )
& ( zfact(U_2956) = one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2956),zero_zero_int)) ) ),
inference(variable_rename,[status(thm)],[f_1097_1]) ).
fof(f_1097_3,plain,
( ! [U_2958] :
( zfact(U_2958) = hAPP_int_int(times_times_int(U_2958),zfact(hAPP_int_int(minus_minus_int(U_2958),one_one_int)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2958),zero_zero_int)) )
& ! [U_2957] :
( zfact(U_2957) = one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2957),zero_zero_int)) ) ),
inference(miniscope,[status(thm)],[f_1097_2]) ).
cnf(f_1097_4,plain,
( zfact(U_2957) = one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2957),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_1097_3]) ).
cnf(f_1097_5,plain,
( zfact(U_2958) = hAPP_int_int(times_times_int(U_2958),zfact(hAPP_int_int(minus_minus_int(U_2958),one_one_int)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2958),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_1097_3]) ).
fof(f_1098_1,plain,
! [A,P_1] :
( inv(P_1,inv(P_1,A)) = A
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),P_1))
| ~ hBOOL(hAPP_int_bool(zprime,P_1))
| ~ is_int(A) ),
inference(fof_nnf,[status(thm)],[fact_1072_inv__inv]) ).
fof(f_1098_2,plain,
! [U_2960,U_2959] :
( inv(U_2959,inv(U_2959,U_2960)) = U_2960
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2960),U_2959))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2960))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),U_2959))
| ~ hBOOL(hAPP_int_bool(zprime,U_2959))
| ~ is_int(U_2960) ),
inference(variable_rename,[status(thm)],[f_1098_1]) ).
fof(f_1098_3,plain,
! [U_2960] :
( ! [U_2959] :
( inv(U_2959,inv(U_2959,U_2960)) = U_2960
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2960),U_2959))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2960))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),U_2959))
| ~ hBOOL(hAPP_int_bool(zprime,U_2959)) )
| ~ is_int(U_2960) ),
inference(miniscope,[status(thm)],[f_1098_2]) ).
cnf(f_1098_4,plain,
( inv(U_2959,inv(U_2959,U_2960)) = U_2960
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2960),U_2959))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2960))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),U_2959))
| ~ hBOOL(hAPP_int_bool(zprime,U_2959))
| ~ is_int(U_2960) ),
inference(clausify,[status(thm)],[f_1098_3]) ).
fof(f_1099_1,plain,
! [J_1,A,P_1] :
( ~ hBOOL(hAPP_int_bool(zcong(J_1,hAPP_int_int(times_times_int(A),multInv(P_1,J_1))),P_1))
| hBOOL(hAPP_int_bool(quadRes(P_1),A))
| hBOOL(hAPP_int_bool(zcong(J_1,zero_zero_int),P_1))
| hBOOL(hAPP_int_bool(zcong(A,zero_zero_int),P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1))
| ~ hBOOL(hAPP_int_bool(zprime,P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1073_MultInvPair__distinct]) ).
fof(f_1099_2,plain,
! [U_2963,U_2962,U_2961] :
( ~ hBOOL(hAPP_int_bool(zcong(U_2963,hAPP_int_int(times_times_int(U_2962),multInv(U_2961,U_2963))),U_2961))
| hBOOL(hAPP_int_bool(quadRes(U_2961),U_2962))
| hBOOL(hAPP_int_bool(zcong(U_2963,zero_zero_int),U_2961))
| hBOOL(hAPP_int_bool(zcong(U_2962,zero_zero_int),U_2961))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_2961))
| ~ hBOOL(hAPP_int_bool(zprime,U_2961)) ),
inference(variable_rename,[status(thm)],[f_1099_1]) ).
cnf(f_1099_3,plain,
( ~ hBOOL(hAPP_int_bool(zcong(U_2963,hAPP_int_int(times_times_int(U_2962),multInv(U_2961,U_2963))),U_2961))
| hBOOL(hAPP_int_bool(quadRes(U_2961),U_2962))
| hBOOL(hAPP_int_bool(zcong(U_2963,zero_zero_int),U_2961))
| hBOOL(hAPP_int_bool(zcong(U_2962,zero_zero_int),U_2961))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_2961))
| ~ hBOOL(hAPP_int_bool(zprime,U_2961)) ),
inference(clausify,[status(thm)],[f_1099_2]) ).
fof(f_1100_1,plain,
! [J_1,K_1,A,P_1] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(multInv(P_1,J_1)),J_1)),K_1),hAPP_int_int(times_times_int(multInv(P_1,J_1)),A)),P_1))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(J_1),K_1),A),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1074_aux______3]) ).
fof(f_1100_2,plain,
! [U_2967,U_2966,U_2965,U_2964] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(multInv(U_2964,U_2967)),U_2967)),U_2966),hAPP_int_int(times_times_int(multInv(U_2964,U_2967)),U_2965)),U_2964))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_2967),U_2966),U_2965),U_2964)) ),
inference(variable_rename,[status(thm)],[f_1100_1]) ).
cnf(f_1100_3,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(multInv(U_2964,U_2967)),U_2967)),U_2966),hAPP_int_int(times_times_int(multInv(U_2964,U_2967)),U_2965)),U_2964))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_2967),U_2966),U_2965),U_2964)) ),
inference(clausify,[status(thm)],[f_1100_2]) ).
fof(f_1101_1,plain,
! [J_1,A,P_1,K_1] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(J_1),K_1),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(A),multInv(P_1,K_1))),K_1)),P_1))
| ~ hBOOL(hAPP_int_bool(zcong(J_1,hAPP_int_int(times_times_int(A),multInv(P_1,K_1))),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1075_aux______1]) ).
fof(f_1101_2,plain,
! [U_2971,U_2970,U_2969,U_2968] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_2971),U_2968),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_2970),multInv(U_2969,U_2968))),U_2968)),U_2969))
| ~ hBOOL(hAPP_int_bool(zcong(U_2971,hAPP_int_int(times_times_int(U_2970),multInv(U_2969,U_2968))),U_2969)) ),
inference(variable_rename,[status(thm)],[f_1101_1]) ).
cnf(f_1101_3,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_2971),U_2968),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_2970),multInv(U_2969,U_2968))),U_2968)),U_2969))
| ~ hBOOL(hAPP_int_bool(zcong(U_2971,hAPP_int_int(times_times_int(U_2970),multInv(U_2969,U_2968))),U_2969)) ),
inference(clausify,[status(thm)],[f_1101_2]) ).
fof(f_1102_1,plain,
! [A,P_1] :
( A != inv(P_1,A)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),hAPP_int_int(minus_minus_int(P_1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A))
| ~ hBOOL(hAPP_int_bool(zprime,P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1076_inv__distinct]) ).
fof(f_1102_2,plain,
! [U_2973,U_2972] :
( U_2973 != inv(U_2972,U_2973)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2973),hAPP_int_int(minus_minus_int(U_2972),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_2973))
| ~ hBOOL(hAPP_int_bool(zprime,U_2972)) ),
inference(variable_rename,[status(thm)],[f_1102_1]) ).
cnf(f_1102_3,plain,
( U_2973 != inv(U_2972,U_2973)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2973),hAPP_int_int(minus_minus_int(U_2972),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_2973))
| ~ hBOOL(hAPP_int_bool(zprime,U_2972)) ),
inference(clausify,[status(thm)],[f_1102_2]) ).
fof(f_1103_1,plain,
! [A,P_1] :
( inv(P_1,A) != one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),hAPP_int_int(minus_minus_int(P_1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A))
| ~ hBOOL(hAPP_int_bool(zprime,P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1077_inv__not__1]) ).
fof(f_1103_2,plain,
! [U_2975,U_2974] :
( inv(U_2974,U_2975) != one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2975),hAPP_int_int(minus_minus_int(U_2974),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_2975))
| ~ hBOOL(hAPP_int_bool(zprime,U_2974)) ),
inference(variable_rename,[status(thm)],[f_1103_1]) ).
cnf(f_1103_3,plain,
( inv(U_2974,U_2975) != one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2975),hAPP_int_int(minus_minus_int(U_2974),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_2975))
| ~ hBOOL(hAPP_int_bool(zprime,U_2974)) ),
inference(clausify,[status(thm)],[f_1103_2]) ).
fof(f_1104_1,plain,
! [A,P_1] :
( inv(P_1,A) != hAPP_int_int(minus_minus_int(P_1),one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),hAPP_int_int(minus_minus_int(P_1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A))
| ~ hBOOL(hAPP_int_bool(zprime,P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1078_inv__not__p__minus__1]) ).
fof(f_1104_2,plain,
! [U_2977,U_2976] :
( inv(U_2976,U_2977) != hAPP_int_int(minus_minus_int(U_2976),one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2977),hAPP_int_int(minus_minus_int(U_2976),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_2977))
| ~ hBOOL(hAPP_int_bool(zprime,U_2976)) ),
inference(variable_rename,[status(thm)],[f_1104_1]) ).
cnf(f_1104_3,plain,
( inv(U_2976,U_2977) != hAPP_int_int(minus_minus_int(U_2976),one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2977),hAPP_int_int(minus_minus_int(U_2976),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_2977))
| ~ hBOOL(hAPP_int_bool(zprime,U_2976)) ),
inference(clausify,[status(thm)],[f_1104_2]) ).
fof(f_1105_1,plain,
! [A,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),inv(P_1,A)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),hAPP_int_int(minus_minus_int(P_1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A))
| ~ hBOOL(hAPP_int_bool(zprime,P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1079_inv__g__1]) ).
fof(f_1105_2,plain,
! [U_2979,U_2978] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),inv(U_2978,U_2979)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2979),hAPP_int_int(minus_minus_int(U_2978),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_2979))
| ~ hBOOL(hAPP_int_bool(zprime,U_2978)) ),
inference(variable_rename,[status(thm)],[f_1105_1]) ).
cnf(f_1105_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),inv(U_2978,U_2979)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2979),hAPP_int_int(minus_minus_int(U_2978),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_2979))
| ~ hBOOL(hAPP_int_bool(zprime,U_2978)) ),
inference(clausify,[status(thm)],[f_1105_2]) ).
fof(f_1106_1,plain,
! [A,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,inv(P_1,A)),hAPP_int_int(minus_minus_int(P_1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),hAPP_int_int(minus_minus_int(P_1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A))
| ~ hBOOL(hAPP_int_bool(zprime,P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1080_inv__less__p__minus__1]) ).
fof(f_1106_2,plain,
! [U_2981,U_2980] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,inv(U_2980,U_2981)),hAPP_int_int(minus_minus_int(U_2980),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2981),hAPP_int_int(minus_minus_int(U_2980),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_2981))
| ~ hBOOL(hAPP_int_bool(zprime,U_2980)) ),
inference(variable_rename,[status(thm)],[f_1106_1]) ).
cnf(f_1106_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,inv(U_2980,U_2981)),hAPP_int_int(minus_minus_int(U_2980),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2981),hAPP_int_int(minus_minus_int(U_2980),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_2981))
| ~ hBOOL(hAPP_int_bool(zprime,U_2980)) ),
inference(clausify,[status(thm)],[f_1106_2]) ).
fof(f_1107_1,plain,
! [X_1,Y_1,P_1] :
( hBOOL(hAPP_int_bool(zcong(multInv(P_1,X_1),multInv(P_1,Y_1)),P_1))
| ~ hBOOL(hAPP_int_bool(zcong(X_1,Y_1),P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1081_MultInv__prop1]) ).
fof(f_1107_2,plain,
! [U_2984,U_2983,U_2982] :
( hBOOL(hAPP_int_bool(zcong(multInv(U_2982,U_2984),multInv(U_2982,U_2983)),U_2982))
| ~ hBOOL(hAPP_int_bool(zcong(U_2984,U_2983),U_2982))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_2982)) ),
inference(variable_rename,[status(thm)],[f_1107_1]) ).
cnf(f_1107_3,plain,
( hBOOL(hAPP_int_bool(zcong(multInv(U_2982,U_2984),multInv(U_2982,U_2983)),U_2982))
| ~ hBOOL(hAPP_int_bool(zcong(U_2984,U_2983),U_2982))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_2982)) ),
inference(clausify,[status(thm)],[f_1107_2]) ).
fof(f_1108_1,plain,
! [A,P_1] :
( inv(P_1,A) != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),hAPP_int_int(minus_minus_int(P_1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A))
| ~ hBOOL(hAPP_int_bool(zprime,P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1082_inv__not__0]) ).
fof(f_1108_2,plain,
! [U_2986,U_2985] :
( inv(U_2985,U_2986) != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2986),hAPP_int_int(minus_minus_int(U_2985),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_2986))
| ~ hBOOL(hAPP_int_bool(zprime,U_2985)) ),
inference(variable_rename,[status(thm)],[f_1108_1]) ).
cnf(f_1108_3,plain,
( inv(U_2985,U_2986) != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2986),hAPP_int_int(minus_minus_int(U_2985),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_2986))
| ~ hBOOL(hAPP_int_bool(zprime,U_2985)) ),
inference(clausify,[status(thm)],[f_1108_2]) ).
fof(f_1109_1,plain,
! [A,J_1,K_1,P_1] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),multInv(P_1,J_1)),hAPP_int_int(times_times_int(A),multInv(P_1,K_1))),P_1))
| ~ hBOOL(hAPP_int_bool(zcong(J_1,K_1),P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1083_MultInv__zcong__prop1]) ).
fof(f_1109_2,plain,
! [U_2990,U_2989,U_2988,U_2987] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_2990),multInv(U_2987,U_2989)),hAPP_int_int(times_times_int(U_2990),multInv(U_2987,U_2988))),U_2987))
| ~ hBOOL(hAPP_int_bool(zcong(U_2989,U_2988),U_2987))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_2987)) ),
inference(variable_rename,[status(thm)],[f_1109_1]) ).
cnf(f_1109_3,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_2990),multInv(U_2987,U_2989)),hAPP_int_int(times_times_int(U_2990),multInv(U_2987,U_2988))),U_2987))
| ~ hBOOL(hAPP_int_bool(zcong(U_2989,U_2988),U_2987))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_2987)) ),
inference(clausify,[status(thm)],[f_1109_2]) ).
fof(f_1110_1,plain,
! [Y_1,X_1,P_1] :
( hBOOL(hAPP_int_bool(zcong(X_1,Y_1),P_1))
| ~ hBOOL(hAPP_int_bool(zcong(multInv(P_1,X_1),multInv(P_1,Y_1)),P_1))
| hBOOL(hAPP_int_bool(zcong(Y_1,zero_zero_int),P_1))
| hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),P_1))
| ~ hBOOL(hAPP_int_bool(zprime,P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1084_MultInv__prop5]) ).
fof(f_1110_2,plain,
! [U_2993,U_2992,U_2991] :
( hBOOL(hAPP_int_bool(zcong(U_2992,U_2993),U_2991))
| ~ hBOOL(hAPP_int_bool(zcong(multInv(U_2991,U_2992),multInv(U_2991,U_2993)),U_2991))
| hBOOL(hAPP_int_bool(zcong(U_2993,zero_zero_int),U_2991))
| hBOOL(hAPP_int_bool(zcong(U_2992,zero_zero_int),U_2991))
| ~ hBOOL(hAPP_int_bool(zprime,U_2991))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_2991)) ),
inference(variable_rename,[status(thm)],[f_1110_1]) ).
cnf(f_1110_3,plain,
( hBOOL(hAPP_int_bool(zcong(U_2992,U_2993),U_2991))
| ~ hBOOL(hAPP_int_bool(zcong(multInv(U_2991,U_2992),multInv(U_2991,U_2993)),U_2991))
| hBOOL(hAPP_int_bool(zcong(U_2993,zero_zero_int),U_2991))
| hBOOL(hAPP_int_bool(zcong(U_2992,zero_zero_int),U_2991))
| ~ hBOOL(hAPP_int_bool(zprime,U_2991))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_2991)) ),
inference(clausify,[status(thm)],[f_1110_2]) ).
fof(f_1111_1,plain,
! [X_1,P_1] :
( hBOOL(hAPP_int_bool(zcong(multInv(P_1,multInv(P_1,X_1)),X_1),P_1))
| hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),P_1))
| ~ hBOOL(hAPP_int_bool(zprime,P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1085_MultInv__prop4]) ).
fof(f_1111_2,plain,
! [U_2995,U_2994] :
( hBOOL(hAPP_int_bool(zcong(multInv(U_2994,multInv(U_2994,U_2995)),U_2995),U_2994))
| hBOOL(hAPP_int_bool(zcong(U_2995,zero_zero_int),U_2994))
| ~ hBOOL(hAPP_int_bool(zprime,U_2994))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_2994)) ),
inference(variable_rename,[status(thm)],[f_1111_1]) ).
cnf(f_1111_3,plain,
( hBOOL(hAPP_int_bool(zcong(multInv(U_2994,multInv(U_2994,U_2995)),U_2995),U_2994))
| hBOOL(hAPP_int_bool(zcong(U_2995,zero_zero_int),U_2994))
| ~ hBOOL(hAPP_int_bool(zprime,U_2994))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_2994)) ),
inference(clausify,[status(thm)],[f_1111_2]) ).
fof(f_1112_1,plain,
! [X_1,P_1] :
( ~ hBOOL(hAPP_int_bool(zcong(multInv(P_1,X_1),zero_zero_int),P_1))
| hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),P_1))
| ~ hBOOL(hAPP_int_bool(zprime,P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1086_MultInv__prop3]) ).
fof(f_1112_2,plain,
! [U_2997,U_2996] :
( ~ hBOOL(hAPP_int_bool(zcong(multInv(U_2996,U_2997),zero_zero_int),U_2996))
| hBOOL(hAPP_int_bool(zcong(U_2997,zero_zero_int),U_2996))
| ~ hBOOL(hAPP_int_bool(zprime,U_2996))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_2996)) ),
inference(variable_rename,[status(thm)],[f_1112_1]) ).
cnf(f_1112_3,plain,
( ~ hBOOL(hAPP_int_bool(zcong(multInv(U_2996,U_2997),zero_zero_int),U_2996))
| hBOOL(hAPP_int_bool(zcong(U_2997,zero_zero_int),U_2996))
| ~ hBOOL(hAPP_int_bool(zprime,U_2996))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_2996)) ),
inference(clausify,[status(thm)],[f_1112_2]) ).
fof(f_1113_1,plain,
! [A,P_1] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),inv(P_1,A)),one_one_int),P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A))
| ~ hBOOL(hAPP_int_bool(zprime,P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1087_inv__is__inv]) ).
fof(f_1113_2,plain,
! [U_2999,U_2998] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_2999),inv(U_2998,U_2999)),one_one_int),U_2998))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2999),U_2998))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2999))
| ~ hBOOL(hAPP_int_bool(zprime,U_2998)) ),
inference(variable_rename,[status(thm)],[f_1113_1]) ).
cnf(f_1113_3,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_2999),inv(U_2998,U_2999)),one_one_int),U_2998))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_2999),U_2998))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_2999))
| ~ hBOOL(hAPP_int_bool(zprime,U_2998)) ),
inference(clausify,[status(thm)],[f_1113_2]) ).
fof(f_1114_1,plain,
! [K_1,A,J_1,P_1] :
( hBOOL(hAPP_int_bool(zcong(K_1,hAPP_int_int(times_times_int(A),multInv(P_1,J_1))),P_1))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(multInv(P_1,J_1)),J_1)),K_1),hAPP_int_int(times_times_int(multInv(P_1,J_1)),A)),P_1))
| hBOOL(hAPP_int_bool(zcong(J_1,zero_zero_int),P_1))
| ~ hBOOL(hAPP_int_bool(zprime,P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1088_aux______4]) ).
fof(f_1114_2,plain,
! [U_3003,U_3002,U_3001,U_3000] :
( hBOOL(hAPP_int_bool(zcong(U_3003,hAPP_int_int(times_times_int(U_3002),multInv(U_3000,U_3001))),U_3000))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(multInv(U_3000,U_3001)),U_3001)),U_3003),hAPP_int_int(times_times_int(multInv(U_3000,U_3001)),U_3002)),U_3000))
| hBOOL(hAPP_int_bool(zcong(U_3001,zero_zero_int),U_3000))
| ~ hBOOL(hAPP_int_bool(zprime,U_3000))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_3000)) ),
inference(variable_rename,[status(thm)],[f_1114_1]) ).
cnf(f_1114_3,plain,
( hBOOL(hAPP_int_bool(zcong(U_3003,hAPP_int_int(times_times_int(U_3002),multInv(U_3000,U_3001))),U_3000))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(multInv(U_3000,U_3001)),U_3001)),U_3003),hAPP_int_int(times_times_int(multInv(U_3000,U_3001)),U_3002)),U_3000))
| hBOOL(hAPP_int_bool(zcong(U_3001,zero_zero_int),U_3000))
| ~ hBOOL(hAPP_int_bool(zprime,U_3000))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_3000)) ),
inference(clausify,[status(thm)],[f_1114_2]) ).
fof(f_1115_1,plain,
! [J_1,A,K_1,P_1] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(J_1),K_1),A),P_1))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(J_1),K_1),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(A),multInv(P_1,K_1))),K_1)),P_1))
| hBOOL(hAPP_int_bool(zcong(K_1,zero_zero_int),P_1))
| ~ hBOOL(hAPP_int_bool(zprime,P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1089_aux______2]) ).
fof(f_1115_2,plain,
! [U_3007,U_3006,U_3005,U_3004] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_3007),U_3005),U_3006),U_3004))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_3007),U_3005),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_3006),multInv(U_3004,U_3005))),U_3005)),U_3004))
| hBOOL(hAPP_int_bool(zcong(U_3005,zero_zero_int),U_3004))
| ~ hBOOL(hAPP_int_bool(zprime,U_3004))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_3004)) ),
inference(variable_rename,[status(thm)],[f_1115_1]) ).
cnf(f_1115_3,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_3007),U_3005),U_3006),U_3004))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_3007),U_3005),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_3006),multInv(U_3004,U_3005))),U_3005)),U_3004))
| hBOOL(hAPP_int_bool(zcong(U_3005,zero_zero_int),U_3004))
| ~ hBOOL(hAPP_int_bool(zprime,U_3004))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_3004)) ),
inference(clausify,[status(thm)],[f_1115_2]) ).
fof(f_1116_1,plain,
! [A,J_1,K_1,P_1] :
( hBOOL(hAPP_int_bool(zcong(K_1,hAPP_int_int(times_times_int(A),multInv(P_1,J_1))),P_1))
| ~ hBOOL(hAPP_int_bool(zcong(J_1,hAPP_int_int(times_times_int(A),multInv(P_1,K_1))),P_1))
| hBOOL(hAPP_int_bool(zcong(J_1,zero_zero_int),P_1))
| hBOOL(hAPP_int_bool(zcong(K_1,zero_zero_int),P_1))
| ~ hBOOL(hAPP_int_bool(zprime,P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1090_MultInv__zcong__prop2]) ).
fof(f_1116_2,plain,
! [U_3011,U_3010,U_3009,U_3008] :
( hBOOL(hAPP_int_bool(zcong(U_3009,hAPP_int_int(times_times_int(U_3011),multInv(U_3008,U_3010))),U_3008))
| ~ hBOOL(hAPP_int_bool(zcong(U_3010,hAPP_int_int(times_times_int(U_3011),multInv(U_3008,U_3009))),U_3008))
| hBOOL(hAPP_int_bool(zcong(U_3010,zero_zero_int),U_3008))
| hBOOL(hAPP_int_bool(zcong(U_3009,zero_zero_int),U_3008))
| ~ hBOOL(hAPP_int_bool(zprime,U_3008))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_3008)) ),
inference(variable_rename,[status(thm)],[f_1116_1]) ).
cnf(f_1116_3,plain,
( hBOOL(hAPP_int_bool(zcong(U_3009,hAPP_int_int(times_times_int(U_3011),multInv(U_3008,U_3010))),U_3008))
| ~ hBOOL(hAPP_int_bool(zcong(U_3010,hAPP_int_int(times_times_int(U_3011),multInv(U_3008,U_3009))),U_3008))
| hBOOL(hAPP_int_bool(zcong(U_3010,zero_zero_int),U_3008))
| hBOOL(hAPP_int_bool(zcong(U_3009,zero_zero_int),U_3008))
| ~ hBOOL(hAPP_int_bool(zprime,U_3008))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_3008)) ),
inference(clausify,[status(thm)],[f_1116_2]) ).
fof(f_1117_1,plain,
! [J_1,K_1,A,P_1] :
( hBOOL(hAPP_int_bool(zcong(J_1,K_1),P_1))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(A),multInv(P_1,J_1)),hAPP_int_int(times_times_int(A),multInv(P_1,K_1))),P_1))
| hBOOL(hAPP_int_bool(zcong(J_1,zero_zero_int),P_1))
| hBOOL(hAPP_int_bool(zcong(K_1,zero_zero_int),P_1))
| hBOOL(hAPP_int_bool(zcong(A,zero_zero_int),P_1))
| ~ hBOOL(hAPP_int_bool(zprime,P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1091_MultInv__zcong__prop3]) ).
fof(f_1117_2,plain,
! [U_3015,U_3014,U_3013,U_3012] :
( hBOOL(hAPP_int_bool(zcong(U_3015,U_3014),U_3012))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_3013),multInv(U_3012,U_3015)),hAPP_int_int(times_times_int(U_3013),multInv(U_3012,U_3014))),U_3012))
| hBOOL(hAPP_int_bool(zcong(U_3015,zero_zero_int),U_3012))
| hBOOL(hAPP_int_bool(zcong(U_3014,zero_zero_int),U_3012))
| hBOOL(hAPP_int_bool(zcong(U_3013,zero_zero_int),U_3012))
| ~ hBOOL(hAPP_int_bool(zprime,U_3012))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_3012)) ),
inference(variable_rename,[status(thm)],[f_1117_1]) ).
cnf(f_1117_3,plain,
( hBOOL(hAPP_int_bool(zcong(U_3015,U_3014),U_3012))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_3013),multInv(U_3012,U_3015)),hAPP_int_int(times_times_int(U_3013),multInv(U_3012,U_3014))),U_3012))
| hBOOL(hAPP_int_bool(zcong(U_3015,zero_zero_int),U_3012))
| hBOOL(hAPP_int_bool(zcong(U_3014,zero_zero_int),U_3012))
| hBOOL(hAPP_int_bool(zcong(U_3013,zero_zero_int),U_3012))
| ~ hBOOL(hAPP_int_bool(zprime,U_3012))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_3012)) ),
inference(clausify,[status(thm)],[f_1117_2]) ).
fof(f_1118_1,plain,
! [X_1,P_1] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X_1),multInv(P_1,X_1))),multInv(P_1,multInv(P_1,X_1))),X_1),P_1))
| hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),P_1))
| ~ hBOOL(hAPP_int_bool(zprime,P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1092_Int2_Oaux____2]) ).
fof(f_1118_2,plain,
! [U_3017,U_3016] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_3017),multInv(U_3016,U_3017))),multInv(U_3016,multInv(U_3016,U_3017))),U_3017),U_3016))
| hBOOL(hAPP_int_bool(zcong(U_3017,zero_zero_int),U_3016))
| ~ hBOOL(hAPP_int_bool(zprime,U_3016))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_3016)) ),
inference(variable_rename,[status(thm)],[f_1118_1]) ).
cnf(f_1118_3,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_3017),multInv(U_3016,U_3017))),multInv(U_3016,multInv(U_3016,U_3017))),U_3017),U_3016))
| hBOOL(hAPP_int_bool(zcong(U_3017,zero_zero_int),U_3016))
| ~ hBOOL(hAPP_int_bool(zprime,U_3016))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_3016)) ),
inference(clausify,[status(thm)],[f_1118_2]) ).
fof(f_1119_1,plain,
! [X_1,P_1] :
( hBOOL(hAPP_int_bool(zcong(multInv(P_1,multInv(P_1,X_1)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(X_1),multInv(P_1,X_1))),multInv(P_1,multInv(P_1,X_1)))),P_1))
| hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),P_1))
| ~ hBOOL(hAPP_int_bool(zprime,P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1093_Int2_Oaux____1]) ).
fof(f_1119_2,plain,
! [U_3019,U_3018] :
( hBOOL(hAPP_int_bool(zcong(multInv(U_3018,multInv(U_3018,U_3019)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_3019),multInv(U_3018,U_3019))),multInv(U_3018,multInv(U_3018,U_3019)))),U_3018))
| hBOOL(hAPP_int_bool(zcong(U_3019,zero_zero_int),U_3018))
| ~ hBOOL(hAPP_int_bool(zprime,U_3018))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_3018)) ),
inference(variable_rename,[status(thm)],[f_1119_1]) ).
cnf(f_1119_3,plain,
( hBOOL(hAPP_int_bool(zcong(multInv(U_3018,multInv(U_3018,U_3019)),hAPP_int_int(times_times_int(hAPP_int_int(times_times_int(U_3019),multInv(U_3018,U_3019))),multInv(U_3018,multInv(U_3018,U_3019)))),U_3018))
| hBOOL(hAPP_int_bool(zcong(U_3019,zero_zero_int),U_3018))
| ~ hBOOL(hAPP_int_bool(zprime,U_3018))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_3018)) ),
inference(clausify,[status(thm)],[f_1119_2]) ).
fof(f_1120_1,plain,
! [X_1,P_1] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(multInv(P_1,X_1)),X_1),one_one_int),P_1))
| hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),P_1))
| ~ hBOOL(hAPP_int_bool(zprime,P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1094_MultInv__prop2a]) ).
fof(f_1120_2,plain,
! [U_3021,U_3020] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(multInv(U_3020,U_3021)),U_3021),one_one_int),U_3020))
| hBOOL(hAPP_int_bool(zcong(U_3021,zero_zero_int),U_3020))
| ~ hBOOL(hAPP_int_bool(zprime,U_3020))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_3020)) ),
inference(variable_rename,[status(thm)],[f_1120_1]) ).
cnf(f_1120_3,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(multInv(U_3020,U_3021)),U_3021),one_one_int),U_3020))
| hBOOL(hAPP_int_bool(zcong(U_3021,zero_zero_int),U_3020))
| ~ hBOOL(hAPP_int_bool(zprime,U_3020))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_3020)) ),
inference(clausify,[status(thm)],[f_1120_2]) ).
fof(f_1121_1,plain,
! [X_1,P_1] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(X_1),multInv(P_1,X_1)),one_one_int),P_1))
| hBOOL(hAPP_int_bool(zcong(X_1,zero_zero_int),P_1))
| ~ hBOOL(hAPP_int_bool(zprime,P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1095_MultInv__prop2]) ).
fof(f_1121_2,plain,
! [U_3023,U_3022] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_3023),multInv(U_3022,U_3023)),one_one_int),U_3022))
| hBOOL(hAPP_int_bool(zcong(U_3023,zero_zero_int),U_3022))
| ~ hBOOL(hAPP_int_bool(zprime,U_3022))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_3022)) ),
inference(variable_rename,[status(thm)],[f_1121_1]) ).
cnf(f_1121_3,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(U_3023),multInv(U_3022,U_3023)),one_one_int),U_3022))
| hBOOL(hAPP_int_bool(zcong(U_3023,zero_zero_int),U_3022))
| ~ hBOOL(hAPP_int_bool(zprime,U_3022))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_3022)) ),
inference(clausify,[status(thm)],[f_1121_2]) ).
fof(f_1122_1,plain,
! [B_2,A_2,P_3] :
( hBOOL(member_int(inv(P_3,B_2),wset(A_2,P_3)))
| ~ hBOOL(member_int(B_2,wset(A_2,P_3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),hAPP_int_int(minus_minus_int(P_3),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),P_3))
| ~ hBOOL(hAPP_int_bool(zprime,P_3)) ),
inference(fof_nnf,[status(thm)],[fact_1096_wset__mem__inv__mem]) ).
fof(f_1122_2,plain,
! [U_3026,U_3025,U_3024] :
( hBOOL(member_int(inv(U_3024,U_3026),wset(U_3025,U_3024)))
| ~ hBOOL(member_int(U_3026,wset(U_3025,U_3024)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3025),hAPP_int_int(minus_minus_int(U_3024),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),U_3024))
| ~ hBOOL(hAPP_int_bool(zprime,U_3024)) ),
inference(variable_rename,[status(thm)],[f_1122_1]) ).
cnf(f_1122_3,plain,
( hBOOL(member_int(inv(U_3024,U_3026),wset(U_3025,U_3024)))
| ~ hBOOL(member_int(U_3026,wset(U_3025,U_3024)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3025),hAPP_int_int(minus_minus_int(U_3024),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),U_3024))
| ~ hBOOL(hAPP_int_bool(zprime,U_3024)) ),
inference(clausify,[status(thm)],[f_1122_2]) ).
fof(f_1123_1,plain,
! [B_2,A_2,P_3] :
( hBOOL(member_int(B_2,wset(A_2,P_3)))
| ~ hBOOL(member_int(inv(P_3,B_2),wset(A_2,P_3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_2),hAPP_int_int(minus_minus_int(P_3),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),B_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),hAPP_int_int(minus_minus_int(P_3),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),P_3))
| ~ hBOOL(hAPP_int_bool(zprime,P_3)) ),
inference(fof_nnf,[status(thm)],[fact_1097_wset__inv__mem__mem]) ).
fof(f_1123_2,plain,
! [U_3029,U_3028,U_3027] :
( hBOOL(member_int(U_3029,wset(U_3028,U_3027)))
| ~ hBOOL(member_int(inv(U_3027,U_3029),wset(U_3028,U_3027)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3029),hAPP_int_int(minus_minus_int(U_3027),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_3029))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3028),hAPP_int_int(minus_minus_int(U_3027),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),U_3027))
| ~ hBOOL(hAPP_int_bool(zprime,U_3027)) ),
inference(variable_rename,[status(thm)],[f_1123_1]) ).
cnf(f_1123_3,plain,
( hBOOL(member_int(U_3029,wset(U_3028,U_3027)))
| ~ hBOOL(member_int(inv(U_3027,U_3029),wset(U_3028,U_3027)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3029),hAPP_int_int(minus_minus_int(U_3027),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_3029))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3028),hAPP_int_int(minus_minus_int(U_3027),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(bit1(bit0(bit1(pls))))),U_3027))
| ~ hBOOL(hAPP_int_bool(zprime,U_3027)) ),
inference(clausify,[status(thm)],[f_1123_2]) ).
fof(f_1124_1,plain,
! [P_3,A_2] :
( hBOOL(member_int(A_2,wset(A_2,P_3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_2)) ),
inference(fof_nnf,[status(thm)],[fact_1098_wset__mem__mem]) ).
fof(f_1124_2,plain,
! [U_3031,U_3030] :
( hBOOL(member_int(U_3030,wset(U_3030,U_3031)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_3030)) ),
inference(variable_rename,[status(thm)],[f_1124_1]) ).
cnf(f_1124_3,plain,
( hBOOL(member_int(U_3030,wset(U_3030,U_3031)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_3030)) ),
inference(clausify,[status(thm)],[f_1124_2]) ).
fof(f_1125_1,plain,
! [B_2,P_3,A_2] :
( hBOOL(member_int(B_2,wset(A_2,P_3)))
| ~ hBOOL(member_int(B_2,wset(hAPP_int_int(minus_minus_int(A_2),one_one_int),P_3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_2)) ),
inference(fof_nnf,[status(thm)],[fact_1099_wset__subset]) ).
fof(f_1125_2,plain,
! [U_3034,U_3033,U_3032] :
( hBOOL(member_int(U_3034,wset(U_3032,U_3033)))
| ~ hBOOL(member_int(U_3034,wset(hAPP_int_int(minus_minus_int(U_3032),one_one_int),U_3033)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_3032)) ),
inference(variable_rename,[status(thm)],[f_1125_1]) ).
cnf(f_1125_3,plain,
( hBOOL(member_int(U_3034,wset(U_3032,U_3033)))
| ~ hBOOL(member_int(U_3034,wset(hAPP_int_int(minus_minus_int(U_3032),one_one_int),U_3033)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_3032)) ),
inference(clausify,[status(thm)],[f_1125_2]) ).
fof(f_1126_1,plain,
! [B_2,A_2,P_3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_2),hAPP_int_int(minus_minus_int(P_3),one_one_int)))
| ~ hBOOL(member_int(B_2,wset(A_2,P_3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),hAPP_int_int(minus_minus_int(P_3),one_one_int)))
| ~ hBOOL(hAPP_int_bool(zprime,P_3)) ),
inference(fof_nnf,[status(thm)],[fact_1100_wset__less]) ).
fof(f_1126_2,plain,
! [U_3037,U_3036,U_3035] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3037),hAPP_int_int(minus_minus_int(U_3035),one_one_int)))
| ~ hBOOL(member_int(U_3037,wset(U_3036,U_3035)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3036),hAPP_int_int(minus_minus_int(U_3035),one_one_int)))
| ~ hBOOL(hAPP_int_bool(zprime,U_3035)) ),
inference(variable_rename,[status(thm)],[f_1126_1]) ).
cnf(f_1126_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3037),hAPP_int_int(minus_minus_int(U_3035),one_one_int)))
| ~ hBOOL(member_int(U_3037,wset(U_3036,U_3035)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3036),hAPP_int_int(minus_minus_int(U_3035),one_one_int)))
| ~ hBOOL(hAPP_int_bool(zprime,U_3035)) ),
inference(clausify,[status(thm)],[f_1126_2]) ).
fof(f_1127_1,plain,
! [B_2,A_2,P_3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),B_2))
| ~ hBOOL(member_int(B_2,wset(A_2,P_3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),hAPP_int_int(minus_minus_int(P_3),one_one_int)))
| ~ hBOOL(hAPP_int_bool(zprime,P_3)) ),
inference(fof_nnf,[status(thm)],[fact_1101_wset__g__1]) ).
fof(f_1127_2,plain,
! [U_3040,U_3039,U_3038] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_3040))
| ~ hBOOL(member_int(U_3040,wset(U_3039,U_3038)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3039),hAPP_int_int(minus_minus_int(U_3038),one_one_int)))
| ~ hBOOL(hAPP_int_bool(zprime,U_3038)) ),
inference(variable_rename,[status(thm)],[f_1127_1]) ).
cnf(f_1127_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_3040))
| ~ hBOOL(member_int(U_3040,wset(U_3039,U_3038)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3039),hAPP_int_int(minus_minus_int(U_3038),one_one_int)))
| ~ hBOOL(hAPP_int_bool(zprime,U_3038)) ),
inference(clausify,[status(thm)],[f_1127_2]) ).
fof(f_1128_1,plain,
! [B_2,P_3,A_2] :
( B_2 = inv(P_3,A_2)
| B_2 = A_2
| ~ hBOOL(member_int(B_2,wset(A_2,P_3)))
| hBOOL(member_int(B_2,wset(hAPP_int_int(minus_minus_int(A_2),one_one_int),P_3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_2))
| ~ is_int(A_2)
| ~ is_int(B_2) ),
inference(fof_nnf,[status(thm)],[fact_1102_wset__mem__imp__or]) ).
fof(f_1128_2,plain,
! [U_3043,U_3042,U_3041] :
( U_3043 = inv(U_3042,U_3041)
| U_3043 = U_3041
| ~ hBOOL(member_int(U_3043,wset(U_3041,U_3042)))
| hBOOL(member_int(U_3043,wset(hAPP_int_int(minus_minus_int(U_3041),one_one_int),U_3042)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_3041))
| ~ is_int(U_3041)
| ~ is_int(U_3043) ),
inference(variable_rename,[status(thm)],[f_1128_1]) ).
cnf(f_1128_3,plain,
( U_3043 = inv(U_3042,U_3041)
| U_3043 = U_3041
| ~ hBOOL(member_int(U_3043,wset(U_3041,U_3042)))
| hBOOL(member_int(U_3043,wset(hAPP_int_int(minus_minus_int(U_3041),one_one_int),U_3042)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_3041))
| ~ is_int(U_3041)
| ~ is_int(U_3043) ),
inference(clausify,[status(thm)],[f_1128_2]) ).
fof(f_1129_1,plain,
! [B_2,A_2,P_3] :
( hBOOL(member_int(B_2,wset(A_2,P_3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),A_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),B_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),hAPP_int_int(minus_minus_int(P_3),one_one_int)))
| ~ hBOOL(hAPP_int_bool(zprime,P_3)) ),
inference(fof_nnf,[status(thm)],[fact_1103_wset__mem]) ).
fof(f_1129_2,plain,
! [U_3046,U_3045,U_3044] :
( hBOOL(member_int(U_3046,wset(U_3045,U_3044)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3046),U_3045))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_3046))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3045),hAPP_int_int(minus_minus_int(U_3044),one_one_int)))
| ~ hBOOL(hAPP_int_bool(zprime,U_3044)) ),
inference(variable_rename,[status(thm)],[f_1129_1]) ).
cnf(f_1129_3,plain,
( hBOOL(member_int(U_3046,wset(U_3045,U_3044)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3046),U_3045))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_3046))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3045),hAPP_int_int(minus_minus_int(U_3044),one_one_int)))
| ~ hBOOL(hAPP_int_bool(zprime,U_3044)) ),
inference(clausify,[status(thm)],[f_1129_2]) ).
fof(f_1130_1,plain,
! [P_2,I_2,K] :
( hBOOL(hAPP_int_bool(P_2,I_2))
| ? [I] :
( ~ hBOOL(hAPP_int_bool(P_2,hAPP_int_int(minus_minus_int(I),one_one_int)))
& hBOOL(hAPP_int_bool(P_2,I))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I),K))
& is_int(I) )
| ~ hBOOL(hAPP_int_bool(P_2,K))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_2),K)) ),
inference(fof_nnf,[status(thm)],[fact_1104_int__le__induct]) ).
fof(f_1130_2,plain,
! [U_3050,U_3049,U_3048] :
( hBOOL(hAPP_int_bool(U_3050,U_3049))
| ? [U_3047] :
( ~ hBOOL(hAPP_int_bool(U_3050,hAPP_int_int(minus_minus_int(U_3047),one_one_int)))
& hBOOL(hAPP_int_bool(U_3050,U_3047))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3047),U_3048))
& is_int(U_3047) )
| ~ hBOOL(hAPP_int_bool(U_3050,U_3048))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3049),U_3048)) ),
inference(variable_rename,[status(thm)],[f_1130_1]) ).
fof(f_1130_3,plain,
! [U_3050,U_3049,U_3048] :
( hBOOL(hAPP_int_bool(U_3050,U_3049))
| ( ~ hBOOL(hAPP_int_bool(U_3050,hAPP_int_int(minus_minus_int(sK24(U_3050,U_3049,U_3048)),one_one_int)))
& hBOOL(hAPP_int_bool(U_3050,sK24(U_3050,U_3049,U_3048)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK24(U_3050,U_3049,U_3048)),U_3048))
& is_int(sK24(U_3050,U_3049,U_3048)) )
| ~ hBOOL(hAPP_int_bool(U_3050,U_3048))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3049),U_3048)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_3047,sK24(U_3050,U_3049,U_3048))],[f_1130_2]) ).
cnf(f_1130_4,plain,
( is_int(sK24(U_3050,U_3049,U_3048))
| hBOOL(hAPP_int_bool(U_3050,U_3049))
| ~ hBOOL(hAPP_int_bool(U_3050,U_3048))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3049),U_3048)) ),
inference(clausify,[status(thm)],[f_1130_3]) ).
cnf(f_1130_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK24(U_3050,U_3049,U_3048)),U_3048))
| hBOOL(hAPP_int_bool(U_3050,U_3049))
| ~ hBOOL(hAPP_int_bool(U_3050,U_3048))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3049),U_3048)) ),
inference(clausify,[status(thm)],[f_1130_3]) ).
cnf(f_1130_6,plain,
( hBOOL(hAPP_int_bool(U_3050,sK24(U_3050,U_3049,U_3048)))
| hBOOL(hAPP_int_bool(U_3050,U_3049))
| ~ hBOOL(hAPP_int_bool(U_3050,U_3048))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3049),U_3048)) ),
inference(clausify,[status(thm)],[f_1130_3]) ).
cnf(f_1130_7,plain,
( ~ hBOOL(hAPP_int_bool(U_3050,hAPP_int_int(minus_minus_int(sK24(U_3050,U_3049,U_3048)),one_one_int)))
| hBOOL(hAPP_int_bool(U_3050,U_3049))
| ~ hBOOL(hAPP_int_bool(U_3050,U_3048))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3049),U_3048)) ),
inference(clausify,[status(thm)],[f_1130_3]) ).
fof(f_1131_1,plain,
! [P_2,I_2,K] :
( hBOOL(hAPP_int_bool(P_2,I_2))
| ? [I] :
( ~ hBOOL(hAPP_int_bool(P_2,hAPP_int_int(minus_minus_int(I),one_one_int)))
& hBOOL(hAPP_int_bool(P_2,I))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I),K))
& is_int(I) )
| ~ hBOOL(hAPP_int_bool(P_2,hAPP_int_int(minus_minus_int(K),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_2),K)) ),
inference(fof_nnf,[status(thm)],[fact_1105_int__less__induct]) ).
fof(f_1131_2,plain,
! [U_3054,U_3053,U_3052] :
( hBOOL(hAPP_int_bool(U_3054,U_3053))
| ? [U_3051] :
( ~ hBOOL(hAPP_int_bool(U_3054,hAPP_int_int(minus_minus_int(U_3051),one_one_int)))
& hBOOL(hAPP_int_bool(U_3054,U_3051))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3051),U_3052))
& is_int(U_3051) )
| ~ hBOOL(hAPP_int_bool(U_3054,hAPP_int_int(minus_minus_int(U_3052),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3053),U_3052)) ),
inference(variable_rename,[status(thm)],[f_1131_1]) ).
fof(f_1131_3,plain,
! [U_3054,U_3053,U_3052] :
( hBOOL(hAPP_int_bool(U_3054,U_3053))
| ( ~ hBOOL(hAPP_int_bool(U_3054,hAPP_int_int(minus_minus_int(sK25(U_3054,U_3053,U_3052)),one_one_int)))
& hBOOL(hAPP_int_bool(U_3054,sK25(U_3054,U_3053,U_3052)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK25(U_3054,U_3053,U_3052)),U_3052))
& is_int(sK25(U_3054,U_3053,U_3052)) )
| ~ hBOOL(hAPP_int_bool(U_3054,hAPP_int_int(minus_minus_int(U_3052),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3053),U_3052)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_3051,sK25(U_3054,U_3053,U_3052))],[f_1131_2]) ).
cnf(f_1131_4,plain,
( is_int(sK25(U_3054,U_3053,U_3052))
| hBOOL(hAPP_int_bool(U_3054,U_3053))
| ~ hBOOL(hAPP_int_bool(U_3054,hAPP_int_int(minus_minus_int(U_3052),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3053),U_3052)) ),
inference(clausify,[status(thm)],[f_1131_3]) ).
cnf(f_1131_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK25(U_3054,U_3053,U_3052)),U_3052))
| hBOOL(hAPP_int_bool(U_3054,U_3053))
| ~ hBOOL(hAPP_int_bool(U_3054,hAPP_int_int(minus_minus_int(U_3052),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3053),U_3052)) ),
inference(clausify,[status(thm)],[f_1131_3]) ).
cnf(f_1131_6,plain,
( hBOOL(hAPP_int_bool(U_3054,sK25(U_3054,U_3053,U_3052)))
| hBOOL(hAPP_int_bool(U_3054,U_3053))
| ~ hBOOL(hAPP_int_bool(U_3054,hAPP_int_int(minus_minus_int(U_3052),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3053),U_3052)) ),
inference(clausify,[status(thm)],[f_1131_3]) ).
cnf(f_1131_7,plain,
( ~ hBOOL(hAPP_int_bool(U_3054,hAPP_int_int(minus_minus_int(sK25(U_3054,U_3053,U_3052)),one_one_int)))
| hBOOL(hAPP_int_bool(U_3054,U_3053))
| ~ hBOOL(hAPP_int_bool(U_3054,hAPP_int_int(minus_minus_int(U_3052),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3053),U_3052)) ),
inference(clausify,[status(thm)],[f_1131_3]) ).
fof(f_1132_1,plain,
! [X_2,P_2] :
( hBOOL(hAPP_int_bool(P_2,X_2))
| ? [A_3] :
( ~ hBOOL(hAPP_int_bool(P_2,A_3))
& ( hBOOL(hAPP_int_bool(P_2,hAPP_int_int(minus_minus_int(A_3),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),A_3)) )
& is_int(A_3) ) ),
inference(fof_nnf,[status(thm)],[fact_1106_d22set__induct__old]) ).
fof(f_1132_2,plain,
! [U_3057,U_3056] :
( hBOOL(hAPP_int_bool(U_3056,U_3057))
| ? [U_3055] :
( ~ hBOOL(hAPP_int_bool(U_3056,U_3055))
& ( hBOOL(hAPP_int_bool(U_3056,hAPP_int_int(minus_minus_int(U_3055),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_3055)) )
& is_int(U_3055) ) ),
inference(variable_rename,[status(thm)],[f_1132_1]) ).
fof(f_1132_3,plain,
! [U_3057,U_3056] :
( hBOOL(hAPP_int_bool(U_3056,U_3057))
| ( ~ hBOOL(hAPP_int_bool(U_3056,sK26(U_3057,U_3056)))
& ( hBOOL(hAPP_int_bool(U_3056,hAPP_int_int(minus_minus_int(sK26(U_3057,U_3056)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),sK26(U_3057,U_3056))) )
& is_int(sK26(U_3057,U_3056)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_3055,sK26(U_3057,U_3056))],[f_1132_2]) ).
cnf(f_1132_4,plain,
( is_int(sK26(U_3057,U_3056))
| hBOOL(hAPP_int_bool(U_3056,U_3057)) ),
inference(clausify,[status(thm)],[f_1132_3]) ).
cnf(f_1132_5,plain,
( hBOOL(hAPP_int_bool(U_3056,hAPP_int_int(minus_minus_int(sK26(U_3057,U_3056)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),sK26(U_3057,U_3056)))
| hBOOL(hAPP_int_bool(U_3056,U_3057)) ),
inference(clausify,[status(thm)],[f_1132_3]) ).
cnf(f_1132_6,plain,
( ~ hBOOL(hAPP_int_bool(U_3056,sK26(U_3057,U_3056)))
| hBOOL(hAPP_int_bool(U_3056,U_3057)) ),
inference(clausify,[status(thm)],[f_1132_3]) ).
fof(f_1133_1,plain,
! [P_2,K,I_2] :
( hBOOL(hAPP_int_bool(P_2,I_2))
| ? [I] :
( ~ hBOOL(hAPP_int_bool(P_2,hAPP_int_int(plus_plus_int(I),one_one_int)))
& hBOOL(hAPP_int_bool(P_2,I))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),I))
& is_int(I) )
| ~ hBOOL(hAPP_int_bool(P_2,K))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),I_2)) ),
inference(fof_nnf,[status(thm)],[fact_1107_int__ge__induct]) ).
fof(f_1133_2,plain,
! [U_3061,U_3060,U_3059] :
( hBOOL(hAPP_int_bool(U_3061,U_3059))
| ? [U_3058] :
( ~ hBOOL(hAPP_int_bool(U_3061,hAPP_int_int(plus_plus_int(U_3058),one_one_int)))
& hBOOL(hAPP_int_bool(U_3061,U_3058))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3060),U_3058))
& is_int(U_3058) )
| ~ hBOOL(hAPP_int_bool(U_3061,U_3060))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3060),U_3059)) ),
inference(variable_rename,[status(thm)],[f_1133_1]) ).
fof(f_1133_3,plain,
! [U_3061,U_3060,U_3059] :
( hBOOL(hAPP_int_bool(U_3061,U_3059))
| ( ~ hBOOL(hAPP_int_bool(U_3061,hAPP_int_int(plus_plus_int(sK27(U_3061,U_3060,U_3059)),one_one_int)))
& hBOOL(hAPP_int_bool(U_3061,sK27(U_3061,U_3060,U_3059)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3060),sK27(U_3061,U_3060,U_3059)))
& is_int(sK27(U_3061,U_3060,U_3059)) )
| ~ hBOOL(hAPP_int_bool(U_3061,U_3060))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3060),U_3059)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_3058,sK27(U_3061,U_3060,U_3059))],[f_1133_2]) ).
cnf(f_1133_4,plain,
( is_int(sK27(U_3061,U_3060,U_3059))
| hBOOL(hAPP_int_bool(U_3061,U_3059))
| ~ hBOOL(hAPP_int_bool(U_3061,U_3060))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3060),U_3059)) ),
inference(clausify,[status(thm)],[f_1133_3]) ).
cnf(f_1133_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3060),sK27(U_3061,U_3060,U_3059)))
| hBOOL(hAPP_int_bool(U_3061,U_3059))
| ~ hBOOL(hAPP_int_bool(U_3061,U_3060))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3060),U_3059)) ),
inference(clausify,[status(thm)],[f_1133_3]) ).
cnf(f_1133_6,plain,
( hBOOL(hAPP_int_bool(U_3061,sK27(U_3061,U_3060,U_3059)))
| hBOOL(hAPP_int_bool(U_3061,U_3059))
| ~ hBOOL(hAPP_int_bool(U_3061,U_3060))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3060),U_3059)) ),
inference(clausify,[status(thm)],[f_1133_3]) ).
cnf(f_1133_7,plain,
( ~ hBOOL(hAPP_int_bool(U_3061,hAPP_int_int(plus_plus_int(sK27(U_3061,U_3060,U_3059)),one_one_int)))
| hBOOL(hAPP_int_bool(U_3061,U_3059))
| ~ hBOOL(hAPP_int_bool(U_3061,U_3060))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3060),U_3059)) ),
inference(clausify,[status(thm)],[f_1133_3]) ).
fof(f_1134_1,plain,
! [P_2,K,I_2] :
( hBOOL(hAPP_int_bool(P_2,I_2))
| ? [I] :
( ~ hBOOL(hAPP_int_bool(P_2,hAPP_int_int(plus_plus_int(I),one_one_int)))
& hBOOL(hAPP_int_bool(P_2,I))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),I))
& is_int(I) )
| ~ hBOOL(hAPP_int_bool(P_2,hAPP_int_int(plus_plus_int(K),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),I_2)) ),
inference(fof_nnf,[status(thm)],[fact_1108_int__gr__induct]) ).
fof(f_1134_2,plain,
! [U_3065,U_3064,U_3063] :
( hBOOL(hAPP_int_bool(U_3065,U_3063))
| ? [U_3062] :
( ~ hBOOL(hAPP_int_bool(U_3065,hAPP_int_int(plus_plus_int(U_3062),one_one_int)))
& hBOOL(hAPP_int_bool(U_3065,U_3062))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3064),U_3062))
& is_int(U_3062) )
| ~ hBOOL(hAPP_int_bool(U_3065,hAPP_int_int(plus_plus_int(U_3064),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3064),U_3063)) ),
inference(variable_rename,[status(thm)],[f_1134_1]) ).
fof(f_1134_3,plain,
! [U_3065,U_3064,U_3063] :
( hBOOL(hAPP_int_bool(U_3065,U_3063))
| ( ~ hBOOL(hAPP_int_bool(U_3065,hAPP_int_int(plus_plus_int(sK28(U_3065,U_3064,U_3063)),one_one_int)))
& hBOOL(hAPP_int_bool(U_3065,sK28(U_3065,U_3064,U_3063)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3064),sK28(U_3065,U_3064,U_3063)))
& is_int(sK28(U_3065,U_3064,U_3063)) )
| ~ hBOOL(hAPP_int_bool(U_3065,hAPP_int_int(plus_plus_int(U_3064),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3064),U_3063)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_3062,sK28(U_3065,U_3064,U_3063))],[f_1134_2]) ).
cnf(f_1134_4,plain,
( is_int(sK28(U_3065,U_3064,U_3063))
| hBOOL(hAPP_int_bool(U_3065,U_3063))
| ~ hBOOL(hAPP_int_bool(U_3065,hAPP_int_int(plus_plus_int(U_3064),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3064),U_3063)) ),
inference(clausify,[status(thm)],[f_1134_3]) ).
cnf(f_1134_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3064),sK28(U_3065,U_3064,U_3063)))
| hBOOL(hAPP_int_bool(U_3065,U_3063))
| ~ hBOOL(hAPP_int_bool(U_3065,hAPP_int_int(plus_plus_int(U_3064),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3064),U_3063)) ),
inference(clausify,[status(thm)],[f_1134_3]) ).
cnf(f_1134_6,plain,
( hBOOL(hAPP_int_bool(U_3065,sK28(U_3065,U_3064,U_3063)))
| hBOOL(hAPP_int_bool(U_3065,U_3063))
| ~ hBOOL(hAPP_int_bool(U_3065,hAPP_int_int(plus_plus_int(U_3064),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3064),U_3063)) ),
inference(clausify,[status(thm)],[f_1134_3]) ).
cnf(f_1134_7,plain,
( ~ hBOOL(hAPP_int_bool(U_3065,hAPP_int_int(plus_plus_int(sK28(U_3065,U_3064,U_3063)),one_one_int)))
| hBOOL(hAPP_int_bool(U_3065,U_3063))
| ~ hBOOL(hAPP_int_bool(U_3065,hAPP_int_int(plus_plus_int(U_3064),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3064),U_3063)) ),
inference(clausify,[status(thm)],[f_1134_3]) ).
fof(f_1135_1,plain,
! [Ma,K,F_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(F_1,Ma)),K)),hAPP_nat_nat(F_1,hAPP_nat_nat(plus_plus_nat(Ma),K))))
| ? [M_2,N_2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F_1,M_2)),hAPP_nat_nat(F_1,N_2)))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_1109_mono__nat__linear__lb]) ).
fof(f_1135_2,plain,
! [U_3070,U_3069,U_3068] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(U_3068,U_3070)),U_3069)),hAPP_nat_nat(U_3068,hAPP_nat_nat(plus_plus_nat(U_3070),U_3069))))
| ? [U_3067,U_3066] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3068,U_3067)),hAPP_nat_nat(U_3068,U_3066)))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3067),U_3066)) ) ),
inference(variable_rename,[status(thm)],[f_1135_1]) ).
fof(f_1135_3,plain,
! [U_3070,U_3069,U_3068] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(U_3068,U_3070)),U_3069)),hAPP_nat_nat(U_3068,hAPP_nat_nat(plus_plus_nat(U_3070),U_3069))))
| ? [U_3066] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3068,sK29(U_3070,U_3069,U_3068))),hAPP_nat_nat(U_3068,U_3066)))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK29(U_3070,U_3069,U_3068)),U_3066)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_3067,sK29(U_3070,U_3069,U_3068))],[f_1135_2]) ).
fof(f_1135_4,plain,
! [U_3070,U_3069,U_3068] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(U_3068,U_3070)),U_3069)),hAPP_nat_nat(U_3068,hAPP_nat_nat(plus_plus_nat(U_3070),U_3069))))
| ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3068,sK29(U_3070,U_3069,U_3068))),hAPP_nat_nat(U_3068,sK30(U_3070,U_3069,U_3068))))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK29(U_3070,U_3069,U_3068)),sK30(U_3070,U_3069,U_3068))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_3066,sK30(U_3070,U_3069,U_3068))],[f_1135_3]) ).
cnf(f_1135_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK29(U_3070,U_3069,U_3068)),sK30(U_3070,U_3069,U_3068)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(U_3068,U_3070)),U_3069)),hAPP_nat_nat(U_3068,hAPP_nat_nat(plus_plus_nat(U_3070),U_3069)))) ),
inference(clausify,[status(thm)],[f_1135_4]) ).
cnf(f_1135_6,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3068,sK29(U_3070,U_3069,U_3068))),hAPP_nat_nat(U_3068,sK30(U_3070,U_3069,U_3068))))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(U_3068,U_3070)),U_3069)),hAPP_nat_nat(U_3068,hAPP_nat_nat(plus_plus_nat(U_3070),U_3069)))) ),
inference(clausify,[status(thm)],[f_1135_4]) ).
fof(f_1136_1,plain,
! [P_3] :
( d22set(hAPP_int_int(minus_minus_int(P_3),number_number_of_int(bit0(bit1(pls))))) = wset(hAPP_int_int(minus_minus_int(P_3),number_number_of_int(bit0(bit1(pls)))),P_3)
| ~ hBOOL(hAPP_int_bool(zprime,P_3)) ),
inference(fof_nnf,[status(thm)],[fact_1110_d22set__eq__wset]) ).
fof(f_1136_2,plain,
! [U_3071] :
( d22set(hAPP_int_int(minus_minus_int(U_3071),number_number_of_int(bit0(bit1(pls))))) = wset(hAPP_int_int(minus_minus_int(U_3071),number_number_of_int(bit0(bit1(pls)))),U_3071)
| ~ hBOOL(hAPP_int_bool(zprime,U_3071)) ),
inference(variable_rename,[status(thm)],[f_1136_1]) ).
cnf(f_1136_3,plain,
( d22set(hAPP_int_int(minus_minus_int(U_3071),number_number_of_int(bit0(bit1(pls))))) = wset(hAPP_int_int(minus_minus_int(U_3071),number_number_of_int(bit0(bit1(pls)))),U_3071)
| ~ hBOOL(hAPP_int_bool(zprime,U_3071)) ),
inference(clausify,[status(thm)],[f_1136_2]) ).
fof(f_1137_1,plain,
! [N,P_2] :
( ? [K_2] :
( hBOOL(hAPP_nat_bool(P_2,K_2))
& ! [I] :
( ~ hBOOL(hAPP_nat_bool(P_2,I))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_2)) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N)) )
| ~ hBOOL(hAPP_nat_bool(P_2,N))
| hBOOL(hAPP_nat_bool(P_2,zero_zero_nat)) ),
inference(fof_nnf,[status(thm)],[fact_1111_ex__least__nat__le]) ).
fof(f_1137_2,plain,
! [U_3075,U_3074] :
( ? [U_3073] :
( hBOOL(hAPP_nat_bool(U_3074,U_3073))
& ! [U_3072] :
( ~ hBOOL(hAPP_nat_bool(U_3074,U_3072))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3072),U_3073)) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3073),U_3075)) )
| ~ hBOOL(hAPP_nat_bool(U_3074,U_3075))
| hBOOL(hAPP_nat_bool(U_3074,zero_zero_nat)) ),
inference(variable_rename,[status(thm)],[f_1137_1]) ).
fof(f_1137_3,plain,
! [U_3075,U_3074] :
( ( hBOOL(hAPP_nat_bool(U_3074,sK31(U_3075,U_3074)))
& ! [U_3072] :
( ~ hBOOL(hAPP_nat_bool(U_3074,U_3072))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3072),sK31(U_3075,U_3074))) )
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK31(U_3075,U_3074)),U_3075)) )
| ~ hBOOL(hAPP_nat_bool(U_3074,U_3075))
| hBOOL(hAPP_nat_bool(U_3074,zero_zero_nat)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_3073,sK31(U_3075,U_3074))],[f_1137_2]) ).
cnf(f_1137_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK31(U_3075,U_3074)),U_3075))
| ~ hBOOL(hAPP_nat_bool(U_3074,U_3075))
| hBOOL(hAPP_nat_bool(U_3074,zero_zero_nat)) ),
inference(clausify,[status(thm)],[f_1137_3]) ).
cnf(f_1137_5,plain,
( ~ hBOOL(hAPP_nat_bool(U_3074,U_3072))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3072),sK31(U_3075,U_3074)))
| ~ hBOOL(hAPP_nat_bool(U_3074,U_3075))
| hBOOL(hAPP_nat_bool(U_3074,zero_zero_nat)) ),
inference(clausify,[status(thm)],[f_1137_3]) ).
cnf(f_1137_6,plain,
( hBOOL(hAPP_nat_bool(U_3074,sK31(U_3075,U_3074)))
| ~ hBOOL(hAPP_nat_bool(U_3074,U_3075))
| hBOOL(hAPP_nat_bool(U_3074,zero_zero_nat)) ),
inference(clausify,[status(thm)],[f_1137_3]) ).
fof(f_1138_1,plain,
! [B_2,A_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),A_2))
| ~ hBOOL(member_int(B_2,d22set(A_2))) ),
inference(fof_nnf,[status(thm)],[fact_1112_d22set__le]) ).
fof(f_1138_2,plain,
! [U_3077,U_3076] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3077),U_3076))
| ~ hBOOL(member_int(U_3077,d22set(U_3076))) ),
inference(variable_rename,[status(thm)],[f_1138_1]) ).
cnf(f_1138_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3077),U_3076))
| ~ hBOOL(member_int(U_3077,d22set(U_3076))) ),
inference(clausify,[status(thm)],[f_1138_2]) ).
fof(f_1139_1,plain,
! [A_2,B_2] :
( ~ hBOOL(member_int(B_2,d22set(A_2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_2),B_2)) ),
inference(fof_nnf,[status(thm)],[fact_1113_d22set__le__swap]) ).
fof(f_1139_2,plain,
! [U_3079,U_3078] :
( ~ hBOOL(member_int(U_3078,d22set(U_3079)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3079),U_3078)) ),
inference(variable_rename,[status(thm)],[f_1139_1]) ).
cnf(f_1139_3,plain,
( ~ hBOOL(member_int(U_3078,d22set(U_3079)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3079),U_3078)) ),
inference(clausify,[status(thm)],[f_1139_2]) ).
fof(f_1140_1,plain,
! [B_2,A_2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),B_2))
| ~ hBOOL(member_int(B_2,d22set(A_2))) ),
inference(fof_nnf,[status(thm)],[fact_1114_d22set__g__1]) ).
fof(f_1140_2,plain,
! [U_3081,U_3080] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_3081))
| ~ hBOOL(member_int(U_3081,d22set(U_3080))) ),
inference(variable_rename,[status(thm)],[f_1140_1]) ).
fof(f_1140_3,plain,
! [U_3081] :
( ! [U_3080] : ~ hBOOL(member_int(U_3081,d22set(U_3080)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_3081)) ),
inference(miniscope,[status(thm)],[f_1140_2]) ).
cnf(f_1140_4,plain,
( ~ hBOOL(member_int(U_3081,d22set(U_3080)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_3081)) ),
inference(clausify,[status(thm)],[f_1140_3]) ).
fof(f_1141_1,plain,
! [A_2,B_2] :
( hBOOL(member_int(B_2,d22set(A_2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_2),A_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),B_2)) ),
inference(fof_nnf,[status(thm)],[fact_1115_d22set__mem]) ).
fof(f_1141_2,plain,
! [U_3083,U_3082] :
( hBOOL(member_int(U_3082,d22set(U_3083)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3082),U_3083))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_3082)) ),
inference(variable_rename,[status(thm)],[f_1141_1]) ).
cnf(f_1141_3,plain,
( hBOOL(member_int(U_3082,d22set(U_3083)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3082),U_3083))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),U_3082)) ),
inference(clausify,[status(thm)],[f_1141_2]) ).
fof(f_1142_1,plain,
! [I_1,J_1] :
( ? [K_2] :
( hAPP_nat_nat(plus_plus_nat(I_1),K_2) = J_1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_1)) ),
inference(fof_nnf,[status(thm)],[fact_1116_less__imp__add__positive]) ).
fof(f_1142_2,plain,
! [U_3086,U_3085] :
( ? [U_3084] :
( hAPP_nat_nat(plus_plus_nat(U_3086),U_3084) = U_3085
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3084)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3086),U_3085)) ),
inference(variable_rename,[status(thm)],[f_1142_1]) ).
fof(f_1142_3,plain,
! [U_3086,U_3085] :
( ( hAPP_nat_nat(plus_plus_nat(U_3086),sK32(U_3086,U_3085)) = U_3085
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK32(U_3086,U_3085))) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3086),U_3085)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_3084,sK32(U_3086,U_3085))],[f_1142_2]) ).
cnf(f_1142_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK32(U_3086,U_3085)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3086),U_3085)) ),
inference(clausify,[status(thm)],[f_1142_3]) ).
cnf(f_1142_5,plain,
( hAPP_nat_nat(plus_plus_nat(U_3086),sK32(U_3086,U_3085)) = U_3085
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3086),U_3085)) ),
inference(clausify,[status(thm)],[f_1142_3]) ).
fof(f_1143_1,plain,
! [A_2,B_2,N] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(A_2),N)),hAPP_nat_int(power_power_int(B_2),N)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_2),B_2)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A_2),B_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(A_2),N)),hAPP_nat_int(power_power_int(B_2),N))) ) )
| N = zero_zero_nat ),
inference(fof_nnf,[status(thm)],[fact_1117_pow__divides__eq__int]) ).
fof(f_1143_2,plain,
! [U_3089,U_3088,U_3087] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_3089),U_3087)),hAPP_nat_int(power_power_int(U_3088),U_3087)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3089),U_3088)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3089),U_3088))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_3089),U_3087)),hAPP_nat_int(power_power_int(U_3088),U_3087))) ) )
| U_3087 = zero_zero_nat ),
inference(variable_rename,[status(thm)],[f_1143_1]) ).
cnf(f_1143_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3089),U_3088))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_3089),U_3087)),hAPP_nat_int(power_power_int(U_3088),U_3087)))
| U_3087 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_1143_2]) ).
cnf(f_1143_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_3089),U_3087)),hAPP_nat_int(power_power_int(U_3088),U_3087)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3089),U_3088))
| U_3087 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_1143_2]) ).
fof(f_1144_1,plain,
! [A] :
( A = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),A)) ),
inference(fof_nnf,[status(thm)],[fact_1118_gcd__lcm__complete__lattice__nat_Otop__le]) ).
fof(f_1144_2,plain,
! [U_3090] :
( U_3090 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),U_3090)) ),
inference(variable_rename,[status(thm)],[f_1144_1]) ).
cnf(f_1144_3,plain,
( U_3090 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),U_3090)) ),
inference(clausify,[status(thm)],[f_1144_2]) ).
fof(f_1145_1,plain,
! [A_2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),A_2))
| A_2 != zero_zero_nat )
& ( A_2 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_1119_gcd__lcm__complete__lattice__nat_Otop__unique]) ).
fof(f_1145_2,plain,
! [U_3091] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),U_3091))
| U_3091 != zero_zero_nat )
& ( U_3091 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),U_3091)) ) ),
inference(variable_rename,[status(thm)],[f_1145_1]) ).
fof(f_1145_3,plain,
( ! [U_3093] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),U_3093))
| U_3093 != zero_zero_nat )
& ! [U_3092] :
( U_3092 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),U_3092)) ) ),
inference(miniscope,[status(thm)],[f_1145_2]) ).
cnf(f_1145_4,plain,
( U_3092 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),U_3092)) ),
inference(clausify,[status(thm)],[f_1145_3]) ).
cnf(f_1145_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),U_3093))
| U_3093 != zero_zero_nat ),
inference(clausify,[status(thm)],[f_1145_3]) ).
fof(f_1146_1,plain,
! [A_2] :
( ( A_2 != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),A_2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),zero_zero_nat)) )
& ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),A_2))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),zero_zero_nat)) )
| A_2 = zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_1120_gcd__lcm__complete__lattice__nat_Oless__top]) ).
fof(f_1146_2,plain,
! [U_3094] :
( ( U_3094 != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),U_3094))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3094),zero_zero_nat)) )
& ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),U_3094))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3094),zero_zero_nat)) )
| U_3094 = zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_1146_1]) ).
fof(f_1146_3,plain,
( ! [U_3096] :
( U_3096 != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),U_3096))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3096),zero_zero_nat)) )
& ! [U_3095] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),U_3095))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3095),zero_zero_nat)) )
| U_3095 = zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_1146_2]) ).
cnf(f_1146_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3095),zero_zero_nat))
| U_3095 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_1146_3]) ).
cnf(f_1146_5,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),U_3095))
| U_3095 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_1146_3]) ).
cnf(f_1146_6,plain,
( U_3096 != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),U_3096))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3096),zero_zero_nat)) ),
inference(clausify,[status(thm)],[f_1146_3]) ).
fof(f_1147_1,plain,
! [A] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),zero_zero_nat)),
inference(fof_nnf,[status(thm)],[fact_1121_gcd__lcm__complete__lattice__nat_Otop__greatest]) ).
fof(f_1147_2,plain,
! [U_3097] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3097),zero_zero_nat)),
inference(variable_rename,[status(thm)],[f_1147_1]) ).
cnf(f_1147_3,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3097),zero_zero_nat)),
inference(clausify,[status(thm)],[f_1147_2]) ).
fof(f_1148_1,plain,
! [A] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),A)) ),
inference(fof_nnf,[status(thm)],[fact_1122_gcd__lcm__complete__lattice__nat_Onot__top__less]) ).
fof(f_1148_2,plain,
! [U_3098] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3098),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),U_3098)) ),
inference(variable_rename,[status(thm)],[f_1148_1]) ).
cnf(f_1148_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3098),zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,zero_zero_nat),U_3098)) ),
inference(clausify,[status(thm)],[f_1148_2]) ).
fof(f_1149_1,plain,
! [A] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),A))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),one_one_nat)) ),
inference(fof_nnf,[status(thm)],[fact_1123_gcd__lcm__complete__lattice__nat_Onot__less__bot]) ).
fof(f_1149_2,plain,
! [U_3099] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),U_3099))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3099),one_one_nat)) ),
inference(variable_rename,[status(thm)],[f_1149_1]) ).
cnf(f_1149_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),U_3099))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3099),one_one_nat)) ),
inference(clausify,[status(thm)],[f_1149_2]) ).
fof(f_1150_1,plain,
! [A] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),A)),
inference(fof_nnf,[status(thm)],[fact_1124_gcd__lcm__complete__lattice__nat_Obot__least]) ).
fof(f_1150_2,plain,
! [U_3100] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),U_3100)),
inference(variable_rename,[status(thm)],[f_1150_1]) ).
cnf(f_1150_3,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),U_3100)),
inference(clausify,[status(thm)],[f_1150_2]) ).
fof(f_1151_1,plain,
! [A_2] :
( ( A_2 != one_one_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),A_2)) )
& ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),one_one_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),A_2)) )
| A_2 = one_one_nat ) ),
inference(fof_nnf,[status(thm)],[fact_1125_gcd__lcm__complete__lattice__nat_Obot__less]) ).
fof(f_1151_2,plain,
! [U_3101] :
( ( U_3101 != one_one_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3101),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),U_3101)) )
& ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3101),one_one_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),U_3101)) )
| U_3101 = one_one_nat ) ),
inference(variable_rename,[status(thm)],[f_1151_1]) ).
fof(f_1151_3,plain,
( ! [U_3103] :
( U_3103 != one_one_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3103),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),U_3103)) )
& ! [U_3102] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3102),one_one_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),U_3102)) )
| U_3102 = one_one_nat ) ),
inference(miniscope,[status(thm)],[f_1151_2]) ).
cnf(f_1151_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),U_3102))
| U_3102 = one_one_nat ),
inference(clausify,[status(thm)],[f_1151_3]) ).
cnf(f_1151_5,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3102),one_one_nat))
| U_3102 = one_one_nat ),
inference(clausify,[status(thm)],[f_1151_3]) ).
cnf(f_1151_6,plain,
( U_3103 != one_one_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3103),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,one_one_nat),U_3103)) ),
inference(clausify,[status(thm)],[f_1151_3]) ).
fof(f_1152_1,plain,
! [A_2] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),one_one_nat))
| A_2 != one_one_nat )
& ( A_2 = one_one_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),one_one_nat)) ) ),
inference(fof_nnf,[status(thm)],[fact_1126_gcd__lcm__complete__lattice__nat_Obot__unique]) ).
fof(f_1152_2,plain,
! [U_3104] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3104),one_one_nat))
| U_3104 != one_one_nat )
& ( U_3104 = one_one_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3104),one_one_nat)) ) ),
inference(variable_rename,[status(thm)],[f_1152_1]) ).
fof(f_1152_3,plain,
( ! [U_3106] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3106),one_one_nat))
| U_3106 != one_one_nat )
& ! [U_3105] :
( U_3105 = one_one_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3105),one_one_nat)) ) ),
inference(miniscope,[status(thm)],[f_1152_2]) ).
cnf(f_1152_4,plain,
( U_3105 = one_one_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3105),one_one_nat)) ),
inference(clausify,[status(thm)],[f_1152_3]) ).
cnf(f_1152_5,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3106),one_one_nat))
| U_3106 != one_one_nat ),
inference(clausify,[status(thm)],[f_1152_3]) ).
fof(f_1153_1,plain,
! [A] :
( A = one_one_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A),one_one_nat)) ),
inference(fof_nnf,[status(thm)],[fact_1127_gcd__lcm__complete__lattice__nat_Ole__bot]) ).
fof(f_1153_2,plain,
! [U_3107] :
( U_3107 = one_one_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3107),one_one_nat)) ),
inference(variable_rename,[status(thm)],[f_1153_1]) ).
cnf(f_1153_3,plain,
( U_3107 = one_one_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3107),one_one_nat)) ),
inference(clausify,[status(thm)],[f_1153_2]) ).
fof(f_1154_1,plain,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M),N_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_1128_dvd__pos__nat]) ).
fof(f_1154_2,plain,
! [U_3109,U_3108] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3109))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3109),U_3108))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3108)) ),
inference(variable_rename,[status(thm)],[f_1154_1]) ).
cnf(f_1154_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3109))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3109),U_3108))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3108)) ),
inference(clausify,[status(thm)],[f_1154_2]) ).
fof(f_1155_1,plain,
! [A_2,B_2,N] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(A_2),N)),hAPP_nat_nat(power_power_nat(B_2),N)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),B_2)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,A_2),B_2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(A_2),N)),hAPP_nat_nat(power_power_nat(B_2),N))) ) )
| N = zero_zero_nat ),
inference(fof_nnf,[status(thm)],[fact_1129_pow__divides__eq__nat]) ).
fof(f_1155_2,plain,
! [U_3112,U_3111,U_3110] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_3112),U_3110)),hAPP_nat_nat(power_power_nat(U_3111),U_3110)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3112),U_3111)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3112),U_3111))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_3112),U_3110)),hAPP_nat_nat(power_power_nat(U_3111),U_3110))) ) )
| U_3110 = zero_zero_nat ),
inference(variable_rename,[status(thm)],[f_1155_1]) ).
cnf(f_1155_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3112),U_3111))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_3112),U_3110)),hAPP_nat_nat(power_power_nat(U_3111),U_3110)))
| U_3110 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_1155_2]) ).
cnf(f_1155_4,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,hAPP_nat_nat(power_power_nat(U_3112),U_3110)),hAPP_nat_nat(power_power_nat(U_3111),U_3110)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3112),U_3111))
| U_3110 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_1155_2]) ).
fof(f_1156_1,plain,
! [A,N_1,B] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,A),B))
| N_1 = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(A),N_1)),hAPP_nat_int(power_power_int(B),N_1))) ),
inference(fof_nnf,[status(thm)],[fact_1130_pow__divides__pow__int]) ).
fof(f_1156_2,plain,
! [U_3115,U_3114,U_3113] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3115),U_3113))
| U_3114 = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_3115),U_3114)),hAPP_nat_int(power_power_int(U_3113),U_3114))) ),
inference(variable_rename,[status(thm)],[f_1156_1]) ).
cnf(f_1156_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3115),U_3113))
| U_3114 = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,hAPP_nat_int(power_power_int(U_3115),U_3114)),hAPP_nat_int(power_power_int(U_3113),U_3114))) ),
inference(clausify,[status(thm)],[f_1156_2]) ).
fof(f_1157_1,plain,
! [M,N_1] :
( N_1 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,M),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_1131_divides__le]) ).
fof(f_1157_2,plain,
! [U_3117,U_3116] :
( U_3116 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3117),U_3116))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3117),U_3116)) ),
inference(variable_rename,[status(thm)],[f_1157_1]) ).
cnf(f_1157_3,plain,
( U_3116 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3117),U_3116))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,U_3117),U_3116)) ),
inference(clausify,[status(thm)],[f_1157_2]) ).
fof(f_1158_1,plain,
! [N_1,M,K_1] :
( N_1 = M
| hAPP_nat_nat(times_times_nat(K_1),N_1) != hAPP_nat_nat(times_times_nat(K_1),M)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1)) ),
inference(fof_nnf,[status(thm)],[fact_1132_mult__left__cancel]) ).
fof(f_1158_2,plain,
! [U_3120,U_3119,U_3118] :
( U_3120 = U_3119
| hAPP_nat_nat(times_times_nat(U_3118),U_3120) != hAPP_nat_nat(times_times_nat(U_3118),U_3119)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3118)) ),
inference(variable_rename,[status(thm)],[f_1158_1]) ).
cnf(f_1158_3,plain,
( U_3120 = U_3119
| hAPP_nat_nat(times_times_nat(U_3118),U_3120) != hAPP_nat_nat(times_times_nat(U_3118),U_3119)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3118)) ),
inference(clausify,[status(thm)],[f_1158_2]) ).
fof(f_1159_1,plain,
! [P_3] : sr(P_3) = 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,P_3))),
inference(fof_nnf,[status(thm)],[fact_1133_SR__def]) ).
fof(f_1159_2,plain,
! [U_3121] : sr(U_3121) = 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,U_3121))),
inference(variable_rename,[status(thm)],[f_1159_1]) ).
cnf(f_1159_3,plain,
sr(U_3121) = 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,U_3121))),
inference(clausify,[status(thm)],[f_1159_2]) ).
fof(f_1160_1,plain,
! [B,A] :
( 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)))),B))),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),A)) = 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(B),one_one_int)),A))),one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A),zero_zero_int)) ),
inference(fof_nnf,[status(thm)],[fact_1134_neg__zmod__mult__2]) ).
fof(f_1160_2,plain,
! [U_3123,U_3122] :
( 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)))),U_3123))),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),U_3122)) = 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(U_3123),one_one_int)),U_3122))),one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3122),zero_zero_int)) ),
inference(variable_rename,[status(thm)],[f_1160_1]) ).
cnf(f_1160_3,plain,
( 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)))),U_3123))),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),U_3122)) = 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(U_3123),one_one_int)),U_3122))),one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3122),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_1160_2]) ).
fof(f_1161_1,plain,
! [V,W] :
( ( hAPP_int_int(div_mod_int(number_number_of_int(bit1(V))),number_number_of_int(bit0(W))) = 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(V)),one_one_int)),number_number_of_int(W)))),one_one_int)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(W))) )
& ( hAPP_int_int(div_mod_int(number_number_of_int(bit1(V))),number_number_of_int(bit0(W))) = 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(V)),number_number_of_int(W)))),one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(W))) ) ),
inference(fof_nnf,[status(thm)],[fact_1135_zmod__number__of__Bit1]) ).
fof(f_1161_2,plain,
! [U_3125,U_3124] :
( ( hAPP_int_int(div_mod_int(number_number_of_int(bit1(U_3125))),number_number_of_int(bit0(U_3124))) = 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(U_3125)),one_one_int)),number_number_of_int(U_3124)))),one_one_int)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(U_3124))) )
& ( hAPP_int_int(div_mod_int(number_number_of_int(bit1(U_3125))),number_number_of_int(bit0(U_3124))) = 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(U_3125)),number_number_of_int(U_3124)))),one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(U_3124))) ) ),
inference(variable_rename,[status(thm)],[f_1161_1]) ).
fof(f_1161_3,plain,
( ! [U_3129,U_3127] :
( hAPP_int_int(div_mod_int(number_number_of_int(bit1(U_3129))),number_number_of_int(bit0(U_3127))) = 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(U_3129)),one_one_int)),number_number_of_int(U_3127)))),one_one_int)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(U_3127))) )
& ! [U_3128,U_3126] :
( hAPP_int_int(div_mod_int(number_number_of_int(bit1(U_3128))),number_number_of_int(bit0(U_3126))) = 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(U_3128)),number_number_of_int(U_3126)))),one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(U_3126))) ) ),
inference(miniscope,[status(thm)],[f_1161_2]) ).
cnf(f_1161_4,plain,
( hAPP_int_int(div_mod_int(number_number_of_int(bit1(U_3128))),number_number_of_int(bit0(U_3126))) = 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(U_3128)),number_number_of_int(U_3126)))),one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(U_3126))) ),
inference(clausify,[status(thm)],[f_1161_3]) ).
cnf(f_1161_5,plain,
( hAPP_int_int(div_mod_int(number_number_of_int(bit1(U_3129))),number_number_of_int(bit0(U_3127))) = 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(U_3129)),one_one_int)),number_number_of_int(U_3127)))),one_one_int)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(U_3127))) ),
inference(clausify,[status(thm)],[f_1161_3]) ).
fof(f_1162_1,plain,
! [X_2,Y_2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X_2)),number_number_of_int(Y_2)))
| hAPP_int_int(div_mod_int(number_number_of_int(Y_2)),number_number_of_int(X_2)) != zero_zero_int )
& ( hAPP_int_int(div_mod_int(number_number_of_int(Y_2)),number_number_of_int(X_2)) = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(X_2)),number_number_of_int(Y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_1136_zdvd__iff__zmod__eq__0__number__of]) ).
fof(f_1162_2,plain,
! [U_3131,U_3130] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(U_3131)),number_number_of_int(U_3130)))
| hAPP_int_int(div_mod_int(number_number_of_int(U_3130)),number_number_of_int(U_3131)) != zero_zero_int )
& ( hAPP_int_int(div_mod_int(number_number_of_int(U_3130)),number_number_of_int(U_3131)) = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(U_3131)),number_number_of_int(U_3130))) ) ),
inference(variable_rename,[status(thm)],[f_1162_1]) ).
fof(f_1162_3,plain,
( ! [U_3135,U_3133] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(U_3135)),number_number_of_int(U_3133)))
| hAPP_int_int(div_mod_int(number_number_of_int(U_3133)),number_number_of_int(U_3135)) != zero_zero_int )
& ! [U_3134,U_3132] :
( hAPP_int_int(div_mod_int(number_number_of_int(U_3132)),number_number_of_int(U_3134)) = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(U_3134)),number_number_of_int(U_3132))) ) ),
inference(miniscope,[status(thm)],[f_1162_2]) ).
cnf(f_1162_4,plain,
( hAPP_int_int(div_mod_int(number_number_of_int(U_3132)),number_number_of_int(U_3134)) = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(U_3134)),number_number_of_int(U_3132))) ),
inference(clausify,[status(thm)],[f_1162_3]) ).
cnf(f_1162_5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,number_number_of_int(U_3135)),number_number_of_int(U_3133)))
| hAPP_int_int(div_mod_int(number_number_of_int(U_3133)),number_number_of_int(U_3135)) != zero_zero_int ),
inference(clausify,[status(thm)],[f_1162_3]) ).
fof(f_1163_1,plain,
! [A,B] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),hAPP_int_int(div_mod_int(A),B)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),zero_zero_int)) ),
inference(fof_nnf,[status(thm)],[fact_1137_neg__mod__bound]) ).
fof(f_1163_2,plain,
! [U_3137,U_3136] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3136),hAPP_int_int(div_mod_int(U_3137),U_3136)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3136),zero_zero_int)) ),
inference(variable_rename,[status(thm)],[f_1163_1]) ).
cnf(f_1163_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3136),hAPP_int_int(div_mod_int(U_3137),U_3136)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3136),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_1163_2]) ).
fof(f_1164_1,plain,
! [A,B] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(div_mod_int(A),B)),B))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B)) ),
inference(fof_nnf,[status(thm)],[fact_1138_pos__mod__bound]) ).
fof(f_1164_2,plain,
! [U_3139,U_3138] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(div_mod_int(U_3139),U_3138)),U_3138))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3138)) ),
inference(variable_rename,[status(thm)],[f_1164_1]) ).
cnf(f_1164_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(div_mod_int(U_3139),U_3138)),U_3138))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3138)) ),
inference(clausify,[status(thm)],[f_1164_2]) ).
fof(f_1165_1,plain,
! [Y_1,X_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(div_mod_int(X_1),Y_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) ),
inference(fof_nnf,[status(thm)],[fact_1139_Divides_Otransfer__nat__int__function__closures_I2_J]) ).
fof(f_1165_2,plain,
! [U_3141,U_3140] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(div_mod_int(U_3140),U_3141)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3141))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3140)) ),
inference(variable_rename,[status(thm)],[f_1165_1]) ).
cnf(f_1165_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(div_mod_int(U_3140),U_3141)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3141))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3140)) ),
inference(clausify,[status(thm)],[f_1165_2]) ).
fof(f_1166_1,plain,
! [K_1,M] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(M),K_1)),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),M)) ),
inference(fof_nnf,[status(thm)],[fact_1140_zmod__le__nonneg__dividend]) ).
fof(f_1166_2,plain,
! [U_3143,U_3142] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(U_3142),U_3143)),U_3142))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3142)) ),
inference(variable_rename,[status(thm)],[f_1166_1]) ).
cnf(f_1166_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(U_3142),U_3143)),U_3142))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3142)) ),
inference(clausify,[status(thm)],[f_1166_2]) ).
fof(f_1167_1,plain,
! [Ma,D] :
( ( ( hAPP_int_int(div_mod_int(Ma),D) = zero_zero_int
| ! [Q_2] :
( Ma != hAPP_int_int(times_times_int(D),Q_2)
| ~ is_int(Q_2) ) )
& ( ? [Q_2] :
( Ma = hAPP_int_int(times_times_int(D),Q_2)
& is_int(Q_2) )
| hAPP_int_int(div_mod_int(Ma),D) != zero_zero_int ) )
| ~ is_int(Ma) ),
inference(fof_nnf,[status(thm)],[fact_1141_zmod__eq__0__iff]) ).
fof(f_1167_2,plain,
! [U_3147,U_3146] :
( ( ( hAPP_int_int(div_mod_int(U_3147),U_3146) = zero_zero_int
| ! [U_3145] :
( U_3147 != hAPP_int_int(times_times_int(U_3146),U_3145)
| ~ is_int(U_3145) ) )
& ( ? [U_3144] :
( U_3147 = hAPP_int_int(times_times_int(U_3146),U_3144)
& is_int(U_3144) )
| hAPP_int_int(div_mod_int(U_3147),U_3146) != zero_zero_int ) )
| ~ is_int(U_3147) ),
inference(variable_rename,[status(thm)],[f_1167_1]) ).
fof(f_1167_3,plain,
! [U_3147] :
( ( ! [U_3149] :
( hAPP_int_int(div_mod_int(U_3147),U_3149) = zero_zero_int
| ! [U_3145] :
( U_3147 != hAPP_int_int(times_times_int(U_3149),U_3145)
| ~ is_int(U_3145) ) )
& ! [U_3148] :
( ? [U_3144] :
( U_3147 = hAPP_int_int(times_times_int(U_3148),U_3144)
& is_int(U_3144) )
| hAPP_int_int(div_mod_int(U_3147),U_3148) != zero_zero_int ) )
| ~ is_int(U_3147) ),
inference(miniscope,[status(thm)],[f_1167_2]) ).
fof(f_1167_4,plain,
! [U_3147] :
( ( ! [U_3149] :
( hAPP_int_int(div_mod_int(U_3147),U_3149) = zero_zero_int
| ! [U_3145] :
( U_3147 != hAPP_int_int(times_times_int(U_3149),U_3145)
| ~ is_int(U_3145) ) )
& ! [U_3148] :
( ( U_3147 = hAPP_int_int(times_times_int(U_3148),sK33(U_3147,U_3148))
& is_int(sK33(U_3147,U_3148)) )
| hAPP_int_int(div_mod_int(U_3147),U_3148) != zero_zero_int ) )
| ~ is_int(U_3147) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_3144,sK33(U_3147,U_3148))],[f_1167_3]) ).
cnf(f_1167_5,plain,
( is_int(sK33(U_3147,U_3148))
| hAPP_int_int(div_mod_int(U_3147),U_3148) != zero_zero_int
| ~ is_int(U_3147) ),
inference(clausify,[status(thm)],[f_1167_4]) ).
cnf(f_1167_6,plain,
( U_3147 = hAPP_int_int(times_times_int(U_3148),sK33(U_3147,U_3148))
| hAPP_int_int(div_mod_int(U_3147),U_3148) != zero_zero_int
| ~ is_int(U_3147) ),
inference(clausify,[status(thm)],[f_1167_4]) ).
cnf(f_1167_7,plain,
( hAPP_int_int(div_mod_int(U_3147),U_3149) = zero_zero_int
| U_3147 != hAPP_int_int(times_times_int(U_3149),U_3145)
| ~ is_int(U_3145)
| ~ is_int(U_3147) ),
inference(clausify,[status(thm)],[f_1167_4]) ).
fof(f_1168_1,plain,
! [X_2,N,Y_2] :
( ( hAPP_int_int(div_mod_int(X_2),N) = hAPP_int_int(div_mod_int(Y_2),N)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,N),hAPP_int_int(minus_minus_int(X_2),Y_2))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,N),hAPP_int_int(minus_minus_int(X_2),Y_2)))
| hAPP_int_int(div_mod_int(X_2),N) != hAPP_int_int(div_mod_int(Y_2),N) ) ),
inference(fof_nnf,[status(thm)],[fact_1142_zmod__eq__dvd__iff]) ).
fof(f_1168_2,plain,
! [U_3152,U_3151,U_3150] :
( ( hAPP_int_int(div_mod_int(U_3152),U_3151) = hAPP_int_int(div_mod_int(U_3150),U_3151)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3151),hAPP_int_int(minus_minus_int(U_3152),U_3150))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3151),hAPP_int_int(minus_minus_int(U_3152),U_3150)))
| hAPP_int_int(div_mod_int(U_3152),U_3151) != hAPP_int_int(div_mod_int(U_3150),U_3151) ) ),
inference(variable_rename,[status(thm)],[f_1168_1]) ).
fof(f_1168_3,plain,
( ! [U_3158,U_3156,U_3154] :
( hAPP_int_int(div_mod_int(U_3158),U_3156) = hAPP_int_int(div_mod_int(U_3154),U_3156)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3156),hAPP_int_int(minus_minus_int(U_3158),U_3154))) )
& ! [U_3157,U_3155,U_3153] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3155),hAPP_int_int(minus_minus_int(U_3157),U_3153)))
| hAPP_int_int(div_mod_int(U_3157),U_3155) != hAPP_int_int(div_mod_int(U_3153),U_3155) ) ),
inference(miniscope,[status(thm)],[f_1168_2]) ).
cnf(f_1168_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3155),hAPP_int_int(minus_minus_int(U_3157),U_3153)))
| hAPP_int_int(div_mod_int(U_3157),U_3155) != hAPP_int_int(div_mod_int(U_3153),U_3155) ),
inference(clausify,[status(thm)],[f_1168_3]) ).
cnf(f_1168_5,plain,
( hAPP_int_int(div_mod_int(U_3158),U_3156) = hAPP_int_int(div_mod_int(U_3154),U_3156)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3156),hAPP_int_int(minus_minus_int(U_3158),U_3154))) ),
inference(clausify,[status(thm)],[f_1168_3]) ).
fof(f_1169_1,plain,
! [X_1,M,Y_1] :
( hBOOL(hAPP_int_bool(zcong(X_1,Y_1),M))
| hAPP_int_int(div_mod_int(X_1),M) != hAPP_int_int(div_mod_int(Y_1),M) ),
inference(fof_nnf,[status(thm)],[fact_1143_Residues_Oaux]) ).
fof(f_1169_2,plain,
! [U_3161,U_3160,U_3159] :
( hBOOL(hAPP_int_bool(zcong(U_3161,U_3159),U_3160))
| hAPP_int_int(div_mod_int(U_3161),U_3160) != hAPP_int_int(div_mod_int(U_3159),U_3160) ),
inference(variable_rename,[status(thm)],[f_1169_1]) ).
cnf(f_1169_3,plain,
( hBOOL(hAPP_int_bool(zcong(U_3161,U_3159),U_3160))
| hAPP_int_int(div_mod_int(U_3161),U_3160) != hAPP_int_int(div_mod_int(U_3159),U_3160) ),
inference(clausify,[status(thm)],[f_1169_2]) ).
fof(f_1170_1,plain,
! [X_1,M] : hBOOL(hAPP_int_bool(zcong(X_1,hAPP_int_int(div_mod_int(X_1),M)),M)),
inference(fof_nnf,[status(thm)],[fact_1144_mod__mod__is__mod]) ).
fof(f_1170_2,plain,
! [U_3163,U_3162] : hBOOL(hAPP_int_bool(zcong(U_3163,hAPP_int_int(div_mod_int(U_3163),U_3162)),U_3162)),
inference(variable_rename,[status(thm)],[f_1170_1]) ).
cnf(f_1170_3,plain,
hBOOL(hAPP_int_bool(zcong(U_3163,hAPP_int_int(div_mod_int(U_3163),U_3162)),U_3162)),
inference(clausify,[status(thm)],[f_1170_2]) ).
fof(f_1171_1,plain,
! [A_2,B_2,Ma] :
( ( hBOOL(hAPP_int_bool(zcong(A_2,B_2),Ma))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(div_mod_int(A_2),Ma),hAPP_int_int(div_mod_int(B_2),Ma)),Ma)) )
& ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(div_mod_int(A_2),Ma),hAPP_int_int(div_mod_int(B_2),Ma)),Ma))
| ~ hBOOL(hAPP_int_bool(zcong(A_2,B_2),Ma)) ) ),
inference(fof_nnf,[status(thm)],[fact_1145_zcong__zmod]) ).
fof(f_1171_2,plain,
! [U_3166,U_3165,U_3164] :
( ( hBOOL(hAPP_int_bool(zcong(U_3166,U_3165),U_3164))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(div_mod_int(U_3166),U_3164),hAPP_int_int(div_mod_int(U_3165),U_3164)),U_3164)) )
& ( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(div_mod_int(U_3166),U_3164),hAPP_int_int(div_mod_int(U_3165),U_3164)),U_3164))
| ~ hBOOL(hAPP_int_bool(zcong(U_3166,U_3165),U_3164)) ) ),
inference(variable_rename,[status(thm)],[f_1171_1]) ).
fof(f_1171_3,plain,
( ! [U_3172,U_3170,U_3168] :
( hBOOL(hAPP_int_bool(zcong(U_3172,U_3170),U_3168))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(div_mod_int(U_3172),U_3168),hAPP_int_int(div_mod_int(U_3170),U_3168)),U_3168)) )
& ! [U_3171,U_3169,U_3167] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(div_mod_int(U_3171),U_3167),hAPP_int_int(div_mod_int(U_3169),U_3167)),U_3167))
| ~ hBOOL(hAPP_int_bool(zcong(U_3171,U_3169),U_3167)) ) ),
inference(miniscope,[status(thm)],[f_1171_2]) ).
cnf(f_1171_4,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(div_mod_int(U_3171),U_3167),hAPP_int_int(div_mod_int(U_3169),U_3167)),U_3167))
| ~ hBOOL(hAPP_int_bool(zcong(U_3171,U_3169),U_3167)) ),
inference(clausify,[status(thm)],[f_1171_3]) ).
cnf(f_1171_5,plain,
( hBOOL(hAPP_int_bool(zcong(U_3172,U_3170),U_3168))
| ~ hBOOL(hAPP_int_bool(zcong(hAPP_int_int(div_mod_int(U_3172),U_3168),hAPP_int_int(div_mod_int(U_3170),U_3168)),U_3168)) ),
inference(clausify,[status(thm)],[f_1171_3]) ).
fof(f_1172_1,plain,
! [K_1,M,N_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),N_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,K_1),hAPP_int_int(div_mod_int(M),N_1))) ),
inference(fof_nnf,[status(thm)],[fact_1146_zdvd__zmod__imp__zdvd]) ).
fof(f_1172_2,plain,
! [U_3175,U_3174,U_3173] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3175),U_3174))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3175),U_3173))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3175),hAPP_int_int(div_mod_int(U_3174),U_3173))) ),
inference(variable_rename,[status(thm)],[f_1172_1]) ).
cnf(f_1172_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3175),U_3174))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3175),U_3173))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3175),hAPP_int_int(div_mod_int(U_3174),U_3173))) ),
inference(clausify,[status(thm)],[f_1172_2]) ).
fof(f_1173_1,plain,
! [N_1,F,M] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,F),hAPP_int_int(div_mod_int(M),N_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,F),N_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,F),M)) ),
inference(fof_nnf,[status(thm)],[fact_1147_zdvd__zmod]) ).
fof(f_1173_2,plain,
! [U_3178,U_3177,U_3176] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3177),hAPP_int_int(div_mod_int(U_3176),U_3178)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3177),U_3178))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3177),U_3176)) ),
inference(variable_rename,[status(thm)],[f_1173_1]) ).
cnf(f_1173_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3177),hAPP_int_int(div_mod_int(U_3176),U_3178)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3177),U_3178))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3177),U_3176)) ),
inference(clausify,[status(thm)],[f_1173_2]) ).
fof(f_1174_1,plain,
! [X_1,M,Y_1] : hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(hAPP_int_int(div_mod_int(X_1),M)),Y_1)),M) = hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(X_1),Y_1)),M),
inference(fof_nnf,[status(thm)],[fact_1148_zpower__zmod]) ).
fof(f_1174_2,plain,
! [U_3181,U_3180,U_3179] : hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(hAPP_int_int(div_mod_int(U_3181),U_3180)),U_3179)),U_3180) = hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(U_3181),U_3179)),U_3180),
inference(variable_rename,[status(thm)],[f_1174_1]) ).
cnf(f_1174_3,plain,
hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(hAPP_int_int(div_mod_int(U_3181),U_3180)),U_3179)),U_3180) = hAPP_int_int(div_mod_int(hAPP_nat_int(power_power_int(U_3181),U_3179)),U_3180),
inference(clausify,[status(thm)],[f_1174_2]) ).
fof(f_1175_1,plain,
! [A,B,C] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(A),B)),C) = hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(A),hAPP_int_int(div_mod_int(B),C))),C),
inference(fof_nnf,[status(thm)],[fact_1149_zmod__zmult1__eq]) ).
fof(f_1175_2,plain,
! [U_3184,U_3183,U_3182] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(U_3184),U_3183)),U_3182) = hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(U_3184),hAPP_int_int(div_mod_int(U_3183),U_3182))),U_3182),
inference(variable_rename,[status(thm)],[f_1175_1]) ).
cnf(f_1175_3,plain,
hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(U_3184),U_3183)),U_3182) = hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(U_3184),hAPP_int_int(div_mod_int(U_3183),U_3182))),U_3182),
inference(clausify,[status(thm)],[f_1175_2]) ).
fof(f_1176_1,plain,
! [A,B,C] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(A),hAPP_int_int(div_mod_int(B),C))),C) = hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(A),B)),C),
inference(fof_nnf,[status(thm)],[fact_1150_zmod__simps_I3_J]) ).
fof(f_1176_2,plain,
! [U_3187,U_3186,U_3185] : hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(U_3187),hAPP_int_int(div_mod_int(U_3186),U_3185))),U_3185) = hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(U_3187),U_3186)),U_3185),
inference(variable_rename,[status(thm)],[f_1176_1]) ).
cnf(f_1176_3,plain,
hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(U_3187),hAPP_int_int(div_mod_int(U_3186),U_3185))),U_3185) = hAPP_int_int(div_mod_int(hAPP_int_int(times_times_int(U_3187),U_3186)),U_3185),
inference(clausify,[status(thm)],[f_1176_2]) ).
fof(f_1177_1,plain,
! [A] : hAPP_int_int(div_mod_int(A),A) = zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_1151_zmod__self]) ).
fof(f_1177_2,plain,
! [U_3188] : hAPP_int_int(div_mod_int(U_3188),U_3188) = zero_zero_int,
inference(variable_rename,[status(thm)],[f_1177_1]) ).
cnf(f_1177_3,plain,
hAPP_int_int(div_mod_int(U_3188),U_3188) = zero_zero_int,
inference(clausify,[status(thm)],[f_1177_2]) ).
fof(f_1178_1,plain,
! [B] : hAPP_int_int(div_mod_int(zero_zero_int),B) = zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_1152_zmod__zero]) ).
fof(f_1178_2,plain,
! [U_3189] : hAPP_int_int(div_mod_int(zero_zero_int),U_3189) = zero_zero_int,
inference(variable_rename,[status(thm)],[f_1178_1]) ).
cnf(f_1178_3,plain,
hAPP_int_int(div_mod_int(zero_zero_int),U_3189) = zero_zero_int,
inference(clausify,[status(thm)],[f_1178_2]) ).
fof(f_1179_1,plain,
! [X_1,Y_1,M] : hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(X_1),hAPP_int_int(div_mod_int(Y_1),M))),M) = hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(X_1),Y_1)),M),
inference(fof_nnf,[status(thm)],[fact_1153_zdiff__zmod__right]) ).
fof(f_1179_2,plain,
! [U_3192,U_3191,U_3190] : hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(U_3192),hAPP_int_int(div_mod_int(U_3191),U_3190))),U_3190) = hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(U_3192),U_3191)),U_3190),
inference(variable_rename,[status(thm)],[f_1179_1]) ).
cnf(f_1179_3,plain,
hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(U_3192),hAPP_int_int(div_mod_int(U_3191),U_3190))),U_3190) = hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(U_3192),U_3191)),U_3190),
inference(clausify,[status(thm)],[f_1179_2]) ).
fof(f_1180_1,plain,
! [X_1,M,Y_1] : hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(hAPP_int_int(div_mod_int(X_1),M)),Y_1)),M) = hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(X_1),Y_1)),M),
inference(fof_nnf,[status(thm)],[fact_1154_zdiff__zmod__left]) ).
fof(f_1180_2,plain,
! [U_3195,U_3194,U_3193] : hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(hAPP_int_int(div_mod_int(U_3195),U_3194)),U_3193)),U_3194) = hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(U_3195),U_3193)),U_3194),
inference(variable_rename,[status(thm)],[f_1180_1]) ).
cnf(f_1180_3,plain,
hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(hAPP_int_int(div_mod_int(U_3195),U_3194)),U_3193)),U_3194) = hAPP_int_int(div_mod_int(hAPP_int_int(minus_minus_int(U_3195),U_3193)),U_3194),
inference(clausify,[status(thm)],[f_1180_2]) ).
fof(f_1181_1,plain,
! [A] : hAPP_int_int(div_mod_int(A),number_number_of_int(min)) = zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_1155_zmod__minus1__right]) ).
fof(f_1181_2,plain,
! [U_3196] : hAPP_int_int(div_mod_int(U_3196),number_number_of_int(min)) = zero_zero_int,
inference(variable_rename,[status(thm)],[f_1181_1]) ).
cnf(f_1181_3,plain,
hAPP_int_int(div_mod_int(U_3196),number_number_of_int(min)) = zero_zero_int,
inference(clausify,[status(thm)],[f_1181_2]) ).
fof(f_1182_1,plain,
! [A,B,M] :
( hAPP_int_int(div_mod_int(hAPP_int_int(div_mod_int(A),B)),M) = hAPP_int_int(div_mod_int(A),M)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,M),B))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M)) ),
inference(fof_nnf,[status(thm)],[fact_1156_zmod__zdvd__zmod]) ).
fof(f_1182_2,plain,
! [U_3199,U_3198,U_3197] :
( hAPP_int_int(div_mod_int(hAPP_int_int(div_mod_int(U_3199),U_3198)),U_3197) = hAPP_int_int(div_mod_int(U_3199),U_3197)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3197),U_3198))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3197)) ),
inference(variable_rename,[status(thm)],[f_1182_1]) ).
cnf(f_1182_3,plain,
( hAPP_int_int(div_mod_int(hAPP_int_int(div_mod_int(U_3199),U_3198)),U_3197) = hAPP_int_int(div_mod_int(U_3199),U_3197)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,U_3197),U_3198))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3197)) ),
inference(clausify,[status(thm)],[f_1182_2]) ).
fof(f_1183_1,plain,
! [A_2,B_2,Ma] :
( ( ( hBOOL(hAPP_int_bool(zcong(A_2,B_2),Ma))
| hAPP_int_int(div_mod_int(A_2),Ma) != hAPP_int_int(div_mod_int(B_2),Ma) )
& ( hAPP_int_int(div_mod_int(A_2),Ma) = hAPP_int_int(div_mod_int(B_2),Ma)
| ~ hBOOL(hAPP_int_bool(zcong(A_2,B_2),Ma)) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ma)) ),
inference(fof_nnf,[status(thm)],[fact_1157_zcong__zmod__eq]) ).
fof(f_1183_2,plain,
! [U_3202,U_3201,U_3200] :
( ( ( hBOOL(hAPP_int_bool(zcong(U_3202,U_3201),U_3200))
| hAPP_int_int(div_mod_int(U_3202),U_3200) != hAPP_int_int(div_mod_int(U_3201),U_3200) )
& ( hAPP_int_int(div_mod_int(U_3202),U_3200) = hAPP_int_int(div_mod_int(U_3201),U_3200)
| ~ hBOOL(hAPP_int_bool(zcong(U_3202,U_3201),U_3200)) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3200)) ),
inference(variable_rename,[status(thm)],[f_1183_1]) ).
cnf(f_1183_3,plain,
( hAPP_int_int(div_mod_int(U_3202),U_3200) = hAPP_int_int(div_mod_int(U_3201),U_3200)
| ~ hBOOL(hAPP_int_bool(zcong(U_3202,U_3201),U_3200))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3200)) ),
inference(clausify,[status(thm)],[f_1183_2]) ).
cnf(f_1183_4,plain,
( hBOOL(hAPP_int_bool(zcong(U_3202,U_3201),U_3200))
| hAPP_int_int(div_mod_int(U_3202),U_3200) != hAPP_int_int(div_mod_int(U_3201),U_3200)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3200)) ),
inference(clausify,[status(thm)],[f_1183_2]) ).
fof(f_1184_1,plain,
! [A,B] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(div_mod_int(A),B)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B)) ),
inference(fof_nnf,[status(thm)],[fact_1158_pos__mod__sign]) ).
fof(f_1184_2,plain,
! [U_3204,U_3203] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(div_mod_int(U_3204),U_3203)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3203)) ),
inference(variable_rename,[status(thm)],[f_1184_1]) ).
cnf(f_1184_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(div_mod_int(U_3204),U_3203)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3203)) ),
inference(clausify,[status(thm)],[f_1184_2]) ).
fof(f_1185_1,plain,
! [A,B] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(div_mod_int(A),B)),B))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(div_mod_int(A),B))) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B)) ),
inference(fof_nnf,[status(thm)],[fact_1159_pos__mod__conj]) ).
fof(f_1185_2,plain,
! [U_3206,U_3205] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(div_mod_int(U_3206),U_3205)),U_3205))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(div_mod_int(U_3206),U_3205))) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3205)) ),
inference(variable_rename,[status(thm)],[f_1185_1]) ).
cnf(f_1185_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(div_mod_int(U_3206),U_3205)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3205)) ),
inference(clausify,[status(thm)],[f_1185_2]) ).
cnf(f_1185_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(div_mod_int(U_3206),U_3205)),U_3205))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3205)) ),
inference(clausify,[status(thm)],[f_1185_2]) ).
fof(f_1186_1,plain,
! [B,A] :
( hAPP_int_int(div_mod_int(A),B) = A
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A),B))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A))
| ~ is_int(A) ),
inference(fof_nnf,[status(thm)],[fact_1160_mod__pos__pos__trivial]) ).
fof(f_1186_2,plain,
! [U_3208,U_3207] :
( hAPP_int_int(div_mod_int(U_3207),U_3208) = U_3207
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3207),U_3208))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3207))
| ~ is_int(U_3207) ),
inference(variable_rename,[status(thm)],[f_1186_1]) ).
cnf(f_1186_3,plain,
( hAPP_int_int(div_mod_int(U_3207),U_3208) = U_3207
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3207),U_3208))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3207))
| ~ is_int(U_3207) ),
inference(clausify,[status(thm)],[f_1186_2]) ).
fof(f_1187_1,plain,
! [A,B] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(A),B)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),zero_zero_int)) ),
inference(fof_nnf,[status(thm)],[fact_1161_neg__mod__sign]) ).
fof(f_1187_2,plain,
! [U_3210,U_3209] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(U_3210),U_3209)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3209),zero_zero_int)) ),
inference(variable_rename,[status(thm)],[f_1187_1]) ).
cnf(f_1187_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(U_3210),U_3209)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3209),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_1187_2]) ).
fof(f_1188_1,plain,
! [A,B] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),hAPP_int_int(div_mod_int(A),B)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(A),B)),zero_zero_int)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),zero_zero_int)) ),
inference(fof_nnf,[status(thm)],[fact_1162_neg__mod__conj]) ).
fof(f_1188_2,plain,
! [U_3212,U_3211] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3211),hAPP_int_int(div_mod_int(U_3212),U_3211)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(U_3212),U_3211)),zero_zero_int)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3211),zero_zero_int)) ),
inference(variable_rename,[status(thm)],[f_1188_1]) ).
cnf(f_1188_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(div_mod_int(U_3212),U_3211)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3211),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_1188_2]) ).
cnf(f_1188_4,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3211),hAPP_int_int(div_mod_int(U_3212),U_3211)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3211),zero_zero_int)) ),
inference(clausify,[status(thm)],[f_1188_2]) ).
fof(f_1189_1,plain,
! [B,A] :
( hAPP_int_int(div_mod_int(A),B) = A
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),A))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A),zero_zero_int))
| ~ is_int(A) ),
inference(fof_nnf,[status(thm)],[fact_1163_mod__neg__neg__trivial]) ).
fof(f_1189_2,plain,
! [U_3214,U_3213] :
( hAPP_int_int(div_mod_int(U_3213),U_3214) = U_3213
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3214),U_3213))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3213),zero_zero_int))
| ~ is_int(U_3213) ),
inference(variable_rename,[status(thm)],[f_1189_1]) ).
cnf(f_1189_3,plain,
( hAPP_int_int(div_mod_int(U_3213),U_3214) = U_3213
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3214),U_3213))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3213),zero_zero_int))
| ~ is_int(U_3213) ),
inference(clausify,[status(thm)],[f_1189_2]) ).
fof(f_1190_1,plain,
! [B,A] :
( hAPP_int_int(div_mod_int(A),B) = hAPP_int_int(plus_plus_int(A),B)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(A),B)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A)) ),
inference(fof_nnf,[status(thm)],[fact_1164_mod__pos__neg__trivial]) ).
fof(f_1190_2,plain,
! [U_3216,U_3215] :
( hAPP_int_int(div_mod_int(U_3215),U_3216) = hAPP_int_int(plus_plus_int(U_3215),U_3216)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(U_3215),U_3216)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3215)) ),
inference(variable_rename,[status(thm)],[f_1190_1]) ).
cnf(f_1190_3,plain,
( hAPP_int_int(div_mod_int(U_3215),U_3216) = hAPP_int_int(plus_plus_int(U_3215),U_3216)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(U_3215),U_3216)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3215)) ),
inference(clausify,[status(thm)],[f_1190_2]) ).
fof(f_1191_1,plain,
! [V,W] : hAPP_int_int(div_mod_int(number_number_of_int(bit0(V))),number_number_of_int(bit0(W))) = hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),hAPP_int_int(div_mod_int(number_number_of_int(V)),number_number_of_int(W))),
inference(fof_nnf,[status(thm)],[fact_1165_zmod__number__of__Bit0]) ).
fof(f_1191_2,plain,
! [U_3218,U_3217] : hAPP_int_int(div_mod_int(number_number_of_int(bit0(U_3218))),number_number_of_int(bit0(U_3217))) = hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),hAPP_int_int(div_mod_int(number_number_of_int(U_3218)),number_number_of_int(U_3217))),
inference(variable_rename,[status(thm)],[f_1191_1]) ).
cnf(f_1191_3,plain,
hAPP_int_int(div_mod_int(number_number_of_int(bit0(U_3218))),number_number_of_int(bit0(U_3217))) = hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),hAPP_int_int(div_mod_int(number_number_of_int(U_3218)),number_number_of_int(U_3217))),
inference(clausify,[status(thm)],[f_1191_2]) ).
fof(f_1192_1,plain,
! [P_2,N,K] :
( ( ( hBOOL(hAPP_int_bool(P_2,hAPP_int_int(div_mod_int(N),K)))
| ( ? [I,J] :
( ~ hBOOL(hAPP_int_bool(P_2,J))
& N = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(K),I)),J)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,J),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),J))
& is_int(J)
& is_int(I) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),zero_zero_int)) )
| ( ? [I,J] :
( ~ hBOOL(hAPP_int_bool(P_2,J))
& N = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(K),I)),J)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,J),K))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),J))
& is_int(J)
& is_int(I) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K)) )
| ( ~ hBOOL(hAPP_int_bool(P_2,N))
& K = zero_zero_int ) )
& ( ( ( ! [I,J] :
( hBOOL(hAPP_int_bool(P_2,J))
| N != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(K),I)),J)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,J),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),J))
| ~ is_int(J)
| ~ is_int(I) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),zero_zero_int)) )
& ( ! [I,J] :
( hBOOL(hAPP_int_bool(P_2,J))
| N != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(K),I)),J)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,J),K))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),J))
| ~ is_int(J)
| ~ is_int(I) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K)) )
& ( hBOOL(hAPP_int_bool(P_2,N))
| K != zero_zero_int ) )
| ~ hBOOL(hAPP_int_bool(P_2,hAPP_int_int(div_mod_int(N),K))) ) )
| ~ is_int(K)
| ~ is_int(N) ),
inference(fof_nnf,[status(thm)],[fact_1166_split__zmod]) ).
fof(f_1192_2,plain,
! [U_3229,U_3228,U_3227] :
( ( ( hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ( ? [U_3226,U_3225] :
( ~ hBOOL(hAPP_int_bool(U_3229,U_3225))
& U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),U_3226)),U_3225)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3225),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),U_3225))
& is_int(U_3225)
& is_int(U_3226) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int)) )
| ( ? [U_3224,U_3223] :
( ~ hBOOL(hAPP_int_bool(U_3229,U_3223))
& U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),U_3224)),U_3223)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3223),U_3227))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3223))
& is_int(U_3223)
& is_int(U_3224) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227)) )
| ( ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
& U_3227 = zero_zero_int ) )
& ( ( ( ! [U_3222,U_3221] :
( hBOOL(hAPP_int_bool(U_3229,U_3221))
| U_3228 != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),U_3222)),U_3221)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3221),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),U_3221))
| ~ is_int(U_3221)
| ~ is_int(U_3222) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int)) )
& ( ! [U_3220,U_3219] :
( hBOOL(hAPP_int_bool(U_3229,U_3219))
| U_3228 != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),U_3220)),U_3219)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3219),U_3227))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3219))
| ~ is_int(U_3219)
| ~ is_int(U_3220) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227)) )
& ( hBOOL(hAPP_int_bool(U_3229,U_3228))
| U_3227 != zero_zero_int ) )
| ~ hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227))) ) )
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(variable_rename,[status(thm)],[f_1192_1]) ).
fof(f_1192_3,plain,
! [U_3229,U_3228,U_3227] :
( ( ( hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ( ? [U_3226,U_3225] :
( ~ hBOOL(hAPP_int_bool(U_3229,U_3225))
& U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),U_3226)),U_3225)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3225),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),U_3225))
& is_int(U_3225)
& is_int(U_3226) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int)) )
| ( ? [U_3223] :
( ~ hBOOL(hAPP_int_bool(U_3229,U_3223))
& U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK34(U_3229,U_3228,U_3227))),U_3223)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3223),U_3227))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3223))
& is_int(U_3223)
& is_int(sK34(U_3229,U_3228,U_3227)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227)) )
| ( ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
& U_3227 = zero_zero_int ) )
& ( ( ( ! [U_3222,U_3221] :
( hBOOL(hAPP_int_bool(U_3229,U_3221))
| U_3228 != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),U_3222)),U_3221)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3221),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),U_3221))
| ~ is_int(U_3221)
| ~ is_int(U_3222) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int)) )
& ( ! [U_3220,U_3219] :
( hBOOL(hAPP_int_bool(U_3229,U_3219))
| U_3228 != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),U_3220)),U_3219)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3219),U_3227))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3219))
| ~ is_int(U_3219)
| ~ is_int(U_3220) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227)) )
& ( hBOOL(hAPP_int_bool(U_3229,U_3228))
| U_3227 != zero_zero_int ) )
| ~ hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227))) ) )
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_3224,sK34(U_3229,U_3228,U_3227))],[f_1192_2]) ).
fof(f_1192_4,plain,
! [U_3229,U_3228,U_3227] :
( ( ( hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ( ? [U_3226,U_3225] :
( ~ hBOOL(hAPP_int_bool(U_3229,U_3225))
& U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),U_3226)),U_3225)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3225),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),U_3225))
& is_int(U_3225)
& is_int(U_3226) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int)) )
| ( ~ hBOOL(hAPP_int_bool(U_3229,sK35(U_3229,U_3228,U_3227)))
& U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK34(U_3229,U_3228,U_3227))),sK35(U_3229,U_3228,U_3227))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK35(U_3229,U_3228,U_3227)),U_3227))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(U_3229,U_3228,U_3227)))
& is_int(sK35(U_3229,U_3228,U_3227))
& is_int(sK34(U_3229,U_3228,U_3227))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227)) )
| ( ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
& U_3227 = zero_zero_int ) )
& ( ( ( ! [U_3222,U_3221] :
( hBOOL(hAPP_int_bool(U_3229,U_3221))
| U_3228 != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),U_3222)),U_3221)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3221),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),U_3221))
| ~ is_int(U_3221)
| ~ is_int(U_3222) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int)) )
& ( ! [U_3220,U_3219] :
( hBOOL(hAPP_int_bool(U_3229,U_3219))
| U_3228 != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),U_3220)),U_3219)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3219),U_3227))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3219))
| ~ is_int(U_3219)
| ~ is_int(U_3220) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227)) )
& ( hBOOL(hAPP_int_bool(U_3229,U_3228))
| U_3227 != zero_zero_int ) )
| ~ hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227))) ) )
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_3223,sK35(U_3229,U_3228,U_3227))],[f_1192_3]) ).
fof(f_1192_5,plain,
! [U_3229,U_3228,U_3227] :
( ( ( hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ( ? [U_3225] :
( ~ hBOOL(hAPP_int_bool(U_3229,U_3225))
& U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK36(U_3229,U_3228,U_3227))),U_3225)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3225),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),U_3225))
& is_int(U_3225)
& is_int(sK36(U_3229,U_3228,U_3227)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int)) )
| ( ~ hBOOL(hAPP_int_bool(U_3229,sK35(U_3229,U_3228,U_3227)))
& U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK34(U_3229,U_3228,U_3227))),sK35(U_3229,U_3228,U_3227))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK35(U_3229,U_3228,U_3227)),U_3227))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(U_3229,U_3228,U_3227)))
& is_int(sK35(U_3229,U_3228,U_3227))
& is_int(sK34(U_3229,U_3228,U_3227))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227)) )
| ( ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
& U_3227 = zero_zero_int ) )
& ( ( ( ! [U_3222,U_3221] :
( hBOOL(hAPP_int_bool(U_3229,U_3221))
| U_3228 != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),U_3222)),U_3221)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3221),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),U_3221))
| ~ is_int(U_3221)
| ~ is_int(U_3222) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int)) )
& ( ! [U_3220,U_3219] :
( hBOOL(hAPP_int_bool(U_3229,U_3219))
| U_3228 != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),U_3220)),U_3219)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3219),U_3227))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3219))
| ~ is_int(U_3219)
| ~ is_int(U_3220) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227)) )
& ( hBOOL(hAPP_int_bool(U_3229,U_3228))
| U_3227 != zero_zero_int ) )
| ~ hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227))) ) )
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_3226,sK36(U_3229,U_3228,U_3227))],[f_1192_4]) ).
fof(f_1192_6,plain,
! [U_3229,U_3228,U_3227] :
( ( ( hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ( ~ hBOOL(hAPP_int_bool(U_3229,sK37(U_3229,U_3228,U_3227)))
& U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK36(U_3229,U_3228,U_3227))),sK37(U_3229,U_3228,U_3227))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK37(U_3229,U_3228,U_3227)),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),sK37(U_3229,U_3228,U_3227)))
& is_int(sK37(U_3229,U_3228,U_3227))
& is_int(sK36(U_3229,U_3228,U_3227))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int)) )
| ( ~ hBOOL(hAPP_int_bool(U_3229,sK35(U_3229,U_3228,U_3227)))
& U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK34(U_3229,U_3228,U_3227))),sK35(U_3229,U_3228,U_3227))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK35(U_3229,U_3228,U_3227)),U_3227))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(U_3229,U_3228,U_3227)))
& is_int(sK35(U_3229,U_3228,U_3227))
& is_int(sK34(U_3229,U_3228,U_3227))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227)) )
| ( ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
& U_3227 = zero_zero_int ) )
& ( ( ( ! [U_3222,U_3221] :
( hBOOL(hAPP_int_bool(U_3229,U_3221))
| U_3228 != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),U_3222)),U_3221)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3221),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),U_3221))
| ~ is_int(U_3221)
| ~ is_int(U_3222) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int)) )
& ( ! [U_3220,U_3219] :
( hBOOL(hAPP_int_bool(U_3229,U_3219))
| U_3228 != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),U_3220)),U_3219)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3219),U_3227))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3219))
| ~ is_int(U_3219)
| ~ is_int(U_3220) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227)) )
& ( hBOOL(hAPP_int_bool(U_3229,U_3228))
| U_3227 != zero_zero_int ) )
| ~ hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227))) ) )
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_3225,sK37(U_3229,U_3228,U_3227))],[f_1192_5]) ).
cnf(f_1192_7,plain,
( hBOOL(hAPP_int_bool(U_3229,U_3228))
| U_3227 != zero_zero_int
| ~ hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_8,plain,
( hBOOL(hAPP_int_bool(U_3229,U_3219))
| U_3228 != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),U_3220)),U_3219)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3219),U_3227))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3219))
| ~ is_int(U_3219)
| ~ is_int(U_3220)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_9,plain,
( hBOOL(hAPP_int_bool(U_3229,U_3221))
| U_3228 != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),U_3222)),U_3221)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3221),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),U_3221))
| ~ is_int(U_3221)
| ~ is_int(U_3222)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_10,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_11,plain,
( is_int(sK34(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_12,plain,
( is_int(sK35(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_13,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(U_3229,U_3228,U_3227)))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_14,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK35(U_3229,U_3228,U_3227)),U_3227))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_15,plain,
( U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK34(U_3229,U_3228,U_3227))),sK35(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_16,plain,
( ~ hBOOL(hAPP_int_bool(U_3229,sK35(U_3229,U_3228,U_3227)))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_17,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_18,plain,
( is_int(sK34(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_19,plain,
( is_int(sK35(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_20,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(U_3229,U_3228,U_3227)))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_21,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK35(U_3229,U_3228,U_3227)),U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_22,plain,
( U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK34(U_3229,U_3228,U_3227))),sK35(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_23,plain,
( ~ hBOOL(hAPP_int_bool(U_3229,sK35(U_3229,U_3228,U_3227)))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_24,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227))
| U_3227 = zero_zero_int
| is_int(sK36(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_25,plain,
( is_int(sK34(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| is_int(sK36(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_26,plain,
( is_int(sK35(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| is_int(sK36(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_27,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(U_3229,U_3228,U_3227)))
| U_3227 = zero_zero_int
| is_int(sK36(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_28,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK35(U_3229,U_3228,U_3227)),U_3227))
| U_3227 = zero_zero_int
| is_int(sK36(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_29,plain,
( U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK34(U_3229,U_3228,U_3227))),sK35(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| is_int(sK36(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_30,plain,
( ~ hBOOL(hAPP_int_bool(U_3229,sK35(U_3229,U_3228,U_3227)))
| U_3227 = zero_zero_int
| is_int(sK36(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_31,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227))
| U_3227 = zero_zero_int
| is_int(sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_32,plain,
( is_int(sK34(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| is_int(sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_33,plain,
( is_int(sK35(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| is_int(sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_34,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(U_3229,U_3228,U_3227)))
| U_3227 = zero_zero_int
| is_int(sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_35,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK35(U_3229,U_3228,U_3227)),U_3227))
| U_3227 = zero_zero_int
| is_int(sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_36,plain,
( U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK34(U_3229,U_3228,U_3227))),sK35(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| is_int(sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_37,plain,
( ~ hBOOL(hAPP_int_bool(U_3229,sK35(U_3229,U_3228,U_3227)))
| U_3227 = zero_zero_int
| is_int(sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_38,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_39,plain,
( is_int(sK34(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_40,plain,
( is_int(sK35(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_41,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(U_3229,U_3228,U_3227)))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_42,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK35(U_3229,U_3228,U_3227)),U_3227))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_43,plain,
( U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK34(U_3229,U_3228,U_3227))),sK35(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_44,plain,
( ~ hBOOL(hAPP_int_bool(U_3229,sK35(U_3229,U_3228,U_3227)))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_45,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK37(U_3229,U_3228,U_3227)),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_46,plain,
( is_int(sK34(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK37(U_3229,U_3228,U_3227)),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_47,plain,
( is_int(sK35(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK37(U_3229,U_3228,U_3227)),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_48,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(U_3229,U_3228,U_3227)))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK37(U_3229,U_3228,U_3227)),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_49,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK35(U_3229,U_3228,U_3227)),U_3227))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK37(U_3229,U_3228,U_3227)),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_50,plain,
( U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK34(U_3229,U_3228,U_3227))),sK35(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK37(U_3229,U_3228,U_3227)),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_51,plain,
( ~ hBOOL(hAPP_int_bool(U_3229,sK35(U_3229,U_3228,U_3227)))
| U_3227 = zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK37(U_3229,U_3228,U_3227)),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_52,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227))
| U_3227 = zero_zero_int
| U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK36(U_3229,U_3228,U_3227))),sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_53,plain,
( is_int(sK34(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK36(U_3229,U_3228,U_3227))),sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_54,plain,
( is_int(sK35(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK36(U_3229,U_3228,U_3227))),sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_55,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(U_3229,U_3228,U_3227)))
| U_3227 = zero_zero_int
| U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK36(U_3229,U_3228,U_3227))),sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_56,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK35(U_3229,U_3228,U_3227)),U_3227))
| U_3227 = zero_zero_int
| U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK36(U_3229,U_3228,U_3227))),sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_57,plain,
( U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK34(U_3229,U_3228,U_3227))),sK35(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK36(U_3229,U_3228,U_3227))),sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_58,plain,
( ~ hBOOL(hAPP_int_bool(U_3229,sK35(U_3229,U_3228,U_3227)))
| U_3227 = zero_zero_int
| U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK36(U_3229,U_3228,U_3227))),sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_59,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227))
| U_3227 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(U_3229,sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_60,plain,
( is_int(sK34(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(U_3229,sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_61,plain,
( is_int(sK35(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(U_3229,sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_62,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(U_3229,U_3228,U_3227)))
| U_3227 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(U_3229,sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_63,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK35(U_3229,U_3228,U_3227)),U_3227))
| U_3227 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(U_3229,sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_64,plain,
( U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK34(U_3229,U_3228,U_3227))),sK35(U_3229,U_3228,U_3227))
| U_3227 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(U_3229,sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_65,plain,
( ~ hBOOL(hAPP_int_bool(U_3229,sK35(U_3229,U_3228,U_3227)))
| U_3227 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(U_3229,sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_66,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| is_int(sK36(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_67,plain,
( is_int(sK34(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| is_int(sK36(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_68,plain,
( is_int(sK35(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| is_int(sK36(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_69,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(U_3229,U_3228,U_3227)))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| is_int(sK36(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_70,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK35(U_3229,U_3228,U_3227)),U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| is_int(sK36(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_71,plain,
( U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK34(U_3229,U_3228,U_3227))),sK35(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| is_int(sK36(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_72,plain,
( ~ hBOOL(hAPP_int_bool(U_3229,sK35(U_3229,U_3228,U_3227)))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| is_int(sK36(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_73,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| is_int(sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_74,plain,
( is_int(sK34(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| is_int(sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_75,plain,
( is_int(sK35(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| is_int(sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_76,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(U_3229,U_3228,U_3227)))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| is_int(sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_77,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK35(U_3229,U_3228,U_3227)),U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| is_int(sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_78,plain,
( U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK34(U_3229,U_3228,U_3227))),sK35(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| is_int(sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_79,plain,
( ~ hBOOL(hAPP_int_bool(U_3229,sK35(U_3229,U_3228,U_3227)))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| is_int(sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_80,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_81,plain,
( is_int(sK34(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_82,plain,
( is_int(sK35(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_83,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(U_3229,U_3228,U_3227)))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_84,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK35(U_3229,U_3228,U_3227)),U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_85,plain,
( U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK34(U_3229,U_3228,U_3227))),sK35(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_86,plain,
( ~ hBOOL(hAPP_int_bool(U_3229,sK35(U_3229,U_3228,U_3227)))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3227),sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_87,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK37(U_3229,U_3228,U_3227)),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_88,plain,
( is_int(sK34(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK37(U_3229,U_3228,U_3227)),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_89,plain,
( is_int(sK35(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK37(U_3229,U_3228,U_3227)),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_90,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(U_3229,U_3228,U_3227)))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK37(U_3229,U_3228,U_3227)),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_91,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK35(U_3229,U_3228,U_3227)),U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK37(U_3229,U_3228,U_3227)),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_92,plain,
( U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK34(U_3229,U_3228,U_3227))),sK35(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK37(U_3229,U_3228,U_3227)),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_93,plain,
( ~ hBOOL(hAPP_int_bool(U_3229,sK35(U_3229,U_3228,U_3227)))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK37(U_3229,U_3228,U_3227)),zero_zero_int))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_94,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK36(U_3229,U_3228,U_3227))),sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_95,plain,
( is_int(sK34(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK36(U_3229,U_3228,U_3227))),sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_96,plain,
( is_int(sK35(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK36(U_3229,U_3228,U_3227))),sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_97,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(U_3229,U_3228,U_3227)))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK36(U_3229,U_3228,U_3227))),sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_98,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK35(U_3229,U_3228,U_3227)),U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK36(U_3229,U_3228,U_3227))),sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_99,plain,
( U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK34(U_3229,U_3228,U_3227))),sK35(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK36(U_3229,U_3228,U_3227))),sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_100,plain,
( ~ hBOOL(hAPP_int_bool(U_3229,sK35(U_3229,U_3228,U_3227)))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK36(U_3229,U_3228,U_3227))),sK37(U_3229,U_3228,U_3227))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_101,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| ~ hBOOL(hAPP_int_bool(U_3229,sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_102,plain,
( is_int(sK34(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| ~ hBOOL(hAPP_int_bool(U_3229,sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_103,plain,
( is_int(sK35(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| ~ hBOOL(hAPP_int_bool(U_3229,sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_104,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(U_3229,U_3228,U_3227)))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| ~ hBOOL(hAPP_int_bool(U_3229,sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_105,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK35(U_3229,U_3228,U_3227)),U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| ~ hBOOL(hAPP_int_bool(U_3229,sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_106,plain,
( U_3228 = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3227),sK34(U_3229,U_3228,U_3227))),sK35(U_3229,U_3228,U_3227))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| ~ hBOOL(hAPP_int_bool(U_3229,sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
cnf(f_1192_107,plain,
( ~ hBOOL(hAPP_int_bool(U_3229,sK35(U_3229,U_3228,U_3227)))
| ~ hBOOL(hAPP_int_bool(U_3229,U_3228))
| ~ hBOOL(hAPP_int_bool(U_3229,sK37(U_3229,U_3228,U_3227)))
| hBOOL(hAPP_int_bool(U_3229,hAPP_int_int(div_mod_int(U_3228),U_3227)))
| ~ is_int(U_3227)
| ~ is_int(U_3228) ),
inference(clausify,[status(thm)],[f_1192_6]) ).
fof(f_1193_1,plain,
! [Q_1,B,R_1,C] :
( 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(B),hAPP_int_int(div_mod_int(Q_1),C))),R_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C)) ),
inference(fof_nnf,[status(thm)],[fact_1167_zmult2__lemma__aux3]) ).
fof(f_1193_2,plain,
! [U_3233,U_3232,U_3231,U_3230] :
( 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(U_3232),hAPP_int_int(div_mod_int(U_3233),U_3230))),U_3231)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3231),U_3232))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3231))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3230)) ),
inference(variable_rename,[status(thm)],[f_1193_1]) ).
cnf(f_1193_3,plain,
( 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(U_3232),hAPP_int_int(div_mod_int(U_3233),U_3230))),U_3231)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3231),U_3232))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3231))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3230)) ),
inference(clausify,[status(thm)],[f_1193_2]) ).
fof(f_1194_1,plain,
! [Q_1,B,R_1,C] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),hAPP_int_int(div_mod_int(Q_1),C))),R_1)),hAPP_int_int(times_times_int(B),C)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C)) ),
inference(fof_nnf,[status(thm)],[fact_1168_zmult2__lemma__aux4]) ).
fof(f_1194_2,plain,
! [U_3237,U_3236,U_3235,U_3234] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3236),hAPP_int_int(div_mod_int(U_3237),U_3234))),U_3235)),hAPP_int_int(times_times_int(U_3236),U_3234)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3235),U_3236))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3235))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3234)) ),
inference(variable_rename,[status(thm)],[f_1194_1]) ).
cnf(f_1194_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3236),hAPP_int_int(div_mod_int(U_3237),U_3234))),U_3235)),hAPP_int_int(times_times_int(U_3236),U_3234)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3235),U_3236))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3235))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3234)) ),
inference(clausify,[status(thm)],[f_1194_2]) ).
fof(f_1195_1,plain,
! [Q_1,B,R_1,C] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(B),C)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),hAPP_int_int(div_mod_int(Q_1),C))),R_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),R_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C)) ),
inference(fof_nnf,[status(thm)],[fact_1169_zmult2__lemma__aux1]) ).
fof(f_1195_2,plain,
! [U_3241,U_3240,U_3239,U_3238] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_3240),U_3238)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3240),hAPP_int_int(div_mod_int(U_3241),U_3238))),U_3239)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3239),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3240),U_3239))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3238)) ),
inference(variable_rename,[status(thm)],[f_1195_1]) ).
cnf(f_1195_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(U_3240),U_3238)),hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3240),hAPP_int_int(div_mod_int(U_3241),U_3238))),U_3239)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3239),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3240),U_3239))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3238)) ),
inference(clausify,[status(thm)],[f_1195_2]) ).
fof(f_1196_1,plain,
! [Q_1,B,R_1,C] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B),hAPP_int_int(div_mod_int(Q_1),C))),R_1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B),R_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),C)) ),
inference(fof_nnf,[status(thm)],[fact_1170_zmult2__lemma__aux2]) ).
fof(f_1196_2,plain,
! [U_3245,U_3244,U_3243,U_3242] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3244),hAPP_int_int(div_mod_int(U_3245),U_3242))),U_3243)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3243),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3244),U_3243))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3242)) ),
inference(variable_rename,[status(thm)],[f_1196_1]) ).
cnf(f_1196_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3244),hAPP_int_int(div_mod_int(U_3245),U_3242))),U_3243)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3243),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3244),U_3243))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3242)) ),
inference(clausify,[status(thm)],[f_1196_2]) ).
fof(f_1197_1,plain,
! [A_1,B_1,Q_3,Y_1] :
( hAPP_int_int(div_mod_int(A_1),B_1) = Y_1
| B_1 = zero_zero_int
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_1),Y_1)) )
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) )
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_1),B_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_1)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1)) )
| A_1 != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(B_1),Q_3)),Y_1)
| ~ is_int(Y_1)
| ~ is_int(B_1) ),
inference(fof_nnf,[status(thm)],[fact_1171_divmod__int__rel__mod__eq]) ).
fof(f_1197_2,plain,
! [U_3249,U_3248,U_3247,U_3246] :
( hAPP_int_int(div_mod_int(U_3249),U_3248) = U_3246
| U_3248 = zero_zero_int
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3246),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3248),U_3246)) )
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3248)) )
| ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3246),U_3248))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3246)) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3248)) )
| U_3249 != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3248),U_3247)),U_3246)
| ~ is_int(U_3246)
| ~ is_int(U_3248) ),
inference(variable_rename,[status(thm)],[f_1197_1]) ).
cnf(f_1197_3,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3248))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3248))
| hAPP_int_int(div_mod_int(U_3249),U_3248) = U_3246
| U_3248 = zero_zero_int
| U_3249 != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3248),U_3247)),U_3246)
| ~ is_int(U_3246)
| ~ is_int(U_3248) ),
inference(clausify,[status(thm)],[f_1197_2]) ).
cnf(f_1197_4,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3246),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3248),U_3246))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3248))
| hAPP_int_int(div_mod_int(U_3249),U_3248) = U_3246
| U_3248 = zero_zero_int
| U_3249 != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3248),U_3247)),U_3246)
| ~ is_int(U_3246)
| ~ is_int(U_3248) ),
inference(clausify,[status(thm)],[f_1197_2]) ).
cnf(f_1197_5,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3248))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3246),U_3248))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3246))
| hAPP_int_int(div_mod_int(U_3249),U_3248) = U_3246
| U_3248 = zero_zero_int
| U_3249 != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3248),U_3247)),U_3246)
| ~ is_int(U_3246)
| ~ is_int(U_3248) ),
inference(clausify,[status(thm)],[f_1197_2]) ).
cnf(f_1197_6,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3246),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3248),U_3246))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3246),U_3248))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3246))
| hAPP_int_int(div_mod_int(U_3249),U_3248) = U_3246
| U_3248 = zero_zero_int
| U_3249 != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(U_3248),U_3247)),U_3246)
| ~ is_int(U_3246)
| ~ is_int(U_3248) ),
inference(clausify,[status(thm)],[f_1197_2]) ).
fof(f_1198_1,plain,
! [X_2] :
( ( hAPP_int_int(div_mod_int(X_2),number_number_of_int(bit0(bit1(pls)))) != zero_zero_int
| hAPP_int_int(div_mod_int(X_2),number_number_of_int(bit0(bit1(pls)))) != one_one_int )
& ( hAPP_int_int(div_mod_int(X_2),number_number_of_int(bit0(bit1(pls)))) = one_one_int
| hAPP_int_int(div_mod_int(X_2),number_number_of_int(bit0(bit1(pls)))) = zero_zero_int ) ),
inference(fof_nnf,[status(thm)],[fact_1172_neq__one__mod__two]) ).
fof(f_1198_2,plain,
! [U_3250] :
( ( hAPP_int_int(div_mod_int(U_3250),number_number_of_int(bit0(bit1(pls)))) != zero_zero_int
| hAPP_int_int(div_mod_int(U_3250),number_number_of_int(bit0(bit1(pls)))) != one_one_int )
& ( hAPP_int_int(div_mod_int(U_3250),number_number_of_int(bit0(bit1(pls)))) = one_one_int
| hAPP_int_int(div_mod_int(U_3250),number_number_of_int(bit0(bit1(pls)))) = zero_zero_int ) ),
inference(variable_rename,[status(thm)],[f_1198_1]) ).
fof(f_1198_3,plain,
( ! [U_3252] :
( hAPP_int_int(div_mod_int(U_3252),number_number_of_int(bit0(bit1(pls)))) != zero_zero_int
| hAPP_int_int(div_mod_int(U_3252),number_number_of_int(bit0(bit1(pls)))) != one_one_int )
& ! [U_3251] :
( hAPP_int_int(div_mod_int(U_3251),number_number_of_int(bit0(bit1(pls)))) = one_one_int
| hAPP_int_int(div_mod_int(U_3251),number_number_of_int(bit0(bit1(pls)))) = zero_zero_int ) ),
inference(miniscope,[status(thm)],[f_1198_2]) ).
cnf(f_1198_4,plain,
( hAPP_int_int(div_mod_int(U_3251),number_number_of_int(bit0(bit1(pls)))) = one_one_int
| hAPP_int_int(div_mod_int(U_3251),number_number_of_int(bit0(bit1(pls)))) = zero_zero_int ),
inference(clausify,[status(thm)],[f_1198_3]) ).
cnf(f_1198_5,plain,
( hAPP_int_int(div_mod_int(U_3252),number_number_of_int(bit0(bit1(pls)))) != zero_zero_int
| hAPP_int_int(div_mod_int(U_3252),number_number_of_int(bit0(bit1(pls)))) != one_one_int ),
inference(clausify,[status(thm)],[f_1198_3]) ).
fof(f_1199_1,plain,
! [B] :
( hAPP_int_int(div_mod_int(number_number_of_int(min)),B) = hAPP_int_int(minus_minus_int(B),one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B)) ),
inference(fof_nnf,[status(thm)],[fact_1173_zmod__minus1]) ).
fof(f_1199_2,plain,
! [U_3253] :
( hAPP_int_int(div_mod_int(number_number_of_int(min)),U_3253) = hAPP_int_int(minus_minus_int(U_3253),one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3253)) ),
inference(variable_rename,[status(thm)],[f_1199_1]) ).
cnf(f_1199_3,plain,
( hAPP_int_int(div_mod_int(number_number_of_int(min)),U_3253) = hAPP_int_int(minus_minus_int(U_3253),one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3253)) ),
inference(clausify,[status(thm)],[f_1199_2]) ).
fof(f_1200_1,plain,
! [B,A] :
( 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)))),B))),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),A)) = 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(B),A)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A)) ),
inference(fof_nnf,[status(thm)],[fact_1174_pos__zmod__mult__2]) ).
fof(f_1200_2,plain,
! [U_3255,U_3254] :
( 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)))),U_3255))),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),U_3254)) = 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(U_3255),U_3254)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3254)) ),
inference(variable_rename,[status(thm)],[f_1200_1]) ).
cnf(f_1200_3,plain,
( 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)))),U_3255))),hAPP_int_int(times_times_int(number_number_of_int(bit0(bit1(pls)))),U_3254)) = 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(U_3255),U_3254)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3254)) ),
inference(clausify,[status(thm)],[f_1200_2]) ).
fof(f_1201_1,plain,
! [M_1,D_1] :
( ? [Q_2] :
( M_1 = hAPP_int_int(times_times_int(D_1),Q_2)
& is_int(Q_2) )
| hAPP_int_int(div_mod_int(M_1),D_1) != zero_zero_int
| ~ is_int(M_1) ),
inference(fof_nnf,[status(thm)],[fact_1175_zmod__eq__0D]) ).
fof(f_1201_2,plain,
! [U_3258,U_3257] :
( ? [U_3256] :
( U_3258 = hAPP_int_int(times_times_int(U_3257),U_3256)
& is_int(U_3256) )
| hAPP_int_int(div_mod_int(U_3258),U_3257) != zero_zero_int
| ~ is_int(U_3258) ),
inference(variable_rename,[status(thm)],[f_1201_1]) ).
fof(f_1201_3,plain,
! [U_3258] :
( ! [U_3257] :
( ? [U_3256] :
( U_3258 = hAPP_int_int(times_times_int(U_3257),U_3256)
& is_int(U_3256) )
| hAPP_int_int(div_mod_int(U_3258),U_3257) != zero_zero_int )
| ~ is_int(U_3258) ),
inference(miniscope,[status(thm)],[f_1201_2]) ).
fof(f_1201_4,plain,
! [U_3258] :
( ! [U_3257] :
( ( U_3258 = hAPP_int_int(times_times_int(U_3257),sK38(U_3258,U_3257))
& is_int(sK38(U_3258,U_3257)) )
| hAPP_int_int(div_mod_int(U_3258),U_3257) != zero_zero_int )
| ~ is_int(U_3258) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_3256,sK38(U_3258,U_3257))],[f_1201_3]) ).
cnf(f_1201_5,plain,
( is_int(sK38(U_3258,U_3257))
| hAPP_int_int(div_mod_int(U_3258),U_3257) != zero_zero_int
| ~ is_int(U_3258) ),
inference(clausify,[status(thm)],[f_1201_4]) ).
cnf(f_1201_6,plain,
( U_3258 = hAPP_int_int(times_times_int(U_3257),sK38(U_3258,U_3257))
| hAPP_int_int(div_mod_int(U_3258),U_3257) != zero_zero_int
| ~ is_int(U_3258) ),
inference(clausify,[status(thm)],[f_1201_4]) ).
fof(f_1202_1,plain,
! [X_1,Y_1,M] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(standardRes(M,X_1)),standardRes(M,Y_1)),hAPP_int_int(times_times_int(X_1),Y_1)),M))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),M)) ),
inference(fof_nnf,[status(thm)],[fact_1176_StandardRes__prop4]) ).
fof(f_1202_2,plain,
! [U_3261,U_3260,U_3259] :
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(standardRes(U_3259,U_3261)),standardRes(U_3259,U_3260)),hAPP_int_int(times_times_int(U_3261),U_3260)),U_3259))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_3259)) ),
inference(variable_rename,[status(thm)],[f_1202_1]) ).
cnf(f_1202_3,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_int_int(times_times_int(standardRes(U_3259,U_3261)),standardRes(U_3259,U_3260)),hAPP_int_int(times_times_int(U_3261),U_3260)),U_3259))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(bit0(bit1(pls)))),U_3259)) ),
inference(clausify,[status(thm)],[f_1202_2]) ).
fof(f_1203_1,plain,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(M),N_1)),N_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_1177_mod__le__divisor]) ).
fof(f_1203_2,plain,
! [U_3263,U_3262] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(U_3263),U_3262)),U_3262))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3262)) ),
inference(variable_rename,[status(thm)],[f_1203_1]) ).
cnf(f_1203_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(U_3263),U_3262)),U_3262))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3262)) ),
inference(clausify,[status(thm)],[f_1203_2]) ).
fof(f_1204_1,plain,
! [M,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(div_mod_nat(M),N_1)),N_1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_1178_mod__less__divisor]) ).
fof(f_1204_2,plain,
! [U_3265,U_3264] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(div_mod_nat(U_3265),U_3264)),U_3264))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3264)) ),
inference(variable_rename,[status(thm)],[f_1204_1]) ).
cnf(f_1204_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(div_mod_nat(U_3265),U_3264)),U_3264))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3264)) ),
inference(clausify,[status(thm)],[f_1204_2]) ).
fof(f_1205_1,plain,
! [Ma,D] :
( ( hAPP_nat_nat(div_mod_nat(Ma),D) = zero_zero_nat
| ! [Q_2] : Ma != hAPP_nat_nat(times_times_nat(D),Q_2) )
& ( ? [Q_2] : Ma = hAPP_nat_nat(times_times_nat(D),Q_2)
| hAPP_nat_nat(div_mod_nat(Ma),D) != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_1179_mod__eq__0__iff]) ).
fof(f_1205_2,plain,
! [U_3269,U_3268] :
( ( hAPP_nat_nat(div_mod_nat(U_3269),U_3268) = zero_zero_nat
| ! [U_3267] : U_3269 != hAPP_nat_nat(times_times_nat(U_3268),U_3267) )
& ( ? [U_3266] : U_3269 = hAPP_nat_nat(times_times_nat(U_3268),U_3266)
| hAPP_nat_nat(div_mod_nat(U_3269),U_3268) != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_1205_1]) ).
fof(f_1205_3,plain,
( ! [U_3273,U_3271] :
( hAPP_nat_nat(div_mod_nat(U_3273),U_3271) = zero_zero_nat
| ! [U_3267] : U_3273 != hAPP_nat_nat(times_times_nat(U_3271),U_3267) )
& ! [U_3272,U_3270] :
( ? [U_3266] : U_3272 = hAPP_nat_nat(times_times_nat(U_3270),U_3266)
| hAPP_nat_nat(div_mod_nat(U_3272),U_3270) != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_1205_2]) ).
fof(f_1205_4,plain,
( ! [U_3273,U_3271] :
( hAPP_nat_nat(div_mod_nat(U_3273),U_3271) = zero_zero_nat
| ! [U_3267] : U_3273 != hAPP_nat_nat(times_times_nat(U_3271),U_3267) )
& ! [U_3272,U_3270] :
( U_3272 = hAPP_nat_nat(times_times_nat(U_3270),sK39(U_3272,U_3270))
| hAPP_nat_nat(div_mod_nat(U_3272),U_3270) != zero_zero_nat ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_3266,sK39(U_3272,U_3270))],[f_1205_3]) ).
cnf(f_1205_5,plain,
( U_3272 = hAPP_nat_nat(times_times_nat(U_3270),sK39(U_3272,U_3270))
| hAPP_nat_nat(div_mod_nat(U_3272),U_3270) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_1205_4]) ).
cnf(f_1205_6,plain,
( hAPP_nat_nat(div_mod_nat(U_3273),U_3271) = zero_zero_nat
| U_3273 != hAPP_nat_nat(times_times_nat(U_3271),U_3267) ),
inference(clausify,[status(thm)],[f_1205_4]) ).
fof(f_1206_1,plain,
! [M,N_1] :
( hAPP_nat_nat(div_mod_nat(M),N_1) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(M),N_1)),N_1)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_1180_mod__geq]) ).
fof(f_1206_2,plain,
! [U_3275,U_3274] :
( hAPP_nat_nat(div_mod_nat(U_3275),U_3274) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(U_3275),U_3274)),U_3274)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3275),U_3274)) ),
inference(variable_rename,[status(thm)],[f_1206_1]) ).
cnf(f_1206_3,plain,
( hAPP_nat_nat(div_mod_nat(U_3275),U_3274) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(U_3275),U_3274)),U_3274)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3275),U_3274)) ),
inference(clausify,[status(thm)],[f_1206_2]) ).
fof(f_1207_1,plain,
! [M,N_1] :
( ( hAPP_nat_nat(div_mod_nat(M),N_1) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(M),N_1)),N_1)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) )
& ( hAPP_nat_nat(div_mod_nat(M),N_1) = M
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_1181_mod__if]) ).
fof(f_1207_2,plain,
! [U_3277,U_3276] :
( ( hAPP_nat_nat(div_mod_nat(U_3277),U_3276) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(U_3277),U_3276)),U_3276)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3277),U_3276)) )
& ( hAPP_nat_nat(div_mod_nat(U_3277),U_3276) = U_3277
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3277),U_3276)) ) ),
inference(variable_rename,[status(thm)],[f_1207_1]) ).
fof(f_1207_3,plain,
( ! [U_3281,U_3279] :
( hAPP_nat_nat(div_mod_nat(U_3281),U_3279) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(U_3281),U_3279)),U_3279)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3281),U_3279)) )
& ! [U_3280,U_3278] :
( hAPP_nat_nat(div_mod_nat(U_3280),U_3278) = U_3280
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3280),U_3278)) ) ),
inference(miniscope,[status(thm)],[f_1207_2]) ).
cnf(f_1207_4,plain,
( hAPP_nat_nat(div_mod_nat(U_3280),U_3278) = U_3280
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3280),U_3278)) ),
inference(clausify,[status(thm)],[f_1207_3]) ).
cnf(f_1207_5,plain,
( hAPP_nat_nat(div_mod_nat(U_3281),U_3279) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(U_3281),U_3279)),U_3279)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3281),U_3279)) ),
inference(clausify,[status(thm)],[f_1207_3]) ).
fof(f_1208_1,plain,
! [K_1,N_1,M] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(K_1),N_1)),M)),N_1) = hAPP_nat_nat(div_mod_nat(M),N_1),
inference(fof_nnf,[status(thm)],[fact_1182_mod__mult__self3]) ).
fof(f_1208_2,plain,
! [U_3284,U_3283,U_3282] : hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_3284),U_3283)),U_3282)),U_3283) = hAPP_nat_nat(div_mod_nat(U_3282),U_3283),
inference(variable_rename,[status(thm)],[f_1208_1]) ).
cnf(f_1208_3,plain,
hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_3284),U_3283)),U_3282)),U_3283) = hAPP_nat_nat(div_mod_nat(U_3282),U_3283),
inference(clausify,[status(thm)],[f_1208_2]) ).
fof(f_1209_1,plain,
! [N_1,M] :
( hAPP_nat_nat(div_mod_nat(M),N_1) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(M),N_1)),N_1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M)) ),
inference(fof_nnf,[status(thm)],[fact_1183_le__mod__geq]) ).
fof(f_1209_2,plain,
! [U_3286,U_3285] :
( hAPP_nat_nat(div_mod_nat(U_3285),U_3286) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(U_3285),U_3286)),U_3286)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3286),U_3285)) ),
inference(variable_rename,[status(thm)],[f_1209_1]) ).
cnf(f_1209_3,plain,
( hAPP_nat_nat(div_mod_nat(U_3285),U_3286) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(minus_minus_nat(U_3285),U_3286)),U_3286)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3286),U_3285)) ),
inference(clausify,[status(thm)],[f_1209_2]) ).
fof(f_1210_1,plain,
! [M,X_1] : standardRes(M,X_1) = hAPP_int_int(div_mod_int(X_1),M),
inference(fof_nnf,[status(thm)],[fact_1184_StandardRes__def]) ).
fof(f_1210_2,plain,
! [U_3288,U_3287] : standardRes(U_3288,U_3287) = hAPP_int_int(div_mod_int(U_3287),U_3288),
inference(variable_rename,[status(thm)],[f_1210_1]) ).
cnf(f_1210_3,plain,
standardRes(U_3288,U_3287) = hAPP_int_int(div_mod_int(U_3287),U_3288),
inference(clausify,[status(thm)],[f_1210_2]) ).
fof(f_1211_1,plain,
! [M,N_1,K_1] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(div_mod_nat(M),N_1)),K_1) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(M),K_1)),hAPP_nat_nat(times_times_nat(N_1),K_1)),
inference(fof_nnf,[status(thm)],[fact_1185_mod__mult__distrib]) ).
fof(f_1211_2,plain,
! [U_3291,U_3290,U_3289] : hAPP_nat_nat(times_times_nat(hAPP_nat_nat(div_mod_nat(U_3291),U_3290)),U_3289) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(U_3291),U_3289)),hAPP_nat_nat(times_times_nat(U_3290),U_3289)),
inference(variable_rename,[status(thm)],[f_1211_1]) ).
cnf(f_1211_3,plain,
hAPP_nat_nat(times_times_nat(hAPP_nat_nat(div_mod_nat(U_3291),U_3290)),U_3289) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(U_3291),U_3289)),hAPP_nat_nat(times_times_nat(U_3290),U_3289)),
inference(clausify,[status(thm)],[f_1211_2]) ).
fof(f_1212_1,plain,
! [K_1,M,N_1] : hAPP_nat_nat(times_times_nat(K_1),hAPP_nat_nat(div_mod_nat(M),N_1)) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(K_1),M)),hAPP_nat_nat(times_times_nat(K_1),N_1)),
inference(fof_nnf,[status(thm)],[fact_1186_mod__mult__distrib2]) ).
fof(f_1212_2,plain,
! [U_3294,U_3293,U_3292] : hAPP_nat_nat(times_times_nat(U_3294),hAPP_nat_nat(div_mod_nat(U_3293),U_3292)) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(U_3294),U_3293)),hAPP_nat_nat(times_times_nat(U_3294),U_3292)),
inference(variable_rename,[status(thm)],[f_1212_1]) ).
cnf(f_1212_3,plain,
hAPP_nat_nat(times_times_nat(U_3294),hAPP_nat_nat(div_mod_nat(U_3293),U_3292)) = hAPP_nat_nat(div_mod_nat(hAPP_nat_nat(times_times_nat(U_3294),U_3293)),hAPP_nat_nat(times_times_nat(U_3294),U_3292)),
inference(clausify,[status(thm)],[f_1212_2]) ).
fof(f_1213_1,plain,
! [M,N_1] :
( hAPP_nat_nat(div_mod_nat(M),N_1) = M
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1)) ),
inference(fof_nnf,[status(thm)],[fact_1187_mod__less]) ).
fof(f_1213_2,plain,
! [U_3296,U_3295] :
( hAPP_nat_nat(div_mod_nat(U_3296),U_3295) = U_3296
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3296),U_3295)) ),
inference(variable_rename,[status(thm)],[f_1213_1]) ).
cnf(f_1213_3,plain,
( hAPP_nat_nat(div_mod_nat(U_3296),U_3295) = U_3296
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3296),U_3295)) ),
inference(clausify,[status(thm)],[f_1213_2]) ).
fof(f_1214_1,plain,
! [M,N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(M),N_1)),M)),
inference(fof_nnf,[status(thm)],[fact_1188_mod__less__eq__dividend]) ).
fof(f_1214_2,plain,
! [U_3298,U_3297] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(U_3298),U_3297)),U_3298)),
inference(variable_rename,[status(thm)],[f_1214_1]) ).
cnf(f_1214_3,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(div_mod_nat(U_3298),U_3297)),U_3298)),
inference(clausify,[status(thm)],[f_1214_2]) ).
fof(f_1215_1,plain,
! [Ma,X_2] :
( ( standardRes(Ma,X_2) = zero_zero_int
| ~ hBOOL(hAPP_int_bool(zcong(X_2,zero_zero_int),Ma)) )
& ( hBOOL(hAPP_int_bool(zcong(X_2,zero_zero_int),Ma))
| standardRes(Ma,X_2) != zero_zero_int ) ),
inference(fof_nnf,[status(thm)],[fact_1189_StandardRes__eq__zcong]) ).
fof(f_1215_2,plain,
! [U_3300,U_3299] :
( ( standardRes(U_3300,U_3299) = zero_zero_int
| ~ hBOOL(hAPP_int_bool(zcong(U_3299,zero_zero_int),U_3300)) )
& ( hBOOL(hAPP_int_bool(zcong(U_3299,zero_zero_int),U_3300))
| standardRes(U_3300,U_3299) != zero_zero_int ) ),
inference(variable_rename,[status(thm)],[f_1215_1]) ).
fof(f_1215_3,plain,
( ! [U_3304,U_3302] :
( standardRes(U_3304,U_3302) = zero_zero_int
| ~ hBOOL(hAPP_int_bool(zcong(U_3302,zero_zero_int),U_3304)) )
& ! [U_3303,U_3301] :
( hBOOL(hAPP_int_bool(zcong(U_3301,zero_zero_int),U_3303))
| standardRes(U_3303,U_3301) != zero_zero_int ) ),
inference(miniscope,[status(thm)],[f_1215_2]) ).
cnf(f_1215_4,plain,
( hBOOL(hAPP_int_bool(zcong(U_3301,zero_zero_int),U_3303))
| standardRes(U_3303,U_3301) != zero_zero_int ),
inference(clausify,[status(thm)],[f_1215_3]) ).
cnf(f_1215_5,plain,
( standardRes(U_3304,U_3302) = zero_zero_int
| ~ hBOOL(hAPP_int_bool(zcong(U_3302,zero_zero_int),U_3304)) ),
inference(clausify,[status(thm)],[f_1215_3]) ).
fof(f_1216_1,plain,
! [X_2,P_3] :
( ( ~ hBOOL(hAPP_int_bool(zcong(X_2,zero_zero_int),P_3))
| standardRes(P_3,X_2) = zero_zero_int )
& ( standardRes(P_3,X_2) != zero_zero_int
| hBOOL(hAPP_int_bool(zcong(X_2,zero_zero_int),P_3)) ) ),
inference(fof_nnf,[status(thm)],[fact_1190_StandardRes__prop3]) ).
fof(f_1216_2,plain,
! [U_3306,U_3305] :
( ( ~ hBOOL(hAPP_int_bool(zcong(U_3306,zero_zero_int),U_3305))
| standardRes(U_3305,U_3306) = zero_zero_int )
& ( standardRes(U_3305,U_3306) != zero_zero_int
| hBOOL(hAPP_int_bool(zcong(U_3306,zero_zero_int),U_3305)) ) ),
inference(variable_rename,[status(thm)],[f_1216_1]) ).
fof(f_1216_3,plain,
( ! [U_3310,U_3308] :
( ~ hBOOL(hAPP_int_bool(zcong(U_3310,zero_zero_int),U_3308))
| standardRes(U_3308,U_3310) = zero_zero_int )
& ! [U_3309,U_3307] :
( standardRes(U_3307,U_3309) != zero_zero_int
| hBOOL(hAPP_int_bool(zcong(U_3309,zero_zero_int),U_3307)) ) ),
inference(miniscope,[status(thm)],[f_1216_2]) ).
cnf(f_1216_4,plain,
( standardRes(U_3307,U_3309) != zero_zero_int
| hBOOL(hAPP_int_bool(zcong(U_3309,zero_zero_int),U_3307)) ),
inference(clausify,[status(thm)],[f_1216_3]) ).
cnf(f_1216_5,plain,
( ~ hBOOL(hAPP_int_bool(zcong(U_3310,zero_zero_int),U_3308))
| standardRes(U_3308,U_3310) = zero_zero_int ),
inference(clausify,[status(thm)],[f_1216_3]) ).
fof(f_1217_1,plain,
! [X_1,M] : hBOOL(hAPP_int_bool(zcong(X_1,standardRes(M,X_1)),M)),
inference(fof_nnf,[status(thm)],[fact_1191_StandardRes__prop1]) ).
fof(f_1217_2,plain,
! [U_3312,U_3311] : hBOOL(hAPP_int_bool(zcong(U_3312,standardRes(U_3311,U_3312)),U_3311)),
inference(variable_rename,[status(thm)],[f_1217_1]) ).
cnf(f_1217_3,plain,
hBOOL(hAPP_int_bool(zcong(U_3312,standardRes(U_3311,U_3312)),U_3311)),
inference(clausify,[status(thm)],[f_1217_2]) ).
fof(f_1218_1,plain,
! [X_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,standardRes(P_1,X_1)),P_1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1192_StandardRes__ubound]) ).
fof(f_1218_2,plain,
! [U_3314,U_3313] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,standardRes(U_3313,U_3314)),U_3313))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3313)) ),
inference(variable_rename,[status(thm)],[f_1218_1]) ).
cnf(f_1218_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,standardRes(U_3313,U_3314)),U_3313))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3313)) ),
inference(clausify,[status(thm)],[f_1218_2]) ).
fof(f_1219_1,plain,
! [X_2,P_3] :
( standardRes(P_3,X_2) = X_2
| ~ hBOOL(member_int(X_2,sr(P_3)))
| ~ is_int(X_2) ),
inference(fof_nnf,[status(thm)],[fact_1193_StandardRes__SR__prop]) ).
fof(f_1219_2,plain,
! [U_3316,U_3315] :
( standardRes(U_3315,U_3316) = U_3316
| ~ hBOOL(member_int(U_3316,sr(U_3315)))
| ~ is_int(U_3316) ),
inference(variable_rename,[status(thm)],[f_1219_1]) ).
fof(f_1219_3,plain,
! [U_3316] :
( ! [U_3315] :
( standardRes(U_3315,U_3316) = U_3316
| ~ hBOOL(member_int(U_3316,sr(U_3315))) )
| ~ is_int(U_3316) ),
inference(miniscope,[status(thm)],[f_1219_2]) ).
cnf(f_1219_4,plain,
( standardRes(U_3315,U_3316) = U_3316
| ~ hBOOL(member_int(U_3316,sr(U_3315)))
| ~ is_int(U_3316) ),
inference(clausify,[status(thm)],[f_1219_3]) ).
fof(f_1220_1,plain,
! [P_2,N,K] :
( ( hBOOL(hAPP_nat_bool(P_2,hAPP_nat_nat(div_mod_nat(N),K)))
| ( ? [I,J] :
( ~ hBOOL(hAPP_nat_bool(P_2,J))
& N = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(K),I)),J)
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K)) )
& K != zero_zero_nat )
| ( ~ hBOOL(hAPP_nat_bool(P_2,N))
& K = zero_zero_nat ) )
& ( ( ( ! [I,J] :
( hBOOL(hAPP_nat_bool(P_2,J))
| N != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(K),I)),J)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K)) )
| K = zero_zero_nat )
& ( hBOOL(hAPP_nat_bool(P_2,N))
| K != zero_zero_nat ) )
| ~ hBOOL(hAPP_nat_bool(P_2,hAPP_nat_nat(div_mod_nat(N),K))) ) ),
inference(fof_nnf,[status(thm)],[fact_1194_split__mod]) ).
fof(f_1220_2,plain,
! [U_3323,U_3322,U_3321] :
( ( hBOOL(hAPP_nat_bool(U_3323,hAPP_nat_nat(div_mod_nat(U_3322),U_3321)))
| ( ? [U_3320,U_3319] :
( ~ hBOOL(hAPP_nat_bool(U_3323,U_3319))
& U_3322 = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_3321),U_3320)),U_3319)
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3319),U_3321)) )
& U_3321 != zero_zero_nat )
| ( ~ hBOOL(hAPP_nat_bool(U_3323,U_3322))
& U_3321 = zero_zero_nat ) )
& ( ( ( ! [U_3318,U_3317] :
( hBOOL(hAPP_nat_bool(U_3323,U_3317))
| U_3322 != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_3321),U_3318)),U_3317)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3317),U_3321)) )
| U_3321 = zero_zero_nat )
& ( hBOOL(hAPP_nat_bool(U_3323,U_3322))
| U_3321 != zero_zero_nat ) )
| ~ hBOOL(hAPP_nat_bool(U_3323,hAPP_nat_nat(div_mod_nat(U_3322),U_3321))) ) ),
inference(variable_rename,[status(thm)],[f_1220_1]) ).
fof(f_1220_3,plain,
( ! [U_3329,U_3327,U_3325] :
( hBOOL(hAPP_nat_bool(U_3329,hAPP_nat_nat(div_mod_nat(U_3327),U_3325)))
| ( ? [U_3320,U_3319] :
( ~ hBOOL(hAPP_nat_bool(U_3329,U_3319))
& U_3327 = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_3325),U_3320)),U_3319)
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3319),U_3325)) )
& U_3325 != zero_zero_nat )
| ( ~ hBOOL(hAPP_nat_bool(U_3329,U_3327))
& U_3325 = zero_zero_nat ) )
& ! [U_3328,U_3326,U_3324] :
( ( ( ! [U_3318,U_3317] :
( hBOOL(hAPP_nat_bool(U_3328,U_3317))
| U_3326 != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_3324),U_3318)),U_3317)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3317),U_3324)) )
| U_3324 = zero_zero_nat )
& ( hBOOL(hAPP_nat_bool(U_3328,U_3326))
| U_3324 != zero_zero_nat ) )
| ~ hBOOL(hAPP_nat_bool(U_3328,hAPP_nat_nat(div_mod_nat(U_3326),U_3324))) ) ),
inference(miniscope,[status(thm)],[f_1220_2]) ).
fof(f_1220_4,plain,
( ! [U_3329,U_3327,U_3325] :
( hBOOL(hAPP_nat_bool(U_3329,hAPP_nat_nat(div_mod_nat(U_3327),U_3325)))
| ( ? [U_3319] :
( ~ hBOOL(hAPP_nat_bool(U_3329,U_3319))
& U_3327 = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_3325),sK40(U_3329,U_3327,U_3325))),U_3319)
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3319),U_3325)) )
& U_3325 != zero_zero_nat )
| ( ~ hBOOL(hAPP_nat_bool(U_3329,U_3327))
& U_3325 = zero_zero_nat ) )
& ! [U_3328,U_3326,U_3324] :
( ( ( ! [U_3318,U_3317] :
( hBOOL(hAPP_nat_bool(U_3328,U_3317))
| U_3326 != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_3324),U_3318)),U_3317)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3317),U_3324)) )
| U_3324 = zero_zero_nat )
& ( hBOOL(hAPP_nat_bool(U_3328,U_3326))
| U_3324 != zero_zero_nat ) )
| ~ hBOOL(hAPP_nat_bool(U_3328,hAPP_nat_nat(div_mod_nat(U_3326),U_3324))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_3320,sK40(U_3329,U_3327,U_3325))],[f_1220_3]) ).
fof(f_1220_5,plain,
( ! [U_3329,U_3327,U_3325] :
( hBOOL(hAPP_nat_bool(U_3329,hAPP_nat_nat(div_mod_nat(U_3327),U_3325)))
| ( ~ hBOOL(hAPP_nat_bool(U_3329,sK41(U_3329,U_3327,U_3325)))
& U_3327 = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_3325),sK40(U_3329,U_3327,U_3325))),sK41(U_3329,U_3327,U_3325))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK41(U_3329,U_3327,U_3325)),U_3325))
& U_3325 != zero_zero_nat )
| ( ~ hBOOL(hAPP_nat_bool(U_3329,U_3327))
& U_3325 = zero_zero_nat ) )
& ! [U_3328,U_3326,U_3324] :
( ( ( ! [U_3318,U_3317] :
( hBOOL(hAPP_nat_bool(U_3328,U_3317))
| U_3326 != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_3324),U_3318)),U_3317)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3317),U_3324)) )
| U_3324 = zero_zero_nat )
& ( hBOOL(hAPP_nat_bool(U_3328,U_3326))
| U_3324 != zero_zero_nat ) )
| ~ hBOOL(hAPP_nat_bool(U_3328,hAPP_nat_nat(div_mod_nat(U_3326),U_3324))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_3319,sK41(U_3329,U_3327,U_3325))],[f_1220_4]) ).
cnf(f_1220_6,plain,
( hBOOL(hAPP_nat_bool(U_3328,U_3326))
| U_3324 != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(U_3328,hAPP_nat_nat(div_mod_nat(U_3326),U_3324))) ),
inference(clausify,[status(thm)],[f_1220_5]) ).
cnf(f_1220_7,plain,
( hBOOL(hAPP_nat_bool(U_3328,U_3317))
| U_3326 != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_3324),U_3318)),U_3317)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3317),U_3324))
| U_3324 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(U_3328,hAPP_nat_nat(div_mod_nat(U_3326),U_3324))) ),
inference(clausify,[status(thm)],[f_1220_5]) ).
cnf(f_1220_8,plain,
( U_3325 != zero_zero_nat
| U_3325 = zero_zero_nat
| hBOOL(hAPP_nat_bool(U_3329,hAPP_nat_nat(div_mod_nat(U_3327),U_3325))) ),
inference(clausify,[status(thm)],[f_1220_5]) ).
cnf(f_1220_9,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK41(U_3329,U_3327,U_3325)),U_3325))
| U_3325 = zero_zero_nat
| hBOOL(hAPP_nat_bool(U_3329,hAPP_nat_nat(div_mod_nat(U_3327),U_3325))) ),
inference(clausify,[status(thm)],[f_1220_5]) ).
cnf(f_1220_10,plain,
( U_3327 = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_3325),sK40(U_3329,U_3327,U_3325))),sK41(U_3329,U_3327,U_3325))
| U_3325 = zero_zero_nat
| hBOOL(hAPP_nat_bool(U_3329,hAPP_nat_nat(div_mod_nat(U_3327),U_3325))) ),
inference(clausify,[status(thm)],[f_1220_5]) ).
cnf(f_1220_11,plain,
( ~ hBOOL(hAPP_nat_bool(U_3329,sK41(U_3329,U_3327,U_3325)))
| U_3325 = zero_zero_nat
| hBOOL(hAPP_nat_bool(U_3329,hAPP_nat_nat(div_mod_nat(U_3327),U_3325))) ),
inference(clausify,[status(thm)],[f_1220_5]) ).
cnf(f_1220_12,plain,
( U_3325 != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(U_3329,U_3327))
| hBOOL(hAPP_nat_bool(U_3329,hAPP_nat_nat(div_mod_nat(U_3327),U_3325))) ),
inference(clausify,[status(thm)],[f_1220_5]) ).
cnf(f_1220_13,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK41(U_3329,U_3327,U_3325)),U_3325))
| ~ hBOOL(hAPP_nat_bool(U_3329,U_3327))
| hBOOL(hAPP_nat_bool(U_3329,hAPP_nat_nat(div_mod_nat(U_3327),U_3325))) ),
inference(clausify,[status(thm)],[f_1220_5]) ).
cnf(f_1220_14,plain,
( U_3327 = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_3325),sK40(U_3329,U_3327,U_3325))),sK41(U_3329,U_3327,U_3325))
| ~ hBOOL(hAPP_nat_bool(U_3329,U_3327))
| hBOOL(hAPP_nat_bool(U_3329,hAPP_nat_nat(div_mod_nat(U_3327),U_3325))) ),
inference(clausify,[status(thm)],[f_1220_5]) ).
cnf(f_1220_15,plain,
( ~ hBOOL(hAPP_nat_bool(U_3329,sK41(U_3329,U_3327,U_3325)))
| ~ hBOOL(hAPP_nat_bool(U_3329,U_3327))
| hBOOL(hAPP_nat_bool(U_3329,hAPP_nat_nat(div_mod_nat(U_3327),U_3325))) ),
inference(clausify,[status(thm)],[f_1220_5]) ).
fof(f_1221_1,plain,
! [Q_1,R_1,B,C] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(B),hAPP_nat_nat(div_mod_nat(Q_1),C))),R_1)),hAPP_nat_nat(times_times_nat(B),C)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,R_1),B))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),C)) ),
inference(fof_nnf,[status(thm)],[fact_1195_mod__lemma]) ).
fof(f_1221_2,plain,
! [U_3333,U_3332,U_3331,U_3330] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_3331),hAPP_nat_nat(div_mod_nat(U_3333),U_3330))),U_3332)),hAPP_nat_nat(times_times_nat(U_3331),U_3330)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3332),U_3331))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3330)) ),
inference(variable_rename,[status(thm)],[f_1221_1]) ).
cnf(f_1221_3,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(times_times_nat(U_3331),hAPP_nat_nat(div_mod_nat(U_3333),U_3330))),U_3332)),hAPP_nat_nat(times_times_nat(U_3331),U_3330)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3332),U_3331))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3330)) ),
inference(clausify,[status(thm)],[f_1221_2]) ).
fof(f_1222_1,plain,
! [X_1,P_1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),standardRes(P_1,X_1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),P_1)) ),
inference(fof_nnf,[status(thm)],[fact_1196_StandardRes__lbound]) ).
fof(f_1222_2,plain,
! [U_3335,U_3334] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),standardRes(U_3334,U_3335)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3334)) ),
inference(variable_rename,[status(thm)],[f_1222_1]) ).
cnf(f_1222_3,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),standardRes(U_3334,U_3335)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3334)) ),
inference(clausify,[status(thm)],[f_1222_2]) ).
fof(f_1223_1,plain,
! [X1,X2,Ma] :
( ( ( standardRes(Ma,X1) = standardRes(Ma,X2)
| ~ hBOOL(hAPP_int_bool(zcong(X1,X2),Ma)) )
& ( hBOOL(hAPP_int_bool(zcong(X1,X2),Ma))
| standardRes(Ma,X1) != standardRes(Ma,X2) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Ma)) ),
inference(fof_nnf,[status(thm)],[fact_1197_StandardRes__prop2]) ).
fof(f_1223_2,plain,
! [U_3338,U_3337,U_3336] :
( ( ( standardRes(U_3336,U_3338) = standardRes(U_3336,U_3337)
| ~ hBOOL(hAPP_int_bool(zcong(U_3338,U_3337),U_3336)) )
& ( hBOOL(hAPP_int_bool(zcong(U_3338,U_3337),U_3336))
| standardRes(U_3336,U_3338) != standardRes(U_3336,U_3337) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3336)) ),
inference(variable_rename,[status(thm)],[f_1223_1]) ).
cnf(f_1223_3,plain,
( hBOOL(hAPP_int_bool(zcong(U_3338,U_3337),U_3336))
| standardRes(U_3336,U_3338) != standardRes(U_3336,U_3337)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3336)) ),
inference(clausify,[status(thm)],[f_1223_2]) ).
cnf(f_1223_4,plain,
( standardRes(U_3336,U_3338) = standardRes(U_3336,U_3337)
| ~ hBOOL(hAPP_int_bool(zcong(U_3338,U_3337),U_3336))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3336)) ),
inference(clausify,[status(thm)],[f_1223_2]) ).
fof(f_1224_1,plain,
! [Q,P] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
| ~ hBOOL(Q)
| ~ hBOOL(P) ),
inference(fof_nnf,[status(thm)],[help_fconj_1_1_U]) ).
fof(f_1224_2,plain,
! [U_3340,U_3339] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_3339),U_3340))
| ~ hBOOL(U_3340)
| ~ hBOOL(U_3339) ),
inference(variable_rename,[status(thm)],[f_1224_1]) ).
fof(f_1224_3,plain,
! [U_3340] :
( ! [U_3339] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_3339),U_3340))
| ~ hBOOL(U_3339) )
| ~ hBOOL(U_3340) ),
inference(miniscope,[status(thm)],[f_1224_2]) ).
cnf(f_1224_4,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_3339),U_3340))
| ~ hBOOL(U_3339)
| ~ hBOOL(U_3340) ),
inference(clausify,[status(thm)],[f_1224_3]) ).
fof(f_1225_1,plain,
! [P,Q] :
( hBOOL(P)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ),
inference(fof_nnf,[status(thm)],[help_fconj_2_1_U]) ).
fof(f_1225_2,plain,
! [U_3342,U_3341] :
( hBOOL(U_3342)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_3342),U_3341)) ),
inference(variable_rename,[status(thm)],[f_1225_1]) ).
fof(f_1225_3,plain,
! [U_3342] :
( ! [U_3341] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_3342),U_3341))
| hBOOL(U_3342) ),
inference(miniscope,[status(thm)],[f_1225_2]) ).
cnf(f_1225_4,plain,
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_3342),U_3341))
| hBOOL(U_3342) ),
inference(clausify,[status(thm)],[f_1225_3]) ).
fof(f_1226_1,plain,
! [P,Q] :
( hBOOL(Q)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ),
inference(fof_nnf,[status(thm)],[help_fconj_3_1_U]) ).
fof(f_1226_2,plain,
! [U_3344,U_3343] :
( hBOOL(U_3343)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_3344),U_3343)) ),
inference(variable_rename,[status(thm)],[f_1226_1]) ).
cnf(f_1226_3,plain,
( hBOOL(U_3343)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_3344),U_3343)) ),
inference(clausify,[status(thm)],[f_1226_2]) ).
fof(f_1227_1,plain,
! [P,Q,R] : hAPP_int_bool(cOMBC_int_int_bool(P,Q),R) = hAPP_int_bool(hAPP_i1948725293t_bool(P,R),Q),
inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U]) ).
fof(f_1227_2,plain,
! [U_3347,U_3346,U_3345] : hAPP_int_bool(cOMBC_int_int_bool(U_3347,U_3346),U_3345) = hAPP_int_bool(hAPP_i1948725293t_bool(U_3347,U_3345),U_3346),
inference(variable_rename,[status(thm)],[f_1227_1]) ).
cnf(f_1227_3,plain,
hAPP_int_bool(cOMBC_int_int_bool(U_3347,U_3346),U_3345) = hAPP_int_bool(hAPP_i1948725293t_bool(U_3347,U_3345),U_3346),
inference(clausify,[status(thm)],[f_1227_2]) ).
fof(f_1228_1,plain,
! [P,Q,R] : hAPP_int_bool(cOMBS_int_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_i68813070l_bool(P,R),hAPP_int_bool(Q,R)),
inference(fof_nnf,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__HOL__Obool_000tc__HOL__Obool_U]) ).
fof(f_1228_2,plain,
! [U_3350,U_3349,U_3348] : hAPP_int_bool(cOMBS_int_bool_bool(U_3350,U_3349),U_3348) = hAPP_bool_bool(hAPP_i68813070l_bool(U_3350,U_3348),hAPP_int_bool(U_3349,U_3348)),
inference(variable_rename,[status(thm)],[f_1228_1]) ).
cnf(f_1228_3,plain,
hAPP_int_bool(cOMBS_int_bool_bool(U_3350,U_3349),U_3348) = hAPP_bool_bool(hAPP_i68813070l_bool(U_3350,U_3348),hAPP_int_bool(U_3349,U_3348)),
inference(clausify,[status(thm)],[f_1228_2]) ).
fof(f_1229_1,plain,
! [P,Q,R] : hAPP_i68813070l_bool(cOMBB_1652995168ol_int(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_int_bool(Q,R)),
inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo]) ).
fof(f_1229_2,plain,
! [U_3353,U_3352,U_3351] : hAPP_i68813070l_bool(cOMBB_1652995168ol_int(U_3353,U_3352),U_3351) = hAPP_b589554111l_bool(U_3353,hAPP_int_bool(U_3352,U_3351)),
inference(variable_rename,[status(thm)],[f_1229_1]) ).
cnf(f_1229_3,plain,
hAPP_i68813070l_bool(cOMBB_1652995168ol_int(U_3353,U_3352),U_3351) = hAPP_b589554111l_bool(U_3353,hAPP_int_bool(U_3352,U_3351)),
inference(clausify,[status(thm)],[f_1229_2]) ).
fof(f_1230_1,negated_conjecture,
~ ? [X,Y] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y),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(negate,[status(cth)],[conj_0]) ).
fof(f_1230_2,negated_conjecture,
! [X,Y] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y),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(fof_nnf,[status(thm)],[f_1230_1]) ).
fof(f_1230_3,negated_conjecture,
! [U_3355,U_3354] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(U_3355),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_3354),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(variable_rename,[status(thm)],[f_1230_2]) ).
cnf(f_1230_4,negated_conjecture,
hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(U_3355),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(U_3354),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(clausify,[status(thm)],[f_1230_3]) ).
cnf(f_441_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_441_6]) ).
cnf(f_914_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_914_4]) ).
cnf(f_914_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_914_5]) ).
cnf(f_914_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_914_6]) ).
cnf(f_914_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_914_7]) ).
cnf(f_914_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_914_8]) ).
cnf(f_914_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_914_9]) ).
cnf(f_914_10_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_914_10]) ).
cnf(f_923_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_923_3]) ).
cnf(f_925_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_925_3]) ).
cnf(f_928_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_928_3]) ).
cnf(f_931_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_931_3]) ).
cnf(f_932_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_932_3]) ).
cnf(f_933_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_933_3]) ).
cnf(f_942_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_942_3]) ).
cnf(f_943_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_943_3]) ).
cnf(f_946_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_946_3]) ).
cnf(f_947_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_947_4]) ).
cnf(f_947_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_947_5]) ).
cnf(f_947_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_947_6]) ).
cnf(f_947_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_947_7]) ).
cnf(f_948_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_948_4]) ).
cnf(f_948_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_948_6]) ).
cnf(f_949_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_949_4]) ).
cnf(f_949_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_949_6]) ).
cnf(f_951_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_951_3]) ).
cnf(f_1087_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_3]) ).
cnf(f_1087_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_4]) ).
cnf(f_1087_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_5]) ).
cnf(f_1087_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_6]) ).
cnf(f_1087_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_7]) ).
cnf(f_1087_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_8]) ).
cnf(f_1087_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_9]) ).
cnf(f_1087_10_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_10]) ).
cnf(f_1087_11_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_11]) ).
cnf(f_1087_12_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_12]) ).
cnf(f_1087_13_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_13]) ).
cnf(f_1087_14_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_14]) ).
cnf(f_1087_15_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_15]) ).
cnf(f_1087_16_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_16]) ).
cnf(f_1087_17_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_17]) ).
cnf(f_1087_18_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_18]) ).
cnf(f_1087_19_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_19]) ).
cnf(f_1087_20_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_20]) ).
cnf(f_1087_21_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_21]) ).
cnf(f_1087_22_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1087_22]) ).
cnf(f_1088_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_3]) ).
cnf(f_1088_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_4]) ).
cnf(f_1088_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_5]) ).
cnf(f_1088_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_6]) ).
cnf(f_1088_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_7]) ).
cnf(f_1088_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_8]) ).
cnf(f_1088_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_9]) ).
cnf(f_1088_10_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_10]) ).
cnf(f_1088_11_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_11]) ).
cnf(f_1088_12_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_12]) ).
cnf(f_1088_13_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_13]) ).
cnf(f_1088_14_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_14]) ).
cnf(f_1088_15_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_15]) ).
cnf(f_1088_16_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_16]) ).
cnf(f_1088_17_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_17]) ).
cnf(f_1088_18_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_18]) ).
cnf(f_1088_19_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_19]) ).
cnf(f_1088_20_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_20]) ).
cnf(f_1088_21_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_21]) ).
cnf(f_1088_22_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1088_22]) ).
cnf(f_1197_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1197_3]) ).
cnf(f_1220_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1220_8]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( undefined_int(Eq_x_0) = undefined_int(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( multInv(Eq_x_0,Eq_x_1) = multInv(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( zfact(Eq_x_0) = zfact(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( bit0(Eq_x_0) = bit0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( bit1(Eq_x_0) = bit1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( number_number_of_int(Eq_x_0) = number_number_of_int(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( legendre(Eq_x_0,Eq_x_1) = legendre(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( standardRes(Eq_x_0,Eq_x_1) = standardRes(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( twoSqu1241645765sum2sq(Eq_x_0) = twoSqu1241645765sum2sq(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( inv(Eq_x_0,Eq_x_1) = inv(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( hAPP_bool_bool(Eq_x_0,Eq_x_1) = hAPP_bool_bool(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( hAPP_int_bool(Eq_x_0,Eq_x_1) = hAPP_int_bool(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( hAPP_int_int(Eq_x_0,Eq_x_1) = hAPP_int_int(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( hAPP_nat_bool(Eq_x_0,Eq_x_1) = hAPP_nat_bool(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( hAPP_nat_int(Eq_x_0,Eq_x_1) = hAPP_nat_int(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( hAPP_real_bool(Eq_x_0,Eq_x_1) = hAPP_real_bool(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( member_int(Eq_x_0,Eq_x_1) = member_int(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( hAPP_i1948725293t_bool(Eq_x_0,Eq_x_1) = hAPP_i1948725293t_bool(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( power_power_int(Eq_x_0) = power_power_int(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( number_number_of_nat(Eq_x_0) = number_number_of_nat(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( plus_plus_int(Eq_x_0) = plus_plus_int(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( times_times_int(Eq_x_0) = times_times_int(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( plus_plus_nat(Eq_x_0) = plus_plus_nat(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( hAPP_nat_nat(Eq_x_0,Eq_x_1) = hAPP_nat_nat(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( power_power_nat(Eq_x_0) = power_power_nat(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( times_times_nat(Eq_x_0) = times_times_nat(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( plus_plus_real(Eq_x_0) = plus_plus_real(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( hAPP_real_real(Eq_x_0,Eq_x_1) = hAPP_real_real(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( power_power_real(Eq_x_0) = power_power_real(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( hAPP_nat_real(Eq_x_0,Eq_x_1) = hAPP_nat_real(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,axiom,
( number267125858f_real(Eq_x_0) = number267125858f_real(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( times_times_real(Eq_x_0) = times_times_real(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( hAPP_n1699378549t_bool(Eq_x_0,Eq_x_1) = hAPP_n1699378549t_bool(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( hAPP_r1134773055l_bool(Eq_x_0,Eq_x_1) = hAPP_r1134773055l_bool(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( collect_int(Eq_x_0) = collect_int(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( product_Pair_int_int(Eq_x_0,Eq_x_1) = product_Pair_int_int(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( zcong(Eq_x_0,Eq_x_1) = zcong(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( quadRes(Eq_x_0) = quadRes(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( minus_minus_int(Eq_x_0) = minus_minus_int(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( minus_minus_real(Eq_x_0) = minus_minus_real(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( minus_minus_nat(Eq_x_0) = minus_minus_nat(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,axiom,
( wset(Eq_x_0,Eq_x_1) = wset(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,axiom,
( d22set(Eq_x_0) = d22set(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,axiom,
( sr(Eq_x_0) = sr(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_48,axiom,
( cOMBB_1652995168ol_int(Eq_x_0,Eq_x_1) = cOMBB_1652995168ol_int(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_49,axiom,
( cOMBC_int_int_bool(Eq_x_0,Eq_x_1) = cOMBC_int_int_bool(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_50,axiom,
( cOMBS_int_bool_bool(Eq_x_0,Eq_x_1) = cOMBS_int_bool_bool(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_51,axiom,
( div_mod_int(Eq_x_0) = div_mod_int(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_52,axiom,
( div_mod_nat(Eq_x_0) = div_mod_nat(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( hAPP_b589554111l_bool(Eq_x_0,Eq_x_1) = hAPP_b589554111l_bool(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_54,axiom,
( hAPP_i68813070l_bool(Eq_x_0,Eq_x_1) = hAPP_i68813070l_bool(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_55,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_56,axiom,
( sK10(Eq_x_0,Eq_x_1,Eq_x_2) = sK10(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_57,axiom,
( sK11(Eq_x_0,Eq_x_1) = sK11(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_58,axiom,
( sK12(Eq_x_0,Eq_x_1) = sK12(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,axiom,
( sK13(Eq_x_0,Eq_x_1) = sK13(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_60,axiom,
( sK14(Eq_x_0,Eq_x_1) = sK14(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_61,axiom,
( sK15(Eq_x_0,Eq_x_1,Eq_x_2) = sK15(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_62,axiom,
( sK16(Eq_x_0,Eq_x_1,Eq_x_2) = sK16(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_63,axiom,
( sK17(Eq_x_0,Eq_x_1) = sK17(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_64,axiom,
( sK18(Eq_x_0) = sK18(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_65,axiom,
( sK19(Eq_x_0) = sK19(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_66,axiom,
( sK20(Eq_x_0,Eq_x_1,Eq_x_2) = sK20(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_67,axiom,
( sK21(Eq_x_0,Eq_x_1,Eq_x_2) = sK21(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_68,axiom,
( sK22(Eq_x_0) = sK22(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_69,axiom,
( sK23(Eq_x_0,Eq_x_1) = sK23(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_70,axiom,
( sK24(Eq_x_0,Eq_x_1,Eq_x_2) = sK24(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_71,axiom,
( sK25(Eq_x_0,Eq_x_1,Eq_x_2) = sK25(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_72,axiom,
( sK26(Eq_x_0,Eq_x_1) = sK26(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_73,axiom,
( sK27(Eq_x_0,Eq_x_1,Eq_x_2) = sK27(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_74,axiom,
( sK28(Eq_x_0,Eq_x_1,Eq_x_2) = sK28(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_75,axiom,
( sK29(Eq_x_0,Eq_x_1,Eq_x_2) = sK29(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,axiom,
( sK30(Eq_x_0,Eq_x_1,Eq_x_2) = sK30(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_77,axiom,
( sK31(Eq_x_0,Eq_x_1) = sK31(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_78,axiom,
( sK32(Eq_x_0,Eq_x_1) = sK32(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_79,axiom,
( sK33(Eq_x_0,Eq_x_1) = sK33(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_80,axiom,
( sK34(Eq_x_0,Eq_x_1,Eq_x_2) = sK34(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_81,axiom,
( sK35(Eq_x_0,Eq_x_1,Eq_x_2) = sK35(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_82,axiom,
( sK36(Eq_x_0,Eq_x_1,Eq_x_2) = sK36(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_83,axiom,
( sK37(Eq_x_0,Eq_x_1,Eq_x_2) = sK37(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_84,axiom,
( sK38(Eq_x_0,Eq_x_1) = sK38(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_85,axiom,
( sK39(Eq_x_0,Eq_x_1) = sK39(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,axiom,
( sK40(Eq_x_0,Eq_x_1,Eq_x_2) = sK40(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_87,axiom,
( sK41(Eq_x_0,Eq_x_1,Eq_x_2) = sK41(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_88,axiom,
( is_int(Eq_y_0)
| ~ is_int(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_89,axiom,
( is_bool(Eq_y_0)
| ~ is_bool(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_90,axiom,
( hBOOL(Eq_y_0)
| ~ hBOOL(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926+3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n001.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 19 19:31:02 UTC 2026
% 0.10/5.38 % CPUTime :
% 228.32/233.64 % SZS status Theorem for theBenchmark
% 228.32/233.64 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------