TPTP Problem File: NUM926+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : NUM926+1 : TPTP v8.2.0. Released v5.3.0.
% Domain : Number Theory
% Problem : Sum of two squares line 258, 100 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : s2s_100_fofmg_l258 [Bla11]
% Status : Theorem
% Rating : 0.22 v8.2.0, 0.19 v8.1.0, 0.14 v7.5.0, 0.16 v7.4.0, 0.23 v7.3.0, 0.17 v7.1.0, 0.22 v7.0.0, 0.20 v6.4.0, 0.27 v6.3.0, 0.29 v6.2.0, 0.36 v6.1.0, 0.27 v6.0.0, 0.30 v5.5.0, 0.41 v5.4.0, 0.46 v5.3.0
% Syntax : Number of formulae : 124 ( 76 unt; 0 def)
% Number of atoms : 183 ( 87 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 67 ( 8 ~; 3 |; 3 &)
% ( 36 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 0 prp; 1-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-2 aty)
% Number of variables : 244 ( 238 !; 6 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 15:34:05
% : Encoded with monomorphized guards.
%------------------------------------------------------------------------------
%----Relevant facts (123)
fof(fact_0_tpos,axiom,
ord_less_eq_int(one_one_int,t) ).
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) ) ).
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) ) ).
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)) ).
fof(fact_4_p,axiom,
zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) ).
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) ).
fof(fact_6_qf1pt,axiom,
twoSqu526106917sum2sq(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)) ).
fof(fact_7_zadd__power2,axiom,
! [A_8,B_4] : power_power_int(plus_plus_int(A_8,B_4),number_number_of_nat(bit0(bit1(pls)))) = plus_plus_int(plus_plus_int(power_power_int(A_8,number_number_of_nat(bit0(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit0(bit1(pls))),A_8),B_4)),power_power_int(B_4,number_number_of_nat(bit0(bit1(pls))))) ).
fof(fact_8_zadd__power3,axiom,
! [A_8,B_4] : power_power_int(plus_plus_int(A_8,B_4),number_number_of_nat(bit1(bit1(pls)))) = plus_plus_int(plus_plus_int(plus_plus_int(power_power_int(A_8,number_number_of_nat(bit1(bit1(pls)))),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),power_power_int(A_8,number_number_of_nat(bit0(bit1(pls))))),B_4)),times_times_int(times_times_int(number_number_of_int(bit1(bit1(pls))),A_8),power_power_int(B_4,number_number_of_nat(bit0(bit1(pls)))))),power_power_int(B_4,number_number_of_nat(bit1(bit1(pls))))) ).
fof(fact_9_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)) ).
fof(fact_10_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)) ).
fof(fact_11_power2__eq__square__number__of,axiom,
! [W_4] : power_power_int(number_number_of_int(W_4),number_number_of_nat(bit0(bit1(pls)))) = times_times_int(number_number_of_int(W_4),number_number_of_int(W_4)) ).
fof(fact_12_power2__eq__square__number__of,axiom,
! [W_4] : power_power_nat(number_number_of_nat(W_4),number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(number_number_of_nat(W_4),number_number_of_nat(W_4)) ).
fof(fact_13_cube__square,axiom,
! [A_8] : times_times_int(A_8,power_power_int(A_8,number_number_of_nat(bit0(bit1(pls))))) = power_power_int(A_8,number_number_of_nat(bit1(bit1(pls)))) ).
fof(fact_14_one__power2,axiom,
power_power_nat(one_one_nat,number_number_of_nat(bit0(bit1(pls)))) = one_one_nat ).
fof(fact_15_one__power2,axiom,
power_power_int(one_one_int,number_number_of_nat(bit0(bit1(pls)))) = one_one_int ).
fof(fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X_7] : times_times_int(X_7,X_7) = power_power_int(X_7,number_number_of_nat(bit0(bit1(pls)))) ).
fof(fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X_7] : times_times_nat(X_7,X_7) = power_power_nat(X_7,number_number_of_nat(bit0(bit1(pls)))) ).
fof(fact_18_power2__eq__square,axiom,
! [A_7] : power_power_int(A_7,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(A_7,A_7) ).
fof(fact_19_power2__eq__square,axiom,
! [A_7] : power_power_nat(A_7,number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(A_7,A_7) ).
fof(fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
! [X_6,N] : power_power_int(X_6,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N)) = times_times_int(power_power_int(X_6,N),power_power_int(X_6,N)) ).
fof(fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
! [X_6,N] : power_power_nat(X_6,times_times_nat(number_number_of_nat(bit0(bit1(pls))),N)) = times_times_nat(power_power_nat(X_6,N),power_power_nat(X_6,N)) ).
fof(fact_22_add__special_I2_J,axiom,
! [W_3] : plus_plus_int(one_one_int,number_number_of_int(W_3)) = number_number_of_int(plus_plus_int(bit1(pls),W_3)) ).
fof(fact_23_add__special_I3_J,axiom,
! [V_3] : plus_plus_int(number_number_of_int(V_3),one_one_int) = number_number_of_int(plus_plus_int(V_3,bit1(pls))) ).
fof(fact_24_one__add__one__is__two,axiom,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))) ).
fof(fact_25__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] : 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) ).
fof(fact_26_zle__refl,axiom,
! [W] : ord_less_eq_int(W,W) ).
fof(fact_27_zle__linear,axiom,
! [Z,W] :
( ord_less_eq_int(Z,W)
| ord_less_eq_int(W,Z) ) ).
fof(fact_28_zless__le,axiom,
! [Z_1,W_1] :
( ord_less_int(Z_1,W_1)
<=> ( ord_less_eq_int(Z_1,W_1)
& Z_1 != W_1 ) ) ).
fof(fact_29_zless__linear,axiom,
! [X_1,Y_1] :
( ord_less_int(X_1,Y_1)
| X_1 = Y_1
| ord_less_int(Y_1,X_1) ) ).
fof(fact_30_zle__trans,axiom,
! [K_1,I,J] :
( ord_less_eq_int(I,J)
=> ( ord_less_eq_int(J,K_1)
=> ord_less_eq_int(I,K_1) ) ) ).
fof(fact_31_zle__antisym,axiom,
! [Z,W] :
( ord_less_eq_int(Z,W)
=> ( ord_less_eq_int(W,Z)
=> Z = W ) ) ).
fof(fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X_5,P_1,Q_1] : power_power_int(power_power_int(X_5,P_1),Q_1) = power_power_int(X_5,times_times_nat(P_1,Q_1)) ).
fof(fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X_5,P_1,Q_1] : power_power_nat(power_power_nat(X_5,P_1),Q_1) = power_power_nat(X_5,times_times_nat(P_1,Q_1)) ).
fof(fact_34_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X_4] : power_power_int(X_4,one_one_nat) = X_4 ).
fof(fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X_4] : power_power_nat(X_4,one_one_nat) = X_4 ).
fof(fact_36_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)) ).
fof(fact_37_le__number__of__eq__not__less,axiom,
! [V_2,W_1] :
( ord_less_eq_nat(number_number_of_nat(V_2),number_number_of_nat(W_1))
<=> ~ ord_less_nat(number_number_of_nat(W_1),number_number_of_nat(V_2)) ) ).
fof(fact_38_le__number__of__eq__not__less,axiom,
! [V_2,W_1] :
( ord_less_eq_int(number_number_of_int(V_2),number_number_of_int(W_1))
<=> ~ ord_less_int(number_number_of_int(W_1),number_number_of_int(V_2)) ) ).
fof(fact_39_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) ) ).
fof(fact_40_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) ) ).
fof(fact_41_zadd__zless__mono,axiom,
! [Z_2,Z,W_2,W] :
( ord_less_int(W_2,W)
=> ( ord_less_eq_int(Z_2,Z)
=> ord_less_int(plus_plus_int(W_2,Z_2),plus_plus_int(W,Z)) ) ) ).
fof(fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X_3,P,Q] : times_times_int(power_power_int(X_3,P),power_power_int(X_3,Q)) = power_power_int(X_3,plus_plus_nat(P,Q)) ).
fof(fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X_3,P,Q] : times_times_nat(power_power_nat(X_3,P),power_power_nat(X_3,Q)) = power_power_nat(X_3,plus_plus_nat(P,Q)) ).
fof(fact_44_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)) ).
fof(fact_45_nat__mult__2,axiom,
! [Z] : times_times_nat(number_number_of_nat(bit0(bit1(pls))),Z) = plus_plus_nat(Z,Z) ).
fof(fact_46_nat__mult__2__right,axiom,
! [Z] : times_times_nat(Z,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(Z,Z) ).
fof(fact_47_nat__1__add__1,axiom,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))) ).
fof(fact_48_less__int__code_I16_J,axiom,
! [K1,K2] :
( ord_less_int(bit1(K1),bit1(K2))
<=> ord_less_int(K1,K2) ) ).
fof(fact_49_rel__simps_I17_J,axiom,
! [K,L] :
( ord_less_int(bit1(K),bit1(L))
<=> ord_less_int(K,L) ) ).
fof(fact_50_less__eq__int__code_I16_J,axiom,
! [K1,K2] :
( ord_less_eq_int(bit1(K1),bit1(K2))
<=> ord_less_eq_int(K1,K2) ) ).
fof(fact_51_rel__simps_I34_J,axiom,
! [K,L] :
( ord_less_eq_int(bit1(K),bit1(L))
<=> ord_less_eq_int(K,L) ) ).
fof(fact_52_rel__simps_I2_J,axiom,
~ ord_less_int(pls,pls) ).
fof(fact_53_less__int__code_I13_J,axiom,
! [K1,K2] :
( ord_less_int(bit0(K1),bit0(K2))
<=> ord_less_int(K1,K2) ) ).
fof(fact_54_rel__simps_I14_J,axiom,
! [K,L] :
( ord_less_int(bit0(K),bit0(L))
<=> ord_less_int(K,L) ) ).
fof(fact_55_rel__simps_I19_J,axiom,
ord_less_eq_int(pls,pls) ).
fof(fact_56_less__eq__int__code_I13_J,axiom,
! [K1,K2] :
( ord_less_eq_int(bit0(K1),bit0(K2))
<=> ord_less_eq_int(K1,K2) ) ).
fof(fact_57_rel__simps_I31_J,axiom,
! [K,L] :
( ord_less_eq_int(bit0(K),bit0(L))
<=> ord_less_eq_int(K,L) ) ).
fof(fact_58_less__number__of__int__code,axiom,
! [K,L] :
( ord_less_int(number_number_of_int(K),number_number_of_int(L))
<=> ord_less_int(K,L) ) ).
fof(fact_59_less__eq__number__of__int__code,axiom,
! [K,L] :
( ord_less_eq_int(number_number_of_int(K),number_number_of_int(L))
<=> ord_less_eq_int(K,L) ) ).
fof(fact_60_zadd__strict__right__mono,axiom,
! [K_1,I,J] :
( ord_less_int(I,J)
=> ord_less_int(plus_plus_int(I,K_1),plus_plus_int(J,K_1)) ) ).
fof(fact_61_zadd__left__mono,axiom,
! [K_1,I,J] :
( ord_less_eq_int(I,J)
=> ord_less_eq_int(plus_plus_int(K_1,I),plus_plus_int(K_1,J)) ) ).
fof(fact_62_add__nat__number__of,axiom,
! [V_1,V] :
( ( ord_less_int(V,pls)
=> plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(V_1) )
& ( ~ ord_less_int(V,pls)
=> ( ( ord_less_int(V_1,pls)
=> plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(V) )
& ( ~ ord_less_int(V_1,pls)
=> plus_plus_nat(number_number_of_nat(V),number_number_of_nat(V_1)) = number_number_of_nat(plus_plus_int(V,V_1)) ) ) ) ) ).
fof(fact_63_nat__numeral__1__eq__1,axiom,
number_number_of_nat(bit1(pls)) = one_one_nat ).
fof(fact_64_Numeral1__eq1__nat,axiom,
one_one_nat = number_number_of_nat(bit1(pls)) ).
fof(fact_65_rel__simps_I29_J,axiom,
! [K] :
( ord_less_eq_int(bit1(K),pls)
<=> ord_less_int(K,pls) ) ).
fof(fact_66_rel__simps_I5_J,axiom,
! [K] :
( ord_less_int(pls,bit1(K))
<=> ord_less_eq_int(pls,K) ) ).
fof(fact_67_less__eq__int__code_I15_J,axiom,
! [K1,K2] :
( ord_less_eq_int(bit1(K1),bit0(K2))
<=> ord_less_int(K1,K2) ) ).
fof(fact_68_rel__simps_I33_J,axiom,
! [K,L] :
( ord_less_eq_int(bit1(K),bit0(L))
<=> ord_less_int(K,L) ) ).
fof(fact_69_less__int__code_I14_J,axiom,
! [K1,K2] :
( ord_less_int(bit0(K1),bit1(K2))
<=> ord_less_eq_int(K1,K2) ) ).
fof(fact_70_rel__simps_I15_J,axiom,
! [K,L] :
( ord_less_int(bit0(K),bit1(L))
<=> ord_less_eq_int(K,L) ) ).
fof(fact_71_zless__imp__add1__zle,axiom,
! [W,Z] :
( ord_less_int(W,Z)
=> ord_less_eq_int(plus_plus_int(W,one_one_int),Z) ) ).
fof(fact_72_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) ) ).
fof(fact_73_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) ) ).
fof(fact_74_zprime__2,axiom,
zprime(number_number_of_int(bit0(bit1(pls)))) ).
fof(fact_75_is__mult__sum2sq,axiom,
! [Y_1,X_1] :
( twoSqu526106917sum2sq(X_1)
=> ( twoSqu526106917sum2sq(Y_1)
=> twoSqu526106917sum2sq(times_times_int(X_1,Y_1)) ) ) ).
fof(fact_76_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)) ).
fof(fact_77_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)) ).
fof(fact_78_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)) ).
fof(fact_79_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)) ).
fof(fact_80_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))) ).
fof(fact_81_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))) ).
fof(fact_82_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) ).
fof(fact_83_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) ).
fof(fact_84_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)) ).
fof(fact_85_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)) ).
fof(fact_86_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) ).
fof(fact_87_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) ).
fof(fact_88_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)) ).
fof(fact_89_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)) ).
fof(fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [A_6,B_3] : times_times_int(A_6,B_3) = times_times_int(B_3,A_6) ).
fof(fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [A_6,B_3] : times_times_nat(A_6,B_3) = times_times_nat(B_3,A_6) ).
fof(fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [A_5,B_2,C_5,D_2] : plus_plus_int(plus_plus_int(A_5,B_2),plus_plus_int(C_5,D_2)) = plus_plus_int(plus_plus_int(A_5,C_5),plus_plus_int(B_2,D_2)) ).
fof(fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [A_5,B_2,C_5,D_2] : plus_plus_nat(plus_plus_nat(A_5,B_2),plus_plus_nat(C_5,D_2)) = plus_plus_nat(plus_plus_nat(A_5,C_5),plus_plus_nat(B_2,D_2)) ).
fof(fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [A_4,B_1,C_4] : plus_plus_int(plus_plus_int(A_4,B_1),C_4) = plus_plus_int(plus_plus_int(A_4,C_4),B_1) ).
fof(fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [A_4,B_1,C_4] : plus_plus_nat(plus_plus_nat(A_4,B_1),C_4) = plus_plus_nat(plus_plus_nat(A_4,C_4),B_1) ).
fof(fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [A_3,B,C_3] : plus_plus_int(plus_plus_int(A_3,B),C_3) = plus_plus_int(A_3,plus_plus_int(B,C_3)) ).
fof(fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [A_3,B,C_3] : plus_plus_nat(plus_plus_nat(A_3,B),C_3) = plus_plus_nat(A_3,plus_plus_nat(B,C_3)) ).
fof(fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [A_2,C_2,D_1] : plus_plus_int(A_2,plus_plus_int(C_2,D_1)) = plus_plus_int(plus_plus_int(A_2,C_2),D_1) ).
fof(fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [A_2,C_2,D_1] : plus_plus_nat(A_2,plus_plus_nat(C_2,D_1)) = plus_plus_nat(plus_plus_nat(A_2,C_2),D_1) ).
fof(fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [A_1,C_1,D] : plus_plus_int(A_1,plus_plus_int(C_1,D)) = plus_plus_int(C_1,plus_plus_int(A_1,D)) ).
fof(fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [A_1,C_1,D] : plus_plus_nat(A_1,plus_plus_nat(C_1,D)) = plus_plus_nat(C_1,plus_plus_nat(A_1,D)) ).
fof(fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [A,C] : plus_plus_int(A,C) = plus_plus_int(C,A) ).
fof(fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [A,C] : plus_plus_nat(A,C) = plus_plus_nat(C,A) ).
fof(fact_104_eq__number__of,axiom,
! [X_2,Y_2] :
( number_number_of_int(X_2) = number_number_of_int(Y_2)
<=> X_2 = Y_2 ) ).
fof(fact_105_number__of__reorient,axiom,
! [W_1,X_2] :
( number_number_of_nat(W_1) = X_2
<=> X_2 = number_number_of_nat(W_1) ) ).
fof(fact_106_number__of__reorient,axiom,
! [W_1,X_2] :
( number_number_of_int(W_1) = X_2
<=> X_2 = number_number_of_int(W_1) ) ).
fof(fact_107_rel__simps_I51_J,axiom,
! [K,L] :
( bit1(K) = bit1(L)
<=> K = L ) ).
fof(fact_108_rel__simps_I48_J,axiom,
! [K,L] :
( bit0(K) = bit0(L)
<=> K = L ) ).
fof(fact_109_zmult__assoc,axiom,
! [Z1,Z2,Z3] : times_times_int(times_times_int(Z1,Z2),Z3) = times_times_int(Z1,times_times_int(Z2,Z3)) ).
fof(fact_110_zmult__commute,axiom,
! [Z,W] : times_times_int(Z,W) = times_times_int(W,Z) ).
fof(fact_111_number__of__is__id,axiom,
! [K_1] : number_number_of_int(K_1) = K_1 ).
fof(fact_112_zadd__assoc,axiom,
! [Z1,Z2,Z3] : plus_plus_int(plus_plus_int(Z1,Z2),Z3) = plus_plus_int(Z1,plus_plus_int(Z2,Z3)) ).
fof(fact_113_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)) ).
fof(fact_114_zadd__commute,axiom,
! [Z,W] : plus_plus_int(Z,W) = plus_plus_int(W,Z) ).
fof(fact_115_rel__simps_I12_J,axiom,
! [K] :
( ord_less_int(bit1(K),pls)
<=> ord_less_int(K,pls) ) ).
fof(fact_116_less__int__code_I15_J,axiom,
! [K1,K2] :
( ord_less_int(bit1(K1),bit0(K2))
<=> ord_less_int(K1,K2) ) ).
fof(fact_117_rel__simps_I16_J,axiom,
! [K,L] :
( ord_less_int(bit1(K),bit0(L))
<=> ord_less_int(K,L) ) ).
fof(fact_118_rel__simps_I10_J,axiom,
! [K] :
( ord_less_int(bit0(K),pls)
<=> ord_less_int(K,pls) ) ).
fof(fact_119_rel__simps_I4_J,axiom,
! [K] :
( ord_less_int(pls,bit0(K))
<=> ord_less_int(pls,K) ) ).
fof(fact_120_rel__simps_I22_J,axiom,
! [K] :
( ord_less_eq_int(pls,bit1(K))
<=> ord_less_eq_int(pls,K) ) ).
fof(fact_121_less__eq__int__code_I14_J,axiom,
! [K1,K2] :
( ord_less_eq_int(bit0(K1),bit1(K2))
<=> ord_less_eq_int(K1,K2) ) ).
fof(fact_122_rel__simps_I32_J,axiom,
! [K,L] :
( ord_less_eq_int(bit0(K),bit1(L))
<=> ord_less_eq_int(K,L) ) ).
%----Conjectures (1)
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) ).
%------------------------------------------------------------------------------