%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM926+2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 08:53:36 AM UTC 2026
% Result : Theorem 48.14s 48.42s
% Output : Proof 48.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(gsy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint,axiom,
! [B_1_1,B_2_1] :
( ( is_int(B_2_1)
& is_int(B_1_1) )
=> is_int(minus_minus_int(B_1_1,B_2_1)) ),
file('theBenchmark.p',gsy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint) ).
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_Oplus__class_Oplus_000tc__Int__Oint,hypothesis,
! [B_1_1,B_2_1] :
( ( is_int(B_2_1)
& is_int(B_1_1) )
=> is_int(plus_plus_int(B_1_1,B_2_1)) ),
file('theBenchmark.p',gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint) ).
fof(gsy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint,hypothesis,
! [B_1_1,B_2_1] :
( ( is_int(B_2_1)
& is_int(B_1_1) )
=> is_int(times_times_int(B_1_1,B_2_1)) ),
file('theBenchmark.p',gsy_c_Groups_Otimes__class_Otimes_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_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_Power_Opower__class_Opower_000tc__Int__Oint,hypothesis,
! [B_1_1,B_2_1] :
( is_int(B_1_1)
=> is_int(power_power_int(B_1_1,B_2_1)) ),
file('theBenchmark.p',gsy_c_Power_Opower__class_Opower_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_TwoSquares__Mirabelle__ccrtsbwhjp_Osum2sq,axiom,
! [B_1_1] : is_int(twoSqu140629262sum2sq(B_1_1)),
file('theBenchmark.p',gsy_c_TwoSquares__Mirabelle__ccrtsbwhjp_Osum2sq) ).
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,
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] :
( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_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,
( ord_less_int(one_one_int,t)
=> ? [X,Y] :
( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_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,
ord_less_int(t,plus_plus_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,
zprime(plus_plus_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,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_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,
twoSqu142715416sum2sq(times_times_int(plus_plus_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_1] : power_power_int(plus_plus_int(A,B_1),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(A,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),A),B_1)),power_power_int(B_1,number_number_of_nat(bit0(bit1(pls))))),
file('theBenchmark.p',fact_7_zadd__power2) ).
fof(fact_8_zadd__power3,axiom,
! [A,B_1] : power_power_int(plus_plus_int(A,B_1),number_number_of_nat(bit1(bit1(pls)))) = plus_plus_int(plus_plus_int(plus_plus_int(power_power_int(A,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(A,number_number_of_nat(bit0(bit1(pls))))),B_1)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),A),power_power_int(B_1,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(B_1,number_number_of_nat(bit1(bit1(pls))))),
file('theBenchmark.p',fact_8_zadd__power3) ).
fof(fact_9_power2__sum,axiom,
! [X_2,Y_2] : power_power_real(plus_plus_real(X_2,Y_2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_real(plus_plus_real(power_power_real(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_real(Y_2,number_number_of_nat(bit0(bit1(pls))))),times_times_real(times_times_real(number267125858f_real(bit0(bit1(pls))),X_2),Y_2)),
file('theBenchmark.p',fact_9_power2__sum) ).
fof(fact_10_power2__sum,axiom,
! [X_2,Y_2] : power_power_nat(plus_plus_nat(X_2,Y_2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(plus_plus_nat(power_power_nat(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(Y_2,number_number_of_nat(bit0(bit1(pls))))),times_times_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] : power_power_int(plus_plus_int(X_2,Y_2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y_2,number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X_2),Y_2)),
file('theBenchmark.p',fact_11_power2__sum) ).
fof(fact_12_power2__eq__square__number__of,axiom,
! [W_15] : power_power_nat(number_number_of_nat(W_15),number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(number_number_of_nat(W_15),number_number_of_nat(W_15)),
file('theBenchmark.p',fact_12_power2__eq__square__number__of) ).
fof(fact_13_power2__eq__square__number__of,axiom,
! [W_15] : power_power_real(number267125858f_real(W_15),number_number_of_nat(bit0(bit1(pls)))) = times_times_real(number267125858f_real(W_15),number267125858f_real(W_15)),
file('theBenchmark.p',fact_13_power2__eq__square__number__of) ).
fof(fact_14_power2__eq__square__number__of,axiom,
! [W_15] : power_power_int(number_number_of_int(W_15),number_number_of_nat(bit0(bit1(pls)))) = times_times_int(number_number_of_int(W_15),number_number_of_int(W_15)),
file('theBenchmark.p',fact_14_power2__eq__square__number__of) ).
fof(fact_15_cube__square,axiom,
! [A] : times_times_int(A,power_power_int(A,number_number_of_nat(bit0(bit1(pls))))) = power_power_int(A,number_number_of_nat(bit1(bit1(pls)))),
file('theBenchmark.p',fact_15_cube__square) ).
fof(fact_16_one__power2,axiom,
power_power_real(one_one_real,number_number_of_nat(bit0(bit1(pls)))) = one_one_real,
file('theBenchmark.p',fact_16_one__power2) ).
fof(fact_17_one__power2,axiom,
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,
power_power_int(one_one_int,number_number_of_nat(bit0(bit1(pls)))) = one_one_int,
file('theBenchmark.p',fact_18_one__power2) ).
fof(fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X_21] : times_times_nat(X_21,X_21) = power_power_nat(X_21,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_21] : times_times_real(X_21,X_21) = power_power_real(X_21,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_21] : times_times_int(X_21,X_21) = power_power_int(X_21,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_57] : power_power_nat(A_57,number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(A_57,A_57),
file('theBenchmark.p',fact_22_power2__eq__square) ).
fof(fact_23_power2__eq__square,axiom,
! [A_57] : power_power_real(A_57,number_number_of_nat(bit0(bit1(pls)))) = times_times_real(A_57,A_57),
file('theBenchmark.p',fact_23_power2__eq__square) ).
fof(fact_24_power2__eq__square,axiom,
! [A_57] : power_power_int(A_57,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(A_57,A_57),
file('theBenchmark.p',fact_24_power2__eq__square) ).
fof(fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
! [X_20,N_38] : power_power_nat(X_20,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_38)) = times_times_nat(power_power_nat(X_20,N_38),power_power_nat(X_20,N_38)),
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_20,N_38] : power_power_real(X_20,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_38)) = times_times_real(power_power_real(X_20,N_38),power_power_real(X_20,N_38)),
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_20,N_38] : power_power_int(X_20,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_38)) = times_times_int(power_power_int(X_20,N_38),power_power_int(X_20,N_38)),
file('theBenchmark.p',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
fof(fact_28_add__special_I2_J,axiom,
! [W_14] : plus_plus_real(one_one_real,number267125858f_real(W_14)) = number267125858f_real(plus_plus_int(bit1(pls),W_14)),
file('theBenchmark.p',fact_28_add__special_I2_J) ).
fof(fact_29_add__special_I2_J,axiom,
! [W_14] : plus_plus_int(one_one_int,number_number_of_int(W_14)) = number_number_of_int(plus_plus_int(bit1(pls),W_14)),
file('theBenchmark.p',fact_29_add__special_I2_J) ).
fof(fact_30_add__special_I3_J,axiom,
! [V_17] : plus_plus_real(number267125858f_real(V_17),one_one_real) = number267125858f_real(plus_plus_int(V_17,bit1(pls))),
file('theBenchmark.p',fact_30_add__special_I3_J) ).
fof(fact_31_add__special_I3_J,axiom,
! [V_17] : plus_plus_int(number_number_of_int(V_17),one_one_int) = number_number_of_int(plus_plus_int(V_17,bit1(pls))),
file('theBenchmark.p',fact_31_add__special_I3_J) ).
fof(fact_32_one__add__one__is__two,axiom,
plus_plus_real(one_one_real,one_one_real) = number267125858f_real(bit0(bit1(pls))),
file('theBenchmark.p',fact_32_one__add__one__is__two) ).
fof(fact_33_one__add__one__is__two,axiom,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(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] :
( is_int(T)
=> plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) != times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),T) ),
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] : ord_less_eq_int(W,W),
file('theBenchmark.p',fact_35_zle__refl) ).
fof(fact_36_zle__linear,axiom,
! [Z,W] :
( ord_less_eq_int(W,Z)
| 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) )
=> ( ord_less_int(Z_1,W_1)
<=> ( Z_1 != W_1
& 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) )
=> ( ord_less_int(Y_1,X_1)
| X_1 = Y_1
| ord_less_int(X_1,Y_1) ) ),
file('theBenchmark.p',fact_38_zless__linear) ).
fof(fact_39_zle__trans,axiom,
! [K,I,J] :
( ord_less_eq_int(I,J)
=> ( ord_less_eq_int(J,K)
=> ord_less_eq_int(I,K) ) ),
file('theBenchmark.p',fact_39_zle__trans) ).
fof(fact_40_zle__antisym,axiom,
! [Z,W] :
( ( is_int(W)
& is_int(Z) )
=> ( ord_less_eq_int(Z,W)
=> ( 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_19,P_3,Q_4] : power_power_nat(power_power_nat(X_19,P_3),Q_4) = power_power_nat(X_19,times_times_nat(P_3,Q_4)),
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_19,P_3,Q_4] : power_power_real(power_power_real(X_19,P_3),Q_4) = power_power_real(X_19,times_times_nat(P_3,Q_4)),
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_19,P_3,Q_4] : power_power_int(power_power_int(X_19,P_3),Q_4) = power_power_int(X_19,times_times_nat(P_3,Q_4)),
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_18] : power_power_nat(X_18,one_one_nat) = X_18,
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_18] : power_power_real(X_18,one_one_nat) = X_18,
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_18] :
( is_int(X_18)
=> power_power_int(X_18,one_one_nat) = X_18 ),
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] : power_power_int(power_power_int(X_1,Y_1),Z) = power_power_int(X_1,times_times_nat(Y_1,Z)),
file('theBenchmark.p',fact_47_zpower__zpower) ).
fof(fact_48_le__number__of__eq__not__less,axiom,
! [V_3,W_1] :
( ord_less_eq_real(number267125858f_real(V_3),number267125858f_real(W_1))
<=> ~ ord_less_real(number267125858f_real(W_1),number267125858f_real(V_3)) ),
file('theBenchmark.p',fact_48_le__number__of__eq__not__less) ).
fof(fact_49_le__number__of__eq__not__less,axiom,
! [V_3,W_1] :
( ord_less_eq_nat(number_number_of_nat(V_3),number_number_of_nat(W_1))
<=> ~ ord_less_nat(number_number_of_nat(W_1),number_number_of_nat(V_3)) ),
file('theBenchmark.p',fact_49_le__number__of__eq__not__less) ).
fof(fact_50_le__number__of__eq__not__less,axiom,
! [V_3,W_1] :
( ord_less_eq_int(number_number_of_int(V_3),number_number_of_int(W_1))
<=> ~ ord_less_int(number_number_of_int(W_1),number_number_of_int(V_3)) ),
file('theBenchmark.p',fact_50_le__number__of__eq__not__less) ).
fof(fact_51_less__number__of,axiom,
! [X_2,Y_2] :
( ord_less_real(number267125858f_real(X_2),number267125858f_real(Y_2))
<=> 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] :
( ord_less_int(number_number_of_int(X_2),number_number_of_int(Y_2))
<=> 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] :
( ord_less_eq_real(number267125858f_real(X_2),number267125858f_real(Y_2))
<=> 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] :
( ord_less_eq_int(number_number_of_int(X_2),number_number_of_int(Y_2))
<=> ord_less_eq_int(X_2,Y_2) ),
file('theBenchmark.p',fact_54_le__number__of) ).
fof(fact_55_zadd__zless__mono,axiom,
! [Z_9,Z,W_13,W] :
( ord_less_int(W_13,W)
=> ( ord_less_eq_int(Z_9,Z)
=> ord_less_int(plus_plus_int(W_13,Z_9),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_17,P_2,Q_3] : times_times_nat(power_power_nat(X_17,P_2),power_power_nat(X_17,Q_3)) = power_power_nat(X_17,plus_plus_nat(P_2,Q_3)),
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_17,P_2,Q_3] : times_times_real(power_power_real(X_17,P_2),power_power_real(X_17,Q_3)) = power_power_real(X_17,plus_plus_nat(P_2,Q_3)),
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_17,P_2,Q_3] : times_times_int(power_power_int(X_17,P_2),power_power_int(X_17,Q_3)) = power_power_int(X_17,plus_plus_nat(P_2,Q_3)),
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] : power_power_int(X_1,plus_plus_nat(Y_1,Z)) = times_times_int(power_power_int(X_1,Y_1),power_power_int(X_1,Z)),
file('theBenchmark.p',fact_59_zpower__zadd__distrib) ).
fof(fact_60_nat__mult__2,axiom,
! [Z] : times_times_nat(number_number_of_nat(bit0(bit1(pls))),Z) = plus_plus_nat(Z,Z),
file('theBenchmark.p',fact_60_nat__mult__2) ).
fof(fact_61_nat__mult__2__right,axiom,
! [Z] : times_times_nat(Z,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(Z,Z),
file('theBenchmark.p',fact_61_nat__mult__2__right) ).
fof(fact_62_nat__1__add__1,axiom,
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] :
( ord_less_int(bit1(K1),bit1(K2))
<=> ord_less_int(K1,K2) ),
file('theBenchmark.p',fact_63_less__int__code_I16_J) ).
fof(fact_64_rel__simps_I17_J,axiom,
! [K_1,L_1] :
( ord_less_int(bit1(K_1),bit1(L_1))
<=> ord_less_int(K_1,L_1) ),
file('theBenchmark.p',fact_64_rel__simps_I17_J) ).
fof(fact_65_less__eq__int__code_I16_J,axiom,
! [K1,K2] :
( ord_less_eq_int(bit1(K1),bit1(K2))
<=> 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_1,L_1] :
( ord_less_eq_int(bit1(K_1),bit1(L_1))
<=> ord_less_eq_int(K_1,L_1) ),
file('theBenchmark.p',fact_66_rel__simps_I34_J) ).
fof(fact_67_rel__simps_I2_J,axiom,
~ 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] :
( ord_less_int(bit0(K1),bit0(K2))
<=> ord_less_int(K1,K2) ),
file('theBenchmark.p',fact_68_less__int__code_I13_J) ).
fof(fact_69_rel__simps_I14_J,axiom,
! [K_1,L_1] :
( ord_less_int(bit0(K_1),bit0(L_1))
<=> ord_less_int(K_1,L_1) ),
file('theBenchmark.p',fact_69_rel__simps_I14_J) ).
fof(fact_70_rel__simps_I19_J,axiom,
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] :
( ord_less_eq_int(bit0(K1),bit0(K2))
<=> 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_1,L_1] :
( ord_less_eq_int(bit0(K_1),bit0(L_1))
<=> ord_less_eq_int(K_1,L_1) ),
file('theBenchmark.p',fact_72_rel__simps_I31_J) ).
fof(fact_73_less__number__of__int__code,axiom,
! [K_1,L_1] :
( ord_less_int(number_number_of_int(K_1),number_number_of_int(L_1))
<=> ord_less_int(K_1,L_1) ),
file('theBenchmark.p',fact_73_less__number__of__int__code) ).
fof(fact_74_less__eq__number__of__int__code,axiom,
! [K_1,L_1] :
( ord_less_eq_int(number_number_of_int(K_1),number_number_of_int(L_1))
<=> ord_less_eq_int(K_1,L_1) ),
file('theBenchmark.p',fact_74_less__eq__number__of__int__code) ).
fof(fact_75_zadd__strict__right__mono,axiom,
! [K,I,J] :
( ord_less_int(I,J)
=> ord_less_int(plus_plus_int(I,K),plus_plus_int(J,K)) ),
file('theBenchmark.p',fact_75_zadd__strict__right__mono) ).
fof(fact_76_zadd__left__mono,axiom,
! [K,I,J] :
( ord_less_eq_int(I,J)
=> ord_less_eq_int(plus_plus_int(K,I),plus_plus_int(K,J)) ),
file('theBenchmark.p',fact_76_zadd__left__mono) ).
fof(fact_77_add__nat__number__of,axiom,
! [V_2,V_1] :
( ( ~ ord_less_int(V_1,pls)
=> ( ( ~ ord_less_int(V_2,pls)
=> plus_plus_nat(number_number_of_nat(V_1),number_number_of_nat(V_2)) = number_number_of_nat(plus_plus_int(V_1,V_2)) )
& ( ord_less_int(V_2,pls)
=> plus_plus_nat(number_number_of_nat(V_1),number_number_of_nat(V_2)) = number_number_of_nat(V_1) ) ) )
& ( ord_less_int(V_1,pls)
=> plus_plus_nat(number_number_of_nat(V_1),number_number_of_nat(V_2)) = number_number_of_nat(V_2) ) ),
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_1] :
( ord_less_eq_int(bit1(K_1),pls)
<=> ord_less_int(K_1,pls) ),
file('theBenchmark.p',fact_80_rel__simps_I29_J) ).
fof(fact_81_rel__simps_I5_J,axiom,
! [K_1] :
( ord_less_int(pls,bit1(K_1))
<=> ord_less_eq_int(pls,K_1) ),
file('theBenchmark.p',fact_81_rel__simps_I5_J) ).
fof(fact_82_less__eq__int__code_I15_J,axiom,
! [K1,K2] :
( ord_less_eq_int(bit1(K1),bit0(K2))
<=> 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_1,L_1] :
( ord_less_eq_int(bit1(K_1),bit0(L_1))
<=> ord_less_int(K_1,L_1) ),
file('theBenchmark.p',fact_83_rel__simps_I33_J) ).
fof(fact_84_less__int__code_I14_J,axiom,
! [K1,K2] :
( ord_less_int(bit0(K1),bit1(K2))
<=> 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_1,L_1] :
( ord_less_int(bit0(K_1),bit1(L_1))
<=> ord_less_eq_int(K_1,L_1) ),
file('theBenchmark.p',fact_85_rel__simps_I15_J) ).
fof(fact_86_zless__imp__add1__zle,axiom,
! [W,Z] :
( ord_less_int(W,Z)
=> ord_less_eq_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] :
( ord_less_eq_int(plus_plus_int(W_1,one_one_int),Z_1)
<=> 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] :
( ord_less_int(W_1,plus_plus_int(Z_1,one_one_int))
<=> ord_less_eq_int(W_1,Z_1) ),
file('theBenchmark.p',fact_88_zle__add1__eq__le) ).
fof(fact_89_zprime__2,axiom,
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] :
( twoSqu142715416sum2sq(X_1)
=> ( twoSqu142715416sum2sq(Y_1)
=> twoSqu142715416sum2sq(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] : times_times_real(times_times_real(Lx_6,Ly_4),times_times_real(Rx_6,Ry_4)) = times_times_real(times_times_real(Lx_6,Rx_6),times_times_real(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] : times_times_nat(times_times_nat(Lx_6,Ly_4),times_times_nat(Rx_6,Ry_4)) = times_times_nat(times_times_nat(Lx_6,Rx_6),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] : times_times_int(times_times_int(Lx_6,Ly_4),times_times_int(Rx_6,Ry_4)) = times_times_int(times_times_int(Lx_6,Rx_6),times_times_int(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] : times_times_real(times_times_real(Lx_5,Ly_3),times_times_real(Rx_5,Ry_3)) = times_times_real(Rx_5,times_times_real(times_times_real(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] : times_times_nat(times_times_nat(Lx_5,Ly_3),times_times_nat(Rx_5,Ry_3)) = times_times_nat(Rx_5,times_times_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] : times_times_int(times_times_int(Lx_5,Ly_3),times_times_int(Rx_5,Ry_3)) = times_times_int(Rx_5,times_times_int(times_times_int(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] : times_times_real(times_times_real(Lx_4,Ly_2),times_times_real(Rx_4,Ry_2)) = times_times_real(Lx_4,times_times_real(Ly_2,times_times_real(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] : times_times_nat(times_times_nat(Lx_4,Ly_2),times_times_nat(Rx_4,Ry_2)) = times_times_nat(Lx_4,times_times_nat(Ly_2,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] : times_times_int(times_times_int(Lx_4,Ly_2),times_times_int(Rx_4,Ry_2)) = times_times_int(Lx_4,times_times_int(Ly_2,times_times_int(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] : times_times_real(times_times_real(Lx_3,Ly_1),Rx_3) = times_times_real(times_times_real(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] : times_times_nat(times_times_nat(Lx_3,Ly_1),Rx_3) = times_times_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] : times_times_int(times_times_int(Lx_3,Ly_1),Rx_3) = times_times_int(times_times_int(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] : times_times_real(times_times_real(Lx_2,Ly),Rx_2) = times_times_real(Lx_2,times_times_real(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] : times_times_nat(times_times_nat(Lx_2,Ly),Rx_2) = times_times_nat(Lx_2,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] : times_times_int(times_times_int(Lx_2,Ly),Rx_2) = times_times_int(Lx_2,times_times_int(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] : times_times_real(Lx_1,times_times_real(Rx_1,Ry_1)) = times_times_real(times_times_real(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] : times_times_nat(Lx_1,times_times_nat(Rx_1,Ry_1)) = times_times_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] : times_times_int(Lx_1,times_times_int(Rx_1,Ry_1)) = times_times_int(times_times_int(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] : times_times_real(Lx,times_times_real(Rx,Ry)) = times_times_real(Rx,times_times_real(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] : times_times_nat(Lx,times_times_nat(Rx,Ry)) = times_times_nat(Rx,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] : times_times_int(Lx,times_times_int(Rx,Ry)) = times_times_int(Rx,times_times_int(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_56,B_17] : times_times_real(A_56,B_17) = times_times_real(B_17,A_56),
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_56,B_17] : times_times_nat(A_56,B_17) = times_times_nat(B_17,A_56),
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_56,B_17] : times_times_int(A_56,B_17) = times_times_int(B_17,A_56),
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_55,B_16,C_10,D_5] : plus_plus_real(plus_plus_real(A_55,B_16),plus_plus_real(C_10,D_5)) = plus_plus_real(plus_plus_real(A_55,C_10),plus_plus_real(B_16,D_5)),
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_55,B_16,C_10,D_5] : plus_plus_nat(plus_plus_nat(A_55,B_16),plus_plus_nat(C_10,D_5)) = plus_plus_nat(plus_plus_nat(A_55,C_10),plus_plus_nat(B_16,D_5)),
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_55,B_16,C_10,D_5] : plus_plus_int(plus_plus_int(A_55,B_16),plus_plus_int(C_10,D_5)) = plus_plus_int(plus_plus_int(A_55,C_10),plus_plus_int(B_16,D_5)),
file('theBenchmark.p',fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_118_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [A_54,B_15,C_9] : plus_plus_real(plus_plus_real(A_54,B_15),C_9) = plus_plus_real(plus_plus_real(A_54,C_9),B_15),
file('theBenchmark.p',fact_118_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_119_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [A_54,B_15,C_9] : plus_plus_nat(plus_plus_nat(A_54,B_15),C_9) = plus_plus_nat(plus_plus_nat(A_54,C_9),B_15),
file('theBenchmark.p',fact_119_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [A_54,B_15,C_9] : plus_plus_int(plus_plus_int(A_54,B_15),C_9) = plus_plus_int(plus_plus_int(A_54,C_9),B_15),
file('theBenchmark.p',fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [A_53,B_14,C_8] : plus_plus_real(plus_plus_real(A_53,B_14),C_8) = plus_plus_real(A_53,plus_plus_real(B_14,C_8)),
file('theBenchmark.p',fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [A_53,B_14,C_8] : plus_plus_nat(plus_plus_nat(A_53,B_14),C_8) = plus_plus_nat(A_53,plus_plus_nat(B_14,C_8)),
file('theBenchmark.p',fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [A_53,B_14,C_8] : plus_plus_int(plus_plus_int(A_53,B_14),C_8) = plus_plus_int(A_53,plus_plus_int(B_14,C_8)),
file('theBenchmark.p',fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [A_52,C_7,D_4] : plus_plus_real(A_52,plus_plus_real(C_7,D_4)) = plus_plus_real(plus_plus_real(A_52,C_7),D_4),
file('theBenchmark.p',fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [A_52,C_7,D_4] : plus_plus_nat(A_52,plus_plus_nat(C_7,D_4)) = plus_plus_nat(plus_plus_nat(A_52,C_7),D_4),
file('theBenchmark.p',fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [A_52,C_7,D_4] : plus_plus_int(A_52,plus_plus_int(C_7,D_4)) = plus_plus_int(plus_plus_int(A_52,C_7),D_4),
file('theBenchmark.p',fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [A_51,C_6,D_3] : plus_plus_real(A_51,plus_plus_real(C_6,D_3)) = plus_plus_real(C_6,plus_plus_real(A_51,D_3)),
file('theBenchmark.p',fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [A_51,C_6,D_3] : plus_plus_nat(A_51,plus_plus_nat(C_6,D_3)) = plus_plus_nat(C_6,plus_plus_nat(A_51,D_3)),
file('theBenchmark.p',fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [A_51,C_6,D_3] : plus_plus_int(A_51,plus_plus_int(C_6,D_3)) = plus_plus_int(C_6,plus_plus_int(A_51,D_3)),
file('theBenchmark.p',fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [A_50,C_5] : plus_plus_real(A_50,C_5) = plus_plus_real(C_5,A_50),
file('theBenchmark.p',fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [A_50,C_5] : plus_plus_nat(A_50,C_5) = plus_plus_nat(C_5,A_50),
file('theBenchmark.p',fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [A_50,C_5] : plus_plus_int(A_50,C_5) = plus_plus_int(C_5,A_50),
file('theBenchmark.p',fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_133_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_133_eq__number__of) ).
fof(fact_134_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_134_eq__number__of) ).
fof(fact_135_number__of__reorient,axiom,
! [W_1,X_2] :
( number267125858f_real(W_1) = X_2
<=> X_2 = number267125858f_real(W_1) ),
file('theBenchmark.p',fact_135_number__of__reorient) ).
fof(fact_136_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_136_number__of__reorient) ).
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_rel__simps_I51_J,axiom,
! [K_1,L_1] :
( ( is_int(L_1)
& is_int(K_1) )
=> ( bit1(K_1) = bit1(L_1)
<=> K_1 = L_1 ) ),
file('theBenchmark.p',fact_138_rel__simps_I51_J) ).
fof(fact_139_rel__simps_I48_J,axiom,
! [K_1,L_1] :
( ( is_int(L_1)
& is_int(K_1) )
=> ( bit0(K_1) = bit0(L_1)
<=> K_1 = L_1 ) ),
file('theBenchmark.p',fact_139_rel__simps_I48_J) ).
fof(fact_140_zmult__assoc,axiom,
! [Z1,Z2,Z3] : times_times_int(times_times_int(Z1,Z2),Z3) = times_times_int(Z1,times_times_int(Z2,Z3)),
file('theBenchmark.p',fact_140_zmult__assoc) ).
fof(fact_141_zmult__commute,axiom,
! [Z,W] : times_times_int(Z,W) = times_times_int(W,Z),
file('theBenchmark.p',fact_141_zmult__commute) ).
fof(fact_142_number__of__is__id,axiom,
! [K] :
( is_int(K)
=> number_number_of_int(K) = K ),
file('theBenchmark.p',fact_142_number__of__is__id) ).
fof(fact_143_zadd__assoc,axiom,
! [Z1,Z2,Z3] : plus_plus_int(plus_plus_int(Z1,Z2),Z3) = plus_plus_int(Z1,plus_plus_int(Z2,Z3)),
file('theBenchmark.p',fact_143_zadd__assoc) ).
fof(fact_144_zadd__left__commute,axiom,
! [X_1,Y_1,Z] : plus_plus_int(X_1,plus_plus_int(Y_1,Z)) = plus_plus_int(Y_1,plus_plus_int(X_1,Z)),
file('theBenchmark.p',fact_144_zadd__left__commute) ).
fof(fact_145_zadd__commute,axiom,
! [Z,W] : plus_plus_int(Z,W) = plus_plus_int(W,Z),
file('theBenchmark.p',fact_145_zadd__commute) ).
fof(fact_146_rel__simps_I12_J,axiom,
! [K_1] :
( ord_less_int(bit1(K_1),pls)
<=> ord_less_int(K_1,pls) ),
file('theBenchmark.p',fact_146_rel__simps_I12_J) ).
fof(fact_147_less__int__code_I15_J,axiom,
! [K1,K2] :
( ord_less_int(bit1(K1),bit0(K2))
<=> ord_less_int(K1,K2) ),
file('theBenchmark.p',fact_147_less__int__code_I15_J) ).
fof(fact_148_rel__simps_I16_J,axiom,
! [K_1,L_1] :
( ord_less_int(bit1(K_1),bit0(L_1))
<=> ord_less_int(K_1,L_1) ),
file('theBenchmark.p',fact_148_rel__simps_I16_J) ).
fof(fact_149_rel__simps_I10_J,axiom,
! [K_1] :
( ord_less_int(bit0(K_1),pls)
<=> ord_less_int(K_1,pls) ),
file('theBenchmark.p',fact_149_rel__simps_I10_J) ).
fof(fact_150_rel__simps_I4_J,axiom,
! [K_1] :
( ord_less_int(pls,bit0(K_1))
<=> ord_less_int(pls,K_1) ),
file('theBenchmark.p',fact_150_rel__simps_I4_J) ).
fof(fact_151_rel__simps_I22_J,axiom,
! [K_1] :
( ord_less_eq_int(pls,bit1(K_1))
<=> ord_less_eq_int(pls,K_1) ),
file('theBenchmark.p',fact_151_rel__simps_I22_J) ).
fof(fact_152_less__eq__int__code_I14_J,axiom,
! [K1,K2] :
( ord_less_eq_int(bit0(K1),bit1(K2))
<=> ord_less_eq_int(K1,K2) ),
file('theBenchmark.p',fact_152_less__eq__int__code_I14_J) ).
fof(fact_153_rel__simps_I32_J,axiom,
! [K_1,L_1] :
( ord_less_eq_int(bit0(K_1),bit1(L_1))
<=> ord_less_eq_int(K_1,L_1) ),
file('theBenchmark.p',fact_153_rel__simps_I32_J) ).
fof(fact_154_rel__simps_I27_J,axiom,
! [K_1] :
( ord_less_eq_int(bit0(K_1),pls)
<=> ord_less_eq_int(K_1,pls) ),
file('theBenchmark.p',fact_154_rel__simps_I27_J) ).
fof(fact_155_rel__simps_I21_J,axiom,
! [K_1] :
( ord_less_eq_int(pls,bit0(K_1))
<=> ord_less_eq_int(pls,K_1) ),
file('theBenchmark.p',fact_155_rel__simps_I21_J) ).
fof(fact_156_zless__add1__eq,axiom,
! [W_1,Z_1] :
( ( is_int(Z_1)
& is_int(W_1) )
=> ( ord_less_int(W_1,plus_plus_int(Z_1,one_one_int))
<=> ( W_1 = Z_1
| ord_less_int(W_1,Z_1) ) ) ),
file('theBenchmark.p',fact_156_zless__add1__eq) ).
fof(fact_157_power__even__eq,axiom,
! [A_49,N_37] : power_power_nat(A_49,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_37)) = power_power_nat(power_power_nat(A_49,N_37),number_number_of_nat(bit0(bit1(pls)))),
file('theBenchmark.p',fact_157_power__even__eq) ).
fof(fact_158_power__even__eq,axiom,
! [A_49,N_37] : power_power_real(A_49,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_37)) = power_power_real(power_power_real(A_49,N_37),number_number_of_nat(bit0(bit1(pls)))),
file('theBenchmark.p',fact_158_power__even__eq) ).
fof(fact_159_power__even__eq,axiom,
! [A_49,N_37] : power_power_int(A_49,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_37)) = power_power_int(power_power_int(A_49,N_37),number_number_of_nat(bit0(bit1(pls)))),
file('theBenchmark.p',fact_159_power__even__eq) ).
fof(fact_160_less__special_I4_J,axiom,
! [X_2] :
( ord_less_real(number267125858f_real(X_2),one_one_real)
<=> ord_less_int(X_2,bit1(pls)) ),
file('theBenchmark.p',fact_160_less__special_I4_J) ).
fof(fact_161_less__special_I4_J,axiom,
! [X_2] :
( ord_less_int(number_number_of_int(X_2),one_one_int)
<=> ord_less_int(X_2,bit1(pls)) ),
file('theBenchmark.p',fact_161_less__special_I4_J) ).
fof(fact_162_less__special_I2_J,axiom,
! [Y_2] :
( ord_less_real(one_one_real,number267125858f_real(Y_2))
<=> ord_less_int(bit1(pls),Y_2) ),
file('theBenchmark.p',fact_162_less__special_I2_J) ).
fof(fact_163_less__special_I2_J,axiom,
! [Y_2] :
( ord_less_int(one_one_int,number_number_of_int(Y_2))
<=> ord_less_int(bit1(pls),Y_2) ),
file('theBenchmark.p',fact_163_less__special_I2_J) ).
fof(fact_164_le__special_I4_J,axiom,
! [X_2] :
( ord_less_eq_real(number267125858f_real(X_2),one_one_real)
<=> ord_less_eq_int(X_2,bit1(pls)) ),
file('theBenchmark.p',fact_164_le__special_I4_J) ).
fof(fact_165_le__special_I4_J,axiom,
! [X_2] :
( ord_less_eq_int(number_number_of_int(X_2),one_one_int)
<=> ord_less_eq_int(X_2,bit1(pls)) ),
file('theBenchmark.p',fact_165_le__special_I4_J) ).
fof(fact_166_le__special_I2_J,axiom,
! [Y_2] :
( ord_less_eq_real(one_one_real,number267125858f_real(Y_2))
<=> ord_less_eq_int(bit1(pls),Y_2) ),
file('theBenchmark.p',fact_166_le__special_I2_J) ).
fof(fact_167_le__special_I2_J,axiom,
! [Y_2] :
( ord_less_eq_int(one_one_int,number_number_of_int(Y_2))
<=> ord_less_eq_int(bit1(pls),Y_2) ),
file('theBenchmark.p',fact_167_le__special_I2_J) ).
fof(fact_168_crossproduct__eq,axiom,
! [W_1,Y_2,X_2,Z_1] :
( plus_plus_real(times_times_real(W_1,Y_2),times_times_real(X_2,Z_1)) = plus_plus_real(times_times_real(W_1,Z_1),times_times_real(X_2,Y_2))
<=> ( Y_2 = Z_1
| W_1 = X_2 ) ),
file('theBenchmark.p',fact_168_crossproduct__eq) ).
fof(fact_169_crossproduct__eq,axiom,
! [W_1,Y_2,X_2,Z_1] :
( plus_plus_nat(times_times_nat(W_1,Y_2),times_times_nat(X_2,Z_1)) = plus_plus_nat(times_times_nat(W_1,Z_1),times_times_nat(X_2,Y_2))
<=> ( Y_2 = Z_1
| W_1 = X_2 ) ),
file('theBenchmark.p',fact_169_crossproduct__eq) ).
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) )
=> ( plus_plus_int(times_times_int(W_1,Y_2),times_times_int(X_2,Z_1)) = plus_plus_int(times_times_int(W_1,Z_1),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_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [A_48,M_12,B_13] : plus_plus_real(times_times_real(A_48,M_12),times_times_real(B_13,M_12)) = times_times_real(plus_plus_real(A_48,B_13),M_12),
file('theBenchmark.p',fact_171_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_172_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [A_48,M_12,B_13] : plus_plus_nat(times_times_nat(A_48,M_12),times_times_nat(B_13,M_12)) = times_times_nat(plus_plus_nat(A_48,B_13),M_12),
file('theBenchmark.p',fact_172_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [A_48,M_12,B_13] : plus_plus_int(times_times_int(A_48,M_12),times_times_int(B_13,M_12)) = times_times_int(plus_plus_int(A_48,B_13),M_12),
file('theBenchmark.p',fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [A_47,B_12,C_4] : times_times_real(plus_plus_real(A_47,B_12),C_4) = plus_plus_real(times_times_real(A_47,C_4),times_times_real(B_12,C_4)),
file('theBenchmark.p',fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [A_47,B_12,C_4] : times_times_nat(plus_plus_nat(A_47,B_12),C_4) = plus_plus_nat(times_times_nat(A_47,C_4),times_times_nat(B_12,C_4)),
file('theBenchmark.p',fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [A_47,B_12,C_4] : times_times_int(plus_plus_int(A_47,B_12),C_4) = plus_plus_int(times_times_int(A_47,C_4),times_times_int(B_12,C_4)),
file('theBenchmark.p',fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_177_crossproduct__noteq,axiom,
! [C,D,A_1,B_2] :
( ( C != D
& A_1 != B_2 )
<=> plus_plus_real(times_times_real(A_1,C),times_times_real(B_2,D)) != plus_plus_real(times_times_real(A_1,D),times_times_real(B_2,C)) ),
file('theBenchmark.p',fact_177_crossproduct__noteq) ).
fof(fact_178_crossproduct__noteq,axiom,
! [C,D,A_1,B_2] :
( ( C != D
& A_1 != B_2 )
<=> plus_plus_nat(times_times_nat(A_1,C),times_times_nat(B_2,D)) != plus_plus_nat(times_times_nat(A_1,D),times_times_nat(B_2,C)) ),
file('theBenchmark.p',fact_178_crossproduct__noteq) ).
fof(fact_179_crossproduct__noteq,axiom,
! [C,D,A_1,B_2] :
( ( is_int(B_2)
& is_int(A_1)
& is_int(D)
& is_int(C) )
=> ( ( C != D
& A_1 != B_2 )
<=> plus_plus_int(times_times_int(A_1,C),times_times_int(B_2,D)) != plus_plus_int(times_times_int(A_1,D),times_times_int(B_2,C)) ) ),
file('theBenchmark.p',fact_179_crossproduct__noteq) ).
fof(fact_180_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [X_16,Y_14,Z_8] : times_times_real(X_16,plus_plus_real(Y_14,Z_8)) = plus_plus_real(times_times_real(X_16,Y_14),times_times_real(X_16,Z_8)),
file('theBenchmark.p',fact_180_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_181_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [X_16,Y_14,Z_8] : times_times_nat(X_16,plus_plus_nat(Y_14,Z_8)) = plus_plus_nat(times_times_nat(X_16,Y_14),times_times_nat(X_16,Z_8)),
file('theBenchmark.p',fact_181_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [X_16,Y_14,Z_8] : times_times_int(X_16,plus_plus_int(Y_14,Z_8)) = plus_plus_int(times_times_int(X_16,Y_14),times_times_int(X_16,Z_8)),
file('theBenchmark.p',fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [A_46] : times_times_real(A_46,one_one_real) = A_46,
file('theBenchmark.p',fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [A_46] : times_times_nat(A_46,one_one_nat) = A_46,
file('theBenchmark.p',fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [A_46] :
( is_int(A_46)
=> times_times_int(A_46,one_one_int) = A_46 ),
file('theBenchmark.p',fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [A_45] : times_times_real(one_one_real,A_45) = A_45,
file('theBenchmark.p',fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [A_45] : times_times_nat(one_one_nat,A_45) = A_45,
file('theBenchmark.p',fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [A_45] :
( is_int(A_45)
=> times_times_int(one_one_int,A_45) = A_45 ),
file('theBenchmark.p',fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [X_15,Y_13,Q_2] : power_power_nat(times_times_nat(X_15,Y_13),Q_2) = times_times_nat(power_power_nat(X_15,Q_2),power_power_nat(Y_13,Q_2)),
file('theBenchmark.p',fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [X_15,Y_13,Q_2] : power_power_real(times_times_real(X_15,Y_13),Q_2) = times_times_real(power_power_real(X_15,Q_2),power_power_real(Y_13,Q_2)),
file('theBenchmark.p',fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [X_15,Y_13,Q_2] : power_power_int(times_times_int(X_15,Y_13),Q_2) = times_times_int(power_power_int(X_15,Q_2),power_power_int(Y_13,Q_2)),
file('theBenchmark.p',fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_192_rel__simps_I46_J,axiom,
! [K] : bit1(K) != pls,
file('theBenchmark.p',fact_192_rel__simps_I46_J) ).
fof(fact_193_rel__simps_I39_J,axiom,
! [L] : pls != bit1(L),
file('theBenchmark.p',fact_193_rel__simps_I39_J) ).
fof(fact_194_rel__simps_I50_J,axiom,
! [K,L] : bit1(K) != bit0(L),
file('theBenchmark.p',fact_194_rel__simps_I50_J) ).
fof(fact_195_rel__simps_I49_J,axiom,
! [K,L] : bit0(K) != bit1(L),
file('theBenchmark.p',fact_195_rel__simps_I49_J) ).
fof(fact_196_rel__simps_I44_J,axiom,
! [K_1] :
( is_int(K_1)
=> ( bit0(K_1) = pls
<=> K_1 = pls ) ),
file('theBenchmark.p',fact_196_rel__simps_I44_J) ).
fof(fact_197_rel__simps_I38_J,axiom,
! [L_1] :
( is_int(L_1)
=> ( pls = bit0(L_1)
<=> pls = L_1 ) ),
file('theBenchmark.p',fact_197_rel__simps_I38_J) ).
fof(fact_198_Bit0__Pls,axiom,
bit0(pls) = pls,
file('theBenchmark.p',fact_198_Bit0__Pls) ).
fof(fact_199_mult__Pls,axiom,
! [W] : times_times_int(pls,W) = pls,
file('theBenchmark.p',fact_199_mult__Pls) ).
fof(fact_200_mult__Bit0,axiom,
! [K,L] : times_times_int(bit0(K),L) = bit0(times_times_int(K,L)),
file('theBenchmark.p',fact_200_mult__Bit0) ).
fof(fact_201_add__Pls__right,axiom,
! [K] :
( is_int(K)
=> plus_plus_int(K,pls) = K ),
file('theBenchmark.p',fact_201_add__Pls__right) ).
fof(fact_202_add__Pls,axiom,
! [K] :
( is_int(K)
=> plus_plus_int(pls,K) = K ),
file('theBenchmark.p',fact_202_add__Pls) ).
fof(fact_203_add__Bit0__Bit0,axiom,
! [K,L] : plus_plus_int(bit0(K),bit0(L)) = bit0(plus_plus_int(K,L)),
file('theBenchmark.p',fact_203_add__Bit0__Bit0) ).
fof(fact_204_Bit0__def,axiom,
! [K] : bit0(K) = plus_plus_int(K,K),
file('theBenchmark.p',fact_204_Bit0__def) ).
fof(fact_205_zmult__1__right,axiom,
! [Z] :
( is_int(Z)
=> times_times_int(Z,one_one_int) = Z ),
file('theBenchmark.p',fact_205_zmult__1__right) ).
fof(fact_206_zmult__1,axiom,
! [Z] :
( is_int(Z)
=> times_times_int(one_one_int,Z) = Z ),
file('theBenchmark.p',fact_206_zmult__1) ).
fof(fact_207_times__numeral__code_I5_J,axiom,
! [V_1,W] : times_times_int(number_number_of_int(V_1),number_number_of_int(W)) = number_number_of_int(times_times_int(V_1,W)),
file('theBenchmark.p',fact_207_times__numeral__code_I5_J) ).
fof(fact_208_zadd__zmult__distrib,axiom,
! [Z1,Z2,W] : times_times_int(plus_plus_int(Z1,Z2),W) = plus_plus_int(times_times_int(Z1,W),times_times_int(Z2,W)),
file('theBenchmark.p',fact_208_zadd__zmult__distrib) ).
fof(fact_209_zadd__zmult__distrib2,axiom,
! [W,Z1,Z2] : times_times_int(W,plus_plus_int(Z1,Z2)) = plus_plus_int(times_times_int(W,Z1),times_times_int(W,Z2)),
file('theBenchmark.p',fact_209_zadd__zmult__distrib2) ).
fof(fact_210_plus__numeral__code_I9_J,axiom,
! [V_1,W] : plus_plus_int(number_number_of_int(V_1),number_number_of_int(W)) = number_number_of_int(plus_plus_int(V_1,W)),
file('theBenchmark.p',fact_210_plus__numeral__code_I9_J) ).
fof(fact_211_semiring__mult__number__of,axiom,
! [V_16,V_15] :
( ord_less_eq_int(pls,V_15)
=> ( ord_less_eq_int(pls,V_16)
=> times_times_real(number267125858f_real(V_15),number267125858f_real(V_16)) = number267125858f_real(times_times_int(V_15,V_16)) ) ),
file('theBenchmark.p',fact_211_semiring__mult__number__of) ).
fof(fact_212_semiring__mult__number__of,axiom,
! [V_16,V_15] :
( ord_less_eq_int(pls,V_15)
=> ( ord_less_eq_int(pls,V_16)
=> times_times_nat(number_number_of_nat(V_15),number_number_of_nat(V_16)) = number_number_of_nat(times_times_int(V_15,V_16)) ) ),
file('theBenchmark.p',fact_212_semiring__mult__number__of) ).
fof(fact_213_semiring__mult__number__of,axiom,
! [V_16,V_15] :
( ord_less_eq_int(pls,V_15)
=> ( ord_less_eq_int(pls,V_16)
=> times_times_int(number_number_of_int(V_15),number_number_of_int(V_16)) = number_number_of_int(times_times_int(V_15,V_16)) ) ),
file('theBenchmark.p',fact_213_semiring__mult__number__of) ).
fof(fact_214_semiring__add__number__of,axiom,
! [V_14,V_13] :
( ord_less_eq_int(pls,V_13)
=> ( ord_less_eq_int(pls,V_14)
=> plus_plus_real(number267125858f_real(V_13),number267125858f_real(V_14)) = number267125858f_real(plus_plus_int(V_13,V_14)) ) ),
file('theBenchmark.p',fact_214_semiring__add__number__of) ).
fof(fact_215_semiring__add__number__of,axiom,
! [V_14,V_13] :
( ord_less_eq_int(pls,V_13)
=> ( ord_less_eq_int(pls,V_14)
=> plus_plus_nat(number_number_of_nat(V_13),number_number_of_nat(V_14)) = number_number_of_nat(plus_plus_int(V_13,V_14)) ) ),
file('theBenchmark.p',fact_215_semiring__add__number__of) ).
fof(fact_216_semiring__add__number__of,axiom,
! [V_14,V_13] :
( ord_less_eq_int(pls,V_13)
=> ( ord_less_eq_int(pls,V_14)
=> plus_plus_int(number_number_of_int(V_13),number_number_of_int(V_14)) = number_number_of_int(plus_plus_int(V_13,V_14)) ) ),
file('theBenchmark.p',fact_216_semiring__add__number__of) ).
fof(fact_217_power2__ge__self,axiom,
! [X_1] : ord_less_eq_int(X_1,power_power_int(X_1,number_number_of_nat(bit0(bit1(pls))))),
file('theBenchmark.p',fact_217_power2__ge__self) ).
fof(fact_218_left__distrib__number__of,axiom,
! [A_44,B_11,V_12] : times_times_real(plus_plus_real(A_44,B_11),number267125858f_real(V_12)) = plus_plus_real(times_times_real(A_44,number267125858f_real(V_12)),times_times_real(B_11,number267125858f_real(V_12))),
file('theBenchmark.p',fact_218_left__distrib__number__of) ).
fof(fact_219_left__distrib__number__of,axiom,
! [A_44,B_11,V_12] : times_times_nat(plus_plus_nat(A_44,B_11),number_number_of_nat(V_12)) = plus_plus_nat(times_times_nat(A_44,number_number_of_nat(V_12)),times_times_nat(B_11,number_number_of_nat(V_12))),
file('theBenchmark.p',fact_219_left__distrib__number__of) ).
fof(fact_220_left__distrib__number__of,axiom,
! [A_44,B_11,V_12] : times_times_int(plus_plus_int(A_44,B_11),number_number_of_int(V_12)) = plus_plus_int(times_times_int(A_44,number_number_of_int(V_12)),times_times_int(B_11,number_number_of_int(V_12))),
file('theBenchmark.p',fact_220_left__distrib__number__of) ).
fof(fact_221_right__distrib__number__of,axiom,
! [V_11,B_10,C_3] : times_times_real(number267125858f_real(V_11),plus_plus_real(B_10,C_3)) = plus_plus_real(times_times_real(number267125858f_real(V_11),B_10),times_times_real(number267125858f_real(V_11),C_3)),
file('theBenchmark.p',fact_221_right__distrib__number__of) ).
fof(fact_222_right__distrib__number__of,axiom,
! [V_11,B_10,C_3] : times_times_nat(number_number_of_nat(V_11),plus_plus_nat(B_10,C_3)) = plus_plus_nat(times_times_nat(number_number_of_nat(V_11),B_10),times_times_nat(number_number_of_nat(V_11),C_3)),
file('theBenchmark.p',fact_222_right__distrib__number__of) ).
fof(fact_223_right__distrib__number__of,axiom,
! [V_11,B_10,C_3] : times_times_int(number_number_of_int(V_11),plus_plus_int(B_10,C_3)) = plus_plus_int(times_times_int(number_number_of_int(V_11),B_10),times_times_int(number_number_of_int(V_11),C_3)),
file('theBenchmark.p',fact_223_right__distrib__number__of) ).
fof(fact_224_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [A_43,M_11] : plus_plus_real(times_times_real(A_43,M_11),M_11) = times_times_real(plus_plus_real(A_43,one_one_real),M_11),
file('theBenchmark.p',fact_224_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [A_43,M_11] : plus_plus_nat(times_times_nat(A_43,M_11),M_11) = times_times_nat(plus_plus_nat(A_43,one_one_nat),M_11),
file('theBenchmark.p',fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [A_43,M_11] : plus_plus_int(times_times_int(A_43,M_11),M_11) = times_times_int(plus_plus_int(A_43,one_one_int),M_11),
file('theBenchmark.p',fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [M_10,A_42] : plus_plus_real(M_10,times_times_real(A_42,M_10)) = times_times_real(plus_plus_real(A_42,one_one_real),M_10),
file('theBenchmark.p',fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [M_10,A_42] : plus_plus_nat(M_10,times_times_nat(A_42,M_10)) = times_times_nat(plus_plus_nat(A_42,one_one_nat),M_10),
file('theBenchmark.p',fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [M_10,A_42] : plus_plus_int(M_10,times_times_int(A_42,M_10)) = times_times_int(plus_plus_int(A_42,one_one_int),M_10),
file('theBenchmark.p',fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [M_9] : plus_plus_real(M_9,M_9) = times_times_real(plus_plus_real(one_one_real,one_one_real),M_9),
file('theBenchmark.p',fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [M_9] : plus_plus_nat(M_9,M_9) = times_times_nat(plus_plus_nat(one_one_nat,one_one_nat),M_9),
file('theBenchmark.p',fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [M_9] : plus_plus_int(M_9,M_9) = times_times_int(plus_plus_int(one_one_int,one_one_int),M_9),
file('theBenchmark.p',fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_233_add__numeral__0,axiom,
! [A_41] : plus_plus_real(number267125858f_real(pls),A_41) = A_41,
file('theBenchmark.p',fact_233_add__numeral__0) ).
fof(fact_234_add__numeral__0,axiom,
! [A_41] :
( is_int(A_41)
=> plus_plus_int(number_number_of_int(pls),A_41) = A_41 ),
file('theBenchmark.p',fact_234_add__numeral__0) ).
fof(fact_235_add__numeral__0__right,axiom,
! [A_40] : plus_plus_real(A_40,number267125858f_real(pls)) = A_40,
file('theBenchmark.p',fact_235_add__numeral__0__right) ).
fof(fact_236_add__numeral__0__right,axiom,
! [A_40] :
( is_int(A_40)
=> plus_plus_int(A_40,number_number_of_int(pls)) = A_40 ),
file('theBenchmark.p',fact_236_add__numeral__0__right) ).
fof(fact_237_mult__number__of__left,axiom,
! [V_10,W_12,Z_7] : times_times_real(number267125858f_real(V_10),times_times_real(number267125858f_real(W_12),Z_7)) = times_times_real(number267125858f_real(times_times_int(V_10,W_12)),Z_7),
file('theBenchmark.p',fact_237_mult__number__of__left) ).
fof(fact_238_mult__number__of__left,axiom,
! [V_10,W_12,Z_7] : times_times_int(number_number_of_int(V_10),times_times_int(number_number_of_int(W_12),Z_7)) = times_times_int(number_number_of_int(times_times_int(V_10,W_12)),Z_7),
file('theBenchmark.p',fact_238_mult__number__of__left) ).
fof(fact_239_arith__simps_I32_J,axiom,
! [V_9,W_11] : times_times_real(number267125858f_real(V_9),number267125858f_real(W_11)) = number267125858f_real(times_times_int(V_9,W_11)),
file('theBenchmark.p',fact_239_arith__simps_I32_J) ).
fof(fact_240_arith__simps_I32_J,axiom,
! [V_9,W_11] : times_times_int(number_number_of_int(V_9),number_number_of_int(W_11)) = number_number_of_int(times_times_int(V_9,W_11)),
file('theBenchmark.p',fact_240_arith__simps_I32_J) ).
fof(fact_241_number__of__mult,axiom,
! [V_8,W_10] : number267125858f_real(times_times_int(V_8,W_10)) = times_times_real(number267125858f_real(V_8),number267125858f_real(W_10)),
file('theBenchmark.p',fact_241_number__of__mult) ).
fof(fact_242_number__of__mult,axiom,
! [V_8,W_10] : number_number_of_int(times_times_int(V_8,W_10)) = times_times_int(number_number_of_int(V_8),number_number_of_int(W_10)),
file('theBenchmark.p',fact_242_number__of__mult) ).
fof(fact_243_add__number__of__left,axiom,
! [V_7,W_9,Z_6] : plus_plus_real(number267125858f_real(V_7),plus_plus_real(number267125858f_real(W_9),Z_6)) = plus_plus_real(number267125858f_real(plus_plus_int(V_7,W_9)),Z_6),
file('theBenchmark.p',fact_243_add__number__of__left) ).
fof(fact_244_add__number__of__left,axiom,
! [V_7,W_9,Z_6] : plus_plus_int(number_number_of_int(V_7),plus_plus_int(number_number_of_int(W_9),Z_6)) = plus_plus_int(number_number_of_int(plus_plus_int(V_7,W_9)),Z_6),
file('theBenchmark.p',fact_244_add__number__of__left) ).
fof(fact_245_add__number__of__eq,axiom,
! [V_6,W_8] : plus_plus_real(number267125858f_real(V_6),number267125858f_real(W_8)) = number267125858f_real(plus_plus_int(V_6,W_8)),
file('theBenchmark.p',fact_245_add__number__of__eq) ).
fof(fact_246_add__number__of__eq,axiom,
! [V_6,W_8] : plus_plus_int(number_number_of_int(V_6),number_number_of_int(W_8)) = number_number_of_int(plus_plus_int(V_6,W_8)),
file('theBenchmark.p',fact_246_add__number__of__eq) ).
fof(fact_247_number__of__add,axiom,
! [V_5,W_7] : number267125858f_real(plus_plus_int(V_5,W_7)) = plus_plus_real(number267125858f_real(V_5),number267125858f_real(W_7)),
file('theBenchmark.p',fact_247_number__of__add) ).
fof(fact_248_number__of__add,axiom,
! [V_5,W_7] : number_number_of_int(plus_plus_int(V_5,W_7)) = plus_plus_int(number_number_of_int(V_5),number_number_of_int(W_7)),
file('theBenchmark.p',fact_248_number__of__add) ).
fof(fact_249_add__Bit1__Bit0,axiom,
! [K,L] : plus_plus_int(bit1(K),bit0(L)) = bit1(plus_plus_int(K,L)),
file('theBenchmark.p',fact_249_add__Bit1__Bit0) ).
fof(fact_250_add__Bit0__Bit1,axiom,
! [K,L] : plus_plus_int(bit0(K),bit1(L)) = bit1(plus_plus_int(K,L)),
file('theBenchmark.p',fact_250_add__Bit0__Bit1) ).
fof(fact_251_Bit1__def,axiom,
! [K] : bit1(K) = plus_plus_int(plus_plus_int(one_one_int,K),K),
file('theBenchmark.p',fact_251_Bit1__def) ).
fof(fact_252_number__of__Bit1,axiom,
! [W_6] : number267125858f_real(bit1(W_6)) = plus_plus_real(plus_plus_real(one_one_real,number267125858f_real(W_6)),number267125858f_real(W_6)),
file('theBenchmark.p',fact_252_number__of__Bit1) ).
fof(fact_253_number__of__Bit1,axiom,
! [W_6] : number_number_of_int(bit1(W_6)) = plus_plus_int(plus_plus_int(one_one_int,number_number_of_int(W_6)),number_number_of_int(W_6)),
file('theBenchmark.p',fact_253_number__of__Bit1) ).
fof(fact_254_mult__numeral__1,axiom,
! [A_39] : times_times_real(number267125858f_real(bit1(pls)),A_39) = A_39,
file('theBenchmark.p',fact_254_mult__numeral__1) ).
fof(fact_255_mult__numeral__1,axiom,
! [A_39] :
( is_int(A_39)
=> times_times_int(number_number_of_int(bit1(pls)),A_39) = A_39 ),
file('theBenchmark.p',fact_255_mult__numeral__1) ).
fof(fact_256_mult__numeral__1__right,axiom,
! [A_38] : times_times_real(A_38,number267125858f_real(bit1(pls))) = A_38,
file('theBenchmark.p',fact_256_mult__numeral__1__right) ).
fof(fact_257_mult__numeral__1__right,axiom,
! [A_38] :
( is_int(A_38)
=> times_times_int(A_38,number_number_of_int(bit1(pls))) = A_38 ),
file('theBenchmark.p',fact_257_mult__numeral__1__right) ).
fof(fact_258_semiring__numeral__1__eq__1,axiom,
number267125858f_real(bit1(pls)) = one_one_real,
file('theBenchmark.p',fact_258_semiring__numeral__1__eq__1) ).
fof(fact_259_semiring__numeral__1__eq__1,axiom,
number_number_of_nat(bit1(pls)) = one_one_nat,
file('theBenchmark.p',fact_259_semiring__numeral__1__eq__1) ).
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_numeral__1__eq__1,axiom,
number267125858f_real(bit1(pls)) = one_one_real,
file('theBenchmark.p',fact_261_numeral__1__eq__1) ).
fof(fact_262_numeral__1__eq__1,axiom,
number_number_of_int(bit1(pls)) = one_one_int,
file('theBenchmark.p',fact_262_numeral__1__eq__1) ).
fof(fact_263_semiring__norm_I110_J,axiom,
one_one_real = number267125858f_real(bit1(pls)),
file('theBenchmark.p',fact_263_semiring__norm_I110_J) ).
fof(fact_264_semiring__norm_I110_J,axiom,
one_one_int = number_number_of_int(bit1(pls)),
file('theBenchmark.p',fact_264_semiring__norm_I110_J) ).
fof(fact_265_one__is__num__one,axiom,
one_one_int = number_number_of_int(bit1(pls)),
file('theBenchmark.p',fact_265_one__is__num__one) ).
fof(fact_266_mult__Bit1,axiom,
! [K,L] : times_times_int(bit1(K),L) = plus_plus_int(bit0(times_times_int(K,L)),L),
file('theBenchmark.p',fact_266_mult__Bit1) ).
fof(fact_267_double__number__of__Bit0,axiom,
! [W_5] : times_times_real(plus_plus_real(one_one_real,one_one_real),number267125858f_real(W_5)) = number267125858f_real(bit0(W_5)),
file('theBenchmark.p',fact_267_double__number__of__Bit0) ).
fof(fact_268_double__number__of__Bit0,axiom,
! [W_5] : times_times_int(plus_plus_int(one_one_int,one_one_int),number_number_of_int(W_5)) = number_number_of_int(bit0(W_5)),
file('theBenchmark.p',fact_268_double__number__of__Bit0) ).
fof(fact_269_power3__eq__cube,axiom,
! [A_37] : power_power_nat(A_37,number_number_of_nat(bit1(bit1(pls)))) = times_times_nat(times_times_nat(A_37,A_37),A_37),
file('theBenchmark.p',fact_269_power3__eq__cube) ).
fof(fact_270_power3__eq__cube,axiom,
! [A_37] : power_power_real(A_37,number_number_of_nat(bit1(bit1(pls)))) = times_times_real(times_times_real(A_37,A_37),A_37),
file('theBenchmark.p',fact_270_power3__eq__cube) ).
fof(fact_271_power3__eq__cube,axiom,
! [A_37] : power_power_int(A_37,number_number_of_nat(bit1(bit1(pls)))) = times_times_int(times_times_int(A_37,A_37),A_37),
file('theBenchmark.p',fact_271_power3__eq__cube) ).
fof(fact_272_quartic__square__square,axiom,
! [X_1] : power_power_int(power_power_int(X_1,number_number_of_nat(bit0(bit1(pls)))),number_number_of_nat(bit0(bit1(pls)))) = power_power_int(X_1,number_number_of_nat(bit0(bit0(bit1(pls))))),
file('theBenchmark.p',fact_272_quartic__square__square) ).
fof(fact_273_semiring__mult__2,axiom,
! [Z_5] : times_times_real(number267125858f_real(bit0(bit1(pls))),Z_5) = plus_plus_real(Z_5,Z_5),
file('theBenchmark.p',fact_273_semiring__mult__2) ).
fof(fact_274_semiring__mult__2,axiom,
! [Z_5] : times_times_nat(number_number_of_nat(bit0(bit1(pls))),Z_5) = plus_plus_nat(Z_5,Z_5),
file('theBenchmark.p',fact_274_semiring__mult__2) ).
fof(fact_275_semiring__mult__2,axiom,
! [Z_5] : times_times_int(number_number_of_int(bit0(bit1(pls))),Z_5) = plus_plus_int(Z_5,Z_5),
file('theBenchmark.p',fact_275_semiring__mult__2) ).
fof(fact_276_mult__2,axiom,
! [Z_4] : times_times_real(number267125858f_real(bit0(bit1(pls))),Z_4) = plus_plus_real(Z_4,Z_4),
file('theBenchmark.p',fact_276_mult__2) ).
fof(fact_277_mult__2,axiom,
! [Z_4] : times_times_int(number_number_of_int(bit0(bit1(pls))),Z_4) = plus_plus_int(Z_4,Z_4),
file('theBenchmark.p',fact_277_mult__2) ).
fof(fact_278_semiring__mult__2__right,axiom,
! [Z_3] : times_times_real(Z_3,number267125858f_real(bit0(bit1(pls)))) = plus_plus_real(Z_3,Z_3),
file('theBenchmark.p',fact_278_semiring__mult__2__right) ).
fof(fact_279_semiring__mult__2__right,axiom,
! [Z_3] : times_times_nat(Z_3,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(Z_3,Z_3),
file('theBenchmark.p',fact_279_semiring__mult__2__right) ).
fof(fact_280_semiring__mult__2__right,axiom,
! [Z_3] : times_times_int(Z_3,number_number_of_int(bit0(bit1(pls)))) = plus_plus_int(Z_3,Z_3),
file('theBenchmark.p',fact_280_semiring__mult__2__right) ).
fof(fact_281_mult__2__right,axiom,
! [Z_2] : times_times_real(Z_2,number267125858f_real(bit0(bit1(pls)))) = plus_plus_real(Z_2,Z_2),
file('theBenchmark.p',fact_281_mult__2__right) ).
fof(fact_282_mult__2__right,axiom,
! [Z_2] : times_times_int(Z_2,number_number_of_int(bit0(bit1(pls)))) = plus_plus_int(Z_2,Z_2),
file('theBenchmark.p',fact_282_mult__2__right) ).
fof(fact_283_semiring__one__add__one__is__two,axiom,
plus_plus_real(one_one_real,one_one_real) = number267125858f_real(bit0(bit1(pls))),
file('theBenchmark.p',fact_283_semiring__one__add__one__is__two) ).
fof(fact_284_semiring__one__add__one__is__two,axiom,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
file('theBenchmark.p',fact_284_semiring__one__add__one__is__two) ).
fof(fact_285_semiring__one__add__one__is__two,axiom,
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_p0,axiom,
ord_less_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
file('theBenchmark.p',fact_286_p0) ).
fof(fact_287__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096,axiom,
dvd_dvd_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int)),
file('theBenchmark.p',fact_287__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096) ).
fof(fact_288_prime__g__5,axiom,
! [P] :
( is_int(P)
=> ( zprime(P)
=> ( P != number_number_of_int(bit0(bit1(pls)))
=> ( P != number_number_of_int(bit1(bit1(pls)))
=> ord_less_eq_int(number_number_of_int(bit1(bit0(bit1(pls)))),P) ) ) ) ),
file('theBenchmark.p',fact_288_prime__g__5) ).
fof(fact_289__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096,axiom,
twoSqu140629262sum2sq(product_Pair_int_int(s,one_one_int)) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),
file('theBenchmark.p',fact_289__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096) ).
fof(fact_290_real__sum__squared__expand,axiom,
! [X_1,Y_1] : power_power_real(plus_plus_real(X_1,Y_1),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_real(plus_plus_real(power_power_real(X_1,number_number_of_nat(bit0(bit1(pls)))),power_power_real(Y_1,number_number_of_nat(bit0(bit1(pls))))),times_times_real(times_times_real(number267125858f_real(bit0(bit1(pls))),X_1),Y_1)),
file('theBenchmark.p',fact_290_real__sum__squared__expand) ).
fof(fact_291_four__x__squared,axiom,
! [X_1] : times_times_real(number267125858f_real(bit0(bit0(bit1(pls)))),power_power_real(X_1,number_number_of_nat(bit0(bit1(pls))))) = power_power_real(times_times_real(number267125858f_real(bit0(bit1(pls))),X_1),number_number_of_nat(bit0(bit1(pls)))),
file('theBenchmark.p',fact_291_four__x__squared) ).
fof(fact_292_power__less__power__Suc,axiom,
! [N_36,A_36] :
( ord_less_real(one_one_real,A_36)
=> ord_less_real(power_power_real(A_36,N_36),times_times_real(A_36,power_power_real(A_36,N_36))) ),
file('theBenchmark.p',fact_292_power__less__power__Suc) ).
fof(fact_293_power__less__power__Suc,axiom,
! [N_36,A_36] :
( ord_less_nat(one_one_nat,A_36)
=> ord_less_nat(power_power_nat(A_36,N_36),times_times_nat(A_36,power_power_nat(A_36,N_36))) ),
file('theBenchmark.p',fact_293_power__less__power__Suc) ).
fof(fact_294_power__less__power__Suc,axiom,
! [N_36,A_36] :
( ord_less_int(one_one_int,A_36)
=> ord_less_int(power_power_int(A_36,N_36),times_times_int(A_36,power_power_int(A_36,N_36))) ),
file('theBenchmark.p',fact_294_power__less__power__Suc) ).
fof(fact_295_power__gt1__lemma,axiom,
! [N_35,A_35] :
( ord_less_real(one_one_real,A_35)
=> ord_less_real(one_one_real,times_times_real(A_35,power_power_real(A_35,N_35))) ),
file('theBenchmark.p',fact_295_power__gt1__lemma) ).
fof(fact_296_power__gt1__lemma,axiom,
! [N_35,A_35] :
( ord_less_nat(one_one_nat,A_35)
=> ord_less_nat(one_one_nat,times_times_nat(A_35,power_power_nat(A_35,N_35))) ),
file('theBenchmark.p',fact_296_power__gt1__lemma) ).
fof(fact_297_power__gt1__lemma,axiom,
! [N_35,A_35] :
( ord_less_int(one_one_int,A_35)
=> ord_less_int(one_one_int,times_times_int(A_35,power_power_int(A_35,N_35))) ),
file('theBenchmark.p',fact_297_power__gt1__lemma) ).
fof(fact_298_power__le__imp__le__exp,axiom,
! [M_8,N_34,A_34] :
( ord_less_real(one_one_real,A_34)
=> ( ord_less_eq_real(power_power_real(A_34,M_8),power_power_real(A_34,N_34))
=> ord_less_eq_nat(M_8,N_34) ) ),
file('theBenchmark.p',fact_298_power__le__imp__le__exp) ).
fof(fact_299_power__le__imp__le__exp,axiom,
! [M_8,N_34,A_34] :
( ord_less_nat(one_one_nat,A_34)
=> ( ord_less_eq_nat(power_power_nat(A_34,M_8),power_power_nat(A_34,N_34))
=> ord_less_eq_nat(M_8,N_34) ) ),
file('theBenchmark.p',fact_299_power__le__imp__le__exp) ).
fof(fact_300_power__le__imp__le__exp,axiom,
! [M_8,N_34,A_34] :
( ord_less_int(one_one_int,A_34)
=> ( ord_less_eq_int(power_power_int(A_34,M_8),power_power_int(A_34,N_34))
=> ord_less_eq_nat(M_8,N_34) ) ),
file('theBenchmark.p',fact_300_power__le__imp__le__exp) ).
fof(fact_301_power__increasing__iff,axiom,
! [X_2,Y_2,B_2] :
( ord_less_real(one_one_real,B_2)
=> ( ord_less_eq_real(power_power_real(B_2,X_2),power_power_real(B_2,Y_2))
<=> ord_less_eq_nat(X_2,Y_2) ) ),
file('theBenchmark.p',fact_301_power__increasing__iff) ).
fof(fact_302_power__increasing__iff,axiom,
! [X_2,Y_2,B_2] :
( ord_less_nat(one_one_nat,B_2)
=> ( ord_less_eq_nat(power_power_nat(B_2,X_2),power_power_nat(B_2,Y_2))
<=> ord_less_eq_nat(X_2,Y_2) ) ),
file('theBenchmark.p',fact_302_power__increasing__iff) ).
fof(fact_303_power__increasing__iff,axiom,
! [X_2,Y_2,B_2] :
( ord_less_int(one_one_int,B_2)
=> ( ord_less_eq_int(power_power_int(B_2,X_2),power_power_int(B_2,Y_2))
<=> ord_less_eq_nat(X_2,Y_2) ) ),
file('theBenchmark.p',fact_303_power__increasing__iff) ).
fof(fact_304__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096,axiom,
zcong(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),power_power_int(s1,number_number_of_nat(bit0(bit1(pls)))),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
file('theBenchmark.p',fact_304__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_305_s0p,axiom,
( zcong(s1,s,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_int(s,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_eq_int(zero_zero_int,s) ),
file('theBenchmark.p',fact_305_s0p) ).
fof(fact_306__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)
=> ( ( zcong(s1,Y,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_int(Y,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_eq_int(zero_zero_int,Y) )
=> Y = X ) )
& zcong(s1,X,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_int(X,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_eq_int(zero_zero_int,X)
& is_int(X) ),
file('theBenchmark.p',fact_306__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_307__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] :
( is_int(S)
=> ~ ( zcong(s1,S,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_int(S,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_eq_int(zero_zero_int,S) ) ),
file('theBenchmark.p',fact_307__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_308_s1,axiom,
zcong(power_power_int(s1,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
file('theBenchmark.p',fact_308_s1) ).
fof(fact_309_power__eq__0__iff,axiom,
! [A_1,N_1] :
( power_power_real(A_1,N_1) = zero_zero_real
<=> ( N_1 != zero_zero_nat
& A_1 = zero_zero_real ) ),
file('theBenchmark.p',fact_309_power__eq__0__iff) ).
fof(fact_310_power__eq__0__iff,axiom,
! [A_1,N_1] :
( power_power_nat(A_1,N_1) = zero_zero_nat
<=> ( N_1 != zero_zero_nat
& A_1 = zero_zero_nat ) ),
file('theBenchmark.p',fact_310_power__eq__0__iff) ).
fof(fact_311_power__eq__0__iff,axiom,
! [A_1,N_1] :
( is_int(A_1)
=> ( power_power_int(A_1,N_1) = zero_zero_int
<=> ( N_1 != zero_zero_nat
& A_1 = zero_zero_int ) ) ),
file('theBenchmark.p',fact_311_power__eq__0__iff) ).
fof(fact_312_le__imp__power__dvd,axiom,
! [A_33,M_7,N_33] :
( ord_less_eq_nat(M_7,N_33)
=> dvd_dvd_nat(power_power_nat(A_33,M_7),power_power_nat(A_33,N_33)) ),
file('theBenchmark.p',fact_312_le__imp__power__dvd) ).
fof(fact_313_le__imp__power__dvd,axiom,
! [A_33,M_7,N_33] :
( ord_less_eq_nat(M_7,N_33)
=> dvd_dvd_int(power_power_int(A_33,M_7),power_power_int(A_33,N_33)) ),
file('theBenchmark.p',fact_313_le__imp__power__dvd) ).
fof(fact_314_le__imp__power__dvd,axiom,
! [A_33,M_7,N_33] :
( ord_less_eq_nat(M_7,N_33)
=> dvd_dvd_real(power_power_real(A_33,M_7),power_power_real(A_33,N_33)) ),
file('theBenchmark.p',fact_314_le__imp__power__dvd) ).
fof(fact_315_dvd__power__le,axiom,
! [N_32,M_6,X_14,Y_12] :
( dvd_dvd_nat(X_14,Y_12)
=> ( ord_less_eq_nat(N_32,M_6)
=> dvd_dvd_nat(power_power_nat(X_14,N_32),power_power_nat(Y_12,M_6)) ) ),
file('theBenchmark.p',fact_315_dvd__power__le) ).
fof(fact_316_dvd__power__le,axiom,
! [N_32,M_6,X_14,Y_12] :
( dvd_dvd_int(X_14,Y_12)
=> ( ord_less_eq_nat(N_32,M_6)
=> dvd_dvd_int(power_power_int(X_14,N_32),power_power_int(Y_12,M_6)) ) ),
file('theBenchmark.p',fact_316_dvd__power__le) ).
fof(fact_317_dvd__power__le,axiom,
! [N_32,M_6,X_14,Y_12] :
( dvd_dvd_real(X_14,Y_12)
=> ( ord_less_eq_nat(N_32,M_6)
=> dvd_dvd_real(power_power_real(X_14,N_32),power_power_real(Y_12,M_6)) ) ),
file('theBenchmark.p',fact_317_dvd__power__le) ).
fof(fact_318_power__le__dvd,axiom,
! [M_5,A_32,N_31,B_9] :
( dvd_dvd_nat(power_power_nat(A_32,N_31),B_9)
=> ( ord_less_eq_nat(M_5,N_31)
=> dvd_dvd_nat(power_power_nat(A_32,M_5),B_9) ) ),
file('theBenchmark.p',fact_318_power__le__dvd) ).
fof(fact_319_power__le__dvd,axiom,
! [M_5,A_32,N_31,B_9] :
( dvd_dvd_int(power_power_int(A_32,N_31),B_9)
=> ( ord_less_eq_nat(M_5,N_31)
=> dvd_dvd_int(power_power_int(A_32,M_5),B_9) ) ),
file('theBenchmark.p',fact_319_power__le__dvd) ).
fof(fact_320_power__le__dvd,axiom,
! [M_5,A_32,N_31,B_9] :
( dvd_dvd_real(power_power_real(A_32,N_31),B_9)
=> ( ord_less_eq_nat(M_5,N_31)
=> dvd_dvd_real(power_power_real(A_32,M_5),B_9) ) ),
file('theBenchmark.p',fact_320_power__le__dvd) ).
fof(fact_321_power__eq__imp__eq__base,axiom,
! [A_31,N_30,B_8] :
( power_power_real(A_31,N_30) = power_power_real(B_8,N_30)
=> ( ord_less_eq_real(zero_zero_real,A_31)
=> ( ord_less_eq_real(zero_zero_real,B_8)
=> ( ord_less_nat(zero_zero_nat,N_30)
=> A_31 = B_8 ) ) ) ),
file('theBenchmark.p',fact_321_power__eq__imp__eq__base) ).
fof(fact_322_power__eq__imp__eq__base,axiom,
! [A_31,N_30,B_8] :
( power_power_nat(A_31,N_30) = power_power_nat(B_8,N_30)
=> ( ord_less_eq_nat(zero_zero_nat,A_31)
=> ( ord_less_eq_nat(zero_zero_nat,B_8)
=> ( ord_less_nat(zero_zero_nat,N_30)
=> A_31 = B_8 ) ) ) ),
file('theBenchmark.p',fact_322_power__eq__imp__eq__base) ).
fof(fact_323_power__eq__imp__eq__base,axiom,
! [A_31,N_30,B_8] :
( ( is_int(B_8)
& is_int(A_31) )
=> ( power_power_int(A_31,N_30) = power_power_int(B_8,N_30)
=> ( ord_less_eq_int(zero_zero_int,A_31)
=> ( ord_less_eq_int(zero_zero_int,B_8)
=> ( ord_less_nat(zero_zero_nat,N_30)
=> A_31 = B_8 ) ) ) ) ),
file('theBenchmark.p',fact_323_power__eq__imp__eq__base) ).
fof(fact_324_zdvd__not__zless,axiom,
! [N,M] :
( ord_less_int(zero_zero_int,M)
=> ( ord_less_int(M,N)
=> ~ dvd_dvd_int(N,M) ) ),
file('theBenchmark.p',fact_324_zdvd__not__zless) ).
fof(fact_325_zdvd__antisym__nonneg,axiom,
! [N,M] :
( ( is_int(M)
& is_int(N) )
=> ( ord_less_eq_int(zero_zero_int,M)
=> ( ord_less_eq_int(zero_zero_int,N)
=> ( dvd_dvd_int(M,N)
=> ( dvd_dvd_int(N,M)
=> M = N ) ) ) ) ),
file('theBenchmark.p',fact_325_zdvd__antisym__nonneg) ).
fof(fact_326_zdvd__mult__cancel,axiom,
! [K,M,N] :
( is_int(K)
=> ( dvd_dvd_int(times_times_int(K,M),times_times_int(K,N))
=> ( K != zero_zero_int
=> dvd_dvd_int(M,N) ) ) ),
file('theBenchmark.p',fact_326_zdvd__mult__cancel) ).
fof(fact_327_dvd__power__same,axiom,
! [N_29,X_13,Y_11] :
( dvd_dvd_nat(X_13,Y_11)
=> dvd_dvd_nat(power_power_nat(X_13,N_29),power_power_nat(Y_11,N_29)) ),
file('theBenchmark.p',fact_327_dvd__power__same) ).
fof(fact_328_dvd__power__same,axiom,
! [N_29,X_13,Y_11] :
( dvd_dvd_int(X_13,Y_11)
=> dvd_dvd_int(power_power_int(X_13,N_29),power_power_int(Y_11,N_29)) ),
file('theBenchmark.p',fact_328_dvd__power__same) ).
fof(fact_329_dvd__power__same,axiom,
! [N_29,X_13,Y_11] :
( dvd_dvd_real(X_13,Y_11)
=> dvd_dvd_real(power_power_real(X_13,N_29),power_power_real(Y_11,N_29)) ),
file('theBenchmark.p',fact_329_dvd__power__same) ).
fof(fact_330_field__power__not__zero,axiom,
! [N_28,A_30] :
( A_30 != zero_zero_real
=> power_power_real(A_30,N_28) != zero_zero_real ),
file('theBenchmark.p',fact_330_field__power__not__zero) ).
fof(fact_331_field__power__not__zero,axiom,
! [N_28,A_30] :
( is_int(A_30)
=> ( A_30 != zero_zero_int
=> power_power_int(A_30,N_28) != zero_zero_int ) ),
file('theBenchmark.p',fact_331_field__power__not__zero) ).
fof(fact_332_power__0__left,axiom,
! [N_27] :
( ( N_27 != zero_zero_nat
=> power_power_real(zero_zero_real,N_27) = zero_zero_real )
& ( N_27 = zero_zero_nat
=> power_power_real(zero_zero_real,N_27) = one_one_real ) ),
file('theBenchmark.p',fact_332_power__0__left) ).
fof(fact_333_power__0__left,axiom,
! [N_27] :
( ( N_27 != zero_zero_nat
=> power_power_nat(zero_zero_nat,N_27) = zero_zero_nat )
& ( N_27 = zero_zero_nat
=> power_power_nat(zero_zero_nat,N_27) = one_one_nat ) ),
file('theBenchmark.p',fact_333_power__0__left) ).
fof(fact_334_power__0__left,axiom,
! [N_27] :
( ( N_27 != zero_zero_nat
=> power_power_int(zero_zero_int,N_27) = zero_zero_int )
& ( N_27 = zero_zero_nat
=> power_power_int(zero_zero_int,N_27) = one_one_int ) ),
file('theBenchmark.p',fact_334_power__0__left) ).
fof(fact_335_zdvd__imp__le,axiom,
! [Z,N] :
( dvd_dvd_int(Z,N)
=> ( ord_less_int(zero_zero_int,N)
=> ord_less_eq_int(Z,N) ) ),
file('theBenchmark.p',fact_335_zdvd__imp__le) ).
fof(fact_336_power__strict__mono,axiom,
! [N_26,A_29,B_7] :
( ord_less_real(A_29,B_7)
=> ( ord_less_eq_real(zero_zero_real,A_29)
=> ( ord_less_nat(zero_zero_nat,N_26)
=> ord_less_real(power_power_real(A_29,N_26),power_power_real(B_7,N_26)) ) ) ),
file('theBenchmark.p',fact_336_power__strict__mono) ).
fof(fact_337_power__strict__mono,axiom,
! [N_26,A_29,B_7] :
( ord_less_nat(A_29,B_7)
=> ( ord_less_eq_nat(zero_zero_nat,A_29)
=> ( ord_less_nat(zero_zero_nat,N_26)
=> ord_less_nat(power_power_nat(A_29,N_26),power_power_nat(B_7,N_26)) ) ) ),
file('theBenchmark.p',fact_337_power__strict__mono) ).
fof(fact_338_power__strict__mono,axiom,
! [N_26,A_29,B_7] :
( ord_less_int(A_29,B_7)
=> ( ord_less_eq_int(zero_zero_int,A_29)
=> ( ord_less_nat(zero_zero_nat,N_26)
=> ord_less_int(power_power_int(A_29,N_26),power_power_int(B_7,N_26)) ) ) ),
file('theBenchmark.p',fact_338_power__strict__mono) ).
fof(fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [A_28] : times_times_real(zero_zero_real,A_28) = zero_zero_real,
file('theBenchmark.p',fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [A_28] : times_times_nat(zero_zero_nat,A_28) = zero_zero_nat,
file('theBenchmark.p',fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [A_28] : times_times_int(zero_zero_int,A_28) = 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_I10_J,axiom,
! [A_27] : times_times_real(A_27,zero_zero_real) = zero_zero_real,
file('theBenchmark.p',fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [A_27] : times_times_nat(A_27,zero_zero_nat) = zero_zero_nat,
file('theBenchmark.p',fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [A_27] : times_times_int(A_27,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_I5_J,axiom,
! [A_26] : plus_plus_real(zero_zero_real,A_26) = A_26,
file('theBenchmark.p',fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [A_26] : plus_plus_nat(zero_zero_nat,A_26) = A_26,
file('theBenchmark.p',fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [A_26] :
( is_int(A_26)
=> plus_plus_int(zero_zero_int,A_26) = A_26 ),
file('theBenchmark.p',fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [A_25] : plus_plus_real(A_25,zero_zero_real) = A_25,
file('theBenchmark.p',fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [A_25] : plus_plus_nat(A_25,zero_zero_nat) = A_25,
file('theBenchmark.p',fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [A_25] :
( is_int(A_25)
=> plus_plus_int(A_25,zero_zero_int) = A_25 ),
file('theBenchmark.p',fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_351_add__0__iff,axiom,
! [B_2,A_1] :
( B_2 = plus_plus_real(B_2,A_1)
<=> A_1 = zero_zero_real ),
file('theBenchmark.p',fact_351_add__0__iff) ).
fof(fact_352_add__0__iff,axiom,
! [B_2,A_1] :
( B_2 = plus_plus_nat(B_2,A_1)
<=> A_1 = zero_zero_nat ),
file('theBenchmark.p',fact_352_add__0__iff) ).
fof(fact_353_add__0__iff,axiom,
! [B_2,A_1] :
( ( is_int(A_1)
& is_int(B_2) )
=> ( B_2 = plus_plus_int(B_2,A_1)
<=> A_1 = zero_zero_int ) ),
file('theBenchmark.p',fact_353_add__0__iff) ).
fof(fact_354_double__eq__0__iff,axiom,
! [A_1] :
( plus_plus_real(A_1,A_1) = zero_zero_real
<=> A_1 = zero_zero_real ),
file('theBenchmark.p',fact_354_double__eq__0__iff) ).
fof(fact_355_double__eq__0__iff,axiom,
! [A_1] :
( is_int(A_1)
=> ( plus_plus_int(A_1,A_1) = zero_zero_int
<=> A_1 = zero_zero_int ) ),
file('theBenchmark.p',fact_355_double__eq__0__iff) ).
fof(fact_356_Pls__def,axiom,
pls = zero_zero_int,
file('theBenchmark.p',fact_356_Pls__def) ).
fof(fact_357_int__0__neq__1,axiom,
zero_zero_int != one_one_int,
file('theBenchmark.p',fact_357_int__0__neq__1) ).
fof(fact_358_zadd__0,axiom,
! [Z] :
( is_int(Z)
=> plus_plus_int(zero_zero_int,Z) = Z ),
file('theBenchmark.p',fact_358_zadd__0) ).
fof(fact_359_zadd__0__right,axiom,
! [Z] :
( is_int(Z)
=> plus_plus_int(Z,zero_zero_int) = Z ),
file('theBenchmark.p',fact_359_zadd__0__right) ).
fof(fact_360_zero__le__power,axiom,
! [N_25,A_24] :
( ord_less_eq_real(zero_zero_real,A_24)
=> ord_less_eq_real(zero_zero_real,power_power_real(A_24,N_25)) ),
file('theBenchmark.p',fact_360_zero__le__power) ).
fof(fact_361_zero__le__power,axiom,
! [N_25,A_24] :
( ord_less_eq_nat(zero_zero_nat,A_24)
=> ord_less_eq_nat(zero_zero_nat,power_power_nat(A_24,N_25)) ),
file('theBenchmark.p',fact_361_zero__le__power) ).
fof(fact_362_zero__le__power,axiom,
! [N_25,A_24] :
( ord_less_eq_int(zero_zero_int,A_24)
=> ord_less_eq_int(zero_zero_int,power_power_int(A_24,N_25)) ),
file('theBenchmark.p',fact_362_zero__le__power) ).
fof(fact_363_power__mono,axiom,
! [N_24,A_23,B_6] :
( ord_less_eq_real(A_23,B_6)
=> ( ord_less_eq_real(zero_zero_real,A_23)
=> ord_less_eq_real(power_power_real(A_23,N_24),power_power_real(B_6,N_24)) ) ),
file('theBenchmark.p',fact_363_power__mono) ).
fof(fact_364_power__mono,axiom,
! [N_24,A_23,B_6] :
( ord_less_eq_nat(A_23,B_6)
=> ( ord_less_eq_nat(zero_zero_nat,A_23)
=> ord_less_eq_nat(power_power_nat(A_23,N_24),power_power_nat(B_6,N_24)) ) ),
file('theBenchmark.p',fact_364_power__mono) ).
fof(fact_365_power__mono,axiom,
! [N_24,A_23,B_6] :
( ord_less_eq_int(A_23,B_6)
=> ( ord_less_eq_int(zero_zero_int,A_23)
=> ord_less_eq_int(power_power_int(A_23,N_24),power_power_int(B_6,N_24)) ) ),
file('theBenchmark.p',fact_365_power__mono) ).
fof(fact_366_zero__less__power,axiom,
! [N_23,A_22] :
( ord_less_real(zero_zero_real,A_22)
=> ord_less_real(zero_zero_real,power_power_real(A_22,N_23)) ),
file('theBenchmark.p',fact_366_zero__less__power) ).
fof(fact_367_zero__less__power,axiom,
! [N_23,A_22] :
( ord_less_nat(zero_zero_nat,A_22)
=> ord_less_nat(zero_zero_nat,power_power_nat(A_22,N_23)) ),
file('theBenchmark.p',fact_367_zero__less__power) ).
fof(fact_368_zero__less__power,axiom,
! [N_23,A_22] :
( ord_less_int(zero_zero_int,A_22)
=> ord_less_int(zero_zero_int,power_power_int(A_22,N_23)) ),
file('theBenchmark.p',fact_368_zero__less__power) ).
fof(fact_369_zcong__zpower__zmult,axiom,
! [Z,X_1,Y_1,P] :
( zcong(power_power_int(X_1,Y_1),one_one_int,P)
=> zcong(power_power_int(X_1,times_times_nat(Y_1,Z)),one_one_int,P) ),
file('theBenchmark.p',fact_369_zcong__zpower__zmult) ).
fof(fact_370_zdvd__reduce,axiom,
! [K_1,N_1,Ma] :
( dvd_dvd_int(K_1,plus_plus_int(N_1,times_times_int(K_1,Ma)))
<=> dvd_dvd_int(K_1,N_1) ),
file('theBenchmark.p',fact_370_zdvd__reduce) ).
fof(fact_371_zdvd__period,axiom,
! [C,X_2,Ta,A_1,D] :
( dvd_dvd_int(A_1,D)
=> ( dvd_dvd_int(A_1,plus_plus_int(X_2,Ta))
<=> dvd_dvd_int(A_1,plus_plus_int(plus_plus_int(X_2,times_times_int(C,D)),Ta)) ) ),
file('theBenchmark.p',fact_371_zdvd__period) ).
fof(fact_372_power__less__imp__less__base,axiom,
! [A_21,N_22,B_5] :
( ord_less_real(power_power_real(A_21,N_22),power_power_real(B_5,N_22))
=> ( ord_less_eq_real(zero_zero_real,B_5)
=> ord_less_real(A_21,B_5) ) ),
file('theBenchmark.p',fact_372_power__less__imp__less__base) ).
fof(fact_373_power__less__imp__less__base,axiom,
! [A_21,N_22,B_5] :
( ord_less_nat(power_power_nat(A_21,N_22),power_power_nat(B_5,N_22))
=> ( ord_less_eq_nat(zero_zero_nat,B_5)
=> ord_less_nat(A_21,B_5) ) ),
file('theBenchmark.p',fact_373_power__less__imp__less__base) ).
fof(fact_374_power__less__imp__less__base,axiom,
! [A_21,N_22,B_5] :
( ord_less_int(power_power_int(A_21,N_22),power_power_int(B_5,N_22))
=> ( ord_less_eq_int(zero_zero_int,B_5)
=> ord_less_int(A_21,B_5) ) ),
file('theBenchmark.p',fact_374_power__less__imp__less__base) ).
fof(fact_375_power__decreasing,axiom,
! [A_20,N_21,N_20] :
( ord_less_eq_nat(N_21,N_20)
=> ( ord_less_eq_real(zero_zero_real,A_20)
=> ( ord_less_eq_real(A_20,one_one_real)
=> ord_less_eq_real(power_power_real(A_20,N_20),power_power_real(A_20,N_21)) ) ) ),
file('theBenchmark.p',fact_375_power__decreasing) ).
fof(fact_376_power__decreasing,axiom,
! [A_20,N_21,N_20] :
( ord_less_eq_nat(N_21,N_20)
=> ( ord_less_eq_nat(zero_zero_nat,A_20)
=> ( ord_less_eq_nat(A_20,one_one_nat)
=> ord_less_eq_nat(power_power_nat(A_20,N_20),power_power_nat(A_20,N_21)) ) ) ),
file('theBenchmark.p',fact_376_power__decreasing) ).
fof(fact_377_power__decreasing,axiom,
! [A_20,N_21,N_20] :
( ord_less_eq_nat(N_21,N_20)
=> ( ord_less_eq_int(zero_zero_int,A_20)
=> ( ord_less_eq_int(A_20,one_one_int)
=> ord_less_eq_int(power_power_int(A_20,N_20),power_power_int(A_20,N_21)) ) ) ),
file('theBenchmark.p',fact_377_power__decreasing) ).
fof(fact_378_power__strict__decreasing,axiom,
! [A_19,N_19,N_18] :
( ord_less_nat(N_19,N_18)
=> ( ord_less_real(zero_zero_real,A_19)
=> ( ord_less_real(A_19,one_one_real)
=> ord_less_real(power_power_real(A_19,N_18),power_power_real(A_19,N_19)) ) ) ),
file('theBenchmark.p',fact_378_power__strict__decreasing) ).
fof(fact_379_power__strict__decreasing,axiom,
! [A_19,N_19,N_18] :
( ord_less_nat(N_19,N_18)
=> ( ord_less_nat(zero_zero_nat,A_19)
=> ( ord_less_nat(A_19,one_one_nat)
=> ord_less_nat(power_power_nat(A_19,N_18),power_power_nat(A_19,N_19)) ) ) ),
file('theBenchmark.p',fact_379_power__strict__decreasing) ).
fof(fact_380_power__strict__decreasing,axiom,
! [A_19,N_19,N_18] :
( ord_less_nat(N_19,N_18)
=> ( ord_less_int(zero_zero_int,A_19)
=> ( ord_less_int(A_19,one_one_int)
=> ord_less_int(power_power_int(A_19,N_18),power_power_int(A_19,N_19)) ) ) ),
file('theBenchmark.p',fact_380_power__strict__decreasing) ).
fof(fact_381_even__less__0__iff,axiom,
! [A_1] :
( ord_less_real(plus_plus_real(A_1,A_1),zero_zero_real)
<=> ord_less_real(A_1,zero_zero_real) ),
file('theBenchmark.p',fact_381_even__less__0__iff) ).
fof(fact_382_even__less__0__iff,axiom,
! [A_1] :
( ord_less_int(plus_plus_int(A_1,A_1),zero_zero_int)
<=> ord_less_int(A_1,zero_zero_int) ),
file('theBenchmark.p',fact_382_even__less__0__iff) ).
fof(fact_383_sum__squares__eq__zero__iff,axiom,
! [X_2,Y_2] :
( plus_plus_real(times_times_real(X_2,X_2),times_times_real(Y_2,Y_2)) = zero_zero_real
<=> ( Y_2 = zero_zero_real
& X_2 = zero_zero_real ) ),
file('theBenchmark.p',fact_383_sum__squares__eq__zero__iff) ).
fof(fact_384_sum__squares__eq__zero__iff,axiom,
! [X_2,Y_2] :
( ( is_int(Y_2)
& is_int(X_2) )
=> ( plus_plus_int(times_times_int(X_2,X_2),times_times_int(Y_2,Y_2)) = zero_zero_int
<=> ( Y_2 = zero_zero_int
& X_2 = zero_zero_int ) ) ),
file('theBenchmark.p',fact_384_sum__squares__eq__zero__iff) ).
fof(fact_385_add__scale__eq__noteq,axiom,
! [C_2,D_2,A_18,B_4,R_3] :
( R_3 != zero_zero_real
=> ( ( C_2 != D_2
& A_18 = B_4 )
=> plus_plus_real(A_18,times_times_real(R_3,C_2)) != plus_plus_real(B_4,times_times_real(R_3,D_2)) ) ),
file('theBenchmark.p',fact_385_add__scale__eq__noteq) ).
fof(fact_386_add__scale__eq__noteq,axiom,
! [C_2,D_2,A_18,B_4,R_3] :
( R_3 != zero_zero_nat
=> ( ( C_2 != D_2
& A_18 = B_4 )
=> plus_plus_nat(A_18,times_times_nat(R_3,C_2)) != plus_plus_nat(B_4,times_times_nat(R_3,D_2)) ) ),
file('theBenchmark.p',fact_386_add__scale__eq__noteq) ).
fof(fact_387_add__scale__eq__noteq,axiom,
! [C_2,D_2,A_18,B_4,R_3] :
( ( is_int(R_3)
& is_int(D_2)
& is_int(C_2) )
=> ( R_3 != zero_zero_int
=> ( ( C_2 != D_2
& A_18 = B_4 )
=> plus_plus_int(A_18,times_times_int(R_3,C_2)) != plus_plus_int(B_4,times_times_int(R_3,D_2)) ) ) ),
file('theBenchmark.p',fact_387_add__scale__eq__noteq) ).
fof(fact_388_zprime__zdvd__power,axiom,
! [A,N,P] :
( zprime(P)
=> ( dvd_dvd_int(P,power_power_int(A,N))
=> dvd_dvd_int(P,A) ) ),
file('theBenchmark.p',fact_388_zprime__zdvd__power) ).
fof(fact_389_semiring__norm_I112_J,axiom,
zero_zero_real = number267125858f_real(pls),
file('theBenchmark.p',fact_389_semiring__norm_I112_J) ).
fof(fact_390_semiring__norm_I112_J,axiom,
zero_zero_int = number_number_of_int(pls),
file('theBenchmark.p',fact_390_semiring__norm_I112_J) ).
fof(fact_391_number__of__Pls,axiom,
number267125858f_real(pls) = zero_zero_real,
file('theBenchmark.p',fact_391_number__of__Pls) ).
fof(fact_392_number__of__Pls,axiom,
number_number_of_int(pls) = zero_zero_int,
file('theBenchmark.p',fact_392_number__of__Pls) ).
fof(fact_393_semiring__numeral__0__eq__0,axiom,
number267125858f_real(pls) = zero_zero_real,
file('theBenchmark.p',fact_393_semiring__numeral__0__eq__0) ).
fof(fact_394_semiring__numeral__0__eq__0,axiom,
number_number_of_nat(pls) = zero_zero_nat,
file('theBenchmark.p',fact_394_semiring__numeral__0__eq__0) ).
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_bin__less__0__simps_I4_J,axiom,
! [W_1] :
( ord_less_int(bit1(W_1),zero_zero_int)
<=> ord_less_int(W_1,zero_zero_int) ),
file('theBenchmark.p',fact_396_bin__less__0__simps_I4_J) ).
fof(fact_397_bin__less__0__simps_I1_J,axiom,
~ ord_less_int(pls,zero_zero_int),
file('theBenchmark.p',fact_397_bin__less__0__simps_I1_J) ).
fof(fact_398_bin__less__0__simps_I3_J,axiom,
! [W_1] :
( ord_less_int(bit0(W_1),zero_zero_int)
<=> ord_less_int(W_1,zero_zero_int) ),
file('theBenchmark.p',fact_398_bin__less__0__simps_I3_J) ).
fof(fact_399_zero__is__num__zero,axiom,
zero_zero_int = number_number_of_int(pls),
file('theBenchmark.p',fact_399_zero__is__num__zero) ).
fof(fact_400_int__0__less__1,axiom,
ord_less_int(zero_zero_int,one_one_int),
file('theBenchmark.p',fact_400_int__0__less__1) ).
fof(fact_401_pos__zmult__pos,axiom,
! [B_1,A] :
( ord_less_int(zero_zero_int,A)
=> ( ord_less_int(zero_zero_int,times_times_int(A,B_1))
=> ord_less_int(zero_zero_int,B_1) ) ),
file('theBenchmark.p',fact_401_pos__zmult__pos) ).
fof(fact_402_zmult__zless__mono2,axiom,
! [K,I,J] :
( ord_less_int(I,J)
=> ( ord_less_int(zero_zero_int,K)
=> ord_less_int(times_times_int(K,I),times_times_int(K,J)) ) ),
file('theBenchmark.p',fact_402_zmult__zless__mono2) ).
fof(fact_403_odd__nonzero,axiom,
! [Z] : plus_plus_int(plus_plus_int(one_one_int,Z),Z) != zero_zero_int,
file('theBenchmark.p',fact_403_odd__nonzero) ).
fof(fact_404_power__Suc__less,axiom,
! [N_17,A_17] :
( ord_less_real(zero_zero_real,A_17)
=> ( ord_less_real(A_17,one_one_real)
=> ord_less_real(times_times_real(A_17,power_power_real(A_17,N_17)),power_power_real(A_17,N_17)) ) ),
file('theBenchmark.p',fact_404_power__Suc__less) ).
fof(fact_405_power__Suc__less,axiom,
! [N_17,A_17] :
( ord_less_nat(zero_zero_nat,A_17)
=> ( ord_less_nat(A_17,one_one_nat)
=> ord_less_nat(times_times_nat(A_17,power_power_nat(A_17,N_17)),power_power_nat(A_17,N_17)) ) ),
file('theBenchmark.p',fact_405_power__Suc__less) ).
fof(fact_406_power__Suc__less,axiom,
! [N_17,A_17] :
( ord_less_int(zero_zero_int,A_17)
=> ( ord_less_int(A_17,one_one_int)
=> ord_less_int(times_times_int(A_17,power_power_int(A_17,N_17)),power_power_int(A_17,N_17)) ) ),
file('theBenchmark.p',fact_406_power__Suc__less) ).
fof(fact_407_zprime__power__zdvd__cancel__left,axiom,
! [N,B_1,A,P] :
( zprime(P)
=> ( ~ dvd_dvd_int(P,A)
=> ( dvd_dvd_int(power_power_int(P,N),times_times_int(A,B_1))
=> dvd_dvd_int(power_power_int(P,N),B_1) ) ) ),
file('theBenchmark.p',fact_407_zprime__power__zdvd__cancel__left) ).
fof(fact_408_zprime__power__zdvd__cancel__right,axiom,
! [N,A,B_1,P] :
( zprime(P)
=> ( ~ dvd_dvd_int(P,B_1)
=> ( dvd_dvd_int(power_power_int(P,N),times_times_int(A,B_1))
=> dvd_dvd_int(power_power_int(P,N),A) ) ) ),
file('theBenchmark.p',fact_408_zprime__power__zdvd__cancel__right) ).
fof(fact_409_sum__squares__ge__zero,axiom,
! [X_12,Y_10] : ord_less_eq_real(zero_zero_real,plus_plus_real(times_times_real(X_12,X_12),times_times_real(Y_10,Y_10))),
file('theBenchmark.p',fact_409_sum__squares__ge__zero) ).
fof(fact_410_sum__squares__ge__zero,axiom,
! [X_12,Y_10] : ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(X_12,X_12),times_times_int(Y_10,Y_10))),
file('theBenchmark.p',fact_410_sum__squares__ge__zero) ).
fof(fact_411_sum__squares__le__zero__iff,axiom,
! [X_2,Y_2] :
( ord_less_eq_real(plus_plus_real(times_times_real(X_2,X_2),times_times_real(Y_2,Y_2)),zero_zero_real)
<=> ( Y_2 = zero_zero_real
& X_2 = zero_zero_real ) ),
file('theBenchmark.p',fact_411_sum__squares__le__zero__iff) ).
fof(fact_412_sum__squares__le__zero__iff,axiom,
! [X_2,Y_2] :
( ( is_int(Y_2)
& is_int(X_2) )
=> ( ord_less_eq_int(plus_plus_int(times_times_int(X_2,X_2),times_times_int(Y_2,Y_2)),zero_zero_int)
<=> ( Y_2 = zero_zero_int
& X_2 = zero_zero_int ) ) ),
file('theBenchmark.p',fact_412_sum__squares__le__zero__iff) ).
fof(fact_413_less__nat__number__of,axiom,
! [V_3,V_4] :
( ord_less_nat(number_number_of_nat(V_3),number_number_of_nat(V_4))
<=> ( ord_less_int(V_3,V_4)
& ( ord_less_int(V_3,V_4)
=> ord_less_int(pls,V_4) ) ) ),
file('theBenchmark.p',fact_413_less__nat__number__of) ).
fof(fact_414_not__sum__squares__lt__zero,axiom,
! [X_11,Y_9] : ~ ord_less_real(plus_plus_real(times_times_real(X_11,X_11),times_times_real(Y_9,Y_9)),zero_zero_real),
file('theBenchmark.p',fact_414_not__sum__squares__lt__zero) ).
fof(fact_415_not__sum__squares__lt__zero,axiom,
! [X_11,Y_9] : ~ ord_less_int(plus_plus_int(times_times_int(X_11,X_11),times_times_int(Y_9,Y_9)),zero_zero_int),
file('theBenchmark.p',fact_415_not__sum__squares__lt__zero) ).
fof(fact_416_sum__squares__gt__zero__iff,axiom,
! [X_2,Y_2] :
( ord_less_real(zero_zero_real,plus_plus_real(times_times_real(X_2,X_2),times_times_real(Y_2,Y_2)))
<=> ( Y_2 != zero_zero_real
| X_2 != zero_zero_real ) ),
file('theBenchmark.p',fact_416_sum__squares__gt__zero__iff) ).
fof(fact_417_sum__squares__gt__zero__iff,axiom,
! [X_2,Y_2] :
( ( is_int(Y_2)
& is_int(X_2) )
=> ( ord_less_int(zero_zero_int,plus_plus_int(times_times_int(X_2,X_2),times_times_int(Y_2,Y_2)))
<=> ( Y_2 != zero_zero_int
| X_2 != zero_zero_int ) ) ),
file('theBenchmark.p',fact_417_sum__squares__gt__zero__iff) ).
fof(fact_418_le__nat__number__of,axiom,
! [V_3,V_4] :
( ord_less_eq_nat(number_number_of_nat(V_3),number_number_of_nat(V_4))
<=> ( ~ ord_less_eq_int(V_3,V_4)
=> ord_less_eq_int(V_3,pls) ) ),
file('theBenchmark.p',fact_418_le__nat__number__of) ).
fof(fact_419_number__of__Bit0,axiom,
! [W_4] : number267125858f_real(bit0(W_4)) = plus_plus_real(plus_plus_real(zero_zero_real,number267125858f_real(W_4)),number267125858f_real(W_4)),
file('theBenchmark.p',fact_419_number__of__Bit0) ).
fof(fact_420_number__of__Bit0,axiom,
! [W_4] : number_number_of_int(bit0(W_4)) = plus_plus_int(plus_plus_int(zero_zero_int,number_number_of_int(W_4)),number_number_of_int(W_4)),
file('theBenchmark.p',fact_420_number__of__Bit0) ).
fof(fact_421_power__one__right,axiom,
! [A_16] : power_power_nat(A_16,one_one_nat) = A_16,
file('theBenchmark.p',fact_421_power__one__right) ).
fof(fact_422_power__one__right,axiom,
! [A_16] : power_power_real(A_16,one_one_nat) = A_16,
file('theBenchmark.p',fact_422_power__one__right) ).
fof(fact_423_power__one__right,axiom,
! [A_16] :
( is_int(A_16)
=> power_power_int(A_16,one_one_nat) = A_16 ),
file('theBenchmark.p',fact_423_power__one__right) ).
fof(fact_424_int__one__le__iff__zero__less,axiom,
! [Z_1] :
( ord_less_eq_int(one_one_int,Z_1)
<=> ord_less_int(zero_zero_int,Z_1) ),
file('theBenchmark.p',fact_424_int__one__le__iff__zero__less) ).
fof(fact_425_pos__zmult__eq__1__iff,axiom,
! [N_1,Ma] :
( ( is_int(Ma)
& is_int(N_1) )
=> ( ord_less_int(zero_zero_int,Ma)
=> ( times_times_int(Ma,N_1) = one_one_int
<=> ( N_1 = one_one_int
& Ma = one_one_int ) ) ) ),
file('theBenchmark.p',fact_425_pos__zmult__eq__1__iff) ).
fof(fact_426_odd__less__0,axiom,
! [Z_1] :
( ord_less_int(plus_plus_int(plus_plus_int(one_one_int,Z_1),Z_1),zero_zero_int)
<=> ord_less_int(Z_1,zero_zero_int) ),
file('theBenchmark.p',fact_426_odd__less__0) ).
fof(fact_427_less__special_I1_J,axiom,
! [Y_2] :
( ord_less_real(zero_zero_real,number267125858f_real(Y_2))
<=> ord_less_int(pls,Y_2) ),
file('theBenchmark.p',fact_427_less__special_I1_J) ).
fof(fact_428_less__special_I1_J,axiom,
! [Y_2] :
( ord_less_int(zero_zero_int,number_number_of_int(Y_2))
<=> ord_less_int(pls,Y_2) ),
file('theBenchmark.p',fact_428_less__special_I1_J) ).
fof(fact_429_less__special_I3_J,axiom,
! [X_2] :
( ord_less_real(number267125858f_real(X_2),zero_zero_real)
<=> ord_less_int(X_2,pls) ),
file('theBenchmark.p',fact_429_less__special_I3_J) ).
fof(fact_430_less__special_I3_J,axiom,
! [X_2] :
( ord_less_int(number_number_of_int(X_2),zero_zero_int)
<=> ord_less_int(X_2,pls) ),
file('theBenchmark.p',fact_430_less__special_I3_J) ).
fof(fact_431_le__special_I1_J,axiom,
! [Y_2] :
( ord_less_eq_real(zero_zero_real,number267125858f_real(Y_2))
<=> ord_less_eq_int(pls,Y_2) ),
file('theBenchmark.p',fact_431_le__special_I1_J) ).
fof(fact_432_le__special_I1_J,axiom,
! [Y_2] :
( ord_less_eq_int(zero_zero_int,number_number_of_int(Y_2))
<=> ord_less_eq_int(pls,Y_2) ),
file('theBenchmark.p',fact_432_le__special_I1_J) ).
fof(fact_433_le__special_I3_J,axiom,
! [X_2] :
( ord_less_eq_real(number267125858f_real(X_2),zero_zero_real)
<=> ord_less_eq_int(X_2,pls) ),
file('theBenchmark.p',fact_433_le__special_I3_J) ).
fof(fact_434_le__special_I3_J,axiom,
! [X_2] :
( ord_less_eq_int(number_number_of_int(X_2),zero_zero_int)
<=> ord_less_eq_int(X_2,pls) ),
file('theBenchmark.p',fact_434_le__special_I3_J) ).
fof(fact_435_le__imp__0__less,axiom,
! [Z] :
( ord_less_eq_int(zero_zero_int,Z)
=> ord_less_int(zero_zero_int,plus_plus_int(one_one_int,Z)) ),
file('theBenchmark.p',fact_435_le__imp__0__less) ).
fof(fact_436_zero__power2,axiom,
power_power_real(zero_zero_real,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real,
file('theBenchmark.p',fact_436_zero__power2) ).
fof(fact_437_zero__power2,axiom,
power_power_nat(zero_zero_nat,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_nat,
file('theBenchmark.p',fact_437_zero__power2) ).
fof(fact_438_zero__power2,axiom,
power_power_int(zero_zero_int,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
file('theBenchmark.p',fact_438_zero__power2) ).
fof(fact_439_zero__eq__power2,axiom,
! [A_1] :
( power_power_real(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real
<=> A_1 = zero_zero_real ),
file('theBenchmark.p',fact_439_zero__eq__power2) ).
fof(fact_440_zero__eq__power2,axiom,
! [A_1] :
( is_int(A_1)
=> ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int
<=> A_1 = zero_zero_int ) ),
file('theBenchmark.p',fact_440_zero__eq__power2) ).
fof(fact_441_zero__le__power2,axiom,
! [A_15] : ord_less_eq_real(zero_zero_real,power_power_real(A_15,number_number_of_nat(bit0(bit1(pls))))),
file('theBenchmark.p',fact_441_zero__le__power2) ).
fof(fact_442_zero__le__power2,axiom,
! [A_15] : ord_less_eq_int(zero_zero_int,power_power_int(A_15,number_number_of_nat(bit0(bit1(pls))))),
file('theBenchmark.p',fact_442_zero__le__power2) ).
fof(fact_443_power2__le__imp__le,axiom,
! [X_10,Y_8] :
( ord_less_eq_real(power_power_real(X_10,number_number_of_nat(bit0(bit1(pls)))),power_power_real(Y_8,number_number_of_nat(bit0(bit1(pls)))))
=> ( ord_less_eq_real(zero_zero_real,Y_8)
=> ord_less_eq_real(X_10,Y_8) ) ),
file('theBenchmark.p',fact_443_power2__le__imp__le) ).
fof(fact_444_power2__le__imp__le,axiom,
! [X_10,Y_8] :
( ord_less_eq_nat(power_power_nat(X_10,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(Y_8,number_number_of_nat(bit0(bit1(pls)))))
=> ( ord_less_eq_nat(zero_zero_nat,Y_8)
=> ord_less_eq_nat(X_10,Y_8) ) ),
file('theBenchmark.p',fact_444_power2__le__imp__le) ).
fof(fact_445_power2__le__imp__le,axiom,
! [X_10,Y_8] :
( ord_less_eq_int(power_power_int(X_10,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y_8,number_number_of_nat(bit0(bit1(pls)))))
=> ( ord_less_eq_int(zero_zero_int,Y_8)
=> ord_less_eq_int(X_10,Y_8) ) ),
file('theBenchmark.p',fact_445_power2__le__imp__le) ).
fof(fact_446_power2__eq__imp__eq,axiom,
! [X_9,Y_7] :
( power_power_real(X_9,number_number_of_nat(bit0(bit1(pls)))) = power_power_real(Y_7,number_number_of_nat(bit0(bit1(pls))))
=> ( ord_less_eq_real(zero_zero_real,X_9)
=> ( ord_less_eq_real(zero_zero_real,Y_7)
=> X_9 = Y_7 ) ) ),
file('theBenchmark.p',fact_446_power2__eq__imp__eq) ).
fof(fact_447_power2__eq__imp__eq,axiom,
! [X_9,Y_7] :
( power_power_nat(X_9,number_number_of_nat(bit0(bit1(pls)))) = power_power_nat(Y_7,number_number_of_nat(bit0(bit1(pls))))
=> ( ord_less_eq_nat(zero_zero_nat,X_9)
=> ( ord_less_eq_nat(zero_zero_nat,Y_7)
=> X_9 = Y_7 ) ) ),
file('theBenchmark.p',fact_447_power2__eq__imp__eq) ).
fof(fact_448_power2__eq__imp__eq,axiom,
! [X_9,Y_7] :
( ( is_int(Y_7)
& is_int(X_9) )
=> ( power_power_int(X_9,number_number_of_nat(bit0(bit1(pls)))) = power_power_int(Y_7,number_number_of_nat(bit0(bit1(pls))))
=> ( ord_less_eq_int(zero_zero_int,X_9)
=> ( ord_less_eq_int(zero_zero_int,Y_7)
=> X_9 = Y_7 ) ) ) ),
file('theBenchmark.p',fact_448_power2__eq__imp__eq) ).
fof(fact_449_power2__less__0,axiom,
! [A_14] : ~ ord_less_real(power_power_real(A_14,number_number_of_nat(bit0(bit1(pls)))),zero_zero_real),
file('theBenchmark.p',fact_449_power2__less__0) ).
fof(fact_450_power2__less__0,axiom,
! [A_14] : ~ ord_less_int(power_power_int(A_14,number_number_of_nat(bit0(bit1(pls)))),zero_zero_int),
file('theBenchmark.p',fact_450_power2__less__0) ).
fof(fact_451_zero__less__power2,axiom,
! [A_1] :
( ord_less_real(zero_zero_real,power_power_real(A_1,number_number_of_nat(bit0(bit1(pls)))))
<=> A_1 != zero_zero_real ),
file('theBenchmark.p',fact_451_zero__less__power2) ).
fof(fact_452_zero__less__power2,axiom,
! [A_1] :
( is_int(A_1)
=> ( ord_less_int(zero_zero_int,power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))))
<=> A_1 != zero_zero_int ) ),
file('theBenchmark.p',fact_452_zero__less__power2) ).
fof(fact_453_sum__power2__eq__zero__iff,axiom,
! [X_2,Y_2] :
( plus_plus_real(power_power_real(X_2,number_number_of_nat(bit0(bit1(pls)))),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_453_sum__power2__eq__zero__iff) ).
fof(fact_454_sum__power2__eq__zero__iff,axiom,
! [X_2,Y_2] :
( ( is_int(Y_2)
& is_int(X_2) )
=> ( plus_plus_int(power_power_int(X_2,number_number_of_nat(bit0(bit1(pls)))),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_454_sum__power2__eq__zero__iff) ).
fof(fact_455_power__commutes,axiom,
! [A_13,N_16] : times_times_nat(power_power_nat(A_13,N_16),A_13) = times_times_nat(A_13,power_power_nat(A_13,N_16)),
file('theBenchmark.p',fact_455_power__commutes) ).
fof(fact_456_power__commutes,axiom,
! [A_13,N_16] : times_times_real(power_power_real(A_13,N_16),A_13) = times_times_real(A_13,power_power_real(A_13,N_16)),
file('theBenchmark.p',fact_456_power__commutes) ).
fof(fact_457_power__commutes,axiom,
! [A_13,N_16] : times_times_int(power_power_int(A_13,N_16),A_13) = times_times_int(A_13,power_power_int(A_13,N_16)),
file('theBenchmark.p',fact_457_power__commutes) ).
fof(fact_458_power__mult__distrib,axiom,
! [A_12,B_3,N_15] : power_power_nat(times_times_nat(A_12,B_3),N_15) = times_times_nat(power_power_nat(A_12,N_15),power_power_nat(B_3,N_15)),
file('theBenchmark.p',fact_458_power__mult__distrib) ).
fof(fact_459_power__mult__distrib,axiom,
! [A_12,B_3,N_15] : power_power_real(times_times_real(A_12,B_3),N_15) = times_times_real(power_power_real(A_12,N_15),power_power_real(B_3,N_15)),
file('theBenchmark.p',fact_459_power__mult__distrib) ).
fof(fact_460_power__mult__distrib,axiom,
! [A_12,B_3,N_15] : power_power_int(times_times_int(A_12,B_3),N_15) = times_times_int(power_power_int(A_12,N_15),power_power_int(B_3,N_15)),
file('theBenchmark.p',fact_460_power__mult__distrib) ).
fof(fact_461_power__add,axiom,
! [A_11,M_4,N_14] : power_power_nat(A_11,plus_plus_nat(M_4,N_14)) = times_times_nat(power_power_nat(A_11,M_4),power_power_nat(A_11,N_14)),
file('theBenchmark.p',fact_461_power__add) ).
fof(fact_462_power__add,axiom,
! [A_11,M_4,N_14] : power_power_real(A_11,plus_plus_nat(M_4,N_14)) = times_times_real(power_power_real(A_11,M_4),power_power_real(A_11,N_14)),
file('theBenchmark.p',fact_462_power__add) ).
fof(fact_463_power__add,axiom,
! [A_11,M_4,N_14] : power_power_int(A_11,plus_plus_nat(M_4,N_14)) = times_times_int(power_power_int(A_11,M_4),power_power_int(A_11,N_14)),
file('theBenchmark.p',fact_463_power__add) ).
fof(fact_464_power__one,axiom,
! [N_13] : power_power_real(one_one_real,N_13) = one_one_real,
file('theBenchmark.p',fact_464_power__one) ).
fof(fact_465_power__one,axiom,
! [N_13] : power_power_nat(one_one_nat,N_13) = one_one_nat,
file('theBenchmark.p',fact_465_power__one) ).
fof(fact_466_power__one,axiom,
! [N_13] : power_power_int(one_one_int,N_13) = one_one_int,
file('theBenchmark.p',fact_466_power__one) ).
fof(fact_467_power__mult,axiom,
! [A_10,M_3,N_12] : power_power_nat(A_10,times_times_nat(M_3,N_12)) = power_power_nat(power_power_nat(A_10,M_3),N_12),
file('theBenchmark.p',fact_467_power__mult) ).
fof(fact_468_power__mult,axiom,
! [A_10,M_3,N_12] : power_power_real(A_10,times_times_nat(M_3,N_12)) = power_power_real(power_power_real(A_10,M_3),N_12),
file('theBenchmark.p',fact_468_power__mult) ).
fof(fact_469_power__mult,axiom,
! [A_10,M_3,N_12] : power_power_int(A_10,times_times_nat(M_3,N_12)) = power_power_int(power_power_int(A_10,M_3),N_12),
file('theBenchmark.p',fact_469_power__mult) ).
fof(fact_470_power2__less__imp__less,axiom,
! [X_8,Y_6] :
( ord_less_real(power_power_real(X_8,number_number_of_nat(bit0(bit1(pls)))),power_power_real(Y_6,number_number_of_nat(bit0(bit1(pls)))))
=> ( ord_less_eq_real(zero_zero_real,Y_6)
=> ord_less_real(X_8,Y_6) ) ),
file('theBenchmark.p',fact_470_power2__less__imp__less) ).
fof(fact_471_power2__less__imp__less,axiom,
! [X_8,Y_6] :
( ord_less_nat(power_power_nat(X_8,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(Y_6,number_number_of_nat(bit0(bit1(pls)))))
=> ( ord_less_eq_nat(zero_zero_nat,Y_6)
=> ord_less_nat(X_8,Y_6) ) ),
file('theBenchmark.p',fact_471_power2__less__imp__less) ).
fof(fact_472_power2__less__imp__less,axiom,
! [X_8,Y_6] :
( ord_less_int(power_power_int(X_8,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y_6,number_number_of_nat(bit0(bit1(pls)))))
=> ( ord_less_eq_int(zero_zero_int,Y_6)
=> ord_less_int(X_8,Y_6) ) ),
file('theBenchmark.p',fact_472_power2__less__imp__less) ).
fof(fact_473_sum__power2__ge__zero,axiom,
! [X_7,Y_5] : ord_less_eq_real(zero_zero_real,plus_plus_real(power_power_real(X_7,number_number_of_nat(bit0(bit1(pls)))),power_power_real(Y_5,number_number_of_nat(bit0(bit1(pls)))))),
file('theBenchmark.p',fact_473_sum__power2__ge__zero) ).
fof(fact_474_sum__power2__ge__zero,axiom,
! [X_7,Y_5] : ord_less_eq_int(zero_zero_int,plus_plus_int(power_power_int(X_7,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y_5,number_number_of_nat(bit0(bit1(pls)))))),
file('theBenchmark.p',fact_474_sum__power2__ge__zero) ).
fof(fact_475_sum__power2__le__zero__iff,axiom,
! [X_2,Y_2] :
( ord_less_eq_real(plus_plus_real(power_power_real(X_2,number_number_of_nat(bit0(bit1(pls)))),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_475_sum__power2__le__zero__iff) ).
fof(fact_476_sum__power2__le__zero__iff,axiom,
! [X_2,Y_2] :
( ( is_int(Y_2)
& is_int(X_2) )
=> ( ord_less_eq_int(plus_plus_int(power_power_int(X_2,number_number_of_nat(bit0(bit1(pls)))),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_476_sum__power2__le__zero__iff) ).
fof(fact_477_not__sum__power2__lt__zero,axiom,
! [X_6,Y_4] : ~ ord_less_real(plus_plus_real(power_power_real(X_6,number_number_of_nat(bit0(bit1(pls)))),power_power_real(Y_4,number_number_of_nat(bit0(bit1(pls))))),zero_zero_real),
file('theBenchmark.p',fact_477_not__sum__power2__lt__zero) ).
fof(fact_478_not__sum__power2__lt__zero,axiom,
! [X_6,Y_4] : ~ ord_less_int(plus_plus_int(power_power_int(X_6,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y_4,number_number_of_nat(bit0(bit1(pls))))),zero_zero_int),
file('theBenchmark.p',fact_478_not__sum__power2__lt__zero) ).
fof(fact_479_sum__power2__gt__zero__iff,axiom,
! [X_2,Y_2] :
( ord_less_real(zero_zero_real,plus_plus_real(power_power_real(X_2,number_number_of_nat(bit0(bit1(pls)))),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_479_sum__power2__gt__zero__iff) ).
fof(fact_480_sum__power2__gt__zero__iff,axiom,
! [X_2,Y_2] :
( ( is_int(Y_2)
& is_int(X_2) )
=> ( ord_less_int(zero_zero_int,plus_plus_int(power_power_int(X_2,number_number_of_nat(bit0(bit1(pls)))),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_480_sum__power2__gt__zero__iff) ).
fof(fact_481_zero__le__even__power_H,axiom,
! [A_9,N_11] : ord_less_eq_real(zero_zero_real,power_power_real(A_9,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_11))),
file('theBenchmark.p',fact_481_zero__le__even__power_H) ).
fof(fact_482_zero__le__even__power_H,axiom,
! [A_9,N_11] : ord_less_eq_int(zero_zero_int,power_power_int(A_9,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_11))),
file('theBenchmark.p',fact_482_zero__le__even__power_H) ).
fof(fact_483_one__le__power,axiom,
! [N_10,A_8] :
( ord_less_eq_real(one_one_real,A_8)
=> ord_less_eq_real(one_one_real,power_power_real(A_8,N_10)) ),
file('theBenchmark.p',fact_483_one__le__power) ).
fof(fact_484_one__le__power,axiom,
! [N_10,A_8] :
( ord_less_eq_nat(one_one_nat,A_8)
=> ord_less_eq_nat(one_one_nat,power_power_nat(A_8,N_10)) ),
file('theBenchmark.p',fact_484_one__le__power) ).
fof(fact_485_one__le__power,axiom,
! [N_10,A_8] :
( ord_less_eq_int(one_one_int,A_8)
=> ord_less_eq_int(one_one_int,power_power_int(A_8,N_10)) ),
file('theBenchmark.p',fact_485_one__le__power) ).
fof(fact_486_power__increasing,axiom,
! [A_7,N_9,N_8] :
( ord_less_eq_nat(N_9,N_8)
=> ( ord_less_eq_real(one_one_real,A_7)
=> ord_less_eq_real(power_power_real(A_7,N_9),power_power_real(A_7,N_8)) ) ),
file('theBenchmark.p',fact_486_power__increasing) ).
fof(fact_487_power__increasing,axiom,
! [A_7,N_9,N_8] :
( ord_less_eq_nat(N_9,N_8)
=> ( ord_less_eq_nat(one_one_nat,A_7)
=> ord_less_eq_nat(power_power_nat(A_7,N_9),power_power_nat(A_7,N_8)) ) ),
file('theBenchmark.p',fact_487_power__increasing) ).
fof(fact_488_power__increasing,axiom,
! [A_7,N_9,N_8] :
( ord_less_eq_nat(N_9,N_8)
=> ( ord_less_eq_int(one_one_int,A_7)
=> ord_less_eq_int(power_power_int(A_7,N_9),power_power_int(A_7,N_8)) ) ),
file('theBenchmark.p',fact_488_power__increasing) ).
fof(fact_489_power__inject__exp,axiom,
! [Ma,N_1,A_1] :
( ord_less_real(one_one_real,A_1)
=> ( power_power_real(A_1,Ma) = power_power_real(A_1,N_1)
<=> Ma = N_1 ) ),
file('theBenchmark.p',fact_489_power__inject__exp) ).
fof(fact_490_power__inject__exp,axiom,
! [Ma,N_1,A_1] :
( ord_less_nat(one_one_nat,A_1)
=> ( power_power_nat(A_1,Ma) = power_power_nat(A_1,N_1)
<=> Ma = N_1 ) ),
file('theBenchmark.p',fact_490_power__inject__exp) ).
fof(fact_491_power__inject__exp,axiom,
! [Ma,N_1,A_1] :
( ord_less_int(one_one_int,A_1)
=> ( power_power_int(A_1,Ma) = power_power_int(A_1,N_1)
<=> Ma = N_1 ) ),
file('theBenchmark.p',fact_491_power__inject__exp) ).
fof(fact_492_power__strict__increasing__iff,axiom,
! [X_2,Y_2,B_2] :
( ord_less_real(one_one_real,B_2)
=> ( ord_less_real(power_power_real(B_2,X_2),power_power_real(B_2,Y_2))
<=> ord_less_nat(X_2,Y_2) ) ),
file('theBenchmark.p',fact_492_power__strict__increasing__iff) ).
fof(fact_493_power__strict__increasing__iff,axiom,
! [X_2,Y_2,B_2] :
( ord_less_nat(one_one_nat,B_2)
=> ( ord_less_nat(power_power_nat(B_2,X_2),power_power_nat(B_2,Y_2))
<=> ord_less_nat(X_2,Y_2) ) ),
file('theBenchmark.p',fact_493_power__strict__increasing__iff) ).
fof(fact_494_power__strict__increasing__iff,axiom,
! [X_2,Y_2,B_2] :
( ord_less_int(one_one_int,B_2)
=> ( ord_less_int(power_power_int(B_2,X_2),power_power_int(B_2,Y_2))
<=> ord_less_nat(X_2,Y_2) ) ),
file('theBenchmark.p',fact_494_power__strict__increasing__iff) ).
fof(fact_495_power__less__imp__less__exp,axiom,
! [M_2,N_7,A_6] :
( ord_less_real(one_one_real,A_6)
=> ( ord_less_real(power_power_real(A_6,M_2),power_power_real(A_6,N_7))
=> ord_less_nat(M_2,N_7) ) ),
file('theBenchmark.p',fact_495_power__less__imp__less__exp) ).
fof(fact_496_power__less__imp__less__exp,axiom,
! [M_2,N_7,A_6] :
( ord_less_nat(one_one_nat,A_6)
=> ( ord_less_nat(power_power_nat(A_6,M_2),power_power_nat(A_6,N_7))
=> ord_less_nat(M_2,N_7) ) ),
file('theBenchmark.p',fact_496_power__less__imp__less__exp) ).
fof(fact_497_power__less__imp__less__exp,axiom,
! [M_2,N_7,A_6] :
( ord_less_int(one_one_int,A_6)
=> ( ord_less_int(power_power_int(A_6,M_2),power_power_int(A_6,N_7))
=> ord_less_nat(M_2,N_7) ) ),
file('theBenchmark.p',fact_497_power__less__imp__less__exp) ).
fof(fact_498_power__strict__increasing,axiom,
! [A_5,N_6,N_5] :
( ord_less_nat(N_6,N_5)
=> ( ord_less_real(one_one_real,A_5)
=> ord_less_real(power_power_real(A_5,N_6),power_power_real(A_5,N_5)) ) ),
file('theBenchmark.p',fact_498_power__strict__increasing) ).
fof(fact_499_power__strict__increasing,axiom,
! [A_5,N_6,N_5] :
( ord_less_nat(N_6,N_5)
=> ( ord_less_nat(one_one_nat,A_5)
=> ord_less_nat(power_power_nat(A_5,N_6),power_power_nat(A_5,N_5)) ) ),
file('theBenchmark.p',fact_499_power__strict__increasing) ).
fof(fact_500_power__strict__increasing,axiom,
! [A_5,N_6,N_5] :
( ord_less_nat(N_6,N_5)
=> ( ord_less_int(one_one_int,A_5)
=> ord_less_int(power_power_int(A_5,N_6),power_power_int(A_5,N_5)) ) ),
file('theBenchmark.p',fact_500_power__strict__increasing) ).
fof(fact_501_s,axiom,
zcong(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
file('theBenchmark.p',fact_501_s) ).
fof(fact_502_Euler_Oaux____1,axiom,
! [Y_1,X_1,P] :
( ~ zcong(X_1,zero_zero_int,P)
=> ( zcong(power_power_int(Y_1,number_number_of_nat(bit0(bit1(pls)))),X_1,P)
=> ~ dvd_dvd_int(P,Y_1) ) ),
file('theBenchmark.p',fact_502_Euler_Oaux____1) ).
fof(fact_503_int__pos__lt__two__imp__zero__or__one,axiom,
! [X_1] :
( is_int(X_1)
=> ( ord_less_eq_int(zero_zero_int,X_1)
=> ( 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_503_int__pos__lt__two__imp__zero__or__one) ).
fof(fact_504_even__power__le__0__imp__0,axiom,
! [A_4,K_3] :
( ord_less_eq_real(power_power_real(A_4,times_times_nat(number_number_of_nat(bit0(bit1(pls))),K_3)),zero_zero_real)
=> A_4 = zero_zero_real ),
file('theBenchmark.p',fact_504_even__power__le__0__imp__0) ).
fof(fact_505_even__power__le__0__imp__0,axiom,
! [A_4,K_3] :
( is_int(A_4)
=> ( ord_less_eq_int(power_power_int(A_4,times_times_nat(number_number_of_nat(bit0(bit1(pls))),K_3)),zero_zero_int)
=> A_4 = zero_zero_int ) ),
file('theBenchmark.p',fact_505_even__power__le__0__imp__0) ).
fof(fact_506_zprime__def,axiom,
! [P_1] :
( is_int(P_1)
=> ( zprime(P_1)
<=> ( ! [M_1] :
( is_int(M_1)
=> ( ( dvd_dvd_int(M_1,P_1)
& ord_less_eq_int(zero_zero_int,M_1) )
=> ( M_1 = P_1
| M_1 = one_one_int ) ) )
& ord_less_int(one_one_int,P_1) ) ) ),
file('theBenchmark.p',fact_506_zprime__def) ).
fof(fact_507__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)
=> ~ zcong(power_power_int(S1,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) ),
file('theBenchmark.p',fact_507__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_) ).
fof(fact_508__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096,axiom,
legendre(number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = one_one_int,
file('theBenchmark.p',fact_508__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096) ).
fof(fact_509_nat__zero__less__power__iff,axiom,
! [X_2,N_1] :
( ord_less_nat(zero_zero_nat,power_power_nat(X_2,N_1))
<=> ( N_1 = zero_zero_nat
| ord_less_nat(zero_zero_nat,X_2) ) ),
file('theBenchmark.p',fact_509_nat__zero__less__power__iff) ).
fof(fact_510_zero__less__power__nat__eq,axiom,
! [X_2,N_1] :
( ord_less_nat(zero_zero_nat,power_power_nat(X_2,N_1))
<=> ( ord_less_nat(zero_zero_nat,X_2)
| N_1 = zero_zero_nat ) ),
file('theBenchmark.p',fact_510_zero__less__power__nat__eq) ).
fof(fact_511_zero__less__power__nat__eq__number__of,axiom,
! [X_2,W_1] :
( ord_less_nat(zero_zero_nat,power_power_nat(X_2,number_number_of_nat(W_1)))
<=> ( ord_less_nat(zero_zero_nat,X_2)
| number_number_of_nat(W_1) = zero_zero_nat ) ),
file('theBenchmark.p',fact_511_zero__less__power__nat__eq__number__of) ).
fof(fact_512_nat__power__less__imp__less,axiom,
! [M,N,I] :
( ord_less_nat(zero_zero_nat,I)
=> ( ord_less_nat(power_power_nat(I,M),power_power_nat(I,N))
=> ord_less_nat(M,N) ) ),
file('theBenchmark.p',fact_512_nat__power__less__imp__less) ).
fof(fact_513_rel__simps_I47_J,axiom,
! [K_1] :
( is_int(K_1)
=> ( bit1(K_1) = min
<=> K_1 = min ) ),
file('theBenchmark.p',fact_513_rel__simps_I47_J) ).
fof(fact_514_rel__simps_I43_J,axiom,
! [L_1] :
( is_int(L_1)
=> ( min = bit1(L_1)
<=> min = L_1 ) ),
file('theBenchmark.p',fact_514_rel__simps_I43_J) ).
fof(fact_515_Bit1__Min,axiom,
bit1(min) = min,
file('theBenchmark.p',fact_515_Bit1__Min) ).
fof(fact_516_rel__simps_I37_J,axiom,
pls != min,
file('theBenchmark.p',fact_516_rel__simps_I37_J) ).
fof(fact_517_rel__simps_I40_J,axiom,
min != pls,
file('theBenchmark.p',fact_517_rel__simps_I40_J) ).
fof(fact_518_rel__simps_I45_J,axiom,
! [K] : bit0(K) != min,
file('theBenchmark.p',fact_518_rel__simps_I45_J) ).
fof(fact_519_rel__simps_I42_J,axiom,
! [L] : min != bit0(L),
file('theBenchmark.p',fact_519_rel__simps_I42_J) ).
fof(fact_520_rel__simps_I7_J,axiom,
~ ord_less_int(min,min),
file('theBenchmark.p',fact_520_rel__simps_I7_J) ).
fof(fact_521_rel__simps_I24_J,axiom,
ord_less_eq_int(min,min),
file('theBenchmark.p',fact_521_rel__simps_I24_J) ).
fof(fact_522_not__real__square__gt__zero,axiom,
! [X_2] :
( ~ ord_less_real(zero_zero_real,times_times_real(X_2,X_2))
<=> X_2 = zero_zero_real ),
file('theBenchmark.p',fact_522_not__real__square__gt__zero) ).
fof(fact_523_rel__simps_I13_J,axiom,
! [K_1] :
( ord_less_int(bit1(K_1),min)
<=> ord_less_int(K_1,min) ),
file('theBenchmark.p',fact_523_rel__simps_I13_J) ).
fof(fact_524_rel__simps_I9_J,axiom,
! [K_1] :
( ord_less_int(min,bit1(K_1))
<=> ord_less_int(min,K_1) ),
file('theBenchmark.p',fact_524_rel__simps_I9_J) ).
fof(fact_525_rel__simps_I3_J,axiom,
~ ord_less_int(pls,min),
file('theBenchmark.p',fact_525_rel__simps_I3_J) ).
fof(fact_526_rel__simps_I6_J,axiom,
ord_less_int(min,pls),
file('theBenchmark.p',fact_526_rel__simps_I6_J) ).
fof(fact_527_rel__simps_I8_J,axiom,
! [K_1] :
( ord_less_int(min,bit0(K_1))
<=> ord_less_int(min,K_1) ),
file('theBenchmark.p',fact_527_rel__simps_I8_J) ).
fof(fact_528_bin__less__0__simps_I2_J,axiom,
ord_less_int(min,zero_zero_int),
file('theBenchmark.p',fact_528_bin__less__0__simps_I2_J) ).
fof(fact_529_rel__simps_I30_J,axiom,
! [K_1] :
( ord_less_eq_int(bit1(K_1),min)
<=> ord_less_eq_int(K_1,min) ),
file('theBenchmark.p',fact_529_rel__simps_I30_J) ).
fof(fact_530_rel__simps_I26_J,axiom,
! [K_1] :
( ord_less_eq_int(min,bit1(K_1))
<=> ord_less_eq_int(min,K_1) ),
file('theBenchmark.p',fact_530_rel__simps_I26_J) ).
fof(fact_531_rel__simps_I20_J,axiom,
~ ord_less_eq_int(pls,min),
file('theBenchmark.p',fact_531_rel__simps_I20_J) ).
fof(fact_532_rel__simps_I23_J,axiom,
ord_less_eq_int(min,pls),
file('theBenchmark.p',fact_532_rel__simps_I23_J) ).
fof(fact_533_rel__simps_I28_J,axiom,
! [K_1] :
( ord_less_eq_int(bit0(K_1),min)
<=> ord_less_eq_int(K_1,min) ),
file('theBenchmark.p',fact_533_rel__simps_I28_J) ).
fof(fact_534_eq__number__of__Pls__Min,axiom,
number_number_of_int(pls) != number_number_of_int(min),
file('theBenchmark.p',fact_534_eq__number__of__Pls__Min) ).
fof(fact_535_power__dvd__imp__le,axiom,
! [I,M,N] :
( dvd_dvd_nat(power_power_nat(I,M),power_power_nat(I,N))
=> ( ord_less_nat(one_one_nat,I)
=> ord_less_eq_nat(M,N) ) ),
file('theBenchmark.p',fact_535_power__dvd__imp__le) ).
fof(fact_536_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [X_5] : power_power_real(X_5,zero_zero_nat) = one_one_real,
file('theBenchmark.p',fact_536_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_537_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [X_5] : power_power_nat(X_5,zero_zero_nat) = one_one_nat,
file('theBenchmark.p',fact_537_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_538_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [X_5] : power_power_int(X_5,zero_zero_nat) = one_one_int,
file('theBenchmark.p',fact_538_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_539_power__0,axiom,
! [A_3] : power_power_real(A_3,zero_zero_nat) = one_one_real,
file('theBenchmark.p',fact_539_power__0) ).
fof(fact_540_power__0,axiom,
! [A_3] : power_power_nat(A_3,zero_zero_nat) = one_one_nat,
file('theBenchmark.p',fact_540_power__0) ).
fof(fact_541_power__0,axiom,
! [A_3] : power_power_int(A_3,zero_zero_nat) = one_one_int,
file('theBenchmark.p',fact_541_power__0) ).
fof(fact_542_nat__number__of__Pls,axiom,
number_number_of_nat(pls) = zero_zero_nat,
file('theBenchmark.p',fact_542_nat__number__of__Pls) ).
fof(fact_543_semiring__norm_I113_J,axiom,
zero_zero_nat = number_number_of_nat(pls),
file('theBenchmark.p',fact_543_semiring__norm_I113_J) ).
fof(fact_544_rel__simps_I25_J,axiom,
! [K_1] :
( ord_less_eq_int(min,bit0(K_1))
<=> ord_less_int(min,K_1) ),
file('theBenchmark.p',fact_544_rel__simps_I25_J) ).
fof(fact_545_rel__simps_I11_J,axiom,
! [K_1] :
( ord_less_int(bit0(K_1),min)
<=> ord_less_eq_int(K_1,min) ),
file('theBenchmark.p',fact_545_rel__simps_I11_J) ).
fof(fact_546_pos__zmult__eq__1__iff__lemma,axiom,
! [M,N] :
( is_int(M)
=> ( times_times_int(M,N) = one_one_int
=> ( M = number_number_of_int(min)
| M = one_one_int ) ) ),
file('theBenchmark.p',fact_546_pos__zmult__eq__1__iff__lemma) ).
fof(fact_547_zmult__eq__1__iff,axiom,
! [Ma,N_1] :
( ( is_int(N_1)
& is_int(Ma) )
=> ( times_times_int(Ma,N_1) = one_one_int
<=> ( ( N_1 = number_number_of_int(min)
& Ma = number_number_of_int(min) )
| ( N_1 = one_one_int
& Ma = one_one_int ) ) ) ),
file('theBenchmark.p',fact_547_zmult__eq__1__iff) ).
fof(fact_548_one__less__power,axiom,
! [N_4,A_2] :
( ord_less_real(one_one_real,A_2)
=> ( ord_less_nat(zero_zero_nat,N_4)
=> ord_less_real(one_one_real,power_power_real(A_2,N_4)) ) ),
file('theBenchmark.p',fact_548_one__less__power) ).
fof(fact_549_one__less__power,axiom,
! [N_4,A_2] :
( ord_less_nat(one_one_nat,A_2)
=> ( ord_less_nat(zero_zero_nat,N_4)
=> ord_less_nat(one_one_nat,power_power_nat(A_2,N_4)) ) ),
file('theBenchmark.p',fact_549_one__less__power) ).
fof(fact_550_one__less__power,axiom,
! [N_4,A_2] :
( ord_less_int(one_one_int,A_2)
=> ( ord_less_nat(zero_zero_nat,N_4)
=> ord_less_int(one_one_int,power_power_int(A_2,N_4)) ) ),
file('theBenchmark.p',fact_550_one__less__power) ).
fof(fact_551_dvd__power,axiom,
! [X_4,N_3] :
( ( X_4 = one_one_nat
| ord_less_nat(zero_zero_nat,N_3) )
=> dvd_dvd_nat(X_4,power_power_nat(X_4,N_3)) ),
file('theBenchmark.p',fact_551_dvd__power) ).
fof(fact_552_dvd__power,axiom,
! [X_4,N_3] :
( ( X_4 = one_one_int
| ord_less_nat(zero_zero_nat,N_3) )
=> dvd_dvd_int(X_4,power_power_int(X_4,N_3)) ),
file('theBenchmark.p',fact_552_dvd__power) ).
fof(fact_553_dvd__power,axiom,
! [X_4,N_3] :
( ( X_4 = one_one_real
| ord_less_nat(zero_zero_nat,N_3) )
=> dvd_dvd_real(X_4,power_power_real(X_4,N_3)) ),
file('theBenchmark.p',fact_553_dvd__power) ).
fof(fact_554_less__0__number__of,axiom,
! [V_3] :
( ord_less_nat(zero_zero_nat,number_number_of_nat(V_3))
<=> ord_less_int(pls,V_3) ),
file('theBenchmark.p',fact_554_less__0__number__of) ).
fof(fact_555_eq__number__of__0,axiom,
! [V_3] :
( number_number_of_nat(V_3) = zero_zero_nat
<=> ord_less_eq_int(V_3,pls) ),
file('theBenchmark.p',fact_555_eq__number__of__0) ).
fof(fact_556_eq__0__number__of,axiom,
! [V_3] :
( zero_zero_nat = number_number_of_nat(V_3)
<=> ord_less_eq_int(V_3,pls) ),
file('theBenchmark.p',fact_556_eq__0__number__of) ).
fof(fact_557_zcong__sym,axiom,
! [A_1,B_2,Ma] :
( zcong(A_1,B_2,Ma)
<=> zcong(B_2,A_1,Ma) ),
file('theBenchmark.p',fact_557_zcong__sym) ).
fof(fact_558_zcong__refl,axiom,
! [K,M] : zcong(K,K,M),
file('theBenchmark.p',fact_558_zcong__refl) ).
fof(fact_559_zcong__trans,axiom,
! [C_1,A,B_1,M] :
( zcong(A,B_1,M)
=> ( zcong(B_1,C_1,M)
=> zcong(A,C_1,M) ) ),
file('theBenchmark.p',fact_559_zcong__trans) ).
fof(fact_560_pos2,axiom,
ord_less_nat(zero_zero_nat,number_number_of_nat(bit0(bit1(pls)))),
file('theBenchmark.p',fact_560_pos2) ).
fof(fact_561_nat__number__of__mult__left,axiom,
! [V_2,K,V_1] :
( ( ~ ord_less_int(V_1,pls)
=> times_times_nat(number_number_of_nat(V_1),times_times_nat(number_number_of_nat(V_2),K)) = times_times_nat(number_number_of_nat(times_times_int(V_1,V_2)),K) )
& ( ord_less_int(V_1,pls)
=> times_times_nat(number_number_of_nat(V_1),times_times_nat(number_number_of_nat(V_2),K)) = zero_zero_nat ) ),
file('theBenchmark.p',fact_561_nat__number__of__mult__left) ).
fof(fact_562_mult__nat__number__of,axiom,
! [V_2,V_1] :
( ( ~ ord_less_int(V_1,pls)
=> times_times_nat(number_number_of_nat(V_1),number_number_of_nat(V_2)) = number_number_of_nat(times_times_int(V_1,V_2)) )
& ( ord_less_int(V_1,pls)
=> times_times_nat(number_number_of_nat(V_1),number_number_of_nat(V_2)) = zero_zero_nat ) ),
file('theBenchmark.p',fact_562_mult__nat__number__of) ).
fof(fact_563_order__le__neq__implies__less,axiom,
! [X_3,Y_3] :
( ord_less_eq_real(X_3,Y_3)
=> ( X_3 != Y_3
=> ord_less_real(X_3,Y_3) ) ),
file('theBenchmark.p',fact_563_order__le__neq__implies__less) ).
fof(fact_564_order__le__neq__implies__less,axiom,
! [X_3,Y_3] :
( ord_less_eq_nat(X_3,Y_3)
=> ( X_3 != Y_3
=> ord_less_nat(X_3,Y_3) ) ),
file('theBenchmark.p',fact_564_order__le__neq__implies__less) ).
fof(fact_565_order__le__neq__implies__less,axiom,
! [X_3,Y_3] :
( ( is_int(Y_3)
& is_int(X_3) )
=> ( ord_less_eq_int(X_3,Y_3)
=> ( X_3 != Y_3
=> ord_less_int(X_3,Y_3) ) ) ),
file('theBenchmark.p',fact_565_order__le__neq__implies__less) ).
fof(fact_566_Euler_Oaux2,axiom,
! [B_1,A,C_1] :
( ord_less_int(A,C_1)
=> ( ord_less_int(B_1,C_1)
=> ( ord_less_eq_int(B_1,A)
| ord_less_eq_int(A,B_1) ) ) ),
file('theBenchmark.p',fact_566_Euler_Oaux2) ).
fof(fact_567_IntPrimes_Ozcong__zero,axiom,
! [A_1,B_2] :
( ( is_int(B_2)
& is_int(A_1) )
=> ( zcong(A_1,B_2,zero_zero_int)
<=> A_1 = B_2 ) ),
file('theBenchmark.p',fact_567_IntPrimes_Ozcong__zero) ).
fof(fact_568_zcong__1,axiom,
! [A,B_1] : zcong(A,B_1,one_one_int),
file('theBenchmark.p',fact_568_zcong__1) ).
fof(fact_569_zcong__zmult,axiom,
! [C_1,D_1,A,B_1,M] :
( zcong(A,B_1,M)
=> ( zcong(C_1,D_1,M)
=> zcong(times_times_int(A,C_1),times_times_int(B_1,D_1),M) ) ),
file('theBenchmark.p',fact_569_zcong__zmult) ).
fof(fact_570_zcong__scalar2,axiom,
! [K,A,B_1,M] :
( zcong(A,B_1,M)
=> zcong(times_times_int(K,A),times_times_int(K,B_1),M) ),
file('theBenchmark.p',fact_570_zcong__scalar2) ).
fof(fact_571_zcong__scalar,axiom,
! [K,A,B_1,M] :
( zcong(A,B_1,M)
=> zcong(times_times_int(A,K),times_times_int(B_1,K),M) ),
file('theBenchmark.p',fact_571_zcong__scalar) ).
fof(fact_572_zcong__zmult__self,axiom,
! [A,M,B_1] : zcong(times_times_int(A,M),times_times_int(B_1,M),M),
file('theBenchmark.p',fact_572_zcong__zmult__self) ).
fof(fact_573_zcong__zadd,axiom,
! [C_1,D_1,A,B_1,M] :
( zcong(A,B_1,M)
=> ( zcong(C_1,D_1,M)
=> zcong(plus_plus_int(A,C_1),plus_plus_int(B_1,D_1),M) ) ),
file('theBenchmark.p',fact_573_zcong__zadd) ).
fof(fact_574_power__m1__even,axiom,
! [N_2] : power_power_real(number267125858f_real(min),times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_2)) = one_one_real,
file('theBenchmark.p',fact_574_power__m1__even) ).
fof(fact_575_power__m1__even,axiom,
! [N_2] : power_power_int(number_number_of_int(min),times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_2)) = one_one_int,
file('theBenchmark.p',fact_575_power__m1__even) ).
fof(fact_576_power__eq__0__iff__number__of,axiom,
! [A_1,W_1] :
( power_power_real(A_1,number_number_of_nat(W_1)) = zero_zero_real
<=> ( number_number_of_nat(W_1) != zero_zero_nat
& A_1 = zero_zero_real ) ),
file('theBenchmark.p',fact_576_power__eq__0__iff__number__of) ).
fof(fact_577_power__eq__0__iff__number__of,axiom,
! [A_1,W_1] :
( power_power_nat(A_1,number_number_of_nat(W_1)) = zero_zero_nat
<=> ( number_number_of_nat(W_1) != zero_zero_nat
& A_1 = zero_zero_nat ) ),
file('theBenchmark.p',fact_577_power__eq__0__iff__number__of) ).
fof(fact_578_power__eq__0__iff__number__of,axiom,
! [A_1,W_1] :
( is_int(A_1)
=> ( power_power_int(A_1,number_number_of_nat(W_1)) = zero_zero_int
<=> ( number_number_of_nat(W_1) != zero_zero_nat
& A_1 = zero_zero_int ) ) ),
file('theBenchmark.p',fact_578_power__eq__0__iff__number__of) ).
fof(fact_579_zcong__not,axiom,
! [B_1,M,A] :
( ord_less_int(zero_zero_int,A)
=> ( ord_less_int(A,M)
=> ( ord_less_int(zero_zero_int,B_1)
=> ( ord_less_int(B_1,A)
=> ~ zcong(A,B_1,M) ) ) ) ),
file('theBenchmark.p',fact_579_zcong__not) ).
fof(fact_580_zcong__iff__lin,axiom,
! [A_1,B_2,Ma] :
( is_int(B_2)
=> ( zcong(A_1,B_2,Ma)
<=> ? [K_2] :
( B_2 = plus_plus_int(A_1,times_times_int(Ma,K_2))
& is_int(K_2) ) ) ),
file('theBenchmark.p',fact_580_zcong__iff__lin) ).
fof(fact_581_power__0__left__number__of,axiom,
! [W_3] :
( ( number_number_of_nat(W_3) != zero_zero_nat
=> power_power_real(zero_zero_real,number_number_of_nat(W_3)) = zero_zero_real )
& ( number_number_of_nat(W_3) = zero_zero_nat
=> power_power_real(zero_zero_real,number_number_of_nat(W_3)) = one_one_real ) ),
file('theBenchmark.p',fact_581_power__0__left__number__of) ).
fof(fact_582_power__0__left__number__of,axiom,
! [W_3] :
( ( number_number_of_nat(W_3) != zero_zero_nat
=> power_power_nat(zero_zero_nat,number_number_of_nat(W_3)) = zero_zero_nat )
& ( number_number_of_nat(W_3) = zero_zero_nat
=> power_power_nat(zero_zero_nat,number_number_of_nat(W_3)) = one_one_nat ) ),
file('theBenchmark.p',fact_582_power__0__left__number__of) ).
fof(fact_583_power__0__left__number__of,axiom,
! [W_3] :
( ( number_number_of_nat(W_3) != zero_zero_nat
=> power_power_int(zero_zero_int,number_number_of_nat(W_3)) = zero_zero_int )
& ( number_number_of_nat(W_3) = zero_zero_nat
=> power_power_int(zero_zero_int,number_number_of_nat(W_3)) = one_one_int ) ),
file('theBenchmark.p',fact_583_power__0__left__number__of) ).
fof(fact_584_zcong__zless__imp__eq,axiom,
! [B_1,M,A] :
( ( is_int(A)
& is_int(B_1) )
=> ( ord_less_eq_int(zero_zero_int,A)
=> ( ord_less_int(A,M)
=> ( ord_less_eq_int(zero_zero_int,B_1)
=> ( ord_less_int(B_1,M)
=> ( zcong(A,B_1,M)
=> A = B_1 ) ) ) ) ) ),
file('theBenchmark.p',fact_584_zcong__zless__imp__eq) ).
fof(fact_585_zcong__zless__0,axiom,
! [M,A] :
( is_int(A)
=> ( ord_less_eq_int(zero_zero_int,A)
=> ( ord_less_int(A,M)
=> ( zcong(A,zero_zero_int,M)
=> A = zero_zero_int ) ) ) ),
file('theBenchmark.p',fact_585_zcong__zless__0) ).
fof(fact_586_zprime__zdvd__zmult,axiom,
! [N,P,M] :
( ord_less_eq_int(zero_zero_int,M)
=> ( zprime(P)
=> ( dvd_dvd_int(P,times_times_int(M,N))
=> ( dvd_dvd_int(P,N)
| dvd_dvd_int(P,M) ) ) ) ),
file('theBenchmark.p',fact_586_zprime__zdvd__zmult) ).
fof(fact_587__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096,axiom,
quadRes(plus_plus_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_587__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096) ).
fof(fact_588__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096,axiom,
dvd_dvd_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min))),
file('theBenchmark.p',fact_588__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096) ).
fof(fact_589_neg__one__power__eq__mod__m,axiom,
! [J,K,M] :
( ord_less_int(number_number_of_int(bit0(bit1(pls))),M)
=> ( zcong(power_power_int(number_number_of_int(min),J),power_power_int(number_number_of_int(min),K),M)
=> power_power_int(number_number_of_int(min),J) = power_power_int(number_number_of_int(min),K) ) ),
file('theBenchmark.p',fact_589_neg__one__power__eq__mod__m) ).
fof(fact_590__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096,axiom,
minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
file('theBenchmark.p',fact_590__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
fof(fact_591__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N,axiom,
( ~ quadRes(plus_plus_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),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) != one_one_int ),
file('theBenchmark.p',fact_591__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N) ).
fof(fact_592_zcong__zdiff,axiom,
! [C_1,D_1,A,B_1,M] :
( zcong(A,B_1,M)
=> ( zcong(C_1,D_1,M)
=> zcong(minus_minus_int(A,C_1),minus_minus_int(B_1,D_1),M) ) ),
file('theBenchmark.p',fact_592_zcong__zdiff) ).
fof(fact_593_diff__bin__simps_I1_J,axiom,
! [K] :
( is_int(K)
=> minus_minus_int(K,pls) = K ),
file('theBenchmark.p',fact_593_diff__bin__simps_I1_J) ).
fof(fact_594_diff__bin__simps_I7_J,axiom,
! [K,L] : minus_minus_int(bit0(K),bit0(L)) = bit0(minus_minus_int(K,L)),
file('theBenchmark.p',fact_594_diff__bin__simps_I7_J) ).
fof(fact_595_zdiff__zmult__distrib,axiom,
! [Z1,Z2,W] : times_times_int(minus_minus_int(Z1,Z2),W) = minus_minus_int(times_times_int(Z1,W),times_times_int(Z2,W)),
file('theBenchmark.p',fact_595_zdiff__zmult__distrib) ).
fof(fact_596_zdiff__zmult__distrib2,axiom,
! [W,Z1,Z2] : times_times_int(W,minus_minus_int(Z1,Z2)) = minus_minus_int(times_times_int(W,Z1),times_times_int(W,Z2)),
file('theBenchmark.p',fact_596_zdiff__zmult__distrib2) ).
fof(fact_597_zdvd__zdiffD,axiom,
! [K,M,N] :
( dvd_dvd_int(K,minus_minus_int(M,N))
=> ( dvd_dvd_int(K,N)
=> dvd_dvd_int(K,M) ) ),
file('theBenchmark.p',fact_597_zdvd__zdiffD) ).
fof(fact_598_number__of__diff,axiom,
! [V,W_2] : number_number_of_int(minus_minus_int(V,W_2)) = minus_minus_int(number_number_of_int(V),number_number_of_int(W_2)),
file('theBenchmark.p',fact_598_number__of__diff) ).
fof(fact_599_diff__bin__simps_I9_J,axiom,
! [K,L] : minus_minus_int(bit1(K),bit0(L)) = bit1(minus_minus_int(K,L)),
file('theBenchmark.p',fact_599_diff__bin__simps_I9_J) ).
fof(fact_600_diff__bin__simps_I10_J,axiom,
! [K,L] : minus_minus_int(bit1(K),bit1(L)) = bit0(minus_minus_int(K,L)),
file('theBenchmark.p',fact_600_diff__bin__simps_I10_J) ).
fof(fact_601_diff__bin__simps_I3_J,axiom,
! [L] : minus_minus_int(pls,bit0(L)) = bit0(minus_minus_int(pls,L)),
file('theBenchmark.p',fact_601_diff__bin__simps_I3_J) ).
fof(fact_602_less__bin__lemma,axiom,
! [K_1,L_1] :
( ord_less_int(K_1,L_1)
<=> ord_less_int(minus_minus_int(K_1,L_1),zero_zero_int) ),
file('theBenchmark.p',fact_602_less__bin__lemma) ).
fof(fact_603_xzgcda__linear__aux1,axiom,
! [A,R_1,B_1,M,C_1,D_1,N] : plus_plus_int(times_times_int(minus_minus_int(A,times_times_int(R_1,B_1)),M),times_times_int(minus_minus_int(C_1,times_times_int(R_1,D_1)),N)) = minus_minus_int(plus_plus_int(times_times_int(A,M),times_times_int(C_1,N)),times_times_int(R_1,plus_plus_int(times_times_int(B_1,M),times_times_int(D_1,N)))),
file('theBenchmark.p',fact_603_xzgcda__linear__aux1) ).
fof(fact_604_zcong__def,axiom,
! [A_1,B_2,Ma] :
( zcong(A_1,B_2,Ma)
<=> dvd_dvd_int(Ma,minus_minus_int(A_1,B_2)) ),
file('theBenchmark.p',fact_604_zcong__def) ).
fof(fact_605_Euler_Oaux1,axiom,
! [A,X_1] :
( is_int(X_1)
=> ( ord_less_int(zero_zero_int,X_1)
=> ( ord_less_int(X_1,A)
=> ( X_1 != minus_minus_int(A,one_one_int)
=> ord_less_int(X_1,minus_minus_int(A,one_one_int)) ) ) ) ),
file('theBenchmark.p',fact_605_Euler_Oaux1) ).
fof(fact_606_zle__diff1__eq,axiom,
! [W_1,Z_1] :
( ord_less_eq_int(W_1,minus_minus_int(Z_1,one_one_int))
<=> ord_less_int(W_1,Z_1) ),
file('theBenchmark.p',fact_606_zle__diff1__eq) ).
fof(fact_607_diff__bin__simps_I4_J,axiom,
! [L] : minus_minus_int(pls,bit1(L)) = bit1(minus_minus_int(min,L)),
file('theBenchmark.p',fact_607_diff__bin__simps_I4_J) ).
fof(fact_608_diff__bin__simps_I6_J,axiom,
! [L] : minus_minus_int(min,bit1(L)) = bit0(minus_minus_int(min,L)),
file('theBenchmark.p',fact_608_diff__bin__simps_I6_J) ).
fof(fact_609_diff__bin__simps_I5_J,axiom,
! [L] : minus_minus_int(min,bit0(L)) = bit1(minus_minus_int(min,L)),
file('theBenchmark.p',fact_609_diff__bin__simps_I5_J) ).
fof(fact_610_inv__not__p__minus__1__aux,axiom,
! [A_1,P_1] :
( zcong(times_times_int(A_1,minus_minus_int(P_1,one_one_int)),one_one_int,P_1)
<=> zcong(A_1,minus_minus_int(P_1,one_one_int),P_1) ),
file('theBenchmark.p',fact_610_inv__not__p__minus__1__aux) ).
fof(fact_611_mult__sum2sq,axiom,
! [A,B_1,P,Q] : times_times_int(twoSqu140629262sum2sq(product_Pair_int_int(A,B_1)),twoSqu140629262sum2sq(product_Pair_int_int(P,Q))) = twoSqu140629262sum2sq(product_Pair_int_int(plus_plus_int(times_times_int(A,P),times_times_int(B_1,Q)),minus_minus_int(times_times_int(A,Q),times_times_int(B_1,P)))),
file('theBenchmark.p',fact_611_mult__sum2sq) ).
fof(fact_612_zcong__square,axiom,
! [A,P] :
( zprime(P)
=> ( ord_less_int(zero_zero_int,A)
=> ( zcong(times_times_int(A,A),one_one_int,P)
=> ( zcong(A,minus_minus_int(P,one_one_int),P)
| zcong(A,one_one_int,P) ) ) ) ),
file('theBenchmark.p',fact_612_zcong__square) ).
fof(fact_613_zcong__square__zless,axiom,
! [A,P] :
( is_int(A)
=> ( zprime(P)
=> ( ord_less_int(zero_zero_int,A)
=> ( ord_less_int(A,P)
=> ( zcong(times_times_int(A,A),one_one_int,P)
=> ( A = minus_minus_int(P,one_one_int)
| A = one_one_int ) ) ) ) ) ),
file('theBenchmark.p',fact_613_zcong__square__zless) ).
fof(fact_614_zspecial__product,axiom,
! [A,B_1] : times_times_int(plus_plus_int(A,B_1),minus_minus_int(A,B_1)) = minus_minus_int(power_power_int(A,number_number_of_nat(bit0(bit1(pls)))),power_power_int(B_1,number_number_of_nat(bit0(bit1(pls))))),
file('theBenchmark.p',fact_614_zspecial__product) ).
fof(fact_615_zdiff__power2,axiom,
! [A,B_1] : power_power_int(minus_minus_int(A,B_1),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(minus_minus_int(power_power_int(A,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),A),B_1)),power_power_int(B_1,number_number_of_nat(bit0(bit1(pls))))),
file('theBenchmark.p',fact_615_zdiff__power2) ).
fof(fact_616_zdiff__power3,axiom,
! [A,B_1] : power_power_int(minus_minus_int(A,B_1),number_number_of_nat(bit1(bit1(pls)))) = minus_minus_int(plus_plus_int(minus_minus_int(power_power_int(A,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(A,number_number_of_nat(bit0(bit1(pls))))),B_1)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),A),power_power_int(B_1,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(B_1,number_number_of_nat(bit1(bit1(pls))))),
file('theBenchmark.p',fact_616_zdiff__power3) ).
fof(fact_617_neg__one__power,axiom,
! [N] :
( power_power_int(number_number_of_int(min),N) = number_number_of_int(min)
| power_power_int(number_number_of_int(min),N) = one_one_int ),
file('theBenchmark.p',fact_617_neg__one__power) ).
fof(fact_618_Legendre__1mod4,axiom,
! [M] :
( zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),M),one_one_int))
=> legendre(number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),M),one_one_int)) = one_one_int ),
file('theBenchmark.p',fact_618_Legendre__1mod4) ).
fof(fact_619_one__not__neg__one__mod__m,axiom,
! [M] :
( ord_less_int(number_number_of_int(bit0(bit1(pls))),M)
=> ~ zcong(one_one_int,number_number_of_int(min),M) ),
file('theBenchmark.p',fact_619_one__not__neg__one__mod__m) ).
fof(fact_620_zcong__neg__1__impl__ne__1,axiom,
! [X_1,P] :
( ord_less_int(number_number_of_int(bit0(bit1(pls))),P)
=> ( zcong(X_1,number_number_of_int(min),P)
=> ~ zcong(X_1,one_one_int,P) ) ),
file('theBenchmark.p',fact_620_zcong__neg__1__impl__ne__1) ).
fof(fact_621_Legendre__def,axiom,
! [A,P] :
( ( ~ zcong(A,zero_zero_int,P)
=> ( ( ~ quadRes(P,A)
=> legendre(A,P) = number_number_of_int(min) )
& ( quadRes(P,A)
=> legendre(A,P) = one_one_int ) ) )
& ( zcong(A,zero_zero_int,P)
=> legendre(A,P) = zero_zero_int ) ),
file('theBenchmark.p',fact_621_Legendre__def) ).
fof(fact_622_divides__cases,axiom,
! [N,M] :
( dvd_dvd_nat(N,M)
=> ( ord_less_eq_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls))),N),M)
| M = N
| M = zero_zero_nat ) ),
file('theBenchmark.p',fact_622_divides__cases) ).
fof(fact_623_divides__antisym,axiom,
! [X_2,Y_2] :
( ( dvd_dvd_nat(Y_2,X_2)
& dvd_dvd_nat(X_2,Y_2) )
<=> X_2 = Y_2 ),
file('theBenchmark.p',fact_623_divides__antisym) ).
fof(fact_624_zcong__eq__trans,axiom,
! [D_1,C_1,A,B_1,M] :
( zcong(A,B_1,M)
=> ( B_1 = C_1
=> ( zcong(C_1,D_1,M)
=> zcong(A,D_1,M) ) ) ),
file('theBenchmark.p',fact_624_zcong__eq__trans) ).
fof(fact_625_mult__eq__if,axiom,
! [N,M] :
( ( M != zero_zero_nat
=> times_times_nat(M,N) = plus_plus_nat(N,times_times_nat(minus_minus_nat(M,one_one_nat),N)) )
& ( M = zero_zero_nat
=> times_times_nat(M,N) = zero_zero_nat ) ),
file('theBenchmark.p',fact_625_mult__eq__if) ).
fof(fact_626_power__eq__if,axiom,
! [P,M] :
( ( M != zero_zero_nat
=> power_power_nat(P,M) = times_times_nat(P,power_power_nat(P,minus_minus_nat(M,one_one_nat))) )
& ( M = zero_zero_nat
=> power_power_nat(P,M) = one_one_nat ) ),
file('theBenchmark.p',fact_626_power__eq__if) ).
fof(fact_627_diff__square,axiom,
! [X_1,Y_1] : minus_minus_nat(power_power_nat(X_1,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(Y_1,number_number_of_nat(bit0(bit1(pls))))) = times_times_nat(plus_plus_nat(X_1,Y_1),minus_minus_nat(X_1,Y_1)),
file('theBenchmark.p',fact_627_diff__square) ).
fof(fact_628_divides__add__revr,axiom,
! [B_1,D_1,A] :
( dvd_dvd_nat(D_1,A)
=> ( dvd_dvd_nat(D_1,plus_plus_nat(A,B_1))
=> dvd_dvd_nat(D_1,B_1) ) ),
file('theBenchmark.p',fact_628_divides__add__revr) ).
fof(fact_629_divides__mul__l,axiom,
! [C_1,A,B_1] :
( dvd_dvd_nat(A,B_1)
=> dvd_dvd_nat(times_times_nat(C_1,A),times_times_nat(C_1,B_1)) ),
file('theBenchmark.p',fact_629_divides__mul__l) ).
fof(fact_630_divides__mul__r,axiom,
! [C_1,A,B_1] :
( dvd_dvd_nat(A,B_1)
=> dvd_dvd_nat(times_times_nat(A,C_1),times_times_nat(B_1,C_1)) ),
file('theBenchmark.p',fact_630_divides__mul__r) ).
fof(fact_631_zcong__id,axiom,
! [M] : zcong(M,zero_zero_int,M),
file('theBenchmark.p',fact_631_zcong__id) ).
fof(fact_632_nat__mult__eq__one,axiom,
! [N_1,Ma] :
( times_times_nat(N_1,Ma) = one_one_nat
<=> ( Ma = one_one_nat
& N_1 = one_one_nat ) ),
file('theBenchmark.p',fact_632_nat__mult__eq__one) ).
fof(fact_633_Int2_Oaux1,axiom,
! [A,B_1,C_1] :
( is_int(A)
=> ( minus_minus_int(A,B_1) = C_1
=> A = plus_plus_int(C_1,B_1) ) ),
file('theBenchmark.p',fact_633_Int2_Oaux1) ).
fof(fact_634_zcong__zmult__prop2,axiom,
! [C,D,A_1,B_2,Ma] :
( zcong(A_1,B_2,Ma)
=> ( zcong(C,times_times_int(D,A_1),Ma)
<=> zcong(C,times_times_int(D,B_2),Ma) ) ),
file('theBenchmark.p',fact_634_zcong__zmult__prop2) ).
fof(fact_635_zcong__zmult__prop1,axiom,
! [C,D,A_1,B_2,Ma] :
( zcong(A_1,B_2,Ma)
=> ( zcong(C,times_times_int(A_1,D),Ma)
<=> zcong(C,times_times_int(B_2,D),Ma) ) ),
file('theBenchmark.p',fact_635_zcong__zmult__prop1) ).
fof(fact_636_zcong__shift,axiom,
! [C_1,A,B_1,M] :
( zcong(A,B_1,M)
=> zcong(plus_plus_int(A,C_1),plus_plus_int(B_1,C_1),M) ),
file('theBenchmark.p',fact_636_zcong__shift) ).
fof(fact_637_nat__power__eq__0__iff,axiom,
! [Ma,N_1] :
( power_power_nat(Ma,N_1) = zero_zero_nat
<=> ( Ma = zero_zero_nat
& N_1 != zero_zero_nat ) ),
file('theBenchmark.p',fact_637_nat__power__eq__0__iff) ).
fof(fact_638_divides__exp,axiom,
! [N,X_1,Y_1] :
( dvd_dvd_nat(X_1,Y_1)
=> dvd_dvd_nat(power_power_nat(X_1,N),power_power_nat(Y_1,N)) ),
file('theBenchmark.p',fact_638_divides__exp) ).
fof(fact_639_zcong__zpower,axiom,
! [Z,X_1,Y_1,M] :
( zcong(X_1,Y_1,M)
=> zcong(power_power_int(X_1,Z),power_power_int(Y_1,Z),M) ),
file('theBenchmark.p',fact_639_zcong__zpower) ).
fof(fact_640_divides__ge,axiom,
! [A,B_1] :
( dvd_dvd_nat(A,B_1)
=> ( ord_less_eq_nat(A,B_1)
| B_1 = zero_zero_nat ) ),
file('theBenchmark.p',fact_640_divides__ge) ).
fof(fact_641_nat__mult__dvd__cancel__disj_H,axiom,
! [Ma,K_1,N_1] :
( dvd_dvd_nat(times_times_nat(Ma,K_1),times_times_nat(N_1,K_1))
<=> ( dvd_dvd_nat(Ma,N_1)
| K_1 = zero_zero_nat ) ),
file('theBenchmark.p',fact_641_nat__mult__dvd__cancel__disj_H) ).
fof(fact_642_zcong__not__zero,axiom,
! [M,X_1] :
( ord_less_int(zero_zero_int,X_1)
=> ( ord_less_int(X_1,M)
=> ~ zcong(X_1,zero_zero_int,M) ) ),
file('theBenchmark.p',fact_642_zcong__not__zero) ).
fof(fact_643_zcong__less__eq,axiom,
! [M,Y_1,X_1] :
( ( is_int(X_1)
& is_int(Y_1) )
=> ( ord_less_int(zero_zero_int,X_1)
=> ( ord_less_int(zero_zero_int,Y_1)
=> ( ord_less_int(zero_zero_int,M)
=> ( zcong(X_1,Y_1,M)
=> ( ord_less_int(X_1,M)
=> ( ord_less_int(Y_1,M)
=> X_1 = Y_1 ) ) ) ) ) ) ),
file('theBenchmark.p',fact_643_zcong__less__eq) ).
fof(fact_644_zdvd__bounds,axiom,
! [N,M] :
( dvd_dvd_int(N,M)
=> ( ord_less_eq_int(N,M)
| ord_less_eq_int(M,zero_zero_int) ) ),
file('theBenchmark.p',fact_644_zdvd__bounds) ).
fof(fact_645_divides__exp2,axiom,
! [X_1,Y_1,N] :
( N != zero_zero_nat
=> ( dvd_dvd_nat(power_power_nat(X_1,N),Y_1)
=> dvd_dvd_nat(X_1,Y_1) ) ),
file('theBenchmark.p',fact_645_divides__exp2) ).
fof(fact_646_divides__rev,axiom,
! [A,N,B_1] :
( dvd_dvd_nat(power_power_nat(A,N),power_power_nat(B_1,N))
=> ( N != zero_zero_nat
=> dvd_dvd_nat(A,B_1) ) ),
file('theBenchmark.p',fact_646_divides__rev) ).
fof(fact_647_zcong__zero__equiv__div,axiom,
! [A_1,Ma] :
( zcong(A_1,zero_zero_int,Ma)
<=> dvd_dvd_int(Ma,A_1) ),
file('theBenchmark.p',fact_647_zcong__zero__equiv__div) ).
fof(fact_648_zcong__eq__zdvd__prop,axiom,
! [X_2,P_1] :
( zcong(X_2,zero_zero_int,P_1)
<=> dvd_dvd_int(P_1,X_2) ),
file('theBenchmark.p',fact_648_zcong__eq__zdvd__prop) ).
fof(fact_649_exp__eq__1,axiom,
! [X_2,N_1] :
( power_power_nat(X_2,N_1) = one_one_nat
<=> ( N_1 = zero_zero_nat
| X_2 = one_one_nat ) ),
file('theBenchmark.p',fact_649_exp__eq__1) ).
fof(fact_650_zprime__zdvd__zmult__better,axiom,
! [M,N,P] :
( zprime(P)
=> ( dvd_dvd_int(P,times_times_int(M,N))
=> ( dvd_dvd_int(P,N)
| dvd_dvd_int(P,M) ) ) ),
file('theBenchmark.p',fact_650_zprime__zdvd__zmult__better) ).
fof(fact_651_Int2_Ozcong__zero,axiom,
! [M,X_1] :
( is_int(X_1)
=> ( ord_less_eq_int(zero_zero_int,X_1)
=> ( ord_less_int(X_1,M)
=> ( zcong(X_1,zero_zero_int,M)
=> X_1 = zero_zero_int ) ) ) ),
file('theBenchmark.p',fact_651_Int2_Ozcong__zero) ).
fof(fact_652_zpower__zdvd__prop1,axiom,
! [P,Y_1,N] :
( ord_less_nat(zero_zero_nat,N)
=> ( dvd_dvd_int(P,Y_1)
=> dvd_dvd_int(P,power_power_int(Y_1,N)) ) ),
file('theBenchmark.p',fact_652_zpower__zdvd__prop1) ).
fof(fact_653_zcong__zmult__prop3,axiom,
! [Y_1,X_1,P] :
( zprime(P)
=> ( ~ zcong(X_1,zero_zero_int,P)
=> ( ~ zcong(Y_1,zero_zero_int,P)
=> ~ zcong(times_times_int(X_1,Y_1),zero_zero_int,P) ) ) ),
file('theBenchmark.p',fact_653_zcong__zmult__prop3) ).
fof(fact_654_divides__div__not,axiom,
! [X_1,Q,N,R_1] :
( X_1 = plus_plus_nat(times_times_nat(Q,N),R_1)
=> ( ord_less_nat(zero_zero_nat,R_1)
=> ( ord_less_nat(R_1,N)
=> ~ dvd_dvd_nat(N,X_1) ) ) ),
file('theBenchmark.p',fact_654_divides__div__not) ).
fof(fact_655_zcong__zprime__prod__zero__contra,axiom,
! [B_1,A,P] :
( zprime(P)
=> ( ord_less_int(zero_zero_int,A)
=> ( ( ~ zcong(B_1,zero_zero_int,P)
& ~ zcong(A,zero_zero_int,P) )
=> ~ zcong(times_times_int(A,B_1),zero_zero_int,P) ) ) ),
file('theBenchmark.p',fact_655_zcong__zprime__prod__zero__contra) ).
fof(fact_656_zcong__zprime__prod__zero,axiom,
! [B_1,A,P] :
( zprime(P)
=> ( ord_less_int(zero_zero_int,A)
=> ( zcong(times_times_int(A,B_1),zero_zero_int,P)
=> ( zcong(B_1,zero_zero_int,P)
| zcong(A,zero_zero_int,P) ) ) ) ),
file('theBenchmark.p',fact_656_zcong__zprime__prod__zero) ).
fof(fact_657_zpower__zdvd__prop2,axiom,
! [Y_1,N,P] :
( zprime(P)
=> ( dvd_dvd_int(P,power_power_int(Y_1,N))
=> ( ord_less_nat(zero_zero_nat,N)
=> dvd_dvd_int(P,Y_1) ) ) ),
file('theBenchmark.p',fact_657_zpower__zdvd__prop2) ).
fof(fact_658_QuadRes__def,axiom,
! [Ma,X_2] :
( quadRes(Ma,X_2)
<=> ? [Y] :
( zcong(power_power_int(Y,number_number_of_nat(bit0(bit1(pls)))),X_2,Ma)
& is_int(Y) ) ),
file('theBenchmark.p',fact_658_QuadRes__def) ).
fof(fact_659_realpow__two__sum__zero__iff,axiom,
! [X_2,Y_2] :
( plus_plus_real(power_power_real(X_2,number_number_of_nat(bit0(bit1(pls)))),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_659_realpow__two__sum__zero__iff) ).
fof(fact_660_self__quotient__aux1,axiom,
! [R_1,Q,A] :
( ord_less_int(zero_zero_int,A)
=> ( A = plus_plus_int(R_1,times_times_int(A,Q))
=> ( ord_less_int(R_1,A)
=> ord_less_eq_int(one_one_int,Q) ) ) ),
file('theBenchmark.p',fact_660_self__quotient__aux1) ).
fof(fact_661_real__zero__not__eq__one,axiom,
zero_zero_real != one_one_real,
file('theBenchmark.p',fact_661_real__zero__not__eq__one) ).
fof(fact_662_real__le__eq__diff,axiom,
! [X_2,Y_2] :
( ord_less_eq_real(X_2,Y_2)
<=> ord_less_eq_real(minus_minus_real(X_2,Y_2),zero_zero_real) ),
file('theBenchmark.p',fact_662_real__le__eq__diff) ).
fof(fact_663_real__less__def,axiom,
! [X_2,Y_2] :
( ord_less_real(X_2,Y_2)
<=> ( X_2 != Y_2
& ord_less_eq_real(X_2,Y_2) ) ),
file('theBenchmark.p',fact_663_real__less__def) ).
fof(fact_664_less__eq__real__def,axiom,
! [X_2,Y_2] :
( ord_less_eq_real(X_2,Y_2)
<=> ( X_2 = Y_2
| ord_less_real(X_2,Y_2) ) ),
file('theBenchmark.p',fact_664_less__eq__real__def) ).
fof(fact_665_real__mult__1,axiom,
! [Z] : times_times_real(one_one_real,Z) = Z,
file('theBenchmark.p',fact_665_real__mult__1) ).
fof(fact_666_real__mult__commute,axiom,
! [Z,W] : times_times_real(Z,W) = times_times_real(W,Z),
file('theBenchmark.p',fact_666_real__mult__commute) ).
fof(fact_667_real__mult__assoc,axiom,
! [Z1,Z2,Z3] : times_times_real(times_times_real(Z1,Z2),Z3) = times_times_real(Z1,times_times_real(Z2,Z3)),
file('theBenchmark.p',fact_667_real__mult__assoc) ).
fof(fact_668_real__add__left__mono,axiom,
! [Z,X_1,Y_1] :
( ord_less_eq_real(X_1,Y_1)
=> ord_less_eq_real(plus_plus_real(Z,X_1),plus_plus_real(Z,Y_1)) ),
file('theBenchmark.p',fact_668_real__add__left__mono) ).
fof(fact_669_real__mult__left__cancel,axiom,
! [A_1,B_2,C] :
( C != zero_zero_real
=> ( times_times_real(C,A_1) = times_times_real(C,B_2)
<=> A_1 = B_2 ) ),
file('theBenchmark.p',fact_669_real__mult__left__cancel) ).
fof(fact_670_real__mult__right__cancel,axiom,
! [A_1,B_2,C] :
( C != zero_zero_real
=> ( times_times_real(A_1,C) = times_times_real(B_2,C)
<=> A_1 = B_2 ) ),
file('theBenchmark.p',fact_670_real__mult__right__cancel) ).
fof(fact_671_real__add__mult__distrib,axiom,
! [Z1,Z2,W] : times_times_real(plus_plus_real(Z1,Z2),W) = plus_plus_real(times_times_real(Z1,W),times_times_real(Z2,W)),
file('theBenchmark.p',fact_671_real__add__mult__distrib) ).
fof(fact_672_real__mult__less__mono2,axiom,
! [X_1,Y_1,Z] :
( ord_less_real(zero_zero_real,Z)
=> ( ord_less_real(X_1,Y_1)
=> ord_less_real(times_times_real(Z,X_1),times_times_real(Z,Y_1)) ) ),
file('theBenchmark.p',fact_672_real__mult__less__mono2) ).
fof(fact_673_real__mult__order,axiom,
! [Y_1,X_1] :
( ord_less_real(zero_zero_real,X_1)
=> ( ord_less_real(zero_zero_real,Y_1)
=> ord_less_real(zero_zero_real,times_times_real(X_1,Y_1)) ) ),
file('theBenchmark.p',fact_673_real__mult__order) ).
fof(fact_674_real__mult__le__cancel__iff2,axiom,
! [X_2,Y_2,Z_1] :
( ord_less_real(zero_zero_real,Z_1)
=> ( ord_less_eq_real(times_times_real(Z_1,X_2),times_times_real(Z_1,Y_2))
<=> ord_less_eq_real(X_2,Y_2) ) ),
file('theBenchmark.p',fact_674_real__mult__le__cancel__iff2) ).
fof(fact_675_real__mult__le__cancel__iff1,axiom,
! [X_2,Y_2,Z_1] :
( ord_less_real(zero_zero_real,Z_1)
=> ( ord_less_eq_real(times_times_real(X_2,Z_1),times_times_real(Y_2,Z_1))
<=> ord_less_eq_real(X_2,Y_2) ) ),
file('theBenchmark.p',fact_675_real__mult__le__cancel__iff1) ).
fof(fact_676_real__mult__less__iff1,axiom,
! [X_2,Y_2,Z_1] :
( ord_less_real(zero_zero_real,Z_1)
=> ( ord_less_real(times_times_real(X_2,Z_1),times_times_real(Y_2,Z_1))
<=> ord_less_real(X_2,Y_2) ) ),
file('theBenchmark.p',fact_676_real__mult__less__iff1) ).
fof(fact_677_real__two__squares__add__zero__iff,axiom,
! [X_2,Y_2] :
( plus_plus_real(times_times_real(X_2,X_2),times_times_real(Y_2,Y_2)) = zero_zero_real
<=> ( Y_2 = zero_zero_real
& X_2 = zero_zero_real ) ),
file('theBenchmark.p',fact_677_real__two__squares__add__zero__iff) ).
fof(fact_678_two__realpow__ge__one,axiom,
! [N] : ord_less_eq_real(one_one_real,power_power_real(number267125858f_real(bit0(bit1(pls))),N)),
file('theBenchmark.p',fact_678_two__realpow__ge__one) ).
fof(fact_679_q__pos__lemma,axiom,
! [B,Q_1,R_2] :
( ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(B,Q_1),R_2))
=> ( ord_less_int(R_2,B)
=> ( ord_less_int(zero_zero_int,B)
=> ord_less_eq_int(zero_zero_int,Q_1) ) ) ),
file('theBenchmark.p',fact_679_q__pos__lemma) ).
fof(fact_680_q__neg__lemma,axiom,
! [B,Q_1,R_2] :
( ord_less_int(plus_plus_int(times_times_int(B,Q_1),R_2),zero_zero_int)
=> ( ord_less_eq_int(zero_zero_int,R_2)
=> ( ord_less_int(zero_zero_int,B)
=> ord_less_eq_int(Q_1,zero_zero_int) ) ) ),
file('theBenchmark.p',fact_680_q__neg__lemma) ).
fof(fact_681_unique__quotient__lemma,axiom,
! [B_1,Q_1,R_2,Q,R_1] :
( ord_less_eq_int(plus_plus_int(times_times_int(B_1,Q_1),R_2),plus_plus_int(times_times_int(B_1,Q),R_1))
=> ( ord_less_eq_int(zero_zero_int,R_2)
=> ( ord_less_int(R_2,B_1)
=> ( ord_less_int(R_1,B_1)
=> ord_less_eq_int(Q_1,Q) ) ) ) ),
file('theBenchmark.p',fact_681_unique__quotient__lemma) ).
fof(fact_682_zdiv__mono2__lemma,axiom,
! [B_1,Q,R_1,B,Q_1,R_2] :
( plus_plus_int(times_times_int(B_1,Q),R_1) = plus_plus_int(times_times_int(B,Q_1),R_2)
=> ( ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(B,Q_1),R_2))
=> ( ord_less_int(R_2,B)
=> ( ord_less_eq_int(zero_zero_int,R_1)
=> ( ord_less_int(zero_zero_int,B)
=> ( ord_less_eq_int(B,B_1)
=> ord_less_eq_int(Q,Q_1) ) ) ) ) ) ),
file('theBenchmark.p',fact_682_zdiv__mono2__lemma) ).
fof(fact_683_unique__quotient__lemma__neg,axiom,
! [B_1,Q_1,R_2,Q,R_1] :
( ord_less_eq_int(plus_plus_int(times_times_int(B_1,Q_1),R_2),plus_plus_int(times_times_int(B_1,Q),R_1))
=> ( ord_less_eq_int(R_1,zero_zero_int)
=> ( ord_less_int(B_1,R_1)
=> ( ord_less_int(B_1,R_2)
=> ord_less_eq_int(Q,Q_1) ) ) ) ),
file('theBenchmark.p',fact_683_unique__quotient__lemma__neg) ).
fof(fact_684_zdiv__mono2__neg__lemma,axiom,
! [B_1,Q,R_1,B,Q_1,R_2] :
( plus_plus_int(times_times_int(B_1,Q),R_1) = plus_plus_int(times_times_int(B,Q_1),R_2)
=> ( ord_less_int(plus_plus_int(times_times_int(B,Q_1),R_2),zero_zero_int)
=> ( ord_less_int(R_1,B_1)
=> ( ord_less_eq_int(zero_zero_int,R_2)
=> ( ord_less_int(zero_zero_int,B)
=> ( ord_less_eq_int(B,B_1)
=> ord_less_eq_int(Q_1,Q) ) ) ) ) ) ),
file('theBenchmark.p',fact_684_zdiv__mono2__neg__lemma) ).
fof(fact_685_self__quotient__aux2,axiom,
! [R_1,Q,A] :
( ord_less_int(zero_zero_int,A)
=> ( A = plus_plus_int(R_1,times_times_int(A,Q))
=> ( ord_less_eq_int(zero_zero_int,R_1)
=> ord_less_eq_int(Q,one_one_int) ) ) ),
file('theBenchmark.p',fact_685_self__quotient__aux2) ).
fof(fact_686_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
ord_less_eq_int(zero_zero_int,number_number_of_int(bit0(bit1(pls)))),
file('theBenchmark.p',fact_686_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
fof(fact_687_real__le__antisym,axiom,
! [Z,W] :
( ord_less_eq_real(Z,W)
=> ( ord_less_eq_real(W,Z)
=> Z = W ) ),
file('theBenchmark.p',fact_687_real__le__antisym) ).
fof(fact_688_real__le__trans,axiom,
! [K,I,J] :
( ord_less_eq_real(I,J)
=> ( ord_less_eq_real(J,K)
=> ord_less_eq_real(I,K) ) ),
file('theBenchmark.p',fact_688_real__le__trans) ).
fof(fact_689_real__le__linear,axiom,
! [Z,W] :
( ord_less_eq_real(W,Z)
| ord_less_eq_real(Z,W) ),
file('theBenchmark.p',fact_689_real__le__linear) ).
fof(fact_690_real__le__refl,axiom,
! [W] : ord_less_eq_real(W,W),
file('theBenchmark.p',fact_690_real__le__refl) ).
fof(fact_691_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
ord_less_eq_int(zero_zero_int,zero_zero_int),
file('theBenchmark.p',fact_691_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
fof(fact_692_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
ord_less_eq_int(zero_zero_int,one_one_int),
file('theBenchmark.p',fact_692_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(fact_693_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
! [Y_1,X_1] :
( ord_less_eq_int(zero_zero_int,X_1)
=> ( ord_less_eq_int(zero_zero_int,Y_1)
=> ord_less_eq_int(zero_zero_int,times_times_int(X_1,Y_1)) ) ),
file('theBenchmark.p',fact_693_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_694_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
! [Y_1,X_1] :
( ord_less_eq_int(zero_zero_int,X_1)
=> ( ord_less_eq_int(zero_zero_int,Y_1)
=> ord_less_eq_int(zero_zero_int,plus_plus_int(X_1,Y_1)) ) ),
file('theBenchmark.p',fact_694_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_695_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [N,X_1] :
( ord_less_eq_int(zero_zero_int,X_1)
=> ord_less_eq_int(zero_zero_int,power_power_int(X_1,N)) ),
file('theBenchmark.p',fact_695_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(fact_696_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
ord_less_eq_int(zero_zero_int,number_number_of_int(bit1(bit1(pls)))),
file('theBenchmark.p',fact_696_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
fof(fact_697_realpow__pos__nth,axiom,
! [A,N] :
( ord_less_nat(zero_zero_nat,N)
=> ( ord_less_real(zero_zero_real,A)
=> ? [R] :
( power_power_real(R,N) = A
& ord_less_real(zero_zero_real,R) ) ) ),
file('theBenchmark.p',fact_697_realpow__pos__nth) ).
fof(conj_0,conjecture,
? [X,Y] : plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_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,
! [B_1_1,B_2_1] :
( is_int(minus_minus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) ),
inference(fof_nnf,[status(thm)],[gsy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( is_int(minus_minus_int(U_1,U_0))
| ~ is_int(U_0)
| ~ is_int(U_1) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_1,U_0] :
( is_int(minus_minus_int(U_1,U_0))
| ~ is_int(U_0)
| ~ is_int(U_1) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
( is_int(minus_minus_int(U_1,U_0))
| ~ is_int(U_0)
| ~ is_int(U_1) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
is_int(one_one_int),
inference(fof_nnf,[status(thm)],[gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint]) ).
fof(f_2_2,plain,
is_int(one_one_int),
inference(definitional_conversion,[status(esa)],[f_2_1]) ).
cnf(f_2_3,plain,
is_int(one_one_int),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [B_1_1,B_2_1] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) ),
inference(fof_nnf,[status(thm)],[gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint]) ).
fof(f_3_2,plain,
! [U_3,U_2] :
( is_int(plus_plus_int(U_3,U_2))
| ~ is_int(U_2)
| ~ is_int(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_2,U_3] :
( is_int(plus_plus_int(U_3,U_2))
| ~ is_int(U_2)
| ~ is_int(U_3) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( is_int(plus_plus_int(U_3,U_2))
| ~ is_int(U_2)
| ~ is_int(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [B_1_1,B_2_1] :
( is_int(times_times_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) ),
inference(fof_nnf,[status(thm)],[gsy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint]) ).
fof(f_4_2,plain,
! [U_5,U_4] :
( is_int(times_times_int(U_5,U_4))
| ~ is_int(U_4)
| ~ is_int(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_5,U_4] :
( is_int(times_times_int(U_5,U_4))
| ~ is_int(U_4)
| ~ is_int(U_5) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( is_int(times_times_int(U_5,U_4))
| ~ is_int(U_4)
| ~ is_int(U_5) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
is_int(zero_zero_int),
inference(fof_nnf,[status(thm)],[gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint]) ).
fof(f_5_2,plain,
is_int(zero_zero_int),
inference(definitional_conversion,[status(esa)],[f_5_1]) ).
cnf(f_5_3,plain,
is_int(zero_zero_int),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
is_int(undefined_int(int)),
inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__Int__Oint]) ).
fof(f_6_2,plain,
is_int(undefined_int(int)),
inference(definitional_conversion,[status(esa)],[f_6_1]) ).
cnf(f_6_3,plain,
is_int(undefined_int(int)),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_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_7_2,plain,
! [U_6] :
( is_int(bit0(U_6))
| ~ is_int(U_6) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_6] :
( is_int(bit0(U_6))
| ~ is_int(U_6) ),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
( is_int(bit0(U_6))
| ~ is_int(U_6) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_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_8_2,plain,
! [U_7] :
( is_int(bit1(U_7))
| ~ is_int(U_7) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_7] :
( is_int(bit1(U_7))
| ~ is_int(U_7) ),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
( is_int(bit1(U_7))
| ~ is_int(U_7) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
is_int(min),
inference(fof_nnf,[status(thm)],[gsy_c_Int_OMin]) ).
fof(f_9_2,plain,
is_int(min),
inference(definitional_conversion,[status(esa)],[f_9_1]) ).
cnf(f_9_3,plain,
is_int(min),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
is_int(pls),
inference(fof_nnf,[status(thm)],[gsy_c_Int_OPls]) ).
fof(f_10_2,plain,
is_int(pls),
inference(definitional_conversion,[status(esa)],[f_10_1]) ).
cnf(f_10_3,plain,
is_int(pls),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_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_11_2,plain,
! [U_8] :
( is_int(number_number_of_int(U_8))
| ~ is_int(U_8) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_8] :
( is_int(number_number_of_int(U_8))
| ~ is_int(U_8) ),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
( is_int(number_number_of_int(U_8))
| ~ is_int(U_8) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [B_1_1,B_2_1] :
( is_int(power_power_int(B_1_1,B_2_1))
| ~ is_int(B_1_1) ),
inference(fof_nnf,[status(thm)],[gsy_c_Power_Opower__class_Opower_000tc__Int__Oint]) ).
fof(f_12_2,plain,
! [U_10,U_9] :
( is_int(power_power_int(U_10,U_9))
| ~ is_int(U_10) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_10] :
( ! [U_9] : is_int(power_power_int(U_10,U_9))
| ~ is_int(U_10) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
! [U_9,U_10] :
( is_int(power_power_int(U_10,U_9))
| ~ is_int(U_10) ),
inference(definitional_conversion,[status(esa)],[f_12_3]) ).
cnf(f_12_5,plain,
( is_int(power_power_int(U_10,U_9))
| ~ is_int(U_10) ),
inference(clausify,[status(thm)],[f_12_4]) ).
fof(f_13_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_13_2,plain,
! [U_12,U_11] :
( is_int(legendre(U_12,U_11))
| ~ is_int(U_11)
| ~ is_int(U_12) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_11,U_12] :
( is_int(legendre(U_12,U_11))
| ~ is_int(U_11)
| ~ is_int(U_12) ),
inference(definitional_conversion,[status(esa)],[f_13_2]) ).
cnf(f_13_4,plain,
( is_int(legendre(U_12,U_11))
| ~ is_int(U_11)
| ~ is_int(U_12) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [B_1_1] : is_int(twoSqu140629262sum2sq(B_1_1)),
inference(fof_nnf,[status(thm)],[gsy_c_TwoSquares__Mirabelle__ccrtsbwhjp_Osum2sq]) ).
fof(f_14_2,plain,
! [U_13] : is_int(twoSqu140629262sum2sq(U_13)),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_13] : is_int(twoSqu140629262sum2sq(U_13)),
inference(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,plain,
is_int(twoSqu140629262sum2sq(U_13)),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
is_int(m),
inference(fof_nnf,[status(thm)],[gsy_v_m]) ).
fof(f_15_2,plain,
is_int(m),
inference(definitional_conversion,[status(esa)],[f_15_1]) ).
cnf(f_15_3,plain,
is_int(m),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
is_int(s1),
inference(fof_nnf,[status(thm)],[gsy_v_s1____]) ).
fof(f_16_2,plain,
is_int(s1),
inference(definitional_conversion,[status(esa)],[f_16_1]) ).
cnf(f_16_3,plain,
is_int(s1),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
is_int(s),
inference(fof_nnf,[status(thm)],[gsy_v_s____]) ).
fof(f_17_2,plain,
is_int(s),
inference(definitional_conversion,[status(esa)],[f_17_1]) ).
cnf(f_17_3,plain,
is_int(s),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
is_int(t),
inference(fof_nnf,[status(thm)],[gsy_v_t____]) ).
fof(f_18_2,plain,
is_int(t),
inference(definitional_conversion,[status(esa)],[f_18_1]) ).
cnf(f_18_3,plain,
is_int(t),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
ord_less_eq_int(one_one_int,t),
inference(fof_nnf,[status(thm)],[fact_0_tpos]) ).
fof(f_19_2,plain,
ord_less_eq_int(one_one_int,t),
inference(definitional_conversion,[status(esa)],[f_19_1]) ).
cnf(f_19_3,plain,
ord_less_eq_int(one_one_int,t),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
( ? [X,Y] :
( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_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_20_2,plain,
( ? [U_15,U_14] :
( plus_plus_int(power_power_int(U_15,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_14,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
& is_int(U_14)
& is_int(U_15) )
| t != one_one_int ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ? [U_15] :
( ? [U_14] :
( plus_plus_int(power_power_int(U_15,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_14,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
& is_int(U_14) )
& is_int(U_15) )
| t != one_one_int ),
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
( ( ? [U_14] :
( plus_plus_int(power_power_int(sK1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_14,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
& is_int(U_14) )
& is_int(sK1) )
| t != one_one_int ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_15,sK1)],[f_20_3]) ).
fof(f_20_5,plain,
( ( plus_plus_int(power_power_int(sK1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK2,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_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_14,sK2)],[f_20_4]) ).
fof(f_20_6,plain,
( ( plus_plus_int(power_power_int(sK1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK2,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
| ~ sP0 )
& ( is_int(sK2)
| ~ sP0 )
& ( is_int(sK1)
| ~ sP0 )
& ( sP0
| t != one_one_int ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_20_5]) ).
cnf(f_20_7,plain,
( sP0
| t != one_one_int ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_8,plain,
( is_int(sK1)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_9,plain,
( is_int(sK2)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_10,plain,
( plus_plus_int(power_power_int(sK1,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK2,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_20_6]) ).
fof(f_21_1,plain,
( ? [X,Y] :
( plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
& is_int(Y)
& is_int(X) )
| ~ 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_21_2,plain,
( ? [U_17,U_16] :
( plus_plus_int(power_power_int(U_17,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_16,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
& is_int(U_16)
& is_int(U_17) )
| ~ ord_less_int(one_one_int,t) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ? [U_17] :
( ? [U_16] :
( plus_plus_int(power_power_int(U_17,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_16,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
& is_int(U_16) )
& is_int(U_17) )
| ~ ord_less_int(one_one_int,t) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
fof(f_21_4,plain,
( ( ? [U_16] :
( plus_plus_int(power_power_int(sK3,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_16,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
& is_int(U_16) )
& is_int(sK3) )
| ~ ord_less_int(one_one_int,t) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_17,sK3)],[f_21_3]) ).
fof(f_21_5,plain,
( ( plus_plus_int(power_power_int(sK3,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK4,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
& is_int(sK4)
& is_int(sK3) )
| ~ ord_less_int(one_one_int,t) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_16,sK4)],[f_21_4]) ).
fof(f_21_6,plain,
( ( plus_plus_int(power_power_int(sK3,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK4,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
| ~ sP1 )
& ( is_int(sK4)
| ~ sP1 )
& ( is_int(sK3)
| ~ sP1 )
& ( sP1
| ~ ord_less_int(one_one_int,t) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_21_5]) ).
cnf(f_21_7,plain,
( sP1
| ~ ord_less_int(one_one_int,t) ),
inference(clausify,[status(thm)],[f_21_6]) ).
cnf(f_21_8,plain,
( is_int(sK3)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_21_6]) ).
cnf(f_21_9,plain,
( is_int(sK4)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_21_6]) ).
cnf(f_21_10,plain,
( plus_plus_int(power_power_int(sK3,number_number_of_nat(bit0(bit1(pls)))),power_power_int(sK4,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_21_6]) ).
fof(f_22_1,plain,
ord_less_int(t,plus_plus_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]) ).
fof(f_22_2,plain,
ord_less_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(definitional_conversion,[status(esa)],[f_22_1]) ).
cnf(f_22_3,plain,
ord_less_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(fof_nnf,[status(thm)],[fact_4_p]) ).
fof(f_23_2,plain,
zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(definitional_conversion,[status(esa)],[f_23_1]) ).
cnf(f_23_3,plain,
zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_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]) ).
fof(f_24_2,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),
inference(definitional_conversion,[status(esa)],[f_24_1]) ).
cnf(f_24_3,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
twoSqu142715416sum2sq(times_times_int(plus_plus_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]) ).
fof(f_25_2,plain,
twoSqu142715416sum2sq(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)),
inference(definitional_conversion,[status(esa)],[f_25_1]) ).
cnf(f_25_3,plain,
twoSqu142715416sum2sq(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [A,B_1] : power_power_int(plus_plus_int(A,B_1),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(A,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),A),B_1)),power_power_int(B_1,number_number_of_nat(bit0(bit1(pls))))),
inference(fof_nnf,[status(thm)],[fact_7_zadd__power2]) ).
fof(f_26_2,plain,
! [U_19,U_18] : power_power_int(plus_plus_int(U_19,U_18),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(U_19,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),U_19),U_18)),power_power_int(U_18,number_number_of_nat(bit0(bit1(pls))))),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_18,U_19] : power_power_int(plus_plus_int(U_19,U_18),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(U_19,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),U_19),U_18)),power_power_int(U_18,number_number_of_nat(bit0(bit1(pls))))),
inference(definitional_conversion,[status(esa)],[f_26_2]) ).
cnf(f_26_4,plain,
power_power_int(plus_plus_int(U_19,U_18),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(U_19,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),U_19),U_18)),power_power_int(U_18,number_number_of_nat(bit0(bit1(pls))))),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A,B_1] : power_power_int(plus_plus_int(A,B_1),number_number_of_nat(bit1(bit1(pls)))) = plus_plus_int(plus_plus_int(plus_plus_int(power_power_int(A,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(A,number_number_of_nat(bit0(bit1(pls))))),B_1)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),A),power_power_int(B_1,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(B_1,number_number_of_nat(bit1(bit1(pls))))),
inference(fof_nnf,[status(thm)],[fact_8_zadd__power3]) ).
fof(f_27_2,plain,
! [U_21,U_20] : power_power_int(plus_plus_int(U_21,U_20),number_number_of_nat(bit1(bit1(pls)))) = plus_plus_int(plus_plus_int(plus_plus_int(power_power_int(U_21,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(U_21,number_number_of_nat(bit0(bit1(pls))))),U_20)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),U_21),power_power_int(U_20,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(U_20,number_number_of_nat(bit1(bit1(pls))))),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_20,U_21] : power_power_int(plus_plus_int(U_21,U_20),number_number_of_nat(bit1(bit1(pls)))) = plus_plus_int(plus_plus_int(plus_plus_int(power_power_int(U_21,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(U_21,number_number_of_nat(bit0(bit1(pls))))),U_20)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),U_21),power_power_int(U_20,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(U_20,number_number_of_nat(bit1(bit1(pls))))),
inference(definitional_conversion,[status(esa)],[f_27_2]) ).
cnf(f_27_4,plain,
power_power_int(plus_plus_int(U_21,U_20),number_number_of_nat(bit1(bit1(pls)))) = plus_plus_int(plus_plus_int(plus_plus_int(power_power_int(U_21,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(U_21,number_number_of_nat(bit0(bit1(pls))))),U_20)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),U_21),power_power_int(U_20,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(U_20,number_number_of_nat(bit1(bit1(pls))))),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [X_2,Y_2] : power_power_real(plus_plus_real(X_2,Y_2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_real(plus_plus_real(power_power_real(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_real(Y_2,number_number_of_nat(bit0(bit1(pls))))),times_times_real(times_times_real(number267125858f_real(bit0(bit1(pls))),X_2),Y_2)),
inference(fof_nnf,[status(thm)],[fact_9_power2__sum]) ).
fof(f_28_2,plain,
! [U_23,U_22] : power_power_real(plus_plus_real(U_23,U_22),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_real(plus_plus_real(power_power_real(U_23,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_22,number_number_of_nat(bit0(bit1(pls))))),times_times_real(times_times_real(number267125858f_real(bit0(bit1(pls))),U_23),U_22)),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_22,U_23] : power_power_real(plus_plus_real(U_23,U_22),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_real(plus_plus_real(power_power_real(U_23,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_22,number_number_of_nat(bit0(bit1(pls))))),times_times_real(times_times_real(number267125858f_real(bit0(bit1(pls))),U_23),U_22)),
inference(definitional_conversion,[status(esa)],[f_28_2]) ).
cnf(f_28_4,plain,
power_power_real(plus_plus_real(U_23,U_22),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_real(plus_plus_real(power_power_real(U_23,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_22,number_number_of_nat(bit0(bit1(pls))))),times_times_real(times_times_real(number267125858f_real(bit0(bit1(pls))),U_23),U_22)),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [X_2,Y_2] : power_power_nat(plus_plus_nat(X_2,Y_2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(plus_plus_nat(power_power_nat(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(Y_2,number_number_of_nat(bit0(bit1(pls))))),times_times_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_29_2,plain,
! [U_25,U_24] : power_power_nat(plus_plus_nat(U_25,U_24),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(plus_plus_nat(power_power_nat(U_25,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(U_24,number_number_of_nat(bit0(bit1(pls))))),times_times_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_25),U_24)),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_24,U_25] : power_power_nat(plus_plus_nat(U_25,U_24),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(plus_plus_nat(power_power_nat(U_25,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(U_24,number_number_of_nat(bit0(bit1(pls))))),times_times_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_25),U_24)),
inference(definitional_conversion,[status(esa)],[f_29_2]) ).
cnf(f_29_4,plain,
power_power_nat(plus_plus_nat(U_25,U_24),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(plus_plus_nat(power_power_nat(U_25,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(U_24,number_number_of_nat(bit0(bit1(pls))))),times_times_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_25),U_24)),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [X_2,Y_2] : power_power_int(plus_plus_int(X_2,Y_2),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y_2,number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),X_2),Y_2)),
inference(fof_nnf,[status(thm)],[fact_11_power2__sum]) ).
fof(f_30_2,plain,
! [U_27,U_26] : power_power_int(plus_plus_int(U_27,U_26),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(U_27,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_26,number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),U_27),U_26)),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_26,U_27] : power_power_int(plus_plus_int(U_27,U_26),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(U_27,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_26,number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),U_27),U_26)),
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,plain,
power_power_int(plus_plus_int(U_27,U_26),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(U_27,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_26,number_number_of_nat(bit0(bit1(pls))))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),U_27),U_26)),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [W_15] : power_power_nat(number_number_of_nat(W_15),number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(number_number_of_nat(W_15),number_number_of_nat(W_15)),
inference(fof_nnf,[status(thm)],[fact_12_power2__eq__square__number__of]) ).
fof(f_31_2,plain,
! [U_28] : power_power_nat(number_number_of_nat(U_28),number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(number_number_of_nat(U_28),number_number_of_nat(U_28)),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_28] : power_power_nat(number_number_of_nat(U_28),number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(number_number_of_nat(U_28),number_number_of_nat(U_28)),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
power_power_nat(number_number_of_nat(U_28),number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(number_number_of_nat(U_28),number_number_of_nat(U_28)),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [W_15] : power_power_real(number267125858f_real(W_15),number_number_of_nat(bit0(bit1(pls)))) = times_times_real(number267125858f_real(W_15),number267125858f_real(W_15)),
inference(fof_nnf,[status(thm)],[fact_13_power2__eq__square__number__of]) ).
fof(f_32_2,plain,
! [U_29] : power_power_real(number267125858f_real(U_29),number_number_of_nat(bit0(bit1(pls)))) = times_times_real(number267125858f_real(U_29),number267125858f_real(U_29)),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_29] : power_power_real(number267125858f_real(U_29),number_number_of_nat(bit0(bit1(pls)))) = times_times_real(number267125858f_real(U_29),number267125858f_real(U_29)),
inference(definitional_conversion,[status(esa)],[f_32_2]) ).
cnf(f_32_4,plain,
power_power_real(number267125858f_real(U_29),number_number_of_nat(bit0(bit1(pls)))) = times_times_real(number267125858f_real(U_29),number267125858f_real(U_29)),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
! [W_15] : power_power_int(number_number_of_int(W_15),number_number_of_nat(bit0(bit1(pls)))) = times_times_int(number_number_of_int(W_15),number_number_of_int(W_15)),
inference(fof_nnf,[status(thm)],[fact_14_power2__eq__square__number__of]) ).
fof(f_33_2,plain,
! [U_30] : power_power_int(number_number_of_int(U_30),number_number_of_nat(bit0(bit1(pls)))) = times_times_int(number_number_of_int(U_30),number_number_of_int(U_30)),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_30] : power_power_int(number_number_of_int(U_30),number_number_of_nat(bit0(bit1(pls)))) = times_times_int(number_number_of_int(U_30),number_number_of_int(U_30)),
inference(definitional_conversion,[status(esa)],[f_33_2]) ).
cnf(f_33_4,plain,
power_power_int(number_number_of_int(U_30),number_number_of_nat(bit0(bit1(pls)))) = times_times_int(number_number_of_int(U_30),number_number_of_int(U_30)),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [A] : times_times_int(A,power_power_int(A,number_number_of_nat(bit0(bit1(pls))))) = power_power_int(A,number_number_of_nat(bit1(bit1(pls)))),
inference(fof_nnf,[status(thm)],[fact_15_cube__square]) ).
fof(f_34_2,plain,
! [U_31] : times_times_int(U_31,power_power_int(U_31,number_number_of_nat(bit0(bit1(pls))))) = power_power_int(U_31,number_number_of_nat(bit1(bit1(pls)))),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_31] : times_times_int(U_31,power_power_int(U_31,number_number_of_nat(bit0(bit1(pls))))) = power_power_int(U_31,number_number_of_nat(bit1(bit1(pls)))),
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
times_times_int(U_31,power_power_int(U_31,number_number_of_nat(bit0(bit1(pls))))) = power_power_int(U_31,number_number_of_nat(bit1(bit1(pls)))),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
power_power_real(one_one_real,number_number_of_nat(bit0(bit1(pls)))) = one_one_real,
inference(fof_nnf,[status(thm)],[fact_16_one__power2]) ).
fof(f_35_2,plain,
power_power_real(one_one_real,number_number_of_nat(bit0(bit1(pls)))) = one_one_real,
inference(definitional_conversion,[status(esa)],[f_35_1]) ).
cnf(f_35_3,plain,
power_power_real(one_one_real,number_number_of_nat(bit0(bit1(pls)))) = one_one_real,
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
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]) ).
fof(f_36_2,plain,
power_power_nat(one_one_nat,number_number_of_nat(bit0(bit1(pls)))) = one_one_nat,
inference(definitional_conversion,[status(esa)],[f_36_1]) ).
cnf(f_36_3,plain,
power_power_nat(one_one_nat,number_number_of_nat(bit0(bit1(pls)))) = one_one_nat,
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
power_power_int(one_one_int,number_number_of_nat(bit0(bit1(pls)))) = one_one_int,
inference(fof_nnf,[status(thm)],[fact_18_one__power2]) ).
fof(f_37_2,plain,
power_power_int(one_one_int,number_number_of_nat(bit0(bit1(pls)))) = one_one_int,
inference(definitional_conversion,[status(esa)],[f_37_1]) ).
cnf(f_37_3,plain,
power_power_int(one_one_int,number_number_of_nat(bit0(bit1(pls)))) = one_one_int,
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [X_21] : times_times_nat(X_21,X_21) = power_power_nat(X_21,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_38_2,plain,
! [U_32] : times_times_nat(U_32,U_32) = power_power_nat(U_32,number_number_of_nat(bit0(bit1(pls)))),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_32] : times_times_nat(U_32,U_32) = power_power_nat(U_32,number_number_of_nat(bit0(bit1(pls)))),
inference(definitional_conversion,[status(esa)],[f_38_2]) ).
cnf(f_38_4,plain,
times_times_nat(U_32,U_32) = power_power_nat(U_32,number_number_of_nat(bit0(bit1(pls)))),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [X_21] : times_times_real(X_21,X_21) = power_power_real(X_21,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_39_2,plain,
! [U_33] : times_times_real(U_33,U_33) = power_power_real(U_33,number_number_of_nat(bit0(bit1(pls)))),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_33] : times_times_real(U_33,U_33) = power_power_real(U_33,number_number_of_nat(bit0(bit1(pls)))),
inference(definitional_conversion,[status(esa)],[f_39_2]) ).
cnf(f_39_4,plain,
times_times_real(U_33,U_33) = power_power_real(U_33,number_number_of_nat(bit0(bit1(pls)))),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [X_21] : times_times_int(X_21,X_21) = power_power_int(X_21,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_40_2,plain,
! [U_34] : times_times_int(U_34,U_34) = power_power_int(U_34,number_number_of_nat(bit0(bit1(pls)))),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_34] : times_times_int(U_34,U_34) = power_power_int(U_34,number_number_of_nat(bit0(bit1(pls)))),
inference(definitional_conversion,[status(esa)],[f_40_2]) ).
cnf(f_40_4,plain,
times_times_int(U_34,U_34) = power_power_int(U_34,number_number_of_nat(bit0(bit1(pls)))),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
! [A_57] : power_power_nat(A_57,number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(A_57,A_57),
inference(fof_nnf,[status(thm)],[fact_22_power2__eq__square]) ).
fof(f_41_2,plain,
! [U_35] : power_power_nat(U_35,number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(U_35,U_35),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_35] : power_power_nat(U_35,number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(U_35,U_35),
inference(definitional_conversion,[status(esa)],[f_41_2]) ).
cnf(f_41_4,plain,
power_power_nat(U_35,number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(U_35,U_35),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [A_57] : power_power_real(A_57,number_number_of_nat(bit0(bit1(pls)))) = times_times_real(A_57,A_57),
inference(fof_nnf,[status(thm)],[fact_23_power2__eq__square]) ).
fof(f_42_2,plain,
! [U_36] : power_power_real(U_36,number_number_of_nat(bit0(bit1(pls)))) = times_times_real(U_36,U_36),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_36] : power_power_real(U_36,number_number_of_nat(bit0(bit1(pls)))) = times_times_real(U_36,U_36),
inference(definitional_conversion,[status(esa)],[f_42_2]) ).
cnf(f_42_4,plain,
power_power_real(U_36,number_number_of_nat(bit0(bit1(pls)))) = times_times_real(U_36,U_36),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
! [A_57] : power_power_int(A_57,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(A_57,A_57),
inference(fof_nnf,[status(thm)],[fact_24_power2__eq__square]) ).
fof(f_43_2,plain,
! [U_37] : power_power_int(U_37,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(U_37,U_37),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_37] : power_power_int(U_37,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(U_37,U_37),
inference(definitional_conversion,[status(esa)],[f_43_2]) ).
cnf(f_43_4,plain,
power_power_int(U_37,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(U_37,U_37),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [X_20,N_38] : power_power_nat(X_20,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_38)) = times_times_nat(power_power_nat(X_20,N_38),power_power_nat(X_20,N_38)),
inference(fof_nnf,[status(thm)],[fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J]) ).
fof(f_44_2,plain,
! [U_39,U_38] : power_power_nat(U_39,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_38)) = times_times_nat(power_power_nat(U_39,U_38),power_power_nat(U_39,U_38)),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_38,U_39] : power_power_nat(U_39,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_38)) = times_times_nat(power_power_nat(U_39,U_38),power_power_nat(U_39,U_38)),
inference(definitional_conversion,[status(esa)],[f_44_2]) ).
cnf(f_44_4,plain,
power_power_nat(U_39,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_38)) = times_times_nat(power_power_nat(U_39,U_38),power_power_nat(U_39,U_38)),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [X_20,N_38] : power_power_real(X_20,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_38)) = times_times_real(power_power_real(X_20,N_38),power_power_real(X_20,N_38)),
inference(fof_nnf,[status(thm)],[fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J]) ).
fof(f_45_2,plain,
! [U_41,U_40] : power_power_real(U_41,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_40)) = times_times_real(power_power_real(U_41,U_40),power_power_real(U_41,U_40)),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_40,U_41] : power_power_real(U_41,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_40)) = times_times_real(power_power_real(U_41,U_40),power_power_real(U_41,U_40)),
inference(definitional_conversion,[status(esa)],[f_45_2]) ).
cnf(f_45_4,plain,
power_power_real(U_41,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_40)) = times_times_real(power_power_real(U_41,U_40),power_power_real(U_41,U_40)),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_1,plain,
! [X_20,N_38] : power_power_int(X_20,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_38)) = times_times_int(power_power_int(X_20,N_38),power_power_int(X_20,N_38)),
inference(fof_nnf,[status(thm)],[fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J]) ).
fof(f_46_2,plain,
! [U_43,U_42] : power_power_int(U_43,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_42)) = times_times_int(power_power_int(U_43,U_42),power_power_int(U_43,U_42)),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_42,U_43] : power_power_int(U_43,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_42)) = times_times_int(power_power_int(U_43,U_42),power_power_int(U_43,U_42)),
inference(definitional_conversion,[status(esa)],[f_46_2]) ).
cnf(f_46_4,plain,
power_power_int(U_43,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_42)) = times_times_int(power_power_int(U_43,U_42),power_power_int(U_43,U_42)),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
! [W_14] : plus_plus_real(one_one_real,number267125858f_real(W_14)) = number267125858f_real(plus_plus_int(bit1(pls),W_14)),
inference(fof_nnf,[status(thm)],[fact_28_add__special_I2_J]) ).
fof(f_47_2,plain,
! [U_44] : plus_plus_real(one_one_real,number267125858f_real(U_44)) = number267125858f_real(plus_plus_int(bit1(pls),U_44)),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_44] : plus_plus_real(one_one_real,number267125858f_real(U_44)) = number267125858f_real(plus_plus_int(bit1(pls),U_44)),
inference(definitional_conversion,[status(esa)],[f_47_2]) ).
cnf(f_47_4,plain,
plus_plus_real(one_one_real,number267125858f_real(U_44)) = number267125858f_real(plus_plus_int(bit1(pls),U_44)),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
! [W_14] : plus_plus_int(one_one_int,number_number_of_int(W_14)) = number_number_of_int(plus_plus_int(bit1(pls),W_14)),
inference(fof_nnf,[status(thm)],[fact_29_add__special_I2_J]) ).
fof(f_48_2,plain,
! [U_45] : plus_plus_int(one_one_int,number_number_of_int(U_45)) = number_number_of_int(plus_plus_int(bit1(pls),U_45)),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_45] : plus_plus_int(one_one_int,number_number_of_int(U_45)) = number_number_of_int(plus_plus_int(bit1(pls),U_45)),
inference(definitional_conversion,[status(esa)],[f_48_2]) ).
cnf(f_48_4,plain,
plus_plus_int(one_one_int,number_number_of_int(U_45)) = number_number_of_int(plus_plus_int(bit1(pls),U_45)),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [V_17] : plus_plus_real(number267125858f_real(V_17),one_one_real) = number267125858f_real(plus_plus_int(V_17,bit1(pls))),
inference(fof_nnf,[status(thm)],[fact_30_add__special_I3_J]) ).
fof(f_49_2,plain,
! [U_46] : plus_plus_real(number267125858f_real(U_46),one_one_real) = number267125858f_real(plus_plus_int(U_46,bit1(pls))),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_46] : plus_plus_real(number267125858f_real(U_46),one_one_real) = number267125858f_real(plus_plus_int(U_46,bit1(pls))),
inference(definitional_conversion,[status(esa)],[f_49_2]) ).
cnf(f_49_4,plain,
plus_plus_real(number267125858f_real(U_46),one_one_real) = number267125858f_real(plus_plus_int(U_46,bit1(pls))),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
! [V_17] : plus_plus_int(number_number_of_int(V_17),one_one_int) = number_number_of_int(plus_plus_int(V_17,bit1(pls))),
inference(fof_nnf,[status(thm)],[fact_31_add__special_I3_J]) ).
fof(f_50_2,plain,
! [U_47] : plus_plus_int(number_number_of_int(U_47),one_one_int) = number_number_of_int(plus_plus_int(U_47,bit1(pls))),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_47] : plus_plus_int(number_number_of_int(U_47),one_one_int) = number_number_of_int(plus_plus_int(U_47,bit1(pls))),
inference(definitional_conversion,[status(esa)],[f_50_2]) ).
cnf(f_50_4,plain,
plus_plus_int(number_number_of_int(U_47),one_one_int) = number_number_of_int(plus_plus_int(U_47,bit1(pls))),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
plus_plus_real(one_one_real,one_one_real) = number267125858f_real(bit0(bit1(pls))),
inference(fof_nnf,[status(thm)],[fact_32_one__add__one__is__two]) ).
fof(f_51_2,plain,
plus_plus_real(one_one_real,one_one_real) = number267125858f_real(bit0(bit1(pls))),
inference(definitional_conversion,[status(esa)],[f_51_1]) ).
cnf(f_51_3,plain,
plus_plus_real(one_one_real,one_one_real) = number267125858f_real(bit0(bit1(pls))),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_1,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
inference(fof_nnf,[status(thm)],[fact_33_one__add__one__is__two]) ).
fof(f_52_2,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
inference(definitional_conversion,[status(esa)],[f_52_1]) ).
cnf(f_52_3,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_1,plain,
? [T] :
( plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),T)
& is_int(T) ),
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_53_2,plain,
? [U_48] :
( plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),U_48)
& is_int(U_48) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
( plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_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_48,sK5)],[f_53_2]) ).
fof(f_53_4,plain,
( plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),sK5)
& is_int(sK5) ),
inference(definitional_conversion,[status(esa)],[f_53_3]) ).
cnf(f_53_5,plain,
is_int(sK5),
inference(clausify,[status(thm)],[f_53_4]) ).
cnf(f_53_6,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),sK5),
inference(clausify,[status(thm)],[f_53_4]) ).
fof(f_54_1,plain,
! [W] : ord_less_eq_int(W,W),
inference(fof_nnf,[status(thm)],[fact_35_zle__refl]) ).
fof(f_54_2,plain,
! [U_49] : ord_less_eq_int(U_49,U_49),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_49] : ord_less_eq_int(U_49,U_49),
inference(definitional_conversion,[status(esa)],[f_54_2]) ).
cnf(f_54_4,plain,
ord_less_eq_int(U_49,U_49),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,plain,
! [Z,W] :
( ord_less_eq_int(W,Z)
| ord_less_eq_int(Z,W) ),
inference(fof_nnf,[status(thm)],[fact_36_zle__linear]) ).
fof(f_55_2,plain,
! [U_51,U_50] :
( ord_less_eq_int(U_50,U_51)
| ord_less_eq_int(U_51,U_50) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_51,U_50] :
( ord_less_eq_int(U_50,U_51)
| ord_less_eq_int(U_51,U_50) ),
inference(definitional_conversion,[status(esa)],[f_55_2]) ).
cnf(f_55_4,plain,
( ord_less_eq_int(U_50,U_51)
| ord_less_eq_int(U_51,U_50) ),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_1,plain,
! [Z_1,W_1] :
( ( ( ord_less_int(Z_1,W_1)
| Z_1 = W_1
| ~ ord_less_eq_int(Z_1,W_1) )
& ( ( Z_1 != W_1
& ord_less_eq_int(Z_1,W_1) )
| ~ 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_56_2,plain,
! [U_53,U_52] :
( ( ( ord_less_int(U_53,U_52)
| U_53 = U_52
| ~ ord_less_eq_int(U_53,U_52) )
& ( ( U_53 != U_52
& ord_less_eq_int(U_53,U_52) )
| ~ ord_less_int(U_53,U_52) ) )
| ~ is_int(U_52)
| ~ is_int(U_53) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
( ! [U_52,U_53] :
( U_53 != U_52
| ~ sP2(U_52,U_53) )
& ! [U_52,U_53] :
( ord_less_eq_int(U_53,U_52)
| ~ sP2(U_52,U_53) )
& ! [U_52,U_53] :
( ord_less_int(U_53,U_52)
| U_53 = U_52
| ~ ord_less_eq_int(U_53,U_52)
| ~ sP3(U_52,U_53) )
& ! [U_52,U_53] :
( sP2(U_52,U_53)
| ~ ord_less_int(U_53,U_52)
| ~ sP3(U_52,U_53) )
& ! [U_52,U_53] :
( sP3(U_52,U_53)
| ~ is_int(U_52)
| ~ is_int(U_53) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2,sP3])],[f_56_2]) ).
cnf(f_56_4,plain,
( sP3(U_52,U_53)
| ~ is_int(U_52)
| ~ is_int(U_53) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_5,plain,
( sP2(U_52,U_53)
| ~ ord_less_int(U_53,U_52)
| ~ sP3(U_52,U_53) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_6,plain,
( ord_less_int(U_53,U_52)
| U_53 = U_52
| ~ ord_less_eq_int(U_53,U_52)
| ~ sP3(U_52,U_53) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_7,plain,
( ord_less_eq_int(U_53,U_52)
| ~ sP2(U_52,U_53) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_8,plain,
( U_53 != U_52
| ~ sP2(U_52,U_53) ),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_1,plain,
! [X_1,Y_1] :
( ord_less_int(Y_1,X_1)
| X_1 = Y_1
| 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_57_2,plain,
! [U_55,U_54] :
( ord_less_int(U_54,U_55)
| U_55 = U_54
| ord_less_int(U_55,U_54)
| ~ is_int(U_54)
| ~ is_int(U_55) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_55,U_54] :
( ord_less_int(U_54,U_55)
| U_55 = U_54
| ord_less_int(U_55,U_54)
| ~ is_int(U_54)
| ~ is_int(U_55) ),
inference(definitional_conversion,[status(esa)],[f_57_2]) ).
cnf(f_57_4,plain,
( ord_less_int(U_54,U_55)
| U_55 = U_54
| ord_less_int(U_55,U_54)
| ~ is_int(U_54)
| ~ is_int(U_55) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
! [K,I,J] :
( ord_less_eq_int(I,K)
| ~ ord_less_eq_int(J,K)
| ~ ord_less_eq_int(I,J) ),
inference(fof_nnf,[status(thm)],[fact_39_zle__trans]) ).
fof(f_58_2,plain,
! [U_58,U_57,U_56] :
( ord_less_eq_int(U_57,U_58)
| ~ ord_less_eq_int(U_56,U_58)
| ~ ord_less_eq_int(U_57,U_56) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_58,U_57,U_56] :
( ord_less_eq_int(U_57,U_58)
| ~ ord_less_eq_int(U_56,U_58)
| ~ ord_less_eq_int(U_57,U_56) ),
inference(definitional_conversion,[status(esa)],[f_58_2]) ).
cnf(f_58_4,plain,
( ord_less_eq_int(U_57,U_58)
| ~ ord_less_eq_int(U_56,U_58)
| ~ ord_less_eq_int(U_57,U_56) ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_1,plain,
! [Z,W] :
( Z = W
| ~ ord_less_eq_int(W,Z)
| ~ ord_less_eq_int(Z,W)
| ~ is_int(W)
| ~ is_int(Z) ),
inference(fof_nnf,[status(thm)],[fact_40_zle__antisym]) ).
fof(f_59_2,plain,
! [U_60,U_59] :
( U_60 = U_59
| ~ ord_less_eq_int(U_59,U_60)
| ~ ord_less_eq_int(U_60,U_59)
| ~ is_int(U_59)
| ~ is_int(U_60) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_59,U_60] :
( U_60 = U_59
| ~ ord_less_eq_int(U_59,U_60)
| ~ ord_less_eq_int(U_60,U_59)
| ~ is_int(U_59)
| ~ is_int(U_60) ),
inference(definitional_conversion,[status(esa)],[f_59_2]) ).
cnf(f_59_4,plain,
( U_60 = U_59
| ~ ord_less_eq_int(U_59,U_60)
| ~ ord_less_eq_int(U_60,U_59)
| ~ is_int(U_59)
| ~ is_int(U_60) ),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_1,plain,
! [X_19,P_3,Q_4] : power_power_nat(power_power_nat(X_19,P_3),Q_4) = power_power_nat(X_19,times_times_nat(P_3,Q_4)),
inference(fof_nnf,[status(thm)],[fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J]) ).
fof(f_60_2,plain,
! [U_63,U_62,U_61] : power_power_nat(power_power_nat(U_63,U_62),U_61) = power_power_nat(U_63,times_times_nat(U_62,U_61)),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_61,U_63,U_62] : power_power_nat(power_power_nat(U_63,U_62),U_61) = power_power_nat(U_63,times_times_nat(U_62,U_61)),
inference(definitional_conversion,[status(esa)],[f_60_2]) ).
cnf(f_60_4,plain,
power_power_nat(power_power_nat(U_63,U_62),U_61) = power_power_nat(U_63,times_times_nat(U_62,U_61)),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
! [X_19,P_3,Q_4] : power_power_real(power_power_real(X_19,P_3),Q_4) = power_power_real(X_19,times_times_nat(P_3,Q_4)),
inference(fof_nnf,[status(thm)],[fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J]) ).
fof(f_61_2,plain,
! [U_66,U_65,U_64] : power_power_real(power_power_real(U_66,U_65),U_64) = power_power_real(U_66,times_times_nat(U_65,U_64)),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
! [U_64,U_65,U_66] : power_power_real(power_power_real(U_66,U_65),U_64) = power_power_real(U_66,times_times_nat(U_65,U_64)),
inference(definitional_conversion,[status(esa)],[f_61_2]) ).
cnf(f_61_4,plain,
power_power_real(power_power_real(U_66,U_65),U_64) = power_power_real(U_66,times_times_nat(U_65,U_64)),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_1,plain,
! [X_19,P_3,Q_4] : power_power_int(power_power_int(X_19,P_3),Q_4) = power_power_int(X_19,times_times_nat(P_3,Q_4)),
inference(fof_nnf,[status(thm)],[fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J]) ).
fof(f_62_2,plain,
! [U_69,U_68,U_67] : power_power_int(power_power_int(U_69,U_68),U_67) = power_power_int(U_69,times_times_nat(U_68,U_67)),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_67,U_68,U_69] : power_power_int(power_power_int(U_69,U_68),U_67) = power_power_int(U_69,times_times_nat(U_68,U_67)),
inference(definitional_conversion,[status(esa)],[f_62_2]) ).
cnf(f_62_4,plain,
power_power_int(power_power_int(U_69,U_68),U_67) = power_power_int(U_69,times_times_nat(U_68,U_67)),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_1,plain,
! [X_18] : power_power_nat(X_18,one_one_nat) = X_18,
inference(fof_nnf,[status(thm)],[fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J]) ).
fof(f_63_2,plain,
! [U_70] : power_power_nat(U_70,one_one_nat) = U_70,
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_70] : power_power_nat(U_70,one_one_nat) = U_70,
inference(definitional_conversion,[status(esa)],[f_63_2]) ).
cnf(f_63_4,plain,
power_power_nat(U_70,one_one_nat) = U_70,
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_1,plain,
! [X_18] : power_power_real(X_18,one_one_nat) = X_18,
inference(fof_nnf,[status(thm)],[fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J]) ).
fof(f_64_2,plain,
! [U_71] : power_power_real(U_71,one_one_nat) = U_71,
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
! [U_71] : power_power_real(U_71,one_one_nat) = U_71,
inference(definitional_conversion,[status(esa)],[f_64_2]) ).
cnf(f_64_4,plain,
power_power_real(U_71,one_one_nat) = U_71,
inference(clausify,[status(thm)],[f_64_3]) ).
fof(f_65_1,plain,
! [X_18] :
( power_power_int(X_18,one_one_nat) = X_18
| ~ is_int(X_18) ),
inference(fof_nnf,[status(thm)],[fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J]) ).
fof(f_65_2,plain,
! [U_72] :
( power_power_int(U_72,one_one_nat) = U_72
| ~ is_int(U_72) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_72] :
( power_power_int(U_72,one_one_nat) = U_72
| ~ is_int(U_72) ),
inference(definitional_conversion,[status(esa)],[f_65_2]) ).
cnf(f_65_4,plain,
( power_power_int(U_72,one_one_nat) = U_72
| ~ is_int(U_72) ),
inference(clausify,[status(thm)],[f_65_3]) ).
fof(f_66_1,plain,
! [X_1,Y_1,Z] : power_power_int(power_power_int(X_1,Y_1),Z) = power_power_int(X_1,times_times_nat(Y_1,Z)),
inference(fof_nnf,[status(thm)],[fact_47_zpower__zpower]) ).
fof(f_66_2,plain,
! [U_75,U_74,U_73] : power_power_int(power_power_int(U_75,U_74),U_73) = power_power_int(U_75,times_times_nat(U_74,U_73)),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_73,U_74,U_75] : power_power_int(power_power_int(U_75,U_74),U_73) = power_power_int(U_75,times_times_nat(U_74,U_73)),
inference(definitional_conversion,[status(esa)],[f_66_2]) ).
cnf(f_66_4,plain,
power_power_int(power_power_int(U_75,U_74),U_73) = power_power_int(U_75,times_times_nat(U_74,U_73)),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_1,plain,
! [V_3,W_1] :
( ( ord_less_eq_real(number267125858f_real(V_3),number267125858f_real(W_1))
| ord_less_real(number267125858f_real(W_1),number267125858f_real(V_3)) )
& ( ~ ord_less_real(number267125858f_real(W_1),number267125858f_real(V_3))
| ~ ord_less_eq_real(number267125858f_real(V_3),number267125858f_real(W_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_48_le__number__of__eq__not__less]) ).
fof(f_67_2,plain,
! [U_77,U_76] :
( ( ord_less_eq_real(number267125858f_real(U_77),number267125858f_real(U_76))
| ord_less_real(number267125858f_real(U_76),number267125858f_real(U_77)) )
& ( ~ ord_less_real(number267125858f_real(U_76),number267125858f_real(U_77))
| ~ ord_less_eq_real(number267125858f_real(U_77),number267125858f_real(U_76)) ) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
( ! [U_81,U_79] :
( ord_less_eq_real(number267125858f_real(U_81),number267125858f_real(U_79))
| ord_less_real(number267125858f_real(U_79),number267125858f_real(U_81)) )
& ! [U_80,U_78] :
( ~ ord_less_real(number267125858f_real(U_78),number267125858f_real(U_80))
| ~ ord_less_eq_real(number267125858f_real(U_80),number267125858f_real(U_78)) ) ),
inference(miniscope,[status(thm)],[f_67_2]) ).
fof(f_67_4,plain,
( ! [U_81,U_79] :
( ord_less_eq_real(number267125858f_real(U_81),number267125858f_real(U_79))
| ord_less_real(number267125858f_real(U_79),number267125858f_real(U_81)) )
& ! [U_80,U_78] :
( ~ ord_less_real(number267125858f_real(U_78),number267125858f_real(U_80))
| ~ ord_less_eq_real(number267125858f_real(U_80),number267125858f_real(U_78)) ) ),
inference(definitional_conversion,[status(esa)],[f_67_3]) ).
cnf(f_67_5,plain,
( ~ ord_less_real(number267125858f_real(U_78),number267125858f_real(U_80))
| ~ ord_less_eq_real(number267125858f_real(U_80),number267125858f_real(U_78)) ),
inference(clausify,[status(thm)],[f_67_4]) ).
cnf(f_67_6,plain,
( ord_less_eq_real(number267125858f_real(U_81),number267125858f_real(U_79))
| ord_less_real(number267125858f_real(U_79),number267125858f_real(U_81)) ),
inference(clausify,[status(thm)],[f_67_4]) ).
fof(f_68_1,plain,
! [V_3,W_1] :
( ( ord_less_eq_nat(number_number_of_nat(V_3),number_number_of_nat(W_1))
| ord_less_nat(number_number_of_nat(W_1),number_number_of_nat(V_3)) )
& ( ~ ord_less_nat(number_number_of_nat(W_1),number_number_of_nat(V_3))
| ~ ord_less_eq_nat(number_number_of_nat(V_3),number_number_of_nat(W_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_49_le__number__of__eq__not__less]) ).
fof(f_68_2,plain,
! [U_83,U_82] :
( ( ord_less_eq_nat(number_number_of_nat(U_83),number_number_of_nat(U_82))
| ord_less_nat(number_number_of_nat(U_82),number_number_of_nat(U_83)) )
& ( ~ ord_less_nat(number_number_of_nat(U_82),number_number_of_nat(U_83))
| ~ ord_less_eq_nat(number_number_of_nat(U_83),number_number_of_nat(U_82)) ) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
( ! [U_87,U_85] :
( ord_less_eq_nat(number_number_of_nat(U_87),number_number_of_nat(U_85))
| ord_less_nat(number_number_of_nat(U_85),number_number_of_nat(U_87)) )
& ! [U_86,U_84] :
( ~ ord_less_nat(number_number_of_nat(U_84),number_number_of_nat(U_86))
| ~ ord_less_eq_nat(number_number_of_nat(U_86),number_number_of_nat(U_84)) ) ),
inference(miniscope,[status(thm)],[f_68_2]) ).
fof(f_68_4,plain,
( ! [U_85,U_87] :
( ord_less_eq_nat(number_number_of_nat(U_87),number_number_of_nat(U_85))
| ord_less_nat(number_number_of_nat(U_85),number_number_of_nat(U_87)) )
& ! [U_86,U_84] :
( ~ ord_less_nat(number_number_of_nat(U_84),number_number_of_nat(U_86))
| ~ ord_less_eq_nat(number_number_of_nat(U_86),number_number_of_nat(U_84)) ) ),
inference(definitional_conversion,[status(esa)],[f_68_3]) ).
cnf(f_68_5,plain,
( ~ ord_less_nat(number_number_of_nat(U_84),number_number_of_nat(U_86))
| ~ ord_less_eq_nat(number_number_of_nat(U_86),number_number_of_nat(U_84)) ),
inference(clausify,[status(thm)],[f_68_4]) ).
cnf(f_68_6,plain,
( ord_less_eq_nat(number_number_of_nat(U_87),number_number_of_nat(U_85))
| ord_less_nat(number_number_of_nat(U_85),number_number_of_nat(U_87)) ),
inference(clausify,[status(thm)],[f_68_4]) ).
fof(f_69_1,plain,
! [V_3,W_1] :
( ( ord_less_eq_int(number_number_of_int(V_3),number_number_of_int(W_1))
| ord_less_int(number_number_of_int(W_1),number_number_of_int(V_3)) )
& ( ~ ord_less_int(number_number_of_int(W_1),number_number_of_int(V_3))
| ~ ord_less_eq_int(number_number_of_int(V_3),number_number_of_int(W_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_50_le__number__of__eq__not__less]) ).
fof(f_69_2,plain,
! [U_89,U_88] :
( ( ord_less_eq_int(number_number_of_int(U_89),number_number_of_int(U_88))
| ord_less_int(number_number_of_int(U_88),number_number_of_int(U_89)) )
& ( ~ ord_less_int(number_number_of_int(U_88),number_number_of_int(U_89))
| ~ ord_less_eq_int(number_number_of_int(U_89),number_number_of_int(U_88)) ) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
( ! [U_93,U_91] :
( ord_less_eq_int(number_number_of_int(U_93),number_number_of_int(U_91))
| ord_less_int(number_number_of_int(U_91),number_number_of_int(U_93)) )
& ! [U_92,U_90] :
( ~ ord_less_int(number_number_of_int(U_90),number_number_of_int(U_92))
| ~ ord_less_eq_int(number_number_of_int(U_92),number_number_of_int(U_90)) ) ),
inference(miniscope,[status(thm)],[f_69_2]) ).
fof(f_69_4,plain,
( ! [U_93,U_91] :
( ord_less_eq_int(number_number_of_int(U_93),number_number_of_int(U_91))
| ord_less_int(number_number_of_int(U_91),number_number_of_int(U_93)) )
& ! [U_92,U_90] :
( ~ ord_less_int(number_number_of_int(U_90),number_number_of_int(U_92))
| ~ ord_less_eq_int(number_number_of_int(U_92),number_number_of_int(U_90)) ) ),
inference(definitional_conversion,[status(esa)],[f_69_3]) ).
cnf(f_69_5,plain,
( ~ ord_less_int(number_number_of_int(U_90),number_number_of_int(U_92))
| ~ ord_less_eq_int(number_number_of_int(U_92),number_number_of_int(U_90)) ),
inference(clausify,[status(thm)],[f_69_4]) ).
cnf(f_69_6,plain,
( ord_less_eq_int(number_number_of_int(U_93),number_number_of_int(U_91))
| ord_less_int(number_number_of_int(U_91),number_number_of_int(U_93)) ),
inference(clausify,[status(thm)],[f_69_4]) ).
fof(f_70_1,plain,
! [X_2,Y_2] :
( ( ord_less_real(number267125858f_real(X_2),number267125858f_real(Y_2))
| ~ ord_less_int(X_2,Y_2) )
& ( ord_less_int(X_2,Y_2)
| ~ ord_less_real(number267125858f_real(X_2),number267125858f_real(Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_51_less__number__of]) ).
fof(f_70_2,plain,
! [U_95,U_94] :
( ( ord_less_real(number267125858f_real(U_95),number267125858f_real(U_94))
| ~ ord_less_int(U_95,U_94) )
& ( ord_less_int(U_95,U_94)
| ~ ord_less_real(number267125858f_real(U_95),number267125858f_real(U_94)) ) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
( ! [U_99,U_97] :
( ord_less_real(number267125858f_real(U_99),number267125858f_real(U_97))
| ~ ord_less_int(U_99,U_97) )
& ! [U_98,U_96] :
( ord_less_int(U_98,U_96)
| ~ ord_less_real(number267125858f_real(U_98),number267125858f_real(U_96)) ) ),
inference(miniscope,[status(thm)],[f_70_2]) ).
fof(f_70_4,plain,
( ! [U_99,U_97] :
( ord_less_real(number267125858f_real(U_99),number267125858f_real(U_97))
| ~ ord_less_int(U_99,U_97) )
& ! [U_98,U_96] :
( ord_less_int(U_98,U_96)
| ~ ord_less_real(number267125858f_real(U_98),number267125858f_real(U_96)) ) ),
inference(definitional_conversion,[status(esa)],[f_70_3]) ).
cnf(f_70_5,plain,
( ord_less_int(U_98,U_96)
| ~ ord_less_real(number267125858f_real(U_98),number267125858f_real(U_96)) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_6,plain,
( ord_less_real(number267125858f_real(U_99),number267125858f_real(U_97))
| ~ ord_less_int(U_99,U_97) ),
inference(clausify,[status(thm)],[f_70_4]) ).
fof(f_71_1,plain,
! [X_2,Y_2] :
( ( ord_less_int(number_number_of_int(X_2),number_number_of_int(Y_2))
| ~ ord_less_int(X_2,Y_2) )
& ( ord_less_int(X_2,Y_2)
| ~ ord_less_int(number_number_of_int(X_2),number_number_of_int(Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_52_less__number__of]) ).
fof(f_71_2,plain,
! [U_101,U_100] :
( ( ord_less_int(number_number_of_int(U_101),number_number_of_int(U_100))
| ~ ord_less_int(U_101,U_100) )
& ( ord_less_int(U_101,U_100)
| ~ ord_less_int(number_number_of_int(U_101),number_number_of_int(U_100)) ) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
( ! [U_105,U_103] :
( ord_less_int(number_number_of_int(U_105),number_number_of_int(U_103))
| ~ ord_less_int(U_105,U_103) )
& ! [U_104,U_102] :
( ord_less_int(U_104,U_102)
| ~ ord_less_int(number_number_of_int(U_104),number_number_of_int(U_102)) ) ),
inference(miniscope,[status(thm)],[f_71_2]) ).
fof(f_71_4,plain,
( ! [U_103,U_105] :
( ord_less_int(number_number_of_int(U_105),number_number_of_int(U_103))
| ~ ord_less_int(U_105,U_103) )
& ! [U_104,U_102] :
( ord_less_int(U_104,U_102)
| ~ ord_less_int(number_number_of_int(U_104),number_number_of_int(U_102)) ) ),
inference(definitional_conversion,[status(esa)],[f_71_3]) ).
cnf(f_71_5,plain,
( ord_less_int(U_104,U_102)
| ~ ord_less_int(number_number_of_int(U_104),number_number_of_int(U_102)) ),
inference(clausify,[status(thm)],[f_71_4]) ).
cnf(f_71_6,plain,
( ord_less_int(number_number_of_int(U_105),number_number_of_int(U_103))
| ~ ord_less_int(U_105,U_103) ),
inference(clausify,[status(thm)],[f_71_4]) ).
fof(f_72_1,plain,
! [X_2,Y_2] :
( ( ord_less_eq_real(number267125858f_real(X_2),number267125858f_real(Y_2))
| ~ ord_less_eq_int(X_2,Y_2) )
& ( ord_less_eq_int(X_2,Y_2)
| ~ ord_less_eq_real(number267125858f_real(X_2),number267125858f_real(Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_53_le__number__of]) ).
fof(f_72_2,plain,
! [U_107,U_106] :
( ( ord_less_eq_real(number267125858f_real(U_107),number267125858f_real(U_106))
| ~ ord_less_eq_int(U_107,U_106) )
& ( ord_less_eq_int(U_107,U_106)
| ~ ord_less_eq_real(number267125858f_real(U_107),number267125858f_real(U_106)) ) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
( ! [U_111,U_109] :
( ord_less_eq_real(number267125858f_real(U_111),number267125858f_real(U_109))
| ~ ord_less_eq_int(U_111,U_109) )
& ! [U_110,U_108] :
( ord_less_eq_int(U_110,U_108)
| ~ ord_less_eq_real(number267125858f_real(U_110),number267125858f_real(U_108)) ) ),
inference(miniscope,[status(thm)],[f_72_2]) ).
fof(f_72_4,plain,
( ! [U_109,U_111] :
( ord_less_eq_real(number267125858f_real(U_111),number267125858f_real(U_109))
| ~ ord_less_eq_int(U_111,U_109) )
& ! [U_110,U_108] :
( ord_less_eq_int(U_110,U_108)
| ~ ord_less_eq_real(number267125858f_real(U_110),number267125858f_real(U_108)) ) ),
inference(definitional_conversion,[status(esa)],[f_72_3]) ).
cnf(f_72_5,plain,
( ord_less_eq_int(U_110,U_108)
| ~ ord_less_eq_real(number267125858f_real(U_110),number267125858f_real(U_108)) ),
inference(clausify,[status(thm)],[f_72_4]) ).
cnf(f_72_6,plain,
( ord_less_eq_real(number267125858f_real(U_111),number267125858f_real(U_109))
| ~ ord_less_eq_int(U_111,U_109) ),
inference(clausify,[status(thm)],[f_72_4]) ).
fof(f_73_1,plain,
! [X_2,Y_2] :
( ( ord_less_eq_int(number_number_of_int(X_2),number_number_of_int(Y_2))
| ~ ord_less_eq_int(X_2,Y_2) )
& ( ord_less_eq_int(X_2,Y_2)
| ~ ord_less_eq_int(number_number_of_int(X_2),number_number_of_int(Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_54_le__number__of]) ).
fof(f_73_2,plain,
! [U_113,U_112] :
( ( ord_less_eq_int(number_number_of_int(U_113),number_number_of_int(U_112))
| ~ ord_less_eq_int(U_113,U_112) )
& ( ord_less_eq_int(U_113,U_112)
| ~ ord_less_eq_int(number_number_of_int(U_113),number_number_of_int(U_112)) ) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
( ! [U_117,U_115] :
( ord_less_eq_int(number_number_of_int(U_117),number_number_of_int(U_115))
| ~ ord_less_eq_int(U_117,U_115) )
& ! [U_116,U_114] :
( ord_less_eq_int(U_116,U_114)
| ~ ord_less_eq_int(number_number_of_int(U_116),number_number_of_int(U_114)) ) ),
inference(miniscope,[status(thm)],[f_73_2]) ).
fof(f_73_4,plain,
( ! [U_115,U_117] :
( ord_less_eq_int(number_number_of_int(U_117),number_number_of_int(U_115))
| ~ ord_less_eq_int(U_117,U_115) )
& ! [U_116,U_114] :
( ord_less_eq_int(U_116,U_114)
| ~ ord_less_eq_int(number_number_of_int(U_116),number_number_of_int(U_114)) ) ),
inference(definitional_conversion,[status(esa)],[f_73_3]) ).
cnf(f_73_5,plain,
( ord_less_eq_int(U_116,U_114)
| ~ ord_less_eq_int(number_number_of_int(U_116),number_number_of_int(U_114)) ),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_6,plain,
( ord_less_eq_int(number_number_of_int(U_117),number_number_of_int(U_115))
| ~ ord_less_eq_int(U_117,U_115) ),
inference(clausify,[status(thm)],[f_73_4]) ).
fof(f_74_1,plain,
! [Z_9,Z,W_13,W] :
( ord_less_int(plus_plus_int(W_13,Z_9),plus_plus_int(W,Z))
| ~ ord_less_eq_int(Z_9,Z)
| ~ ord_less_int(W_13,W) ),
inference(fof_nnf,[status(thm)],[fact_55_zadd__zless__mono]) ).
fof(f_74_2,plain,
! [U_121,U_120,U_119,U_118] :
( ord_less_int(plus_plus_int(U_119,U_121),plus_plus_int(U_118,U_120))
| ~ ord_less_eq_int(U_121,U_120)
| ~ ord_less_int(U_119,U_118) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
! [U_118,U_119,U_120,U_121] :
( ord_less_int(plus_plus_int(U_119,U_121),plus_plus_int(U_118,U_120))
| ~ ord_less_eq_int(U_121,U_120)
| ~ ord_less_int(U_119,U_118) ),
inference(definitional_conversion,[status(esa)],[f_74_2]) ).
cnf(f_74_4,plain,
( ord_less_int(plus_plus_int(U_119,U_121),plus_plus_int(U_118,U_120))
| ~ ord_less_eq_int(U_121,U_120)
| ~ ord_less_int(U_119,U_118) ),
inference(clausify,[status(thm)],[f_74_3]) ).
fof(f_75_1,plain,
! [X_17,P_2,Q_3] : times_times_nat(power_power_nat(X_17,P_2),power_power_nat(X_17,Q_3)) = power_power_nat(X_17,plus_plus_nat(P_2,Q_3)),
inference(fof_nnf,[status(thm)],[fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J]) ).
fof(f_75_2,plain,
! [U_124,U_123,U_122] : times_times_nat(power_power_nat(U_124,U_123),power_power_nat(U_124,U_122)) = power_power_nat(U_124,plus_plus_nat(U_123,U_122)),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
! [U_124,U_123,U_122] : times_times_nat(power_power_nat(U_124,U_123),power_power_nat(U_124,U_122)) = power_power_nat(U_124,plus_plus_nat(U_123,U_122)),
inference(definitional_conversion,[status(esa)],[f_75_2]) ).
cnf(f_75_4,plain,
times_times_nat(power_power_nat(U_124,U_123),power_power_nat(U_124,U_122)) = power_power_nat(U_124,plus_plus_nat(U_123,U_122)),
inference(clausify,[status(thm)],[f_75_3]) ).
fof(f_76_1,plain,
! [X_17,P_2,Q_3] : times_times_real(power_power_real(X_17,P_2),power_power_real(X_17,Q_3)) = power_power_real(X_17,plus_plus_nat(P_2,Q_3)),
inference(fof_nnf,[status(thm)],[fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J]) ).
fof(f_76_2,plain,
! [U_127,U_126,U_125] : times_times_real(power_power_real(U_127,U_126),power_power_real(U_127,U_125)) = power_power_real(U_127,plus_plus_nat(U_126,U_125)),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
! [U_125,U_126,U_127] : times_times_real(power_power_real(U_127,U_126),power_power_real(U_127,U_125)) = power_power_real(U_127,plus_plus_nat(U_126,U_125)),
inference(definitional_conversion,[status(esa)],[f_76_2]) ).
cnf(f_76_4,plain,
times_times_real(power_power_real(U_127,U_126),power_power_real(U_127,U_125)) = power_power_real(U_127,plus_plus_nat(U_126,U_125)),
inference(clausify,[status(thm)],[f_76_3]) ).
fof(f_77_1,plain,
! [X_17,P_2,Q_3] : times_times_int(power_power_int(X_17,P_2),power_power_int(X_17,Q_3)) = power_power_int(X_17,plus_plus_nat(P_2,Q_3)),
inference(fof_nnf,[status(thm)],[fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J]) ).
fof(f_77_2,plain,
! [U_130,U_129,U_128] : times_times_int(power_power_int(U_130,U_129),power_power_int(U_130,U_128)) = power_power_int(U_130,plus_plus_nat(U_129,U_128)),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
! [U_128,U_129,U_130] : times_times_int(power_power_int(U_130,U_129),power_power_int(U_130,U_128)) = power_power_int(U_130,plus_plus_nat(U_129,U_128)),
inference(definitional_conversion,[status(esa)],[f_77_2]) ).
cnf(f_77_4,plain,
times_times_int(power_power_int(U_130,U_129),power_power_int(U_130,U_128)) = power_power_int(U_130,plus_plus_nat(U_129,U_128)),
inference(clausify,[status(thm)],[f_77_3]) ).
fof(f_78_1,plain,
! [X_1,Y_1,Z] : power_power_int(X_1,plus_plus_nat(Y_1,Z)) = times_times_int(power_power_int(X_1,Y_1),power_power_int(X_1,Z)),
inference(fof_nnf,[status(thm)],[fact_59_zpower__zadd__distrib]) ).
fof(f_78_2,plain,
! [U_133,U_132,U_131] : power_power_int(U_133,plus_plus_nat(U_132,U_131)) = times_times_int(power_power_int(U_133,U_132),power_power_int(U_133,U_131)),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
! [U_131,U_132,U_133] : power_power_int(U_133,plus_plus_nat(U_132,U_131)) = times_times_int(power_power_int(U_133,U_132),power_power_int(U_133,U_131)),
inference(definitional_conversion,[status(esa)],[f_78_2]) ).
cnf(f_78_4,plain,
power_power_int(U_133,plus_plus_nat(U_132,U_131)) = times_times_int(power_power_int(U_133,U_132),power_power_int(U_133,U_131)),
inference(clausify,[status(thm)],[f_78_3]) ).
fof(f_79_1,plain,
! [Z] : times_times_nat(number_number_of_nat(bit0(bit1(pls))),Z) = plus_plus_nat(Z,Z),
inference(fof_nnf,[status(thm)],[fact_60_nat__mult__2]) ).
fof(f_79_2,plain,
! [U_134] : times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_134) = plus_plus_nat(U_134,U_134),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
! [U_134] : times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_134) = plus_plus_nat(U_134,U_134),
inference(definitional_conversion,[status(esa)],[f_79_2]) ).
cnf(f_79_4,plain,
times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_134) = plus_plus_nat(U_134,U_134),
inference(clausify,[status(thm)],[f_79_3]) ).
fof(f_80_1,plain,
! [Z] : times_times_nat(Z,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(Z,Z),
inference(fof_nnf,[status(thm)],[fact_61_nat__mult__2__right]) ).
fof(f_80_2,plain,
! [U_135] : times_times_nat(U_135,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(U_135,U_135),
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
! [U_135] : times_times_nat(U_135,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(U_135,U_135),
inference(definitional_conversion,[status(esa)],[f_80_2]) ).
cnf(f_80_4,plain,
times_times_nat(U_135,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(U_135,U_135),
inference(clausify,[status(thm)],[f_80_3]) ).
fof(f_81_1,plain,
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]) ).
fof(f_81_2,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(definitional_conversion,[status(esa)],[f_81_1]) ).
cnf(f_81_3,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_1,plain,
! [K1,K2] :
( ( ord_less_int(bit1(K1),bit1(K2))
| ~ ord_less_int(K1,K2) )
& ( ord_less_int(K1,K2)
| ~ ord_less_int(bit1(K1),bit1(K2)) ) ),
inference(fof_nnf,[status(thm)],[fact_63_less__int__code_I16_J]) ).
fof(f_82_2,plain,
! [U_137,U_136] :
( ( ord_less_int(bit1(U_137),bit1(U_136))
| ~ ord_less_int(U_137,U_136) )
& ( ord_less_int(U_137,U_136)
| ~ ord_less_int(bit1(U_137),bit1(U_136)) ) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
( ! [U_141,U_139] :
( ord_less_int(bit1(U_141),bit1(U_139))
| ~ ord_less_int(U_141,U_139) )
& ! [U_140,U_138] :
( ord_less_int(U_140,U_138)
| ~ ord_less_int(bit1(U_140),bit1(U_138)) ) ),
inference(miniscope,[status(thm)],[f_82_2]) ).
fof(f_82_4,plain,
( ! [U_139,U_141] :
( ord_less_int(bit1(U_141),bit1(U_139))
| ~ ord_less_int(U_141,U_139) )
& ! [U_140,U_138] :
( ord_less_int(U_140,U_138)
| ~ ord_less_int(bit1(U_140),bit1(U_138)) ) ),
inference(definitional_conversion,[status(esa)],[f_82_3]) ).
cnf(f_82_5,plain,
( ord_less_int(U_140,U_138)
| ~ ord_less_int(bit1(U_140),bit1(U_138)) ),
inference(clausify,[status(thm)],[f_82_4]) ).
cnf(f_82_6,plain,
( ord_less_int(bit1(U_141),bit1(U_139))
| ~ ord_less_int(U_141,U_139) ),
inference(clausify,[status(thm)],[f_82_4]) ).
fof(f_83_1,plain,
! [K_1,L_1] :
( ( ord_less_int(bit1(K_1),bit1(L_1))
| ~ ord_less_int(K_1,L_1) )
& ( ord_less_int(K_1,L_1)
| ~ ord_less_int(bit1(K_1),bit1(L_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_64_rel__simps_I17_J]) ).
fof(f_83_2,plain,
! [U_143,U_142] :
( ( ord_less_int(bit1(U_143),bit1(U_142))
| ~ ord_less_int(U_143,U_142) )
& ( ord_less_int(U_143,U_142)
| ~ ord_less_int(bit1(U_143),bit1(U_142)) ) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
( ! [U_147,U_145] :
( ord_less_int(bit1(U_147),bit1(U_145))
| ~ ord_less_int(U_147,U_145) )
& ! [U_146,U_144] :
( ord_less_int(U_146,U_144)
| ~ ord_less_int(bit1(U_146),bit1(U_144)) ) ),
inference(miniscope,[status(thm)],[f_83_2]) ).
fof(f_83_4,plain,
( ! [U_145,U_147] :
( ord_less_int(bit1(U_147),bit1(U_145))
| ~ ord_less_int(U_147,U_145) )
& ! [U_144,U_146] :
( ord_less_int(U_146,U_144)
| ~ ord_less_int(bit1(U_146),bit1(U_144)) ) ),
inference(definitional_conversion,[status(esa)],[f_83_3]) ).
cnf(f_83_5,plain,
( ord_less_int(U_146,U_144)
| ~ ord_less_int(bit1(U_146),bit1(U_144)) ),
inference(clausify,[status(thm)],[f_83_4]) ).
cnf(f_83_6,plain,
( ord_less_int(bit1(U_147),bit1(U_145))
| ~ ord_less_int(U_147,U_145) ),
inference(clausify,[status(thm)],[f_83_4]) ).
fof(f_84_1,plain,
! [K1,K2] :
( ( ord_less_eq_int(bit1(K1),bit1(K2))
| ~ ord_less_eq_int(K1,K2) )
& ( ord_less_eq_int(K1,K2)
| ~ ord_less_eq_int(bit1(K1),bit1(K2)) ) ),
inference(fof_nnf,[status(thm)],[fact_65_less__eq__int__code_I16_J]) ).
fof(f_84_2,plain,
! [U_149,U_148] :
( ( ord_less_eq_int(bit1(U_149),bit1(U_148))
| ~ ord_less_eq_int(U_149,U_148) )
& ( ord_less_eq_int(U_149,U_148)
| ~ ord_less_eq_int(bit1(U_149),bit1(U_148)) ) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
( ! [U_153,U_151] :
( ord_less_eq_int(bit1(U_153),bit1(U_151))
| ~ ord_less_eq_int(U_153,U_151) )
& ! [U_152,U_150] :
( ord_less_eq_int(U_152,U_150)
| ~ ord_less_eq_int(bit1(U_152),bit1(U_150)) ) ),
inference(miniscope,[status(thm)],[f_84_2]) ).
fof(f_84_4,plain,
( ! [U_151,U_153] :
( ord_less_eq_int(bit1(U_153),bit1(U_151))
| ~ ord_less_eq_int(U_153,U_151) )
& ! [U_150,U_152] :
( ord_less_eq_int(U_152,U_150)
| ~ ord_less_eq_int(bit1(U_152),bit1(U_150)) ) ),
inference(definitional_conversion,[status(esa)],[f_84_3]) ).
cnf(f_84_5,plain,
( ord_less_eq_int(U_152,U_150)
| ~ ord_less_eq_int(bit1(U_152),bit1(U_150)) ),
inference(clausify,[status(thm)],[f_84_4]) ).
cnf(f_84_6,plain,
( ord_less_eq_int(bit1(U_153),bit1(U_151))
| ~ ord_less_eq_int(U_153,U_151) ),
inference(clausify,[status(thm)],[f_84_4]) ).
fof(f_85_1,plain,
! [K_1,L_1] :
( ( ord_less_eq_int(bit1(K_1),bit1(L_1))
| ~ ord_less_eq_int(K_1,L_1) )
& ( ord_less_eq_int(K_1,L_1)
| ~ ord_less_eq_int(bit1(K_1),bit1(L_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_66_rel__simps_I34_J]) ).
fof(f_85_2,plain,
! [U_155,U_154] :
( ( ord_less_eq_int(bit1(U_155),bit1(U_154))
| ~ ord_less_eq_int(U_155,U_154) )
& ( ord_less_eq_int(U_155,U_154)
| ~ ord_less_eq_int(bit1(U_155),bit1(U_154)) ) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
( ! [U_159,U_157] :
( ord_less_eq_int(bit1(U_159),bit1(U_157))
| ~ ord_less_eq_int(U_159,U_157) )
& ! [U_158,U_156] :
( ord_less_eq_int(U_158,U_156)
| ~ ord_less_eq_int(bit1(U_158),bit1(U_156)) ) ),
inference(miniscope,[status(thm)],[f_85_2]) ).
fof(f_85_4,plain,
( ! [U_159,U_157] :
( ord_less_eq_int(bit1(U_159),bit1(U_157))
| ~ ord_less_eq_int(U_159,U_157) )
& ! [U_158,U_156] :
( ord_less_eq_int(U_158,U_156)
| ~ ord_less_eq_int(bit1(U_158),bit1(U_156)) ) ),
inference(definitional_conversion,[status(esa)],[f_85_3]) ).
cnf(f_85_5,plain,
( ord_less_eq_int(U_158,U_156)
| ~ ord_less_eq_int(bit1(U_158),bit1(U_156)) ),
inference(clausify,[status(thm)],[f_85_4]) ).
cnf(f_85_6,plain,
( ord_less_eq_int(bit1(U_159),bit1(U_157))
| ~ ord_less_eq_int(U_159,U_157) ),
inference(clausify,[status(thm)],[f_85_4]) ).
fof(f_86_1,plain,
~ ord_less_int(pls,pls),
inference(fof_nnf,[status(thm)],[fact_67_rel__simps_I2_J]) ).
fof(f_86_2,plain,
~ ord_less_int(pls,pls),
inference(definitional_conversion,[status(esa)],[f_86_1]) ).
cnf(f_86_3,plain,
~ ord_less_int(pls,pls),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_1,plain,
! [K1,K2] :
( ( ord_less_int(bit0(K1),bit0(K2))
| ~ ord_less_int(K1,K2) )
& ( ord_less_int(K1,K2)
| ~ ord_less_int(bit0(K1),bit0(K2)) ) ),
inference(fof_nnf,[status(thm)],[fact_68_less__int__code_I13_J]) ).
fof(f_87_2,plain,
! [U_161,U_160] :
( ( ord_less_int(bit0(U_161),bit0(U_160))
| ~ ord_less_int(U_161,U_160) )
& ( ord_less_int(U_161,U_160)
| ~ ord_less_int(bit0(U_161),bit0(U_160)) ) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
fof(f_87_3,plain,
( ! [U_165,U_163] :
( ord_less_int(bit0(U_165),bit0(U_163))
| ~ ord_less_int(U_165,U_163) )
& ! [U_164,U_162] :
( ord_less_int(U_164,U_162)
| ~ ord_less_int(bit0(U_164),bit0(U_162)) ) ),
inference(miniscope,[status(thm)],[f_87_2]) ).
fof(f_87_4,plain,
( ! [U_163,U_165] :
( ord_less_int(bit0(U_165),bit0(U_163))
| ~ ord_less_int(U_165,U_163) )
& ! [U_164,U_162] :
( ord_less_int(U_164,U_162)
| ~ ord_less_int(bit0(U_164),bit0(U_162)) ) ),
inference(definitional_conversion,[status(esa)],[f_87_3]) ).
cnf(f_87_5,plain,
( ord_less_int(U_164,U_162)
| ~ ord_less_int(bit0(U_164),bit0(U_162)) ),
inference(clausify,[status(thm)],[f_87_4]) ).
cnf(f_87_6,plain,
( ord_less_int(bit0(U_165),bit0(U_163))
| ~ ord_less_int(U_165,U_163) ),
inference(clausify,[status(thm)],[f_87_4]) ).
fof(f_88_1,plain,
! [K_1,L_1] :
( ( ord_less_int(bit0(K_1),bit0(L_1))
| ~ ord_less_int(K_1,L_1) )
& ( ord_less_int(K_1,L_1)
| ~ ord_less_int(bit0(K_1),bit0(L_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_69_rel__simps_I14_J]) ).
fof(f_88_2,plain,
! [U_167,U_166] :
( ( ord_less_int(bit0(U_167),bit0(U_166))
| ~ ord_less_int(U_167,U_166) )
& ( ord_less_int(U_167,U_166)
| ~ ord_less_int(bit0(U_167),bit0(U_166)) ) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
( ! [U_171,U_169] :
( ord_less_int(bit0(U_171),bit0(U_169))
| ~ ord_less_int(U_171,U_169) )
& ! [U_170,U_168] :
( ord_less_int(U_170,U_168)
| ~ ord_less_int(bit0(U_170),bit0(U_168)) ) ),
inference(miniscope,[status(thm)],[f_88_2]) ).
fof(f_88_4,plain,
( ! [U_169,U_171] :
( ord_less_int(bit0(U_171),bit0(U_169))
| ~ ord_less_int(U_171,U_169) )
& ! [U_168,U_170] :
( ord_less_int(U_170,U_168)
| ~ ord_less_int(bit0(U_170),bit0(U_168)) ) ),
inference(definitional_conversion,[status(esa)],[f_88_3]) ).
cnf(f_88_5,plain,
( ord_less_int(U_170,U_168)
| ~ ord_less_int(bit0(U_170),bit0(U_168)) ),
inference(clausify,[status(thm)],[f_88_4]) ).
cnf(f_88_6,plain,
( ord_less_int(bit0(U_171),bit0(U_169))
| ~ ord_less_int(U_171,U_169) ),
inference(clausify,[status(thm)],[f_88_4]) ).
fof(f_89_1,plain,
ord_less_eq_int(pls,pls),
inference(fof_nnf,[status(thm)],[fact_70_rel__simps_I19_J]) ).
fof(f_89_2,plain,
ord_less_eq_int(pls,pls),
inference(definitional_conversion,[status(esa)],[f_89_1]) ).
cnf(f_89_3,plain,
ord_less_eq_int(pls,pls),
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_1,plain,
! [K1,K2] :
( ( ord_less_eq_int(bit0(K1),bit0(K2))
| ~ ord_less_eq_int(K1,K2) )
& ( ord_less_eq_int(K1,K2)
| ~ ord_less_eq_int(bit0(K1),bit0(K2)) ) ),
inference(fof_nnf,[status(thm)],[fact_71_less__eq__int__code_I13_J]) ).
fof(f_90_2,plain,
! [U_173,U_172] :
( ( ord_less_eq_int(bit0(U_173),bit0(U_172))
| ~ ord_less_eq_int(U_173,U_172) )
& ( ord_less_eq_int(U_173,U_172)
| ~ ord_less_eq_int(bit0(U_173),bit0(U_172)) ) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
( ! [U_177,U_175] :
( ord_less_eq_int(bit0(U_177),bit0(U_175))
| ~ ord_less_eq_int(U_177,U_175) )
& ! [U_176,U_174] :
( ord_less_eq_int(U_176,U_174)
| ~ ord_less_eq_int(bit0(U_176),bit0(U_174)) ) ),
inference(miniscope,[status(thm)],[f_90_2]) ).
fof(f_90_4,plain,
( ! [U_175,U_177] :
( ord_less_eq_int(bit0(U_177),bit0(U_175))
| ~ ord_less_eq_int(U_177,U_175) )
& ! [U_176,U_174] :
( ord_less_eq_int(U_176,U_174)
| ~ ord_less_eq_int(bit0(U_176),bit0(U_174)) ) ),
inference(definitional_conversion,[status(esa)],[f_90_3]) ).
cnf(f_90_5,plain,
( ord_less_eq_int(U_176,U_174)
| ~ ord_less_eq_int(bit0(U_176),bit0(U_174)) ),
inference(clausify,[status(thm)],[f_90_4]) ).
cnf(f_90_6,plain,
( ord_less_eq_int(bit0(U_177),bit0(U_175))
| ~ ord_less_eq_int(U_177,U_175) ),
inference(clausify,[status(thm)],[f_90_4]) ).
fof(f_91_1,plain,
! [K_1,L_1] :
( ( ord_less_eq_int(bit0(K_1),bit0(L_1))
| ~ ord_less_eq_int(K_1,L_1) )
& ( ord_less_eq_int(K_1,L_1)
| ~ ord_less_eq_int(bit0(K_1),bit0(L_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_72_rel__simps_I31_J]) ).
fof(f_91_2,plain,
! [U_179,U_178] :
( ( ord_less_eq_int(bit0(U_179),bit0(U_178))
| ~ ord_less_eq_int(U_179,U_178) )
& ( ord_less_eq_int(U_179,U_178)
| ~ ord_less_eq_int(bit0(U_179),bit0(U_178)) ) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
( ! [U_183,U_181] :
( ord_less_eq_int(bit0(U_183),bit0(U_181))
| ~ ord_less_eq_int(U_183,U_181) )
& ! [U_182,U_180] :
( ord_less_eq_int(U_182,U_180)
| ~ ord_less_eq_int(bit0(U_182),bit0(U_180)) ) ),
inference(miniscope,[status(thm)],[f_91_2]) ).
fof(f_91_4,plain,
( ! [U_181,U_183] :
( ord_less_eq_int(bit0(U_183),bit0(U_181))
| ~ ord_less_eq_int(U_183,U_181) )
& ! [U_182,U_180] :
( ord_less_eq_int(U_182,U_180)
| ~ ord_less_eq_int(bit0(U_182),bit0(U_180)) ) ),
inference(definitional_conversion,[status(esa)],[f_91_3]) ).
cnf(f_91_5,plain,
( ord_less_eq_int(U_182,U_180)
| ~ ord_less_eq_int(bit0(U_182),bit0(U_180)) ),
inference(clausify,[status(thm)],[f_91_4]) ).
cnf(f_91_6,plain,
( ord_less_eq_int(bit0(U_183),bit0(U_181))
| ~ ord_less_eq_int(U_183,U_181) ),
inference(clausify,[status(thm)],[f_91_4]) ).
fof(f_92_1,plain,
! [K_1,L_1] :
( ( ord_less_int(number_number_of_int(K_1),number_number_of_int(L_1))
| ~ ord_less_int(K_1,L_1) )
& ( ord_less_int(K_1,L_1)
| ~ ord_less_int(number_number_of_int(K_1),number_number_of_int(L_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_73_less__number__of__int__code]) ).
fof(f_92_2,plain,
! [U_185,U_184] :
( ( ord_less_int(number_number_of_int(U_185),number_number_of_int(U_184))
| ~ ord_less_int(U_185,U_184) )
& ( ord_less_int(U_185,U_184)
| ~ ord_less_int(number_number_of_int(U_185),number_number_of_int(U_184)) ) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
( ! [U_189,U_187] :
( ord_less_int(number_number_of_int(U_189),number_number_of_int(U_187))
| ~ ord_less_int(U_189,U_187) )
& ! [U_188,U_186] :
( ord_less_int(U_188,U_186)
| ~ ord_less_int(number_number_of_int(U_188),number_number_of_int(U_186)) ) ),
inference(miniscope,[status(thm)],[f_92_2]) ).
fof(f_92_4,plain,
( ! [U_187,U_189] :
( ord_less_int(number_number_of_int(U_189),number_number_of_int(U_187))
| ~ ord_less_int(U_189,U_187) )
& ! [U_186,U_188] :
( ord_less_int(U_188,U_186)
| ~ ord_less_int(number_number_of_int(U_188),number_number_of_int(U_186)) ) ),
inference(definitional_conversion,[status(esa)],[f_92_3]) ).
cnf(f_92_5,plain,
( ord_less_int(U_188,U_186)
| ~ ord_less_int(number_number_of_int(U_188),number_number_of_int(U_186)) ),
inference(clausify,[status(thm)],[f_92_4]) ).
cnf(f_92_6,plain,
( ord_less_int(number_number_of_int(U_189),number_number_of_int(U_187))
| ~ ord_less_int(U_189,U_187) ),
inference(clausify,[status(thm)],[f_92_4]) ).
fof(f_93_1,plain,
! [K_1,L_1] :
( ( ord_less_eq_int(number_number_of_int(K_1),number_number_of_int(L_1))
| ~ ord_less_eq_int(K_1,L_1) )
& ( ord_less_eq_int(K_1,L_1)
| ~ ord_less_eq_int(number_number_of_int(K_1),number_number_of_int(L_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_74_less__eq__number__of__int__code]) ).
fof(f_93_2,plain,
! [U_191,U_190] :
( ( ord_less_eq_int(number_number_of_int(U_191),number_number_of_int(U_190))
| ~ ord_less_eq_int(U_191,U_190) )
& ( ord_less_eq_int(U_191,U_190)
| ~ ord_less_eq_int(number_number_of_int(U_191),number_number_of_int(U_190)) ) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
( ! [U_195,U_193] :
( ord_less_eq_int(number_number_of_int(U_195),number_number_of_int(U_193))
| ~ ord_less_eq_int(U_195,U_193) )
& ! [U_194,U_192] :
( ord_less_eq_int(U_194,U_192)
| ~ ord_less_eq_int(number_number_of_int(U_194),number_number_of_int(U_192)) ) ),
inference(miniscope,[status(thm)],[f_93_2]) ).
fof(f_93_4,plain,
( ! [U_193,U_195] :
( ord_less_eq_int(number_number_of_int(U_195),number_number_of_int(U_193))
| ~ ord_less_eq_int(U_195,U_193) )
& ! [U_192,U_194] :
( ord_less_eq_int(U_194,U_192)
| ~ ord_less_eq_int(number_number_of_int(U_194),number_number_of_int(U_192)) ) ),
inference(definitional_conversion,[status(esa)],[f_93_3]) ).
cnf(f_93_5,plain,
( ord_less_eq_int(U_194,U_192)
| ~ ord_less_eq_int(number_number_of_int(U_194),number_number_of_int(U_192)) ),
inference(clausify,[status(thm)],[f_93_4]) ).
cnf(f_93_6,plain,
( ord_less_eq_int(number_number_of_int(U_195),number_number_of_int(U_193))
| ~ ord_less_eq_int(U_195,U_193) ),
inference(clausify,[status(thm)],[f_93_4]) ).
fof(f_94_1,plain,
! [K,I,J] :
( ord_less_int(plus_plus_int(I,K),plus_plus_int(J,K))
| ~ ord_less_int(I,J) ),
inference(fof_nnf,[status(thm)],[fact_75_zadd__strict__right__mono]) ).
fof(f_94_2,plain,
! [U_198,U_197,U_196] :
( ord_less_int(plus_plus_int(U_197,U_198),plus_plus_int(U_196,U_198))
| ~ ord_less_int(U_197,U_196) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
! [U_197,U_196,U_198] :
( ord_less_int(plus_plus_int(U_197,U_198),plus_plus_int(U_196,U_198))
| ~ ord_less_int(U_197,U_196) ),
inference(definitional_conversion,[status(esa)],[f_94_2]) ).
cnf(f_94_4,plain,
( ord_less_int(plus_plus_int(U_197,U_198),plus_plus_int(U_196,U_198))
| ~ ord_less_int(U_197,U_196) ),
inference(clausify,[status(thm)],[f_94_3]) ).
fof(f_95_1,plain,
! [K,I,J] :
( ord_less_eq_int(plus_plus_int(K,I),plus_plus_int(K,J))
| ~ ord_less_eq_int(I,J) ),
inference(fof_nnf,[status(thm)],[fact_76_zadd__left__mono]) ).
fof(f_95_2,plain,
! [U_201,U_200,U_199] :
( ord_less_eq_int(plus_plus_int(U_201,U_200),plus_plus_int(U_201,U_199))
| ~ ord_less_eq_int(U_200,U_199) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
! [U_199,U_200,U_201] :
( ord_less_eq_int(plus_plus_int(U_201,U_200),plus_plus_int(U_201,U_199))
| ~ ord_less_eq_int(U_200,U_199) ),
inference(definitional_conversion,[status(esa)],[f_95_2]) ).
cnf(f_95_4,plain,
( ord_less_eq_int(plus_plus_int(U_201,U_200),plus_plus_int(U_201,U_199))
| ~ ord_less_eq_int(U_200,U_199) ),
inference(clausify,[status(thm)],[f_95_3]) ).
fof(f_96_1,plain,
! [V_2,V_1] :
( ( ( ( plus_plus_nat(number_number_of_nat(V_1),number_number_of_nat(V_2)) = number_number_of_nat(plus_plus_int(V_1,V_2))
| ord_less_int(V_2,pls) )
& ( plus_plus_nat(number_number_of_nat(V_1),number_number_of_nat(V_2)) = number_number_of_nat(V_1)
| ~ ord_less_int(V_2,pls) ) )
| ord_less_int(V_1,pls) )
& ( plus_plus_nat(number_number_of_nat(V_1),number_number_of_nat(V_2)) = number_number_of_nat(V_2)
| ~ ord_less_int(V_1,pls) ) ),
inference(fof_nnf,[status(thm)],[fact_77_add__nat__number__of]) ).
fof(f_96_2,plain,
! [U_203,U_202] :
( ( ( ( plus_plus_nat(number_number_of_nat(U_202),number_number_of_nat(U_203)) = number_number_of_nat(plus_plus_int(U_202,U_203))
| ord_less_int(U_203,pls) )
& ( plus_plus_nat(number_number_of_nat(U_202),number_number_of_nat(U_203)) = number_number_of_nat(U_202)
| ~ ord_less_int(U_203,pls) ) )
| ord_less_int(U_202,pls) )
& ( plus_plus_nat(number_number_of_nat(U_202),number_number_of_nat(U_203)) = number_number_of_nat(U_203)
| ~ ord_less_int(U_202,pls) ) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
( ! [U_207,U_205] :
( ( ( plus_plus_nat(number_number_of_nat(U_205),number_number_of_nat(U_207)) = number_number_of_nat(plus_plus_int(U_205,U_207))
| ord_less_int(U_207,pls) )
& ( plus_plus_nat(number_number_of_nat(U_205),number_number_of_nat(U_207)) = number_number_of_nat(U_205)
| ~ ord_less_int(U_207,pls) ) )
| ord_less_int(U_205,pls) )
& ! [U_206,U_204] :
( plus_plus_nat(number_number_of_nat(U_204),number_number_of_nat(U_206)) = number_number_of_nat(U_206)
| ~ ord_less_int(U_204,pls) ) ),
inference(miniscope,[status(thm)],[f_96_2]) ).
fof(f_96_4,plain,
( ! [U_207,U_205] :
( plus_plus_nat(number_number_of_nat(U_205),number_number_of_nat(U_207)) = number_number_of_nat(plus_plus_int(U_205,U_207))
| ord_less_int(U_207,pls)
| ~ sP4(U_207,U_205) )
& ! [U_207,U_205] :
( plus_plus_nat(number_number_of_nat(U_205),number_number_of_nat(U_207)) = number_number_of_nat(U_205)
| ~ ord_less_int(U_207,pls)
| ~ sP4(U_207,U_205) )
& ! [U_207,U_205] :
( sP4(U_207,U_205)
| ord_less_int(U_205,pls) )
& ! [U_206,U_204] :
( plus_plus_nat(number_number_of_nat(U_204),number_number_of_nat(U_206)) = number_number_of_nat(U_206)
| ~ ord_less_int(U_204,pls) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_96_3]) ).
cnf(f_96_5,plain,
( plus_plus_nat(number_number_of_nat(U_204),number_number_of_nat(U_206)) = number_number_of_nat(U_206)
| ~ ord_less_int(U_204,pls) ),
inference(clausify,[status(thm)],[f_96_4]) ).
cnf(f_96_6,plain,
( sP4(U_207,U_205)
| ord_less_int(U_205,pls) ),
inference(clausify,[status(thm)],[f_96_4]) ).
cnf(f_96_7,plain,
( plus_plus_nat(number_number_of_nat(U_205),number_number_of_nat(U_207)) = number_number_of_nat(U_205)
| ~ ord_less_int(U_207,pls)
| ~ sP4(U_207,U_205) ),
inference(clausify,[status(thm)],[f_96_4]) ).
cnf(f_96_8,plain,
( plus_plus_nat(number_number_of_nat(U_205),number_number_of_nat(U_207)) = number_number_of_nat(plus_plus_int(U_205,U_207))
| ord_less_int(U_207,pls)
| ~ sP4(U_207,U_205) ),
inference(clausify,[status(thm)],[f_96_4]) ).
fof(f_97_1,plain,
number_number_of_nat(bit1(pls)) = one_one_nat,
inference(fof_nnf,[status(thm)],[fact_78_nat__numeral__1__eq__1]) ).
fof(f_97_2,plain,
number_number_of_nat(bit1(pls)) = one_one_nat,
inference(definitional_conversion,[status(esa)],[f_97_1]) ).
cnf(f_97_3,plain,
number_number_of_nat(bit1(pls)) = one_one_nat,
inference(clausify,[status(thm)],[f_97_2]) ).
fof(f_98_1,plain,
one_one_nat = number_number_of_nat(bit1(pls)),
inference(fof_nnf,[status(thm)],[fact_79_Numeral1__eq1__nat]) ).
fof(f_98_2,plain,
one_one_nat = number_number_of_nat(bit1(pls)),
inference(definitional_conversion,[status(esa)],[f_98_1]) ).
cnf(f_98_3,plain,
one_one_nat = number_number_of_nat(bit1(pls)),
inference(clausify,[status(thm)],[f_98_2]) ).
fof(f_99_1,plain,
! [K_1] :
( ( ord_less_eq_int(bit1(K_1),pls)
| ~ ord_less_int(K_1,pls) )
& ( ord_less_int(K_1,pls)
| ~ ord_less_eq_int(bit1(K_1),pls) ) ),
inference(fof_nnf,[status(thm)],[fact_80_rel__simps_I29_J]) ).
fof(f_99_2,plain,
! [U_208] :
( ( ord_less_eq_int(bit1(U_208),pls)
| ~ ord_less_int(U_208,pls) )
& ( ord_less_int(U_208,pls)
| ~ ord_less_eq_int(bit1(U_208),pls) ) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
( ! [U_210] :
( ord_less_eq_int(bit1(U_210),pls)
| ~ ord_less_int(U_210,pls) )
& ! [U_209] :
( ord_less_int(U_209,pls)
| ~ ord_less_eq_int(bit1(U_209),pls) ) ),
inference(miniscope,[status(thm)],[f_99_2]) ).
fof(f_99_4,plain,
( ! [U_210] :
( ord_less_eq_int(bit1(U_210),pls)
| ~ ord_less_int(U_210,pls) )
& ! [U_209] :
( ord_less_int(U_209,pls)
| ~ ord_less_eq_int(bit1(U_209),pls) ) ),
inference(definitional_conversion,[status(esa)],[f_99_3]) ).
cnf(f_99_5,plain,
( ord_less_int(U_209,pls)
| ~ ord_less_eq_int(bit1(U_209),pls) ),
inference(clausify,[status(thm)],[f_99_4]) ).
cnf(f_99_6,plain,
( ord_less_eq_int(bit1(U_210),pls)
| ~ ord_less_int(U_210,pls) ),
inference(clausify,[status(thm)],[f_99_4]) ).
fof(f_100_1,plain,
! [K_1] :
( ( ord_less_int(pls,bit1(K_1))
| ~ ord_less_eq_int(pls,K_1) )
& ( ord_less_eq_int(pls,K_1)
| ~ ord_less_int(pls,bit1(K_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_81_rel__simps_I5_J]) ).
fof(f_100_2,plain,
! [U_211] :
( ( ord_less_int(pls,bit1(U_211))
| ~ ord_less_eq_int(pls,U_211) )
& ( ord_less_eq_int(pls,U_211)
| ~ ord_less_int(pls,bit1(U_211)) ) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
( ! [U_213] :
( ord_less_int(pls,bit1(U_213))
| ~ ord_less_eq_int(pls,U_213) )
& ! [U_212] :
( ord_less_eq_int(pls,U_212)
| ~ ord_less_int(pls,bit1(U_212)) ) ),
inference(miniscope,[status(thm)],[f_100_2]) ).
fof(f_100_4,plain,
( ! [U_213] :
( ord_less_int(pls,bit1(U_213))
| ~ ord_less_eq_int(pls,U_213) )
& ! [U_212] :
( ord_less_eq_int(pls,U_212)
| ~ ord_less_int(pls,bit1(U_212)) ) ),
inference(definitional_conversion,[status(esa)],[f_100_3]) ).
cnf(f_100_5,plain,
( ord_less_eq_int(pls,U_212)
| ~ ord_less_int(pls,bit1(U_212)) ),
inference(clausify,[status(thm)],[f_100_4]) ).
cnf(f_100_6,plain,
( ord_less_int(pls,bit1(U_213))
| ~ ord_less_eq_int(pls,U_213) ),
inference(clausify,[status(thm)],[f_100_4]) ).
fof(f_101_1,plain,
! [K1,K2] :
( ( ord_less_eq_int(bit1(K1),bit0(K2))
| ~ ord_less_int(K1,K2) )
& ( ord_less_int(K1,K2)
| ~ ord_less_eq_int(bit1(K1),bit0(K2)) ) ),
inference(fof_nnf,[status(thm)],[fact_82_less__eq__int__code_I15_J]) ).
fof(f_101_2,plain,
! [U_215,U_214] :
( ( ord_less_eq_int(bit1(U_215),bit0(U_214))
| ~ ord_less_int(U_215,U_214) )
& ( ord_less_int(U_215,U_214)
| ~ ord_less_eq_int(bit1(U_215),bit0(U_214)) ) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
( ! [U_219,U_217] :
( ord_less_eq_int(bit1(U_219),bit0(U_217))
| ~ ord_less_int(U_219,U_217) )
& ! [U_218,U_216] :
( ord_less_int(U_218,U_216)
| ~ ord_less_eq_int(bit1(U_218),bit0(U_216)) ) ),
inference(miniscope,[status(thm)],[f_101_2]) ).
fof(f_101_4,plain,
( ! [U_219,U_217] :
( ord_less_eq_int(bit1(U_219),bit0(U_217))
| ~ ord_less_int(U_219,U_217) )
& ! [U_218,U_216] :
( ord_less_int(U_218,U_216)
| ~ ord_less_eq_int(bit1(U_218),bit0(U_216)) ) ),
inference(definitional_conversion,[status(esa)],[f_101_3]) ).
cnf(f_101_5,plain,
( ord_less_int(U_218,U_216)
| ~ ord_less_eq_int(bit1(U_218),bit0(U_216)) ),
inference(clausify,[status(thm)],[f_101_4]) ).
cnf(f_101_6,plain,
( ord_less_eq_int(bit1(U_219),bit0(U_217))
| ~ ord_less_int(U_219,U_217) ),
inference(clausify,[status(thm)],[f_101_4]) ).
fof(f_102_1,plain,
! [K_1,L_1] :
( ( ord_less_eq_int(bit1(K_1),bit0(L_1))
| ~ ord_less_int(K_1,L_1) )
& ( ord_less_int(K_1,L_1)
| ~ ord_less_eq_int(bit1(K_1),bit0(L_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_83_rel__simps_I33_J]) ).
fof(f_102_2,plain,
! [U_221,U_220] :
( ( ord_less_eq_int(bit1(U_221),bit0(U_220))
| ~ ord_less_int(U_221,U_220) )
& ( ord_less_int(U_221,U_220)
| ~ ord_less_eq_int(bit1(U_221),bit0(U_220)) ) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
( ! [U_225,U_223] :
( ord_less_eq_int(bit1(U_225),bit0(U_223))
| ~ ord_less_int(U_225,U_223) )
& ! [U_224,U_222] :
( ord_less_int(U_224,U_222)
| ~ ord_less_eq_int(bit1(U_224),bit0(U_222)) ) ),
inference(miniscope,[status(thm)],[f_102_2]) ).
fof(f_102_4,plain,
( ! [U_223,U_225] :
( ord_less_eq_int(bit1(U_225),bit0(U_223))
| ~ ord_less_int(U_225,U_223) )
& ! [U_222,U_224] :
( ord_less_int(U_224,U_222)
| ~ ord_less_eq_int(bit1(U_224),bit0(U_222)) ) ),
inference(definitional_conversion,[status(esa)],[f_102_3]) ).
cnf(f_102_5,plain,
( ord_less_int(U_224,U_222)
| ~ ord_less_eq_int(bit1(U_224),bit0(U_222)) ),
inference(clausify,[status(thm)],[f_102_4]) ).
cnf(f_102_6,plain,
( ord_less_eq_int(bit1(U_225),bit0(U_223))
| ~ ord_less_int(U_225,U_223) ),
inference(clausify,[status(thm)],[f_102_4]) ).
fof(f_103_1,plain,
! [K1,K2] :
( ( ord_less_int(bit0(K1),bit1(K2))
| ~ ord_less_eq_int(K1,K2) )
& ( ord_less_eq_int(K1,K2)
| ~ ord_less_int(bit0(K1),bit1(K2)) ) ),
inference(fof_nnf,[status(thm)],[fact_84_less__int__code_I14_J]) ).
fof(f_103_2,plain,
! [U_227,U_226] :
( ( ord_less_int(bit0(U_227),bit1(U_226))
| ~ ord_less_eq_int(U_227,U_226) )
& ( ord_less_eq_int(U_227,U_226)
| ~ ord_less_int(bit0(U_227),bit1(U_226)) ) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
( ! [U_231,U_229] :
( ord_less_int(bit0(U_231),bit1(U_229))
| ~ ord_less_eq_int(U_231,U_229) )
& ! [U_230,U_228] :
( ord_less_eq_int(U_230,U_228)
| ~ ord_less_int(bit0(U_230),bit1(U_228)) ) ),
inference(miniscope,[status(thm)],[f_103_2]) ).
fof(f_103_4,plain,
( ! [U_229,U_231] :
( ord_less_int(bit0(U_231),bit1(U_229))
| ~ ord_less_eq_int(U_231,U_229) )
& ! [U_230,U_228] :
( ord_less_eq_int(U_230,U_228)
| ~ ord_less_int(bit0(U_230),bit1(U_228)) ) ),
inference(definitional_conversion,[status(esa)],[f_103_3]) ).
cnf(f_103_5,plain,
( ord_less_eq_int(U_230,U_228)
| ~ ord_less_int(bit0(U_230),bit1(U_228)) ),
inference(clausify,[status(thm)],[f_103_4]) ).
cnf(f_103_6,plain,
( ord_less_int(bit0(U_231),bit1(U_229))
| ~ ord_less_eq_int(U_231,U_229) ),
inference(clausify,[status(thm)],[f_103_4]) ).
fof(f_104_1,plain,
! [K_1,L_1] :
( ( ord_less_int(bit0(K_1),bit1(L_1))
| ~ ord_less_eq_int(K_1,L_1) )
& ( ord_less_eq_int(K_1,L_1)
| ~ ord_less_int(bit0(K_1),bit1(L_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_85_rel__simps_I15_J]) ).
fof(f_104_2,plain,
! [U_233,U_232] :
( ( ord_less_int(bit0(U_233),bit1(U_232))
| ~ ord_less_eq_int(U_233,U_232) )
& ( ord_less_eq_int(U_233,U_232)
| ~ ord_less_int(bit0(U_233),bit1(U_232)) ) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
( ! [U_237,U_235] :
( ord_less_int(bit0(U_237),bit1(U_235))
| ~ ord_less_eq_int(U_237,U_235) )
& ! [U_236,U_234] :
( ord_less_eq_int(U_236,U_234)
| ~ ord_less_int(bit0(U_236),bit1(U_234)) ) ),
inference(miniscope,[status(thm)],[f_104_2]) ).
fof(f_104_4,plain,
( ! [U_235,U_237] :
( ord_less_int(bit0(U_237),bit1(U_235))
| ~ ord_less_eq_int(U_237,U_235) )
& ! [U_234,U_236] :
( ord_less_eq_int(U_236,U_234)
| ~ ord_less_int(bit0(U_236),bit1(U_234)) ) ),
inference(definitional_conversion,[status(esa)],[f_104_3]) ).
cnf(f_104_5,plain,
( ord_less_eq_int(U_236,U_234)
| ~ ord_less_int(bit0(U_236),bit1(U_234)) ),
inference(clausify,[status(thm)],[f_104_4]) ).
cnf(f_104_6,plain,
( ord_less_int(bit0(U_237),bit1(U_235))
| ~ ord_less_eq_int(U_237,U_235) ),
inference(clausify,[status(thm)],[f_104_4]) ).
fof(f_105_1,plain,
! [W,Z] :
( ord_less_eq_int(plus_plus_int(W,one_one_int),Z)
| ~ ord_less_int(W,Z) ),
inference(fof_nnf,[status(thm)],[fact_86_zless__imp__add1__zle]) ).
fof(f_105_2,plain,
! [U_239,U_238] :
( ord_less_eq_int(plus_plus_int(U_239,one_one_int),U_238)
| ~ ord_less_int(U_239,U_238) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
! [U_239,U_238] :
( ord_less_eq_int(plus_plus_int(U_239,one_one_int),U_238)
| ~ ord_less_int(U_239,U_238) ),
inference(definitional_conversion,[status(esa)],[f_105_2]) ).
cnf(f_105_4,plain,
( ord_less_eq_int(plus_plus_int(U_239,one_one_int),U_238)
| ~ ord_less_int(U_239,U_238) ),
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_1,plain,
! [W_1,Z_1] :
( ( ord_less_eq_int(plus_plus_int(W_1,one_one_int),Z_1)
| ~ ord_less_int(W_1,Z_1) )
& ( ord_less_int(W_1,Z_1)
| ~ ord_less_eq_int(plus_plus_int(W_1,one_one_int),Z_1) ) ),
inference(fof_nnf,[status(thm)],[fact_87_add1__zle__eq]) ).
fof(f_106_2,plain,
! [U_241,U_240] :
( ( ord_less_eq_int(plus_plus_int(U_241,one_one_int),U_240)
| ~ ord_less_int(U_241,U_240) )
& ( ord_less_int(U_241,U_240)
| ~ ord_less_eq_int(plus_plus_int(U_241,one_one_int),U_240) ) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
( ! [U_245,U_243] :
( ord_less_eq_int(plus_plus_int(U_245,one_one_int),U_243)
| ~ ord_less_int(U_245,U_243) )
& ! [U_244,U_242] :
( ord_less_int(U_244,U_242)
| ~ ord_less_eq_int(plus_plus_int(U_244,one_one_int),U_242) ) ),
inference(miniscope,[status(thm)],[f_106_2]) ).
fof(f_106_4,plain,
( ! [U_245,U_243] :
( ord_less_eq_int(plus_plus_int(U_245,one_one_int),U_243)
| ~ ord_less_int(U_245,U_243) )
& ! [U_244,U_242] :
( ord_less_int(U_244,U_242)
| ~ ord_less_eq_int(plus_plus_int(U_244,one_one_int),U_242) ) ),
inference(definitional_conversion,[status(esa)],[f_106_3]) ).
cnf(f_106_5,plain,
( ord_less_int(U_244,U_242)
| ~ ord_less_eq_int(plus_plus_int(U_244,one_one_int),U_242) ),
inference(clausify,[status(thm)],[f_106_4]) ).
cnf(f_106_6,plain,
( ord_less_eq_int(plus_plus_int(U_245,one_one_int),U_243)
| ~ ord_less_int(U_245,U_243) ),
inference(clausify,[status(thm)],[f_106_4]) ).
fof(f_107_1,plain,
! [W_1,Z_1] :
( ( ord_less_int(W_1,plus_plus_int(Z_1,one_one_int))
| ~ ord_less_eq_int(W_1,Z_1) )
& ( ord_less_eq_int(W_1,Z_1)
| ~ ord_less_int(W_1,plus_plus_int(Z_1,one_one_int)) ) ),
inference(fof_nnf,[status(thm)],[fact_88_zle__add1__eq__le]) ).
fof(f_107_2,plain,
! [U_247,U_246] :
( ( ord_less_int(U_247,plus_plus_int(U_246,one_one_int))
| ~ ord_less_eq_int(U_247,U_246) )
& ( ord_less_eq_int(U_247,U_246)
| ~ ord_less_int(U_247,plus_plus_int(U_246,one_one_int)) ) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
( ! [U_251,U_249] :
( ord_less_int(U_251,plus_plus_int(U_249,one_one_int))
| ~ ord_less_eq_int(U_251,U_249) )
& ! [U_250,U_248] :
( ord_less_eq_int(U_250,U_248)
| ~ ord_less_int(U_250,plus_plus_int(U_248,one_one_int)) ) ),
inference(miniscope,[status(thm)],[f_107_2]) ).
fof(f_107_4,plain,
( ! [U_249,U_251] :
( ord_less_int(U_251,plus_plus_int(U_249,one_one_int))
| ~ ord_less_eq_int(U_251,U_249) )
& ! [U_248,U_250] :
( ord_less_eq_int(U_250,U_248)
| ~ ord_less_int(U_250,plus_plus_int(U_248,one_one_int)) ) ),
inference(definitional_conversion,[status(esa)],[f_107_3]) ).
cnf(f_107_5,plain,
( ord_less_eq_int(U_250,U_248)
| ~ ord_less_int(U_250,plus_plus_int(U_248,one_one_int)) ),
inference(clausify,[status(thm)],[f_107_4]) ).
cnf(f_107_6,plain,
( ord_less_int(U_251,plus_plus_int(U_249,one_one_int))
| ~ ord_less_eq_int(U_251,U_249) ),
inference(clausify,[status(thm)],[f_107_4]) ).
fof(f_108_1,plain,
zprime(number_number_of_int(bit0(bit1(pls)))),
inference(fof_nnf,[status(thm)],[fact_89_zprime__2]) ).
fof(f_108_2,plain,
zprime(number_number_of_int(bit0(bit1(pls)))),
inference(definitional_conversion,[status(esa)],[f_108_1]) ).
cnf(f_108_3,plain,
zprime(number_number_of_int(bit0(bit1(pls)))),
inference(clausify,[status(thm)],[f_108_2]) ).
fof(f_109_1,plain,
! [Y_1,X_1] :
( twoSqu142715416sum2sq(times_times_int(X_1,Y_1))
| ~ twoSqu142715416sum2sq(Y_1)
| ~ twoSqu142715416sum2sq(X_1) ),
inference(fof_nnf,[status(thm)],[fact_90_is__mult__sum2sq]) ).
fof(f_109_2,plain,
! [U_253,U_252] :
( twoSqu142715416sum2sq(times_times_int(U_252,U_253))
| ~ twoSqu142715416sum2sq(U_253)
| ~ twoSqu142715416sum2sq(U_252) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
! [U_252,U_253] :
( twoSqu142715416sum2sq(times_times_int(U_252,U_253))
| ~ twoSqu142715416sum2sq(U_253)
| ~ twoSqu142715416sum2sq(U_252) ),
inference(definitional_conversion,[status(esa)],[f_109_2]) ).
cnf(f_109_4,plain,
( twoSqu142715416sum2sq(times_times_int(U_252,U_253))
| ~ twoSqu142715416sum2sq(U_253)
| ~ twoSqu142715416sum2sq(U_252) ),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_1,plain,
! [Lx_6,Ly_4,Rx_6,Ry_4] : times_times_real(times_times_real(Lx_6,Ly_4),times_times_real(Rx_6,Ry_4)) = times_times_real(times_times_real(Lx_6,Rx_6),times_times_real(Ly_4,Ry_4)),
inference(fof_nnf,[status(thm)],[fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J]) ).
fof(f_110_2,plain,
! [U_257,U_256,U_255,U_254] : times_times_real(times_times_real(U_257,U_256),times_times_real(U_255,U_254)) = times_times_real(times_times_real(U_257,U_255),times_times_real(U_256,U_254)),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
! [U_254,U_255,U_256,U_257] : times_times_real(times_times_real(U_257,U_256),times_times_real(U_255,U_254)) = times_times_real(times_times_real(U_257,U_255),times_times_real(U_256,U_254)),
inference(definitional_conversion,[status(esa)],[f_110_2]) ).
cnf(f_110_4,plain,
times_times_real(times_times_real(U_257,U_256),times_times_real(U_255,U_254)) = times_times_real(times_times_real(U_257,U_255),times_times_real(U_256,U_254)),
inference(clausify,[status(thm)],[f_110_3]) ).
fof(f_111_1,plain,
! [Lx_6,Ly_4,Rx_6,Ry_4] : times_times_nat(times_times_nat(Lx_6,Ly_4),times_times_nat(Rx_6,Ry_4)) = times_times_nat(times_times_nat(Lx_6,Rx_6),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_111_2,plain,
! [U_261,U_260,U_259,U_258] : times_times_nat(times_times_nat(U_261,U_260),times_times_nat(U_259,U_258)) = times_times_nat(times_times_nat(U_261,U_259),times_times_nat(U_260,U_258)),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
! [U_261,U_259,U_260,U_258] : times_times_nat(times_times_nat(U_261,U_260),times_times_nat(U_259,U_258)) = times_times_nat(times_times_nat(U_261,U_259),times_times_nat(U_260,U_258)),
inference(definitional_conversion,[status(esa)],[f_111_2]) ).
cnf(f_111_4,plain,
times_times_nat(times_times_nat(U_261,U_260),times_times_nat(U_259,U_258)) = times_times_nat(times_times_nat(U_261,U_259),times_times_nat(U_260,U_258)),
inference(clausify,[status(thm)],[f_111_3]) ).
fof(f_112_1,plain,
! [Lx_6,Ly_4,Rx_6,Ry_4] : times_times_int(times_times_int(Lx_6,Ly_4),times_times_int(Rx_6,Ry_4)) = times_times_int(times_times_int(Lx_6,Rx_6),times_times_int(Ly_4,Ry_4)),
inference(fof_nnf,[status(thm)],[fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J]) ).
fof(f_112_2,plain,
! [U_265,U_264,U_263,U_262] : times_times_int(times_times_int(U_265,U_264),times_times_int(U_263,U_262)) = times_times_int(times_times_int(U_265,U_263),times_times_int(U_264,U_262)),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
! [U_262,U_263,U_264,U_265] : times_times_int(times_times_int(U_265,U_264),times_times_int(U_263,U_262)) = times_times_int(times_times_int(U_265,U_263),times_times_int(U_264,U_262)),
inference(definitional_conversion,[status(esa)],[f_112_2]) ).
cnf(f_112_4,plain,
times_times_int(times_times_int(U_265,U_264),times_times_int(U_263,U_262)) = times_times_int(times_times_int(U_265,U_263),times_times_int(U_264,U_262)),
inference(clausify,[status(thm)],[f_112_3]) ).
fof(f_113_1,plain,
! [Lx_5,Ly_3,Rx_5,Ry_3] : times_times_real(times_times_real(Lx_5,Ly_3),times_times_real(Rx_5,Ry_3)) = times_times_real(Rx_5,times_times_real(times_times_real(Lx_5,Ly_3),Ry_3)),
inference(fof_nnf,[status(thm)],[fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J]) ).
fof(f_113_2,plain,
! [U_269,U_268,U_267,U_266] : times_times_real(times_times_real(U_269,U_268),times_times_real(U_267,U_266)) = times_times_real(U_267,times_times_real(times_times_real(U_269,U_268),U_266)),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
! [U_266,U_267,U_268,U_269] : times_times_real(times_times_real(U_269,U_268),times_times_real(U_267,U_266)) = times_times_real(U_267,times_times_real(times_times_real(U_269,U_268),U_266)),
inference(definitional_conversion,[status(esa)],[f_113_2]) ).
cnf(f_113_4,plain,
times_times_real(times_times_real(U_269,U_268),times_times_real(U_267,U_266)) = times_times_real(U_267,times_times_real(times_times_real(U_269,U_268),U_266)),
inference(clausify,[status(thm)],[f_113_3]) ).
fof(f_114_1,plain,
! [Lx_5,Ly_3,Rx_5,Ry_3] : times_times_nat(times_times_nat(Lx_5,Ly_3),times_times_nat(Rx_5,Ry_3)) = times_times_nat(Rx_5,times_times_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_114_2,plain,
! [U_273,U_272,U_271,U_270] : times_times_nat(times_times_nat(U_273,U_272),times_times_nat(U_271,U_270)) = times_times_nat(U_271,times_times_nat(times_times_nat(U_273,U_272),U_270)),
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
! [U_271,U_270,U_272,U_273] : times_times_nat(times_times_nat(U_273,U_272),times_times_nat(U_271,U_270)) = times_times_nat(U_271,times_times_nat(times_times_nat(U_273,U_272),U_270)),
inference(definitional_conversion,[status(esa)],[f_114_2]) ).
cnf(f_114_4,plain,
times_times_nat(times_times_nat(U_273,U_272),times_times_nat(U_271,U_270)) = times_times_nat(U_271,times_times_nat(times_times_nat(U_273,U_272),U_270)),
inference(clausify,[status(thm)],[f_114_3]) ).
fof(f_115_1,plain,
! [Lx_5,Ly_3,Rx_5,Ry_3] : times_times_int(times_times_int(Lx_5,Ly_3),times_times_int(Rx_5,Ry_3)) = times_times_int(Rx_5,times_times_int(times_times_int(Lx_5,Ly_3),Ry_3)),
inference(fof_nnf,[status(thm)],[fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J]) ).
fof(f_115_2,plain,
! [U_277,U_276,U_275,U_274] : times_times_int(times_times_int(U_277,U_276),times_times_int(U_275,U_274)) = times_times_int(U_275,times_times_int(times_times_int(U_277,U_276),U_274)),
inference(variable_rename,[status(thm)],[f_115_1]) ).
fof(f_115_3,plain,
! [U_275,U_274,U_276,U_277] : times_times_int(times_times_int(U_277,U_276),times_times_int(U_275,U_274)) = times_times_int(U_275,times_times_int(times_times_int(U_277,U_276),U_274)),
inference(definitional_conversion,[status(esa)],[f_115_2]) ).
cnf(f_115_4,plain,
times_times_int(times_times_int(U_277,U_276),times_times_int(U_275,U_274)) = times_times_int(U_275,times_times_int(times_times_int(U_277,U_276),U_274)),
inference(clausify,[status(thm)],[f_115_3]) ).
fof(f_116_1,plain,
! [Lx_4,Ly_2,Rx_4,Ry_2] : times_times_real(times_times_real(Lx_4,Ly_2),times_times_real(Rx_4,Ry_2)) = times_times_real(Lx_4,times_times_real(Ly_2,times_times_real(Rx_4,Ry_2))),
inference(fof_nnf,[status(thm)],[fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J]) ).
fof(f_116_2,plain,
! [U_281,U_280,U_279,U_278] : times_times_real(times_times_real(U_281,U_280),times_times_real(U_279,U_278)) = times_times_real(U_281,times_times_real(U_280,times_times_real(U_279,U_278))),
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
! [U_279,U_278,U_280,U_281] : times_times_real(times_times_real(U_281,U_280),times_times_real(U_279,U_278)) = times_times_real(U_281,times_times_real(U_280,times_times_real(U_279,U_278))),
inference(definitional_conversion,[status(esa)],[f_116_2]) ).
cnf(f_116_4,plain,
times_times_real(times_times_real(U_281,U_280),times_times_real(U_279,U_278)) = times_times_real(U_281,times_times_real(U_280,times_times_real(U_279,U_278))),
inference(clausify,[status(thm)],[f_116_3]) ).
fof(f_117_1,plain,
! [Lx_4,Ly_2,Rx_4,Ry_2] : times_times_nat(times_times_nat(Lx_4,Ly_2),times_times_nat(Rx_4,Ry_2)) = times_times_nat(Lx_4,times_times_nat(Ly_2,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_117_2,plain,
! [U_285,U_284,U_283,U_282] : times_times_nat(times_times_nat(U_285,U_284),times_times_nat(U_283,U_282)) = times_times_nat(U_285,times_times_nat(U_284,times_times_nat(U_283,U_282))),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
! [U_282,U_283,U_284,U_285] : times_times_nat(times_times_nat(U_285,U_284),times_times_nat(U_283,U_282)) = times_times_nat(U_285,times_times_nat(U_284,times_times_nat(U_283,U_282))),
inference(definitional_conversion,[status(esa)],[f_117_2]) ).
cnf(f_117_4,plain,
times_times_nat(times_times_nat(U_285,U_284),times_times_nat(U_283,U_282)) = times_times_nat(U_285,times_times_nat(U_284,times_times_nat(U_283,U_282))),
inference(clausify,[status(thm)],[f_117_3]) ).
fof(f_118_1,plain,
! [Lx_4,Ly_2,Rx_4,Ry_2] : times_times_int(times_times_int(Lx_4,Ly_2),times_times_int(Rx_4,Ry_2)) = times_times_int(Lx_4,times_times_int(Ly_2,times_times_int(Rx_4,Ry_2))),
inference(fof_nnf,[status(thm)],[fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J]) ).
fof(f_118_2,plain,
! [U_289,U_288,U_287,U_286] : times_times_int(times_times_int(U_289,U_288),times_times_int(U_287,U_286)) = times_times_int(U_289,times_times_int(U_288,times_times_int(U_287,U_286))),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
! [U_287,U_286,U_288,U_289] : times_times_int(times_times_int(U_289,U_288),times_times_int(U_287,U_286)) = times_times_int(U_289,times_times_int(U_288,times_times_int(U_287,U_286))),
inference(definitional_conversion,[status(esa)],[f_118_2]) ).
cnf(f_118_4,plain,
times_times_int(times_times_int(U_289,U_288),times_times_int(U_287,U_286)) = times_times_int(U_289,times_times_int(U_288,times_times_int(U_287,U_286))),
inference(clausify,[status(thm)],[f_118_3]) ).
fof(f_119_1,plain,
! [Lx_3,Ly_1,Rx_3] : times_times_real(times_times_real(Lx_3,Ly_1),Rx_3) = times_times_real(times_times_real(Lx_3,Rx_3),Ly_1),
inference(fof_nnf,[status(thm)],[fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J]) ).
fof(f_119_2,plain,
! [U_292,U_291,U_290] : times_times_real(times_times_real(U_292,U_291),U_290) = times_times_real(times_times_real(U_292,U_290),U_291),
inference(variable_rename,[status(thm)],[f_119_1]) ).
fof(f_119_3,plain,
! [U_290,U_291,U_292] : times_times_real(times_times_real(U_292,U_291),U_290) = times_times_real(times_times_real(U_292,U_290),U_291),
inference(definitional_conversion,[status(esa)],[f_119_2]) ).
cnf(f_119_4,plain,
times_times_real(times_times_real(U_292,U_291),U_290) = times_times_real(times_times_real(U_292,U_290),U_291),
inference(clausify,[status(thm)],[f_119_3]) ).
fof(f_120_1,plain,
! [Lx_3,Ly_1,Rx_3] : times_times_nat(times_times_nat(Lx_3,Ly_1),Rx_3) = times_times_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_120_2,plain,
! [U_295,U_294,U_293] : times_times_nat(times_times_nat(U_295,U_294),U_293) = times_times_nat(times_times_nat(U_295,U_293),U_294),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
! [U_293,U_294,U_295] : times_times_nat(times_times_nat(U_295,U_294),U_293) = times_times_nat(times_times_nat(U_295,U_293),U_294),
inference(definitional_conversion,[status(esa)],[f_120_2]) ).
cnf(f_120_4,plain,
times_times_nat(times_times_nat(U_295,U_294),U_293) = times_times_nat(times_times_nat(U_295,U_293),U_294),
inference(clausify,[status(thm)],[f_120_3]) ).
fof(f_121_1,plain,
! [Lx_3,Ly_1,Rx_3] : times_times_int(times_times_int(Lx_3,Ly_1),Rx_3) = times_times_int(times_times_int(Lx_3,Rx_3),Ly_1),
inference(fof_nnf,[status(thm)],[fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J]) ).
fof(f_121_2,plain,
! [U_298,U_297,U_296] : times_times_int(times_times_int(U_298,U_297),U_296) = times_times_int(times_times_int(U_298,U_296),U_297),
inference(variable_rename,[status(thm)],[f_121_1]) ).
fof(f_121_3,plain,
! [U_296,U_297,U_298] : times_times_int(times_times_int(U_298,U_297),U_296) = times_times_int(times_times_int(U_298,U_296),U_297),
inference(definitional_conversion,[status(esa)],[f_121_2]) ).
cnf(f_121_4,plain,
times_times_int(times_times_int(U_298,U_297),U_296) = times_times_int(times_times_int(U_298,U_296),U_297),
inference(clausify,[status(thm)],[f_121_3]) ).
fof(f_122_1,plain,
! [Lx_2,Ly,Rx_2] : times_times_real(times_times_real(Lx_2,Ly),Rx_2) = times_times_real(Lx_2,times_times_real(Ly,Rx_2)),
inference(fof_nnf,[status(thm)],[fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J]) ).
fof(f_122_2,plain,
! [U_301,U_300,U_299] : times_times_real(times_times_real(U_301,U_300),U_299) = times_times_real(U_301,times_times_real(U_300,U_299)),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
! [U_299,U_300,U_301] : times_times_real(times_times_real(U_301,U_300),U_299) = times_times_real(U_301,times_times_real(U_300,U_299)),
inference(definitional_conversion,[status(esa)],[f_122_2]) ).
cnf(f_122_4,plain,
times_times_real(times_times_real(U_301,U_300),U_299) = times_times_real(U_301,times_times_real(U_300,U_299)),
inference(clausify,[status(thm)],[f_122_3]) ).
fof(f_123_1,plain,
! [Lx_2,Ly,Rx_2] : times_times_nat(times_times_nat(Lx_2,Ly),Rx_2) = times_times_nat(Lx_2,times_times_nat(Ly,Rx_2)),
inference(fof_nnf,[status(thm)],[fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J]) ).
fof(f_123_2,plain,
! [U_304,U_303,U_302] : times_times_nat(times_times_nat(U_304,U_303),U_302) = times_times_nat(U_304,times_times_nat(U_303,U_302)),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
! [U_302,U_303,U_304] : times_times_nat(times_times_nat(U_304,U_303),U_302) = times_times_nat(U_304,times_times_nat(U_303,U_302)),
inference(definitional_conversion,[status(esa)],[f_123_2]) ).
cnf(f_123_4,plain,
times_times_nat(times_times_nat(U_304,U_303),U_302) = times_times_nat(U_304,times_times_nat(U_303,U_302)),
inference(clausify,[status(thm)],[f_123_3]) ).
fof(f_124_1,plain,
! [Lx_2,Ly,Rx_2] : times_times_int(times_times_int(Lx_2,Ly),Rx_2) = times_times_int(Lx_2,times_times_int(Ly,Rx_2)),
inference(fof_nnf,[status(thm)],[fact_105_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J]) ).
fof(f_124_2,plain,
! [U_307,U_306,U_305] : times_times_int(times_times_int(U_307,U_306),U_305) = times_times_int(U_307,times_times_int(U_306,U_305)),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
! [U_305,U_306,U_307] : times_times_int(times_times_int(U_307,U_306),U_305) = times_times_int(U_307,times_times_int(U_306,U_305)),
inference(definitional_conversion,[status(esa)],[f_124_2]) ).
cnf(f_124_4,plain,
times_times_int(times_times_int(U_307,U_306),U_305) = times_times_int(U_307,times_times_int(U_306,U_305)),
inference(clausify,[status(thm)],[f_124_3]) ).
fof(f_125_1,plain,
! [Lx_1,Rx_1,Ry_1] : times_times_real(Lx_1,times_times_real(Rx_1,Ry_1)) = times_times_real(times_times_real(Lx_1,Rx_1),Ry_1),
inference(fof_nnf,[status(thm)],[fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J]) ).
fof(f_125_2,plain,
! [U_310,U_309,U_308] : times_times_real(U_310,times_times_real(U_309,U_308)) = times_times_real(times_times_real(U_310,U_309),U_308),
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
! [U_308,U_309,U_310] : times_times_real(U_310,times_times_real(U_309,U_308)) = times_times_real(times_times_real(U_310,U_309),U_308),
inference(definitional_conversion,[status(esa)],[f_125_2]) ).
cnf(f_125_4,plain,
times_times_real(U_310,times_times_real(U_309,U_308)) = times_times_real(times_times_real(U_310,U_309),U_308),
inference(clausify,[status(thm)],[f_125_3]) ).
fof(f_126_1,plain,
! [Lx_1,Rx_1,Ry_1] : times_times_nat(Lx_1,times_times_nat(Rx_1,Ry_1)) = times_times_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_126_2,plain,
! [U_313,U_312,U_311] : times_times_nat(U_313,times_times_nat(U_312,U_311)) = times_times_nat(times_times_nat(U_313,U_312),U_311),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
! [U_311,U_312,U_313] : times_times_nat(U_313,times_times_nat(U_312,U_311)) = times_times_nat(times_times_nat(U_313,U_312),U_311),
inference(definitional_conversion,[status(esa)],[f_126_2]) ).
cnf(f_126_4,plain,
times_times_nat(U_313,times_times_nat(U_312,U_311)) = times_times_nat(times_times_nat(U_313,U_312),U_311),
inference(clausify,[status(thm)],[f_126_3]) ).
fof(f_127_1,plain,
! [Lx_1,Rx_1,Ry_1] : times_times_int(Lx_1,times_times_int(Rx_1,Ry_1)) = times_times_int(times_times_int(Lx_1,Rx_1),Ry_1),
inference(fof_nnf,[status(thm)],[fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J]) ).
fof(f_127_2,plain,
! [U_316,U_315,U_314] : times_times_int(U_316,times_times_int(U_315,U_314)) = times_times_int(times_times_int(U_316,U_315),U_314),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
! [U_314,U_315,U_316] : times_times_int(U_316,times_times_int(U_315,U_314)) = times_times_int(times_times_int(U_316,U_315),U_314),
inference(definitional_conversion,[status(esa)],[f_127_2]) ).
cnf(f_127_4,plain,
times_times_int(U_316,times_times_int(U_315,U_314)) = times_times_int(times_times_int(U_316,U_315),U_314),
inference(clausify,[status(thm)],[f_127_3]) ).
fof(f_128_1,plain,
! [Lx,Rx,Ry] : times_times_real(Lx,times_times_real(Rx,Ry)) = times_times_real(Rx,times_times_real(Lx,Ry)),
inference(fof_nnf,[status(thm)],[fact_109_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J]) ).
fof(f_128_2,plain,
! [U_319,U_318,U_317] : times_times_real(U_319,times_times_real(U_318,U_317)) = times_times_real(U_318,times_times_real(U_319,U_317)),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
! [U_317,U_318,U_319] : times_times_real(U_319,times_times_real(U_318,U_317)) = times_times_real(U_318,times_times_real(U_319,U_317)),
inference(definitional_conversion,[status(esa)],[f_128_2]) ).
cnf(f_128_4,plain,
times_times_real(U_319,times_times_real(U_318,U_317)) = times_times_real(U_318,times_times_real(U_319,U_317)),
inference(clausify,[status(thm)],[f_128_3]) ).
fof(f_129_1,plain,
! [Lx,Rx,Ry] : times_times_nat(Lx,times_times_nat(Rx,Ry)) = times_times_nat(Rx,times_times_nat(Lx,Ry)),
inference(fof_nnf,[status(thm)],[fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J]) ).
fof(f_129_2,plain,
! [U_322,U_321,U_320] : times_times_nat(U_322,times_times_nat(U_321,U_320)) = times_times_nat(U_321,times_times_nat(U_322,U_320)),
inference(variable_rename,[status(thm)],[f_129_1]) ).
fof(f_129_3,plain,
! [U_320,U_321,U_322] : times_times_nat(U_322,times_times_nat(U_321,U_320)) = times_times_nat(U_321,times_times_nat(U_322,U_320)),
inference(definitional_conversion,[status(esa)],[f_129_2]) ).
cnf(f_129_4,plain,
times_times_nat(U_322,times_times_nat(U_321,U_320)) = times_times_nat(U_321,times_times_nat(U_322,U_320)),
inference(clausify,[status(thm)],[f_129_3]) ).
fof(f_130_1,plain,
! [Lx,Rx,Ry] : times_times_int(Lx,times_times_int(Rx,Ry)) = times_times_int(Rx,times_times_int(Lx,Ry)),
inference(fof_nnf,[status(thm)],[fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J]) ).
fof(f_130_2,plain,
! [U_325,U_324,U_323] : times_times_int(U_325,times_times_int(U_324,U_323)) = times_times_int(U_324,times_times_int(U_325,U_323)),
inference(variable_rename,[status(thm)],[f_130_1]) ).
fof(f_130_3,plain,
! [U_324,U_325,U_323] : times_times_int(U_325,times_times_int(U_324,U_323)) = times_times_int(U_324,times_times_int(U_325,U_323)),
inference(definitional_conversion,[status(esa)],[f_130_2]) ).
cnf(f_130_4,plain,
times_times_int(U_325,times_times_int(U_324,U_323)) = times_times_int(U_324,times_times_int(U_325,U_323)),
inference(clausify,[status(thm)],[f_130_3]) ).
fof(f_131_1,plain,
! [A_56,B_17] : times_times_real(A_56,B_17) = times_times_real(B_17,A_56),
inference(fof_nnf,[status(thm)],[fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).
fof(f_131_2,plain,
! [U_327,U_326] : times_times_real(U_327,U_326) = times_times_real(U_326,U_327),
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
! [U_326,U_327] : times_times_real(U_327,U_326) = times_times_real(U_326,U_327),
inference(definitional_conversion,[status(esa)],[f_131_2]) ).
cnf(f_131_4,plain,
times_times_real(U_327,U_326) = times_times_real(U_326,U_327),
inference(clausify,[status(thm)],[f_131_3]) ).
fof(f_132_1,plain,
! [A_56,B_17] : times_times_nat(A_56,B_17) = times_times_nat(B_17,A_56),
inference(fof_nnf,[status(thm)],[fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).
fof(f_132_2,plain,
! [U_329,U_328] : times_times_nat(U_329,U_328) = times_times_nat(U_328,U_329),
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
! [U_328,U_329] : times_times_nat(U_329,U_328) = times_times_nat(U_328,U_329),
inference(definitional_conversion,[status(esa)],[f_132_2]) ).
cnf(f_132_4,plain,
times_times_nat(U_329,U_328) = times_times_nat(U_328,U_329),
inference(clausify,[status(thm)],[f_132_3]) ).
fof(f_133_1,plain,
! [A_56,B_17] : times_times_int(A_56,B_17) = times_times_int(B_17,A_56),
inference(fof_nnf,[status(thm)],[fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).
fof(f_133_2,plain,
! [U_331,U_330] : times_times_int(U_331,U_330) = times_times_int(U_330,U_331),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
! [U_330,U_331] : times_times_int(U_331,U_330) = times_times_int(U_330,U_331),
inference(definitional_conversion,[status(esa)],[f_133_2]) ).
cnf(f_133_4,plain,
times_times_int(U_331,U_330) = times_times_int(U_330,U_331),
inference(clausify,[status(thm)],[f_133_3]) ).
fof(f_134_1,plain,
! [A_55,B_16,C_10,D_5] : plus_plus_real(plus_plus_real(A_55,B_16),plus_plus_real(C_10,D_5)) = plus_plus_real(plus_plus_real(A_55,C_10),plus_plus_real(B_16,D_5)),
inference(fof_nnf,[status(thm)],[fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).
fof(f_134_2,plain,
! [U_335,U_334,U_333,U_332] : plus_plus_real(plus_plus_real(U_335,U_334),plus_plus_real(U_333,U_332)) = plus_plus_real(plus_plus_real(U_335,U_333),plus_plus_real(U_334,U_332)),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
! [U_332,U_333,U_334,U_335] : plus_plus_real(plus_plus_real(U_335,U_334),plus_plus_real(U_333,U_332)) = plus_plus_real(plus_plus_real(U_335,U_333),plus_plus_real(U_334,U_332)),
inference(definitional_conversion,[status(esa)],[f_134_2]) ).
cnf(f_134_4,plain,
plus_plus_real(plus_plus_real(U_335,U_334),plus_plus_real(U_333,U_332)) = plus_plus_real(plus_plus_real(U_335,U_333),plus_plus_real(U_334,U_332)),
inference(clausify,[status(thm)],[f_134_3]) ).
fof(f_135_1,plain,
! [A_55,B_16,C_10,D_5] : plus_plus_nat(plus_plus_nat(A_55,B_16),plus_plus_nat(C_10,D_5)) = plus_plus_nat(plus_plus_nat(A_55,C_10),plus_plus_nat(B_16,D_5)),
inference(fof_nnf,[status(thm)],[fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).
fof(f_135_2,plain,
! [U_339,U_338,U_337,U_336] : plus_plus_nat(plus_plus_nat(U_339,U_338),plus_plus_nat(U_337,U_336)) = plus_plus_nat(plus_plus_nat(U_339,U_337),plus_plus_nat(U_338,U_336)),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
! [U_336,U_337,U_338,U_339] : plus_plus_nat(plus_plus_nat(U_339,U_338),plus_plus_nat(U_337,U_336)) = plus_plus_nat(plus_plus_nat(U_339,U_337),plus_plus_nat(U_338,U_336)),
inference(definitional_conversion,[status(esa)],[f_135_2]) ).
cnf(f_135_4,plain,
plus_plus_nat(plus_plus_nat(U_339,U_338),plus_plus_nat(U_337,U_336)) = plus_plus_nat(plus_plus_nat(U_339,U_337),plus_plus_nat(U_338,U_336)),
inference(clausify,[status(thm)],[f_135_3]) ).
fof(f_136_1,plain,
! [A_55,B_16,C_10,D_5] : plus_plus_int(plus_plus_int(A_55,B_16),plus_plus_int(C_10,D_5)) = plus_plus_int(plus_plus_int(A_55,C_10),plus_plus_int(B_16,D_5)),
inference(fof_nnf,[status(thm)],[fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).
fof(f_136_2,plain,
! [U_343,U_342,U_341,U_340] : plus_plus_int(plus_plus_int(U_343,U_342),plus_plus_int(U_341,U_340)) = plus_plus_int(plus_plus_int(U_343,U_341),plus_plus_int(U_342,U_340)),
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
! [U_340,U_341,U_342,U_343] : plus_plus_int(plus_plus_int(U_343,U_342),plus_plus_int(U_341,U_340)) = plus_plus_int(plus_plus_int(U_343,U_341),plus_plus_int(U_342,U_340)),
inference(definitional_conversion,[status(esa)],[f_136_2]) ).
cnf(f_136_4,plain,
plus_plus_int(plus_plus_int(U_343,U_342),plus_plus_int(U_341,U_340)) = plus_plus_int(plus_plus_int(U_343,U_341),plus_plus_int(U_342,U_340)),
inference(clausify,[status(thm)],[f_136_3]) ).
fof(f_137_1,plain,
! [A_54,B_15,C_9] : plus_plus_real(plus_plus_real(A_54,B_15),C_9) = plus_plus_real(plus_plus_real(A_54,C_9),B_15),
inference(fof_nnf,[status(thm)],[fact_118_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).
fof(f_137_2,plain,
! [U_346,U_345,U_344] : plus_plus_real(plus_plus_real(U_346,U_345),U_344) = plus_plus_real(plus_plus_real(U_346,U_344),U_345),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
! [U_345,U_344,U_346] : plus_plus_real(plus_plus_real(U_346,U_345),U_344) = plus_plus_real(plus_plus_real(U_346,U_344),U_345),
inference(definitional_conversion,[status(esa)],[f_137_2]) ).
cnf(f_137_4,plain,
plus_plus_real(plus_plus_real(U_346,U_345),U_344) = plus_plus_real(plus_plus_real(U_346,U_344),U_345),
inference(clausify,[status(thm)],[f_137_3]) ).
fof(f_138_1,plain,
! [A_54,B_15,C_9] : plus_plus_nat(plus_plus_nat(A_54,B_15),C_9) = plus_plus_nat(plus_plus_nat(A_54,C_9),B_15),
inference(fof_nnf,[status(thm)],[fact_119_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).
fof(f_138_2,plain,
! [U_349,U_348,U_347] : plus_plus_nat(plus_plus_nat(U_349,U_348),U_347) = plus_plus_nat(plus_plus_nat(U_349,U_347),U_348),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
! [U_347,U_348,U_349] : plus_plus_nat(plus_plus_nat(U_349,U_348),U_347) = plus_plus_nat(plus_plus_nat(U_349,U_347),U_348),
inference(definitional_conversion,[status(esa)],[f_138_2]) ).
cnf(f_138_4,plain,
plus_plus_nat(plus_plus_nat(U_349,U_348),U_347) = plus_plus_nat(plus_plus_nat(U_349,U_347),U_348),
inference(clausify,[status(thm)],[f_138_3]) ).
fof(f_139_1,plain,
! [A_54,B_15,C_9] : plus_plus_int(plus_plus_int(A_54,B_15),C_9) = plus_plus_int(plus_plus_int(A_54,C_9),B_15),
inference(fof_nnf,[status(thm)],[fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).
fof(f_139_2,plain,
! [U_352,U_351,U_350] : plus_plus_int(plus_plus_int(U_352,U_351),U_350) = plus_plus_int(plus_plus_int(U_352,U_350),U_351),
inference(variable_rename,[status(thm)],[f_139_1]) ).
fof(f_139_3,plain,
! [U_350,U_351,U_352] : plus_plus_int(plus_plus_int(U_352,U_351),U_350) = plus_plus_int(plus_plus_int(U_352,U_350),U_351),
inference(definitional_conversion,[status(esa)],[f_139_2]) ).
cnf(f_139_4,plain,
plus_plus_int(plus_plus_int(U_352,U_351),U_350) = plus_plus_int(plus_plus_int(U_352,U_350),U_351),
inference(clausify,[status(thm)],[f_139_3]) ).
fof(f_140_1,plain,
! [A_53,B_14,C_8] : plus_plus_real(plus_plus_real(A_53,B_14),C_8) = plus_plus_real(A_53,plus_plus_real(B_14,C_8)),
inference(fof_nnf,[status(thm)],[fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).
fof(f_140_2,plain,
! [U_355,U_354,U_353] : plus_plus_real(plus_plus_real(U_355,U_354),U_353) = plus_plus_real(U_355,plus_plus_real(U_354,U_353)),
inference(variable_rename,[status(thm)],[f_140_1]) ).
fof(f_140_3,plain,
! [U_353,U_354,U_355] : plus_plus_real(plus_plus_real(U_355,U_354),U_353) = plus_plus_real(U_355,plus_plus_real(U_354,U_353)),
inference(definitional_conversion,[status(esa)],[f_140_2]) ).
cnf(f_140_4,plain,
plus_plus_real(plus_plus_real(U_355,U_354),U_353) = plus_plus_real(U_355,plus_plus_real(U_354,U_353)),
inference(clausify,[status(thm)],[f_140_3]) ).
fof(f_141_1,plain,
! [A_53,B_14,C_8] : plus_plus_nat(plus_plus_nat(A_53,B_14),C_8) = plus_plus_nat(A_53,plus_plus_nat(B_14,C_8)),
inference(fof_nnf,[status(thm)],[fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).
fof(f_141_2,plain,
! [U_358,U_357,U_356] : plus_plus_nat(plus_plus_nat(U_358,U_357),U_356) = plus_plus_nat(U_358,plus_plus_nat(U_357,U_356)),
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
! [U_356,U_357,U_358] : plus_plus_nat(plus_plus_nat(U_358,U_357),U_356) = plus_plus_nat(U_358,plus_plus_nat(U_357,U_356)),
inference(definitional_conversion,[status(esa)],[f_141_2]) ).
cnf(f_141_4,plain,
plus_plus_nat(plus_plus_nat(U_358,U_357),U_356) = plus_plus_nat(U_358,plus_plus_nat(U_357,U_356)),
inference(clausify,[status(thm)],[f_141_3]) ).
fof(f_142_1,plain,
! [A_53,B_14,C_8] : plus_plus_int(plus_plus_int(A_53,B_14),C_8) = plus_plus_int(A_53,plus_plus_int(B_14,C_8)),
inference(fof_nnf,[status(thm)],[fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).
fof(f_142_2,plain,
! [U_361,U_360,U_359] : plus_plus_int(plus_plus_int(U_361,U_360),U_359) = plus_plus_int(U_361,plus_plus_int(U_360,U_359)),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
! [U_359,U_360,U_361] : plus_plus_int(plus_plus_int(U_361,U_360),U_359) = plus_plus_int(U_361,plus_plus_int(U_360,U_359)),
inference(definitional_conversion,[status(esa)],[f_142_2]) ).
cnf(f_142_4,plain,
plus_plus_int(plus_plus_int(U_361,U_360),U_359) = plus_plus_int(U_361,plus_plus_int(U_360,U_359)),
inference(clausify,[status(thm)],[f_142_3]) ).
fof(f_143_1,plain,
! [A_52,C_7,D_4] : plus_plus_real(A_52,plus_plus_real(C_7,D_4)) = plus_plus_real(plus_plus_real(A_52,C_7),D_4),
inference(fof_nnf,[status(thm)],[fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).
fof(f_143_2,plain,
! [U_364,U_363,U_362] : plus_plus_real(U_364,plus_plus_real(U_363,U_362)) = plus_plus_real(plus_plus_real(U_364,U_363),U_362),
inference(variable_rename,[status(thm)],[f_143_1]) ).
fof(f_143_3,plain,
! [U_362,U_363,U_364] : plus_plus_real(U_364,plus_plus_real(U_363,U_362)) = plus_plus_real(plus_plus_real(U_364,U_363),U_362),
inference(definitional_conversion,[status(esa)],[f_143_2]) ).
cnf(f_143_4,plain,
plus_plus_real(U_364,plus_plus_real(U_363,U_362)) = plus_plus_real(plus_plus_real(U_364,U_363),U_362),
inference(clausify,[status(thm)],[f_143_3]) ).
fof(f_144_1,plain,
! [A_52,C_7,D_4] : plus_plus_nat(A_52,plus_plus_nat(C_7,D_4)) = plus_plus_nat(plus_plus_nat(A_52,C_7),D_4),
inference(fof_nnf,[status(thm)],[fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).
fof(f_144_2,plain,
! [U_367,U_366,U_365] : plus_plus_nat(U_367,plus_plus_nat(U_366,U_365)) = plus_plus_nat(plus_plus_nat(U_367,U_366),U_365),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
! [U_365,U_366,U_367] : plus_plus_nat(U_367,plus_plus_nat(U_366,U_365)) = plus_plus_nat(plus_plus_nat(U_367,U_366),U_365),
inference(definitional_conversion,[status(esa)],[f_144_2]) ).
cnf(f_144_4,plain,
plus_plus_nat(U_367,plus_plus_nat(U_366,U_365)) = plus_plus_nat(plus_plus_nat(U_367,U_366),U_365),
inference(clausify,[status(thm)],[f_144_3]) ).
fof(f_145_1,plain,
! [A_52,C_7,D_4] : plus_plus_int(A_52,plus_plus_int(C_7,D_4)) = plus_plus_int(plus_plus_int(A_52,C_7),D_4),
inference(fof_nnf,[status(thm)],[fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).
fof(f_145_2,plain,
! [U_370,U_369,U_368] : plus_plus_int(U_370,plus_plus_int(U_369,U_368)) = plus_plus_int(plus_plus_int(U_370,U_369),U_368),
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
! [U_368,U_369,U_370] : plus_plus_int(U_370,plus_plus_int(U_369,U_368)) = plus_plus_int(plus_plus_int(U_370,U_369),U_368),
inference(definitional_conversion,[status(esa)],[f_145_2]) ).
cnf(f_145_4,plain,
plus_plus_int(U_370,plus_plus_int(U_369,U_368)) = plus_plus_int(plus_plus_int(U_370,U_369),U_368),
inference(clausify,[status(thm)],[f_145_3]) ).
fof(f_146_1,plain,
! [A_51,C_6,D_3] : plus_plus_real(A_51,plus_plus_real(C_6,D_3)) = plus_plus_real(C_6,plus_plus_real(A_51,D_3)),
inference(fof_nnf,[status(thm)],[fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).
fof(f_146_2,plain,
! [U_373,U_372,U_371] : plus_plus_real(U_373,plus_plus_real(U_372,U_371)) = plus_plus_real(U_372,plus_plus_real(U_373,U_371)),
inference(variable_rename,[status(thm)],[f_146_1]) ).
fof(f_146_3,plain,
! [U_371,U_372,U_373] : plus_plus_real(U_373,plus_plus_real(U_372,U_371)) = plus_plus_real(U_372,plus_plus_real(U_373,U_371)),
inference(definitional_conversion,[status(esa)],[f_146_2]) ).
cnf(f_146_4,plain,
plus_plus_real(U_373,plus_plus_real(U_372,U_371)) = plus_plus_real(U_372,plus_plus_real(U_373,U_371)),
inference(clausify,[status(thm)],[f_146_3]) ).
fof(f_147_1,plain,
! [A_51,C_6,D_3] : plus_plus_nat(A_51,plus_plus_nat(C_6,D_3)) = plus_plus_nat(C_6,plus_plus_nat(A_51,D_3)),
inference(fof_nnf,[status(thm)],[fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).
fof(f_147_2,plain,
! [U_376,U_375,U_374] : plus_plus_nat(U_376,plus_plus_nat(U_375,U_374)) = plus_plus_nat(U_375,plus_plus_nat(U_376,U_374)),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
! [U_374,U_375,U_376] : plus_plus_nat(U_376,plus_plus_nat(U_375,U_374)) = plus_plus_nat(U_375,plus_plus_nat(U_376,U_374)),
inference(definitional_conversion,[status(esa)],[f_147_2]) ).
cnf(f_147_4,plain,
plus_plus_nat(U_376,plus_plus_nat(U_375,U_374)) = plus_plus_nat(U_375,plus_plus_nat(U_376,U_374)),
inference(clausify,[status(thm)],[f_147_3]) ).
fof(f_148_1,plain,
! [A_51,C_6,D_3] : plus_plus_int(A_51,plus_plus_int(C_6,D_3)) = plus_plus_int(C_6,plus_plus_int(A_51,D_3)),
inference(fof_nnf,[status(thm)],[fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).
fof(f_148_2,plain,
! [U_379,U_378,U_377] : plus_plus_int(U_379,plus_plus_int(U_378,U_377)) = plus_plus_int(U_378,plus_plus_int(U_379,U_377)),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_377,U_378,U_379] : plus_plus_int(U_379,plus_plus_int(U_378,U_377)) = plus_plus_int(U_378,plus_plus_int(U_379,U_377)),
inference(definitional_conversion,[status(esa)],[f_148_2]) ).
cnf(f_148_4,plain,
plus_plus_int(U_379,plus_plus_int(U_378,U_377)) = plus_plus_int(U_378,plus_plus_int(U_379,U_377)),
inference(clausify,[status(thm)],[f_148_3]) ).
fof(f_149_1,plain,
! [A_50,C_5] : plus_plus_real(A_50,C_5) = plus_plus_real(C_5,A_50),
inference(fof_nnf,[status(thm)],[fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
fof(f_149_2,plain,
! [U_381,U_380] : plus_plus_real(U_381,U_380) = plus_plus_real(U_380,U_381),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
! [U_380,U_381] : plus_plus_real(U_381,U_380) = plus_plus_real(U_380,U_381),
inference(definitional_conversion,[status(esa)],[f_149_2]) ).
cnf(f_149_4,plain,
plus_plus_real(U_381,U_380) = plus_plus_real(U_380,U_381),
inference(clausify,[status(thm)],[f_149_3]) ).
fof(f_150_1,plain,
! [A_50,C_5] : plus_plus_nat(A_50,C_5) = plus_plus_nat(C_5,A_50),
inference(fof_nnf,[status(thm)],[fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
fof(f_150_2,plain,
! [U_383,U_382] : plus_plus_nat(U_383,U_382) = plus_plus_nat(U_382,U_383),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
! [U_382,U_383] : plus_plus_nat(U_383,U_382) = plus_plus_nat(U_382,U_383),
inference(definitional_conversion,[status(esa)],[f_150_2]) ).
cnf(f_150_4,plain,
plus_plus_nat(U_383,U_382) = plus_plus_nat(U_382,U_383),
inference(clausify,[status(thm)],[f_150_3]) ).
fof(f_151_1,plain,
! [A_50,C_5] : plus_plus_int(A_50,C_5) = plus_plus_int(C_5,A_50),
inference(fof_nnf,[status(thm)],[fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
fof(f_151_2,plain,
! [U_385,U_384] : plus_plus_int(U_385,U_384) = plus_plus_int(U_384,U_385),
inference(variable_rename,[status(thm)],[f_151_1]) ).
fof(f_151_3,plain,
! [U_384,U_385] : plus_plus_int(U_385,U_384) = plus_plus_int(U_384,U_385),
inference(definitional_conversion,[status(esa)],[f_151_2]) ).
cnf(f_151_4,plain,
plus_plus_int(U_385,U_384) = plus_plus_int(U_384,U_385),
inference(clausify,[status(thm)],[f_151_3]) ).
fof(f_152_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_133_eq__number__of]) ).
fof(f_152_2,plain,
! [U_387,U_386] :
( ( ( number267125858f_real(U_387) = number267125858f_real(U_386)
| U_387 != U_386 )
& ( U_387 = U_386
| number267125858f_real(U_387) != number267125858f_real(U_386) ) )
| ~ is_int(U_386)
| ~ is_int(U_387) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
( ! [U_386,U_387] :
( number267125858f_real(U_387) = number267125858f_real(U_386)
| U_387 != U_386
| ~ sP5(U_386,U_387) )
& ! [U_386,U_387] :
( U_387 = U_386
| number267125858f_real(U_387) != number267125858f_real(U_386)
| ~ sP5(U_386,U_387) )
& ! [U_386,U_387] :
( sP5(U_386,U_387)
| ~ is_int(U_386)
| ~ is_int(U_387) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_152_2]) ).
cnf(f_152_4,plain,
( sP5(U_386,U_387)
| ~ is_int(U_386)
| ~ is_int(U_387) ),
inference(clausify,[status(thm)],[f_152_3]) ).
cnf(f_152_5,plain,
( U_387 = U_386
| number267125858f_real(U_387) != number267125858f_real(U_386)
| ~ sP5(U_386,U_387) ),
inference(clausify,[status(thm)],[f_152_3]) ).
cnf(f_152_6,plain,
( number267125858f_real(U_387) = number267125858f_real(U_386)
| U_387 != U_386
| ~ sP5(U_386,U_387) ),
inference(clausify,[status(thm)],[f_152_3]) ).
fof(f_153_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_134_eq__number__of]) ).
fof(f_153_2,plain,
! [U_389,U_388] :
( ( ( number_number_of_int(U_389) = number_number_of_int(U_388)
| U_389 != U_388 )
& ( U_389 = U_388
| number_number_of_int(U_389) != number_number_of_int(U_388) ) )
| ~ is_int(U_388)
| ~ is_int(U_389) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
( ! [U_389,U_388] :
( number_number_of_int(U_389) = number_number_of_int(U_388)
| U_389 != U_388
| ~ sP6(U_389,U_388) )
& ! [U_389,U_388] :
( U_389 = U_388
| number_number_of_int(U_389) != number_number_of_int(U_388)
| ~ sP6(U_389,U_388) )
& ! [U_389,U_388] :
( sP6(U_389,U_388)
| ~ is_int(U_388)
| ~ is_int(U_389) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_153_2]) ).
cnf(f_153_4,plain,
( sP6(U_389,U_388)
| ~ is_int(U_388)
| ~ is_int(U_389) ),
inference(clausify,[status(thm)],[f_153_3]) ).
cnf(f_153_5,plain,
( U_389 = U_388
| number_number_of_int(U_389) != number_number_of_int(U_388)
| ~ sP6(U_389,U_388) ),
inference(clausify,[status(thm)],[f_153_3]) ).
cnf(f_153_6,plain,
( number_number_of_int(U_389) = number_number_of_int(U_388)
| U_389 != U_388
| ~ sP6(U_389,U_388) ),
inference(clausify,[status(thm)],[f_153_3]) ).
fof(f_154_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_135_number__of__reorient]) ).
fof(f_154_2,plain,
! [U_391,U_390] :
( ( number267125858f_real(U_391) = U_390
| U_390 != number267125858f_real(U_391) )
& ( U_390 = number267125858f_real(U_391)
| number267125858f_real(U_391) != U_390 ) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
fof(f_154_3,plain,
( ! [U_395,U_393] :
( number267125858f_real(U_395) = U_393
| U_393 != number267125858f_real(U_395) )
& ! [U_394,U_392] :
( U_392 = number267125858f_real(U_394)
| number267125858f_real(U_394) != U_392 ) ),
inference(miniscope,[status(thm)],[f_154_2]) ).
fof(f_154_4,plain,
( ! [U_393,U_395] :
( number267125858f_real(U_395) = U_393
| U_393 != number267125858f_real(U_395) )
& ! [U_394,U_392] :
( U_392 = number267125858f_real(U_394)
| number267125858f_real(U_394) != U_392 ) ),
inference(definitional_conversion,[status(esa)],[f_154_3]) ).
cnf(f_154_5,plain,
( U_392 = number267125858f_real(U_394)
| number267125858f_real(U_394) != U_392 ),
inference(clausify,[status(thm)],[f_154_4]) ).
cnf(f_154_6,plain,
( number267125858f_real(U_395) = U_393
| U_393 != number267125858f_real(U_395) ),
inference(clausify,[status(thm)],[f_154_4]) ).
fof(f_155_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_136_number__of__reorient]) ).
fof(f_155_2,plain,
! [U_397,U_396] :
( ( ( number_number_of_int(U_397) = U_396
| U_396 != number_number_of_int(U_397) )
& ( U_396 = number_number_of_int(U_397)
| number_number_of_int(U_397) != U_396 ) )
| ~ is_int(U_396) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
( ! [U_396,U_397] :
( number_number_of_int(U_397) = U_396
| U_396 != number_number_of_int(U_397)
| ~ sP7(U_396,U_397) )
& ! [U_396,U_397] :
( U_396 = number_number_of_int(U_397)
| number_number_of_int(U_397) != U_396
| ~ sP7(U_396,U_397) )
& ! [U_396,U_397] :
( sP7(U_396,U_397)
| ~ is_int(U_396) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_155_2]) ).
cnf(f_155_4,plain,
( sP7(U_396,U_397)
| ~ is_int(U_396) ),
inference(clausify,[status(thm)],[f_155_3]) ).
cnf(f_155_5,plain,
( U_396 = number_number_of_int(U_397)
| number_number_of_int(U_397) != U_396
| ~ sP7(U_396,U_397) ),
inference(clausify,[status(thm)],[f_155_3]) ).
cnf(f_155_6,plain,
( number_number_of_int(U_397) = U_396
| U_396 != number_number_of_int(U_397)
| ~ sP7(U_396,U_397) ),
inference(clausify,[status(thm)],[f_155_3]) ).
fof(f_156_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_156_2,plain,
! [U_399,U_398] :
( ( number_number_of_nat(U_399) = U_398
| U_398 != number_number_of_nat(U_399) )
& ( U_398 = number_number_of_nat(U_399)
| number_number_of_nat(U_399) != U_398 ) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
( ! [U_403,U_401] :
( number_number_of_nat(U_403) = U_401
| U_401 != number_number_of_nat(U_403) )
& ! [U_402,U_400] :
( U_400 = number_number_of_nat(U_402)
| number_number_of_nat(U_402) != U_400 ) ),
inference(miniscope,[status(thm)],[f_156_2]) ).
fof(f_156_4,plain,
( ! [U_401,U_403] :
( number_number_of_nat(U_403) = U_401
| U_401 != number_number_of_nat(U_403) )
& ! [U_400,U_402] :
( U_400 = number_number_of_nat(U_402)
| number_number_of_nat(U_402) != U_400 ) ),
inference(definitional_conversion,[status(esa)],[f_156_3]) ).
cnf(f_156_5,plain,
( U_400 = number_number_of_nat(U_402)
| number_number_of_nat(U_402) != U_400 ),
inference(clausify,[status(thm)],[f_156_4]) ).
cnf(f_156_6,plain,
( number_number_of_nat(U_403) = U_401
| U_401 != number_number_of_nat(U_403) ),
inference(clausify,[status(thm)],[f_156_4]) ).
fof(f_157_1,plain,
! [K_1,L_1] :
( ( ( bit1(K_1) = bit1(L_1)
| K_1 != L_1 )
& ( K_1 = L_1
| bit1(K_1) != bit1(L_1) ) )
| ~ is_int(L_1)
| ~ is_int(K_1) ),
inference(fof_nnf,[status(thm)],[fact_138_rel__simps_I51_J]) ).
fof(f_157_2,plain,
! [U_405,U_404] :
( ( ( bit1(U_405) = bit1(U_404)
| U_405 != U_404 )
& ( U_405 = U_404
| bit1(U_405) != bit1(U_404) ) )
| ~ is_int(U_404)
| ~ is_int(U_405) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
( ! [U_405,U_404] :
( bit1(U_405) = bit1(U_404)
| U_405 != U_404
| ~ sP8(U_405,U_404) )
& ! [U_405,U_404] :
( U_405 = U_404
| bit1(U_405) != bit1(U_404)
| ~ sP8(U_405,U_404) )
& ! [U_405,U_404] :
( sP8(U_405,U_404)
| ~ is_int(U_404)
| ~ is_int(U_405) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_157_2]) ).
cnf(f_157_4,plain,
( sP8(U_405,U_404)
| ~ is_int(U_404)
| ~ is_int(U_405) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_5,plain,
( U_405 = U_404
| bit1(U_405) != bit1(U_404)
| ~ sP8(U_405,U_404) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_6,plain,
( bit1(U_405) = bit1(U_404)
| U_405 != U_404
| ~ sP8(U_405,U_404) ),
inference(clausify,[status(thm)],[f_157_3]) ).
fof(f_158_1,plain,
! [K_1,L_1] :
( ( ( bit0(K_1) = bit0(L_1)
| K_1 != L_1 )
& ( K_1 = L_1
| bit0(K_1) != bit0(L_1) ) )
| ~ is_int(L_1)
| ~ is_int(K_1) ),
inference(fof_nnf,[status(thm)],[fact_139_rel__simps_I48_J]) ).
fof(f_158_2,plain,
! [U_407,U_406] :
( ( ( bit0(U_407) = bit0(U_406)
| U_407 != U_406 )
& ( U_407 = U_406
| bit0(U_407) != bit0(U_406) ) )
| ~ is_int(U_406)
| ~ is_int(U_407) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
( ! [U_406,U_407] :
( bit0(U_407) = bit0(U_406)
| U_407 != U_406
| ~ sP9(U_406,U_407) )
& ! [U_406,U_407] :
( U_407 = U_406
| bit0(U_407) != bit0(U_406)
| ~ sP9(U_406,U_407) )
& ! [U_406,U_407] :
( sP9(U_406,U_407)
| ~ is_int(U_406)
| ~ is_int(U_407) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_158_2]) ).
cnf(f_158_4,plain,
( sP9(U_406,U_407)
| ~ is_int(U_406)
| ~ is_int(U_407) ),
inference(clausify,[status(thm)],[f_158_3]) ).
cnf(f_158_5,plain,
( U_407 = U_406
| bit0(U_407) != bit0(U_406)
| ~ sP9(U_406,U_407) ),
inference(clausify,[status(thm)],[f_158_3]) ).
cnf(f_158_6,plain,
( bit0(U_407) = bit0(U_406)
| U_407 != U_406
| ~ sP9(U_406,U_407) ),
inference(clausify,[status(thm)],[f_158_3]) ).
fof(f_159_1,plain,
! [Z1,Z2,Z3] : times_times_int(times_times_int(Z1,Z2),Z3) = times_times_int(Z1,times_times_int(Z2,Z3)),
inference(fof_nnf,[status(thm)],[fact_140_zmult__assoc]) ).
fof(f_159_2,plain,
! [U_410,U_409,U_408] : times_times_int(times_times_int(U_410,U_409),U_408) = times_times_int(U_410,times_times_int(U_409,U_408)),
inference(variable_rename,[status(thm)],[f_159_1]) ).
fof(f_159_3,plain,
! [U_409,U_410,U_408] : times_times_int(times_times_int(U_410,U_409),U_408) = times_times_int(U_410,times_times_int(U_409,U_408)),
inference(definitional_conversion,[status(esa)],[f_159_2]) ).
cnf(f_159_4,plain,
times_times_int(times_times_int(U_410,U_409),U_408) = times_times_int(U_410,times_times_int(U_409,U_408)),
inference(clausify,[status(thm)],[f_159_3]) ).
fof(f_160_1,plain,
! [Z,W] : times_times_int(Z,W) = times_times_int(W,Z),
inference(fof_nnf,[status(thm)],[fact_141_zmult__commute]) ).
fof(f_160_2,plain,
! [U_412,U_411] : times_times_int(U_412,U_411) = times_times_int(U_411,U_412),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
! [U_411,U_412] : times_times_int(U_412,U_411) = times_times_int(U_411,U_412),
inference(definitional_conversion,[status(esa)],[f_160_2]) ).
cnf(f_160_4,plain,
times_times_int(U_412,U_411) = times_times_int(U_411,U_412),
inference(clausify,[status(thm)],[f_160_3]) ).
fof(f_161_1,plain,
! [K] :
( number_number_of_int(K) = K
| ~ is_int(K) ),
inference(fof_nnf,[status(thm)],[fact_142_number__of__is__id]) ).
fof(f_161_2,plain,
! [U_413] :
( number_number_of_int(U_413) = U_413
| ~ is_int(U_413) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
fof(f_161_3,plain,
! [U_413] :
( number_number_of_int(U_413) = U_413
| ~ is_int(U_413) ),
inference(definitional_conversion,[status(esa)],[f_161_2]) ).
cnf(f_161_4,plain,
( number_number_of_int(U_413) = U_413
| ~ is_int(U_413) ),
inference(clausify,[status(thm)],[f_161_3]) ).
fof(f_162_1,plain,
! [Z1,Z2,Z3] : plus_plus_int(plus_plus_int(Z1,Z2),Z3) = plus_plus_int(Z1,plus_plus_int(Z2,Z3)),
inference(fof_nnf,[status(thm)],[fact_143_zadd__assoc]) ).
fof(f_162_2,plain,
! [U_416,U_415,U_414] : plus_plus_int(plus_plus_int(U_416,U_415),U_414) = plus_plus_int(U_416,plus_plus_int(U_415,U_414)),
inference(variable_rename,[status(thm)],[f_162_1]) ).
fof(f_162_3,plain,
! [U_414,U_415,U_416] : plus_plus_int(plus_plus_int(U_416,U_415),U_414) = plus_plus_int(U_416,plus_plus_int(U_415,U_414)),
inference(definitional_conversion,[status(esa)],[f_162_2]) ).
cnf(f_162_4,plain,
plus_plus_int(plus_plus_int(U_416,U_415),U_414) = plus_plus_int(U_416,plus_plus_int(U_415,U_414)),
inference(clausify,[status(thm)],[f_162_3]) ).
fof(f_163_1,plain,
! [X_1,Y_1,Z] : plus_plus_int(X_1,plus_plus_int(Y_1,Z)) = plus_plus_int(Y_1,plus_plus_int(X_1,Z)),
inference(fof_nnf,[status(thm)],[fact_144_zadd__left__commute]) ).
fof(f_163_2,plain,
! [U_419,U_418,U_417] : plus_plus_int(U_419,plus_plus_int(U_418,U_417)) = plus_plus_int(U_418,plus_plus_int(U_419,U_417)),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
! [U_417,U_418,U_419] : plus_plus_int(U_419,plus_plus_int(U_418,U_417)) = plus_plus_int(U_418,plus_plus_int(U_419,U_417)),
inference(definitional_conversion,[status(esa)],[f_163_2]) ).
cnf(f_163_4,plain,
plus_plus_int(U_419,plus_plus_int(U_418,U_417)) = plus_plus_int(U_418,plus_plus_int(U_419,U_417)),
inference(clausify,[status(thm)],[f_163_3]) ).
fof(f_164_1,plain,
! [Z,W] : plus_plus_int(Z,W) = plus_plus_int(W,Z),
inference(fof_nnf,[status(thm)],[fact_145_zadd__commute]) ).
fof(f_164_2,plain,
! [U_421,U_420] : plus_plus_int(U_421,U_420) = plus_plus_int(U_420,U_421),
inference(variable_rename,[status(thm)],[f_164_1]) ).
fof(f_164_3,plain,
! [U_421,U_420] : plus_plus_int(U_421,U_420) = plus_plus_int(U_420,U_421),
inference(definitional_conversion,[status(esa)],[f_164_2]) ).
cnf(f_164_4,plain,
plus_plus_int(U_421,U_420) = plus_plus_int(U_420,U_421),
inference(clausify,[status(thm)],[f_164_3]) ).
fof(f_165_1,plain,
! [K_1] :
( ( ord_less_int(bit1(K_1),pls)
| ~ ord_less_int(K_1,pls) )
& ( ord_less_int(K_1,pls)
| ~ ord_less_int(bit1(K_1),pls) ) ),
inference(fof_nnf,[status(thm)],[fact_146_rel__simps_I12_J]) ).
fof(f_165_2,plain,
! [U_422] :
( ( ord_less_int(bit1(U_422),pls)
| ~ ord_less_int(U_422,pls) )
& ( ord_less_int(U_422,pls)
| ~ ord_less_int(bit1(U_422),pls) ) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
fof(f_165_3,plain,
( ! [U_424] :
( ord_less_int(bit1(U_424),pls)
| ~ ord_less_int(U_424,pls) )
& ! [U_423] :
( ord_less_int(U_423,pls)
| ~ ord_less_int(bit1(U_423),pls) ) ),
inference(miniscope,[status(thm)],[f_165_2]) ).
fof(f_165_4,plain,
( ! [U_424] :
( ord_less_int(bit1(U_424),pls)
| ~ ord_less_int(U_424,pls) )
& ! [U_423] :
( ord_less_int(U_423,pls)
| ~ ord_less_int(bit1(U_423),pls) ) ),
inference(definitional_conversion,[status(esa)],[f_165_3]) ).
cnf(f_165_5,plain,
( ord_less_int(U_423,pls)
| ~ ord_less_int(bit1(U_423),pls) ),
inference(clausify,[status(thm)],[f_165_4]) ).
cnf(f_165_6,plain,
( ord_less_int(bit1(U_424),pls)
| ~ ord_less_int(U_424,pls) ),
inference(clausify,[status(thm)],[f_165_4]) ).
fof(f_166_1,plain,
! [K1,K2] :
( ( ord_less_int(bit1(K1),bit0(K2))
| ~ ord_less_int(K1,K2) )
& ( ord_less_int(K1,K2)
| ~ ord_less_int(bit1(K1),bit0(K2)) ) ),
inference(fof_nnf,[status(thm)],[fact_147_less__int__code_I15_J]) ).
fof(f_166_2,plain,
! [U_426,U_425] :
( ( ord_less_int(bit1(U_426),bit0(U_425))
| ~ ord_less_int(U_426,U_425) )
& ( ord_less_int(U_426,U_425)
| ~ ord_less_int(bit1(U_426),bit0(U_425)) ) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
fof(f_166_3,plain,
( ! [U_430,U_428] :
( ord_less_int(bit1(U_430),bit0(U_428))
| ~ ord_less_int(U_430,U_428) )
& ! [U_429,U_427] :
( ord_less_int(U_429,U_427)
| ~ ord_less_int(bit1(U_429),bit0(U_427)) ) ),
inference(miniscope,[status(thm)],[f_166_2]) ).
fof(f_166_4,plain,
( ! [U_430,U_428] :
( ord_less_int(bit1(U_430),bit0(U_428))
| ~ ord_less_int(U_430,U_428) )
& ! [U_427,U_429] :
( ord_less_int(U_429,U_427)
| ~ ord_less_int(bit1(U_429),bit0(U_427)) ) ),
inference(definitional_conversion,[status(esa)],[f_166_3]) ).
cnf(f_166_5,plain,
( ord_less_int(U_429,U_427)
| ~ ord_less_int(bit1(U_429),bit0(U_427)) ),
inference(clausify,[status(thm)],[f_166_4]) ).
cnf(f_166_6,plain,
( ord_less_int(bit1(U_430),bit0(U_428))
| ~ ord_less_int(U_430,U_428) ),
inference(clausify,[status(thm)],[f_166_4]) ).
fof(f_167_1,plain,
! [K_1,L_1] :
( ( ord_less_int(bit1(K_1),bit0(L_1))
| ~ ord_less_int(K_1,L_1) )
& ( ord_less_int(K_1,L_1)
| ~ ord_less_int(bit1(K_1),bit0(L_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_148_rel__simps_I16_J]) ).
fof(f_167_2,plain,
! [U_432,U_431] :
( ( ord_less_int(bit1(U_432),bit0(U_431))
| ~ ord_less_int(U_432,U_431) )
& ( ord_less_int(U_432,U_431)
| ~ ord_less_int(bit1(U_432),bit0(U_431)) ) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
fof(f_167_3,plain,
( ! [U_436,U_434] :
( ord_less_int(bit1(U_436),bit0(U_434))
| ~ ord_less_int(U_436,U_434) )
& ! [U_435,U_433] :
( ord_less_int(U_435,U_433)
| ~ ord_less_int(bit1(U_435),bit0(U_433)) ) ),
inference(miniscope,[status(thm)],[f_167_2]) ).
fof(f_167_4,plain,
( ! [U_434,U_436] :
( ord_less_int(bit1(U_436),bit0(U_434))
| ~ ord_less_int(U_436,U_434) )
& ! [U_433,U_435] :
( ord_less_int(U_435,U_433)
| ~ ord_less_int(bit1(U_435),bit0(U_433)) ) ),
inference(definitional_conversion,[status(esa)],[f_167_3]) ).
cnf(f_167_5,plain,
( ord_less_int(U_435,U_433)
| ~ ord_less_int(bit1(U_435),bit0(U_433)) ),
inference(clausify,[status(thm)],[f_167_4]) ).
cnf(f_167_6,plain,
( ord_less_int(bit1(U_436),bit0(U_434))
| ~ ord_less_int(U_436,U_434) ),
inference(clausify,[status(thm)],[f_167_4]) ).
fof(f_168_1,plain,
! [K_1] :
( ( ord_less_int(bit0(K_1),pls)
| ~ ord_less_int(K_1,pls) )
& ( ord_less_int(K_1,pls)
| ~ ord_less_int(bit0(K_1),pls) ) ),
inference(fof_nnf,[status(thm)],[fact_149_rel__simps_I10_J]) ).
fof(f_168_2,plain,
! [U_437] :
( ( ord_less_int(bit0(U_437),pls)
| ~ ord_less_int(U_437,pls) )
& ( ord_less_int(U_437,pls)
| ~ ord_less_int(bit0(U_437),pls) ) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
fof(f_168_3,plain,
( ! [U_439] :
( ord_less_int(bit0(U_439),pls)
| ~ ord_less_int(U_439,pls) )
& ! [U_438] :
( ord_less_int(U_438,pls)
| ~ ord_less_int(bit0(U_438),pls) ) ),
inference(miniscope,[status(thm)],[f_168_2]) ).
fof(f_168_4,plain,
( ! [U_439] :
( ord_less_int(bit0(U_439),pls)
| ~ ord_less_int(U_439,pls) )
& ! [U_438] :
( ord_less_int(U_438,pls)
| ~ ord_less_int(bit0(U_438),pls) ) ),
inference(definitional_conversion,[status(esa)],[f_168_3]) ).
cnf(f_168_5,plain,
( ord_less_int(U_438,pls)
| ~ ord_less_int(bit0(U_438),pls) ),
inference(clausify,[status(thm)],[f_168_4]) ).
cnf(f_168_6,plain,
( ord_less_int(bit0(U_439),pls)
| ~ ord_less_int(U_439,pls) ),
inference(clausify,[status(thm)],[f_168_4]) ).
fof(f_169_1,plain,
! [K_1] :
( ( ord_less_int(pls,bit0(K_1))
| ~ ord_less_int(pls,K_1) )
& ( ord_less_int(pls,K_1)
| ~ ord_less_int(pls,bit0(K_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_150_rel__simps_I4_J]) ).
fof(f_169_2,plain,
! [U_440] :
( ( ord_less_int(pls,bit0(U_440))
| ~ ord_less_int(pls,U_440) )
& ( ord_less_int(pls,U_440)
| ~ ord_less_int(pls,bit0(U_440)) ) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
( ! [U_442] :
( ord_less_int(pls,bit0(U_442))
| ~ ord_less_int(pls,U_442) )
& ! [U_441] :
( ord_less_int(pls,U_441)
| ~ ord_less_int(pls,bit0(U_441)) ) ),
inference(miniscope,[status(thm)],[f_169_2]) ).
fof(f_169_4,plain,
( ! [U_442] :
( ord_less_int(pls,bit0(U_442))
| ~ ord_less_int(pls,U_442) )
& ! [U_441] :
( ord_less_int(pls,U_441)
| ~ ord_less_int(pls,bit0(U_441)) ) ),
inference(definitional_conversion,[status(esa)],[f_169_3]) ).
cnf(f_169_5,plain,
( ord_less_int(pls,U_441)
| ~ ord_less_int(pls,bit0(U_441)) ),
inference(clausify,[status(thm)],[f_169_4]) ).
cnf(f_169_6,plain,
( ord_less_int(pls,bit0(U_442))
| ~ ord_less_int(pls,U_442) ),
inference(clausify,[status(thm)],[f_169_4]) ).
fof(f_170_1,plain,
! [K_1] :
( ( ord_less_eq_int(pls,bit1(K_1))
| ~ ord_less_eq_int(pls,K_1) )
& ( ord_less_eq_int(pls,K_1)
| ~ ord_less_eq_int(pls,bit1(K_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_151_rel__simps_I22_J]) ).
fof(f_170_2,plain,
! [U_443] :
( ( ord_less_eq_int(pls,bit1(U_443))
| ~ ord_less_eq_int(pls,U_443) )
& ( ord_less_eq_int(pls,U_443)
| ~ ord_less_eq_int(pls,bit1(U_443)) ) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
( ! [U_445] :
( ord_less_eq_int(pls,bit1(U_445))
| ~ ord_less_eq_int(pls,U_445) )
& ! [U_444] :
( ord_less_eq_int(pls,U_444)
| ~ ord_less_eq_int(pls,bit1(U_444)) ) ),
inference(miniscope,[status(thm)],[f_170_2]) ).
fof(f_170_4,plain,
( ! [U_445] :
( ord_less_eq_int(pls,bit1(U_445))
| ~ ord_less_eq_int(pls,U_445) )
& ! [U_444] :
( ord_less_eq_int(pls,U_444)
| ~ ord_less_eq_int(pls,bit1(U_444)) ) ),
inference(definitional_conversion,[status(esa)],[f_170_3]) ).
cnf(f_170_5,plain,
( ord_less_eq_int(pls,U_444)
| ~ ord_less_eq_int(pls,bit1(U_444)) ),
inference(clausify,[status(thm)],[f_170_4]) ).
cnf(f_170_6,plain,
( ord_less_eq_int(pls,bit1(U_445))
| ~ ord_less_eq_int(pls,U_445) ),
inference(clausify,[status(thm)],[f_170_4]) ).
fof(f_171_1,plain,
! [K1,K2] :
( ( ord_less_eq_int(bit0(K1),bit1(K2))
| ~ ord_less_eq_int(K1,K2) )
& ( ord_less_eq_int(K1,K2)
| ~ ord_less_eq_int(bit0(K1),bit1(K2)) ) ),
inference(fof_nnf,[status(thm)],[fact_152_less__eq__int__code_I14_J]) ).
fof(f_171_2,plain,
! [U_447,U_446] :
( ( ord_less_eq_int(bit0(U_447),bit1(U_446))
| ~ ord_less_eq_int(U_447,U_446) )
& ( ord_less_eq_int(U_447,U_446)
| ~ ord_less_eq_int(bit0(U_447),bit1(U_446)) ) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
fof(f_171_3,plain,
( ! [U_451,U_449] :
( ord_less_eq_int(bit0(U_451),bit1(U_449))
| ~ ord_less_eq_int(U_451,U_449) )
& ! [U_450,U_448] :
( ord_less_eq_int(U_450,U_448)
| ~ ord_less_eq_int(bit0(U_450),bit1(U_448)) ) ),
inference(miniscope,[status(thm)],[f_171_2]) ).
fof(f_171_4,plain,
( ! [U_449,U_451] :
( ord_less_eq_int(bit0(U_451),bit1(U_449))
| ~ ord_less_eq_int(U_451,U_449) )
& ! [U_448,U_450] :
( ord_less_eq_int(U_450,U_448)
| ~ ord_less_eq_int(bit0(U_450),bit1(U_448)) ) ),
inference(definitional_conversion,[status(esa)],[f_171_3]) ).
cnf(f_171_5,plain,
( ord_less_eq_int(U_450,U_448)
| ~ ord_less_eq_int(bit0(U_450),bit1(U_448)) ),
inference(clausify,[status(thm)],[f_171_4]) ).
cnf(f_171_6,plain,
( ord_less_eq_int(bit0(U_451),bit1(U_449))
| ~ ord_less_eq_int(U_451,U_449) ),
inference(clausify,[status(thm)],[f_171_4]) ).
fof(f_172_1,plain,
! [K_1,L_1] :
( ( ord_less_eq_int(bit0(K_1),bit1(L_1))
| ~ ord_less_eq_int(K_1,L_1) )
& ( ord_less_eq_int(K_1,L_1)
| ~ ord_less_eq_int(bit0(K_1),bit1(L_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_153_rel__simps_I32_J]) ).
fof(f_172_2,plain,
! [U_453,U_452] :
( ( ord_less_eq_int(bit0(U_453),bit1(U_452))
| ~ ord_less_eq_int(U_453,U_452) )
& ( ord_less_eq_int(U_453,U_452)
| ~ ord_less_eq_int(bit0(U_453),bit1(U_452)) ) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
fof(f_172_3,plain,
( ! [U_457,U_455] :
( ord_less_eq_int(bit0(U_457),bit1(U_455))
| ~ ord_less_eq_int(U_457,U_455) )
& ! [U_456,U_454] :
( ord_less_eq_int(U_456,U_454)
| ~ ord_less_eq_int(bit0(U_456),bit1(U_454)) ) ),
inference(miniscope,[status(thm)],[f_172_2]) ).
fof(f_172_4,plain,
( ! [U_455,U_457] :
( ord_less_eq_int(bit0(U_457),bit1(U_455))
| ~ ord_less_eq_int(U_457,U_455) )
& ! [U_454,U_456] :
( ord_less_eq_int(U_456,U_454)
| ~ ord_less_eq_int(bit0(U_456),bit1(U_454)) ) ),
inference(definitional_conversion,[status(esa)],[f_172_3]) ).
cnf(f_172_5,plain,
( ord_less_eq_int(U_456,U_454)
| ~ ord_less_eq_int(bit0(U_456),bit1(U_454)) ),
inference(clausify,[status(thm)],[f_172_4]) ).
cnf(f_172_6,plain,
( ord_less_eq_int(bit0(U_457),bit1(U_455))
| ~ ord_less_eq_int(U_457,U_455) ),
inference(clausify,[status(thm)],[f_172_4]) ).
fof(f_173_1,plain,
! [K_1] :
( ( ord_less_eq_int(bit0(K_1),pls)
| ~ ord_less_eq_int(K_1,pls) )
& ( ord_less_eq_int(K_1,pls)
| ~ ord_less_eq_int(bit0(K_1),pls) ) ),
inference(fof_nnf,[status(thm)],[fact_154_rel__simps_I27_J]) ).
fof(f_173_2,plain,
! [U_458] :
( ( ord_less_eq_int(bit0(U_458),pls)
| ~ ord_less_eq_int(U_458,pls) )
& ( ord_less_eq_int(U_458,pls)
| ~ ord_less_eq_int(bit0(U_458),pls) ) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
( ! [U_460] :
( ord_less_eq_int(bit0(U_460),pls)
| ~ ord_less_eq_int(U_460,pls) )
& ! [U_459] :
( ord_less_eq_int(U_459,pls)
| ~ ord_less_eq_int(bit0(U_459),pls) ) ),
inference(miniscope,[status(thm)],[f_173_2]) ).
fof(f_173_4,plain,
( ! [U_460] :
( ord_less_eq_int(bit0(U_460),pls)
| ~ ord_less_eq_int(U_460,pls) )
& ! [U_459] :
( ord_less_eq_int(U_459,pls)
| ~ ord_less_eq_int(bit0(U_459),pls) ) ),
inference(definitional_conversion,[status(esa)],[f_173_3]) ).
cnf(f_173_5,plain,
( ord_less_eq_int(U_459,pls)
| ~ ord_less_eq_int(bit0(U_459),pls) ),
inference(clausify,[status(thm)],[f_173_4]) ).
cnf(f_173_6,plain,
( ord_less_eq_int(bit0(U_460),pls)
| ~ ord_less_eq_int(U_460,pls) ),
inference(clausify,[status(thm)],[f_173_4]) ).
fof(f_174_1,plain,
! [K_1] :
( ( ord_less_eq_int(pls,bit0(K_1))
| ~ ord_less_eq_int(pls,K_1) )
& ( ord_less_eq_int(pls,K_1)
| ~ ord_less_eq_int(pls,bit0(K_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_155_rel__simps_I21_J]) ).
fof(f_174_2,plain,
! [U_461] :
( ( ord_less_eq_int(pls,bit0(U_461))
| ~ ord_less_eq_int(pls,U_461) )
& ( ord_less_eq_int(pls,U_461)
| ~ ord_less_eq_int(pls,bit0(U_461)) ) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
fof(f_174_3,plain,
( ! [U_463] :
( ord_less_eq_int(pls,bit0(U_463))
| ~ ord_less_eq_int(pls,U_463) )
& ! [U_462] :
( ord_less_eq_int(pls,U_462)
| ~ ord_less_eq_int(pls,bit0(U_462)) ) ),
inference(miniscope,[status(thm)],[f_174_2]) ).
fof(f_174_4,plain,
( ! [U_463] :
( ord_less_eq_int(pls,bit0(U_463))
| ~ ord_less_eq_int(pls,U_463) )
& ! [U_462] :
( ord_less_eq_int(pls,U_462)
| ~ ord_less_eq_int(pls,bit0(U_462)) ) ),
inference(definitional_conversion,[status(esa)],[f_174_3]) ).
cnf(f_174_5,plain,
( ord_less_eq_int(pls,U_462)
| ~ ord_less_eq_int(pls,bit0(U_462)) ),
inference(clausify,[status(thm)],[f_174_4]) ).
cnf(f_174_6,plain,
( ord_less_eq_int(pls,bit0(U_463))
| ~ ord_less_eq_int(pls,U_463) ),
inference(clausify,[status(thm)],[f_174_4]) ).
fof(f_175_1,plain,
! [W_1,Z_1] :
( ( ( ord_less_int(W_1,plus_plus_int(Z_1,one_one_int))
| ( W_1 != Z_1
& ~ ord_less_int(W_1,Z_1) ) )
& ( W_1 = Z_1
| ord_less_int(W_1,Z_1)
| ~ ord_less_int(W_1,plus_plus_int(Z_1,one_one_int)) ) )
| ~ is_int(Z_1)
| ~ is_int(W_1) ),
inference(fof_nnf,[status(thm)],[fact_156_zless__add1__eq]) ).
fof(f_175_2,plain,
! [U_465,U_464] :
( ( ( ord_less_int(U_465,plus_plus_int(U_464,one_one_int))
| ( U_465 != U_464
& ~ ord_less_int(U_465,U_464) ) )
& ( U_465 = U_464
| ord_less_int(U_465,U_464)
| ~ ord_less_int(U_465,plus_plus_int(U_464,one_one_int)) ) )
| ~ is_int(U_464)
| ~ is_int(U_465) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
fof(f_175_3,plain,
( ! [U_464,U_465] :
( U_465 != U_464
| ~ sP10(U_464,U_465) )
& ! [U_464,U_465] :
( ~ ord_less_int(U_465,U_464)
| ~ sP10(U_464,U_465) )
& ! [U_464,U_465] :
( ord_less_int(U_465,plus_plus_int(U_464,one_one_int))
| sP10(U_464,U_465)
| ~ sP11(U_464,U_465) )
& ! [U_464,U_465] :
( U_465 = U_464
| ord_less_int(U_465,U_464)
| ~ ord_less_int(U_465,plus_plus_int(U_464,one_one_int))
| ~ sP11(U_464,U_465) )
& ! [U_464,U_465] :
( sP11(U_464,U_465)
| ~ is_int(U_464)
| ~ is_int(U_465) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10,sP11])],[f_175_2]) ).
cnf(f_175_4,plain,
( sP11(U_464,U_465)
| ~ is_int(U_464)
| ~ is_int(U_465) ),
inference(clausify,[status(thm)],[f_175_3]) ).
cnf(f_175_5,plain,
( U_465 = U_464
| ord_less_int(U_465,U_464)
| ~ ord_less_int(U_465,plus_plus_int(U_464,one_one_int))
| ~ sP11(U_464,U_465) ),
inference(clausify,[status(thm)],[f_175_3]) ).
cnf(f_175_6,plain,
( ord_less_int(U_465,plus_plus_int(U_464,one_one_int))
| sP10(U_464,U_465)
| ~ sP11(U_464,U_465) ),
inference(clausify,[status(thm)],[f_175_3]) ).
cnf(f_175_7,plain,
( ~ ord_less_int(U_465,U_464)
| ~ sP10(U_464,U_465) ),
inference(clausify,[status(thm)],[f_175_3]) ).
cnf(f_175_8,plain,
( U_465 != U_464
| ~ sP10(U_464,U_465) ),
inference(clausify,[status(thm)],[f_175_3]) ).
fof(f_176_1,plain,
! [A_49,N_37] : power_power_nat(A_49,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_37)) = power_power_nat(power_power_nat(A_49,N_37),number_number_of_nat(bit0(bit1(pls)))),
inference(fof_nnf,[status(thm)],[fact_157_power__even__eq]) ).
fof(f_176_2,plain,
! [U_467,U_466] : power_power_nat(U_467,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_466)) = power_power_nat(power_power_nat(U_467,U_466),number_number_of_nat(bit0(bit1(pls)))),
inference(variable_rename,[status(thm)],[f_176_1]) ).
fof(f_176_3,plain,
! [U_467,U_466] : power_power_nat(U_467,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_466)) = power_power_nat(power_power_nat(U_467,U_466),number_number_of_nat(bit0(bit1(pls)))),
inference(definitional_conversion,[status(esa)],[f_176_2]) ).
cnf(f_176_4,plain,
power_power_nat(U_467,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_466)) = power_power_nat(power_power_nat(U_467,U_466),number_number_of_nat(bit0(bit1(pls)))),
inference(clausify,[status(thm)],[f_176_3]) ).
fof(f_177_1,plain,
! [A_49,N_37] : power_power_real(A_49,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_37)) = power_power_real(power_power_real(A_49,N_37),number_number_of_nat(bit0(bit1(pls)))),
inference(fof_nnf,[status(thm)],[fact_158_power__even__eq]) ).
fof(f_177_2,plain,
! [U_469,U_468] : power_power_real(U_469,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_468)) = power_power_real(power_power_real(U_469,U_468),number_number_of_nat(bit0(bit1(pls)))),
inference(variable_rename,[status(thm)],[f_177_1]) ).
fof(f_177_3,plain,
! [U_469,U_468] : power_power_real(U_469,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_468)) = power_power_real(power_power_real(U_469,U_468),number_number_of_nat(bit0(bit1(pls)))),
inference(definitional_conversion,[status(esa)],[f_177_2]) ).
cnf(f_177_4,plain,
power_power_real(U_469,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_468)) = power_power_real(power_power_real(U_469,U_468),number_number_of_nat(bit0(bit1(pls)))),
inference(clausify,[status(thm)],[f_177_3]) ).
fof(f_178_1,plain,
! [A_49,N_37] : power_power_int(A_49,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_37)) = power_power_int(power_power_int(A_49,N_37),number_number_of_nat(bit0(bit1(pls)))),
inference(fof_nnf,[status(thm)],[fact_159_power__even__eq]) ).
fof(f_178_2,plain,
! [U_471,U_470] : power_power_int(U_471,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_470)) = power_power_int(power_power_int(U_471,U_470),number_number_of_nat(bit0(bit1(pls)))),
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
! [U_470,U_471] : power_power_int(U_471,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_470)) = power_power_int(power_power_int(U_471,U_470),number_number_of_nat(bit0(bit1(pls)))),
inference(definitional_conversion,[status(esa)],[f_178_2]) ).
cnf(f_178_4,plain,
power_power_int(U_471,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_470)) = power_power_int(power_power_int(U_471,U_470),number_number_of_nat(bit0(bit1(pls)))),
inference(clausify,[status(thm)],[f_178_3]) ).
fof(f_179_1,plain,
! [X_2] :
( ( ord_less_real(number267125858f_real(X_2),one_one_real)
| ~ ord_less_int(X_2,bit1(pls)) )
& ( ord_less_int(X_2,bit1(pls))
| ~ ord_less_real(number267125858f_real(X_2),one_one_real) ) ),
inference(fof_nnf,[status(thm)],[fact_160_less__special_I4_J]) ).
fof(f_179_2,plain,
! [U_472] :
( ( ord_less_real(number267125858f_real(U_472),one_one_real)
| ~ ord_less_int(U_472,bit1(pls)) )
& ( ord_less_int(U_472,bit1(pls))
| ~ ord_less_real(number267125858f_real(U_472),one_one_real) ) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
fof(f_179_3,plain,
( ! [U_474] :
( ord_less_real(number267125858f_real(U_474),one_one_real)
| ~ ord_less_int(U_474,bit1(pls)) )
& ! [U_473] :
( ord_less_int(U_473,bit1(pls))
| ~ ord_less_real(number267125858f_real(U_473),one_one_real) ) ),
inference(miniscope,[status(thm)],[f_179_2]) ).
fof(f_179_4,plain,
( ! [U_474] :
( ord_less_real(number267125858f_real(U_474),one_one_real)
| ~ ord_less_int(U_474,bit1(pls)) )
& ! [U_473] :
( ord_less_int(U_473,bit1(pls))
| ~ ord_less_real(number267125858f_real(U_473),one_one_real) ) ),
inference(definitional_conversion,[status(esa)],[f_179_3]) ).
cnf(f_179_5,plain,
( ord_less_int(U_473,bit1(pls))
| ~ ord_less_real(number267125858f_real(U_473),one_one_real) ),
inference(clausify,[status(thm)],[f_179_4]) ).
cnf(f_179_6,plain,
( ord_less_real(number267125858f_real(U_474),one_one_real)
| ~ ord_less_int(U_474,bit1(pls)) ),
inference(clausify,[status(thm)],[f_179_4]) ).
fof(f_180_1,plain,
! [X_2] :
( ( ord_less_int(number_number_of_int(X_2),one_one_int)
| ~ ord_less_int(X_2,bit1(pls)) )
& ( ord_less_int(X_2,bit1(pls))
| ~ ord_less_int(number_number_of_int(X_2),one_one_int) ) ),
inference(fof_nnf,[status(thm)],[fact_161_less__special_I4_J]) ).
fof(f_180_2,plain,
! [U_475] :
( ( ord_less_int(number_number_of_int(U_475),one_one_int)
| ~ ord_less_int(U_475,bit1(pls)) )
& ( ord_less_int(U_475,bit1(pls))
| ~ ord_less_int(number_number_of_int(U_475),one_one_int) ) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
fof(f_180_3,plain,
( ! [U_477] :
( ord_less_int(number_number_of_int(U_477),one_one_int)
| ~ ord_less_int(U_477,bit1(pls)) )
& ! [U_476] :
( ord_less_int(U_476,bit1(pls))
| ~ ord_less_int(number_number_of_int(U_476),one_one_int) ) ),
inference(miniscope,[status(thm)],[f_180_2]) ).
fof(f_180_4,plain,
( ! [U_477] :
( ord_less_int(number_number_of_int(U_477),one_one_int)
| ~ ord_less_int(U_477,bit1(pls)) )
& ! [U_476] :
( ord_less_int(U_476,bit1(pls))
| ~ ord_less_int(number_number_of_int(U_476),one_one_int) ) ),
inference(definitional_conversion,[status(esa)],[f_180_3]) ).
cnf(f_180_5,plain,
( ord_less_int(U_476,bit1(pls))
| ~ ord_less_int(number_number_of_int(U_476),one_one_int) ),
inference(clausify,[status(thm)],[f_180_4]) ).
cnf(f_180_6,plain,
( ord_less_int(number_number_of_int(U_477),one_one_int)
| ~ ord_less_int(U_477,bit1(pls)) ),
inference(clausify,[status(thm)],[f_180_4]) ).
fof(f_181_1,plain,
! [Y_2] :
( ( ord_less_real(one_one_real,number267125858f_real(Y_2))
| ~ ord_less_int(bit1(pls),Y_2) )
& ( ord_less_int(bit1(pls),Y_2)
| ~ ord_less_real(one_one_real,number267125858f_real(Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_162_less__special_I2_J]) ).
fof(f_181_2,plain,
! [U_478] :
( ( ord_less_real(one_one_real,number267125858f_real(U_478))
| ~ ord_less_int(bit1(pls),U_478) )
& ( ord_less_int(bit1(pls),U_478)
| ~ ord_less_real(one_one_real,number267125858f_real(U_478)) ) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
( ! [U_480] :
( ord_less_real(one_one_real,number267125858f_real(U_480))
| ~ ord_less_int(bit1(pls),U_480) )
& ! [U_479] :
( ord_less_int(bit1(pls),U_479)
| ~ ord_less_real(one_one_real,number267125858f_real(U_479)) ) ),
inference(miniscope,[status(thm)],[f_181_2]) ).
fof(f_181_4,plain,
( ! [U_480] :
( ord_less_real(one_one_real,number267125858f_real(U_480))
| ~ ord_less_int(bit1(pls),U_480) )
& ! [U_479] :
( ord_less_int(bit1(pls),U_479)
| ~ ord_less_real(one_one_real,number267125858f_real(U_479)) ) ),
inference(definitional_conversion,[status(esa)],[f_181_3]) ).
cnf(f_181_5,plain,
( ord_less_int(bit1(pls),U_479)
| ~ ord_less_real(one_one_real,number267125858f_real(U_479)) ),
inference(clausify,[status(thm)],[f_181_4]) ).
cnf(f_181_6,plain,
( ord_less_real(one_one_real,number267125858f_real(U_480))
| ~ ord_less_int(bit1(pls),U_480) ),
inference(clausify,[status(thm)],[f_181_4]) ).
fof(f_182_1,plain,
! [Y_2] :
( ( ord_less_int(one_one_int,number_number_of_int(Y_2))
| ~ ord_less_int(bit1(pls),Y_2) )
& ( ord_less_int(bit1(pls),Y_2)
| ~ ord_less_int(one_one_int,number_number_of_int(Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_163_less__special_I2_J]) ).
fof(f_182_2,plain,
! [U_481] :
( ( ord_less_int(one_one_int,number_number_of_int(U_481))
| ~ ord_less_int(bit1(pls),U_481) )
& ( ord_less_int(bit1(pls),U_481)
| ~ ord_less_int(one_one_int,number_number_of_int(U_481)) ) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
fof(f_182_3,plain,
( ! [U_483] :
( ord_less_int(one_one_int,number_number_of_int(U_483))
| ~ ord_less_int(bit1(pls),U_483) )
& ! [U_482] :
( ord_less_int(bit1(pls),U_482)
| ~ ord_less_int(one_one_int,number_number_of_int(U_482)) ) ),
inference(miniscope,[status(thm)],[f_182_2]) ).
fof(f_182_4,plain,
( ! [U_483] :
( ord_less_int(one_one_int,number_number_of_int(U_483))
| ~ ord_less_int(bit1(pls),U_483) )
& ! [U_482] :
( ord_less_int(bit1(pls),U_482)
| ~ ord_less_int(one_one_int,number_number_of_int(U_482)) ) ),
inference(definitional_conversion,[status(esa)],[f_182_3]) ).
cnf(f_182_5,plain,
( ord_less_int(bit1(pls),U_482)
| ~ ord_less_int(one_one_int,number_number_of_int(U_482)) ),
inference(clausify,[status(thm)],[f_182_4]) ).
cnf(f_182_6,plain,
( ord_less_int(one_one_int,number_number_of_int(U_483))
| ~ ord_less_int(bit1(pls),U_483) ),
inference(clausify,[status(thm)],[f_182_4]) ).
fof(f_183_1,plain,
! [X_2] :
( ( ord_less_eq_real(number267125858f_real(X_2),one_one_real)
| ~ ord_less_eq_int(X_2,bit1(pls)) )
& ( ord_less_eq_int(X_2,bit1(pls))
| ~ ord_less_eq_real(number267125858f_real(X_2),one_one_real) ) ),
inference(fof_nnf,[status(thm)],[fact_164_le__special_I4_J]) ).
fof(f_183_2,plain,
! [U_484] :
( ( ord_less_eq_real(number267125858f_real(U_484),one_one_real)
| ~ ord_less_eq_int(U_484,bit1(pls)) )
& ( ord_less_eq_int(U_484,bit1(pls))
| ~ ord_less_eq_real(number267125858f_real(U_484),one_one_real) ) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
( ! [U_486] :
( ord_less_eq_real(number267125858f_real(U_486),one_one_real)
| ~ ord_less_eq_int(U_486,bit1(pls)) )
& ! [U_485] :
( ord_less_eq_int(U_485,bit1(pls))
| ~ ord_less_eq_real(number267125858f_real(U_485),one_one_real) ) ),
inference(miniscope,[status(thm)],[f_183_2]) ).
fof(f_183_4,plain,
( ! [U_486] :
( ord_less_eq_real(number267125858f_real(U_486),one_one_real)
| ~ ord_less_eq_int(U_486,bit1(pls)) )
& ! [U_485] :
( ord_less_eq_int(U_485,bit1(pls))
| ~ ord_less_eq_real(number267125858f_real(U_485),one_one_real) ) ),
inference(definitional_conversion,[status(esa)],[f_183_3]) ).
cnf(f_183_5,plain,
( ord_less_eq_int(U_485,bit1(pls))
| ~ ord_less_eq_real(number267125858f_real(U_485),one_one_real) ),
inference(clausify,[status(thm)],[f_183_4]) ).
cnf(f_183_6,plain,
( ord_less_eq_real(number267125858f_real(U_486),one_one_real)
| ~ ord_less_eq_int(U_486,bit1(pls)) ),
inference(clausify,[status(thm)],[f_183_4]) ).
fof(f_184_1,plain,
! [X_2] :
( ( ord_less_eq_int(number_number_of_int(X_2),one_one_int)
| ~ ord_less_eq_int(X_2,bit1(pls)) )
& ( ord_less_eq_int(X_2,bit1(pls))
| ~ ord_less_eq_int(number_number_of_int(X_2),one_one_int) ) ),
inference(fof_nnf,[status(thm)],[fact_165_le__special_I4_J]) ).
fof(f_184_2,plain,
! [U_487] :
( ( ord_less_eq_int(number_number_of_int(U_487),one_one_int)
| ~ ord_less_eq_int(U_487,bit1(pls)) )
& ( ord_less_eq_int(U_487,bit1(pls))
| ~ ord_less_eq_int(number_number_of_int(U_487),one_one_int) ) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
fof(f_184_3,plain,
( ! [U_489] :
( ord_less_eq_int(number_number_of_int(U_489),one_one_int)
| ~ ord_less_eq_int(U_489,bit1(pls)) )
& ! [U_488] :
( ord_less_eq_int(U_488,bit1(pls))
| ~ ord_less_eq_int(number_number_of_int(U_488),one_one_int) ) ),
inference(miniscope,[status(thm)],[f_184_2]) ).
fof(f_184_4,plain,
( ! [U_489] :
( ord_less_eq_int(number_number_of_int(U_489),one_one_int)
| ~ ord_less_eq_int(U_489,bit1(pls)) )
& ! [U_488] :
( ord_less_eq_int(U_488,bit1(pls))
| ~ ord_less_eq_int(number_number_of_int(U_488),one_one_int) ) ),
inference(definitional_conversion,[status(esa)],[f_184_3]) ).
cnf(f_184_5,plain,
( ord_less_eq_int(U_488,bit1(pls))
| ~ ord_less_eq_int(number_number_of_int(U_488),one_one_int) ),
inference(clausify,[status(thm)],[f_184_4]) ).
cnf(f_184_6,plain,
( ord_less_eq_int(number_number_of_int(U_489),one_one_int)
| ~ ord_less_eq_int(U_489,bit1(pls)) ),
inference(clausify,[status(thm)],[f_184_4]) ).
fof(f_185_1,plain,
! [Y_2] :
( ( ord_less_eq_real(one_one_real,number267125858f_real(Y_2))
| ~ ord_less_eq_int(bit1(pls),Y_2) )
& ( ord_less_eq_int(bit1(pls),Y_2)
| ~ ord_less_eq_real(one_one_real,number267125858f_real(Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_166_le__special_I2_J]) ).
fof(f_185_2,plain,
! [U_490] :
( ( ord_less_eq_real(one_one_real,number267125858f_real(U_490))
| ~ ord_less_eq_int(bit1(pls),U_490) )
& ( ord_less_eq_int(bit1(pls),U_490)
| ~ ord_less_eq_real(one_one_real,number267125858f_real(U_490)) ) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
fof(f_185_3,plain,
( ! [U_492] :
( ord_less_eq_real(one_one_real,number267125858f_real(U_492))
| ~ ord_less_eq_int(bit1(pls),U_492) )
& ! [U_491] :
( ord_less_eq_int(bit1(pls),U_491)
| ~ ord_less_eq_real(one_one_real,number267125858f_real(U_491)) ) ),
inference(miniscope,[status(thm)],[f_185_2]) ).
fof(f_185_4,plain,
( ! [U_492] :
( ord_less_eq_real(one_one_real,number267125858f_real(U_492))
| ~ ord_less_eq_int(bit1(pls),U_492) )
& ! [U_491] :
( ord_less_eq_int(bit1(pls),U_491)
| ~ ord_less_eq_real(one_one_real,number267125858f_real(U_491)) ) ),
inference(definitional_conversion,[status(esa)],[f_185_3]) ).
cnf(f_185_5,plain,
( ord_less_eq_int(bit1(pls),U_491)
| ~ ord_less_eq_real(one_one_real,number267125858f_real(U_491)) ),
inference(clausify,[status(thm)],[f_185_4]) ).
cnf(f_185_6,plain,
( ord_less_eq_real(one_one_real,number267125858f_real(U_492))
| ~ ord_less_eq_int(bit1(pls),U_492) ),
inference(clausify,[status(thm)],[f_185_4]) ).
fof(f_186_1,plain,
! [Y_2] :
( ( ord_less_eq_int(one_one_int,number_number_of_int(Y_2))
| ~ ord_less_eq_int(bit1(pls),Y_2) )
& ( ord_less_eq_int(bit1(pls),Y_2)
| ~ ord_less_eq_int(one_one_int,number_number_of_int(Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_167_le__special_I2_J]) ).
fof(f_186_2,plain,
! [U_493] :
( ( ord_less_eq_int(one_one_int,number_number_of_int(U_493))
| ~ ord_less_eq_int(bit1(pls),U_493) )
& ( ord_less_eq_int(bit1(pls),U_493)
| ~ ord_less_eq_int(one_one_int,number_number_of_int(U_493)) ) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
fof(f_186_3,plain,
( ! [U_495] :
( ord_less_eq_int(one_one_int,number_number_of_int(U_495))
| ~ ord_less_eq_int(bit1(pls),U_495) )
& ! [U_494] :
( ord_less_eq_int(bit1(pls),U_494)
| ~ ord_less_eq_int(one_one_int,number_number_of_int(U_494)) ) ),
inference(miniscope,[status(thm)],[f_186_2]) ).
fof(f_186_4,plain,
( ! [U_495] :
( ord_less_eq_int(one_one_int,number_number_of_int(U_495))
| ~ ord_less_eq_int(bit1(pls),U_495) )
& ! [U_494] :
( ord_less_eq_int(bit1(pls),U_494)
| ~ ord_less_eq_int(one_one_int,number_number_of_int(U_494)) ) ),
inference(definitional_conversion,[status(esa)],[f_186_3]) ).
cnf(f_186_5,plain,
( ord_less_eq_int(bit1(pls),U_494)
| ~ ord_less_eq_int(one_one_int,number_number_of_int(U_494)) ),
inference(clausify,[status(thm)],[f_186_4]) ).
cnf(f_186_6,plain,
( ord_less_eq_int(one_one_int,number_number_of_int(U_495))
| ~ ord_less_eq_int(bit1(pls),U_495) ),
inference(clausify,[status(thm)],[f_186_4]) ).
fof(f_187_1,plain,
! [W_1,Y_2,X_2,Z_1] :
( ( plus_plus_real(times_times_real(W_1,Y_2),times_times_real(X_2,Z_1)) = plus_plus_real(times_times_real(W_1,Z_1),times_times_real(X_2,Y_2))
| ( Y_2 != Z_1
& W_1 != X_2 ) )
& ( Y_2 = Z_1
| W_1 = X_2
| plus_plus_real(times_times_real(W_1,Y_2),times_times_real(X_2,Z_1)) != plus_plus_real(times_times_real(W_1,Z_1),times_times_real(X_2,Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_168_crossproduct__eq]) ).
fof(f_187_2,plain,
! [U_499,U_498,U_497,U_496] :
( ( plus_plus_real(times_times_real(U_499,U_498),times_times_real(U_497,U_496)) = plus_plus_real(times_times_real(U_499,U_496),times_times_real(U_497,U_498))
| ( U_498 != U_496
& U_499 != U_497 ) )
& ( U_498 = U_496
| U_499 = U_497
| plus_plus_real(times_times_real(U_499,U_498),times_times_real(U_497,U_496)) != plus_plus_real(times_times_real(U_499,U_496),times_times_real(U_497,U_498)) ) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
fof(f_187_3,plain,
( ! [U_507,U_505,U_503,U_501] :
( plus_plus_real(times_times_real(U_507,U_505),times_times_real(U_503,U_501)) = plus_plus_real(times_times_real(U_507,U_501),times_times_real(U_503,U_505))
| ( U_505 != U_501
& U_507 != U_503 ) )
& ! [U_506,U_504,U_502,U_500] :
( U_504 = U_500
| U_506 = U_502
| plus_plus_real(times_times_real(U_506,U_504),times_times_real(U_502,U_500)) != plus_plus_real(times_times_real(U_506,U_500),times_times_real(U_502,U_504)) ) ),
inference(miniscope,[status(thm)],[f_187_2]) ).
fof(f_187_4,plain,
( ! [U_503,U_501,U_507,U_505] :
( U_505 != U_501
| ~ sP12(U_503,U_501,U_507,U_505) )
& ! [U_503,U_501,U_507,U_505] :
( U_507 != U_503
| ~ sP12(U_503,U_501,U_507,U_505) )
& ! [U_503,U_501,U_507,U_505] :
( plus_plus_real(times_times_real(U_507,U_505),times_times_real(U_503,U_501)) = plus_plus_real(times_times_real(U_507,U_501),times_times_real(U_503,U_505))
| sP12(U_503,U_501,U_507,U_505) )
& ! [U_506,U_502,U_500,U_504] :
( U_504 = U_500
| U_506 = U_502
| plus_plus_real(times_times_real(U_506,U_504),times_times_real(U_502,U_500)) != plus_plus_real(times_times_real(U_506,U_500),times_times_real(U_502,U_504)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_187_3]) ).
cnf(f_187_5,plain,
( U_504 = U_500
| U_506 = U_502
| plus_plus_real(times_times_real(U_506,U_504),times_times_real(U_502,U_500)) != plus_plus_real(times_times_real(U_506,U_500),times_times_real(U_502,U_504)) ),
inference(clausify,[status(thm)],[f_187_4]) ).
cnf(f_187_6,plain,
( plus_plus_real(times_times_real(U_507,U_505),times_times_real(U_503,U_501)) = plus_plus_real(times_times_real(U_507,U_501),times_times_real(U_503,U_505))
| sP12(U_503,U_501,U_507,U_505) ),
inference(clausify,[status(thm)],[f_187_4]) ).
cnf(f_187_7,plain,
( U_507 != U_503
| ~ sP12(U_503,U_501,U_507,U_505) ),
inference(clausify,[status(thm)],[f_187_4]) ).
cnf(f_187_8,plain,
( U_505 != U_501
| ~ sP12(U_503,U_501,U_507,U_505) ),
inference(clausify,[status(thm)],[f_187_4]) ).
fof(f_188_1,plain,
! [W_1,Y_2,X_2,Z_1] :
( ( plus_plus_nat(times_times_nat(W_1,Y_2),times_times_nat(X_2,Z_1)) = plus_plus_nat(times_times_nat(W_1,Z_1),times_times_nat(X_2,Y_2))
| ( Y_2 != Z_1
& W_1 != X_2 ) )
& ( Y_2 = Z_1
| W_1 = X_2
| plus_plus_nat(times_times_nat(W_1,Y_2),times_times_nat(X_2,Z_1)) != plus_plus_nat(times_times_nat(W_1,Z_1),times_times_nat(X_2,Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_169_crossproduct__eq]) ).
fof(f_188_2,plain,
! [U_511,U_510,U_509,U_508] :
( ( plus_plus_nat(times_times_nat(U_511,U_510),times_times_nat(U_509,U_508)) = plus_plus_nat(times_times_nat(U_511,U_508),times_times_nat(U_509,U_510))
| ( U_510 != U_508
& U_511 != U_509 ) )
& ( U_510 = U_508
| U_511 = U_509
| plus_plus_nat(times_times_nat(U_511,U_510),times_times_nat(U_509,U_508)) != plus_plus_nat(times_times_nat(U_511,U_508),times_times_nat(U_509,U_510)) ) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
fof(f_188_3,plain,
( ! [U_519,U_517,U_515,U_513] :
( plus_plus_nat(times_times_nat(U_519,U_517),times_times_nat(U_515,U_513)) = plus_plus_nat(times_times_nat(U_519,U_513),times_times_nat(U_515,U_517))
| ( U_517 != U_513
& U_519 != U_515 ) )
& ! [U_518,U_516,U_514,U_512] :
( U_516 = U_512
| U_518 = U_514
| plus_plus_nat(times_times_nat(U_518,U_516),times_times_nat(U_514,U_512)) != plus_plus_nat(times_times_nat(U_518,U_512),times_times_nat(U_514,U_516)) ) ),
inference(miniscope,[status(thm)],[f_188_2]) ).
fof(f_188_4,plain,
( ! [U_515,U_513,U_519,U_517] :
( U_517 != U_513
| ~ sP13(U_515,U_513,U_519,U_517) )
& ! [U_515,U_513,U_519,U_517] :
( U_519 != U_515
| ~ sP13(U_515,U_513,U_519,U_517) )
& ! [U_515,U_513,U_519,U_517] :
( plus_plus_nat(times_times_nat(U_519,U_517),times_times_nat(U_515,U_513)) = plus_plus_nat(times_times_nat(U_519,U_513),times_times_nat(U_515,U_517))
| sP13(U_515,U_513,U_519,U_517) )
& ! [U_514,U_518,U_512,U_516] :
( U_516 = U_512
| U_518 = U_514
| plus_plus_nat(times_times_nat(U_518,U_516),times_times_nat(U_514,U_512)) != plus_plus_nat(times_times_nat(U_518,U_512),times_times_nat(U_514,U_516)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13])],[f_188_3]) ).
cnf(f_188_5,plain,
( U_516 = U_512
| U_518 = U_514
| plus_plus_nat(times_times_nat(U_518,U_516),times_times_nat(U_514,U_512)) != plus_plus_nat(times_times_nat(U_518,U_512),times_times_nat(U_514,U_516)) ),
inference(clausify,[status(thm)],[f_188_4]) ).
cnf(f_188_6,plain,
( plus_plus_nat(times_times_nat(U_519,U_517),times_times_nat(U_515,U_513)) = plus_plus_nat(times_times_nat(U_519,U_513),times_times_nat(U_515,U_517))
| sP13(U_515,U_513,U_519,U_517) ),
inference(clausify,[status(thm)],[f_188_4]) ).
cnf(f_188_7,plain,
( U_519 != U_515
| ~ sP13(U_515,U_513,U_519,U_517) ),
inference(clausify,[status(thm)],[f_188_4]) ).
cnf(f_188_8,plain,
( U_517 != U_513
| ~ sP13(U_515,U_513,U_519,U_517) ),
inference(clausify,[status(thm)],[f_188_4]) ).
fof(f_189_1,plain,
! [W_1,Y_2,X_2,Z_1] :
( ( ( plus_plus_int(times_times_int(W_1,Y_2),times_times_int(X_2,Z_1)) = plus_plus_int(times_times_int(W_1,Z_1),times_times_int(X_2,Y_2))
| ( Y_2 != Z_1
& W_1 != X_2 ) )
& ( Y_2 = Z_1
| W_1 = X_2
| plus_plus_int(times_times_int(W_1,Y_2),times_times_int(X_2,Z_1)) != plus_plus_int(times_times_int(W_1,Z_1),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_189_2,plain,
! [U_523,U_522,U_521,U_520] :
( ( ( plus_plus_int(times_times_int(U_523,U_522),times_times_int(U_521,U_520)) = plus_plus_int(times_times_int(U_523,U_520),times_times_int(U_521,U_522))
| ( U_522 != U_520
& U_523 != U_521 ) )
& ( U_522 = U_520
| U_523 = U_521
| plus_plus_int(times_times_int(U_523,U_522),times_times_int(U_521,U_520)) != plus_plus_int(times_times_int(U_523,U_520),times_times_int(U_521,U_522)) ) )
| ~ is_int(U_520)
| ~ is_int(U_521)
| ~ is_int(U_522)
| ~ is_int(U_523) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
fof(f_189_3,plain,
( ! [U_520,U_521,U_522,U_523] :
( U_522 != U_520
| ~ sP14(U_520,U_521,U_522,U_523) )
& ! [U_520,U_521,U_522,U_523] :
( U_523 != U_521
| ~ sP14(U_520,U_521,U_522,U_523) )
& ! [U_520,U_521,U_522,U_523] :
( plus_plus_int(times_times_int(U_523,U_522),times_times_int(U_521,U_520)) = plus_plus_int(times_times_int(U_523,U_520),times_times_int(U_521,U_522))
| sP14(U_520,U_521,U_522,U_523)
| ~ sP15(U_520,U_521,U_522,U_523) )
& ! [U_520,U_521,U_522,U_523] :
( U_522 = U_520
| U_523 = U_521
| plus_plus_int(times_times_int(U_523,U_522),times_times_int(U_521,U_520)) != plus_plus_int(times_times_int(U_523,U_520),times_times_int(U_521,U_522))
| ~ sP15(U_520,U_521,U_522,U_523) )
& ! [U_520,U_521,U_522,U_523] :
( sP15(U_520,U_521,U_522,U_523)
| ~ is_int(U_520)
| ~ is_int(U_521)
| ~ is_int(U_522)
| ~ is_int(U_523) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14,sP15])],[f_189_2]) ).
cnf(f_189_4,plain,
( sP15(U_520,U_521,U_522,U_523)
| ~ is_int(U_520)
| ~ is_int(U_521)
| ~ is_int(U_522)
| ~ is_int(U_523) ),
inference(clausify,[status(thm)],[f_189_3]) ).
cnf(f_189_5,plain,
( U_522 = U_520
| U_523 = U_521
| plus_plus_int(times_times_int(U_523,U_522),times_times_int(U_521,U_520)) != plus_plus_int(times_times_int(U_523,U_520),times_times_int(U_521,U_522))
| ~ sP15(U_520,U_521,U_522,U_523) ),
inference(clausify,[status(thm)],[f_189_3]) ).
cnf(f_189_6,plain,
( plus_plus_int(times_times_int(U_523,U_522),times_times_int(U_521,U_520)) = plus_plus_int(times_times_int(U_523,U_520),times_times_int(U_521,U_522))
| sP14(U_520,U_521,U_522,U_523)
| ~ sP15(U_520,U_521,U_522,U_523) ),
inference(clausify,[status(thm)],[f_189_3]) ).
cnf(f_189_7,plain,
( U_523 != U_521
| ~ sP14(U_520,U_521,U_522,U_523) ),
inference(clausify,[status(thm)],[f_189_3]) ).
cnf(f_189_8,plain,
( U_522 != U_520
| ~ sP14(U_520,U_521,U_522,U_523) ),
inference(clausify,[status(thm)],[f_189_3]) ).
fof(f_190_1,plain,
! [A_48,M_12,B_13] : plus_plus_real(times_times_real(A_48,M_12),times_times_real(B_13,M_12)) = times_times_real(plus_plus_real(A_48,B_13),M_12),
inference(fof_nnf,[status(thm)],[fact_171_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J]) ).
fof(f_190_2,plain,
! [U_526,U_525,U_524] : plus_plus_real(times_times_real(U_526,U_525),times_times_real(U_524,U_525)) = times_times_real(plus_plus_real(U_526,U_524),U_525),
inference(variable_rename,[status(thm)],[f_190_1]) ).
fof(f_190_3,plain,
! [U_526,U_524,U_525] : plus_plus_real(times_times_real(U_526,U_525),times_times_real(U_524,U_525)) = times_times_real(plus_plus_real(U_526,U_524),U_525),
inference(definitional_conversion,[status(esa)],[f_190_2]) ).
cnf(f_190_4,plain,
plus_plus_real(times_times_real(U_526,U_525),times_times_real(U_524,U_525)) = times_times_real(plus_plus_real(U_526,U_524),U_525),
inference(clausify,[status(thm)],[f_190_3]) ).
fof(f_191_1,plain,
! [A_48,M_12,B_13] : plus_plus_nat(times_times_nat(A_48,M_12),times_times_nat(B_13,M_12)) = times_times_nat(plus_plus_nat(A_48,B_13),M_12),
inference(fof_nnf,[status(thm)],[fact_172_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J]) ).
fof(f_191_2,plain,
! [U_529,U_528,U_527] : plus_plus_nat(times_times_nat(U_529,U_528),times_times_nat(U_527,U_528)) = times_times_nat(plus_plus_nat(U_529,U_527),U_528),
inference(variable_rename,[status(thm)],[f_191_1]) ).
fof(f_191_3,plain,
! [U_527,U_528,U_529] : plus_plus_nat(times_times_nat(U_529,U_528),times_times_nat(U_527,U_528)) = times_times_nat(plus_plus_nat(U_529,U_527),U_528),
inference(definitional_conversion,[status(esa)],[f_191_2]) ).
cnf(f_191_4,plain,
plus_plus_nat(times_times_nat(U_529,U_528),times_times_nat(U_527,U_528)) = times_times_nat(plus_plus_nat(U_529,U_527),U_528),
inference(clausify,[status(thm)],[f_191_3]) ).
fof(f_192_1,plain,
! [A_48,M_12,B_13] : plus_plus_int(times_times_int(A_48,M_12),times_times_int(B_13,M_12)) = times_times_int(plus_plus_int(A_48,B_13),M_12),
inference(fof_nnf,[status(thm)],[fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J]) ).
fof(f_192_2,plain,
! [U_532,U_531,U_530] : plus_plus_int(times_times_int(U_532,U_531),times_times_int(U_530,U_531)) = times_times_int(plus_plus_int(U_532,U_530),U_531),
inference(variable_rename,[status(thm)],[f_192_1]) ).
fof(f_192_3,plain,
! [U_530,U_531,U_532] : plus_plus_int(times_times_int(U_532,U_531),times_times_int(U_530,U_531)) = times_times_int(plus_plus_int(U_532,U_530),U_531),
inference(definitional_conversion,[status(esa)],[f_192_2]) ).
cnf(f_192_4,plain,
plus_plus_int(times_times_int(U_532,U_531),times_times_int(U_530,U_531)) = times_times_int(plus_plus_int(U_532,U_530),U_531),
inference(clausify,[status(thm)],[f_192_3]) ).
fof(f_193_1,plain,
! [A_47,B_12,C_4] : times_times_real(plus_plus_real(A_47,B_12),C_4) = plus_plus_real(times_times_real(A_47,C_4),times_times_real(B_12,C_4)),
inference(fof_nnf,[status(thm)],[fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J]) ).
fof(f_193_2,plain,
! [U_535,U_534,U_533] : times_times_real(plus_plus_real(U_535,U_534),U_533) = plus_plus_real(times_times_real(U_535,U_533),times_times_real(U_534,U_533)),
inference(variable_rename,[status(thm)],[f_193_1]) ).
fof(f_193_3,plain,
! [U_533,U_534,U_535] : times_times_real(plus_plus_real(U_535,U_534),U_533) = plus_plus_real(times_times_real(U_535,U_533),times_times_real(U_534,U_533)),
inference(definitional_conversion,[status(esa)],[f_193_2]) ).
cnf(f_193_4,plain,
times_times_real(plus_plus_real(U_535,U_534),U_533) = plus_plus_real(times_times_real(U_535,U_533),times_times_real(U_534,U_533)),
inference(clausify,[status(thm)],[f_193_3]) ).
fof(f_194_1,plain,
! [A_47,B_12,C_4] : times_times_nat(plus_plus_nat(A_47,B_12),C_4) = plus_plus_nat(times_times_nat(A_47,C_4),times_times_nat(B_12,C_4)),
inference(fof_nnf,[status(thm)],[fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J]) ).
fof(f_194_2,plain,
! [U_538,U_537,U_536] : times_times_nat(plus_plus_nat(U_538,U_537),U_536) = plus_plus_nat(times_times_nat(U_538,U_536),times_times_nat(U_537,U_536)),
inference(variable_rename,[status(thm)],[f_194_1]) ).
fof(f_194_3,plain,
! [U_536,U_537,U_538] : times_times_nat(plus_plus_nat(U_538,U_537),U_536) = plus_plus_nat(times_times_nat(U_538,U_536),times_times_nat(U_537,U_536)),
inference(definitional_conversion,[status(esa)],[f_194_2]) ).
cnf(f_194_4,plain,
times_times_nat(plus_plus_nat(U_538,U_537),U_536) = plus_plus_nat(times_times_nat(U_538,U_536),times_times_nat(U_537,U_536)),
inference(clausify,[status(thm)],[f_194_3]) ).
fof(f_195_1,plain,
! [A_47,B_12,C_4] : times_times_int(plus_plus_int(A_47,B_12),C_4) = plus_plus_int(times_times_int(A_47,C_4),times_times_int(B_12,C_4)),
inference(fof_nnf,[status(thm)],[fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J]) ).
fof(f_195_2,plain,
! [U_541,U_540,U_539] : times_times_int(plus_plus_int(U_541,U_540),U_539) = plus_plus_int(times_times_int(U_541,U_539),times_times_int(U_540,U_539)),
inference(variable_rename,[status(thm)],[f_195_1]) ).
fof(f_195_3,plain,
! [U_539,U_540,U_541] : times_times_int(plus_plus_int(U_541,U_540),U_539) = plus_plus_int(times_times_int(U_541,U_539),times_times_int(U_540,U_539)),
inference(definitional_conversion,[status(esa)],[f_195_2]) ).
cnf(f_195_4,plain,
times_times_int(plus_plus_int(U_541,U_540),U_539) = plus_plus_int(times_times_int(U_541,U_539),times_times_int(U_540,U_539)),
inference(clausify,[status(thm)],[f_195_3]) ).
fof(f_196_1,plain,
! [C,D,A_1,B_2] :
( ( ( C != D
& A_1 != B_2 )
| plus_plus_real(times_times_real(A_1,C),times_times_real(B_2,D)) = plus_plus_real(times_times_real(A_1,D),times_times_real(B_2,C)) )
& ( plus_plus_real(times_times_real(A_1,C),times_times_real(B_2,D)) != plus_plus_real(times_times_real(A_1,D),times_times_real(B_2,C))
| C = D
| A_1 = B_2 ) ),
inference(fof_nnf,[status(thm)],[fact_177_crossproduct__noteq]) ).
fof(f_196_2,plain,
! [U_545,U_544,U_543,U_542] :
( ( ( U_545 != U_544
& U_543 != U_542 )
| plus_plus_real(times_times_real(U_543,U_545),times_times_real(U_542,U_544)) = plus_plus_real(times_times_real(U_543,U_544),times_times_real(U_542,U_545)) )
& ( plus_plus_real(times_times_real(U_543,U_545),times_times_real(U_542,U_544)) != plus_plus_real(times_times_real(U_543,U_544),times_times_real(U_542,U_545))
| U_545 = U_544
| U_543 = U_542 ) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
fof(f_196_3,plain,
( ! [U_553,U_551,U_549,U_547] :
( ( U_553 != U_551
& U_549 != U_547 )
| plus_plus_real(times_times_real(U_549,U_553),times_times_real(U_547,U_551)) = plus_plus_real(times_times_real(U_549,U_551),times_times_real(U_547,U_553)) )
& ! [U_552,U_550,U_548,U_546] :
( plus_plus_real(times_times_real(U_548,U_552),times_times_real(U_546,U_550)) != plus_plus_real(times_times_real(U_548,U_550),times_times_real(U_546,U_552))
| U_552 = U_550
| U_548 = U_546 ) ),
inference(miniscope,[status(thm)],[f_196_2]) ).
fof(f_196_4,plain,
( ! [U_549,U_547,U_553,U_551] :
( U_553 != U_551
| ~ sP16(U_549,U_547,U_553,U_551) )
& ! [U_549,U_547,U_553,U_551] :
( U_549 != U_547
| ~ sP16(U_549,U_547,U_553,U_551) )
& ! [U_549,U_547,U_553,U_551] :
( sP16(U_549,U_547,U_553,U_551)
| plus_plus_real(times_times_real(U_549,U_553),times_times_real(U_547,U_551)) = plus_plus_real(times_times_real(U_549,U_551),times_times_real(U_547,U_553)) )
& ! [U_548,U_552,U_546,U_550] :
( plus_plus_real(times_times_real(U_548,U_552),times_times_real(U_546,U_550)) != plus_plus_real(times_times_real(U_548,U_550),times_times_real(U_546,U_552))
| U_552 = U_550
| U_548 = U_546 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_196_3]) ).
cnf(f_196_5,plain,
( plus_plus_real(times_times_real(U_548,U_552),times_times_real(U_546,U_550)) != plus_plus_real(times_times_real(U_548,U_550),times_times_real(U_546,U_552))
| U_552 = U_550
| U_548 = U_546 ),
inference(clausify,[status(thm)],[f_196_4]) ).
cnf(f_196_6,plain,
( sP16(U_549,U_547,U_553,U_551)
| plus_plus_real(times_times_real(U_549,U_553),times_times_real(U_547,U_551)) = plus_plus_real(times_times_real(U_549,U_551),times_times_real(U_547,U_553)) ),
inference(clausify,[status(thm)],[f_196_4]) ).
cnf(f_196_7,plain,
( U_549 != U_547
| ~ sP16(U_549,U_547,U_553,U_551) ),
inference(clausify,[status(thm)],[f_196_4]) ).
cnf(f_196_8,plain,
( U_553 != U_551
| ~ sP16(U_549,U_547,U_553,U_551) ),
inference(clausify,[status(thm)],[f_196_4]) ).
fof(f_197_1,plain,
! [C,D,A_1,B_2] :
( ( ( C != D
& A_1 != B_2 )
| plus_plus_nat(times_times_nat(A_1,C),times_times_nat(B_2,D)) = plus_plus_nat(times_times_nat(A_1,D),times_times_nat(B_2,C)) )
& ( plus_plus_nat(times_times_nat(A_1,C),times_times_nat(B_2,D)) != plus_plus_nat(times_times_nat(A_1,D),times_times_nat(B_2,C))
| C = D
| A_1 = B_2 ) ),
inference(fof_nnf,[status(thm)],[fact_178_crossproduct__noteq]) ).
fof(f_197_2,plain,
! [U_557,U_556,U_555,U_554] :
( ( ( U_557 != U_556
& U_555 != U_554 )
| plus_plus_nat(times_times_nat(U_555,U_557),times_times_nat(U_554,U_556)) = plus_plus_nat(times_times_nat(U_555,U_556),times_times_nat(U_554,U_557)) )
& ( plus_plus_nat(times_times_nat(U_555,U_557),times_times_nat(U_554,U_556)) != plus_plus_nat(times_times_nat(U_555,U_556),times_times_nat(U_554,U_557))
| U_557 = U_556
| U_555 = U_554 ) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
fof(f_197_3,plain,
( ! [U_565,U_563,U_561,U_559] :
( ( U_565 != U_563
& U_561 != U_559 )
| plus_plus_nat(times_times_nat(U_561,U_565),times_times_nat(U_559,U_563)) = plus_plus_nat(times_times_nat(U_561,U_563),times_times_nat(U_559,U_565)) )
& ! [U_564,U_562,U_560,U_558] :
( plus_plus_nat(times_times_nat(U_560,U_564),times_times_nat(U_558,U_562)) != plus_plus_nat(times_times_nat(U_560,U_562),times_times_nat(U_558,U_564))
| U_564 = U_562
| U_560 = U_558 ) ),
inference(miniscope,[status(thm)],[f_197_2]) ).
fof(f_197_4,plain,
( ! [U_561,U_559,U_565,U_563] :
( U_565 != U_563
| ~ sP17(U_561,U_559,U_565,U_563) )
& ! [U_561,U_559,U_565,U_563] :
( U_561 != U_559
| ~ sP17(U_561,U_559,U_565,U_563) )
& ! [U_561,U_559,U_565,U_563] :
( sP17(U_561,U_559,U_565,U_563)
| plus_plus_nat(times_times_nat(U_561,U_565),times_times_nat(U_559,U_563)) = plus_plus_nat(times_times_nat(U_561,U_563),times_times_nat(U_559,U_565)) )
& ! [U_560,U_564,U_558,U_562] :
( plus_plus_nat(times_times_nat(U_560,U_564),times_times_nat(U_558,U_562)) != plus_plus_nat(times_times_nat(U_560,U_562),times_times_nat(U_558,U_564))
| U_564 = U_562
| U_560 = U_558 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_197_3]) ).
cnf(f_197_5,plain,
( plus_plus_nat(times_times_nat(U_560,U_564),times_times_nat(U_558,U_562)) != plus_plus_nat(times_times_nat(U_560,U_562),times_times_nat(U_558,U_564))
| U_564 = U_562
| U_560 = U_558 ),
inference(clausify,[status(thm)],[f_197_4]) ).
cnf(f_197_6,plain,
( sP17(U_561,U_559,U_565,U_563)
| plus_plus_nat(times_times_nat(U_561,U_565),times_times_nat(U_559,U_563)) = plus_plus_nat(times_times_nat(U_561,U_563),times_times_nat(U_559,U_565)) ),
inference(clausify,[status(thm)],[f_197_4]) ).
cnf(f_197_7,plain,
( U_561 != U_559
| ~ sP17(U_561,U_559,U_565,U_563) ),
inference(clausify,[status(thm)],[f_197_4]) ).
cnf(f_197_8,plain,
( U_565 != U_563
| ~ sP17(U_561,U_559,U_565,U_563) ),
inference(clausify,[status(thm)],[f_197_4]) ).
fof(f_198_1,plain,
! [C,D,A_1,B_2] :
( ( ( ( C != D
& A_1 != B_2 )
| plus_plus_int(times_times_int(A_1,C),times_times_int(B_2,D)) = plus_plus_int(times_times_int(A_1,D),times_times_int(B_2,C)) )
& ( plus_plus_int(times_times_int(A_1,C),times_times_int(B_2,D)) != plus_plus_int(times_times_int(A_1,D),times_times_int(B_2,C))
| C = D
| A_1 = B_2 ) )
| ~ is_int(B_2)
| ~ is_int(A_1)
| ~ is_int(D)
| ~ is_int(C) ),
inference(fof_nnf,[status(thm)],[fact_179_crossproduct__noteq]) ).
fof(f_198_2,plain,
! [U_569,U_568,U_567,U_566] :
( ( ( ( U_569 != U_568
& U_567 != U_566 )
| plus_plus_int(times_times_int(U_567,U_569),times_times_int(U_566,U_568)) = plus_plus_int(times_times_int(U_567,U_568),times_times_int(U_566,U_569)) )
& ( plus_plus_int(times_times_int(U_567,U_569),times_times_int(U_566,U_568)) != plus_plus_int(times_times_int(U_567,U_568),times_times_int(U_566,U_569))
| U_569 = U_568
| U_567 = U_566 ) )
| ~ is_int(U_566)
| ~ is_int(U_567)
| ~ is_int(U_568)
| ~ is_int(U_569) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
fof(f_198_3,plain,
( ! [U_568,U_567,U_566,U_569] :
( U_569 != U_568
| ~ sP18(U_568,U_567,U_566,U_569) )
& ! [U_568,U_567,U_566,U_569] :
( U_567 != U_566
| ~ sP18(U_568,U_567,U_566,U_569) )
& ! [U_568,U_567,U_566,U_569] :
( sP18(U_568,U_567,U_566,U_569)
| plus_plus_int(times_times_int(U_567,U_569),times_times_int(U_566,U_568)) = plus_plus_int(times_times_int(U_567,U_568),times_times_int(U_566,U_569))
| ~ sP19(U_568,U_567,U_566,U_569) )
& ! [U_568,U_567,U_566,U_569] :
( plus_plus_int(times_times_int(U_567,U_569),times_times_int(U_566,U_568)) != plus_plus_int(times_times_int(U_567,U_568),times_times_int(U_566,U_569))
| U_569 = U_568
| U_567 = U_566
| ~ sP19(U_568,U_567,U_566,U_569) )
& ! [U_568,U_567,U_566,U_569] :
( sP19(U_568,U_567,U_566,U_569)
| ~ is_int(U_566)
| ~ is_int(U_567)
| ~ is_int(U_568)
| ~ is_int(U_569) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18,sP19])],[f_198_2]) ).
cnf(f_198_4,plain,
( sP19(U_568,U_567,U_566,U_569)
| ~ is_int(U_566)
| ~ is_int(U_567)
| ~ is_int(U_568)
| ~ is_int(U_569) ),
inference(clausify,[status(thm)],[f_198_3]) ).
cnf(f_198_5,plain,
( plus_plus_int(times_times_int(U_567,U_569),times_times_int(U_566,U_568)) != plus_plus_int(times_times_int(U_567,U_568),times_times_int(U_566,U_569))
| U_569 = U_568
| U_567 = U_566
| ~ sP19(U_568,U_567,U_566,U_569) ),
inference(clausify,[status(thm)],[f_198_3]) ).
cnf(f_198_6,plain,
( sP18(U_568,U_567,U_566,U_569)
| plus_plus_int(times_times_int(U_567,U_569),times_times_int(U_566,U_568)) = plus_plus_int(times_times_int(U_567,U_568),times_times_int(U_566,U_569))
| ~ sP19(U_568,U_567,U_566,U_569) ),
inference(clausify,[status(thm)],[f_198_3]) ).
cnf(f_198_7,plain,
( U_567 != U_566
| ~ sP18(U_568,U_567,U_566,U_569) ),
inference(clausify,[status(thm)],[f_198_3]) ).
cnf(f_198_8,plain,
( U_569 != U_568
| ~ sP18(U_568,U_567,U_566,U_569) ),
inference(clausify,[status(thm)],[f_198_3]) ).
fof(f_199_1,plain,
! [X_16,Y_14,Z_8] : times_times_real(X_16,plus_plus_real(Y_14,Z_8)) = plus_plus_real(times_times_real(X_16,Y_14),times_times_real(X_16,Z_8)),
inference(fof_nnf,[status(thm)],[fact_180_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J]) ).
fof(f_199_2,plain,
! [U_572,U_571,U_570] : times_times_real(U_572,plus_plus_real(U_571,U_570)) = plus_plus_real(times_times_real(U_572,U_571),times_times_real(U_572,U_570)),
inference(variable_rename,[status(thm)],[f_199_1]) ).
fof(f_199_3,plain,
! [U_572,U_571,U_570] : times_times_real(U_572,plus_plus_real(U_571,U_570)) = plus_plus_real(times_times_real(U_572,U_571),times_times_real(U_572,U_570)),
inference(definitional_conversion,[status(esa)],[f_199_2]) ).
cnf(f_199_4,plain,
times_times_real(U_572,plus_plus_real(U_571,U_570)) = plus_plus_real(times_times_real(U_572,U_571),times_times_real(U_572,U_570)),
inference(clausify,[status(thm)],[f_199_3]) ).
fof(f_200_1,plain,
! [X_16,Y_14,Z_8] : times_times_nat(X_16,plus_plus_nat(Y_14,Z_8)) = plus_plus_nat(times_times_nat(X_16,Y_14),times_times_nat(X_16,Z_8)),
inference(fof_nnf,[status(thm)],[fact_181_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J]) ).
fof(f_200_2,plain,
! [U_575,U_574,U_573] : times_times_nat(U_575,plus_plus_nat(U_574,U_573)) = plus_plus_nat(times_times_nat(U_575,U_574),times_times_nat(U_575,U_573)),
inference(variable_rename,[status(thm)],[f_200_1]) ).
fof(f_200_3,plain,
! [U_575,U_573,U_574] : times_times_nat(U_575,plus_plus_nat(U_574,U_573)) = plus_plus_nat(times_times_nat(U_575,U_574),times_times_nat(U_575,U_573)),
inference(definitional_conversion,[status(esa)],[f_200_2]) ).
cnf(f_200_4,plain,
times_times_nat(U_575,plus_plus_nat(U_574,U_573)) = plus_plus_nat(times_times_nat(U_575,U_574),times_times_nat(U_575,U_573)),
inference(clausify,[status(thm)],[f_200_3]) ).
fof(f_201_1,plain,
! [X_16,Y_14,Z_8] : times_times_int(X_16,plus_plus_int(Y_14,Z_8)) = plus_plus_int(times_times_int(X_16,Y_14),times_times_int(X_16,Z_8)),
inference(fof_nnf,[status(thm)],[fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J]) ).
fof(f_201_2,plain,
! [U_578,U_577,U_576] : times_times_int(U_578,plus_plus_int(U_577,U_576)) = plus_plus_int(times_times_int(U_578,U_577),times_times_int(U_578,U_576)),
inference(variable_rename,[status(thm)],[f_201_1]) ).
fof(f_201_3,plain,
! [U_577,U_576,U_578] : times_times_int(U_578,plus_plus_int(U_577,U_576)) = plus_plus_int(times_times_int(U_578,U_577),times_times_int(U_578,U_576)),
inference(definitional_conversion,[status(esa)],[f_201_2]) ).
cnf(f_201_4,plain,
times_times_int(U_578,plus_plus_int(U_577,U_576)) = plus_plus_int(times_times_int(U_578,U_577),times_times_int(U_578,U_576)),
inference(clausify,[status(thm)],[f_201_3]) ).
fof(f_202_1,plain,
! [A_46] : times_times_real(A_46,one_one_real) = A_46,
inference(fof_nnf,[status(thm)],[fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J]) ).
fof(f_202_2,plain,
! [U_579] : times_times_real(U_579,one_one_real) = U_579,
inference(variable_rename,[status(thm)],[f_202_1]) ).
fof(f_202_3,plain,
! [U_579] : times_times_real(U_579,one_one_real) = U_579,
inference(definitional_conversion,[status(esa)],[f_202_2]) ).
cnf(f_202_4,plain,
times_times_real(U_579,one_one_real) = U_579,
inference(clausify,[status(thm)],[f_202_3]) ).
fof(f_203_1,plain,
! [A_46] : times_times_nat(A_46,one_one_nat) = A_46,
inference(fof_nnf,[status(thm)],[fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J]) ).
fof(f_203_2,plain,
! [U_580] : times_times_nat(U_580,one_one_nat) = U_580,
inference(variable_rename,[status(thm)],[f_203_1]) ).
fof(f_203_3,plain,
! [U_580] : times_times_nat(U_580,one_one_nat) = U_580,
inference(definitional_conversion,[status(esa)],[f_203_2]) ).
cnf(f_203_4,plain,
times_times_nat(U_580,one_one_nat) = U_580,
inference(clausify,[status(thm)],[f_203_3]) ).
fof(f_204_1,plain,
! [A_46] :
( times_times_int(A_46,one_one_int) = A_46
| ~ is_int(A_46) ),
inference(fof_nnf,[status(thm)],[fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J]) ).
fof(f_204_2,plain,
! [U_581] :
( times_times_int(U_581,one_one_int) = U_581
| ~ is_int(U_581) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
fof(f_204_3,plain,
! [U_581] :
( times_times_int(U_581,one_one_int) = U_581
| ~ is_int(U_581) ),
inference(definitional_conversion,[status(esa)],[f_204_2]) ).
cnf(f_204_4,plain,
( times_times_int(U_581,one_one_int) = U_581
| ~ is_int(U_581) ),
inference(clausify,[status(thm)],[f_204_3]) ).
fof(f_205_1,plain,
! [A_45] : times_times_real(one_one_real,A_45) = A_45,
inference(fof_nnf,[status(thm)],[fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J]) ).
fof(f_205_2,plain,
! [U_582] : times_times_real(one_one_real,U_582) = U_582,
inference(variable_rename,[status(thm)],[f_205_1]) ).
fof(f_205_3,plain,
! [U_582] : times_times_real(one_one_real,U_582) = U_582,
inference(definitional_conversion,[status(esa)],[f_205_2]) ).
cnf(f_205_4,plain,
times_times_real(one_one_real,U_582) = U_582,
inference(clausify,[status(thm)],[f_205_3]) ).
fof(f_206_1,plain,
! [A_45] : times_times_nat(one_one_nat,A_45) = A_45,
inference(fof_nnf,[status(thm)],[fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J]) ).
fof(f_206_2,plain,
! [U_583] : times_times_nat(one_one_nat,U_583) = U_583,
inference(variable_rename,[status(thm)],[f_206_1]) ).
fof(f_206_3,plain,
! [U_583] : times_times_nat(one_one_nat,U_583) = U_583,
inference(definitional_conversion,[status(esa)],[f_206_2]) ).
cnf(f_206_4,plain,
times_times_nat(one_one_nat,U_583) = U_583,
inference(clausify,[status(thm)],[f_206_3]) ).
fof(f_207_1,plain,
! [A_45] :
( times_times_int(one_one_int,A_45) = A_45
| ~ is_int(A_45) ),
inference(fof_nnf,[status(thm)],[fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J]) ).
fof(f_207_2,plain,
! [U_584] :
( times_times_int(one_one_int,U_584) = U_584
| ~ is_int(U_584) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
fof(f_207_3,plain,
! [U_584] :
( times_times_int(one_one_int,U_584) = U_584
| ~ is_int(U_584) ),
inference(definitional_conversion,[status(esa)],[f_207_2]) ).
cnf(f_207_4,plain,
( times_times_int(one_one_int,U_584) = U_584
| ~ is_int(U_584) ),
inference(clausify,[status(thm)],[f_207_3]) ).
fof(f_208_1,plain,
! [X_15,Y_13,Q_2] : power_power_nat(times_times_nat(X_15,Y_13),Q_2) = times_times_nat(power_power_nat(X_15,Q_2),power_power_nat(Y_13,Q_2)),
inference(fof_nnf,[status(thm)],[fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J]) ).
fof(f_208_2,plain,
! [U_587,U_586,U_585] : power_power_nat(times_times_nat(U_587,U_586),U_585) = times_times_nat(power_power_nat(U_587,U_585),power_power_nat(U_586,U_585)),
inference(variable_rename,[status(thm)],[f_208_1]) ).
fof(f_208_3,plain,
! [U_585,U_586,U_587] : power_power_nat(times_times_nat(U_587,U_586),U_585) = times_times_nat(power_power_nat(U_587,U_585),power_power_nat(U_586,U_585)),
inference(definitional_conversion,[status(esa)],[f_208_2]) ).
cnf(f_208_4,plain,
power_power_nat(times_times_nat(U_587,U_586),U_585) = times_times_nat(power_power_nat(U_587,U_585),power_power_nat(U_586,U_585)),
inference(clausify,[status(thm)],[f_208_3]) ).
fof(f_209_1,plain,
! [X_15,Y_13,Q_2] : power_power_real(times_times_real(X_15,Y_13),Q_2) = times_times_real(power_power_real(X_15,Q_2),power_power_real(Y_13,Q_2)),
inference(fof_nnf,[status(thm)],[fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J]) ).
fof(f_209_2,plain,
! [U_590,U_589,U_588] : power_power_real(times_times_real(U_590,U_589),U_588) = times_times_real(power_power_real(U_590,U_588),power_power_real(U_589,U_588)),
inference(variable_rename,[status(thm)],[f_209_1]) ).
fof(f_209_3,plain,
! [U_588,U_589,U_590] : power_power_real(times_times_real(U_590,U_589),U_588) = times_times_real(power_power_real(U_590,U_588),power_power_real(U_589,U_588)),
inference(definitional_conversion,[status(esa)],[f_209_2]) ).
cnf(f_209_4,plain,
power_power_real(times_times_real(U_590,U_589),U_588) = times_times_real(power_power_real(U_590,U_588),power_power_real(U_589,U_588)),
inference(clausify,[status(thm)],[f_209_3]) ).
fof(f_210_1,plain,
! [X_15,Y_13,Q_2] : power_power_int(times_times_int(X_15,Y_13),Q_2) = times_times_int(power_power_int(X_15,Q_2),power_power_int(Y_13,Q_2)),
inference(fof_nnf,[status(thm)],[fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J]) ).
fof(f_210_2,plain,
! [U_593,U_592,U_591] : power_power_int(times_times_int(U_593,U_592),U_591) = times_times_int(power_power_int(U_593,U_591),power_power_int(U_592,U_591)),
inference(variable_rename,[status(thm)],[f_210_1]) ).
fof(f_210_3,plain,
! [U_591,U_592,U_593] : power_power_int(times_times_int(U_593,U_592),U_591) = times_times_int(power_power_int(U_593,U_591),power_power_int(U_592,U_591)),
inference(definitional_conversion,[status(esa)],[f_210_2]) ).
cnf(f_210_4,plain,
power_power_int(times_times_int(U_593,U_592),U_591) = times_times_int(power_power_int(U_593,U_591),power_power_int(U_592,U_591)),
inference(clausify,[status(thm)],[f_210_3]) ).
fof(f_211_1,plain,
! [K] : bit1(K) != pls,
inference(fof_nnf,[status(thm)],[fact_192_rel__simps_I46_J]) ).
fof(f_211_2,plain,
! [U_594] : bit1(U_594) != pls,
inference(variable_rename,[status(thm)],[f_211_1]) ).
fof(f_211_3,plain,
! [U_594] : bit1(U_594) != pls,
inference(definitional_conversion,[status(esa)],[f_211_2]) ).
cnf(f_211_4,plain,
bit1(U_594) != pls,
inference(clausify,[status(thm)],[f_211_3]) ).
fof(f_212_1,plain,
! [L] : pls != bit1(L),
inference(fof_nnf,[status(thm)],[fact_193_rel__simps_I39_J]) ).
fof(f_212_2,plain,
! [U_595] : pls != bit1(U_595),
inference(variable_rename,[status(thm)],[f_212_1]) ).
fof(f_212_3,plain,
! [U_595] : pls != bit1(U_595),
inference(definitional_conversion,[status(esa)],[f_212_2]) ).
cnf(f_212_4,plain,
pls != bit1(U_595),
inference(clausify,[status(thm)],[f_212_3]) ).
fof(f_213_1,plain,
! [K,L] : bit1(K) != bit0(L),
inference(fof_nnf,[status(thm)],[fact_194_rel__simps_I50_J]) ).
fof(f_213_2,plain,
! [U_597,U_596] : bit1(U_597) != bit0(U_596),
inference(variable_rename,[status(thm)],[f_213_1]) ).
fof(f_213_3,plain,
! [U_596,U_597] : bit1(U_597) != bit0(U_596),
inference(definitional_conversion,[status(esa)],[f_213_2]) ).
cnf(f_213_4,plain,
bit1(U_597) != bit0(U_596),
inference(clausify,[status(thm)],[f_213_3]) ).
fof(f_214_1,plain,
! [K,L] : bit0(K) != bit1(L),
inference(fof_nnf,[status(thm)],[fact_195_rel__simps_I49_J]) ).
fof(f_214_2,plain,
! [U_599,U_598] : bit0(U_599) != bit1(U_598),
inference(variable_rename,[status(thm)],[f_214_1]) ).
fof(f_214_3,plain,
! [U_598,U_599] : bit0(U_599) != bit1(U_598),
inference(definitional_conversion,[status(esa)],[f_214_2]) ).
cnf(f_214_4,plain,
bit0(U_599) != bit1(U_598),
inference(clausify,[status(thm)],[f_214_3]) ).
fof(f_215_1,plain,
! [K_1] :
( ( ( bit0(K_1) = pls
| K_1 != pls )
& ( K_1 = pls
| bit0(K_1) != pls ) )
| ~ is_int(K_1) ),
inference(fof_nnf,[status(thm)],[fact_196_rel__simps_I44_J]) ).
fof(f_215_2,plain,
! [U_600] :
( ( ( bit0(U_600) = pls
| U_600 != pls )
& ( U_600 = pls
| bit0(U_600) != pls ) )
| ~ is_int(U_600) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
fof(f_215_3,plain,
( ! [U_600] :
( bit0(U_600) = pls
| U_600 != pls
| ~ sP20(U_600) )
& ! [U_600] :
( U_600 = pls
| bit0(U_600) != pls
| ~ sP20(U_600) )
& ! [U_600] :
( sP20(U_600)
| ~ is_int(U_600) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20])],[f_215_2]) ).
cnf(f_215_4,plain,
( sP20(U_600)
| ~ is_int(U_600) ),
inference(clausify,[status(thm)],[f_215_3]) ).
cnf(f_215_5,plain,
( U_600 = pls
| bit0(U_600) != pls
| ~ sP20(U_600) ),
inference(clausify,[status(thm)],[f_215_3]) ).
cnf(f_215_6,plain,
( bit0(U_600) = pls
| U_600 != pls
| ~ sP20(U_600) ),
inference(clausify,[status(thm)],[f_215_3]) ).
fof(f_216_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_197_rel__simps_I38_J]) ).
fof(f_216_2,plain,
! [U_601] :
( ( ( pls = bit0(U_601)
| pls != U_601 )
& ( pls = U_601
| pls != bit0(U_601) ) )
| ~ is_int(U_601) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
fof(f_216_3,plain,
( ! [U_601] :
( pls = bit0(U_601)
| pls != U_601
| ~ sP21(U_601) )
& ! [U_601] :
( pls = U_601
| pls != bit0(U_601)
| ~ sP21(U_601) )
& ! [U_601] :
( sP21(U_601)
| ~ is_int(U_601) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21])],[f_216_2]) ).
cnf(f_216_4,plain,
( sP21(U_601)
| ~ is_int(U_601) ),
inference(clausify,[status(thm)],[f_216_3]) ).
cnf(f_216_5,plain,
( pls = U_601
| pls != bit0(U_601)
| ~ sP21(U_601) ),
inference(clausify,[status(thm)],[f_216_3]) ).
cnf(f_216_6,plain,
( pls = bit0(U_601)
| pls != U_601
| ~ sP21(U_601) ),
inference(clausify,[status(thm)],[f_216_3]) ).
fof(f_217_1,plain,
bit0(pls) = pls,
inference(fof_nnf,[status(thm)],[fact_198_Bit0__Pls]) ).
fof(f_217_2,plain,
bit0(pls) = pls,
inference(definitional_conversion,[status(esa)],[f_217_1]) ).
cnf(f_217_3,plain,
bit0(pls) = pls,
inference(clausify,[status(thm)],[f_217_2]) ).
fof(f_218_1,plain,
! [W] : times_times_int(pls,W) = pls,
inference(fof_nnf,[status(thm)],[fact_199_mult__Pls]) ).
fof(f_218_2,plain,
! [U_602] : times_times_int(pls,U_602) = pls,
inference(variable_rename,[status(thm)],[f_218_1]) ).
fof(f_218_3,plain,
! [U_602] : times_times_int(pls,U_602) = pls,
inference(definitional_conversion,[status(esa)],[f_218_2]) ).
cnf(f_218_4,plain,
times_times_int(pls,U_602) = pls,
inference(clausify,[status(thm)],[f_218_3]) ).
fof(f_219_1,plain,
! [K,L] : times_times_int(bit0(K),L) = bit0(times_times_int(K,L)),
inference(fof_nnf,[status(thm)],[fact_200_mult__Bit0]) ).
fof(f_219_2,plain,
! [U_604,U_603] : times_times_int(bit0(U_604),U_603) = bit0(times_times_int(U_604,U_603)),
inference(variable_rename,[status(thm)],[f_219_1]) ).
fof(f_219_3,plain,
! [U_603,U_604] : times_times_int(bit0(U_604),U_603) = bit0(times_times_int(U_604,U_603)),
inference(definitional_conversion,[status(esa)],[f_219_2]) ).
cnf(f_219_4,plain,
times_times_int(bit0(U_604),U_603) = bit0(times_times_int(U_604,U_603)),
inference(clausify,[status(thm)],[f_219_3]) ).
fof(f_220_1,plain,
! [K] :
( plus_plus_int(K,pls) = K
| ~ is_int(K) ),
inference(fof_nnf,[status(thm)],[fact_201_add__Pls__right]) ).
fof(f_220_2,plain,
! [U_605] :
( plus_plus_int(U_605,pls) = U_605
| ~ is_int(U_605) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
fof(f_220_3,plain,
! [U_605] :
( plus_plus_int(U_605,pls) = U_605
| ~ is_int(U_605) ),
inference(definitional_conversion,[status(esa)],[f_220_2]) ).
cnf(f_220_4,plain,
( plus_plus_int(U_605,pls) = U_605
| ~ is_int(U_605) ),
inference(clausify,[status(thm)],[f_220_3]) ).
fof(f_221_1,plain,
! [K] :
( plus_plus_int(pls,K) = K
| ~ is_int(K) ),
inference(fof_nnf,[status(thm)],[fact_202_add__Pls]) ).
fof(f_221_2,plain,
! [U_606] :
( plus_plus_int(pls,U_606) = U_606
| ~ is_int(U_606) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
fof(f_221_3,plain,
! [U_606] :
( plus_plus_int(pls,U_606) = U_606
| ~ is_int(U_606) ),
inference(definitional_conversion,[status(esa)],[f_221_2]) ).
cnf(f_221_4,plain,
( plus_plus_int(pls,U_606) = U_606
| ~ is_int(U_606) ),
inference(clausify,[status(thm)],[f_221_3]) ).
fof(f_222_1,plain,
! [K,L] : plus_plus_int(bit0(K),bit0(L)) = bit0(plus_plus_int(K,L)),
inference(fof_nnf,[status(thm)],[fact_203_add__Bit0__Bit0]) ).
fof(f_222_2,plain,
! [U_608,U_607] : plus_plus_int(bit0(U_608),bit0(U_607)) = bit0(plus_plus_int(U_608,U_607)),
inference(variable_rename,[status(thm)],[f_222_1]) ).
fof(f_222_3,plain,
! [U_607,U_608] : plus_plus_int(bit0(U_608),bit0(U_607)) = bit0(plus_plus_int(U_608,U_607)),
inference(definitional_conversion,[status(esa)],[f_222_2]) ).
cnf(f_222_4,plain,
plus_plus_int(bit0(U_608),bit0(U_607)) = bit0(plus_plus_int(U_608,U_607)),
inference(clausify,[status(thm)],[f_222_3]) ).
fof(f_223_1,plain,
! [K] : bit0(K) = plus_plus_int(K,K),
inference(fof_nnf,[status(thm)],[fact_204_Bit0__def]) ).
fof(f_223_2,plain,
! [U_609] : bit0(U_609) = plus_plus_int(U_609,U_609),
inference(variable_rename,[status(thm)],[f_223_1]) ).
fof(f_223_3,plain,
! [U_609] : bit0(U_609) = plus_plus_int(U_609,U_609),
inference(definitional_conversion,[status(esa)],[f_223_2]) ).
cnf(f_223_4,plain,
bit0(U_609) = plus_plus_int(U_609,U_609),
inference(clausify,[status(thm)],[f_223_3]) ).
fof(f_224_1,plain,
! [Z] :
( times_times_int(Z,one_one_int) = Z
| ~ is_int(Z) ),
inference(fof_nnf,[status(thm)],[fact_205_zmult__1__right]) ).
fof(f_224_2,plain,
! [U_610] :
( times_times_int(U_610,one_one_int) = U_610
| ~ is_int(U_610) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
fof(f_224_3,plain,
! [U_610] :
( times_times_int(U_610,one_one_int) = U_610
| ~ is_int(U_610) ),
inference(definitional_conversion,[status(esa)],[f_224_2]) ).
cnf(f_224_4,plain,
( times_times_int(U_610,one_one_int) = U_610
| ~ is_int(U_610) ),
inference(clausify,[status(thm)],[f_224_3]) ).
fof(f_225_1,plain,
! [Z] :
( times_times_int(one_one_int,Z) = Z
| ~ is_int(Z) ),
inference(fof_nnf,[status(thm)],[fact_206_zmult__1]) ).
fof(f_225_2,plain,
! [U_611] :
( times_times_int(one_one_int,U_611) = U_611
| ~ is_int(U_611) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
fof(f_225_3,plain,
! [U_611] :
( times_times_int(one_one_int,U_611) = U_611
| ~ is_int(U_611) ),
inference(definitional_conversion,[status(esa)],[f_225_2]) ).
cnf(f_225_4,plain,
( times_times_int(one_one_int,U_611) = U_611
| ~ is_int(U_611) ),
inference(clausify,[status(thm)],[f_225_3]) ).
fof(f_226_1,plain,
! [V_1,W] : times_times_int(number_number_of_int(V_1),number_number_of_int(W)) = number_number_of_int(times_times_int(V_1,W)),
inference(fof_nnf,[status(thm)],[fact_207_times__numeral__code_I5_J]) ).
fof(f_226_2,plain,
! [U_613,U_612] : times_times_int(number_number_of_int(U_613),number_number_of_int(U_612)) = number_number_of_int(times_times_int(U_613,U_612)),
inference(variable_rename,[status(thm)],[f_226_1]) ).
fof(f_226_3,plain,
! [U_612,U_613] : times_times_int(number_number_of_int(U_613),number_number_of_int(U_612)) = number_number_of_int(times_times_int(U_613,U_612)),
inference(definitional_conversion,[status(esa)],[f_226_2]) ).
cnf(f_226_4,plain,
times_times_int(number_number_of_int(U_613),number_number_of_int(U_612)) = number_number_of_int(times_times_int(U_613,U_612)),
inference(clausify,[status(thm)],[f_226_3]) ).
fof(f_227_1,plain,
! [Z1,Z2,W] : times_times_int(plus_plus_int(Z1,Z2),W) = plus_plus_int(times_times_int(Z1,W),times_times_int(Z2,W)),
inference(fof_nnf,[status(thm)],[fact_208_zadd__zmult__distrib]) ).
fof(f_227_2,plain,
! [U_616,U_615,U_614] : times_times_int(plus_plus_int(U_616,U_615),U_614) = plus_plus_int(times_times_int(U_616,U_614),times_times_int(U_615,U_614)),
inference(variable_rename,[status(thm)],[f_227_1]) ).
fof(f_227_3,plain,
! [U_614,U_615,U_616] : times_times_int(plus_plus_int(U_616,U_615),U_614) = plus_plus_int(times_times_int(U_616,U_614),times_times_int(U_615,U_614)),
inference(definitional_conversion,[status(esa)],[f_227_2]) ).
cnf(f_227_4,plain,
times_times_int(plus_plus_int(U_616,U_615),U_614) = plus_plus_int(times_times_int(U_616,U_614),times_times_int(U_615,U_614)),
inference(clausify,[status(thm)],[f_227_3]) ).
fof(f_228_1,plain,
! [W,Z1,Z2] : times_times_int(W,plus_plus_int(Z1,Z2)) = plus_plus_int(times_times_int(W,Z1),times_times_int(W,Z2)),
inference(fof_nnf,[status(thm)],[fact_209_zadd__zmult__distrib2]) ).
fof(f_228_2,plain,
! [U_619,U_618,U_617] : times_times_int(U_619,plus_plus_int(U_618,U_617)) = plus_plus_int(times_times_int(U_619,U_618),times_times_int(U_619,U_617)),
inference(variable_rename,[status(thm)],[f_228_1]) ).
fof(f_228_3,plain,
! [U_617,U_618,U_619] : times_times_int(U_619,plus_plus_int(U_618,U_617)) = plus_plus_int(times_times_int(U_619,U_618),times_times_int(U_619,U_617)),
inference(definitional_conversion,[status(esa)],[f_228_2]) ).
cnf(f_228_4,plain,
times_times_int(U_619,plus_plus_int(U_618,U_617)) = plus_plus_int(times_times_int(U_619,U_618),times_times_int(U_619,U_617)),
inference(clausify,[status(thm)],[f_228_3]) ).
fof(f_229_1,plain,
! [V_1,W] : plus_plus_int(number_number_of_int(V_1),number_number_of_int(W)) = number_number_of_int(plus_plus_int(V_1,W)),
inference(fof_nnf,[status(thm)],[fact_210_plus__numeral__code_I9_J]) ).
fof(f_229_2,plain,
! [U_621,U_620] : plus_plus_int(number_number_of_int(U_621),number_number_of_int(U_620)) = number_number_of_int(plus_plus_int(U_621,U_620)),
inference(variable_rename,[status(thm)],[f_229_1]) ).
fof(f_229_3,plain,
! [U_620,U_621] : plus_plus_int(number_number_of_int(U_621),number_number_of_int(U_620)) = number_number_of_int(plus_plus_int(U_621,U_620)),
inference(definitional_conversion,[status(esa)],[f_229_2]) ).
cnf(f_229_4,plain,
plus_plus_int(number_number_of_int(U_621),number_number_of_int(U_620)) = number_number_of_int(plus_plus_int(U_621,U_620)),
inference(clausify,[status(thm)],[f_229_3]) ).
fof(f_230_1,plain,
! [V_16,V_15] :
( times_times_real(number267125858f_real(V_15),number267125858f_real(V_16)) = number267125858f_real(times_times_int(V_15,V_16))
| ~ ord_less_eq_int(pls,V_16)
| ~ ord_less_eq_int(pls,V_15) ),
inference(fof_nnf,[status(thm)],[fact_211_semiring__mult__number__of]) ).
fof(f_230_2,plain,
! [U_623,U_622] :
( times_times_real(number267125858f_real(U_622),number267125858f_real(U_623)) = number267125858f_real(times_times_int(U_622,U_623))
| ~ ord_less_eq_int(pls,U_623)
| ~ ord_less_eq_int(pls,U_622) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
fof(f_230_3,plain,
! [U_623,U_622] :
( times_times_real(number267125858f_real(U_622),number267125858f_real(U_623)) = number267125858f_real(times_times_int(U_622,U_623))
| ~ ord_less_eq_int(pls,U_623)
| ~ ord_less_eq_int(pls,U_622) ),
inference(definitional_conversion,[status(esa)],[f_230_2]) ).
cnf(f_230_4,plain,
( times_times_real(number267125858f_real(U_622),number267125858f_real(U_623)) = number267125858f_real(times_times_int(U_622,U_623))
| ~ ord_less_eq_int(pls,U_623)
| ~ ord_less_eq_int(pls,U_622) ),
inference(clausify,[status(thm)],[f_230_3]) ).
fof(f_231_1,plain,
! [V_16,V_15] :
( times_times_nat(number_number_of_nat(V_15),number_number_of_nat(V_16)) = number_number_of_nat(times_times_int(V_15,V_16))
| ~ ord_less_eq_int(pls,V_16)
| ~ ord_less_eq_int(pls,V_15) ),
inference(fof_nnf,[status(thm)],[fact_212_semiring__mult__number__of]) ).
fof(f_231_2,plain,
! [U_625,U_624] :
( times_times_nat(number_number_of_nat(U_624),number_number_of_nat(U_625)) = number_number_of_nat(times_times_int(U_624,U_625))
| ~ ord_less_eq_int(pls,U_625)
| ~ ord_less_eq_int(pls,U_624) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
fof(f_231_3,plain,
! [U_625,U_624] :
( times_times_nat(number_number_of_nat(U_624),number_number_of_nat(U_625)) = number_number_of_nat(times_times_int(U_624,U_625))
| ~ ord_less_eq_int(pls,U_625)
| ~ ord_less_eq_int(pls,U_624) ),
inference(definitional_conversion,[status(esa)],[f_231_2]) ).
cnf(f_231_4,plain,
( times_times_nat(number_number_of_nat(U_624),number_number_of_nat(U_625)) = number_number_of_nat(times_times_int(U_624,U_625))
| ~ ord_less_eq_int(pls,U_625)
| ~ ord_less_eq_int(pls,U_624) ),
inference(clausify,[status(thm)],[f_231_3]) ).
fof(f_232_1,plain,
! [V_16,V_15] :
( times_times_int(number_number_of_int(V_15),number_number_of_int(V_16)) = number_number_of_int(times_times_int(V_15,V_16))
| ~ ord_less_eq_int(pls,V_16)
| ~ ord_less_eq_int(pls,V_15) ),
inference(fof_nnf,[status(thm)],[fact_213_semiring__mult__number__of]) ).
fof(f_232_2,plain,
! [U_627,U_626] :
( times_times_int(number_number_of_int(U_626),number_number_of_int(U_627)) = number_number_of_int(times_times_int(U_626,U_627))
| ~ ord_less_eq_int(pls,U_627)
| ~ ord_less_eq_int(pls,U_626) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
fof(f_232_3,plain,
! [U_627,U_626] :
( times_times_int(number_number_of_int(U_626),number_number_of_int(U_627)) = number_number_of_int(times_times_int(U_626,U_627))
| ~ ord_less_eq_int(pls,U_627)
| ~ ord_less_eq_int(pls,U_626) ),
inference(definitional_conversion,[status(esa)],[f_232_2]) ).
cnf(f_232_4,plain,
( times_times_int(number_number_of_int(U_626),number_number_of_int(U_627)) = number_number_of_int(times_times_int(U_626,U_627))
| ~ ord_less_eq_int(pls,U_627)
| ~ ord_less_eq_int(pls,U_626) ),
inference(clausify,[status(thm)],[f_232_3]) ).
fof(f_233_1,plain,
! [V_14,V_13] :
( plus_plus_real(number267125858f_real(V_13),number267125858f_real(V_14)) = number267125858f_real(plus_plus_int(V_13,V_14))
| ~ ord_less_eq_int(pls,V_14)
| ~ ord_less_eq_int(pls,V_13) ),
inference(fof_nnf,[status(thm)],[fact_214_semiring__add__number__of]) ).
fof(f_233_2,plain,
! [U_629,U_628] :
( plus_plus_real(number267125858f_real(U_628),number267125858f_real(U_629)) = number267125858f_real(plus_plus_int(U_628,U_629))
| ~ ord_less_eq_int(pls,U_629)
| ~ ord_less_eq_int(pls,U_628) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
fof(f_233_3,plain,
! [U_629,U_628] :
( plus_plus_real(number267125858f_real(U_628),number267125858f_real(U_629)) = number267125858f_real(plus_plus_int(U_628,U_629))
| ~ ord_less_eq_int(pls,U_629)
| ~ ord_less_eq_int(pls,U_628) ),
inference(definitional_conversion,[status(esa)],[f_233_2]) ).
cnf(f_233_4,plain,
( plus_plus_real(number267125858f_real(U_628),number267125858f_real(U_629)) = number267125858f_real(plus_plus_int(U_628,U_629))
| ~ ord_less_eq_int(pls,U_629)
| ~ ord_less_eq_int(pls,U_628) ),
inference(clausify,[status(thm)],[f_233_3]) ).
fof(f_234_1,plain,
! [V_14,V_13] :
( plus_plus_nat(number_number_of_nat(V_13),number_number_of_nat(V_14)) = number_number_of_nat(plus_plus_int(V_13,V_14))
| ~ ord_less_eq_int(pls,V_14)
| ~ ord_less_eq_int(pls,V_13) ),
inference(fof_nnf,[status(thm)],[fact_215_semiring__add__number__of]) ).
fof(f_234_2,plain,
! [U_631,U_630] :
( plus_plus_nat(number_number_of_nat(U_630),number_number_of_nat(U_631)) = number_number_of_nat(plus_plus_int(U_630,U_631))
| ~ ord_less_eq_int(pls,U_631)
| ~ ord_less_eq_int(pls,U_630) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
fof(f_234_3,plain,
! [U_630,U_631] :
( plus_plus_nat(number_number_of_nat(U_630),number_number_of_nat(U_631)) = number_number_of_nat(plus_plus_int(U_630,U_631))
| ~ ord_less_eq_int(pls,U_631)
| ~ ord_less_eq_int(pls,U_630) ),
inference(definitional_conversion,[status(esa)],[f_234_2]) ).
cnf(f_234_4,plain,
( plus_plus_nat(number_number_of_nat(U_630),number_number_of_nat(U_631)) = number_number_of_nat(plus_plus_int(U_630,U_631))
| ~ ord_less_eq_int(pls,U_631)
| ~ ord_less_eq_int(pls,U_630) ),
inference(clausify,[status(thm)],[f_234_3]) ).
fof(f_235_1,plain,
! [V_14,V_13] :
( plus_plus_int(number_number_of_int(V_13),number_number_of_int(V_14)) = number_number_of_int(plus_plus_int(V_13,V_14))
| ~ ord_less_eq_int(pls,V_14)
| ~ ord_less_eq_int(pls,V_13) ),
inference(fof_nnf,[status(thm)],[fact_216_semiring__add__number__of]) ).
fof(f_235_2,plain,
! [U_633,U_632] :
( plus_plus_int(number_number_of_int(U_632),number_number_of_int(U_633)) = number_number_of_int(plus_plus_int(U_632,U_633))
| ~ ord_less_eq_int(pls,U_633)
| ~ ord_less_eq_int(pls,U_632) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
fof(f_235_3,plain,
! [U_632,U_633] :
( plus_plus_int(number_number_of_int(U_632),number_number_of_int(U_633)) = number_number_of_int(plus_plus_int(U_632,U_633))
| ~ ord_less_eq_int(pls,U_633)
| ~ ord_less_eq_int(pls,U_632) ),
inference(definitional_conversion,[status(esa)],[f_235_2]) ).
cnf(f_235_4,plain,
( plus_plus_int(number_number_of_int(U_632),number_number_of_int(U_633)) = number_number_of_int(plus_plus_int(U_632,U_633))
| ~ ord_less_eq_int(pls,U_633)
| ~ ord_less_eq_int(pls,U_632) ),
inference(clausify,[status(thm)],[f_235_3]) ).
fof(f_236_1,plain,
! [X_1] : ord_less_eq_int(X_1,power_power_int(X_1,number_number_of_nat(bit0(bit1(pls))))),
inference(fof_nnf,[status(thm)],[fact_217_power2__ge__self]) ).
fof(f_236_2,plain,
! [U_634] : ord_less_eq_int(U_634,power_power_int(U_634,number_number_of_nat(bit0(bit1(pls))))),
inference(variable_rename,[status(thm)],[f_236_1]) ).
fof(f_236_3,plain,
! [U_634] : ord_less_eq_int(U_634,power_power_int(U_634,number_number_of_nat(bit0(bit1(pls))))),
inference(definitional_conversion,[status(esa)],[f_236_2]) ).
cnf(f_236_4,plain,
ord_less_eq_int(U_634,power_power_int(U_634,number_number_of_nat(bit0(bit1(pls))))),
inference(clausify,[status(thm)],[f_236_3]) ).
fof(f_237_1,plain,
! [A_44,B_11,V_12] : times_times_real(plus_plus_real(A_44,B_11),number267125858f_real(V_12)) = plus_plus_real(times_times_real(A_44,number267125858f_real(V_12)),times_times_real(B_11,number267125858f_real(V_12))),
inference(fof_nnf,[status(thm)],[fact_218_left__distrib__number__of]) ).
fof(f_237_2,plain,
! [U_637,U_636,U_635] : times_times_real(plus_plus_real(U_637,U_636),number267125858f_real(U_635)) = plus_plus_real(times_times_real(U_637,number267125858f_real(U_635)),times_times_real(U_636,number267125858f_real(U_635))),
inference(variable_rename,[status(thm)],[f_237_1]) ).
fof(f_237_3,plain,
! [U_635,U_636,U_637] : times_times_real(plus_plus_real(U_637,U_636),number267125858f_real(U_635)) = plus_plus_real(times_times_real(U_637,number267125858f_real(U_635)),times_times_real(U_636,number267125858f_real(U_635))),
inference(definitional_conversion,[status(esa)],[f_237_2]) ).
cnf(f_237_4,plain,
times_times_real(plus_plus_real(U_637,U_636),number267125858f_real(U_635)) = plus_plus_real(times_times_real(U_637,number267125858f_real(U_635)),times_times_real(U_636,number267125858f_real(U_635))),
inference(clausify,[status(thm)],[f_237_3]) ).
fof(f_238_1,plain,
! [A_44,B_11,V_12] : times_times_nat(plus_plus_nat(A_44,B_11),number_number_of_nat(V_12)) = plus_plus_nat(times_times_nat(A_44,number_number_of_nat(V_12)),times_times_nat(B_11,number_number_of_nat(V_12))),
inference(fof_nnf,[status(thm)],[fact_219_left__distrib__number__of]) ).
fof(f_238_2,plain,
! [U_640,U_639,U_638] : times_times_nat(plus_plus_nat(U_640,U_639),number_number_of_nat(U_638)) = plus_plus_nat(times_times_nat(U_640,number_number_of_nat(U_638)),times_times_nat(U_639,number_number_of_nat(U_638))),
inference(variable_rename,[status(thm)],[f_238_1]) ).
fof(f_238_3,plain,
! [U_638,U_639,U_640] : times_times_nat(plus_plus_nat(U_640,U_639),number_number_of_nat(U_638)) = plus_plus_nat(times_times_nat(U_640,number_number_of_nat(U_638)),times_times_nat(U_639,number_number_of_nat(U_638))),
inference(definitional_conversion,[status(esa)],[f_238_2]) ).
cnf(f_238_4,plain,
times_times_nat(plus_plus_nat(U_640,U_639),number_number_of_nat(U_638)) = plus_plus_nat(times_times_nat(U_640,number_number_of_nat(U_638)),times_times_nat(U_639,number_number_of_nat(U_638))),
inference(clausify,[status(thm)],[f_238_3]) ).
fof(f_239_1,plain,
! [A_44,B_11,V_12] : times_times_int(plus_plus_int(A_44,B_11),number_number_of_int(V_12)) = plus_plus_int(times_times_int(A_44,number_number_of_int(V_12)),times_times_int(B_11,number_number_of_int(V_12))),
inference(fof_nnf,[status(thm)],[fact_220_left__distrib__number__of]) ).
fof(f_239_2,plain,
! [U_643,U_642,U_641] : times_times_int(plus_plus_int(U_643,U_642),number_number_of_int(U_641)) = plus_plus_int(times_times_int(U_643,number_number_of_int(U_641)),times_times_int(U_642,number_number_of_int(U_641))),
inference(variable_rename,[status(thm)],[f_239_1]) ).
fof(f_239_3,plain,
! [U_641,U_642,U_643] : times_times_int(plus_plus_int(U_643,U_642),number_number_of_int(U_641)) = plus_plus_int(times_times_int(U_643,number_number_of_int(U_641)),times_times_int(U_642,number_number_of_int(U_641))),
inference(definitional_conversion,[status(esa)],[f_239_2]) ).
cnf(f_239_4,plain,
times_times_int(plus_plus_int(U_643,U_642),number_number_of_int(U_641)) = plus_plus_int(times_times_int(U_643,number_number_of_int(U_641)),times_times_int(U_642,number_number_of_int(U_641))),
inference(clausify,[status(thm)],[f_239_3]) ).
fof(f_240_1,plain,
! [V_11,B_10,C_3] : times_times_real(number267125858f_real(V_11),plus_plus_real(B_10,C_3)) = plus_plus_real(times_times_real(number267125858f_real(V_11),B_10),times_times_real(number267125858f_real(V_11),C_3)),
inference(fof_nnf,[status(thm)],[fact_221_right__distrib__number__of]) ).
fof(f_240_2,plain,
! [U_646,U_645,U_644] : times_times_real(number267125858f_real(U_646),plus_plus_real(U_645,U_644)) = plus_plus_real(times_times_real(number267125858f_real(U_646),U_645),times_times_real(number267125858f_real(U_646),U_644)),
inference(variable_rename,[status(thm)],[f_240_1]) ).
fof(f_240_3,plain,
! [U_644,U_645,U_646] : times_times_real(number267125858f_real(U_646),plus_plus_real(U_645,U_644)) = plus_plus_real(times_times_real(number267125858f_real(U_646),U_645),times_times_real(number267125858f_real(U_646),U_644)),
inference(definitional_conversion,[status(esa)],[f_240_2]) ).
cnf(f_240_4,plain,
times_times_real(number267125858f_real(U_646),plus_plus_real(U_645,U_644)) = plus_plus_real(times_times_real(number267125858f_real(U_646),U_645),times_times_real(number267125858f_real(U_646),U_644)),
inference(clausify,[status(thm)],[f_240_3]) ).
fof(f_241_1,plain,
! [V_11,B_10,C_3] : times_times_nat(number_number_of_nat(V_11),plus_plus_nat(B_10,C_3)) = plus_plus_nat(times_times_nat(number_number_of_nat(V_11),B_10),times_times_nat(number_number_of_nat(V_11),C_3)),
inference(fof_nnf,[status(thm)],[fact_222_right__distrib__number__of]) ).
fof(f_241_2,plain,
! [U_649,U_648,U_647] : times_times_nat(number_number_of_nat(U_649),plus_plus_nat(U_648,U_647)) = plus_plus_nat(times_times_nat(number_number_of_nat(U_649),U_648),times_times_nat(number_number_of_nat(U_649),U_647)),
inference(variable_rename,[status(thm)],[f_241_1]) ).
fof(f_241_3,plain,
! [U_647,U_648,U_649] : times_times_nat(number_number_of_nat(U_649),plus_plus_nat(U_648,U_647)) = plus_plus_nat(times_times_nat(number_number_of_nat(U_649),U_648),times_times_nat(number_number_of_nat(U_649),U_647)),
inference(definitional_conversion,[status(esa)],[f_241_2]) ).
cnf(f_241_4,plain,
times_times_nat(number_number_of_nat(U_649),plus_plus_nat(U_648,U_647)) = plus_plus_nat(times_times_nat(number_number_of_nat(U_649),U_648),times_times_nat(number_number_of_nat(U_649),U_647)),
inference(clausify,[status(thm)],[f_241_3]) ).
fof(f_242_1,plain,
! [V_11,B_10,C_3] : times_times_int(number_number_of_int(V_11),plus_plus_int(B_10,C_3)) = plus_plus_int(times_times_int(number_number_of_int(V_11),B_10),times_times_int(number_number_of_int(V_11),C_3)),
inference(fof_nnf,[status(thm)],[fact_223_right__distrib__number__of]) ).
fof(f_242_2,plain,
! [U_652,U_651,U_650] : times_times_int(number_number_of_int(U_652),plus_plus_int(U_651,U_650)) = plus_plus_int(times_times_int(number_number_of_int(U_652),U_651),times_times_int(number_number_of_int(U_652),U_650)),
inference(variable_rename,[status(thm)],[f_242_1]) ).
fof(f_242_3,plain,
! [U_650,U_651,U_652] : times_times_int(number_number_of_int(U_652),plus_plus_int(U_651,U_650)) = plus_plus_int(times_times_int(number_number_of_int(U_652),U_651),times_times_int(number_number_of_int(U_652),U_650)),
inference(definitional_conversion,[status(esa)],[f_242_2]) ).
cnf(f_242_4,plain,
times_times_int(number_number_of_int(U_652),plus_plus_int(U_651,U_650)) = plus_plus_int(times_times_int(number_number_of_int(U_652),U_651),times_times_int(number_number_of_int(U_652),U_650)),
inference(clausify,[status(thm)],[f_242_3]) ).
fof(f_243_1,plain,
! [A_43,M_11] : plus_plus_real(times_times_real(A_43,M_11),M_11) = times_times_real(plus_plus_real(A_43,one_one_real),M_11),
inference(fof_nnf,[status(thm)],[fact_224_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J]) ).
fof(f_243_2,plain,
! [U_654,U_653] : plus_plus_real(times_times_real(U_654,U_653),U_653) = times_times_real(plus_plus_real(U_654,one_one_real),U_653),
inference(variable_rename,[status(thm)],[f_243_1]) ).
fof(f_243_3,plain,
! [U_653,U_654] : plus_plus_real(times_times_real(U_654,U_653),U_653) = times_times_real(plus_plus_real(U_654,one_one_real),U_653),
inference(definitional_conversion,[status(esa)],[f_243_2]) ).
cnf(f_243_4,plain,
plus_plus_real(times_times_real(U_654,U_653),U_653) = times_times_real(plus_plus_real(U_654,one_one_real),U_653),
inference(clausify,[status(thm)],[f_243_3]) ).
fof(f_244_1,plain,
! [A_43,M_11] : plus_plus_nat(times_times_nat(A_43,M_11),M_11) = times_times_nat(plus_plus_nat(A_43,one_one_nat),M_11),
inference(fof_nnf,[status(thm)],[fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J]) ).
fof(f_244_2,plain,
! [U_656,U_655] : plus_plus_nat(times_times_nat(U_656,U_655),U_655) = times_times_nat(plus_plus_nat(U_656,one_one_nat),U_655),
inference(variable_rename,[status(thm)],[f_244_1]) ).
fof(f_244_3,plain,
! [U_655,U_656] : plus_plus_nat(times_times_nat(U_656,U_655),U_655) = times_times_nat(plus_plus_nat(U_656,one_one_nat),U_655),
inference(definitional_conversion,[status(esa)],[f_244_2]) ).
cnf(f_244_4,plain,
plus_plus_nat(times_times_nat(U_656,U_655),U_655) = times_times_nat(plus_plus_nat(U_656,one_one_nat),U_655),
inference(clausify,[status(thm)],[f_244_3]) ).
fof(f_245_1,plain,
! [A_43,M_11] : plus_plus_int(times_times_int(A_43,M_11),M_11) = times_times_int(plus_plus_int(A_43,one_one_int),M_11),
inference(fof_nnf,[status(thm)],[fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J]) ).
fof(f_245_2,plain,
! [U_658,U_657] : plus_plus_int(times_times_int(U_658,U_657),U_657) = times_times_int(plus_plus_int(U_658,one_one_int),U_657),
inference(variable_rename,[status(thm)],[f_245_1]) ).
fof(f_245_3,plain,
! [U_657,U_658] : plus_plus_int(times_times_int(U_658,U_657),U_657) = times_times_int(plus_plus_int(U_658,one_one_int),U_657),
inference(definitional_conversion,[status(esa)],[f_245_2]) ).
cnf(f_245_4,plain,
plus_plus_int(times_times_int(U_658,U_657),U_657) = times_times_int(plus_plus_int(U_658,one_one_int),U_657),
inference(clausify,[status(thm)],[f_245_3]) ).
fof(f_246_1,plain,
! [M_10,A_42] : plus_plus_real(M_10,times_times_real(A_42,M_10)) = times_times_real(plus_plus_real(A_42,one_one_real),M_10),
inference(fof_nnf,[status(thm)],[fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J]) ).
fof(f_246_2,plain,
! [U_660,U_659] : plus_plus_real(U_660,times_times_real(U_659,U_660)) = times_times_real(plus_plus_real(U_659,one_one_real),U_660),
inference(variable_rename,[status(thm)],[f_246_1]) ).
fof(f_246_3,plain,
! [U_659,U_660] : plus_plus_real(U_660,times_times_real(U_659,U_660)) = times_times_real(plus_plus_real(U_659,one_one_real),U_660),
inference(definitional_conversion,[status(esa)],[f_246_2]) ).
cnf(f_246_4,plain,
plus_plus_real(U_660,times_times_real(U_659,U_660)) = times_times_real(plus_plus_real(U_659,one_one_real),U_660),
inference(clausify,[status(thm)],[f_246_3]) ).
fof(f_247_1,plain,
! [M_10,A_42] : plus_plus_nat(M_10,times_times_nat(A_42,M_10)) = times_times_nat(plus_plus_nat(A_42,one_one_nat),M_10),
inference(fof_nnf,[status(thm)],[fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J]) ).
fof(f_247_2,plain,
! [U_662,U_661] : plus_plus_nat(U_662,times_times_nat(U_661,U_662)) = times_times_nat(plus_plus_nat(U_661,one_one_nat),U_662),
inference(variable_rename,[status(thm)],[f_247_1]) ).
fof(f_247_3,plain,
! [U_661,U_662] : plus_plus_nat(U_662,times_times_nat(U_661,U_662)) = times_times_nat(plus_plus_nat(U_661,one_one_nat),U_662),
inference(definitional_conversion,[status(esa)],[f_247_2]) ).
cnf(f_247_4,plain,
plus_plus_nat(U_662,times_times_nat(U_661,U_662)) = times_times_nat(plus_plus_nat(U_661,one_one_nat),U_662),
inference(clausify,[status(thm)],[f_247_3]) ).
fof(f_248_1,plain,
! [M_10,A_42] : plus_plus_int(M_10,times_times_int(A_42,M_10)) = times_times_int(plus_plus_int(A_42,one_one_int),M_10),
inference(fof_nnf,[status(thm)],[fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J]) ).
fof(f_248_2,plain,
! [U_664,U_663] : plus_plus_int(U_664,times_times_int(U_663,U_664)) = times_times_int(plus_plus_int(U_663,one_one_int),U_664),
inference(variable_rename,[status(thm)],[f_248_1]) ).
fof(f_248_3,plain,
! [U_663,U_664] : plus_plus_int(U_664,times_times_int(U_663,U_664)) = times_times_int(plus_plus_int(U_663,one_one_int),U_664),
inference(definitional_conversion,[status(esa)],[f_248_2]) ).
cnf(f_248_4,plain,
plus_plus_int(U_664,times_times_int(U_663,U_664)) = times_times_int(plus_plus_int(U_663,one_one_int),U_664),
inference(clausify,[status(thm)],[f_248_3]) ).
fof(f_249_1,plain,
! [M_9] : plus_plus_real(M_9,M_9) = times_times_real(plus_plus_real(one_one_real,one_one_real),M_9),
inference(fof_nnf,[status(thm)],[fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).
fof(f_249_2,plain,
! [U_665] : plus_plus_real(U_665,U_665) = times_times_real(plus_plus_real(one_one_real,one_one_real),U_665),
inference(variable_rename,[status(thm)],[f_249_1]) ).
fof(f_249_3,plain,
! [U_665] : plus_plus_real(U_665,U_665) = times_times_real(plus_plus_real(one_one_real,one_one_real),U_665),
inference(definitional_conversion,[status(esa)],[f_249_2]) ).
cnf(f_249_4,plain,
plus_plus_real(U_665,U_665) = times_times_real(plus_plus_real(one_one_real,one_one_real),U_665),
inference(clausify,[status(thm)],[f_249_3]) ).
fof(f_250_1,plain,
! [M_9] : plus_plus_nat(M_9,M_9) = times_times_nat(plus_plus_nat(one_one_nat,one_one_nat),M_9),
inference(fof_nnf,[status(thm)],[fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).
fof(f_250_2,plain,
! [U_666] : plus_plus_nat(U_666,U_666) = times_times_nat(plus_plus_nat(one_one_nat,one_one_nat),U_666),
inference(variable_rename,[status(thm)],[f_250_1]) ).
fof(f_250_3,plain,
! [U_666] : plus_plus_nat(U_666,U_666) = times_times_nat(plus_plus_nat(one_one_nat,one_one_nat),U_666),
inference(definitional_conversion,[status(esa)],[f_250_2]) ).
cnf(f_250_4,plain,
plus_plus_nat(U_666,U_666) = times_times_nat(plus_plus_nat(one_one_nat,one_one_nat),U_666),
inference(clausify,[status(thm)],[f_250_3]) ).
fof(f_251_1,plain,
! [M_9] : plus_plus_int(M_9,M_9) = times_times_int(plus_plus_int(one_one_int,one_one_int),M_9),
inference(fof_nnf,[status(thm)],[fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).
fof(f_251_2,plain,
! [U_667] : plus_plus_int(U_667,U_667) = times_times_int(plus_plus_int(one_one_int,one_one_int),U_667),
inference(variable_rename,[status(thm)],[f_251_1]) ).
fof(f_251_3,plain,
! [U_667] : plus_plus_int(U_667,U_667) = times_times_int(plus_plus_int(one_one_int,one_one_int),U_667),
inference(definitional_conversion,[status(esa)],[f_251_2]) ).
cnf(f_251_4,plain,
plus_plus_int(U_667,U_667) = times_times_int(plus_plus_int(one_one_int,one_one_int),U_667),
inference(clausify,[status(thm)],[f_251_3]) ).
fof(f_252_1,plain,
! [A_41] : plus_plus_real(number267125858f_real(pls),A_41) = A_41,
inference(fof_nnf,[status(thm)],[fact_233_add__numeral__0]) ).
fof(f_252_2,plain,
! [U_668] : plus_plus_real(number267125858f_real(pls),U_668) = U_668,
inference(variable_rename,[status(thm)],[f_252_1]) ).
fof(f_252_3,plain,
! [U_668] : plus_plus_real(number267125858f_real(pls),U_668) = U_668,
inference(definitional_conversion,[status(esa)],[f_252_2]) ).
cnf(f_252_4,plain,
plus_plus_real(number267125858f_real(pls),U_668) = U_668,
inference(clausify,[status(thm)],[f_252_3]) ).
fof(f_253_1,plain,
! [A_41] :
( plus_plus_int(number_number_of_int(pls),A_41) = A_41
| ~ is_int(A_41) ),
inference(fof_nnf,[status(thm)],[fact_234_add__numeral__0]) ).
fof(f_253_2,plain,
! [U_669] :
( plus_plus_int(number_number_of_int(pls),U_669) = U_669
| ~ is_int(U_669) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
fof(f_253_3,plain,
! [U_669] :
( plus_plus_int(number_number_of_int(pls),U_669) = U_669
| ~ is_int(U_669) ),
inference(definitional_conversion,[status(esa)],[f_253_2]) ).
cnf(f_253_4,plain,
( plus_plus_int(number_number_of_int(pls),U_669) = U_669
| ~ is_int(U_669) ),
inference(clausify,[status(thm)],[f_253_3]) ).
fof(f_254_1,plain,
! [A_40] : plus_plus_real(A_40,number267125858f_real(pls)) = A_40,
inference(fof_nnf,[status(thm)],[fact_235_add__numeral__0__right]) ).
fof(f_254_2,plain,
! [U_670] : plus_plus_real(U_670,number267125858f_real(pls)) = U_670,
inference(variable_rename,[status(thm)],[f_254_1]) ).
fof(f_254_3,plain,
! [U_670] : plus_plus_real(U_670,number267125858f_real(pls)) = U_670,
inference(definitional_conversion,[status(esa)],[f_254_2]) ).
cnf(f_254_4,plain,
plus_plus_real(U_670,number267125858f_real(pls)) = U_670,
inference(clausify,[status(thm)],[f_254_3]) ).
fof(f_255_1,plain,
! [A_40] :
( plus_plus_int(A_40,number_number_of_int(pls)) = A_40
| ~ is_int(A_40) ),
inference(fof_nnf,[status(thm)],[fact_236_add__numeral__0__right]) ).
fof(f_255_2,plain,
! [U_671] :
( plus_plus_int(U_671,number_number_of_int(pls)) = U_671
| ~ is_int(U_671) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
fof(f_255_3,plain,
! [U_671] :
( plus_plus_int(U_671,number_number_of_int(pls)) = U_671
| ~ is_int(U_671) ),
inference(definitional_conversion,[status(esa)],[f_255_2]) ).
cnf(f_255_4,plain,
( plus_plus_int(U_671,number_number_of_int(pls)) = U_671
| ~ is_int(U_671) ),
inference(clausify,[status(thm)],[f_255_3]) ).
fof(f_256_1,plain,
! [V_10,W_12,Z_7] : times_times_real(number267125858f_real(V_10),times_times_real(number267125858f_real(W_12),Z_7)) = times_times_real(number267125858f_real(times_times_int(V_10,W_12)),Z_7),
inference(fof_nnf,[status(thm)],[fact_237_mult__number__of__left]) ).
fof(f_256_2,plain,
! [U_674,U_673,U_672] : times_times_real(number267125858f_real(U_674),times_times_real(number267125858f_real(U_673),U_672)) = times_times_real(number267125858f_real(times_times_int(U_674,U_673)),U_672),
inference(variable_rename,[status(thm)],[f_256_1]) ).
fof(f_256_3,plain,
! [U_672,U_673,U_674] : times_times_real(number267125858f_real(U_674),times_times_real(number267125858f_real(U_673),U_672)) = times_times_real(number267125858f_real(times_times_int(U_674,U_673)),U_672),
inference(definitional_conversion,[status(esa)],[f_256_2]) ).
cnf(f_256_4,plain,
times_times_real(number267125858f_real(U_674),times_times_real(number267125858f_real(U_673),U_672)) = times_times_real(number267125858f_real(times_times_int(U_674,U_673)),U_672),
inference(clausify,[status(thm)],[f_256_3]) ).
fof(f_257_1,plain,
! [V_10,W_12,Z_7] : times_times_int(number_number_of_int(V_10),times_times_int(number_number_of_int(W_12),Z_7)) = times_times_int(number_number_of_int(times_times_int(V_10,W_12)),Z_7),
inference(fof_nnf,[status(thm)],[fact_238_mult__number__of__left]) ).
fof(f_257_2,plain,
! [U_677,U_676,U_675] : times_times_int(number_number_of_int(U_677),times_times_int(number_number_of_int(U_676),U_675)) = times_times_int(number_number_of_int(times_times_int(U_677,U_676)),U_675),
inference(variable_rename,[status(thm)],[f_257_1]) ).
fof(f_257_3,plain,
! [U_675,U_676,U_677] : times_times_int(number_number_of_int(U_677),times_times_int(number_number_of_int(U_676),U_675)) = times_times_int(number_number_of_int(times_times_int(U_677,U_676)),U_675),
inference(definitional_conversion,[status(esa)],[f_257_2]) ).
cnf(f_257_4,plain,
times_times_int(number_number_of_int(U_677),times_times_int(number_number_of_int(U_676),U_675)) = times_times_int(number_number_of_int(times_times_int(U_677,U_676)),U_675),
inference(clausify,[status(thm)],[f_257_3]) ).
fof(f_258_1,plain,
! [V_9,W_11] : times_times_real(number267125858f_real(V_9),number267125858f_real(W_11)) = number267125858f_real(times_times_int(V_9,W_11)),
inference(fof_nnf,[status(thm)],[fact_239_arith__simps_I32_J]) ).
fof(f_258_2,plain,
! [U_679,U_678] : times_times_real(number267125858f_real(U_679),number267125858f_real(U_678)) = number267125858f_real(times_times_int(U_679,U_678)),
inference(variable_rename,[status(thm)],[f_258_1]) ).
fof(f_258_3,plain,
! [U_679,U_678] : times_times_real(number267125858f_real(U_679),number267125858f_real(U_678)) = number267125858f_real(times_times_int(U_679,U_678)),
inference(definitional_conversion,[status(esa)],[f_258_2]) ).
cnf(f_258_4,plain,
times_times_real(number267125858f_real(U_679),number267125858f_real(U_678)) = number267125858f_real(times_times_int(U_679,U_678)),
inference(clausify,[status(thm)],[f_258_3]) ).
fof(f_259_1,plain,
! [V_9,W_11] : times_times_int(number_number_of_int(V_9),number_number_of_int(W_11)) = number_number_of_int(times_times_int(V_9,W_11)),
inference(fof_nnf,[status(thm)],[fact_240_arith__simps_I32_J]) ).
fof(f_259_2,plain,
! [U_681,U_680] : times_times_int(number_number_of_int(U_681),number_number_of_int(U_680)) = number_number_of_int(times_times_int(U_681,U_680)),
inference(variable_rename,[status(thm)],[f_259_1]) ).
fof(f_259_3,plain,
! [U_680,U_681] : times_times_int(number_number_of_int(U_681),number_number_of_int(U_680)) = number_number_of_int(times_times_int(U_681,U_680)),
inference(definitional_conversion,[status(esa)],[f_259_2]) ).
cnf(f_259_4,plain,
times_times_int(number_number_of_int(U_681),number_number_of_int(U_680)) = number_number_of_int(times_times_int(U_681,U_680)),
inference(clausify,[status(thm)],[f_259_3]) ).
fof(f_260_1,plain,
! [V_8,W_10] : number267125858f_real(times_times_int(V_8,W_10)) = times_times_real(number267125858f_real(V_8),number267125858f_real(W_10)),
inference(fof_nnf,[status(thm)],[fact_241_number__of__mult]) ).
fof(f_260_2,plain,
! [U_683,U_682] : number267125858f_real(times_times_int(U_683,U_682)) = times_times_real(number267125858f_real(U_683),number267125858f_real(U_682)),
inference(variable_rename,[status(thm)],[f_260_1]) ).
fof(f_260_3,plain,
! [U_682,U_683] : number267125858f_real(times_times_int(U_683,U_682)) = times_times_real(number267125858f_real(U_683),number267125858f_real(U_682)),
inference(definitional_conversion,[status(esa)],[f_260_2]) ).
cnf(f_260_4,plain,
number267125858f_real(times_times_int(U_683,U_682)) = times_times_real(number267125858f_real(U_683),number267125858f_real(U_682)),
inference(clausify,[status(thm)],[f_260_3]) ).
fof(f_261_1,plain,
! [V_8,W_10] : number_number_of_int(times_times_int(V_8,W_10)) = times_times_int(number_number_of_int(V_8),number_number_of_int(W_10)),
inference(fof_nnf,[status(thm)],[fact_242_number__of__mult]) ).
fof(f_261_2,plain,
! [U_685,U_684] : number_number_of_int(times_times_int(U_685,U_684)) = times_times_int(number_number_of_int(U_685),number_number_of_int(U_684)),
inference(variable_rename,[status(thm)],[f_261_1]) ).
fof(f_261_3,plain,
! [U_684,U_685] : number_number_of_int(times_times_int(U_685,U_684)) = times_times_int(number_number_of_int(U_685),number_number_of_int(U_684)),
inference(definitional_conversion,[status(esa)],[f_261_2]) ).
cnf(f_261_4,plain,
number_number_of_int(times_times_int(U_685,U_684)) = times_times_int(number_number_of_int(U_685),number_number_of_int(U_684)),
inference(clausify,[status(thm)],[f_261_3]) ).
fof(f_262_1,plain,
! [V_7,W_9,Z_6] : plus_plus_real(number267125858f_real(V_7),plus_plus_real(number267125858f_real(W_9),Z_6)) = plus_plus_real(number267125858f_real(plus_plus_int(V_7,W_9)),Z_6),
inference(fof_nnf,[status(thm)],[fact_243_add__number__of__left]) ).
fof(f_262_2,plain,
! [U_688,U_687,U_686] : plus_plus_real(number267125858f_real(U_688),plus_plus_real(number267125858f_real(U_687),U_686)) = plus_plus_real(number267125858f_real(plus_plus_int(U_688,U_687)),U_686),
inference(variable_rename,[status(thm)],[f_262_1]) ).
fof(f_262_3,plain,
! [U_686,U_687,U_688] : plus_plus_real(number267125858f_real(U_688),plus_plus_real(number267125858f_real(U_687),U_686)) = plus_plus_real(number267125858f_real(plus_plus_int(U_688,U_687)),U_686),
inference(definitional_conversion,[status(esa)],[f_262_2]) ).
cnf(f_262_4,plain,
plus_plus_real(number267125858f_real(U_688),plus_plus_real(number267125858f_real(U_687),U_686)) = plus_plus_real(number267125858f_real(plus_plus_int(U_688,U_687)),U_686),
inference(clausify,[status(thm)],[f_262_3]) ).
fof(f_263_1,plain,
! [V_7,W_9,Z_6] : plus_plus_int(number_number_of_int(V_7),plus_plus_int(number_number_of_int(W_9),Z_6)) = plus_plus_int(number_number_of_int(plus_plus_int(V_7,W_9)),Z_6),
inference(fof_nnf,[status(thm)],[fact_244_add__number__of__left]) ).
fof(f_263_2,plain,
! [U_691,U_690,U_689] : plus_plus_int(number_number_of_int(U_691),plus_plus_int(number_number_of_int(U_690),U_689)) = plus_plus_int(number_number_of_int(plus_plus_int(U_691,U_690)),U_689),
inference(variable_rename,[status(thm)],[f_263_1]) ).
fof(f_263_3,plain,
! [U_689,U_690,U_691] : plus_plus_int(number_number_of_int(U_691),plus_plus_int(number_number_of_int(U_690),U_689)) = plus_plus_int(number_number_of_int(plus_plus_int(U_691,U_690)),U_689),
inference(definitional_conversion,[status(esa)],[f_263_2]) ).
cnf(f_263_4,plain,
plus_plus_int(number_number_of_int(U_691),plus_plus_int(number_number_of_int(U_690),U_689)) = plus_plus_int(number_number_of_int(plus_plus_int(U_691,U_690)),U_689),
inference(clausify,[status(thm)],[f_263_3]) ).
fof(f_264_1,plain,
! [V_6,W_8] : plus_plus_real(number267125858f_real(V_6),number267125858f_real(W_8)) = number267125858f_real(plus_plus_int(V_6,W_8)),
inference(fof_nnf,[status(thm)],[fact_245_add__number__of__eq]) ).
fof(f_264_2,plain,
! [U_693,U_692] : plus_plus_real(number267125858f_real(U_693),number267125858f_real(U_692)) = number267125858f_real(plus_plus_int(U_693,U_692)),
inference(variable_rename,[status(thm)],[f_264_1]) ).
fof(f_264_3,plain,
! [U_692,U_693] : plus_plus_real(number267125858f_real(U_693),number267125858f_real(U_692)) = number267125858f_real(plus_plus_int(U_693,U_692)),
inference(definitional_conversion,[status(esa)],[f_264_2]) ).
cnf(f_264_4,plain,
plus_plus_real(number267125858f_real(U_693),number267125858f_real(U_692)) = number267125858f_real(plus_plus_int(U_693,U_692)),
inference(clausify,[status(thm)],[f_264_3]) ).
fof(f_265_1,plain,
! [V_6,W_8] : plus_plus_int(number_number_of_int(V_6),number_number_of_int(W_8)) = number_number_of_int(plus_plus_int(V_6,W_8)),
inference(fof_nnf,[status(thm)],[fact_246_add__number__of__eq]) ).
fof(f_265_2,plain,
! [U_695,U_694] : plus_plus_int(number_number_of_int(U_695),number_number_of_int(U_694)) = number_number_of_int(plus_plus_int(U_695,U_694)),
inference(variable_rename,[status(thm)],[f_265_1]) ).
fof(f_265_3,plain,
! [U_694,U_695] : plus_plus_int(number_number_of_int(U_695),number_number_of_int(U_694)) = number_number_of_int(plus_plus_int(U_695,U_694)),
inference(definitional_conversion,[status(esa)],[f_265_2]) ).
cnf(f_265_4,plain,
plus_plus_int(number_number_of_int(U_695),number_number_of_int(U_694)) = number_number_of_int(plus_plus_int(U_695,U_694)),
inference(clausify,[status(thm)],[f_265_3]) ).
fof(f_266_1,plain,
! [V_5,W_7] : number267125858f_real(plus_plus_int(V_5,W_7)) = plus_plus_real(number267125858f_real(V_5),number267125858f_real(W_7)),
inference(fof_nnf,[status(thm)],[fact_247_number__of__add]) ).
fof(f_266_2,plain,
! [U_697,U_696] : number267125858f_real(plus_plus_int(U_697,U_696)) = plus_plus_real(number267125858f_real(U_697),number267125858f_real(U_696)),
inference(variable_rename,[status(thm)],[f_266_1]) ).
fof(f_266_3,plain,
! [U_696,U_697] : number267125858f_real(plus_plus_int(U_697,U_696)) = plus_plus_real(number267125858f_real(U_697),number267125858f_real(U_696)),
inference(definitional_conversion,[status(esa)],[f_266_2]) ).
cnf(f_266_4,plain,
number267125858f_real(plus_plus_int(U_697,U_696)) = plus_plus_real(number267125858f_real(U_697),number267125858f_real(U_696)),
inference(clausify,[status(thm)],[f_266_3]) ).
fof(f_267_1,plain,
! [V_5,W_7] : number_number_of_int(plus_plus_int(V_5,W_7)) = plus_plus_int(number_number_of_int(V_5),number_number_of_int(W_7)),
inference(fof_nnf,[status(thm)],[fact_248_number__of__add]) ).
fof(f_267_2,plain,
! [U_699,U_698] : number_number_of_int(plus_plus_int(U_699,U_698)) = plus_plus_int(number_number_of_int(U_699),number_number_of_int(U_698)),
inference(variable_rename,[status(thm)],[f_267_1]) ).
fof(f_267_3,plain,
! [U_698,U_699] : number_number_of_int(plus_plus_int(U_699,U_698)) = plus_plus_int(number_number_of_int(U_699),number_number_of_int(U_698)),
inference(definitional_conversion,[status(esa)],[f_267_2]) ).
cnf(f_267_4,plain,
number_number_of_int(plus_plus_int(U_699,U_698)) = plus_plus_int(number_number_of_int(U_699),number_number_of_int(U_698)),
inference(clausify,[status(thm)],[f_267_3]) ).
fof(f_268_1,plain,
! [K,L] : plus_plus_int(bit1(K),bit0(L)) = bit1(plus_plus_int(K,L)),
inference(fof_nnf,[status(thm)],[fact_249_add__Bit1__Bit0]) ).
fof(f_268_2,plain,
! [U_701,U_700] : plus_plus_int(bit1(U_701),bit0(U_700)) = bit1(plus_plus_int(U_701,U_700)),
inference(variable_rename,[status(thm)],[f_268_1]) ).
fof(f_268_3,plain,
! [U_700,U_701] : plus_plus_int(bit1(U_701),bit0(U_700)) = bit1(plus_plus_int(U_701,U_700)),
inference(definitional_conversion,[status(esa)],[f_268_2]) ).
cnf(f_268_4,plain,
plus_plus_int(bit1(U_701),bit0(U_700)) = bit1(plus_plus_int(U_701,U_700)),
inference(clausify,[status(thm)],[f_268_3]) ).
fof(f_269_1,plain,
! [K,L] : plus_plus_int(bit0(K),bit1(L)) = bit1(plus_plus_int(K,L)),
inference(fof_nnf,[status(thm)],[fact_250_add__Bit0__Bit1]) ).
fof(f_269_2,plain,
! [U_703,U_702] : plus_plus_int(bit0(U_703),bit1(U_702)) = bit1(plus_plus_int(U_703,U_702)),
inference(variable_rename,[status(thm)],[f_269_1]) ).
fof(f_269_3,plain,
! [U_702,U_703] : plus_plus_int(bit0(U_703),bit1(U_702)) = bit1(plus_plus_int(U_703,U_702)),
inference(definitional_conversion,[status(esa)],[f_269_2]) ).
cnf(f_269_4,plain,
plus_plus_int(bit0(U_703),bit1(U_702)) = bit1(plus_plus_int(U_703,U_702)),
inference(clausify,[status(thm)],[f_269_3]) ).
fof(f_270_1,plain,
! [K] : bit1(K) = plus_plus_int(plus_plus_int(one_one_int,K),K),
inference(fof_nnf,[status(thm)],[fact_251_Bit1__def]) ).
fof(f_270_2,plain,
! [U_704] : bit1(U_704) = plus_plus_int(plus_plus_int(one_one_int,U_704),U_704),
inference(variable_rename,[status(thm)],[f_270_1]) ).
fof(f_270_3,plain,
! [U_704] : bit1(U_704) = plus_plus_int(plus_plus_int(one_one_int,U_704),U_704),
inference(definitional_conversion,[status(esa)],[f_270_2]) ).
cnf(f_270_4,plain,
bit1(U_704) = plus_plus_int(plus_plus_int(one_one_int,U_704),U_704),
inference(clausify,[status(thm)],[f_270_3]) ).
fof(f_271_1,plain,
! [W_6] : number267125858f_real(bit1(W_6)) = plus_plus_real(plus_plus_real(one_one_real,number267125858f_real(W_6)),number267125858f_real(W_6)),
inference(fof_nnf,[status(thm)],[fact_252_number__of__Bit1]) ).
fof(f_271_2,plain,
! [U_705] : number267125858f_real(bit1(U_705)) = plus_plus_real(plus_plus_real(one_one_real,number267125858f_real(U_705)),number267125858f_real(U_705)),
inference(variable_rename,[status(thm)],[f_271_1]) ).
fof(f_271_3,plain,
! [U_705] : number267125858f_real(bit1(U_705)) = plus_plus_real(plus_plus_real(one_one_real,number267125858f_real(U_705)),number267125858f_real(U_705)),
inference(definitional_conversion,[status(esa)],[f_271_2]) ).
cnf(f_271_4,plain,
number267125858f_real(bit1(U_705)) = plus_plus_real(plus_plus_real(one_one_real,number267125858f_real(U_705)),number267125858f_real(U_705)),
inference(clausify,[status(thm)],[f_271_3]) ).
fof(f_272_1,plain,
! [W_6] : number_number_of_int(bit1(W_6)) = plus_plus_int(plus_plus_int(one_one_int,number_number_of_int(W_6)),number_number_of_int(W_6)),
inference(fof_nnf,[status(thm)],[fact_253_number__of__Bit1]) ).
fof(f_272_2,plain,
! [U_706] : number_number_of_int(bit1(U_706)) = plus_plus_int(plus_plus_int(one_one_int,number_number_of_int(U_706)),number_number_of_int(U_706)),
inference(variable_rename,[status(thm)],[f_272_1]) ).
fof(f_272_3,plain,
! [U_706] : number_number_of_int(bit1(U_706)) = plus_plus_int(plus_plus_int(one_one_int,number_number_of_int(U_706)),number_number_of_int(U_706)),
inference(definitional_conversion,[status(esa)],[f_272_2]) ).
cnf(f_272_4,plain,
number_number_of_int(bit1(U_706)) = plus_plus_int(plus_plus_int(one_one_int,number_number_of_int(U_706)),number_number_of_int(U_706)),
inference(clausify,[status(thm)],[f_272_3]) ).
fof(f_273_1,plain,
! [A_39] : times_times_real(number267125858f_real(bit1(pls)),A_39) = A_39,
inference(fof_nnf,[status(thm)],[fact_254_mult__numeral__1]) ).
fof(f_273_2,plain,
! [U_707] : times_times_real(number267125858f_real(bit1(pls)),U_707) = U_707,
inference(variable_rename,[status(thm)],[f_273_1]) ).
fof(f_273_3,plain,
! [U_707] : times_times_real(number267125858f_real(bit1(pls)),U_707) = U_707,
inference(definitional_conversion,[status(esa)],[f_273_2]) ).
cnf(f_273_4,plain,
times_times_real(number267125858f_real(bit1(pls)),U_707) = U_707,
inference(clausify,[status(thm)],[f_273_3]) ).
fof(f_274_1,plain,
! [A_39] :
( times_times_int(number_number_of_int(bit1(pls)),A_39) = A_39
| ~ is_int(A_39) ),
inference(fof_nnf,[status(thm)],[fact_255_mult__numeral__1]) ).
fof(f_274_2,plain,
! [U_708] :
( times_times_int(number_number_of_int(bit1(pls)),U_708) = U_708
| ~ is_int(U_708) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
fof(f_274_3,plain,
! [U_708] :
( times_times_int(number_number_of_int(bit1(pls)),U_708) = U_708
| ~ is_int(U_708) ),
inference(definitional_conversion,[status(esa)],[f_274_2]) ).
cnf(f_274_4,plain,
( times_times_int(number_number_of_int(bit1(pls)),U_708) = U_708
| ~ is_int(U_708) ),
inference(clausify,[status(thm)],[f_274_3]) ).
fof(f_275_1,plain,
! [A_38] : times_times_real(A_38,number267125858f_real(bit1(pls))) = A_38,
inference(fof_nnf,[status(thm)],[fact_256_mult__numeral__1__right]) ).
fof(f_275_2,plain,
! [U_709] : times_times_real(U_709,number267125858f_real(bit1(pls))) = U_709,
inference(variable_rename,[status(thm)],[f_275_1]) ).
fof(f_275_3,plain,
! [U_709] : times_times_real(U_709,number267125858f_real(bit1(pls))) = U_709,
inference(definitional_conversion,[status(esa)],[f_275_2]) ).
cnf(f_275_4,plain,
times_times_real(U_709,number267125858f_real(bit1(pls))) = U_709,
inference(clausify,[status(thm)],[f_275_3]) ).
fof(f_276_1,plain,
! [A_38] :
( times_times_int(A_38,number_number_of_int(bit1(pls))) = A_38
| ~ is_int(A_38) ),
inference(fof_nnf,[status(thm)],[fact_257_mult__numeral__1__right]) ).
fof(f_276_2,plain,
! [U_710] :
( times_times_int(U_710,number_number_of_int(bit1(pls))) = U_710
| ~ is_int(U_710) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
fof(f_276_3,plain,
! [U_710] :
( times_times_int(U_710,number_number_of_int(bit1(pls))) = U_710
| ~ is_int(U_710) ),
inference(definitional_conversion,[status(esa)],[f_276_2]) ).
cnf(f_276_4,plain,
( times_times_int(U_710,number_number_of_int(bit1(pls))) = U_710
| ~ is_int(U_710) ),
inference(clausify,[status(thm)],[f_276_3]) ).
fof(f_277_1,plain,
number267125858f_real(bit1(pls)) = one_one_real,
inference(fof_nnf,[status(thm)],[fact_258_semiring__numeral__1__eq__1]) ).
fof(f_277_2,plain,
number267125858f_real(bit1(pls)) = one_one_real,
inference(definitional_conversion,[status(esa)],[f_277_1]) ).
cnf(f_277_3,plain,
number267125858f_real(bit1(pls)) = one_one_real,
inference(clausify,[status(thm)],[f_277_2]) ).
fof(f_278_1,plain,
number_number_of_nat(bit1(pls)) = one_one_nat,
inference(fof_nnf,[status(thm)],[fact_259_semiring__numeral__1__eq__1]) ).
fof(f_278_2,plain,
number_number_of_nat(bit1(pls)) = one_one_nat,
inference(definitional_conversion,[status(esa)],[f_278_1]) ).
cnf(f_278_3,plain,
number_number_of_nat(bit1(pls)) = one_one_nat,
inference(clausify,[status(thm)],[f_278_2]) ).
fof(f_279_1,plain,
number_number_of_int(bit1(pls)) = one_one_int,
inference(fof_nnf,[status(thm)],[fact_260_semiring__numeral__1__eq__1]) ).
fof(f_279_2,plain,
number_number_of_int(bit1(pls)) = one_one_int,
inference(definitional_conversion,[status(esa)],[f_279_1]) ).
cnf(f_279_3,plain,
number_number_of_int(bit1(pls)) = one_one_int,
inference(clausify,[status(thm)],[f_279_2]) ).
fof(f_280_1,plain,
number267125858f_real(bit1(pls)) = one_one_real,
inference(fof_nnf,[status(thm)],[fact_261_numeral__1__eq__1]) ).
fof(f_280_2,plain,
number267125858f_real(bit1(pls)) = one_one_real,
inference(definitional_conversion,[status(esa)],[f_280_1]) ).
cnf(f_280_3,plain,
number267125858f_real(bit1(pls)) = one_one_real,
inference(clausify,[status(thm)],[f_280_2]) ).
fof(f_281_1,plain,
number_number_of_int(bit1(pls)) = one_one_int,
inference(fof_nnf,[status(thm)],[fact_262_numeral__1__eq__1]) ).
fof(f_281_2,plain,
number_number_of_int(bit1(pls)) = one_one_int,
inference(definitional_conversion,[status(esa)],[f_281_1]) ).
cnf(f_281_3,plain,
number_number_of_int(bit1(pls)) = one_one_int,
inference(clausify,[status(thm)],[f_281_2]) ).
fof(f_282_1,plain,
one_one_real = number267125858f_real(bit1(pls)),
inference(fof_nnf,[status(thm)],[fact_263_semiring__norm_I110_J]) ).
fof(f_282_2,plain,
one_one_real = number267125858f_real(bit1(pls)),
inference(definitional_conversion,[status(esa)],[f_282_1]) ).
cnf(f_282_3,plain,
one_one_real = number267125858f_real(bit1(pls)),
inference(clausify,[status(thm)],[f_282_2]) ).
fof(f_283_1,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(fof_nnf,[status(thm)],[fact_264_semiring__norm_I110_J]) ).
fof(f_283_2,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(definitional_conversion,[status(esa)],[f_283_1]) ).
cnf(f_283_3,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(clausify,[status(thm)],[f_283_2]) ).
fof(f_284_1,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(fof_nnf,[status(thm)],[fact_265_one__is__num__one]) ).
fof(f_284_2,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(definitional_conversion,[status(esa)],[f_284_1]) ).
cnf(f_284_3,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(clausify,[status(thm)],[f_284_2]) ).
fof(f_285_1,plain,
! [K,L] : times_times_int(bit1(K),L) = plus_plus_int(bit0(times_times_int(K,L)),L),
inference(fof_nnf,[status(thm)],[fact_266_mult__Bit1]) ).
fof(f_285_2,plain,
! [U_712,U_711] : times_times_int(bit1(U_712),U_711) = plus_plus_int(bit0(times_times_int(U_712,U_711)),U_711),
inference(variable_rename,[status(thm)],[f_285_1]) ).
fof(f_285_3,plain,
! [U_711,U_712] : times_times_int(bit1(U_712),U_711) = plus_plus_int(bit0(times_times_int(U_712,U_711)),U_711),
inference(definitional_conversion,[status(esa)],[f_285_2]) ).
cnf(f_285_4,plain,
times_times_int(bit1(U_712),U_711) = plus_plus_int(bit0(times_times_int(U_712,U_711)),U_711),
inference(clausify,[status(thm)],[f_285_3]) ).
fof(f_286_1,plain,
! [W_5] : times_times_real(plus_plus_real(one_one_real,one_one_real),number267125858f_real(W_5)) = number267125858f_real(bit0(W_5)),
inference(fof_nnf,[status(thm)],[fact_267_double__number__of__Bit0]) ).
fof(f_286_2,plain,
! [U_713] : times_times_real(plus_plus_real(one_one_real,one_one_real),number267125858f_real(U_713)) = number267125858f_real(bit0(U_713)),
inference(variable_rename,[status(thm)],[f_286_1]) ).
fof(f_286_3,plain,
! [U_713] : times_times_real(plus_plus_real(one_one_real,one_one_real),number267125858f_real(U_713)) = number267125858f_real(bit0(U_713)),
inference(definitional_conversion,[status(esa)],[f_286_2]) ).
cnf(f_286_4,plain,
times_times_real(plus_plus_real(one_one_real,one_one_real),number267125858f_real(U_713)) = number267125858f_real(bit0(U_713)),
inference(clausify,[status(thm)],[f_286_3]) ).
fof(f_287_1,plain,
! [W_5] : times_times_int(plus_plus_int(one_one_int,one_one_int),number_number_of_int(W_5)) = number_number_of_int(bit0(W_5)),
inference(fof_nnf,[status(thm)],[fact_268_double__number__of__Bit0]) ).
fof(f_287_2,plain,
! [U_714] : times_times_int(plus_plus_int(one_one_int,one_one_int),number_number_of_int(U_714)) = number_number_of_int(bit0(U_714)),
inference(variable_rename,[status(thm)],[f_287_1]) ).
fof(f_287_3,plain,
! [U_714] : times_times_int(plus_plus_int(one_one_int,one_one_int),number_number_of_int(U_714)) = number_number_of_int(bit0(U_714)),
inference(definitional_conversion,[status(esa)],[f_287_2]) ).
cnf(f_287_4,plain,
times_times_int(plus_plus_int(one_one_int,one_one_int),number_number_of_int(U_714)) = number_number_of_int(bit0(U_714)),
inference(clausify,[status(thm)],[f_287_3]) ).
fof(f_288_1,plain,
! [A_37] : power_power_nat(A_37,number_number_of_nat(bit1(bit1(pls)))) = times_times_nat(times_times_nat(A_37,A_37),A_37),
inference(fof_nnf,[status(thm)],[fact_269_power3__eq__cube]) ).
fof(f_288_2,plain,
! [U_715] : power_power_nat(U_715,number_number_of_nat(bit1(bit1(pls)))) = times_times_nat(times_times_nat(U_715,U_715),U_715),
inference(variable_rename,[status(thm)],[f_288_1]) ).
fof(f_288_3,plain,
! [U_715] : power_power_nat(U_715,number_number_of_nat(bit1(bit1(pls)))) = times_times_nat(times_times_nat(U_715,U_715),U_715),
inference(definitional_conversion,[status(esa)],[f_288_2]) ).
cnf(f_288_4,plain,
power_power_nat(U_715,number_number_of_nat(bit1(bit1(pls)))) = times_times_nat(times_times_nat(U_715,U_715),U_715),
inference(clausify,[status(thm)],[f_288_3]) ).
fof(f_289_1,plain,
! [A_37] : power_power_real(A_37,number_number_of_nat(bit1(bit1(pls)))) = times_times_real(times_times_real(A_37,A_37),A_37),
inference(fof_nnf,[status(thm)],[fact_270_power3__eq__cube]) ).
fof(f_289_2,plain,
! [U_716] : power_power_real(U_716,number_number_of_nat(bit1(bit1(pls)))) = times_times_real(times_times_real(U_716,U_716),U_716),
inference(variable_rename,[status(thm)],[f_289_1]) ).
fof(f_289_3,plain,
! [U_716] : power_power_real(U_716,number_number_of_nat(bit1(bit1(pls)))) = times_times_real(times_times_real(U_716,U_716),U_716),
inference(definitional_conversion,[status(esa)],[f_289_2]) ).
cnf(f_289_4,plain,
power_power_real(U_716,number_number_of_nat(bit1(bit1(pls)))) = times_times_real(times_times_real(U_716,U_716),U_716),
inference(clausify,[status(thm)],[f_289_3]) ).
fof(f_290_1,plain,
! [A_37] : power_power_int(A_37,number_number_of_nat(bit1(bit1(pls)))) = times_times_int(times_times_int(A_37,A_37),A_37),
inference(fof_nnf,[status(thm)],[fact_271_power3__eq__cube]) ).
fof(f_290_2,plain,
! [U_717] : power_power_int(U_717,number_number_of_nat(bit1(bit1(pls)))) = times_times_int(times_times_int(U_717,U_717),U_717),
inference(variable_rename,[status(thm)],[f_290_1]) ).
fof(f_290_3,plain,
! [U_717] : power_power_int(U_717,number_number_of_nat(bit1(bit1(pls)))) = times_times_int(times_times_int(U_717,U_717),U_717),
inference(definitional_conversion,[status(esa)],[f_290_2]) ).
cnf(f_290_4,plain,
power_power_int(U_717,number_number_of_nat(bit1(bit1(pls)))) = times_times_int(times_times_int(U_717,U_717),U_717),
inference(clausify,[status(thm)],[f_290_3]) ).
fof(f_291_1,plain,
! [X_1] : power_power_int(power_power_int(X_1,number_number_of_nat(bit0(bit1(pls)))),number_number_of_nat(bit0(bit1(pls)))) = power_power_int(X_1,number_number_of_nat(bit0(bit0(bit1(pls))))),
inference(fof_nnf,[status(thm)],[fact_272_quartic__square__square]) ).
fof(f_291_2,plain,
! [U_718] : power_power_int(power_power_int(U_718,number_number_of_nat(bit0(bit1(pls)))),number_number_of_nat(bit0(bit1(pls)))) = power_power_int(U_718,number_number_of_nat(bit0(bit0(bit1(pls))))),
inference(variable_rename,[status(thm)],[f_291_1]) ).
fof(f_291_3,plain,
! [U_718] : power_power_int(power_power_int(U_718,number_number_of_nat(bit0(bit1(pls)))),number_number_of_nat(bit0(bit1(pls)))) = power_power_int(U_718,number_number_of_nat(bit0(bit0(bit1(pls))))),
inference(definitional_conversion,[status(esa)],[f_291_2]) ).
cnf(f_291_4,plain,
power_power_int(power_power_int(U_718,number_number_of_nat(bit0(bit1(pls)))),number_number_of_nat(bit0(bit1(pls)))) = power_power_int(U_718,number_number_of_nat(bit0(bit0(bit1(pls))))),
inference(clausify,[status(thm)],[f_291_3]) ).
fof(f_292_1,plain,
! [Z_5] : times_times_real(number267125858f_real(bit0(bit1(pls))),Z_5) = plus_plus_real(Z_5,Z_5),
inference(fof_nnf,[status(thm)],[fact_273_semiring__mult__2]) ).
fof(f_292_2,plain,
! [U_719] : times_times_real(number267125858f_real(bit0(bit1(pls))),U_719) = plus_plus_real(U_719,U_719),
inference(variable_rename,[status(thm)],[f_292_1]) ).
fof(f_292_3,plain,
! [U_719] : times_times_real(number267125858f_real(bit0(bit1(pls))),U_719) = plus_plus_real(U_719,U_719),
inference(definitional_conversion,[status(esa)],[f_292_2]) ).
cnf(f_292_4,plain,
times_times_real(number267125858f_real(bit0(bit1(pls))),U_719) = plus_plus_real(U_719,U_719),
inference(clausify,[status(thm)],[f_292_3]) ).
fof(f_293_1,plain,
! [Z_5] : times_times_nat(number_number_of_nat(bit0(bit1(pls))),Z_5) = plus_plus_nat(Z_5,Z_5),
inference(fof_nnf,[status(thm)],[fact_274_semiring__mult__2]) ).
fof(f_293_2,plain,
! [U_720] : times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_720) = plus_plus_nat(U_720,U_720),
inference(variable_rename,[status(thm)],[f_293_1]) ).
fof(f_293_3,plain,
! [U_720] : times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_720) = plus_plus_nat(U_720,U_720),
inference(definitional_conversion,[status(esa)],[f_293_2]) ).
cnf(f_293_4,plain,
times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_720) = plus_plus_nat(U_720,U_720),
inference(clausify,[status(thm)],[f_293_3]) ).
fof(f_294_1,plain,
! [Z_5] : times_times_int(number_number_of_int(bit0(bit1(pls))),Z_5) = plus_plus_int(Z_5,Z_5),
inference(fof_nnf,[status(thm)],[fact_275_semiring__mult__2]) ).
fof(f_294_2,plain,
! [U_721] : times_times_int(number_number_of_int(bit0(bit1(pls))),U_721) = plus_plus_int(U_721,U_721),
inference(variable_rename,[status(thm)],[f_294_1]) ).
fof(f_294_3,plain,
! [U_721] : times_times_int(number_number_of_int(bit0(bit1(pls))),U_721) = plus_plus_int(U_721,U_721),
inference(definitional_conversion,[status(esa)],[f_294_2]) ).
cnf(f_294_4,plain,
times_times_int(number_number_of_int(bit0(bit1(pls))),U_721) = plus_plus_int(U_721,U_721),
inference(clausify,[status(thm)],[f_294_3]) ).
fof(f_295_1,plain,
! [Z_4] : times_times_real(number267125858f_real(bit0(bit1(pls))),Z_4) = plus_plus_real(Z_4,Z_4),
inference(fof_nnf,[status(thm)],[fact_276_mult__2]) ).
fof(f_295_2,plain,
! [U_722] : times_times_real(number267125858f_real(bit0(bit1(pls))),U_722) = plus_plus_real(U_722,U_722),
inference(variable_rename,[status(thm)],[f_295_1]) ).
fof(f_295_3,plain,
! [U_722] : times_times_real(number267125858f_real(bit0(bit1(pls))),U_722) = plus_plus_real(U_722,U_722),
inference(definitional_conversion,[status(esa)],[f_295_2]) ).
cnf(f_295_4,plain,
times_times_real(number267125858f_real(bit0(bit1(pls))),U_722) = plus_plus_real(U_722,U_722),
inference(clausify,[status(thm)],[f_295_3]) ).
fof(f_296_1,plain,
! [Z_4] : times_times_int(number_number_of_int(bit0(bit1(pls))),Z_4) = plus_plus_int(Z_4,Z_4),
inference(fof_nnf,[status(thm)],[fact_277_mult__2]) ).
fof(f_296_2,plain,
! [U_723] : times_times_int(number_number_of_int(bit0(bit1(pls))),U_723) = plus_plus_int(U_723,U_723),
inference(variable_rename,[status(thm)],[f_296_1]) ).
fof(f_296_3,plain,
! [U_723] : times_times_int(number_number_of_int(bit0(bit1(pls))),U_723) = plus_plus_int(U_723,U_723),
inference(definitional_conversion,[status(esa)],[f_296_2]) ).
cnf(f_296_4,plain,
times_times_int(number_number_of_int(bit0(bit1(pls))),U_723) = plus_plus_int(U_723,U_723),
inference(clausify,[status(thm)],[f_296_3]) ).
fof(f_297_1,plain,
! [Z_3] : times_times_real(Z_3,number267125858f_real(bit0(bit1(pls)))) = plus_plus_real(Z_3,Z_3),
inference(fof_nnf,[status(thm)],[fact_278_semiring__mult__2__right]) ).
fof(f_297_2,plain,
! [U_724] : times_times_real(U_724,number267125858f_real(bit0(bit1(pls)))) = plus_plus_real(U_724,U_724),
inference(variable_rename,[status(thm)],[f_297_1]) ).
fof(f_297_3,plain,
! [U_724] : times_times_real(U_724,number267125858f_real(bit0(bit1(pls)))) = plus_plus_real(U_724,U_724),
inference(definitional_conversion,[status(esa)],[f_297_2]) ).
cnf(f_297_4,plain,
times_times_real(U_724,number267125858f_real(bit0(bit1(pls)))) = plus_plus_real(U_724,U_724),
inference(clausify,[status(thm)],[f_297_3]) ).
fof(f_298_1,plain,
! [Z_3] : times_times_nat(Z_3,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(Z_3,Z_3),
inference(fof_nnf,[status(thm)],[fact_279_semiring__mult__2__right]) ).
fof(f_298_2,plain,
! [U_725] : times_times_nat(U_725,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(U_725,U_725),
inference(variable_rename,[status(thm)],[f_298_1]) ).
fof(f_298_3,plain,
! [U_725] : times_times_nat(U_725,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(U_725,U_725),
inference(definitional_conversion,[status(esa)],[f_298_2]) ).
cnf(f_298_4,plain,
times_times_nat(U_725,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(U_725,U_725),
inference(clausify,[status(thm)],[f_298_3]) ).
fof(f_299_1,plain,
! [Z_3] : times_times_int(Z_3,number_number_of_int(bit0(bit1(pls)))) = plus_plus_int(Z_3,Z_3),
inference(fof_nnf,[status(thm)],[fact_280_semiring__mult__2__right]) ).
fof(f_299_2,plain,
! [U_726] : times_times_int(U_726,number_number_of_int(bit0(bit1(pls)))) = plus_plus_int(U_726,U_726),
inference(variable_rename,[status(thm)],[f_299_1]) ).
fof(f_299_3,plain,
! [U_726] : times_times_int(U_726,number_number_of_int(bit0(bit1(pls)))) = plus_plus_int(U_726,U_726),
inference(definitional_conversion,[status(esa)],[f_299_2]) ).
cnf(f_299_4,plain,
times_times_int(U_726,number_number_of_int(bit0(bit1(pls)))) = plus_plus_int(U_726,U_726),
inference(clausify,[status(thm)],[f_299_3]) ).
fof(f_300_1,plain,
! [Z_2] : times_times_real(Z_2,number267125858f_real(bit0(bit1(pls)))) = plus_plus_real(Z_2,Z_2),
inference(fof_nnf,[status(thm)],[fact_281_mult__2__right]) ).
fof(f_300_2,plain,
! [U_727] : times_times_real(U_727,number267125858f_real(bit0(bit1(pls)))) = plus_plus_real(U_727,U_727),
inference(variable_rename,[status(thm)],[f_300_1]) ).
fof(f_300_3,plain,
! [U_727] : times_times_real(U_727,number267125858f_real(bit0(bit1(pls)))) = plus_plus_real(U_727,U_727),
inference(definitional_conversion,[status(esa)],[f_300_2]) ).
cnf(f_300_4,plain,
times_times_real(U_727,number267125858f_real(bit0(bit1(pls)))) = plus_plus_real(U_727,U_727),
inference(clausify,[status(thm)],[f_300_3]) ).
fof(f_301_1,plain,
! [Z_2] : times_times_int(Z_2,number_number_of_int(bit0(bit1(pls)))) = plus_plus_int(Z_2,Z_2),
inference(fof_nnf,[status(thm)],[fact_282_mult__2__right]) ).
fof(f_301_2,plain,
! [U_728] : times_times_int(U_728,number_number_of_int(bit0(bit1(pls)))) = plus_plus_int(U_728,U_728),
inference(variable_rename,[status(thm)],[f_301_1]) ).
fof(f_301_3,plain,
! [U_728] : times_times_int(U_728,number_number_of_int(bit0(bit1(pls)))) = plus_plus_int(U_728,U_728),
inference(definitional_conversion,[status(esa)],[f_301_2]) ).
cnf(f_301_4,plain,
times_times_int(U_728,number_number_of_int(bit0(bit1(pls)))) = plus_plus_int(U_728,U_728),
inference(clausify,[status(thm)],[f_301_3]) ).
fof(f_302_1,plain,
plus_plus_real(one_one_real,one_one_real) = number267125858f_real(bit0(bit1(pls))),
inference(fof_nnf,[status(thm)],[fact_283_semiring__one__add__one__is__two]) ).
fof(f_302_2,plain,
plus_plus_real(one_one_real,one_one_real) = number267125858f_real(bit0(bit1(pls))),
inference(definitional_conversion,[status(esa)],[f_302_1]) ).
cnf(f_302_3,plain,
plus_plus_real(one_one_real,one_one_real) = number267125858f_real(bit0(bit1(pls))),
inference(clausify,[status(thm)],[f_302_2]) ).
fof(f_303_1,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(fof_nnf,[status(thm)],[fact_284_semiring__one__add__one__is__two]) ).
fof(f_303_2,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(definitional_conversion,[status(esa)],[f_303_1]) ).
cnf(f_303_3,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(clausify,[status(thm)],[f_303_2]) ).
fof(f_304_1,plain,
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]) ).
fof(f_304_2,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
inference(definitional_conversion,[status(esa)],[f_304_1]) ).
cnf(f_304_3,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
inference(clausify,[status(thm)],[f_304_2]) ).
fof(f_305_1,plain,
ord_less_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(fof_nnf,[status(thm)],[fact_286_p0]) ).
fof(f_305_2,plain,
ord_less_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(definitional_conversion,[status(esa)],[f_305_1]) ).
cnf(f_305_3,plain,
ord_less_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(clausify,[status(thm)],[f_305_2]) ).
fof(f_306_1,plain,
dvd_dvd_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int)),
inference(fof_nnf,[status(thm)],[fact_287__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096]) ).
fof(f_306_2,plain,
dvd_dvd_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int)),
inference(definitional_conversion,[status(esa)],[f_306_1]) ).
cnf(f_306_3,plain,
dvd_dvd_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int)),
inference(clausify,[status(thm)],[f_306_2]) ).
fof(f_307_1,plain,
! [P] :
( ord_less_eq_int(number_number_of_int(bit1(bit0(bit1(pls)))),P)
| P = number_number_of_int(bit1(bit1(pls)))
| P = number_number_of_int(bit0(bit1(pls)))
| ~ zprime(P)
| ~ is_int(P) ),
inference(fof_nnf,[status(thm)],[fact_288_prime__g__5]) ).
fof(f_307_2,plain,
! [U_729] :
( ord_less_eq_int(number_number_of_int(bit1(bit0(bit1(pls)))),U_729)
| U_729 = number_number_of_int(bit1(bit1(pls)))
| U_729 = number_number_of_int(bit0(bit1(pls)))
| ~ zprime(U_729)
| ~ is_int(U_729) ),
inference(variable_rename,[status(thm)],[f_307_1]) ).
fof(f_307_3,plain,
! [U_729] :
( ord_less_eq_int(number_number_of_int(bit1(bit0(bit1(pls)))),U_729)
| U_729 = number_number_of_int(bit1(bit1(pls)))
| U_729 = number_number_of_int(bit0(bit1(pls)))
| ~ zprime(U_729)
| ~ is_int(U_729) ),
inference(definitional_conversion,[status(esa)],[f_307_2]) ).
cnf(f_307_4,plain,
( ord_less_eq_int(number_number_of_int(bit1(bit0(bit1(pls)))),U_729)
| U_729 = number_number_of_int(bit1(bit1(pls)))
| U_729 = number_number_of_int(bit0(bit1(pls)))
| ~ zprime(U_729)
| ~ is_int(U_729) ),
inference(clausify,[status(thm)],[f_307_3]) ).
fof(f_308_1,plain,
twoSqu140629262sum2sq(product_Pair_int_int(s,one_one_int)) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),
inference(fof_nnf,[status(thm)],[fact_289__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096]) ).
fof(f_308_2,plain,
twoSqu140629262sum2sq(product_Pair_int_int(s,one_one_int)) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),
inference(definitional_conversion,[status(esa)],[f_308_1]) ).
cnf(f_308_3,plain,
twoSqu140629262sum2sq(product_Pair_int_int(s,one_one_int)) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),
inference(clausify,[status(thm)],[f_308_2]) ).
fof(f_309_1,plain,
! [X_1,Y_1] : power_power_real(plus_plus_real(X_1,Y_1),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_real(plus_plus_real(power_power_real(X_1,number_number_of_nat(bit0(bit1(pls)))),power_power_real(Y_1,number_number_of_nat(bit0(bit1(pls))))),times_times_real(times_times_real(number267125858f_real(bit0(bit1(pls))),X_1),Y_1)),
inference(fof_nnf,[status(thm)],[fact_290_real__sum__squared__expand]) ).
fof(f_309_2,plain,
! [U_731,U_730] : power_power_real(plus_plus_real(U_731,U_730),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_real(plus_plus_real(power_power_real(U_731,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_730,number_number_of_nat(bit0(bit1(pls))))),times_times_real(times_times_real(number267125858f_real(bit0(bit1(pls))),U_731),U_730)),
inference(variable_rename,[status(thm)],[f_309_1]) ).
fof(f_309_3,plain,
! [U_731,U_730] : power_power_real(plus_plus_real(U_731,U_730),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_real(plus_plus_real(power_power_real(U_731,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_730,number_number_of_nat(bit0(bit1(pls))))),times_times_real(times_times_real(number267125858f_real(bit0(bit1(pls))),U_731),U_730)),
inference(definitional_conversion,[status(esa)],[f_309_2]) ).
cnf(f_309_4,plain,
power_power_real(plus_plus_real(U_731,U_730),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_real(plus_plus_real(power_power_real(U_731,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_730,number_number_of_nat(bit0(bit1(pls))))),times_times_real(times_times_real(number267125858f_real(bit0(bit1(pls))),U_731),U_730)),
inference(clausify,[status(thm)],[f_309_3]) ).
fof(f_310_1,plain,
! [X_1] : times_times_real(number267125858f_real(bit0(bit0(bit1(pls)))),power_power_real(X_1,number_number_of_nat(bit0(bit1(pls))))) = power_power_real(times_times_real(number267125858f_real(bit0(bit1(pls))),X_1),number_number_of_nat(bit0(bit1(pls)))),
inference(fof_nnf,[status(thm)],[fact_291_four__x__squared]) ).
fof(f_310_2,plain,
! [U_732] : times_times_real(number267125858f_real(bit0(bit0(bit1(pls)))),power_power_real(U_732,number_number_of_nat(bit0(bit1(pls))))) = power_power_real(times_times_real(number267125858f_real(bit0(bit1(pls))),U_732),number_number_of_nat(bit0(bit1(pls)))),
inference(variable_rename,[status(thm)],[f_310_1]) ).
fof(f_310_3,plain,
! [U_732] : times_times_real(number267125858f_real(bit0(bit0(bit1(pls)))),power_power_real(U_732,number_number_of_nat(bit0(bit1(pls))))) = power_power_real(times_times_real(number267125858f_real(bit0(bit1(pls))),U_732),number_number_of_nat(bit0(bit1(pls)))),
inference(definitional_conversion,[status(esa)],[f_310_2]) ).
cnf(f_310_4,plain,
times_times_real(number267125858f_real(bit0(bit0(bit1(pls)))),power_power_real(U_732,number_number_of_nat(bit0(bit1(pls))))) = power_power_real(times_times_real(number267125858f_real(bit0(bit1(pls))),U_732),number_number_of_nat(bit0(bit1(pls)))),
inference(clausify,[status(thm)],[f_310_3]) ).
fof(f_311_1,plain,
! [N_36,A_36] :
( ord_less_real(power_power_real(A_36,N_36),times_times_real(A_36,power_power_real(A_36,N_36)))
| ~ ord_less_real(one_one_real,A_36) ),
inference(fof_nnf,[status(thm)],[fact_292_power__less__power__Suc]) ).
fof(f_311_2,plain,
! [U_734,U_733] :
( ord_less_real(power_power_real(U_733,U_734),times_times_real(U_733,power_power_real(U_733,U_734)))
| ~ ord_less_real(one_one_real,U_733) ),
inference(variable_rename,[status(thm)],[f_311_1]) ).
fof(f_311_3,plain,
! [U_733,U_734] :
( ord_less_real(power_power_real(U_733,U_734),times_times_real(U_733,power_power_real(U_733,U_734)))
| ~ ord_less_real(one_one_real,U_733) ),
inference(definitional_conversion,[status(esa)],[f_311_2]) ).
cnf(f_311_4,plain,
( ord_less_real(power_power_real(U_733,U_734),times_times_real(U_733,power_power_real(U_733,U_734)))
| ~ ord_less_real(one_one_real,U_733) ),
inference(clausify,[status(thm)],[f_311_3]) ).
fof(f_312_1,plain,
! [N_36,A_36] :
( ord_less_nat(power_power_nat(A_36,N_36),times_times_nat(A_36,power_power_nat(A_36,N_36)))
| ~ ord_less_nat(one_one_nat,A_36) ),
inference(fof_nnf,[status(thm)],[fact_293_power__less__power__Suc]) ).
fof(f_312_2,plain,
! [U_736,U_735] :
( ord_less_nat(power_power_nat(U_735,U_736),times_times_nat(U_735,power_power_nat(U_735,U_736)))
| ~ ord_less_nat(one_one_nat,U_735) ),
inference(variable_rename,[status(thm)],[f_312_1]) ).
fof(f_312_3,plain,
! [U_735,U_736] :
( ord_less_nat(power_power_nat(U_735,U_736),times_times_nat(U_735,power_power_nat(U_735,U_736)))
| ~ ord_less_nat(one_one_nat,U_735) ),
inference(definitional_conversion,[status(esa)],[f_312_2]) ).
cnf(f_312_4,plain,
( ord_less_nat(power_power_nat(U_735,U_736),times_times_nat(U_735,power_power_nat(U_735,U_736)))
| ~ ord_less_nat(one_one_nat,U_735) ),
inference(clausify,[status(thm)],[f_312_3]) ).
fof(f_313_1,plain,
! [N_36,A_36] :
( ord_less_int(power_power_int(A_36,N_36),times_times_int(A_36,power_power_int(A_36,N_36)))
| ~ ord_less_int(one_one_int,A_36) ),
inference(fof_nnf,[status(thm)],[fact_294_power__less__power__Suc]) ).
fof(f_313_2,plain,
! [U_738,U_737] :
( ord_less_int(power_power_int(U_737,U_738),times_times_int(U_737,power_power_int(U_737,U_738)))
| ~ ord_less_int(one_one_int,U_737) ),
inference(variable_rename,[status(thm)],[f_313_1]) ).
fof(f_313_3,plain,
! [U_737,U_738] :
( ord_less_int(power_power_int(U_737,U_738),times_times_int(U_737,power_power_int(U_737,U_738)))
| ~ ord_less_int(one_one_int,U_737) ),
inference(definitional_conversion,[status(esa)],[f_313_2]) ).
cnf(f_313_4,plain,
( ord_less_int(power_power_int(U_737,U_738),times_times_int(U_737,power_power_int(U_737,U_738)))
| ~ ord_less_int(one_one_int,U_737) ),
inference(clausify,[status(thm)],[f_313_3]) ).
fof(f_314_1,plain,
! [N_35,A_35] :
( ord_less_real(one_one_real,times_times_real(A_35,power_power_real(A_35,N_35)))
| ~ ord_less_real(one_one_real,A_35) ),
inference(fof_nnf,[status(thm)],[fact_295_power__gt1__lemma]) ).
fof(f_314_2,plain,
! [U_740,U_739] :
( ord_less_real(one_one_real,times_times_real(U_739,power_power_real(U_739,U_740)))
| ~ ord_less_real(one_one_real,U_739) ),
inference(variable_rename,[status(thm)],[f_314_1]) ).
fof(f_314_3,plain,
! [U_739,U_740] :
( ord_less_real(one_one_real,times_times_real(U_739,power_power_real(U_739,U_740)))
| ~ ord_less_real(one_one_real,U_739) ),
inference(definitional_conversion,[status(esa)],[f_314_2]) ).
cnf(f_314_4,plain,
( ord_less_real(one_one_real,times_times_real(U_739,power_power_real(U_739,U_740)))
| ~ ord_less_real(one_one_real,U_739) ),
inference(clausify,[status(thm)],[f_314_3]) ).
fof(f_315_1,plain,
! [N_35,A_35] :
( ord_less_nat(one_one_nat,times_times_nat(A_35,power_power_nat(A_35,N_35)))
| ~ ord_less_nat(one_one_nat,A_35) ),
inference(fof_nnf,[status(thm)],[fact_296_power__gt1__lemma]) ).
fof(f_315_2,plain,
! [U_742,U_741] :
( ord_less_nat(one_one_nat,times_times_nat(U_741,power_power_nat(U_741,U_742)))
| ~ ord_less_nat(one_one_nat,U_741) ),
inference(variable_rename,[status(thm)],[f_315_1]) ).
fof(f_315_3,plain,
! [U_742,U_741] :
( ord_less_nat(one_one_nat,times_times_nat(U_741,power_power_nat(U_741,U_742)))
| ~ ord_less_nat(one_one_nat,U_741) ),
inference(definitional_conversion,[status(esa)],[f_315_2]) ).
cnf(f_315_4,plain,
( ord_less_nat(one_one_nat,times_times_nat(U_741,power_power_nat(U_741,U_742)))
| ~ ord_less_nat(one_one_nat,U_741) ),
inference(clausify,[status(thm)],[f_315_3]) ).
fof(f_316_1,plain,
! [N_35,A_35] :
( ord_less_int(one_one_int,times_times_int(A_35,power_power_int(A_35,N_35)))
| ~ ord_less_int(one_one_int,A_35) ),
inference(fof_nnf,[status(thm)],[fact_297_power__gt1__lemma]) ).
fof(f_316_2,plain,
! [U_744,U_743] :
( ord_less_int(one_one_int,times_times_int(U_743,power_power_int(U_743,U_744)))
| ~ ord_less_int(one_one_int,U_743) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
fof(f_316_3,plain,
! [U_743,U_744] :
( ord_less_int(one_one_int,times_times_int(U_743,power_power_int(U_743,U_744)))
| ~ ord_less_int(one_one_int,U_743) ),
inference(definitional_conversion,[status(esa)],[f_316_2]) ).
cnf(f_316_4,plain,
( ord_less_int(one_one_int,times_times_int(U_743,power_power_int(U_743,U_744)))
| ~ ord_less_int(one_one_int,U_743) ),
inference(clausify,[status(thm)],[f_316_3]) ).
fof(f_317_1,plain,
! [M_8,N_34,A_34] :
( ord_less_eq_nat(M_8,N_34)
| ~ ord_less_eq_real(power_power_real(A_34,M_8),power_power_real(A_34,N_34))
| ~ ord_less_real(one_one_real,A_34) ),
inference(fof_nnf,[status(thm)],[fact_298_power__le__imp__le__exp]) ).
fof(f_317_2,plain,
! [U_747,U_746,U_745] :
( ord_less_eq_nat(U_747,U_746)
| ~ ord_less_eq_real(power_power_real(U_745,U_747),power_power_real(U_745,U_746))
| ~ ord_less_real(one_one_real,U_745) ),
inference(variable_rename,[status(thm)],[f_317_1]) ).
fof(f_317_3,plain,
! [U_745,U_746,U_747] :
( ord_less_eq_nat(U_747,U_746)
| ~ ord_less_eq_real(power_power_real(U_745,U_747),power_power_real(U_745,U_746))
| ~ ord_less_real(one_one_real,U_745) ),
inference(definitional_conversion,[status(esa)],[f_317_2]) ).
cnf(f_317_4,plain,
( ord_less_eq_nat(U_747,U_746)
| ~ ord_less_eq_real(power_power_real(U_745,U_747),power_power_real(U_745,U_746))
| ~ ord_less_real(one_one_real,U_745) ),
inference(clausify,[status(thm)],[f_317_3]) ).
fof(f_318_1,plain,
! [M_8,N_34,A_34] :
( ord_less_eq_nat(M_8,N_34)
| ~ ord_less_eq_nat(power_power_nat(A_34,M_8),power_power_nat(A_34,N_34))
| ~ ord_less_nat(one_one_nat,A_34) ),
inference(fof_nnf,[status(thm)],[fact_299_power__le__imp__le__exp]) ).
fof(f_318_2,plain,
! [U_750,U_749,U_748] :
( ord_less_eq_nat(U_750,U_749)
| ~ ord_less_eq_nat(power_power_nat(U_748,U_750),power_power_nat(U_748,U_749))
| ~ ord_less_nat(one_one_nat,U_748) ),
inference(variable_rename,[status(thm)],[f_318_1]) ).
fof(f_318_3,plain,
! [U_748,U_749,U_750] :
( ord_less_eq_nat(U_750,U_749)
| ~ ord_less_eq_nat(power_power_nat(U_748,U_750),power_power_nat(U_748,U_749))
| ~ ord_less_nat(one_one_nat,U_748) ),
inference(definitional_conversion,[status(esa)],[f_318_2]) ).
cnf(f_318_4,plain,
( ord_less_eq_nat(U_750,U_749)
| ~ ord_less_eq_nat(power_power_nat(U_748,U_750),power_power_nat(U_748,U_749))
| ~ ord_less_nat(one_one_nat,U_748) ),
inference(clausify,[status(thm)],[f_318_3]) ).
fof(f_319_1,plain,
! [M_8,N_34,A_34] :
( ord_less_eq_nat(M_8,N_34)
| ~ ord_less_eq_int(power_power_int(A_34,M_8),power_power_int(A_34,N_34))
| ~ ord_less_int(one_one_int,A_34) ),
inference(fof_nnf,[status(thm)],[fact_300_power__le__imp__le__exp]) ).
fof(f_319_2,plain,
! [U_753,U_752,U_751] :
( ord_less_eq_nat(U_753,U_752)
| ~ ord_less_eq_int(power_power_int(U_751,U_753),power_power_int(U_751,U_752))
| ~ ord_less_int(one_one_int,U_751) ),
inference(variable_rename,[status(thm)],[f_319_1]) ).
fof(f_319_3,plain,
! [U_752,U_751,U_753] :
( ord_less_eq_nat(U_753,U_752)
| ~ ord_less_eq_int(power_power_int(U_751,U_753),power_power_int(U_751,U_752))
| ~ ord_less_int(one_one_int,U_751) ),
inference(definitional_conversion,[status(esa)],[f_319_2]) ).
cnf(f_319_4,plain,
( ord_less_eq_nat(U_753,U_752)
| ~ ord_less_eq_int(power_power_int(U_751,U_753),power_power_int(U_751,U_752))
| ~ ord_less_int(one_one_int,U_751) ),
inference(clausify,[status(thm)],[f_319_3]) ).
fof(f_320_1,plain,
! [X_2,Y_2,B_2] :
( ( ( ord_less_eq_real(power_power_real(B_2,X_2),power_power_real(B_2,Y_2))
| ~ ord_less_eq_nat(X_2,Y_2) )
& ( ord_less_eq_nat(X_2,Y_2)
| ~ ord_less_eq_real(power_power_real(B_2,X_2),power_power_real(B_2,Y_2)) ) )
| ~ ord_less_real(one_one_real,B_2) ),
inference(fof_nnf,[status(thm)],[fact_301_power__increasing__iff]) ).
fof(f_320_2,plain,
! [U_756,U_755,U_754] :
( ( ( ord_less_eq_real(power_power_real(U_754,U_756),power_power_real(U_754,U_755))
| ~ ord_less_eq_nat(U_756,U_755) )
& ( ord_less_eq_nat(U_756,U_755)
| ~ ord_less_eq_real(power_power_real(U_754,U_756),power_power_real(U_754,U_755)) ) )
| ~ ord_less_real(one_one_real,U_754) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
fof(f_320_3,plain,
( ! [U_754,U_755,U_756] :
( ord_less_eq_real(power_power_real(U_754,U_756),power_power_real(U_754,U_755))
| ~ ord_less_eq_nat(U_756,U_755)
| ~ sP22(U_754,U_755,U_756) )
& ! [U_754,U_755,U_756] :
( ord_less_eq_nat(U_756,U_755)
| ~ ord_less_eq_real(power_power_real(U_754,U_756),power_power_real(U_754,U_755))
| ~ sP22(U_754,U_755,U_756) )
& ! [U_754,U_755,U_756] :
( sP22(U_754,U_755,U_756)
| ~ ord_less_real(one_one_real,U_754) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP22])],[f_320_2]) ).
cnf(f_320_4,plain,
( sP22(U_754,U_755,U_756)
| ~ ord_less_real(one_one_real,U_754) ),
inference(clausify,[status(thm)],[f_320_3]) ).
cnf(f_320_5,plain,
( ord_less_eq_nat(U_756,U_755)
| ~ ord_less_eq_real(power_power_real(U_754,U_756),power_power_real(U_754,U_755))
| ~ sP22(U_754,U_755,U_756) ),
inference(clausify,[status(thm)],[f_320_3]) ).
cnf(f_320_6,plain,
( ord_less_eq_real(power_power_real(U_754,U_756),power_power_real(U_754,U_755))
| ~ ord_less_eq_nat(U_756,U_755)
| ~ sP22(U_754,U_755,U_756) ),
inference(clausify,[status(thm)],[f_320_3]) ).
fof(f_321_1,plain,
! [X_2,Y_2,B_2] :
( ( ( ord_less_eq_nat(power_power_nat(B_2,X_2),power_power_nat(B_2,Y_2))
| ~ ord_less_eq_nat(X_2,Y_2) )
& ( ord_less_eq_nat(X_2,Y_2)
| ~ ord_less_eq_nat(power_power_nat(B_2,X_2),power_power_nat(B_2,Y_2)) ) )
| ~ ord_less_nat(one_one_nat,B_2) ),
inference(fof_nnf,[status(thm)],[fact_302_power__increasing__iff]) ).
fof(f_321_2,plain,
! [U_759,U_758,U_757] :
( ( ( ord_less_eq_nat(power_power_nat(U_757,U_759),power_power_nat(U_757,U_758))
| ~ ord_less_eq_nat(U_759,U_758) )
& ( ord_less_eq_nat(U_759,U_758)
| ~ ord_less_eq_nat(power_power_nat(U_757,U_759),power_power_nat(U_757,U_758)) ) )
| ~ ord_less_nat(one_one_nat,U_757) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
fof(f_321_3,plain,
( ! [U_759,U_758,U_757] :
( ord_less_eq_nat(power_power_nat(U_757,U_759),power_power_nat(U_757,U_758))
| ~ ord_less_eq_nat(U_759,U_758)
| ~ sP23(U_759,U_758,U_757) )
& ! [U_759,U_758,U_757] :
( ord_less_eq_nat(U_759,U_758)
| ~ ord_less_eq_nat(power_power_nat(U_757,U_759),power_power_nat(U_757,U_758))
| ~ sP23(U_759,U_758,U_757) )
& ! [U_759,U_758,U_757] :
( sP23(U_759,U_758,U_757)
| ~ ord_less_nat(one_one_nat,U_757) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23])],[f_321_2]) ).
cnf(f_321_4,plain,
( sP23(U_759,U_758,U_757)
| ~ ord_less_nat(one_one_nat,U_757) ),
inference(clausify,[status(thm)],[f_321_3]) ).
cnf(f_321_5,plain,
( ord_less_eq_nat(U_759,U_758)
| ~ ord_less_eq_nat(power_power_nat(U_757,U_759),power_power_nat(U_757,U_758))
| ~ sP23(U_759,U_758,U_757) ),
inference(clausify,[status(thm)],[f_321_3]) ).
cnf(f_321_6,plain,
( ord_less_eq_nat(power_power_nat(U_757,U_759),power_power_nat(U_757,U_758))
| ~ ord_less_eq_nat(U_759,U_758)
| ~ sP23(U_759,U_758,U_757) ),
inference(clausify,[status(thm)],[f_321_3]) ).
fof(f_322_1,plain,
! [X_2,Y_2,B_2] :
( ( ( ord_less_eq_int(power_power_int(B_2,X_2),power_power_int(B_2,Y_2))
| ~ ord_less_eq_nat(X_2,Y_2) )
& ( ord_less_eq_nat(X_2,Y_2)
| ~ ord_less_eq_int(power_power_int(B_2,X_2),power_power_int(B_2,Y_2)) ) )
| ~ ord_less_int(one_one_int,B_2) ),
inference(fof_nnf,[status(thm)],[fact_303_power__increasing__iff]) ).
fof(f_322_2,plain,
! [U_762,U_761,U_760] :
( ( ( ord_less_eq_int(power_power_int(U_760,U_762),power_power_int(U_760,U_761))
| ~ ord_less_eq_nat(U_762,U_761) )
& ( ord_less_eq_nat(U_762,U_761)
| ~ ord_less_eq_int(power_power_int(U_760,U_762),power_power_int(U_760,U_761)) ) )
| ~ ord_less_int(one_one_int,U_760) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
fof(f_322_3,plain,
( ! [U_762,U_760,U_761] :
( ord_less_eq_int(power_power_int(U_760,U_762),power_power_int(U_760,U_761))
| ~ ord_less_eq_nat(U_762,U_761)
| ~ sP24(U_762,U_760,U_761) )
& ! [U_762,U_760,U_761] :
( ord_less_eq_nat(U_762,U_761)
| ~ ord_less_eq_int(power_power_int(U_760,U_762),power_power_int(U_760,U_761))
| ~ sP24(U_762,U_760,U_761) )
& ! [U_762,U_760,U_761] :
( sP24(U_762,U_760,U_761)
| ~ ord_less_int(one_one_int,U_760) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24])],[f_322_2]) ).
cnf(f_322_4,plain,
( sP24(U_762,U_760,U_761)
| ~ ord_less_int(one_one_int,U_760) ),
inference(clausify,[status(thm)],[f_322_3]) ).
cnf(f_322_5,plain,
( ord_less_eq_nat(U_762,U_761)
| ~ ord_less_eq_int(power_power_int(U_760,U_762),power_power_int(U_760,U_761))
| ~ sP24(U_762,U_760,U_761) ),
inference(clausify,[status(thm)],[f_322_3]) ).
cnf(f_322_6,plain,
( ord_less_eq_int(power_power_int(U_760,U_762),power_power_int(U_760,U_761))
| ~ ord_less_eq_nat(U_762,U_761)
| ~ sP24(U_762,U_760,U_761) ),
inference(clausify,[status(thm)],[f_322_3]) ).
fof(f_323_1,plain,
zcong(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),power_power_int(s1,number_number_of_nat(bit0(bit1(pls)))),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(fof_nnf,[status(thm)],[fact_304__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096]) ).
fof(f_323_2,plain,
zcong(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),power_power_int(s1,number_number_of_nat(bit0(bit1(pls)))),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(definitional_conversion,[status(esa)],[f_323_1]) ).
cnf(f_323_3,plain,
zcong(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),power_power_int(s1,number_number_of_nat(bit0(bit1(pls)))),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(clausify,[status(thm)],[f_323_2]) ).
fof(f_324_1,plain,
( zcong(s1,s,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_int(s,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_eq_int(zero_zero_int,s) ),
inference(fof_nnf,[status(thm)],[fact_305_s0p]) ).
fof(f_324_2,plain,
( zcong(s1,s,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_int(s,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_eq_int(zero_zero_int,s) ),
inference(definitional_conversion,[status(esa)],[f_324_1]) ).
cnf(f_324_3,plain,
ord_less_eq_int(zero_zero_int,s),
inference(clausify,[status(thm)],[f_324_2]) ).
cnf(f_324_4,plain,
ord_less_int(s,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(clausify,[status(thm)],[f_324_2]) ).
cnf(f_324_5,plain,
zcong(s1,s,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(clausify,[status(thm)],[f_324_2]) ).
fof(f_325_1,plain,
? [X] :
( ! [Y] :
( Y = X
| ~ zcong(s1,Y,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| ~ ord_less_int(Y,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| ~ ord_less_eq_int(zero_zero_int,Y)
| ~ is_int(Y) )
& zcong(s1,X,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_int(X,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_eq_int(zero_zero_int,X)
& is_int(X) ),
inference(fof_nnf,[status(thm)],[fact_306__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_325_2,plain,
? [U_764] :
( ! [U_763] :
( U_763 = U_764
| ~ zcong(s1,U_763,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| ~ ord_less_int(U_763,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| ~ ord_less_eq_int(zero_zero_int,U_763)
| ~ is_int(U_763) )
& zcong(s1,U_764,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_int(U_764,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_eq_int(zero_zero_int,U_764)
& is_int(U_764) ),
inference(variable_rename,[status(thm)],[f_325_1]) ).
fof(f_325_3,plain,
( ! [U_763] :
( U_763 = sK6
| ~ zcong(s1,U_763,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| ~ ord_less_int(U_763,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| ~ ord_less_eq_int(zero_zero_int,U_763)
| ~ is_int(U_763) )
& zcong(s1,sK6,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_int(sK6,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_eq_int(zero_zero_int,sK6)
& is_int(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_764,sK6)],[f_325_2]) ).
fof(f_325_4,plain,
( ! [U_763] :
( U_763 = sK6
| ~ zcong(s1,U_763,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| ~ ord_less_int(U_763,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| ~ ord_less_eq_int(zero_zero_int,U_763)
| ~ is_int(U_763) )
& zcong(s1,sK6,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_int(sK6,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_eq_int(zero_zero_int,sK6)
& is_int(sK6) ),
inference(definitional_conversion,[status(esa)],[f_325_3]) ).
cnf(f_325_5,plain,
is_int(sK6),
inference(clausify,[status(thm)],[f_325_4]) ).
cnf(f_325_6,plain,
ord_less_eq_int(zero_zero_int,sK6),
inference(clausify,[status(thm)],[f_325_4]) ).
cnf(f_325_7,plain,
ord_less_int(sK6,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(clausify,[status(thm)],[f_325_4]) ).
cnf(f_325_8,plain,
zcong(s1,sK6,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(clausify,[status(thm)],[f_325_4]) ).
cnf(f_325_9,plain,
( U_763 = sK6
| ~ zcong(s1,U_763,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| ~ ord_less_int(U_763,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| ~ ord_less_eq_int(zero_zero_int,U_763)
| ~ is_int(U_763) ),
inference(clausify,[status(thm)],[f_325_4]) ).
fof(f_326_1,plain,
? [S] :
( zcong(s1,S,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_int(S,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_eq_int(zero_zero_int,S)
& is_int(S) ),
inference(fof_nnf,[status(thm)],[fact_307__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_326_2,plain,
? [U_765] :
( zcong(s1,U_765,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_int(U_765,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_eq_int(zero_zero_int,U_765)
& is_int(U_765) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
fof(f_326_3,plain,
( zcong(s1,sK7,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_int(sK7,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_eq_int(zero_zero_int,sK7)
& is_int(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_765,sK7)],[f_326_2]) ).
fof(f_326_4,plain,
( zcong(s1,sK7,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_int(sK7,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& ord_less_eq_int(zero_zero_int,sK7)
& is_int(sK7) ),
inference(definitional_conversion,[status(esa)],[f_326_3]) ).
cnf(f_326_5,plain,
is_int(sK7),
inference(clausify,[status(thm)],[f_326_4]) ).
cnf(f_326_6,plain,
ord_less_eq_int(zero_zero_int,sK7),
inference(clausify,[status(thm)],[f_326_4]) ).
cnf(f_326_7,plain,
ord_less_int(sK7,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(clausify,[status(thm)],[f_326_4]) ).
cnf(f_326_8,plain,
zcong(s1,sK7,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(clausify,[status(thm)],[f_326_4]) ).
fof(f_327_1,plain,
zcong(power_power_int(s1,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(fof_nnf,[status(thm)],[fact_308_s1]) ).
fof(f_327_2,plain,
zcong(power_power_int(s1,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(definitional_conversion,[status(esa)],[f_327_1]) ).
cnf(f_327_3,plain,
zcong(power_power_int(s1,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(clausify,[status(thm)],[f_327_2]) ).
fof(f_328_1,plain,
! [A_1,N_1] :
( ( power_power_real(A_1,N_1) = zero_zero_real
| N_1 = zero_zero_nat
| A_1 != zero_zero_real )
& ( ( N_1 != zero_zero_nat
& A_1 = zero_zero_real )
| power_power_real(A_1,N_1) != zero_zero_real ) ),
inference(fof_nnf,[status(thm)],[fact_309_power__eq__0__iff]) ).
fof(f_328_2,plain,
! [U_767,U_766] :
( ( power_power_real(U_767,U_766) = zero_zero_real
| U_766 = zero_zero_nat
| U_767 != zero_zero_real )
& ( ( U_766 != zero_zero_nat
& U_767 = zero_zero_real )
| power_power_real(U_767,U_766) != zero_zero_real ) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
fof(f_328_3,plain,
( ! [U_771,U_769] :
( power_power_real(U_771,U_769) = zero_zero_real
| U_769 = zero_zero_nat
| U_771 != zero_zero_real )
& ! [U_770,U_768] :
( ( U_768 != zero_zero_nat
& U_770 = zero_zero_real )
| power_power_real(U_770,U_768) != zero_zero_real ) ),
inference(miniscope,[status(thm)],[f_328_2]) ).
fof(f_328_4,plain,
( ! [U_770,U_768] :
( U_768 != zero_zero_nat
| ~ sP25(U_770,U_768) )
& ! [U_770,U_768] :
( U_770 = zero_zero_real
| ~ sP25(U_770,U_768) )
& ! [U_771,U_769] :
( power_power_real(U_771,U_769) = zero_zero_real
| U_769 = zero_zero_nat
| U_771 != zero_zero_real )
& ! [U_770,U_768] :
( sP25(U_770,U_768)
| power_power_real(U_770,U_768) != zero_zero_real ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25])],[f_328_3]) ).
cnf(f_328_5,plain,
( sP25(U_770,U_768)
| power_power_real(U_770,U_768) != zero_zero_real ),
inference(clausify,[status(thm)],[f_328_4]) ).
cnf(f_328_6,plain,
( power_power_real(U_771,U_769) = zero_zero_real
| U_769 = zero_zero_nat
| U_771 != zero_zero_real ),
inference(clausify,[status(thm)],[f_328_4]) ).
cnf(f_328_7,plain,
( U_770 = zero_zero_real
| ~ sP25(U_770,U_768) ),
inference(clausify,[status(thm)],[f_328_4]) ).
cnf(f_328_8,plain,
( U_768 != zero_zero_nat
| ~ sP25(U_770,U_768) ),
inference(clausify,[status(thm)],[f_328_4]) ).
fof(f_329_1,plain,
! [A_1,N_1] :
( ( power_power_nat(A_1,N_1) = zero_zero_nat
| N_1 = zero_zero_nat
| A_1 != zero_zero_nat )
& ( ( N_1 != zero_zero_nat
& A_1 = zero_zero_nat )
| power_power_nat(A_1,N_1) != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_310_power__eq__0__iff]) ).
fof(f_329_2,plain,
! [U_773,U_772] :
( ( power_power_nat(U_773,U_772) = zero_zero_nat
| U_772 = zero_zero_nat
| U_773 != zero_zero_nat )
& ( ( U_772 != zero_zero_nat
& U_773 = zero_zero_nat )
| power_power_nat(U_773,U_772) != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_329_1]) ).
fof(f_329_3,plain,
( ! [U_777,U_775] :
( power_power_nat(U_777,U_775) = zero_zero_nat
| U_775 = zero_zero_nat
| U_777 != zero_zero_nat )
& ! [U_776,U_774] :
( ( U_774 != zero_zero_nat
& U_776 = zero_zero_nat )
| power_power_nat(U_776,U_774) != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_329_2]) ).
fof(f_329_4,plain,
( ! [U_774,U_776] :
( U_774 != zero_zero_nat
| ~ sP26(U_774,U_776) )
& ! [U_774,U_776] :
( U_776 = zero_zero_nat
| ~ sP26(U_774,U_776) )
& ! [U_775,U_777] :
( power_power_nat(U_777,U_775) = zero_zero_nat
| U_775 = zero_zero_nat
| U_777 != zero_zero_nat )
& ! [U_774,U_776] :
( sP26(U_774,U_776)
| power_power_nat(U_776,U_774) != zero_zero_nat ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP26])],[f_329_3]) ).
cnf(f_329_5,plain,
( sP26(U_774,U_776)
| power_power_nat(U_776,U_774) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_329_4]) ).
cnf(f_329_6,plain,
( power_power_nat(U_777,U_775) = zero_zero_nat
| U_775 = zero_zero_nat
| U_777 != zero_zero_nat ),
inference(clausify,[status(thm)],[f_329_4]) ).
cnf(f_329_7,plain,
( U_776 = zero_zero_nat
| ~ sP26(U_774,U_776) ),
inference(clausify,[status(thm)],[f_329_4]) ).
cnf(f_329_8,plain,
( U_774 != zero_zero_nat
| ~ sP26(U_774,U_776) ),
inference(clausify,[status(thm)],[f_329_4]) ).
fof(f_330_1,plain,
! [A_1,N_1] :
( ( ( power_power_int(A_1,N_1) = zero_zero_int
| N_1 = zero_zero_nat
| A_1 != zero_zero_int )
& ( ( N_1 != zero_zero_nat
& A_1 = zero_zero_int )
| power_power_int(A_1,N_1) != zero_zero_int ) )
| ~ is_int(A_1) ),
inference(fof_nnf,[status(thm)],[fact_311_power__eq__0__iff]) ).
fof(f_330_2,plain,
! [U_779,U_778] :
( ( ( power_power_int(U_779,U_778) = zero_zero_int
| U_778 = zero_zero_nat
| U_779 != zero_zero_int )
& ( ( U_778 != zero_zero_nat
& U_779 = zero_zero_int )
| power_power_int(U_779,U_778) != zero_zero_int ) )
| ~ is_int(U_779) ),
inference(variable_rename,[status(thm)],[f_330_1]) ).
fof(f_330_3,plain,
! [U_779] :
( ( ! [U_781] :
( power_power_int(U_779,U_781) = zero_zero_int
| U_781 = zero_zero_nat
| U_779 != zero_zero_int )
& ! [U_780] :
( ( U_780 != zero_zero_nat
& U_779 = zero_zero_int )
| power_power_int(U_779,U_780) != zero_zero_int ) )
| ~ is_int(U_779) ),
inference(miniscope,[status(thm)],[f_330_2]) ).
fof(f_330_4,plain,
( ! [U_779,U_780] :
( U_780 != zero_zero_nat
| ~ sP27(U_779,U_780) )
& ! [U_779,U_780] :
( U_779 = zero_zero_int
| ~ sP27(U_779,U_780) )
& ! [U_779,U_781,U_780] :
( power_power_int(U_779,U_781) = zero_zero_int
| U_781 = zero_zero_nat
| U_779 != zero_zero_int
| ~ sP28(U_779,U_781,U_780) )
& ! [U_779,U_781,U_780] :
( sP27(U_779,U_780)
| power_power_int(U_779,U_780) != zero_zero_int
| ~ sP28(U_779,U_781,U_780) )
& ! [U_779,U_781,U_780] :
( sP28(U_779,U_781,U_780)
| ~ is_int(U_779) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP27,sP28])],[f_330_3]) ).
cnf(f_330_5,plain,
( sP28(U_779,U_781,U_780)
| ~ is_int(U_779) ),
inference(clausify,[status(thm)],[f_330_4]) ).
cnf(f_330_6,plain,
( sP27(U_779,U_780)
| power_power_int(U_779,U_780) != zero_zero_int
| ~ sP28(U_779,U_781,U_780) ),
inference(clausify,[status(thm)],[f_330_4]) ).
cnf(f_330_7,plain,
( power_power_int(U_779,U_781) = zero_zero_int
| U_781 = zero_zero_nat
| U_779 != zero_zero_int
| ~ sP28(U_779,U_781,U_780) ),
inference(clausify,[status(thm)],[f_330_4]) ).
cnf(f_330_8,plain,
( U_779 = zero_zero_int
| ~ sP27(U_779,U_780) ),
inference(clausify,[status(thm)],[f_330_4]) ).
cnf(f_330_9,plain,
( U_780 != zero_zero_nat
| ~ sP27(U_779,U_780) ),
inference(clausify,[status(thm)],[f_330_4]) ).
fof(f_331_1,plain,
! [A_33,M_7,N_33] :
( dvd_dvd_nat(power_power_nat(A_33,M_7),power_power_nat(A_33,N_33))
| ~ ord_less_eq_nat(M_7,N_33) ),
inference(fof_nnf,[status(thm)],[fact_312_le__imp__power__dvd]) ).
fof(f_331_2,plain,
! [U_784,U_783,U_782] :
( dvd_dvd_nat(power_power_nat(U_784,U_783),power_power_nat(U_784,U_782))
| ~ ord_less_eq_nat(U_783,U_782) ),
inference(variable_rename,[status(thm)],[f_331_1]) ).
fof(f_331_3,plain,
! [U_782,U_784,U_783] :
( dvd_dvd_nat(power_power_nat(U_784,U_783),power_power_nat(U_784,U_782))
| ~ ord_less_eq_nat(U_783,U_782) ),
inference(definitional_conversion,[status(esa)],[f_331_2]) ).
cnf(f_331_4,plain,
( dvd_dvd_nat(power_power_nat(U_784,U_783),power_power_nat(U_784,U_782))
| ~ ord_less_eq_nat(U_783,U_782) ),
inference(clausify,[status(thm)],[f_331_3]) ).
fof(f_332_1,plain,
! [A_33,M_7,N_33] :
( dvd_dvd_int(power_power_int(A_33,M_7),power_power_int(A_33,N_33))
| ~ ord_less_eq_nat(M_7,N_33) ),
inference(fof_nnf,[status(thm)],[fact_313_le__imp__power__dvd]) ).
fof(f_332_2,plain,
! [U_787,U_786,U_785] :
( dvd_dvd_int(power_power_int(U_787,U_786),power_power_int(U_787,U_785))
| ~ ord_less_eq_nat(U_786,U_785) ),
inference(variable_rename,[status(thm)],[f_332_1]) ).
fof(f_332_3,plain,
! [U_787,U_786,U_785] :
( dvd_dvd_int(power_power_int(U_787,U_786),power_power_int(U_787,U_785))
| ~ ord_less_eq_nat(U_786,U_785) ),
inference(definitional_conversion,[status(esa)],[f_332_2]) ).
cnf(f_332_4,plain,
( dvd_dvd_int(power_power_int(U_787,U_786),power_power_int(U_787,U_785))
| ~ ord_less_eq_nat(U_786,U_785) ),
inference(clausify,[status(thm)],[f_332_3]) ).
fof(f_333_1,plain,
! [A_33,M_7,N_33] :
( dvd_dvd_real(power_power_real(A_33,M_7),power_power_real(A_33,N_33))
| ~ ord_less_eq_nat(M_7,N_33) ),
inference(fof_nnf,[status(thm)],[fact_314_le__imp__power__dvd]) ).
fof(f_333_2,plain,
! [U_790,U_789,U_788] :
( dvd_dvd_real(power_power_real(U_790,U_789),power_power_real(U_790,U_788))
| ~ ord_less_eq_nat(U_789,U_788) ),
inference(variable_rename,[status(thm)],[f_333_1]) ).
fof(f_333_3,plain,
! [U_789,U_788,U_790] :
( dvd_dvd_real(power_power_real(U_790,U_789),power_power_real(U_790,U_788))
| ~ ord_less_eq_nat(U_789,U_788) ),
inference(definitional_conversion,[status(esa)],[f_333_2]) ).
cnf(f_333_4,plain,
( dvd_dvd_real(power_power_real(U_790,U_789),power_power_real(U_790,U_788))
| ~ ord_less_eq_nat(U_789,U_788) ),
inference(clausify,[status(thm)],[f_333_3]) ).
fof(f_334_1,plain,
! [N_32,M_6,X_14,Y_12] :
( dvd_dvd_nat(power_power_nat(X_14,N_32),power_power_nat(Y_12,M_6))
| ~ ord_less_eq_nat(N_32,M_6)
| ~ dvd_dvd_nat(X_14,Y_12) ),
inference(fof_nnf,[status(thm)],[fact_315_dvd__power__le]) ).
fof(f_334_2,plain,
! [U_794,U_793,U_792,U_791] :
( dvd_dvd_nat(power_power_nat(U_792,U_794),power_power_nat(U_791,U_793))
| ~ ord_less_eq_nat(U_794,U_793)
| ~ dvd_dvd_nat(U_792,U_791) ),
inference(variable_rename,[status(thm)],[f_334_1]) ).
fof(f_334_3,plain,
! [U_791,U_792,U_793,U_794] :
( dvd_dvd_nat(power_power_nat(U_792,U_794),power_power_nat(U_791,U_793))
| ~ ord_less_eq_nat(U_794,U_793)
| ~ dvd_dvd_nat(U_792,U_791) ),
inference(definitional_conversion,[status(esa)],[f_334_2]) ).
cnf(f_334_4,plain,
( dvd_dvd_nat(power_power_nat(U_792,U_794),power_power_nat(U_791,U_793))
| ~ ord_less_eq_nat(U_794,U_793)
| ~ dvd_dvd_nat(U_792,U_791) ),
inference(clausify,[status(thm)],[f_334_3]) ).
fof(f_335_1,plain,
! [N_32,M_6,X_14,Y_12] :
( dvd_dvd_int(power_power_int(X_14,N_32),power_power_int(Y_12,M_6))
| ~ ord_less_eq_nat(N_32,M_6)
| ~ dvd_dvd_int(X_14,Y_12) ),
inference(fof_nnf,[status(thm)],[fact_316_dvd__power__le]) ).
fof(f_335_2,plain,
! [U_798,U_797,U_796,U_795] :
( dvd_dvd_int(power_power_int(U_796,U_798),power_power_int(U_795,U_797))
| ~ ord_less_eq_nat(U_798,U_797)
| ~ dvd_dvd_int(U_796,U_795) ),
inference(variable_rename,[status(thm)],[f_335_1]) ).
fof(f_335_3,plain,
! [U_795,U_796,U_797,U_798] :
( dvd_dvd_int(power_power_int(U_796,U_798),power_power_int(U_795,U_797))
| ~ ord_less_eq_nat(U_798,U_797)
| ~ dvd_dvd_int(U_796,U_795) ),
inference(definitional_conversion,[status(esa)],[f_335_2]) ).
cnf(f_335_4,plain,
( dvd_dvd_int(power_power_int(U_796,U_798),power_power_int(U_795,U_797))
| ~ ord_less_eq_nat(U_798,U_797)
| ~ dvd_dvd_int(U_796,U_795) ),
inference(clausify,[status(thm)],[f_335_3]) ).
fof(f_336_1,plain,
! [N_32,M_6,X_14,Y_12] :
( dvd_dvd_real(power_power_real(X_14,N_32),power_power_real(Y_12,M_6))
| ~ ord_less_eq_nat(N_32,M_6)
| ~ dvd_dvd_real(X_14,Y_12) ),
inference(fof_nnf,[status(thm)],[fact_317_dvd__power__le]) ).
fof(f_336_2,plain,
! [U_802,U_801,U_800,U_799] :
( dvd_dvd_real(power_power_real(U_800,U_802),power_power_real(U_799,U_801))
| ~ ord_less_eq_nat(U_802,U_801)
| ~ dvd_dvd_real(U_800,U_799) ),
inference(variable_rename,[status(thm)],[f_336_1]) ).
fof(f_336_3,plain,
! [U_800,U_799,U_801,U_802] :
( dvd_dvd_real(power_power_real(U_800,U_802),power_power_real(U_799,U_801))
| ~ ord_less_eq_nat(U_802,U_801)
| ~ dvd_dvd_real(U_800,U_799) ),
inference(definitional_conversion,[status(esa)],[f_336_2]) ).
cnf(f_336_4,plain,
( dvd_dvd_real(power_power_real(U_800,U_802),power_power_real(U_799,U_801))
| ~ ord_less_eq_nat(U_802,U_801)
| ~ dvd_dvd_real(U_800,U_799) ),
inference(clausify,[status(thm)],[f_336_3]) ).
fof(f_337_1,plain,
! [M_5,A_32,N_31,B_9] :
( dvd_dvd_nat(power_power_nat(A_32,M_5),B_9)
| ~ ord_less_eq_nat(M_5,N_31)
| ~ dvd_dvd_nat(power_power_nat(A_32,N_31),B_9) ),
inference(fof_nnf,[status(thm)],[fact_318_power__le__dvd]) ).
fof(f_337_2,plain,
! [U_806,U_805,U_804,U_803] :
( dvd_dvd_nat(power_power_nat(U_805,U_806),U_803)
| ~ ord_less_eq_nat(U_806,U_804)
| ~ dvd_dvd_nat(power_power_nat(U_805,U_804),U_803) ),
inference(variable_rename,[status(thm)],[f_337_1]) ).
fof(f_337_3,plain,
! [U_805,U_804,U_803,U_806] :
( dvd_dvd_nat(power_power_nat(U_805,U_806),U_803)
| ~ ord_less_eq_nat(U_806,U_804)
| ~ dvd_dvd_nat(power_power_nat(U_805,U_804),U_803) ),
inference(definitional_conversion,[status(esa)],[f_337_2]) ).
cnf(f_337_4,plain,
( dvd_dvd_nat(power_power_nat(U_805,U_806),U_803)
| ~ ord_less_eq_nat(U_806,U_804)
| ~ dvd_dvd_nat(power_power_nat(U_805,U_804),U_803) ),
inference(clausify,[status(thm)],[f_337_3]) ).
fof(f_338_1,plain,
! [M_5,A_32,N_31,B_9] :
( dvd_dvd_int(power_power_int(A_32,M_5),B_9)
| ~ ord_less_eq_nat(M_5,N_31)
| ~ dvd_dvd_int(power_power_int(A_32,N_31),B_9) ),
inference(fof_nnf,[status(thm)],[fact_319_power__le__dvd]) ).
fof(f_338_2,plain,
! [U_810,U_809,U_808,U_807] :
( dvd_dvd_int(power_power_int(U_809,U_810),U_807)
| ~ ord_less_eq_nat(U_810,U_808)
| ~ dvd_dvd_int(power_power_int(U_809,U_808),U_807) ),
inference(variable_rename,[status(thm)],[f_338_1]) ).
fof(f_338_3,plain,
! [U_807,U_809,U_808,U_810] :
( dvd_dvd_int(power_power_int(U_809,U_810),U_807)
| ~ ord_less_eq_nat(U_810,U_808)
| ~ dvd_dvd_int(power_power_int(U_809,U_808),U_807) ),
inference(definitional_conversion,[status(esa)],[f_338_2]) ).
cnf(f_338_4,plain,
( dvd_dvd_int(power_power_int(U_809,U_810),U_807)
| ~ ord_less_eq_nat(U_810,U_808)
| ~ dvd_dvd_int(power_power_int(U_809,U_808),U_807) ),
inference(clausify,[status(thm)],[f_338_3]) ).
fof(f_339_1,plain,
! [M_5,A_32,N_31,B_9] :
( dvd_dvd_real(power_power_real(A_32,M_5),B_9)
| ~ ord_less_eq_nat(M_5,N_31)
| ~ dvd_dvd_real(power_power_real(A_32,N_31),B_9) ),
inference(fof_nnf,[status(thm)],[fact_320_power__le__dvd]) ).
fof(f_339_2,plain,
! [U_814,U_813,U_812,U_811] :
( dvd_dvd_real(power_power_real(U_813,U_814),U_811)
| ~ ord_less_eq_nat(U_814,U_812)
| ~ dvd_dvd_real(power_power_real(U_813,U_812),U_811) ),
inference(variable_rename,[status(thm)],[f_339_1]) ).
fof(f_339_3,plain,
! [U_811,U_812,U_813,U_814] :
( dvd_dvd_real(power_power_real(U_813,U_814),U_811)
| ~ ord_less_eq_nat(U_814,U_812)
| ~ dvd_dvd_real(power_power_real(U_813,U_812),U_811) ),
inference(definitional_conversion,[status(esa)],[f_339_2]) ).
cnf(f_339_4,plain,
( dvd_dvd_real(power_power_real(U_813,U_814),U_811)
| ~ ord_less_eq_nat(U_814,U_812)
| ~ dvd_dvd_real(power_power_real(U_813,U_812),U_811) ),
inference(clausify,[status(thm)],[f_339_3]) ).
fof(f_340_1,plain,
! [A_31,N_30,B_8] :
( A_31 = B_8
| ~ ord_less_nat(zero_zero_nat,N_30)
| ~ ord_less_eq_real(zero_zero_real,B_8)
| ~ ord_less_eq_real(zero_zero_real,A_31)
| power_power_real(A_31,N_30) != power_power_real(B_8,N_30) ),
inference(fof_nnf,[status(thm)],[fact_321_power__eq__imp__eq__base]) ).
fof(f_340_2,plain,
! [U_817,U_816,U_815] :
( U_817 = U_815
| ~ ord_less_nat(zero_zero_nat,U_816)
| ~ ord_less_eq_real(zero_zero_real,U_815)
| ~ ord_less_eq_real(zero_zero_real,U_817)
| power_power_real(U_817,U_816) != power_power_real(U_815,U_816) ),
inference(variable_rename,[status(thm)],[f_340_1]) ).
fof(f_340_3,plain,
! [U_815,U_816,U_817] :
( U_817 = U_815
| ~ ord_less_nat(zero_zero_nat,U_816)
| ~ ord_less_eq_real(zero_zero_real,U_815)
| ~ ord_less_eq_real(zero_zero_real,U_817)
| power_power_real(U_817,U_816) != power_power_real(U_815,U_816) ),
inference(definitional_conversion,[status(esa)],[f_340_2]) ).
cnf(f_340_4,plain,
( U_817 = U_815
| ~ ord_less_nat(zero_zero_nat,U_816)
| ~ ord_less_eq_real(zero_zero_real,U_815)
| ~ ord_less_eq_real(zero_zero_real,U_817)
| power_power_real(U_817,U_816) != power_power_real(U_815,U_816) ),
inference(clausify,[status(thm)],[f_340_3]) ).
fof(f_341_1,plain,
! [A_31,N_30,B_8] :
( A_31 = B_8
| ~ ord_less_nat(zero_zero_nat,N_30)
| ~ ord_less_eq_nat(zero_zero_nat,B_8)
| ~ ord_less_eq_nat(zero_zero_nat,A_31)
| power_power_nat(A_31,N_30) != power_power_nat(B_8,N_30) ),
inference(fof_nnf,[status(thm)],[fact_322_power__eq__imp__eq__base]) ).
fof(f_341_2,plain,
! [U_820,U_819,U_818] :
( U_820 = U_818
| ~ ord_less_nat(zero_zero_nat,U_819)
| ~ ord_less_eq_nat(zero_zero_nat,U_818)
| ~ ord_less_eq_nat(zero_zero_nat,U_820)
| power_power_nat(U_820,U_819) != power_power_nat(U_818,U_819) ),
inference(variable_rename,[status(thm)],[f_341_1]) ).
fof(f_341_3,plain,
! [U_820,U_818,U_819] :
( U_820 = U_818
| ~ ord_less_nat(zero_zero_nat,U_819)
| ~ ord_less_eq_nat(zero_zero_nat,U_818)
| ~ ord_less_eq_nat(zero_zero_nat,U_820)
| power_power_nat(U_820,U_819) != power_power_nat(U_818,U_819) ),
inference(definitional_conversion,[status(esa)],[f_341_2]) ).
cnf(f_341_4,plain,
( U_820 = U_818
| ~ ord_less_nat(zero_zero_nat,U_819)
| ~ ord_less_eq_nat(zero_zero_nat,U_818)
| ~ ord_less_eq_nat(zero_zero_nat,U_820)
| power_power_nat(U_820,U_819) != power_power_nat(U_818,U_819) ),
inference(clausify,[status(thm)],[f_341_3]) ).
fof(f_342_1,plain,
! [A_31,N_30,B_8] :
( A_31 = B_8
| ~ ord_less_nat(zero_zero_nat,N_30)
| ~ ord_less_eq_int(zero_zero_int,B_8)
| ~ ord_less_eq_int(zero_zero_int,A_31)
| power_power_int(A_31,N_30) != power_power_int(B_8,N_30)
| ~ is_int(B_8)
| ~ is_int(A_31) ),
inference(fof_nnf,[status(thm)],[fact_323_power__eq__imp__eq__base]) ).
fof(f_342_2,plain,
! [U_823,U_822,U_821] :
( U_823 = U_821
| ~ ord_less_nat(zero_zero_nat,U_822)
| ~ ord_less_eq_int(zero_zero_int,U_821)
| ~ ord_less_eq_int(zero_zero_int,U_823)
| power_power_int(U_823,U_822) != power_power_int(U_821,U_822)
| ~ is_int(U_821)
| ~ is_int(U_823) ),
inference(variable_rename,[status(thm)],[f_342_1]) ).
fof(f_342_3,plain,
! [U_823,U_821,U_822] :
( U_823 = U_821
| ~ ord_less_nat(zero_zero_nat,U_822)
| ~ ord_less_eq_int(zero_zero_int,U_821)
| ~ ord_less_eq_int(zero_zero_int,U_823)
| power_power_int(U_823,U_822) != power_power_int(U_821,U_822)
| ~ is_int(U_821)
| ~ is_int(U_823) ),
inference(definitional_conversion,[status(esa)],[f_342_2]) ).
cnf(f_342_4,plain,
( U_823 = U_821
| ~ ord_less_nat(zero_zero_nat,U_822)
| ~ ord_less_eq_int(zero_zero_int,U_821)
| ~ ord_less_eq_int(zero_zero_int,U_823)
| power_power_int(U_823,U_822) != power_power_int(U_821,U_822)
| ~ is_int(U_821)
| ~ is_int(U_823) ),
inference(clausify,[status(thm)],[f_342_3]) ).
fof(f_343_1,plain,
! [N,M] :
( ~ dvd_dvd_int(N,M)
| ~ ord_less_int(M,N)
| ~ ord_less_int(zero_zero_int,M) ),
inference(fof_nnf,[status(thm)],[fact_324_zdvd__not__zless]) ).
fof(f_343_2,plain,
! [U_825,U_824] :
( ~ dvd_dvd_int(U_825,U_824)
| ~ ord_less_int(U_824,U_825)
| ~ ord_less_int(zero_zero_int,U_824) ),
inference(variable_rename,[status(thm)],[f_343_1]) ).
fof(f_343_3,plain,
! [U_824,U_825] :
( ~ dvd_dvd_int(U_825,U_824)
| ~ ord_less_int(U_824,U_825)
| ~ ord_less_int(zero_zero_int,U_824) ),
inference(definitional_conversion,[status(esa)],[f_343_2]) ).
cnf(f_343_4,plain,
( ~ dvd_dvd_int(U_825,U_824)
| ~ ord_less_int(U_824,U_825)
| ~ ord_less_int(zero_zero_int,U_824) ),
inference(clausify,[status(thm)],[f_343_3]) ).
fof(f_344_1,plain,
! [N,M] :
( M = N
| ~ dvd_dvd_int(N,M)
| ~ dvd_dvd_int(M,N)
| ~ ord_less_eq_int(zero_zero_int,N)
| ~ ord_less_eq_int(zero_zero_int,M)
| ~ is_int(M)
| ~ is_int(N) ),
inference(fof_nnf,[status(thm)],[fact_325_zdvd__antisym__nonneg]) ).
fof(f_344_2,plain,
! [U_827,U_826] :
( U_826 = U_827
| ~ dvd_dvd_int(U_827,U_826)
| ~ dvd_dvd_int(U_826,U_827)
| ~ ord_less_eq_int(zero_zero_int,U_827)
| ~ ord_less_eq_int(zero_zero_int,U_826)
| ~ is_int(U_826)
| ~ is_int(U_827) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
fof(f_344_3,plain,
! [U_827,U_826] :
( U_826 = U_827
| ~ dvd_dvd_int(U_827,U_826)
| ~ dvd_dvd_int(U_826,U_827)
| ~ ord_less_eq_int(zero_zero_int,U_827)
| ~ ord_less_eq_int(zero_zero_int,U_826)
| ~ is_int(U_826)
| ~ is_int(U_827) ),
inference(definitional_conversion,[status(esa)],[f_344_2]) ).
cnf(f_344_4,plain,
( U_826 = U_827
| ~ dvd_dvd_int(U_827,U_826)
| ~ dvd_dvd_int(U_826,U_827)
| ~ ord_less_eq_int(zero_zero_int,U_827)
| ~ ord_less_eq_int(zero_zero_int,U_826)
| ~ is_int(U_826)
| ~ is_int(U_827) ),
inference(clausify,[status(thm)],[f_344_3]) ).
fof(f_345_1,plain,
! [K,M,N] :
( dvd_dvd_int(M,N)
| K = zero_zero_int
| ~ dvd_dvd_int(times_times_int(K,M),times_times_int(K,N))
| ~ is_int(K) ),
inference(fof_nnf,[status(thm)],[fact_326_zdvd__mult__cancel]) ).
fof(f_345_2,plain,
! [U_830,U_829,U_828] :
( dvd_dvd_int(U_829,U_828)
| U_830 = zero_zero_int
| ~ dvd_dvd_int(times_times_int(U_830,U_829),times_times_int(U_830,U_828))
| ~ is_int(U_830) ),
inference(variable_rename,[status(thm)],[f_345_1]) ).
fof(f_345_3,plain,
! [U_830] :
( ! [U_829,U_828] :
( dvd_dvd_int(U_829,U_828)
| U_830 = zero_zero_int
| ~ dvd_dvd_int(times_times_int(U_830,U_829),times_times_int(U_830,U_828)) )
| ~ is_int(U_830) ),
inference(miniscope,[status(thm)],[f_345_2]) ).
fof(f_345_4,plain,
! [U_828,U_830,U_829] :
( dvd_dvd_int(U_829,U_828)
| U_830 = zero_zero_int
| ~ dvd_dvd_int(times_times_int(U_830,U_829),times_times_int(U_830,U_828))
| ~ is_int(U_830) ),
inference(definitional_conversion,[status(esa)],[f_345_3]) ).
cnf(f_345_5,plain,
( dvd_dvd_int(U_829,U_828)
| U_830 = zero_zero_int
| ~ dvd_dvd_int(times_times_int(U_830,U_829),times_times_int(U_830,U_828))
| ~ is_int(U_830) ),
inference(clausify,[status(thm)],[f_345_4]) ).
fof(f_346_1,plain,
! [N_29,X_13,Y_11] :
( dvd_dvd_nat(power_power_nat(X_13,N_29),power_power_nat(Y_11,N_29))
| ~ dvd_dvd_nat(X_13,Y_11) ),
inference(fof_nnf,[status(thm)],[fact_327_dvd__power__same]) ).
fof(f_346_2,plain,
! [U_833,U_832,U_831] :
( dvd_dvd_nat(power_power_nat(U_832,U_833),power_power_nat(U_831,U_833))
| ~ dvd_dvd_nat(U_832,U_831) ),
inference(variable_rename,[status(thm)],[f_346_1]) ).
fof(f_346_3,plain,
! [U_831,U_833,U_832] :
( dvd_dvd_nat(power_power_nat(U_832,U_833),power_power_nat(U_831,U_833))
| ~ dvd_dvd_nat(U_832,U_831) ),
inference(definitional_conversion,[status(esa)],[f_346_2]) ).
cnf(f_346_4,plain,
( dvd_dvd_nat(power_power_nat(U_832,U_833),power_power_nat(U_831,U_833))
| ~ dvd_dvd_nat(U_832,U_831) ),
inference(clausify,[status(thm)],[f_346_3]) ).
fof(f_347_1,plain,
! [N_29,X_13,Y_11] :
( dvd_dvd_int(power_power_int(X_13,N_29),power_power_int(Y_11,N_29))
| ~ dvd_dvd_int(X_13,Y_11) ),
inference(fof_nnf,[status(thm)],[fact_328_dvd__power__same]) ).
fof(f_347_2,plain,
! [U_836,U_835,U_834] :
( dvd_dvd_int(power_power_int(U_835,U_836),power_power_int(U_834,U_836))
| ~ dvd_dvd_int(U_835,U_834) ),
inference(variable_rename,[status(thm)],[f_347_1]) ).
fof(f_347_3,plain,
! [U_835,U_836,U_834] :
( dvd_dvd_int(power_power_int(U_835,U_836),power_power_int(U_834,U_836))
| ~ dvd_dvd_int(U_835,U_834) ),
inference(definitional_conversion,[status(esa)],[f_347_2]) ).
cnf(f_347_4,plain,
( dvd_dvd_int(power_power_int(U_835,U_836),power_power_int(U_834,U_836))
| ~ dvd_dvd_int(U_835,U_834) ),
inference(clausify,[status(thm)],[f_347_3]) ).
fof(f_348_1,plain,
! [N_29,X_13,Y_11] :
( dvd_dvd_real(power_power_real(X_13,N_29),power_power_real(Y_11,N_29))
| ~ dvd_dvd_real(X_13,Y_11) ),
inference(fof_nnf,[status(thm)],[fact_329_dvd__power__same]) ).
fof(f_348_2,plain,
! [U_839,U_838,U_837] :
( dvd_dvd_real(power_power_real(U_838,U_839),power_power_real(U_837,U_839))
| ~ dvd_dvd_real(U_838,U_837) ),
inference(variable_rename,[status(thm)],[f_348_1]) ).
fof(f_348_3,plain,
! [U_838,U_837,U_839] :
( dvd_dvd_real(power_power_real(U_838,U_839),power_power_real(U_837,U_839))
| ~ dvd_dvd_real(U_838,U_837) ),
inference(definitional_conversion,[status(esa)],[f_348_2]) ).
cnf(f_348_4,plain,
( dvd_dvd_real(power_power_real(U_838,U_839),power_power_real(U_837,U_839))
| ~ dvd_dvd_real(U_838,U_837) ),
inference(clausify,[status(thm)],[f_348_3]) ).
fof(f_349_1,plain,
! [N_28,A_30] :
( power_power_real(A_30,N_28) != zero_zero_real
| A_30 = zero_zero_real ),
inference(fof_nnf,[status(thm)],[fact_330_field__power__not__zero]) ).
fof(f_349_2,plain,
! [U_841,U_840] :
( power_power_real(U_840,U_841) != zero_zero_real
| U_840 = zero_zero_real ),
inference(variable_rename,[status(thm)],[f_349_1]) ).
fof(f_349_3,plain,
! [U_841,U_840] :
( power_power_real(U_840,U_841) != zero_zero_real
| U_840 = zero_zero_real ),
inference(definitional_conversion,[status(esa)],[f_349_2]) ).
cnf(f_349_4,plain,
( power_power_real(U_840,U_841) != zero_zero_real
| U_840 = zero_zero_real ),
inference(clausify,[status(thm)],[f_349_3]) ).
fof(f_350_1,plain,
! [N_28,A_30] :
( power_power_int(A_30,N_28) != zero_zero_int
| A_30 = zero_zero_int
| ~ is_int(A_30) ),
inference(fof_nnf,[status(thm)],[fact_331_field__power__not__zero]) ).
fof(f_350_2,plain,
! [U_843,U_842] :
( power_power_int(U_842,U_843) != zero_zero_int
| U_842 = zero_zero_int
| ~ is_int(U_842) ),
inference(variable_rename,[status(thm)],[f_350_1]) ).
fof(f_350_3,plain,
! [U_843,U_842] :
( power_power_int(U_842,U_843) != zero_zero_int
| U_842 = zero_zero_int
| ~ is_int(U_842) ),
inference(definitional_conversion,[status(esa)],[f_350_2]) ).
cnf(f_350_4,plain,
( power_power_int(U_842,U_843) != zero_zero_int
| U_842 = zero_zero_int
| ~ is_int(U_842) ),
inference(clausify,[status(thm)],[f_350_3]) ).
fof(f_351_1,plain,
! [N_27] :
( ( power_power_real(zero_zero_real,N_27) = zero_zero_real
| N_27 = zero_zero_nat )
& ( power_power_real(zero_zero_real,N_27) = one_one_real
| N_27 != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_332_power__0__left]) ).
fof(f_351_2,plain,
! [U_844] :
( ( power_power_real(zero_zero_real,U_844) = zero_zero_real
| U_844 = zero_zero_nat )
& ( power_power_real(zero_zero_real,U_844) = one_one_real
| U_844 != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_351_1]) ).
fof(f_351_3,plain,
( ! [U_846] :
( power_power_real(zero_zero_real,U_846) = zero_zero_real
| U_846 = zero_zero_nat )
& ! [U_845] :
( power_power_real(zero_zero_real,U_845) = one_one_real
| U_845 != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_351_2]) ).
fof(f_351_4,plain,
( ! [U_846] :
( power_power_real(zero_zero_real,U_846) = zero_zero_real
| U_846 = zero_zero_nat )
& ! [U_845] :
( power_power_real(zero_zero_real,U_845) = one_one_real
| U_845 != zero_zero_nat ) ),
inference(definitional_conversion,[status(esa)],[f_351_3]) ).
cnf(f_351_5,plain,
( power_power_real(zero_zero_real,U_845) = one_one_real
| U_845 != zero_zero_nat ),
inference(clausify,[status(thm)],[f_351_4]) ).
cnf(f_351_6,plain,
( power_power_real(zero_zero_real,U_846) = zero_zero_real
| U_846 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_351_4]) ).
fof(f_352_1,plain,
! [N_27] :
( ( power_power_nat(zero_zero_nat,N_27) = zero_zero_nat
| N_27 = zero_zero_nat )
& ( power_power_nat(zero_zero_nat,N_27) = one_one_nat
| N_27 != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_333_power__0__left]) ).
fof(f_352_2,plain,
! [U_847] :
( ( power_power_nat(zero_zero_nat,U_847) = zero_zero_nat
| U_847 = zero_zero_nat )
& ( power_power_nat(zero_zero_nat,U_847) = one_one_nat
| U_847 != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_352_1]) ).
fof(f_352_3,plain,
( ! [U_849] :
( power_power_nat(zero_zero_nat,U_849) = zero_zero_nat
| U_849 = zero_zero_nat )
& ! [U_848] :
( power_power_nat(zero_zero_nat,U_848) = one_one_nat
| U_848 != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_352_2]) ).
fof(f_352_4,plain,
( ! [U_849] :
( power_power_nat(zero_zero_nat,U_849) = zero_zero_nat
| U_849 = zero_zero_nat )
& ! [U_848] :
( power_power_nat(zero_zero_nat,U_848) = one_one_nat
| U_848 != zero_zero_nat ) ),
inference(definitional_conversion,[status(esa)],[f_352_3]) ).
cnf(f_352_5,plain,
( power_power_nat(zero_zero_nat,U_848) = one_one_nat
| U_848 != zero_zero_nat ),
inference(clausify,[status(thm)],[f_352_4]) ).
cnf(f_352_6,plain,
( power_power_nat(zero_zero_nat,U_849) = zero_zero_nat
| U_849 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_352_4]) ).
fof(f_353_1,plain,
! [N_27] :
( ( power_power_int(zero_zero_int,N_27) = zero_zero_int
| N_27 = zero_zero_nat )
& ( power_power_int(zero_zero_int,N_27) = one_one_int
| N_27 != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_334_power__0__left]) ).
fof(f_353_2,plain,
! [U_850] :
( ( power_power_int(zero_zero_int,U_850) = zero_zero_int
| U_850 = zero_zero_nat )
& ( power_power_int(zero_zero_int,U_850) = one_one_int
| U_850 != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_353_1]) ).
fof(f_353_3,plain,
( ! [U_852] :
( power_power_int(zero_zero_int,U_852) = zero_zero_int
| U_852 = zero_zero_nat )
& ! [U_851] :
( power_power_int(zero_zero_int,U_851) = one_one_int
| U_851 != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_353_2]) ).
fof(f_353_4,plain,
( ! [U_852] :
( power_power_int(zero_zero_int,U_852) = zero_zero_int
| U_852 = zero_zero_nat )
& ! [U_851] :
( power_power_int(zero_zero_int,U_851) = one_one_int
| U_851 != zero_zero_nat ) ),
inference(definitional_conversion,[status(esa)],[f_353_3]) ).
cnf(f_353_5,plain,
( power_power_int(zero_zero_int,U_851) = one_one_int
| U_851 != zero_zero_nat ),
inference(clausify,[status(thm)],[f_353_4]) ).
cnf(f_353_6,plain,
( power_power_int(zero_zero_int,U_852) = zero_zero_int
| U_852 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_353_4]) ).
fof(f_354_1,plain,
! [Z,N] :
( ord_less_eq_int(Z,N)
| ~ ord_less_int(zero_zero_int,N)
| ~ dvd_dvd_int(Z,N) ),
inference(fof_nnf,[status(thm)],[fact_335_zdvd__imp__le]) ).
fof(f_354_2,plain,
! [U_854,U_853] :
( ord_less_eq_int(U_854,U_853)
| ~ ord_less_int(zero_zero_int,U_853)
| ~ dvd_dvd_int(U_854,U_853) ),
inference(variable_rename,[status(thm)],[f_354_1]) ).
fof(f_354_3,plain,
! [U_853,U_854] :
( ord_less_eq_int(U_854,U_853)
| ~ ord_less_int(zero_zero_int,U_853)
| ~ dvd_dvd_int(U_854,U_853) ),
inference(definitional_conversion,[status(esa)],[f_354_2]) ).
cnf(f_354_4,plain,
( ord_less_eq_int(U_854,U_853)
| ~ ord_less_int(zero_zero_int,U_853)
| ~ dvd_dvd_int(U_854,U_853) ),
inference(clausify,[status(thm)],[f_354_3]) ).
fof(f_355_1,plain,
! [N_26,A_29,B_7] :
( ord_less_real(power_power_real(A_29,N_26),power_power_real(B_7,N_26))
| ~ ord_less_nat(zero_zero_nat,N_26)
| ~ ord_less_eq_real(zero_zero_real,A_29)
| ~ ord_less_real(A_29,B_7) ),
inference(fof_nnf,[status(thm)],[fact_336_power__strict__mono]) ).
fof(f_355_2,plain,
! [U_857,U_856,U_855] :
( ord_less_real(power_power_real(U_856,U_857),power_power_real(U_855,U_857))
| ~ ord_less_nat(zero_zero_nat,U_857)
| ~ ord_less_eq_real(zero_zero_real,U_856)
| ~ ord_less_real(U_856,U_855) ),
inference(variable_rename,[status(thm)],[f_355_1]) ).
fof(f_355_3,plain,
! [U_856,U_855,U_857] :
( ord_less_real(power_power_real(U_856,U_857),power_power_real(U_855,U_857))
| ~ ord_less_nat(zero_zero_nat,U_857)
| ~ ord_less_eq_real(zero_zero_real,U_856)
| ~ ord_less_real(U_856,U_855) ),
inference(definitional_conversion,[status(esa)],[f_355_2]) ).
cnf(f_355_4,plain,
( ord_less_real(power_power_real(U_856,U_857),power_power_real(U_855,U_857))
| ~ ord_less_nat(zero_zero_nat,U_857)
| ~ ord_less_eq_real(zero_zero_real,U_856)
| ~ ord_less_real(U_856,U_855) ),
inference(clausify,[status(thm)],[f_355_3]) ).
fof(f_356_1,plain,
! [N_26,A_29,B_7] :
( ord_less_nat(power_power_nat(A_29,N_26),power_power_nat(B_7,N_26))
| ~ ord_less_nat(zero_zero_nat,N_26)
| ~ ord_less_eq_nat(zero_zero_nat,A_29)
| ~ ord_less_nat(A_29,B_7) ),
inference(fof_nnf,[status(thm)],[fact_337_power__strict__mono]) ).
fof(f_356_2,plain,
! [U_860,U_859,U_858] :
( ord_less_nat(power_power_nat(U_859,U_860),power_power_nat(U_858,U_860))
| ~ ord_less_nat(zero_zero_nat,U_860)
| ~ ord_less_eq_nat(zero_zero_nat,U_859)
| ~ ord_less_nat(U_859,U_858) ),
inference(variable_rename,[status(thm)],[f_356_1]) ).
fof(f_356_3,plain,
! [U_859,U_858,U_860] :
( ord_less_nat(power_power_nat(U_859,U_860),power_power_nat(U_858,U_860))
| ~ ord_less_nat(zero_zero_nat,U_860)
| ~ ord_less_eq_nat(zero_zero_nat,U_859)
| ~ ord_less_nat(U_859,U_858) ),
inference(definitional_conversion,[status(esa)],[f_356_2]) ).
cnf(f_356_4,plain,
( ord_less_nat(power_power_nat(U_859,U_860),power_power_nat(U_858,U_860))
| ~ ord_less_nat(zero_zero_nat,U_860)
| ~ ord_less_eq_nat(zero_zero_nat,U_859)
| ~ ord_less_nat(U_859,U_858) ),
inference(clausify,[status(thm)],[f_356_3]) ).
fof(f_357_1,plain,
! [N_26,A_29,B_7] :
( ord_less_int(power_power_int(A_29,N_26),power_power_int(B_7,N_26))
| ~ ord_less_nat(zero_zero_nat,N_26)
| ~ ord_less_eq_int(zero_zero_int,A_29)
| ~ ord_less_int(A_29,B_7) ),
inference(fof_nnf,[status(thm)],[fact_338_power__strict__mono]) ).
fof(f_357_2,plain,
! [U_863,U_862,U_861] :
( ord_less_int(power_power_int(U_862,U_863),power_power_int(U_861,U_863))
| ~ ord_less_nat(zero_zero_nat,U_863)
| ~ ord_less_eq_int(zero_zero_int,U_862)
| ~ ord_less_int(U_862,U_861) ),
inference(variable_rename,[status(thm)],[f_357_1]) ).
fof(f_357_3,plain,
! [U_862,U_861,U_863] :
( ord_less_int(power_power_int(U_862,U_863),power_power_int(U_861,U_863))
| ~ ord_less_nat(zero_zero_nat,U_863)
| ~ ord_less_eq_int(zero_zero_int,U_862)
| ~ ord_less_int(U_862,U_861) ),
inference(definitional_conversion,[status(esa)],[f_357_2]) ).
cnf(f_357_4,plain,
( ord_less_int(power_power_int(U_862,U_863),power_power_int(U_861,U_863))
| ~ ord_less_nat(zero_zero_nat,U_863)
| ~ ord_less_eq_int(zero_zero_int,U_862)
| ~ ord_less_int(U_862,U_861) ),
inference(clausify,[status(thm)],[f_357_3]) ).
fof(f_358_1,plain,
! [A_28] : times_times_real(zero_zero_real,A_28) = zero_zero_real,
inference(fof_nnf,[status(thm)],[fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J]) ).
fof(f_358_2,plain,
! [U_864] : times_times_real(zero_zero_real,U_864) = zero_zero_real,
inference(variable_rename,[status(thm)],[f_358_1]) ).
fof(f_358_3,plain,
! [U_864] : times_times_real(zero_zero_real,U_864) = zero_zero_real,
inference(definitional_conversion,[status(esa)],[f_358_2]) ).
cnf(f_358_4,plain,
times_times_real(zero_zero_real,U_864) = zero_zero_real,
inference(clausify,[status(thm)],[f_358_3]) ).
fof(f_359_1,plain,
! [A_28] : times_times_nat(zero_zero_nat,A_28) = zero_zero_nat,
inference(fof_nnf,[status(thm)],[fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J]) ).
fof(f_359_2,plain,
! [U_865] : times_times_nat(zero_zero_nat,U_865) = zero_zero_nat,
inference(variable_rename,[status(thm)],[f_359_1]) ).
fof(f_359_3,plain,
! [U_865] : times_times_nat(zero_zero_nat,U_865) = zero_zero_nat,
inference(definitional_conversion,[status(esa)],[f_359_2]) ).
cnf(f_359_4,plain,
times_times_nat(zero_zero_nat,U_865) = zero_zero_nat,
inference(clausify,[status(thm)],[f_359_3]) ).
fof(f_360_1,plain,
! [A_28] : times_times_int(zero_zero_int,A_28) = zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J]) ).
fof(f_360_2,plain,
! [U_866] : times_times_int(zero_zero_int,U_866) = zero_zero_int,
inference(variable_rename,[status(thm)],[f_360_1]) ).
fof(f_360_3,plain,
! [U_866] : times_times_int(zero_zero_int,U_866) = zero_zero_int,
inference(definitional_conversion,[status(esa)],[f_360_2]) ).
cnf(f_360_4,plain,
times_times_int(zero_zero_int,U_866) = zero_zero_int,
inference(clausify,[status(thm)],[f_360_3]) ).
fof(f_361_1,plain,
! [A_27] : times_times_real(A_27,zero_zero_real) = zero_zero_real,
inference(fof_nnf,[status(thm)],[fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).
fof(f_361_2,plain,
! [U_867] : times_times_real(U_867,zero_zero_real) = zero_zero_real,
inference(variable_rename,[status(thm)],[f_361_1]) ).
fof(f_361_3,plain,
! [U_867] : times_times_real(U_867,zero_zero_real) = zero_zero_real,
inference(definitional_conversion,[status(esa)],[f_361_2]) ).
cnf(f_361_4,plain,
times_times_real(U_867,zero_zero_real) = zero_zero_real,
inference(clausify,[status(thm)],[f_361_3]) ).
fof(f_362_1,plain,
! [A_27] : times_times_nat(A_27,zero_zero_nat) = zero_zero_nat,
inference(fof_nnf,[status(thm)],[fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).
fof(f_362_2,plain,
! [U_868] : times_times_nat(U_868,zero_zero_nat) = zero_zero_nat,
inference(variable_rename,[status(thm)],[f_362_1]) ).
fof(f_362_3,plain,
! [U_868] : times_times_nat(U_868,zero_zero_nat) = zero_zero_nat,
inference(definitional_conversion,[status(esa)],[f_362_2]) ).
cnf(f_362_4,plain,
times_times_nat(U_868,zero_zero_nat) = zero_zero_nat,
inference(clausify,[status(thm)],[f_362_3]) ).
fof(f_363_1,plain,
! [A_27] : times_times_int(A_27,zero_zero_int) = zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).
fof(f_363_2,plain,
! [U_869] : times_times_int(U_869,zero_zero_int) = zero_zero_int,
inference(variable_rename,[status(thm)],[f_363_1]) ).
fof(f_363_3,plain,
! [U_869] : times_times_int(U_869,zero_zero_int) = zero_zero_int,
inference(definitional_conversion,[status(esa)],[f_363_2]) ).
cnf(f_363_4,plain,
times_times_int(U_869,zero_zero_int) = zero_zero_int,
inference(clausify,[status(thm)],[f_363_3]) ).
fof(f_364_1,plain,
! [A_26] : plus_plus_real(zero_zero_real,A_26) = A_26,
inference(fof_nnf,[status(thm)],[fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J]) ).
fof(f_364_2,plain,
! [U_870] : plus_plus_real(zero_zero_real,U_870) = U_870,
inference(variable_rename,[status(thm)],[f_364_1]) ).
fof(f_364_3,plain,
! [U_870] : plus_plus_real(zero_zero_real,U_870) = U_870,
inference(definitional_conversion,[status(esa)],[f_364_2]) ).
cnf(f_364_4,plain,
plus_plus_real(zero_zero_real,U_870) = U_870,
inference(clausify,[status(thm)],[f_364_3]) ).
fof(f_365_1,plain,
! [A_26] : plus_plus_nat(zero_zero_nat,A_26) = A_26,
inference(fof_nnf,[status(thm)],[fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J]) ).
fof(f_365_2,plain,
! [U_871] : plus_plus_nat(zero_zero_nat,U_871) = U_871,
inference(variable_rename,[status(thm)],[f_365_1]) ).
fof(f_365_3,plain,
! [U_871] : plus_plus_nat(zero_zero_nat,U_871) = U_871,
inference(definitional_conversion,[status(esa)],[f_365_2]) ).
cnf(f_365_4,plain,
plus_plus_nat(zero_zero_nat,U_871) = U_871,
inference(clausify,[status(thm)],[f_365_3]) ).
fof(f_366_1,plain,
! [A_26] :
( plus_plus_int(zero_zero_int,A_26) = A_26
| ~ is_int(A_26) ),
inference(fof_nnf,[status(thm)],[fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J]) ).
fof(f_366_2,plain,
! [U_872] :
( plus_plus_int(zero_zero_int,U_872) = U_872
| ~ is_int(U_872) ),
inference(variable_rename,[status(thm)],[f_366_1]) ).
fof(f_366_3,plain,
! [U_872] :
( plus_plus_int(zero_zero_int,U_872) = U_872
| ~ is_int(U_872) ),
inference(definitional_conversion,[status(esa)],[f_366_2]) ).
cnf(f_366_4,plain,
( plus_plus_int(zero_zero_int,U_872) = U_872
| ~ is_int(U_872) ),
inference(clausify,[status(thm)],[f_366_3]) ).
fof(f_367_1,plain,
! [A_25] : plus_plus_real(A_25,zero_zero_real) = A_25,
inference(fof_nnf,[status(thm)],[fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J]) ).
fof(f_367_2,plain,
! [U_873] : plus_plus_real(U_873,zero_zero_real) = U_873,
inference(variable_rename,[status(thm)],[f_367_1]) ).
fof(f_367_3,plain,
! [U_873] : plus_plus_real(U_873,zero_zero_real) = U_873,
inference(definitional_conversion,[status(esa)],[f_367_2]) ).
cnf(f_367_4,plain,
plus_plus_real(U_873,zero_zero_real) = U_873,
inference(clausify,[status(thm)],[f_367_3]) ).
fof(f_368_1,plain,
! [A_25] : plus_plus_nat(A_25,zero_zero_nat) = A_25,
inference(fof_nnf,[status(thm)],[fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J]) ).
fof(f_368_2,plain,
! [U_874] : plus_plus_nat(U_874,zero_zero_nat) = U_874,
inference(variable_rename,[status(thm)],[f_368_1]) ).
fof(f_368_3,plain,
! [U_874] : plus_plus_nat(U_874,zero_zero_nat) = U_874,
inference(definitional_conversion,[status(esa)],[f_368_2]) ).
cnf(f_368_4,plain,
plus_plus_nat(U_874,zero_zero_nat) = U_874,
inference(clausify,[status(thm)],[f_368_3]) ).
fof(f_369_1,plain,
! [A_25] :
( plus_plus_int(A_25,zero_zero_int) = A_25
| ~ is_int(A_25) ),
inference(fof_nnf,[status(thm)],[fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J]) ).
fof(f_369_2,plain,
! [U_875] :
( plus_plus_int(U_875,zero_zero_int) = U_875
| ~ is_int(U_875) ),
inference(variable_rename,[status(thm)],[f_369_1]) ).
fof(f_369_3,plain,
! [U_875] :
( plus_plus_int(U_875,zero_zero_int) = U_875
| ~ is_int(U_875) ),
inference(definitional_conversion,[status(esa)],[f_369_2]) ).
cnf(f_369_4,plain,
( plus_plus_int(U_875,zero_zero_int) = U_875
| ~ is_int(U_875) ),
inference(clausify,[status(thm)],[f_369_3]) ).
fof(f_370_1,plain,
! [B_2,A_1] :
( ( B_2 = plus_plus_real(B_2,A_1)
| A_1 != zero_zero_real )
& ( A_1 = zero_zero_real
| B_2 != plus_plus_real(B_2,A_1) ) ),
inference(fof_nnf,[status(thm)],[fact_351_add__0__iff]) ).
fof(f_370_2,plain,
! [U_877,U_876] :
( ( U_877 = plus_plus_real(U_877,U_876)
| U_876 != zero_zero_real )
& ( U_876 = zero_zero_real
| U_877 != plus_plus_real(U_877,U_876) ) ),
inference(variable_rename,[status(thm)],[f_370_1]) ).
fof(f_370_3,plain,
( ! [U_881,U_879] :
( U_881 = plus_plus_real(U_881,U_879)
| U_879 != zero_zero_real )
& ! [U_880,U_878] :
( U_878 = zero_zero_real
| U_880 != plus_plus_real(U_880,U_878) ) ),
inference(miniscope,[status(thm)],[f_370_2]) ).
fof(f_370_4,plain,
( ! [U_879,U_881] :
( U_881 = plus_plus_real(U_881,U_879)
| U_879 != zero_zero_real )
& ! [U_880,U_878] :
( U_878 = zero_zero_real
| U_880 != plus_plus_real(U_880,U_878) ) ),
inference(definitional_conversion,[status(esa)],[f_370_3]) ).
cnf(f_370_5,plain,
( U_878 = zero_zero_real
| U_880 != plus_plus_real(U_880,U_878) ),
inference(clausify,[status(thm)],[f_370_4]) ).
cnf(f_370_6,plain,
( U_881 = plus_plus_real(U_881,U_879)
| U_879 != zero_zero_real ),
inference(clausify,[status(thm)],[f_370_4]) ).
fof(f_371_1,plain,
! [B_2,A_1] :
( ( B_2 = plus_plus_nat(B_2,A_1)
| A_1 != zero_zero_nat )
& ( A_1 = zero_zero_nat
| B_2 != plus_plus_nat(B_2,A_1) ) ),
inference(fof_nnf,[status(thm)],[fact_352_add__0__iff]) ).
fof(f_371_2,plain,
! [U_883,U_882] :
( ( U_883 = plus_plus_nat(U_883,U_882)
| U_882 != zero_zero_nat )
& ( U_882 = zero_zero_nat
| U_883 != plus_plus_nat(U_883,U_882) ) ),
inference(variable_rename,[status(thm)],[f_371_1]) ).
fof(f_371_3,plain,
( ! [U_887,U_885] :
( U_887 = plus_plus_nat(U_887,U_885)
| U_885 != zero_zero_nat )
& ! [U_886,U_884] :
( U_884 = zero_zero_nat
| U_886 != plus_plus_nat(U_886,U_884) ) ),
inference(miniscope,[status(thm)],[f_371_2]) ).
fof(f_371_4,plain,
( ! [U_887,U_885] :
( U_887 = plus_plus_nat(U_887,U_885)
| U_885 != zero_zero_nat )
& ! [U_886,U_884] :
( U_884 = zero_zero_nat
| U_886 != plus_plus_nat(U_886,U_884) ) ),
inference(definitional_conversion,[status(esa)],[f_371_3]) ).
cnf(f_371_5,plain,
( U_884 = zero_zero_nat
| U_886 != plus_plus_nat(U_886,U_884) ),
inference(clausify,[status(thm)],[f_371_4]) ).
cnf(f_371_6,plain,
( U_887 = plus_plus_nat(U_887,U_885)
| U_885 != zero_zero_nat ),
inference(clausify,[status(thm)],[f_371_4]) ).
fof(f_372_1,plain,
! [B_2,A_1] :
( ( ( B_2 = plus_plus_int(B_2,A_1)
| A_1 != zero_zero_int )
& ( A_1 = zero_zero_int
| B_2 != plus_plus_int(B_2,A_1) ) )
| ~ is_int(A_1)
| ~ is_int(B_2) ),
inference(fof_nnf,[status(thm)],[fact_353_add__0__iff]) ).
fof(f_372_2,plain,
! [U_889,U_888] :
( ( ( U_889 = plus_plus_int(U_889,U_888)
| U_888 != zero_zero_int )
& ( U_888 = zero_zero_int
| U_889 != plus_plus_int(U_889,U_888) ) )
| ~ is_int(U_888)
| ~ is_int(U_889) ),
inference(variable_rename,[status(thm)],[f_372_1]) ).
fof(f_372_3,plain,
( ! [U_889,U_888] :
( U_889 = plus_plus_int(U_889,U_888)
| U_888 != zero_zero_int
| ~ sP29(U_889,U_888) )
& ! [U_889,U_888] :
( U_888 = zero_zero_int
| U_889 != plus_plus_int(U_889,U_888)
| ~ sP29(U_889,U_888) )
& ! [U_889,U_888] :
( sP29(U_889,U_888)
| ~ is_int(U_888)
| ~ is_int(U_889) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP29])],[f_372_2]) ).
cnf(f_372_4,plain,
( sP29(U_889,U_888)
| ~ is_int(U_888)
| ~ is_int(U_889) ),
inference(clausify,[status(thm)],[f_372_3]) ).
cnf(f_372_5,plain,
( U_888 = zero_zero_int
| U_889 != plus_plus_int(U_889,U_888)
| ~ sP29(U_889,U_888) ),
inference(clausify,[status(thm)],[f_372_3]) ).
cnf(f_372_6,plain,
( U_889 = plus_plus_int(U_889,U_888)
| U_888 != zero_zero_int
| ~ sP29(U_889,U_888) ),
inference(clausify,[status(thm)],[f_372_3]) ).
fof(f_373_1,plain,
! [A_1] :
( ( plus_plus_real(A_1,A_1) = zero_zero_real
| A_1 != zero_zero_real )
& ( A_1 = zero_zero_real
| plus_plus_real(A_1,A_1) != zero_zero_real ) ),
inference(fof_nnf,[status(thm)],[fact_354_double__eq__0__iff]) ).
fof(f_373_2,plain,
! [U_890] :
( ( plus_plus_real(U_890,U_890) = zero_zero_real
| U_890 != zero_zero_real )
& ( U_890 = zero_zero_real
| plus_plus_real(U_890,U_890) != zero_zero_real ) ),
inference(variable_rename,[status(thm)],[f_373_1]) ).
fof(f_373_3,plain,
( ! [U_892] :
( plus_plus_real(U_892,U_892) = zero_zero_real
| U_892 != zero_zero_real )
& ! [U_891] :
( U_891 = zero_zero_real
| plus_plus_real(U_891,U_891) != zero_zero_real ) ),
inference(miniscope,[status(thm)],[f_373_2]) ).
fof(f_373_4,plain,
( ! [U_892] :
( plus_plus_real(U_892,U_892) = zero_zero_real
| U_892 != zero_zero_real )
& ! [U_891] :
( U_891 = zero_zero_real
| plus_plus_real(U_891,U_891) != zero_zero_real ) ),
inference(definitional_conversion,[status(esa)],[f_373_3]) ).
cnf(f_373_5,plain,
( U_891 = zero_zero_real
| plus_plus_real(U_891,U_891) != zero_zero_real ),
inference(clausify,[status(thm)],[f_373_4]) ).
cnf(f_373_6,plain,
( plus_plus_real(U_892,U_892) = zero_zero_real
| U_892 != zero_zero_real ),
inference(clausify,[status(thm)],[f_373_4]) ).
fof(f_374_1,plain,
! [A_1] :
( ( ( plus_plus_int(A_1,A_1) = zero_zero_int
| A_1 != zero_zero_int )
& ( A_1 = zero_zero_int
| plus_plus_int(A_1,A_1) != zero_zero_int ) )
| ~ is_int(A_1) ),
inference(fof_nnf,[status(thm)],[fact_355_double__eq__0__iff]) ).
fof(f_374_2,plain,
! [U_893] :
( ( ( plus_plus_int(U_893,U_893) = zero_zero_int
| U_893 != zero_zero_int )
& ( U_893 = zero_zero_int
| plus_plus_int(U_893,U_893) != zero_zero_int ) )
| ~ is_int(U_893) ),
inference(variable_rename,[status(thm)],[f_374_1]) ).
fof(f_374_3,plain,
( ! [U_893] :
( plus_plus_int(U_893,U_893) = zero_zero_int
| U_893 != zero_zero_int
| ~ sP30(U_893) )
& ! [U_893] :
( U_893 = zero_zero_int
| plus_plus_int(U_893,U_893) != zero_zero_int
| ~ sP30(U_893) )
& ! [U_893] :
( sP30(U_893)
| ~ is_int(U_893) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP30])],[f_374_2]) ).
cnf(f_374_4,plain,
( sP30(U_893)
| ~ is_int(U_893) ),
inference(clausify,[status(thm)],[f_374_3]) ).
cnf(f_374_5,plain,
( U_893 = zero_zero_int
| plus_plus_int(U_893,U_893) != zero_zero_int
| ~ sP30(U_893) ),
inference(clausify,[status(thm)],[f_374_3]) ).
cnf(f_374_6,plain,
( plus_plus_int(U_893,U_893) = zero_zero_int
| U_893 != zero_zero_int
| ~ sP30(U_893) ),
inference(clausify,[status(thm)],[f_374_3]) ).
fof(f_375_1,plain,
pls = zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_356_Pls__def]) ).
fof(f_375_2,plain,
pls = zero_zero_int,
inference(definitional_conversion,[status(esa)],[f_375_1]) ).
cnf(f_375_3,plain,
pls = zero_zero_int,
inference(clausify,[status(thm)],[f_375_2]) ).
fof(f_376_1,plain,
zero_zero_int != one_one_int,
inference(fof_nnf,[status(thm)],[fact_357_int__0__neq__1]) ).
fof(f_376_2,plain,
zero_zero_int != one_one_int,
inference(definitional_conversion,[status(esa)],[f_376_1]) ).
cnf(f_376_3,plain,
zero_zero_int != one_one_int,
inference(clausify,[status(thm)],[f_376_2]) ).
fof(f_377_1,plain,
! [Z] :
( plus_plus_int(zero_zero_int,Z) = Z
| ~ is_int(Z) ),
inference(fof_nnf,[status(thm)],[fact_358_zadd__0]) ).
fof(f_377_2,plain,
! [U_894] :
( plus_plus_int(zero_zero_int,U_894) = U_894
| ~ is_int(U_894) ),
inference(variable_rename,[status(thm)],[f_377_1]) ).
fof(f_377_3,plain,
! [U_894] :
( plus_plus_int(zero_zero_int,U_894) = U_894
| ~ is_int(U_894) ),
inference(definitional_conversion,[status(esa)],[f_377_2]) ).
cnf(f_377_4,plain,
( plus_plus_int(zero_zero_int,U_894) = U_894
| ~ is_int(U_894) ),
inference(clausify,[status(thm)],[f_377_3]) ).
fof(f_378_1,plain,
! [Z] :
( plus_plus_int(Z,zero_zero_int) = Z
| ~ is_int(Z) ),
inference(fof_nnf,[status(thm)],[fact_359_zadd__0__right]) ).
fof(f_378_2,plain,
! [U_895] :
( plus_plus_int(U_895,zero_zero_int) = U_895
| ~ is_int(U_895) ),
inference(variable_rename,[status(thm)],[f_378_1]) ).
fof(f_378_3,plain,
! [U_895] :
( plus_plus_int(U_895,zero_zero_int) = U_895
| ~ is_int(U_895) ),
inference(definitional_conversion,[status(esa)],[f_378_2]) ).
cnf(f_378_4,plain,
( plus_plus_int(U_895,zero_zero_int) = U_895
| ~ is_int(U_895) ),
inference(clausify,[status(thm)],[f_378_3]) ).
fof(f_379_1,plain,
! [N_25,A_24] :
( ord_less_eq_real(zero_zero_real,power_power_real(A_24,N_25))
| ~ ord_less_eq_real(zero_zero_real,A_24) ),
inference(fof_nnf,[status(thm)],[fact_360_zero__le__power]) ).
fof(f_379_2,plain,
! [U_897,U_896] :
( ord_less_eq_real(zero_zero_real,power_power_real(U_896,U_897))
| ~ ord_less_eq_real(zero_zero_real,U_896) ),
inference(variable_rename,[status(thm)],[f_379_1]) ).
fof(f_379_3,plain,
! [U_897,U_896] :
( ord_less_eq_real(zero_zero_real,power_power_real(U_896,U_897))
| ~ ord_less_eq_real(zero_zero_real,U_896) ),
inference(definitional_conversion,[status(esa)],[f_379_2]) ).
cnf(f_379_4,plain,
( ord_less_eq_real(zero_zero_real,power_power_real(U_896,U_897))
| ~ ord_less_eq_real(zero_zero_real,U_896) ),
inference(clausify,[status(thm)],[f_379_3]) ).
fof(f_380_1,plain,
! [N_25,A_24] :
( ord_less_eq_nat(zero_zero_nat,power_power_nat(A_24,N_25))
| ~ ord_less_eq_nat(zero_zero_nat,A_24) ),
inference(fof_nnf,[status(thm)],[fact_361_zero__le__power]) ).
fof(f_380_2,plain,
! [U_899,U_898] :
( ord_less_eq_nat(zero_zero_nat,power_power_nat(U_898,U_899))
| ~ ord_less_eq_nat(zero_zero_nat,U_898) ),
inference(variable_rename,[status(thm)],[f_380_1]) ).
fof(f_380_3,plain,
! [U_899,U_898] :
( ord_less_eq_nat(zero_zero_nat,power_power_nat(U_898,U_899))
| ~ ord_less_eq_nat(zero_zero_nat,U_898) ),
inference(definitional_conversion,[status(esa)],[f_380_2]) ).
cnf(f_380_4,plain,
( ord_less_eq_nat(zero_zero_nat,power_power_nat(U_898,U_899))
| ~ ord_less_eq_nat(zero_zero_nat,U_898) ),
inference(clausify,[status(thm)],[f_380_3]) ).
fof(f_381_1,plain,
! [N_25,A_24] :
( ord_less_eq_int(zero_zero_int,power_power_int(A_24,N_25))
| ~ ord_less_eq_int(zero_zero_int,A_24) ),
inference(fof_nnf,[status(thm)],[fact_362_zero__le__power]) ).
fof(f_381_2,plain,
! [U_901,U_900] :
( ord_less_eq_int(zero_zero_int,power_power_int(U_900,U_901))
| ~ ord_less_eq_int(zero_zero_int,U_900) ),
inference(variable_rename,[status(thm)],[f_381_1]) ).
fof(f_381_3,plain,
! [U_901,U_900] :
( ord_less_eq_int(zero_zero_int,power_power_int(U_900,U_901))
| ~ ord_less_eq_int(zero_zero_int,U_900) ),
inference(definitional_conversion,[status(esa)],[f_381_2]) ).
cnf(f_381_4,plain,
( ord_less_eq_int(zero_zero_int,power_power_int(U_900,U_901))
| ~ ord_less_eq_int(zero_zero_int,U_900) ),
inference(clausify,[status(thm)],[f_381_3]) ).
fof(f_382_1,plain,
! [N_24,A_23,B_6] :
( ord_less_eq_real(power_power_real(A_23,N_24),power_power_real(B_6,N_24))
| ~ ord_less_eq_real(zero_zero_real,A_23)
| ~ ord_less_eq_real(A_23,B_6) ),
inference(fof_nnf,[status(thm)],[fact_363_power__mono]) ).
fof(f_382_2,plain,
! [U_904,U_903,U_902] :
( ord_less_eq_real(power_power_real(U_903,U_904),power_power_real(U_902,U_904))
| ~ ord_less_eq_real(zero_zero_real,U_903)
| ~ ord_less_eq_real(U_903,U_902) ),
inference(variable_rename,[status(thm)],[f_382_1]) ).
fof(f_382_3,plain,
! [U_902,U_903,U_904] :
( ord_less_eq_real(power_power_real(U_903,U_904),power_power_real(U_902,U_904))
| ~ ord_less_eq_real(zero_zero_real,U_903)
| ~ ord_less_eq_real(U_903,U_902) ),
inference(definitional_conversion,[status(esa)],[f_382_2]) ).
cnf(f_382_4,plain,
( ord_less_eq_real(power_power_real(U_903,U_904),power_power_real(U_902,U_904))
| ~ ord_less_eq_real(zero_zero_real,U_903)
| ~ ord_less_eq_real(U_903,U_902) ),
inference(clausify,[status(thm)],[f_382_3]) ).
fof(f_383_1,plain,
! [N_24,A_23,B_6] :
( ord_less_eq_nat(power_power_nat(A_23,N_24),power_power_nat(B_6,N_24))
| ~ ord_less_eq_nat(zero_zero_nat,A_23)
| ~ ord_less_eq_nat(A_23,B_6) ),
inference(fof_nnf,[status(thm)],[fact_364_power__mono]) ).
fof(f_383_2,plain,
! [U_907,U_906,U_905] :
( ord_less_eq_nat(power_power_nat(U_906,U_907),power_power_nat(U_905,U_907))
| ~ ord_less_eq_nat(zero_zero_nat,U_906)
| ~ ord_less_eq_nat(U_906,U_905) ),
inference(variable_rename,[status(thm)],[f_383_1]) ).
fof(f_383_3,plain,
! [U_905,U_906,U_907] :
( ord_less_eq_nat(power_power_nat(U_906,U_907),power_power_nat(U_905,U_907))
| ~ ord_less_eq_nat(zero_zero_nat,U_906)
| ~ ord_less_eq_nat(U_906,U_905) ),
inference(definitional_conversion,[status(esa)],[f_383_2]) ).
cnf(f_383_4,plain,
( ord_less_eq_nat(power_power_nat(U_906,U_907),power_power_nat(U_905,U_907))
| ~ ord_less_eq_nat(zero_zero_nat,U_906)
| ~ ord_less_eq_nat(U_906,U_905) ),
inference(clausify,[status(thm)],[f_383_3]) ).
fof(f_384_1,plain,
! [N_24,A_23,B_6] :
( ord_less_eq_int(power_power_int(A_23,N_24),power_power_int(B_6,N_24))
| ~ ord_less_eq_int(zero_zero_int,A_23)
| ~ ord_less_eq_int(A_23,B_6) ),
inference(fof_nnf,[status(thm)],[fact_365_power__mono]) ).
fof(f_384_2,plain,
! [U_910,U_909,U_908] :
( ord_less_eq_int(power_power_int(U_909,U_910),power_power_int(U_908,U_910))
| ~ ord_less_eq_int(zero_zero_int,U_909)
| ~ ord_less_eq_int(U_909,U_908) ),
inference(variable_rename,[status(thm)],[f_384_1]) ).
fof(f_384_3,plain,
! [U_909,U_908,U_910] :
( ord_less_eq_int(power_power_int(U_909,U_910),power_power_int(U_908,U_910))
| ~ ord_less_eq_int(zero_zero_int,U_909)
| ~ ord_less_eq_int(U_909,U_908) ),
inference(definitional_conversion,[status(esa)],[f_384_2]) ).
cnf(f_384_4,plain,
( ord_less_eq_int(power_power_int(U_909,U_910),power_power_int(U_908,U_910))
| ~ ord_less_eq_int(zero_zero_int,U_909)
| ~ ord_less_eq_int(U_909,U_908) ),
inference(clausify,[status(thm)],[f_384_3]) ).
fof(f_385_1,plain,
! [N_23,A_22] :
( ord_less_real(zero_zero_real,power_power_real(A_22,N_23))
| ~ ord_less_real(zero_zero_real,A_22) ),
inference(fof_nnf,[status(thm)],[fact_366_zero__less__power]) ).
fof(f_385_2,plain,
! [U_912,U_911] :
( ord_less_real(zero_zero_real,power_power_real(U_911,U_912))
| ~ ord_less_real(zero_zero_real,U_911) ),
inference(variable_rename,[status(thm)],[f_385_1]) ).
fof(f_385_3,plain,
! [U_912,U_911] :
( ord_less_real(zero_zero_real,power_power_real(U_911,U_912))
| ~ ord_less_real(zero_zero_real,U_911) ),
inference(definitional_conversion,[status(esa)],[f_385_2]) ).
cnf(f_385_4,plain,
( ord_less_real(zero_zero_real,power_power_real(U_911,U_912))
| ~ ord_less_real(zero_zero_real,U_911) ),
inference(clausify,[status(thm)],[f_385_3]) ).
fof(f_386_1,plain,
! [N_23,A_22] :
( ord_less_nat(zero_zero_nat,power_power_nat(A_22,N_23))
| ~ ord_less_nat(zero_zero_nat,A_22) ),
inference(fof_nnf,[status(thm)],[fact_367_zero__less__power]) ).
fof(f_386_2,plain,
! [U_914,U_913] :
( ord_less_nat(zero_zero_nat,power_power_nat(U_913,U_914))
| ~ ord_less_nat(zero_zero_nat,U_913) ),
inference(variable_rename,[status(thm)],[f_386_1]) ).
fof(f_386_3,plain,
! [U_913,U_914] :
( ord_less_nat(zero_zero_nat,power_power_nat(U_913,U_914))
| ~ ord_less_nat(zero_zero_nat,U_913) ),
inference(definitional_conversion,[status(esa)],[f_386_2]) ).
cnf(f_386_4,plain,
( ord_less_nat(zero_zero_nat,power_power_nat(U_913,U_914))
| ~ ord_less_nat(zero_zero_nat,U_913) ),
inference(clausify,[status(thm)],[f_386_3]) ).
fof(f_387_1,plain,
! [N_23,A_22] :
( ord_less_int(zero_zero_int,power_power_int(A_22,N_23))
| ~ ord_less_int(zero_zero_int,A_22) ),
inference(fof_nnf,[status(thm)],[fact_368_zero__less__power]) ).
fof(f_387_2,plain,
! [U_916,U_915] :
( ord_less_int(zero_zero_int,power_power_int(U_915,U_916))
| ~ ord_less_int(zero_zero_int,U_915) ),
inference(variable_rename,[status(thm)],[f_387_1]) ).
fof(f_387_3,plain,
! [U_915,U_916] :
( ord_less_int(zero_zero_int,power_power_int(U_915,U_916))
| ~ ord_less_int(zero_zero_int,U_915) ),
inference(definitional_conversion,[status(esa)],[f_387_2]) ).
cnf(f_387_4,plain,
( ord_less_int(zero_zero_int,power_power_int(U_915,U_916))
| ~ ord_less_int(zero_zero_int,U_915) ),
inference(clausify,[status(thm)],[f_387_3]) ).
fof(f_388_1,plain,
! [Z,X_1,Y_1,P] :
( zcong(power_power_int(X_1,times_times_nat(Y_1,Z)),one_one_int,P)
| ~ zcong(power_power_int(X_1,Y_1),one_one_int,P) ),
inference(fof_nnf,[status(thm)],[fact_369_zcong__zpower__zmult]) ).
fof(f_388_2,plain,
! [U_920,U_919,U_918,U_917] :
( zcong(power_power_int(U_919,times_times_nat(U_918,U_920)),one_one_int,U_917)
| ~ zcong(power_power_int(U_919,U_918),one_one_int,U_917) ),
inference(variable_rename,[status(thm)],[f_388_1]) ).
fof(f_388_3,plain,
! [U_917,U_918,U_919,U_920] :
( zcong(power_power_int(U_919,times_times_nat(U_918,U_920)),one_one_int,U_917)
| ~ zcong(power_power_int(U_919,U_918),one_one_int,U_917) ),
inference(definitional_conversion,[status(esa)],[f_388_2]) ).
cnf(f_388_4,plain,
( zcong(power_power_int(U_919,times_times_nat(U_918,U_920)),one_one_int,U_917)
| ~ zcong(power_power_int(U_919,U_918),one_one_int,U_917) ),
inference(clausify,[status(thm)],[f_388_3]) ).
fof(f_389_1,plain,
! [K_1,N_1,Ma] :
( ( dvd_dvd_int(K_1,plus_plus_int(N_1,times_times_int(K_1,Ma)))
| ~ dvd_dvd_int(K_1,N_1) )
& ( dvd_dvd_int(K_1,N_1)
| ~ dvd_dvd_int(K_1,plus_plus_int(N_1,times_times_int(K_1,Ma))) ) ),
inference(fof_nnf,[status(thm)],[fact_370_zdvd__reduce]) ).
fof(f_389_2,plain,
! [U_923,U_922,U_921] :
( ( dvd_dvd_int(U_923,plus_plus_int(U_922,times_times_int(U_923,U_921)))
| ~ dvd_dvd_int(U_923,U_922) )
& ( dvd_dvd_int(U_923,U_922)
| ~ dvd_dvd_int(U_923,plus_plus_int(U_922,times_times_int(U_923,U_921))) ) ),
inference(variable_rename,[status(thm)],[f_389_1]) ).
fof(f_389_3,plain,
( ! [U_929,U_927] :
( ! [U_925] : dvd_dvd_int(U_929,plus_plus_int(U_927,times_times_int(U_929,U_925)))
| ~ dvd_dvd_int(U_929,U_927) )
& ! [U_928,U_926] :
( ! [U_924] : ~ dvd_dvd_int(U_928,plus_plus_int(U_926,times_times_int(U_928,U_924)))
| dvd_dvd_int(U_928,U_926) ) ),
inference(miniscope,[status(thm)],[f_389_2]) ).
fof(f_389_4,plain,
( ! [U_929,U_925,U_927] :
( dvd_dvd_int(U_929,plus_plus_int(U_927,times_times_int(U_929,U_925)))
| ~ dvd_dvd_int(U_929,U_927) )
& ! [U_928,U_926,U_924] :
( ~ dvd_dvd_int(U_928,plus_plus_int(U_926,times_times_int(U_928,U_924)))
| dvd_dvd_int(U_928,U_926) ) ),
inference(definitional_conversion,[status(esa)],[f_389_3]) ).
cnf(f_389_5,plain,
( ~ dvd_dvd_int(U_928,plus_plus_int(U_926,times_times_int(U_928,U_924)))
| dvd_dvd_int(U_928,U_926) ),
inference(clausify,[status(thm)],[f_389_4]) ).
cnf(f_389_6,plain,
( dvd_dvd_int(U_929,plus_plus_int(U_927,times_times_int(U_929,U_925)))
| ~ dvd_dvd_int(U_929,U_927) ),
inference(clausify,[status(thm)],[f_389_4]) ).
fof(f_390_1,plain,
! [C,X_2,Ta,A_1,D] :
( ( ( dvd_dvd_int(A_1,plus_plus_int(X_2,Ta))
| ~ dvd_dvd_int(A_1,plus_plus_int(plus_plus_int(X_2,times_times_int(C,D)),Ta)) )
& ( dvd_dvd_int(A_1,plus_plus_int(plus_plus_int(X_2,times_times_int(C,D)),Ta))
| ~ dvd_dvd_int(A_1,plus_plus_int(X_2,Ta)) ) )
| ~ dvd_dvd_int(A_1,D) ),
inference(fof_nnf,[status(thm)],[fact_371_zdvd__period]) ).
fof(f_390_2,plain,
! [U_934,U_933,U_932,U_931,U_930] :
( ( ( dvd_dvd_int(U_931,plus_plus_int(U_933,U_932))
| ~ dvd_dvd_int(U_931,plus_plus_int(plus_plus_int(U_933,times_times_int(U_934,U_930)),U_932)) )
& ( dvd_dvd_int(U_931,plus_plus_int(plus_plus_int(U_933,times_times_int(U_934,U_930)),U_932))
| ~ dvd_dvd_int(U_931,plus_plus_int(U_933,U_932)) ) )
| ~ dvd_dvd_int(U_931,U_930) ),
inference(variable_rename,[status(thm)],[f_390_1]) ).
fof(f_390_3,plain,
( ! [U_930,U_932,U_931,U_933,U_934] :
( dvd_dvd_int(U_931,plus_plus_int(U_933,U_932))
| ~ dvd_dvd_int(U_931,plus_plus_int(plus_plus_int(U_933,times_times_int(U_934,U_930)),U_932))
| ~ sP31(U_930,U_932,U_931,U_933,U_934) )
& ! [U_930,U_932,U_931,U_933,U_934] :
( dvd_dvd_int(U_931,plus_plus_int(plus_plus_int(U_933,times_times_int(U_934,U_930)),U_932))
| ~ dvd_dvd_int(U_931,plus_plus_int(U_933,U_932))
| ~ sP31(U_930,U_932,U_931,U_933,U_934) )
& ! [U_930,U_932,U_931,U_933,U_934] :
( sP31(U_930,U_932,U_931,U_933,U_934)
| ~ dvd_dvd_int(U_931,U_930) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP31])],[f_390_2]) ).
cnf(f_390_4,plain,
( sP31(U_930,U_932,U_931,U_933,U_934)
| ~ dvd_dvd_int(U_931,U_930) ),
inference(clausify,[status(thm)],[f_390_3]) ).
cnf(f_390_5,plain,
( dvd_dvd_int(U_931,plus_plus_int(plus_plus_int(U_933,times_times_int(U_934,U_930)),U_932))
| ~ dvd_dvd_int(U_931,plus_plus_int(U_933,U_932))
| ~ sP31(U_930,U_932,U_931,U_933,U_934) ),
inference(clausify,[status(thm)],[f_390_3]) ).
cnf(f_390_6,plain,
( dvd_dvd_int(U_931,plus_plus_int(U_933,U_932))
| ~ dvd_dvd_int(U_931,plus_plus_int(plus_plus_int(U_933,times_times_int(U_934,U_930)),U_932))
| ~ sP31(U_930,U_932,U_931,U_933,U_934) ),
inference(clausify,[status(thm)],[f_390_3]) ).
fof(f_391_1,plain,
! [A_21,N_22,B_5] :
( ord_less_real(A_21,B_5)
| ~ ord_less_eq_real(zero_zero_real,B_5)
| ~ ord_less_real(power_power_real(A_21,N_22),power_power_real(B_5,N_22)) ),
inference(fof_nnf,[status(thm)],[fact_372_power__less__imp__less__base]) ).
fof(f_391_2,plain,
! [U_937,U_936,U_935] :
( ord_less_real(U_937,U_935)
| ~ ord_less_eq_real(zero_zero_real,U_935)
| ~ ord_less_real(power_power_real(U_937,U_936),power_power_real(U_935,U_936)) ),
inference(variable_rename,[status(thm)],[f_391_1]) ).
fof(f_391_3,plain,
! [U_935,U_937,U_936] :
( ord_less_real(U_937,U_935)
| ~ ord_less_eq_real(zero_zero_real,U_935)
| ~ ord_less_real(power_power_real(U_937,U_936),power_power_real(U_935,U_936)) ),
inference(definitional_conversion,[status(esa)],[f_391_2]) ).
cnf(f_391_4,plain,
( ord_less_real(U_937,U_935)
| ~ ord_less_eq_real(zero_zero_real,U_935)
| ~ ord_less_real(power_power_real(U_937,U_936),power_power_real(U_935,U_936)) ),
inference(clausify,[status(thm)],[f_391_3]) ).
fof(f_392_1,plain,
! [A_21,N_22,B_5] :
( ord_less_nat(A_21,B_5)
| ~ ord_less_eq_nat(zero_zero_nat,B_5)
| ~ ord_less_nat(power_power_nat(A_21,N_22),power_power_nat(B_5,N_22)) ),
inference(fof_nnf,[status(thm)],[fact_373_power__less__imp__less__base]) ).
fof(f_392_2,plain,
! [U_940,U_939,U_938] :
( ord_less_nat(U_940,U_938)
| ~ ord_less_eq_nat(zero_zero_nat,U_938)
| ~ ord_less_nat(power_power_nat(U_940,U_939),power_power_nat(U_938,U_939)) ),
inference(variable_rename,[status(thm)],[f_392_1]) ).
fof(f_392_3,plain,
! [U_938,U_939,U_940] :
( ord_less_nat(U_940,U_938)
| ~ ord_less_eq_nat(zero_zero_nat,U_938)
| ~ ord_less_nat(power_power_nat(U_940,U_939),power_power_nat(U_938,U_939)) ),
inference(definitional_conversion,[status(esa)],[f_392_2]) ).
cnf(f_392_4,plain,
( ord_less_nat(U_940,U_938)
| ~ ord_less_eq_nat(zero_zero_nat,U_938)
| ~ ord_less_nat(power_power_nat(U_940,U_939),power_power_nat(U_938,U_939)) ),
inference(clausify,[status(thm)],[f_392_3]) ).
fof(f_393_1,plain,
! [A_21,N_22,B_5] :
( ord_less_int(A_21,B_5)
| ~ ord_less_eq_int(zero_zero_int,B_5)
| ~ ord_less_int(power_power_int(A_21,N_22),power_power_int(B_5,N_22)) ),
inference(fof_nnf,[status(thm)],[fact_374_power__less__imp__less__base]) ).
fof(f_393_2,plain,
! [U_943,U_942,U_941] :
( ord_less_int(U_943,U_941)
| ~ ord_less_eq_int(zero_zero_int,U_941)
| ~ ord_less_int(power_power_int(U_943,U_942),power_power_int(U_941,U_942)) ),
inference(variable_rename,[status(thm)],[f_393_1]) ).
fof(f_393_3,plain,
! [U_942,U_941,U_943] :
( ord_less_int(U_943,U_941)
| ~ ord_less_eq_int(zero_zero_int,U_941)
| ~ ord_less_int(power_power_int(U_943,U_942),power_power_int(U_941,U_942)) ),
inference(definitional_conversion,[status(esa)],[f_393_2]) ).
cnf(f_393_4,plain,
( ord_less_int(U_943,U_941)
| ~ ord_less_eq_int(zero_zero_int,U_941)
| ~ ord_less_int(power_power_int(U_943,U_942),power_power_int(U_941,U_942)) ),
inference(clausify,[status(thm)],[f_393_3]) ).
fof(f_394_1,plain,
! [A_20,N_21,N_20] :
( ord_less_eq_real(power_power_real(A_20,N_20),power_power_real(A_20,N_21))
| ~ ord_less_eq_real(A_20,one_one_real)
| ~ ord_less_eq_real(zero_zero_real,A_20)
| ~ ord_less_eq_nat(N_21,N_20) ),
inference(fof_nnf,[status(thm)],[fact_375_power__decreasing]) ).
fof(f_394_2,plain,
! [U_946,U_945,U_944] :
( ord_less_eq_real(power_power_real(U_946,U_944),power_power_real(U_946,U_945))
| ~ ord_less_eq_real(U_946,one_one_real)
| ~ ord_less_eq_real(zero_zero_real,U_946)
| ~ ord_less_eq_nat(U_945,U_944) ),
inference(variable_rename,[status(thm)],[f_394_1]) ).
fof(f_394_3,plain,
! [U_944,U_945,U_946] :
( ord_less_eq_real(power_power_real(U_946,U_944),power_power_real(U_946,U_945))
| ~ ord_less_eq_real(U_946,one_one_real)
| ~ ord_less_eq_real(zero_zero_real,U_946)
| ~ ord_less_eq_nat(U_945,U_944) ),
inference(definitional_conversion,[status(esa)],[f_394_2]) ).
cnf(f_394_4,plain,
( ord_less_eq_real(power_power_real(U_946,U_944),power_power_real(U_946,U_945))
| ~ ord_less_eq_real(U_946,one_one_real)
| ~ ord_less_eq_real(zero_zero_real,U_946)
| ~ ord_less_eq_nat(U_945,U_944) ),
inference(clausify,[status(thm)],[f_394_3]) ).
fof(f_395_1,plain,
! [A_20,N_21,N_20] :
( ord_less_eq_nat(power_power_nat(A_20,N_20),power_power_nat(A_20,N_21))
| ~ ord_less_eq_nat(A_20,one_one_nat)
| ~ ord_less_eq_nat(zero_zero_nat,A_20)
| ~ ord_less_eq_nat(N_21,N_20) ),
inference(fof_nnf,[status(thm)],[fact_376_power__decreasing]) ).
fof(f_395_2,plain,
! [U_949,U_948,U_947] :
( ord_less_eq_nat(power_power_nat(U_949,U_947),power_power_nat(U_949,U_948))
| ~ ord_less_eq_nat(U_949,one_one_nat)
| ~ ord_less_eq_nat(zero_zero_nat,U_949)
| ~ ord_less_eq_nat(U_948,U_947) ),
inference(variable_rename,[status(thm)],[f_395_1]) ).
fof(f_395_3,plain,
! [U_948,U_947,U_949] :
( ord_less_eq_nat(power_power_nat(U_949,U_947),power_power_nat(U_949,U_948))
| ~ ord_less_eq_nat(U_949,one_one_nat)
| ~ ord_less_eq_nat(zero_zero_nat,U_949)
| ~ ord_less_eq_nat(U_948,U_947) ),
inference(definitional_conversion,[status(esa)],[f_395_2]) ).
cnf(f_395_4,plain,
( ord_less_eq_nat(power_power_nat(U_949,U_947),power_power_nat(U_949,U_948))
| ~ ord_less_eq_nat(U_949,one_one_nat)
| ~ ord_less_eq_nat(zero_zero_nat,U_949)
| ~ ord_less_eq_nat(U_948,U_947) ),
inference(clausify,[status(thm)],[f_395_3]) ).
fof(f_396_1,plain,
! [A_20,N_21,N_20] :
( ord_less_eq_int(power_power_int(A_20,N_20),power_power_int(A_20,N_21))
| ~ ord_less_eq_int(A_20,one_one_int)
| ~ ord_less_eq_int(zero_zero_int,A_20)
| ~ ord_less_eq_nat(N_21,N_20) ),
inference(fof_nnf,[status(thm)],[fact_377_power__decreasing]) ).
fof(f_396_2,plain,
! [U_952,U_951,U_950] :
( ord_less_eq_int(power_power_int(U_952,U_950),power_power_int(U_952,U_951))
| ~ ord_less_eq_int(U_952,one_one_int)
| ~ ord_less_eq_int(zero_zero_int,U_952)
| ~ ord_less_eq_nat(U_951,U_950) ),
inference(variable_rename,[status(thm)],[f_396_1]) ).
fof(f_396_3,plain,
! [U_951,U_950,U_952] :
( ord_less_eq_int(power_power_int(U_952,U_950),power_power_int(U_952,U_951))
| ~ ord_less_eq_int(U_952,one_one_int)
| ~ ord_less_eq_int(zero_zero_int,U_952)
| ~ ord_less_eq_nat(U_951,U_950) ),
inference(definitional_conversion,[status(esa)],[f_396_2]) ).
cnf(f_396_4,plain,
( ord_less_eq_int(power_power_int(U_952,U_950),power_power_int(U_952,U_951))
| ~ ord_less_eq_int(U_952,one_one_int)
| ~ ord_less_eq_int(zero_zero_int,U_952)
| ~ ord_less_eq_nat(U_951,U_950) ),
inference(clausify,[status(thm)],[f_396_3]) ).
fof(f_397_1,plain,
! [A_19,N_19,N_18] :
( ord_less_real(power_power_real(A_19,N_18),power_power_real(A_19,N_19))
| ~ ord_less_real(A_19,one_one_real)
| ~ ord_less_real(zero_zero_real,A_19)
| ~ ord_less_nat(N_19,N_18) ),
inference(fof_nnf,[status(thm)],[fact_378_power__strict__decreasing]) ).
fof(f_397_2,plain,
! [U_955,U_954,U_953] :
( ord_less_real(power_power_real(U_955,U_953),power_power_real(U_955,U_954))
| ~ ord_less_real(U_955,one_one_real)
| ~ ord_less_real(zero_zero_real,U_955)
| ~ ord_less_nat(U_954,U_953) ),
inference(variable_rename,[status(thm)],[f_397_1]) ).
fof(f_397_3,plain,
! [U_954,U_953,U_955] :
( ord_less_real(power_power_real(U_955,U_953),power_power_real(U_955,U_954))
| ~ ord_less_real(U_955,one_one_real)
| ~ ord_less_real(zero_zero_real,U_955)
| ~ ord_less_nat(U_954,U_953) ),
inference(definitional_conversion,[status(esa)],[f_397_2]) ).
cnf(f_397_4,plain,
( ord_less_real(power_power_real(U_955,U_953),power_power_real(U_955,U_954))
| ~ ord_less_real(U_955,one_one_real)
| ~ ord_less_real(zero_zero_real,U_955)
| ~ ord_less_nat(U_954,U_953) ),
inference(clausify,[status(thm)],[f_397_3]) ).
fof(f_398_1,plain,
! [A_19,N_19,N_18] :
( ord_less_nat(power_power_nat(A_19,N_18),power_power_nat(A_19,N_19))
| ~ ord_less_nat(A_19,one_one_nat)
| ~ ord_less_nat(zero_zero_nat,A_19)
| ~ ord_less_nat(N_19,N_18) ),
inference(fof_nnf,[status(thm)],[fact_379_power__strict__decreasing]) ).
fof(f_398_2,plain,
! [U_958,U_957,U_956] :
( ord_less_nat(power_power_nat(U_958,U_956),power_power_nat(U_958,U_957))
| ~ ord_less_nat(U_958,one_one_nat)
| ~ ord_less_nat(zero_zero_nat,U_958)
| ~ ord_less_nat(U_957,U_956) ),
inference(variable_rename,[status(thm)],[f_398_1]) ).
fof(f_398_3,plain,
! [U_957,U_956,U_958] :
( ord_less_nat(power_power_nat(U_958,U_956),power_power_nat(U_958,U_957))
| ~ ord_less_nat(U_958,one_one_nat)
| ~ ord_less_nat(zero_zero_nat,U_958)
| ~ ord_less_nat(U_957,U_956) ),
inference(definitional_conversion,[status(esa)],[f_398_2]) ).
cnf(f_398_4,plain,
( ord_less_nat(power_power_nat(U_958,U_956),power_power_nat(U_958,U_957))
| ~ ord_less_nat(U_958,one_one_nat)
| ~ ord_less_nat(zero_zero_nat,U_958)
| ~ ord_less_nat(U_957,U_956) ),
inference(clausify,[status(thm)],[f_398_3]) ).
fof(f_399_1,plain,
! [A_19,N_19,N_18] :
( ord_less_int(power_power_int(A_19,N_18),power_power_int(A_19,N_19))
| ~ ord_less_int(A_19,one_one_int)
| ~ ord_less_int(zero_zero_int,A_19)
| ~ ord_less_nat(N_19,N_18) ),
inference(fof_nnf,[status(thm)],[fact_380_power__strict__decreasing]) ).
fof(f_399_2,plain,
! [U_961,U_960,U_959] :
( ord_less_int(power_power_int(U_961,U_959),power_power_int(U_961,U_960))
| ~ ord_less_int(U_961,one_one_int)
| ~ ord_less_int(zero_zero_int,U_961)
| ~ ord_less_nat(U_960,U_959) ),
inference(variable_rename,[status(thm)],[f_399_1]) ).
fof(f_399_3,plain,
! [U_960,U_959,U_961] :
( ord_less_int(power_power_int(U_961,U_959),power_power_int(U_961,U_960))
| ~ ord_less_int(U_961,one_one_int)
| ~ ord_less_int(zero_zero_int,U_961)
| ~ ord_less_nat(U_960,U_959) ),
inference(definitional_conversion,[status(esa)],[f_399_2]) ).
cnf(f_399_4,plain,
( ord_less_int(power_power_int(U_961,U_959),power_power_int(U_961,U_960))
| ~ ord_less_int(U_961,one_one_int)
| ~ ord_less_int(zero_zero_int,U_961)
| ~ ord_less_nat(U_960,U_959) ),
inference(clausify,[status(thm)],[f_399_3]) ).
fof(f_400_1,plain,
! [A_1] :
( ( ord_less_real(plus_plus_real(A_1,A_1),zero_zero_real)
| ~ ord_less_real(A_1,zero_zero_real) )
& ( ord_less_real(A_1,zero_zero_real)
| ~ ord_less_real(plus_plus_real(A_1,A_1),zero_zero_real) ) ),
inference(fof_nnf,[status(thm)],[fact_381_even__less__0__iff]) ).
fof(f_400_2,plain,
! [U_962] :
( ( ord_less_real(plus_plus_real(U_962,U_962),zero_zero_real)
| ~ ord_less_real(U_962,zero_zero_real) )
& ( ord_less_real(U_962,zero_zero_real)
| ~ ord_less_real(plus_plus_real(U_962,U_962),zero_zero_real) ) ),
inference(variable_rename,[status(thm)],[f_400_1]) ).
fof(f_400_3,plain,
( ! [U_964] :
( ord_less_real(plus_plus_real(U_964,U_964),zero_zero_real)
| ~ ord_less_real(U_964,zero_zero_real) )
& ! [U_963] :
( ord_less_real(U_963,zero_zero_real)
| ~ ord_less_real(plus_plus_real(U_963,U_963),zero_zero_real) ) ),
inference(miniscope,[status(thm)],[f_400_2]) ).
fof(f_400_4,plain,
( ! [U_964] :
( ord_less_real(plus_plus_real(U_964,U_964),zero_zero_real)
| ~ ord_less_real(U_964,zero_zero_real) )
& ! [U_963] :
( ord_less_real(U_963,zero_zero_real)
| ~ ord_less_real(plus_plus_real(U_963,U_963),zero_zero_real) ) ),
inference(definitional_conversion,[status(esa)],[f_400_3]) ).
cnf(f_400_5,plain,
( ord_less_real(U_963,zero_zero_real)
| ~ ord_less_real(plus_plus_real(U_963,U_963),zero_zero_real) ),
inference(clausify,[status(thm)],[f_400_4]) ).
cnf(f_400_6,plain,
( ord_less_real(plus_plus_real(U_964,U_964),zero_zero_real)
| ~ ord_less_real(U_964,zero_zero_real) ),
inference(clausify,[status(thm)],[f_400_4]) ).
fof(f_401_1,plain,
! [A_1] :
( ( ord_less_int(plus_plus_int(A_1,A_1),zero_zero_int)
| ~ ord_less_int(A_1,zero_zero_int) )
& ( ord_less_int(A_1,zero_zero_int)
| ~ ord_less_int(plus_plus_int(A_1,A_1),zero_zero_int) ) ),
inference(fof_nnf,[status(thm)],[fact_382_even__less__0__iff]) ).
fof(f_401_2,plain,
! [U_965] :
( ( ord_less_int(plus_plus_int(U_965,U_965),zero_zero_int)
| ~ ord_less_int(U_965,zero_zero_int) )
& ( ord_less_int(U_965,zero_zero_int)
| ~ ord_less_int(plus_plus_int(U_965,U_965),zero_zero_int) ) ),
inference(variable_rename,[status(thm)],[f_401_1]) ).
fof(f_401_3,plain,
( ! [U_967] :
( ord_less_int(plus_plus_int(U_967,U_967),zero_zero_int)
| ~ ord_less_int(U_967,zero_zero_int) )
& ! [U_966] :
( ord_less_int(U_966,zero_zero_int)
| ~ ord_less_int(plus_plus_int(U_966,U_966),zero_zero_int) ) ),
inference(miniscope,[status(thm)],[f_401_2]) ).
fof(f_401_4,plain,
( ! [U_967] :
( ord_less_int(plus_plus_int(U_967,U_967),zero_zero_int)
| ~ ord_less_int(U_967,zero_zero_int) )
& ! [U_966] :
( ord_less_int(U_966,zero_zero_int)
| ~ ord_less_int(plus_plus_int(U_966,U_966),zero_zero_int) ) ),
inference(definitional_conversion,[status(esa)],[f_401_3]) ).
cnf(f_401_5,plain,
( ord_less_int(U_966,zero_zero_int)
| ~ ord_less_int(plus_plus_int(U_966,U_966),zero_zero_int) ),
inference(clausify,[status(thm)],[f_401_4]) ).
cnf(f_401_6,plain,
( ord_less_int(plus_plus_int(U_967,U_967),zero_zero_int)
| ~ ord_less_int(U_967,zero_zero_int) ),
inference(clausify,[status(thm)],[f_401_4]) ).
fof(f_402_1,plain,
! [X_2,Y_2] :
( ( plus_plus_real(times_times_real(X_2,X_2),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 )
| plus_plus_real(times_times_real(X_2,X_2),times_times_real(Y_2,Y_2)) != zero_zero_real ) ),
inference(fof_nnf,[status(thm)],[fact_383_sum__squares__eq__zero__iff]) ).
fof(f_402_2,plain,
! [U_969,U_968] :
( ( plus_plus_real(times_times_real(U_969,U_969),times_times_real(U_968,U_968)) = zero_zero_real
| U_968 != zero_zero_real
| U_969 != zero_zero_real )
& ( ( U_968 = zero_zero_real
& U_969 = zero_zero_real )
| plus_plus_real(times_times_real(U_969,U_969),times_times_real(U_968,U_968)) != zero_zero_real ) ),
inference(variable_rename,[status(thm)],[f_402_1]) ).
fof(f_402_3,plain,
( ! [U_973,U_971] :
( plus_plus_real(times_times_real(U_973,U_973),times_times_real(U_971,U_971)) = zero_zero_real
| U_971 != zero_zero_real
| U_973 != zero_zero_real )
& ! [U_972,U_970] :
( ( U_970 = zero_zero_real
& U_972 = zero_zero_real )
| plus_plus_real(times_times_real(U_972,U_972),times_times_real(U_970,U_970)) != zero_zero_real ) ),
inference(miniscope,[status(thm)],[f_402_2]) ).
fof(f_402_4,plain,
( ! [U_970,U_972] :
( U_970 = zero_zero_real
| ~ sP32(U_970,U_972) )
& ! [U_970,U_972] :
( U_972 = zero_zero_real
| ~ sP32(U_970,U_972) )
& ! [U_973,U_971] :
( plus_plus_real(times_times_real(U_973,U_973),times_times_real(U_971,U_971)) = zero_zero_real
| U_971 != zero_zero_real
| U_973 != zero_zero_real )
& ! [U_970,U_972] :
( sP32(U_970,U_972)
| plus_plus_real(times_times_real(U_972,U_972),times_times_real(U_970,U_970)) != zero_zero_real ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP32])],[f_402_3]) ).
cnf(f_402_5,plain,
( sP32(U_970,U_972)
| plus_plus_real(times_times_real(U_972,U_972),times_times_real(U_970,U_970)) != zero_zero_real ),
inference(clausify,[status(thm)],[f_402_4]) ).
cnf(f_402_6,plain,
( plus_plus_real(times_times_real(U_973,U_973),times_times_real(U_971,U_971)) = zero_zero_real
| U_971 != zero_zero_real
| U_973 != zero_zero_real ),
inference(clausify,[status(thm)],[f_402_4]) ).
cnf(f_402_7,plain,
( U_972 = zero_zero_real
| ~ sP32(U_970,U_972) ),
inference(clausify,[status(thm)],[f_402_4]) ).
cnf(f_402_8,plain,
( U_970 = zero_zero_real
| ~ sP32(U_970,U_972) ),
inference(clausify,[status(thm)],[f_402_4]) ).
fof(f_403_1,plain,
! [X_2,Y_2] :
( ( ( plus_plus_int(times_times_int(X_2,X_2),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 )
| plus_plus_int(times_times_int(X_2,X_2),times_times_int(Y_2,Y_2)) != zero_zero_int ) )
| ~ is_int(Y_2)
| ~ is_int(X_2) ),
inference(fof_nnf,[status(thm)],[fact_384_sum__squares__eq__zero__iff]) ).
fof(f_403_2,plain,
! [U_975,U_974] :
( ( ( plus_plus_int(times_times_int(U_975,U_975),times_times_int(U_974,U_974)) = zero_zero_int
| U_974 != zero_zero_int
| U_975 != zero_zero_int )
& ( ( U_974 = zero_zero_int
& U_975 = zero_zero_int )
| plus_plus_int(times_times_int(U_975,U_975),times_times_int(U_974,U_974)) != zero_zero_int ) )
| ~ is_int(U_974)
| ~ is_int(U_975) ),
inference(variable_rename,[status(thm)],[f_403_1]) ).
fof(f_403_3,plain,
( ! [U_975,U_974] :
( U_974 = zero_zero_int
| ~ sP33(U_975,U_974) )
& ! [U_975,U_974] :
( U_975 = zero_zero_int
| ~ sP33(U_975,U_974) )
& ! [U_975,U_974] :
( plus_plus_int(times_times_int(U_975,U_975),times_times_int(U_974,U_974)) = zero_zero_int
| U_974 != zero_zero_int
| U_975 != zero_zero_int
| ~ sP34(U_975,U_974) )
& ! [U_975,U_974] :
( sP33(U_975,U_974)
| plus_plus_int(times_times_int(U_975,U_975),times_times_int(U_974,U_974)) != zero_zero_int
| ~ sP34(U_975,U_974) )
& ! [U_975,U_974] :
( sP34(U_975,U_974)
| ~ is_int(U_974)
| ~ is_int(U_975) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP33,sP34])],[f_403_2]) ).
cnf(f_403_4,plain,
( sP34(U_975,U_974)
| ~ is_int(U_974)
| ~ is_int(U_975) ),
inference(clausify,[status(thm)],[f_403_3]) ).
cnf(f_403_5,plain,
( sP33(U_975,U_974)
| plus_plus_int(times_times_int(U_975,U_975),times_times_int(U_974,U_974)) != zero_zero_int
| ~ sP34(U_975,U_974) ),
inference(clausify,[status(thm)],[f_403_3]) ).
cnf(f_403_6,plain,
( plus_plus_int(times_times_int(U_975,U_975),times_times_int(U_974,U_974)) = zero_zero_int
| U_974 != zero_zero_int
| U_975 != zero_zero_int
| ~ sP34(U_975,U_974) ),
inference(clausify,[status(thm)],[f_403_3]) ).
cnf(f_403_7,plain,
( U_975 = zero_zero_int
| ~ sP33(U_975,U_974) ),
inference(clausify,[status(thm)],[f_403_3]) ).
cnf(f_403_8,plain,
( U_974 = zero_zero_int
| ~ sP33(U_975,U_974) ),
inference(clausify,[status(thm)],[f_403_3]) ).
fof(f_404_1,plain,
! [C_2,D_2,A_18,B_4,R_3] :
( plus_plus_real(A_18,times_times_real(R_3,C_2)) != plus_plus_real(B_4,times_times_real(R_3,D_2))
| C_2 = D_2
| A_18 != B_4
| R_3 = zero_zero_real ),
inference(fof_nnf,[status(thm)],[fact_385_add__scale__eq__noteq]) ).
fof(f_404_2,plain,
! [U_980,U_979,U_978,U_977,U_976] :
( plus_plus_real(U_978,times_times_real(U_976,U_980)) != plus_plus_real(U_977,times_times_real(U_976,U_979))
| U_980 = U_979
| U_978 != U_977
| U_976 = zero_zero_real ),
inference(variable_rename,[status(thm)],[f_404_1]) ).
fof(f_404_3,plain,
! [U_977,U_980,U_978,U_976,U_979] :
( plus_plus_real(U_978,times_times_real(U_976,U_980)) != plus_plus_real(U_977,times_times_real(U_976,U_979))
| U_980 = U_979
| U_978 != U_977
| U_976 = zero_zero_real ),
inference(definitional_conversion,[status(esa)],[f_404_2]) ).
cnf(f_404_4,plain,
( plus_plus_real(U_978,times_times_real(U_976,U_980)) != plus_plus_real(U_977,times_times_real(U_976,U_979))
| U_980 = U_979
| U_978 != U_977
| U_976 = zero_zero_real ),
inference(clausify,[status(thm)],[f_404_3]) ).
fof(f_405_1,plain,
! [C_2,D_2,A_18,B_4,R_3] :
( plus_plus_nat(A_18,times_times_nat(R_3,C_2)) != plus_plus_nat(B_4,times_times_nat(R_3,D_2))
| C_2 = D_2
| A_18 != B_4
| R_3 = zero_zero_nat ),
inference(fof_nnf,[status(thm)],[fact_386_add__scale__eq__noteq]) ).
fof(f_405_2,plain,
! [U_985,U_984,U_983,U_982,U_981] :
( plus_plus_nat(U_983,times_times_nat(U_981,U_985)) != plus_plus_nat(U_982,times_times_nat(U_981,U_984))
| U_985 = U_984
| U_983 != U_982
| U_981 = zero_zero_nat ),
inference(variable_rename,[status(thm)],[f_405_1]) ).
fof(f_405_3,plain,
! [U_981,U_982,U_984,U_983,U_985] :
( plus_plus_nat(U_983,times_times_nat(U_981,U_985)) != plus_plus_nat(U_982,times_times_nat(U_981,U_984))
| U_985 = U_984
| U_983 != U_982
| U_981 = zero_zero_nat ),
inference(definitional_conversion,[status(esa)],[f_405_2]) ).
cnf(f_405_4,plain,
( plus_plus_nat(U_983,times_times_nat(U_981,U_985)) != plus_plus_nat(U_982,times_times_nat(U_981,U_984))
| U_985 = U_984
| U_983 != U_982
| U_981 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_405_3]) ).
fof(f_406_1,plain,
! [C_2,D_2,A_18,B_4,R_3] :
( plus_plus_int(A_18,times_times_int(R_3,C_2)) != plus_plus_int(B_4,times_times_int(R_3,D_2))
| C_2 = D_2
| A_18 != B_4
| R_3 = zero_zero_int
| ~ is_int(R_3)
| ~ is_int(D_2)
| ~ is_int(C_2) ),
inference(fof_nnf,[status(thm)],[fact_387_add__scale__eq__noteq]) ).
fof(f_406_2,plain,
! [U_990,U_989,U_988,U_987,U_986] :
( plus_plus_int(U_988,times_times_int(U_986,U_990)) != plus_plus_int(U_987,times_times_int(U_986,U_989))
| U_990 = U_989
| U_988 != U_987
| U_986 = zero_zero_int
| ~ is_int(U_986)
| ~ is_int(U_989)
| ~ is_int(U_990) ),
inference(variable_rename,[status(thm)],[f_406_1]) ).
fof(f_406_3,plain,
! [U_986,U_987,U_988,U_989,U_990] :
( plus_plus_int(U_988,times_times_int(U_986,U_990)) != plus_plus_int(U_987,times_times_int(U_986,U_989))
| U_990 = U_989
| U_988 != U_987
| U_986 = zero_zero_int
| ~ is_int(U_986)
| ~ is_int(U_989)
| ~ is_int(U_990) ),
inference(definitional_conversion,[status(esa)],[f_406_2]) ).
cnf(f_406_4,plain,
( plus_plus_int(U_988,times_times_int(U_986,U_990)) != plus_plus_int(U_987,times_times_int(U_986,U_989))
| U_990 = U_989
| U_988 != U_987
| U_986 = zero_zero_int
| ~ is_int(U_986)
| ~ is_int(U_989)
| ~ is_int(U_990) ),
inference(clausify,[status(thm)],[f_406_3]) ).
fof(f_407_1,plain,
! [A,N,P] :
( dvd_dvd_int(P,A)
| ~ dvd_dvd_int(P,power_power_int(A,N))
| ~ zprime(P) ),
inference(fof_nnf,[status(thm)],[fact_388_zprime__zdvd__power]) ).
fof(f_407_2,plain,
! [U_993,U_992,U_991] :
( dvd_dvd_int(U_991,U_993)
| ~ dvd_dvd_int(U_991,power_power_int(U_993,U_992))
| ~ zprime(U_991) ),
inference(variable_rename,[status(thm)],[f_407_1]) ).
fof(f_407_3,plain,
! [U_993,U_991,U_992] :
( dvd_dvd_int(U_991,U_993)
| ~ dvd_dvd_int(U_991,power_power_int(U_993,U_992))
| ~ zprime(U_991) ),
inference(definitional_conversion,[status(esa)],[f_407_2]) ).
cnf(f_407_4,plain,
( dvd_dvd_int(U_991,U_993)
| ~ dvd_dvd_int(U_991,power_power_int(U_993,U_992))
| ~ zprime(U_991) ),
inference(clausify,[status(thm)],[f_407_3]) ).
fof(f_408_1,plain,
zero_zero_real = number267125858f_real(pls),
inference(fof_nnf,[status(thm)],[fact_389_semiring__norm_I112_J]) ).
fof(f_408_2,plain,
zero_zero_real = number267125858f_real(pls),
inference(definitional_conversion,[status(esa)],[f_408_1]) ).
cnf(f_408_3,plain,
zero_zero_real = number267125858f_real(pls),
inference(clausify,[status(thm)],[f_408_2]) ).
fof(f_409_1,plain,
zero_zero_int = number_number_of_int(pls),
inference(fof_nnf,[status(thm)],[fact_390_semiring__norm_I112_J]) ).
fof(f_409_2,plain,
zero_zero_int = number_number_of_int(pls),
inference(definitional_conversion,[status(esa)],[f_409_1]) ).
cnf(f_409_3,plain,
zero_zero_int = number_number_of_int(pls),
inference(clausify,[status(thm)],[f_409_2]) ).
fof(f_410_1,plain,
number267125858f_real(pls) = zero_zero_real,
inference(fof_nnf,[status(thm)],[fact_391_number__of__Pls]) ).
fof(f_410_2,plain,
number267125858f_real(pls) = zero_zero_real,
inference(definitional_conversion,[status(esa)],[f_410_1]) ).
cnf(f_410_3,plain,
number267125858f_real(pls) = zero_zero_real,
inference(clausify,[status(thm)],[f_410_2]) ).
fof(f_411_1,plain,
number_number_of_int(pls) = zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_392_number__of__Pls]) ).
fof(f_411_2,plain,
number_number_of_int(pls) = zero_zero_int,
inference(definitional_conversion,[status(esa)],[f_411_1]) ).
cnf(f_411_3,plain,
number_number_of_int(pls) = zero_zero_int,
inference(clausify,[status(thm)],[f_411_2]) ).
fof(f_412_1,plain,
number267125858f_real(pls) = zero_zero_real,
inference(fof_nnf,[status(thm)],[fact_393_semiring__numeral__0__eq__0]) ).
fof(f_412_2,plain,
number267125858f_real(pls) = zero_zero_real,
inference(definitional_conversion,[status(esa)],[f_412_1]) ).
cnf(f_412_3,plain,
number267125858f_real(pls) = zero_zero_real,
inference(clausify,[status(thm)],[f_412_2]) ).
fof(f_413_1,plain,
number_number_of_nat(pls) = zero_zero_nat,
inference(fof_nnf,[status(thm)],[fact_394_semiring__numeral__0__eq__0]) ).
fof(f_413_2,plain,
number_number_of_nat(pls) = zero_zero_nat,
inference(definitional_conversion,[status(esa)],[f_413_1]) ).
cnf(f_413_3,plain,
number_number_of_nat(pls) = zero_zero_nat,
inference(clausify,[status(thm)],[f_413_2]) ).
fof(f_414_1,plain,
number_number_of_int(pls) = zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_395_semiring__numeral__0__eq__0]) ).
fof(f_414_2,plain,
number_number_of_int(pls) = zero_zero_int,
inference(definitional_conversion,[status(esa)],[f_414_1]) ).
cnf(f_414_3,plain,
number_number_of_int(pls) = zero_zero_int,
inference(clausify,[status(thm)],[f_414_2]) ).
fof(f_415_1,plain,
! [W_1] :
( ( ord_less_int(bit1(W_1),zero_zero_int)
| ~ ord_less_int(W_1,zero_zero_int) )
& ( ord_less_int(W_1,zero_zero_int)
| ~ ord_less_int(bit1(W_1),zero_zero_int) ) ),
inference(fof_nnf,[status(thm)],[fact_396_bin__less__0__simps_I4_J]) ).
fof(f_415_2,plain,
! [U_994] :
( ( ord_less_int(bit1(U_994),zero_zero_int)
| ~ ord_less_int(U_994,zero_zero_int) )
& ( ord_less_int(U_994,zero_zero_int)
| ~ ord_less_int(bit1(U_994),zero_zero_int) ) ),
inference(variable_rename,[status(thm)],[f_415_1]) ).
fof(f_415_3,plain,
( ! [U_996] :
( ord_less_int(bit1(U_996),zero_zero_int)
| ~ ord_less_int(U_996,zero_zero_int) )
& ! [U_995] :
( ord_less_int(U_995,zero_zero_int)
| ~ ord_less_int(bit1(U_995),zero_zero_int) ) ),
inference(miniscope,[status(thm)],[f_415_2]) ).
fof(f_415_4,plain,
( ! [U_996] :
( ord_less_int(bit1(U_996),zero_zero_int)
| ~ ord_less_int(U_996,zero_zero_int) )
& ! [U_995] :
( ord_less_int(U_995,zero_zero_int)
| ~ ord_less_int(bit1(U_995),zero_zero_int) ) ),
inference(definitional_conversion,[status(esa)],[f_415_3]) ).
cnf(f_415_5,plain,
( ord_less_int(U_995,zero_zero_int)
| ~ ord_less_int(bit1(U_995),zero_zero_int) ),
inference(clausify,[status(thm)],[f_415_4]) ).
cnf(f_415_6,plain,
( ord_less_int(bit1(U_996),zero_zero_int)
| ~ ord_less_int(U_996,zero_zero_int) ),
inference(clausify,[status(thm)],[f_415_4]) ).
fof(f_416_1,plain,
~ ord_less_int(pls,zero_zero_int),
inference(fof_nnf,[status(thm)],[fact_397_bin__less__0__simps_I1_J]) ).
fof(f_416_2,plain,
~ ord_less_int(pls,zero_zero_int),
inference(definitional_conversion,[status(esa)],[f_416_1]) ).
cnf(f_416_3,plain,
~ ord_less_int(pls,zero_zero_int),
inference(clausify,[status(thm)],[f_416_2]) ).
fof(f_417_1,plain,
! [W_1] :
( ( ord_less_int(bit0(W_1),zero_zero_int)
| ~ ord_less_int(W_1,zero_zero_int) )
& ( ord_less_int(W_1,zero_zero_int)
| ~ ord_less_int(bit0(W_1),zero_zero_int) ) ),
inference(fof_nnf,[status(thm)],[fact_398_bin__less__0__simps_I3_J]) ).
fof(f_417_2,plain,
! [U_997] :
( ( ord_less_int(bit0(U_997),zero_zero_int)
| ~ ord_less_int(U_997,zero_zero_int) )
& ( ord_less_int(U_997,zero_zero_int)
| ~ ord_less_int(bit0(U_997),zero_zero_int) ) ),
inference(variable_rename,[status(thm)],[f_417_1]) ).
fof(f_417_3,plain,
( ! [U_999] :
( ord_less_int(bit0(U_999),zero_zero_int)
| ~ ord_less_int(U_999,zero_zero_int) )
& ! [U_998] :
( ord_less_int(U_998,zero_zero_int)
| ~ ord_less_int(bit0(U_998),zero_zero_int) ) ),
inference(miniscope,[status(thm)],[f_417_2]) ).
fof(f_417_4,plain,
( ! [U_999] :
( ord_less_int(bit0(U_999),zero_zero_int)
| ~ ord_less_int(U_999,zero_zero_int) )
& ! [U_998] :
( ord_less_int(U_998,zero_zero_int)
| ~ ord_less_int(bit0(U_998),zero_zero_int) ) ),
inference(definitional_conversion,[status(esa)],[f_417_3]) ).
cnf(f_417_5,plain,
( ord_less_int(U_998,zero_zero_int)
| ~ ord_less_int(bit0(U_998),zero_zero_int) ),
inference(clausify,[status(thm)],[f_417_4]) ).
cnf(f_417_6,plain,
( ord_less_int(bit0(U_999),zero_zero_int)
| ~ ord_less_int(U_999,zero_zero_int) ),
inference(clausify,[status(thm)],[f_417_4]) ).
fof(f_418_1,plain,
zero_zero_int = number_number_of_int(pls),
inference(fof_nnf,[status(thm)],[fact_399_zero__is__num__zero]) ).
fof(f_418_2,plain,
zero_zero_int = number_number_of_int(pls),
inference(definitional_conversion,[status(esa)],[f_418_1]) ).
cnf(f_418_3,plain,
zero_zero_int = number_number_of_int(pls),
inference(clausify,[status(thm)],[f_418_2]) ).
fof(f_419_1,plain,
ord_less_int(zero_zero_int,one_one_int),
inference(fof_nnf,[status(thm)],[fact_400_int__0__less__1]) ).
fof(f_419_2,plain,
ord_less_int(zero_zero_int,one_one_int),
inference(definitional_conversion,[status(esa)],[f_419_1]) ).
cnf(f_419_3,plain,
ord_less_int(zero_zero_int,one_one_int),
inference(clausify,[status(thm)],[f_419_2]) ).
fof(f_420_1,plain,
! [B_1,A] :
( ord_less_int(zero_zero_int,B_1)
| ~ ord_less_int(zero_zero_int,times_times_int(A,B_1))
| ~ ord_less_int(zero_zero_int,A) ),
inference(fof_nnf,[status(thm)],[fact_401_pos__zmult__pos]) ).
fof(f_420_2,plain,
! [U_1001,U_1000] :
( ord_less_int(zero_zero_int,U_1001)
| ~ ord_less_int(zero_zero_int,times_times_int(U_1000,U_1001))
| ~ ord_less_int(zero_zero_int,U_1000) ),
inference(variable_rename,[status(thm)],[f_420_1]) ).
fof(f_420_3,plain,
! [U_1001,U_1000] :
( ord_less_int(zero_zero_int,U_1001)
| ~ ord_less_int(zero_zero_int,times_times_int(U_1000,U_1001))
| ~ ord_less_int(zero_zero_int,U_1000) ),
inference(definitional_conversion,[status(esa)],[f_420_2]) ).
cnf(f_420_4,plain,
( ord_less_int(zero_zero_int,U_1001)
| ~ ord_less_int(zero_zero_int,times_times_int(U_1000,U_1001))
| ~ ord_less_int(zero_zero_int,U_1000) ),
inference(clausify,[status(thm)],[f_420_3]) ).
fof(f_421_1,plain,
! [K,I,J] :
( ord_less_int(times_times_int(K,I),times_times_int(K,J))
| ~ ord_less_int(zero_zero_int,K)
| ~ ord_less_int(I,J) ),
inference(fof_nnf,[status(thm)],[fact_402_zmult__zless__mono2]) ).
fof(f_421_2,plain,
! [U_1004,U_1003,U_1002] :
( ord_less_int(times_times_int(U_1004,U_1003),times_times_int(U_1004,U_1002))
| ~ ord_less_int(zero_zero_int,U_1004)
| ~ ord_less_int(U_1003,U_1002) ),
inference(variable_rename,[status(thm)],[f_421_1]) ).
fof(f_421_3,plain,
! [U_1003,U_1002,U_1004] :
( ord_less_int(times_times_int(U_1004,U_1003),times_times_int(U_1004,U_1002))
| ~ ord_less_int(zero_zero_int,U_1004)
| ~ ord_less_int(U_1003,U_1002) ),
inference(definitional_conversion,[status(esa)],[f_421_2]) ).
cnf(f_421_4,plain,
( ord_less_int(times_times_int(U_1004,U_1003),times_times_int(U_1004,U_1002))
| ~ ord_less_int(zero_zero_int,U_1004)
| ~ ord_less_int(U_1003,U_1002) ),
inference(clausify,[status(thm)],[f_421_3]) ).
fof(f_422_1,plain,
! [Z] : plus_plus_int(plus_plus_int(one_one_int,Z),Z) != zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_403_odd__nonzero]) ).
fof(f_422_2,plain,
! [U_1005] : plus_plus_int(plus_plus_int(one_one_int,U_1005),U_1005) != zero_zero_int,
inference(variable_rename,[status(thm)],[f_422_1]) ).
fof(f_422_3,plain,
! [U_1005] : plus_plus_int(plus_plus_int(one_one_int,U_1005),U_1005) != zero_zero_int,
inference(definitional_conversion,[status(esa)],[f_422_2]) ).
cnf(f_422_4,plain,
plus_plus_int(plus_plus_int(one_one_int,U_1005),U_1005) != zero_zero_int,
inference(clausify,[status(thm)],[f_422_3]) ).
fof(f_423_1,plain,
! [N_17,A_17] :
( ord_less_real(times_times_real(A_17,power_power_real(A_17,N_17)),power_power_real(A_17,N_17))
| ~ ord_less_real(A_17,one_one_real)
| ~ ord_less_real(zero_zero_real,A_17) ),
inference(fof_nnf,[status(thm)],[fact_404_power__Suc__less]) ).
fof(f_423_2,plain,
! [U_1007,U_1006] :
( ord_less_real(times_times_real(U_1006,power_power_real(U_1006,U_1007)),power_power_real(U_1006,U_1007))
| ~ ord_less_real(U_1006,one_one_real)
| ~ ord_less_real(zero_zero_real,U_1006) ),
inference(variable_rename,[status(thm)],[f_423_1]) ).
fof(f_423_3,plain,
! [U_1006,U_1007] :
( ord_less_real(times_times_real(U_1006,power_power_real(U_1006,U_1007)),power_power_real(U_1006,U_1007))
| ~ ord_less_real(U_1006,one_one_real)
| ~ ord_less_real(zero_zero_real,U_1006) ),
inference(definitional_conversion,[status(esa)],[f_423_2]) ).
cnf(f_423_4,plain,
( ord_less_real(times_times_real(U_1006,power_power_real(U_1006,U_1007)),power_power_real(U_1006,U_1007))
| ~ ord_less_real(U_1006,one_one_real)
| ~ ord_less_real(zero_zero_real,U_1006) ),
inference(clausify,[status(thm)],[f_423_3]) ).
fof(f_424_1,plain,
! [N_17,A_17] :
( ord_less_nat(times_times_nat(A_17,power_power_nat(A_17,N_17)),power_power_nat(A_17,N_17))
| ~ ord_less_nat(A_17,one_one_nat)
| ~ ord_less_nat(zero_zero_nat,A_17) ),
inference(fof_nnf,[status(thm)],[fact_405_power__Suc__less]) ).
fof(f_424_2,plain,
! [U_1009,U_1008] :
( ord_less_nat(times_times_nat(U_1008,power_power_nat(U_1008,U_1009)),power_power_nat(U_1008,U_1009))
| ~ ord_less_nat(U_1008,one_one_nat)
| ~ ord_less_nat(zero_zero_nat,U_1008) ),
inference(variable_rename,[status(thm)],[f_424_1]) ).
fof(f_424_3,plain,
! [U_1008,U_1009] :
( ord_less_nat(times_times_nat(U_1008,power_power_nat(U_1008,U_1009)),power_power_nat(U_1008,U_1009))
| ~ ord_less_nat(U_1008,one_one_nat)
| ~ ord_less_nat(zero_zero_nat,U_1008) ),
inference(definitional_conversion,[status(esa)],[f_424_2]) ).
cnf(f_424_4,plain,
( ord_less_nat(times_times_nat(U_1008,power_power_nat(U_1008,U_1009)),power_power_nat(U_1008,U_1009))
| ~ ord_less_nat(U_1008,one_one_nat)
| ~ ord_less_nat(zero_zero_nat,U_1008) ),
inference(clausify,[status(thm)],[f_424_3]) ).
fof(f_425_1,plain,
! [N_17,A_17] :
( ord_less_int(times_times_int(A_17,power_power_int(A_17,N_17)),power_power_int(A_17,N_17))
| ~ ord_less_int(A_17,one_one_int)
| ~ ord_less_int(zero_zero_int,A_17) ),
inference(fof_nnf,[status(thm)],[fact_406_power__Suc__less]) ).
fof(f_425_2,plain,
! [U_1011,U_1010] :
( ord_less_int(times_times_int(U_1010,power_power_int(U_1010,U_1011)),power_power_int(U_1010,U_1011))
| ~ ord_less_int(U_1010,one_one_int)
| ~ ord_less_int(zero_zero_int,U_1010) ),
inference(variable_rename,[status(thm)],[f_425_1]) ).
fof(f_425_3,plain,
! [U_1010,U_1011] :
( ord_less_int(times_times_int(U_1010,power_power_int(U_1010,U_1011)),power_power_int(U_1010,U_1011))
| ~ ord_less_int(U_1010,one_one_int)
| ~ ord_less_int(zero_zero_int,U_1010) ),
inference(definitional_conversion,[status(esa)],[f_425_2]) ).
cnf(f_425_4,plain,
( ord_less_int(times_times_int(U_1010,power_power_int(U_1010,U_1011)),power_power_int(U_1010,U_1011))
| ~ ord_less_int(U_1010,one_one_int)
| ~ ord_less_int(zero_zero_int,U_1010) ),
inference(clausify,[status(thm)],[f_425_3]) ).
fof(f_426_1,plain,
! [N,B_1,A,P] :
( dvd_dvd_int(power_power_int(P,N),B_1)
| ~ dvd_dvd_int(power_power_int(P,N),times_times_int(A,B_1))
| dvd_dvd_int(P,A)
| ~ zprime(P) ),
inference(fof_nnf,[status(thm)],[fact_407_zprime__power__zdvd__cancel__left]) ).
fof(f_426_2,plain,
! [U_1015,U_1014,U_1013,U_1012] :
( dvd_dvd_int(power_power_int(U_1012,U_1015),U_1014)
| ~ dvd_dvd_int(power_power_int(U_1012,U_1015),times_times_int(U_1013,U_1014))
| dvd_dvd_int(U_1012,U_1013)
| ~ zprime(U_1012) ),
inference(variable_rename,[status(thm)],[f_426_1]) ).
fof(f_426_3,plain,
! [U_1012,U_1013,U_1014,U_1015] :
( dvd_dvd_int(power_power_int(U_1012,U_1015),U_1014)
| ~ dvd_dvd_int(power_power_int(U_1012,U_1015),times_times_int(U_1013,U_1014))
| dvd_dvd_int(U_1012,U_1013)
| ~ zprime(U_1012) ),
inference(definitional_conversion,[status(esa)],[f_426_2]) ).
cnf(f_426_4,plain,
( dvd_dvd_int(power_power_int(U_1012,U_1015),U_1014)
| ~ dvd_dvd_int(power_power_int(U_1012,U_1015),times_times_int(U_1013,U_1014))
| dvd_dvd_int(U_1012,U_1013)
| ~ zprime(U_1012) ),
inference(clausify,[status(thm)],[f_426_3]) ).
fof(f_427_1,plain,
! [N,A,B_1,P] :
( dvd_dvd_int(power_power_int(P,N),A)
| ~ dvd_dvd_int(power_power_int(P,N),times_times_int(A,B_1))
| dvd_dvd_int(P,B_1)
| ~ zprime(P) ),
inference(fof_nnf,[status(thm)],[fact_408_zprime__power__zdvd__cancel__right]) ).
fof(f_427_2,plain,
! [U_1019,U_1018,U_1017,U_1016] :
( dvd_dvd_int(power_power_int(U_1016,U_1019),U_1018)
| ~ dvd_dvd_int(power_power_int(U_1016,U_1019),times_times_int(U_1018,U_1017))
| dvd_dvd_int(U_1016,U_1017)
| ~ zprime(U_1016) ),
inference(variable_rename,[status(thm)],[f_427_1]) ).
fof(f_427_3,plain,
! [U_1016,U_1017,U_1018,U_1019] :
( dvd_dvd_int(power_power_int(U_1016,U_1019),U_1018)
| ~ dvd_dvd_int(power_power_int(U_1016,U_1019),times_times_int(U_1018,U_1017))
| dvd_dvd_int(U_1016,U_1017)
| ~ zprime(U_1016) ),
inference(definitional_conversion,[status(esa)],[f_427_2]) ).
cnf(f_427_4,plain,
( dvd_dvd_int(power_power_int(U_1016,U_1019),U_1018)
| ~ dvd_dvd_int(power_power_int(U_1016,U_1019),times_times_int(U_1018,U_1017))
| dvd_dvd_int(U_1016,U_1017)
| ~ zprime(U_1016) ),
inference(clausify,[status(thm)],[f_427_3]) ).
fof(f_428_1,plain,
! [X_12,Y_10] : ord_less_eq_real(zero_zero_real,plus_plus_real(times_times_real(X_12,X_12),times_times_real(Y_10,Y_10))),
inference(fof_nnf,[status(thm)],[fact_409_sum__squares__ge__zero]) ).
fof(f_428_2,plain,
! [U_1021,U_1020] : ord_less_eq_real(zero_zero_real,plus_plus_real(times_times_real(U_1021,U_1021),times_times_real(U_1020,U_1020))),
inference(variable_rename,[status(thm)],[f_428_1]) ).
fof(f_428_3,plain,
! [U_1020,U_1021] : ord_less_eq_real(zero_zero_real,plus_plus_real(times_times_real(U_1021,U_1021),times_times_real(U_1020,U_1020))),
inference(definitional_conversion,[status(esa)],[f_428_2]) ).
cnf(f_428_4,plain,
ord_less_eq_real(zero_zero_real,plus_plus_real(times_times_real(U_1021,U_1021),times_times_real(U_1020,U_1020))),
inference(clausify,[status(thm)],[f_428_3]) ).
fof(f_429_1,plain,
! [X_12,Y_10] : ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(X_12,X_12),times_times_int(Y_10,Y_10))),
inference(fof_nnf,[status(thm)],[fact_410_sum__squares__ge__zero]) ).
fof(f_429_2,plain,
! [U_1023,U_1022] : ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(U_1023,U_1023),times_times_int(U_1022,U_1022))),
inference(variable_rename,[status(thm)],[f_429_1]) ).
fof(f_429_3,plain,
! [U_1022,U_1023] : ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(U_1023,U_1023),times_times_int(U_1022,U_1022))),
inference(definitional_conversion,[status(esa)],[f_429_2]) ).
cnf(f_429_4,plain,
ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(U_1023,U_1023),times_times_int(U_1022,U_1022))),
inference(clausify,[status(thm)],[f_429_3]) ).
fof(f_430_1,plain,
! [X_2,Y_2] :
( ( ord_less_eq_real(plus_plus_real(times_times_real(X_2,X_2),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 )
| ~ ord_less_eq_real(plus_plus_real(times_times_real(X_2,X_2),times_times_real(Y_2,Y_2)),zero_zero_real) ) ),
inference(fof_nnf,[status(thm)],[fact_411_sum__squares__le__zero__iff]) ).
fof(f_430_2,plain,
! [U_1025,U_1024] :
( ( ord_less_eq_real(plus_plus_real(times_times_real(U_1025,U_1025),times_times_real(U_1024,U_1024)),zero_zero_real)
| U_1024 != zero_zero_real
| U_1025 != zero_zero_real )
& ( ( U_1024 = zero_zero_real
& U_1025 = zero_zero_real )
| ~ ord_less_eq_real(plus_plus_real(times_times_real(U_1025,U_1025),times_times_real(U_1024,U_1024)),zero_zero_real) ) ),
inference(variable_rename,[status(thm)],[f_430_1]) ).
fof(f_430_3,plain,
( ! [U_1029,U_1027] :
( ord_less_eq_real(plus_plus_real(times_times_real(U_1029,U_1029),times_times_real(U_1027,U_1027)),zero_zero_real)
| U_1027 != zero_zero_real
| U_1029 != zero_zero_real )
& ! [U_1028,U_1026] :
( ( U_1026 = zero_zero_real
& U_1028 = zero_zero_real )
| ~ ord_less_eq_real(plus_plus_real(times_times_real(U_1028,U_1028),times_times_real(U_1026,U_1026)),zero_zero_real) ) ),
inference(miniscope,[status(thm)],[f_430_2]) ).
fof(f_430_4,plain,
( ! [U_1028,U_1026] :
( U_1026 = zero_zero_real
| ~ sP35(U_1028,U_1026) )
& ! [U_1028,U_1026] :
( U_1028 = zero_zero_real
| ~ sP35(U_1028,U_1026) )
& ! [U_1027,U_1029] :
( ord_less_eq_real(plus_plus_real(times_times_real(U_1029,U_1029),times_times_real(U_1027,U_1027)),zero_zero_real)
| U_1027 != zero_zero_real
| U_1029 != zero_zero_real )
& ! [U_1028,U_1026] :
( sP35(U_1028,U_1026)
| ~ ord_less_eq_real(plus_plus_real(times_times_real(U_1028,U_1028),times_times_real(U_1026,U_1026)),zero_zero_real) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP35])],[f_430_3]) ).
cnf(f_430_5,plain,
( sP35(U_1028,U_1026)
| ~ ord_less_eq_real(plus_plus_real(times_times_real(U_1028,U_1028),times_times_real(U_1026,U_1026)),zero_zero_real) ),
inference(clausify,[status(thm)],[f_430_4]) ).
cnf(f_430_6,plain,
( ord_less_eq_real(plus_plus_real(times_times_real(U_1029,U_1029),times_times_real(U_1027,U_1027)),zero_zero_real)
| U_1027 != zero_zero_real
| U_1029 != zero_zero_real ),
inference(clausify,[status(thm)],[f_430_4]) ).
cnf(f_430_7,plain,
( U_1028 = zero_zero_real
| ~ sP35(U_1028,U_1026) ),
inference(clausify,[status(thm)],[f_430_4]) ).
cnf(f_430_8,plain,
( U_1026 = zero_zero_real
| ~ sP35(U_1028,U_1026) ),
inference(clausify,[status(thm)],[f_430_4]) ).
fof(f_431_1,plain,
! [X_2,Y_2] :
( ( ( ord_less_eq_int(plus_plus_int(times_times_int(X_2,X_2),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 )
| ~ ord_less_eq_int(plus_plus_int(times_times_int(X_2,X_2),times_times_int(Y_2,Y_2)),zero_zero_int) ) )
| ~ is_int(Y_2)
| ~ is_int(X_2) ),
inference(fof_nnf,[status(thm)],[fact_412_sum__squares__le__zero__iff]) ).
fof(f_431_2,plain,
! [U_1031,U_1030] :
( ( ( ord_less_eq_int(plus_plus_int(times_times_int(U_1031,U_1031),times_times_int(U_1030,U_1030)),zero_zero_int)
| U_1030 != zero_zero_int
| U_1031 != zero_zero_int )
& ( ( U_1030 = zero_zero_int
& U_1031 = zero_zero_int )
| ~ ord_less_eq_int(plus_plus_int(times_times_int(U_1031,U_1031),times_times_int(U_1030,U_1030)),zero_zero_int) ) )
| ~ is_int(U_1030)
| ~ is_int(U_1031) ),
inference(variable_rename,[status(thm)],[f_431_1]) ).
fof(f_431_3,plain,
( ! [U_1031,U_1030] :
( U_1030 = zero_zero_int
| ~ sP36(U_1031,U_1030) )
& ! [U_1031,U_1030] :
( U_1031 = zero_zero_int
| ~ sP36(U_1031,U_1030) )
& ! [U_1031,U_1030] :
( ord_less_eq_int(plus_plus_int(times_times_int(U_1031,U_1031),times_times_int(U_1030,U_1030)),zero_zero_int)
| U_1030 != zero_zero_int
| U_1031 != zero_zero_int
| ~ sP37(U_1031,U_1030) )
& ! [U_1031,U_1030] :
( sP36(U_1031,U_1030)
| ~ ord_less_eq_int(plus_plus_int(times_times_int(U_1031,U_1031),times_times_int(U_1030,U_1030)),zero_zero_int)
| ~ sP37(U_1031,U_1030) )
& ! [U_1031,U_1030] :
( sP37(U_1031,U_1030)
| ~ is_int(U_1030)
| ~ is_int(U_1031) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP36,sP37])],[f_431_2]) ).
cnf(f_431_4,plain,
( sP37(U_1031,U_1030)
| ~ is_int(U_1030)
| ~ is_int(U_1031) ),
inference(clausify,[status(thm)],[f_431_3]) ).
cnf(f_431_5,plain,
( sP36(U_1031,U_1030)
| ~ ord_less_eq_int(plus_plus_int(times_times_int(U_1031,U_1031),times_times_int(U_1030,U_1030)),zero_zero_int)
| ~ sP37(U_1031,U_1030) ),
inference(clausify,[status(thm)],[f_431_3]) ).
cnf(f_431_6,plain,
( ord_less_eq_int(plus_plus_int(times_times_int(U_1031,U_1031),times_times_int(U_1030,U_1030)),zero_zero_int)
| U_1030 != zero_zero_int
| U_1031 != zero_zero_int
| ~ sP37(U_1031,U_1030) ),
inference(clausify,[status(thm)],[f_431_3]) ).
cnf(f_431_7,plain,
( U_1031 = zero_zero_int
| ~ sP36(U_1031,U_1030) ),
inference(clausify,[status(thm)],[f_431_3]) ).
cnf(f_431_8,plain,
( U_1030 = zero_zero_int
| ~ sP36(U_1031,U_1030) ),
inference(clausify,[status(thm)],[f_431_3]) ).
fof(f_432_1,plain,
! [V_3,V_4] :
( ( ord_less_nat(number_number_of_nat(V_3),number_number_of_nat(V_4))
| ~ ord_less_int(V_3,V_4)
| ( ~ ord_less_int(pls,V_4)
& ord_less_int(V_3,V_4) ) )
& ( ( ord_less_int(V_3,V_4)
& ( ord_less_int(pls,V_4)
| ~ ord_less_int(V_3,V_4) ) )
| ~ ord_less_nat(number_number_of_nat(V_3),number_number_of_nat(V_4)) ) ),
inference(fof_nnf,[status(thm)],[fact_413_less__nat__number__of]) ).
fof(f_432_2,plain,
! [U_1033,U_1032] :
( ( ord_less_nat(number_number_of_nat(U_1033),number_number_of_nat(U_1032))
| ~ ord_less_int(U_1033,U_1032)
| ( ~ ord_less_int(pls,U_1032)
& ord_less_int(U_1033,U_1032) ) )
& ( ( ord_less_int(U_1033,U_1032)
& ( ord_less_int(pls,U_1032)
| ~ ord_less_int(U_1033,U_1032) ) )
| ~ ord_less_nat(number_number_of_nat(U_1033),number_number_of_nat(U_1032)) ) ),
inference(variable_rename,[status(thm)],[f_432_1]) ).
fof(f_432_3,plain,
( ! [U_1037,U_1035] :
( ord_less_nat(number_number_of_nat(U_1037),number_number_of_nat(U_1035))
| ~ ord_less_int(U_1037,U_1035)
| ( ~ ord_less_int(pls,U_1035)
& ord_less_int(U_1037,U_1035) ) )
& ! [U_1036,U_1034] :
( ( ord_less_int(U_1036,U_1034)
& ( ord_less_int(pls,U_1034)
| ~ ord_less_int(U_1036,U_1034) ) )
| ~ ord_less_nat(number_number_of_nat(U_1036),number_number_of_nat(U_1034)) ) ),
inference(miniscope,[status(thm)],[f_432_2]) ).
fof(f_432_4,plain,
( ! [U_1035,U_1037] :
( ~ ord_less_int(pls,U_1035)
| ~ sP39(U_1035,U_1037) )
& ! [U_1035,U_1037] :
( ord_less_int(U_1037,U_1035)
| ~ sP39(U_1035,U_1037) )
& ! [U_1034,U_1036] :
( ord_less_int(U_1036,U_1034)
| ~ sP38(U_1034,U_1036) )
& ! [U_1034,U_1036] :
( ord_less_int(pls,U_1034)
| ~ ord_less_int(U_1036,U_1034)
| ~ sP38(U_1034,U_1036) )
& ! [U_1035,U_1037] :
( ord_less_nat(number_number_of_nat(U_1037),number_number_of_nat(U_1035))
| ~ ord_less_int(U_1037,U_1035)
| sP39(U_1035,U_1037) )
& ! [U_1034,U_1036] :
( sP38(U_1034,U_1036)
| ~ ord_less_nat(number_number_of_nat(U_1036),number_number_of_nat(U_1034)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP38,sP39])],[f_432_3]) ).
cnf(f_432_5,plain,
( sP38(U_1034,U_1036)
| ~ ord_less_nat(number_number_of_nat(U_1036),number_number_of_nat(U_1034)) ),
inference(clausify,[status(thm)],[f_432_4]) ).
cnf(f_432_6,plain,
( ord_less_nat(number_number_of_nat(U_1037),number_number_of_nat(U_1035))
| ~ ord_less_int(U_1037,U_1035)
| sP39(U_1035,U_1037) ),
inference(clausify,[status(thm)],[f_432_4]) ).
cnf(f_432_7,plain,
( ord_less_int(pls,U_1034)
| ~ ord_less_int(U_1036,U_1034)
| ~ sP38(U_1034,U_1036) ),
inference(clausify,[status(thm)],[f_432_4]) ).
cnf(f_432_8,plain,
( ord_less_int(U_1036,U_1034)
| ~ sP38(U_1034,U_1036) ),
inference(clausify,[status(thm)],[f_432_4]) ).
cnf(f_432_9,plain,
( ord_less_int(U_1037,U_1035)
| ~ sP39(U_1035,U_1037) ),
inference(clausify,[status(thm)],[f_432_4]) ).
cnf(f_432_10,plain,
( ~ ord_less_int(pls,U_1035)
| ~ sP39(U_1035,U_1037) ),
inference(clausify,[status(thm)],[f_432_4]) ).
fof(f_433_1,plain,
! [X_11,Y_9] : ~ ord_less_real(plus_plus_real(times_times_real(X_11,X_11),times_times_real(Y_9,Y_9)),zero_zero_real),
inference(fof_nnf,[status(thm)],[fact_414_not__sum__squares__lt__zero]) ).
fof(f_433_2,plain,
! [U_1039,U_1038] : ~ ord_less_real(plus_plus_real(times_times_real(U_1039,U_1039),times_times_real(U_1038,U_1038)),zero_zero_real),
inference(variable_rename,[status(thm)],[f_433_1]) ).
fof(f_433_3,plain,
! [U_1039,U_1038] : ~ ord_less_real(plus_plus_real(times_times_real(U_1039,U_1039),times_times_real(U_1038,U_1038)),zero_zero_real),
inference(definitional_conversion,[status(esa)],[f_433_2]) ).
cnf(f_433_4,plain,
~ ord_less_real(plus_plus_real(times_times_real(U_1039,U_1039),times_times_real(U_1038,U_1038)),zero_zero_real),
inference(clausify,[status(thm)],[f_433_3]) ).
fof(f_434_1,plain,
! [X_11,Y_9] : ~ ord_less_int(plus_plus_int(times_times_int(X_11,X_11),times_times_int(Y_9,Y_9)),zero_zero_int),
inference(fof_nnf,[status(thm)],[fact_415_not__sum__squares__lt__zero]) ).
fof(f_434_2,plain,
! [U_1041,U_1040] : ~ ord_less_int(plus_plus_int(times_times_int(U_1041,U_1041),times_times_int(U_1040,U_1040)),zero_zero_int),
inference(variable_rename,[status(thm)],[f_434_1]) ).
fof(f_434_3,plain,
! [U_1040,U_1041] : ~ ord_less_int(plus_plus_int(times_times_int(U_1041,U_1041),times_times_int(U_1040,U_1040)),zero_zero_int),
inference(definitional_conversion,[status(esa)],[f_434_2]) ).
cnf(f_434_4,plain,
~ ord_less_int(plus_plus_int(times_times_int(U_1041,U_1041),times_times_int(U_1040,U_1040)),zero_zero_int),
inference(clausify,[status(thm)],[f_434_3]) ).
fof(f_435_1,plain,
! [X_2,Y_2] :
( ( ord_less_real(zero_zero_real,plus_plus_real(times_times_real(X_2,X_2),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
| ~ ord_less_real(zero_zero_real,plus_plus_real(times_times_real(X_2,X_2),times_times_real(Y_2,Y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_416_sum__squares__gt__zero__iff]) ).
fof(f_435_2,plain,
! [U_1043,U_1042] :
( ( ord_less_real(zero_zero_real,plus_plus_real(times_times_real(U_1043,U_1043),times_times_real(U_1042,U_1042)))
| ( U_1042 = zero_zero_real
& U_1043 = zero_zero_real ) )
& ( U_1042 != zero_zero_real
| U_1043 != zero_zero_real
| ~ ord_less_real(zero_zero_real,plus_plus_real(times_times_real(U_1043,U_1043),times_times_real(U_1042,U_1042))) ) ),
inference(variable_rename,[status(thm)],[f_435_1]) ).
fof(f_435_3,plain,
( ! [U_1047,U_1045] :
( ord_less_real(zero_zero_real,plus_plus_real(times_times_real(U_1047,U_1047),times_times_real(U_1045,U_1045)))
| ( U_1045 = zero_zero_real
& U_1047 = zero_zero_real ) )
& ! [U_1046,U_1044] :
( U_1044 != zero_zero_real
| U_1046 != zero_zero_real
| ~ ord_less_real(zero_zero_real,plus_plus_real(times_times_real(U_1046,U_1046),times_times_real(U_1044,U_1044))) ) ),
inference(miniscope,[status(thm)],[f_435_2]) ).
fof(f_435_4,plain,
( ! [U_1045,U_1047] :
( U_1045 = zero_zero_real
| ~ sP40(U_1045,U_1047) )
& ! [U_1045,U_1047] :
( U_1047 = zero_zero_real
| ~ sP40(U_1045,U_1047) )
& ! [U_1045,U_1047] :
( ord_less_real(zero_zero_real,plus_plus_real(times_times_real(U_1047,U_1047),times_times_real(U_1045,U_1045)))
| sP40(U_1045,U_1047) )
& ! [U_1046,U_1044] :
( U_1044 != zero_zero_real
| U_1046 != zero_zero_real
| ~ ord_less_real(zero_zero_real,plus_plus_real(times_times_real(U_1046,U_1046),times_times_real(U_1044,U_1044))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP40])],[f_435_3]) ).
cnf(f_435_5,plain,
( U_1044 != zero_zero_real
| U_1046 != zero_zero_real
| ~ ord_less_real(zero_zero_real,plus_plus_real(times_times_real(U_1046,U_1046),times_times_real(U_1044,U_1044))) ),
inference(clausify,[status(thm)],[f_435_4]) ).
cnf(f_435_6,plain,
( ord_less_real(zero_zero_real,plus_plus_real(times_times_real(U_1047,U_1047),times_times_real(U_1045,U_1045)))
| sP40(U_1045,U_1047) ),
inference(clausify,[status(thm)],[f_435_4]) ).
cnf(f_435_7,plain,
( U_1047 = zero_zero_real
| ~ sP40(U_1045,U_1047) ),
inference(clausify,[status(thm)],[f_435_4]) ).
cnf(f_435_8,plain,
( U_1045 = zero_zero_real
| ~ sP40(U_1045,U_1047) ),
inference(clausify,[status(thm)],[f_435_4]) ).
fof(f_436_1,plain,
! [X_2,Y_2] :
( ( ( ord_less_int(zero_zero_int,plus_plus_int(times_times_int(X_2,X_2),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
| ~ ord_less_int(zero_zero_int,plus_plus_int(times_times_int(X_2,X_2),times_times_int(Y_2,Y_2))) ) )
| ~ is_int(Y_2)
| ~ is_int(X_2) ),
inference(fof_nnf,[status(thm)],[fact_417_sum__squares__gt__zero__iff]) ).
fof(f_436_2,plain,
! [U_1049,U_1048] :
( ( ( ord_less_int(zero_zero_int,plus_plus_int(times_times_int(U_1049,U_1049),times_times_int(U_1048,U_1048)))
| ( U_1048 = zero_zero_int
& U_1049 = zero_zero_int ) )
& ( U_1048 != zero_zero_int
| U_1049 != zero_zero_int
| ~ ord_less_int(zero_zero_int,plus_plus_int(times_times_int(U_1049,U_1049),times_times_int(U_1048,U_1048))) ) )
| ~ is_int(U_1048)
| ~ is_int(U_1049) ),
inference(variable_rename,[status(thm)],[f_436_1]) ).
fof(f_436_3,plain,
( ! [U_1048,U_1049] :
( U_1048 = zero_zero_int
| ~ sP41(U_1048,U_1049) )
& ! [U_1048,U_1049] :
( U_1049 = zero_zero_int
| ~ sP41(U_1048,U_1049) )
& ! [U_1048,U_1049] :
( ord_less_int(zero_zero_int,plus_plus_int(times_times_int(U_1049,U_1049),times_times_int(U_1048,U_1048)))
| sP41(U_1048,U_1049)
| ~ sP42(U_1048,U_1049) )
& ! [U_1048,U_1049] :
( U_1048 != zero_zero_int
| U_1049 != zero_zero_int
| ~ ord_less_int(zero_zero_int,plus_plus_int(times_times_int(U_1049,U_1049),times_times_int(U_1048,U_1048)))
| ~ sP42(U_1048,U_1049) )
& ! [U_1048,U_1049] :
( sP42(U_1048,U_1049)
| ~ is_int(U_1048)
| ~ is_int(U_1049) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP41,sP42])],[f_436_2]) ).
cnf(f_436_4,plain,
( sP42(U_1048,U_1049)
| ~ is_int(U_1048)
| ~ is_int(U_1049) ),
inference(clausify,[status(thm)],[f_436_3]) ).
cnf(f_436_5,plain,
( U_1048 != zero_zero_int
| U_1049 != zero_zero_int
| ~ ord_less_int(zero_zero_int,plus_plus_int(times_times_int(U_1049,U_1049),times_times_int(U_1048,U_1048)))
| ~ sP42(U_1048,U_1049) ),
inference(clausify,[status(thm)],[f_436_3]) ).
cnf(f_436_6,plain,
( ord_less_int(zero_zero_int,plus_plus_int(times_times_int(U_1049,U_1049),times_times_int(U_1048,U_1048)))
| sP41(U_1048,U_1049)
| ~ sP42(U_1048,U_1049) ),
inference(clausify,[status(thm)],[f_436_3]) ).
cnf(f_436_7,plain,
( U_1049 = zero_zero_int
| ~ sP41(U_1048,U_1049) ),
inference(clausify,[status(thm)],[f_436_3]) ).
cnf(f_436_8,plain,
( U_1048 = zero_zero_int
| ~ sP41(U_1048,U_1049) ),
inference(clausify,[status(thm)],[f_436_3]) ).
fof(f_437_1,plain,
! [V_3,V_4] :
( ( ord_less_eq_nat(number_number_of_nat(V_3),number_number_of_nat(V_4))
| ( ~ ord_less_eq_int(V_3,pls)
& ~ ord_less_eq_int(V_3,V_4) ) )
& ( ord_less_eq_int(V_3,pls)
| ord_less_eq_int(V_3,V_4)
| ~ ord_less_eq_nat(number_number_of_nat(V_3),number_number_of_nat(V_4)) ) ),
inference(fof_nnf,[status(thm)],[fact_418_le__nat__number__of]) ).
fof(f_437_2,plain,
! [U_1051,U_1050] :
( ( ord_less_eq_nat(number_number_of_nat(U_1051),number_number_of_nat(U_1050))
| ( ~ ord_less_eq_int(U_1051,pls)
& ~ ord_less_eq_int(U_1051,U_1050) ) )
& ( ord_less_eq_int(U_1051,pls)
| ord_less_eq_int(U_1051,U_1050)
| ~ ord_less_eq_nat(number_number_of_nat(U_1051),number_number_of_nat(U_1050)) ) ),
inference(variable_rename,[status(thm)],[f_437_1]) ).
fof(f_437_3,plain,
( ! [U_1055,U_1053] :
( ord_less_eq_nat(number_number_of_nat(U_1055),number_number_of_nat(U_1053))
| ( ~ ord_less_eq_int(U_1055,pls)
& ~ ord_less_eq_int(U_1055,U_1053) ) )
& ! [U_1054,U_1052] :
( ord_less_eq_int(U_1054,pls)
| ord_less_eq_int(U_1054,U_1052)
| ~ ord_less_eq_nat(number_number_of_nat(U_1054),number_number_of_nat(U_1052)) ) ),
inference(miniscope,[status(thm)],[f_437_2]) ).
fof(f_437_4,plain,
( ! [U_1053,U_1055] :
( ~ ord_less_eq_int(U_1055,pls)
| ~ sP43(U_1053,U_1055) )
& ! [U_1053,U_1055] :
( ~ ord_less_eq_int(U_1055,U_1053)
| ~ sP43(U_1053,U_1055) )
& ! [U_1053,U_1055] :
( ord_less_eq_nat(number_number_of_nat(U_1055),number_number_of_nat(U_1053))
| sP43(U_1053,U_1055) )
& ! [U_1054,U_1052] :
( ord_less_eq_int(U_1054,pls)
| ord_less_eq_int(U_1054,U_1052)
| ~ ord_less_eq_nat(number_number_of_nat(U_1054),number_number_of_nat(U_1052)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP43])],[f_437_3]) ).
cnf(f_437_5,plain,
( ord_less_eq_int(U_1054,pls)
| ord_less_eq_int(U_1054,U_1052)
| ~ ord_less_eq_nat(number_number_of_nat(U_1054),number_number_of_nat(U_1052)) ),
inference(clausify,[status(thm)],[f_437_4]) ).
cnf(f_437_6,plain,
( ord_less_eq_nat(number_number_of_nat(U_1055),number_number_of_nat(U_1053))
| sP43(U_1053,U_1055) ),
inference(clausify,[status(thm)],[f_437_4]) ).
cnf(f_437_7,plain,
( ~ ord_less_eq_int(U_1055,U_1053)
| ~ sP43(U_1053,U_1055) ),
inference(clausify,[status(thm)],[f_437_4]) ).
cnf(f_437_8,plain,
( ~ ord_less_eq_int(U_1055,pls)
| ~ sP43(U_1053,U_1055) ),
inference(clausify,[status(thm)],[f_437_4]) ).
fof(f_438_1,plain,
! [W_4] : number267125858f_real(bit0(W_4)) = plus_plus_real(plus_plus_real(zero_zero_real,number267125858f_real(W_4)),number267125858f_real(W_4)),
inference(fof_nnf,[status(thm)],[fact_419_number__of__Bit0]) ).
fof(f_438_2,plain,
! [U_1056] : number267125858f_real(bit0(U_1056)) = plus_plus_real(plus_plus_real(zero_zero_real,number267125858f_real(U_1056)),number267125858f_real(U_1056)),
inference(variable_rename,[status(thm)],[f_438_1]) ).
fof(f_438_3,plain,
! [U_1056] : number267125858f_real(bit0(U_1056)) = plus_plus_real(plus_plus_real(zero_zero_real,number267125858f_real(U_1056)),number267125858f_real(U_1056)),
inference(definitional_conversion,[status(esa)],[f_438_2]) ).
cnf(f_438_4,plain,
number267125858f_real(bit0(U_1056)) = plus_plus_real(plus_plus_real(zero_zero_real,number267125858f_real(U_1056)),number267125858f_real(U_1056)),
inference(clausify,[status(thm)],[f_438_3]) ).
fof(f_439_1,plain,
! [W_4] : number_number_of_int(bit0(W_4)) = plus_plus_int(plus_plus_int(zero_zero_int,number_number_of_int(W_4)),number_number_of_int(W_4)),
inference(fof_nnf,[status(thm)],[fact_420_number__of__Bit0]) ).
fof(f_439_2,plain,
! [U_1057] : number_number_of_int(bit0(U_1057)) = plus_plus_int(plus_plus_int(zero_zero_int,number_number_of_int(U_1057)),number_number_of_int(U_1057)),
inference(variable_rename,[status(thm)],[f_439_1]) ).
fof(f_439_3,plain,
! [U_1057] : number_number_of_int(bit0(U_1057)) = plus_plus_int(plus_plus_int(zero_zero_int,number_number_of_int(U_1057)),number_number_of_int(U_1057)),
inference(definitional_conversion,[status(esa)],[f_439_2]) ).
cnf(f_439_4,plain,
number_number_of_int(bit0(U_1057)) = plus_plus_int(plus_plus_int(zero_zero_int,number_number_of_int(U_1057)),number_number_of_int(U_1057)),
inference(clausify,[status(thm)],[f_439_3]) ).
fof(f_440_1,plain,
! [A_16] : power_power_nat(A_16,one_one_nat) = A_16,
inference(fof_nnf,[status(thm)],[fact_421_power__one__right]) ).
fof(f_440_2,plain,
! [U_1058] : power_power_nat(U_1058,one_one_nat) = U_1058,
inference(variable_rename,[status(thm)],[f_440_1]) ).
fof(f_440_3,plain,
! [U_1058] : power_power_nat(U_1058,one_one_nat) = U_1058,
inference(definitional_conversion,[status(esa)],[f_440_2]) ).
cnf(f_440_4,plain,
power_power_nat(U_1058,one_one_nat) = U_1058,
inference(clausify,[status(thm)],[f_440_3]) ).
fof(f_441_1,plain,
! [A_16] : power_power_real(A_16,one_one_nat) = A_16,
inference(fof_nnf,[status(thm)],[fact_422_power__one__right]) ).
fof(f_441_2,plain,
! [U_1059] : power_power_real(U_1059,one_one_nat) = U_1059,
inference(variable_rename,[status(thm)],[f_441_1]) ).
fof(f_441_3,plain,
! [U_1059] : power_power_real(U_1059,one_one_nat) = U_1059,
inference(definitional_conversion,[status(esa)],[f_441_2]) ).
cnf(f_441_4,plain,
power_power_real(U_1059,one_one_nat) = U_1059,
inference(clausify,[status(thm)],[f_441_3]) ).
fof(f_442_1,plain,
! [A_16] :
( power_power_int(A_16,one_one_nat) = A_16
| ~ is_int(A_16) ),
inference(fof_nnf,[status(thm)],[fact_423_power__one__right]) ).
fof(f_442_2,plain,
! [U_1060] :
( power_power_int(U_1060,one_one_nat) = U_1060
| ~ is_int(U_1060) ),
inference(variable_rename,[status(thm)],[f_442_1]) ).
fof(f_442_3,plain,
! [U_1060] :
( power_power_int(U_1060,one_one_nat) = U_1060
| ~ is_int(U_1060) ),
inference(definitional_conversion,[status(esa)],[f_442_2]) ).
cnf(f_442_4,plain,
( power_power_int(U_1060,one_one_nat) = U_1060
| ~ is_int(U_1060) ),
inference(clausify,[status(thm)],[f_442_3]) ).
fof(f_443_1,plain,
! [Z_1] :
( ( ord_less_eq_int(one_one_int,Z_1)
| ~ ord_less_int(zero_zero_int,Z_1) )
& ( ord_less_int(zero_zero_int,Z_1)
| ~ ord_less_eq_int(one_one_int,Z_1) ) ),
inference(fof_nnf,[status(thm)],[fact_424_int__one__le__iff__zero__less]) ).
fof(f_443_2,plain,
! [U_1061] :
( ( ord_less_eq_int(one_one_int,U_1061)
| ~ ord_less_int(zero_zero_int,U_1061) )
& ( ord_less_int(zero_zero_int,U_1061)
| ~ ord_less_eq_int(one_one_int,U_1061) ) ),
inference(variable_rename,[status(thm)],[f_443_1]) ).
fof(f_443_3,plain,
( ! [U_1063] :
( ord_less_eq_int(one_one_int,U_1063)
| ~ ord_less_int(zero_zero_int,U_1063) )
& ! [U_1062] :
( ord_less_int(zero_zero_int,U_1062)
| ~ ord_less_eq_int(one_one_int,U_1062) ) ),
inference(miniscope,[status(thm)],[f_443_2]) ).
fof(f_443_4,plain,
( ! [U_1063] :
( ord_less_eq_int(one_one_int,U_1063)
| ~ ord_less_int(zero_zero_int,U_1063) )
& ! [U_1062] :
( ord_less_int(zero_zero_int,U_1062)
| ~ ord_less_eq_int(one_one_int,U_1062) ) ),
inference(definitional_conversion,[status(esa)],[f_443_3]) ).
cnf(f_443_5,plain,
( ord_less_int(zero_zero_int,U_1062)
| ~ ord_less_eq_int(one_one_int,U_1062) ),
inference(clausify,[status(thm)],[f_443_4]) ).
cnf(f_443_6,plain,
( ord_less_eq_int(one_one_int,U_1063)
| ~ ord_less_int(zero_zero_int,U_1063) ),
inference(clausify,[status(thm)],[f_443_4]) ).
fof(f_444_1,plain,
! [N_1,Ma] :
( ( ( times_times_int(Ma,N_1) = one_one_int
| N_1 != one_one_int
| Ma != one_one_int )
& ( ( N_1 = one_one_int
& Ma = one_one_int )
| times_times_int(Ma,N_1) != one_one_int ) )
| ~ ord_less_int(zero_zero_int,Ma)
| ~ is_int(Ma)
| ~ is_int(N_1) ),
inference(fof_nnf,[status(thm)],[fact_425_pos__zmult__eq__1__iff]) ).
fof(f_444_2,plain,
! [U_1065,U_1064] :
( ( ( times_times_int(U_1064,U_1065) = one_one_int
| U_1065 != one_one_int
| U_1064 != one_one_int )
& ( ( U_1065 = one_one_int
& U_1064 = one_one_int )
| times_times_int(U_1064,U_1065) != one_one_int ) )
| ~ ord_less_int(zero_zero_int,U_1064)
| ~ is_int(U_1064)
| ~ is_int(U_1065) ),
inference(variable_rename,[status(thm)],[f_444_1]) ).
fof(f_444_3,plain,
( ! [U_1065,U_1064] :
( U_1065 = one_one_int
| ~ sP44(U_1065,U_1064) )
& ! [U_1065,U_1064] :
( U_1064 = one_one_int
| ~ sP44(U_1065,U_1064) )
& ! [U_1065,U_1064] :
( times_times_int(U_1064,U_1065) = one_one_int
| U_1065 != one_one_int
| U_1064 != one_one_int
| ~ sP45(U_1065,U_1064) )
& ! [U_1065,U_1064] :
( sP44(U_1065,U_1064)
| times_times_int(U_1064,U_1065) != one_one_int
| ~ sP45(U_1065,U_1064) )
& ! [U_1065,U_1064] :
( sP45(U_1065,U_1064)
| ~ ord_less_int(zero_zero_int,U_1064)
| ~ is_int(U_1064)
| ~ is_int(U_1065) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP44,sP45])],[f_444_2]) ).
cnf(f_444_4,plain,
( sP45(U_1065,U_1064)
| ~ ord_less_int(zero_zero_int,U_1064)
| ~ is_int(U_1064)
| ~ is_int(U_1065) ),
inference(clausify,[status(thm)],[f_444_3]) ).
cnf(f_444_5,plain,
( sP44(U_1065,U_1064)
| times_times_int(U_1064,U_1065) != one_one_int
| ~ sP45(U_1065,U_1064) ),
inference(clausify,[status(thm)],[f_444_3]) ).
cnf(f_444_6,plain,
( times_times_int(U_1064,U_1065) = one_one_int
| U_1065 != one_one_int
| U_1064 != one_one_int
| ~ sP45(U_1065,U_1064) ),
inference(clausify,[status(thm)],[f_444_3]) ).
cnf(f_444_7,plain,
( U_1064 = one_one_int
| ~ sP44(U_1065,U_1064) ),
inference(clausify,[status(thm)],[f_444_3]) ).
cnf(f_444_8,plain,
( U_1065 = one_one_int
| ~ sP44(U_1065,U_1064) ),
inference(clausify,[status(thm)],[f_444_3]) ).
fof(f_445_1,plain,
! [Z_1] :
( ( ord_less_int(plus_plus_int(plus_plus_int(one_one_int,Z_1),Z_1),zero_zero_int)
| ~ ord_less_int(Z_1,zero_zero_int) )
& ( ord_less_int(Z_1,zero_zero_int)
| ~ ord_less_int(plus_plus_int(plus_plus_int(one_one_int,Z_1),Z_1),zero_zero_int) ) ),
inference(fof_nnf,[status(thm)],[fact_426_odd__less__0]) ).
fof(f_445_2,plain,
! [U_1066] :
( ( ord_less_int(plus_plus_int(plus_plus_int(one_one_int,U_1066),U_1066),zero_zero_int)
| ~ ord_less_int(U_1066,zero_zero_int) )
& ( ord_less_int(U_1066,zero_zero_int)
| ~ ord_less_int(plus_plus_int(plus_plus_int(one_one_int,U_1066),U_1066),zero_zero_int) ) ),
inference(variable_rename,[status(thm)],[f_445_1]) ).
fof(f_445_3,plain,
( ! [U_1068] :
( ord_less_int(plus_plus_int(plus_plus_int(one_one_int,U_1068),U_1068),zero_zero_int)
| ~ ord_less_int(U_1068,zero_zero_int) )
& ! [U_1067] :
( ord_less_int(U_1067,zero_zero_int)
| ~ ord_less_int(plus_plus_int(plus_plus_int(one_one_int,U_1067),U_1067),zero_zero_int) ) ),
inference(miniscope,[status(thm)],[f_445_2]) ).
fof(f_445_4,plain,
( ! [U_1068] :
( ord_less_int(plus_plus_int(plus_plus_int(one_one_int,U_1068),U_1068),zero_zero_int)
| ~ ord_less_int(U_1068,zero_zero_int) )
& ! [U_1067] :
( ord_less_int(U_1067,zero_zero_int)
| ~ ord_less_int(plus_plus_int(plus_plus_int(one_one_int,U_1067),U_1067),zero_zero_int) ) ),
inference(definitional_conversion,[status(esa)],[f_445_3]) ).
cnf(f_445_5,plain,
( ord_less_int(U_1067,zero_zero_int)
| ~ ord_less_int(plus_plus_int(plus_plus_int(one_one_int,U_1067),U_1067),zero_zero_int) ),
inference(clausify,[status(thm)],[f_445_4]) ).
cnf(f_445_6,plain,
( ord_less_int(plus_plus_int(plus_plus_int(one_one_int,U_1068),U_1068),zero_zero_int)
| ~ ord_less_int(U_1068,zero_zero_int) ),
inference(clausify,[status(thm)],[f_445_4]) ).
fof(f_446_1,plain,
! [Y_2] :
( ( ord_less_real(zero_zero_real,number267125858f_real(Y_2))
| ~ ord_less_int(pls,Y_2) )
& ( ord_less_int(pls,Y_2)
| ~ ord_less_real(zero_zero_real,number267125858f_real(Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_427_less__special_I1_J]) ).
fof(f_446_2,plain,
! [U_1069] :
( ( ord_less_real(zero_zero_real,number267125858f_real(U_1069))
| ~ ord_less_int(pls,U_1069) )
& ( ord_less_int(pls,U_1069)
| ~ ord_less_real(zero_zero_real,number267125858f_real(U_1069)) ) ),
inference(variable_rename,[status(thm)],[f_446_1]) ).
fof(f_446_3,plain,
( ! [U_1071] :
( ord_less_real(zero_zero_real,number267125858f_real(U_1071))
| ~ ord_less_int(pls,U_1071) )
& ! [U_1070] :
( ord_less_int(pls,U_1070)
| ~ ord_less_real(zero_zero_real,number267125858f_real(U_1070)) ) ),
inference(miniscope,[status(thm)],[f_446_2]) ).
fof(f_446_4,plain,
( ! [U_1071] :
( ord_less_real(zero_zero_real,number267125858f_real(U_1071))
| ~ ord_less_int(pls,U_1071) )
& ! [U_1070] :
( ord_less_int(pls,U_1070)
| ~ ord_less_real(zero_zero_real,number267125858f_real(U_1070)) ) ),
inference(definitional_conversion,[status(esa)],[f_446_3]) ).
cnf(f_446_5,plain,
( ord_less_int(pls,U_1070)
| ~ ord_less_real(zero_zero_real,number267125858f_real(U_1070)) ),
inference(clausify,[status(thm)],[f_446_4]) ).
cnf(f_446_6,plain,
( ord_less_real(zero_zero_real,number267125858f_real(U_1071))
| ~ ord_less_int(pls,U_1071) ),
inference(clausify,[status(thm)],[f_446_4]) ).
fof(f_447_1,plain,
! [Y_2] :
( ( ord_less_int(zero_zero_int,number_number_of_int(Y_2))
| ~ ord_less_int(pls,Y_2) )
& ( ord_less_int(pls,Y_2)
| ~ ord_less_int(zero_zero_int,number_number_of_int(Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_428_less__special_I1_J]) ).
fof(f_447_2,plain,
! [U_1072] :
( ( ord_less_int(zero_zero_int,number_number_of_int(U_1072))
| ~ ord_less_int(pls,U_1072) )
& ( ord_less_int(pls,U_1072)
| ~ ord_less_int(zero_zero_int,number_number_of_int(U_1072)) ) ),
inference(variable_rename,[status(thm)],[f_447_1]) ).
fof(f_447_3,plain,
( ! [U_1074] :
( ord_less_int(zero_zero_int,number_number_of_int(U_1074))
| ~ ord_less_int(pls,U_1074) )
& ! [U_1073] :
( ord_less_int(pls,U_1073)
| ~ ord_less_int(zero_zero_int,number_number_of_int(U_1073)) ) ),
inference(miniscope,[status(thm)],[f_447_2]) ).
fof(f_447_4,plain,
( ! [U_1074] :
( ord_less_int(zero_zero_int,number_number_of_int(U_1074))
| ~ ord_less_int(pls,U_1074) )
& ! [U_1073] :
( ord_less_int(pls,U_1073)
| ~ ord_less_int(zero_zero_int,number_number_of_int(U_1073)) ) ),
inference(definitional_conversion,[status(esa)],[f_447_3]) ).
cnf(f_447_5,plain,
( ord_less_int(pls,U_1073)
| ~ ord_less_int(zero_zero_int,number_number_of_int(U_1073)) ),
inference(clausify,[status(thm)],[f_447_4]) ).
cnf(f_447_6,plain,
( ord_less_int(zero_zero_int,number_number_of_int(U_1074))
| ~ ord_less_int(pls,U_1074) ),
inference(clausify,[status(thm)],[f_447_4]) ).
fof(f_448_1,plain,
! [X_2] :
( ( ord_less_real(number267125858f_real(X_2),zero_zero_real)
| ~ ord_less_int(X_2,pls) )
& ( ord_less_int(X_2,pls)
| ~ ord_less_real(number267125858f_real(X_2),zero_zero_real) ) ),
inference(fof_nnf,[status(thm)],[fact_429_less__special_I3_J]) ).
fof(f_448_2,plain,
! [U_1075] :
( ( ord_less_real(number267125858f_real(U_1075),zero_zero_real)
| ~ ord_less_int(U_1075,pls) )
& ( ord_less_int(U_1075,pls)
| ~ ord_less_real(number267125858f_real(U_1075),zero_zero_real) ) ),
inference(variable_rename,[status(thm)],[f_448_1]) ).
fof(f_448_3,plain,
( ! [U_1077] :
( ord_less_real(number267125858f_real(U_1077),zero_zero_real)
| ~ ord_less_int(U_1077,pls) )
& ! [U_1076] :
( ord_less_int(U_1076,pls)
| ~ ord_less_real(number267125858f_real(U_1076),zero_zero_real) ) ),
inference(miniscope,[status(thm)],[f_448_2]) ).
fof(f_448_4,plain,
( ! [U_1077] :
( ord_less_real(number267125858f_real(U_1077),zero_zero_real)
| ~ ord_less_int(U_1077,pls) )
& ! [U_1076] :
( ord_less_int(U_1076,pls)
| ~ ord_less_real(number267125858f_real(U_1076),zero_zero_real) ) ),
inference(definitional_conversion,[status(esa)],[f_448_3]) ).
cnf(f_448_5,plain,
( ord_less_int(U_1076,pls)
| ~ ord_less_real(number267125858f_real(U_1076),zero_zero_real) ),
inference(clausify,[status(thm)],[f_448_4]) ).
cnf(f_448_6,plain,
( ord_less_real(number267125858f_real(U_1077),zero_zero_real)
| ~ ord_less_int(U_1077,pls) ),
inference(clausify,[status(thm)],[f_448_4]) ).
fof(f_449_1,plain,
! [X_2] :
( ( ord_less_int(number_number_of_int(X_2),zero_zero_int)
| ~ ord_less_int(X_2,pls) )
& ( ord_less_int(X_2,pls)
| ~ ord_less_int(number_number_of_int(X_2),zero_zero_int) ) ),
inference(fof_nnf,[status(thm)],[fact_430_less__special_I3_J]) ).
fof(f_449_2,plain,
! [U_1078] :
( ( ord_less_int(number_number_of_int(U_1078),zero_zero_int)
| ~ ord_less_int(U_1078,pls) )
& ( ord_less_int(U_1078,pls)
| ~ ord_less_int(number_number_of_int(U_1078),zero_zero_int) ) ),
inference(variable_rename,[status(thm)],[f_449_1]) ).
fof(f_449_3,plain,
( ! [U_1080] :
( ord_less_int(number_number_of_int(U_1080),zero_zero_int)
| ~ ord_less_int(U_1080,pls) )
& ! [U_1079] :
( ord_less_int(U_1079,pls)
| ~ ord_less_int(number_number_of_int(U_1079),zero_zero_int) ) ),
inference(miniscope,[status(thm)],[f_449_2]) ).
fof(f_449_4,plain,
( ! [U_1080] :
( ord_less_int(number_number_of_int(U_1080),zero_zero_int)
| ~ ord_less_int(U_1080,pls) )
& ! [U_1079] :
( ord_less_int(U_1079,pls)
| ~ ord_less_int(number_number_of_int(U_1079),zero_zero_int) ) ),
inference(definitional_conversion,[status(esa)],[f_449_3]) ).
cnf(f_449_5,plain,
( ord_less_int(U_1079,pls)
| ~ ord_less_int(number_number_of_int(U_1079),zero_zero_int) ),
inference(clausify,[status(thm)],[f_449_4]) ).
cnf(f_449_6,plain,
( ord_less_int(number_number_of_int(U_1080),zero_zero_int)
| ~ ord_less_int(U_1080,pls) ),
inference(clausify,[status(thm)],[f_449_4]) ).
fof(f_450_1,plain,
! [Y_2] :
( ( ord_less_eq_real(zero_zero_real,number267125858f_real(Y_2))
| ~ ord_less_eq_int(pls,Y_2) )
& ( ord_less_eq_int(pls,Y_2)
| ~ ord_less_eq_real(zero_zero_real,number267125858f_real(Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_431_le__special_I1_J]) ).
fof(f_450_2,plain,
! [U_1081] :
( ( ord_less_eq_real(zero_zero_real,number267125858f_real(U_1081))
| ~ ord_less_eq_int(pls,U_1081) )
& ( ord_less_eq_int(pls,U_1081)
| ~ ord_less_eq_real(zero_zero_real,number267125858f_real(U_1081)) ) ),
inference(variable_rename,[status(thm)],[f_450_1]) ).
fof(f_450_3,plain,
( ! [U_1083] :
( ord_less_eq_real(zero_zero_real,number267125858f_real(U_1083))
| ~ ord_less_eq_int(pls,U_1083) )
& ! [U_1082] :
( ord_less_eq_int(pls,U_1082)
| ~ ord_less_eq_real(zero_zero_real,number267125858f_real(U_1082)) ) ),
inference(miniscope,[status(thm)],[f_450_2]) ).
fof(f_450_4,plain,
( ! [U_1083] :
( ord_less_eq_real(zero_zero_real,number267125858f_real(U_1083))
| ~ ord_less_eq_int(pls,U_1083) )
& ! [U_1082] :
( ord_less_eq_int(pls,U_1082)
| ~ ord_less_eq_real(zero_zero_real,number267125858f_real(U_1082)) ) ),
inference(definitional_conversion,[status(esa)],[f_450_3]) ).
cnf(f_450_5,plain,
( ord_less_eq_int(pls,U_1082)
| ~ ord_less_eq_real(zero_zero_real,number267125858f_real(U_1082)) ),
inference(clausify,[status(thm)],[f_450_4]) ).
cnf(f_450_6,plain,
( ord_less_eq_real(zero_zero_real,number267125858f_real(U_1083))
| ~ ord_less_eq_int(pls,U_1083) ),
inference(clausify,[status(thm)],[f_450_4]) ).
fof(f_451_1,plain,
! [Y_2] :
( ( ord_less_eq_int(zero_zero_int,number_number_of_int(Y_2))
| ~ ord_less_eq_int(pls,Y_2) )
& ( ord_less_eq_int(pls,Y_2)
| ~ ord_less_eq_int(zero_zero_int,number_number_of_int(Y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_432_le__special_I1_J]) ).
fof(f_451_2,plain,
! [U_1084] :
( ( ord_less_eq_int(zero_zero_int,number_number_of_int(U_1084))
| ~ ord_less_eq_int(pls,U_1084) )
& ( ord_less_eq_int(pls,U_1084)
| ~ ord_less_eq_int(zero_zero_int,number_number_of_int(U_1084)) ) ),
inference(variable_rename,[status(thm)],[f_451_1]) ).
fof(f_451_3,plain,
( ! [U_1086] :
( ord_less_eq_int(zero_zero_int,number_number_of_int(U_1086))
| ~ ord_less_eq_int(pls,U_1086) )
& ! [U_1085] :
( ord_less_eq_int(pls,U_1085)
| ~ ord_less_eq_int(zero_zero_int,number_number_of_int(U_1085)) ) ),
inference(miniscope,[status(thm)],[f_451_2]) ).
fof(f_451_4,plain,
( ! [U_1086] :
( ord_less_eq_int(zero_zero_int,number_number_of_int(U_1086))
| ~ ord_less_eq_int(pls,U_1086) )
& ! [U_1085] :
( ord_less_eq_int(pls,U_1085)
| ~ ord_less_eq_int(zero_zero_int,number_number_of_int(U_1085)) ) ),
inference(definitional_conversion,[status(esa)],[f_451_3]) ).
cnf(f_451_5,plain,
( ord_less_eq_int(pls,U_1085)
| ~ ord_less_eq_int(zero_zero_int,number_number_of_int(U_1085)) ),
inference(clausify,[status(thm)],[f_451_4]) ).
cnf(f_451_6,plain,
( ord_less_eq_int(zero_zero_int,number_number_of_int(U_1086))
| ~ ord_less_eq_int(pls,U_1086) ),
inference(clausify,[status(thm)],[f_451_4]) ).
fof(f_452_1,plain,
! [X_2] :
( ( ord_less_eq_real(number267125858f_real(X_2),zero_zero_real)
| ~ ord_less_eq_int(X_2,pls) )
& ( ord_less_eq_int(X_2,pls)
| ~ ord_less_eq_real(number267125858f_real(X_2),zero_zero_real) ) ),
inference(fof_nnf,[status(thm)],[fact_433_le__special_I3_J]) ).
fof(f_452_2,plain,
! [U_1087] :
( ( ord_less_eq_real(number267125858f_real(U_1087),zero_zero_real)
| ~ ord_less_eq_int(U_1087,pls) )
& ( ord_less_eq_int(U_1087,pls)
| ~ ord_less_eq_real(number267125858f_real(U_1087),zero_zero_real) ) ),
inference(variable_rename,[status(thm)],[f_452_1]) ).
fof(f_452_3,plain,
( ! [U_1089] :
( ord_less_eq_real(number267125858f_real(U_1089),zero_zero_real)
| ~ ord_less_eq_int(U_1089,pls) )
& ! [U_1088] :
( ord_less_eq_int(U_1088,pls)
| ~ ord_less_eq_real(number267125858f_real(U_1088),zero_zero_real) ) ),
inference(miniscope,[status(thm)],[f_452_2]) ).
fof(f_452_4,plain,
( ! [U_1089] :
( ord_less_eq_real(number267125858f_real(U_1089),zero_zero_real)
| ~ ord_less_eq_int(U_1089,pls) )
& ! [U_1088] :
( ord_less_eq_int(U_1088,pls)
| ~ ord_less_eq_real(number267125858f_real(U_1088),zero_zero_real) ) ),
inference(definitional_conversion,[status(esa)],[f_452_3]) ).
cnf(f_452_5,plain,
( ord_less_eq_int(U_1088,pls)
| ~ ord_less_eq_real(number267125858f_real(U_1088),zero_zero_real) ),
inference(clausify,[status(thm)],[f_452_4]) ).
cnf(f_452_6,plain,
( ord_less_eq_real(number267125858f_real(U_1089),zero_zero_real)
| ~ ord_less_eq_int(U_1089,pls) ),
inference(clausify,[status(thm)],[f_452_4]) ).
fof(f_453_1,plain,
! [X_2] :
( ( ord_less_eq_int(number_number_of_int(X_2),zero_zero_int)
| ~ ord_less_eq_int(X_2,pls) )
& ( ord_less_eq_int(X_2,pls)
| ~ ord_less_eq_int(number_number_of_int(X_2),zero_zero_int) ) ),
inference(fof_nnf,[status(thm)],[fact_434_le__special_I3_J]) ).
fof(f_453_2,plain,
! [U_1090] :
( ( ord_less_eq_int(number_number_of_int(U_1090),zero_zero_int)
| ~ ord_less_eq_int(U_1090,pls) )
& ( ord_less_eq_int(U_1090,pls)
| ~ ord_less_eq_int(number_number_of_int(U_1090),zero_zero_int) ) ),
inference(variable_rename,[status(thm)],[f_453_1]) ).
fof(f_453_3,plain,
( ! [U_1092] :
( ord_less_eq_int(number_number_of_int(U_1092),zero_zero_int)
| ~ ord_less_eq_int(U_1092,pls) )
& ! [U_1091] :
( ord_less_eq_int(U_1091,pls)
| ~ ord_less_eq_int(number_number_of_int(U_1091),zero_zero_int) ) ),
inference(miniscope,[status(thm)],[f_453_2]) ).
fof(f_453_4,plain,
( ! [U_1092] :
( ord_less_eq_int(number_number_of_int(U_1092),zero_zero_int)
| ~ ord_less_eq_int(U_1092,pls) )
& ! [U_1091] :
( ord_less_eq_int(U_1091,pls)
| ~ ord_less_eq_int(number_number_of_int(U_1091),zero_zero_int) ) ),
inference(definitional_conversion,[status(esa)],[f_453_3]) ).
cnf(f_453_5,plain,
( ord_less_eq_int(U_1091,pls)
| ~ ord_less_eq_int(number_number_of_int(U_1091),zero_zero_int) ),
inference(clausify,[status(thm)],[f_453_4]) ).
cnf(f_453_6,plain,
( ord_less_eq_int(number_number_of_int(U_1092),zero_zero_int)
| ~ ord_less_eq_int(U_1092,pls) ),
inference(clausify,[status(thm)],[f_453_4]) ).
fof(f_454_1,plain,
! [Z] :
( ord_less_int(zero_zero_int,plus_plus_int(one_one_int,Z))
| ~ ord_less_eq_int(zero_zero_int,Z) ),
inference(fof_nnf,[status(thm)],[fact_435_le__imp__0__less]) ).
fof(f_454_2,plain,
! [U_1093] :
( ord_less_int(zero_zero_int,plus_plus_int(one_one_int,U_1093))
| ~ ord_less_eq_int(zero_zero_int,U_1093) ),
inference(variable_rename,[status(thm)],[f_454_1]) ).
fof(f_454_3,plain,
! [U_1093] :
( ord_less_int(zero_zero_int,plus_plus_int(one_one_int,U_1093))
| ~ ord_less_eq_int(zero_zero_int,U_1093) ),
inference(definitional_conversion,[status(esa)],[f_454_2]) ).
cnf(f_454_4,plain,
( ord_less_int(zero_zero_int,plus_plus_int(one_one_int,U_1093))
| ~ ord_less_eq_int(zero_zero_int,U_1093) ),
inference(clausify,[status(thm)],[f_454_3]) ).
fof(f_455_1,plain,
power_power_real(zero_zero_real,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real,
inference(fof_nnf,[status(thm)],[fact_436_zero__power2]) ).
fof(f_455_2,plain,
power_power_real(zero_zero_real,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real,
inference(definitional_conversion,[status(esa)],[f_455_1]) ).
cnf(f_455_3,plain,
power_power_real(zero_zero_real,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real,
inference(clausify,[status(thm)],[f_455_2]) ).
fof(f_456_1,plain,
power_power_nat(zero_zero_nat,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_nat,
inference(fof_nnf,[status(thm)],[fact_437_zero__power2]) ).
fof(f_456_2,plain,
power_power_nat(zero_zero_nat,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_nat,
inference(definitional_conversion,[status(esa)],[f_456_1]) ).
cnf(f_456_3,plain,
power_power_nat(zero_zero_nat,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_nat,
inference(clausify,[status(thm)],[f_456_2]) ).
fof(f_457_1,plain,
power_power_int(zero_zero_int,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(fof_nnf,[status(thm)],[fact_438_zero__power2]) ).
fof(f_457_2,plain,
power_power_int(zero_zero_int,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(definitional_conversion,[status(esa)],[f_457_1]) ).
cnf(f_457_3,plain,
power_power_int(zero_zero_int,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(clausify,[status(thm)],[f_457_2]) ).
fof(f_458_1,plain,
! [A_1] :
( ( power_power_real(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real
| A_1 != zero_zero_real )
& ( A_1 = zero_zero_real
| power_power_real(A_1,number_number_of_nat(bit0(bit1(pls)))) != zero_zero_real ) ),
inference(fof_nnf,[status(thm)],[fact_439_zero__eq__power2]) ).
fof(f_458_2,plain,
! [U_1094] :
( ( power_power_real(U_1094,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real
| U_1094 != zero_zero_real )
& ( U_1094 = zero_zero_real
| power_power_real(U_1094,number_number_of_nat(bit0(bit1(pls)))) != zero_zero_real ) ),
inference(variable_rename,[status(thm)],[f_458_1]) ).
fof(f_458_3,plain,
( ! [U_1096] :
( power_power_real(U_1096,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real
| U_1096 != zero_zero_real )
& ! [U_1095] :
( U_1095 = zero_zero_real
| power_power_real(U_1095,number_number_of_nat(bit0(bit1(pls)))) != zero_zero_real ) ),
inference(miniscope,[status(thm)],[f_458_2]) ).
fof(f_458_4,plain,
( ! [U_1096] :
( power_power_real(U_1096,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real
| U_1096 != zero_zero_real )
& ! [U_1095] :
( U_1095 = zero_zero_real
| power_power_real(U_1095,number_number_of_nat(bit0(bit1(pls)))) != zero_zero_real ) ),
inference(definitional_conversion,[status(esa)],[f_458_3]) ).
cnf(f_458_5,plain,
( U_1095 = zero_zero_real
| power_power_real(U_1095,number_number_of_nat(bit0(bit1(pls)))) != zero_zero_real ),
inference(clausify,[status(thm)],[f_458_4]) ).
cnf(f_458_6,plain,
( power_power_real(U_1096,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real
| U_1096 != zero_zero_real ),
inference(clausify,[status(thm)],[f_458_4]) ).
fof(f_459_1,plain,
! [A_1] :
( ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int
| A_1 != zero_zero_int )
& ( A_1 = zero_zero_int
| power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ) )
| ~ is_int(A_1) ),
inference(fof_nnf,[status(thm)],[fact_440_zero__eq__power2]) ).
fof(f_459_2,plain,
! [U_1097] :
( ( ( power_power_int(U_1097,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int
| U_1097 != zero_zero_int )
& ( U_1097 = zero_zero_int
| power_power_int(U_1097,number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ) )
| ~ is_int(U_1097) ),
inference(variable_rename,[status(thm)],[f_459_1]) ).
fof(f_459_3,plain,
( ! [U_1097] :
( power_power_int(U_1097,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int
| U_1097 != zero_zero_int
| ~ sP46(U_1097) )
& ! [U_1097] :
( U_1097 = zero_zero_int
| power_power_int(U_1097,number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int
| ~ sP46(U_1097) )
& ! [U_1097] :
( sP46(U_1097)
| ~ is_int(U_1097) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP46])],[f_459_2]) ).
cnf(f_459_4,plain,
( sP46(U_1097)
| ~ is_int(U_1097) ),
inference(clausify,[status(thm)],[f_459_3]) ).
cnf(f_459_5,plain,
( U_1097 = zero_zero_int
| power_power_int(U_1097,number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int
| ~ sP46(U_1097) ),
inference(clausify,[status(thm)],[f_459_3]) ).
cnf(f_459_6,plain,
( power_power_int(U_1097,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int
| U_1097 != zero_zero_int
| ~ sP46(U_1097) ),
inference(clausify,[status(thm)],[f_459_3]) ).
fof(f_460_1,plain,
! [A_15] : ord_less_eq_real(zero_zero_real,power_power_real(A_15,number_number_of_nat(bit0(bit1(pls))))),
inference(fof_nnf,[status(thm)],[fact_441_zero__le__power2]) ).
fof(f_460_2,plain,
! [U_1098] : ord_less_eq_real(zero_zero_real,power_power_real(U_1098,number_number_of_nat(bit0(bit1(pls))))),
inference(variable_rename,[status(thm)],[f_460_1]) ).
fof(f_460_3,plain,
! [U_1098] : ord_less_eq_real(zero_zero_real,power_power_real(U_1098,number_number_of_nat(bit0(bit1(pls))))),
inference(definitional_conversion,[status(esa)],[f_460_2]) ).
cnf(f_460_4,plain,
ord_less_eq_real(zero_zero_real,power_power_real(U_1098,number_number_of_nat(bit0(bit1(pls))))),
inference(clausify,[status(thm)],[f_460_3]) ).
fof(f_461_1,plain,
! [A_15] : ord_less_eq_int(zero_zero_int,power_power_int(A_15,number_number_of_nat(bit0(bit1(pls))))),
inference(fof_nnf,[status(thm)],[fact_442_zero__le__power2]) ).
fof(f_461_2,plain,
! [U_1099] : ord_less_eq_int(zero_zero_int,power_power_int(U_1099,number_number_of_nat(bit0(bit1(pls))))),
inference(variable_rename,[status(thm)],[f_461_1]) ).
fof(f_461_3,plain,
! [U_1099] : ord_less_eq_int(zero_zero_int,power_power_int(U_1099,number_number_of_nat(bit0(bit1(pls))))),
inference(definitional_conversion,[status(esa)],[f_461_2]) ).
cnf(f_461_4,plain,
ord_less_eq_int(zero_zero_int,power_power_int(U_1099,number_number_of_nat(bit0(bit1(pls))))),
inference(clausify,[status(thm)],[f_461_3]) ).
fof(f_462_1,plain,
! [X_10,Y_8] :
( ord_less_eq_real(X_10,Y_8)
| ~ ord_less_eq_real(zero_zero_real,Y_8)
| ~ ord_less_eq_real(power_power_real(X_10,number_number_of_nat(bit0(bit1(pls)))),power_power_real(Y_8,number_number_of_nat(bit0(bit1(pls))))) ),
inference(fof_nnf,[status(thm)],[fact_443_power2__le__imp__le]) ).
fof(f_462_2,plain,
! [U_1101,U_1100] :
( ord_less_eq_real(U_1101,U_1100)
| ~ ord_less_eq_real(zero_zero_real,U_1100)
| ~ ord_less_eq_real(power_power_real(U_1101,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1100,number_number_of_nat(bit0(bit1(pls))))) ),
inference(variable_rename,[status(thm)],[f_462_1]) ).
fof(f_462_3,plain,
! [U_1101,U_1100] :
( ord_less_eq_real(U_1101,U_1100)
| ~ ord_less_eq_real(zero_zero_real,U_1100)
| ~ ord_less_eq_real(power_power_real(U_1101,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1100,number_number_of_nat(bit0(bit1(pls))))) ),
inference(definitional_conversion,[status(esa)],[f_462_2]) ).
cnf(f_462_4,plain,
( ord_less_eq_real(U_1101,U_1100)
| ~ ord_less_eq_real(zero_zero_real,U_1100)
| ~ ord_less_eq_real(power_power_real(U_1101,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1100,number_number_of_nat(bit0(bit1(pls))))) ),
inference(clausify,[status(thm)],[f_462_3]) ).
fof(f_463_1,plain,
! [X_10,Y_8] :
( ord_less_eq_nat(X_10,Y_8)
| ~ ord_less_eq_nat(zero_zero_nat,Y_8)
| ~ ord_less_eq_nat(power_power_nat(X_10,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(Y_8,number_number_of_nat(bit0(bit1(pls))))) ),
inference(fof_nnf,[status(thm)],[fact_444_power2__le__imp__le]) ).
fof(f_463_2,plain,
! [U_1103,U_1102] :
( ord_less_eq_nat(U_1103,U_1102)
| ~ ord_less_eq_nat(zero_zero_nat,U_1102)
| ~ ord_less_eq_nat(power_power_nat(U_1103,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(U_1102,number_number_of_nat(bit0(bit1(pls))))) ),
inference(variable_rename,[status(thm)],[f_463_1]) ).
fof(f_463_3,plain,
! [U_1103,U_1102] :
( ord_less_eq_nat(U_1103,U_1102)
| ~ ord_less_eq_nat(zero_zero_nat,U_1102)
| ~ ord_less_eq_nat(power_power_nat(U_1103,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(U_1102,number_number_of_nat(bit0(bit1(pls))))) ),
inference(definitional_conversion,[status(esa)],[f_463_2]) ).
cnf(f_463_4,plain,
( ord_less_eq_nat(U_1103,U_1102)
| ~ ord_less_eq_nat(zero_zero_nat,U_1102)
| ~ ord_less_eq_nat(power_power_nat(U_1103,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(U_1102,number_number_of_nat(bit0(bit1(pls))))) ),
inference(clausify,[status(thm)],[f_463_3]) ).
fof(f_464_1,plain,
! [X_10,Y_8] :
( ord_less_eq_int(X_10,Y_8)
| ~ ord_less_eq_int(zero_zero_int,Y_8)
| ~ ord_less_eq_int(power_power_int(X_10,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y_8,number_number_of_nat(bit0(bit1(pls))))) ),
inference(fof_nnf,[status(thm)],[fact_445_power2__le__imp__le]) ).
fof(f_464_2,plain,
! [U_1105,U_1104] :
( ord_less_eq_int(U_1105,U_1104)
| ~ ord_less_eq_int(zero_zero_int,U_1104)
| ~ ord_less_eq_int(power_power_int(U_1105,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1104,number_number_of_nat(bit0(bit1(pls))))) ),
inference(variable_rename,[status(thm)],[f_464_1]) ).
fof(f_464_3,plain,
! [U_1105,U_1104] :
( ord_less_eq_int(U_1105,U_1104)
| ~ ord_less_eq_int(zero_zero_int,U_1104)
| ~ ord_less_eq_int(power_power_int(U_1105,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1104,number_number_of_nat(bit0(bit1(pls))))) ),
inference(definitional_conversion,[status(esa)],[f_464_2]) ).
cnf(f_464_4,plain,
( ord_less_eq_int(U_1105,U_1104)
| ~ ord_less_eq_int(zero_zero_int,U_1104)
| ~ ord_less_eq_int(power_power_int(U_1105,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1104,number_number_of_nat(bit0(bit1(pls))))) ),
inference(clausify,[status(thm)],[f_464_3]) ).
fof(f_465_1,plain,
! [X_9,Y_7] :
( X_9 = Y_7
| ~ ord_less_eq_real(zero_zero_real,Y_7)
| ~ ord_less_eq_real(zero_zero_real,X_9)
| power_power_real(X_9,number_number_of_nat(bit0(bit1(pls)))) != power_power_real(Y_7,number_number_of_nat(bit0(bit1(pls)))) ),
inference(fof_nnf,[status(thm)],[fact_446_power2__eq__imp__eq]) ).
fof(f_465_2,plain,
! [U_1107,U_1106] :
( U_1107 = U_1106
| ~ ord_less_eq_real(zero_zero_real,U_1106)
| ~ ord_less_eq_real(zero_zero_real,U_1107)
| power_power_real(U_1107,number_number_of_nat(bit0(bit1(pls)))) != power_power_real(U_1106,number_number_of_nat(bit0(bit1(pls)))) ),
inference(variable_rename,[status(thm)],[f_465_1]) ).
fof(f_465_3,plain,
! [U_1107,U_1106] :
( U_1107 = U_1106
| ~ ord_less_eq_real(zero_zero_real,U_1106)
| ~ ord_less_eq_real(zero_zero_real,U_1107)
| power_power_real(U_1107,number_number_of_nat(bit0(bit1(pls)))) != power_power_real(U_1106,number_number_of_nat(bit0(bit1(pls)))) ),
inference(definitional_conversion,[status(esa)],[f_465_2]) ).
cnf(f_465_4,plain,
( U_1107 = U_1106
| ~ ord_less_eq_real(zero_zero_real,U_1106)
| ~ ord_less_eq_real(zero_zero_real,U_1107)
| power_power_real(U_1107,number_number_of_nat(bit0(bit1(pls)))) != power_power_real(U_1106,number_number_of_nat(bit0(bit1(pls)))) ),
inference(clausify,[status(thm)],[f_465_3]) ).
fof(f_466_1,plain,
! [X_9,Y_7] :
( X_9 = Y_7
| ~ ord_less_eq_nat(zero_zero_nat,Y_7)
| ~ ord_less_eq_nat(zero_zero_nat,X_9)
| power_power_nat(X_9,number_number_of_nat(bit0(bit1(pls)))) != power_power_nat(Y_7,number_number_of_nat(bit0(bit1(pls)))) ),
inference(fof_nnf,[status(thm)],[fact_447_power2__eq__imp__eq]) ).
fof(f_466_2,plain,
! [U_1109,U_1108] :
( U_1109 = U_1108
| ~ ord_less_eq_nat(zero_zero_nat,U_1108)
| ~ ord_less_eq_nat(zero_zero_nat,U_1109)
| power_power_nat(U_1109,number_number_of_nat(bit0(bit1(pls)))) != power_power_nat(U_1108,number_number_of_nat(bit0(bit1(pls)))) ),
inference(variable_rename,[status(thm)],[f_466_1]) ).
fof(f_466_3,plain,
! [U_1109,U_1108] :
( U_1109 = U_1108
| ~ ord_less_eq_nat(zero_zero_nat,U_1108)
| ~ ord_less_eq_nat(zero_zero_nat,U_1109)
| power_power_nat(U_1109,number_number_of_nat(bit0(bit1(pls)))) != power_power_nat(U_1108,number_number_of_nat(bit0(bit1(pls)))) ),
inference(definitional_conversion,[status(esa)],[f_466_2]) ).
cnf(f_466_4,plain,
( U_1109 = U_1108
| ~ ord_less_eq_nat(zero_zero_nat,U_1108)
| ~ ord_less_eq_nat(zero_zero_nat,U_1109)
| power_power_nat(U_1109,number_number_of_nat(bit0(bit1(pls)))) != power_power_nat(U_1108,number_number_of_nat(bit0(bit1(pls)))) ),
inference(clausify,[status(thm)],[f_466_3]) ).
fof(f_467_1,plain,
! [X_9,Y_7] :
( X_9 = Y_7
| ~ ord_less_eq_int(zero_zero_int,Y_7)
| ~ ord_less_eq_int(zero_zero_int,X_9)
| power_power_int(X_9,number_number_of_nat(bit0(bit1(pls)))) != power_power_int(Y_7,number_number_of_nat(bit0(bit1(pls))))
| ~ is_int(Y_7)
| ~ is_int(X_9) ),
inference(fof_nnf,[status(thm)],[fact_448_power2__eq__imp__eq]) ).
fof(f_467_2,plain,
! [U_1111,U_1110] :
( U_1111 = U_1110
| ~ ord_less_eq_int(zero_zero_int,U_1110)
| ~ ord_less_eq_int(zero_zero_int,U_1111)
| power_power_int(U_1111,number_number_of_nat(bit0(bit1(pls)))) != power_power_int(U_1110,number_number_of_nat(bit0(bit1(pls))))
| ~ is_int(U_1110)
| ~ is_int(U_1111) ),
inference(variable_rename,[status(thm)],[f_467_1]) ).
fof(f_467_3,plain,
! [U_1111,U_1110] :
( U_1111 = U_1110
| ~ ord_less_eq_int(zero_zero_int,U_1110)
| ~ ord_less_eq_int(zero_zero_int,U_1111)
| power_power_int(U_1111,number_number_of_nat(bit0(bit1(pls)))) != power_power_int(U_1110,number_number_of_nat(bit0(bit1(pls))))
| ~ is_int(U_1110)
| ~ is_int(U_1111) ),
inference(definitional_conversion,[status(esa)],[f_467_2]) ).
cnf(f_467_4,plain,
( U_1111 = U_1110
| ~ ord_less_eq_int(zero_zero_int,U_1110)
| ~ ord_less_eq_int(zero_zero_int,U_1111)
| power_power_int(U_1111,number_number_of_nat(bit0(bit1(pls)))) != power_power_int(U_1110,number_number_of_nat(bit0(bit1(pls))))
| ~ is_int(U_1110)
| ~ is_int(U_1111) ),
inference(clausify,[status(thm)],[f_467_3]) ).
fof(f_468_1,plain,
! [A_14] : ~ ord_less_real(power_power_real(A_14,number_number_of_nat(bit0(bit1(pls)))),zero_zero_real),
inference(fof_nnf,[status(thm)],[fact_449_power2__less__0]) ).
fof(f_468_2,plain,
! [U_1112] : ~ ord_less_real(power_power_real(U_1112,number_number_of_nat(bit0(bit1(pls)))),zero_zero_real),
inference(variable_rename,[status(thm)],[f_468_1]) ).
fof(f_468_3,plain,
! [U_1112] : ~ ord_less_real(power_power_real(U_1112,number_number_of_nat(bit0(bit1(pls)))),zero_zero_real),
inference(definitional_conversion,[status(esa)],[f_468_2]) ).
cnf(f_468_4,plain,
~ ord_less_real(power_power_real(U_1112,number_number_of_nat(bit0(bit1(pls)))),zero_zero_real),
inference(clausify,[status(thm)],[f_468_3]) ).
fof(f_469_1,plain,
! [A_14] : ~ ord_less_int(power_power_int(A_14,number_number_of_nat(bit0(bit1(pls)))),zero_zero_int),
inference(fof_nnf,[status(thm)],[fact_450_power2__less__0]) ).
fof(f_469_2,plain,
! [U_1113] : ~ ord_less_int(power_power_int(U_1113,number_number_of_nat(bit0(bit1(pls)))),zero_zero_int),
inference(variable_rename,[status(thm)],[f_469_1]) ).
fof(f_469_3,plain,
! [U_1113] : ~ ord_less_int(power_power_int(U_1113,number_number_of_nat(bit0(bit1(pls)))),zero_zero_int),
inference(definitional_conversion,[status(esa)],[f_469_2]) ).
cnf(f_469_4,plain,
~ ord_less_int(power_power_int(U_1113,number_number_of_nat(bit0(bit1(pls)))),zero_zero_int),
inference(clausify,[status(thm)],[f_469_3]) ).
fof(f_470_1,plain,
! [A_1] :
( ( ord_less_real(zero_zero_real,power_power_real(A_1,number_number_of_nat(bit0(bit1(pls)))))
| A_1 = zero_zero_real )
& ( A_1 != zero_zero_real
| ~ ord_less_real(zero_zero_real,power_power_real(A_1,number_number_of_nat(bit0(bit1(pls))))) ) ),
inference(fof_nnf,[status(thm)],[fact_451_zero__less__power2]) ).
fof(f_470_2,plain,
! [U_1114] :
( ( ord_less_real(zero_zero_real,power_power_real(U_1114,number_number_of_nat(bit0(bit1(pls)))))
| U_1114 = zero_zero_real )
& ( U_1114 != zero_zero_real
| ~ ord_less_real(zero_zero_real,power_power_real(U_1114,number_number_of_nat(bit0(bit1(pls))))) ) ),
inference(variable_rename,[status(thm)],[f_470_1]) ).
fof(f_470_3,plain,
( ! [U_1116] :
( ord_less_real(zero_zero_real,power_power_real(U_1116,number_number_of_nat(bit0(bit1(pls)))))
| U_1116 = zero_zero_real )
& ! [U_1115] :
( U_1115 != zero_zero_real
| ~ ord_less_real(zero_zero_real,power_power_real(U_1115,number_number_of_nat(bit0(bit1(pls))))) ) ),
inference(miniscope,[status(thm)],[f_470_2]) ).
fof(f_470_4,plain,
( ! [U_1116] :
( ord_less_real(zero_zero_real,power_power_real(U_1116,number_number_of_nat(bit0(bit1(pls)))))
| U_1116 = zero_zero_real )
& ! [U_1115] :
( U_1115 != zero_zero_real
| ~ ord_less_real(zero_zero_real,power_power_real(U_1115,number_number_of_nat(bit0(bit1(pls))))) ) ),
inference(definitional_conversion,[status(esa)],[f_470_3]) ).
cnf(f_470_5,plain,
( U_1115 != zero_zero_real
| ~ ord_less_real(zero_zero_real,power_power_real(U_1115,number_number_of_nat(bit0(bit1(pls))))) ),
inference(clausify,[status(thm)],[f_470_4]) ).
cnf(f_470_6,plain,
( ord_less_real(zero_zero_real,power_power_real(U_1116,number_number_of_nat(bit0(bit1(pls)))))
| U_1116 = zero_zero_real ),
inference(clausify,[status(thm)],[f_470_4]) ).
fof(f_471_1,plain,
! [A_1] :
( ( ( ord_less_int(zero_zero_int,power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))))
| A_1 = zero_zero_int )
& ( A_1 != zero_zero_int
| ~ ord_less_int(zero_zero_int,power_power_int(A_1,number_number_of_nat(bit0(bit1(pls))))) ) )
| ~ is_int(A_1) ),
inference(fof_nnf,[status(thm)],[fact_452_zero__less__power2]) ).
fof(f_471_2,plain,
! [U_1117] :
( ( ( ord_less_int(zero_zero_int,power_power_int(U_1117,number_number_of_nat(bit0(bit1(pls)))))
| U_1117 = zero_zero_int )
& ( U_1117 != zero_zero_int
| ~ ord_less_int(zero_zero_int,power_power_int(U_1117,number_number_of_nat(bit0(bit1(pls))))) ) )
| ~ is_int(U_1117) ),
inference(variable_rename,[status(thm)],[f_471_1]) ).
fof(f_471_3,plain,
( ! [U_1117] :
( ord_less_int(zero_zero_int,power_power_int(U_1117,number_number_of_nat(bit0(bit1(pls)))))
| U_1117 = zero_zero_int
| ~ sP47(U_1117) )
& ! [U_1117] :
( U_1117 != zero_zero_int
| ~ ord_less_int(zero_zero_int,power_power_int(U_1117,number_number_of_nat(bit0(bit1(pls)))))
| ~ sP47(U_1117) )
& ! [U_1117] :
( sP47(U_1117)
| ~ is_int(U_1117) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP47])],[f_471_2]) ).
cnf(f_471_4,plain,
( sP47(U_1117)
| ~ is_int(U_1117) ),
inference(clausify,[status(thm)],[f_471_3]) ).
cnf(f_471_5,plain,
( U_1117 != zero_zero_int
| ~ ord_less_int(zero_zero_int,power_power_int(U_1117,number_number_of_nat(bit0(bit1(pls)))))
| ~ sP47(U_1117) ),
inference(clausify,[status(thm)],[f_471_3]) ).
cnf(f_471_6,plain,
( ord_less_int(zero_zero_int,power_power_int(U_1117,number_number_of_nat(bit0(bit1(pls)))))
| U_1117 = zero_zero_int
| ~ sP47(U_1117) ),
inference(clausify,[status(thm)],[f_471_3]) ).
fof(f_472_1,plain,
! [X_2,Y_2] :
( ( plus_plus_real(power_power_real(X_2,number_number_of_nat(bit0(bit1(pls)))),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 )
| plus_plus_real(power_power_real(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_real(Y_2,number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ) ),
inference(fof_nnf,[status(thm)],[fact_453_sum__power2__eq__zero__iff]) ).
fof(f_472_2,plain,
! [U_1119,U_1118] :
( ( plus_plus_real(power_power_real(U_1119,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1118,number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| U_1118 != zero_zero_real
| U_1119 != zero_zero_real )
& ( ( U_1118 = zero_zero_real
& U_1119 = zero_zero_real )
| plus_plus_real(power_power_real(U_1119,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1118,number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ) ),
inference(variable_rename,[status(thm)],[f_472_1]) ).
fof(f_472_3,plain,
( ! [U_1123,U_1121] :
( plus_plus_real(power_power_real(U_1123,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1121,number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| U_1121 != zero_zero_real
| U_1123 != zero_zero_real )
& ! [U_1122,U_1120] :
( ( U_1120 = zero_zero_real
& U_1122 = zero_zero_real )
| plus_plus_real(power_power_real(U_1122,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1120,number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ) ),
inference(miniscope,[status(thm)],[f_472_2]) ).
fof(f_472_4,plain,
( ! [U_1122,U_1120] :
( U_1120 = zero_zero_real
| ~ sP48(U_1122,U_1120) )
& ! [U_1122,U_1120] :
( U_1122 = zero_zero_real
| ~ sP48(U_1122,U_1120) )
& ! [U_1123,U_1121] :
( plus_plus_real(power_power_real(U_1123,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1121,number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| U_1121 != zero_zero_real
| U_1123 != zero_zero_real )
& ! [U_1122,U_1120] :
( sP48(U_1122,U_1120)
| plus_plus_real(power_power_real(U_1122,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1120,number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP48])],[f_472_3]) ).
cnf(f_472_5,plain,
( sP48(U_1122,U_1120)
| plus_plus_real(power_power_real(U_1122,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1120,number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ),
inference(clausify,[status(thm)],[f_472_4]) ).
cnf(f_472_6,plain,
( plus_plus_real(power_power_real(U_1123,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1121,number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| U_1121 != zero_zero_real
| U_1123 != zero_zero_real ),
inference(clausify,[status(thm)],[f_472_4]) ).
cnf(f_472_7,plain,
( U_1122 = zero_zero_real
| ~ sP48(U_1122,U_1120) ),
inference(clausify,[status(thm)],[f_472_4]) ).
cnf(f_472_8,plain,
( U_1120 = zero_zero_real
| ~ sP48(U_1122,U_1120) ),
inference(clausify,[status(thm)],[f_472_4]) ).
fof(f_473_1,plain,
! [X_2,Y_2] :
( ( ( plus_plus_int(power_power_int(X_2,number_number_of_nat(bit0(bit1(pls)))),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 )
| plus_plus_int(power_power_int(X_2,number_number_of_nat(bit0(bit1(pls)))),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_454_sum__power2__eq__zero__iff]) ).
fof(f_473_2,plain,
! [U_1125,U_1124] :
( ( ( plus_plus_int(power_power_int(U_1125,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1124,number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int
| U_1124 != zero_zero_int
| U_1125 != zero_zero_int )
& ( ( U_1124 = zero_zero_int
& U_1125 = zero_zero_int )
| plus_plus_int(power_power_int(U_1125,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1124,number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int ) )
| ~ is_int(U_1124)
| ~ is_int(U_1125) ),
inference(variable_rename,[status(thm)],[f_473_1]) ).
fof(f_473_3,plain,
( ! [U_1125,U_1124] :
( U_1124 = zero_zero_int
| ~ sP49(U_1125,U_1124) )
& ! [U_1125,U_1124] :
( U_1125 = zero_zero_int
| ~ sP49(U_1125,U_1124) )
& ! [U_1125,U_1124] :
( plus_plus_int(power_power_int(U_1125,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1124,number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int
| U_1124 != zero_zero_int
| U_1125 != zero_zero_int
| ~ sP50(U_1125,U_1124) )
& ! [U_1125,U_1124] :
( sP49(U_1125,U_1124)
| plus_plus_int(power_power_int(U_1125,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1124,number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int
| ~ sP50(U_1125,U_1124) )
& ! [U_1125,U_1124] :
( sP50(U_1125,U_1124)
| ~ is_int(U_1124)
| ~ is_int(U_1125) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49,sP50])],[f_473_2]) ).
cnf(f_473_4,plain,
( sP50(U_1125,U_1124)
| ~ is_int(U_1124)
| ~ is_int(U_1125) ),
inference(clausify,[status(thm)],[f_473_3]) ).
cnf(f_473_5,plain,
( sP49(U_1125,U_1124)
| plus_plus_int(power_power_int(U_1125,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1124,number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int
| ~ sP50(U_1125,U_1124) ),
inference(clausify,[status(thm)],[f_473_3]) ).
cnf(f_473_6,plain,
( plus_plus_int(power_power_int(U_1125,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1124,number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int
| U_1124 != zero_zero_int
| U_1125 != zero_zero_int
| ~ sP50(U_1125,U_1124) ),
inference(clausify,[status(thm)],[f_473_3]) ).
cnf(f_473_7,plain,
( U_1125 = zero_zero_int
| ~ sP49(U_1125,U_1124) ),
inference(clausify,[status(thm)],[f_473_3]) ).
cnf(f_473_8,plain,
( U_1124 = zero_zero_int
| ~ sP49(U_1125,U_1124) ),
inference(clausify,[status(thm)],[f_473_3]) ).
fof(f_474_1,plain,
! [A_13,N_16] : times_times_nat(power_power_nat(A_13,N_16),A_13) = times_times_nat(A_13,power_power_nat(A_13,N_16)),
inference(fof_nnf,[status(thm)],[fact_455_power__commutes]) ).
fof(f_474_2,plain,
! [U_1127,U_1126] : times_times_nat(power_power_nat(U_1127,U_1126),U_1127) = times_times_nat(U_1127,power_power_nat(U_1127,U_1126)),
inference(variable_rename,[status(thm)],[f_474_1]) ).
fof(f_474_3,plain,
! [U_1127,U_1126] : times_times_nat(power_power_nat(U_1127,U_1126),U_1127) = times_times_nat(U_1127,power_power_nat(U_1127,U_1126)),
inference(definitional_conversion,[status(esa)],[f_474_2]) ).
cnf(f_474_4,plain,
times_times_nat(power_power_nat(U_1127,U_1126),U_1127) = times_times_nat(U_1127,power_power_nat(U_1127,U_1126)),
inference(clausify,[status(thm)],[f_474_3]) ).
fof(f_475_1,plain,
! [A_13,N_16] : times_times_real(power_power_real(A_13,N_16),A_13) = times_times_real(A_13,power_power_real(A_13,N_16)),
inference(fof_nnf,[status(thm)],[fact_456_power__commutes]) ).
fof(f_475_2,plain,
! [U_1129,U_1128] : times_times_real(power_power_real(U_1129,U_1128),U_1129) = times_times_real(U_1129,power_power_real(U_1129,U_1128)),
inference(variable_rename,[status(thm)],[f_475_1]) ).
fof(f_475_3,plain,
! [U_1129,U_1128] : times_times_real(power_power_real(U_1129,U_1128),U_1129) = times_times_real(U_1129,power_power_real(U_1129,U_1128)),
inference(definitional_conversion,[status(esa)],[f_475_2]) ).
cnf(f_475_4,plain,
times_times_real(power_power_real(U_1129,U_1128),U_1129) = times_times_real(U_1129,power_power_real(U_1129,U_1128)),
inference(clausify,[status(thm)],[f_475_3]) ).
fof(f_476_1,plain,
! [A_13,N_16] : times_times_int(power_power_int(A_13,N_16),A_13) = times_times_int(A_13,power_power_int(A_13,N_16)),
inference(fof_nnf,[status(thm)],[fact_457_power__commutes]) ).
fof(f_476_2,plain,
! [U_1131,U_1130] : times_times_int(power_power_int(U_1131,U_1130),U_1131) = times_times_int(U_1131,power_power_int(U_1131,U_1130)),
inference(variable_rename,[status(thm)],[f_476_1]) ).
fof(f_476_3,plain,
! [U_1130,U_1131] : times_times_int(power_power_int(U_1131,U_1130),U_1131) = times_times_int(U_1131,power_power_int(U_1131,U_1130)),
inference(definitional_conversion,[status(esa)],[f_476_2]) ).
cnf(f_476_4,plain,
times_times_int(power_power_int(U_1131,U_1130),U_1131) = times_times_int(U_1131,power_power_int(U_1131,U_1130)),
inference(clausify,[status(thm)],[f_476_3]) ).
fof(f_477_1,plain,
! [A_12,B_3,N_15] : power_power_nat(times_times_nat(A_12,B_3),N_15) = times_times_nat(power_power_nat(A_12,N_15),power_power_nat(B_3,N_15)),
inference(fof_nnf,[status(thm)],[fact_458_power__mult__distrib]) ).
fof(f_477_2,plain,
! [U_1134,U_1133,U_1132] : power_power_nat(times_times_nat(U_1134,U_1133),U_1132) = times_times_nat(power_power_nat(U_1134,U_1132),power_power_nat(U_1133,U_1132)),
inference(variable_rename,[status(thm)],[f_477_1]) ).
fof(f_477_3,plain,
! [U_1133,U_1134,U_1132] : power_power_nat(times_times_nat(U_1134,U_1133),U_1132) = times_times_nat(power_power_nat(U_1134,U_1132),power_power_nat(U_1133,U_1132)),
inference(definitional_conversion,[status(esa)],[f_477_2]) ).
cnf(f_477_4,plain,
power_power_nat(times_times_nat(U_1134,U_1133),U_1132) = times_times_nat(power_power_nat(U_1134,U_1132),power_power_nat(U_1133,U_1132)),
inference(clausify,[status(thm)],[f_477_3]) ).
fof(f_478_1,plain,
! [A_12,B_3,N_15] : power_power_real(times_times_real(A_12,B_3),N_15) = times_times_real(power_power_real(A_12,N_15),power_power_real(B_3,N_15)),
inference(fof_nnf,[status(thm)],[fact_459_power__mult__distrib]) ).
fof(f_478_2,plain,
! [U_1137,U_1136,U_1135] : power_power_real(times_times_real(U_1137,U_1136),U_1135) = times_times_real(power_power_real(U_1137,U_1135),power_power_real(U_1136,U_1135)),
inference(variable_rename,[status(thm)],[f_478_1]) ).
fof(f_478_3,plain,
! [U_1135,U_1136,U_1137] : power_power_real(times_times_real(U_1137,U_1136),U_1135) = times_times_real(power_power_real(U_1137,U_1135),power_power_real(U_1136,U_1135)),
inference(definitional_conversion,[status(esa)],[f_478_2]) ).
cnf(f_478_4,plain,
power_power_real(times_times_real(U_1137,U_1136),U_1135) = times_times_real(power_power_real(U_1137,U_1135),power_power_real(U_1136,U_1135)),
inference(clausify,[status(thm)],[f_478_3]) ).
fof(f_479_1,plain,
! [A_12,B_3,N_15] : power_power_int(times_times_int(A_12,B_3),N_15) = times_times_int(power_power_int(A_12,N_15),power_power_int(B_3,N_15)),
inference(fof_nnf,[status(thm)],[fact_460_power__mult__distrib]) ).
fof(f_479_2,plain,
! [U_1140,U_1139,U_1138] : power_power_int(times_times_int(U_1140,U_1139),U_1138) = times_times_int(power_power_int(U_1140,U_1138),power_power_int(U_1139,U_1138)),
inference(variable_rename,[status(thm)],[f_479_1]) ).
fof(f_479_3,plain,
! [U_1138,U_1139,U_1140] : power_power_int(times_times_int(U_1140,U_1139),U_1138) = times_times_int(power_power_int(U_1140,U_1138),power_power_int(U_1139,U_1138)),
inference(definitional_conversion,[status(esa)],[f_479_2]) ).
cnf(f_479_4,plain,
power_power_int(times_times_int(U_1140,U_1139),U_1138) = times_times_int(power_power_int(U_1140,U_1138),power_power_int(U_1139,U_1138)),
inference(clausify,[status(thm)],[f_479_3]) ).
fof(f_480_1,plain,
! [A_11,M_4,N_14] : power_power_nat(A_11,plus_plus_nat(M_4,N_14)) = times_times_nat(power_power_nat(A_11,M_4),power_power_nat(A_11,N_14)),
inference(fof_nnf,[status(thm)],[fact_461_power__add]) ).
fof(f_480_2,plain,
! [U_1143,U_1142,U_1141] : power_power_nat(U_1143,plus_plus_nat(U_1142,U_1141)) = times_times_nat(power_power_nat(U_1143,U_1142),power_power_nat(U_1143,U_1141)),
inference(variable_rename,[status(thm)],[f_480_1]) ).
fof(f_480_3,plain,
! [U_1141,U_1142,U_1143] : power_power_nat(U_1143,plus_plus_nat(U_1142,U_1141)) = times_times_nat(power_power_nat(U_1143,U_1142),power_power_nat(U_1143,U_1141)),
inference(definitional_conversion,[status(esa)],[f_480_2]) ).
cnf(f_480_4,plain,
power_power_nat(U_1143,plus_plus_nat(U_1142,U_1141)) = times_times_nat(power_power_nat(U_1143,U_1142),power_power_nat(U_1143,U_1141)),
inference(clausify,[status(thm)],[f_480_3]) ).
fof(f_481_1,plain,
! [A_11,M_4,N_14] : power_power_real(A_11,plus_plus_nat(M_4,N_14)) = times_times_real(power_power_real(A_11,M_4),power_power_real(A_11,N_14)),
inference(fof_nnf,[status(thm)],[fact_462_power__add]) ).
fof(f_481_2,plain,
! [U_1146,U_1145,U_1144] : power_power_real(U_1146,plus_plus_nat(U_1145,U_1144)) = times_times_real(power_power_real(U_1146,U_1145),power_power_real(U_1146,U_1144)),
inference(variable_rename,[status(thm)],[f_481_1]) ).
fof(f_481_3,plain,
! [U_1144,U_1145,U_1146] : power_power_real(U_1146,plus_plus_nat(U_1145,U_1144)) = times_times_real(power_power_real(U_1146,U_1145),power_power_real(U_1146,U_1144)),
inference(definitional_conversion,[status(esa)],[f_481_2]) ).
cnf(f_481_4,plain,
power_power_real(U_1146,plus_plus_nat(U_1145,U_1144)) = times_times_real(power_power_real(U_1146,U_1145),power_power_real(U_1146,U_1144)),
inference(clausify,[status(thm)],[f_481_3]) ).
fof(f_482_1,plain,
! [A_11,M_4,N_14] : power_power_int(A_11,plus_plus_nat(M_4,N_14)) = times_times_int(power_power_int(A_11,M_4),power_power_int(A_11,N_14)),
inference(fof_nnf,[status(thm)],[fact_463_power__add]) ).
fof(f_482_2,plain,
! [U_1149,U_1148,U_1147] : power_power_int(U_1149,plus_plus_nat(U_1148,U_1147)) = times_times_int(power_power_int(U_1149,U_1148),power_power_int(U_1149,U_1147)),
inference(variable_rename,[status(thm)],[f_482_1]) ).
fof(f_482_3,plain,
! [U_1147,U_1148,U_1149] : power_power_int(U_1149,plus_plus_nat(U_1148,U_1147)) = times_times_int(power_power_int(U_1149,U_1148),power_power_int(U_1149,U_1147)),
inference(definitional_conversion,[status(esa)],[f_482_2]) ).
cnf(f_482_4,plain,
power_power_int(U_1149,plus_plus_nat(U_1148,U_1147)) = times_times_int(power_power_int(U_1149,U_1148),power_power_int(U_1149,U_1147)),
inference(clausify,[status(thm)],[f_482_3]) ).
fof(f_483_1,plain,
! [N_13] : power_power_real(one_one_real,N_13) = one_one_real,
inference(fof_nnf,[status(thm)],[fact_464_power__one]) ).
fof(f_483_2,plain,
! [U_1150] : power_power_real(one_one_real,U_1150) = one_one_real,
inference(variable_rename,[status(thm)],[f_483_1]) ).
fof(f_483_3,plain,
! [U_1150] : power_power_real(one_one_real,U_1150) = one_one_real,
inference(definitional_conversion,[status(esa)],[f_483_2]) ).
cnf(f_483_4,plain,
power_power_real(one_one_real,U_1150) = one_one_real,
inference(clausify,[status(thm)],[f_483_3]) ).
fof(f_484_1,plain,
! [N_13] : power_power_nat(one_one_nat,N_13) = one_one_nat,
inference(fof_nnf,[status(thm)],[fact_465_power__one]) ).
fof(f_484_2,plain,
! [U_1151] : power_power_nat(one_one_nat,U_1151) = one_one_nat,
inference(variable_rename,[status(thm)],[f_484_1]) ).
fof(f_484_3,plain,
! [U_1151] : power_power_nat(one_one_nat,U_1151) = one_one_nat,
inference(definitional_conversion,[status(esa)],[f_484_2]) ).
cnf(f_484_4,plain,
power_power_nat(one_one_nat,U_1151) = one_one_nat,
inference(clausify,[status(thm)],[f_484_3]) ).
fof(f_485_1,plain,
! [N_13] : power_power_int(one_one_int,N_13) = one_one_int,
inference(fof_nnf,[status(thm)],[fact_466_power__one]) ).
fof(f_485_2,plain,
! [U_1152] : power_power_int(one_one_int,U_1152) = one_one_int,
inference(variable_rename,[status(thm)],[f_485_1]) ).
fof(f_485_3,plain,
! [U_1152] : power_power_int(one_one_int,U_1152) = one_one_int,
inference(definitional_conversion,[status(esa)],[f_485_2]) ).
cnf(f_485_4,plain,
power_power_int(one_one_int,U_1152) = one_one_int,
inference(clausify,[status(thm)],[f_485_3]) ).
fof(f_486_1,plain,
! [A_10,M_3,N_12] : power_power_nat(A_10,times_times_nat(M_3,N_12)) = power_power_nat(power_power_nat(A_10,M_3),N_12),
inference(fof_nnf,[status(thm)],[fact_467_power__mult]) ).
fof(f_486_2,plain,
! [U_1155,U_1154,U_1153] : power_power_nat(U_1155,times_times_nat(U_1154,U_1153)) = power_power_nat(power_power_nat(U_1155,U_1154),U_1153),
inference(variable_rename,[status(thm)],[f_486_1]) ).
fof(f_486_3,plain,
! [U_1153,U_1154,U_1155] : power_power_nat(U_1155,times_times_nat(U_1154,U_1153)) = power_power_nat(power_power_nat(U_1155,U_1154),U_1153),
inference(definitional_conversion,[status(esa)],[f_486_2]) ).
cnf(f_486_4,plain,
power_power_nat(U_1155,times_times_nat(U_1154,U_1153)) = power_power_nat(power_power_nat(U_1155,U_1154),U_1153),
inference(clausify,[status(thm)],[f_486_3]) ).
fof(f_487_1,plain,
! [A_10,M_3,N_12] : power_power_real(A_10,times_times_nat(M_3,N_12)) = power_power_real(power_power_real(A_10,M_3),N_12),
inference(fof_nnf,[status(thm)],[fact_468_power__mult]) ).
fof(f_487_2,plain,
! [U_1158,U_1157,U_1156] : power_power_real(U_1158,times_times_nat(U_1157,U_1156)) = power_power_real(power_power_real(U_1158,U_1157),U_1156),
inference(variable_rename,[status(thm)],[f_487_1]) ).
fof(f_487_3,plain,
! [U_1156,U_1157,U_1158] : power_power_real(U_1158,times_times_nat(U_1157,U_1156)) = power_power_real(power_power_real(U_1158,U_1157),U_1156),
inference(definitional_conversion,[status(esa)],[f_487_2]) ).
cnf(f_487_4,plain,
power_power_real(U_1158,times_times_nat(U_1157,U_1156)) = power_power_real(power_power_real(U_1158,U_1157),U_1156),
inference(clausify,[status(thm)],[f_487_3]) ).
fof(f_488_1,plain,
! [A_10,M_3,N_12] : power_power_int(A_10,times_times_nat(M_3,N_12)) = power_power_int(power_power_int(A_10,M_3),N_12),
inference(fof_nnf,[status(thm)],[fact_469_power__mult]) ).
fof(f_488_2,plain,
! [U_1161,U_1160,U_1159] : power_power_int(U_1161,times_times_nat(U_1160,U_1159)) = power_power_int(power_power_int(U_1161,U_1160),U_1159),
inference(variable_rename,[status(thm)],[f_488_1]) ).
fof(f_488_3,plain,
! [U_1159,U_1160,U_1161] : power_power_int(U_1161,times_times_nat(U_1160,U_1159)) = power_power_int(power_power_int(U_1161,U_1160),U_1159),
inference(definitional_conversion,[status(esa)],[f_488_2]) ).
cnf(f_488_4,plain,
power_power_int(U_1161,times_times_nat(U_1160,U_1159)) = power_power_int(power_power_int(U_1161,U_1160),U_1159),
inference(clausify,[status(thm)],[f_488_3]) ).
fof(f_489_1,plain,
! [X_8,Y_6] :
( ord_less_real(X_8,Y_6)
| ~ ord_less_eq_real(zero_zero_real,Y_6)
| ~ ord_less_real(power_power_real(X_8,number_number_of_nat(bit0(bit1(pls)))),power_power_real(Y_6,number_number_of_nat(bit0(bit1(pls))))) ),
inference(fof_nnf,[status(thm)],[fact_470_power2__less__imp__less]) ).
fof(f_489_2,plain,
! [U_1163,U_1162] :
( ord_less_real(U_1163,U_1162)
| ~ ord_less_eq_real(zero_zero_real,U_1162)
| ~ ord_less_real(power_power_real(U_1163,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1162,number_number_of_nat(bit0(bit1(pls))))) ),
inference(variable_rename,[status(thm)],[f_489_1]) ).
fof(f_489_3,plain,
! [U_1163,U_1162] :
( ord_less_real(U_1163,U_1162)
| ~ ord_less_eq_real(zero_zero_real,U_1162)
| ~ ord_less_real(power_power_real(U_1163,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1162,number_number_of_nat(bit0(bit1(pls))))) ),
inference(definitional_conversion,[status(esa)],[f_489_2]) ).
cnf(f_489_4,plain,
( ord_less_real(U_1163,U_1162)
| ~ ord_less_eq_real(zero_zero_real,U_1162)
| ~ ord_less_real(power_power_real(U_1163,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1162,number_number_of_nat(bit0(bit1(pls))))) ),
inference(clausify,[status(thm)],[f_489_3]) ).
fof(f_490_1,plain,
! [X_8,Y_6] :
( ord_less_nat(X_8,Y_6)
| ~ ord_less_eq_nat(zero_zero_nat,Y_6)
| ~ ord_less_nat(power_power_nat(X_8,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(Y_6,number_number_of_nat(bit0(bit1(pls))))) ),
inference(fof_nnf,[status(thm)],[fact_471_power2__less__imp__less]) ).
fof(f_490_2,plain,
! [U_1165,U_1164] :
( ord_less_nat(U_1165,U_1164)
| ~ ord_less_eq_nat(zero_zero_nat,U_1164)
| ~ ord_less_nat(power_power_nat(U_1165,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(U_1164,number_number_of_nat(bit0(bit1(pls))))) ),
inference(variable_rename,[status(thm)],[f_490_1]) ).
fof(f_490_3,plain,
! [U_1165,U_1164] :
( ord_less_nat(U_1165,U_1164)
| ~ ord_less_eq_nat(zero_zero_nat,U_1164)
| ~ ord_less_nat(power_power_nat(U_1165,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(U_1164,number_number_of_nat(bit0(bit1(pls))))) ),
inference(definitional_conversion,[status(esa)],[f_490_2]) ).
cnf(f_490_4,plain,
( ord_less_nat(U_1165,U_1164)
| ~ ord_less_eq_nat(zero_zero_nat,U_1164)
| ~ ord_less_nat(power_power_nat(U_1165,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(U_1164,number_number_of_nat(bit0(bit1(pls))))) ),
inference(clausify,[status(thm)],[f_490_3]) ).
fof(f_491_1,plain,
! [X_8,Y_6] :
( ord_less_int(X_8,Y_6)
| ~ ord_less_eq_int(zero_zero_int,Y_6)
| ~ ord_less_int(power_power_int(X_8,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y_6,number_number_of_nat(bit0(bit1(pls))))) ),
inference(fof_nnf,[status(thm)],[fact_472_power2__less__imp__less]) ).
fof(f_491_2,plain,
! [U_1167,U_1166] :
( ord_less_int(U_1167,U_1166)
| ~ ord_less_eq_int(zero_zero_int,U_1166)
| ~ ord_less_int(power_power_int(U_1167,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1166,number_number_of_nat(bit0(bit1(pls))))) ),
inference(variable_rename,[status(thm)],[f_491_1]) ).
fof(f_491_3,plain,
! [U_1167,U_1166] :
( ord_less_int(U_1167,U_1166)
| ~ ord_less_eq_int(zero_zero_int,U_1166)
| ~ ord_less_int(power_power_int(U_1167,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1166,number_number_of_nat(bit0(bit1(pls))))) ),
inference(definitional_conversion,[status(esa)],[f_491_2]) ).
cnf(f_491_4,plain,
( ord_less_int(U_1167,U_1166)
| ~ ord_less_eq_int(zero_zero_int,U_1166)
| ~ ord_less_int(power_power_int(U_1167,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1166,number_number_of_nat(bit0(bit1(pls))))) ),
inference(clausify,[status(thm)],[f_491_3]) ).
fof(f_492_1,plain,
! [X_7,Y_5] : ord_less_eq_real(zero_zero_real,plus_plus_real(power_power_real(X_7,number_number_of_nat(bit0(bit1(pls)))),power_power_real(Y_5,number_number_of_nat(bit0(bit1(pls)))))),
inference(fof_nnf,[status(thm)],[fact_473_sum__power2__ge__zero]) ).
fof(f_492_2,plain,
! [U_1169,U_1168] : ord_less_eq_real(zero_zero_real,plus_plus_real(power_power_real(U_1169,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1168,number_number_of_nat(bit0(bit1(pls)))))),
inference(variable_rename,[status(thm)],[f_492_1]) ).
fof(f_492_3,plain,
! [U_1169,U_1168] : ord_less_eq_real(zero_zero_real,plus_plus_real(power_power_real(U_1169,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1168,number_number_of_nat(bit0(bit1(pls)))))),
inference(definitional_conversion,[status(esa)],[f_492_2]) ).
cnf(f_492_4,plain,
ord_less_eq_real(zero_zero_real,plus_plus_real(power_power_real(U_1169,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1168,number_number_of_nat(bit0(bit1(pls)))))),
inference(clausify,[status(thm)],[f_492_3]) ).
fof(f_493_1,plain,
! [X_7,Y_5] : ord_less_eq_int(zero_zero_int,plus_plus_int(power_power_int(X_7,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y_5,number_number_of_nat(bit0(bit1(pls)))))),
inference(fof_nnf,[status(thm)],[fact_474_sum__power2__ge__zero]) ).
fof(f_493_2,plain,
! [U_1171,U_1170] : ord_less_eq_int(zero_zero_int,plus_plus_int(power_power_int(U_1171,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1170,number_number_of_nat(bit0(bit1(pls)))))),
inference(variable_rename,[status(thm)],[f_493_1]) ).
fof(f_493_3,plain,
! [U_1170,U_1171] : ord_less_eq_int(zero_zero_int,plus_plus_int(power_power_int(U_1171,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1170,number_number_of_nat(bit0(bit1(pls)))))),
inference(definitional_conversion,[status(esa)],[f_493_2]) ).
cnf(f_493_4,plain,
ord_less_eq_int(zero_zero_int,plus_plus_int(power_power_int(U_1171,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1170,number_number_of_nat(bit0(bit1(pls)))))),
inference(clausify,[status(thm)],[f_493_3]) ).
fof(f_494_1,plain,
! [X_2,Y_2] :
( ( ord_less_eq_real(plus_plus_real(power_power_real(X_2,number_number_of_nat(bit0(bit1(pls)))),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 )
| ~ ord_less_eq_real(plus_plus_real(power_power_real(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_real(Y_2,number_number_of_nat(bit0(bit1(pls))))),zero_zero_real) ) ),
inference(fof_nnf,[status(thm)],[fact_475_sum__power2__le__zero__iff]) ).
fof(f_494_2,plain,
! [U_1173,U_1172] :
( ( ord_less_eq_real(plus_plus_real(power_power_real(U_1173,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1172,number_number_of_nat(bit0(bit1(pls))))),zero_zero_real)
| U_1172 != zero_zero_real
| U_1173 != zero_zero_real )
& ( ( U_1172 = zero_zero_real
& U_1173 = zero_zero_real )
| ~ ord_less_eq_real(plus_plus_real(power_power_real(U_1173,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1172,number_number_of_nat(bit0(bit1(pls))))),zero_zero_real) ) ),
inference(variable_rename,[status(thm)],[f_494_1]) ).
fof(f_494_3,plain,
( ! [U_1177,U_1175] :
( ord_less_eq_real(plus_plus_real(power_power_real(U_1177,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1175,number_number_of_nat(bit0(bit1(pls))))),zero_zero_real)
| U_1175 != zero_zero_real
| U_1177 != zero_zero_real )
& ! [U_1176,U_1174] :
( ( U_1174 = zero_zero_real
& U_1176 = zero_zero_real )
| ~ ord_less_eq_real(plus_plus_real(power_power_real(U_1176,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1174,number_number_of_nat(bit0(bit1(pls))))),zero_zero_real) ) ),
inference(miniscope,[status(thm)],[f_494_2]) ).
fof(f_494_4,plain,
( ! [U_1176,U_1174] :
( U_1174 = zero_zero_real
| ~ sP51(U_1176,U_1174) )
& ! [U_1176,U_1174] :
( U_1176 = zero_zero_real
| ~ sP51(U_1176,U_1174) )
& ! [U_1177,U_1175] :
( ord_less_eq_real(plus_plus_real(power_power_real(U_1177,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1175,number_number_of_nat(bit0(bit1(pls))))),zero_zero_real)
| U_1175 != zero_zero_real
| U_1177 != zero_zero_real )
& ! [U_1176,U_1174] :
( sP51(U_1176,U_1174)
| ~ ord_less_eq_real(plus_plus_real(power_power_real(U_1176,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1174,number_number_of_nat(bit0(bit1(pls))))),zero_zero_real) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP51])],[f_494_3]) ).
cnf(f_494_5,plain,
( sP51(U_1176,U_1174)
| ~ ord_less_eq_real(plus_plus_real(power_power_real(U_1176,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1174,number_number_of_nat(bit0(bit1(pls))))),zero_zero_real) ),
inference(clausify,[status(thm)],[f_494_4]) ).
cnf(f_494_6,plain,
( ord_less_eq_real(plus_plus_real(power_power_real(U_1177,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1175,number_number_of_nat(bit0(bit1(pls))))),zero_zero_real)
| U_1175 != zero_zero_real
| U_1177 != zero_zero_real ),
inference(clausify,[status(thm)],[f_494_4]) ).
cnf(f_494_7,plain,
( U_1176 = zero_zero_real
| ~ sP51(U_1176,U_1174) ),
inference(clausify,[status(thm)],[f_494_4]) ).
cnf(f_494_8,plain,
( U_1174 = zero_zero_real
| ~ sP51(U_1176,U_1174) ),
inference(clausify,[status(thm)],[f_494_4]) ).
fof(f_495_1,plain,
! [X_2,Y_2] :
( ( ( ord_less_eq_int(plus_plus_int(power_power_int(X_2,number_number_of_nat(bit0(bit1(pls)))),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 )
| ~ ord_less_eq_int(plus_plus_int(power_power_int(X_2,number_number_of_nat(bit0(bit1(pls)))),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_476_sum__power2__le__zero__iff]) ).
fof(f_495_2,plain,
! [U_1179,U_1178] :
( ( ( ord_less_eq_int(plus_plus_int(power_power_int(U_1179,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1178,number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)
| U_1178 != zero_zero_int
| U_1179 != zero_zero_int )
& ( ( U_1178 = zero_zero_int
& U_1179 = zero_zero_int )
| ~ ord_less_eq_int(plus_plus_int(power_power_int(U_1179,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1178,number_number_of_nat(bit0(bit1(pls))))),zero_zero_int) ) )
| ~ is_int(U_1178)
| ~ is_int(U_1179) ),
inference(variable_rename,[status(thm)],[f_495_1]) ).
fof(f_495_3,plain,
( ! [U_1178,U_1179] :
( U_1178 = zero_zero_int
| ~ sP52(U_1178,U_1179) )
& ! [U_1178,U_1179] :
( U_1179 = zero_zero_int
| ~ sP52(U_1178,U_1179) )
& ! [U_1178,U_1179] :
( ord_less_eq_int(plus_plus_int(power_power_int(U_1179,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1178,number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)
| U_1178 != zero_zero_int
| U_1179 != zero_zero_int
| ~ sP53(U_1178,U_1179) )
& ! [U_1178,U_1179] :
( sP52(U_1178,U_1179)
| ~ ord_less_eq_int(plus_plus_int(power_power_int(U_1179,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1178,number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)
| ~ sP53(U_1178,U_1179) )
& ! [U_1178,U_1179] :
( sP53(U_1178,U_1179)
| ~ is_int(U_1178)
| ~ is_int(U_1179) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP52,sP53])],[f_495_2]) ).
cnf(f_495_4,plain,
( sP53(U_1178,U_1179)
| ~ is_int(U_1178)
| ~ is_int(U_1179) ),
inference(clausify,[status(thm)],[f_495_3]) ).
cnf(f_495_5,plain,
( sP52(U_1178,U_1179)
| ~ ord_less_eq_int(plus_plus_int(power_power_int(U_1179,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1178,number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)
| ~ sP53(U_1178,U_1179) ),
inference(clausify,[status(thm)],[f_495_3]) ).
cnf(f_495_6,plain,
( ord_less_eq_int(plus_plus_int(power_power_int(U_1179,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1178,number_number_of_nat(bit0(bit1(pls))))),zero_zero_int)
| U_1178 != zero_zero_int
| U_1179 != zero_zero_int
| ~ sP53(U_1178,U_1179) ),
inference(clausify,[status(thm)],[f_495_3]) ).
cnf(f_495_7,plain,
( U_1179 = zero_zero_int
| ~ sP52(U_1178,U_1179) ),
inference(clausify,[status(thm)],[f_495_3]) ).
cnf(f_495_8,plain,
( U_1178 = zero_zero_int
| ~ sP52(U_1178,U_1179) ),
inference(clausify,[status(thm)],[f_495_3]) ).
fof(f_496_1,plain,
! [X_6,Y_4] : ~ ord_less_real(plus_plus_real(power_power_real(X_6,number_number_of_nat(bit0(bit1(pls)))),power_power_real(Y_4,number_number_of_nat(bit0(bit1(pls))))),zero_zero_real),
inference(fof_nnf,[status(thm)],[fact_477_not__sum__power2__lt__zero]) ).
fof(f_496_2,plain,
! [U_1181,U_1180] : ~ ord_less_real(plus_plus_real(power_power_real(U_1181,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1180,number_number_of_nat(bit0(bit1(pls))))),zero_zero_real),
inference(variable_rename,[status(thm)],[f_496_1]) ).
fof(f_496_3,plain,
! [U_1181,U_1180] : ~ ord_less_real(plus_plus_real(power_power_real(U_1181,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1180,number_number_of_nat(bit0(bit1(pls))))),zero_zero_real),
inference(definitional_conversion,[status(esa)],[f_496_2]) ).
cnf(f_496_4,plain,
~ ord_less_real(plus_plus_real(power_power_real(U_1181,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1180,number_number_of_nat(bit0(bit1(pls))))),zero_zero_real),
inference(clausify,[status(thm)],[f_496_3]) ).
fof(f_497_1,plain,
! [X_6,Y_4] : ~ ord_less_int(plus_plus_int(power_power_int(X_6,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y_4,number_number_of_nat(bit0(bit1(pls))))),zero_zero_int),
inference(fof_nnf,[status(thm)],[fact_478_not__sum__power2__lt__zero]) ).
fof(f_497_2,plain,
! [U_1183,U_1182] : ~ ord_less_int(plus_plus_int(power_power_int(U_1183,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1182,number_number_of_nat(bit0(bit1(pls))))),zero_zero_int),
inference(variable_rename,[status(thm)],[f_497_1]) ).
fof(f_497_3,plain,
! [U_1182,U_1183] : ~ ord_less_int(plus_plus_int(power_power_int(U_1183,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1182,number_number_of_nat(bit0(bit1(pls))))),zero_zero_int),
inference(definitional_conversion,[status(esa)],[f_497_2]) ).
cnf(f_497_4,plain,
~ ord_less_int(plus_plus_int(power_power_int(U_1183,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1182,number_number_of_nat(bit0(bit1(pls))))),zero_zero_int),
inference(clausify,[status(thm)],[f_497_3]) ).
fof(f_498_1,plain,
! [X_2,Y_2] :
( ( ord_less_real(zero_zero_real,plus_plus_real(power_power_real(X_2,number_number_of_nat(bit0(bit1(pls)))),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
| ~ ord_less_real(zero_zero_real,plus_plus_real(power_power_real(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_real(Y_2,number_number_of_nat(bit0(bit1(pls)))))) ) ),
inference(fof_nnf,[status(thm)],[fact_479_sum__power2__gt__zero__iff]) ).
fof(f_498_2,plain,
! [U_1185,U_1184] :
( ( ord_less_real(zero_zero_real,plus_plus_real(power_power_real(U_1185,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1184,number_number_of_nat(bit0(bit1(pls))))))
| ( U_1184 = zero_zero_real
& U_1185 = zero_zero_real ) )
& ( U_1184 != zero_zero_real
| U_1185 != zero_zero_real
| ~ ord_less_real(zero_zero_real,plus_plus_real(power_power_real(U_1185,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1184,number_number_of_nat(bit0(bit1(pls)))))) ) ),
inference(variable_rename,[status(thm)],[f_498_1]) ).
fof(f_498_3,plain,
( ! [U_1189,U_1187] :
( ord_less_real(zero_zero_real,plus_plus_real(power_power_real(U_1189,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1187,number_number_of_nat(bit0(bit1(pls))))))
| ( U_1187 = zero_zero_real
& U_1189 = zero_zero_real ) )
& ! [U_1188,U_1186] :
( U_1186 != zero_zero_real
| U_1188 != zero_zero_real
| ~ ord_less_real(zero_zero_real,plus_plus_real(power_power_real(U_1188,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1186,number_number_of_nat(bit0(bit1(pls)))))) ) ),
inference(miniscope,[status(thm)],[f_498_2]) ).
fof(f_498_4,plain,
( ! [U_1187,U_1189] :
( U_1187 = zero_zero_real
| ~ sP54(U_1187,U_1189) )
& ! [U_1187,U_1189] :
( U_1189 = zero_zero_real
| ~ sP54(U_1187,U_1189) )
& ! [U_1187,U_1189] :
( ord_less_real(zero_zero_real,plus_plus_real(power_power_real(U_1189,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1187,number_number_of_nat(bit0(bit1(pls))))))
| sP54(U_1187,U_1189) )
& ! [U_1186,U_1188] :
( U_1186 != zero_zero_real
| U_1188 != zero_zero_real
| ~ ord_less_real(zero_zero_real,plus_plus_real(power_power_real(U_1188,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1186,number_number_of_nat(bit0(bit1(pls)))))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP54])],[f_498_3]) ).
cnf(f_498_5,plain,
( U_1186 != zero_zero_real
| U_1188 != zero_zero_real
| ~ ord_less_real(zero_zero_real,plus_plus_real(power_power_real(U_1188,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1186,number_number_of_nat(bit0(bit1(pls)))))) ),
inference(clausify,[status(thm)],[f_498_4]) ).
cnf(f_498_6,plain,
( ord_less_real(zero_zero_real,plus_plus_real(power_power_real(U_1189,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1187,number_number_of_nat(bit0(bit1(pls))))))
| sP54(U_1187,U_1189) ),
inference(clausify,[status(thm)],[f_498_4]) ).
cnf(f_498_7,plain,
( U_1189 = zero_zero_real
| ~ sP54(U_1187,U_1189) ),
inference(clausify,[status(thm)],[f_498_4]) ).
cnf(f_498_8,plain,
( U_1187 = zero_zero_real
| ~ sP54(U_1187,U_1189) ),
inference(clausify,[status(thm)],[f_498_4]) ).
fof(f_499_1,plain,
! [X_2,Y_2] :
( ( ( ord_less_int(zero_zero_int,plus_plus_int(power_power_int(X_2,number_number_of_nat(bit0(bit1(pls)))),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
| ~ ord_less_int(zero_zero_int,plus_plus_int(power_power_int(X_2,number_number_of_nat(bit0(bit1(pls)))),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_480_sum__power2__gt__zero__iff]) ).
fof(f_499_2,plain,
! [U_1191,U_1190] :
( ( ( ord_less_int(zero_zero_int,plus_plus_int(power_power_int(U_1191,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1190,number_number_of_nat(bit0(bit1(pls))))))
| ( U_1190 = zero_zero_int
& U_1191 = zero_zero_int ) )
& ( U_1190 != zero_zero_int
| U_1191 != zero_zero_int
| ~ ord_less_int(zero_zero_int,plus_plus_int(power_power_int(U_1191,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1190,number_number_of_nat(bit0(bit1(pls)))))) ) )
| ~ is_int(U_1190)
| ~ is_int(U_1191) ),
inference(variable_rename,[status(thm)],[f_499_1]) ).
fof(f_499_3,plain,
( ! [U_1190,U_1191] :
( U_1190 = zero_zero_int
| ~ sP55(U_1190,U_1191) )
& ! [U_1190,U_1191] :
( U_1191 = zero_zero_int
| ~ sP55(U_1190,U_1191) )
& ! [U_1190,U_1191] :
( ord_less_int(zero_zero_int,plus_plus_int(power_power_int(U_1191,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1190,number_number_of_nat(bit0(bit1(pls))))))
| sP55(U_1190,U_1191)
| ~ sP56(U_1190,U_1191) )
& ! [U_1190,U_1191] :
( U_1190 != zero_zero_int
| U_1191 != zero_zero_int
| ~ ord_less_int(zero_zero_int,plus_plus_int(power_power_int(U_1191,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1190,number_number_of_nat(bit0(bit1(pls))))))
| ~ sP56(U_1190,U_1191) )
& ! [U_1190,U_1191] :
( sP56(U_1190,U_1191)
| ~ is_int(U_1190)
| ~ is_int(U_1191) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP55,sP56])],[f_499_2]) ).
cnf(f_499_4,plain,
( sP56(U_1190,U_1191)
| ~ is_int(U_1190)
| ~ is_int(U_1191) ),
inference(clausify,[status(thm)],[f_499_3]) ).
cnf(f_499_5,plain,
( U_1190 != zero_zero_int
| U_1191 != zero_zero_int
| ~ ord_less_int(zero_zero_int,plus_plus_int(power_power_int(U_1191,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1190,number_number_of_nat(bit0(bit1(pls))))))
| ~ sP56(U_1190,U_1191) ),
inference(clausify,[status(thm)],[f_499_3]) ).
cnf(f_499_6,plain,
( ord_less_int(zero_zero_int,plus_plus_int(power_power_int(U_1191,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1190,number_number_of_nat(bit0(bit1(pls))))))
| sP55(U_1190,U_1191)
| ~ sP56(U_1190,U_1191) ),
inference(clausify,[status(thm)],[f_499_3]) ).
cnf(f_499_7,plain,
( U_1191 = zero_zero_int
| ~ sP55(U_1190,U_1191) ),
inference(clausify,[status(thm)],[f_499_3]) ).
cnf(f_499_8,plain,
( U_1190 = zero_zero_int
| ~ sP55(U_1190,U_1191) ),
inference(clausify,[status(thm)],[f_499_3]) ).
fof(f_500_1,plain,
! [A_9,N_11] : ord_less_eq_real(zero_zero_real,power_power_real(A_9,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_11))),
inference(fof_nnf,[status(thm)],[fact_481_zero__le__even__power_H]) ).
fof(f_500_2,plain,
! [U_1193,U_1192] : ord_less_eq_real(zero_zero_real,power_power_real(U_1193,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1192))),
inference(variable_rename,[status(thm)],[f_500_1]) ).
fof(f_500_3,plain,
! [U_1193,U_1192] : ord_less_eq_real(zero_zero_real,power_power_real(U_1193,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1192))),
inference(definitional_conversion,[status(esa)],[f_500_2]) ).
cnf(f_500_4,plain,
ord_less_eq_real(zero_zero_real,power_power_real(U_1193,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1192))),
inference(clausify,[status(thm)],[f_500_3]) ).
fof(f_501_1,plain,
! [A_9,N_11] : ord_less_eq_int(zero_zero_int,power_power_int(A_9,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_11))),
inference(fof_nnf,[status(thm)],[fact_482_zero__le__even__power_H]) ).
fof(f_501_2,plain,
! [U_1195,U_1194] : ord_less_eq_int(zero_zero_int,power_power_int(U_1195,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1194))),
inference(variable_rename,[status(thm)],[f_501_1]) ).
fof(f_501_3,plain,
! [U_1194,U_1195] : ord_less_eq_int(zero_zero_int,power_power_int(U_1195,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1194))),
inference(definitional_conversion,[status(esa)],[f_501_2]) ).
cnf(f_501_4,plain,
ord_less_eq_int(zero_zero_int,power_power_int(U_1195,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1194))),
inference(clausify,[status(thm)],[f_501_3]) ).
fof(f_502_1,plain,
! [N_10,A_8] :
( ord_less_eq_real(one_one_real,power_power_real(A_8,N_10))
| ~ ord_less_eq_real(one_one_real,A_8) ),
inference(fof_nnf,[status(thm)],[fact_483_one__le__power]) ).
fof(f_502_2,plain,
! [U_1197,U_1196] :
( ord_less_eq_real(one_one_real,power_power_real(U_1196,U_1197))
| ~ ord_less_eq_real(one_one_real,U_1196) ),
inference(variable_rename,[status(thm)],[f_502_1]) ).
fof(f_502_3,plain,
! [U_1197,U_1196] :
( ord_less_eq_real(one_one_real,power_power_real(U_1196,U_1197))
| ~ ord_less_eq_real(one_one_real,U_1196) ),
inference(definitional_conversion,[status(esa)],[f_502_2]) ).
cnf(f_502_4,plain,
( ord_less_eq_real(one_one_real,power_power_real(U_1196,U_1197))
| ~ ord_less_eq_real(one_one_real,U_1196) ),
inference(clausify,[status(thm)],[f_502_3]) ).
fof(f_503_1,plain,
! [N_10,A_8] :
( ord_less_eq_nat(one_one_nat,power_power_nat(A_8,N_10))
| ~ ord_less_eq_nat(one_one_nat,A_8) ),
inference(fof_nnf,[status(thm)],[fact_484_one__le__power]) ).
fof(f_503_2,plain,
! [U_1199,U_1198] :
( ord_less_eq_nat(one_one_nat,power_power_nat(U_1198,U_1199))
| ~ ord_less_eq_nat(one_one_nat,U_1198) ),
inference(variable_rename,[status(thm)],[f_503_1]) ).
fof(f_503_3,plain,
! [U_1198,U_1199] :
( ord_less_eq_nat(one_one_nat,power_power_nat(U_1198,U_1199))
| ~ ord_less_eq_nat(one_one_nat,U_1198) ),
inference(definitional_conversion,[status(esa)],[f_503_2]) ).
cnf(f_503_4,plain,
( ord_less_eq_nat(one_one_nat,power_power_nat(U_1198,U_1199))
| ~ ord_less_eq_nat(one_one_nat,U_1198) ),
inference(clausify,[status(thm)],[f_503_3]) ).
fof(f_504_1,plain,
! [N_10,A_8] :
( ord_less_eq_int(one_one_int,power_power_int(A_8,N_10))
| ~ ord_less_eq_int(one_one_int,A_8) ),
inference(fof_nnf,[status(thm)],[fact_485_one__le__power]) ).
fof(f_504_2,plain,
! [U_1201,U_1200] :
( ord_less_eq_int(one_one_int,power_power_int(U_1200,U_1201))
| ~ ord_less_eq_int(one_one_int,U_1200) ),
inference(variable_rename,[status(thm)],[f_504_1]) ).
fof(f_504_3,plain,
! [U_1200,U_1201] :
( ord_less_eq_int(one_one_int,power_power_int(U_1200,U_1201))
| ~ ord_less_eq_int(one_one_int,U_1200) ),
inference(definitional_conversion,[status(esa)],[f_504_2]) ).
cnf(f_504_4,plain,
( ord_less_eq_int(one_one_int,power_power_int(U_1200,U_1201))
| ~ ord_less_eq_int(one_one_int,U_1200) ),
inference(clausify,[status(thm)],[f_504_3]) ).
fof(f_505_1,plain,
! [A_7,N_9,N_8] :
( ord_less_eq_real(power_power_real(A_7,N_9),power_power_real(A_7,N_8))
| ~ ord_less_eq_real(one_one_real,A_7)
| ~ ord_less_eq_nat(N_9,N_8) ),
inference(fof_nnf,[status(thm)],[fact_486_power__increasing]) ).
fof(f_505_2,plain,
! [U_1204,U_1203,U_1202] :
( ord_less_eq_real(power_power_real(U_1204,U_1203),power_power_real(U_1204,U_1202))
| ~ ord_less_eq_real(one_one_real,U_1204)
| ~ ord_less_eq_nat(U_1203,U_1202) ),
inference(variable_rename,[status(thm)],[f_505_1]) ).
fof(f_505_3,plain,
! [U_1202,U_1203,U_1204] :
( ord_less_eq_real(power_power_real(U_1204,U_1203),power_power_real(U_1204,U_1202))
| ~ ord_less_eq_real(one_one_real,U_1204)
| ~ ord_less_eq_nat(U_1203,U_1202) ),
inference(definitional_conversion,[status(esa)],[f_505_2]) ).
cnf(f_505_4,plain,
( ord_less_eq_real(power_power_real(U_1204,U_1203),power_power_real(U_1204,U_1202))
| ~ ord_less_eq_real(one_one_real,U_1204)
| ~ ord_less_eq_nat(U_1203,U_1202) ),
inference(clausify,[status(thm)],[f_505_3]) ).
fof(f_506_1,plain,
! [A_7,N_9,N_8] :
( ord_less_eq_nat(power_power_nat(A_7,N_9),power_power_nat(A_7,N_8))
| ~ ord_less_eq_nat(one_one_nat,A_7)
| ~ ord_less_eq_nat(N_9,N_8) ),
inference(fof_nnf,[status(thm)],[fact_487_power__increasing]) ).
fof(f_506_2,plain,
! [U_1207,U_1206,U_1205] :
( ord_less_eq_nat(power_power_nat(U_1207,U_1206),power_power_nat(U_1207,U_1205))
| ~ ord_less_eq_nat(one_one_nat,U_1207)
| ~ ord_less_eq_nat(U_1206,U_1205) ),
inference(variable_rename,[status(thm)],[f_506_1]) ).
fof(f_506_3,plain,
! [U_1205,U_1206,U_1207] :
( ord_less_eq_nat(power_power_nat(U_1207,U_1206),power_power_nat(U_1207,U_1205))
| ~ ord_less_eq_nat(one_one_nat,U_1207)
| ~ ord_less_eq_nat(U_1206,U_1205) ),
inference(definitional_conversion,[status(esa)],[f_506_2]) ).
cnf(f_506_4,plain,
( ord_less_eq_nat(power_power_nat(U_1207,U_1206),power_power_nat(U_1207,U_1205))
| ~ ord_less_eq_nat(one_one_nat,U_1207)
| ~ ord_less_eq_nat(U_1206,U_1205) ),
inference(clausify,[status(thm)],[f_506_3]) ).
fof(f_507_1,plain,
! [A_7,N_9,N_8] :
( ord_less_eq_int(power_power_int(A_7,N_9),power_power_int(A_7,N_8))
| ~ ord_less_eq_int(one_one_int,A_7)
| ~ ord_less_eq_nat(N_9,N_8) ),
inference(fof_nnf,[status(thm)],[fact_488_power__increasing]) ).
fof(f_507_2,plain,
! [U_1210,U_1209,U_1208] :
( ord_less_eq_int(power_power_int(U_1210,U_1209),power_power_int(U_1210,U_1208))
| ~ ord_less_eq_int(one_one_int,U_1210)
| ~ ord_less_eq_nat(U_1209,U_1208) ),
inference(variable_rename,[status(thm)],[f_507_1]) ).
fof(f_507_3,plain,
! [U_1208,U_1209,U_1210] :
( ord_less_eq_int(power_power_int(U_1210,U_1209),power_power_int(U_1210,U_1208))
| ~ ord_less_eq_int(one_one_int,U_1210)
| ~ ord_less_eq_nat(U_1209,U_1208) ),
inference(definitional_conversion,[status(esa)],[f_507_2]) ).
cnf(f_507_4,plain,
( ord_less_eq_int(power_power_int(U_1210,U_1209),power_power_int(U_1210,U_1208))
| ~ ord_less_eq_int(one_one_int,U_1210)
| ~ ord_less_eq_nat(U_1209,U_1208) ),
inference(clausify,[status(thm)],[f_507_3]) ).
fof(f_508_1,plain,
! [Ma,N_1,A_1] :
( ( ( power_power_real(A_1,Ma) = power_power_real(A_1,N_1)
| Ma != N_1 )
& ( Ma = N_1
| power_power_real(A_1,Ma) != power_power_real(A_1,N_1) ) )
| ~ ord_less_real(one_one_real,A_1) ),
inference(fof_nnf,[status(thm)],[fact_489_power__inject__exp]) ).
fof(f_508_2,plain,
! [U_1213,U_1212,U_1211] :
( ( ( power_power_real(U_1211,U_1213) = power_power_real(U_1211,U_1212)
| U_1213 != U_1212 )
& ( U_1213 = U_1212
| power_power_real(U_1211,U_1213) != power_power_real(U_1211,U_1212) ) )
| ~ ord_less_real(one_one_real,U_1211) ),
inference(variable_rename,[status(thm)],[f_508_1]) ).
fof(f_508_3,plain,
( ! [U_1211,U_1212,U_1213] :
( power_power_real(U_1211,U_1213) = power_power_real(U_1211,U_1212)
| U_1213 != U_1212
| ~ sP57(U_1211,U_1212,U_1213) )
& ! [U_1211,U_1212,U_1213] :
( U_1213 = U_1212
| power_power_real(U_1211,U_1213) != power_power_real(U_1211,U_1212)
| ~ sP57(U_1211,U_1212,U_1213) )
& ! [U_1211,U_1212,U_1213] :
( sP57(U_1211,U_1212,U_1213)
| ~ ord_less_real(one_one_real,U_1211) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP57])],[f_508_2]) ).
cnf(f_508_4,plain,
( sP57(U_1211,U_1212,U_1213)
| ~ ord_less_real(one_one_real,U_1211) ),
inference(clausify,[status(thm)],[f_508_3]) ).
cnf(f_508_5,plain,
( U_1213 = U_1212
| power_power_real(U_1211,U_1213) != power_power_real(U_1211,U_1212)
| ~ sP57(U_1211,U_1212,U_1213) ),
inference(clausify,[status(thm)],[f_508_3]) ).
cnf(f_508_6,plain,
( power_power_real(U_1211,U_1213) = power_power_real(U_1211,U_1212)
| U_1213 != U_1212
| ~ sP57(U_1211,U_1212,U_1213) ),
inference(clausify,[status(thm)],[f_508_3]) ).
fof(f_509_1,plain,
! [Ma,N_1,A_1] :
( ( ( power_power_nat(A_1,Ma) = power_power_nat(A_1,N_1)
| Ma != N_1 )
& ( Ma = N_1
| power_power_nat(A_1,Ma) != power_power_nat(A_1,N_1) ) )
| ~ ord_less_nat(one_one_nat,A_1) ),
inference(fof_nnf,[status(thm)],[fact_490_power__inject__exp]) ).
fof(f_509_2,plain,
! [U_1216,U_1215,U_1214] :
( ( ( power_power_nat(U_1214,U_1216) = power_power_nat(U_1214,U_1215)
| U_1216 != U_1215 )
& ( U_1216 = U_1215
| power_power_nat(U_1214,U_1216) != power_power_nat(U_1214,U_1215) ) )
| ~ ord_less_nat(one_one_nat,U_1214) ),
inference(variable_rename,[status(thm)],[f_509_1]) ).
fof(f_509_3,plain,
( ! [U_1216,U_1215,U_1214] :
( power_power_nat(U_1214,U_1216) = power_power_nat(U_1214,U_1215)
| U_1216 != U_1215
| ~ sP58(U_1216,U_1215,U_1214) )
& ! [U_1216,U_1215,U_1214] :
( U_1216 = U_1215
| power_power_nat(U_1214,U_1216) != power_power_nat(U_1214,U_1215)
| ~ sP58(U_1216,U_1215,U_1214) )
& ! [U_1216,U_1215,U_1214] :
( sP58(U_1216,U_1215,U_1214)
| ~ ord_less_nat(one_one_nat,U_1214) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP58])],[f_509_2]) ).
cnf(f_509_4,plain,
( sP58(U_1216,U_1215,U_1214)
| ~ ord_less_nat(one_one_nat,U_1214) ),
inference(clausify,[status(thm)],[f_509_3]) ).
cnf(f_509_5,plain,
( U_1216 = U_1215
| power_power_nat(U_1214,U_1216) != power_power_nat(U_1214,U_1215)
| ~ sP58(U_1216,U_1215,U_1214) ),
inference(clausify,[status(thm)],[f_509_3]) ).
cnf(f_509_6,plain,
( power_power_nat(U_1214,U_1216) = power_power_nat(U_1214,U_1215)
| U_1216 != U_1215
| ~ sP58(U_1216,U_1215,U_1214) ),
inference(clausify,[status(thm)],[f_509_3]) ).
fof(f_510_1,plain,
! [Ma,N_1,A_1] :
( ( ( power_power_int(A_1,Ma) = power_power_int(A_1,N_1)
| Ma != N_1 )
& ( Ma = N_1
| power_power_int(A_1,Ma) != power_power_int(A_1,N_1) ) )
| ~ ord_less_int(one_one_int,A_1) ),
inference(fof_nnf,[status(thm)],[fact_491_power__inject__exp]) ).
fof(f_510_2,plain,
! [U_1219,U_1218,U_1217] :
( ( ( power_power_int(U_1217,U_1219) = power_power_int(U_1217,U_1218)
| U_1219 != U_1218 )
& ( U_1219 = U_1218
| power_power_int(U_1217,U_1219) != power_power_int(U_1217,U_1218) ) )
| ~ ord_less_int(one_one_int,U_1217) ),
inference(variable_rename,[status(thm)],[f_510_1]) ).
fof(f_510_3,plain,
( ! [U_1218,U_1219,U_1217] :
( power_power_int(U_1217,U_1219) = power_power_int(U_1217,U_1218)
| U_1219 != U_1218
| ~ sP59(U_1218,U_1219,U_1217) )
& ! [U_1218,U_1219,U_1217] :
( U_1219 = U_1218
| power_power_int(U_1217,U_1219) != power_power_int(U_1217,U_1218)
| ~ sP59(U_1218,U_1219,U_1217) )
& ! [U_1218,U_1219,U_1217] :
( sP59(U_1218,U_1219,U_1217)
| ~ ord_less_int(one_one_int,U_1217) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP59])],[f_510_2]) ).
cnf(f_510_4,plain,
( sP59(U_1218,U_1219,U_1217)
| ~ ord_less_int(one_one_int,U_1217) ),
inference(clausify,[status(thm)],[f_510_3]) ).
cnf(f_510_5,plain,
( U_1219 = U_1218
| power_power_int(U_1217,U_1219) != power_power_int(U_1217,U_1218)
| ~ sP59(U_1218,U_1219,U_1217) ),
inference(clausify,[status(thm)],[f_510_3]) ).
cnf(f_510_6,plain,
( power_power_int(U_1217,U_1219) = power_power_int(U_1217,U_1218)
| U_1219 != U_1218
| ~ sP59(U_1218,U_1219,U_1217) ),
inference(clausify,[status(thm)],[f_510_3]) ).
fof(f_511_1,plain,
! [X_2,Y_2,B_2] :
( ( ( ord_less_real(power_power_real(B_2,X_2),power_power_real(B_2,Y_2))
| ~ ord_less_nat(X_2,Y_2) )
& ( ord_less_nat(X_2,Y_2)
| ~ ord_less_real(power_power_real(B_2,X_2),power_power_real(B_2,Y_2)) ) )
| ~ ord_less_real(one_one_real,B_2) ),
inference(fof_nnf,[status(thm)],[fact_492_power__strict__increasing__iff]) ).
fof(f_511_2,plain,
! [U_1222,U_1221,U_1220] :
( ( ( ord_less_real(power_power_real(U_1220,U_1222),power_power_real(U_1220,U_1221))
| ~ ord_less_nat(U_1222,U_1221) )
& ( ord_less_nat(U_1222,U_1221)
| ~ ord_less_real(power_power_real(U_1220,U_1222),power_power_real(U_1220,U_1221)) ) )
| ~ ord_less_real(one_one_real,U_1220) ),
inference(variable_rename,[status(thm)],[f_511_1]) ).
fof(f_511_3,plain,
( ! [U_1221,U_1222,U_1220] :
( ord_less_real(power_power_real(U_1220,U_1222),power_power_real(U_1220,U_1221))
| ~ ord_less_nat(U_1222,U_1221)
| ~ sP60(U_1221,U_1222,U_1220) )
& ! [U_1221,U_1222,U_1220] :
( ord_less_nat(U_1222,U_1221)
| ~ ord_less_real(power_power_real(U_1220,U_1222),power_power_real(U_1220,U_1221))
| ~ sP60(U_1221,U_1222,U_1220) )
& ! [U_1221,U_1222,U_1220] :
( sP60(U_1221,U_1222,U_1220)
| ~ ord_less_real(one_one_real,U_1220) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP60])],[f_511_2]) ).
cnf(f_511_4,plain,
( sP60(U_1221,U_1222,U_1220)
| ~ ord_less_real(one_one_real,U_1220) ),
inference(clausify,[status(thm)],[f_511_3]) ).
cnf(f_511_5,plain,
( ord_less_nat(U_1222,U_1221)
| ~ ord_less_real(power_power_real(U_1220,U_1222),power_power_real(U_1220,U_1221))
| ~ sP60(U_1221,U_1222,U_1220) ),
inference(clausify,[status(thm)],[f_511_3]) ).
cnf(f_511_6,plain,
( ord_less_real(power_power_real(U_1220,U_1222),power_power_real(U_1220,U_1221))
| ~ ord_less_nat(U_1222,U_1221)
| ~ sP60(U_1221,U_1222,U_1220) ),
inference(clausify,[status(thm)],[f_511_3]) ).
fof(f_512_1,plain,
! [X_2,Y_2,B_2] :
( ( ( ord_less_nat(power_power_nat(B_2,X_2),power_power_nat(B_2,Y_2))
| ~ ord_less_nat(X_2,Y_2) )
& ( ord_less_nat(X_2,Y_2)
| ~ ord_less_nat(power_power_nat(B_2,X_2),power_power_nat(B_2,Y_2)) ) )
| ~ ord_less_nat(one_one_nat,B_2) ),
inference(fof_nnf,[status(thm)],[fact_493_power__strict__increasing__iff]) ).
fof(f_512_2,plain,
! [U_1225,U_1224,U_1223] :
( ( ( ord_less_nat(power_power_nat(U_1223,U_1225),power_power_nat(U_1223,U_1224))
| ~ ord_less_nat(U_1225,U_1224) )
& ( ord_less_nat(U_1225,U_1224)
| ~ ord_less_nat(power_power_nat(U_1223,U_1225),power_power_nat(U_1223,U_1224)) ) )
| ~ ord_less_nat(one_one_nat,U_1223) ),
inference(variable_rename,[status(thm)],[f_512_1]) ).
fof(f_512_3,plain,
( ! [U_1224,U_1225,U_1223] :
( ord_less_nat(power_power_nat(U_1223,U_1225),power_power_nat(U_1223,U_1224))
| ~ ord_less_nat(U_1225,U_1224)
| ~ sP61(U_1224,U_1225,U_1223) )
& ! [U_1224,U_1225,U_1223] :
( ord_less_nat(U_1225,U_1224)
| ~ ord_less_nat(power_power_nat(U_1223,U_1225),power_power_nat(U_1223,U_1224))
| ~ sP61(U_1224,U_1225,U_1223) )
& ! [U_1224,U_1225,U_1223] :
( sP61(U_1224,U_1225,U_1223)
| ~ ord_less_nat(one_one_nat,U_1223) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP61])],[f_512_2]) ).
cnf(f_512_4,plain,
( sP61(U_1224,U_1225,U_1223)
| ~ ord_less_nat(one_one_nat,U_1223) ),
inference(clausify,[status(thm)],[f_512_3]) ).
cnf(f_512_5,plain,
( ord_less_nat(U_1225,U_1224)
| ~ ord_less_nat(power_power_nat(U_1223,U_1225),power_power_nat(U_1223,U_1224))
| ~ sP61(U_1224,U_1225,U_1223) ),
inference(clausify,[status(thm)],[f_512_3]) ).
cnf(f_512_6,plain,
( ord_less_nat(power_power_nat(U_1223,U_1225),power_power_nat(U_1223,U_1224))
| ~ ord_less_nat(U_1225,U_1224)
| ~ sP61(U_1224,U_1225,U_1223) ),
inference(clausify,[status(thm)],[f_512_3]) ).
fof(f_513_1,plain,
! [X_2,Y_2,B_2] :
( ( ( ord_less_int(power_power_int(B_2,X_2),power_power_int(B_2,Y_2))
| ~ ord_less_nat(X_2,Y_2) )
& ( ord_less_nat(X_2,Y_2)
| ~ ord_less_int(power_power_int(B_2,X_2),power_power_int(B_2,Y_2)) ) )
| ~ ord_less_int(one_one_int,B_2) ),
inference(fof_nnf,[status(thm)],[fact_494_power__strict__increasing__iff]) ).
fof(f_513_2,plain,
! [U_1228,U_1227,U_1226] :
( ( ( ord_less_int(power_power_int(U_1226,U_1228),power_power_int(U_1226,U_1227))
| ~ ord_less_nat(U_1228,U_1227) )
& ( ord_less_nat(U_1228,U_1227)
| ~ ord_less_int(power_power_int(U_1226,U_1228),power_power_int(U_1226,U_1227)) ) )
| ~ ord_less_int(one_one_int,U_1226) ),
inference(variable_rename,[status(thm)],[f_513_1]) ).
fof(f_513_3,plain,
( ! [U_1227,U_1228,U_1226] :
( ord_less_int(power_power_int(U_1226,U_1228),power_power_int(U_1226,U_1227))
| ~ ord_less_nat(U_1228,U_1227)
| ~ sP62(U_1227,U_1228,U_1226) )
& ! [U_1227,U_1228,U_1226] :
( ord_less_nat(U_1228,U_1227)
| ~ ord_less_int(power_power_int(U_1226,U_1228),power_power_int(U_1226,U_1227))
| ~ sP62(U_1227,U_1228,U_1226) )
& ! [U_1227,U_1228,U_1226] :
( sP62(U_1227,U_1228,U_1226)
| ~ ord_less_int(one_one_int,U_1226) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP62])],[f_513_2]) ).
cnf(f_513_4,plain,
( sP62(U_1227,U_1228,U_1226)
| ~ ord_less_int(one_one_int,U_1226) ),
inference(clausify,[status(thm)],[f_513_3]) ).
cnf(f_513_5,plain,
( ord_less_nat(U_1228,U_1227)
| ~ ord_less_int(power_power_int(U_1226,U_1228),power_power_int(U_1226,U_1227))
| ~ sP62(U_1227,U_1228,U_1226) ),
inference(clausify,[status(thm)],[f_513_3]) ).
cnf(f_513_6,plain,
( ord_less_int(power_power_int(U_1226,U_1228),power_power_int(U_1226,U_1227))
| ~ ord_less_nat(U_1228,U_1227)
| ~ sP62(U_1227,U_1228,U_1226) ),
inference(clausify,[status(thm)],[f_513_3]) ).
fof(f_514_1,plain,
! [M_2,N_7,A_6] :
( ord_less_nat(M_2,N_7)
| ~ ord_less_real(power_power_real(A_6,M_2),power_power_real(A_6,N_7))
| ~ ord_less_real(one_one_real,A_6) ),
inference(fof_nnf,[status(thm)],[fact_495_power__less__imp__less__exp]) ).
fof(f_514_2,plain,
! [U_1231,U_1230,U_1229] :
( ord_less_nat(U_1231,U_1230)
| ~ ord_less_real(power_power_real(U_1229,U_1231),power_power_real(U_1229,U_1230))
| ~ ord_less_real(one_one_real,U_1229) ),
inference(variable_rename,[status(thm)],[f_514_1]) ).
fof(f_514_3,plain,
! [U_1230,U_1231,U_1229] :
( ord_less_nat(U_1231,U_1230)
| ~ ord_less_real(power_power_real(U_1229,U_1231),power_power_real(U_1229,U_1230))
| ~ ord_less_real(one_one_real,U_1229) ),
inference(definitional_conversion,[status(esa)],[f_514_2]) ).
cnf(f_514_4,plain,
( ord_less_nat(U_1231,U_1230)
| ~ ord_less_real(power_power_real(U_1229,U_1231),power_power_real(U_1229,U_1230))
| ~ ord_less_real(one_one_real,U_1229) ),
inference(clausify,[status(thm)],[f_514_3]) ).
fof(f_515_1,plain,
! [M_2,N_7,A_6] :
( ord_less_nat(M_2,N_7)
| ~ ord_less_nat(power_power_nat(A_6,M_2),power_power_nat(A_6,N_7))
| ~ ord_less_nat(one_one_nat,A_6) ),
inference(fof_nnf,[status(thm)],[fact_496_power__less__imp__less__exp]) ).
fof(f_515_2,plain,
! [U_1234,U_1233,U_1232] :
( ord_less_nat(U_1234,U_1233)
| ~ ord_less_nat(power_power_nat(U_1232,U_1234),power_power_nat(U_1232,U_1233))
| ~ ord_less_nat(one_one_nat,U_1232) ),
inference(variable_rename,[status(thm)],[f_515_1]) ).
fof(f_515_3,plain,
! [U_1234,U_1232,U_1233] :
( ord_less_nat(U_1234,U_1233)
| ~ ord_less_nat(power_power_nat(U_1232,U_1234),power_power_nat(U_1232,U_1233))
| ~ ord_less_nat(one_one_nat,U_1232) ),
inference(definitional_conversion,[status(esa)],[f_515_2]) ).
cnf(f_515_4,plain,
( ord_less_nat(U_1234,U_1233)
| ~ ord_less_nat(power_power_nat(U_1232,U_1234),power_power_nat(U_1232,U_1233))
| ~ ord_less_nat(one_one_nat,U_1232) ),
inference(clausify,[status(thm)],[f_515_3]) ).
fof(f_516_1,plain,
! [M_2,N_7,A_6] :
( ord_less_nat(M_2,N_7)
| ~ ord_less_int(power_power_int(A_6,M_2),power_power_int(A_6,N_7))
| ~ ord_less_int(one_one_int,A_6) ),
inference(fof_nnf,[status(thm)],[fact_497_power__less__imp__less__exp]) ).
fof(f_516_2,plain,
! [U_1237,U_1236,U_1235] :
( ord_less_nat(U_1237,U_1236)
| ~ ord_less_int(power_power_int(U_1235,U_1237),power_power_int(U_1235,U_1236))
| ~ ord_less_int(one_one_int,U_1235) ),
inference(variable_rename,[status(thm)],[f_516_1]) ).
fof(f_516_3,plain,
! [U_1235,U_1236,U_1237] :
( ord_less_nat(U_1237,U_1236)
| ~ ord_less_int(power_power_int(U_1235,U_1237),power_power_int(U_1235,U_1236))
| ~ ord_less_int(one_one_int,U_1235) ),
inference(definitional_conversion,[status(esa)],[f_516_2]) ).
cnf(f_516_4,plain,
( ord_less_nat(U_1237,U_1236)
| ~ ord_less_int(power_power_int(U_1235,U_1237),power_power_int(U_1235,U_1236))
| ~ ord_less_int(one_one_int,U_1235) ),
inference(clausify,[status(thm)],[f_516_3]) ).
fof(f_517_1,plain,
! [A_5,N_6,N_5] :
( ord_less_real(power_power_real(A_5,N_6),power_power_real(A_5,N_5))
| ~ ord_less_real(one_one_real,A_5)
| ~ ord_less_nat(N_6,N_5) ),
inference(fof_nnf,[status(thm)],[fact_498_power__strict__increasing]) ).
fof(f_517_2,plain,
! [U_1240,U_1239,U_1238] :
( ord_less_real(power_power_real(U_1240,U_1239),power_power_real(U_1240,U_1238))
| ~ ord_less_real(one_one_real,U_1240)
| ~ ord_less_nat(U_1239,U_1238) ),
inference(variable_rename,[status(thm)],[f_517_1]) ).
fof(f_517_3,plain,
! [U_1239,U_1238,U_1240] :
( ord_less_real(power_power_real(U_1240,U_1239),power_power_real(U_1240,U_1238))
| ~ ord_less_real(one_one_real,U_1240)
| ~ ord_less_nat(U_1239,U_1238) ),
inference(definitional_conversion,[status(esa)],[f_517_2]) ).
cnf(f_517_4,plain,
( ord_less_real(power_power_real(U_1240,U_1239),power_power_real(U_1240,U_1238))
| ~ ord_less_real(one_one_real,U_1240)
| ~ ord_less_nat(U_1239,U_1238) ),
inference(clausify,[status(thm)],[f_517_3]) ).
fof(f_518_1,plain,
! [A_5,N_6,N_5] :
( ord_less_nat(power_power_nat(A_5,N_6),power_power_nat(A_5,N_5))
| ~ ord_less_nat(one_one_nat,A_5)
| ~ ord_less_nat(N_6,N_5) ),
inference(fof_nnf,[status(thm)],[fact_499_power__strict__increasing]) ).
fof(f_518_2,plain,
! [U_1243,U_1242,U_1241] :
( ord_less_nat(power_power_nat(U_1243,U_1242),power_power_nat(U_1243,U_1241))
| ~ ord_less_nat(one_one_nat,U_1243)
| ~ ord_less_nat(U_1242,U_1241) ),
inference(variable_rename,[status(thm)],[f_518_1]) ).
fof(f_518_3,plain,
! [U_1242,U_1241,U_1243] :
( ord_less_nat(power_power_nat(U_1243,U_1242),power_power_nat(U_1243,U_1241))
| ~ ord_less_nat(one_one_nat,U_1243)
| ~ ord_less_nat(U_1242,U_1241) ),
inference(definitional_conversion,[status(esa)],[f_518_2]) ).
cnf(f_518_4,plain,
( ord_less_nat(power_power_nat(U_1243,U_1242),power_power_nat(U_1243,U_1241))
| ~ ord_less_nat(one_one_nat,U_1243)
| ~ ord_less_nat(U_1242,U_1241) ),
inference(clausify,[status(thm)],[f_518_3]) ).
fof(f_519_1,plain,
! [A_5,N_6,N_5] :
( ord_less_int(power_power_int(A_5,N_6),power_power_int(A_5,N_5))
| ~ ord_less_int(one_one_int,A_5)
| ~ ord_less_nat(N_6,N_5) ),
inference(fof_nnf,[status(thm)],[fact_500_power__strict__increasing]) ).
fof(f_519_2,plain,
! [U_1246,U_1245,U_1244] :
( ord_less_int(power_power_int(U_1246,U_1245),power_power_int(U_1246,U_1244))
| ~ ord_less_int(one_one_int,U_1246)
| ~ ord_less_nat(U_1245,U_1244) ),
inference(variable_rename,[status(thm)],[f_519_1]) ).
fof(f_519_3,plain,
! [U_1245,U_1244,U_1246] :
( ord_less_int(power_power_int(U_1246,U_1245),power_power_int(U_1246,U_1244))
| ~ ord_less_int(one_one_int,U_1246)
| ~ ord_less_nat(U_1245,U_1244) ),
inference(definitional_conversion,[status(esa)],[f_519_2]) ).
cnf(f_519_4,plain,
( ord_less_int(power_power_int(U_1246,U_1245),power_power_int(U_1246,U_1244))
| ~ ord_less_int(one_one_int,U_1246)
| ~ ord_less_nat(U_1245,U_1244) ),
inference(clausify,[status(thm)],[f_519_3]) ).
fof(f_520_1,plain,
zcong(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(fof_nnf,[status(thm)],[fact_501_s]) ).
fof(f_520_2,plain,
zcong(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(definitional_conversion,[status(esa)],[f_520_1]) ).
cnf(f_520_3,plain,
zcong(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(clausify,[status(thm)],[f_520_2]) ).
fof(f_521_1,plain,
! [Y_1,X_1,P] :
( ~ dvd_dvd_int(P,Y_1)
| ~ zcong(power_power_int(Y_1,number_number_of_nat(bit0(bit1(pls)))),X_1,P)
| zcong(X_1,zero_zero_int,P) ),
inference(fof_nnf,[status(thm)],[fact_502_Euler_Oaux____1]) ).
fof(f_521_2,plain,
! [U_1249,U_1248,U_1247] :
( ~ dvd_dvd_int(U_1247,U_1249)
| ~ zcong(power_power_int(U_1249,number_number_of_nat(bit0(bit1(pls)))),U_1248,U_1247)
| zcong(U_1248,zero_zero_int,U_1247) ),
inference(variable_rename,[status(thm)],[f_521_1]) ).
fof(f_521_3,plain,
! [U_1249,U_1247,U_1248] :
( ~ dvd_dvd_int(U_1247,U_1249)
| ~ zcong(power_power_int(U_1249,number_number_of_nat(bit0(bit1(pls)))),U_1248,U_1247)
| zcong(U_1248,zero_zero_int,U_1247) ),
inference(definitional_conversion,[status(esa)],[f_521_2]) ).
cnf(f_521_4,plain,
( ~ dvd_dvd_int(U_1247,U_1249)
| ~ zcong(power_power_int(U_1249,number_number_of_nat(bit0(bit1(pls)))),U_1248,U_1247)
| zcong(U_1248,zero_zero_int,U_1247) ),
inference(clausify,[status(thm)],[f_521_3]) ).
fof(f_522_1,plain,
! [X_1] :
( X_1 = one_one_int
| X_1 = zero_zero_int
| ~ ord_less_int(X_1,number_number_of_int(bit0(bit1(pls))))
| ~ ord_less_eq_int(zero_zero_int,X_1)
| ~ is_int(X_1) ),
inference(fof_nnf,[status(thm)],[fact_503_int__pos__lt__two__imp__zero__or__one]) ).
fof(f_522_2,plain,
! [U_1250] :
( U_1250 = one_one_int
| U_1250 = zero_zero_int
| ~ ord_less_int(U_1250,number_number_of_int(bit0(bit1(pls))))
| ~ ord_less_eq_int(zero_zero_int,U_1250)
| ~ is_int(U_1250) ),
inference(variable_rename,[status(thm)],[f_522_1]) ).
fof(f_522_3,plain,
! [U_1250] :
( U_1250 = one_one_int
| U_1250 = zero_zero_int
| ~ ord_less_int(U_1250,number_number_of_int(bit0(bit1(pls))))
| ~ ord_less_eq_int(zero_zero_int,U_1250)
| ~ is_int(U_1250) ),
inference(definitional_conversion,[status(esa)],[f_522_2]) ).
cnf(f_522_4,plain,
( U_1250 = one_one_int
| U_1250 = zero_zero_int
| ~ ord_less_int(U_1250,number_number_of_int(bit0(bit1(pls))))
| ~ ord_less_eq_int(zero_zero_int,U_1250)
| ~ is_int(U_1250) ),
inference(clausify,[status(thm)],[f_522_3]) ).
fof(f_523_1,plain,
! [A_4,K_3] :
( A_4 = zero_zero_real
| ~ ord_less_eq_real(power_power_real(A_4,times_times_nat(number_number_of_nat(bit0(bit1(pls))),K_3)),zero_zero_real) ),
inference(fof_nnf,[status(thm)],[fact_504_even__power__le__0__imp__0]) ).
fof(f_523_2,plain,
! [U_1252,U_1251] :
( U_1252 = zero_zero_real
| ~ ord_less_eq_real(power_power_real(U_1252,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1251)),zero_zero_real) ),
inference(variable_rename,[status(thm)],[f_523_1]) ).
fof(f_523_3,plain,
! [U_1252] :
( ! [U_1251] : ~ ord_less_eq_real(power_power_real(U_1252,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1251)),zero_zero_real)
| U_1252 = zero_zero_real ),
inference(miniscope,[status(thm)],[f_523_2]) ).
fof(f_523_4,plain,
! [U_1252,U_1251] :
( ~ ord_less_eq_real(power_power_real(U_1252,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1251)),zero_zero_real)
| U_1252 = zero_zero_real ),
inference(definitional_conversion,[status(esa)],[f_523_3]) ).
cnf(f_523_5,plain,
( ~ ord_less_eq_real(power_power_real(U_1252,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1251)),zero_zero_real)
| U_1252 = zero_zero_real ),
inference(clausify,[status(thm)],[f_523_4]) ).
fof(f_524_1,plain,
! [A_4,K_3] :
( A_4 = zero_zero_int
| ~ ord_less_eq_int(power_power_int(A_4,times_times_nat(number_number_of_nat(bit0(bit1(pls))),K_3)),zero_zero_int)
| ~ is_int(A_4) ),
inference(fof_nnf,[status(thm)],[fact_505_even__power__le__0__imp__0]) ).
fof(f_524_2,plain,
! [U_1254,U_1253] :
( U_1254 = zero_zero_int
| ~ ord_less_eq_int(power_power_int(U_1254,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1253)),zero_zero_int)
| ~ is_int(U_1254) ),
inference(variable_rename,[status(thm)],[f_524_1]) ).
fof(f_524_3,plain,
! [U_1254] :
( ! [U_1253] : ~ ord_less_eq_int(power_power_int(U_1254,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1253)),zero_zero_int)
| U_1254 = zero_zero_int
| ~ is_int(U_1254) ),
inference(miniscope,[status(thm)],[f_524_2]) ).
fof(f_524_4,plain,
! [U_1254,U_1253] :
( ~ ord_less_eq_int(power_power_int(U_1254,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1253)),zero_zero_int)
| U_1254 = zero_zero_int
| ~ is_int(U_1254) ),
inference(definitional_conversion,[status(esa)],[f_524_3]) ).
cnf(f_524_5,plain,
( ~ ord_less_eq_int(power_power_int(U_1254,times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1253)),zero_zero_int)
| U_1254 = zero_zero_int
| ~ is_int(U_1254) ),
inference(clausify,[status(thm)],[f_524_4]) ).
fof(f_525_1,plain,
! [P_1] :
( ( ( zprime(P_1)
| ? [M_1] :
( M_1 != P_1
& M_1 != one_one_int
& dvd_dvd_int(M_1,P_1)
& ord_less_eq_int(zero_zero_int,M_1)
& is_int(M_1) )
| ~ ord_less_int(one_one_int,P_1) )
& ( ( ! [M_1] :
( M_1 = P_1
| M_1 = one_one_int
| ~ dvd_dvd_int(M_1,P_1)
| ~ ord_less_eq_int(zero_zero_int,M_1)
| ~ is_int(M_1) )
& ord_less_int(one_one_int,P_1) )
| ~ zprime(P_1) ) )
| ~ is_int(P_1) ),
inference(fof_nnf,[status(thm)],[fact_506_zprime__def]) ).
fof(f_525_2,plain,
! [U_1257] :
( ( ( zprime(U_1257)
| ? [U_1256] :
( U_1256 != U_1257
& U_1256 != one_one_int
& dvd_dvd_int(U_1256,U_1257)
& ord_less_eq_int(zero_zero_int,U_1256)
& is_int(U_1256) )
| ~ ord_less_int(one_one_int,U_1257) )
& ( ( ! [U_1255] :
( U_1255 = U_1257
| U_1255 = one_one_int
| ~ dvd_dvd_int(U_1255,U_1257)
| ~ ord_less_eq_int(zero_zero_int,U_1255)
| ~ is_int(U_1255) )
& ord_less_int(one_one_int,U_1257) )
| ~ zprime(U_1257) ) )
| ~ is_int(U_1257) ),
inference(variable_rename,[status(thm)],[f_525_1]) ).
fof(f_525_3,plain,
! [U_1257] :
( ( ( zprime(U_1257)
| ( sK8(U_1257) != U_1257
& sK8(U_1257) != one_one_int
& dvd_dvd_int(sK8(U_1257),U_1257)
& ord_less_eq_int(zero_zero_int,sK8(U_1257))
& is_int(sK8(U_1257)) )
| ~ ord_less_int(one_one_int,U_1257) )
& ( ( ! [U_1255] :
( U_1255 = U_1257
| U_1255 = one_one_int
| ~ dvd_dvd_int(U_1255,U_1257)
| ~ ord_less_eq_int(zero_zero_int,U_1255)
| ~ is_int(U_1255) )
& ord_less_int(one_one_int,U_1257) )
| ~ zprime(U_1257) ) )
| ~ is_int(U_1257) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_1256,sK8(U_1257))],[f_525_2]) ).
fof(f_525_4,plain,
( ! [U_1257] :
( sK8(U_1257) != U_1257
| ~ sP64(U_1257) )
& ! [U_1257] :
( sK8(U_1257) != one_one_int
| ~ sP64(U_1257) )
& ! [U_1257] :
( dvd_dvd_int(sK8(U_1257),U_1257)
| ~ sP64(U_1257) )
& ! [U_1257] :
( ord_less_eq_int(zero_zero_int,sK8(U_1257))
| ~ sP64(U_1257) )
& ! [U_1257] :
( is_int(sK8(U_1257))
| ~ sP64(U_1257) )
& ! [U_1255,U_1257] :
( U_1255 = U_1257
| U_1255 = one_one_int
| ~ dvd_dvd_int(U_1255,U_1257)
| ~ ord_less_eq_int(zero_zero_int,U_1255)
| ~ is_int(U_1255)
| ~ sP63(U_1255,U_1257) )
& ! [U_1255,U_1257] :
( ord_less_int(one_one_int,U_1257)
| ~ sP63(U_1255,U_1257) )
& ! [U_1255,U_1257] :
( zprime(U_1257)
| sP64(U_1257)
| ~ ord_less_int(one_one_int,U_1257)
| ~ sP65(U_1255,U_1257) )
& ! [U_1255,U_1257] :
( sP63(U_1255,U_1257)
| ~ zprime(U_1257)
| ~ sP65(U_1255,U_1257) )
& ! [U_1255,U_1257] :
( sP65(U_1255,U_1257)
| ~ is_int(U_1257) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP63,sP64,sP65])],[f_525_3]) ).
cnf(f_525_5,plain,
( sP65(U_1255,U_1257)
| ~ is_int(U_1257) ),
inference(clausify,[status(thm)],[f_525_4]) ).
cnf(f_525_6,plain,
( sP63(U_1255,U_1257)
| ~ zprime(U_1257)
| ~ sP65(U_1255,U_1257) ),
inference(clausify,[status(thm)],[f_525_4]) ).
cnf(f_525_7,plain,
( zprime(U_1257)
| sP64(U_1257)
| ~ ord_less_int(one_one_int,U_1257)
| ~ sP65(U_1255,U_1257) ),
inference(clausify,[status(thm)],[f_525_4]) ).
cnf(f_525_8,plain,
( ord_less_int(one_one_int,U_1257)
| ~ sP63(U_1255,U_1257) ),
inference(clausify,[status(thm)],[f_525_4]) ).
cnf(f_525_9,plain,
( U_1255 = U_1257
| U_1255 = one_one_int
| ~ dvd_dvd_int(U_1255,U_1257)
| ~ ord_less_eq_int(zero_zero_int,U_1255)
| ~ is_int(U_1255)
| ~ sP63(U_1255,U_1257) ),
inference(clausify,[status(thm)],[f_525_4]) ).
cnf(f_525_10,plain,
( is_int(sK8(U_1257))
| ~ sP64(U_1257) ),
inference(clausify,[status(thm)],[f_525_4]) ).
cnf(f_525_11,plain,
( ord_less_eq_int(zero_zero_int,sK8(U_1257))
| ~ sP64(U_1257) ),
inference(clausify,[status(thm)],[f_525_4]) ).
cnf(f_525_12,plain,
( dvd_dvd_int(sK8(U_1257),U_1257)
| ~ sP64(U_1257) ),
inference(clausify,[status(thm)],[f_525_4]) ).
cnf(f_525_13,plain,
( sK8(U_1257) != one_one_int
| ~ sP64(U_1257) ),
inference(clausify,[status(thm)],[f_525_4]) ).
cnf(f_525_14,plain,
( sK8(U_1257) != U_1257
| ~ sP64(U_1257) ),
inference(clausify,[status(thm)],[f_525_4]) ).
fof(f_526_1,plain,
? [S1] :
( zcong(power_power_int(S1,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min),plus_plus_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_507__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_]) ).
fof(f_526_2,plain,
? [U_1258] :
( zcong(power_power_int(U_1258,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& is_int(U_1258) ),
inference(variable_rename,[status(thm)],[f_526_1]) ).
fof(f_526_3,plain,
( zcong(power_power_int(sK9,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min),plus_plus_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_1258,sK9)],[f_526_2]) ).
fof(f_526_4,plain,
( zcong(power_power_int(sK9,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
& is_int(sK9) ),
inference(definitional_conversion,[status(esa)],[f_526_3]) ).
cnf(f_526_5,plain,
is_int(sK9),
inference(clausify,[status(thm)],[f_526_4]) ).
cnf(f_526_6,plain,
zcong(power_power_int(sK9,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(clausify,[status(thm)],[f_526_4]) ).
fof(f_527_1,plain,
legendre(number_number_of_int(min),plus_plus_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_508__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096]) ).
fof(f_527_2,plain,
legendre(number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = one_one_int,
inference(definitional_conversion,[status(esa)],[f_527_1]) ).
cnf(f_527_3,plain,
legendre(number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = one_one_int,
inference(clausify,[status(thm)],[f_527_2]) ).
fof(f_528_1,plain,
! [X_2,N_1] :
( ( ord_less_nat(zero_zero_nat,power_power_nat(X_2,N_1))
| ( N_1 != zero_zero_nat
& ~ ord_less_nat(zero_zero_nat,X_2) ) )
& ( N_1 = zero_zero_nat
| ord_less_nat(zero_zero_nat,X_2)
| ~ ord_less_nat(zero_zero_nat,power_power_nat(X_2,N_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_509_nat__zero__less__power__iff]) ).
fof(f_528_2,plain,
! [U_1260,U_1259] :
( ( ord_less_nat(zero_zero_nat,power_power_nat(U_1260,U_1259))
| ( U_1259 != zero_zero_nat
& ~ ord_less_nat(zero_zero_nat,U_1260) ) )
& ( U_1259 = zero_zero_nat
| ord_less_nat(zero_zero_nat,U_1260)
| ~ ord_less_nat(zero_zero_nat,power_power_nat(U_1260,U_1259)) ) ),
inference(variable_rename,[status(thm)],[f_528_1]) ).
fof(f_528_3,plain,
( ! [U_1264,U_1262] :
( ord_less_nat(zero_zero_nat,power_power_nat(U_1264,U_1262))
| ( U_1262 != zero_zero_nat
& ~ ord_less_nat(zero_zero_nat,U_1264) ) )
& ! [U_1263,U_1261] :
( U_1261 = zero_zero_nat
| ord_less_nat(zero_zero_nat,U_1263)
| ~ ord_less_nat(zero_zero_nat,power_power_nat(U_1263,U_1261)) ) ),
inference(miniscope,[status(thm)],[f_528_2]) ).
fof(f_528_4,plain,
( ! [U_1264,U_1262] :
( U_1262 != zero_zero_nat
| ~ sP66(U_1264,U_1262) )
& ! [U_1264,U_1262] :
( ~ ord_less_nat(zero_zero_nat,U_1264)
| ~ sP66(U_1264,U_1262) )
& ! [U_1264,U_1262] :
( ord_less_nat(zero_zero_nat,power_power_nat(U_1264,U_1262))
| sP66(U_1264,U_1262) )
& ! [U_1261,U_1263] :
( U_1261 = zero_zero_nat
| ord_less_nat(zero_zero_nat,U_1263)
| ~ ord_less_nat(zero_zero_nat,power_power_nat(U_1263,U_1261)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP66])],[f_528_3]) ).
cnf(f_528_5,plain,
( U_1261 = zero_zero_nat
| ord_less_nat(zero_zero_nat,U_1263)
| ~ ord_less_nat(zero_zero_nat,power_power_nat(U_1263,U_1261)) ),
inference(clausify,[status(thm)],[f_528_4]) ).
cnf(f_528_6,plain,
( ord_less_nat(zero_zero_nat,power_power_nat(U_1264,U_1262))
| sP66(U_1264,U_1262) ),
inference(clausify,[status(thm)],[f_528_4]) ).
cnf(f_528_7,plain,
( ~ ord_less_nat(zero_zero_nat,U_1264)
| ~ sP66(U_1264,U_1262) ),
inference(clausify,[status(thm)],[f_528_4]) ).
cnf(f_528_8,plain,
( U_1262 != zero_zero_nat
| ~ sP66(U_1264,U_1262) ),
inference(clausify,[status(thm)],[f_528_4]) ).
fof(f_529_1,plain,
! [X_2,N_1] :
( ( ord_less_nat(zero_zero_nat,power_power_nat(X_2,N_1))
| ( ~ ord_less_nat(zero_zero_nat,X_2)
& N_1 != zero_zero_nat ) )
& ( ord_less_nat(zero_zero_nat,X_2)
| N_1 = zero_zero_nat
| ~ ord_less_nat(zero_zero_nat,power_power_nat(X_2,N_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_510_zero__less__power__nat__eq]) ).
fof(f_529_2,plain,
! [U_1266,U_1265] :
( ( ord_less_nat(zero_zero_nat,power_power_nat(U_1266,U_1265))
| ( ~ ord_less_nat(zero_zero_nat,U_1266)
& U_1265 != zero_zero_nat ) )
& ( ord_less_nat(zero_zero_nat,U_1266)
| U_1265 = zero_zero_nat
| ~ ord_less_nat(zero_zero_nat,power_power_nat(U_1266,U_1265)) ) ),
inference(variable_rename,[status(thm)],[f_529_1]) ).
fof(f_529_3,plain,
( ! [U_1270,U_1268] :
( ord_less_nat(zero_zero_nat,power_power_nat(U_1270,U_1268))
| ( ~ ord_less_nat(zero_zero_nat,U_1270)
& U_1268 != zero_zero_nat ) )
& ! [U_1269,U_1267] :
( ord_less_nat(zero_zero_nat,U_1269)
| U_1267 = zero_zero_nat
| ~ ord_less_nat(zero_zero_nat,power_power_nat(U_1269,U_1267)) ) ),
inference(miniscope,[status(thm)],[f_529_2]) ).
fof(f_529_4,plain,
( ! [U_1268,U_1270] :
( ~ ord_less_nat(zero_zero_nat,U_1270)
| ~ sP67(U_1268,U_1270) )
& ! [U_1268,U_1270] :
( U_1268 != zero_zero_nat
| ~ sP67(U_1268,U_1270) )
& ! [U_1268,U_1270] :
( ord_less_nat(zero_zero_nat,power_power_nat(U_1270,U_1268))
| sP67(U_1268,U_1270) )
& ! [U_1269,U_1267] :
( ord_less_nat(zero_zero_nat,U_1269)
| U_1267 = zero_zero_nat
| ~ ord_less_nat(zero_zero_nat,power_power_nat(U_1269,U_1267)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP67])],[f_529_3]) ).
cnf(f_529_5,plain,
( ord_less_nat(zero_zero_nat,U_1269)
| U_1267 = zero_zero_nat
| ~ ord_less_nat(zero_zero_nat,power_power_nat(U_1269,U_1267)) ),
inference(clausify,[status(thm)],[f_529_4]) ).
cnf(f_529_6,plain,
( ord_less_nat(zero_zero_nat,power_power_nat(U_1270,U_1268))
| sP67(U_1268,U_1270) ),
inference(clausify,[status(thm)],[f_529_4]) ).
cnf(f_529_7,plain,
( U_1268 != zero_zero_nat
| ~ sP67(U_1268,U_1270) ),
inference(clausify,[status(thm)],[f_529_4]) ).
cnf(f_529_8,plain,
( ~ ord_less_nat(zero_zero_nat,U_1270)
| ~ sP67(U_1268,U_1270) ),
inference(clausify,[status(thm)],[f_529_4]) ).
fof(f_530_1,plain,
! [X_2,W_1] :
( ( ord_less_nat(zero_zero_nat,power_power_nat(X_2,number_number_of_nat(W_1)))
| ( ~ ord_less_nat(zero_zero_nat,X_2)
& number_number_of_nat(W_1) != zero_zero_nat ) )
& ( ord_less_nat(zero_zero_nat,X_2)
| number_number_of_nat(W_1) = zero_zero_nat
| ~ ord_less_nat(zero_zero_nat,power_power_nat(X_2,number_number_of_nat(W_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_511_zero__less__power__nat__eq__number__of]) ).
fof(f_530_2,plain,
! [U_1272,U_1271] :
( ( ord_less_nat(zero_zero_nat,power_power_nat(U_1272,number_number_of_nat(U_1271)))
| ( ~ ord_less_nat(zero_zero_nat,U_1272)
& number_number_of_nat(U_1271) != zero_zero_nat ) )
& ( ord_less_nat(zero_zero_nat,U_1272)
| number_number_of_nat(U_1271) = zero_zero_nat
| ~ ord_less_nat(zero_zero_nat,power_power_nat(U_1272,number_number_of_nat(U_1271))) ) ),
inference(variable_rename,[status(thm)],[f_530_1]) ).
fof(f_530_3,plain,
( ! [U_1276,U_1274] :
( ord_less_nat(zero_zero_nat,power_power_nat(U_1276,number_number_of_nat(U_1274)))
| ( ~ ord_less_nat(zero_zero_nat,U_1276)
& number_number_of_nat(U_1274) != zero_zero_nat ) )
& ! [U_1275,U_1273] :
( ord_less_nat(zero_zero_nat,U_1275)
| number_number_of_nat(U_1273) = zero_zero_nat
| ~ ord_less_nat(zero_zero_nat,power_power_nat(U_1275,number_number_of_nat(U_1273))) ) ),
inference(miniscope,[status(thm)],[f_530_2]) ).
fof(f_530_4,plain,
( ! [U_1276,U_1274] :
( ~ ord_less_nat(zero_zero_nat,U_1276)
| ~ sP68(U_1276,U_1274) )
& ! [U_1276,U_1274] :
( number_number_of_nat(U_1274) != zero_zero_nat
| ~ sP68(U_1276,U_1274) )
& ! [U_1276,U_1274] :
( ord_less_nat(zero_zero_nat,power_power_nat(U_1276,number_number_of_nat(U_1274)))
| sP68(U_1276,U_1274) )
& ! [U_1275,U_1273] :
( ord_less_nat(zero_zero_nat,U_1275)
| number_number_of_nat(U_1273) = zero_zero_nat
| ~ ord_less_nat(zero_zero_nat,power_power_nat(U_1275,number_number_of_nat(U_1273))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP68])],[f_530_3]) ).
cnf(f_530_5,plain,
( ord_less_nat(zero_zero_nat,U_1275)
| number_number_of_nat(U_1273) = zero_zero_nat
| ~ ord_less_nat(zero_zero_nat,power_power_nat(U_1275,number_number_of_nat(U_1273))) ),
inference(clausify,[status(thm)],[f_530_4]) ).
cnf(f_530_6,plain,
( ord_less_nat(zero_zero_nat,power_power_nat(U_1276,number_number_of_nat(U_1274)))
| sP68(U_1276,U_1274) ),
inference(clausify,[status(thm)],[f_530_4]) ).
cnf(f_530_7,plain,
( number_number_of_nat(U_1274) != zero_zero_nat
| ~ sP68(U_1276,U_1274) ),
inference(clausify,[status(thm)],[f_530_4]) ).
cnf(f_530_8,plain,
( ~ ord_less_nat(zero_zero_nat,U_1276)
| ~ sP68(U_1276,U_1274) ),
inference(clausify,[status(thm)],[f_530_4]) ).
fof(f_531_1,plain,
! [M,N,I] :
( ord_less_nat(M,N)
| ~ ord_less_nat(power_power_nat(I,M),power_power_nat(I,N))
| ~ ord_less_nat(zero_zero_nat,I) ),
inference(fof_nnf,[status(thm)],[fact_512_nat__power__less__imp__less]) ).
fof(f_531_2,plain,
! [U_1279,U_1278,U_1277] :
( ord_less_nat(U_1279,U_1278)
| ~ ord_less_nat(power_power_nat(U_1277,U_1279),power_power_nat(U_1277,U_1278))
| ~ ord_less_nat(zero_zero_nat,U_1277) ),
inference(variable_rename,[status(thm)],[f_531_1]) ).
fof(f_531_3,plain,
! [U_1277,U_1279,U_1278] :
( ord_less_nat(U_1279,U_1278)
| ~ ord_less_nat(power_power_nat(U_1277,U_1279),power_power_nat(U_1277,U_1278))
| ~ ord_less_nat(zero_zero_nat,U_1277) ),
inference(definitional_conversion,[status(esa)],[f_531_2]) ).
cnf(f_531_4,plain,
( ord_less_nat(U_1279,U_1278)
| ~ ord_less_nat(power_power_nat(U_1277,U_1279),power_power_nat(U_1277,U_1278))
| ~ ord_less_nat(zero_zero_nat,U_1277) ),
inference(clausify,[status(thm)],[f_531_3]) ).
fof(f_532_1,plain,
! [K_1] :
( ( ( bit1(K_1) = min
| K_1 != min )
& ( K_1 = min
| bit1(K_1) != min ) )
| ~ is_int(K_1) ),
inference(fof_nnf,[status(thm)],[fact_513_rel__simps_I47_J]) ).
fof(f_532_2,plain,
! [U_1280] :
( ( ( bit1(U_1280) = min
| U_1280 != min )
& ( U_1280 = min
| bit1(U_1280) != min ) )
| ~ is_int(U_1280) ),
inference(variable_rename,[status(thm)],[f_532_1]) ).
fof(f_532_3,plain,
( ! [U_1280] :
( bit1(U_1280) = min
| U_1280 != min
| ~ sP69(U_1280) )
& ! [U_1280] :
( U_1280 = min
| bit1(U_1280) != min
| ~ sP69(U_1280) )
& ! [U_1280] :
( sP69(U_1280)
| ~ is_int(U_1280) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP69])],[f_532_2]) ).
cnf(f_532_4,plain,
( sP69(U_1280)
| ~ is_int(U_1280) ),
inference(clausify,[status(thm)],[f_532_3]) ).
cnf(f_532_5,plain,
( U_1280 = min
| bit1(U_1280) != min
| ~ sP69(U_1280) ),
inference(clausify,[status(thm)],[f_532_3]) ).
cnf(f_532_6,plain,
( bit1(U_1280) = min
| U_1280 != min
| ~ sP69(U_1280) ),
inference(clausify,[status(thm)],[f_532_3]) ).
fof(f_533_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_514_rel__simps_I43_J]) ).
fof(f_533_2,plain,
! [U_1281] :
( ( ( min = bit1(U_1281)
| min != U_1281 )
& ( min = U_1281
| min != bit1(U_1281) ) )
| ~ is_int(U_1281) ),
inference(variable_rename,[status(thm)],[f_533_1]) ).
fof(f_533_3,plain,
( ! [U_1281] :
( min = bit1(U_1281)
| min != U_1281
| ~ sP70(U_1281) )
& ! [U_1281] :
( min = U_1281
| min != bit1(U_1281)
| ~ sP70(U_1281) )
& ! [U_1281] :
( sP70(U_1281)
| ~ is_int(U_1281) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP70])],[f_533_2]) ).
cnf(f_533_4,plain,
( sP70(U_1281)
| ~ is_int(U_1281) ),
inference(clausify,[status(thm)],[f_533_3]) ).
cnf(f_533_5,plain,
( min = U_1281
| min != bit1(U_1281)
| ~ sP70(U_1281) ),
inference(clausify,[status(thm)],[f_533_3]) ).
cnf(f_533_6,plain,
( min = bit1(U_1281)
| min != U_1281
| ~ sP70(U_1281) ),
inference(clausify,[status(thm)],[f_533_3]) ).
fof(f_534_1,plain,
bit1(min) = min,
inference(fof_nnf,[status(thm)],[fact_515_Bit1__Min]) ).
fof(f_534_2,plain,
bit1(min) = min,
inference(definitional_conversion,[status(esa)],[f_534_1]) ).
cnf(f_534_3,plain,
bit1(min) = min,
inference(clausify,[status(thm)],[f_534_2]) ).
fof(f_535_1,plain,
pls != min,
inference(fof_nnf,[status(thm)],[fact_516_rel__simps_I37_J]) ).
fof(f_535_2,plain,
pls != min,
inference(definitional_conversion,[status(esa)],[f_535_1]) ).
cnf(f_535_3,plain,
pls != min,
inference(clausify,[status(thm)],[f_535_2]) ).
fof(f_536_1,plain,
min != pls,
inference(fof_nnf,[status(thm)],[fact_517_rel__simps_I40_J]) ).
fof(f_536_2,plain,
min != pls,
inference(definitional_conversion,[status(esa)],[f_536_1]) ).
cnf(f_536_3,plain,
min != pls,
inference(clausify,[status(thm)],[f_536_2]) ).
fof(f_537_1,plain,
! [K] : bit0(K) != min,
inference(fof_nnf,[status(thm)],[fact_518_rel__simps_I45_J]) ).
fof(f_537_2,plain,
! [U_1282] : bit0(U_1282) != min,
inference(variable_rename,[status(thm)],[f_537_1]) ).
fof(f_537_3,plain,
! [U_1282] : bit0(U_1282) != min,
inference(definitional_conversion,[status(esa)],[f_537_2]) ).
cnf(f_537_4,plain,
bit0(U_1282) != min,
inference(clausify,[status(thm)],[f_537_3]) ).
fof(f_538_1,plain,
! [L] : min != bit0(L),
inference(fof_nnf,[status(thm)],[fact_519_rel__simps_I42_J]) ).
fof(f_538_2,plain,
! [U_1283] : min != bit0(U_1283),
inference(variable_rename,[status(thm)],[f_538_1]) ).
fof(f_538_3,plain,
! [U_1283] : min != bit0(U_1283),
inference(definitional_conversion,[status(esa)],[f_538_2]) ).
cnf(f_538_4,plain,
min != bit0(U_1283),
inference(clausify,[status(thm)],[f_538_3]) ).
fof(f_539_1,plain,
~ ord_less_int(min,min),
inference(fof_nnf,[status(thm)],[fact_520_rel__simps_I7_J]) ).
fof(f_539_2,plain,
~ ord_less_int(min,min),
inference(definitional_conversion,[status(esa)],[f_539_1]) ).
cnf(f_539_3,plain,
~ ord_less_int(min,min),
inference(clausify,[status(thm)],[f_539_2]) ).
fof(f_540_1,plain,
ord_less_eq_int(min,min),
inference(fof_nnf,[status(thm)],[fact_521_rel__simps_I24_J]) ).
fof(f_540_2,plain,
ord_less_eq_int(min,min),
inference(definitional_conversion,[status(esa)],[f_540_1]) ).
cnf(f_540_3,plain,
ord_less_eq_int(min,min),
inference(clausify,[status(thm)],[f_540_2]) ).
fof(f_541_1,plain,
! [X_2] :
( ( ~ ord_less_real(zero_zero_real,times_times_real(X_2,X_2))
| X_2 != zero_zero_real )
& ( X_2 = zero_zero_real
| ord_less_real(zero_zero_real,times_times_real(X_2,X_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_522_not__real__square__gt__zero]) ).
fof(f_541_2,plain,
! [U_1284] :
( ( ~ ord_less_real(zero_zero_real,times_times_real(U_1284,U_1284))
| U_1284 != zero_zero_real )
& ( U_1284 = zero_zero_real
| ord_less_real(zero_zero_real,times_times_real(U_1284,U_1284)) ) ),
inference(variable_rename,[status(thm)],[f_541_1]) ).
fof(f_541_3,plain,
( ! [U_1286] :
( ~ ord_less_real(zero_zero_real,times_times_real(U_1286,U_1286))
| U_1286 != zero_zero_real )
& ! [U_1285] :
( U_1285 = zero_zero_real
| ord_less_real(zero_zero_real,times_times_real(U_1285,U_1285)) ) ),
inference(miniscope,[status(thm)],[f_541_2]) ).
fof(f_541_4,plain,
( ! [U_1286] :
( ~ ord_less_real(zero_zero_real,times_times_real(U_1286,U_1286))
| U_1286 != zero_zero_real )
& ! [U_1285] :
( U_1285 = zero_zero_real
| ord_less_real(zero_zero_real,times_times_real(U_1285,U_1285)) ) ),
inference(definitional_conversion,[status(esa)],[f_541_3]) ).
cnf(f_541_5,plain,
( U_1285 = zero_zero_real
| ord_less_real(zero_zero_real,times_times_real(U_1285,U_1285)) ),
inference(clausify,[status(thm)],[f_541_4]) ).
cnf(f_541_6,plain,
( ~ ord_less_real(zero_zero_real,times_times_real(U_1286,U_1286))
| U_1286 != zero_zero_real ),
inference(clausify,[status(thm)],[f_541_4]) ).
fof(f_542_1,plain,
! [K_1] :
( ( ord_less_int(bit1(K_1),min)
| ~ ord_less_int(K_1,min) )
& ( ord_less_int(K_1,min)
| ~ ord_less_int(bit1(K_1),min) ) ),
inference(fof_nnf,[status(thm)],[fact_523_rel__simps_I13_J]) ).
fof(f_542_2,plain,
! [U_1287] :
( ( ord_less_int(bit1(U_1287),min)
| ~ ord_less_int(U_1287,min) )
& ( ord_less_int(U_1287,min)
| ~ ord_less_int(bit1(U_1287),min) ) ),
inference(variable_rename,[status(thm)],[f_542_1]) ).
fof(f_542_3,plain,
( ! [U_1289] :
( ord_less_int(bit1(U_1289),min)
| ~ ord_less_int(U_1289,min) )
& ! [U_1288] :
( ord_less_int(U_1288,min)
| ~ ord_less_int(bit1(U_1288),min) ) ),
inference(miniscope,[status(thm)],[f_542_2]) ).
fof(f_542_4,plain,
( ! [U_1289] :
( ord_less_int(bit1(U_1289),min)
| ~ ord_less_int(U_1289,min) )
& ! [U_1288] :
( ord_less_int(U_1288,min)
| ~ ord_less_int(bit1(U_1288),min) ) ),
inference(definitional_conversion,[status(esa)],[f_542_3]) ).
cnf(f_542_5,plain,
( ord_less_int(U_1288,min)
| ~ ord_less_int(bit1(U_1288),min) ),
inference(clausify,[status(thm)],[f_542_4]) ).
cnf(f_542_6,plain,
( ord_less_int(bit1(U_1289),min)
| ~ ord_less_int(U_1289,min) ),
inference(clausify,[status(thm)],[f_542_4]) ).
fof(f_543_1,plain,
! [K_1] :
( ( ord_less_int(min,bit1(K_1))
| ~ ord_less_int(min,K_1) )
& ( ord_less_int(min,K_1)
| ~ ord_less_int(min,bit1(K_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_524_rel__simps_I9_J]) ).
fof(f_543_2,plain,
! [U_1290] :
( ( ord_less_int(min,bit1(U_1290))
| ~ ord_less_int(min,U_1290) )
& ( ord_less_int(min,U_1290)
| ~ ord_less_int(min,bit1(U_1290)) ) ),
inference(variable_rename,[status(thm)],[f_543_1]) ).
fof(f_543_3,plain,
( ! [U_1292] :
( ord_less_int(min,bit1(U_1292))
| ~ ord_less_int(min,U_1292) )
& ! [U_1291] :
( ord_less_int(min,U_1291)
| ~ ord_less_int(min,bit1(U_1291)) ) ),
inference(miniscope,[status(thm)],[f_543_2]) ).
fof(f_543_4,plain,
( ! [U_1292] :
( ord_less_int(min,bit1(U_1292))
| ~ ord_less_int(min,U_1292) )
& ! [U_1291] :
( ord_less_int(min,U_1291)
| ~ ord_less_int(min,bit1(U_1291)) ) ),
inference(definitional_conversion,[status(esa)],[f_543_3]) ).
cnf(f_543_5,plain,
( ord_less_int(min,U_1291)
| ~ ord_less_int(min,bit1(U_1291)) ),
inference(clausify,[status(thm)],[f_543_4]) ).
cnf(f_543_6,plain,
( ord_less_int(min,bit1(U_1292))
| ~ ord_less_int(min,U_1292) ),
inference(clausify,[status(thm)],[f_543_4]) ).
fof(f_544_1,plain,
~ ord_less_int(pls,min),
inference(fof_nnf,[status(thm)],[fact_525_rel__simps_I3_J]) ).
fof(f_544_2,plain,
~ ord_less_int(pls,min),
inference(definitional_conversion,[status(esa)],[f_544_1]) ).
cnf(f_544_3,plain,
~ ord_less_int(pls,min),
inference(clausify,[status(thm)],[f_544_2]) ).
fof(f_545_1,plain,
ord_less_int(min,pls),
inference(fof_nnf,[status(thm)],[fact_526_rel__simps_I6_J]) ).
fof(f_545_2,plain,
ord_less_int(min,pls),
inference(definitional_conversion,[status(esa)],[f_545_1]) ).
cnf(f_545_3,plain,
ord_less_int(min,pls),
inference(clausify,[status(thm)],[f_545_2]) ).
fof(f_546_1,plain,
! [K_1] :
( ( ord_less_int(min,bit0(K_1))
| ~ ord_less_int(min,K_1) )
& ( ord_less_int(min,K_1)
| ~ ord_less_int(min,bit0(K_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_527_rel__simps_I8_J]) ).
fof(f_546_2,plain,
! [U_1293] :
( ( ord_less_int(min,bit0(U_1293))
| ~ ord_less_int(min,U_1293) )
& ( ord_less_int(min,U_1293)
| ~ ord_less_int(min,bit0(U_1293)) ) ),
inference(variable_rename,[status(thm)],[f_546_1]) ).
fof(f_546_3,plain,
( ! [U_1295] :
( ord_less_int(min,bit0(U_1295))
| ~ ord_less_int(min,U_1295) )
& ! [U_1294] :
( ord_less_int(min,U_1294)
| ~ ord_less_int(min,bit0(U_1294)) ) ),
inference(miniscope,[status(thm)],[f_546_2]) ).
fof(f_546_4,plain,
( ! [U_1295] :
( ord_less_int(min,bit0(U_1295))
| ~ ord_less_int(min,U_1295) )
& ! [U_1294] :
( ord_less_int(min,U_1294)
| ~ ord_less_int(min,bit0(U_1294)) ) ),
inference(definitional_conversion,[status(esa)],[f_546_3]) ).
cnf(f_546_5,plain,
( ord_less_int(min,U_1294)
| ~ ord_less_int(min,bit0(U_1294)) ),
inference(clausify,[status(thm)],[f_546_4]) ).
cnf(f_546_6,plain,
( ord_less_int(min,bit0(U_1295))
| ~ ord_less_int(min,U_1295) ),
inference(clausify,[status(thm)],[f_546_4]) ).
fof(f_547_1,plain,
ord_less_int(min,zero_zero_int),
inference(fof_nnf,[status(thm)],[fact_528_bin__less__0__simps_I2_J]) ).
fof(f_547_2,plain,
ord_less_int(min,zero_zero_int),
inference(definitional_conversion,[status(esa)],[f_547_1]) ).
cnf(f_547_3,plain,
ord_less_int(min,zero_zero_int),
inference(clausify,[status(thm)],[f_547_2]) ).
fof(f_548_1,plain,
! [K_1] :
( ( ord_less_eq_int(bit1(K_1),min)
| ~ ord_less_eq_int(K_1,min) )
& ( ord_less_eq_int(K_1,min)
| ~ ord_less_eq_int(bit1(K_1),min) ) ),
inference(fof_nnf,[status(thm)],[fact_529_rel__simps_I30_J]) ).
fof(f_548_2,plain,
! [U_1296] :
( ( ord_less_eq_int(bit1(U_1296),min)
| ~ ord_less_eq_int(U_1296,min) )
& ( ord_less_eq_int(U_1296,min)
| ~ ord_less_eq_int(bit1(U_1296),min) ) ),
inference(variable_rename,[status(thm)],[f_548_1]) ).
fof(f_548_3,plain,
( ! [U_1298] :
( ord_less_eq_int(bit1(U_1298),min)
| ~ ord_less_eq_int(U_1298,min) )
& ! [U_1297] :
( ord_less_eq_int(U_1297,min)
| ~ ord_less_eq_int(bit1(U_1297),min) ) ),
inference(miniscope,[status(thm)],[f_548_2]) ).
fof(f_548_4,plain,
( ! [U_1298] :
( ord_less_eq_int(bit1(U_1298),min)
| ~ ord_less_eq_int(U_1298,min) )
& ! [U_1297] :
( ord_less_eq_int(U_1297,min)
| ~ ord_less_eq_int(bit1(U_1297),min) ) ),
inference(definitional_conversion,[status(esa)],[f_548_3]) ).
cnf(f_548_5,plain,
( ord_less_eq_int(U_1297,min)
| ~ ord_less_eq_int(bit1(U_1297),min) ),
inference(clausify,[status(thm)],[f_548_4]) ).
cnf(f_548_6,plain,
( ord_less_eq_int(bit1(U_1298),min)
| ~ ord_less_eq_int(U_1298,min) ),
inference(clausify,[status(thm)],[f_548_4]) ).
fof(f_549_1,plain,
! [K_1] :
( ( ord_less_eq_int(min,bit1(K_1))
| ~ ord_less_eq_int(min,K_1) )
& ( ord_less_eq_int(min,K_1)
| ~ ord_less_eq_int(min,bit1(K_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_530_rel__simps_I26_J]) ).
fof(f_549_2,plain,
! [U_1299] :
( ( ord_less_eq_int(min,bit1(U_1299))
| ~ ord_less_eq_int(min,U_1299) )
& ( ord_less_eq_int(min,U_1299)
| ~ ord_less_eq_int(min,bit1(U_1299)) ) ),
inference(variable_rename,[status(thm)],[f_549_1]) ).
fof(f_549_3,plain,
( ! [U_1301] :
( ord_less_eq_int(min,bit1(U_1301))
| ~ ord_less_eq_int(min,U_1301) )
& ! [U_1300] :
( ord_less_eq_int(min,U_1300)
| ~ ord_less_eq_int(min,bit1(U_1300)) ) ),
inference(miniscope,[status(thm)],[f_549_2]) ).
fof(f_549_4,plain,
( ! [U_1301] :
( ord_less_eq_int(min,bit1(U_1301))
| ~ ord_less_eq_int(min,U_1301) )
& ! [U_1300] :
( ord_less_eq_int(min,U_1300)
| ~ ord_less_eq_int(min,bit1(U_1300)) ) ),
inference(definitional_conversion,[status(esa)],[f_549_3]) ).
cnf(f_549_5,plain,
( ord_less_eq_int(min,U_1300)
| ~ ord_less_eq_int(min,bit1(U_1300)) ),
inference(clausify,[status(thm)],[f_549_4]) ).
cnf(f_549_6,plain,
( ord_less_eq_int(min,bit1(U_1301))
| ~ ord_less_eq_int(min,U_1301) ),
inference(clausify,[status(thm)],[f_549_4]) ).
fof(f_550_1,plain,
~ ord_less_eq_int(pls,min),
inference(fof_nnf,[status(thm)],[fact_531_rel__simps_I20_J]) ).
fof(f_550_2,plain,
~ ord_less_eq_int(pls,min),
inference(definitional_conversion,[status(esa)],[f_550_1]) ).
cnf(f_550_3,plain,
~ ord_less_eq_int(pls,min),
inference(clausify,[status(thm)],[f_550_2]) ).
fof(f_551_1,plain,
ord_less_eq_int(min,pls),
inference(fof_nnf,[status(thm)],[fact_532_rel__simps_I23_J]) ).
fof(f_551_2,plain,
ord_less_eq_int(min,pls),
inference(definitional_conversion,[status(esa)],[f_551_1]) ).
cnf(f_551_3,plain,
ord_less_eq_int(min,pls),
inference(clausify,[status(thm)],[f_551_2]) ).
fof(f_552_1,plain,
! [K_1] :
( ( ord_less_eq_int(bit0(K_1),min)
| ~ ord_less_eq_int(K_1,min) )
& ( ord_less_eq_int(K_1,min)
| ~ ord_less_eq_int(bit0(K_1),min) ) ),
inference(fof_nnf,[status(thm)],[fact_533_rel__simps_I28_J]) ).
fof(f_552_2,plain,
! [U_1302] :
( ( ord_less_eq_int(bit0(U_1302),min)
| ~ ord_less_eq_int(U_1302,min) )
& ( ord_less_eq_int(U_1302,min)
| ~ ord_less_eq_int(bit0(U_1302),min) ) ),
inference(variable_rename,[status(thm)],[f_552_1]) ).
fof(f_552_3,plain,
( ! [U_1304] :
( ord_less_eq_int(bit0(U_1304),min)
| ~ ord_less_eq_int(U_1304,min) )
& ! [U_1303] :
( ord_less_eq_int(U_1303,min)
| ~ ord_less_eq_int(bit0(U_1303),min) ) ),
inference(miniscope,[status(thm)],[f_552_2]) ).
fof(f_552_4,plain,
( ! [U_1304] :
( ord_less_eq_int(bit0(U_1304),min)
| ~ ord_less_eq_int(U_1304,min) )
& ! [U_1303] :
( ord_less_eq_int(U_1303,min)
| ~ ord_less_eq_int(bit0(U_1303),min) ) ),
inference(definitional_conversion,[status(esa)],[f_552_3]) ).
cnf(f_552_5,plain,
( ord_less_eq_int(U_1303,min)
| ~ ord_less_eq_int(bit0(U_1303),min) ),
inference(clausify,[status(thm)],[f_552_4]) ).
cnf(f_552_6,plain,
( ord_less_eq_int(bit0(U_1304),min)
| ~ ord_less_eq_int(U_1304,min) ),
inference(clausify,[status(thm)],[f_552_4]) ).
fof(f_553_1,plain,
number_number_of_int(pls) != number_number_of_int(min),
inference(fof_nnf,[status(thm)],[fact_534_eq__number__of__Pls__Min]) ).
fof(f_553_2,plain,
number_number_of_int(pls) != number_number_of_int(min),
inference(definitional_conversion,[status(esa)],[f_553_1]) ).
cnf(f_553_3,plain,
number_number_of_int(pls) != number_number_of_int(min),
inference(clausify,[status(thm)],[f_553_2]) ).
fof(f_554_1,plain,
! [I,M,N] :
( ord_less_eq_nat(M,N)
| ~ ord_less_nat(one_one_nat,I)
| ~ dvd_dvd_nat(power_power_nat(I,M),power_power_nat(I,N)) ),
inference(fof_nnf,[status(thm)],[fact_535_power__dvd__imp__le]) ).
fof(f_554_2,plain,
! [U_1307,U_1306,U_1305] :
( ord_less_eq_nat(U_1306,U_1305)
| ~ ord_less_nat(one_one_nat,U_1307)
| ~ dvd_dvd_nat(power_power_nat(U_1307,U_1306),power_power_nat(U_1307,U_1305)) ),
inference(variable_rename,[status(thm)],[f_554_1]) ).
fof(f_554_3,plain,
! [U_1306,U_1305,U_1307] :
( ord_less_eq_nat(U_1306,U_1305)
| ~ ord_less_nat(one_one_nat,U_1307)
| ~ dvd_dvd_nat(power_power_nat(U_1307,U_1306),power_power_nat(U_1307,U_1305)) ),
inference(definitional_conversion,[status(esa)],[f_554_2]) ).
cnf(f_554_4,plain,
( ord_less_eq_nat(U_1306,U_1305)
| ~ ord_less_nat(one_one_nat,U_1307)
| ~ dvd_dvd_nat(power_power_nat(U_1307,U_1306),power_power_nat(U_1307,U_1305)) ),
inference(clausify,[status(thm)],[f_554_3]) ).
fof(f_555_1,plain,
! [X_5] : power_power_real(X_5,zero_zero_nat) = one_one_real,
inference(fof_nnf,[status(thm)],[fact_536_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J]) ).
fof(f_555_2,plain,
! [U_1308] : power_power_real(U_1308,zero_zero_nat) = one_one_real,
inference(variable_rename,[status(thm)],[f_555_1]) ).
fof(f_555_3,plain,
! [U_1308] : power_power_real(U_1308,zero_zero_nat) = one_one_real,
inference(definitional_conversion,[status(esa)],[f_555_2]) ).
cnf(f_555_4,plain,
power_power_real(U_1308,zero_zero_nat) = one_one_real,
inference(clausify,[status(thm)],[f_555_3]) ).
fof(f_556_1,plain,
! [X_5] : power_power_nat(X_5,zero_zero_nat) = one_one_nat,
inference(fof_nnf,[status(thm)],[fact_537_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J]) ).
fof(f_556_2,plain,
! [U_1309] : power_power_nat(U_1309,zero_zero_nat) = one_one_nat,
inference(variable_rename,[status(thm)],[f_556_1]) ).
fof(f_556_3,plain,
! [U_1309] : power_power_nat(U_1309,zero_zero_nat) = one_one_nat,
inference(definitional_conversion,[status(esa)],[f_556_2]) ).
cnf(f_556_4,plain,
power_power_nat(U_1309,zero_zero_nat) = one_one_nat,
inference(clausify,[status(thm)],[f_556_3]) ).
fof(f_557_1,plain,
! [X_5] : power_power_int(X_5,zero_zero_nat) = one_one_int,
inference(fof_nnf,[status(thm)],[fact_538_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J]) ).
fof(f_557_2,plain,
! [U_1310] : power_power_int(U_1310,zero_zero_nat) = one_one_int,
inference(variable_rename,[status(thm)],[f_557_1]) ).
fof(f_557_3,plain,
! [U_1310] : power_power_int(U_1310,zero_zero_nat) = one_one_int,
inference(definitional_conversion,[status(esa)],[f_557_2]) ).
cnf(f_557_4,plain,
power_power_int(U_1310,zero_zero_nat) = one_one_int,
inference(clausify,[status(thm)],[f_557_3]) ).
fof(f_558_1,plain,
! [A_3] : power_power_real(A_3,zero_zero_nat) = one_one_real,
inference(fof_nnf,[status(thm)],[fact_539_power__0]) ).
fof(f_558_2,plain,
! [U_1311] : power_power_real(U_1311,zero_zero_nat) = one_one_real,
inference(variable_rename,[status(thm)],[f_558_1]) ).
fof(f_558_3,plain,
! [U_1311] : power_power_real(U_1311,zero_zero_nat) = one_one_real,
inference(definitional_conversion,[status(esa)],[f_558_2]) ).
cnf(f_558_4,plain,
power_power_real(U_1311,zero_zero_nat) = one_one_real,
inference(clausify,[status(thm)],[f_558_3]) ).
fof(f_559_1,plain,
! [A_3] : power_power_nat(A_3,zero_zero_nat) = one_one_nat,
inference(fof_nnf,[status(thm)],[fact_540_power__0]) ).
fof(f_559_2,plain,
! [U_1312] : power_power_nat(U_1312,zero_zero_nat) = one_one_nat,
inference(variable_rename,[status(thm)],[f_559_1]) ).
fof(f_559_3,plain,
! [U_1312] : power_power_nat(U_1312,zero_zero_nat) = one_one_nat,
inference(definitional_conversion,[status(esa)],[f_559_2]) ).
cnf(f_559_4,plain,
power_power_nat(U_1312,zero_zero_nat) = one_one_nat,
inference(clausify,[status(thm)],[f_559_3]) ).
fof(f_560_1,plain,
! [A_3] : power_power_int(A_3,zero_zero_nat) = one_one_int,
inference(fof_nnf,[status(thm)],[fact_541_power__0]) ).
fof(f_560_2,plain,
! [U_1313] : power_power_int(U_1313,zero_zero_nat) = one_one_int,
inference(variable_rename,[status(thm)],[f_560_1]) ).
fof(f_560_3,plain,
! [U_1313] : power_power_int(U_1313,zero_zero_nat) = one_one_int,
inference(definitional_conversion,[status(esa)],[f_560_2]) ).
cnf(f_560_4,plain,
power_power_int(U_1313,zero_zero_nat) = one_one_int,
inference(clausify,[status(thm)],[f_560_3]) ).
fof(f_561_1,plain,
number_number_of_nat(pls) = zero_zero_nat,
inference(fof_nnf,[status(thm)],[fact_542_nat__number__of__Pls]) ).
fof(f_561_2,plain,
number_number_of_nat(pls) = zero_zero_nat,
inference(definitional_conversion,[status(esa)],[f_561_1]) ).
cnf(f_561_3,plain,
number_number_of_nat(pls) = zero_zero_nat,
inference(clausify,[status(thm)],[f_561_2]) ).
fof(f_562_1,plain,
zero_zero_nat = number_number_of_nat(pls),
inference(fof_nnf,[status(thm)],[fact_543_semiring__norm_I113_J]) ).
fof(f_562_2,plain,
zero_zero_nat = number_number_of_nat(pls),
inference(definitional_conversion,[status(esa)],[f_562_1]) ).
cnf(f_562_3,plain,
zero_zero_nat = number_number_of_nat(pls),
inference(clausify,[status(thm)],[f_562_2]) ).
fof(f_563_1,plain,
! [K_1] :
( ( ord_less_eq_int(min,bit0(K_1))
| ~ ord_less_int(min,K_1) )
& ( ord_less_int(min,K_1)
| ~ ord_less_eq_int(min,bit0(K_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_544_rel__simps_I25_J]) ).
fof(f_563_2,plain,
! [U_1314] :
( ( ord_less_eq_int(min,bit0(U_1314))
| ~ ord_less_int(min,U_1314) )
& ( ord_less_int(min,U_1314)
| ~ ord_less_eq_int(min,bit0(U_1314)) ) ),
inference(variable_rename,[status(thm)],[f_563_1]) ).
fof(f_563_3,plain,
( ! [U_1316] :
( ord_less_eq_int(min,bit0(U_1316))
| ~ ord_less_int(min,U_1316) )
& ! [U_1315] :
( ord_less_int(min,U_1315)
| ~ ord_less_eq_int(min,bit0(U_1315)) ) ),
inference(miniscope,[status(thm)],[f_563_2]) ).
fof(f_563_4,plain,
( ! [U_1316] :
( ord_less_eq_int(min,bit0(U_1316))
| ~ ord_less_int(min,U_1316) )
& ! [U_1315] :
( ord_less_int(min,U_1315)
| ~ ord_less_eq_int(min,bit0(U_1315)) ) ),
inference(definitional_conversion,[status(esa)],[f_563_3]) ).
cnf(f_563_5,plain,
( ord_less_int(min,U_1315)
| ~ ord_less_eq_int(min,bit0(U_1315)) ),
inference(clausify,[status(thm)],[f_563_4]) ).
cnf(f_563_6,plain,
( ord_less_eq_int(min,bit0(U_1316))
| ~ ord_less_int(min,U_1316) ),
inference(clausify,[status(thm)],[f_563_4]) ).
fof(f_564_1,plain,
! [K_1] :
( ( ord_less_int(bit0(K_1),min)
| ~ ord_less_eq_int(K_1,min) )
& ( ord_less_eq_int(K_1,min)
| ~ ord_less_int(bit0(K_1),min) ) ),
inference(fof_nnf,[status(thm)],[fact_545_rel__simps_I11_J]) ).
fof(f_564_2,plain,
! [U_1317] :
( ( ord_less_int(bit0(U_1317),min)
| ~ ord_less_eq_int(U_1317,min) )
& ( ord_less_eq_int(U_1317,min)
| ~ ord_less_int(bit0(U_1317),min) ) ),
inference(variable_rename,[status(thm)],[f_564_1]) ).
fof(f_564_3,plain,
( ! [U_1319] :
( ord_less_int(bit0(U_1319),min)
| ~ ord_less_eq_int(U_1319,min) )
& ! [U_1318] :
( ord_less_eq_int(U_1318,min)
| ~ ord_less_int(bit0(U_1318),min) ) ),
inference(miniscope,[status(thm)],[f_564_2]) ).
fof(f_564_4,plain,
( ! [U_1319] :
( ord_less_int(bit0(U_1319),min)
| ~ ord_less_eq_int(U_1319,min) )
& ! [U_1318] :
( ord_less_eq_int(U_1318,min)
| ~ ord_less_int(bit0(U_1318),min) ) ),
inference(definitional_conversion,[status(esa)],[f_564_3]) ).
cnf(f_564_5,plain,
( ord_less_eq_int(U_1318,min)
| ~ ord_less_int(bit0(U_1318),min) ),
inference(clausify,[status(thm)],[f_564_4]) ).
cnf(f_564_6,plain,
( ord_less_int(bit0(U_1319),min)
| ~ ord_less_eq_int(U_1319,min) ),
inference(clausify,[status(thm)],[f_564_4]) ).
fof(f_565_1,plain,
! [M,N] :
( M = number_number_of_int(min)
| M = one_one_int
| times_times_int(M,N) != one_one_int
| ~ is_int(M) ),
inference(fof_nnf,[status(thm)],[fact_546_pos__zmult__eq__1__iff__lemma]) ).
fof(f_565_2,plain,
! [U_1321,U_1320] :
( U_1321 = number_number_of_int(min)
| U_1321 = one_one_int
| times_times_int(U_1321,U_1320) != one_one_int
| ~ is_int(U_1321) ),
inference(variable_rename,[status(thm)],[f_565_1]) ).
fof(f_565_3,plain,
! [U_1321] :
( ! [U_1320] : times_times_int(U_1321,U_1320) != one_one_int
| U_1321 = number_number_of_int(min)
| U_1321 = one_one_int
| ~ is_int(U_1321) ),
inference(miniscope,[status(thm)],[f_565_2]) ).
fof(f_565_4,plain,
! [U_1321,U_1320] :
( times_times_int(U_1321,U_1320) != one_one_int
| U_1321 = number_number_of_int(min)
| U_1321 = one_one_int
| ~ is_int(U_1321) ),
inference(definitional_conversion,[status(esa)],[f_565_3]) ).
cnf(f_565_5,plain,
( times_times_int(U_1321,U_1320) != one_one_int
| U_1321 = number_number_of_int(min)
| U_1321 = one_one_int
| ~ is_int(U_1321) ),
inference(clausify,[status(thm)],[f_565_4]) ).
fof(f_566_1,plain,
! [Ma,N_1] :
( ( ( times_times_int(Ma,N_1) = one_one_int
| ( ( N_1 != number_number_of_int(min)
| Ma != number_number_of_int(min) )
& ( N_1 != one_one_int
| Ma != one_one_int ) ) )
& ( ( N_1 = number_number_of_int(min)
& Ma = number_number_of_int(min) )
| ( N_1 = one_one_int
& Ma = one_one_int )
| times_times_int(Ma,N_1) != one_one_int ) )
| ~ is_int(N_1)
| ~ is_int(Ma) ),
inference(fof_nnf,[status(thm)],[fact_547_zmult__eq__1__iff]) ).
fof(f_566_2,plain,
! [U_1323,U_1322] :
( ( ( times_times_int(U_1323,U_1322) = one_one_int
| ( ( U_1322 != number_number_of_int(min)
| U_1323 != number_number_of_int(min) )
& ( U_1322 != one_one_int
| U_1323 != one_one_int ) ) )
& ( ( U_1322 = number_number_of_int(min)
& U_1323 = number_number_of_int(min) )
| ( U_1322 = one_one_int
& U_1323 = one_one_int )
| times_times_int(U_1323,U_1322) != one_one_int ) )
| ~ is_int(U_1322)
| ~ is_int(U_1323) ),
inference(variable_rename,[status(thm)],[f_566_1]) ).
fof(f_566_3,plain,
( ! [U_1323,U_1322] :
( U_1322 != number_number_of_int(min)
| U_1323 != number_number_of_int(min)
| ~ sP73(U_1323,U_1322) )
& ! [U_1323,U_1322] :
( U_1322 != one_one_int
| U_1323 != one_one_int
| ~ sP73(U_1323,U_1322) )
& ! [U_1323,U_1322] :
( U_1322 = number_number_of_int(min)
| ~ sP72(U_1323,U_1322) )
& ! [U_1323,U_1322] :
( U_1323 = number_number_of_int(min)
| ~ sP72(U_1323,U_1322) )
& ! [U_1323,U_1322] :
( U_1322 = one_one_int
| ~ sP71(U_1323,U_1322) )
& ! [U_1323,U_1322] :
( U_1323 = one_one_int
| ~ sP71(U_1323,U_1322) )
& ! [U_1323,U_1322] :
( times_times_int(U_1323,U_1322) = one_one_int
| sP73(U_1323,U_1322)
| ~ sP74(U_1323,U_1322) )
& ! [U_1323,U_1322] :
( sP72(U_1323,U_1322)
| sP71(U_1323,U_1322)
| times_times_int(U_1323,U_1322) != one_one_int
| ~ sP74(U_1323,U_1322) )
& ! [U_1323,U_1322] :
( sP74(U_1323,U_1322)
| ~ is_int(U_1322)
| ~ is_int(U_1323) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP71,sP72,sP73,sP74])],[f_566_2]) ).
cnf(f_566_4,plain,
( sP74(U_1323,U_1322)
| ~ is_int(U_1322)
| ~ is_int(U_1323) ),
inference(clausify,[status(thm)],[f_566_3]) ).
cnf(f_566_5,plain,
( sP72(U_1323,U_1322)
| sP71(U_1323,U_1322)
| times_times_int(U_1323,U_1322) != one_one_int
| ~ sP74(U_1323,U_1322) ),
inference(clausify,[status(thm)],[f_566_3]) ).
cnf(f_566_6,plain,
( times_times_int(U_1323,U_1322) = one_one_int
| sP73(U_1323,U_1322)
| ~ sP74(U_1323,U_1322) ),
inference(clausify,[status(thm)],[f_566_3]) ).
cnf(f_566_7,plain,
( U_1323 = one_one_int
| ~ sP71(U_1323,U_1322) ),
inference(clausify,[status(thm)],[f_566_3]) ).
cnf(f_566_8,plain,
( U_1322 = one_one_int
| ~ sP71(U_1323,U_1322) ),
inference(clausify,[status(thm)],[f_566_3]) ).
cnf(f_566_9,plain,
( U_1323 = number_number_of_int(min)
| ~ sP72(U_1323,U_1322) ),
inference(clausify,[status(thm)],[f_566_3]) ).
cnf(f_566_10,plain,
( U_1322 = number_number_of_int(min)
| ~ sP72(U_1323,U_1322) ),
inference(clausify,[status(thm)],[f_566_3]) ).
cnf(f_566_11,plain,
( U_1322 != one_one_int
| U_1323 != one_one_int
| ~ sP73(U_1323,U_1322) ),
inference(clausify,[status(thm)],[f_566_3]) ).
cnf(f_566_12,plain,
( U_1322 != number_number_of_int(min)
| U_1323 != number_number_of_int(min)
| ~ sP73(U_1323,U_1322) ),
inference(clausify,[status(thm)],[f_566_3]) ).
fof(f_567_1,plain,
! [N_4,A_2] :
( ord_less_real(one_one_real,power_power_real(A_2,N_4))
| ~ ord_less_nat(zero_zero_nat,N_4)
| ~ ord_less_real(one_one_real,A_2) ),
inference(fof_nnf,[status(thm)],[fact_548_one__less__power]) ).
fof(f_567_2,plain,
! [U_1325,U_1324] :
( ord_less_real(one_one_real,power_power_real(U_1324,U_1325))
| ~ ord_less_nat(zero_zero_nat,U_1325)
| ~ ord_less_real(one_one_real,U_1324) ),
inference(variable_rename,[status(thm)],[f_567_1]) ).
fof(f_567_3,plain,
! [U_1325,U_1324] :
( ord_less_real(one_one_real,power_power_real(U_1324,U_1325))
| ~ ord_less_nat(zero_zero_nat,U_1325)
| ~ ord_less_real(one_one_real,U_1324) ),
inference(definitional_conversion,[status(esa)],[f_567_2]) ).
cnf(f_567_4,plain,
( ord_less_real(one_one_real,power_power_real(U_1324,U_1325))
| ~ ord_less_nat(zero_zero_nat,U_1325)
| ~ ord_less_real(one_one_real,U_1324) ),
inference(clausify,[status(thm)],[f_567_3]) ).
fof(f_568_1,plain,
! [N_4,A_2] :
( ord_less_nat(one_one_nat,power_power_nat(A_2,N_4))
| ~ ord_less_nat(zero_zero_nat,N_4)
| ~ ord_less_nat(one_one_nat,A_2) ),
inference(fof_nnf,[status(thm)],[fact_549_one__less__power]) ).
fof(f_568_2,plain,
! [U_1327,U_1326] :
( ord_less_nat(one_one_nat,power_power_nat(U_1326,U_1327))
| ~ ord_less_nat(zero_zero_nat,U_1327)
| ~ ord_less_nat(one_one_nat,U_1326) ),
inference(variable_rename,[status(thm)],[f_568_1]) ).
fof(f_568_3,plain,
! [U_1327,U_1326] :
( ord_less_nat(one_one_nat,power_power_nat(U_1326,U_1327))
| ~ ord_less_nat(zero_zero_nat,U_1327)
| ~ ord_less_nat(one_one_nat,U_1326) ),
inference(definitional_conversion,[status(esa)],[f_568_2]) ).
cnf(f_568_4,plain,
( ord_less_nat(one_one_nat,power_power_nat(U_1326,U_1327))
| ~ ord_less_nat(zero_zero_nat,U_1327)
| ~ ord_less_nat(one_one_nat,U_1326) ),
inference(clausify,[status(thm)],[f_568_3]) ).
fof(f_569_1,plain,
! [N_4,A_2] :
( ord_less_int(one_one_int,power_power_int(A_2,N_4))
| ~ ord_less_nat(zero_zero_nat,N_4)
| ~ ord_less_int(one_one_int,A_2) ),
inference(fof_nnf,[status(thm)],[fact_550_one__less__power]) ).
fof(f_569_2,plain,
! [U_1329,U_1328] :
( ord_less_int(one_one_int,power_power_int(U_1328,U_1329))
| ~ ord_less_nat(zero_zero_nat,U_1329)
| ~ ord_less_int(one_one_int,U_1328) ),
inference(variable_rename,[status(thm)],[f_569_1]) ).
fof(f_569_3,plain,
! [U_1329,U_1328] :
( ord_less_int(one_one_int,power_power_int(U_1328,U_1329))
| ~ ord_less_nat(zero_zero_nat,U_1329)
| ~ ord_less_int(one_one_int,U_1328) ),
inference(definitional_conversion,[status(esa)],[f_569_2]) ).
cnf(f_569_4,plain,
( ord_less_int(one_one_int,power_power_int(U_1328,U_1329))
| ~ ord_less_nat(zero_zero_nat,U_1329)
| ~ ord_less_int(one_one_int,U_1328) ),
inference(clausify,[status(thm)],[f_569_3]) ).
fof(f_570_1,plain,
! [X_4,N_3] :
( dvd_dvd_nat(X_4,power_power_nat(X_4,N_3))
| ( X_4 != one_one_nat
& ~ ord_less_nat(zero_zero_nat,N_3) ) ),
inference(fof_nnf,[status(thm)],[fact_551_dvd__power]) ).
fof(f_570_2,plain,
! [U_1331,U_1330] :
( dvd_dvd_nat(U_1331,power_power_nat(U_1331,U_1330))
| ( U_1331 != one_one_nat
& ~ ord_less_nat(zero_zero_nat,U_1330) ) ),
inference(variable_rename,[status(thm)],[f_570_1]) ).
fof(f_570_3,plain,
( ! [U_1330,U_1331] :
( U_1331 != one_one_nat
| ~ sP75(U_1330,U_1331) )
& ! [U_1330,U_1331] :
( ~ ord_less_nat(zero_zero_nat,U_1330)
| ~ sP75(U_1330,U_1331) )
& ! [U_1330,U_1331] :
( dvd_dvd_nat(U_1331,power_power_nat(U_1331,U_1330))
| sP75(U_1330,U_1331) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP75])],[f_570_2]) ).
cnf(f_570_4,plain,
( dvd_dvd_nat(U_1331,power_power_nat(U_1331,U_1330))
| sP75(U_1330,U_1331) ),
inference(clausify,[status(thm)],[f_570_3]) ).
cnf(f_570_5,plain,
( ~ ord_less_nat(zero_zero_nat,U_1330)
| ~ sP75(U_1330,U_1331) ),
inference(clausify,[status(thm)],[f_570_3]) ).
cnf(f_570_6,plain,
( U_1331 != one_one_nat
| ~ sP75(U_1330,U_1331) ),
inference(clausify,[status(thm)],[f_570_3]) ).
fof(f_571_1,plain,
! [X_4,N_3] :
( dvd_dvd_int(X_4,power_power_int(X_4,N_3))
| ( X_4 != one_one_int
& ~ ord_less_nat(zero_zero_nat,N_3) ) ),
inference(fof_nnf,[status(thm)],[fact_552_dvd__power]) ).
fof(f_571_2,plain,
! [U_1333,U_1332] :
( dvd_dvd_int(U_1333,power_power_int(U_1333,U_1332))
| ( U_1333 != one_one_int
& ~ ord_less_nat(zero_zero_nat,U_1332) ) ),
inference(variable_rename,[status(thm)],[f_571_1]) ).
fof(f_571_3,plain,
( ! [U_1332,U_1333] :
( U_1333 != one_one_int
| ~ sP76(U_1332,U_1333) )
& ! [U_1332,U_1333] :
( ~ ord_less_nat(zero_zero_nat,U_1332)
| ~ sP76(U_1332,U_1333) )
& ! [U_1332,U_1333] :
( dvd_dvd_int(U_1333,power_power_int(U_1333,U_1332))
| sP76(U_1332,U_1333) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP76])],[f_571_2]) ).
cnf(f_571_4,plain,
( dvd_dvd_int(U_1333,power_power_int(U_1333,U_1332))
| sP76(U_1332,U_1333) ),
inference(clausify,[status(thm)],[f_571_3]) ).
cnf(f_571_5,plain,
( ~ ord_less_nat(zero_zero_nat,U_1332)
| ~ sP76(U_1332,U_1333) ),
inference(clausify,[status(thm)],[f_571_3]) ).
cnf(f_571_6,plain,
( U_1333 != one_one_int
| ~ sP76(U_1332,U_1333) ),
inference(clausify,[status(thm)],[f_571_3]) ).
fof(f_572_1,plain,
! [X_4,N_3] :
( dvd_dvd_real(X_4,power_power_real(X_4,N_3))
| ( X_4 != one_one_real
& ~ ord_less_nat(zero_zero_nat,N_3) ) ),
inference(fof_nnf,[status(thm)],[fact_553_dvd__power]) ).
fof(f_572_2,plain,
! [U_1335,U_1334] :
( dvd_dvd_real(U_1335,power_power_real(U_1335,U_1334))
| ( U_1335 != one_one_real
& ~ ord_less_nat(zero_zero_nat,U_1334) ) ),
inference(variable_rename,[status(thm)],[f_572_1]) ).
fof(f_572_3,plain,
( ! [U_1335,U_1334] :
( U_1335 != one_one_real
| ~ sP77(U_1335,U_1334) )
& ! [U_1335,U_1334] :
( ~ ord_less_nat(zero_zero_nat,U_1334)
| ~ sP77(U_1335,U_1334) )
& ! [U_1335,U_1334] :
( dvd_dvd_real(U_1335,power_power_real(U_1335,U_1334))
| sP77(U_1335,U_1334) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP77])],[f_572_2]) ).
cnf(f_572_4,plain,
( dvd_dvd_real(U_1335,power_power_real(U_1335,U_1334))
| sP77(U_1335,U_1334) ),
inference(clausify,[status(thm)],[f_572_3]) ).
cnf(f_572_5,plain,
( ~ ord_less_nat(zero_zero_nat,U_1334)
| ~ sP77(U_1335,U_1334) ),
inference(clausify,[status(thm)],[f_572_3]) ).
cnf(f_572_6,plain,
( U_1335 != one_one_real
| ~ sP77(U_1335,U_1334) ),
inference(clausify,[status(thm)],[f_572_3]) ).
fof(f_573_1,plain,
! [V_3] :
( ( ord_less_nat(zero_zero_nat,number_number_of_nat(V_3))
| ~ ord_less_int(pls,V_3) )
& ( ord_less_int(pls,V_3)
| ~ ord_less_nat(zero_zero_nat,number_number_of_nat(V_3)) ) ),
inference(fof_nnf,[status(thm)],[fact_554_less__0__number__of]) ).
fof(f_573_2,plain,
! [U_1336] :
( ( ord_less_nat(zero_zero_nat,number_number_of_nat(U_1336))
| ~ ord_less_int(pls,U_1336) )
& ( ord_less_int(pls,U_1336)
| ~ ord_less_nat(zero_zero_nat,number_number_of_nat(U_1336)) ) ),
inference(variable_rename,[status(thm)],[f_573_1]) ).
fof(f_573_3,plain,
( ! [U_1338] :
( ord_less_nat(zero_zero_nat,number_number_of_nat(U_1338))
| ~ ord_less_int(pls,U_1338) )
& ! [U_1337] :
( ord_less_int(pls,U_1337)
| ~ ord_less_nat(zero_zero_nat,number_number_of_nat(U_1337)) ) ),
inference(miniscope,[status(thm)],[f_573_2]) ).
fof(f_573_4,plain,
( ! [U_1338] :
( ord_less_nat(zero_zero_nat,number_number_of_nat(U_1338))
| ~ ord_less_int(pls,U_1338) )
& ! [U_1337] :
( ord_less_int(pls,U_1337)
| ~ ord_less_nat(zero_zero_nat,number_number_of_nat(U_1337)) ) ),
inference(definitional_conversion,[status(esa)],[f_573_3]) ).
cnf(f_573_5,plain,
( ord_less_int(pls,U_1337)
| ~ ord_less_nat(zero_zero_nat,number_number_of_nat(U_1337)) ),
inference(clausify,[status(thm)],[f_573_4]) ).
cnf(f_573_6,plain,
( ord_less_nat(zero_zero_nat,number_number_of_nat(U_1338))
| ~ ord_less_int(pls,U_1338) ),
inference(clausify,[status(thm)],[f_573_4]) ).
fof(f_574_1,plain,
! [V_3] :
( ( number_number_of_nat(V_3) = zero_zero_nat
| ~ ord_less_eq_int(V_3,pls) )
& ( ord_less_eq_int(V_3,pls)
| number_number_of_nat(V_3) != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_555_eq__number__of__0]) ).
fof(f_574_2,plain,
! [U_1339] :
( ( number_number_of_nat(U_1339) = zero_zero_nat
| ~ ord_less_eq_int(U_1339,pls) )
& ( ord_less_eq_int(U_1339,pls)
| number_number_of_nat(U_1339) != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_574_1]) ).
fof(f_574_3,plain,
( ! [U_1341] :
( number_number_of_nat(U_1341) = zero_zero_nat
| ~ ord_less_eq_int(U_1341,pls) )
& ! [U_1340] :
( ord_less_eq_int(U_1340,pls)
| number_number_of_nat(U_1340) != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_574_2]) ).
fof(f_574_4,plain,
( ! [U_1341] :
( number_number_of_nat(U_1341) = zero_zero_nat
| ~ ord_less_eq_int(U_1341,pls) )
& ! [U_1340] :
( ord_less_eq_int(U_1340,pls)
| number_number_of_nat(U_1340) != zero_zero_nat ) ),
inference(definitional_conversion,[status(esa)],[f_574_3]) ).
cnf(f_574_5,plain,
( ord_less_eq_int(U_1340,pls)
| number_number_of_nat(U_1340) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_574_4]) ).
cnf(f_574_6,plain,
( number_number_of_nat(U_1341) = zero_zero_nat
| ~ ord_less_eq_int(U_1341,pls) ),
inference(clausify,[status(thm)],[f_574_4]) ).
fof(f_575_1,plain,
! [V_3] :
( ( zero_zero_nat = number_number_of_nat(V_3)
| ~ ord_less_eq_int(V_3,pls) )
& ( ord_less_eq_int(V_3,pls)
| zero_zero_nat != number_number_of_nat(V_3) ) ),
inference(fof_nnf,[status(thm)],[fact_556_eq__0__number__of]) ).
fof(f_575_2,plain,
! [U_1342] :
( ( zero_zero_nat = number_number_of_nat(U_1342)
| ~ ord_less_eq_int(U_1342,pls) )
& ( ord_less_eq_int(U_1342,pls)
| zero_zero_nat != number_number_of_nat(U_1342) ) ),
inference(variable_rename,[status(thm)],[f_575_1]) ).
fof(f_575_3,plain,
( ! [U_1344] :
( zero_zero_nat = number_number_of_nat(U_1344)
| ~ ord_less_eq_int(U_1344,pls) )
& ! [U_1343] :
( ord_less_eq_int(U_1343,pls)
| zero_zero_nat != number_number_of_nat(U_1343) ) ),
inference(miniscope,[status(thm)],[f_575_2]) ).
fof(f_575_4,plain,
( ! [U_1344] :
( zero_zero_nat = number_number_of_nat(U_1344)
| ~ ord_less_eq_int(U_1344,pls) )
& ! [U_1343] :
( ord_less_eq_int(U_1343,pls)
| zero_zero_nat != number_number_of_nat(U_1343) ) ),
inference(definitional_conversion,[status(esa)],[f_575_3]) ).
cnf(f_575_5,plain,
( ord_less_eq_int(U_1343,pls)
| zero_zero_nat != number_number_of_nat(U_1343) ),
inference(clausify,[status(thm)],[f_575_4]) ).
cnf(f_575_6,plain,
( zero_zero_nat = number_number_of_nat(U_1344)
| ~ ord_less_eq_int(U_1344,pls) ),
inference(clausify,[status(thm)],[f_575_4]) ).
fof(f_576_1,plain,
! [A_1,B_2,Ma] :
( ( zcong(A_1,B_2,Ma)
| ~ zcong(B_2,A_1,Ma) )
& ( zcong(B_2,A_1,Ma)
| ~ zcong(A_1,B_2,Ma) ) ),
inference(fof_nnf,[status(thm)],[fact_557_zcong__sym]) ).
fof(f_576_2,plain,
! [U_1347,U_1346,U_1345] :
( ( zcong(U_1347,U_1346,U_1345)
| ~ zcong(U_1346,U_1347,U_1345) )
& ( zcong(U_1346,U_1347,U_1345)
| ~ zcong(U_1347,U_1346,U_1345) ) ),
inference(variable_rename,[status(thm)],[f_576_1]) ).
fof(f_576_3,plain,
( ! [U_1353,U_1351,U_1349] :
( zcong(U_1353,U_1351,U_1349)
| ~ zcong(U_1351,U_1353,U_1349) )
& ! [U_1352,U_1350,U_1348] :
( zcong(U_1350,U_1352,U_1348)
| ~ zcong(U_1352,U_1350,U_1348) ) ),
inference(miniscope,[status(thm)],[f_576_2]) ).
fof(f_576_4,plain,
( ! [U_1353,U_1351,U_1349] :
( zcong(U_1353,U_1351,U_1349)
| ~ zcong(U_1351,U_1353,U_1349) )
& ! [U_1352,U_1348,U_1350] :
( zcong(U_1350,U_1352,U_1348)
| ~ zcong(U_1352,U_1350,U_1348) ) ),
inference(definitional_conversion,[status(esa)],[f_576_3]) ).
cnf(f_576_5,plain,
( zcong(U_1350,U_1352,U_1348)
| ~ zcong(U_1352,U_1350,U_1348) ),
inference(clausify,[status(thm)],[f_576_4]) ).
cnf(f_576_6,plain,
( zcong(U_1353,U_1351,U_1349)
| ~ zcong(U_1351,U_1353,U_1349) ),
inference(clausify,[status(thm)],[f_576_4]) ).
fof(f_577_1,plain,
! [K,M] : zcong(K,K,M),
inference(fof_nnf,[status(thm)],[fact_558_zcong__refl]) ).
fof(f_577_2,plain,
! [U_1355,U_1354] : zcong(U_1355,U_1355,U_1354),
inference(variable_rename,[status(thm)],[f_577_1]) ).
fof(f_577_3,plain,
! [U_1354,U_1355] : zcong(U_1355,U_1355,U_1354),
inference(definitional_conversion,[status(esa)],[f_577_2]) ).
cnf(f_577_4,plain,
zcong(U_1355,U_1355,U_1354),
inference(clausify,[status(thm)],[f_577_3]) ).
fof(f_578_1,plain,
! [C_1,A,B_1,M] :
( zcong(A,C_1,M)
| ~ zcong(B_1,C_1,M)
| ~ zcong(A,B_1,M) ),
inference(fof_nnf,[status(thm)],[fact_559_zcong__trans]) ).
fof(f_578_2,plain,
! [U_1359,U_1358,U_1357,U_1356] :
( zcong(U_1358,U_1359,U_1356)
| ~ zcong(U_1357,U_1359,U_1356)
| ~ zcong(U_1358,U_1357,U_1356) ),
inference(variable_rename,[status(thm)],[f_578_1]) ).
fof(f_578_3,plain,
! [U_1357,U_1356,U_1358,U_1359] :
( zcong(U_1358,U_1359,U_1356)
| ~ zcong(U_1357,U_1359,U_1356)
| ~ zcong(U_1358,U_1357,U_1356) ),
inference(definitional_conversion,[status(esa)],[f_578_2]) ).
cnf(f_578_4,plain,
( zcong(U_1358,U_1359,U_1356)
| ~ zcong(U_1357,U_1359,U_1356)
| ~ zcong(U_1358,U_1357,U_1356) ),
inference(clausify,[status(thm)],[f_578_3]) ).
fof(f_579_1,plain,
ord_less_nat(zero_zero_nat,number_number_of_nat(bit0(bit1(pls)))),
inference(fof_nnf,[status(thm)],[fact_560_pos2]) ).
fof(f_579_2,plain,
ord_less_nat(zero_zero_nat,number_number_of_nat(bit0(bit1(pls)))),
inference(definitional_conversion,[status(esa)],[f_579_1]) ).
cnf(f_579_3,plain,
ord_less_nat(zero_zero_nat,number_number_of_nat(bit0(bit1(pls)))),
inference(clausify,[status(thm)],[f_579_2]) ).
fof(f_580_1,plain,
! [V_2,K,V_1] :
( ( times_times_nat(number_number_of_nat(V_1),times_times_nat(number_number_of_nat(V_2),K)) = times_times_nat(number_number_of_nat(times_times_int(V_1,V_2)),K)
| ord_less_int(V_1,pls) )
& ( times_times_nat(number_number_of_nat(V_1),times_times_nat(number_number_of_nat(V_2),K)) = zero_zero_nat
| ~ ord_less_int(V_1,pls) ) ),
inference(fof_nnf,[status(thm)],[fact_561_nat__number__of__mult__left]) ).
fof(f_580_2,plain,
! [U_1362,U_1361,U_1360] :
( ( times_times_nat(number_number_of_nat(U_1360),times_times_nat(number_number_of_nat(U_1362),U_1361)) = times_times_nat(number_number_of_nat(times_times_int(U_1360,U_1362)),U_1361)
| ord_less_int(U_1360,pls) )
& ( times_times_nat(number_number_of_nat(U_1360),times_times_nat(number_number_of_nat(U_1362),U_1361)) = zero_zero_nat
| ~ ord_less_int(U_1360,pls) ) ),
inference(variable_rename,[status(thm)],[f_580_1]) ).
fof(f_580_3,plain,
( ! [U_1368,U_1366,U_1364] :
( times_times_nat(number_number_of_nat(U_1364),times_times_nat(number_number_of_nat(U_1368),U_1366)) = times_times_nat(number_number_of_nat(times_times_int(U_1364,U_1368)),U_1366)
| ord_less_int(U_1364,pls) )
& ! [U_1367,U_1365,U_1363] :
( times_times_nat(number_number_of_nat(U_1363),times_times_nat(number_number_of_nat(U_1367),U_1365)) = zero_zero_nat
| ~ ord_less_int(U_1363,pls) ) ),
inference(miniscope,[status(thm)],[f_580_2]) ).
fof(f_580_4,plain,
( ! [U_1364,U_1366,U_1368] :
( times_times_nat(number_number_of_nat(U_1364),times_times_nat(number_number_of_nat(U_1368),U_1366)) = times_times_nat(number_number_of_nat(times_times_int(U_1364,U_1368)),U_1366)
| ord_less_int(U_1364,pls) )
& ! [U_1367,U_1365,U_1363] :
( times_times_nat(number_number_of_nat(U_1363),times_times_nat(number_number_of_nat(U_1367),U_1365)) = zero_zero_nat
| ~ ord_less_int(U_1363,pls) ) ),
inference(definitional_conversion,[status(esa)],[f_580_3]) ).
cnf(f_580_5,plain,
( times_times_nat(number_number_of_nat(U_1363),times_times_nat(number_number_of_nat(U_1367),U_1365)) = zero_zero_nat
| ~ ord_less_int(U_1363,pls) ),
inference(clausify,[status(thm)],[f_580_4]) ).
cnf(f_580_6,plain,
( times_times_nat(number_number_of_nat(U_1364),times_times_nat(number_number_of_nat(U_1368),U_1366)) = times_times_nat(number_number_of_nat(times_times_int(U_1364,U_1368)),U_1366)
| ord_less_int(U_1364,pls) ),
inference(clausify,[status(thm)],[f_580_4]) ).
fof(f_581_1,plain,
! [V_2,V_1] :
( ( times_times_nat(number_number_of_nat(V_1),number_number_of_nat(V_2)) = number_number_of_nat(times_times_int(V_1,V_2))
| ord_less_int(V_1,pls) )
& ( times_times_nat(number_number_of_nat(V_1),number_number_of_nat(V_2)) = zero_zero_nat
| ~ ord_less_int(V_1,pls) ) ),
inference(fof_nnf,[status(thm)],[fact_562_mult__nat__number__of]) ).
fof(f_581_2,plain,
! [U_1370,U_1369] :
( ( times_times_nat(number_number_of_nat(U_1369),number_number_of_nat(U_1370)) = number_number_of_nat(times_times_int(U_1369,U_1370))
| ord_less_int(U_1369,pls) )
& ( times_times_nat(number_number_of_nat(U_1369),number_number_of_nat(U_1370)) = zero_zero_nat
| ~ ord_less_int(U_1369,pls) ) ),
inference(variable_rename,[status(thm)],[f_581_1]) ).
fof(f_581_3,plain,
( ! [U_1374,U_1372] :
( times_times_nat(number_number_of_nat(U_1372),number_number_of_nat(U_1374)) = number_number_of_nat(times_times_int(U_1372,U_1374))
| ord_less_int(U_1372,pls) )
& ! [U_1373,U_1371] :
( times_times_nat(number_number_of_nat(U_1371),number_number_of_nat(U_1373)) = zero_zero_nat
| ~ ord_less_int(U_1371,pls) ) ),
inference(miniscope,[status(thm)],[f_581_2]) ).
fof(f_581_4,plain,
( ! [U_1372,U_1374] :
( times_times_nat(number_number_of_nat(U_1372),number_number_of_nat(U_1374)) = number_number_of_nat(times_times_int(U_1372,U_1374))
| ord_less_int(U_1372,pls) )
& ! [U_1373,U_1371] :
( times_times_nat(number_number_of_nat(U_1371),number_number_of_nat(U_1373)) = zero_zero_nat
| ~ ord_less_int(U_1371,pls) ) ),
inference(definitional_conversion,[status(esa)],[f_581_3]) ).
cnf(f_581_5,plain,
( times_times_nat(number_number_of_nat(U_1371),number_number_of_nat(U_1373)) = zero_zero_nat
| ~ ord_less_int(U_1371,pls) ),
inference(clausify,[status(thm)],[f_581_4]) ).
cnf(f_581_6,plain,
( times_times_nat(number_number_of_nat(U_1372),number_number_of_nat(U_1374)) = number_number_of_nat(times_times_int(U_1372,U_1374))
| ord_less_int(U_1372,pls) ),
inference(clausify,[status(thm)],[f_581_4]) ).
fof(f_582_1,plain,
! [X_3,Y_3] :
( ord_less_real(X_3,Y_3)
| X_3 = Y_3
| ~ ord_less_eq_real(X_3,Y_3) ),
inference(fof_nnf,[status(thm)],[fact_563_order__le__neq__implies__less]) ).
fof(f_582_2,plain,
! [U_1376,U_1375] :
( ord_less_real(U_1376,U_1375)
| U_1376 = U_1375
| ~ ord_less_eq_real(U_1376,U_1375) ),
inference(variable_rename,[status(thm)],[f_582_1]) ).
fof(f_582_3,plain,
! [U_1376,U_1375] :
( ord_less_real(U_1376,U_1375)
| U_1376 = U_1375
| ~ ord_less_eq_real(U_1376,U_1375) ),
inference(definitional_conversion,[status(esa)],[f_582_2]) ).
cnf(f_582_4,plain,
( ord_less_real(U_1376,U_1375)
| U_1376 = U_1375
| ~ ord_less_eq_real(U_1376,U_1375) ),
inference(clausify,[status(thm)],[f_582_3]) ).
fof(f_583_1,plain,
! [X_3,Y_3] :
( ord_less_nat(X_3,Y_3)
| X_3 = Y_3
| ~ ord_less_eq_nat(X_3,Y_3) ),
inference(fof_nnf,[status(thm)],[fact_564_order__le__neq__implies__less]) ).
fof(f_583_2,plain,
! [U_1378,U_1377] :
( ord_less_nat(U_1378,U_1377)
| U_1378 = U_1377
| ~ ord_less_eq_nat(U_1378,U_1377) ),
inference(variable_rename,[status(thm)],[f_583_1]) ).
fof(f_583_3,plain,
! [U_1377,U_1378] :
( ord_less_nat(U_1378,U_1377)
| U_1378 = U_1377
| ~ ord_less_eq_nat(U_1378,U_1377) ),
inference(definitional_conversion,[status(esa)],[f_583_2]) ).
cnf(f_583_4,plain,
( ord_less_nat(U_1378,U_1377)
| U_1378 = U_1377
| ~ ord_less_eq_nat(U_1378,U_1377) ),
inference(clausify,[status(thm)],[f_583_3]) ).
fof(f_584_1,plain,
! [X_3,Y_3] :
( ord_less_int(X_3,Y_3)
| X_3 = Y_3
| ~ ord_less_eq_int(X_3,Y_3)
| ~ is_int(Y_3)
| ~ is_int(X_3) ),
inference(fof_nnf,[status(thm)],[fact_565_order__le__neq__implies__less]) ).
fof(f_584_2,plain,
! [U_1380,U_1379] :
( ord_less_int(U_1380,U_1379)
| U_1380 = U_1379
| ~ ord_less_eq_int(U_1380,U_1379)
| ~ is_int(U_1379)
| ~ is_int(U_1380) ),
inference(variable_rename,[status(thm)],[f_584_1]) ).
fof(f_584_3,plain,
! [U_1379,U_1380] :
( ord_less_int(U_1380,U_1379)
| U_1380 = U_1379
| ~ ord_less_eq_int(U_1380,U_1379)
| ~ is_int(U_1379)
| ~ is_int(U_1380) ),
inference(definitional_conversion,[status(esa)],[f_584_2]) ).
cnf(f_584_4,plain,
( ord_less_int(U_1380,U_1379)
| U_1380 = U_1379
| ~ ord_less_eq_int(U_1380,U_1379)
| ~ is_int(U_1379)
| ~ is_int(U_1380) ),
inference(clausify,[status(thm)],[f_584_3]) ).
fof(f_585_1,plain,
! [B_1,A,C_1] :
( ord_less_eq_int(B_1,A)
| ord_less_eq_int(A,B_1)
| ~ ord_less_int(B_1,C_1)
| ~ ord_less_int(A,C_1) ),
inference(fof_nnf,[status(thm)],[fact_566_Euler_Oaux2]) ).
fof(f_585_2,plain,
! [U_1383,U_1382,U_1381] :
( ord_less_eq_int(U_1383,U_1382)
| ord_less_eq_int(U_1382,U_1383)
| ~ ord_less_int(U_1383,U_1381)
| ~ ord_less_int(U_1382,U_1381) ),
inference(variable_rename,[status(thm)],[f_585_1]) ).
fof(f_585_3,plain,
! [U_1383,U_1382,U_1381] :
( ord_less_eq_int(U_1383,U_1382)
| ord_less_eq_int(U_1382,U_1383)
| ~ ord_less_int(U_1383,U_1381)
| ~ ord_less_int(U_1382,U_1381) ),
inference(definitional_conversion,[status(esa)],[f_585_2]) ).
cnf(f_585_4,plain,
( ord_less_eq_int(U_1383,U_1382)
| ord_less_eq_int(U_1382,U_1383)
| ~ ord_less_int(U_1383,U_1381)
| ~ ord_less_int(U_1382,U_1381) ),
inference(clausify,[status(thm)],[f_585_3]) ).
fof(f_586_1,plain,
! [A_1,B_2] :
( ( ( zcong(A_1,B_2,zero_zero_int)
| A_1 != B_2 )
& ( A_1 = B_2
| ~ zcong(A_1,B_2,zero_zero_int) ) )
| ~ is_int(B_2)
| ~ is_int(A_1) ),
inference(fof_nnf,[status(thm)],[fact_567_IntPrimes_Ozcong__zero]) ).
fof(f_586_2,plain,
! [U_1385,U_1384] :
( ( ( zcong(U_1385,U_1384,zero_zero_int)
| U_1385 != U_1384 )
& ( U_1385 = U_1384
| ~ zcong(U_1385,U_1384,zero_zero_int) ) )
| ~ is_int(U_1384)
| ~ is_int(U_1385) ),
inference(variable_rename,[status(thm)],[f_586_1]) ).
fof(f_586_3,plain,
( ! [U_1385,U_1384] :
( zcong(U_1385,U_1384,zero_zero_int)
| U_1385 != U_1384
| ~ sP78(U_1385,U_1384) )
& ! [U_1385,U_1384] :
( U_1385 = U_1384
| ~ zcong(U_1385,U_1384,zero_zero_int)
| ~ sP78(U_1385,U_1384) )
& ! [U_1385,U_1384] :
( sP78(U_1385,U_1384)
| ~ is_int(U_1384)
| ~ is_int(U_1385) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP78])],[f_586_2]) ).
cnf(f_586_4,plain,
( sP78(U_1385,U_1384)
| ~ is_int(U_1384)
| ~ is_int(U_1385) ),
inference(clausify,[status(thm)],[f_586_3]) ).
cnf(f_586_5,plain,
( U_1385 = U_1384
| ~ zcong(U_1385,U_1384,zero_zero_int)
| ~ sP78(U_1385,U_1384) ),
inference(clausify,[status(thm)],[f_586_3]) ).
cnf(f_586_6,plain,
( zcong(U_1385,U_1384,zero_zero_int)
| U_1385 != U_1384
| ~ sP78(U_1385,U_1384) ),
inference(clausify,[status(thm)],[f_586_3]) ).
fof(f_587_1,plain,
! [A,B_1] : zcong(A,B_1,one_one_int),
inference(fof_nnf,[status(thm)],[fact_568_zcong__1]) ).
fof(f_587_2,plain,
! [U_1387,U_1386] : zcong(U_1387,U_1386,one_one_int),
inference(variable_rename,[status(thm)],[f_587_1]) ).
fof(f_587_3,plain,
! [U_1387,U_1386] : zcong(U_1387,U_1386,one_one_int),
inference(definitional_conversion,[status(esa)],[f_587_2]) ).
cnf(f_587_4,plain,
zcong(U_1387,U_1386,one_one_int),
inference(clausify,[status(thm)],[f_587_3]) ).
fof(f_588_1,plain,
! [C_1,D_1,A,B_1,M] :
( zcong(times_times_int(A,C_1),times_times_int(B_1,D_1),M)
| ~ zcong(C_1,D_1,M)
| ~ zcong(A,B_1,M) ),
inference(fof_nnf,[status(thm)],[fact_569_zcong__zmult]) ).
fof(f_588_2,plain,
! [U_1392,U_1391,U_1390,U_1389,U_1388] :
( zcong(times_times_int(U_1390,U_1392),times_times_int(U_1389,U_1391),U_1388)
| ~ zcong(U_1392,U_1391,U_1388)
| ~ zcong(U_1390,U_1389,U_1388) ),
inference(variable_rename,[status(thm)],[f_588_1]) ).
fof(f_588_3,plain,
! [U_1392,U_1388,U_1389,U_1390,U_1391] :
( zcong(times_times_int(U_1390,U_1392),times_times_int(U_1389,U_1391),U_1388)
| ~ zcong(U_1392,U_1391,U_1388)
| ~ zcong(U_1390,U_1389,U_1388) ),
inference(definitional_conversion,[status(esa)],[f_588_2]) ).
cnf(f_588_4,plain,
( zcong(times_times_int(U_1390,U_1392),times_times_int(U_1389,U_1391),U_1388)
| ~ zcong(U_1392,U_1391,U_1388)
| ~ zcong(U_1390,U_1389,U_1388) ),
inference(clausify,[status(thm)],[f_588_3]) ).
fof(f_589_1,plain,
! [K,A,B_1,M] :
( zcong(times_times_int(K,A),times_times_int(K,B_1),M)
| ~ zcong(A,B_1,M) ),
inference(fof_nnf,[status(thm)],[fact_570_zcong__scalar2]) ).
fof(f_589_2,plain,
! [U_1396,U_1395,U_1394,U_1393] :
( zcong(times_times_int(U_1396,U_1395),times_times_int(U_1396,U_1394),U_1393)
| ~ zcong(U_1395,U_1394,U_1393) ),
inference(variable_rename,[status(thm)],[f_589_1]) ).
fof(f_589_3,plain,
! [U_1395,U_1394,U_1393,U_1396] :
( zcong(times_times_int(U_1396,U_1395),times_times_int(U_1396,U_1394),U_1393)
| ~ zcong(U_1395,U_1394,U_1393) ),
inference(definitional_conversion,[status(esa)],[f_589_2]) ).
cnf(f_589_4,plain,
( zcong(times_times_int(U_1396,U_1395),times_times_int(U_1396,U_1394),U_1393)
| ~ zcong(U_1395,U_1394,U_1393) ),
inference(clausify,[status(thm)],[f_589_3]) ).
fof(f_590_1,plain,
! [K,A,B_1,M] :
( zcong(times_times_int(A,K),times_times_int(B_1,K),M)
| ~ zcong(A,B_1,M) ),
inference(fof_nnf,[status(thm)],[fact_571_zcong__scalar]) ).
fof(f_590_2,plain,
! [U_1400,U_1399,U_1398,U_1397] :
( zcong(times_times_int(U_1399,U_1400),times_times_int(U_1398,U_1400),U_1397)
| ~ zcong(U_1399,U_1398,U_1397) ),
inference(variable_rename,[status(thm)],[f_590_1]) ).
fof(f_590_3,plain,
! [U_1398,U_1397,U_1399,U_1400] :
( zcong(times_times_int(U_1399,U_1400),times_times_int(U_1398,U_1400),U_1397)
| ~ zcong(U_1399,U_1398,U_1397) ),
inference(definitional_conversion,[status(esa)],[f_590_2]) ).
cnf(f_590_4,plain,
( zcong(times_times_int(U_1399,U_1400),times_times_int(U_1398,U_1400),U_1397)
| ~ zcong(U_1399,U_1398,U_1397) ),
inference(clausify,[status(thm)],[f_590_3]) ).
fof(f_591_1,plain,
! [A,M,B_1] : zcong(times_times_int(A,M),times_times_int(B_1,M),M),
inference(fof_nnf,[status(thm)],[fact_572_zcong__zmult__self]) ).
fof(f_591_2,plain,
! [U_1403,U_1402,U_1401] : zcong(times_times_int(U_1403,U_1402),times_times_int(U_1401,U_1402),U_1402),
inference(variable_rename,[status(thm)],[f_591_1]) ).
fof(f_591_3,plain,
! [U_1402,U_1401,U_1403] : zcong(times_times_int(U_1403,U_1402),times_times_int(U_1401,U_1402),U_1402),
inference(definitional_conversion,[status(esa)],[f_591_2]) ).
cnf(f_591_4,plain,
zcong(times_times_int(U_1403,U_1402),times_times_int(U_1401,U_1402),U_1402),
inference(clausify,[status(thm)],[f_591_3]) ).
fof(f_592_1,plain,
! [C_1,D_1,A,B_1,M] :
( zcong(plus_plus_int(A,C_1),plus_plus_int(B_1,D_1),M)
| ~ zcong(C_1,D_1,M)
| ~ zcong(A,B_1,M) ),
inference(fof_nnf,[status(thm)],[fact_573_zcong__zadd]) ).
fof(f_592_2,plain,
! [U_1408,U_1407,U_1406,U_1405,U_1404] :
( zcong(plus_plus_int(U_1406,U_1408),plus_plus_int(U_1405,U_1407),U_1404)
| ~ zcong(U_1408,U_1407,U_1404)
| ~ zcong(U_1406,U_1405,U_1404) ),
inference(variable_rename,[status(thm)],[f_592_1]) ).
fof(f_592_3,plain,
! [U_1405,U_1404,U_1406,U_1407,U_1408] :
( zcong(plus_plus_int(U_1406,U_1408),plus_plus_int(U_1405,U_1407),U_1404)
| ~ zcong(U_1408,U_1407,U_1404)
| ~ zcong(U_1406,U_1405,U_1404) ),
inference(definitional_conversion,[status(esa)],[f_592_2]) ).
cnf(f_592_4,plain,
( zcong(plus_plus_int(U_1406,U_1408),plus_plus_int(U_1405,U_1407),U_1404)
| ~ zcong(U_1408,U_1407,U_1404)
| ~ zcong(U_1406,U_1405,U_1404) ),
inference(clausify,[status(thm)],[f_592_3]) ).
fof(f_593_1,plain,
! [N_2] : power_power_real(number267125858f_real(min),times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_2)) = one_one_real,
inference(fof_nnf,[status(thm)],[fact_574_power__m1__even]) ).
fof(f_593_2,plain,
! [U_1409] : power_power_real(number267125858f_real(min),times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1409)) = one_one_real,
inference(variable_rename,[status(thm)],[f_593_1]) ).
fof(f_593_3,plain,
! [U_1409] : power_power_real(number267125858f_real(min),times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1409)) = one_one_real,
inference(definitional_conversion,[status(esa)],[f_593_2]) ).
cnf(f_593_4,plain,
power_power_real(number267125858f_real(min),times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1409)) = one_one_real,
inference(clausify,[status(thm)],[f_593_3]) ).
fof(f_594_1,plain,
! [N_2] : power_power_int(number_number_of_int(min),times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_2)) = one_one_int,
inference(fof_nnf,[status(thm)],[fact_575_power__m1__even]) ).
fof(f_594_2,plain,
! [U_1410] : power_power_int(number_number_of_int(min),times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1410)) = one_one_int,
inference(variable_rename,[status(thm)],[f_594_1]) ).
fof(f_594_3,plain,
! [U_1410] : power_power_int(number_number_of_int(min),times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1410)) = one_one_int,
inference(definitional_conversion,[status(esa)],[f_594_2]) ).
cnf(f_594_4,plain,
power_power_int(number_number_of_int(min),times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1410)) = one_one_int,
inference(clausify,[status(thm)],[f_594_3]) ).
fof(f_595_1,plain,
! [A_1,W_1] :
( ( power_power_real(A_1,number_number_of_nat(W_1)) = zero_zero_real
| number_number_of_nat(W_1) = zero_zero_nat
| A_1 != zero_zero_real )
& ( ( number_number_of_nat(W_1) != zero_zero_nat
& A_1 = zero_zero_real )
| power_power_real(A_1,number_number_of_nat(W_1)) != zero_zero_real ) ),
inference(fof_nnf,[status(thm)],[fact_576_power__eq__0__iff__number__of]) ).
fof(f_595_2,plain,
! [U_1412,U_1411] :
( ( power_power_real(U_1412,number_number_of_nat(U_1411)) = zero_zero_real
| number_number_of_nat(U_1411) = zero_zero_nat
| U_1412 != zero_zero_real )
& ( ( number_number_of_nat(U_1411) != zero_zero_nat
& U_1412 = zero_zero_real )
| power_power_real(U_1412,number_number_of_nat(U_1411)) != zero_zero_real ) ),
inference(variable_rename,[status(thm)],[f_595_1]) ).
fof(f_595_3,plain,
( ! [U_1416,U_1414] :
( power_power_real(U_1416,number_number_of_nat(U_1414)) = zero_zero_real
| number_number_of_nat(U_1414) = zero_zero_nat
| U_1416 != zero_zero_real )
& ! [U_1415,U_1413] :
( ( number_number_of_nat(U_1413) != zero_zero_nat
& U_1415 = zero_zero_real )
| power_power_real(U_1415,number_number_of_nat(U_1413)) != zero_zero_real ) ),
inference(miniscope,[status(thm)],[f_595_2]) ).
fof(f_595_4,plain,
( ! [U_1415,U_1413] :
( number_number_of_nat(U_1413) != zero_zero_nat
| ~ sP79(U_1415,U_1413) )
& ! [U_1415,U_1413] :
( U_1415 = zero_zero_real
| ~ sP79(U_1415,U_1413) )
& ! [U_1416,U_1414] :
( power_power_real(U_1416,number_number_of_nat(U_1414)) = zero_zero_real
| number_number_of_nat(U_1414) = zero_zero_nat
| U_1416 != zero_zero_real )
& ! [U_1415,U_1413] :
( sP79(U_1415,U_1413)
| power_power_real(U_1415,number_number_of_nat(U_1413)) != zero_zero_real ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP79])],[f_595_3]) ).
cnf(f_595_5,plain,
( sP79(U_1415,U_1413)
| power_power_real(U_1415,number_number_of_nat(U_1413)) != zero_zero_real ),
inference(clausify,[status(thm)],[f_595_4]) ).
cnf(f_595_6,plain,
( power_power_real(U_1416,number_number_of_nat(U_1414)) = zero_zero_real
| number_number_of_nat(U_1414) = zero_zero_nat
| U_1416 != zero_zero_real ),
inference(clausify,[status(thm)],[f_595_4]) ).
cnf(f_595_7,plain,
( U_1415 = zero_zero_real
| ~ sP79(U_1415,U_1413) ),
inference(clausify,[status(thm)],[f_595_4]) ).
cnf(f_595_8,plain,
( number_number_of_nat(U_1413) != zero_zero_nat
| ~ sP79(U_1415,U_1413) ),
inference(clausify,[status(thm)],[f_595_4]) ).
fof(f_596_1,plain,
! [A_1,W_1] :
( ( power_power_nat(A_1,number_number_of_nat(W_1)) = zero_zero_nat
| number_number_of_nat(W_1) = zero_zero_nat
| A_1 != zero_zero_nat )
& ( ( number_number_of_nat(W_1) != zero_zero_nat
& A_1 = zero_zero_nat )
| power_power_nat(A_1,number_number_of_nat(W_1)) != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_577_power__eq__0__iff__number__of]) ).
fof(f_596_2,plain,
! [U_1418,U_1417] :
( ( power_power_nat(U_1418,number_number_of_nat(U_1417)) = zero_zero_nat
| number_number_of_nat(U_1417) = zero_zero_nat
| U_1418 != zero_zero_nat )
& ( ( number_number_of_nat(U_1417) != zero_zero_nat
& U_1418 = zero_zero_nat )
| power_power_nat(U_1418,number_number_of_nat(U_1417)) != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_596_1]) ).
fof(f_596_3,plain,
( ! [U_1422,U_1420] :
( power_power_nat(U_1422,number_number_of_nat(U_1420)) = zero_zero_nat
| number_number_of_nat(U_1420) = zero_zero_nat
| U_1422 != zero_zero_nat )
& ! [U_1421,U_1419] :
( ( number_number_of_nat(U_1419) != zero_zero_nat
& U_1421 = zero_zero_nat )
| power_power_nat(U_1421,number_number_of_nat(U_1419)) != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_596_2]) ).
fof(f_596_4,plain,
( ! [U_1421,U_1419] :
( number_number_of_nat(U_1419) != zero_zero_nat
| ~ sP80(U_1421,U_1419) )
& ! [U_1421,U_1419] :
( U_1421 = zero_zero_nat
| ~ sP80(U_1421,U_1419) )
& ! [U_1422,U_1420] :
( power_power_nat(U_1422,number_number_of_nat(U_1420)) = zero_zero_nat
| number_number_of_nat(U_1420) = zero_zero_nat
| U_1422 != zero_zero_nat )
& ! [U_1421,U_1419] :
( sP80(U_1421,U_1419)
| power_power_nat(U_1421,number_number_of_nat(U_1419)) != zero_zero_nat ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP80])],[f_596_3]) ).
cnf(f_596_5,plain,
( sP80(U_1421,U_1419)
| power_power_nat(U_1421,number_number_of_nat(U_1419)) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_596_4]) ).
cnf(f_596_6,plain,
( power_power_nat(U_1422,number_number_of_nat(U_1420)) = zero_zero_nat
| number_number_of_nat(U_1420) = zero_zero_nat
| U_1422 != zero_zero_nat ),
inference(clausify,[status(thm)],[f_596_4]) ).
cnf(f_596_7,plain,
( U_1421 = zero_zero_nat
| ~ sP80(U_1421,U_1419) ),
inference(clausify,[status(thm)],[f_596_4]) ).
cnf(f_596_8,plain,
( number_number_of_nat(U_1419) != zero_zero_nat
| ~ sP80(U_1421,U_1419) ),
inference(clausify,[status(thm)],[f_596_4]) ).
fof(f_597_1,plain,
! [A_1,W_1] :
( ( ( power_power_int(A_1,number_number_of_nat(W_1)) = zero_zero_int
| number_number_of_nat(W_1) = zero_zero_nat
| A_1 != zero_zero_int )
& ( ( number_number_of_nat(W_1) != zero_zero_nat
& A_1 = zero_zero_int )
| power_power_int(A_1,number_number_of_nat(W_1)) != zero_zero_int ) )
| ~ is_int(A_1) ),
inference(fof_nnf,[status(thm)],[fact_578_power__eq__0__iff__number__of]) ).
fof(f_597_2,plain,
! [U_1424,U_1423] :
( ( ( power_power_int(U_1424,number_number_of_nat(U_1423)) = zero_zero_int
| number_number_of_nat(U_1423) = zero_zero_nat
| U_1424 != zero_zero_int )
& ( ( number_number_of_nat(U_1423) != zero_zero_nat
& U_1424 = zero_zero_int )
| power_power_int(U_1424,number_number_of_nat(U_1423)) != zero_zero_int ) )
| ~ is_int(U_1424) ),
inference(variable_rename,[status(thm)],[f_597_1]) ).
fof(f_597_3,plain,
! [U_1424] :
( ( ! [U_1426] :
( power_power_int(U_1424,number_number_of_nat(U_1426)) = zero_zero_int
| number_number_of_nat(U_1426) = zero_zero_nat
| U_1424 != zero_zero_int )
& ! [U_1425] :
( ( number_number_of_nat(U_1425) != zero_zero_nat
& U_1424 = zero_zero_int )
| power_power_int(U_1424,number_number_of_nat(U_1425)) != zero_zero_int ) )
| ~ is_int(U_1424) ),
inference(miniscope,[status(thm)],[f_597_2]) ).
fof(f_597_4,plain,
( ! [U_1424,U_1425] :
( number_number_of_nat(U_1425) != zero_zero_nat
| ~ sP81(U_1424,U_1425) )
& ! [U_1424,U_1425] :
( U_1424 = zero_zero_int
| ~ sP81(U_1424,U_1425) )
& ! [U_1424,U_1425,U_1426] :
( power_power_int(U_1424,number_number_of_nat(U_1426)) = zero_zero_int
| number_number_of_nat(U_1426) = zero_zero_nat
| U_1424 != zero_zero_int
| ~ sP82(U_1424,U_1425,U_1426) )
& ! [U_1424,U_1425,U_1426] :
( sP81(U_1424,U_1425)
| power_power_int(U_1424,number_number_of_nat(U_1425)) != zero_zero_int
| ~ sP82(U_1424,U_1425,U_1426) )
& ! [U_1424,U_1425,U_1426] :
( sP82(U_1424,U_1425,U_1426)
| ~ is_int(U_1424) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP81,sP82])],[f_597_3]) ).
cnf(f_597_5,plain,
( sP82(U_1424,U_1425,U_1426)
| ~ is_int(U_1424) ),
inference(clausify,[status(thm)],[f_597_4]) ).
cnf(f_597_6,plain,
( sP81(U_1424,U_1425)
| power_power_int(U_1424,number_number_of_nat(U_1425)) != zero_zero_int
| ~ sP82(U_1424,U_1425,U_1426) ),
inference(clausify,[status(thm)],[f_597_4]) ).
cnf(f_597_7,plain,
( power_power_int(U_1424,number_number_of_nat(U_1426)) = zero_zero_int
| number_number_of_nat(U_1426) = zero_zero_nat
| U_1424 != zero_zero_int
| ~ sP82(U_1424,U_1425,U_1426) ),
inference(clausify,[status(thm)],[f_597_4]) ).
cnf(f_597_8,plain,
( U_1424 = zero_zero_int
| ~ sP81(U_1424,U_1425) ),
inference(clausify,[status(thm)],[f_597_4]) ).
cnf(f_597_9,plain,
( number_number_of_nat(U_1425) != zero_zero_nat
| ~ sP81(U_1424,U_1425) ),
inference(clausify,[status(thm)],[f_597_4]) ).
fof(f_598_1,plain,
! [B_1,M,A] :
( ~ zcong(A,B_1,M)
| ~ ord_less_int(B_1,A)
| ~ ord_less_int(zero_zero_int,B_1)
| ~ ord_less_int(A,M)
| ~ ord_less_int(zero_zero_int,A) ),
inference(fof_nnf,[status(thm)],[fact_579_zcong__not]) ).
fof(f_598_2,plain,
! [U_1429,U_1428,U_1427] :
( ~ zcong(U_1427,U_1429,U_1428)
| ~ ord_less_int(U_1429,U_1427)
| ~ ord_less_int(zero_zero_int,U_1429)
| ~ ord_less_int(U_1427,U_1428)
| ~ ord_less_int(zero_zero_int,U_1427) ),
inference(variable_rename,[status(thm)],[f_598_1]) ).
fof(f_598_3,plain,
! [U_1428,U_1429,U_1427] :
( ~ zcong(U_1427,U_1429,U_1428)
| ~ ord_less_int(U_1429,U_1427)
| ~ ord_less_int(zero_zero_int,U_1429)
| ~ ord_less_int(U_1427,U_1428)
| ~ ord_less_int(zero_zero_int,U_1427) ),
inference(definitional_conversion,[status(esa)],[f_598_2]) ).
cnf(f_598_4,plain,
( ~ zcong(U_1427,U_1429,U_1428)
| ~ ord_less_int(U_1429,U_1427)
| ~ ord_less_int(zero_zero_int,U_1429)
| ~ ord_less_int(U_1427,U_1428)
| ~ ord_less_int(zero_zero_int,U_1427) ),
inference(clausify,[status(thm)],[f_598_3]) ).
fof(f_599_1,plain,
! [A_1,B_2,Ma] :
( ( ( zcong(A_1,B_2,Ma)
| ! [K_2] :
( B_2 != plus_plus_int(A_1,times_times_int(Ma,K_2))
| ~ is_int(K_2) ) )
& ( ? [K_2] :
( B_2 = plus_plus_int(A_1,times_times_int(Ma,K_2))
& is_int(K_2) )
| ~ zcong(A_1,B_2,Ma) ) )
| ~ is_int(B_2) ),
inference(fof_nnf,[status(thm)],[fact_580_zcong__iff__lin]) ).
fof(f_599_2,plain,
! [U_1434,U_1433,U_1432] :
( ( ( zcong(U_1434,U_1433,U_1432)
| ! [U_1431] :
( U_1433 != plus_plus_int(U_1434,times_times_int(U_1432,U_1431))
| ~ is_int(U_1431) ) )
& ( ? [U_1430] :
( U_1433 = plus_plus_int(U_1434,times_times_int(U_1432,U_1430))
& is_int(U_1430) )
| ~ zcong(U_1434,U_1433,U_1432) ) )
| ~ is_int(U_1433) ),
inference(variable_rename,[status(thm)],[f_599_1]) ).
fof(f_599_3,plain,
! [U_1434,U_1433] :
( ( ! [U_1436] :
( zcong(U_1434,U_1433,U_1436)
| ! [U_1431] :
( U_1433 != plus_plus_int(U_1434,times_times_int(U_1436,U_1431))
| ~ is_int(U_1431) ) )
& ! [U_1435] :
( ? [U_1430] :
( U_1433 = plus_plus_int(U_1434,times_times_int(U_1435,U_1430))
& is_int(U_1430) )
| ~ zcong(U_1434,U_1433,U_1435) ) )
| ~ is_int(U_1433) ),
inference(miniscope,[status(thm)],[f_599_2]) ).
fof(f_599_4,plain,
! [U_1434,U_1433] :
( ( ! [U_1436] :
( zcong(U_1434,U_1433,U_1436)
| ! [U_1431] :
( U_1433 != plus_plus_int(U_1434,times_times_int(U_1436,U_1431))
| ~ is_int(U_1431) ) )
& ! [U_1435] :
( ( U_1433 = plus_plus_int(U_1434,times_times_int(U_1435,sK10(U_1434,U_1433,U_1435)))
& is_int(sK10(U_1434,U_1433,U_1435)) )
| ~ zcong(U_1434,U_1433,U_1435) ) )
| ~ is_int(U_1433) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_1430,sK10(U_1434,U_1433,U_1435))],[f_599_3]) ).
fof(f_599_5,plain,
( ! [U_1433,U_1434,U_1435] :
( U_1433 = plus_plus_int(U_1434,times_times_int(U_1435,sK10(U_1434,U_1433,U_1435)))
| ~ sP83(U_1433,U_1434,U_1435) )
& ! [U_1433,U_1434,U_1435] :
( is_int(sK10(U_1434,U_1433,U_1435))
| ~ sP83(U_1433,U_1434,U_1435) )
& ! [U_1431,U_1433,U_1434,U_1435,U_1436] :
( zcong(U_1434,U_1433,U_1436)
| U_1433 != plus_plus_int(U_1434,times_times_int(U_1436,U_1431))
| ~ is_int(U_1431)
| ~ sP84(U_1431,U_1433,U_1434,U_1435,U_1436) )
& ! [U_1431,U_1433,U_1434,U_1435,U_1436] :
( sP83(U_1433,U_1434,U_1435)
| ~ zcong(U_1434,U_1433,U_1435)
| ~ sP84(U_1431,U_1433,U_1434,U_1435,U_1436) )
& ! [U_1431,U_1433,U_1434,U_1435,U_1436] :
( sP84(U_1431,U_1433,U_1434,U_1435,U_1436)
| ~ is_int(U_1433) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP83,sP84])],[f_599_4]) ).
cnf(f_599_6,plain,
( sP84(U_1431,U_1433,U_1434,U_1435,U_1436)
| ~ is_int(U_1433) ),
inference(clausify,[status(thm)],[f_599_5]) ).
cnf(f_599_7,plain,
( sP83(U_1433,U_1434,U_1435)
| ~ zcong(U_1434,U_1433,U_1435)
| ~ sP84(U_1431,U_1433,U_1434,U_1435,U_1436) ),
inference(clausify,[status(thm)],[f_599_5]) ).
cnf(f_599_8,plain,
( zcong(U_1434,U_1433,U_1436)
| U_1433 != plus_plus_int(U_1434,times_times_int(U_1436,U_1431))
| ~ is_int(U_1431)
| ~ sP84(U_1431,U_1433,U_1434,U_1435,U_1436) ),
inference(clausify,[status(thm)],[f_599_5]) ).
cnf(f_599_9,plain,
( is_int(sK10(U_1434,U_1433,U_1435))
| ~ sP83(U_1433,U_1434,U_1435) ),
inference(clausify,[status(thm)],[f_599_5]) ).
cnf(f_599_10,plain,
( U_1433 = plus_plus_int(U_1434,times_times_int(U_1435,sK10(U_1434,U_1433,U_1435)))
| ~ sP83(U_1433,U_1434,U_1435) ),
inference(clausify,[status(thm)],[f_599_5]) ).
fof(f_600_1,plain,
! [W_3] :
( ( power_power_real(zero_zero_real,number_number_of_nat(W_3)) = zero_zero_real
| number_number_of_nat(W_3) = zero_zero_nat )
& ( power_power_real(zero_zero_real,number_number_of_nat(W_3)) = one_one_real
| number_number_of_nat(W_3) != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_581_power__0__left__number__of]) ).
fof(f_600_2,plain,
! [U_1437] :
( ( power_power_real(zero_zero_real,number_number_of_nat(U_1437)) = zero_zero_real
| number_number_of_nat(U_1437) = zero_zero_nat )
& ( power_power_real(zero_zero_real,number_number_of_nat(U_1437)) = one_one_real
| number_number_of_nat(U_1437) != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_600_1]) ).
fof(f_600_3,plain,
( ! [U_1439] :
( power_power_real(zero_zero_real,number_number_of_nat(U_1439)) = zero_zero_real
| number_number_of_nat(U_1439) = zero_zero_nat )
& ! [U_1438] :
( power_power_real(zero_zero_real,number_number_of_nat(U_1438)) = one_one_real
| number_number_of_nat(U_1438) != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_600_2]) ).
fof(f_600_4,plain,
( ! [U_1439] :
( power_power_real(zero_zero_real,number_number_of_nat(U_1439)) = zero_zero_real
| number_number_of_nat(U_1439) = zero_zero_nat )
& ! [U_1438] :
( power_power_real(zero_zero_real,number_number_of_nat(U_1438)) = one_one_real
| number_number_of_nat(U_1438) != zero_zero_nat ) ),
inference(definitional_conversion,[status(esa)],[f_600_3]) ).
cnf(f_600_5,plain,
( power_power_real(zero_zero_real,number_number_of_nat(U_1438)) = one_one_real
| number_number_of_nat(U_1438) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_600_4]) ).
cnf(f_600_6,plain,
( power_power_real(zero_zero_real,number_number_of_nat(U_1439)) = zero_zero_real
| number_number_of_nat(U_1439) = zero_zero_nat ),
inference(clausify,[status(thm)],[f_600_4]) ).
fof(f_601_1,plain,
! [W_3] :
( ( power_power_nat(zero_zero_nat,number_number_of_nat(W_3)) = zero_zero_nat
| number_number_of_nat(W_3) = zero_zero_nat )
& ( power_power_nat(zero_zero_nat,number_number_of_nat(W_3)) = one_one_nat
| number_number_of_nat(W_3) != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_582_power__0__left__number__of]) ).
fof(f_601_2,plain,
! [U_1440] :
( ( power_power_nat(zero_zero_nat,number_number_of_nat(U_1440)) = zero_zero_nat
| number_number_of_nat(U_1440) = zero_zero_nat )
& ( power_power_nat(zero_zero_nat,number_number_of_nat(U_1440)) = one_one_nat
| number_number_of_nat(U_1440) != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_601_1]) ).
fof(f_601_3,plain,
( ! [U_1442] :
( power_power_nat(zero_zero_nat,number_number_of_nat(U_1442)) = zero_zero_nat
| number_number_of_nat(U_1442) = zero_zero_nat )
& ! [U_1441] :
( power_power_nat(zero_zero_nat,number_number_of_nat(U_1441)) = one_one_nat
| number_number_of_nat(U_1441) != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_601_2]) ).
fof(f_601_4,plain,
( ! [U_1442] :
( power_power_nat(zero_zero_nat,number_number_of_nat(U_1442)) = zero_zero_nat
| number_number_of_nat(U_1442) = zero_zero_nat )
& ! [U_1441] :
( power_power_nat(zero_zero_nat,number_number_of_nat(U_1441)) = one_one_nat
| number_number_of_nat(U_1441) != zero_zero_nat ) ),
inference(definitional_conversion,[status(esa)],[f_601_3]) ).
cnf(f_601_5,plain,
( power_power_nat(zero_zero_nat,number_number_of_nat(U_1441)) = one_one_nat
| number_number_of_nat(U_1441) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_601_4]) ).
cnf(f_601_6,plain,
( power_power_nat(zero_zero_nat,number_number_of_nat(U_1442)) = zero_zero_nat
| number_number_of_nat(U_1442) = zero_zero_nat ),
inference(clausify,[status(thm)],[f_601_4]) ).
fof(f_602_1,plain,
! [W_3] :
( ( power_power_int(zero_zero_int,number_number_of_nat(W_3)) = zero_zero_int
| number_number_of_nat(W_3) = zero_zero_nat )
& ( power_power_int(zero_zero_int,number_number_of_nat(W_3)) = one_one_int
| number_number_of_nat(W_3) != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_583_power__0__left__number__of]) ).
fof(f_602_2,plain,
! [U_1443] :
( ( power_power_int(zero_zero_int,number_number_of_nat(U_1443)) = zero_zero_int
| number_number_of_nat(U_1443) = zero_zero_nat )
& ( power_power_int(zero_zero_int,number_number_of_nat(U_1443)) = one_one_int
| number_number_of_nat(U_1443) != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_602_1]) ).
fof(f_602_3,plain,
( ! [U_1445] :
( power_power_int(zero_zero_int,number_number_of_nat(U_1445)) = zero_zero_int
| number_number_of_nat(U_1445) = zero_zero_nat )
& ! [U_1444] :
( power_power_int(zero_zero_int,number_number_of_nat(U_1444)) = one_one_int
| number_number_of_nat(U_1444) != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_602_2]) ).
fof(f_602_4,plain,
( ! [U_1445] :
( power_power_int(zero_zero_int,number_number_of_nat(U_1445)) = zero_zero_int
| number_number_of_nat(U_1445) = zero_zero_nat )
& ! [U_1444] :
( power_power_int(zero_zero_int,number_number_of_nat(U_1444)) = one_one_int
| number_number_of_nat(U_1444) != zero_zero_nat ) ),
inference(definitional_conversion,[status(esa)],[f_602_3]) ).
cnf(f_602_5,plain,
( power_power_int(zero_zero_int,number_number_of_nat(U_1444)) = one_one_int
| number_number_of_nat(U_1444) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_602_4]) ).
cnf(f_602_6,plain,
( power_power_int(zero_zero_int,number_number_of_nat(U_1445)) = zero_zero_int
| number_number_of_nat(U_1445) = zero_zero_nat ),
inference(clausify,[status(thm)],[f_602_4]) ).
fof(f_603_1,plain,
! [B_1,M,A] :
( A = B_1
| ~ zcong(A,B_1,M)
| ~ ord_less_int(B_1,M)
| ~ ord_less_eq_int(zero_zero_int,B_1)
| ~ ord_less_int(A,M)
| ~ ord_less_eq_int(zero_zero_int,A)
| ~ is_int(A)
| ~ is_int(B_1) ),
inference(fof_nnf,[status(thm)],[fact_584_zcong__zless__imp__eq]) ).
fof(f_603_2,plain,
! [U_1448,U_1447,U_1446] :
( U_1446 = U_1448
| ~ zcong(U_1446,U_1448,U_1447)
| ~ ord_less_int(U_1448,U_1447)
| ~ ord_less_eq_int(zero_zero_int,U_1448)
| ~ ord_less_int(U_1446,U_1447)
| ~ ord_less_eq_int(zero_zero_int,U_1446)
| ~ is_int(U_1446)
| ~ is_int(U_1448) ),
inference(variable_rename,[status(thm)],[f_603_1]) ).
fof(f_603_3,plain,
! [U_1447,U_1448,U_1446] :
( U_1446 = U_1448
| ~ zcong(U_1446,U_1448,U_1447)
| ~ ord_less_int(U_1448,U_1447)
| ~ ord_less_eq_int(zero_zero_int,U_1448)
| ~ ord_less_int(U_1446,U_1447)
| ~ ord_less_eq_int(zero_zero_int,U_1446)
| ~ is_int(U_1446)
| ~ is_int(U_1448) ),
inference(definitional_conversion,[status(esa)],[f_603_2]) ).
cnf(f_603_4,plain,
( U_1446 = U_1448
| ~ zcong(U_1446,U_1448,U_1447)
| ~ ord_less_int(U_1448,U_1447)
| ~ ord_less_eq_int(zero_zero_int,U_1448)
| ~ ord_less_int(U_1446,U_1447)
| ~ ord_less_eq_int(zero_zero_int,U_1446)
| ~ is_int(U_1446)
| ~ is_int(U_1448) ),
inference(clausify,[status(thm)],[f_603_3]) ).
fof(f_604_1,plain,
! [M,A] :
( A = zero_zero_int
| ~ zcong(A,zero_zero_int,M)
| ~ ord_less_int(A,M)
| ~ ord_less_eq_int(zero_zero_int,A)
| ~ is_int(A) ),
inference(fof_nnf,[status(thm)],[fact_585_zcong__zless__0]) ).
fof(f_604_2,plain,
! [U_1450,U_1449] :
( U_1449 = zero_zero_int
| ~ zcong(U_1449,zero_zero_int,U_1450)
| ~ ord_less_int(U_1449,U_1450)
| ~ ord_less_eq_int(zero_zero_int,U_1449)
| ~ is_int(U_1449) ),
inference(variable_rename,[status(thm)],[f_604_1]) ).
fof(f_604_3,plain,
! [U_1449,U_1450] :
( U_1449 = zero_zero_int
| ~ zcong(U_1449,zero_zero_int,U_1450)
| ~ ord_less_int(U_1449,U_1450)
| ~ ord_less_eq_int(zero_zero_int,U_1449)
| ~ is_int(U_1449) ),
inference(definitional_conversion,[status(esa)],[f_604_2]) ).
cnf(f_604_4,plain,
( U_1449 = zero_zero_int
| ~ zcong(U_1449,zero_zero_int,U_1450)
| ~ ord_less_int(U_1449,U_1450)
| ~ ord_less_eq_int(zero_zero_int,U_1449)
| ~ is_int(U_1449) ),
inference(clausify,[status(thm)],[f_604_3]) ).
fof(f_605_1,plain,
! [N,P,M] :
( dvd_dvd_int(P,N)
| dvd_dvd_int(P,M)
| ~ dvd_dvd_int(P,times_times_int(M,N))
| ~ zprime(P)
| ~ ord_less_eq_int(zero_zero_int,M) ),
inference(fof_nnf,[status(thm)],[fact_586_zprime__zdvd__zmult]) ).
fof(f_605_2,plain,
! [U_1453,U_1452,U_1451] :
( dvd_dvd_int(U_1452,U_1453)
| dvd_dvd_int(U_1452,U_1451)
| ~ dvd_dvd_int(U_1452,times_times_int(U_1451,U_1453))
| ~ zprime(U_1452)
| ~ ord_less_eq_int(zero_zero_int,U_1451) ),
inference(variable_rename,[status(thm)],[f_605_1]) ).
fof(f_605_3,plain,
! [U_1453,U_1452,U_1451] :
( dvd_dvd_int(U_1452,U_1453)
| dvd_dvd_int(U_1452,U_1451)
| ~ dvd_dvd_int(U_1452,times_times_int(U_1451,U_1453))
| ~ zprime(U_1452)
| ~ ord_less_eq_int(zero_zero_int,U_1451) ),
inference(definitional_conversion,[status(esa)],[f_605_2]) ).
cnf(f_605_4,plain,
( dvd_dvd_int(U_1452,U_1453)
| dvd_dvd_int(U_1452,U_1451)
| ~ dvd_dvd_int(U_1452,times_times_int(U_1451,U_1453))
| ~ zprime(U_1452)
| ~ ord_less_eq_int(zero_zero_int,U_1451) ),
inference(clausify,[status(thm)],[f_605_3]) ).
fof(f_606_1,plain,
quadRes(plus_plus_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_587__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096]) ).
fof(f_606_2,plain,
quadRes(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),number_number_of_int(min)),
inference(definitional_conversion,[status(esa)],[f_606_1]) ).
cnf(f_606_3,plain,
quadRes(plus_plus_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_606_2]) ).
fof(f_607_1,plain,
dvd_dvd_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min))),
inference(fof_nnf,[status(thm)],[fact_588__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096]) ).
fof(f_607_2,plain,
dvd_dvd_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min))),
inference(definitional_conversion,[status(esa)],[f_607_1]) ).
cnf(f_607_3,plain,
dvd_dvd_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min))),
inference(clausify,[status(thm)],[f_607_2]) ).
fof(f_608_1,plain,
! [J,K,M] :
( power_power_int(number_number_of_int(min),J) = power_power_int(number_number_of_int(min),K)
| ~ zcong(power_power_int(number_number_of_int(min),J),power_power_int(number_number_of_int(min),K),M)
| ~ ord_less_int(number_number_of_int(bit0(bit1(pls))),M) ),
inference(fof_nnf,[status(thm)],[fact_589_neg__one__power__eq__mod__m]) ).
fof(f_608_2,plain,
! [U_1456,U_1455,U_1454] :
( power_power_int(number_number_of_int(min),U_1456) = power_power_int(number_number_of_int(min),U_1455)
| ~ zcong(power_power_int(number_number_of_int(min),U_1456),power_power_int(number_number_of_int(min),U_1455),U_1454)
| ~ ord_less_int(number_number_of_int(bit0(bit1(pls))),U_1454) ),
inference(variable_rename,[status(thm)],[f_608_1]) ).
fof(f_608_3,plain,
! [U_1454,U_1455,U_1456] :
( power_power_int(number_number_of_int(min),U_1456) = power_power_int(number_number_of_int(min),U_1455)
| ~ zcong(power_power_int(number_number_of_int(min),U_1456),power_power_int(number_number_of_int(min),U_1455),U_1454)
| ~ ord_less_int(number_number_of_int(bit0(bit1(pls))),U_1454) ),
inference(definitional_conversion,[status(esa)],[f_608_2]) ).
cnf(f_608_4,plain,
( power_power_int(number_number_of_int(min),U_1456) = power_power_int(number_number_of_int(min),U_1455)
| ~ zcong(power_power_int(number_number_of_int(min),U_1456),power_power_int(number_number_of_int(min),U_1455),U_1454)
| ~ ord_less_int(number_number_of_int(bit0(bit1(pls))),U_1454) ),
inference(clausify,[status(thm)],[f_608_3]) ).
fof(f_609_1,plain,
minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
inference(fof_nnf,[status(thm)],[fact_590__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096]) ).
fof(f_609_2,plain,
minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
inference(definitional_conversion,[status(esa)],[f_609_1]) ).
cnf(f_609_3,plain,
minus_minus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)) = plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
inference(clausify,[status(thm)],[f_609_2]) ).
fof(f_610_1,plain,
( legendre(number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) != one_one_int
| quadRes(plus_plus_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_591__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N]) ).
fof(f_610_2,plain,
( legendre(number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) != one_one_int
| quadRes(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),number_number_of_int(min)) ),
inference(definitional_conversion,[status(esa)],[f_610_1]) ).
cnf(f_610_3,plain,
( legendre(number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) != one_one_int
| quadRes(plus_plus_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_610_2]) ).
fof(f_611_1,plain,
! [C_1,D_1,A,B_1,M] :
( zcong(minus_minus_int(A,C_1),minus_minus_int(B_1,D_1),M)
| ~ zcong(C_1,D_1,M)
| ~ zcong(A,B_1,M) ),
inference(fof_nnf,[status(thm)],[fact_592_zcong__zdiff]) ).
fof(f_611_2,plain,
! [U_1461,U_1460,U_1459,U_1458,U_1457] :
( zcong(minus_minus_int(U_1459,U_1461),minus_minus_int(U_1458,U_1460),U_1457)
| ~ zcong(U_1461,U_1460,U_1457)
| ~ zcong(U_1459,U_1458,U_1457) ),
inference(variable_rename,[status(thm)],[f_611_1]) ).
fof(f_611_3,plain,
! [U_1458,U_1457,U_1459,U_1460,U_1461] :
( zcong(minus_minus_int(U_1459,U_1461),minus_minus_int(U_1458,U_1460),U_1457)
| ~ zcong(U_1461,U_1460,U_1457)
| ~ zcong(U_1459,U_1458,U_1457) ),
inference(definitional_conversion,[status(esa)],[f_611_2]) ).
cnf(f_611_4,plain,
( zcong(minus_minus_int(U_1459,U_1461),minus_minus_int(U_1458,U_1460),U_1457)
| ~ zcong(U_1461,U_1460,U_1457)
| ~ zcong(U_1459,U_1458,U_1457) ),
inference(clausify,[status(thm)],[f_611_3]) ).
fof(f_612_1,plain,
! [K] :
( minus_minus_int(K,pls) = K
| ~ is_int(K) ),
inference(fof_nnf,[status(thm)],[fact_593_diff__bin__simps_I1_J]) ).
fof(f_612_2,plain,
! [U_1462] :
( minus_minus_int(U_1462,pls) = U_1462
| ~ is_int(U_1462) ),
inference(variable_rename,[status(thm)],[f_612_1]) ).
fof(f_612_3,plain,
! [U_1462] :
( minus_minus_int(U_1462,pls) = U_1462
| ~ is_int(U_1462) ),
inference(definitional_conversion,[status(esa)],[f_612_2]) ).
cnf(f_612_4,plain,
( minus_minus_int(U_1462,pls) = U_1462
| ~ is_int(U_1462) ),
inference(clausify,[status(thm)],[f_612_3]) ).
fof(f_613_1,plain,
! [K,L] : minus_minus_int(bit0(K),bit0(L)) = bit0(minus_minus_int(K,L)),
inference(fof_nnf,[status(thm)],[fact_594_diff__bin__simps_I7_J]) ).
fof(f_613_2,plain,
! [U_1464,U_1463] : minus_minus_int(bit0(U_1464),bit0(U_1463)) = bit0(minus_minus_int(U_1464,U_1463)),
inference(variable_rename,[status(thm)],[f_613_1]) ).
fof(f_613_3,plain,
! [U_1463,U_1464] : minus_minus_int(bit0(U_1464),bit0(U_1463)) = bit0(minus_minus_int(U_1464,U_1463)),
inference(definitional_conversion,[status(esa)],[f_613_2]) ).
cnf(f_613_4,plain,
minus_minus_int(bit0(U_1464),bit0(U_1463)) = bit0(minus_minus_int(U_1464,U_1463)),
inference(clausify,[status(thm)],[f_613_3]) ).
fof(f_614_1,plain,
! [Z1,Z2,W] : times_times_int(minus_minus_int(Z1,Z2),W) = minus_minus_int(times_times_int(Z1,W),times_times_int(Z2,W)),
inference(fof_nnf,[status(thm)],[fact_595_zdiff__zmult__distrib]) ).
fof(f_614_2,plain,
! [U_1467,U_1466,U_1465] : times_times_int(minus_minus_int(U_1467,U_1466),U_1465) = minus_minus_int(times_times_int(U_1467,U_1465),times_times_int(U_1466,U_1465)),
inference(variable_rename,[status(thm)],[f_614_1]) ).
fof(f_614_3,plain,
! [U_1465,U_1466,U_1467] : times_times_int(minus_minus_int(U_1467,U_1466),U_1465) = minus_minus_int(times_times_int(U_1467,U_1465),times_times_int(U_1466,U_1465)),
inference(definitional_conversion,[status(esa)],[f_614_2]) ).
cnf(f_614_4,plain,
times_times_int(minus_minus_int(U_1467,U_1466),U_1465) = minus_minus_int(times_times_int(U_1467,U_1465),times_times_int(U_1466,U_1465)),
inference(clausify,[status(thm)],[f_614_3]) ).
fof(f_615_1,plain,
! [W,Z1,Z2] : times_times_int(W,minus_minus_int(Z1,Z2)) = minus_minus_int(times_times_int(W,Z1),times_times_int(W,Z2)),
inference(fof_nnf,[status(thm)],[fact_596_zdiff__zmult__distrib2]) ).
fof(f_615_2,plain,
! [U_1470,U_1469,U_1468] : times_times_int(U_1470,minus_minus_int(U_1469,U_1468)) = minus_minus_int(times_times_int(U_1470,U_1469),times_times_int(U_1470,U_1468)),
inference(variable_rename,[status(thm)],[f_615_1]) ).
fof(f_615_3,plain,
! [U_1470,U_1469,U_1468] : times_times_int(U_1470,minus_minus_int(U_1469,U_1468)) = minus_minus_int(times_times_int(U_1470,U_1469),times_times_int(U_1470,U_1468)),
inference(definitional_conversion,[status(esa)],[f_615_2]) ).
cnf(f_615_4,plain,
times_times_int(U_1470,minus_minus_int(U_1469,U_1468)) = minus_minus_int(times_times_int(U_1470,U_1469),times_times_int(U_1470,U_1468)),
inference(clausify,[status(thm)],[f_615_3]) ).
fof(f_616_1,plain,
! [K,M,N] :
( dvd_dvd_int(K,M)
| ~ dvd_dvd_int(K,N)
| ~ dvd_dvd_int(K,minus_minus_int(M,N)) ),
inference(fof_nnf,[status(thm)],[fact_597_zdvd__zdiffD]) ).
fof(f_616_2,plain,
! [U_1473,U_1472,U_1471] :
( dvd_dvd_int(U_1473,U_1472)
| ~ dvd_dvd_int(U_1473,U_1471)
| ~ dvd_dvd_int(U_1473,minus_minus_int(U_1472,U_1471)) ),
inference(variable_rename,[status(thm)],[f_616_1]) ).
fof(f_616_3,plain,
! [U_1471,U_1472,U_1473] :
( dvd_dvd_int(U_1473,U_1472)
| ~ dvd_dvd_int(U_1473,U_1471)
| ~ dvd_dvd_int(U_1473,minus_minus_int(U_1472,U_1471)) ),
inference(definitional_conversion,[status(esa)],[f_616_2]) ).
cnf(f_616_4,plain,
( dvd_dvd_int(U_1473,U_1472)
| ~ dvd_dvd_int(U_1473,U_1471)
| ~ dvd_dvd_int(U_1473,minus_minus_int(U_1472,U_1471)) ),
inference(clausify,[status(thm)],[f_616_3]) ).
fof(f_617_1,plain,
! [V,W_2] : number_number_of_int(minus_minus_int(V,W_2)) = minus_minus_int(number_number_of_int(V),number_number_of_int(W_2)),
inference(fof_nnf,[status(thm)],[fact_598_number__of__diff]) ).
fof(f_617_2,plain,
! [U_1475,U_1474] : number_number_of_int(minus_minus_int(U_1475,U_1474)) = minus_minus_int(number_number_of_int(U_1475),number_number_of_int(U_1474)),
inference(variable_rename,[status(thm)],[f_617_1]) ).
fof(f_617_3,plain,
! [U_1474,U_1475] : number_number_of_int(minus_minus_int(U_1475,U_1474)) = minus_minus_int(number_number_of_int(U_1475),number_number_of_int(U_1474)),
inference(definitional_conversion,[status(esa)],[f_617_2]) ).
cnf(f_617_4,plain,
number_number_of_int(minus_minus_int(U_1475,U_1474)) = minus_minus_int(number_number_of_int(U_1475),number_number_of_int(U_1474)),
inference(clausify,[status(thm)],[f_617_3]) ).
fof(f_618_1,plain,
! [K,L] : minus_minus_int(bit1(K),bit0(L)) = bit1(minus_minus_int(K,L)),
inference(fof_nnf,[status(thm)],[fact_599_diff__bin__simps_I9_J]) ).
fof(f_618_2,plain,
! [U_1477,U_1476] : minus_minus_int(bit1(U_1477),bit0(U_1476)) = bit1(minus_minus_int(U_1477,U_1476)),
inference(variable_rename,[status(thm)],[f_618_1]) ).
fof(f_618_3,plain,
! [U_1476,U_1477] : minus_minus_int(bit1(U_1477),bit0(U_1476)) = bit1(minus_minus_int(U_1477,U_1476)),
inference(definitional_conversion,[status(esa)],[f_618_2]) ).
cnf(f_618_4,plain,
minus_minus_int(bit1(U_1477),bit0(U_1476)) = bit1(minus_minus_int(U_1477,U_1476)),
inference(clausify,[status(thm)],[f_618_3]) ).
fof(f_619_1,plain,
! [K,L] : minus_minus_int(bit1(K),bit1(L)) = bit0(minus_minus_int(K,L)),
inference(fof_nnf,[status(thm)],[fact_600_diff__bin__simps_I10_J]) ).
fof(f_619_2,plain,
! [U_1479,U_1478] : minus_minus_int(bit1(U_1479),bit1(U_1478)) = bit0(minus_minus_int(U_1479,U_1478)),
inference(variable_rename,[status(thm)],[f_619_1]) ).
fof(f_619_3,plain,
! [U_1478,U_1479] : minus_minus_int(bit1(U_1479),bit1(U_1478)) = bit0(minus_minus_int(U_1479,U_1478)),
inference(definitional_conversion,[status(esa)],[f_619_2]) ).
cnf(f_619_4,plain,
minus_minus_int(bit1(U_1479),bit1(U_1478)) = bit0(minus_minus_int(U_1479,U_1478)),
inference(clausify,[status(thm)],[f_619_3]) ).
fof(f_620_1,plain,
! [L] : minus_minus_int(pls,bit0(L)) = bit0(minus_minus_int(pls,L)),
inference(fof_nnf,[status(thm)],[fact_601_diff__bin__simps_I3_J]) ).
fof(f_620_2,plain,
! [U_1480] : minus_minus_int(pls,bit0(U_1480)) = bit0(minus_minus_int(pls,U_1480)),
inference(variable_rename,[status(thm)],[f_620_1]) ).
fof(f_620_3,plain,
! [U_1480] : minus_minus_int(pls,bit0(U_1480)) = bit0(minus_minus_int(pls,U_1480)),
inference(definitional_conversion,[status(esa)],[f_620_2]) ).
cnf(f_620_4,plain,
minus_minus_int(pls,bit0(U_1480)) = bit0(minus_minus_int(pls,U_1480)),
inference(clausify,[status(thm)],[f_620_3]) ).
fof(f_621_1,plain,
! [K_1,L_1] :
( ( ord_less_int(K_1,L_1)
| ~ ord_less_int(minus_minus_int(K_1,L_1),zero_zero_int) )
& ( ord_less_int(minus_minus_int(K_1,L_1),zero_zero_int)
| ~ ord_less_int(K_1,L_1) ) ),
inference(fof_nnf,[status(thm)],[fact_602_less__bin__lemma]) ).
fof(f_621_2,plain,
! [U_1482,U_1481] :
( ( ord_less_int(U_1482,U_1481)
| ~ ord_less_int(minus_minus_int(U_1482,U_1481),zero_zero_int) )
& ( ord_less_int(minus_minus_int(U_1482,U_1481),zero_zero_int)
| ~ ord_less_int(U_1482,U_1481) ) ),
inference(variable_rename,[status(thm)],[f_621_1]) ).
fof(f_621_3,plain,
( ! [U_1486,U_1484] :
( ord_less_int(U_1486,U_1484)
| ~ ord_less_int(minus_minus_int(U_1486,U_1484),zero_zero_int) )
& ! [U_1485,U_1483] :
( ord_less_int(minus_minus_int(U_1485,U_1483),zero_zero_int)
| ~ ord_less_int(U_1485,U_1483) ) ),
inference(miniscope,[status(thm)],[f_621_2]) ).
fof(f_621_4,plain,
( ! [U_1484,U_1486] :
( ord_less_int(U_1486,U_1484)
| ~ ord_less_int(minus_minus_int(U_1486,U_1484),zero_zero_int) )
& ! [U_1485,U_1483] :
( ord_less_int(minus_minus_int(U_1485,U_1483),zero_zero_int)
| ~ ord_less_int(U_1485,U_1483) ) ),
inference(definitional_conversion,[status(esa)],[f_621_3]) ).
cnf(f_621_5,plain,
( ord_less_int(minus_minus_int(U_1485,U_1483),zero_zero_int)
| ~ ord_less_int(U_1485,U_1483) ),
inference(clausify,[status(thm)],[f_621_4]) ).
cnf(f_621_6,plain,
( ord_less_int(U_1486,U_1484)
| ~ ord_less_int(minus_minus_int(U_1486,U_1484),zero_zero_int) ),
inference(clausify,[status(thm)],[f_621_4]) ).
fof(f_622_1,plain,
! [A,R_1,B_1,M,C_1,D_1,N] : plus_plus_int(times_times_int(minus_minus_int(A,times_times_int(R_1,B_1)),M),times_times_int(minus_minus_int(C_1,times_times_int(R_1,D_1)),N)) = minus_minus_int(plus_plus_int(times_times_int(A,M),times_times_int(C_1,N)),times_times_int(R_1,plus_plus_int(times_times_int(B_1,M),times_times_int(D_1,N)))),
inference(fof_nnf,[status(thm)],[fact_603_xzgcda__linear__aux1]) ).
fof(f_622_2,plain,
! [U_1493,U_1492,U_1491,U_1490,U_1489,U_1488,U_1487] : plus_plus_int(times_times_int(minus_minus_int(U_1493,times_times_int(U_1492,U_1491)),U_1490),times_times_int(minus_minus_int(U_1489,times_times_int(U_1492,U_1488)),U_1487)) = minus_minus_int(plus_plus_int(times_times_int(U_1493,U_1490),times_times_int(U_1489,U_1487)),times_times_int(U_1492,plus_plus_int(times_times_int(U_1491,U_1490),times_times_int(U_1488,U_1487)))),
inference(variable_rename,[status(thm)],[f_622_1]) ).
fof(f_622_3,plain,
! [U_1487,U_1488,U_1489,U_1490,U_1491,U_1492,U_1493] : plus_plus_int(times_times_int(minus_minus_int(U_1493,times_times_int(U_1492,U_1491)),U_1490),times_times_int(minus_minus_int(U_1489,times_times_int(U_1492,U_1488)),U_1487)) = minus_minus_int(plus_plus_int(times_times_int(U_1493,U_1490),times_times_int(U_1489,U_1487)),times_times_int(U_1492,plus_plus_int(times_times_int(U_1491,U_1490),times_times_int(U_1488,U_1487)))),
inference(definitional_conversion,[status(esa)],[f_622_2]) ).
cnf(f_622_4,plain,
plus_plus_int(times_times_int(minus_minus_int(U_1493,times_times_int(U_1492,U_1491)),U_1490),times_times_int(minus_minus_int(U_1489,times_times_int(U_1492,U_1488)),U_1487)) = minus_minus_int(plus_plus_int(times_times_int(U_1493,U_1490),times_times_int(U_1489,U_1487)),times_times_int(U_1492,plus_plus_int(times_times_int(U_1491,U_1490),times_times_int(U_1488,U_1487)))),
inference(clausify,[status(thm)],[f_622_3]) ).
fof(f_623_1,plain,
! [A_1,B_2,Ma] :
( ( zcong(A_1,B_2,Ma)
| ~ dvd_dvd_int(Ma,minus_minus_int(A_1,B_2)) )
& ( dvd_dvd_int(Ma,minus_minus_int(A_1,B_2))
| ~ zcong(A_1,B_2,Ma) ) ),
inference(fof_nnf,[status(thm)],[fact_604_zcong__def]) ).
fof(f_623_2,plain,
! [U_1496,U_1495,U_1494] :
( ( zcong(U_1496,U_1495,U_1494)
| ~ dvd_dvd_int(U_1494,minus_minus_int(U_1496,U_1495)) )
& ( dvd_dvd_int(U_1494,minus_minus_int(U_1496,U_1495))
| ~ zcong(U_1496,U_1495,U_1494) ) ),
inference(variable_rename,[status(thm)],[f_623_1]) ).
fof(f_623_3,plain,
( ! [U_1502,U_1500,U_1498] :
( zcong(U_1502,U_1500,U_1498)
| ~ dvd_dvd_int(U_1498,minus_minus_int(U_1502,U_1500)) )
& ! [U_1501,U_1499,U_1497] :
( dvd_dvd_int(U_1497,minus_minus_int(U_1501,U_1499))
| ~ zcong(U_1501,U_1499,U_1497) ) ),
inference(miniscope,[status(thm)],[f_623_2]) ).
fof(f_623_4,plain,
( ! [U_1502,U_1498,U_1500] :
( zcong(U_1502,U_1500,U_1498)
| ~ dvd_dvd_int(U_1498,minus_minus_int(U_1502,U_1500)) )
& ! [U_1501,U_1497,U_1499] :
( dvd_dvd_int(U_1497,minus_minus_int(U_1501,U_1499))
| ~ zcong(U_1501,U_1499,U_1497) ) ),
inference(definitional_conversion,[status(esa)],[f_623_3]) ).
cnf(f_623_5,plain,
( dvd_dvd_int(U_1497,minus_minus_int(U_1501,U_1499))
| ~ zcong(U_1501,U_1499,U_1497) ),
inference(clausify,[status(thm)],[f_623_4]) ).
cnf(f_623_6,plain,
( zcong(U_1502,U_1500,U_1498)
| ~ dvd_dvd_int(U_1498,minus_minus_int(U_1502,U_1500)) ),
inference(clausify,[status(thm)],[f_623_4]) ).
fof(f_624_1,plain,
! [A,X_1] :
( ord_less_int(X_1,minus_minus_int(A,one_one_int))
| X_1 = minus_minus_int(A,one_one_int)
| ~ ord_less_int(X_1,A)
| ~ ord_less_int(zero_zero_int,X_1)
| ~ is_int(X_1) ),
inference(fof_nnf,[status(thm)],[fact_605_Euler_Oaux1]) ).
fof(f_624_2,plain,
! [U_1504,U_1503] :
( ord_less_int(U_1503,minus_minus_int(U_1504,one_one_int))
| U_1503 = minus_minus_int(U_1504,one_one_int)
| ~ ord_less_int(U_1503,U_1504)
| ~ ord_less_int(zero_zero_int,U_1503)
| ~ is_int(U_1503) ),
inference(variable_rename,[status(thm)],[f_624_1]) ).
fof(f_624_3,plain,
! [U_1504,U_1503] :
( ord_less_int(U_1503,minus_minus_int(U_1504,one_one_int))
| U_1503 = minus_minus_int(U_1504,one_one_int)
| ~ ord_less_int(U_1503,U_1504)
| ~ ord_less_int(zero_zero_int,U_1503)
| ~ is_int(U_1503) ),
inference(definitional_conversion,[status(esa)],[f_624_2]) ).
cnf(f_624_4,plain,
( ord_less_int(U_1503,minus_minus_int(U_1504,one_one_int))
| U_1503 = minus_minus_int(U_1504,one_one_int)
| ~ ord_less_int(U_1503,U_1504)
| ~ ord_less_int(zero_zero_int,U_1503)
| ~ is_int(U_1503) ),
inference(clausify,[status(thm)],[f_624_3]) ).
fof(f_625_1,plain,
! [W_1,Z_1] :
( ( ord_less_eq_int(W_1,minus_minus_int(Z_1,one_one_int))
| ~ ord_less_int(W_1,Z_1) )
& ( ord_less_int(W_1,Z_1)
| ~ ord_less_eq_int(W_1,minus_minus_int(Z_1,one_one_int)) ) ),
inference(fof_nnf,[status(thm)],[fact_606_zle__diff1__eq]) ).
fof(f_625_2,plain,
! [U_1506,U_1505] :
( ( ord_less_eq_int(U_1506,minus_minus_int(U_1505,one_one_int))
| ~ ord_less_int(U_1506,U_1505) )
& ( ord_less_int(U_1506,U_1505)
| ~ ord_less_eq_int(U_1506,minus_minus_int(U_1505,one_one_int)) ) ),
inference(variable_rename,[status(thm)],[f_625_1]) ).
fof(f_625_3,plain,
( ! [U_1510,U_1508] :
( ord_less_eq_int(U_1510,minus_minus_int(U_1508,one_one_int))
| ~ ord_less_int(U_1510,U_1508) )
& ! [U_1509,U_1507] :
( ord_less_int(U_1509,U_1507)
| ~ ord_less_eq_int(U_1509,minus_minus_int(U_1507,one_one_int)) ) ),
inference(miniscope,[status(thm)],[f_625_2]) ).
fof(f_625_4,plain,
( ! [U_1510,U_1508] :
( ord_less_eq_int(U_1510,minus_minus_int(U_1508,one_one_int))
| ~ ord_less_int(U_1510,U_1508) )
& ! [U_1509,U_1507] :
( ord_less_int(U_1509,U_1507)
| ~ ord_less_eq_int(U_1509,minus_minus_int(U_1507,one_one_int)) ) ),
inference(definitional_conversion,[status(esa)],[f_625_3]) ).
cnf(f_625_5,plain,
( ord_less_int(U_1509,U_1507)
| ~ ord_less_eq_int(U_1509,minus_minus_int(U_1507,one_one_int)) ),
inference(clausify,[status(thm)],[f_625_4]) ).
cnf(f_625_6,plain,
( ord_less_eq_int(U_1510,minus_minus_int(U_1508,one_one_int))
| ~ ord_less_int(U_1510,U_1508) ),
inference(clausify,[status(thm)],[f_625_4]) ).
fof(f_626_1,plain,
! [L] : minus_minus_int(pls,bit1(L)) = bit1(minus_minus_int(min,L)),
inference(fof_nnf,[status(thm)],[fact_607_diff__bin__simps_I4_J]) ).
fof(f_626_2,plain,
! [U_1511] : minus_minus_int(pls,bit1(U_1511)) = bit1(minus_minus_int(min,U_1511)),
inference(variable_rename,[status(thm)],[f_626_1]) ).
fof(f_626_3,plain,
! [U_1511] : minus_minus_int(pls,bit1(U_1511)) = bit1(minus_minus_int(min,U_1511)),
inference(definitional_conversion,[status(esa)],[f_626_2]) ).
cnf(f_626_4,plain,
minus_minus_int(pls,bit1(U_1511)) = bit1(minus_minus_int(min,U_1511)),
inference(clausify,[status(thm)],[f_626_3]) ).
fof(f_627_1,plain,
! [L] : minus_minus_int(min,bit1(L)) = bit0(minus_minus_int(min,L)),
inference(fof_nnf,[status(thm)],[fact_608_diff__bin__simps_I6_J]) ).
fof(f_627_2,plain,
! [U_1512] : minus_minus_int(min,bit1(U_1512)) = bit0(minus_minus_int(min,U_1512)),
inference(variable_rename,[status(thm)],[f_627_1]) ).
fof(f_627_3,plain,
! [U_1512] : minus_minus_int(min,bit1(U_1512)) = bit0(minus_minus_int(min,U_1512)),
inference(definitional_conversion,[status(esa)],[f_627_2]) ).
cnf(f_627_4,plain,
minus_minus_int(min,bit1(U_1512)) = bit0(minus_minus_int(min,U_1512)),
inference(clausify,[status(thm)],[f_627_3]) ).
fof(f_628_1,plain,
! [L] : minus_minus_int(min,bit0(L)) = bit1(minus_minus_int(min,L)),
inference(fof_nnf,[status(thm)],[fact_609_diff__bin__simps_I5_J]) ).
fof(f_628_2,plain,
! [U_1513] : minus_minus_int(min,bit0(U_1513)) = bit1(minus_minus_int(min,U_1513)),
inference(variable_rename,[status(thm)],[f_628_1]) ).
fof(f_628_3,plain,
! [U_1513] : minus_minus_int(min,bit0(U_1513)) = bit1(minus_minus_int(min,U_1513)),
inference(definitional_conversion,[status(esa)],[f_628_2]) ).
cnf(f_628_4,plain,
minus_minus_int(min,bit0(U_1513)) = bit1(minus_minus_int(min,U_1513)),
inference(clausify,[status(thm)],[f_628_3]) ).
fof(f_629_1,plain,
! [A_1,P_1] :
( ( zcong(times_times_int(A_1,minus_minus_int(P_1,one_one_int)),one_one_int,P_1)
| ~ zcong(A_1,minus_minus_int(P_1,one_one_int),P_1) )
& ( zcong(A_1,minus_minus_int(P_1,one_one_int),P_1)
| ~ zcong(times_times_int(A_1,minus_minus_int(P_1,one_one_int)),one_one_int,P_1) ) ),
inference(fof_nnf,[status(thm)],[fact_610_inv__not__p__minus__1__aux]) ).
fof(f_629_2,plain,
! [U_1515,U_1514] :
( ( zcong(times_times_int(U_1515,minus_minus_int(U_1514,one_one_int)),one_one_int,U_1514)
| ~ zcong(U_1515,minus_minus_int(U_1514,one_one_int),U_1514) )
& ( zcong(U_1515,minus_minus_int(U_1514,one_one_int),U_1514)
| ~ zcong(times_times_int(U_1515,minus_minus_int(U_1514,one_one_int)),one_one_int,U_1514) ) ),
inference(variable_rename,[status(thm)],[f_629_1]) ).
fof(f_629_3,plain,
( ! [U_1519,U_1517] :
( zcong(times_times_int(U_1519,minus_minus_int(U_1517,one_one_int)),one_one_int,U_1517)
| ~ zcong(U_1519,minus_minus_int(U_1517,one_one_int),U_1517) )
& ! [U_1518,U_1516] :
( zcong(U_1518,minus_minus_int(U_1516,one_one_int),U_1516)
| ~ zcong(times_times_int(U_1518,minus_minus_int(U_1516,one_one_int)),one_one_int,U_1516) ) ),
inference(miniscope,[status(thm)],[f_629_2]) ).
fof(f_629_4,plain,
( ! [U_1519,U_1517] :
( zcong(times_times_int(U_1519,minus_minus_int(U_1517,one_one_int)),one_one_int,U_1517)
| ~ zcong(U_1519,minus_minus_int(U_1517,one_one_int),U_1517) )
& ! [U_1518,U_1516] :
( zcong(U_1518,minus_minus_int(U_1516,one_one_int),U_1516)
| ~ zcong(times_times_int(U_1518,minus_minus_int(U_1516,one_one_int)),one_one_int,U_1516) ) ),
inference(definitional_conversion,[status(esa)],[f_629_3]) ).
cnf(f_629_5,plain,
( zcong(U_1518,minus_minus_int(U_1516,one_one_int),U_1516)
| ~ zcong(times_times_int(U_1518,minus_minus_int(U_1516,one_one_int)),one_one_int,U_1516) ),
inference(clausify,[status(thm)],[f_629_4]) ).
cnf(f_629_6,plain,
( zcong(times_times_int(U_1519,minus_minus_int(U_1517,one_one_int)),one_one_int,U_1517)
| ~ zcong(U_1519,minus_minus_int(U_1517,one_one_int),U_1517) ),
inference(clausify,[status(thm)],[f_629_4]) ).
fof(f_630_1,plain,
! [A,B_1,P,Q] : times_times_int(twoSqu140629262sum2sq(product_Pair_int_int(A,B_1)),twoSqu140629262sum2sq(product_Pair_int_int(P,Q))) = twoSqu140629262sum2sq(product_Pair_int_int(plus_plus_int(times_times_int(A,P),times_times_int(B_1,Q)),minus_minus_int(times_times_int(A,Q),times_times_int(B_1,P)))),
inference(fof_nnf,[status(thm)],[fact_611_mult__sum2sq]) ).
fof(f_630_2,plain,
! [U_1523,U_1522,U_1521,U_1520] : times_times_int(twoSqu140629262sum2sq(product_Pair_int_int(U_1523,U_1522)),twoSqu140629262sum2sq(product_Pair_int_int(U_1521,U_1520))) = twoSqu140629262sum2sq(product_Pair_int_int(plus_plus_int(times_times_int(U_1523,U_1521),times_times_int(U_1522,U_1520)),minus_minus_int(times_times_int(U_1523,U_1520),times_times_int(U_1522,U_1521)))),
inference(variable_rename,[status(thm)],[f_630_1]) ).
fof(f_630_3,plain,
! [U_1520,U_1521,U_1522,U_1523] : times_times_int(twoSqu140629262sum2sq(product_Pair_int_int(U_1523,U_1522)),twoSqu140629262sum2sq(product_Pair_int_int(U_1521,U_1520))) = twoSqu140629262sum2sq(product_Pair_int_int(plus_plus_int(times_times_int(U_1523,U_1521),times_times_int(U_1522,U_1520)),minus_minus_int(times_times_int(U_1523,U_1520),times_times_int(U_1522,U_1521)))),
inference(definitional_conversion,[status(esa)],[f_630_2]) ).
cnf(f_630_4,plain,
times_times_int(twoSqu140629262sum2sq(product_Pair_int_int(U_1523,U_1522)),twoSqu140629262sum2sq(product_Pair_int_int(U_1521,U_1520))) = twoSqu140629262sum2sq(product_Pair_int_int(plus_plus_int(times_times_int(U_1523,U_1521),times_times_int(U_1522,U_1520)),minus_minus_int(times_times_int(U_1523,U_1520),times_times_int(U_1522,U_1521)))),
inference(clausify,[status(thm)],[f_630_3]) ).
fof(f_631_1,plain,
! [A,P] :
( zcong(A,minus_minus_int(P,one_one_int),P)
| zcong(A,one_one_int,P)
| ~ zcong(times_times_int(A,A),one_one_int,P)
| ~ ord_less_int(zero_zero_int,A)
| ~ zprime(P) ),
inference(fof_nnf,[status(thm)],[fact_612_zcong__square]) ).
fof(f_631_2,plain,
! [U_1525,U_1524] :
( zcong(U_1525,minus_minus_int(U_1524,one_one_int),U_1524)
| zcong(U_1525,one_one_int,U_1524)
| ~ zcong(times_times_int(U_1525,U_1525),one_one_int,U_1524)
| ~ ord_less_int(zero_zero_int,U_1525)
| ~ zprime(U_1524) ),
inference(variable_rename,[status(thm)],[f_631_1]) ).
fof(f_631_3,plain,
! [U_1525,U_1524] :
( zcong(U_1525,minus_minus_int(U_1524,one_one_int),U_1524)
| zcong(U_1525,one_one_int,U_1524)
| ~ zcong(times_times_int(U_1525,U_1525),one_one_int,U_1524)
| ~ ord_less_int(zero_zero_int,U_1525)
| ~ zprime(U_1524) ),
inference(definitional_conversion,[status(esa)],[f_631_2]) ).
cnf(f_631_4,plain,
( zcong(U_1525,minus_minus_int(U_1524,one_one_int),U_1524)
| zcong(U_1525,one_one_int,U_1524)
| ~ zcong(times_times_int(U_1525,U_1525),one_one_int,U_1524)
| ~ ord_less_int(zero_zero_int,U_1525)
| ~ zprime(U_1524) ),
inference(clausify,[status(thm)],[f_631_3]) ).
fof(f_632_1,plain,
! [A,P] :
( A = minus_minus_int(P,one_one_int)
| A = one_one_int
| ~ zcong(times_times_int(A,A),one_one_int,P)
| ~ ord_less_int(A,P)
| ~ ord_less_int(zero_zero_int,A)
| ~ zprime(P)
| ~ is_int(A) ),
inference(fof_nnf,[status(thm)],[fact_613_zcong__square__zless]) ).
fof(f_632_2,plain,
! [U_1527,U_1526] :
( U_1527 = minus_minus_int(U_1526,one_one_int)
| U_1527 = one_one_int
| ~ zcong(times_times_int(U_1527,U_1527),one_one_int,U_1526)
| ~ ord_less_int(U_1527,U_1526)
| ~ ord_less_int(zero_zero_int,U_1527)
| ~ zprime(U_1526)
| ~ is_int(U_1527) ),
inference(variable_rename,[status(thm)],[f_632_1]) ).
fof(f_632_3,plain,
! [U_1527] :
( ! [U_1526] :
( U_1527 = minus_minus_int(U_1526,one_one_int)
| U_1527 = one_one_int
| ~ zcong(times_times_int(U_1527,U_1527),one_one_int,U_1526)
| ~ ord_less_int(U_1527,U_1526)
| ~ ord_less_int(zero_zero_int,U_1527)
| ~ zprime(U_1526) )
| ~ is_int(U_1527) ),
inference(miniscope,[status(thm)],[f_632_2]) ).
fof(f_632_4,plain,
! [U_1527,U_1526] :
( U_1527 = minus_minus_int(U_1526,one_one_int)
| U_1527 = one_one_int
| ~ zcong(times_times_int(U_1527,U_1527),one_one_int,U_1526)
| ~ ord_less_int(U_1527,U_1526)
| ~ ord_less_int(zero_zero_int,U_1527)
| ~ zprime(U_1526)
| ~ is_int(U_1527) ),
inference(definitional_conversion,[status(esa)],[f_632_3]) ).
cnf(f_632_5,plain,
( U_1527 = minus_minus_int(U_1526,one_one_int)
| U_1527 = one_one_int
| ~ zcong(times_times_int(U_1527,U_1527),one_one_int,U_1526)
| ~ ord_less_int(U_1527,U_1526)
| ~ ord_less_int(zero_zero_int,U_1527)
| ~ zprime(U_1526)
| ~ is_int(U_1527) ),
inference(clausify,[status(thm)],[f_632_4]) ).
fof(f_633_1,plain,
! [A,B_1] : times_times_int(plus_plus_int(A,B_1),minus_minus_int(A,B_1)) = minus_minus_int(power_power_int(A,number_number_of_nat(bit0(bit1(pls)))),power_power_int(B_1,number_number_of_nat(bit0(bit1(pls))))),
inference(fof_nnf,[status(thm)],[fact_614_zspecial__product]) ).
fof(f_633_2,plain,
! [U_1529,U_1528] : times_times_int(plus_plus_int(U_1529,U_1528),minus_minus_int(U_1529,U_1528)) = minus_minus_int(power_power_int(U_1529,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1528,number_number_of_nat(bit0(bit1(pls))))),
inference(variable_rename,[status(thm)],[f_633_1]) ).
fof(f_633_3,plain,
! [U_1528,U_1529] : times_times_int(plus_plus_int(U_1529,U_1528),minus_minus_int(U_1529,U_1528)) = minus_minus_int(power_power_int(U_1529,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1528,number_number_of_nat(bit0(bit1(pls))))),
inference(definitional_conversion,[status(esa)],[f_633_2]) ).
cnf(f_633_4,plain,
times_times_int(plus_plus_int(U_1529,U_1528),minus_minus_int(U_1529,U_1528)) = minus_minus_int(power_power_int(U_1529,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1528,number_number_of_nat(bit0(bit1(pls))))),
inference(clausify,[status(thm)],[f_633_3]) ).
fof(f_634_1,plain,
! [A,B_1] : power_power_int(minus_minus_int(A,B_1),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(minus_minus_int(power_power_int(A,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),A),B_1)),power_power_int(B_1,number_number_of_nat(bit0(bit1(pls))))),
inference(fof_nnf,[status(thm)],[fact_615_zdiff__power2]) ).
fof(f_634_2,plain,
! [U_1531,U_1530] : power_power_int(minus_minus_int(U_1531,U_1530),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(minus_minus_int(power_power_int(U_1531,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),U_1531),U_1530)),power_power_int(U_1530,number_number_of_nat(bit0(bit1(pls))))),
inference(variable_rename,[status(thm)],[f_634_1]) ).
fof(f_634_3,plain,
! [U_1531,U_1530] : power_power_int(minus_minus_int(U_1531,U_1530),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(minus_minus_int(power_power_int(U_1531,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),U_1531),U_1530)),power_power_int(U_1530,number_number_of_nat(bit0(bit1(pls))))),
inference(definitional_conversion,[status(esa)],[f_634_2]) ).
cnf(f_634_4,plain,
power_power_int(minus_minus_int(U_1531,U_1530),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(minus_minus_int(power_power_int(U_1531,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),U_1531),U_1530)),power_power_int(U_1530,number_number_of_nat(bit0(bit1(pls))))),
inference(clausify,[status(thm)],[f_634_3]) ).
fof(f_635_1,plain,
! [A,B_1] : power_power_int(minus_minus_int(A,B_1),number_number_of_nat(bit1(bit1(pls)))) = minus_minus_int(plus_plus_int(minus_minus_int(power_power_int(A,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(A,number_number_of_nat(bit0(bit1(pls))))),B_1)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),A),power_power_int(B_1,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(B_1,number_number_of_nat(bit1(bit1(pls))))),
inference(fof_nnf,[status(thm)],[fact_616_zdiff__power3]) ).
fof(f_635_2,plain,
! [U_1533,U_1532] : power_power_int(minus_minus_int(U_1533,U_1532),number_number_of_nat(bit1(bit1(pls)))) = minus_minus_int(plus_plus_int(minus_minus_int(power_power_int(U_1533,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(U_1533,number_number_of_nat(bit0(bit1(pls))))),U_1532)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),U_1533),power_power_int(U_1532,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(U_1532,number_number_of_nat(bit1(bit1(pls))))),
inference(variable_rename,[status(thm)],[f_635_1]) ).
fof(f_635_3,plain,
! [U_1532,U_1533] : power_power_int(minus_minus_int(U_1533,U_1532),number_number_of_nat(bit1(bit1(pls)))) = minus_minus_int(plus_plus_int(minus_minus_int(power_power_int(U_1533,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(U_1533,number_number_of_nat(bit0(bit1(pls))))),U_1532)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),U_1533),power_power_int(U_1532,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(U_1532,number_number_of_nat(bit1(bit1(pls))))),
inference(definitional_conversion,[status(esa)],[f_635_2]) ).
cnf(f_635_4,plain,
power_power_int(minus_minus_int(U_1533,U_1532),number_number_of_nat(bit1(bit1(pls)))) = minus_minus_int(plus_plus_int(minus_minus_int(power_power_int(U_1533,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(U_1533,number_number_of_nat(bit0(bit1(pls))))),U_1532)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),U_1533),power_power_int(U_1532,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(U_1532,number_number_of_nat(bit1(bit1(pls))))),
inference(clausify,[status(thm)],[f_635_3]) ).
fof(f_636_1,plain,
! [N] :
( power_power_int(number_number_of_int(min),N) = number_number_of_int(min)
| power_power_int(number_number_of_int(min),N) = one_one_int ),
inference(fof_nnf,[status(thm)],[fact_617_neg__one__power]) ).
fof(f_636_2,plain,
! [U_1534] :
( power_power_int(number_number_of_int(min),U_1534) = number_number_of_int(min)
| power_power_int(number_number_of_int(min),U_1534) = one_one_int ),
inference(variable_rename,[status(thm)],[f_636_1]) ).
fof(f_636_3,plain,
! [U_1534] :
( power_power_int(number_number_of_int(min),U_1534) = number_number_of_int(min)
| power_power_int(number_number_of_int(min),U_1534) = one_one_int ),
inference(definitional_conversion,[status(esa)],[f_636_2]) ).
cnf(f_636_4,plain,
( power_power_int(number_number_of_int(min),U_1534) = number_number_of_int(min)
| power_power_int(number_number_of_int(min),U_1534) = one_one_int ),
inference(clausify,[status(thm)],[f_636_3]) ).
fof(f_637_1,plain,
! [M] :
( legendre(number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),M),one_one_int)) = one_one_int
| ~ zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),M),one_one_int)) ),
inference(fof_nnf,[status(thm)],[fact_618_Legendre__1mod4]) ).
fof(f_637_2,plain,
! [U_1535] :
( legendre(number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),U_1535),one_one_int)) = one_one_int
| ~ zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),U_1535),one_one_int)) ),
inference(variable_rename,[status(thm)],[f_637_1]) ).
fof(f_637_3,plain,
! [U_1535] :
( legendre(number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),U_1535),one_one_int)) = one_one_int
| ~ zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),U_1535),one_one_int)) ),
inference(definitional_conversion,[status(esa)],[f_637_2]) ).
cnf(f_637_4,plain,
( legendre(number_number_of_int(min),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),U_1535),one_one_int)) = one_one_int
| ~ zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),U_1535),one_one_int)) ),
inference(clausify,[status(thm)],[f_637_3]) ).
fof(f_638_1,plain,
! [M] :
( ~ zcong(one_one_int,number_number_of_int(min),M)
| ~ ord_less_int(number_number_of_int(bit0(bit1(pls))),M) ),
inference(fof_nnf,[status(thm)],[fact_619_one__not__neg__one__mod__m]) ).
fof(f_638_2,plain,
! [U_1536] :
( ~ zcong(one_one_int,number_number_of_int(min),U_1536)
| ~ ord_less_int(number_number_of_int(bit0(bit1(pls))),U_1536) ),
inference(variable_rename,[status(thm)],[f_638_1]) ).
fof(f_638_3,plain,
! [U_1536] :
( ~ zcong(one_one_int,number_number_of_int(min),U_1536)
| ~ ord_less_int(number_number_of_int(bit0(bit1(pls))),U_1536) ),
inference(definitional_conversion,[status(esa)],[f_638_2]) ).
cnf(f_638_4,plain,
( ~ zcong(one_one_int,number_number_of_int(min),U_1536)
| ~ ord_less_int(number_number_of_int(bit0(bit1(pls))),U_1536) ),
inference(clausify,[status(thm)],[f_638_3]) ).
fof(f_639_1,plain,
! [X_1,P] :
( ~ zcong(X_1,one_one_int,P)
| ~ zcong(X_1,number_number_of_int(min),P)
| ~ ord_less_int(number_number_of_int(bit0(bit1(pls))),P) ),
inference(fof_nnf,[status(thm)],[fact_620_zcong__neg__1__impl__ne__1]) ).
fof(f_639_2,plain,
! [U_1538,U_1537] :
( ~ zcong(U_1538,one_one_int,U_1537)
| ~ zcong(U_1538,number_number_of_int(min),U_1537)
| ~ ord_less_int(number_number_of_int(bit0(bit1(pls))),U_1537) ),
inference(variable_rename,[status(thm)],[f_639_1]) ).
fof(f_639_3,plain,
! [U_1537,U_1538] :
( ~ zcong(U_1538,one_one_int,U_1537)
| ~ zcong(U_1538,number_number_of_int(min),U_1537)
| ~ ord_less_int(number_number_of_int(bit0(bit1(pls))),U_1537) ),
inference(definitional_conversion,[status(esa)],[f_639_2]) ).
cnf(f_639_4,plain,
( ~ zcong(U_1538,one_one_int,U_1537)
| ~ zcong(U_1538,number_number_of_int(min),U_1537)
| ~ ord_less_int(number_number_of_int(bit0(bit1(pls))),U_1537) ),
inference(clausify,[status(thm)],[f_639_3]) ).
fof(f_640_1,plain,
! [A,P] :
( ( ( ( legendre(A,P) = number_number_of_int(min)
| quadRes(P,A) )
& ( legendre(A,P) = one_one_int
| ~ quadRes(P,A) ) )
| zcong(A,zero_zero_int,P) )
& ( legendre(A,P) = zero_zero_int
| ~ zcong(A,zero_zero_int,P) ) ),
inference(fof_nnf,[status(thm)],[fact_621_Legendre__def]) ).
fof(f_640_2,plain,
! [U_1540,U_1539] :
( ( ( ( legendre(U_1540,U_1539) = number_number_of_int(min)
| quadRes(U_1539,U_1540) )
& ( legendre(U_1540,U_1539) = one_one_int
| ~ quadRes(U_1539,U_1540) ) )
| zcong(U_1540,zero_zero_int,U_1539) )
& ( legendre(U_1540,U_1539) = zero_zero_int
| ~ zcong(U_1540,zero_zero_int,U_1539) ) ),
inference(variable_rename,[status(thm)],[f_640_1]) ).
fof(f_640_3,plain,
( ! [U_1544,U_1542] :
( ( ( legendre(U_1544,U_1542) = number_number_of_int(min)
| quadRes(U_1542,U_1544) )
& ( legendre(U_1544,U_1542) = one_one_int
| ~ quadRes(U_1542,U_1544) ) )
| zcong(U_1544,zero_zero_int,U_1542) )
& ! [U_1543,U_1541] :
( legendre(U_1543,U_1541) = zero_zero_int
| ~ zcong(U_1543,zero_zero_int,U_1541) ) ),
inference(miniscope,[status(thm)],[f_640_2]) ).
fof(f_640_4,plain,
( ! [U_1542,U_1544] :
( legendre(U_1544,U_1542) = number_number_of_int(min)
| quadRes(U_1542,U_1544)
| ~ sP85(U_1542,U_1544) )
& ! [U_1542,U_1544] :
( legendre(U_1544,U_1542) = one_one_int
| ~ quadRes(U_1542,U_1544)
| ~ sP85(U_1542,U_1544) )
& ! [U_1542,U_1544] :
( sP85(U_1542,U_1544)
| zcong(U_1544,zero_zero_int,U_1542) )
& ! [U_1541,U_1543] :
( legendre(U_1543,U_1541) = zero_zero_int
| ~ zcong(U_1543,zero_zero_int,U_1541) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP85])],[f_640_3]) ).
cnf(f_640_5,plain,
( legendre(U_1543,U_1541) = zero_zero_int
| ~ zcong(U_1543,zero_zero_int,U_1541) ),
inference(clausify,[status(thm)],[f_640_4]) ).
cnf(f_640_6,plain,
( sP85(U_1542,U_1544)
| zcong(U_1544,zero_zero_int,U_1542) ),
inference(clausify,[status(thm)],[f_640_4]) ).
cnf(f_640_7,plain,
( legendre(U_1544,U_1542) = one_one_int
| ~ quadRes(U_1542,U_1544)
| ~ sP85(U_1542,U_1544) ),
inference(clausify,[status(thm)],[f_640_4]) ).
cnf(f_640_8,plain,
( legendre(U_1544,U_1542) = number_number_of_int(min)
| quadRes(U_1542,U_1544)
| ~ sP85(U_1542,U_1544) ),
inference(clausify,[status(thm)],[f_640_4]) ).
fof(f_641_1,plain,
! [N,M] :
( ord_less_eq_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls))),N),M)
| M = N
| M = zero_zero_nat
| ~ dvd_dvd_nat(N,M) ),
inference(fof_nnf,[status(thm)],[fact_622_divides__cases]) ).
fof(f_641_2,plain,
! [U_1546,U_1545] :
( ord_less_eq_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1546),U_1545)
| U_1545 = U_1546
| U_1545 = zero_zero_nat
| ~ dvd_dvd_nat(U_1546,U_1545) ),
inference(variable_rename,[status(thm)],[f_641_1]) ).
fof(f_641_3,plain,
! [U_1546,U_1545] :
( ord_less_eq_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1546),U_1545)
| U_1545 = U_1546
| U_1545 = zero_zero_nat
| ~ dvd_dvd_nat(U_1546,U_1545) ),
inference(definitional_conversion,[status(esa)],[f_641_2]) ).
cnf(f_641_4,plain,
( ord_less_eq_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls))),U_1546),U_1545)
| U_1545 = U_1546
| U_1545 = zero_zero_nat
| ~ dvd_dvd_nat(U_1546,U_1545) ),
inference(clausify,[status(thm)],[f_641_3]) ).
fof(f_642_1,plain,
! [X_2,Y_2] :
( ( ( dvd_dvd_nat(Y_2,X_2)
& dvd_dvd_nat(X_2,Y_2) )
| X_2 != Y_2 )
& ( X_2 = Y_2
| ~ dvd_dvd_nat(Y_2,X_2)
| ~ dvd_dvd_nat(X_2,Y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_623_divides__antisym]) ).
fof(f_642_2,plain,
! [U_1548,U_1547] :
( ( ( dvd_dvd_nat(U_1547,U_1548)
& dvd_dvd_nat(U_1548,U_1547) )
| U_1548 != U_1547 )
& ( U_1548 = U_1547
| ~ dvd_dvd_nat(U_1547,U_1548)
| ~ dvd_dvd_nat(U_1548,U_1547) ) ),
inference(variable_rename,[status(thm)],[f_642_1]) ).
fof(f_642_3,plain,
( ! [U_1552,U_1550] :
( ( dvd_dvd_nat(U_1550,U_1552)
& dvd_dvd_nat(U_1552,U_1550) )
| U_1552 != U_1550 )
& ! [U_1551,U_1549] :
( U_1551 = U_1549
| ~ dvd_dvd_nat(U_1549,U_1551)
| ~ dvd_dvd_nat(U_1551,U_1549) ) ),
inference(miniscope,[status(thm)],[f_642_2]) ).
fof(f_642_4,plain,
( ! [U_1550,U_1552] :
( dvd_dvd_nat(U_1550,U_1552)
| ~ sP86(U_1550,U_1552) )
& ! [U_1550,U_1552] :
( dvd_dvd_nat(U_1552,U_1550)
| ~ sP86(U_1550,U_1552) )
& ! [U_1550,U_1552] :
( sP86(U_1550,U_1552)
| U_1552 != U_1550 )
& ! [U_1549,U_1551] :
( U_1551 = U_1549
| ~ dvd_dvd_nat(U_1549,U_1551)
| ~ dvd_dvd_nat(U_1551,U_1549) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP86])],[f_642_3]) ).
cnf(f_642_5,plain,
( U_1551 = U_1549
| ~ dvd_dvd_nat(U_1549,U_1551)
| ~ dvd_dvd_nat(U_1551,U_1549) ),
inference(clausify,[status(thm)],[f_642_4]) ).
cnf(f_642_6,plain,
( sP86(U_1550,U_1552)
| U_1552 != U_1550 ),
inference(clausify,[status(thm)],[f_642_4]) ).
cnf(f_642_7,plain,
( dvd_dvd_nat(U_1552,U_1550)
| ~ sP86(U_1550,U_1552) ),
inference(clausify,[status(thm)],[f_642_4]) ).
cnf(f_642_8,plain,
( dvd_dvd_nat(U_1550,U_1552)
| ~ sP86(U_1550,U_1552) ),
inference(clausify,[status(thm)],[f_642_4]) ).
fof(f_643_1,plain,
! [D_1,C_1,A,B_1,M] :
( zcong(A,D_1,M)
| ~ zcong(C_1,D_1,M)
| B_1 != C_1
| ~ zcong(A,B_1,M) ),
inference(fof_nnf,[status(thm)],[fact_624_zcong__eq__trans]) ).
fof(f_643_2,plain,
! [U_1557,U_1556,U_1555,U_1554,U_1553] :
( zcong(U_1555,U_1557,U_1553)
| ~ zcong(U_1556,U_1557,U_1553)
| U_1554 != U_1556
| ~ zcong(U_1555,U_1554,U_1553) ),
inference(variable_rename,[status(thm)],[f_643_1]) ).
fof(f_643_3,plain,
! [U_1554,U_1553,U_1555,U_1556,U_1557] :
( zcong(U_1555,U_1557,U_1553)
| ~ zcong(U_1556,U_1557,U_1553)
| U_1554 != U_1556
| ~ zcong(U_1555,U_1554,U_1553) ),
inference(definitional_conversion,[status(esa)],[f_643_2]) ).
cnf(f_643_4,plain,
( zcong(U_1555,U_1557,U_1553)
| ~ zcong(U_1556,U_1557,U_1553)
| U_1554 != U_1556
| ~ zcong(U_1555,U_1554,U_1553) ),
inference(clausify,[status(thm)],[f_643_3]) ).
fof(f_644_1,plain,
! [N,M] :
( ( times_times_nat(M,N) = plus_plus_nat(N,times_times_nat(minus_minus_nat(M,one_one_nat),N))
| M = zero_zero_nat )
& ( times_times_nat(M,N) = zero_zero_nat
| M != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_625_mult__eq__if]) ).
fof(f_644_2,plain,
! [U_1559,U_1558] :
( ( times_times_nat(U_1558,U_1559) = plus_plus_nat(U_1559,times_times_nat(minus_minus_nat(U_1558,one_one_nat),U_1559))
| U_1558 = zero_zero_nat )
& ( times_times_nat(U_1558,U_1559) = zero_zero_nat
| U_1558 != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_644_1]) ).
fof(f_644_3,plain,
( ! [U_1563,U_1561] :
( times_times_nat(U_1561,U_1563) = plus_plus_nat(U_1563,times_times_nat(minus_minus_nat(U_1561,one_one_nat),U_1563))
| U_1561 = zero_zero_nat )
& ! [U_1562,U_1560] :
( times_times_nat(U_1560,U_1562) = zero_zero_nat
| U_1560 != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_644_2]) ).
fof(f_644_4,plain,
( ! [U_1561,U_1563] :
( times_times_nat(U_1561,U_1563) = plus_plus_nat(U_1563,times_times_nat(minus_minus_nat(U_1561,one_one_nat),U_1563))
| U_1561 = zero_zero_nat )
& ! [U_1560,U_1562] :
( times_times_nat(U_1560,U_1562) = zero_zero_nat
| U_1560 != zero_zero_nat ) ),
inference(definitional_conversion,[status(esa)],[f_644_3]) ).
cnf(f_644_5,plain,
( times_times_nat(U_1560,U_1562) = zero_zero_nat
| U_1560 != zero_zero_nat ),
inference(clausify,[status(thm)],[f_644_4]) ).
cnf(f_644_6,plain,
( times_times_nat(U_1561,U_1563) = plus_plus_nat(U_1563,times_times_nat(minus_minus_nat(U_1561,one_one_nat),U_1563))
| U_1561 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_644_4]) ).
fof(f_645_1,plain,
! [P,M] :
( ( power_power_nat(P,M) = times_times_nat(P,power_power_nat(P,minus_minus_nat(M,one_one_nat)))
| M = zero_zero_nat )
& ( power_power_nat(P,M) = one_one_nat
| M != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_626_power__eq__if]) ).
fof(f_645_2,plain,
! [U_1565,U_1564] :
( ( power_power_nat(U_1565,U_1564) = times_times_nat(U_1565,power_power_nat(U_1565,minus_minus_nat(U_1564,one_one_nat)))
| U_1564 = zero_zero_nat )
& ( power_power_nat(U_1565,U_1564) = one_one_nat
| U_1564 != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_645_1]) ).
fof(f_645_3,plain,
( ! [U_1569,U_1567] :
( power_power_nat(U_1569,U_1567) = times_times_nat(U_1569,power_power_nat(U_1569,minus_minus_nat(U_1567,one_one_nat)))
| U_1567 = zero_zero_nat )
& ! [U_1568,U_1566] :
( power_power_nat(U_1568,U_1566) = one_one_nat
| U_1566 != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_645_2]) ).
fof(f_645_4,plain,
( ! [U_1567,U_1569] :
( power_power_nat(U_1569,U_1567) = times_times_nat(U_1569,power_power_nat(U_1569,minus_minus_nat(U_1567,one_one_nat)))
| U_1567 = zero_zero_nat )
& ! [U_1566,U_1568] :
( power_power_nat(U_1568,U_1566) = one_one_nat
| U_1566 != zero_zero_nat ) ),
inference(definitional_conversion,[status(esa)],[f_645_3]) ).
cnf(f_645_5,plain,
( power_power_nat(U_1568,U_1566) = one_one_nat
| U_1566 != zero_zero_nat ),
inference(clausify,[status(thm)],[f_645_4]) ).
cnf(f_645_6,plain,
( power_power_nat(U_1569,U_1567) = times_times_nat(U_1569,power_power_nat(U_1569,minus_minus_nat(U_1567,one_one_nat)))
| U_1567 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_645_4]) ).
fof(f_646_1,plain,
! [X_1,Y_1] : minus_minus_nat(power_power_nat(X_1,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(Y_1,number_number_of_nat(bit0(bit1(pls))))) = times_times_nat(plus_plus_nat(X_1,Y_1),minus_minus_nat(X_1,Y_1)),
inference(fof_nnf,[status(thm)],[fact_627_diff__square]) ).
fof(f_646_2,plain,
! [U_1571,U_1570] : minus_minus_nat(power_power_nat(U_1571,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(U_1570,number_number_of_nat(bit0(bit1(pls))))) = times_times_nat(plus_plus_nat(U_1571,U_1570),minus_minus_nat(U_1571,U_1570)),
inference(variable_rename,[status(thm)],[f_646_1]) ).
fof(f_646_3,plain,
! [U_1570,U_1571] : minus_minus_nat(power_power_nat(U_1571,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(U_1570,number_number_of_nat(bit0(bit1(pls))))) = times_times_nat(plus_plus_nat(U_1571,U_1570),minus_minus_nat(U_1571,U_1570)),
inference(definitional_conversion,[status(esa)],[f_646_2]) ).
cnf(f_646_4,plain,
minus_minus_nat(power_power_nat(U_1571,number_number_of_nat(bit0(bit1(pls)))),power_power_nat(U_1570,number_number_of_nat(bit0(bit1(pls))))) = times_times_nat(plus_plus_nat(U_1571,U_1570),minus_minus_nat(U_1571,U_1570)),
inference(clausify,[status(thm)],[f_646_3]) ).
fof(f_647_1,plain,
! [B_1,D_1,A] :
( dvd_dvd_nat(D_1,B_1)
| ~ dvd_dvd_nat(D_1,plus_plus_nat(A,B_1))
| ~ dvd_dvd_nat(D_1,A) ),
inference(fof_nnf,[status(thm)],[fact_628_divides__add__revr]) ).
fof(f_647_2,plain,
! [U_1574,U_1573,U_1572] :
( dvd_dvd_nat(U_1573,U_1574)
| ~ dvd_dvd_nat(U_1573,plus_plus_nat(U_1572,U_1574))
| ~ dvd_dvd_nat(U_1573,U_1572) ),
inference(variable_rename,[status(thm)],[f_647_1]) ).
fof(f_647_3,plain,
! [U_1573,U_1572,U_1574] :
( dvd_dvd_nat(U_1573,U_1574)
| ~ dvd_dvd_nat(U_1573,plus_plus_nat(U_1572,U_1574))
| ~ dvd_dvd_nat(U_1573,U_1572) ),
inference(definitional_conversion,[status(esa)],[f_647_2]) ).
cnf(f_647_4,plain,
( dvd_dvd_nat(U_1573,U_1574)
| ~ dvd_dvd_nat(U_1573,plus_plus_nat(U_1572,U_1574))
| ~ dvd_dvd_nat(U_1573,U_1572) ),
inference(clausify,[status(thm)],[f_647_3]) ).
fof(f_648_1,plain,
! [C_1,A,B_1] :
( dvd_dvd_nat(times_times_nat(C_1,A),times_times_nat(C_1,B_1))
| ~ dvd_dvd_nat(A,B_1) ),
inference(fof_nnf,[status(thm)],[fact_629_divides__mul__l]) ).
fof(f_648_2,plain,
! [U_1577,U_1576,U_1575] :
( dvd_dvd_nat(times_times_nat(U_1577,U_1576),times_times_nat(U_1577,U_1575))
| ~ dvd_dvd_nat(U_1576,U_1575) ),
inference(variable_rename,[status(thm)],[f_648_1]) ).
fof(f_648_3,plain,
! [U_1577,U_1576,U_1575] :
( dvd_dvd_nat(times_times_nat(U_1577,U_1576),times_times_nat(U_1577,U_1575))
| ~ dvd_dvd_nat(U_1576,U_1575) ),
inference(definitional_conversion,[status(esa)],[f_648_2]) ).
cnf(f_648_4,plain,
( dvd_dvd_nat(times_times_nat(U_1577,U_1576),times_times_nat(U_1577,U_1575))
| ~ dvd_dvd_nat(U_1576,U_1575) ),
inference(clausify,[status(thm)],[f_648_3]) ).
fof(f_649_1,plain,
! [C_1,A,B_1] :
( dvd_dvd_nat(times_times_nat(A,C_1),times_times_nat(B_1,C_1))
| ~ dvd_dvd_nat(A,B_1) ),
inference(fof_nnf,[status(thm)],[fact_630_divides__mul__r]) ).
fof(f_649_2,plain,
! [U_1580,U_1579,U_1578] :
( dvd_dvd_nat(times_times_nat(U_1579,U_1580),times_times_nat(U_1578,U_1580))
| ~ dvd_dvd_nat(U_1579,U_1578) ),
inference(variable_rename,[status(thm)],[f_649_1]) ).
fof(f_649_3,plain,
! [U_1579,U_1578,U_1580] :
( dvd_dvd_nat(times_times_nat(U_1579,U_1580),times_times_nat(U_1578,U_1580))
| ~ dvd_dvd_nat(U_1579,U_1578) ),
inference(definitional_conversion,[status(esa)],[f_649_2]) ).
cnf(f_649_4,plain,
( dvd_dvd_nat(times_times_nat(U_1579,U_1580),times_times_nat(U_1578,U_1580))
| ~ dvd_dvd_nat(U_1579,U_1578) ),
inference(clausify,[status(thm)],[f_649_3]) ).
fof(f_650_1,plain,
! [M] : zcong(M,zero_zero_int,M),
inference(fof_nnf,[status(thm)],[fact_631_zcong__id]) ).
fof(f_650_2,plain,
! [U_1581] : zcong(U_1581,zero_zero_int,U_1581),
inference(variable_rename,[status(thm)],[f_650_1]) ).
fof(f_650_3,plain,
! [U_1581] : zcong(U_1581,zero_zero_int,U_1581),
inference(definitional_conversion,[status(esa)],[f_650_2]) ).
cnf(f_650_4,plain,
zcong(U_1581,zero_zero_int,U_1581),
inference(clausify,[status(thm)],[f_650_3]) ).
fof(f_651_1,plain,
! [N_1,Ma] :
( ( times_times_nat(N_1,Ma) = one_one_nat
| Ma != one_one_nat
| N_1 != one_one_nat )
& ( ( Ma = one_one_nat
& N_1 = one_one_nat )
| times_times_nat(N_1,Ma) != one_one_nat ) ),
inference(fof_nnf,[status(thm)],[fact_632_nat__mult__eq__one]) ).
fof(f_651_2,plain,
! [U_1583,U_1582] :
( ( times_times_nat(U_1583,U_1582) = one_one_nat
| U_1582 != one_one_nat
| U_1583 != one_one_nat )
& ( ( U_1582 = one_one_nat
& U_1583 = one_one_nat )
| times_times_nat(U_1583,U_1582) != one_one_nat ) ),
inference(variable_rename,[status(thm)],[f_651_1]) ).
fof(f_651_3,plain,
( ! [U_1587,U_1585] :
( times_times_nat(U_1587,U_1585) = one_one_nat
| U_1585 != one_one_nat
| U_1587 != one_one_nat )
& ! [U_1586,U_1584] :
( ( U_1584 = one_one_nat
& U_1586 = one_one_nat )
| times_times_nat(U_1586,U_1584) != one_one_nat ) ),
inference(miniscope,[status(thm)],[f_651_2]) ).
fof(f_651_4,plain,
( ! [U_1586,U_1584] :
( U_1584 = one_one_nat
| ~ sP87(U_1586,U_1584) )
& ! [U_1586,U_1584] :
( U_1586 = one_one_nat
| ~ sP87(U_1586,U_1584) )
& ! [U_1585,U_1587] :
( times_times_nat(U_1587,U_1585) = one_one_nat
| U_1585 != one_one_nat
| U_1587 != one_one_nat )
& ! [U_1586,U_1584] :
( sP87(U_1586,U_1584)
| times_times_nat(U_1586,U_1584) != one_one_nat ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP87])],[f_651_3]) ).
cnf(f_651_5,plain,
( sP87(U_1586,U_1584)
| times_times_nat(U_1586,U_1584) != one_one_nat ),
inference(clausify,[status(thm)],[f_651_4]) ).
cnf(f_651_6,plain,
( times_times_nat(U_1587,U_1585) = one_one_nat
| U_1585 != one_one_nat
| U_1587 != one_one_nat ),
inference(clausify,[status(thm)],[f_651_4]) ).
cnf(f_651_7,plain,
( U_1586 = one_one_nat
| ~ sP87(U_1586,U_1584) ),
inference(clausify,[status(thm)],[f_651_4]) ).
cnf(f_651_8,plain,
( U_1584 = one_one_nat
| ~ sP87(U_1586,U_1584) ),
inference(clausify,[status(thm)],[f_651_4]) ).
fof(f_652_1,plain,
! [A,B_1,C_1] :
( A = plus_plus_int(C_1,B_1)
| minus_minus_int(A,B_1) != C_1
| ~ is_int(A) ),
inference(fof_nnf,[status(thm)],[fact_633_Int2_Oaux1]) ).
fof(f_652_2,plain,
! [U_1590,U_1589,U_1588] :
( U_1590 = plus_plus_int(U_1588,U_1589)
| minus_minus_int(U_1590,U_1589) != U_1588
| ~ is_int(U_1590) ),
inference(variable_rename,[status(thm)],[f_652_1]) ).
fof(f_652_3,plain,
! [U_1590] :
( ! [U_1589,U_1588] :
( U_1590 = plus_plus_int(U_1588,U_1589)
| minus_minus_int(U_1590,U_1589) != U_1588 )
| ~ is_int(U_1590) ),
inference(miniscope,[status(thm)],[f_652_2]) ).
fof(f_652_4,plain,
! [U_1588,U_1589,U_1590] :
( U_1590 = plus_plus_int(U_1588,U_1589)
| minus_minus_int(U_1590,U_1589) != U_1588
| ~ is_int(U_1590) ),
inference(definitional_conversion,[status(esa)],[f_652_3]) ).
cnf(f_652_5,plain,
( U_1590 = plus_plus_int(U_1588,U_1589)
| minus_minus_int(U_1590,U_1589) != U_1588
| ~ is_int(U_1590) ),
inference(clausify,[status(thm)],[f_652_4]) ).
fof(f_653_1,plain,
! [C,D,A_1,B_2,Ma] :
( ( ( zcong(C,times_times_int(D,A_1),Ma)
| ~ zcong(C,times_times_int(D,B_2),Ma) )
& ( zcong(C,times_times_int(D,B_2),Ma)
| ~ zcong(C,times_times_int(D,A_1),Ma) ) )
| ~ zcong(A_1,B_2,Ma) ),
inference(fof_nnf,[status(thm)],[fact_634_zcong__zmult__prop2]) ).
fof(f_653_2,plain,
! [U_1595,U_1594,U_1593,U_1592,U_1591] :
( ( ( zcong(U_1595,times_times_int(U_1594,U_1593),U_1591)
| ~ zcong(U_1595,times_times_int(U_1594,U_1592),U_1591) )
& ( zcong(U_1595,times_times_int(U_1594,U_1592),U_1591)
| ~ zcong(U_1595,times_times_int(U_1594,U_1593),U_1591) ) )
| ~ zcong(U_1593,U_1592,U_1591) ),
inference(variable_rename,[status(thm)],[f_653_1]) ).
fof(f_653_3,plain,
( ! [U_1593,U_1592,U_1591,U_1594,U_1595] :
( zcong(U_1595,times_times_int(U_1594,U_1593),U_1591)
| ~ zcong(U_1595,times_times_int(U_1594,U_1592),U_1591)
| ~ sP88(U_1593,U_1592,U_1591,U_1594,U_1595) )
& ! [U_1593,U_1592,U_1591,U_1594,U_1595] :
( zcong(U_1595,times_times_int(U_1594,U_1592),U_1591)
| ~ zcong(U_1595,times_times_int(U_1594,U_1593),U_1591)
| ~ sP88(U_1593,U_1592,U_1591,U_1594,U_1595) )
& ! [U_1593,U_1592,U_1591,U_1594,U_1595] :
( sP88(U_1593,U_1592,U_1591,U_1594,U_1595)
| ~ zcong(U_1593,U_1592,U_1591) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP88])],[f_653_2]) ).
cnf(f_653_4,plain,
( sP88(U_1593,U_1592,U_1591,U_1594,U_1595)
| ~ zcong(U_1593,U_1592,U_1591) ),
inference(clausify,[status(thm)],[f_653_3]) ).
cnf(f_653_5,plain,
( zcong(U_1595,times_times_int(U_1594,U_1592),U_1591)
| ~ zcong(U_1595,times_times_int(U_1594,U_1593),U_1591)
| ~ sP88(U_1593,U_1592,U_1591,U_1594,U_1595) ),
inference(clausify,[status(thm)],[f_653_3]) ).
cnf(f_653_6,plain,
( zcong(U_1595,times_times_int(U_1594,U_1593),U_1591)
| ~ zcong(U_1595,times_times_int(U_1594,U_1592),U_1591)
| ~ sP88(U_1593,U_1592,U_1591,U_1594,U_1595) ),
inference(clausify,[status(thm)],[f_653_3]) ).
fof(f_654_1,plain,
! [C,D,A_1,B_2,Ma] :
( ( ( zcong(C,times_times_int(A_1,D),Ma)
| ~ zcong(C,times_times_int(B_2,D),Ma) )
& ( zcong(C,times_times_int(B_2,D),Ma)
| ~ zcong(C,times_times_int(A_1,D),Ma) ) )
| ~ zcong(A_1,B_2,Ma) ),
inference(fof_nnf,[status(thm)],[fact_635_zcong__zmult__prop1]) ).
fof(f_654_2,plain,
! [U_1600,U_1599,U_1598,U_1597,U_1596] :
( ( ( zcong(U_1600,times_times_int(U_1598,U_1599),U_1596)
| ~ zcong(U_1600,times_times_int(U_1597,U_1599),U_1596) )
& ( zcong(U_1600,times_times_int(U_1597,U_1599),U_1596)
| ~ zcong(U_1600,times_times_int(U_1598,U_1599),U_1596) ) )
| ~ zcong(U_1598,U_1597,U_1596) ),
inference(variable_rename,[status(thm)],[f_654_1]) ).
fof(f_654_3,plain,
( ! [U_1600,U_1598,U_1596,U_1599,U_1597] :
( zcong(U_1600,times_times_int(U_1598,U_1599),U_1596)
| ~ zcong(U_1600,times_times_int(U_1597,U_1599),U_1596)
| ~ sP89(U_1600,U_1598,U_1596,U_1599,U_1597) )
& ! [U_1600,U_1598,U_1596,U_1599,U_1597] :
( zcong(U_1600,times_times_int(U_1597,U_1599),U_1596)
| ~ zcong(U_1600,times_times_int(U_1598,U_1599),U_1596)
| ~ sP89(U_1600,U_1598,U_1596,U_1599,U_1597) )
& ! [U_1600,U_1598,U_1596,U_1599,U_1597] :
( sP89(U_1600,U_1598,U_1596,U_1599,U_1597)
| ~ zcong(U_1598,U_1597,U_1596) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP89])],[f_654_2]) ).
cnf(f_654_4,plain,
( sP89(U_1600,U_1598,U_1596,U_1599,U_1597)
| ~ zcong(U_1598,U_1597,U_1596) ),
inference(clausify,[status(thm)],[f_654_3]) ).
cnf(f_654_5,plain,
( zcong(U_1600,times_times_int(U_1597,U_1599),U_1596)
| ~ zcong(U_1600,times_times_int(U_1598,U_1599),U_1596)
| ~ sP89(U_1600,U_1598,U_1596,U_1599,U_1597) ),
inference(clausify,[status(thm)],[f_654_3]) ).
cnf(f_654_6,plain,
( zcong(U_1600,times_times_int(U_1598,U_1599),U_1596)
| ~ zcong(U_1600,times_times_int(U_1597,U_1599),U_1596)
| ~ sP89(U_1600,U_1598,U_1596,U_1599,U_1597) ),
inference(clausify,[status(thm)],[f_654_3]) ).
fof(f_655_1,plain,
! [C_1,A,B_1,M] :
( zcong(plus_plus_int(A,C_1),plus_plus_int(B_1,C_1),M)
| ~ zcong(A,B_1,M) ),
inference(fof_nnf,[status(thm)],[fact_636_zcong__shift]) ).
fof(f_655_2,plain,
! [U_1604,U_1603,U_1602,U_1601] :
( zcong(plus_plus_int(U_1603,U_1604),plus_plus_int(U_1602,U_1604),U_1601)
| ~ zcong(U_1603,U_1602,U_1601) ),
inference(variable_rename,[status(thm)],[f_655_1]) ).
fof(f_655_3,plain,
! [U_1601,U_1603,U_1602,U_1604] :
( zcong(plus_plus_int(U_1603,U_1604),plus_plus_int(U_1602,U_1604),U_1601)
| ~ zcong(U_1603,U_1602,U_1601) ),
inference(definitional_conversion,[status(esa)],[f_655_2]) ).
cnf(f_655_4,plain,
( zcong(plus_plus_int(U_1603,U_1604),plus_plus_int(U_1602,U_1604),U_1601)
| ~ zcong(U_1603,U_1602,U_1601) ),
inference(clausify,[status(thm)],[f_655_3]) ).
fof(f_656_1,plain,
! [Ma,N_1] :
( ( power_power_nat(Ma,N_1) = zero_zero_nat
| Ma != zero_zero_nat
| N_1 = zero_zero_nat )
& ( ( Ma = zero_zero_nat
& N_1 != zero_zero_nat )
| power_power_nat(Ma,N_1) != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[fact_637_nat__power__eq__0__iff]) ).
fof(f_656_2,plain,
! [U_1606,U_1605] :
( ( power_power_nat(U_1606,U_1605) = zero_zero_nat
| U_1606 != zero_zero_nat
| U_1605 = zero_zero_nat )
& ( ( U_1606 = zero_zero_nat
& U_1605 != zero_zero_nat )
| power_power_nat(U_1606,U_1605) != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[f_656_1]) ).
fof(f_656_3,plain,
( ! [U_1610,U_1608] :
( power_power_nat(U_1610,U_1608) = zero_zero_nat
| U_1610 != zero_zero_nat
| U_1608 = zero_zero_nat )
& ! [U_1609,U_1607] :
( ( U_1609 = zero_zero_nat
& U_1607 != zero_zero_nat )
| power_power_nat(U_1609,U_1607) != zero_zero_nat ) ),
inference(miniscope,[status(thm)],[f_656_2]) ).
fof(f_656_4,plain,
( ! [U_1609,U_1607] :
( U_1609 = zero_zero_nat
| ~ sP90(U_1609,U_1607) )
& ! [U_1609,U_1607] :
( U_1607 != zero_zero_nat
| ~ sP90(U_1609,U_1607) )
& ! [U_1608,U_1610] :
( power_power_nat(U_1610,U_1608) = zero_zero_nat
| U_1610 != zero_zero_nat
| U_1608 = zero_zero_nat )
& ! [U_1609,U_1607] :
( sP90(U_1609,U_1607)
| power_power_nat(U_1609,U_1607) != zero_zero_nat ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP90])],[f_656_3]) ).
cnf(f_656_5,plain,
( sP90(U_1609,U_1607)
| power_power_nat(U_1609,U_1607) != zero_zero_nat ),
inference(clausify,[status(thm)],[f_656_4]) ).
cnf(f_656_6,plain,
( power_power_nat(U_1610,U_1608) = zero_zero_nat
| U_1610 != zero_zero_nat
| U_1608 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_656_4]) ).
cnf(f_656_7,plain,
( U_1607 != zero_zero_nat
| ~ sP90(U_1609,U_1607) ),
inference(clausify,[status(thm)],[f_656_4]) ).
cnf(f_656_8,plain,
( U_1609 = zero_zero_nat
| ~ sP90(U_1609,U_1607) ),
inference(clausify,[status(thm)],[f_656_4]) ).
fof(f_657_1,plain,
! [N,X_1,Y_1] :
( dvd_dvd_nat(power_power_nat(X_1,N),power_power_nat(Y_1,N))
| ~ dvd_dvd_nat(X_1,Y_1) ),
inference(fof_nnf,[status(thm)],[fact_638_divides__exp]) ).
fof(f_657_2,plain,
! [U_1613,U_1612,U_1611] :
( dvd_dvd_nat(power_power_nat(U_1612,U_1613),power_power_nat(U_1611,U_1613))
| ~ dvd_dvd_nat(U_1612,U_1611) ),
inference(variable_rename,[status(thm)],[f_657_1]) ).
fof(f_657_3,plain,
! [U_1612,U_1611,U_1613] :
( dvd_dvd_nat(power_power_nat(U_1612,U_1613),power_power_nat(U_1611,U_1613))
| ~ dvd_dvd_nat(U_1612,U_1611) ),
inference(definitional_conversion,[status(esa)],[f_657_2]) ).
cnf(f_657_4,plain,
( dvd_dvd_nat(power_power_nat(U_1612,U_1613),power_power_nat(U_1611,U_1613))
| ~ dvd_dvd_nat(U_1612,U_1611) ),
inference(clausify,[status(thm)],[f_657_3]) ).
fof(f_658_1,plain,
! [Z,X_1,Y_1,M] :
( zcong(power_power_int(X_1,Z),power_power_int(Y_1,Z),M)
| ~ zcong(X_1,Y_1,M) ),
inference(fof_nnf,[status(thm)],[fact_639_zcong__zpower]) ).
fof(f_658_2,plain,
! [U_1617,U_1616,U_1615,U_1614] :
( zcong(power_power_int(U_1616,U_1617),power_power_int(U_1615,U_1617),U_1614)
| ~ zcong(U_1616,U_1615,U_1614) ),
inference(variable_rename,[status(thm)],[f_658_1]) ).
fof(f_658_3,plain,
! [U_1615,U_1616,U_1617,U_1614] :
( zcong(power_power_int(U_1616,U_1617),power_power_int(U_1615,U_1617),U_1614)
| ~ zcong(U_1616,U_1615,U_1614) ),
inference(definitional_conversion,[status(esa)],[f_658_2]) ).
cnf(f_658_4,plain,
( zcong(power_power_int(U_1616,U_1617),power_power_int(U_1615,U_1617),U_1614)
| ~ zcong(U_1616,U_1615,U_1614) ),
inference(clausify,[status(thm)],[f_658_3]) ).
fof(f_659_1,plain,
! [A,B_1] :
( ord_less_eq_nat(A,B_1)
| B_1 = zero_zero_nat
| ~ dvd_dvd_nat(A,B_1) ),
inference(fof_nnf,[status(thm)],[fact_640_divides__ge]) ).
fof(f_659_2,plain,
! [U_1619,U_1618] :
( ord_less_eq_nat(U_1619,U_1618)
| U_1618 = zero_zero_nat
| ~ dvd_dvd_nat(U_1619,U_1618) ),
inference(variable_rename,[status(thm)],[f_659_1]) ).
fof(f_659_3,plain,
! [U_1619,U_1618] :
( ord_less_eq_nat(U_1619,U_1618)
| U_1618 = zero_zero_nat
| ~ dvd_dvd_nat(U_1619,U_1618) ),
inference(definitional_conversion,[status(esa)],[f_659_2]) ).
cnf(f_659_4,plain,
( ord_less_eq_nat(U_1619,U_1618)
| U_1618 = zero_zero_nat
| ~ dvd_dvd_nat(U_1619,U_1618) ),
inference(clausify,[status(thm)],[f_659_3]) ).
fof(f_660_1,plain,
! [Ma,K_1,N_1] :
( ( dvd_dvd_nat(times_times_nat(Ma,K_1),times_times_nat(N_1,K_1))
| ( ~ dvd_dvd_nat(Ma,N_1)
& K_1 != zero_zero_nat ) )
& ( dvd_dvd_nat(Ma,N_1)
| K_1 = zero_zero_nat
| ~ dvd_dvd_nat(times_times_nat(Ma,K_1),times_times_nat(N_1,K_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_641_nat__mult__dvd__cancel__disj_H]) ).
fof(f_660_2,plain,
! [U_1622,U_1621,U_1620] :
( ( dvd_dvd_nat(times_times_nat(U_1622,U_1621),times_times_nat(U_1620,U_1621))
| ( ~ dvd_dvd_nat(U_1622,U_1620)
& U_1621 != zero_zero_nat ) )
& ( dvd_dvd_nat(U_1622,U_1620)
| U_1621 = zero_zero_nat
| ~ dvd_dvd_nat(times_times_nat(U_1622,U_1621),times_times_nat(U_1620,U_1621)) ) ),
inference(variable_rename,[status(thm)],[f_660_1]) ).
fof(f_660_3,plain,
( ! [U_1628,U_1626,U_1624] :
( dvd_dvd_nat(times_times_nat(U_1628,U_1626),times_times_nat(U_1624,U_1626))
| ( ~ dvd_dvd_nat(U_1628,U_1624)
& U_1626 != zero_zero_nat ) )
& ! [U_1627,U_1625,U_1623] :
( dvd_dvd_nat(U_1627,U_1623)
| U_1625 = zero_zero_nat
| ~ dvd_dvd_nat(times_times_nat(U_1627,U_1625),times_times_nat(U_1623,U_1625)) ) ),
inference(miniscope,[status(thm)],[f_660_2]) ).
fof(f_660_4,plain,
( ! [U_1624,U_1626,U_1628] :
( ~ dvd_dvd_nat(U_1628,U_1624)
| ~ sP91(U_1624,U_1626,U_1628) )
& ! [U_1624,U_1626,U_1628] :
( U_1626 != zero_zero_nat
| ~ sP91(U_1624,U_1626,U_1628) )
& ! [U_1624,U_1626,U_1628] :
( dvd_dvd_nat(times_times_nat(U_1628,U_1626),times_times_nat(U_1624,U_1626))
| sP91(U_1624,U_1626,U_1628) )
& ! [U_1625,U_1623,U_1627] :
( dvd_dvd_nat(U_1627,U_1623)
| U_1625 = zero_zero_nat
| ~ dvd_dvd_nat(times_times_nat(U_1627,U_1625),times_times_nat(U_1623,U_1625)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP91])],[f_660_3]) ).
cnf(f_660_5,plain,
( dvd_dvd_nat(U_1627,U_1623)
| U_1625 = zero_zero_nat
| ~ dvd_dvd_nat(times_times_nat(U_1627,U_1625),times_times_nat(U_1623,U_1625)) ),
inference(clausify,[status(thm)],[f_660_4]) ).
cnf(f_660_6,plain,
( dvd_dvd_nat(times_times_nat(U_1628,U_1626),times_times_nat(U_1624,U_1626))
| sP91(U_1624,U_1626,U_1628) ),
inference(clausify,[status(thm)],[f_660_4]) ).
cnf(f_660_7,plain,
( U_1626 != zero_zero_nat
| ~ sP91(U_1624,U_1626,U_1628) ),
inference(clausify,[status(thm)],[f_660_4]) ).
cnf(f_660_8,plain,
( ~ dvd_dvd_nat(U_1628,U_1624)
| ~ sP91(U_1624,U_1626,U_1628) ),
inference(clausify,[status(thm)],[f_660_4]) ).
fof(f_661_1,plain,
! [M,X_1] :
( ~ zcong(X_1,zero_zero_int,M)
| ~ ord_less_int(X_1,M)
| ~ ord_less_int(zero_zero_int,X_1) ),
inference(fof_nnf,[status(thm)],[fact_642_zcong__not__zero]) ).
fof(f_661_2,plain,
! [U_1630,U_1629] :
( ~ zcong(U_1629,zero_zero_int,U_1630)
| ~ ord_less_int(U_1629,U_1630)
| ~ ord_less_int(zero_zero_int,U_1629) ),
inference(variable_rename,[status(thm)],[f_661_1]) ).
fof(f_661_3,plain,
! [U_1629,U_1630] :
( ~ zcong(U_1629,zero_zero_int,U_1630)
| ~ ord_less_int(U_1629,U_1630)
| ~ ord_less_int(zero_zero_int,U_1629) ),
inference(definitional_conversion,[status(esa)],[f_661_2]) ).
cnf(f_661_4,plain,
( ~ zcong(U_1629,zero_zero_int,U_1630)
| ~ ord_less_int(U_1629,U_1630)
| ~ ord_less_int(zero_zero_int,U_1629) ),
inference(clausify,[status(thm)],[f_661_3]) ).
fof(f_662_1,plain,
! [M,Y_1,X_1] :
( X_1 = Y_1
| ~ ord_less_int(Y_1,M)
| ~ ord_less_int(X_1,M)
| ~ zcong(X_1,Y_1,M)
| ~ ord_less_int(zero_zero_int,M)
| ~ ord_less_int(zero_zero_int,Y_1)
| ~ ord_less_int(zero_zero_int,X_1)
| ~ is_int(X_1)
| ~ is_int(Y_1) ),
inference(fof_nnf,[status(thm)],[fact_643_zcong__less__eq]) ).
fof(f_662_2,plain,
! [U_1633,U_1632,U_1631] :
( U_1631 = U_1632
| ~ ord_less_int(U_1632,U_1633)
| ~ ord_less_int(U_1631,U_1633)
| ~ zcong(U_1631,U_1632,U_1633)
| ~ ord_less_int(zero_zero_int,U_1633)
| ~ ord_less_int(zero_zero_int,U_1632)
| ~ ord_less_int(zero_zero_int,U_1631)
| ~ is_int(U_1631)
| ~ is_int(U_1632) ),
inference(variable_rename,[status(thm)],[f_662_1]) ).
fof(f_662_3,plain,
! [U_1631,U_1633,U_1632] :
( U_1631 = U_1632
| ~ ord_less_int(U_1632,U_1633)
| ~ ord_less_int(U_1631,U_1633)
| ~ zcong(U_1631,U_1632,U_1633)
| ~ ord_less_int(zero_zero_int,U_1633)
| ~ ord_less_int(zero_zero_int,U_1632)
| ~ ord_less_int(zero_zero_int,U_1631)
| ~ is_int(U_1631)
| ~ is_int(U_1632) ),
inference(definitional_conversion,[status(esa)],[f_662_2]) ).
cnf(f_662_4,plain,
( U_1631 = U_1632
| ~ ord_less_int(U_1632,U_1633)
| ~ ord_less_int(U_1631,U_1633)
| ~ zcong(U_1631,U_1632,U_1633)
| ~ ord_less_int(zero_zero_int,U_1633)
| ~ ord_less_int(zero_zero_int,U_1632)
| ~ ord_less_int(zero_zero_int,U_1631)
| ~ is_int(U_1631)
| ~ is_int(U_1632) ),
inference(clausify,[status(thm)],[f_662_3]) ).
fof(f_663_1,plain,
! [N,M] :
( ord_less_eq_int(N,M)
| ord_less_eq_int(M,zero_zero_int)
| ~ dvd_dvd_int(N,M) ),
inference(fof_nnf,[status(thm)],[fact_644_zdvd__bounds]) ).
fof(f_663_2,plain,
! [U_1635,U_1634] :
( ord_less_eq_int(U_1635,U_1634)
| ord_less_eq_int(U_1634,zero_zero_int)
| ~ dvd_dvd_int(U_1635,U_1634) ),
inference(variable_rename,[status(thm)],[f_663_1]) ).
fof(f_663_3,plain,
! [U_1635,U_1634] :
( ord_less_eq_int(U_1635,U_1634)
| ord_less_eq_int(U_1634,zero_zero_int)
| ~ dvd_dvd_int(U_1635,U_1634) ),
inference(definitional_conversion,[status(esa)],[f_663_2]) ).
cnf(f_663_4,plain,
( ord_less_eq_int(U_1635,U_1634)
| ord_less_eq_int(U_1634,zero_zero_int)
| ~ dvd_dvd_int(U_1635,U_1634) ),
inference(clausify,[status(thm)],[f_663_3]) ).
fof(f_664_1,plain,
! [X_1,Y_1,N] :
( dvd_dvd_nat(X_1,Y_1)
| ~ dvd_dvd_nat(power_power_nat(X_1,N),Y_1)
| N = zero_zero_nat ),
inference(fof_nnf,[status(thm)],[fact_645_divides__exp2]) ).
fof(f_664_2,plain,
! [U_1638,U_1637,U_1636] :
( dvd_dvd_nat(U_1638,U_1637)
| ~ dvd_dvd_nat(power_power_nat(U_1638,U_1636),U_1637)
| U_1636 = zero_zero_nat ),
inference(variable_rename,[status(thm)],[f_664_1]) ).
fof(f_664_3,plain,
! [U_1636,U_1638,U_1637] :
( dvd_dvd_nat(U_1638,U_1637)
| ~ dvd_dvd_nat(power_power_nat(U_1638,U_1636),U_1637)
| U_1636 = zero_zero_nat ),
inference(definitional_conversion,[status(esa)],[f_664_2]) ).
cnf(f_664_4,plain,
( dvd_dvd_nat(U_1638,U_1637)
| ~ dvd_dvd_nat(power_power_nat(U_1638,U_1636),U_1637)
| U_1636 = zero_zero_nat ),
inference(clausify,[status(thm)],[f_664_3]) ).
fof(f_665_1,plain,
! [A,N,B_1] :
( dvd_dvd_nat(A,B_1)
| N = zero_zero_nat
| ~ dvd_dvd_nat(power_power_nat(A,N),power_power_nat(B_1,N)) ),
inference(fof_nnf,[status(thm)],[fact_646_divides__rev]) ).
fof(f_665_2,plain,
! [U_1641,U_1640,U_1639] :
( dvd_dvd_nat(U_1641,U_1639)
| U_1640 = zero_zero_nat
| ~ dvd_dvd_nat(power_power_nat(U_1641,U_1640),power_power_nat(U_1639,U_1640)) ),
inference(variable_rename,[status(thm)],[f_665_1]) ).
fof(f_665_3,plain,
! [U_1641,U_1640,U_1639] :
( dvd_dvd_nat(U_1641,U_1639)
| U_1640 = zero_zero_nat
| ~ dvd_dvd_nat(power_power_nat(U_1641,U_1640),power_power_nat(U_1639,U_1640)) ),
inference(definitional_conversion,[status(esa)],[f_665_2]) ).
cnf(f_665_4,plain,
( dvd_dvd_nat(U_1641,U_1639)
| U_1640 = zero_zero_nat
| ~ dvd_dvd_nat(power_power_nat(U_1641,U_1640),power_power_nat(U_1639,U_1640)) ),
inference(clausify,[status(thm)],[f_665_3]) ).
fof(f_666_1,plain,
! [A_1,Ma] :
( ( zcong(A_1,zero_zero_int,Ma)
| ~ dvd_dvd_int(Ma,A_1) )
& ( dvd_dvd_int(Ma,A_1)
| ~ zcong(A_1,zero_zero_int,Ma) ) ),
inference(fof_nnf,[status(thm)],[fact_647_zcong__zero__equiv__div]) ).
fof(f_666_2,plain,
! [U_1643,U_1642] :
( ( zcong(U_1643,zero_zero_int,U_1642)
| ~ dvd_dvd_int(U_1642,U_1643) )
& ( dvd_dvd_int(U_1642,U_1643)
| ~ zcong(U_1643,zero_zero_int,U_1642) ) ),
inference(variable_rename,[status(thm)],[f_666_1]) ).
fof(f_666_3,plain,
( ! [U_1647,U_1645] :
( zcong(U_1647,zero_zero_int,U_1645)
| ~ dvd_dvd_int(U_1645,U_1647) )
& ! [U_1646,U_1644] :
( dvd_dvd_int(U_1644,U_1646)
| ~ zcong(U_1646,zero_zero_int,U_1644) ) ),
inference(miniscope,[status(thm)],[f_666_2]) ).
fof(f_666_4,plain,
( ! [U_1645,U_1647] :
( zcong(U_1647,zero_zero_int,U_1645)
| ~ dvd_dvd_int(U_1645,U_1647) )
& ! [U_1646,U_1644] :
( dvd_dvd_int(U_1644,U_1646)
| ~ zcong(U_1646,zero_zero_int,U_1644) ) ),
inference(definitional_conversion,[status(esa)],[f_666_3]) ).
cnf(f_666_5,plain,
( dvd_dvd_int(U_1644,U_1646)
| ~ zcong(U_1646,zero_zero_int,U_1644) ),
inference(clausify,[status(thm)],[f_666_4]) ).
cnf(f_666_6,plain,
( zcong(U_1647,zero_zero_int,U_1645)
| ~ dvd_dvd_int(U_1645,U_1647) ),
inference(clausify,[status(thm)],[f_666_4]) ).
fof(f_667_1,plain,
! [X_2,P_1] :
( ( zcong(X_2,zero_zero_int,P_1)
| ~ dvd_dvd_int(P_1,X_2) )
& ( dvd_dvd_int(P_1,X_2)
| ~ zcong(X_2,zero_zero_int,P_1) ) ),
inference(fof_nnf,[status(thm)],[fact_648_zcong__eq__zdvd__prop]) ).
fof(f_667_2,plain,
! [U_1649,U_1648] :
( ( zcong(U_1649,zero_zero_int,U_1648)
| ~ dvd_dvd_int(U_1648,U_1649) )
& ( dvd_dvd_int(U_1648,U_1649)
| ~ zcong(U_1649,zero_zero_int,U_1648) ) ),
inference(variable_rename,[status(thm)],[f_667_1]) ).
fof(f_667_3,plain,
( ! [U_1653,U_1651] :
( zcong(U_1653,zero_zero_int,U_1651)
| ~ dvd_dvd_int(U_1651,U_1653) )
& ! [U_1652,U_1650] :
( dvd_dvd_int(U_1650,U_1652)
| ~ zcong(U_1652,zero_zero_int,U_1650) ) ),
inference(miniscope,[status(thm)],[f_667_2]) ).
fof(f_667_4,plain,
( ! [U_1653,U_1651] :
( zcong(U_1653,zero_zero_int,U_1651)
| ~ dvd_dvd_int(U_1651,U_1653) )
& ! [U_1652,U_1650] :
( dvd_dvd_int(U_1650,U_1652)
| ~ zcong(U_1652,zero_zero_int,U_1650) ) ),
inference(definitional_conversion,[status(esa)],[f_667_3]) ).
cnf(f_667_5,plain,
( dvd_dvd_int(U_1650,U_1652)
| ~ zcong(U_1652,zero_zero_int,U_1650) ),
inference(clausify,[status(thm)],[f_667_4]) ).
cnf(f_667_6,plain,
( zcong(U_1653,zero_zero_int,U_1651)
| ~ dvd_dvd_int(U_1651,U_1653) ),
inference(clausify,[status(thm)],[f_667_4]) ).
fof(f_668_1,plain,
! [X_2,N_1] :
( ( power_power_nat(X_2,N_1) = one_one_nat
| ( N_1 != zero_zero_nat
& X_2 != one_one_nat ) )
& ( N_1 = zero_zero_nat
| X_2 = one_one_nat
| power_power_nat(X_2,N_1) != one_one_nat ) ),
inference(fof_nnf,[status(thm)],[fact_649_exp__eq__1]) ).
fof(f_668_2,plain,
! [U_1655,U_1654] :
( ( power_power_nat(U_1655,U_1654) = one_one_nat
| ( U_1654 != zero_zero_nat
& U_1655 != one_one_nat ) )
& ( U_1654 = zero_zero_nat
| U_1655 = one_one_nat
| power_power_nat(U_1655,U_1654) != one_one_nat ) ),
inference(variable_rename,[status(thm)],[f_668_1]) ).
fof(f_668_3,plain,
( ! [U_1659,U_1657] :
( power_power_nat(U_1659,U_1657) = one_one_nat
| ( U_1657 != zero_zero_nat
& U_1659 != one_one_nat ) )
& ! [U_1658,U_1656] :
( U_1656 = zero_zero_nat
| U_1658 = one_one_nat
| power_power_nat(U_1658,U_1656) != one_one_nat ) ),
inference(miniscope,[status(thm)],[f_668_2]) ).
fof(f_668_4,plain,
( ! [U_1659,U_1657] :
( U_1657 != zero_zero_nat
| ~ sP92(U_1659,U_1657) )
& ! [U_1659,U_1657] :
( U_1659 != one_one_nat
| ~ sP92(U_1659,U_1657) )
& ! [U_1659,U_1657] :
( power_power_nat(U_1659,U_1657) = one_one_nat
| sP92(U_1659,U_1657) )
& ! [U_1658,U_1656] :
( U_1656 = zero_zero_nat
| U_1658 = one_one_nat
| power_power_nat(U_1658,U_1656) != one_one_nat ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP92])],[f_668_3]) ).
cnf(f_668_5,plain,
( U_1656 = zero_zero_nat
| U_1658 = one_one_nat
| power_power_nat(U_1658,U_1656) != one_one_nat ),
inference(clausify,[status(thm)],[f_668_4]) ).
cnf(f_668_6,plain,
( power_power_nat(U_1659,U_1657) = one_one_nat
| sP92(U_1659,U_1657) ),
inference(clausify,[status(thm)],[f_668_4]) ).
cnf(f_668_7,plain,
( U_1659 != one_one_nat
| ~ sP92(U_1659,U_1657) ),
inference(clausify,[status(thm)],[f_668_4]) ).
cnf(f_668_8,plain,
( U_1657 != zero_zero_nat
| ~ sP92(U_1659,U_1657) ),
inference(clausify,[status(thm)],[f_668_4]) ).
fof(f_669_1,plain,
! [M,N,P] :
( dvd_dvd_int(P,N)
| dvd_dvd_int(P,M)
| ~ dvd_dvd_int(P,times_times_int(M,N))
| ~ zprime(P) ),
inference(fof_nnf,[status(thm)],[fact_650_zprime__zdvd__zmult__better]) ).
fof(f_669_2,plain,
! [U_1662,U_1661,U_1660] :
( dvd_dvd_int(U_1660,U_1661)
| dvd_dvd_int(U_1660,U_1662)
| ~ dvd_dvd_int(U_1660,times_times_int(U_1662,U_1661))
| ~ zprime(U_1660) ),
inference(variable_rename,[status(thm)],[f_669_1]) ).
fof(f_669_3,plain,
! [U_1660,U_1661,U_1662] :
( dvd_dvd_int(U_1660,U_1661)
| dvd_dvd_int(U_1660,U_1662)
| ~ dvd_dvd_int(U_1660,times_times_int(U_1662,U_1661))
| ~ zprime(U_1660) ),
inference(definitional_conversion,[status(esa)],[f_669_2]) ).
cnf(f_669_4,plain,
( dvd_dvd_int(U_1660,U_1661)
| dvd_dvd_int(U_1660,U_1662)
| ~ dvd_dvd_int(U_1660,times_times_int(U_1662,U_1661))
| ~ zprime(U_1660) ),
inference(clausify,[status(thm)],[f_669_3]) ).
fof(f_670_1,plain,
! [M,X_1] :
( X_1 = zero_zero_int
| ~ zcong(X_1,zero_zero_int,M)
| ~ ord_less_int(X_1,M)
| ~ ord_less_eq_int(zero_zero_int,X_1)
| ~ is_int(X_1) ),
inference(fof_nnf,[status(thm)],[fact_651_Int2_Ozcong__zero]) ).
fof(f_670_2,plain,
! [U_1664,U_1663] :
( U_1663 = zero_zero_int
| ~ zcong(U_1663,zero_zero_int,U_1664)
| ~ ord_less_int(U_1663,U_1664)
| ~ ord_less_eq_int(zero_zero_int,U_1663)
| ~ is_int(U_1663) ),
inference(variable_rename,[status(thm)],[f_670_1]) ).
fof(f_670_3,plain,
! [U_1663,U_1664] :
( U_1663 = zero_zero_int
| ~ zcong(U_1663,zero_zero_int,U_1664)
| ~ ord_less_int(U_1663,U_1664)
| ~ ord_less_eq_int(zero_zero_int,U_1663)
| ~ is_int(U_1663) ),
inference(definitional_conversion,[status(esa)],[f_670_2]) ).
cnf(f_670_4,plain,
( U_1663 = zero_zero_int
| ~ zcong(U_1663,zero_zero_int,U_1664)
| ~ ord_less_int(U_1663,U_1664)
| ~ ord_less_eq_int(zero_zero_int,U_1663)
| ~ is_int(U_1663) ),
inference(clausify,[status(thm)],[f_670_3]) ).
fof(f_671_1,plain,
! [P,Y_1,N] :
( dvd_dvd_int(P,power_power_int(Y_1,N))
| ~ dvd_dvd_int(P,Y_1)
| ~ ord_less_nat(zero_zero_nat,N) ),
inference(fof_nnf,[status(thm)],[fact_652_zpower__zdvd__prop1]) ).
fof(f_671_2,plain,
! [U_1667,U_1666,U_1665] :
( dvd_dvd_int(U_1667,power_power_int(U_1666,U_1665))
| ~ dvd_dvd_int(U_1667,U_1666)
| ~ ord_less_nat(zero_zero_nat,U_1665) ),
inference(variable_rename,[status(thm)],[f_671_1]) ).
fof(f_671_3,plain,
! [U_1665,U_1667,U_1666] :
( dvd_dvd_int(U_1667,power_power_int(U_1666,U_1665))
| ~ dvd_dvd_int(U_1667,U_1666)
| ~ ord_less_nat(zero_zero_nat,U_1665) ),
inference(definitional_conversion,[status(esa)],[f_671_2]) ).
cnf(f_671_4,plain,
( dvd_dvd_int(U_1667,power_power_int(U_1666,U_1665))
| ~ dvd_dvd_int(U_1667,U_1666)
| ~ ord_less_nat(zero_zero_nat,U_1665) ),
inference(clausify,[status(thm)],[f_671_3]) ).
fof(f_672_1,plain,
! [Y_1,X_1,P] :
( ~ zcong(times_times_int(X_1,Y_1),zero_zero_int,P)
| zcong(Y_1,zero_zero_int,P)
| zcong(X_1,zero_zero_int,P)
| ~ zprime(P) ),
inference(fof_nnf,[status(thm)],[fact_653_zcong__zmult__prop3]) ).
fof(f_672_2,plain,
! [U_1670,U_1669,U_1668] :
( ~ zcong(times_times_int(U_1669,U_1670),zero_zero_int,U_1668)
| zcong(U_1670,zero_zero_int,U_1668)
| zcong(U_1669,zero_zero_int,U_1668)
| ~ zprime(U_1668) ),
inference(variable_rename,[status(thm)],[f_672_1]) ).
fof(f_672_3,plain,
! [U_1669,U_1668,U_1670] :
( ~ zcong(times_times_int(U_1669,U_1670),zero_zero_int,U_1668)
| zcong(U_1670,zero_zero_int,U_1668)
| zcong(U_1669,zero_zero_int,U_1668)
| ~ zprime(U_1668) ),
inference(definitional_conversion,[status(esa)],[f_672_2]) ).
cnf(f_672_4,plain,
( ~ zcong(times_times_int(U_1669,U_1670),zero_zero_int,U_1668)
| zcong(U_1670,zero_zero_int,U_1668)
| zcong(U_1669,zero_zero_int,U_1668)
| ~ zprime(U_1668) ),
inference(clausify,[status(thm)],[f_672_3]) ).
fof(f_673_1,plain,
! [X_1,Q,N,R_1] :
( ~ dvd_dvd_nat(N,X_1)
| ~ ord_less_nat(R_1,N)
| ~ ord_less_nat(zero_zero_nat,R_1)
| X_1 != plus_plus_nat(times_times_nat(Q,N),R_1) ),
inference(fof_nnf,[status(thm)],[fact_654_divides__div__not]) ).
fof(f_673_2,plain,
! [U_1674,U_1673,U_1672,U_1671] :
( ~ dvd_dvd_nat(U_1672,U_1674)
| ~ ord_less_nat(U_1671,U_1672)
| ~ ord_less_nat(zero_zero_nat,U_1671)
| U_1674 != plus_plus_nat(times_times_nat(U_1673,U_1672),U_1671) ),
inference(variable_rename,[status(thm)],[f_673_1]) ).
fof(f_673_3,plain,
! [U_1671,U_1673,U_1672,U_1674] :
( ~ dvd_dvd_nat(U_1672,U_1674)
| ~ ord_less_nat(U_1671,U_1672)
| ~ ord_less_nat(zero_zero_nat,U_1671)
| U_1674 != plus_plus_nat(times_times_nat(U_1673,U_1672),U_1671) ),
inference(definitional_conversion,[status(esa)],[f_673_2]) ).
cnf(f_673_4,plain,
( ~ dvd_dvd_nat(U_1672,U_1674)
| ~ ord_less_nat(U_1671,U_1672)
| ~ ord_less_nat(zero_zero_nat,U_1671)
| U_1674 != plus_plus_nat(times_times_nat(U_1673,U_1672),U_1671) ),
inference(clausify,[status(thm)],[f_673_3]) ).
fof(f_674_1,plain,
! [B_1,A,P] :
( ~ zcong(times_times_int(A,B_1),zero_zero_int,P)
| zcong(B_1,zero_zero_int,P)
| zcong(A,zero_zero_int,P)
| ~ ord_less_int(zero_zero_int,A)
| ~ zprime(P) ),
inference(fof_nnf,[status(thm)],[fact_655_zcong__zprime__prod__zero__contra]) ).
fof(f_674_2,plain,
! [U_1677,U_1676,U_1675] :
( ~ zcong(times_times_int(U_1676,U_1677),zero_zero_int,U_1675)
| zcong(U_1677,zero_zero_int,U_1675)
| zcong(U_1676,zero_zero_int,U_1675)
| ~ ord_less_int(zero_zero_int,U_1676)
| ~ zprime(U_1675) ),
inference(variable_rename,[status(thm)],[f_674_1]) ).
fof(f_674_3,plain,
! [U_1677,U_1675,U_1676] :
( ~ zcong(times_times_int(U_1676,U_1677),zero_zero_int,U_1675)
| zcong(U_1677,zero_zero_int,U_1675)
| zcong(U_1676,zero_zero_int,U_1675)
| ~ ord_less_int(zero_zero_int,U_1676)
| ~ zprime(U_1675) ),
inference(definitional_conversion,[status(esa)],[f_674_2]) ).
cnf(f_674_4,plain,
( ~ zcong(times_times_int(U_1676,U_1677),zero_zero_int,U_1675)
| zcong(U_1677,zero_zero_int,U_1675)
| zcong(U_1676,zero_zero_int,U_1675)
| ~ ord_less_int(zero_zero_int,U_1676)
| ~ zprime(U_1675) ),
inference(clausify,[status(thm)],[f_674_3]) ).
fof(f_675_1,plain,
! [B_1,A,P] :
( zcong(B_1,zero_zero_int,P)
| zcong(A,zero_zero_int,P)
| ~ zcong(times_times_int(A,B_1),zero_zero_int,P)
| ~ ord_less_int(zero_zero_int,A)
| ~ zprime(P) ),
inference(fof_nnf,[status(thm)],[fact_656_zcong__zprime__prod__zero]) ).
fof(f_675_2,plain,
! [U_1680,U_1679,U_1678] :
( zcong(U_1680,zero_zero_int,U_1678)
| zcong(U_1679,zero_zero_int,U_1678)
| ~ zcong(times_times_int(U_1679,U_1680),zero_zero_int,U_1678)
| ~ ord_less_int(zero_zero_int,U_1679)
| ~ zprime(U_1678) ),
inference(variable_rename,[status(thm)],[f_675_1]) ).
fof(f_675_3,plain,
! [U_1680,U_1678,U_1679] :
( zcong(U_1680,zero_zero_int,U_1678)
| zcong(U_1679,zero_zero_int,U_1678)
| ~ zcong(times_times_int(U_1679,U_1680),zero_zero_int,U_1678)
| ~ ord_less_int(zero_zero_int,U_1679)
| ~ zprime(U_1678) ),
inference(definitional_conversion,[status(esa)],[f_675_2]) ).
cnf(f_675_4,plain,
( zcong(U_1680,zero_zero_int,U_1678)
| zcong(U_1679,zero_zero_int,U_1678)
| ~ zcong(times_times_int(U_1679,U_1680),zero_zero_int,U_1678)
| ~ ord_less_int(zero_zero_int,U_1679)
| ~ zprime(U_1678) ),
inference(clausify,[status(thm)],[f_675_3]) ).
fof(f_676_1,plain,
! [Y_1,N,P] :
( dvd_dvd_int(P,Y_1)
| ~ ord_less_nat(zero_zero_nat,N)
| ~ dvd_dvd_int(P,power_power_int(Y_1,N))
| ~ zprime(P) ),
inference(fof_nnf,[status(thm)],[fact_657_zpower__zdvd__prop2]) ).
fof(f_676_2,plain,
! [U_1683,U_1682,U_1681] :
( dvd_dvd_int(U_1681,U_1683)
| ~ ord_less_nat(zero_zero_nat,U_1682)
| ~ dvd_dvd_int(U_1681,power_power_int(U_1683,U_1682))
| ~ zprime(U_1681) ),
inference(variable_rename,[status(thm)],[f_676_1]) ).
fof(f_676_3,plain,
! [U_1683,U_1682,U_1681] :
( dvd_dvd_int(U_1681,U_1683)
| ~ ord_less_nat(zero_zero_nat,U_1682)
| ~ dvd_dvd_int(U_1681,power_power_int(U_1683,U_1682))
| ~ zprime(U_1681) ),
inference(definitional_conversion,[status(esa)],[f_676_2]) ).
cnf(f_676_4,plain,
( dvd_dvd_int(U_1681,U_1683)
| ~ ord_less_nat(zero_zero_nat,U_1682)
| ~ dvd_dvd_int(U_1681,power_power_int(U_1683,U_1682))
| ~ zprime(U_1681) ),
inference(clausify,[status(thm)],[f_676_3]) ).
fof(f_677_1,plain,
! [Ma,X_2] :
( ( quadRes(Ma,X_2)
| ! [Y] :
( ~ zcong(power_power_int(Y,number_number_of_nat(bit0(bit1(pls)))),X_2,Ma)
| ~ is_int(Y) ) )
& ( ? [Y] :
( zcong(power_power_int(Y,number_number_of_nat(bit0(bit1(pls)))),X_2,Ma)
& is_int(Y) )
| ~ quadRes(Ma,X_2) ) ),
inference(fof_nnf,[status(thm)],[fact_658_QuadRes__def]) ).
fof(f_677_2,plain,
! [U_1687,U_1686] :
( ( quadRes(U_1687,U_1686)
| ! [U_1685] :
( ~ zcong(power_power_int(U_1685,number_number_of_nat(bit0(bit1(pls)))),U_1686,U_1687)
| ~ is_int(U_1685) ) )
& ( ? [U_1684] :
( zcong(power_power_int(U_1684,number_number_of_nat(bit0(bit1(pls)))),U_1686,U_1687)
& is_int(U_1684) )
| ~ quadRes(U_1687,U_1686) ) ),
inference(variable_rename,[status(thm)],[f_677_1]) ).
fof(f_677_3,plain,
( ! [U_1691,U_1689] :
( quadRes(U_1691,U_1689)
| ! [U_1685] :
( ~ zcong(power_power_int(U_1685,number_number_of_nat(bit0(bit1(pls)))),U_1689,U_1691)
| ~ is_int(U_1685) ) )
& ! [U_1690,U_1688] :
( ? [U_1684] :
( zcong(power_power_int(U_1684,number_number_of_nat(bit0(bit1(pls)))),U_1688,U_1690)
& is_int(U_1684) )
| ~ quadRes(U_1690,U_1688) ) ),
inference(miniscope,[status(thm)],[f_677_2]) ).
fof(f_677_4,plain,
( ! [U_1691,U_1689] :
( quadRes(U_1691,U_1689)
| ! [U_1685] :
( ~ zcong(power_power_int(U_1685,number_number_of_nat(bit0(bit1(pls)))),U_1689,U_1691)
| ~ is_int(U_1685) ) )
& ! [U_1690,U_1688] :
( ( zcong(power_power_int(sK11(U_1690,U_1688),number_number_of_nat(bit0(bit1(pls)))),U_1688,U_1690)
& is_int(sK11(U_1690,U_1688)) )
| ~ quadRes(U_1690,U_1688) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_1684,sK11(U_1690,U_1688))],[f_677_3]) ).
fof(f_677_5,plain,
( ! [U_1690,U_1688] :
( zcong(power_power_int(sK11(U_1690,U_1688),number_number_of_nat(bit0(bit1(pls)))),U_1688,U_1690)
| ~ sP93(U_1690,U_1688) )
& ! [U_1690,U_1688] :
( is_int(sK11(U_1690,U_1688))
| ~ sP93(U_1690,U_1688) )
& ! [U_1685,U_1691,U_1689] :
( quadRes(U_1691,U_1689)
| ~ zcong(power_power_int(U_1685,number_number_of_nat(bit0(bit1(pls)))),U_1689,U_1691)
| ~ is_int(U_1685) )
& ! [U_1690,U_1688] :
( sP93(U_1690,U_1688)
| ~ quadRes(U_1690,U_1688) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP93])],[f_677_4]) ).
cnf(f_677_6,plain,
( sP93(U_1690,U_1688)
| ~ quadRes(U_1690,U_1688) ),
inference(clausify,[status(thm)],[f_677_5]) ).
cnf(f_677_7,plain,
( quadRes(U_1691,U_1689)
| ~ zcong(power_power_int(U_1685,number_number_of_nat(bit0(bit1(pls)))),U_1689,U_1691)
| ~ is_int(U_1685) ),
inference(clausify,[status(thm)],[f_677_5]) ).
cnf(f_677_8,plain,
( is_int(sK11(U_1690,U_1688))
| ~ sP93(U_1690,U_1688) ),
inference(clausify,[status(thm)],[f_677_5]) ).
cnf(f_677_9,plain,
( zcong(power_power_int(sK11(U_1690,U_1688),number_number_of_nat(bit0(bit1(pls)))),U_1688,U_1690)
| ~ sP93(U_1690,U_1688) ),
inference(clausify,[status(thm)],[f_677_5]) ).
fof(f_678_1,plain,
! [X_2,Y_2] :
( ( plus_plus_real(power_power_real(X_2,number_number_of_nat(bit0(bit1(pls)))),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 )
| plus_plus_real(power_power_real(X_2,number_number_of_nat(bit0(bit1(pls)))),power_power_real(Y_2,number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ) ),
inference(fof_nnf,[status(thm)],[fact_659_realpow__two__sum__zero__iff]) ).
fof(f_678_2,plain,
! [U_1693,U_1692] :
( ( plus_plus_real(power_power_real(U_1693,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1692,number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| U_1692 != zero_zero_real
| U_1693 != zero_zero_real )
& ( ( U_1692 = zero_zero_real
& U_1693 = zero_zero_real )
| plus_plus_real(power_power_real(U_1693,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1692,number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ) ),
inference(variable_rename,[status(thm)],[f_678_1]) ).
fof(f_678_3,plain,
( ! [U_1697,U_1695] :
( plus_plus_real(power_power_real(U_1697,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1695,number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| U_1695 != zero_zero_real
| U_1697 != zero_zero_real )
& ! [U_1696,U_1694] :
( ( U_1694 = zero_zero_real
& U_1696 = zero_zero_real )
| plus_plus_real(power_power_real(U_1696,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1694,number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ) ),
inference(miniscope,[status(thm)],[f_678_2]) ).
fof(f_678_4,plain,
( ! [U_1696,U_1694] :
( U_1694 = zero_zero_real
| ~ sP94(U_1696,U_1694) )
& ! [U_1696,U_1694] :
( U_1696 = zero_zero_real
| ~ sP94(U_1696,U_1694) )
& ! [U_1695,U_1697] :
( plus_plus_real(power_power_real(U_1697,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1695,number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| U_1695 != zero_zero_real
| U_1697 != zero_zero_real )
& ! [U_1696,U_1694] :
( sP94(U_1696,U_1694)
| plus_plus_real(power_power_real(U_1696,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1694,number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP94])],[f_678_3]) ).
cnf(f_678_5,plain,
( sP94(U_1696,U_1694)
| plus_plus_real(power_power_real(U_1696,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1694,number_number_of_nat(bit0(bit1(pls))))) != zero_zero_real ),
inference(clausify,[status(thm)],[f_678_4]) ).
cnf(f_678_6,plain,
( plus_plus_real(power_power_real(U_1697,number_number_of_nat(bit0(bit1(pls)))),power_power_real(U_1695,number_number_of_nat(bit0(bit1(pls))))) = zero_zero_real
| U_1695 != zero_zero_real
| U_1697 != zero_zero_real ),
inference(clausify,[status(thm)],[f_678_4]) ).
cnf(f_678_7,plain,
( U_1696 = zero_zero_real
| ~ sP94(U_1696,U_1694) ),
inference(clausify,[status(thm)],[f_678_4]) ).
cnf(f_678_8,plain,
( U_1694 = zero_zero_real
| ~ sP94(U_1696,U_1694) ),
inference(clausify,[status(thm)],[f_678_4]) ).
fof(f_679_1,plain,
! [R_1,Q,A] :
( ord_less_eq_int(one_one_int,Q)
| ~ ord_less_int(R_1,A)
| A != plus_plus_int(R_1,times_times_int(A,Q))
| ~ ord_less_int(zero_zero_int,A) ),
inference(fof_nnf,[status(thm)],[fact_660_self__quotient__aux1]) ).
fof(f_679_2,plain,
! [U_1700,U_1699,U_1698] :
( ord_less_eq_int(one_one_int,U_1699)
| ~ ord_less_int(U_1700,U_1698)
| U_1698 != plus_plus_int(U_1700,times_times_int(U_1698,U_1699))
| ~ ord_less_int(zero_zero_int,U_1698) ),
inference(variable_rename,[status(thm)],[f_679_1]) ).
fof(f_679_3,plain,
! [U_1699,U_1700,U_1698] :
( ord_less_eq_int(one_one_int,U_1699)
| ~ ord_less_int(U_1700,U_1698)
| U_1698 != plus_plus_int(U_1700,times_times_int(U_1698,U_1699))
| ~ ord_less_int(zero_zero_int,U_1698) ),
inference(definitional_conversion,[status(esa)],[f_679_2]) ).
cnf(f_679_4,plain,
( ord_less_eq_int(one_one_int,U_1699)
| ~ ord_less_int(U_1700,U_1698)
| U_1698 != plus_plus_int(U_1700,times_times_int(U_1698,U_1699))
| ~ ord_less_int(zero_zero_int,U_1698) ),
inference(clausify,[status(thm)],[f_679_3]) ).
fof(f_680_1,plain,
zero_zero_real != one_one_real,
inference(fof_nnf,[status(thm)],[fact_661_real__zero__not__eq__one]) ).
fof(f_680_2,plain,
zero_zero_real != one_one_real,
inference(definitional_conversion,[status(esa)],[f_680_1]) ).
cnf(f_680_3,plain,
zero_zero_real != one_one_real,
inference(clausify,[status(thm)],[f_680_2]) ).
fof(f_681_1,plain,
! [X_2,Y_2] :
( ( ord_less_eq_real(X_2,Y_2)
| ~ ord_less_eq_real(minus_minus_real(X_2,Y_2),zero_zero_real) )
& ( ord_less_eq_real(minus_minus_real(X_2,Y_2),zero_zero_real)
| ~ ord_less_eq_real(X_2,Y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_662_real__le__eq__diff]) ).
fof(f_681_2,plain,
! [U_1702,U_1701] :
( ( ord_less_eq_real(U_1702,U_1701)
| ~ ord_less_eq_real(minus_minus_real(U_1702,U_1701),zero_zero_real) )
& ( ord_less_eq_real(minus_minus_real(U_1702,U_1701),zero_zero_real)
| ~ ord_less_eq_real(U_1702,U_1701) ) ),
inference(variable_rename,[status(thm)],[f_681_1]) ).
fof(f_681_3,plain,
( ! [U_1706,U_1704] :
( ord_less_eq_real(U_1706,U_1704)
| ~ ord_less_eq_real(minus_minus_real(U_1706,U_1704),zero_zero_real) )
& ! [U_1705,U_1703] :
( ord_less_eq_real(minus_minus_real(U_1705,U_1703),zero_zero_real)
| ~ ord_less_eq_real(U_1705,U_1703) ) ),
inference(miniscope,[status(thm)],[f_681_2]) ).
fof(f_681_4,plain,
( ! [U_1706,U_1704] :
( ord_less_eq_real(U_1706,U_1704)
| ~ ord_less_eq_real(minus_minus_real(U_1706,U_1704),zero_zero_real) )
& ! [U_1705,U_1703] :
( ord_less_eq_real(minus_minus_real(U_1705,U_1703),zero_zero_real)
| ~ ord_less_eq_real(U_1705,U_1703) ) ),
inference(definitional_conversion,[status(esa)],[f_681_3]) ).
cnf(f_681_5,plain,
( ord_less_eq_real(minus_minus_real(U_1705,U_1703),zero_zero_real)
| ~ ord_less_eq_real(U_1705,U_1703) ),
inference(clausify,[status(thm)],[f_681_4]) ).
cnf(f_681_6,plain,
( ord_less_eq_real(U_1706,U_1704)
| ~ ord_less_eq_real(minus_minus_real(U_1706,U_1704),zero_zero_real) ),
inference(clausify,[status(thm)],[f_681_4]) ).
fof(f_682_1,plain,
! [X_2,Y_2] :
( ( ord_less_real(X_2,Y_2)
| X_2 = Y_2
| ~ ord_less_eq_real(X_2,Y_2) )
& ( ( X_2 != Y_2
& ord_less_eq_real(X_2,Y_2) )
| ~ ord_less_real(X_2,Y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_663_real__less__def]) ).
fof(f_682_2,plain,
! [U_1708,U_1707] :
( ( ord_less_real(U_1708,U_1707)
| U_1708 = U_1707
| ~ ord_less_eq_real(U_1708,U_1707) )
& ( ( U_1708 != U_1707
& ord_less_eq_real(U_1708,U_1707) )
| ~ ord_less_real(U_1708,U_1707) ) ),
inference(variable_rename,[status(thm)],[f_682_1]) ).
fof(f_682_3,plain,
( ! [U_1712,U_1710] :
( ord_less_real(U_1712,U_1710)
| U_1712 = U_1710
| ~ ord_less_eq_real(U_1712,U_1710) )
& ! [U_1711,U_1709] :
( ( U_1711 != U_1709
& ord_less_eq_real(U_1711,U_1709) )
| ~ ord_less_real(U_1711,U_1709) ) ),
inference(miniscope,[status(thm)],[f_682_2]) ).
fof(f_682_4,plain,
( ! [U_1711,U_1709] :
( U_1711 != U_1709
| ~ sP95(U_1711,U_1709) )
& ! [U_1711,U_1709] :
( ord_less_eq_real(U_1711,U_1709)
| ~ sP95(U_1711,U_1709) )
& ! [U_1712,U_1710] :
( ord_less_real(U_1712,U_1710)
| U_1712 = U_1710
| ~ ord_less_eq_real(U_1712,U_1710) )
& ! [U_1711,U_1709] :
( sP95(U_1711,U_1709)
| ~ ord_less_real(U_1711,U_1709) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP95])],[f_682_3]) ).
cnf(f_682_5,plain,
( sP95(U_1711,U_1709)
| ~ ord_less_real(U_1711,U_1709) ),
inference(clausify,[status(thm)],[f_682_4]) ).
cnf(f_682_6,plain,
( ord_less_real(U_1712,U_1710)
| U_1712 = U_1710
| ~ ord_less_eq_real(U_1712,U_1710) ),
inference(clausify,[status(thm)],[f_682_4]) ).
cnf(f_682_7,plain,
( ord_less_eq_real(U_1711,U_1709)
| ~ sP95(U_1711,U_1709) ),
inference(clausify,[status(thm)],[f_682_4]) ).
cnf(f_682_8,plain,
( U_1711 != U_1709
| ~ sP95(U_1711,U_1709) ),
inference(clausify,[status(thm)],[f_682_4]) ).
fof(f_683_1,plain,
! [X_2,Y_2] :
( ( ord_less_eq_real(X_2,Y_2)
| ( X_2 != Y_2
& ~ ord_less_real(X_2,Y_2) ) )
& ( X_2 = Y_2
| ord_less_real(X_2,Y_2)
| ~ ord_less_eq_real(X_2,Y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_664_less__eq__real__def]) ).
fof(f_683_2,plain,
! [U_1714,U_1713] :
( ( ord_less_eq_real(U_1714,U_1713)
| ( U_1714 != U_1713
& ~ ord_less_real(U_1714,U_1713) ) )
& ( U_1714 = U_1713
| ord_less_real(U_1714,U_1713)
| ~ ord_less_eq_real(U_1714,U_1713) ) ),
inference(variable_rename,[status(thm)],[f_683_1]) ).
fof(f_683_3,plain,
( ! [U_1718,U_1716] :
( ord_less_eq_real(U_1718,U_1716)
| ( U_1718 != U_1716
& ~ ord_less_real(U_1718,U_1716) ) )
& ! [U_1717,U_1715] :
( U_1717 = U_1715
| ord_less_real(U_1717,U_1715)
| ~ ord_less_eq_real(U_1717,U_1715) ) ),
inference(miniscope,[status(thm)],[f_683_2]) ).
fof(f_683_4,plain,
( ! [U_1716,U_1718] :
( U_1718 != U_1716
| ~ sP96(U_1716,U_1718) )
& ! [U_1716,U_1718] :
( ~ ord_less_real(U_1718,U_1716)
| ~ sP96(U_1716,U_1718) )
& ! [U_1716,U_1718] :
( ord_less_eq_real(U_1718,U_1716)
| sP96(U_1716,U_1718) )
& ! [U_1717,U_1715] :
( U_1717 = U_1715
| ord_less_real(U_1717,U_1715)
| ~ ord_less_eq_real(U_1717,U_1715) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP96])],[f_683_3]) ).
cnf(f_683_5,plain,
( U_1717 = U_1715
| ord_less_real(U_1717,U_1715)
| ~ ord_less_eq_real(U_1717,U_1715) ),
inference(clausify,[status(thm)],[f_683_4]) ).
cnf(f_683_6,plain,
( ord_less_eq_real(U_1718,U_1716)
| sP96(U_1716,U_1718) ),
inference(clausify,[status(thm)],[f_683_4]) ).
cnf(f_683_7,plain,
( ~ ord_less_real(U_1718,U_1716)
| ~ sP96(U_1716,U_1718) ),
inference(clausify,[status(thm)],[f_683_4]) ).
cnf(f_683_8,plain,
( U_1718 != U_1716
| ~ sP96(U_1716,U_1718) ),
inference(clausify,[status(thm)],[f_683_4]) ).
fof(f_684_1,plain,
! [Z] : times_times_real(one_one_real,Z) = Z,
inference(fof_nnf,[status(thm)],[fact_665_real__mult__1]) ).
fof(f_684_2,plain,
! [U_1719] : times_times_real(one_one_real,U_1719) = U_1719,
inference(variable_rename,[status(thm)],[f_684_1]) ).
fof(f_684_3,plain,
! [U_1719] : times_times_real(one_one_real,U_1719) = U_1719,
inference(definitional_conversion,[status(esa)],[f_684_2]) ).
cnf(f_684_4,plain,
times_times_real(one_one_real,U_1719) = U_1719,
inference(clausify,[status(thm)],[f_684_3]) ).
fof(f_685_1,plain,
! [Z,W] : times_times_real(Z,W) = times_times_real(W,Z),
inference(fof_nnf,[status(thm)],[fact_666_real__mult__commute]) ).
fof(f_685_2,plain,
! [U_1721,U_1720] : times_times_real(U_1721,U_1720) = times_times_real(U_1720,U_1721),
inference(variable_rename,[status(thm)],[f_685_1]) ).
fof(f_685_3,plain,
! [U_1721,U_1720] : times_times_real(U_1721,U_1720) = times_times_real(U_1720,U_1721),
inference(definitional_conversion,[status(esa)],[f_685_2]) ).
cnf(f_685_4,plain,
times_times_real(U_1721,U_1720) = times_times_real(U_1720,U_1721),
inference(clausify,[status(thm)],[f_685_3]) ).
fof(f_686_1,plain,
! [Z1,Z2,Z3] : times_times_real(times_times_real(Z1,Z2),Z3) = times_times_real(Z1,times_times_real(Z2,Z3)),
inference(fof_nnf,[status(thm)],[fact_667_real__mult__assoc]) ).
fof(f_686_2,plain,
! [U_1724,U_1723,U_1722] : times_times_real(times_times_real(U_1724,U_1723),U_1722) = times_times_real(U_1724,times_times_real(U_1723,U_1722)),
inference(variable_rename,[status(thm)],[f_686_1]) ).
fof(f_686_3,plain,
! [U_1722,U_1723,U_1724] : times_times_real(times_times_real(U_1724,U_1723),U_1722) = times_times_real(U_1724,times_times_real(U_1723,U_1722)),
inference(definitional_conversion,[status(esa)],[f_686_2]) ).
cnf(f_686_4,plain,
times_times_real(times_times_real(U_1724,U_1723),U_1722) = times_times_real(U_1724,times_times_real(U_1723,U_1722)),
inference(clausify,[status(thm)],[f_686_3]) ).
fof(f_687_1,plain,
! [Z,X_1,Y_1] :
( ord_less_eq_real(plus_plus_real(Z,X_1),plus_plus_real(Z,Y_1))
| ~ ord_less_eq_real(X_1,Y_1) ),
inference(fof_nnf,[status(thm)],[fact_668_real__add__left__mono]) ).
fof(f_687_2,plain,
! [U_1727,U_1726,U_1725] :
( ord_less_eq_real(plus_plus_real(U_1727,U_1726),plus_plus_real(U_1727,U_1725))
| ~ ord_less_eq_real(U_1726,U_1725) ),
inference(variable_rename,[status(thm)],[f_687_1]) ).
fof(f_687_3,plain,
! [U_1726,U_1725,U_1727] :
( ord_less_eq_real(plus_plus_real(U_1727,U_1726),plus_plus_real(U_1727,U_1725))
| ~ ord_less_eq_real(U_1726,U_1725) ),
inference(definitional_conversion,[status(esa)],[f_687_2]) ).
cnf(f_687_4,plain,
( ord_less_eq_real(plus_plus_real(U_1727,U_1726),plus_plus_real(U_1727,U_1725))
| ~ ord_less_eq_real(U_1726,U_1725) ),
inference(clausify,[status(thm)],[f_687_3]) ).
fof(f_688_1,plain,
! [A_1,B_2,C] :
( ( ( times_times_real(C,A_1) = times_times_real(C,B_2)
| A_1 != B_2 )
& ( A_1 = B_2
| times_times_real(C,A_1) != times_times_real(C,B_2) ) )
| C = zero_zero_real ),
inference(fof_nnf,[status(thm)],[fact_669_real__mult__left__cancel]) ).
fof(f_688_2,plain,
! [U_1730,U_1729,U_1728] :
( ( ( times_times_real(U_1728,U_1730) = times_times_real(U_1728,U_1729)
| U_1730 != U_1729 )
& ( U_1730 = U_1729
| times_times_real(U_1728,U_1730) != times_times_real(U_1728,U_1729) ) )
| U_1728 = zero_zero_real ),
inference(variable_rename,[status(thm)],[f_688_1]) ).
fof(f_688_3,plain,
( ! [U_1728,U_1729,U_1730] :
( times_times_real(U_1728,U_1730) = times_times_real(U_1728,U_1729)
| U_1730 != U_1729
| ~ sP97(U_1728,U_1729,U_1730) )
& ! [U_1728,U_1729,U_1730] :
( U_1730 = U_1729
| times_times_real(U_1728,U_1730) != times_times_real(U_1728,U_1729)
| ~ sP97(U_1728,U_1729,U_1730) )
& ! [U_1728,U_1729,U_1730] :
( sP97(U_1728,U_1729,U_1730)
| U_1728 = zero_zero_real ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP97])],[f_688_2]) ).
cnf(f_688_4,plain,
( sP97(U_1728,U_1729,U_1730)
| U_1728 = zero_zero_real ),
inference(clausify,[status(thm)],[f_688_3]) ).
cnf(f_688_5,plain,
( U_1730 = U_1729
| times_times_real(U_1728,U_1730) != times_times_real(U_1728,U_1729)
| ~ sP97(U_1728,U_1729,U_1730) ),
inference(clausify,[status(thm)],[f_688_3]) ).
cnf(f_688_6,plain,
( times_times_real(U_1728,U_1730) = times_times_real(U_1728,U_1729)
| U_1730 != U_1729
| ~ sP97(U_1728,U_1729,U_1730) ),
inference(clausify,[status(thm)],[f_688_3]) ).
fof(f_689_1,plain,
! [A_1,B_2,C] :
( ( ( times_times_real(A_1,C) = times_times_real(B_2,C)
| A_1 != B_2 )
& ( A_1 = B_2
| times_times_real(A_1,C) != times_times_real(B_2,C) ) )
| C = zero_zero_real ),
inference(fof_nnf,[status(thm)],[fact_670_real__mult__right__cancel]) ).
fof(f_689_2,plain,
! [U_1733,U_1732,U_1731] :
( ( ( times_times_real(U_1733,U_1731) = times_times_real(U_1732,U_1731)
| U_1733 != U_1732 )
& ( U_1733 = U_1732
| times_times_real(U_1733,U_1731) != times_times_real(U_1732,U_1731) ) )
| U_1731 = zero_zero_real ),
inference(variable_rename,[status(thm)],[f_689_1]) ).
fof(f_689_3,plain,
( ! [U_1731,U_1732,U_1733] :
( times_times_real(U_1733,U_1731) = times_times_real(U_1732,U_1731)
| U_1733 != U_1732
| ~ sP98(U_1731,U_1732,U_1733) )
& ! [U_1731,U_1732,U_1733] :
( U_1733 = U_1732
| times_times_real(U_1733,U_1731) != times_times_real(U_1732,U_1731)
| ~ sP98(U_1731,U_1732,U_1733) )
& ! [U_1731,U_1732,U_1733] :
( sP98(U_1731,U_1732,U_1733)
| U_1731 = zero_zero_real ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP98])],[f_689_2]) ).
cnf(f_689_4,plain,
( sP98(U_1731,U_1732,U_1733)
| U_1731 = zero_zero_real ),
inference(clausify,[status(thm)],[f_689_3]) ).
cnf(f_689_5,plain,
( U_1733 = U_1732
| times_times_real(U_1733,U_1731) != times_times_real(U_1732,U_1731)
| ~ sP98(U_1731,U_1732,U_1733) ),
inference(clausify,[status(thm)],[f_689_3]) ).
cnf(f_689_6,plain,
( times_times_real(U_1733,U_1731) = times_times_real(U_1732,U_1731)
| U_1733 != U_1732
| ~ sP98(U_1731,U_1732,U_1733) ),
inference(clausify,[status(thm)],[f_689_3]) ).
fof(f_690_1,plain,
! [Z1,Z2,W] : times_times_real(plus_plus_real(Z1,Z2),W) = plus_plus_real(times_times_real(Z1,W),times_times_real(Z2,W)),
inference(fof_nnf,[status(thm)],[fact_671_real__add__mult__distrib]) ).
fof(f_690_2,plain,
! [U_1736,U_1735,U_1734] : times_times_real(plus_plus_real(U_1736,U_1735),U_1734) = plus_plus_real(times_times_real(U_1736,U_1734),times_times_real(U_1735,U_1734)),
inference(variable_rename,[status(thm)],[f_690_1]) ).
fof(f_690_3,plain,
! [U_1735,U_1736,U_1734] : times_times_real(plus_plus_real(U_1736,U_1735),U_1734) = plus_plus_real(times_times_real(U_1736,U_1734),times_times_real(U_1735,U_1734)),
inference(definitional_conversion,[status(esa)],[f_690_2]) ).
cnf(f_690_4,plain,
times_times_real(plus_plus_real(U_1736,U_1735),U_1734) = plus_plus_real(times_times_real(U_1736,U_1734),times_times_real(U_1735,U_1734)),
inference(clausify,[status(thm)],[f_690_3]) ).
fof(f_691_1,plain,
! [X_1,Y_1,Z] :
( ord_less_real(times_times_real(Z,X_1),times_times_real(Z,Y_1))
| ~ ord_less_real(X_1,Y_1)
| ~ ord_less_real(zero_zero_real,Z) ),
inference(fof_nnf,[status(thm)],[fact_672_real__mult__less__mono2]) ).
fof(f_691_2,plain,
! [U_1739,U_1738,U_1737] :
( ord_less_real(times_times_real(U_1737,U_1739),times_times_real(U_1737,U_1738))
| ~ ord_less_real(U_1739,U_1738)
| ~ ord_less_real(zero_zero_real,U_1737) ),
inference(variable_rename,[status(thm)],[f_691_1]) ).
fof(f_691_3,plain,
! [U_1737,U_1738,U_1739] :
( ord_less_real(times_times_real(U_1737,U_1739),times_times_real(U_1737,U_1738))
| ~ ord_less_real(U_1739,U_1738)
| ~ ord_less_real(zero_zero_real,U_1737) ),
inference(definitional_conversion,[status(esa)],[f_691_2]) ).
cnf(f_691_4,plain,
( ord_less_real(times_times_real(U_1737,U_1739),times_times_real(U_1737,U_1738))
| ~ ord_less_real(U_1739,U_1738)
| ~ ord_less_real(zero_zero_real,U_1737) ),
inference(clausify,[status(thm)],[f_691_3]) ).
fof(f_692_1,plain,
! [Y_1,X_1] :
( ord_less_real(zero_zero_real,times_times_real(X_1,Y_1))
| ~ ord_less_real(zero_zero_real,Y_1)
| ~ ord_less_real(zero_zero_real,X_1) ),
inference(fof_nnf,[status(thm)],[fact_673_real__mult__order]) ).
fof(f_692_2,plain,
! [U_1741,U_1740] :
( ord_less_real(zero_zero_real,times_times_real(U_1740,U_1741))
| ~ ord_less_real(zero_zero_real,U_1741)
| ~ ord_less_real(zero_zero_real,U_1740) ),
inference(variable_rename,[status(thm)],[f_692_1]) ).
fof(f_692_3,plain,
! [U_1741,U_1740] :
( ord_less_real(zero_zero_real,times_times_real(U_1740,U_1741))
| ~ ord_less_real(zero_zero_real,U_1741)
| ~ ord_less_real(zero_zero_real,U_1740) ),
inference(definitional_conversion,[status(esa)],[f_692_2]) ).
cnf(f_692_4,plain,
( ord_less_real(zero_zero_real,times_times_real(U_1740,U_1741))
| ~ ord_less_real(zero_zero_real,U_1741)
| ~ ord_less_real(zero_zero_real,U_1740) ),
inference(clausify,[status(thm)],[f_692_3]) ).
fof(f_693_1,plain,
! [X_2,Y_2,Z_1] :
( ( ( ord_less_eq_real(times_times_real(Z_1,X_2),times_times_real(Z_1,Y_2))
| ~ ord_less_eq_real(X_2,Y_2) )
& ( ord_less_eq_real(X_2,Y_2)
| ~ ord_less_eq_real(times_times_real(Z_1,X_2),times_times_real(Z_1,Y_2)) ) )
| ~ ord_less_real(zero_zero_real,Z_1) ),
inference(fof_nnf,[status(thm)],[fact_674_real__mult__le__cancel__iff2]) ).
fof(f_693_2,plain,
! [U_1744,U_1743,U_1742] :
( ( ( ord_less_eq_real(times_times_real(U_1742,U_1744),times_times_real(U_1742,U_1743))
| ~ ord_less_eq_real(U_1744,U_1743) )
& ( ord_less_eq_real(U_1744,U_1743)
| ~ ord_less_eq_real(times_times_real(U_1742,U_1744),times_times_real(U_1742,U_1743)) ) )
| ~ ord_less_real(zero_zero_real,U_1742) ),
inference(variable_rename,[status(thm)],[f_693_1]) ).
fof(f_693_3,plain,
( ! [U_1743,U_1742,U_1744] :
( ord_less_eq_real(times_times_real(U_1742,U_1744),times_times_real(U_1742,U_1743))
| ~ ord_less_eq_real(U_1744,U_1743)
| ~ sP99(U_1743,U_1742,U_1744) )
& ! [U_1743,U_1742,U_1744] :
( ord_less_eq_real(U_1744,U_1743)
| ~ ord_less_eq_real(times_times_real(U_1742,U_1744),times_times_real(U_1742,U_1743))
| ~ sP99(U_1743,U_1742,U_1744) )
& ! [U_1743,U_1742,U_1744] :
( sP99(U_1743,U_1742,U_1744)
| ~ ord_less_real(zero_zero_real,U_1742) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP99])],[f_693_2]) ).
cnf(f_693_4,plain,
( sP99(U_1743,U_1742,U_1744)
| ~ ord_less_real(zero_zero_real,U_1742) ),
inference(clausify,[status(thm)],[f_693_3]) ).
cnf(f_693_5,plain,
( ord_less_eq_real(U_1744,U_1743)
| ~ ord_less_eq_real(times_times_real(U_1742,U_1744),times_times_real(U_1742,U_1743))
| ~ sP99(U_1743,U_1742,U_1744) ),
inference(clausify,[status(thm)],[f_693_3]) ).
cnf(f_693_6,plain,
( ord_less_eq_real(times_times_real(U_1742,U_1744),times_times_real(U_1742,U_1743))
| ~ ord_less_eq_real(U_1744,U_1743)
| ~ sP99(U_1743,U_1742,U_1744) ),
inference(clausify,[status(thm)],[f_693_3]) ).
fof(f_694_1,plain,
! [X_2,Y_2,Z_1] :
( ( ( ord_less_eq_real(times_times_real(X_2,Z_1),times_times_real(Y_2,Z_1))
| ~ ord_less_eq_real(X_2,Y_2) )
& ( ord_less_eq_real(X_2,Y_2)
| ~ ord_less_eq_real(times_times_real(X_2,Z_1),times_times_real(Y_2,Z_1)) ) )
| ~ ord_less_real(zero_zero_real,Z_1) ),
inference(fof_nnf,[status(thm)],[fact_675_real__mult__le__cancel__iff1]) ).
fof(f_694_2,plain,
! [U_1747,U_1746,U_1745] :
( ( ( ord_less_eq_real(times_times_real(U_1747,U_1745),times_times_real(U_1746,U_1745))
| ~ ord_less_eq_real(U_1747,U_1746) )
& ( ord_less_eq_real(U_1747,U_1746)
| ~ ord_less_eq_real(times_times_real(U_1747,U_1745),times_times_real(U_1746,U_1745)) ) )
| ~ ord_less_real(zero_zero_real,U_1745) ),
inference(variable_rename,[status(thm)],[f_694_1]) ).
fof(f_694_3,plain,
( ! [U_1746,U_1747,U_1745] :
( ord_less_eq_real(times_times_real(U_1747,U_1745),times_times_real(U_1746,U_1745))
| ~ ord_less_eq_real(U_1747,U_1746)
| ~ sP100(U_1746,U_1747,U_1745) )
& ! [U_1746,U_1747,U_1745] :
( ord_less_eq_real(U_1747,U_1746)
| ~ ord_less_eq_real(times_times_real(U_1747,U_1745),times_times_real(U_1746,U_1745))
| ~ sP100(U_1746,U_1747,U_1745) )
& ! [U_1746,U_1747,U_1745] :
( sP100(U_1746,U_1747,U_1745)
| ~ ord_less_real(zero_zero_real,U_1745) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP100])],[f_694_2]) ).
cnf(f_694_4,plain,
( sP100(U_1746,U_1747,U_1745)
| ~ ord_less_real(zero_zero_real,U_1745) ),
inference(clausify,[status(thm)],[f_694_3]) ).
cnf(f_694_5,plain,
( ord_less_eq_real(U_1747,U_1746)
| ~ ord_less_eq_real(times_times_real(U_1747,U_1745),times_times_real(U_1746,U_1745))
| ~ sP100(U_1746,U_1747,U_1745) ),
inference(clausify,[status(thm)],[f_694_3]) ).
cnf(f_694_6,plain,
( ord_less_eq_real(times_times_real(U_1747,U_1745),times_times_real(U_1746,U_1745))
| ~ ord_less_eq_real(U_1747,U_1746)
| ~ sP100(U_1746,U_1747,U_1745) ),
inference(clausify,[status(thm)],[f_694_3]) ).
fof(f_695_1,plain,
! [X_2,Y_2,Z_1] :
( ( ( ord_less_real(times_times_real(X_2,Z_1),times_times_real(Y_2,Z_1))
| ~ ord_less_real(X_2,Y_2) )
& ( ord_less_real(X_2,Y_2)
| ~ ord_less_real(times_times_real(X_2,Z_1),times_times_real(Y_2,Z_1)) ) )
| ~ ord_less_real(zero_zero_real,Z_1) ),
inference(fof_nnf,[status(thm)],[fact_676_real__mult__less__iff1]) ).
fof(f_695_2,plain,
! [U_1750,U_1749,U_1748] :
( ( ( ord_less_real(times_times_real(U_1750,U_1748),times_times_real(U_1749,U_1748))
| ~ ord_less_real(U_1750,U_1749) )
& ( ord_less_real(U_1750,U_1749)
| ~ ord_less_real(times_times_real(U_1750,U_1748),times_times_real(U_1749,U_1748)) ) )
| ~ ord_less_real(zero_zero_real,U_1748) ),
inference(variable_rename,[status(thm)],[f_695_1]) ).
fof(f_695_3,plain,
( ! [U_1750,U_1749,U_1748] :
( ord_less_real(times_times_real(U_1750,U_1748),times_times_real(U_1749,U_1748))
| ~ ord_less_real(U_1750,U_1749)
| ~ sP101(U_1750,U_1749,U_1748) )
& ! [U_1750,U_1749,U_1748] :
( ord_less_real(U_1750,U_1749)
| ~ ord_less_real(times_times_real(U_1750,U_1748),times_times_real(U_1749,U_1748))
| ~ sP101(U_1750,U_1749,U_1748) )
& ! [U_1750,U_1749,U_1748] :
( sP101(U_1750,U_1749,U_1748)
| ~ ord_less_real(zero_zero_real,U_1748) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP101])],[f_695_2]) ).
cnf(f_695_4,plain,
( sP101(U_1750,U_1749,U_1748)
| ~ ord_less_real(zero_zero_real,U_1748) ),
inference(clausify,[status(thm)],[f_695_3]) ).
cnf(f_695_5,plain,
( ord_less_real(U_1750,U_1749)
| ~ ord_less_real(times_times_real(U_1750,U_1748),times_times_real(U_1749,U_1748))
| ~ sP101(U_1750,U_1749,U_1748) ),
inference(clausify,[status(thm)],[f_695_3]) ).
cnf(f_695_6,plain,
( ord_less_real(times_times_real(U_1750,U_1748),times_times_real(U_1749,U_1748))
| ~ ord_less_real(U_1750,U_1749)
| ~ sP101(U_1750,U_1749,U_1748) ),
inference(clausify,[status(thm)],[f_695_3]) ).
fof(f_696_1,plain,
! [X_2,Y_2] :
( ( plus_plus_real(times_times_real(X_2,X_2),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 )
| plus_plus_real(times_times_real(X_2,X_2),times_times_real(Y_2,Y_2)) != zero_zero_real ) ),
inference(fof_nnf,[status(thm)],[fact_677_real__two__squares__add__zero__iff]) ).
fof(f_696_2,plain,
! [U_1752,U_1751] :
( ( plus_plus_real(times_times_real(U_1752,U_1752),times_times_real(U_1751,U_1751)) = zero_zero_real
| U_1751 != zero_zero_real
| U_1752 != zero_zero_real )
& ( ( U_1751 = zero_zero_real
& U_1752 = zero_zero_real )
| plus_plus_real(times_times_real(U_1752,U_1752),times_times_real(U_1751,U_1751)) != zero_zero_real ) ),
inference(variable_rename,[status(thm)],[f_696_1]) ).
fof(f_696_3,plain,
( ! [U_1756,U_1754] :
( plus_plus_real(times_times_real(U_1756,U_1756),times_times_real(U_1754,U_1754)) = zero_zero_real
| U_1754 != zero_zero_real
| U_1756 != zero_zero_real )
& ! [U_1755,U_1753] :
( ( U_1753 = zero_zero_real
& U_1755 = zero_zero_real )
| plus_plus_real(times_times_real(U_1755,U_1755),times_times_real(U_1753,U_1753)) != zero_zero_real ) ),
inference(miniscope,[status(thm)],[f_696_2]) ).
fof(f_696_4,plain,
( ! [U_1753,U_1755] :
( U_1753 = zero_zero_real
| ~ sP102(U_1753,U_1755) )
& ! [U_1753,U_1755] :
( U_1755 = zero_zero_real
| ~ sP102(U_1753,U_1755) )
& ! [U_1756,U_1754] :
( plus_plus_real(times_times_real(U_1756,U_1756),times_times_real(U_1754,U_1754)) = zero_zero_real
| U_1754 != zero_zero_real
| U_1756 != zero_zero_real )
& ! [U_1753,U_1755] :
( sP102(U_1753,U_1755)
| plus_plus_real(times_times_real(U_1755,U_1755),times_times_real(U_1753,U_1753)) != zero_zero_real ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP102])],[f_696_3]) ).
cnf(f_696_5,plain,
( sP102(U_1753,U_1755)
| plus_plus_real(times_times_real(U_1755,U_1755),times_times_real(U_1753,U_1753)) != zero_zero_real ),
inference(clausify,[status(thm)],[f_696_4]) ).
cnf(f_696_6,plain,
( plus_plus_real(times_times_real(U_1756,U_1756),times_times_real(U_1754,U_1754)) = zero_zero_real
| U_1754 != zero_zero_real
| U_1756 != zero_zero_real ),
inference(clausify,[status(thm)],[f_696_4]) ).
cnf(f_696_7,plain,
( U_1755 = zero_zero_real
| ~ sP102(U_1753,U_1755) ),
inference(clausify,[status(thm)],[f_696_4]) ).
cnf(f_696_8,plain,
( U_1753 = zero_zero_real
| ~ sP102(U_1753,U_1755) ),
inference(clausify,[status(thm)],[f_696_4]) ).
fof(f_697_1,plain,
! [N] : ord_less_eq_real(one_one_real,power_power_real(number267125858f_real(bit0(bit1(pls))),N)),
inference(fof_nnf,[status(thm)],[fact_678_two__realpow__ge__one]) ).
fof(f_697_2,plain,
! [U_1757] : ord_less_eq_real(one_one_real,power_power_real(number267125858f_real(bit0(bit1(pls))),U_1757)),
inference(variable_rename,[status(thm)],[f_697_1]) ).
fof(f_697_3,plain,
! [U_1757] : ord_less_eq_real(one_one_real,power_power_real(number267125858f_real(bit0(bit1(pls))),U_1757)),
inference(definitional_conversion,[status(esa)],[f_697_2]) ).
cnf(f_697_4,plain,
ord_less_eq_real(one_one_real,power_power_real(number267125858f_real(bit0(bit1(pls))),U_1757)),
inference(clausify,[status(thm)],[f_697_3]) ).
fof(f_698_1,plain,
! [B,Q_1,R_2] :
( ord_less_eq_int(zero_zero_int,Q_1)
| ~ ord_less_int(zero_zero_int,B)
| ~ ord_less_int(R_2,B)
| ~ ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(B,Q_1),R_2)) ),
inference(fof_nnf,[status(thm)],[fact_679_q__pos__lemma]) ).
fof(f_698_2,plain,
! [U_1760,U_1759,U_1758] :
( ord_less_eq_int(zero_zero_int,U_1759)
| ~ ord_less_int(zero_zero_int,U_1760)
| ~ ord_less_int(U_1758,U_1760)
| ~ ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(U_1760,U_1759),U_1758)) ),
inference(variable_rename,[status(thm)],[f_698_1]) ).
fof(f_698_3,plain,
! [U_1758,U_1760,U_1759] :
( ord_less_eq_int(zero_zero_int,U_1759)
| ~ ord_less_int(zero_zero_int,U_1760)
| ~ ord_less_int(U_1758,U_1760)
| ~ ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(U_1760,U_1759),U_1758)) ),
inference(definitional_conversion,[status(esa)],[f_698_2]) ).
cnf(f_698_4,plain,
( ord_less_eq_int(zero_zero_int,U_1759)
| ~ ord_less_int(zero_zero_int,U_1760)
| ~ ord_less_int(U_1758,U_1760)
| ~ ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(U_1760,U_1759),U_1758)) ),
inference(clausify,[status(thm)],[f_698_3]) ).
fof(f_699_1,plain,
! [B,Q_1,R_2] :
( ord_less_eq_int(Q_1,zero_zero_int)
| ~ ord_less_int(zero_zero_int,B)
| ~ ord_less_eq_int(zero_zero_int,R_2)
| ~ ord_less_int(plus_plus_int(times_times_int(B,Q_1),R_2),zero_zero_int) ),
inference(fof_nnf,[status(thm)],[fact_680_q__neg__lemma]) ).
fof(f_699_2,plain,
! [U_1763,U_1762,U_1761] :
( ord_less_eq_int(U_1762,zero_zero_int)
| ~ ord_less_int(zero_zero_int,U_1763)
| ~ ord_less_eq_int(zero_zero_int,U_1761)
| ~ ord_less_int(plus_plus_int(times_times_int(U_1763,U_1762),U_1761),zero_zero_int) ),
inference(variable_rename,[status(thm)],[f_699_1]) ).
fof(f_699_3,plain,
! [U_1761,U_1762,U_1763] :
( ord_less_eq_int(U_1762,zero_zero_int)
| ~ ord_less_int(zero_zero_int,U_1763)
| ~ ord_less_eq_int(zero_zero_int,U_1761)
| ~ ord_less_int(plus_plus_int(times_times_int(U_1763,U_1762),U_1761),zero_zero_int) ),
inference(definitional_conversion,[status(esa)],[f_699_2]) ).
cnf(f_699_4,plain,
( ord_less_eq_int(U_1762,zero_zero_int)
| ~ ord_less_int(zero_zero_int,U_1763)
| ~ ord_less_eq_int(zero_zero_int,U_1761)
| ~ ord_less_int(plus_plus_int(times_times_int(U_1763,U_1762),U_1761),zero_zero_int) ),
inference(clausify,[status(thm)],[f_699_3]) ).
fof(f_700_1,plain,
! [B_1,Q_1,R_2,Q,R_1] :
( ord_less_eq_int(Q_1,Q)
| ~ ord_less_int(R_1,B_1)
| ~ ord_less_int(R_2,B_1)
| ~ ord_less_eq_int(zero_zero_int,R_2)
| ~ ord_less_eq_int(plus_plus_int(times_times_int(B_1,Q_1),R_2),plus_plus_int(times_times_int(B_1,Q),R_1)) ),
inference(fof_nnf,[status(thm)],[fact_681_unique__quotient__lemma]) ).
fof(f_700_2,plain,
! [U_1768,U_1767,U_1766,U_1765,U_1764] :
( ord_less_eq_int(U_1767,U_1765)
| ~ ord_less_int(U_1764,U_1768)
| ~ ord_less_int(U_1766,U_1768)
| ~ ord_less_eq_int(zero_zero_int,U_1766)
| ~ ord_less_eq_int(plus_plus_int(times_times_int(U_1768,U_1767),U_1766),plus_plus_int(times_times_int(U_1768,U_1765),U_1764)) ),
inference(variable_rename,[status(thm)],[f_700_1]) ).
fof(f_700_3,plain,
! [U_1766,U_1764,U_1767,U_1765,U_1768] :
( ord_less_eq_int(U_1767,U_1765)
| ~ ord_less_int(U_1764,U_1768)
| ~ ord_less_int(U_1766,U_1768)
| ~ ord_less_eq_int(zero_zero_int,U_1766)
| ~ ord_less_eq_int(plus_plus_int(times_times_int(U_1768,U_1767),U_1766),plus_plus_int(times_times_int(U_1768,U_1765),U_1764)) ),
inference(definitional_conversion,[status(esa)],[f_700_2]) ).
cnf(f_700_4,plain,
( ord_less_eq_int(U_1767,U_1765)
| ~ ord_less_int(U_1764,U_1768)
| ~ ord_less_int(U_1766,U_1768)
| ~ ord_less_eq_int(zero_zero_int,U_1766)
| ~ ord_less_eq_int(plus_plus_int(times_times_int(U_1768,U_1767),U_1766),plus_plus_int(times_times_int(U_1768,U_1765),U_1764)) ),
inference(clausify,[status(thm)],[f_700_3]) ).
fof(f_701_1,plain,
! [B_1,Q,R_1,B,Q_1,R_2] :
( ord_less_eq_int(Q,Q_1)
| ~ ord_less_eq_int(B,B_1)
| ~ ord_less_int(zero_zero_int,B)
| ~ ord_less_eq_int(zero_zero_int,R_1)
| ~ ord_less_int(R_2,B)
| ~ ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(B,Q_1),R_2))
| plus_plus_int(times_times_int(B_1,Q),R_1) != plus_plus_int(times_times_int(B,Q_1),R_2) ),
inference(fof_nnf,[status(thm)],[fact_682_zdiv__mono2__lemma]) ).
fof(f_701_2,plain,
! [U_1774,U_1773,U_1772,U_1771,U_1770,U_1769] :
( ord_less_eq_int(U_1773,U_1770)
| ~ ord_less_eq_int(U_1771,U_1774)
| ~ ord_less_int(zero_zero_int,U_1771)
| ~ ord_less_eq_int(zero_zero_int,U_1772)
| ~ ord_less_int(U_1769,U_1771)
| ~ ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(U_1771,U_1770),U_1769))
| plus_plus_int(times_times_int(U_1774,U_1773),U_1772) != plus_plus_int(times_times_int(U_1771,U_1770),U_1769) ),
inference(variable_rename,[status(thm)],[f_701_1]) ).
fof(f_701_3,plain,
! [U_1769,U_1771,U_1772,U_1773,U_1774,U_1770] :
( ord_less_eq_int(U_1773,U_1770)
| ~ ord_less_eq_int(U_1771,U_1774)
| ~ ord_less_int(zero_zero_int,U_1771)
| ~ ord_less_eq_int(zero_zero_int,U_1772)
| ~ ord_less_int(U_1769,U_1771)
| ~ ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(U_1771,U_1770),U_1769))
| plus_plus_int(times_times_int(U_1774,U_1773),U_1772) != plus_plus_int(times_times_int(U_1771,U_1770),U_1769) ),
inference(definitional_conversion,[status(esa)],[f_701_2]) ).
cnf(f_701_4,plain,
( ord_less_eq_int(U_1773,U_1770)
| ~ ord_less_eq_int(U_1771,U_1774)
| ~ ord_less_int(zero_zero_int,U_1771)
| ~ ord_less_eq_int(zero_zero_int,U_1772)
| ~ ord_less_int(U_1769,U_1771)
| ~ ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(U_1771,U_1770),U_1769))
| plus_plus_int(times_times_int(U_1774,U_1773),U_1772) != plus_plus_int(times_times_int(U_1771,U_1770),U_1769) ),
inference(clausify,[status(thm)],[f_701_3]) ).
fof(f_702_1,plain,
! [B_1,Q_1,R_2,Q,R_1] :
( ord_less_eq_int(Q,Q_1)
| ~ ord_less_int(B_1,R_2)
| ~ ord_less_int(B_1,R_1)
| ~ ord_less_eq_int(R_1,zero_zero_int)
| ~ ord_less_eq_int(plus_plus_int(times_times_int(B_1,Q_1),R_2),plus_plus_int(times_times_int(B_1,Q),R_1)) ),
inference(fof_nnf,[status(thm)],[fact_683_unique__quotient__lemma__neg]) ).
fof(f_702_2,plain,
! [U_1779,U_1778,U_1777,U_1776,U_1775] :
( ord_less_eq_int(U_1776,U_1778)
| ~ ord_less_int(U_1779,U_1777)
| ~ ord_less_int(U_1779,U_1775)
| ~ ord_less_eq_int(U_1775,zero_zero_int)
| ~ ord_less_eq_int(plus_plus_int(times_times_int(U_1779,U_1778),U_1777),plus_plus_int(times_times_int(U_1779,U_1776),U_1775)) ),
inference(variable_rename,[status(thm)],[f_702_1]) ).
fof(f_702_3,plain,
! [U_1778,U_1777,U_1775,U_1776,U_1779] :
( ord_less_eq_int(U_1776,U_1778)
| ~ ord_less_int(U_1779,U_1777)
| ~ ord_less_int(U_1779,U_1775)
| ~ ord_less_eq_int(U_1775,zero_zero_int)
| ~ ord_less_eq_int(plus_plus_int(times_times_int(U_1779,U_1778),U_1777),plus_plus_int(times_times_int(U_1779,U_1776),U_1775)) ),
inference(definitional_conversion,[status(esa)],[f_702_2]) ).
cnf(f_702_4,plain,
( ord_less_eq_int(U_1776,U_1778)
| ~ ord_less_int(U_1779,U_1777)
| ~ ord_less_int(U_1779,U_1775)
| ~ ord_less_eq_int(U_1775,zero_zero_int)
| ~ ord_less_eq_int(plus_plus_int(times_times_int(U_1779,U_1778),U_1777),plus_plus_int(times_times_int(U_1779,U_1776),U_1775)) ),
inference(clausify,[status(thm)],[f_702_3]) ).
fof(f_703_1,plain,
! [B_1,Q,R_1,B,Q_1,R_2] :
( ord_less_eq_int(Q_1,Q)
| ~ ord_less_eq_int(B,B_1)
| ~ ord_less_int(zero_zero_int,B)
| ~ ord_less_eq_int(zero_zero_int,R_2)
| ~ ord_less_int(R_1,B_1)
| ~ ord_less_int(plus_plus_int(times_times_int(B,Q_1),R_2),zero_zero_int)
| plus_plus_int(times_times_int(B_1,Q),R_1) != plus_plus_int(times_times_int(B,Q_1),R_2) ),
inference(fof_nnf,[status(thm)],[fact_684_zdiv__mono2__neg__lemma]) ).
fof(f_703_2,plain,
! [U_1785,U_1784,U_1783,U_1782,U_1781,U_1780] :
( ord_less_eq_int(U_1781,U_1784)
| ~ ord_less_eq_int(U_1782,U_1785)
| ~ ord_less_int(zero_zero_int,U_1782)
| ~ ord_less_eq_int(zero_zero_int,U_1780)
| ~ ord_less_int(U_1783,U_1785)
| ~ ord_less_int(plus_plus_int(times_times_int(U_1782,U_1781),U_1780),zero_zero_int)
| plus_plus_int(times_times_int(U_1785,U_1784),U_1783) != plus_plus_int(times_times_int(U_1782,U_1781),U_1780) ),
inference(variable_rename,[status(thm)],[f_703_1]) ).
fof(f_703_3,plain,
! [U_1781,U_1785,U_1780,U_1784,U_1782,U_1783] :
( ord_less_eq_int(U_1781,U_1784)
| ~ ord_less_eq_int(U_1782,U_1785)
| ~ ord_less_int(zero_zero_int,U_1782)
| ~ ord_less_eq_int(zero_zero_int,U_1780)
| ~ ord_less_int(U_1783,U_1785)
| ~ ord_less_int(plus_plus_int(times_times_int(U_1782,U_1781),U_1780),zero_zero_int)
| plus_plus_int(times_times_int(U_1785,U_1784),U_1783) != plus_plus_int(times_times_int(U_1782,U_1781),U_1780) ),
inference(definitional_conversion,[status(esa)],[f_703_2]) ).
cnf(f_703_4,plain,
( ord_less_eq_int(U_1781,U_1784)
| ~ ord_less_eq_int(U_1782,U_1785)
| ~ ord_less_int(zero_zero_int,U_1782)
| ~ ord_less_eq_int(zero_zero_int,U_1780)
| ~ ord_less_int(U_1783,U_1785)
| ~ ord_less_int(plus_plus_int(times_times_int(U_1782,U_1781),U_1780),zero_zero_int)
| plus_plus_int(times_times_int(U_1785,U_1784),U_1783) != plus_plus_int(times_times_int(U_1782,U_1781),U_1780) ),
inference(clausify,[status(thm)],[f_703_3]) ).
fof(f_704_1,plain,
! [R_1,Q,A] :
( ord_less_eq_int(Q,one_one_int)
| ~ ord_less_eq_int(zero_zero_int,R_1)
| A != plus_plus_int(R_1,times_times_int(A,Q))
| ~ ord_less_int(zero_zero_int,A) ),
inference(fof_nnf,[status(thm)],[fact_685_self__quotient__aux2]) ).
fof(f_704_2,plain,
! [U_1788,U_1787,U_1786] :
( ord_less_eq_int(U_1787,one_one_int)
| ~ ord_less_eq_int(zero_zero_int,U_1788)
| U_1786 != plus_plus_int(U_1788,times_times_int(U_1786,U_1787))
| ~ ord_less_int(zero_zero_int,U_1786) ),
inference(variable_rename,[status(thm)],[f_704_1]) ).
fof(f_704_3,plain,
! [U_1786,U_1787,U_1788] :
( ord_less_eq_int(U_1787,one_one_int)
| ~ ord_less_eq_int(zero_zero_int,U_1788)
| U_1786 != plus_plus_int(U_1788,times_times_int(U_1786,U_1787))
| ~ ord_less_int(zero_zero_int,U_1786) ),
inference(definitional_conversion,[status(esa)],[f_704_2]) ).
cnf(f_704_4,plain,
( ord_less_eq_int(U_1787,one_one_int)
| ~ ord_less_eq_int(zero_zero_int,U_1788)
| U_1786 != plus_plus_int(U_1788,times_times_int(U_1786,U_1787))
| ~ ord_less_int(zero_zero_int,U_1786) ),
inference(clausify,[status(thm)],[f_704_3]) ).
fof(f_705_1,plain,
ord_less_eq_int(zero_zero_int,number_number_of_int(bit0(bit1(pls)))),
inference(fof_nnf,[status(thm)],[fact_686_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J]) ).
fof(f_705_2,plain,
ord_less_eq_int(zero_zero_int,number_number_of_int(bit0(bit1(pls)))),
inference(definitional_conversion,[status(esa)],[f_705_1]) ).
cnf(f_705_3,plain,
ord_less_eq_int(zero_zero_int,number_number_of_int(bit0(bit1(pls)))),
inference(clausify,[status(thm)],[f_705_2]) ).
fof(f_706_1,plain,
! [Z,W] :
( Z = W
| ~ ord_less_eq_real(W,Z)
| ~ ord_less_eq_real(Z,W) ),
inference(fof_nnf,[status(thm)],[fact_687_real__le__antisym]) ).
fof(f_706_2,plain,
! [U_1790,U_1789] :
( U_1790 = U_1789
| ~ ord_less_eq_real(U_1789,U_1790)
| ~ ord_less_eq_real(U_1790,U_1789) ),
inference(variable_rename,[status(thm)],[f_706_1]) ).
fof(f_706_3,plain,
! [U_1790,U_1789] :
( U_1790 = U_1789
| ~ ord_less_eq_real(U_1789,U_1790)
| ~ ord_less_eq_real(U_1790,U_1789) ),
inference(definitional_conversion,[status(esa)],[f_706_2]) ).
cnf(f_706_4,plain,
( U_1790 = U_1789
| ~ ord_less_eq_real(U_1789,U_1790)
| ~ ord_less_eq_real(U_1790,U_1789) ),
inference(clausify,[status(thm)],[f_706_3]) ).
fof(f_707_1,plain,
! [K,I,J] :
( ord_less_eq_real(I,K)
| ~ ord_less_eq_real(J,K)
| ~ ord_less_eq_real(I,J) ),
inference(fof_nnf,[status(thm)],[fact_688_real__le__trans]) ).
fof(f_707_2,plain,
! [U_1793,U_1792,U_1791] :
( ord_less_eq_real(U_1792,U_1793)
| ~ ord_less_eq_real(U_1791,U_1793)
| ~ ord_less_eq_real(U_1792,U_1791) ),
inference(variable_rename,[status(thm)],[f_707_1]) ).
fof(f_707_3,plain,
! [U_1792,U_1791,U_1793] :
( ord_less_eq_real(U_1792,U_1793)
| ~ ord_less_eq_real(U_1791,U_1793)
| ~ ord_less_eq_real(U_1792,U_1791) ),
inference(definitional_conversion,[status(esa)],[f_707_2]) ).
cnf(f_707_4,plain,
( ord_less_eq_real(U_1792,U_1793)
| ~ ord_less_eq_real(U_1791,U_1793)
| ~ ord_less_eq_real(U_1792,U_1791) ),
inference(clausify,[status(thm)],[f_707_3]) ).
fof(f_708_1,plain,
! [Z,W] :
( ord_less_eq_real(W,Z)
| ord_less_eq_real(Z,W) ),
inference(fof_nnf,[status(thm)],[fact_689_real__le__linear]) ).
fof(f_708_2,plain,
! [U_1795,U_1794] :
( ord_less_eq_real(U_1794,U_1795)
| ord_less_eq_real(U_1795,U_1794) ),
inference(variable_rename,[status(thm)],[f_708_1]) ).
fof(f_708_3,plain,
! [U_1794,U_1795] :
( ord_less_eq_real(U_1794,U_1795)
| ord_less_eq_real(U_1795,U_1794) ),
inference(definitional_conversion,[status(esa)],[f_708_2]) ).
cnf(f_708_4,plain,
( ord_less_eq_real(U_1794,U_1795)
| ord_less_eq_real(U_1795,U_1794) ),
inference(clausify,[status(thm)],[f_708_3]) ).
fof(f_709_1,plain,
! [W] : ord_less_eq_real(W,W),
inference(fof_nnf,[status(thm)],[fact_690_real__le__refl]) ).
fof(f_709_2,plain,
! [U_1796] : ord_less_eq_real(U_1796,U_1796),
inference(variable_rename,[status(thm)],[f_709_1]) ).
fof(f_709_3,plain,
! [U_1796] : ord_less_eq_real(U_1796,U_1796),
inference(definitional_conversion,[status(esa)],[f_709_2]) ).
cnf(f_709_4,plain,
ord_less_eq_real(U_1796,U_1796),
inference(clausify,[status(thm)],[f_709_3]) ).
fof(f_710_1,plain,
ord_less_eq_int(zero_zero_int,zero_zero_int),
inference(fof_nnf,[status(thm)],[fact_691_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]) ).
fof(f_710_2,plain,
ord_less_eq_int(zero_zero_int,zero_zero_int),
inference(definitional_conversion,[status(esa)],[f_710_1]) ).
cnf(f_710_3,plain,
ord_less_eq_int(zero_zero_int,zero_zero_int),
inference(clausify,[status(thm)],[f_710_2]) ).
fof(f_711_1,plain,
ord_less_eq_int(zero_zero_int,one_one_int),
inference(fof_nnf,[status(thm)],[fact_692_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]) ).
fof(f_711_2,plain,
ord_less_eq_int(zero_zero_int,one_one_int),
inference(definitional_conversion,[status(esa)],[f_711_1]) ).
cnf(f_711_3,plain,
ord_less_eq_int(zero_zero_int,one_one_int),
inference(clausify,[status(thm)],[f_711_2]) ).
fof(f_712_1,plain,
! [Y_1,X_1] :
( ord_less_eq_int(zero_zero_int,times_times_int(X_1,Y_1))
| ~ ord_less_eq_int(zero_zero_int,Y_1)
| ~ ord_less_eq_int(zero_zero_int,X_1) ),
inference(fof_nnf,[status(thm)],[fact_693_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J]) ).
fof(f_712_2,plain,
! [U_1798,U_1797] :
( ord_less_eq_int(zero_zero_int,times_times_int(U_1797,U_1798))
| ~ ord_less_eq_int(zero_zero_int,U_1798)
| ~ ord_less_eq_int(zero_zero_int,U_1797) ),
inference(variable_rename,[status(thm)],[f_712_1]) ).
fof(f_712_3,plain,
! [U_1797,U_1798] :
( ord_less_eq_int(zero_zero_int,times_times_int(U_1797,U_1798))
| ~ ord_less_eq_int(zero_zero_int,U_1798)
| ~ ord_less_eq_int(zero_zero_int,U_1797) ),
inference(definitional_conversion,[status(esa)],[f_712_2]) ).
cnf(f_712_4,plain,
( ord_less_eq_int(zero_zero_int,times_times_int(U_1797,U_1798))
| ~ ord_less_eq_int(zero_zero_int,U_1798)
| ~ ord_less_eq_int(zero_zero_int,U_1797) ),
inference(clausify,[status(thm)],[f_712_3]) ).
fof(f_713_1,plain,
! [Y_1,X_1] :
( ord_less_eq_int(zero_zero_int,plus_plus_int(X_1,Y_1))
| ~ ord_less_eq_int(zero_zero_int,Y_1)
| ~ ord_less_eq_int(zero_zero_int,X_1) ),
inference(fof_nnf,[status(thm)],[fact_694_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J]) ).
fof(f_713_2,plain,
! [U_1800,U_1799] :
( ord_less_eq_int(zero_zero_int,plus_plus_int(U_1799,U_1800))
| ~ ord_less_eq_int(zero_zero_int,U_1800)
| ~ ord_less_eq_int(zero_zero_int,U_1799) ),
inference(variable_rename,[status(thm)],[f_713_1]) ).
fof(f_713_3,plain,
! [U_1800,U_1799] :
( ord_less_eq_int(zero_zero_int,plus_plus_int(U_1799,U_1800))
| ~ ord_less_eq_int(zero_zero_int,U_1800)
| ~ ord_less_eq_int(zero_zero_int,U_1799) ),
inference(definitional_conversion,[status(esa)],[f_713_2]) ).
cnf(f_713_4,plain,
( ord_less_eq_int(zero_zero_int,plus_plus_int(U_1799,U_1800))
| ~ ord_less_eq_int(zero_zero_int,U_1800)
| ~ ord_less_eq_int(zero_zero_int,U_1799) ),
inference(clausify,[status(thm)],[f_713_3]) ).
fof(f_714_1,plain,
! [N,X_1] :
( ord_less_eq_int(zero_zero_int,power_power_int(X_1,N))
| ~ ord_less_eq_int(zero_zero_int,X_1) ),
inference(fof_nnf,[status(thm)],[fact_695_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J]) ).
fof(f_714_2,plain,
! [U_1802,U_1801] :
( ord_less_eq_int(zero_zero_int,power_power_int(U_1801,U_1802))
| ~ ord_less_eq_int(zero_zero_int,U_1801) ),
inference(variable_rename,[status(thm)],[f_714_1]) ).
fof(f_714_3,plain,
! [U_1802,U_1801] :
( ord_less_eq_int(zero_zero_int,power_power_int(U_1801,U_1802))
| ~ ord_less_eq_int(zero_zero_int,U_1801) ),
inference(definitional_conversion,[status(esa)],[f_714_2]) ).
cnf(f_714_4,plain,
( ord_less_eq_int(zero_zero_int,power_power_int(U_1801,U_1802))
| ~ ord_less_eq_int(zero_zero_int,U_1801) ),
inference(clausify,[status(thm)],[f_714_3]) ).
fof(f_715_1,plain,
ord_less_eq_int(zero_zero_int,number_number_of_int(bit1(bit1(pls)))),
inference(fof_nnf,[status(thm)],[fact_696_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J]) ).
fof(f_715_2,plain,
ord_less_eq_int(zero_zero_int,number_number_of_int(bit1(bit1(pls)))),
inference(definitional_conversion,[status(esa)],[f_715_1]) ).
cnf(f_715_3,plain,
ord_less_eq_int(zero_zero_int,number_number_of_int(bit1(bit1(pls)))),
inference(clausify,[status(thm)],[f_715_2]) ).
fof(f_716_1,plain,
! [A,N] :
( ? [R] :
( power_power_real(R,N) = A
& ord_less_real(zero_zero_real,R) )
| ~ ord_less_real(zero_zero_real,A)
| ~ ord_less_nat(zero_zero_nat,N) ),
inference(fof_nnf,[status(thm)],[fact_697_realpow__pos__nth]) ).
fof(f_716_2,plain,
! [U_1805,U_1804] :
( ? [U_1803] :
( power_power_real(U_1803,U_1804) = U_1805
& ord_less_real(zero_zero_real,U_1803) )
| ~ ord_less_real(zero_zero_real,U_1805)
| ~ ord_less_nat(zero_zero_nat,U_1804) ),
inference(variable_rename,[status(thm)],[f_716_1]) ).
fof(f_716_3,plain,
! [U_1805,U_1804] :
( ( power_power_real(sK12(U_1805,U_1804),U_1804) = U_1805
& ord_less_real(zero_zero_real,sK12(U_1805,U_1804)) )
| ~ ord_less_real(zero_zero_real,U_1805)
| ~ ord_less_nat(zero_zero_nat,U_1804) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_1803,sK12(U_1805,U_1804))],[f_716_2]) ).
fof(f_716_4,plain,
( ! [U_1804,U_1805] :
( power_power_real(sK12(U_1805,U_1804),U_1804) = U_1805
| ~ sP103(U_1804,U_1805) )
& ! [U_1804,U_1805] :
( ord_less_real(zero_zero_real,sK12(U_1805,U_1804))
| ~ sP103(U_1804,U_1805) )
& ! [U_1804,U_1805] :
( sP103(U_1804,U_1805)
| ~ ord_less_real(zero_zero_real,U_1805)
| ~ ord_less_nat(zero_zero_nat,U_1804) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP103])],[f_716_3]) ).
cnf(f_716_5,plain,
( sP103(U_1804,U_1805)
| ~ ord_less_real(zero_zero_real,U_1805)
| ~ ord_less_nat(zero_zero_nat,U_1804) ),
inference(clausify,[status(thm)],[f_716_4]) ).
cnf(f_716_6,plain,
( ord_less_real(zero_zero_real,sK12(U_1805,U_1804))
| ~ sP103(U_1804,U_1805) ),
inference(clausify,[status(thm)],[f_716_4]) ).
cnf(f_716_7,plain,
( power_power_real(sK12(U_1805,U_1804),U_1804) = U_1805
| ~ sP103(U_1804,U_1805) ),
inference(clausify,[status(thm)],[f_716_4]) ).
fof(f_717_1,negated_conjecture,
~ ? [X,Y] : plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
inference(negate,[status(cth)],[conj_0]) ).
fof(f_717_2,negated_conjecture,
! [X,Y] : plus_plus_int(power_power_int(X,number_number_of_nat(bit0(bit1(pls)))),power_power_int(Y,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
inference(fof_nnf,[status(thm)],[f_717_1]) ).
fof(f_717_3,negated_conjecture,
! [U_1807,U_1806] : plus_plus_int(power_power_int(U_1807,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1806,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
inference(variable_rename,[status(thm)],[f_717_2]) ).
fof(f_717_4,negated_conjecture,
! [U_1806,U_1807] : plus_plus_int(power_power_int(U_1807,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1806,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
inference(definitional_conversion,[status(esa)],[f_717_3]) ).
cnf(f_717_5,negated_conjecture,
plus_plus_int(power_power_int(U_1807,number_number_of_nat(bit0(bit1(pls)))),power_power_int(U_1806,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),
inference(clausify,[status(thm)],[f_717_4]) ).
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,
( minus_minus_int(Eq_x_0,Eq_x_1) = minus_minus_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_5,axiom,
( plus_plus_int(Eq_x_0,Eq_x_1) = plus_plus_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_6,axiom,
( times_times_int(Eq_x_0,Eq_x_1) = times_times_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_7,axiom,
( undefined_int(Eq_x_0) = undefined_int(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( bit0(Eq_x_0) = bit0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( bit1(Eq_x_0) = bit1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,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_11,axiom,
( power_power_int(Eq_x_0,Eq_x_1) = power_power_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_12,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_13,axiom,
( twoSqu140629262sum2sq(Eq_x_0) = twoSqu140629262sum2sq(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,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_15,axiom,
( plus_plus_real(Eq_x_0,Eq_x_1) = plus_plus_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_16,axiom,
( power_power_real(Eq_x_0,Eq_x_1) = power_power_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_17,axiom,
( number267125858f_real(Eq_x_0) = number267125858f_real(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( times_times_real(Eq_x_0,Eq_x_1) = times_times_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_19,axiom,
( plus_plus_nat(Eq_x_0,Eq_x_1) = plus_plus_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_20,axiom,
( power_power_nat(Eq_x_0,Eq_x_1) = power_power_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_21,axiom,
( times_times_nat(Eq_x_0,Eq_x_1) = times_times_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_22,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_23,axiom,
( minus_minus_nat(Eq_x_0,Eq_x_1) = minus_minus_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_24,axiom,
( minus_minus_real(Eq_x_0,Eq_x_1) = minus_minus_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_25,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,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_27,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_28,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_29,axiom,
( is_int(Eq_y_0)
| ~ is_int(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( ord_less_eq_int(Eq_y_0,Eq_y_1)
| ~ ord_less_eq_int(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( ord_less_int(Eq_y_0,Eq_y_1)
| ~ ord_less_int(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( zprime(Eq_y_0)
| ~ zprime(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( twoSqu142715416sum2sq(Eq_y_0)
| ~ twoSqu142715416sum2sq(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( ord_less_eq_real(Eq_y_0,Eq_y_1)
| ~ ord_less_eq_real(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( ord_less_real(Eq_y_0,Eq_y_1)
| ~ ord_less_real(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( ord_less_eq_nat(Eq_y_0,Eq_y_1)
| ~ ord_less_eq_nat(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( ord_less_nat(Eq_y_0,Eq_y_1)
| ~ ord_less_nat(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( dvd_dvd_int(Eq_y_0,Eq_y_1)
| ~ dvd_dvd_int(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( zcong(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ zcong(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( dvd_dvd_nat(Eq_y_0,Eq_y_1)
| ~ dvd_dvd_nat(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,axiom,
( dvd_dvd_real(Eq_y_0,Eq_y_1)
| ~ dvd_dvd_real(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_42,axiom,
( quadRes(Eq_y_0,Eq_y_1)
| ~ quadRes(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,axiom,
( sP2(Eq_y_0,Eq_y_1)
| ~ sP2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,axiom,
( sP3(Eq_y_0,Eq_y_1)
| ~ sP3(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_45,axiom,
( sP4(Eq_y_0,Eq_y_1)
| ~ sP4(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_46,axiom,
( sP5(Eq_y_0,Eq_y_1)
| ~ sP5(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_47,axiom,
( sP6(Eq_y_0,Eq_y_1)
| ~ sP6(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( sP7(Eq_y_0,Eq_y_1)
| ~ sP7(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_49,axiom,
( sP8(Eq_y_0,Eq_y_1)
| ~ sP8(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,axiom,
( sP9(Eq_y_0,Eq_y_1)
| ~ sP9(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_51,axiom,
( sP10(Eq_y_0,Eq_y_1)
| ~ sP10(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_52,axiom,
( sP11(Eq_y_0,Eq_y_1)
| ~ sP11(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_53,axiom,
( sP12(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_54,axiom,
( sP13(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP13(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_55,axiom,
( sP14(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP14(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_56,axiom,
( sP15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_57,axiom,
( sP16(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP16(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_58,axiom,
( sP17(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP17(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_59,axiom,
( sP18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP18(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_60,axiom,
( sP19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_61,axiom,
( sP20(Eq_y_0)
| ~ sP20(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_62,axiom,
( sP21(Eq_y_0)
| ~ sP21(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_63,axiom,
( sP22(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP22(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_64,axiom,
( sP23(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP23(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_65,axiom,
( sP24(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP24(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_66,axiom,
( sP25(Eq_y_0,Eq_y_1)
| ~ sP25(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_67,axiom,
( sP26(Eq_y_0,Eq_y_1)
| ~ sP26(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_68,axiom,
( sP27(Eq_y_0,Eq_y_1)
| ~ sP27(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_69,axiom,
( sP28(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP28(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_70,axiom,
( sP29(Eq_y_0,Eq_y_1)
| ~ sP29(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_71,axiom,
( sP30(Eq_y_0)
| ~ sP30(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_72,axiom,
( sP31(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP31(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_73,axiom,
( sP32(Eq_y_0,Eq_y_1)
| ~ sP32(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_74,axiom,
( sP33(Eq_y_0,Eq_y_1)
| ~ sP33(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_75,axiom,
( sP34(Eq_y_0,Eq_y_1)
| ~ sP34(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_76,axiom,
( sP35(Eq_y_0,Eq_y_1)
| ~ sP35(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_77,axiom,
( sP36(Eq_y_0,Eq_y_1)
| ~ sP36(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_78,axiom,
( sP37(Eq_y_0,Eq_y_1)
| ~ sP37(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_79,axiom,
( sP38(Eq_y_0,Eq_y_1)
| ~ sP38(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_80,axiom,
( sP39(Eq_y_0,Eq_y_1)
| ~ sP39(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_81,axiom,
( sP40(Eq_y_0,Eq_y_1)
| ~ sP40(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_82,axiom,
( sP41(Eq_y_0,Eq_y_1)
| ~ sP41(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_83,axiom,
( sP42(Eq_y_0,Eq_y_1)
| ~ sP42(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_84,axiom,
( sP43(Eq_y_0,Eq_y_1)
| ~ sP43(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_85,axiom,
( sP44(Eq_y_0,Eq_y_1)
| ~ sP44(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_86,axiom,
( sP45(Eq_y_0,Eq_y_1)
| ~ sP45(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_87,axiom,
( sP46(Eq_y_0)
| ~ sP46(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_88,axiom,
( sP47(Eq_y_0)
| ~ sP47(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_89,axiom,
( sP48(Eq_y_0,Eq_y_1)
| ~ sP48(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_90,axiom,
( sP49(Eq_y_0,Eq_y_1)
| ~ sP49(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_91,axiom,
( sP50(Eq_y_0,Eq_y_1)
| ~ sP50(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_92,axiom,
( sP51(Eq_y_0,Eq_y_1)
| ~ sP51(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_93,axiom,
( sP52(Eq_y_0,Eq_y_1)
| ~ sP52(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_94,axiom,
( sP53(Eq_y_0,Eq_y_1)
| ~ sP53(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_95,axiom,
( sP54(Eq_y_0,Eq_y_1)
| ~ sP54(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_96,axiom,
( sP55(Eq_y_0,Eq_y_1)
| ~ sP55(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_97,axiom,
( sP56(Eq_y_0,Eq_y_1)
| ~ sP56(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_98,axiom,
( sP57(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP57(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_99,axiom,
( sP58(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP58(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_100,axiom,
( sP59(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP59(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_101,axiom,
( sP60(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP60(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_102,axiom,
( sP61(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP61(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_103,axiom,
( sP62(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP62(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_104,axiom,
( sP63(Eq_y_0,Eq_y_1)
| ~ sP63(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_105,axiom,
( sP64(Eq_y_0)
| ~ sP64(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_106,axiom,
( sP65(Eq_y_0,Eq_y_1)
| ~ sP65(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_107,axiom,
( sP66(Eq_y_0,Eq_y_1)
| ~ sP66(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_108,axiom,
( sP67(Eq_y_0,Eq_y_1)
| ~ sP67(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_109,axiom,
( sP68(Eq_y_0,Eq_y_1)
| ~ sP68(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_110,axiom,
( sP69(Eq_y_0)
| ~ sP69(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_111,axiom,
( sP70(Eq_y_0)
| ~ sP70(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_112,axiom,
( sP71(Eq_y_0,Eq_y_1)
| ~ sP71(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_113,axiom,
( sP72(Eq_y_0,Eq_y_1)
| ~ sP72(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_114,axiom,
( sP73(Eq_y_0,Eq_y_1)
| ~ sP73(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_115,axiom,
( sP74(Eq_y_0,Eq_y_1)
| ~ sP74(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_116,axiom,
( sP75(Eq_y_0,Eq_y_1)
| ~ sP75(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_117,axiom,
( sP76(Eq_y_0,Eq_y_1)
| ~ sP76(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_118,axiom,
( sP77(Eq_y_0,Eq_y_1)
| ~ sP77(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_119,axiom,
( sP78(Eq_y_0,Eq_y_1)
| ~ sP78(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_120,axiom,
( sP79(Eq_y_0,Eq_y_1)
| ~ sP79(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_121,axiom,
( sP80(Eq_y_0,Eq_y_1)
| ~ sP80(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_122,axiom,
( sP81(Eq_y_0,Eq_y_1)
| ~ sP81(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_123,axiom,
( sP82(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP82(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_124,axiom,
( sP83(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP83(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_125,axiom,
( sP84(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP84(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_126,axiom,
( sP85(Eq_y_0,Eq_y_1)
| ~ sP85(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_127,axiom,
( sP86(Eq_y_0,Eq_y_1)
| ~ sP86(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_128,axiom,
( sP87(Eq_y_0,Eq_y_1)
| ~ sP87(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_129,axiom,
( sP88(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP88(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_130,axiom,
( sP89(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP89(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_131,axiom,
( sP90(Eq_y_0,Eq_y_1)
| ~ sP90(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_132,axiom,
( sP91(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP91(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_133,axiom,
( sP92(Eq_y_0,Eq_y_1)
| ~ sP92(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_134,axiom,
( sP93(Eq_y_0,Eq_y_1)
| ~ sP93(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_135,axiom,
( sP94(Eq_y_0,Eq_y_1)
| ~ sP94(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_136,axiom,
( sP95(Eq_y_0,Eq_y_1)
| ~ sP95(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_137,axiom,
( sP96(Eq_y_0,Eq_y_1)
| ~ sP96(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_138,axiom,
( sP97(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP97(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_139,axiom,
( sP98(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP98(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_140,axiom,
( sP99(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP99(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_141,axiom,
( sP100(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP100(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_142,axiom,
( sP101(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP101(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_143,axiom,
( sP102(Eq_y_0,Eq_y_1)
| ~ sP102(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_144,axiom,
( sP103(Eq_y_0,Eq_y_1)
| ~ sP103(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM926+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.02 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 19:27:45 UTC 2026
% 0.08/0.36 % CPUTime :
% 48.14/48.42 % SZS status Theorem for theBenchmark
% 48.14/48.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------