TSTP Solution File: NUM926+2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM926+2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 10:25:50 EDT 2023
% Result : Theorem 4.15s 4.18s
% Output : CNFRefutation 4.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM926+2 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 08:45:02 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 4.01/4.13 %-------------------------------------------
% 4.01/4.13 % File :CSE---1.6
% 4.01/4.13 % Problem :theBenchmark
% 4.01/4.13 % Transform :cnf
% 4.01/4.13 % Format :tptp:raw
% 4.01/4.13 % Command :java -jar mcs_scs.jar %d %s
% 4.01/4.13
% 4.01/4.13 % Result :Theorem 3.260000s
% 4.01/4.13 % Output :CNFRefutation 3.260000s
% 4.01/4.13 %-------------------------------------------
% 4.01/4.13 %------------------------------------------------------------------------------
% 4.01/4.13 % File : NUM926+2 : TPTP v8.1.2. Released v5.3.0.
% 4.01/4.13 % Domain : Number Theory
% 4.01/4.13 % Problem : Sum of two squares line 258, 500 axioms selected
% 4.01/4.13 % Version : Especial.
% 4.01/4.13 % English :
% 4.01/4.13
% 4.01/4.13 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 4.01/4.13 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 4.01/4.13 % Source : [Bla11]
% 4.01/4.13 % Names : s2s_500_fofmg_l258 [Bla11]
% 4.01/4.13
% 4.01/4.13 % Status : Theorem
% 4.01/4.13 % Rating : 0.47 v8.1.0, 0.42 v7.5.0, 0.44 v7.4.0, 0.43 v7.3.0, 0.45 v7.2.0, 0.41 v7.1.0, 0.39 v7.0.0, 0.33 v6.4.0, 0.38 v6.3.0, 0.46 v6.2.0, 0.48 v6.1.0, 0.57 v6.0.0, 0.61 v5.5.0, 0.74 v5.4.0, 0.79 v5.3.0
% 4.01/4.13 % Syntax : Number of formulae : 717 ( 332 unt; 0 def)
% 4.01/4.13 % Number of atoms : 1509 ( 570 equ)
% 4.01/4.13 % Maximal formula atoms : 9 ( 2 avg)
% 4.01/4.13 % Number of connectives : 910 ( 118 ~; 36 |; 101 &)
% 4.01/4.13 % ( 161 <=>; 494 =>; 0 <=; 0 <~>)
% 4.01/4.13 % Maximal formula depth : 13 ( 4 avg)
% 4.01/4.13 % Maximal term depth : 10 ( 2 avg)
% 4.01/4.13 % Number of predicates : 15 ( 14 usr; 0 prp; 1-3 aty)
% 4.01/4.13 % Number of functors : 34 ( 34 usr; 13 con; 0-2 aty)
% 4.01/4.13 % Number of variables : 1371 (1361 !; 10 ?)
% 4.01/4.13 % SPC : FOF_THM_RFO_SEQ
% 4.01/4.13
% 4.01/4.13 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 4.01/4.13 % 2011-08-09 14:39:04
% 4.01/4.13 %------------------------------------------------------------------------------
% 4.01/4.13 %----Explicit typings (18)
% 4.01/4.13 fof(gsy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint,axiom,
% 4.01/4.13 ! [B_1_1,B_2_1] :
% 4.01/4.13 ( ( is_int(B_1_1)
% 4.01/4.13 & is_int(B_2_1) )
% 4.01/4.14 => is_int(minus_minus_int(B_1_1,B_2_1)) ) ).
% 4.01/4.14
% 4.01/4.14 fof(gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint,hypothesis,
% 4.01/4.14 is_int(one_one_int) ).
% 4.01/4.14
% 4.01/4.14 fof(gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint,hypothesis,
% 4.01/4.14 ! [B_1_1,B_2_1] :
% 4.01/4.14 ( ( is_int(B_1_1)
% 4.01/4.14 & is_int(B_2_1) )
% 4.01/4.14 => is_int(plus_plus_int(B_1_1,B_2_1)) ) ).
% 4.01/4.14
% 4.01/4.14 fof(gsy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint,hypothesis,
% 4.01/4.14 ! [B_1_1,B_2_1] :
% 4.01/4.14 ( ( is_int(B_1_1)
% 4.01/4.14 & is_int(B_2_1) )
% 4.01/4.14 => is_int(times_times_int(B_1_1,B_2_1)) ) ).
% 4.01/4.14
% 4.01/4.14 fof(gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint,axiom,
% 4.01/4.14 is_int(zero_zero_int) ).
% 4.01/4.14
% 4.01/4.14 fof(gsy_c_HOL_Oundefined_000tc__Int__Oint,axiom,
% 4.01/4.14 is_int(undefined_int(int)) ).
% 4.01/4.14
% 4.01/4.14 fof(gsy_c_Int_OBit0,hypothesis,
% 4.01/4.14 ! [B_1_1] :
% 4.01/4.14 ( is_int(B_1_1)
% 4.01/4.14 => is_int(bit0(B_1_1)) ) ).
% 4.01/4.14
% 4.01/4.14 fof(gsy_c_Int_OBit1,hypothesis,
% 4.01/4.14 ! [B_1_1] :
% 4.01/4.14 ( is_int(B_1_1)
% 4.01/4.14 => is_int(bit1(B_1_1)) ) ).
% 4.01/4.14
% 4.01/4.14 fof(gsy_c_Int_OMin,axiom,
% 4.01/4.14 is_int(min) ).
% 4.01/4.14
% 4.01/4.14 fof(gsy_c_Int_OPls,hypothesis,
% 4.01/4.14 is_int(pls) ).
% 4.01/4.14
% 4.01/4.14 fof(gsy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint,hypothesis,
% 4.01/4.14 ! [B_1_1] :
% 4.01/4.14 ( is_int(B_1_1)
% 4.01/4.14 => is_int(number_number_of_int(B_1_1)) ) ).
% 4.01/4.14
% 4.01/4.14 fof(gsy_c_Power_Opower__class_Opower_000tc__Int__Oint,hypothesis,
% 4.01/4.14 ! [B_1_1,B_2_1] :
% 4.01/4.14 ( is_int(B_1_1)
% 4.01/4.14 => is_int(power_power_int(B_1_1,B_2_1)) ) ).
% 4.01/4.14
% 4.01/4.14 fof(gsy_c_Residues_OLegendre,axiom,
% 4.01/4.14 ! [B_1_1,B_2_1] :
% 4.01/4.14 ( ( is_int(B_1_1)
% 4.01/4.14 & is_int(B_2_1) )
% 4.01/4.14 => is_int(legendre(B_1_1,B_2_1)) ) ).
% 4.01/4.14
% 4.01/4.14 fof(gsy_c_TwoSquares__Mirabelle__ccrtsbwhjp_Osum2sq,axiom,
% 4.01/4.14 ! [B_1_1] : is_int(twoSqu140629262sum2sq(B_1_1)) ).
% 4.01/4.14
% 4.01/4.14 fof(gsy_v_m,hypothesis,
% 4.01/4.14 is_int(m) ).
% 4.01/4.14
% 4.01/4.14 fof(gsy_v_s1____,axiom,
% 4.01/4.14 is_int(s1) ).
% 4.01/4.14
% 4.01/4.14 fof(gsy_v_s____,axiom,
% 4.01/4.14 is_int(s) ).
% 4.01/4.14
% 4.01/4.14 fof(gsy_v_t____,axiom,
% 4.01/4.14 is_int(t) ).
% 4.01/4.14
% 4.01/4.14 %----Relevant facts (698)
% 4.01/4.14 fof(fact_0_tpos,axiom,
% 4.01/4.14 ord_less_eq_int(one_one_int,t) ).
% 4.01/4.14
% 4.01/4.14 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,
% 4.01/4.14 ( t = one_one_int
% 4.01/4.14 => ? [X,Y] :
% 4.01/4.14 ( is_int(X)
% 4.01/4.14 & is_int(Y)
% 4.01/4.14 & 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) ) ) ).
% 4.01/4.14
% 4.01/4.14 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,
% 4.01/4.14 ( ord_less_int(one_one_int,t)
% 4.01/4.14 => ? [X,Y] :
% 4.01/4.14 ( is_int(X)
% 4.01/4.14 & is_int(Y)
% 4.01/4.14 & 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) ) ) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_3_t__l__p,axiom,
% 4.01/4.14 ord_less_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_4_p,axiom,
% 4.01/4.14 zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_5_t,axiom,
% 4.01/4.14 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) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_6_qf1pt,axiom,
% 4.01/4.14 twoSqu142715416sum2sq(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_7_zadd__power2,axiom,
% 4.01/4.14 ! [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))))) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_8_zadd__power3,axiom,
% 4.01/4.14 ! [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))))) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_9_power2__sum,axiom,
% 4.01/4.14 ! [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)) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_10_power2__sum,axiom,
% 4.01/4.14 ! [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)) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_11_power2__sum,axiom,
% 4.01/4.14 ! [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)) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_12_power2__eq__square__number__of,axiom,
% 4.01/4.14 ! [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)) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_13_power2__eq__square__number__of,axiom,
% 4.01/4.14 ! [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)) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_14_power2__eq__square__number__of,axiom,
% 4.01/4.14 ! [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)) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_15_cube__square,axiom,
% 4.01/4.14 ! [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)))) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_16_one__power2,axiom,
% 4.01/4.14 power_power_real(one_one_real,number_number_of_nat(bit0(bit1(pls)))) = one_one_real ).
% 4.01/4.14
% 4.01/4.14 fof(fact_17_one__power2,axiom,
% 4.01/4.14 power_power_nat(one_one_nat,number_number_of_nat(bit0(bit1(pls)))) = one_one_nat ).
% 4.01/4.14
% 4.01/4.14 fof(fact_18_one__power2,axiom,
% 4.01/4.14 power_power_int(one_one_int,number_number_of_nat(bit0(bit1(pls)))) = one_one_int ).
% 4.01/4.14
% 4.01/4.14 fof(fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 4.01/4.14 ! [X_21] : times_times_nat(X_21,X_21) = power_power_nat(X_21,number_number_of_nat(bit0(bit1(pls)))) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 4.01/4.14 ! [X_21] : times_times_real(X_21,X_21) = power_power_real(X_21,number_number_of_nat(bit0(bit1(pls)))) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 4.01/4.14 ! [X_21] : times_times_int(X_21,X_21) = power_power_int(X_21,number_number_of_nat(bit0(bit1(pls)))) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_22_power2__eq__square,axiom,
% 4.01/4.14 ! [A_57] : power_power_nat(A_57,number_number_of_nat(bit0(bit1(pls)))) = times_times_nat(A_57,A_57) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_23_power2__eq__square,axiom,
% 4.01/4.14 ! [A_57] : power_power_real(A_57,number_number_of_nat(bit0(bit1(pls)))) = times_times_real(A_57,A_57) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_24_power2__eq__square,axiom,
% 4.01/4.14 ! [A_57] : power_power_int(A_57,number_number_of_nat(bit0(bit1(pls)))) = times_times_int(A_57,A_57) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 4.01/4.14 ! [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)) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 4.01/4.14 ! [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)) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 4.01/4.14 ! [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)) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_28_add__special_I2_J,axiom,
% 4.01/4.14 ! [W_14] : plus_plus_real(one_one_real,number267125858f_real(W_14)) = number267125858f_real(plus_plus_int(bit1(pls),W_14)) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_29_add__special_I2_J,axiom,
% 4.01/4.14 ! [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)) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_30_add__special_I3_J,axiom,
% 4.01/4.14 ! [V_17] : plus_plus_real(number267125858f_real(V_17),one_one_real) = number267125858f_real(plus_plus_int(V_17,bit1(pls))) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_31_add__special_I3_J,axiom,
% 4.01/4.14 ! [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))) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_32_one__add__one__is__two,axiom,
% 4.01/4.14 plus_plus_real(one_one_real,one_one_real) = number267125858f_real(bit0(bit1(pls))) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_33_one__add__one__is__two,axiom,
% 4.01/4.14 plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))) ).
% 4.01/4.14
% 4.01/4.14 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,
% 4.01/4.14 ~ ! [T] :
% 4.01/4.14 ( is_int(T)
% 4.01/4.14 => 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) ) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_35_zle__refl,axiom,
% 4.01/4.14 ! [W] : ord_less_eq_int(W,W) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_36_zle__linear,axiom,
% 4.01/4.14 ! [Z,W] :
% 4.01/4.14 ( ord_less_eq_int(Z,W)
% 4.01/4.14 | ord_less_eq_int(W,Z) ) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_37_zless__le,axiom,
% 4.01/4.14 ! [Z_1,W_1] :
% 4.01/4.14 ( ( is_int(Z_1)
% 4.01/4.14 & is_int(W_1) )
% 4.01/4.14 => ( ord_less_int(Z_1,W_1)
% 4.01/4.14 <=> ( ord_less_eq_int(Z_1,W_1)
% 4.01/4.14 & Z_1 != W_1 ) ) ) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_38_zless__linear,axiom,
% 4.01/4.14 ! [X_1,Y_1] :
% 4.01/4.14 ( ( is_int(X_1)
% 4.01/4.14 & is_int(Y_1) )
% 4.01/4.14 => ( ord_less_int(X_1,Y_1)
% 4.01/4.14 | X_1 = Y_1
% 4.01/4.14 | ord_less_int(Y_1,X_1) ) ) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_39_zle__trans,axiom,
% 4.01/4.14 ! [K,I,J] :
% 4.01/4.14 ( ord_less_eq_int(I,J)
% 4.01/4.14 => ( ord_less_eq_int(J,K)
% 4.01/4.14 => ord_less_eq_int(I,K) ) ) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_40_zle__antisym,axiom,
% 4.01/4.14 ! [Z,W] :
% 4.01/4.14 ( ( is_int(Z)
% 4.01/4.14 & is_int(W) )
% 4.01/4.14 => ( ord_less_eq_int(Z,W)
% 4.01/4.14 => ( ord_less_eq_int(W,Z)
% 4.01/4.14 => Z = W ) ) ) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 4.01/4.14 ! [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)) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 4.01/4.14 ! [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)) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 4.01/4.14 ! [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)) ).
% 4.01/4.14
% 4.01/4.14 fof(fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 4.01/4.14 ! [X_18] : power_power_nat(X_18,one_one_nat) = X_18 ).
% 4.01/4.14
% 4.01/4.15 fof(fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 4.01/4.15 ! [X_18] : power_power_real(X_18,one_one_nat) = X_18 ).
% 4.01/4.15
% 4.01/4.15 fof(fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 4.01/4.15 ! [X_18] :
% 4.01/4.15 ( is_int(X_18)
% 4.01/4.15 => power_power_int(X_18,one_one_nat) = X_18 ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_47_zpower__zpower,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_48_le__number__of__eq__not__less,axiom,
% 4.01/4.15 ! [V_3,W_1] :
% 4.01/4.15 ( ord_less_eq_real(number267125858f_real(V_3),number267125858f_real(W_1))
% 4.01/4.15 <=> ~ ord_less_real(number267125858f_real(W_1),number267125858f_real(V_3)) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_49_le__number__of__eq__not__less,axiom,
% 4.01/4.15 ! [V_3,W_1] :
% 4.01/4.15 ( ord_less_eq_nat(number_number_of_nat(V_3),number_number_of_nat(W_1))
% 4.01/4.15 <=> ~ ord_less_nat(number_number_of_nat(W_1),number_number_of_nat(V_3)) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_50_le__number__of__eq__not__less,axiom,
% 4.01/4.15 ! [V_3,W_1] :
% 4.01/4.15 ( ord_less_eq_int(number_number_of_int(V_3),number_number_of_int(W_1))
% 4.01/4.15 <=> ~ ord_less_int(number_number_of_int(W_1),number_number_of_int(V_3)) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_51_less__number__of,axiom,
% 4.01/4.15 ! [X_2,Y_2] :
% 4.01/4.15 ( ord_less_real(number267125858f_real(X_2),number267125858f_real(Y_2))
% 4.01/4.15 <=> ord_less_int(X_2,Y_2) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_52_less__number__of,axiom,
% 4.01/4.15 ! [X_2,Y_2] :
% 4.01/4.15 ( ord_less_int(number_number_of_int(X_2),number_number_of_int(Y_2))
% 4.01/4.15 <=> ord_less_int(X_2,Y_2) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_53_le__number__of,axiom,
% 4.01/4.15 ! [X_2,Y_2] :
% 4.01/4.15 ( ord_less_eq_real(number267125858f_real(X_2),number267125858f_real(Y_2))
% 4.01/4.15 <=> ord_less_eq_int(X_2,Y_2) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_54_le__number__of,axiom,
% 4.01/4.15 ! [X_2,Y_2] :
% 4.01/4.15 ( ord_less_eq_int(number_number_of_int(X_2),number_number_of_int(Y_2))
% 4.01/4.15 <=> ord_less_eq_int(X_2,Y_2) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_55_zadd__zless__mono,axiom,
% 4.01/4.15 ! [Z_9,Z,W_13,W] :
% 4.01/4.15 ( ord_less_int(W_13,W)
% 4.01/4.15 => ( ord_less_eq_int(Z_9,Z)
% 4.01/4.15 => ord_less_int(plus_plus_int(W_13,Z_9),plus_plus_int(W,Z)) ) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_59_zpower__zadd__distrib,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_60_nat__mult__2,axiom,
% 4.01/4.15 ! [Z] : times_times_nat(number_number_of_nat(bit0(bit1(pls))),Z) = plus_plus_nat(Z,Z) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_61_nat__mult__2__right,axiom,
% 4.01/4.15 ! [Z] : times_times_nat(Z,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(Z,Z) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_62_nat__1__add__1,axiom,
% 4.01/4.15 plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_63_less__int__code_I16_J,axiom,
% 4.01/4.15 ! [K1,K2] :
% 4.01/4.15 ( ord_less_int(bit1(K1),bit1(K2))
% 4.01/4.15 <=> ord_less_int(K1,K2) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_64_rel__simps_I17_J,axiom,
% 4.01/4.15 ! [K_1,L_1] :
% 4.01/4.15 ( ord_less_int(bit1(K_1),bit1(L_1))
% 4.01/4.15 <=> ord_less_int(K_1,L_1) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_65_less__eq__int__code_I16_J,axiom,
% 4.01/4.15 ! [K1,K2] :
% 4.01/4.15 ( ord_less_eq_int(bit1(K1),bit1(K2))
% 4.01/4.15 <=> ord_less_eq_int(K1,K2) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_66_rel__simps_I34_J,axiom,
% 4.01/4.15 ! [K_1,L_1] :
% 4.01/4.15 ( ord_less_eq_int(bit1(K_1),bit1(L_1))
% 4.01/4.15 <=> ord_less_eq_int(K_1,L_1) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_67_rel__simps_I2_J,axiom,
% 4.01/4.15 ~ ord_less_int(pls,pls) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_68_less__int__code_I13_J,axiom,
% 4.01/4.15 ! [K1,K2] :
% 4.01/4.15 ( ord_less_int(bit0(K1),bit0(K2))
% 4.01/4.15 <=> ord_less_int(K1,K2) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_69_rel__simps_I14_J,axiom,
% 4.01/4.15 ! [K_1,L_1] :
% 4.01/4.15 ( ord_less_int(bit0(K_1),bit0(L_1))
% 4.01/4.15 <=> ord_less_int(K_1,L_1) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_70_rel__simps_I19_J,axiom,
% 4.01/4.15 ord_less_eq_int(pls,pls) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_71_less__eq__int__code_I13_J,axiom,
% 4.01/4.15 ! [K1,K2] :
% 4.01/4.15 ( ord_less_eq_int(bit0(K1),bit0(K2))
% 4.01/4.15 <=> ord_less_eq_int(K1,K2) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_72_rel__simps_I31_J,axiom,
% 4.01/4.15 ! [K_1,L_1] :
% 4.01/4.15 ( ord_less_eq_int(bit0(K_1),bit0(L_1))
% 4.01/4.15 <=> ord_less_eq_int(K_1,L_1) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_73_less__number__of__int__code,axiom,
% 4.01/4.15 ! [K_1,L_1] :
% 4.01/4.15 ( ord_less_int(number_number_of_int(K_1),number_number_of_int(L_1))
% 4.01/4.15 <=> ord_less_int(K_1,L_1) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_74_less__eq__number__of__int__code,axiom,
% 4.01/4.15 ! [K_1,L_1] :
% 4.01/4.15 ( ord_less_eq_int(number_number_of_int(K_1),number_number_of_int(L_1))
% 4.01/4.15 <=> ord_less_eq_int(K_1,L_1) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_75_zadd__strict__right__mono,axiom,
% 4.01/4.15 ! [K,I,J] :
% 4.01/4.15 ( ord_less_int(I,J)
% 4.01/4.15 => ord_less_int(plus_plus_int(I,K),plus_plus_int(J,K)) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_76_zadd__left__mono,axiom,
% 4.01/4.15 ! [K,I,J] :
% 4.01/4.15 ( ord_less_eq_int(I,J)
% 4.01/4.15 => ord_less_eq_int(plus_plus_int(K,I),plus_plus_int(K,J)) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_77_add__nat__number__of,axiom,
% 4.01/4.15 ! [V_2,V_1] :
% 4.01/4.15 ( ( ord_less_int(V_1,pls)
% 4.01/4.15 => plus_plus_nat(number_number_of_nat(V_1),number_number_of_nat(V_2)) = number_number_of_nat(V_2) )
% 4.01/4.15 & ( ~ ord_less_int(V_1,pls)
% 4.01/4.15 => ( ( ord_less_int(V_2,pls)
% 4.01/4.15 => plus_plus_nat(number_number_of_nat(V_1),number_number_of_nat(V_2)) = number_number_of_nat(V_1) )
% 4.01/4.15 & ( ~ ord_less_int(V_2,pls)
% 4.01/4.15 => 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)) ) ) ) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_78_nat__numeral__1__eq__1,axiom,
% 4.01/4.15 number_number_of_nat(bit1(pls)) = one_one_nat ).
% 4.01/4.15
% 4.01/4.15 fof(fact_79_Numeral1__eq1__nat,axiom,
% 4.01/4.15 one_one_nat = number_number_of_nat(bit1(pls)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_80_rel__simps_I29_J,axiom,
% 4.01/4.15 ! [K_1] :
% 4.01/4.15 ( ord_less_eq_int(bit1(K_1),pls)
% 4.01/4.15 <=> ord_less_int(K_1,pls) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_81_rel__simps_I5_J,axiom,
% 4.01/4.15 ! [K_1] :
% 4.01/4.15 ( ord_less_int(pls,bit1(K_1))
% 4.01/4.15 <=> ord_less_eq_int(pls,K_1) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_82_less__eq__int__code_I15_J,axiom,
% 4.01/4.15 ! [K1,K2] :
% 4.01/4.15 ( ord_less_eq_int(bit1(K1),bit0(K2))
% 4.01/4.15 <=> ord_less_int(K1,K2) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_83_rel__simps_I33_J,axiom,
% 4.01/4.15 ! [K_1,L_1] :
% 4.01/4.15 ( ord_less_eq_int(bit1(K_1),bit0(L_1))
% 4.01/4.15 <=> ord_less_int(K_1,L_1) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_84_less__int__code_I14_J,axiom,
% 4.01/4.15 ! [K1,K2] :
% 4.01/4.15 ( ord_less_int(bit0(K1),bit1(K2))
% 4.01/4.15 <=> ord_less_eq_int(K1,K2) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_85_rel__simps_I15_J,axiom,
% 4.01/4.15 ! [K_1,L_1] :
% 4.01/4.15 ( ord_less_int(bit0(K_1),bit1(L_1))
% 4.01/4.15 <=> ord_less_eq_int(K_1,L_1) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_86_zless__imp__add1__zle,axiom,
% 4.01/4.15 ! [W,Z] :
% 4.01/4.15 ( ord_less_int(W,Z)
% 4.01/4.15 => ord_less_eq_int(plus_plus_int(W,one_one_int),Z) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_87_add1__zle__eq,axiom,
% 4.01/4.15 ! [W_1,Z_1] :
% 4.01/4.15 ( ord_less_eq_int(plus_plus_int(W_1,one_one_int),Z_1)
% 4.01/4.15 <=> ord_less_int(W_1,Z_1) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_88_zle__add1__eq__le,axiom,
% 4.01/4.15 ! [W_1,Z_1] :
% 4.01/4.15 ( ord_less_int(W_1,plus_plus_int(Z_1,one_one_int))
% 4.01/4.15 <=> ord_less_eq_int(W_1,Z_1) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_89_zprime__2,axiom,
% 4.01/4.15 zprime(number_number_of_int(bit0(bit1(pls)))) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_90_is__mult__sum2sq,axiom,
% 4.01/4.15 ! [Y_1,X_1] :
% 4.01/4.15 ( twoSqu142715416sum2sq(X_1)
% 4.01/4.15 => ( twoSqu142715416sum2sq(Y_1)
% 4.01/4.15 => twoSqu142715416sum2sq(times_times_int(X_1,Y_1)) ) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 4.01/4.15 ! [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))) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 4.01/4.15 ! [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))) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 4.01/4.15 ! [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))) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 4.01/4.15 ! [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) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 4.01/4.15 ! [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) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 4.01/4.15 ! [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) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_105_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 4.01/4.15 ! [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) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_107_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 4.01/4.15 ! [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) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 4.01/4.15 ! [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) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_109_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 4.01/4.15 ! [Lx,Rx,Ry] : times_times_real(Lx,times_times_real(Rx,Ry)) = times_times_real(Rx,times_times_real(Lx,Ry)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 4.01/4.15 ! [Lx,Rx,Ry] : times_times_nat(Lx,times_times_nat(Rx,Ry)) = times_times_nat(Rx,times_times_nat(Lx,Ry)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 4.01/4.15 ! [Lx,Rx,Ry] : times_times_int(Lx,times_times_int(Rx,Ry)) = times_times_int(Rx,times_times_int(Lx,Ry)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 4.01/4.15 ! [A_56,B_17] : times_times_real(A_56,B_17) = times_times_real(B_17,A_56) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 4.01/4.15 ! [A_56,B_17] : times_times_nat(A_56,B_17) = times_times_nat(B_17,A_56) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 4.01/4.15 ! [A_56,B_17] : times_times_int(A_56,B_17) = times_times_int(B_17,A_56) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_118_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 4.01/4.15 ! [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) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_119_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 4.01/4.15 ! [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) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 4.01/4.15 ! [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) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 4.01/4.15 ! [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) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 4.01/4.15 ! [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) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 4.01/4.15 ! [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) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 4.01/4.15 ! [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)) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 4.01/4.15 ! [A_50,C_5] : plus_plus_real(A_50,C_5) = plus_plus_real(C_5,A_50) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 4.01/4.15 ! [A_50,C_5] : plus_plus_nat(A_50,C_5) = plus_plus_nat(C_5,A_50) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 4.01/4.15 ! [A_50,C_5] : plus_plus_int(A_50,C_5) = plus_plus_int(C_5,A_50) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_133_eq__number__of,axiom,
% 4.01/4.15 ! [X_2,Y_2] :
% 4.01/4.15 ( ( is_int(X_2)
% 4.01/4.15 & is_int(Y_2) )
% 4.01/4.15 => ( number267125858f_real(X_2) = number267125858f_real(Y_2)
% 4.01/4.15 <=> X_2 = Y_2 ) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_134_eq__number__of,axiom,
% 4.01/4.15 ! [X_2,Y_2] :
% 4.01/4.15 ( ( is_int(X_2)
% 4.01/4.15 & is_int(Y_2) )
% 4.01/4.15 => ( number_number_of_int(X_2) = number_number_of_int(Y_2)
% 4.01/4.15 <=> X_2 = Y_2 ) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_135_number__of__reorient,axiom,
% 4.01/4.15 ! [W_1,X_2] :
% 4.01/4.15 ( number267125858f_real(W_1) = X_2
% 4.01/4.15 <=> X_2 = number267125858f_real(W_1) ) ).
% 4.01/4.15
% 4.01/4.15 fof(fact_136_number__of__reorient,axiom,
% 4.01/4.15 ! [W_1,X_2] :
% 4.01/4.16 ( is_int(X_2)
% 4.01/4.16 => ( number_number_of_int(W_1) = X_2
% 4.01/4.16 <=> X_2 = number_number_of_int(W_1) ) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_137_number__of__reorient,axiom,
% 4.01/4.16 ! [W_1,X_2] :
% 4.01/4.16 ( number_number_of_nat(W_1) = X_2
% 4.01/4.16 <=> X_2 = number_number_of_nat(W_1) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_138_rel__simps_I51_J,axiom,
% 4.01/4.16 ! [K_1,L_1] :
% 4.01/4.16 ( ( is_int(K_1)
% 4.01/4.16 & is_int(L_1) )
% 4.01/4.16 => ( bit1(K_1) = bit1(L_1)
% 4.01/4.16 <=> K_1 = L_1 ) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_139_rel__simps_I48_J,axiom,
% 4.01/4.16 ! [K_1,L_1] :
% 4.01/4.16 ( ( is_int(K_1)
% 4.01/4.16 & is_int(L_1) )
% 4.01/4.16 => ( bit0(K_1) = bit0(L_1)
% 4.01/4.16 <=> K_1 = L_1 ) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_140_zmult__assoc,axiom,
% 4.01/4.16 ! [Z1,Z2,Z3] : times_times_int(times_times_int(Z1,Z2),Z3) = times_times_int(Z1,times_times_int(Z2,Z3)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_141_zmult__commute,axiom,
% 4.01/4.16 ! [Z,W] : times_times_int(Z,W) = times_times_int(W,Z) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_142_number__of__is__id,axiom,
% 4.01/4.16 ! [K] :
% 4.01/4.16 ( is_int(K)
% 4.01/4.16 => number_number_of_int(K) = K ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_143_zadd__assoc,axiom,
% 4.01/4.16 ! [Z1,Z2,Z3] : plus_plus_int(plus_plus_int(Z1,Z2),Z3) = plus_plus_int(Z1,plus_plus_int(Z2,Z3)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_144_zadd__left__commute,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_145_zadd__commute,axiom,
% 4.01/4.16 ! [Z,W] : plus_plus_int(Z,W) = plus_plus_int(W,Z) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_146_rel__simps_I12_J,axiom,
% 4.01/4.16 ! [K_1] :
% 4.01/4.16 ( ord_less_int(bit1(K_1),pls)
% 4.01/4.16 <=> ord_less_int(K_1,pls) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_147_less__int__code_I15_J,axiom,
% 4.01/4.16 ! [K1,K2] :
% 4.01/4.16 ( ord_less_int(bit1(K1),bit0(K2))
% 4.01/4.16 <=> ord_less_int(K1,K2) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_148_rel__simps_I16_J,axiom,
% 4.01/4.16 ! [K_1,L_1] :
% 4.01/4.16 ( ord_less_int(bit1(K_1),bit0(L_1))
% 4.01/4.16 <=> ord_less_int(K_1,L_1) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_149_rel__simps_I10_J,axiom,
% 4.01/4.16 ! [K_1] :
% 4.01/4.16 ( ord_less_int(bit0(K_1),pls)
% 4.01/4.16 <=> ord_less_int(K_1,pls) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_150_rel__simps_I4_J,axiom,
% 4.01/4.16 ! [K_1] :
% 4.01/4.16 ( ord_less_int(pls,bit0(K_1))
% 4.01/4.16 <=> ord_less_int(pls,K_1) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_151_rel__simps_I22_J,axiom,
% 4.01/4.16 ! [K_1] :
% 4.01/4.16 ( ord_less_eq_int(pls,bit1(K_1))
% 4.01/4.16 <=> ord_less_eq_int(pls,K_1) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_152_less__eq__int__code_I14_J,axiom,
% 4.01/4.16 ! [K1,K2] :
% 4.01/4.16 ( ord_less_eq_int(bit0(K1),bit1(K2))
% 4.01/4.16 <=> ord_less_eq_int(K1,K2) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_153_rel__simps_I32_J,axiom,
% 4.01/4.16 ! [K_1,L_1] :
% 4.01/4.16 ( ord_less_eq_int(bit0(K_1),bit1(L_1))
% 4.01/4.16 <=> ord_less_eq_int(K_1,L_1) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_154_rel__simps_I27_J,axiom,
% 4.01/4.16 ! [K_1] :
% 4.01/4.16 ( ord_less_eq_int(bit0(K_1),pls)
% 4.01/4.16 <=> ord_less_eq_int(K_1,pls) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_155_rel__simps_I21_J,axiom,
% 4.01/4.16 ! [K_1] :
% 4.01/4.16 ( ord_less_eq_int(pls,bit0(K_1))
% 4.01/4.16 <=> ord_less_eq_int(pls,K_1) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_156_zless__add1__eq,axiom,
% 4.01/4.16 ! [W_1,Z_1] :
% 4.01/4.16 ( ( is_int(W_1)
% 4.01/4.16 & is_int(Z_1) )
% 4.01/4.16 => ( ord_less_int(W_1,plus_plus_int(Z_1,one_one_int))
% 4.01/4.16 <=> ( ord_less_int(W_1,Z_1)
% 4.01/4.16 | W_1 = Z_1 ) ) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_157_power__even__eq,axiom,
% 4.01/4.16 ! [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)))) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_158_power__even__eq,axiom,
% 4.01/4.16 ! [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)))) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_159_power__even__eq,axiom,
% 4.01/4.16 ! [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)))) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_160_less__special_I4_J,axiom,
% 4.01/4.16 ! [X_2] :
% 4.01/4.16 ( ord_less_real(number267125858f_real(X_2),one_one_real)
% 4.01/4.16 <=> ord_less_int(X_2,bit1(pls)) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_161_less__special_I4_J,axiom,
% 4.01/4.16 ! [X_2] :
% 4.01/4.16 ( ord_less_int(number_number_of_int(X_2),one_one_int)
% 4.01/4.16 <=> ord_less_int(X_2,bit1(pls)) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_162_less__special_I2_J,axiom,
% 4.01/4.16 ! [Y_2] :
% 4.01/4.16 ( ord_less_real(one_one_real,number267125858f_real(Y_2))
% 4.01/4.16 <=> ord_less_int(bit1(pls),Y_2) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_163_less__special_I2_J,axiom,
% 4.01/4.16 ! [Y_2] :
% 4.01/4.16 ( ord_less_int(one_one_int,number_number_of_int(Y_2))
% 4.01/4.16 <=> ord_less_int(bit1(pls),Y_2) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_164_le__special_I4_J,axiom,
% 4.01/4.16 ! [X_2] :
% 4.01/4.16 ( ord_less_eq_real(number267125858f_real(X_2),one_one_real)
% 4.01/4.16 <=> ord_less_eq_int(X_2,bit1(pls)) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_165_le__special_I4_J,axiom,
% 4.01/4.16 ! [X_2] :
% 4.01/4.16 ( ord_less_eq_int(number_number_of_int(X_2),one_one_int)
% 4.01/4.16 <=> ord_less_eq_int(X_2,bit1(pls)) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_166_le__special_I2_J,axiom,
% 4.01/4.16 ! [Y_2] :
% 4.01/4.16 ( ord_less_eq_real(one_one_real,number267125858f_real(Y_2))
% 4.01/4.16 <=> ord_less_eq_int(bit1(pls),Y_2) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_167_le__special_I2_J,axiom,
% 4.01/4.16 ! [Y_2] :
% 4.01/4.16 ( ord_less_eq_int(one_one_int,number_number_of_int(Y_2))
% 4.01/4.16 <=> ord_less_eq_int(bit1(pls),Y_2) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_168_crossproduct__eq,axiom,
% 4.01/4.16 ! [W_1,Y_2,X_2,Z_1] :
% 4.01/4.16 ( 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))
% 4.01/4.16 <=> ( W_1 = X_2
% 4.01/4.16 | Y_2 = Z_1 ) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_169_crossproduct__eq,axiom,
% 4.01/4.16 ! [W_1,Y_2,X_2,Z_1] :
% 4.01/4.16 ( 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))
% 4.01/4.16 <=> ( W_1 = X_2
% 4.01/4.16 | Y_2 = Z_1 ) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_170_crossproduct__eq,axiom,
% 4.01/4.16 ! [W_1,Y_2,X_2,Z_1] :
% 4.01/4.16 ( ( is_int(W_1)
% 4.01/4.16 & is_int(Y_2)
% 4.01/4.16 & is_int(X_2)
% 4.01/4.16 & is_int(Z_1) )
% 4.01/4.16 => ( 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))
% 4.01/4.16 <=> ( W_1 = X_2
% 4.01/4.16 | Y_2 = Z_1 ) ) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_171_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 4.01/4.16 ! [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) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_172_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 4.01/4.16 ! [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) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 4.01/4.16 ! [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) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_177_crossproduct__noteq,axiom,
% 4.01/4.16 ! [C,D,A_1,B_2] :
% 4.01/4.16 ( ( A_1 != B_2
% 4.01/4.16 & C != D )
% 4.01/4.16 <=> 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)) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_178_crossproduct__noteq,axiom,
% 4.01/4.16 ! [C,D,A_1,B_2] :
% 4.01/4.16 ( ( A_1 != B_2
% 4.01/4.16 & C != D )
% 4.01/4.16 <=> 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)) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_179_crossproduct__noteq,axiom,
% 4.01/4.16 ! [C,D,A_1,B_2] :
% 4.01/4.16 ( ( is_int(C)
% 4.01/4.16 & is_int(D)
% 4.01/4.16 & is_int(A_1)
% 4.01/4.16 & is_int(B_2) )
% 4.01/4.16 => ( ( A_1 != B_2
% 4.01/4.16 & C != D )
% 4.01/4.16 <=> 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)) ) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_180_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_181_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 4.01/4.16 ! [A_46] : times_times_real(A_46,one_one_real) = A_46 ).
% 4.01/4.16
% 4.01/4.16 fof(fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 4.01/4.16 ! [A_46] : times_times_nat(A_46,one_one_nat) = A_46 ).
% 4.01/4.16
% 4.01/4.16 fof(fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 4.01/4.16 ! [A_46] :
% 4.01/4.16 ( is_int(A_46)
% 4.01/4.16 => times_times_int(A_46,one_one_int) = A_46 ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 4.01/4.16 ! [A_45] : times_times_real(one_one_real,A_45) = A_45 ).
% 4.01/4.16
% 4.01/4.16 fof(fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 4.01/4.16 ! [A_45] : times_times_nat(one_one_nat,A_45) = A_45 ).
% 4.01/4.16
% 4.01/4.16 fof(fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 4.01/4.16 ! [A_45] :
% 4.01/4.16 ( is_int(A_45)
% 4.01/4.16 => times_times_int(one_one_int,A_45) = A_45 ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_192_rel__simps_I46_J,axiom,
% 4.01/4.16 ! [K] : bit1(K) != pls ).
% 4.01/4.16
% 4.01/4.16 fof(fact_193_rel__simps_I39_J,axiom,
% 4.01/4.16 ! [L] : pls != bit1(L) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_194_rel__simps_I50_J,axiom,
% 4.01/4.16 ! [K,L] : bit1(K) != bit0(L) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_195_rel__simps_I49_J,axiom,
% 4.01/4.16 ! [K,L] : bit0(K) != bit1(L) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_196_rel__simps_I44_J,axiom,
% 4.01/4.16 ! [K_1] :
% 4.01/4.16 ( is_int(K_1)
% 4.01/4.16 => ( bit0(K_1) = pls
% 4.01/4.16 <=> K_1 = pls ) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_197_rel__simps_I38_J,axiom,
% 4.01/4.16 ! [L_1] :
% 4.01/4.16 ( is_int(L_1)
% 4.01/4.16 => ( pls = bit0(L_1)
% 4.01/4.16 <=> pls = L_1 ) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_198_Bit0__Pls,axiom,
% 4.01/4.16 bit0(pls) = pls ).
% 4.01/4.16
% 4.01/4.16 fof(fact_199_mult__Pls,axiom,
% 4.01/4.16 ! [W] : times_times_int(pls,W) = pls ).
% 4.01/4.16
% 4.01/4.16 fof(fact_200_mult__Bit0,axiom,
% 4.01/4.16 ! [K,L] : times_times_int(bit0(K),L) = bit0(times_times_int(K,L)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_201_add__Pls__right,axiom,
% 4.01/4.16 ! [K] :
% 4.01/4.16 ( is_int(K)
% 4.01/4.16 => plus_plus_int(K,pls) = K ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_202_add__Pls,axiom,
% 4.01/4.16 ! [K] :
% 4.01/4.16 ( is_int(K)
% 4.01/4.16 => plus_plus_int(pls,K) = K ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_203_add__Bit0__Bit0,axiom,
% 4.01/4.16 ! [K,L] : plus_plus_int(bit0(K),bit0(L)) = bit0(plus_plus_int(K,L)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_204_Bit0__def,axiom,
% 4.01/4.16 ! [K] : bit0(K) = plus_plus_int(K,K) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_205_zmult__1__right,axiom,
% 4.01/4.16 ! [Z] :
% 4.01/4.16 ( is_int(Z)
% 4.01/4.16 => times_times_int(Z,one_one_int) = Z ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_206_zmult__1,axiom,
% 4.01/4.16 ! [Z] :
% 4.01/4.16 ( is_int(Z)
% 4.01/4.16 => times_times_int(one_one_int,Z) = Z ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_207_times__numeral__code_I5_J,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_208_zadd__zmult__distrib,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_209_zadd__zmult__distrib2,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_210_plus__numeral__code_I9_J,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_211_semiring__mult__number__of,axiom,
% 4.01/4.16 ! [V_16,V_15] :
% 4.01/4.16 ( ord_less_eq_int(pls,V_15)
% 4.01/4.16 => ( ord_less_eq_int(pls,V_16)
% 4.01/4.16 => times_times_real(number267125858f_real(V_15),number267125858f_real(V_16)) = number267125858f_real(times_times_int(V_15,V_16)) ) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_212_semiring__mult__number__of,axiom,
% 4.01/4.16 ! [V_16,V_15] :
% 4.01/4.16 ( ord_less_eq_int(pls,V_15)
% 4.01/4.16 => ( ord_less_eq_int(pls,V_16)
% 4.01/4.16 => 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)) ) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_213_semiring__mult__number__of,axiom,
% 4.01/4.16 ! [V_16,V_15] :
% 4.01/4.16 ( ord_less_eq_int(pls,V_15)
% 4.01/4.16 => ( ord_less_eq_int(pls,V_16)
% 4.01/4.16 => 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)) ) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_214_semiring__add__number__of,axiom,
% 4.01/4.16 ! [V_14,V_13] :
% 4.01/4.16 ( ord_less_eq_int(pls,V_13)
% 4.01/4.16 => ( ord_less_eq_int(pls,V_14)
% 4.01/4.16 => plus_plus_real(number267125858f_real(V_13),number267125858f_real(V_14)) = number267125858f_real(plus_plus_int(V_13,V_14)) ) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_215_semiring__add__number__of,axiom,
% 4.01/4.16 ! [V_14,V_13] :
% 4.01/4.16 ( ord_less_eq_int(pls,V_13)
% 4.01/4.16 => ( ord_less_eq_int(pls,V_14)
% 4.01/4.16 => 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)) ) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_216_semiring__add__number__of,axiom,
% 4.01/4.16 ! [V_14,V_13] :
% 4.01/4.16 ( ord_less_eq_int(pls,V_13)
% 4.01/4.16 => ( ord_less_eq_int(pls,V_14)
% 4.01/4.16 => 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)) ) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_217_power2__ge__self,axiom,
% 4.01/4.16 ! [X_1] : ord_less_eq_int(X_1,power_power_int(X_1,number_number_of_nat(bit0(bit1(pls))))) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_218_left__distrib__number__of,axiom,
% 4.01/4.16 ! [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))) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_219_left__distrib__number__of,axiom,
% 4.01/4.16 ! [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))) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_220_left__distrib__number__of,axiom,
% 4.01/4.16 ! [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))) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_221_right__distrib__number__of,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_222_right__distrib__number__of,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_223_right__distrib__number__of,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_224_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 4.01/4.16 ! [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) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 4.01/4.16 ! [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) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 4.01/4.16 ! [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) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 4.01/4.16 ! [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) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 4.01/4.16 ! [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) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 4.01/4.16 ! [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) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 4.01/4.16 ! [M_9] : plus_plus_real(M_9,M_9) = times_times_real(plus_plus_real(one_one_real,one_one_real),M_9) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 4.01/4.16 ! [M_9] : plus_plus_nat(M_9,M_9) = times_times_nat(plus_plus_nat(one_one_nat,one_one_nat),M_9) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 4.01/4.16 ! [M_9] : plus_plus_int(M_9,M_9) = times_times_int(plus_plus_int(one_one_int,one_one_int),M_9) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_233_add__numeral__0,axiom,
% 4.01/4.16 ! [A_41] : plus_plus_real(number267125858f_real(pls),A_41) = A_41 ).
% 4.01/4.16
% 4.01/4.16 fof(fact_234_add__numeral__0,axiom,
% 4.01/4.16 ! [A_41] :
% 4.01/4.16 ( is_int(A_41)
% 4.01/4.16 => plus_plus_int(number_number_of_int(pls),A_41) = A_41 ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_235_add__numeral__0__right,axiom,
% 4.01/4.16 ! [A_40] : plus_plus_real(A_40,number267125858f_real(pls)) = A_40 ).
% 4.01/4.16
% 4.01/4.16 fof(fact_236_add__numeral__0__right,axiom,
% 4.01/4.16 ! [A_40] :
% 4.01/4.16 ( is_int(A_40)
% 4.01/4.16 => plus_plus_int(A_40,number_number_of_int(pls)) = A_40 ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_237_mult__number__of__left,axiom,
% 4.01/4.16 ! [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) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_238_mult__number__of__left,axiom,
% 4.01/4.16 ! [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) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_239_arith__simps_I32_J,axiom,
% 4.01/4.16 ! [V_9,W_11] : times_times_real(number267125858f_real(V_9),number267125858f_real(W_11)) = number267125858f_real(times_times_int(V_9,W_11)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_240_arith__simps_I32_J,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_241_number__of__mult,axiom,
% 4.01/4.16 ! [V_8,W_10] : number267125858f_real(times_times_int(V_8,W_10)) = times_times_real(number267125858f_real(V_8),number267125858f_real(W_10)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_242_number__of__mult,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_243_add__number__of__left,axiom,
% 4.01/4.16 ! [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) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_244_add__number__of__left,axiom,
% 4.01/4.16 ! [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) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_245_add__number__of__eq,axiom,
% 4.01/4.16 ! [V_6,W_8] : plus_plus_real(number267125858f_real(V_6),number267125858f_real(W_8)) = number267125858f_real(plus_plus_int(V_6,W_8)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_246_add__number__of__eq,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_247_number__of__add,axiom,
% 4.01/4.16 ! [V_5,W_7] : number267125858f_real(plus_plus_int(V_5,W_7)) = plus_plus_real(number267125858f_real(V_5),number267125858f_real(W_7)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_248_number__of__add,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_249_add__Bit1__Bit0,axiom,
% 4.01/4.16 ! [K,L] : plus_plus_int(bit1(K),bit0(L)) = bit1(plus_plus_int(K,L)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_250_add__Bit0__Bit1,axiom,
% 4.01/4.16 ! [K,L] : plus_plus_int(bit0(K),bit1(L)) = bit1(plus_plus_int(K,L)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_251_Bit1__def,axiom,
% 4.01/4.16 ! [K] : bit1(K) = plus_plus_int(plus_plus_int(one_one_int,K),K) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_252_number__of__Bit1,axiom,
% 4.01/4.16 ! [W_6] : number267125858f_real(bit1(W_6)) = plus_plus_real(plus_plus_real(one_one_real,number267125858f_real(W_6)),number267125858f_real(W_6)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_253_number__of__Bit1,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_254_mult__numeral__1,axiom,
% 4.01/4.16 ! [A_39] : times_times_real(number267125858f_real(bit1(pls)),A_39) = A_39 ).
% 4.01/4.16
% 4.01/4.16 fof(fact_255_mult__numeral__1,axiom,
% 4.01/4.16 ! [A_39] :
% 4.01/4.16 ( is_int(A_39)
% 4.01/4.16 => times_times_int(number_number_of_int(bit1(pls)),A_39) = A_39 ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_256_mult__numeral__1__right,axiom,
% 4.01/4.16 ! [A_38] : times_times_real(A_38,number267125858f_real(bit1(pls))) = A_38 ).
% 4.01/4.16
% 4.01/4.16 fof(fact_257_mult__numeral__1__right,axiom,
% 4.01/4.16 ! [A_38] :
% 4.01/4.16 ( is_int(A_38)
% 4.01/4.16 => times_times_int(A_38,number_number_of_int(bit1(pls))) = A_38 ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_258_semiring__numeral__1__eq__1,axiom,
% 4.01/4.16 number267125858f_real(bit1(pls)) = one_one_real ).
% 4.01/4.16
% 4.01/4.16 fof(fact_259_semiring__numeral__1__eq__1,axiom,
% 4.01/4.16 number_number_of_nat(bit1(pls)) = one_one_nat ).
% 4.01/4.16
% 4.01/4.16 fof(fact_260_semiring__numeral__1__eq__1,axiom,
% 4.01/4.16 number_number_of_int(bit1(pls)) = one_one_int ).
% 4.01/4.16
% 4.01/4.16 fof(fact_261_numeral__1__eq__1,axiom,
% 4.01/4.16 number267125858f_real(bit1(pls)) = one_one_real ).
% 4.01/4.16
% 4.01/4.16 fof(fact_262_numeral__1__eq__1,axiom,
% 4.01/4.16 number_number_of_int(bit1(pls)) = one_one_int ).
% 4.01/4.16
% 4.01/4.16 fof(fact_263_semiring__norm_I110_J,axiom,
% 4.01/4.16 one_one_real = number267125858f_real(bit1(pls)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_264_semiring__norm_I110_J,axiom,
% 4.01/4.16 one_one_int = number_number_of_int(bit1(pls)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_265_one__is__num__one,axiom,
% 4.01/4.16 one_one_int = number_number_of_int(bit1(pls)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_266_mult__Bit1,axiom,
% 4.01/4.16 ! [K,L] : times_times_int(bit1(K),L) = plus_plus_int(bit0(times_times_int(K,L)),L) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_267_double__number__of__Bit0,axiom,
% 4.01/4.16 ! [W_5] : times_times_real(plus_plus_real(one_one_real,one_one_real),number267125858f_real(W_5)) = number267125858f_real(bit0(W_5)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_268_double__number__of__Bit0,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_269_power3__eq__cube,axiom,
% 4.01/4.16 ! [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) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_270_power3__eq__cube,axiom,
% 4.01/4.16 ! [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) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_271_power3__eq__cube,axiom,
% 4.01/4.16 ! [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) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_272_quartic__square__square,axiom,
% 4.01/4.16 ! [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))))) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_273_semiring__mult__2,axiom,
% 4.01/4.16 ! [Z_5] : times_times_real(number267125858f_real(bit0(bit1(pls))),Z_5) = plus_plus_real(Z_5,Z_5) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_274_semiring__mult__2,axiom,
% 4.01/4.16 ! [Z_5] : times_times_nat(number_number_of_nat(bit0(bit1(pls))),Z_5) = plus_plus_nat(Z_5,Z_5) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_275_semiring__mult__2,axiom,
% 4.01/4.16 ! [Z_5] : times_times_int(number_number_of_int(bit0(bit1(pls))),Z_5) = plus_plus_int(Z_5,Z_5) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_276_mult__2,axiom,
% 4.01/4.16 ! [Z_4] : times_times_real(number267125858f_real(bit0(bit1(pls))),Z_4) = plus_plus_real(Z_4,Z_4) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_277_mult__2,axiom,
% 4.01/4.16 ! [Z_4] : times_times_int(number_number_of_int(bit0(bit1(pls))),Z_4) = plus_plus_int(Z_4,Z_4) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_278_semiring__mult__2__right,axiom,
% 4.01/4.16 ! [Z_3] : times_times_real(Z_3,number267125858f_real(bit0(bit1(pls)))) = plus_plus_real(Z_3,Z_3) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_279_semiring__mult__2__right,axiom,
% 4.01/4.16 ! [Z_3] : times_times_nat(Z_3,number_number_of_nat(bit0(bit1(pls)))) = plus_plus_nat(Z_3,Z_3) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_280_semiring__mult__2__right,axiom,
% 4.01/4.16 ! [Z_3] : times_times_int(Z_3,number_number_of_int(bit0(bit1(pls)))) = plus_plus_int(Z_3,Z_3) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_281_mult__2__right,axiom,
% 4.01/4.16 ! [Z_2] : times_times_real(Z_2,number267125858f_real(bit0(bit1(pls)))) = plus_plus_real(Z_2,Z_2) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_282_mult__2__right,axiom,
% 4.01/4.16 ! [Z_2] : times_times_int(Z_2,number_number_of_int(bit0(bit1(pls)))) = plus_plus_int(Z_2,Z_2) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_283_semiring__one__add__one__is__two,axiom,
% 4.01/4.16 plus_plus_real(one_one_real,one_one_real) = number267125858f_real(bit0(bit1(pls))) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_284_semiring__one__add__one__is__two,axiom,
% 4.01/4.16 plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_285_semiring__one__add__one__is__two,axiom,
% 4.01/4.16 plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_286_p0,axiom,
% 4.01/4.16 ord_less_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_287__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096,axiom,
% 4.01/4.16 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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_288_prime__g__5,axiom,
% 4.01/4.16 ! [P] :
% 4.01/4.16 ( is_int(P)
% 4.01/4.16 => ( zprime(P)
% 4.01/4.16 => ( P != number_number_of_int(bit0(bit1(pls)))
% 4.01/4.16 => ( P != number_number_of_int(bit1(bit1(pls)))
% 4.01/4.16 => ord_less_eq_int(number_number_of_int(bit1(bit0(bit1(pls)))),P) ) ) ) ) ).
% 4.01/4.16
% 4.01/4.16 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,
% 4.01/4.16 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) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_290_real__sum__squared__expand,axiom,
% 4.01/4.16 ! [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)) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_291_four__x__squared,axiom,
% 4.01/4.16 ! [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)))) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_292_power__less__power__Suc,axiom,
% 4.01/4.16 ! [N_36,A_36] :
% 4.01/4.16 ( ord_less_real(one_one_real,A_36)
% 4.01/4.16 => ord_less_real(power_power_real(A_36,N_36),times_times_real(A_36,power_power_real(A_36,N_36))) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_293_power__less__power__Suc,axiom,
% 4.01/4.16 ! [N_36,A_36] :
% 4.01/4.16 ( ord_less_nat(one_one_nat,A_36)
% 4.01/4.16 => ord_less_nat(power_power_nat(A_36,N_36),times_times_nat(A_36,power_power_nat(A_36,N_36))) ) ).
% 4.01/4.16
% 4.01/4.16 fof(fact_294_power__less__power__Suc,axiom,
% 4.01/4.16 ! [N_36,A_36] :
% 4.01/4.16 ( ord_less_int(one_one_int,A_36)
% 4.01/4.16 => ord_less_int(power_power_int(A_36,N_36),times_times_int(A_36,power_power_int(A_36,N_36))) ) ).
% 4.01/4.16
% 4.15/4.17 fof(fact_295_power__gt1__lemma,axiom,
% 4.15/4.17 ! [N_35,A_35] :
% 4.15/4.17 ( ord_less_real(one_one_real,A_35)
% 4.15/4.17 => ord_less_real(one_one_real,times_times_real(A_35,power_power_real(A_35,N_35))) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_296_power__gt1__lemma,axiom,
% 4.15/4.17 ! [N_35,A_35] :
% 4.15/4.17 ( ord_less_nat(one_one_nat,A_35)
% 4.15/4.17 => ord_less_nat(one_one_nat,times_times_nat(A_35,power_power_nat(A_35,N_35))) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_297_power__gt1__lemma,axiom,
% 4.15/4.17 ! [N_35,A_35] :
% 4.15/4.17 ( ord_less_int(one_one_int,A_35)
% 4.15/4.17 => ord_less_int(one_one_int,times_times_int(A_35,power_power_int(A_35,N_35))) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_298_power__le__imp__le__exp,axiom,
% 4.15/4.17 ! [M_8,N_34,A_34] :
% 4.15/4.17 ( ord_less_real(one_one_real,A_34)
% 4.15/4.17 => ( ord_less_eq_real(power_power_real(A_34,M_8),power_power_real(A_34,N_34))
% 4.15/4.17 => ord_less_eq_nat(M_8,N_34) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_299_power__le__imp__le__exp,axiom,
% 4.15/4.17 ! [M_8,N_34,A_34] :
% 4.15/4.17 ( ord_less_nat(one_one_nat,A_34)
% 4.15/4.17 => ( ord_less_eq_nat(power_power_nat(A_34,M_8),power_power_nat(A_34,N_34))
% 4.15/4.17 => ord_less_eq_nat(M_8,N_34) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_300_power__le__imp__le__exp,axiom,
% 4.15/4.17 ! [M_8,N_34,A_34] :
% 4.15/4.17 ( ord_less_int(one_one_int,A_34)
% 4.15/4.17 => ( ord_less_eq_int(power_power_int(A_34,M_8),power_power_int(A_34,N_34))
% 4.15/4.17 => ord_less_eq_nat(M_8,N_34) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_301_power__increasing__iff,axiom,
% 4.15/4.17 ! [X_2,Y_2,B_2] :
% 4.15/4.17 ( ord_less_real(one_one_real,B_2)
% 4.15/4.17 => ( ord_less_eq_real(power_power_real(B_2,X_2),power_power_real(B_2,Y_2))
% 4.15/4.17 <=> ord_less_eq_nat(X_2,Y_2) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_302_power__increasing__iff,axiom,
% 4.15/4.17 ! [X_2,Y_2,B_2] :
% 4.15/4.17 ( ord_less_nat(one_one_nat,B_2)
% 4.15/4.17 => ( ord_less_eq_nat(power_power_nat(B_2,X_2),power_power_nat(B_2,Y_2))
% 4.15/4.17 <=> ord_less_eq_nat(X_2,Y_2) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_303_power__increasing__iff,axiom,
% 4.15/4.17 ! [X_2,Y_2,B_2] :
% 4.15/4.17 ( ord_less_int(one_one_int,B_2)
% 4.15/4.17 => ( ord_less_eq_int(power_power_int(B_2,X_2),power_power_int(B_2,Y_2))
% 4.15/4.17 <=> ord_less_eq_nat(X_2,Y_2) ) ) ).
% 4.15/4.17
% 4.15/4.17 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,
% 4.15/4.17 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)) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_305_s0p,axiom,
% 4.15/4.17 ( ord_less_eq_int(zero_zero_int,s)
% 4.15/4.17 & ord_less_int(s,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
% 4.15/4.17 & zcong(s1,s,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) ) ).
% 4.15/4.17
% 4.15/4.17 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,
% 4.15/4.17 ? [X] :
% 4.15/4.17 ( is_int(X)
% 4.15/4.17 & ord_less_eq_int(zero_zero_int,X)
% 4.15/4.17 & ord_less_int(X,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
% 4.15/4.17 & zcong(s1,X,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
% 4.15/4.17 & ! [Y] :
% 4.15/4.17 ( is_int(Y)
% 4.15/4.17 => ( ( ord_less_eq_int(zero_zero_int,Y)
% 4.15/4.17 & ord_less_int(Y,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
% 4.15/4.17 & zcong(s1,Y,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) )
% 4.15/4.17 => Y = X ) ) ) ).
% 4.15/4.17
% 4.15/4.17 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,
% 4.15/4.17 ~ ! [S] :
% 4.15/4.17 ( is_int(S)
% 4.15/4.17 => ~ ( ord_less_eq_int(zero_zero_int,S)
% 4.15/4.17 & ord_less_int(S,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
% 4.15/4.17 & zcong(s1,S,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_308_s1,axiom,
% 4.15/4.17 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)) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_309_power__eq__0__iff,axiom,
% 4.15/4.17 ! [A_1,N_1] :
% 4.15/4.17 ( power_power_real(A_1,N_1) = zero_zero_real
% 4.15/4.17 <=> ( A_1 = zero_zero_real
% 4.15/4.17 & N_1 != zero_zero_nat ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_310_power__eq__0__iff,axiom,
% 4.15/4.17 ! [A_1,N_1] :
% 4.15/4.17 ( power_power_nat(A_1,N_1) = zero_zero_nat
% 4.15/4.17 <=> ( A_1 = zero_zero_nat
% 4.15/4.17 & N_1 != zero_zero_nat ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_311_power__eq__0__iff,axiom,
% 4.15/4.17 ! [A_1,N_1] :
% 4.15/4.17 ( is_int(A_1)
% 4.15/4.17 => ( power_power_int(A_1,N_1) = zero_zero_int
% 4.15/4.17 <=> ( A_1 = zero_zero_int
% 4.15/4.17 & N_1 != zero_zero_nat ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_312_le__imp__power__dvd,axiom,
% 4.15/4.17 ! [A_33,M_7,N_33] :
% 4.15/4.17 ( ord_less_eq_nat(M_7,N_33)
% 4.15/4.17 => dvd_dvd_nat(power_power_nat(A_33,M_7),power_power_nat(A_33,N_33)) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_313_le__imp__power__dvd,axiom,
% 4.15/4.17 ! [A_33,M_7,N_33] :
% 4.15/4.17 ( ord_less_eq_nat(M_7,N_33)
% 4.15/4.17 => dvd_dvd_int(power_power_int(A_33,M_7),power_power_int(A_33,N_33)) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_314_le__imp__power__dvd,axiom,
% 4.15/4.17 ! [A_33,M_7,N_33] :
% 4.15/4.17 ( ord_less_eq_nat(M_7,N_33)
% 4.15/4.17 => dvd_dvd_real(power_power_real(A_33,M_7),power_power_real(A_33,N_33)) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_315_dvd__power__le,axiom,
% 4.15/4.17 ! [N_32,M_6,X_14,Y_12] :
% 4.15/4.17 ( dvd_dvd_nat(X_14,Y_12)
% 4.15/4.17 => ( ord_less_eq_nat(N_32,M_6)
% 4.15/4.17 => dvd_dvd_nat(power_power_nat(X_14,N_32),power_power_nat(Y_12,M_6)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_316_dvd__power__le,axiom,
% 4.15/4.17 ! [N_32,M_6,X_14,Y_12] :
% 4.15/4.17 ( dvd_dvd_int(X_14,Y_12)
% 4.15/4.17 => ( ord_less_eq_nat(N_32,M_6)
% 4.15/4.17 => dvd_dvd_int(power_power_int(X_14,N_32),power_power_int(Y_12,M_6)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_317_dvd__power__le,axiom,
% 4.15/4.17 ! [N_32,M_6,X_14,Y_12] :
% 4.15/4.17 ( dvd_dvd_real(X_14,Y_12)
% 4.15/4.17 => ( ord_less_eq_nat(N_32,M_6)
% 4.15/4.17 => dvd_dvd_real(power_power_real(X_14,N_32),power_power_real(Y_12,M_6)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_318_power__le__dvd,axiom,
% 4.15/4.17 ! [M_5,A_32,N_31,B_9] :
% 4.15/4.17 ( dvd_dvd_nat(power_power_nat(A_32,N_31),B_9)
% 4.15/4.17 => ( ord_less_eq_nat(M_5,N_31)
% 4.15/4.17 => dvd_dvd_nat(power_power_nat(A_32,M_5),B_9) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_319_power__le__dvd,axiom,
% 4.15/4.17 ! [M_5,A_32,N_31,B_9] :
% 4.15/4.17 ( dvd_dvd_int(power_power_int(A_32,N_31),B_9)
% 4.15/4.17 => ( ord_less_eq_nat(M_5,N_31)
% 4.15/4.17 => dvd_dvd_int(power_power_int(A_32,M_5),B_9) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_320_power__le__dvd,axiom,
% 4.15/4.17 ! [M_5,A_32,N_31,B_9] :
% 4.15/4.17 ( dvd_dvd_real(power_power_real(A_32,N_31),B_9)
% 4.15/4.17 => ( ord_less_eq_nat(M_5,N_31)
% 4.15/4.17 => dvd_dvd_real(power_power_real(A_32,M_5),B_9) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_321_power__eq__imp__eq__base,axiom,
% 4.15/4.17 ! [A_31,N_30,B_8] :
% 4.15/4.17 ( power_power_real(A_31,N_30) = power_power_real(B_8,N_30)
% 4.15/4.17 => ( ord_less_eq_real(zero_zero_real,A_31)
% 4.15/4.17 => ( ord_less_eq_real(zero_zero_real,B_8)
% 4.15/4.17 => ( ord_less_nat(zero_zero_nat,N_30)
% 4.15/4.17 => A_31 = B_8 ) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_322_power__eq__imp__eq__base,axiom,
% 4.15/4.17 ! [A_31,N_30,B_8] :
% 4.15/4.17 ( power_power_nat(A_31,N_30) = power_power_nat(B_8,N_30)
% 4.15/4.17 => ( ord_less_eq_nat(zero_zero_nat,A_31)
% 4.15/4.17 => ( ord_less_eq_nat(zero_zero_nat,B_8)
% 4.15/4.17 => ( ord_less_nat(zero_zero_nat,N_30)
% 4.15/4.17 => A_31 = B_8 ) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_323_power__eq__imp__eq__base,axiom,
% 4.15/4.17 ! [A_31,N_30,B_8] :
% 4.15/4.17 ( ( is_int(A_31)
% 4.15/4.17 & is_int(B_8) )
% 4.15/4.17 => ( power_power_int(A_31,N_30) = power_power_int(B_8,N_30)
% 4.15/4.17 => ( ord_less_eq_int(zero_zero_int,A_31)
% 4.15/4.17 => ( ord_less_eq_int(zero_zero_int,B_8)
% 4.15/4.17 => ( ord_less_nat(zero_zero_nat,N_30)
% 4.15/4.17 => A_31 = B_8 ) ) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_324_zdvd__not__zless,axiom,
% 4.15/4.17 ! [N,M] :
% 4.15/4.17 ( ord_less_int(zero_zero_int,M)
% 4.15/4.17 => ( ord_less_int(M,N)
% 4.15/4.17 => ~ dvd_dvd_int(N,M) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_325_zdvd__antisym__nonneg,axiom,
% 4.15/4.17 ! [N,M] :
% 4.15/4.17 ( ( is_int(N)
% 4.15/4.17 & is_int(M) )
% 4.15/4.17 => ( ord_less_eq_int(zero_zero_int,M)
% 4.15/4.17 => ( ord_less_eq_int(zero_zero_int,N)
% 4.15/4.17 => ( dvd_dvd_int(M,N)
% 4.15/4.17 => ( dvd_dvd_int(N,M)
% 4.15/4.17 => M = N ) ) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_326_zdvd__mult__cancel,axiom,
% 4.15/4.17 ! [K,M,N] :
% 4.15/4.17 ( is_int(K)
% 4.15/4.17 => ( dvd_dvd_int(times_times_int(K,M),times_times_int(K,N))
% 4.15/4.17 => ( K != zero_zero_int
% 4.15/4.17 => dvd_dvd_int(M,N) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_327_dvd__power__same,axiom,
% 4.15/4.17 ! [N_29,X_13,Y_11] :
% 4.15/4.17 ( dvd_dvd_nat(X_13,Y_11)
% 4.15/4.17 => dvd_dvd_nat(power_power_nat(X_13,N_29),power_power_nat(Y_11,N_29)) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_328_dvd__power__same,axiom,
% 4.15/4.17 ! [N_29,X_13,Y_11] :
% 4.15/4.17 ( dvd_dvd_int(X_13,Y_11)
% 4.15/4.17 => dvd_dvd_int(power_power_int(X_13,N_29),power_power_int(Y_11,N_29)) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_329_dvd__power__same,axiom,
% 4.15/4.17 ! [N_29,X_13,Y_11] :
% 4.15/4.17 ( dvd_dvd_real(X_13,Y_11)
% 4.15/4.17 => dvd_dvd_real(power_power_real(X_13,N_29),power_power_real(Y_11,N_29)) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_330_field__power__not__zero,axiom,
% 4.15/4.17 ! [N_28,A_30] :
% 4.15/4.17 ( A_30 != zero_zero_real
% 4.15/4.17 => power_power_real(A_30,N_28) != zero_zero_real ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_331_field__power__not__zero,axiom,
% 4.15/4.17 ! [N_28,A_30] :
% 4.15/4.17 ( is_int(A_30)
% 4.15/4.17 => ( A_30 != zero_zero_int
% 4.15/4.17 => power_power_int(A_30,N_28) != zero_zero_int ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_332_power__0__left,axiom,
% 4.15/4.17 ! [N_27] :
% 4.15/4.17 ( ( N_27 = zero_zero_nat
% 4.15/4.17 => power_power_real(zero_zero_real,N_27) = one_one_real )
% 4.15/4.17 & ( N_27 != zero_zero_nat
% 4.15/4.17 => power_power_real(zero_zero_real,N_27) = zero_zero_real ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_333_power__0__left,axiom,
% 4.15/4.17 ! [N_27] :
% 4.15/4.17 ( ( N_27 = zero_zero_nat
% 4.15/4.17 => power_power_nat(zero_zero_nat,N_27) = one_one_nat )
% 4.15/4.17 & ( N_27 != zero_zero_nat
% 4.15/4.17 => power_power_nat(zero_zero_nat,N_27) = zero_zero_nat ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_334_power__0__left,axiom,
% 4.15/4.17 ! [N_27] :
% 4.15/4.17 ( ( N_27 = zero_zero_nat
% 4.15/4.17 => power_power_int(zero_zero_int,N_27) = one_one_int )
% 4.15/4.17 & ( N_27 != zero_zero_nat
% 4.15/4.17 => power_power_int(zero_zero_int,N_27) = zero_zero_int ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_335_zdvd__imp__le,axiom,
% 4.15/4.17 ! [Z,N] :
% 4.15/4.17 ( dvd_dvd_int(Z,N)
% 4.15/4.17 => ( ord_less_int(zero_zero_int,N)
% 4.15/4.17 => ord_less_eq_int(Z,N) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_336_power__strict__mono,axiom,
% 4.15/4.17 ! [N_26,A_29,B_7] :
% 4.15/4.17 ( ord_less_real(A_29,B_7)
% 4.15/4.17 => ( ord_less_eq_real(zero_zero_real,A_29)
% 4.15/4.17 => ( ord_less_nat(zero_zero_nat,N_26)
% 4.15/4.17 => ord_less_real(power_power_real(A_29,N_26),power_power_real(B_7,N_26)) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_337_power__strict__mono,axiom,
% 4.15/4.17 ! [N_26,A_29,B_7] :
% 4.15/4.17 ( ord_less_nat(A_29,B_7)
% 4.15/4.17 => ( ord_less_eq_nat(zero_zero_nat,A_29)
% 4.15/4.17 => ( ord_less_nat(zero_zero_nat,N_26)
% 4.15/4.17 => ord_less_nat(power_power_nat(A_29,N_26),power_power_nat(B_7,N_26)) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_338_power__strict__mono,axiom,
% 4.15/4.17 ! [N_26,A_29,B_7] :
% 4.15/4.17 ( ord_less_int(A_29,B_7)
% 4.15/4.17 => ( ord_less_eq_int(zero_zero_int,A_29)
% 4.15/4.17 => ( ord_less_nat(zero_zero_nat,N_26)
% 4.15/4.17 => ord_less_int(power_power_int(A_29,N_26),power_power_int(B_7,N_26)) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 4.15/4.17 ! [A_28] : times_times_real(zero_zero_real,A_28) = zero_zero_real ).
% 4.15/4.17
% 4.15/4.17 fof(fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 4.15/4.17 ! [A_28] : times_times_nat(zero_zero_nat,A_28) = zero_zero_nat ).
% 4.15/4.17
% 4.15/4.17 fof(fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 4.15/4.17 ! [A_28] : times_times_int(zero_zero_int,A_28) = zero_zero_int ).
% 4.15/4.17
% 4.15/4.17 fof(fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 4.15/4.17 ! [A_27] : times_times_real(A_27,zero_zero_real) = zero_zero_real ).
% 4.15/4.17
% 4.15/4.17 fof(fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 4.15/4.17 ! [A_27] : times_times_nat(A_27,zero_zero_nat) = zero_zero_nat ).
% 4.15/4.17
% 4.15/4.17 fof(fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 4.15/4.17 ! [A_27] : times_times_int(A_27,zero_zero_int) = zero_zero_int ).
% 4.15/4.17
% 4.15/4.17 fof(fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 4.15/4.17 ! [A_26] : plus_plus_real(zero_zero_real,A_26) = A_26 ).
% 4.15/4.17
% 4.15/4.17 fof(fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 4.15/4.17 ! [A_26] : plus_plus_nat(zero_zero_nat,A_26) = A_26 ).
% 4.15/4.17
% 4.15/4.17 fof(fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 4.15/4.17 ! [A_26] :
% 4.15/4.17 ( is_int(A_26)
% 4.15/4.17 => plus_plus_int(zero_zero_int,A_26) = A_26 ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 4.15/4.17 ! [A_25] : plus_plus_real(A_25,zero_zero_real) = A_25 ).
% 4.15/4.17
% 4.15/4.17 fof(fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 4.15/4.17 ! [A_25] : plus_plus_nat(A_25,zero_zero_nat) = A_25 ).
% 4.15/4.17
% 4.15/4.17 fof(fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 4.15/4.17 ! [A_25] :
% 4.15/4.17 ( is_int(A_25)
% 4.15/4.17 => plus_plus_int(A_25,zero_zero_int) = A_25 ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_351_add__0__iff,axiom,
% 4.15/4.17 ! [B_2,A_1] :
% 4.15/4.17 ( B_2 = plus_plus_real(B_2,A_1)
% 4.15/4.17 <=> A_1 = zero_zero_real ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_352_add__0__iff,axiom,
% 4.15/4.17 ! [B_2,A_1] :
% 4.15/4.17 ( B_2 = plus_plus_nat(B_2,A_1)
% 4.15/4.17 <=> A_1 = zero_zero_nat ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_353_add__0__iff,axiom,
% 4.15/4.17 ! [B_2,A_1] :
% 4.15/4.17 ( ( is_int(B_2)
% 4.15/4.17 & is_int(A_1) )
% 4.15/4.17 => ( B_2 = plus_plus_int(B_2,A_1)
% 4.15/4.17 <=> A_1 = zero_zero_int ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_354_double__eq__0__iff,axiom,
% 4.15/4.17 ! [A_1] :
% 4.15/4.17 ( plus_plus_real(A_1,A_1) = zero_zero_real
% 4.15/4.17 <=> A_1 = zero_zero_real ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_355_double__eq__0__iff,axiom,
% 4.15/4.17 ! [A_1] :
% 4.15/4.17 ( is_int(A_1)
% 4.15/4.17 => ( plus_plus_int(A_1,A_1) = zero_zero_int
% 4.15/4.17 <=> A_1 = zero_zero_int ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_356_Pls__def,axiom,
% 4.15/4.17 pls = zero_zero_int ).
% 4.15/4.17
% 4.15/4.17 fof(fact_357_int__0__neq__1,axiom,
% 4.15/4.17 zero_zero_int != one_one_int ).
% 4.15/4.17
% 4.15/4.17 fof(fact_358_zadd__0,axiom,
% 4.15/4.17 ! [Z] :
% 4.15/4.17 ( is_int(Z)
% 4.15/4.17 => plus_plus_int(zero_zero_int,Z) = Z ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_359_zadd__0__right,axiom,
% 4.15/4.17 ! [Z] :
% 4.15/4.17 ( is_int(Z)
% 4.15/4.17 => plus_plus_int(Z,zero_zero_int) = Z ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_360_zero__le__power,axiom,
% 4.15/4.17 ! [N_25,A_24] :
% 4.15/4.17 ( ord_less_eq_real(zero_zero_real,A_24)
% 4.15/4.17 => ord_less_eq_real(zero_zero_real,power_power_real(A_24,N_25)) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_361_zero__le__power,axiom,
% 4.15/4.17 ! [N_25,A_24] :
% 4.15/4.17 ( ord_less_eq_nat(zero_zero_nat,A_24)
% 4.15/4.17 => ord_less_eq_nat(zero_zero_nat,power_power_nat(A_24,N_25)) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_362_zero__le__power,axiom,
% 4.15/4.17 ! [N_25,A_24] :
% 4.15/4.17 ( ord_less_eq_int(zero_zero_int,A_24)
% 4.15/4.17 => ord_less_eq_int(zero_zero_int,power_power_int(A_24,N_25)) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_363_power__mono,axiom,
% 4.15/4.17 ! [N_24,A_23,B_6] :
% 4.15/4.17 ( ord_less_eq_real(A_23,B_6)
% 4.15/4.17 => ( ord_less_eq_real(zero_zero_real,A_23)
% 4.15/4.17 => ord_less_eq_real(power_power_real(A_23,N_24),power_power_real(B_6,N_24)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_364_power__mono,axiom,
% 4.15/4.17 ! [N_24,A_23,B_6] :
% 4.15/4.17 ( ord_less_eq_nat(A_23,B_6)
% 4.15/4.17 => ( ord_less_eq_nat(zero_zero_nat,A_23)
% 4.15/4.17 => ord_less_eq_nat(power_power_nat(A_23,N_24),power_power_nat(B_6,N_24)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_365_power__mono,axiom,
% 4.15/4.17 ! [N_24,A_23,B_6] :
% 4.15/4.17 ( ord_less_eq_int(A_23,B_6)
% 4.15/4.17 => ( ord_less_eq_int(zero_zero_int,A_23)
% 4.15/4.17 => ord_less_eq_int(power_power_int(A_23,N_24),power_power_int(B_6,N_24)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_366_zero__less__power,axiom,
% 4.15/4.17 ! [N_23,A_22] :
% 4.15/4.17 ( ord_less_real(zero_zero_real,A_22)
% 4.15/4.17 => ord_less_real(zero_zero_real,power_power_real(A_22,N_23)) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_367_zero__less__power,axiom,
% 4.15/4.17 ! [N_23,A_22] :
% 4.15/4.17 ( ord_less_nat(zero_zero_nat,A_22)
% 4.15/4.17 => ord_less_nat(zero_zero_nat,power_power_nat(A_22,N_23)) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_368_zero__less__power,axiom,
% 4.15/4.17 ! [N_23,A_22] :
% 4.15/4.17 ( ord_less_int(zero_zero_int,A_22)
% 4.15/4.17 => ord_less_int(zero_zero_int,power_power_int(A_22,N_23)) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_369_zcong__zpower__zmult,axiom,
% 4.15/4.17 ! [Z,X_1,Y_1,P] :
% 4.15/4.17 ( zcong(power_power_int(X_1,Y_1),one_one_int,P)
% 4.15/4.17 => zcong(power_power_int(X_1,times_times_nat(Y_1,Z)),one_one_int,P) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_370_zdvd__reduce,axiom,
% 4.15/4.17 ! [K_1,N_1,Ma] :
% 4.15/4.17 ( dvd_dvd_int(K_1,plus_plus_int(N_1,times_times_int(K_1,Ma)))
% 4.15/4.17 <=> dvd_dvd_int(K_1,N_1) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_371_zdvd__period,axiom,
% 4.15/4.17 ! [C,X_2,Ta,A_1,D] :
% 4.15/4.17 ( dvd_dvd_int(A_1,D)
% 4.15/4.17 => ( dvd_dvd_int(A_1,plus_plus_int(X_2,Ta))
% 4.15/4.17 <=> dvd_dvd_int(A_1,plus_plus_int(plus_plus_int(X_2,times_times_int(C,D)),Ta)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_372_power__less__imp__less__base,axiom,
% 4.15/4.17 ! [A_21,N_22,B_5] :
% 4.15/4.17 ( ord_less_real(power_power_real(A_21,N_22),power_power_real(B_5,N_22))
% 4.15/4.17 => ( ord_less_eq_real(zero_zero_real,B_5)
% 4.15/4.17 => ord_less_real(A_21,B_5) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_373_power__less__imp__less__base,axiom,
% 4.15/4.17 ! [A_21,N_22,B_5] :
% 4.15/4.17 ( ord_less_nat(power_power_nat(A_21,N_22),power_power_nat(B_5,N_22))
% 4.15/4.17 => ( ord_less_eq_nat(zero_zero_nat,B_5)
% 4.15/4.17 => ord_less_nat(A_21,B_5) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_374_power__less__imp__less__base,axiom,
% 4.15/4.17 ! [A_21,N_22,B_5] :
% 4.15/4.17 ( ord_less_int(power_power_int(A_21,N_22),power_power_int(B_5,N_22))
% 4.15/4.17 => ( ord_less_eq_int(zero_zero_int,B_5)
% 4.15/4.17 => ord_less_int(A_21,B_5) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_375_power__decreasing,axiom,
% 4.15/4.17 ! [A_20,N_21,N_20] :
% 4.15/4.17 ( ord_less_eq_nat(N_21,N_20)
% 4.15/4.17 => ( ord_less_eq_real(zero_zero_real,A_20)
% 4.15/4.17 => ( ord_less_eq_real(A_20,one_one_real)
% 4.15/4.17 => ord_less_eq_real(power_power_real(A_20,N_20),power_power_real(A_20,N_21)) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_376_power__decreasing,axiom,
% 4.15/4.17 ! [A_20,N_21,N_20] :
% 4.15/4.17 ( ord_less_eq_nat(N_21,N_20)
% 4.15/4.17 => ( ord_less_eq_nat(zero_zero_nat,A_20)
% 4.15/4.17 => ( ord_less_eq_nat(A_20,one_one_nat)
% 4.15/4.17 => ord_less_eq_nat(power_power_nat(A_20,N_20),power_power_nat(A_20,N_21)) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_377_power__decreasing,axiom,
% 4.15/4.17 ! [A_20,N_21,N_20] :
% 4.15/4.17 ( ord_less_eq_nat(N_21,N_20)
% 4.15/4.17 => ( ord_less_eq_int(zero_zero_int,A_20)
% 4.15/4.17 => ( ord_less_eq_int(A_20,one_one_int)
% 4.15/4.17 => ord_less_eq_int(power_power_int(A_20,N_20),power_power_int(A_20,N_21)) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_378_power__strict__decreasing,axiom,
% 4.15/4.17 ! [A_19,N_19,N_18] :
% 4.15/4.17 ( ord_less_nat(N_19,N_18)
% 4.15/4.17 => ( ord_less_real(zero_zero_real,A_19)
% 4.15/4.17 => ( ord_less_real(A_19,one_one_real)
% 4.15/4.17 => ord_less_real(power_power_real(A_19,N_18),power_power_real(A_19,N_19)) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_379_power__strict__decreasing,axiom,
% 4.15/4.17 ! [A_19,N_19,N_18] :
% 4.15/4.17 ( ord_less_nat(N_19,N_18)
% 4.15/4.17 => ( ord_less_nat(zero_zero_nat,A_19)
% 4.15/4.17 => ( ord_less_nat(A_19,one_one_nat)
% 4.15/4.17 => ord_less_nat(power_power_nat(A_19,N_18),power_power_nat(A_19,N_19)) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_380_power__strict__decreasing,axiom,
% 4.15/4.17 ! [A_19,N_19,N_18] :
% 4.15/4.17 ( ord_less_nat(N_19,N_18)
% 4.15/4.17 => ( ord_less_int(zero_zero_int,A_19)
% 4.15/4.17 => ( ord_less_int(A_19,one_one_int)
% 4.15/4.17 => ord_less_int(power_power_int(A_19,N_18),power_power_int(A_19,N_19)) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_381_even__less__0__iff,axiom,
% 4.15/4.17 ! [A_1] :
% 4.15/4.17 ( ord_less_real(plus_plus_real(A_1,A_1),zero_zero_real)
% 4.15/4.17 <=> ord_less_real(A_1,zero_zero_real) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_382_even__less__0__iff,axiom,
% 4.15/4.17 ! [A_1] :
% 4.15/4.17 ( ord_less_int(plus_plus_int(A_1,A_1),zero_zero_int)
% 4.15/4.17 <=> ord_less_int(A_1,zero_zero_int) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_383_sum__squares__eq__zero__iff,axiom,
% 4.15/4.17 ! [X_2,Y_2] :
% 4.15/4.17 ( plus_plus_real(times_times_real(X_2,X_2),times_times_real(Y_2,Y_2)) = zero_zero_real
% 4.15/4.17 <=> ( X_2 = zero_zero_real
% 4.15/4.17 & Y_2 = zero_zero_real ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_384_sum__squares__eq__zero__iff,axiom,
% 4.15/4.17 ! [X_2,Y_2] :
% 4.15/4.17 ( ( is_int(X_2)
% 4.15/4.17 & is_int(Y_2) )
% 4.15/4.17 => ( plus_plus_int(times_times_int(X_2,X_2),times_times_int(Y_2,Y_2)) = zero_zero_int
% 4.15/4.17 <=> ( X_2 = zero_zero_int
% 4.15/4.17 & Y_2 = zero_zero_int ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_385_add__scale__eq__noteq,axiom,
% 4.15/4.17 ! [C_2,D_2,A_18,B_4,R_3] :
% 4.15/4.17 ( R_3 != zero_zero_real
% 4.15/4.17 => ( ( A_18 = B_4
% 4.15/4.17 & C_2 != D_2 )
% 4.15/4.17 => plus_plus_real(A_18,times_times_real(R_3,C_2)) != plus_plus_real(B_4,times_times_real(R_3,D_2)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_386_add__scale__eq__noteq,axiom,
% 4.15/4.17 ! [C_2,D_2,A_18,B_4,R_3] :
% 4.15/4.17 ( R_3 != zero_zero_nat
% 4.15/4.17 => ( ( A_18 = B_4
% 4.15/4.17 & C_2 != D_2 )
% 4.15/4.17 => plus_plus_nat(A_18,times_times_nat(R_3,C_2)) != plus_plus_nat(B_4,times_times_nat(R_3,D_2)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_387_add__scale__eq__noteq,axiom,
% 4.15/4.17 ! [C_2,D_2,A_18,B_4,R_3] :
% 4.15/4.17 ( ( is_int(C_2)
% 4.15/4.17 & is_int(D_2)
% 4.15/4.17 & is_int(R_3) )
% 4.15/4.17 => ( R_3 != zero_zero_int
% 4.15/4.17 => ( ( A_18 = B_4
% 4.15/4.17 & C_2 != D_2 )
% 4.15/4.17 => plus_plus_int(A_18,times_times_int(R_3,C_2)) != plus_plus_int(B_4,times_times_int(R_3,D_2)) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_388_zprime__zdvd__power,axiom,
% 4.15/4.17 ! [A,N,P] :
% 4.15/4.17 ( zprime(P)
% 4.15/4.17 => ( dvd_dvd_int(P,power_power_int(A,N))
% 4.15/4.17 => dvd_dvd_int(P,A) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_389_semiring__norm_I112_J,axiom,
% 4.15/4.17 zero_zero_real = number267125858f_real(pls) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_390_semiring__norm_I112_J,axiom,
% 4.15/4.17 zero_zero_int = number_number_of_int(pls) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_391_number__of__Pls,axiom,
% 4.15/4.17 number267125858f_real(pls) = zero_zero_real ).
% 4.15/4.17
% 4.15/4.17 fof(fact_392_number__of__Pls,axiom,
% 4.15/4.17 number_number_of_int(pls) = zero_zero_int ).
% 4.15/4.17
% 4.15/4.17 fof(fact_393_semiring__numeral__0__eq__0,axiom,
% 4.15/4.17 number267125858f_real(pls) = zero_zero_real ).
% 4.15/4.17
% 4.15/4.17 fof(fact_394_semiring__numeral__0__eq__0,axiom,
% 4.15/4.17 number_number_of_nat(pls) = zero_zero_nat ).
% 4.15/4.17
% 4.15/4.17 fof(fact_395_semiring__numeral__0__eq__0,axiom,
% 4.15/4.17 number_number_of_int(pls) = zero_zero_int ).
% 4.15/4.17
% 4.15/4.17 fof(fact_396_bin__less__0__simps_I4_J,axiom,
% 4.15/4.17 ! [W_1] :
% 4.15/4.17 ( ord_less_int(bit1(W_1),zero_zero_int)
% 4.15/4.17 <=> ord_less_int(W_1,zero_zero_int) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_397_bin__less__0__simps_I1_J,axiom,
% 4.15/4.17 ~ ord_less_int(pls,zero_zero_int) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_398_bin__less__0__simps_I3_J,axiom,
% 4.15/4.17 ! [W_1] :
% 4.15/4.17 ( ord_less_int(bit0(W_1),zero_zero_int)
% 4.15/4.17 <=> ord_less_int(W_1,zero_zero_int) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_399_zero__is__num__zero,axiom,
% 4.15/4.17 zero_zero_int = number_number_of_int(pls) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_400_int__0__less__1,axiom,
% 4.15/4.17 ord_less_int(zero_zero_int,one_one_int) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_401_pos__zmult__pos,axiom,
% 4.15/4.17 ! [B_1,A] :
% 4.15/4.17 ( ord_less_int(zero_zero_int,A)
% 4.15/4.17 => ( ord_less_int(zero_zero_int,times_times_int(A,B_1))
% 4.15/4.17 => ord_less_int(zero_zero_int,B_1) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_402_zmult__zless__mono2,axiom,
% 4.15/4.17 ! [K,I,J] :
% 4.15/4.17 ( ord_less_int(I,J)
% 4.15/4.17 => ( ord_less_int(zero_zero_int,K)
% 4.15/4.17 => ord_less_int(times_times_int(K,I),times_times_int(K,J)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_403_odd__nonzero,axiom,
% 4.15/4.17 ! [Z] : plus_plus_int(plus_plus_int(one_one_int,Z),Z) != zero_zero_int ).
% 4.15/4.17
% 4.15/4.17 fof(fact_404_power__Suc__less,axiom,
% 4.15/4.17 ! [N_17,A_17] :
% 4.15/4.17 ( ord_less_real(zero_zero_real,A_17)
% 4.15/4.17 => ( ord_less_real(A_17,one_one_real)
% 4.15/4.17 => ord_less_real(times_times_real(A_17,power_power_real(A_17,N_17)),power_power_real(A_17,N_17)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_405_power__Suc__less,axiom,
% 4.15/4.17 ! [N_17,A_17] :
% 4.15/4.17 ( ord_less_nat(zero_zero_nat,A_17)
% 4.15/4.17 => ( ord_less_nat(A_17,one_one_nat)
% 4.15/4.17 => ord_less_nat(times_times_nat(A_17,power_power_nat(A_17,N_17)),power_power_nat(A_17,N_17)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_406_power__Suc__less,axiom,
% 4.15/4.17 ! [N_17,A_17] :
% 4.15/4.17 ( ord_less_int(zero_zero_int,A_17)
% 4.15/4.17 => ( ord_less_int(A_17,one_one_int)
% 4.15/4.17 => ord_less_int(times_times_int(A_17,power_power_int(A_17,N_17)),power_power_int(A_17,N_17)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_407_zprime__power__zdvd__cancel__left,axiom,
% 4.15/4.17 ! [N,B_1,A,P] :
% 4.15/4.17 ( zprime(P)
% 4.15/4.17 => ( ~ dvd_dvd_int(P,A)
% 4.15/4.17 => ( dvd_dvd_int(power_power_int(P,N),times_times_int(A,B_1))
% 4.15/4.17 => dvd_dvd_int(power_power_int(P,N),B_1) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_408_zprime__power__zdvd__cancel__right,axiom,
% 4.15/4.17 ! [N,A,B_1,P] :
% 4.15/4.17 ( zprime(P)
% 4.15/4.17 => ( ~ dvd_dvd_int(P,B_1)
% 4.15/4.17 => ( dvd_dvd_int(power_power_int(P,N),times_times_int(A,B_1))
% 4.15/4.17 => dvd_dvd_int(power_power_int(P,N),A) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_409_sum__squares__ge__zero,axiom,
% 4.15/4.17 ! [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))) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_410_sum__squares__ge__zero,axiom,
% 4.15/4.17 ! [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))) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_411_sum__squares__le__zero__iff,axiom,
% 4.15/4.17 ! [X_2,Y_2] :
% 4.15/4.17 ( ord_less_eq_real(plus_plus_real(times_times_real(X_2,X_2),times_times_real(Y_2,Y_2)),zero_zero_real)
% 4.15/4.17 <=> ( X_2 = zero_zero_real
% 4.15/4.17 & Y_2 = zero_zero_real ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_412_sum__squares__le__zero__iff,axiom,
% 4.15/4.17 ! [X_2,Y_2] :
% 4.15/4.17 ( ( is_int(X_2)
% 4.15/4.17 & is_int(Y_2) )
% 4.15/4.17 => ( ord_less_eq_int(plus_plus_int(times_times_int(X_2,X_2),times_times_int(Y_2,Y_2)),zero_zero_int)
% 4.15/4.17 <=> ( X_2 = zero_zero_int
% 4.15/4.17 & Y_2 = zero_zero_int ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_413_less__nat__number__of,axiom,
% 4.15/4.17 ! [V_3,V_4] :
% 4.15/4.17 ( ord_less_nat(number_number_of_nat(V_3),number_number_of_nat(V_4))
% 4.15/4.17 <=> ( ( ord_less_int(V_3,V_4)
% 4.15/4.17 => ord_less_int(pls,V_4) )
% 4.15/4.17 & ord_less_int(V_3,V_4) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_414_not__sum__squares__lt__zero,axiom,
% 4.15/4.17 ! [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) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_415_not__sum__squares__lt__zero,axiom,
% 4.15/4.17 ! [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) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_416_sum__squares__gt__zero__iff,axiom,
% 4.15/4.17 ! [X_2,Y_2] :
% 4.15/4.17 ( ord_less_real(zero_zero_real,plus_plus_real(times_times_real(X_2,X_2),times_times_real(Y_2,Y_2)))
% 4.15/4.17 <=> ( X_2 != zero_zero_real
% 4.15/4.17 | Y_2 != zero_zero_real ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_417_sum__squares__gt__zero__iff,axiom,
% 4.15/4.17 ! [X_2,Y_2] :
% 4.15/4.17 ( ( is_int(X_2)
% 4.15/4.17 & is_int(Y_2) )
% 4.15/4.17 => ( ord_less_int(zero_zero_int,plus_plus_int(times_times_int(X_2,X_2),times_times_int(Y_2,Y_2)))
% 4.15/4.17 <=> ( X_2 != zero_zero_int
% 4.15/4.17 | Y_2 != zero_zero_int ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_418_le__nat__number__of,axiom,
% 4.15/4.17 ! [V_3,V_4] :
% 4.15/4.17 ( ord_less_eq_nat(number_number_of_nat(V_3),number_number_of_nat(V_4))
% 4.15/4.17 <=> ( ~ ord_less_eq_int(V_3,V_4)
% 4.15/4.17 => ord_less_eq_int(V_3,pls) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_419_number__of__Bit0,axiom,
% 4.15/4.17 ! [W_4] : number267125858f_real(bit0(W_4)) = plus_plus_real(plus_plus_real(zero_zero_real,number267125858f_real(W_4)),number267125858f_real(W_4)) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_420_number__of__Bit0,axiom,
% 4.15/4.17 ! [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)) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_421_power__one__right,axiom,
% 4.15/4.17 ! [A_16] : power_power_nat(A_16,one_one_nat) = A_16 ).
% 4.15/4.17
% 4.15/4.17 fof(fact_422_power__one__right,axiom,
% 4.15/4.17 ! [A_16] : power_power_real(A_16,one_one_nat) = A_16 ).
% 4.15/4.17
% 4.15/4.17 fof(fact_423_power__one__right,axiom,
% 4.15/4.17 ! [A_16] :
% 4.15/4.17 ( is_int(A_16)
% 4.15/4.17 => power_power_int(A_16,one_one_nat) = A_16 ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_424_int__one__le__iff__zero__less,axiom,
% 4.15/4.17 ! [Z_1] :
% 4.15/4.17 ( ord_less_eq_int(one_one_int,Z_1)
% 4.15/4.17 <=> ord_less_int(zero_zero_int,Z_1) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_425_pos__zmult__eq__1__iff,axiom,
% 4.15/4.17 ! [N_1,Ma] :
% 4.15/4.17 ( ( is_int(N_1)
% 4.15/4.17 & is_int(Ma) )
% 4.15/4.17 => ( ord_less_int(zero_zero_int,Ma)
% 4.15/4.17 => ( times_times_int(Ma,N_1) = one_one_int
% 4.15/4.17 <=> ( Ma = one_one_int
% 4.15/4.17 & N_1 = one_one_int ) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_426_odd__less__0,axiom,
% 4.15/4.17 ! [Z_1] :
% 4.15/4.17 ( ord_less_int(plus_plus_int(plus_plus_int(one_one_int,Z_1),Z_1),zero_zero_int)
% 4.15/4.17 <=> ord_less_int(Z_1,zero_zero_int) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_427_less__special_I1_J,axiom,
% 4.15/4.17 ! [Y_2] :
% 4.15/4.17 ( ord_less_real(zero_zero_real,number267125858f_real(Y_2))
% 4.15/4.17 <=> ord_less_int(pls,Y_2) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_428_less__special_I1_J,axiom,
% 4.15/4.17 ! [Y_2] :
% 4.15/4.17 ( ord_less_int(zero_zero_int,number_number_of_int(Y_2))
% 4.15/4.17 <=> ord_less_int(pls,Y_2) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_429_less__special_I3_J,axiom,
% 4.15/4.17 ! [X_2] :
% 4.15/4.17 ( ord_less_real(number267125858f_real(X_2),zero_zero_real)
% 4.15/4.17 <=> ord_less_int(X_2,pls) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_430_less__special_I3_J,axiom,
% 4.15/4.17 ! [X_2] :
% 4.15/4.17 ( ord_less_int(number_number_of_int(X_2),zero_zero_int)
% 4.15/4.17 <=> ord_less_int(X_2,pls) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_431_le__special_I1_J,axiom,
% 4.15/4.17 ! [Y_2] :
% 4.15/4.17 ( ord_less_eq_real(zero_zero_real,number267125858f_real(Y_2))
% 4.15/4.17 <=> ord_less_eq_int(pls,Y_2) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_432_le__special_I1_J,axiom,
% 4.15/4.17 ! [Y_2] :
% 4.15/4.17 ( ord_less_eq_int(zero_zero_int,number_number_of_int(Y_2))
% 4.15/4.17 <=> ord_less_eq_int(pls,Y_2) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_433_le__special_I3_J,axiom,
% 4.15/4.17 ! [X_2] :
% 4.15/4.17 ( ord_less_eq_real(number267125858f_real(X_2),zero_zero_real)
% 4.15/4.17 <=> ord_less_eq_int(X_2,pls) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_434_le__special_I3_J,axiom,
% 4.15/4.17 ! [X_2] :
% 4.15/4.17 ( ord_less_eq_int(number_number_of_int(X_2),zero_zero_int)
% 4.15/4.17 <=> ord_less_eq_int(X_2,pls) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_435_le__imp__0__less,axiom,
% 4.15/4.17 ! [Z] :
% 4.15/4.17 ( ord_less_eq_int(zero_zero_int,Z)
% 4.15/4.17 => ord_less_int(zero_zero_int,plus_plus_int(one_one_int,Z)) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_436_zero__power2,axiom,
% 4.15/4.17 power_power_real(zero_zero_real,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real ).
% 4.15/4.17
% 4.15/4.17 fof(fact_437_zero__power2,axiom,
% 4.15/4.17 power_power_nat(zero_zero_nat,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_nat ).
% 4.15/4.17
% 4.15/4.17 fof(fact_438_zero__power2,axiom,
% 4.15/4.17 power_power_int(zero_zero_int,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int ).
% 4.15/4.17
% 4.15/4.17 fof(fact_439_zero__eq__power2,axiom,
% 4.15/4.17 ! [A_1] :
% 4.15/4.17 ( power_power_real(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_real
% 4.15/4.17 <=> A_1 = zero_zero_real ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_440_zero__eq__power2,axiom,
% 4.15/4.17 ! [A_1] :
% 4.15/4.17 ( is_int(A_1)
% 4.15/4.17 => ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int
% 4.15/4.17 <=> A_1 = zero_zero_int ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_441_zero__le__power2,axiom,
% 4.15/4.17 ! [A_15] : ord_less_eq_real(zero_zero_real,power_power_real(A_15,number_number_of_nat(bit0(bit1(pls))))) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_442_zero__le__power2,axiom,
% 4.15/4.17 ! [A_15] : ord_less_eq_int(zero_zero_int,power_power_int(A_15,number_number_of_nat(bit0(bit1(pls))))) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_443_power2__le__imp__le,axiom,
% 4.15/4.17 ! [X_10,Y_8] :
% 4.15/4.17 ( 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)))))
% 4.15/4.17 => ( ord_less_eq_real(zero_zero_real,Y_8)
% 4.15/4.17 => ord_less_eq_real(X_10,Y_8) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_444_power2__le__imp__le,axiom,
% 4.15/4.17 ! [X_10,Y_8] :
% 4.15/4.17 ( 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)))))
% 4.15/4.17 => ( ord_less_eq_nat(zero_zero_nat,Y_8)
% 4.15/4.17 => ord_less_eq_nat(X_10,Y_8) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_445_power2__le__imp__le,axiom,
% 4.15/4.17 ! [X_10,Y_8] :
% 4.15/4.17 ( 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)))))
% 4.15/4.17 => ( ord_less_eq_int(zero_zero_int,Y_8)
% 4.15/4.17 => ord_less_eq_int(X_10,Y_8) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_446_power2__eq__imp__eq,axiom,
% 4.15/4.17 ! [X_9,Y_7] :
% 4.15/4.17 ( power_power_real(X_9,number_number_of_nat(bit0(bit1(pls)))) = power_power_real(Y_7,number_number_of_nat(bit0(bit1(pls))))
% 4.15/4.17 => ( ord_less_eq_real(zero_zero_real,X_9)
% 4.15/4.17 => ( ord_less_eq_real(zero_zero_real,Y_7)
% 4.15/4.17 => X_9 = Y_7 ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_447_power2__eq__imp__eq,axiom,
% 4.15/4.17 ! [X_9,Y_7] :
% 4.15/4.17 ( power_power_nat(X_9,number_number_of_nat(bit0(bit1(pls)))) = power_power_nat(Y_7,number_number_of_nat(bit0(bit1(pls))))
% 4.15/4.17 => ( ord_less_eq_nat(zero_zero_nat,X_9)
% 4.15/4.17 => ( ord_less_eq_nat(zero_zero_nat,Y_7)
% 4.15/4.17 => X_9 = Y_7 ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_448_power2__eq__imp__eq,axiom,
% 4.15/4.17 ! [X_9,Y_7] :
% 4.15/4.17 ( ( is_int(X_9)
% 4.15/4.17 & is_int(Y_7) )
% 4.15/4.17 => ( power_power_int(X_9,number_number_of_nat(bit0(bit1(pls)))) = power_power_int(Y_7,number_number_of_nat(bit0(bit1(pls))))
% 4.15/4.17 => ( ord_less_eq_int(zero_zero_int,X_9)
% 4.15/4.17 => ( ord_less_eq_int(zero_zero_int,Y_7)
% 4.15/4.17 => X_9 = Y_7 ) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_449_power2__less__0,axiom,
% 4.15/4.17 ! [A_14] : ~ ord_less_real(power_power_real(A_14,number_number_of_nat(bit0(bit1(pls)))),zero_zero_real) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_450_power2__less__0,axiom,
% 4.15/4.17 ! [A_14] : ~ ord_less_int(power_power_int(A_14,number_number_of_nat(bit0(bit1(pls)))),zero_zero_int) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_451_zero__less__power2,axiom,
% 4.15/4.17 ! [A_1] :
% 4.15/4.17 ( ord_less_real(zero_zero_real,power_power_real(A_1,number_number_of_nat(bit0(bit1(pls)))))
% 4.15/4.17 <=> A_1 != zero_zero_real ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_452_zero__less__power2,axiom,
% 4.15/4.17 ! [A_1] :
% 4.15/4.17 ( is_int(A_1)
% 4.15/4.17 => ( ord_less_int(zero_zero_int,power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))))
% 4.15/4.17 <=> A_1 != zero_zero_int ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_453_sum__power2__eq__zero__iff,axiom,
% 4.15/4.17 ! [X_2,Y_2] :
% 4.15/4.17 ( 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
% 4.15/4.17 <=> ( X_2 = zero_zero_real
% 4.15/4.17 & Y_2 = zero_zero_real ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_454_sum__power2__eq__zero__iff,axiom,
% 4.15/4.17 ! [X_2,Y_2] :
% 4.15/4.17 ( ( is_int(X_2)
% 4.15/4.17 & is_int(Y_2) )
% 4.15/4.17 => ( 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
% 4.15/4.17 <=> ( X_2 = zero_zero_int
% 4.15/4.17 & Y_2 = zero_zero_int ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_455_power__commutes,axiom,
% 4.15/4.17 ! [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)) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_456_power__commutes,axiom,
% 4.15/4.17 ! [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)) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_457_power__commutes,axiom,
% 4.15/4.17 ! [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)) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_458_power__mult__distrib,axiom,
% 4.15/4.17 ! [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)) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_459_power__mult__distrib,axiom,
% 4.15/4.17 ! [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)) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_460_power__mult__distrib,axiom,
% 4.15/4.17 ! [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)) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_461_power__add,axiom,
% 4.15/4.17 ! [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)) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_462_power__add,axiom,
% 4.15/4.17 ! [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)) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_463_power__add,axiom,
% 4.15/4.17 ! [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)) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_464_power__one,axiom,
% 4.15/4.17 ! [N_13] : power_power_real(one_one_real,N_13) = one_one_real ).
% 4.15/4.17
% 4.15/4.17 fof(fact_465_power__one,axiom,
% 4.15/4.17 ! [N_13] : power_power_nat(one_one_nat,N_13) = one_one_nat ).
% 4.15/4.17
% 4.15/4.17 fof(fact_466_power__one,axiom,
% 4.15/4.17 ! [N_13] : power_power_int(one_one_int,N_13) = one_one_int ).
% 4.15/4.17
% 4.15/4.17 fof(fact_467_power__mult,axiom,
% 4.15/4.17 ! [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) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_468_power__mult,axiom,
% 4.15/4.17 ! [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) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_469_power__mult,axiom,
% 4.15/4.17 ! [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) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_470_power2__less__imp__less,axiom,
% 4.15/4.17 ! [X_8,Y_6] :
% 4.15/4.17 ( 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)))))
% 4.15/4.17 => ( ord_less_eq_real(zero_zero_real,Y_6)
% 4.15/4.17 => ord_less_real(X_8,Y_6) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_471_power2__less__imp__less,axiom,
% 4.15/4.17 ! [X_8,Y_6] :
% 4.15/4.17 ( 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)))))
% 4.15/4.17 => ( ord_less_eq_nat(zero_zero_nat,Y_6)
% 4.15/4.17 => ord_less_nat(X_8,Y_6) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_472_power2__less__imp__less,axiom,
% 4.15/4.17 ! [X_8,Y_6] :
% 4.15/4.17 ( 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)))))
% 4.15/4.17 => ( ord_less_eq_int(zero_zero_int,Y_6)
% 4.15/4.17 => ord_less_int(X_8,Y_6) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_473_sum__power2__ge__zero,axiom,
% 4.15/4.17 ! [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)))))) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_474_sum__power2__ge__zero,axiom,
% 4.15/4.17 ! [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)))))) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_475_sum__power2__le__zero__iff,axiom,
% 4.15/4.17 ! [X_2,Y_2] :
% 4.15/4.17 ( 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)
% 4.15/4.17 <=> ( X_2 = zero_zero_real
% 4.15/4.17 & Y_2 = zero_zero_real ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_476_sum__power2__le__zero__iff,axiom,
% 4.15/4.17 ! [X_2,Y_2] :
% 4.15/4.17 ( ( is_int(X_2)
% 4.15/4.17 & is_int(Y_2) )
% 4.15/4.17 => ( 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)
% 4.15/4.17 <=> ( X_2 = zero_zero_int
% 4.15/4.17 & Y_2 = zero_zero_int ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_477_not__sum__power2__lt__zero,axiom,
% 4.15/4.17 ! [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) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_478_not__sum__power2__lt__zero,axiom,
% 4.15/4.17 ! [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) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_479_sum__power2__gt__zero__iff,axiom,
% 4.15/4.17 ! [X_2,Y_2] :
% 4.15/4.17 ( 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))))))
% 4.15/4.17 <=> ( X_2 != zero_zero_real
% 4.15/4.17 | Y_2 != zero_zero_real ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_480_sum__power2__gt__zero__iff,axiom,
% 4.15/4.17 ! [X_2,Y_2] :
% 4.15/4.17 ( ( is_int(X_2)
% 4.15/4.17 & is_int(Y_2) )
% 4.15/4.17 => ( 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))))))
% 4.15/4.17 <=> ( X_2 != zero_zero_int
% 4.15/4.17 | Y_2 != zero_zero_int ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_481_zero__le__even__power_H,axiom,
% 4.15/4.17 ! [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))) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_482_zero__le__even__power_H,axiom,
% 4.15/4.17 ! [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))) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_483_one__le__power,axiom,
% 4.15/4.17 ! [N_10,A_8] :
% 4.15/4.17 ( ord_less_eq_real(one_one_real,A_8)
% 4.15/4.17 => ord_less_eq_real(one_one_real,power_power_real(A_8,N_10)) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_484_one__le__power,axiom,
% 4.15/4.17 ! [N_10,A_8] :
% 4.15/4.17 ( ord_less_eq_nat(one_one_nat,A_8)
% 4.15/4.17 => ord_less_eq_nat(one_one_nat,power_power_nat(A_8,N_10)) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_485_one__le__power,axiom,
% 4.15/4.17 ! [N_10,A_8] :
% 4.15/4.17 ( ord_less_eq_int(one_one_int,A_8)
% 4.15/4.17 => ord_less_eq_int(one_one_int,power_power_int(A_8,N_10)) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_486_power__increasing,axiom,
% 4.15/4.17 ! [A_7,N_9,N_8] :
% 4.15/4.17 ( ord_less_eq_nat(N_9,N_8)
% 4.15/4.17 => ( ord_less_eq_real(one_one_real,A_7)
% 4.15/4.17 => ord_less_eq_real(power_power_real(A_7,N_9),power_power_real(A_7,N_8)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_487_power__increasing,axiom,
% 4.15/4.17 ! [A_7,N_9,N_8] :
% 4.15/4.17 ( ord_less_eq_nat(N_9,N_8)
% 4.15/4.17 => ( ord_less_eq_nat(one_one_nat,A_7)
% 4.15/4.17 => ord_less_eq_nat(power_power_nat(A_7,N_9),power_power_nat(A_7,N_8)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_488_power__increasing,axiom,
% 4.15/4.17 ! [A_7,N_9,N_8] :
% 4.15/4.17 ( ord_less_eq_nat(N_9,N_8)
% 4.15/4.17 => ( ord_less_eq_int(one_one_int,A_7)
% 4.15/4.17 => ord_less_eq_int(power_power_int(A_7,N_9),power_power_int(A_7,N_8)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_489_power__inject__exp,axiom,
% 4.15/4.17 ! [Ma,N_1,A_1] :
% 4.15/4.17 ( ord_less_real(one_one_real,A_1)
% 4.15/4.17 => ( power_power_real(A_1,Ma) = power_power_real(A_1,N_1)
% 4.15/4.17 <=> Ma = N_1 ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_490_power__inject__exp,axiom,
% 4.15/4.17 ! [Ma,N_1,A_1] :
% 4.15/4.17 ( ord_less_nat(one_one_nat,A_1)
% 4.15/4.17 => ( power_power_nat(A_1,Ma) = power_power_nat(A_1,N_1)
% 4.15/4.17 <=> Ma = N_1 ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_491_power__inject__exp,axiom,
% 4.15/4.17 ! [Ma,N_1,A_1] :
% 4.15/4.17 ( ord_less_int(one_one_int,A_1)
% 4.15/4.17 => ( power_power_int(A_1,Ma) = power_power_int(A_1,N_1)
% 4.15/4.17 <=> Ma = N_1 ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_492_power__strict__increasing__iff,axiom,
% 4.15/4.17 ! [X_2,Y_2,B_2] :
% 4.15/4.17 ( ord_less_real(one_one_real,B_2)
% 4.15/4.17 => ( ord_less_real(power_power_real(B_2,X_2),power_power_real(B_2,Y_2))
% 4.15/4.17 <=> ord_less_nat(X_2,Y_2) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_493_power__strict__increasing__iff,axiom,
% 4.15/4.17 ! [X_2,Y_2,B_2] :
% 4.15/4.17 ( ord_less_nat(one_one_nat,B_2)
% 4.15/4.17 => ( ord_less_nat(power_power_nat(B_2,X_2),power_power_nat(B_2,Y_2))
% 4.15/4.17 <=> ord_less_nat(X_2,Y_2) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_494_power__strict__increasing__iff,axiom,
% 4.15/4.17 ! [X_2,Y_2,B_2] :
% 4.15/4.17 ( ord_less_int(one_one_int,B_2)
% 4.15/4.17 => ( ord_less_int(power_power_int(B_2,X_2),power_power_int(B_2,Y_2))
% 4.15/4.17 <=> ord_less_nat(X_2,Y_2) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_495_power__less__imp__less__exp,axiom,
% 4.15/4.17 ! [M_2,N_7,A_6] :
% 4.15/4.17 ( ord_less_real(one_one_real,A_6)
% 4.15/4.17 => ( ord_less_real(power_power_real(A_6,M_2),power_power_real(A_6,N_7))
% 4.15/4.17 => ord_less_nat(M_2,N_7) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_496_power__less__imp__less__exp,axiom,
% 4.15/4.17 ! [M_2,N_7,A_6] :
% 4.15/4.17 ( ord_less_nat(one_one_nat,A_6)
% 4.15/4.17 => ( ord_less_nat(power_power_nat(A_6,M_2),power_power_nat(A_6,N_7))
% 4.15/4.17 => ord_less_nat(M_2,N_7) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_497_power__less__imp__less__exp,axiom,
% 4.15/4.17 ! [M_2,N_7,A_6] :
% 4.15/4.17 ( ord_less_int(one_one_int,A_6)
% 4.15/4.17 => ( ord_less_int(power_power_int(A_6,M_2),power_power_int(A_6,N_7))
% 4.15/4.17 => ord_less_nat(M_2,N_7) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_498_power__strict__increasing,axiom,
% 4.15/4.17 ! [A_5,N_6,N_5] :
% 4.15/4.17 ( ord_less_nat(N_6,N_5)
% 4.15/4.17 => ( ord_less_real(one_one_real,A_5)
% 4.15/4.17 => ord_less_real(power_power_real(A_5,N_6),power_power_real(A_5,N_5)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_499_power__strict__increasing,axiom,
% 4.15/4.17 ! [A_5,N_6,N_5] :
% 4.15/4.17 ( ord_less_nat(N_6,N_5)
% 4.15/4.17 => ( ord_less_nat(one_one_nat,A_5)
% 4.15/4.17 => ord_less_nat(power_power_nat(A_5,N_6),power_power_nat(A_5,N_5)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_500_power__strict__increasing,axiom,
% 4.15/4.17 ! [A_5,N_6,N_5] :
% 4.15/4.17 ( ord_less_nat(N_6,N_5)
% 4.15/4.17 => ( ord_less_int(one_one_int,A_5)
% 4.15/4.17 => ord_less_int(power_power_int(A_5,N_6),power_power_int(A_5,N_5)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_501_s,axiom,
% 4.15/4.17 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)) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_502_Euler_Oaux____1,axiom,
% 4.15/4.17 ! [Y_1,X_1,P] :
% 4.15/4.17 ( ~ zcong(X_1,zero_zero_int,P)
% 4.15/4.17 => ( zcong(power_power_int(Y_1,number_number_of_nat(bit0(bit1(pls)))),X_1,P)
% 4.15/4.17 => ~ dvd_dvd_int(P,Y_1) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_503_int__pos__lt__two__imp__zero__or__one,axiom,
% 4.15/4.17 ! [X_1] :
% 4.15/4.17 ( is_int(X_1)
% 4.15/4.17 => ( ord_less_eq_int(zero_zero_int,X_1)
% 4.15/4.17 => ( ord_less_int(X_1,number_number_of_int(bit0(bit1(pls))))
% 4.15/4.17 => ( X_1 = zero_zero_int
% 4.15/4.17 | X_1 = one_one_int ) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_504_even__power__le__0__imp__0,axiom,
% 4.15/4.17 ! [A_4,K_3] :
% 4.15/4.17 ( ord_less_eq_real(power_power_real(A_4,times_times_nat(number_number_of_nat(bit0(bit1(pls))),K_3)),zero_zero_real)
% 4.15/4.17 => A_4 = zero_zero_real ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_505_even__power__le__0__imp__0,axiom,
% 4.15/4.17 ! [A_4,K_3] :
% 4.15/4.17 ( is_int(A_4)
% 4.15/4.17 => ( ord_less_eq_int(power_power_int(A_4,times_times_nat(number_number_of_nat(bit0(bit1(pls))),K_3)),zero_zero_int)
% 4.15/4.17 => A_4 = zero_zero_int ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_506_zprime__def,axiom,
% 4.15/4.17 ! [P_1] :
% 4.15/4.17 ( is_int(P_1)
% 4.15/4.17 => ( zprime(P_1)
% 4.15/4.17 <=> ( ord_less_int(one_one_int,P_1)
% 4.15/4.17 & ! [M_1] :
% 4.15/4.17 ( is_int(M_1)
% 4.15/4.17 => ( ( ord_less_eq_int(zero_zero_int,M_1)
% 4.15/4.17 & dvd_dvd_int(M_1,P_1) )
% 4.15/4.17 => ( M_1 = one_one_int
% 4.15/4.17 | M_1 = P_1 ) ) ) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 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,
% 4.15/4.17 ~ ! [S1] :
% 4.15/4.17 ( is_int(S1)
% 4.15/4.17 => ~ 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)) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_508__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096,axiom,
% 4.15/4.17 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 ).
% 4.15/4.17
% 4.15/4.17 fof(fact_509_nat__zero__less__power__iff,axiom,
% 4.15/4.17 ! [X_2,N_1] :
% 4.15/4.17 ( ord_less_nat(zero_zero_nat,power_power_nat(X_2,N_1))
% 4.15/4.17 <=> ( ord_less_nat(zero_zero_nat,X_2)
% 4.15/4.17 | N_1 = zero_zero_nat ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_510_zero__less__power__nat__eq,axiom,
% 4.15/4.17 ! [X_2,N_1] :
% 4.15/4.17 ( ord_less_nat(zero_zero_nat,power_power_nat(X_2,N_1))
% 4.15/4.17 <=> ( N_1 = zero_zero_nat
% 4.15/4.17 | ord_less_nat(zero_zero_nat,X_2) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_511_zero__less__power__nat__eq__number__of,axiom,
% 4.15/4.17 ! [X_2,W_1] :
% 4.15/4.17 ( ord_less_nat(zero_zero_nat,power_power_nat(X_2,number_number_of_nat(W_1)))
% 4.15/4.17 <=> ( number_number_of_nat(W_1) = zero_zero_nat
% 4.15/4.17 | ord_less_nat(zero_zero_nat,X_2) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_512_nat__power__less__imp__less,axiom,
% 4.15/4.17 ! [M,N,I] :
% 4.15/4.17 ( ord_less_nat(zero_zero_nat,I)
% 4.15/4.17 => ( ord_less_nat(power_power_nat(I,M),power_power_nat(I,N))
% 4.15/4.17 => ord_less_nat(M,N) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_513_rel__simps_I47_J,axiom,
% 4.15/4.17 ! [K_1] :
% 4.15/4.17 ( is_int(K_1)
% 4.15/4.17 => ( bit1(K_1) = min
% 4.15/4.17 <=> K_1 = min ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_514_rel__simps_I43_J,axiom,
% 4.15/4.17 ! [L_1] :
% 4.15/4.17 ( is_int(L_1)
% 4.15/4.17 => ( min = bit1(L_1)
% 4.15/4.17 <=> min = L_1 ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_515_Bit1__Min,axiom,
% 4.15/4.17 bit1(min) = min ).
% 4.15/4.17
% 4.15/4.17 fof(fact_516_rel__simps_I37_J,axiom,
% 4.15/4.17 pls != min ).
% 4.15/4.17
% 4.15/4.17 fof(fact_517_rel__simps_I40_J,axiom,
% 4.15/4.17 min != pls ).
% 4.15/4.17
% 4.15/4.17 fof(fact_518_rel__simps_I45_J,axiom,
% 4.15/4.17 ! [K] : bit0(K) != min ).
% 4.15/4.17
% 4.15/4.17 fof(fact_519_rel__simps_I42_J,axiom,
% 4.15/4.17 ! [L] : min != bit0(L) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_520_rel__simps_I7_J,axiom,
% 4.15/4.17 ~ ord_less_int(min,min) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_521_rel__simps_I24_J,axiom,
% 4.15/4.17 ord_less_eq_int(min,min) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_522_not__real__square__gt__zero,axiom,
% 4.15/4.17 ! [X_2] :
% 4.15/4.17 ( ~ ord_less_real(zero_zero_real,times_times_real(X_2,X_2))
% 4.15/4.17 <=> X_2 = zero_zero_real ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_523_rel__simps_I13_J,axiom,
% 4.15/4.17 ! [K_1] :
% 4.15/4.17 ( ord_less_int(bit1(K_1),min)
% 4.15/4.17 <=> ord_less_int(K_1,min) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_524_rel__simps_I9_J,axiom,
% 4.15/4.17 ! [K_1] :
% 4.15/4.17 ( ord_less_int(min,bit1(K_1))
% 4.15/4.17 <=> ord_less_int(min,K_1) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_525_rel__simps_I3_J,axiom,
% 4.15/4.17 ~ ord_less_int(pls,min) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_526_rel__simps_I6_J,axiom,
% 4.15/4.17 ord_less_int(min,pls) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_527_rel__simps_I8_J,axiom,
% 4.15/4.17 ! [K_1] :
% 4.15/4.17 ( ord_less_int(min,bit0(K_1))
% 4.15/4.17 <=> ord_less_int(min,K_1) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_528_bin__less__0__simps_I2_J,axiom,
% 4.15/4.17 ord_less_int(min,zero_zero_int) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_529_rel__simps_I30_J,axiom,
% 4.15/4.17 ! [K_1] :
% 4.15/4.17 ( ord_less_eq_int(bit1(K_1),min)
% 4.15/4.17 <=> ord_less_eq_int(K_1,min) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_530_rel__simps_I26_J,axiom,
% 4.15/4.17 ! [K_1] :
% 4.15/4.17 ( ord_less_eq_int(min,bit1(K_1))
% 4.15/4.17 <=> ord_less_eq_int(min,K_1) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_531_rel__simps_I20_J,axiom,
% 4.15/4.17 ~ ord_less_eq_int(pls,min) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_532_rel__simps_I23_J,axiom,
% 4.15/4.17 ord_less_eq_int(min,pls) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_533_rel__simps_I28_J,axiom,
% 4.15/4.17 ! [K_1] :
% 4.15/4.17 ( ord_less_eq_int(bit0(K_1),min)
% 4.15/4.17 <=> ord_less_eq_int(K_1,min) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_534_eq__number__of__Pls__Min,axiom,
% 4.15/4.17 number_number_of_int(pls) != number_number_of_int(min) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_535_power__dvd__imp__le,axiom,
% 4.15/4.17 ! [I,M,N] :
% 4.15/4.17 ( dvd_dvd_nat(power_power_nat(I,M),power_power_nat(I,N))
% 4.15/4.17 => ( ord_less_nat(one_one_nat,I)
% 4.15/4.17 => ord_less_eq_nat(M,N) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_536_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 4.15/4.17 ! [X_5] : power_power_real(X_5,zero_zero_nat) = one_one_real ).
% 4.15/4.17
% 4.15/4.17 fof(fact_537_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 4.15/4.17 ! [X_5] : power_power_nat(X_5,zero_zero_nat) = one_one_nat ).
% 4.15/4.17
% 4.15/4.17 fof(fact_538_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 4.15/4.17 ! [X_5] : power_power_int(X_5,zero_zero_nat) = one_one_int ).
% 4.15/4.17
% 4.15/4.17 fof(fact_539_power__0,axiom,
% 4.15/4.17 ! [A_3] : power_power_real(A_3,zero_zero_nat) = one_one_real ).
% 4.15/4.17
% 4.15/4.17 fof(fact_540_power__0,axiom,
% 4.15/4.17 ! [A_3] : power_power_nat(A_3,zero_zero_nat) = one_one_nat ).
% 4.15/4.17
% 4.15/4.17 fof(fact_541_power__0,axiom,
% 4.15/4.17 ! [A_3] : power_power_int(A_3,zero_zero_nat) = one_one_int ).
% 4.15/4.17
% 4.15/4.17 fof(fact_542_nat__number__of__Pls,axiom,
% 4.15/4.17 number_number_of_nat(pls) = zero_zero_nat ).
% 4.15/4.17
% 4.15/4.17 fof(fact_543_semiring__norm_I113_J,axiom,
% 4.15/4.17 zero_zero_nat = number_number_of_nat(pls) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_544_rel__simps_I25_J,axiom,
% 4.15/4.17 ! [K_1] :
% 4.15/4.17 ( ord_less_eq_int(min,bit0(K_1))
% 4.15/4.17 <=> ord_less_int(min,K_1) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_545_rel__simps_I11_J,axiom,
% 4.15/4.17 ! [K_1] :
% 4.15/4.17 ( ord_less_int(bit0(K_1),min)
% 4.15/4.17 <=> ord_less_eq_int(K_1,min) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_546_pos__zmult__eq__1__iff__lemma,axiom,
% 4.15/4.17 ! [M,N] :
% 4.15/4.17 ( is_int(M)
% 4.15/4.17 => ( times_times_int(M,N) = one_one_int
% 4.15/4.17 => ( M = one_one_int
% 4.15/4.17 | M = number_number_of_int(min) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_547_zmult__eq__1__iff,axiom,
% 4.15/4.17 ! [Ma,N_1] :
% 4.15/4.17 ( ( is_int(Ma)
% 4.15/4.17 & is_int(N_1) )
% 4.15/4.17 => ( times_times_int(Ma,N_1) = one_one_int
% 4.15/4.17 <=> ( ( Ma = one_one_int
% 4.15/4.17 & N_1 = one_one_int )
% 4.15/4.17 | ( Ma = number_number_of_int(min)
% 4.15/4.17 & N_1 = number_number_of_int(min) ) ) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_548_one__less__power,axiom,
% 4.15/4.17 ! [N_4,A_2] :
% 4.15/4.17 ( ord_less_real(one_one_real,A_2)
% 4.15/4.17 => ( ord_less_nat(zero_zero_nat,N_4)
% 4.15/4.17 => ord_less_real(one_one_real,power_power_real(A_2,N_4)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_549_one__less__power,axiom,
% 4.15/4.17 ! [N_4,A_2] :
% 4.15/4.17 ( ord_less_nat(one_one_nat,A_2)
% 4.15/4.17 => ( ord_less_nat(zero_zero_nat,N_4)
% 4.15/4.17 => ord_less_nat(one_one_nat,power_power_nat(A_2,N_4)) ) ) ).
% 4.15/4.17
% 4.15/4.17 fof(fact_550_one__less__power,axiom,
% 4.15/4.17 ! [N_4,A_2] :
% 4.15/4.17 ( ord_less_int(one_one_int,A_2)
% 4.15/4.17 => ( ord_less_nat(zero_zero_nat,N_4)
% 4.15/4.18 => ord_less_int(one_one_int,power_power_int(A_2,N_4)) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_551_dvd__power,axiom,
% 4.15/4.18 ! [X_4,N_3] :
% 4.15/4.18 ( ( ord_less_nat(zero_zero_nat,N_3)
% 4.15/4.18 | X_4 = one_one_nat )
% 4.15/4.18 => dvd_dvd_nat(X_4,power_power_nat(X_4,N_3)) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_552_dvd__power,axiom,
% 4.15/4.18 ! [X_4,N_3] :
% 4.15/4.18 ( ( ord_less_nat(zero_zero_nat,N_3)
% 4.15/4.18 | X_4 = one_one_int )
% 4.15/4.18 => dvd_dvd_int(X_4,power_power_int(X_4,N_3)) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_553_dvd__power,axiom,
% 4.15/4.18 ! [X_4,N_3] :
% 4.15/4.18 ( ( ord_less_nat(zero_zero_nat,N_3)
% 4.15/4.18 | X_4 = one_one_real )
% 4.15/4.18 => dvd_dvd_real(X_4,power_power_real(X_4,N_3)) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_554_less__0__number__of,axiom,
% 4.15/4.18 ! [V_3] :
% 4.15/4.18 ( ord_less_nat(zero_zero_nat,number_number_of_nat(V_3))
% 4.15/4.18 <=> ord_less_int(pls,V_3) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_555_eq__number__of__0,axiom,
% 4.15/4.18 ! [V_3] :
% 4.15/4.18 ( number_number_of_nat(V_3) = zero_zero_nat
% 4.15/4.18 <=> ord_less_eq_int(V_3,pls) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_556_eq__0__number__of,axiom,
% 4.15/4.18 ! [V_3] :
% 4.15/4.18 ( zero_zero_nat = number_number_of_nat(V_3)
% 4.15/4.18 <=> ord_less_eq_int(V_3,pls) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_557_zcong__sym,axiom,
% 4.15/4.18 ! [A_1,B_2,Ma] :
% 4.15/4.18 ( zcong(A_1,B_2,Ma)
% 4.15/4.18 <=> zcong(B_2,A_1,Ma) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_558_zcong__refl,axiom,
% 4.15/4.18 ! [K,M] : zcong(K,K,M) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_559_zcong__trans,axiom,
% 4.15/4.18 ! [C_1,A,B_1,M] :
% 4.15/4.18 ( zcong(A,B_1,M)
% 4.15/4.18 => ( zcong(B_1,C_1,M)
% 4.15/4.18 => zcong(A,C_1,M) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_560_pos2,axiom,
% 4.15/4.18 ord_less_nat(zero_zero_nat,number_number_of_nat(bit0(bit1(pls)))) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_561_nat__number__of__mult__left,axiom,
% 4.15/4.18 ! [V_2,K,V_1] :
% 4.15/4.18 ( ( ord_less_int(V_1,pls)
% 4.15/4.18 => times_times_nat(number_number_of_nat(V_1),times_times_nat(number_number_of_nat(V_2),K)) = zero_zero_nat )
% 4.15/4.18 & ( ~ ord_less_int(V_1,pls)
% 4.15/4.18 => 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) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_562_mult__nat__number__of,axiom,
% 4.15/4.18 ! [V_2,V_1] :
% 4.15/4.18 ( ( ord_less_int(V_1,pls)
% 4.15/4.18 => times_times_nat(number_number_of_nat(V_1),number_number_of_nat(V_2)) = zero_zero_nat )
% 4.15/4.18 & ( ~ ord_less_int(V_1,pls)
% 4.15/4.18 => 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)) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_563_order__le__neq__implies__less,axiom,
% 4.15/4.18 ! [X_3,Y_3] :
% 4.15/4.18 ( ord_less_eq_real(X_3,Y_3)
% 4.15/4.18 => ( X_3 != Y_3
% 4.15/4.18 => ord_less_real(X_3,Y_3) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_564_order__le__neq__implies__less,axiom,
% 4.15/4.18 ! [X_3,Y_3] :
% 4.15/4.18 ( ord_less_eq_nat(X_3,Y_3)
% 4.15/4.18 => ( X_3 != Y_3
% 4.15/4.18 => ord_less_nat(X_3,Y_3) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_565_order__le__neq__implies__less,axiom,
% 4.15/4.18 ! [X_3,Y_3] :
% 4.15/4.18 ( ( is_int(X_3)
% 4.15/4.18 & is_int(Y_3) )
% 4.15/4.18 => ( ord_less_eq_int(X_3,Y_3)
% 4.15/4.18 => ( X_3 != Y_3
% 4.15/4.18 => ord_less_int(X_3,Y_3) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_566_Euler_Oaux2,axiom,
% 4.15/4.18 ! [B_1,A,C_1] :
% 4.15/4.18 ( ord_less_int(A,C_1)
% 4.15/4.18 => ( ord_less_int(B_1,C_1)
% 4.15/4.18 => ( ord_less_eq_int(A,B_1)
% 4.15/4.18 | ord_less_eq_int(B_1,A) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_567_IntPrimes_Ozcong__zero,axiom,
% 4.15/4.18 ! [A_1,B_2] :
% 4.15/4.18 ( ( is_int(A_1)
% 4.15/4.18 & is_int(B_2) )
% 4.15/4.18 => ( zcong(A_1,B_2,zero_zero_int)
% 4.15/4.18 <=> A_1 = B_2 ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_568_zcong__1,axiom,
% 4.15/4.18 ! [A,B_1] : zcong(A,B_1,one_one_int) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_569_zcong__zmult,axiom,
% 4.15/4.18 ! [C_1,D_1,A,B_1,M] :
% 4.15/4.18 ( zcong(A,B_1,M)
% 4.15/4.18 => ( zcong(C_1,D_1,M)
% 4.15/4.18 => zcong(times_times_int(A,C_1),times_times_int(B_1,D_1),M) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_570_zcong__scalar2,axiom,
% 4.15/4.18 ! [K,A,B_1,M] :
% 4.15/4.18 ( zcong(A,B_1,M)
% 4.15/4.18 => zcong(times_times_int(K,A),times_times_int(K,B_1),M) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_571_zcong__scalar,axiom,
% 4.15/4.18 ! [K,A,B_1,M] :
% 4.15/4.18 ( zcong(A,B_1,M)
% 4.15/4.18 => zcong(times_times_int(A,K),times_times_int(B_1,K),M) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_572_zcong__zmult__self,axiom,
% 4.15/4.18 ! [A,M,B_1] : zcong(times_times_int(A,M),times_times_int(B_1,M),M) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_573_zcong__zadd,axiom,
% 4.15/4.18 ! [C_1,D_1,A,B_1,M] :
% 4.15/4.18 ( zcong(A,B_1,M)
% 4.15/4.18 => ( zcong(C_1,D_1,M)
% 4.15/4.18 => zcong(plus_plus_int(A,C_1),plus_plus_int(B_1,D_1),M) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_574_power__m1__even,axiom,
% 4.15/4.18 ! [N_2] : power_power_real(number267125858f_real(min),times_times_nat(number_number_of_nat(bit0(bit1(pls))),N_2)) = one_one_real ).
% 4.15/4.18
% 4.15/4.18 fof(fact_575_power__m1__even,axiom,
% 4.15/4.18 ! [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 ).
% 4.15/4.18
% 4.15/4.18 fof(fact_576_power__eq__0__iff__number__of,axiom,
% 4.15/4.18 ! [A_1,W_1] :
% 4.15/4.18 ( power_power_real(A_1,number_number_of_nat(W_1)) = zero_zero_real
% 4.15/4.18 <=> ( A_1 = zero_zero_real
% 4.15/4.18 & number_number_of_nat(W_1) != zero_zero_nat ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_577_power__eq__0__iff__number__of,axiom,
% 4.15/4.18 ! [A_1,W_1] :
% 4.15/4.18 ( power_power_nat(A_1,number_number_of_nat(W_1)) = zero_zero_nat
% 4.15/4.18 <=> ( A_1 = zero_zero_nat
% 4.15/4.18 & number_number_of_nat(W_1) != zero_zero_nat ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_578_power__eq__0__iff__number__of,axiom,
% 4.15/4.18 ! [A_1,W_1] :
% 4.15/4.18 ( is_int(A_1)
% 4.15/4.18 => ( power_power_int(A_1,number_number_of_nat(W_1)) = zero_zero_int
% 4.15/4.18 <=> ( A_1 = zero_zero_int
% 4.15/4.18 & number_number_of_nat(W_1) != zero_zero_nat ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_579_zcong__not,axiom,
% 4.15/4.18 ! [B_1,M,A] :
% 4.15/4.18 ( ord_less_int(zero_zero_int,A)
% 4.15/4.18 => ( ord_less_int(A,M)
% 4.15/4.18 => ( ord_less_int(zero_zero_int,B_1)
% 4.15/4.18 => ( ord_less_int(B_1,A)
% 4.15/4.18 => ~ zcong(A,B_1,M) ) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_580_zcong__iff__lin,axiom,
% 4.15/4.18 ! [A_1,B_2,Ma] :
% 4.15/4.18 ( is_int(B_2)
% 4.15/4.18 => ( zcong(A_1,B_2,Ma)
% 4.15/4.18 <=> ? [K_2] :
% 4.15/4.18 ( is_int(K_2)
% 4.15/4.18 & B_2 = plus_plus_int(A_1,times_times_int(Ma,K_2)) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_581_power__0__left__number__of,axiom,
% 4.15/4.18 ! [W_3] :
% 4.15/4.18 ( ( number_number_of_nat(W_3) = zero_zero_nat
% 4.15/4.18 => power_power_real(zero_zero_real,number_number_of_nat(W_3)) = one_one_real )
% 4.15/4.18 & ( number_number_of_nat(W_3) != zero_zero_nat
% 4.15/4.18 => power_power_real(zero_zero_real,number_number_of_nat(W_3)) = zero_zero_real ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_582_power__0__left__number__of,axiom,
% 4.15/4.18 ! [W_3] :
% 4.15/4.18 ( ( number_number_of_nat(W_3) = zero_zero_nat
% 4.15/4.18 => power_power_nat(zero_zero_nat,number_number_of_nat(W_3)) = one_one_nat )
% 4.15/4.18 & ( number_number_of_nat(W_3) != zero_zero_nat
% 4.15/4.18 => power_power_nat(zero_zero_nat,number_number_of_nat(W_3)) = zero_zero_nat ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_583_power__0__left__number__of,axiom,
% 4.15/4.18 ! [W_3] :
% 4.15/4.18 ( ( number_number_of_nat(W_3) = zero_zero_nat
% 4.15/4.18 => power_power_int(zero_zero_int,number_number_of_nat(W_3)) = one_one_int )
% 4.15/4.18 & ( number_number_of_nat(W_3) != zero_zero_nat
% 4.15/4.18 => power_power_int(zero_zero_int,number_number_of_nat(W_3)) = zero_zero_int ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_584_zcong__zless__imp__eq,axiom,
% 4.15/4.18 ! [B_1,M,A] :
% 4.15/4.18 ( ( is_int(B_1)
% 4.15/4.18 & is_int(A) )
% 4.15/4.18 => ( ord_less_eq_int(zero_zero_int,A)
% 4.15/4.18 => ( ord_less_int(A,M)
% 4.15/4.18 => ( ord_less_eq_int(zero_zero_int,B_1)
% 4.15/4.18 => ( ord_less_int(B_1,M)
% 4.15/4.18 => ( zcong(A,B_1,M)
% 4.15/4.18 => A = B_1 ) ) ) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_585_zcong__zless__0,axiom,
% 4.15/4.18 ! [M,A] :
% 4.15/4.18 ( is_int(A)
% 4.15/4.18 => ( ord_less_eq_int(zero_zero_int,A)
% 4.15/4.18 => ( ord_less_int(A,M)
% 4.15/4.18 => ( zcong(A,zero_zero_int,M)
% 4.15/4.18 => A = zero_zero_int ) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_586_zprime__zdvd__zmult,axiom,
% 4.15/4.18 ! [N,P,M] :
% 4.15/4.18 ( ord_less_eq_int(zero_zero_int,M)
% 4.15/4.18 => ( zprime(P)
% 4.15/4.18 => ( dvd_dvd_int(P,times_times_int(M,N))
% 4.15/4.18 => ( dvd_dvd_int(P,M)
% 4.15/4.18 | dvd_dvd_int(P,N) ) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_587__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096,axiom,
% 4.15/4.18 quadRes(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),number_number_of_int(min)) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_588__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096,axiom,
% 4.15/4.18 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))) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_589_neg__one__power__eq__mod__m,axiom,
% 4.15/4.18 ! [J,K,M] :
% 4.15/4.18 ( ord_less_int(number_number_of_int(bit0(bit1(pls))),M)
% 4.15/4.18 => ( zcong(power_power_int(number_number_of_int(min),J),power_power_int(number_number_of_int(min),K),M)
% 4.15/4.18 => power_power_int(number_number_of_int(min),J) = power_power_int(number_number_of_int(min),K) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_590__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096,axiom,
% 4.15/4.18 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) ).
% 4.15/4.18
% 4.15/4.18 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,
% 4.15/4.18 ( ~ quadRes(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),number_number_of_int(min))
% 4.15/4.18 => 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 ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_592_zcong__zdiff,axiom,
% 4.15/4.18 ! [C_1,D_1,A,B_1,M] :
% 4.15/4.18 ( zcong(A,B_1,M)
% 4.15/4.18 => ( zcong(C_1,D_1,M)
% 4.15/4.18 => zcong(minus_minus_int(A,C_1),minus_minus_int(B_1,D_1),M) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_593_diff__bin__simps_I1_J,axiom,
% 4.15/4.18 ! [K] :
% 4.15/4.18 ( is_int(K)
% 4.15/4.18 => minus_minus_int(K,pls) = K ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_594_diff__bin__simps_I7_J,axiom,
% 4.15/4.18 ! [K,L] : minus_minus_int(bit0(K),bit0(L)) = bit0(minus_minus_int(K,L)) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_595_zdiff__zmult__distrib,axiom,
% 4.15/4.18 ! [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)) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_596_zdiff__zmult__distrib2,axiom,
% 4.15/4.18 ! [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)) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_597_zdvd__zdiffD,axiom,
% 4.15/4.18 ! [K,M,N] :
% 4.15/4.18 ( dvd_dvd_int(K,minus_minus_int(M,N))
% 4.15/4.18 => ( dvd_dvd_int(K,N)
% 4.15/4.18 => dvd_dvd_int(K,M) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_598_number__of__diff,axiom,
% 4.15/4.18 ! [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)) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_599_diff__bin__simps_I9_J,axiom,
% 4.15/4.18 ! [K,L] : minus_minus_int(bit1(K),bit0(L)) = bit1(minus_minus_int(K,L)) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_600_diff__bin__simps_I10_J,axiom,
% 4.15/4.18 ! [K,L] : minus_minus_int(bit1(K),bit1(L)) = bit0(minus_minus_int(K,L)) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_601_diff__bin__simps_I3_J,axiom,
% 4.15/4.18 ! [L] : minus_minus_int(pls,bit0(L)) = bit0(minus_minus_int(pls,L)) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_602_less__bin__lemma,axiom,
% 4.15/4.18 ! [K_1,L_1] :
% 4.15/4.18 ( ord_less_int(K_1,L_1)
% 4.15/4.18 <=> ord_less_int(minus_minus_int(K_1,L_1),zero_zero_int) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_603_xzgcda__linear__aux1,axiom,
% 4.15/4.18 ! [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)))) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_604_zcong__def,axiom,
% 4.15/4.18 ! [A_1,B_2,Ma] :
% 4.15/4.18 ( zcong(A_1,B_2,Ma)
% 4.15/4.18 <=> dvd_dvd_int(Ma,minus_minus_int(A_1,B_2)) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_605_Euler_Oaux1,axiom,
% 4.15/4.18 ! [A,X_1] :
% 4.15/4.18 ( is_int(X_1)
% 4.15/4.18 => ( ord_less_int(zero_zero_int,X_1)
% 4.15/4.18 => ( ord_less_int(X_1,A)
% 4.15/4.18 => ( X_1 != minus_minus_int(A,one_one_int)
% 4.15/4.18 => ord_less_int(X_1,minus_minus_int(A,one_one_int)) ) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_606_zle__diff1__eq,axiom,
% 4.15/4.18 ! [W_1,Z_1] :
% 4.15/4.18 ( ord_less_eq_int(W_1,minus_minus_int(Z_1,one_one_int))
% 4.15/4.18 <=> ord_less_int(W_1,Z_1) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_607_diff__bin__simps_I4_J,axiom,
% 4.15/4.18 ! [L] : minus_minus_int(pls,bit1(L)) = bit1(minus_minus_int(min,L)) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_608_diff__bin__simps_I6_J,axiom,
% 4.15/4.18 ! [L] : minus_minus_int(min,bit1(L)) = bit0(minus_minus_int(min,L)) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_609_diff__bin__simps_I5_J,axiom,
% 4.15/4.18 ! [L] : minus_minus_int(min,bit0(L)) = bit1(minus_minus_int(min,L)) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_610_inv__not__p__minus__1__aux,axiom,
% 4.15/4.18 ! [A_1,P_1] :
% 4.15/4.18 ( zcong(times_times_int(A_1,minus_minus_int(P_1,one_one_int)),one_one_int,P_1)
% 4.15/4.18 <=> zcong(A_1,minus_minus_int(P_1,one_one_int),P_1) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_611_mult__sum2sq,axiom,
% 4.15/4.18 ! [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)))) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_612_zcong__square,axiom,
% 4.15/4.18 ! [A,P] :
% 4.15/4.18 ( zprime(P)
% 4.15/4.18 => ( ord_less_int(zero_zero_int,A)
% 4.15/4.18 => ( zcong(times_times_int(A,A),one_one_int,P)
% 4.15/4.18 => ( zcong(A,one_one_int,P)
% 4.15/4.18 | zcong(A,minus_minus_int(P,one_one_int),P) ) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_613_zcong__square__zless,axiom,
% 4.15/4.18 ! [A,P] :
% 4.15/4.18 ( is_int(A)
% 4.15/4.18 => ( zprime(P)
% 4.15/4.18 => ( ord_less_int(zero_zero_int,A)
% 4.15/4.18 => ( ord_less_int(A,P)
% 4.15/4.18 => ( zcong(times_times_int(A,A),one_one_int,P)
% 4.15/4.18 => ( A = one_one_int
% 4.15/4.18 | A = minus_minus_int(P,one_one_int) ) ) ) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_614_zspecial__product,axiom,
% 4.15/4.18 ! [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))))) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_615_zdiff__power2,axiom,
% 4.15/4.18 ! [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))))) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_616_zdiff__power3,axiom,
% 4.15/4.18 ! [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))))) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_617_neg__one__power,axiom,
% 4.15/4.18 ! [N] :
% 4.15/4.18 ( power_power_int(number_number_of_int(min),N) = one_one_int
% 4.15/4.18 | power_power_int(number_number_of_int(min),N) = number_number_of_int(min) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_618_Legendre__1mod4,axiom,
% 4.15/4.18 ! [M] :
% 4.15/4.18 ( zprime(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),M),one_one_int))
% 4.15/4.18 => 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 ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_619_one__not__neg__one__mod__m,axiom,
% 4.15/4.18 ! [M] :
% 4.15/4.18 ( ord_less_int(number_number_of_int(bit0(bit1(pls))),M)
% 4.15/4.18 => ~ zcong(one_one_int,number_number_of_int(min),M) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_620_zcong__neg__1__impl__ne__1,axiom,
% 4.15/4.18 ! [X_1,P] :
% 4.15/4.18 ( ord_less_int(number_number_of_int(bit0(bit1(pls))),P)
% 4.15/4.18 => ( zcong(X_1,number_number_of_int(min),P)
% 4.15/4.18 => ~ zcong(X_1,one_one_int,P) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_621_Legendre__def,axiom,
% 4.15/4.18 ! [A,P] :
% 4.15/4.18 ( ( zcong(A,zero_zero_int,P)
% 4.15/4.18 => legendre(A,P) = zero_zero_int )
% 4.15/4.18 & ( ~ zcong(A,zero_zero_int,P)
% 4.15/4.18 => ( ( quadRes(P,A)
% 4.15/4.18 => legendre(A,P) = one_one_int )
% 4.15/4.18 & ( ~ quadRes(P,A)
% 4.15/4.18 => legendre(A,P) = number_number_of_int(min) ) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_622_divides__cases,axiom,
% 4.15/4.18 ! [N,M] :
% 4.15/4.18 ( dvd_dvd_nat(N,M)
% 4.15/4.18 => ( M = zero_zero_nat
% 4.15/4.18 | M = N
% 4.15/4.18 | ord_less_eq_nat(times_times_nat(number_number_of_nat(bit0(bit1(pls))),N),M) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_623_divides__antisym,axiom,
% 4.15/4.18 ! [X_2,Y_2] :
% 4.15/4.18 ( ( dvd_dvd_nat(X_2,Y_2)
% 4.15/4.18 & dvd_dvd_nat(Y_2,X_2) )
% 4.15/4.18 <=> X_2 = Y_2 ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_624_zcong__eq__trans,axiom,
% 4.15/4.18 ! [D_1,C_1,A,B_1,M] :
% 4.15/4.18 ( zcong(A,B_1,M)
% 4.15/4.18 => ( B_1 = C_1
% 4.15/4.18 => ( zcong(C_1,D_1,M)
% 4.15/4.18 => zcong(A,D_1,M) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_625_mult__eq__if,axiom,
% 4.15/4.18 ! [N,M] :
% 4.15/4.18 ( ( M = zero_zero_nat
% 4.15/4.18 => times_times_nat(M,N) = zero_zero_nat )
% 4.15/4.18 & ( M != zero_zero_nat
% 4.15/4.18 => times_times_nat(M,N) = plus_plus_nat(N,times_times_nat(minus_minus_nat(M,one_one_nat),N)) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_626_power__eq__if,axiom,
% 4.15/4.18 ! [P,M] :
% 4.15/4.18 ( ( M = zero_zero_nat
% 4.15/4.18 => power_power_nat(P,M) = one_one_nat )
% 4.15/4.18 & ( M != zero_zero_nat
% 4.15/4.18 => power_power_nat(P,M) = times_times_nat(P,power_power_nat(P,minus_minus_nat(M,one_one_nat))) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_627_diff__square,axiom,
% 4.15/4.18 ! [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)) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_628_divides__add__revr,axiom,
% 4.15/4.18 ! [B_1,D_1,A] :
% 4.15/4.18 ( dvd_dvd_nat(D_1,A)
% 4.15/4.18 => ( dvd_dvd_nat(D_1,plus_plus_nat(A,B_1))
% 4.15/4.18 => dvd_dvd_nat(D_1,B_1) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_629_divides__mul__l,axiom,
% 4.15/4.18 ! [C_1,A,B_1] :
% 4.15/4.18 ( dvd_dvd_nat(A,B_1)
% 4.15/4.18 => dvd_dvd_nat(times_times_nat(C_1,A),times_times_nat(C_1,B_1)) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_630_divides__mul__r,axiom,
% 4.15/4.18 ! [C_1,A,B_1] :
% 4.15/4.18 ( dvd_dvd_nat(A,B_1)
% 4.15/4.18 => dvd_dvd_nat(times_times_nat(A,C_1),times_times_nat(B_1,C_1)) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_631_zcong__id,axiom,
% 4.15/4.18 ! [M] : zcong(M,zero_zero_int,M) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_632_nat__mult__eq__one,axiom,
% 4.15/4.18 ! [N_1,Ma] :
% 4.15/4.18 ( times_times_nat(N_1,Ma) = one_one_nat
% 4.15/4.18 <=> ( N_1 = one_one_nat
% 4.15/4.18 & Ma = one_one_nat ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_633_Int2_Oaux1,axiom,
% 4.15/4.18 ! [A,B_1,C_1] :
% 4.15/4.18 ( is_int(A)
% 4.15/4.18 => ( minus_minus_int(A,B_1) = C_1
% 4.15/4.18 => A = plus_plus_int(C_1,B_1) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_634_zcong__zmult__prop2,axiom,
% 4.15/4.18 ! [C,D,A_1,B_2,Ma] :
% 4.15/4.18 ( zcong(A_1,B_2,Ma)
% 4.15/4.18 => ( zcong(C,times_times_int(D,A_1),Ma)
% 4.15/4.18 <=> zcong(C,times_times_int(D,B_2),Ma) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_635_zcong__zmult__prop1,axiom,
% 4.15/4.18 ! [C,D,A_1,B_2,Ma] :
% 4.15/4.18 ( zcong(A_1,B_2,Ma)
% 4.15/4.18 => ( zcong(C,times_times_int(A_1,D),Ma)
% 4.15/4.18 <=> zcong(C,times_times_int(B_2,D),Ma) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_636_zcong__shift,axiom,
% 4.15/4.18 ! [C_1,A,B_1,M] :
% 4.15/4.18 ( zcong(A,B_1,M)
% 4.15/4.18 => zcong(plus_plus_int(A,C_1),plus_plus_int(B_1,C_1),M) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_637_nat__power__eq__0__iff,axiom,
% 4.15/4.18 ! [Ma,N_1] :
% 4.15/4.18 ( power_power_nat(Ma,N_1) = zero_zero_nat
% 4.15/4.18 <=> ( N_1 != zero_zero_nat
% 4.15/4.18 & Ma = zero_zero_nat ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_638_divides__exp,axiom,
% 4.15/4.18 ! [N,X_1,Y_1] :
% 4.15/4.18 ( dvd_dvd_nat(X_1,Y_1)
% 4.15/4.18 => dvd_dvd_nat(power_power_nat(X_1,N),power_power_nat(Y_1,N)) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_639_zcong__zpower,axiom,
% 4.15/4.18 ! [Z,X_1,Y_1,M] :
% 4.15/4.18 ( zcong(X_1,Y_1,M)
% 4.15/4.18 => zcong(power_power_int(X_1,Z),power_power_int(Y_1,Z),M) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_640_divides__ge,axiom,
% 4.15/4.18 ! [A,B_1] :
% 4.15/4.18 ( dvd_dvd_nat(A,B_1)
% 4.15/4.18 => ( B_1 = zero_zero_nat
% 4.15/4.18 | ord_less_eq_nat(A,B_1) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_641_nat__mult__dvd__cancel__disj_H,axiom,
% 4.15/4.18 ! [Ma,K_1,N_1] :
% 4.15/4.18 ( dvd_dvd_nat(times_times_nat(Ma,K_1),times_times_nat(N_1,K_1))
% 4.15/4.18 <=> ( K_1 = zero_zero_nat
% 4.15/4.18 | dvd_dvd_nat(Ma,N_1) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_642_zcong__not__zero,axiom,
% 4.15/4.18 ! [M,X_1] :
% 4.15/4.18 ( ord_less_int(zero_zero_int,X_1)
% 4.15/4.18 => ( ord_less_int(X_1,M)
% 4.15/4.18 => ~ zcong(X_1,zero_zero_int,M) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_643_zcong__less__eq,axiom,
% 4.15/4.18 ! [M,Y_1,X_1] :
% 4.15/4.18 ( ( is_int(Y_1)
% 4.15/4.18 & is_int(X_1) )
% 4.15/4.18 => ( ord_less_int(zero_zero_int,X_1)
% 4.15/4.18 => ( ord_less_int(zero_zero_int,Y_1)
% 4.15/4.18 => ( ord_less_int(zero_zero_int,M)
% 4.15/4.18 => ( zcong(X_1,Y_1,M)
% 4.15/4.18 => ( ord_less_int(X_1,M)
% 4.15/4.18 => ( ord_less_int(Y_1,M)
% 4.15/4.18 => X_1 = Y_1 ) ) ) ) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_644_zdvd__bounds,axiom,
% 4.15/4.18 ! [N,M] :
% 4.15/4.18 ( dvd_dvd_int(N,M)
% 4.15/4.18 => ( ord_less_eq_int(M,zero_zero_int)
% 4.15/4.18 | ord_less_eq_int(N,M) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_645_divides__exp2,axiom,
% 4.15/4.18 ! [X_1,Y_1,N] :
% 4.15/4.18 ( N != zero_zero_nat
% 4.15/4.18 => ( dvd_dvd_nat(power_power_nat(X_1,N),Y_1)
% 4.15/4.18 => dvd_dvd_nat(X_1,Y_1) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_646_divides__rev,axiom,
% 4.15/4.18 ! [A,N,B_1] :
% 4.15/4.18 ( dvd_dvd_nat(power_power_nat(A,N),power_power_nat(B_1,N))
% 4.15/4.18 => ( N != zero_zero_nat
% 4.15/4.18 => dvd_dvd_nat(A,B_1) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_647_zcong__zero__equiv__div,axiom,
% 4.15/4.18 ! [A_1,Ma] :
% 4.15/4.18 ( zcong(A_1,zero_zero_int,Ma)
% 4.15/4.18 <=> dvd_dvd_int(Ma,A_1) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_648_zcong__eq__zdvd__prop,axiom,
% 4.15/4.18 ! [X_2,P_1] :
% 4.15/4.18 ( zcong(X_2,zero_zero_int,P_1)
% 4.15/4.18 <=> dvd_dvd_int(P_1,X_2) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_649_exp__eq__1,axiom,
% 4.15/4.18 ! [X_2,N_1] :
% 4.15/4.18 ( power_power_nat(X_2,N_1) = one_one_nat
% 4.15/4.18 <=> ( X_2 = one_one_nat
% 4.15/4.18 | N_1 = zero_zero_nat ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_650_zprime__zdvd__zmult__better,axiom,
% 4.15/4.18 ! [M,N,P] :
% 4.15/4.18 ( zprime(P)
% 4.15/4.18 => ( dvd_dvd_int(P,times_times_int(M,N))
% 4.15/4.18 => ( dvd_dvd_int(P,M)
% 4.15/4.18 | dvd_dvd_int(P,N) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_651_Int2_Ozcong__zero,axiom,
% 4.15/4.18 ! [M,X_1] :
% 4.15/4.18 ( is_int(X_1)
% 4.15/4.18 => ( ord_less_eq_int(zero_zero_int,X_1)
% 4.15/4.18 => ( ord_less_int(X_1,M)
% 4.15/4.18 => ( zcong(X_1,zero_zero_int,M)
% 4.15/4.18 => X_1 = zero_zero_int ) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_652_zpower__zdvd__prop1,axiom,
% 4.15/4.18 ! [P,Y_1,N] :
% 4.15/4.18 ( ord_less_nat(zero_zero_nat,N)
% 4.15/4.18 => ( dvd_dvd_int(P,Y_1)
% 4.15/4.18 => dvd_dvd_int(P,power_power_int(Y_1,N)) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_653_zcong__zmult__prop3,axiom,
% 4.15/4.18 ! [Y_1,X_1,P] :
% 4.15/4.18 ( zprime(P)
% 4.15/4.18 => ( ~ zcong(X_1,zero_zero_int,P)
% 4.15/4.18 => ( ~ zcong(Y_1,zero_zero_int,P)
% 4.15/4.18 => ~ zcong(times_times_int(X_1,Y_1),zero_zero_int,P) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_654_divides__div__not,axiom,
% 4.15/4.18 ! [X_1,Q,N,R_1] :
% 4.15/4.18 ( X_1 = plus_plus_nat(times_times_nat(Q,N),R_1)
% 4.15/4.18 => ( ord_less_nat(zero_zero_nat,R_1)
% 4.15/4.18 => ( ord_less_nat(R_1,N)
% 4.15/4.18 => ~ dvd_dvd_nat(N,X_1) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_655_zcong__zprime__prod__zero__contra,axiom,
% 4.15/4.18 ! [B_1,A,P] :
% 4.15/4.18 ( zprime(P)
% 4.15/4.18 => ( ord_less_int(zero_zero_int,A)
% 4.15/4.18 => ( ( ~ zcong(A,zero_zero_int,P)
% 4.15/4.18 & ~ zcong(B_1,zero_zero_int,P) )
% 4.15/4.18 => ~ zcong(times_times_int(A,B_1),zero_zero_int,P) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_656_zcong__zprime__prod__zero,axiom,
% 4.15/4.18 ! [B_1,A,P] :
% 4.15/4.18 ( zprime(P)
% 4.15/4.18 => ( ord_less_int(zero_zero_int,A)
% 4.15/4.18 => ( zcong(times_times_int(A,B_1),zero_zero_int,P)
% 4.15/4.18 => ( zcong(A,zero_zero_int,P)
% 4.15/4.18 | zcong(B_1,zero_zero_int,P) ) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_657_zpower__zdvd__prop2,axiom,
% 4.15/4.18 ! [Y_1,N,P] :
% 4.15/4.18 ( zprime(P)
% 4.15/4.18 => ( dvd_dvd_int(P,power_power_int(Y_1,N))
% 4.15/4.18 => ( ord_less_nat(zero_zero_nat,N)
% 4.15/4.18 => dvd_dvd_int(P,Y_1) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_658_QuadRes__def,axiom,
% 4.15/4.18 ! [Ma,X_2] :
% 4.15/4.18 ( quadRes(Ma,X_2)
% 4.15/4.18 <=> ? [Y] :
% 4.15/4.18 ( is_int(Y)
% 4.15/4.18 & zcong(power_power_int(Y,number_number_of_nat(bit0(bit1(pls)))),X_2,Ma) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_659_realpow__two__sum__zero__iff,axiom,
% 4.15/4.18 ! [X_2,Y_2] :
% 4.15/4.18 ( 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
% 4.15/4.18 <=> ( X_2 = zero_zero_real
% 4.15/4.18 & Y_2 = zero_zero_real ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_660_self__quotient__aux1,axiom,
% 4.15/4.18 ! [R_1,Q,A] :
% 4.15/4.18 ( ord_less_int(zero_zero_int,A)
% 4.15/4.18 => ( A = plus_plus_int(R_1,times_times_int(A,Q))
% 4.15/4.18 => ( ord_less_int(R_1,A)
% 4.15/4.18 => ord_less_eq_int(one_one_int,Q) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_661_real__zero__not__eq__one,axiom,
% 4.15/4.18 zero_zero_real != one_one_real ).
% 4.15/4.18
% 4.15/4.18 fof(fact_662_real__le__eq__diff,axiom,
% 4.15/4.18 ! [X_2,Y_2] :
% 4.15/4.18 ( ord_less_eq_real(X_2,Y_2)
% 4.15/4.18 <=> ord_less_eq_real(minus_minus_real(X_2,Y_2),zero_zero_real) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_663_real__less__def,axiom,
% 4.15/4.18 ! [X_2,Y_2] :
% 4.15/4.18 ( ord_less_real(X_2,Y_2)
% 4.15/4.18 <=> ( ord_less_eq_real(X_2,Y_2)
% 4.15/4.18 & X_2 != Y_2 ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_664_less__eq__real__def,axiom,
% 4.15/4.18 ! [X_2,Y_2] :
% 4.15/4.18 ( ord_less_eq_real(X_2,Y_2)
% 4.15/4.18 <=> ( ord_less_real(X_2,Y_2)
% 4.15/4.18 | X_2 = Y_2 ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_665_real__mult__1,axiom,
% 4.15/4.18 ! [Z] : times_times_real(one_one_real,Z) = Z ).
% 4.15/4.18
% 4.15/4.18 fof(fact_666_real__mult__commute,axiom,
% 4.15/4.18 ! [Z,W] : times_times_real(Z,W) = times_times_real(W,Z) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_667_real__mult__assoc,axiom,
% 4.15/4.18 ! [Z1,Z2,Z3] : times_times_real(times_times_real(Z1,Z2),Z3) = times_times_real(Z1,times_times_real(Z2,Z3)) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_668_real__add__left__mono,axiom,
% 4.15/4.18 ! [Z,X_1,Y_1] :
% 4.15/4.18 ( ord_less_eq_real(X_1,Y_1)
% 4.15/4.18 => ord_less_eq_real(plus_plus_real(Z,X_1),plus_plus_real(Z,Y_1)) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_669_real__mult__left__cancel,axiom,
% 4.15/4.18 ! [A_1,B_2,C] :
% 4.15/4.18 ( C != zero_zero_real
% 4.15/4.18 => ( times_times_real(C,A_1) = times_times_real(C,B_2)
% 4.15/4.18 <=> A_1 = B_2 ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_670_real__mult__right__cancel,axiom,
% 4.15/4.18 ! [A_1,B_2,C] :
% 4.15/4.18 ( C != zero_zero_real
% 4.15/4.18 => ( times_times_real(A_1,C) = times_times_real(B_2,C)
% 4.15/4.18 <=> A_1 = B_2 ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_671_real__add__mult__distrib,axiom,
% 4.15/4.18 ! [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)) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_672_real__mult__less__mono2,axiom,
% 4.15/4.18 ! [X_1,Y_1,Z] :
% 4.15/4.18 ( ord_less_real(zero_zero_real,Z)
% 4.15/4.18 => ( ord_less_real(X_1,Y_1)
% 4.15/4.18 => ord_less_real(times_times_real(Z,X_1),times_times_real(Z,Y_1)) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_673_real__mult__order,axiom,
% 4.15/4.18 ! [Y_1,X_1] :
% 4.15/4.18 ( ord_less_real(zero_zero_real,X_1)
% 4.15/4.18 => ( ord_less_real(zero_zero_real,Y_1)
% 4.15/4.18 => ord_less_real(zero_zero_real,times_times_real(X_1,Y_1)) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_674_real__mult__le__cancel__iff2,axiom,
% 4.15/4.18 ! [X_2,Y_2,Z_1] :
% 4.15/4.18 ( ord_less_real(zero_zero_real,Z_1)
% 4.15/4.18 => ( ord_less_eq_real(times_times_real(Z_1,X_2),times_times_real(Z_1,Y_2))
% 4.15/4.18 <=> ord_less_eq_real(X_2,Y_2) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_675_real__mult__le__cancel__iff1,axiom,
% 4.15/4.18 ! [X_2,Y_2,Z_1] :
% 4.15/4.18 ( ord_less_real(zero_zero_real,Z_1)
% 4.15/4.18 => ( ord_less_eq_real(times_times_real(X_2,Z_1),times_times_real(Y_2,Z_1))
% 4.15/4.18 <=> ord_less_eq_real(X_2,Y_2) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_676_real__mult__less__iff1,axiom,
% 4.15/4.18 ! [X_2,Y_2,Z_1] :
% 4.15/4.18 ( ord_less_real(zero_zero_real,Z_1)
% 4.15/4.18 => ( ord_less_real(times_times_real(X_2,Z_1),times_times_real(Y_2,Z_1))
% 4.15/4.18 <=> ord_less_real(X_2,Y_2) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_677_real__two__squares__add__zero__iff,axiom,
% 4.15/4.18 ! [X_2,Y_2] :
% 4.15/4.18 ( plus_plus_real(times_times_real(X_2,X_2),times_times_real(Y_2,Y_2)) = zero_zero_real
% 4.15/4.18 <=> ( X_2 = zero_zero_real
% 4.15/4.18 & Y_2 = zero_zero_real ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_678_two__realpow__ge__one,axiom,
% 4.15/4.18 ! [N] : ord_less_eq_real(one_one_real,power_power_real(number267125858f_real(bit0(bit1(pls))),N)) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_679_q__pos__lemma,axiom,
% 4.15/4.18 ! [B,Q_1,R_2] :
% 4.15/4.18 ( ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(B,Q_1),R_2))
% 4.15/4.18 => ( ord_less_int(R_2,B)
% 4.15/4.18 => ( ord_less_int(zero_zero_int,B)
% 4.15/4.18 => ord_less_eq_int(zero_zero_int,Q_1) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_680_q__neg__lemma,axiom,
% 4.15/4.18 ! [B,Q_1,R_2] :
% 4.15/4.18 ( ord_less_int(plus_plus_int(times_times_int(B,Q_1),R_2),zero_zero_int)
% 4.15/4.18 => ( ord_less_eq_int(zero_zero_int,R_2)
% 4.15/4.18 => ( ord_less_int(zero_zero_int,B)
% 4.15/4.18 => ord_less_eq_int(Q_1,zero_zero_int) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_681_unique__quotient__lemma,axiom,
% 4.15/4.18 ! [B_1,Q_1,R_2,Q,R_1] :
% 4.15/4.18 ( 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))
% 4.15/4.18 => ( ord_less_eq_int(zero_zero_int,R_2)
% 4.15/4.18 => ( ord_less_int(R_2,B_1)
% 4.15/4.18 => ( ord_less_int(R_1,B_1)
% 4.15/4.18 => ord_less_eq_int(Q_1,Q) ) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_682_zdiv__mono2__lemma,axiom,
% 4.15/4.18 ! [B_1,Q,R_1,B,Q_1,R_2] :
% 4.15/4.18 ( plus_plus_int(times_times_int(B_1,Q),R_1) = plus_plus_int(times_times_int(B,Q_1),R_2)
% 4.15/4.18 => ( ord_less_eq_int(zero_zero_int,plus_plus_int(times_times_int(B,Q_1),R_2))
% 4.15/4.18 => ( ord_less_int(R_2,B)
% 4.15/4.18 => ( ord_less_eq_int(zero_zero_int,R_1)
% 4.15/4.18 => ( ord_less_int(zero_zero_int,B)
% 4.15/4.18 => ( ord_less_eq_int(B,B_1)
% 4.15/4.18 => ord_less_eq_int(Q,Q_1) ) ) ) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_683_unique__quotient__lemma__neg,axiom,
% 4.15/4.18 ! [B_1,Q_1,R_2,Q,R_1] :
% 4.15/4.18 ( 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))
% 4.15/4.18 => ( ord_less_eq_int(R_1,zero_zero_int)
% 4.15/4.18 => ( ord_less_int(B_1,R_1)
% 4.15/4.18 => ( ord_less_int(B_1,R_2)
% 4.15/4.18 => ord_less_eq_int(Q,Q_1) ) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_684_zdiv__mono2__neg__lemma,axiom,
% 4.15/4.18 ! [B_1,Q,R_1,B,Q_1,R_2] :
% 4.15/4.18 ( plus_plus_int(times_times_int(B_1,Q),R_1) = plus_plus_int(times_times_int(B,Q_1),R_2)
% 4.15/4.18 => ( ord_less_int(plus_plus_int(times_times_int(B,Q_1),R_2),zero_zero_int)
% 4.15/4.18 => ( ord_less_int(R_1,B_1)
% 4.15/4.18 => ( ord_less_eq_int(zero_zero_int,R_2)
% 4.15/4.18 => ( ord_less_int(zero_zero_int,B)
% 4.15/4.18 => ( ord_less_eq_int(B,B_1)
% 4.15/4.18 => ord_less_eq_int(Q_1,Q) ) ) ) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_685_self__quotient__aux2,axiom,
% 4.15/4.18 ! [R_1,Q,A] :
% 4.15/4.18 ( ord_less_int(zero_zero_int,A)
% 4.15/4.18 => ( A = plus_plus_int(R_1,times_times_int(A,Q))
% 4.15/4.18 => ( ord_less_eq_int(zero_zero_int,R_1)
% 4.15/4.18 => ord_less_eq_int(Q,one_one_int) ) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_686_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 4.15/4.18 ord_less_eq_int(zero_zero_int,number_number_of_int(bit0(bit1(pls)))) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_687_real__le__antisym,axiom,
% 4.15/4.18 ! [Z,W] :
% 4.15/4.18 ( ord_less_eq_real(Z,W)
% 4.15/4.18 => ( ord_less_eq_real(W,Z)
% 4.15/4.18 => Z = W ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_688_real__le__trans,axiom,
% 4.15/4.18 ! [K,I,J] :
% 4.15/4.18 ( ord_less_eq_real(I,J)
% 4.15/4.18 => ( ord_less_eq_real(J,K)
% 4.15/4.18 => ord_less_eq_real(I,K) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_689_real__le__linear,axiom,
% 4.15/4.18 ! [Z,W] :
% 4.15/4.18 ( ord_less_eq_real(Z,W)
% 4.15/4.18 | ord_less_eq_real(W,Z) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_690_real__le__refl,axiom,
% 4.15/4.18 ! [W] : ord_less_eq_real(W,W) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_691_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 4.15/4.18 ord_less_eq_int(zero_zero_int,zero_zero_int) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_692_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 4.15/4.18 ord_less_eq_int(zero_zero_int,one_one_int) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_693_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 4.15/4.18 ! [Y_1,X_1] :
% 4.15/4.18 ( ord_less_eq_int(zero_zero_int,X_1)
% 4.15/4.18 => ( ord_less_eq_int(zero_zero_int,Y_1)
% 4.15/4.18 => ord_less_eq_int(zero_zero_int,times_times_int(X_1,Y_1)) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_694_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 4.15/4.18 ! [Y_1,X_1] :
% 4.15/4.18 ( ord_less_eq_int(zero_zero_int,X_1)
% 4.15/4.18 => ( ord_less_eq_int(zero_zero_int,Y_1)
% 4.15/4.18 => ord_less_eq_int(zero_zero_int,plus_plus_int(X_1,Y_1)) ) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_695_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 4.15/4.18 ! [N,X_1] :
% 4.15/4.18 ( ord_less_eq_int(zero_zero_int,X_1)
% 4.15/4.18 => ord_less_eq_int(zero_zero_int,power_power_int(X_1,N)) ) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_696_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 4.15/4.18 ord_less_eq_int(zero_zero_int,number_number_of_int(bit1(bit1(pls)))) ).
% 4.15/4.18
% 4.15/4.18 fof(fact_697_realpow__pos__nth,axiom,
% 4.15/4.18 ! [A,N] :
% 4.15/4.18 ( ord_less_nat(zero_zero_nat,N)
% 4.15/4.18 => ( ord_less_real(zero_zero_real,A)
% 4.15/4.18 => ? [R] :
% 4.15/4.18 ( ord_less_real(zero_zero_real,R)
% 4.15/4.18 & power_power_real(R,N) = A ) ) ) ).
% 4.15/4.18
% 4.15/4.18 %----Conjectures (1)
% 4.15/4.18 fof(conj_0,conjecture,
% 4.15/4.18 ? [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) ).
% 4.15/4.18
% 4.15/4.18 %------------------------------------------------------------------------------
% 4.15/4.18 %-------------------------------------------
% 4.15/4.18 % Proof found
% 4.15/4.18 % SZS status Theorem for theBenchmark
% 4.15/4.18 % SZS output start Proof
% 4.22/4.19 %ClaNum:1010(EqnAxiom:70)
% 4.22/4.19 %VarNum:3270(SingletonVarNum:1353)
% 4.22/4.19 %MaxLitNum:9
% 4.22/4.19 %MaxfuncDepth:8
% 4.22/4.19 %SharedTerms:164
% 4.22/4.19 %goalClause: 415
% 4.22/4.19 %singleGoalClaCount:1
% 4.22/4.19 [71]E(a1,a27)
% 4.22/4.19 [82]P1(a24)
% 4.22/4.19 [83]P1(a27)
% 4.22/4.19 [84]P1(a4)
% 4.22/4.19 [85]P1(a1)
% 4.22/4.19 [86]P1(a5)
% 4.22/4.19 [87]P1(a28)
% 4.22/4.19 [88]P1(a29)
% 4.22/4.19 [89]P1(a37)
% 4.22/4.19 [90]P1(a6)
% 4.22/4.19 [91]P1(a14)
% 4.22/4.19 [92]P1(a15)
% 4.22/4.19 [93]P1(a16)
% 4.22/4.19 [97]P5(a24,a37)
% 4.22/4.19 [98]P5(a27,a24)
% 4.22/4.19 [100]P5(a27,a29)
% 4.22/4.19 [101]P5(a27,a14)
% 4.22/4.19 [102]P5(a27,a15)
% 4.22/4.19 [104]P5(a4,a1)
% 4.22/4.19 [106]P6(a27,a24)
% 4.22/4.19 [107]P6(a4,a27)
% 4.22/4.19 [108]P6(a4,a1)
% 4.22/4.19 [392]~E(a24,a27)
% 4.22/4.19 [394]~E(a4,a1)
% 4.22/4.19 [395]~E(a25,a43)
% 4.22/4.19 [397]~P5(a1,a4)
% 4.22/4.19 [398]~P6(a4,a4)
% 4.22/4.19 [399]~P6(a1,a27)
% 4.22/4.19 [400]~P6(a1,a4)
% 4.22/4.19 [401]~P6(a1,a1)
% 4.22/4.19 [77]E(f2(a1),a27)
% 4.22/4.19 [79]E(f23(a1),a44)
% 4.22/4.19 [81]E(f3(a1),a43)
% 4.22/4.19 [94]P1(f38(a18))
% 4.22/4.19 [96]E(f30(a1,a1),a1)
% 4.22/4.19 [396]~E(f2(a4),f2(a1))
% 4.22/4.19 [151]E(f30(f30(a24,a4),a4),a4)
% 4.22/4.19 [174]E(f2(f30(f30(a24,a1),a1)),a24)
% 4.22/4.19 [176]E(f23(f30(f30(a24,a1),a1)),a26)
% 4.22/4.19 [178]E(f3(f30(f30(a24,a1),a1)),a25)
% 4.22/4.19 [300]E(f2(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),f30(a24,a24))
% 4.22/4.19 [302]E(f3(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),f32(a25,a25))
% 4.22/4.19 [304]E(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),f33(a26,a26))
% 4.22/4.19 [305]P14(f2(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))
% 4.22/4.19 [312]P5(a27,f2(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))
% 4.22/4.19 [313]P10(a44,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))
% 4.22/4.19 [337]P5(a27,f2(f30(f30(a24,f30(f30(a24,a1),a1)),f30(f30(a24,a1),a1))))
% 4.22/4.19 [307]E(f31(a27,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a27)
% 4.22/4.19 [309]E(f34(a43,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a43)
% 4.22/4.19 [311]E(f35(a44,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a44)
% 4.22/4.19 [354]E(f20(f31(a29,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f2(a4)),f30(f31(a29,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a24))
% 4.22/4.19 [369]P14(f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))
% 4.22/4.19 [370]P6(a27,f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))
% 4.22/4.19 [371]P6(a29,f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))
% 4.22/4.19 [372]P6(a37,f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))
% 4.22/4.19 [373]P6(a14,f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))
% 4.22/4.19 [374]P6(a15,f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))
% 4.22/4.19 [376]P11(f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24),f2(a4))
% 4.22/4.19 [378]P9(a28,a29,f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))
% 4.22/4.19 [379]P9(a28,a14,f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))
% 4.22/4.19 [380]P9(a28,a15,f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))
% 4.22/4.19 [383]P9(f31(a28,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f2(a4),f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))
% 4.22/4.19 [384]P9(f31(a29,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f2(a4),f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))
% 4.22/4.19 [385]P9(f31(a16,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f2(a4),f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))
% 4.22/4.19 [386]P2(f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24),f30(f31(a29,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a24))
% 4.22/4.19 [387]P2(f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24),f20(f31(a29,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f2(a4)))
% 4.22/4.19 [388]P9(f31(a29,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(a28,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))
% 4.22/4.19 [375]E(f19(f2(a4),f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24)),a24)
% 4.22/4.19 [377]E(f40(f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24),a37),f39(f36(a29,a24)))
% 4.22/4.19 [381]E(f40(f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24),a37),f30(f31(a29,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a24))
% 4.22/4.19 [382]E(f40(f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24),a6),f30(f31(a29,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a24))
% 4.22/4.19 [389]P13(f40(f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24),a37))
% 4.22/4.19 [138]P5(x1381,x1381)
% 4.22/4.19 [139]P7(x1391,x1391)
% 4.22/4.19 [156]P9(x1561,a27,x1561)
% 4.22/4.19 [95]P1(f39(x951))
% 4.22/4.19 [109]E(f40(x1091,a27),a27)
% 4.22/4.19 [111]E(f31(x1111,a44),a24)
% 4.22/4.19 [113]E(f34(x1131,a44),a25)
% 4.22/4.19 [114]E(f41(x1141,a43),a43)
% 4.22/4.19 [116]E(f35(x1161,a44),a26)
% 4.22/4.19 [117]E(f42(x1171,a44),a44)
% 4.22/4.19 [118]E(f40(a27,x1181),a27)
% 4.22/4.19 [119]E(f40(a1,x1191),a1)
% 4.22/4.19 [120]E(f31(a24,x1201),a24)
% 4.22/4.19 [121]E(f34(a25,x1211),a25)
% 4.22/4.19 [122]E(f41(a43,x1221),a43)
% 4.22/4.19 [123]E(f35(a26,x1231),a26)
% 4.22/4.19 [124]E(f42(a44,x1241),a44)
% 4.22/4.19 [125]E(f32(x1251,a43),x1251)
% 4.22/4.19 [127]E(f34(x1271,a26),x1271)
% 4.22/4.19 [128]E(f41(x1281,a25),x1281)
% 4.22/4.19 [129]E(f33(x1291,a44),x1291)
% 4.22/4.19 [131]E(f35(x1311,a26),x1311)
% 4.22/4.19 [132]E(f42(x1321,a26),x1321)
% 4.22/4.19 [133]E(f32(a43,x1331),x1331)
% 4.22/4.19 [135]E(f41(a25,x1351),x1351)
% 4.22/4.19 [136]E(f33(a44,x1361),x1361)
% 4.22/4.19 [137]E(f42(a26,x1371),x1371)
% 4.22/4.19 [403]~E(f30(x4031,x4031),a4)
% 4.22/4.19 [140]E(f32(x1401,f3(a1)),x1401)
% 4.22/4.19 [141]E(f32(f3(a1),x1411),x1411)
% 4.22/4.19 [152]E(f30(x1521,x1521),f40(f30(a24,a24),x1521))
% 4.22/4.19 [153]E(f32(x1531,x1531),f41(f32(a25,a25),x1531))
% 4.22/4.19 [154]E(f33(x1541,x1541),f42(f33(a26,a26),x1541))
% 4.22/4.19 [179]E(f40(f30(a24,a24),f2(x1791)),f2(f30(x1791,x1791)))
% 4.22/4.19 [180]E(f41(f32(a25,a25),f3(x1801)),f3(f30(x1801,x1801)))
% 4.22/4.19 [225]E(f30(f30(a27,f2(x2251)),f2(x2251)),f2(f30(x2251,x2251)))
% 4.22/4.19 [226]E(f32(f32(a43,f3(x2261)),f3(x2261)),f3(f30(x2261,x2261)))
% 4.22/4.19 [227]E(f30(f20(a1,x2271),f20(a1,x2271)),f20(a1,f30(x2271,x2271)))
% 4.22/4.19 [279]E(f30(f30(a24,f20(a4,x2791)),f20(a4,x2791)),f20(a4,f30(x2791,x2791)))
% 4.22/4.19 [405]~E(f30(f30(a24,x4051),x4051),a27)
% 4.22/4.19 [406]~E(f30(f30(a24,x4061),x4061),a1)
% 4.22/4.19 [261]E(f30(f30(a24,f2(x2611)),f2(x2611)),f2(f30(f30(a24,x2611),x2611)))
% 4.22/4.19 [262]E(f32(f32(a25,f3(x2621)),f3(x2621)),f3(f30(f30(a24,x2621),x2621)))
% 4.22/4.19 [280]E(f20(a4,f30(f30(a24,x2801),x2801)),f30(f20(a4,x2801),f20(a4,x2801)))
% 4.22/4.19 [293]E(f30(f30(a24,f20(a4,x2931)),f20(a4,x2931)),f20(a1,f30(f30(a24,x2931),x2931)))
% 4.22/4.19 [281]E(f41(x2811,f3(f30(f30(a24,a1),a1))),x2811)
% 4.22/4.19 [282]E(f41(f3(f30(f30(a24,a1),a1)),x2821),x2821)
% 4.22/4.19 [289]E(f2(f30(f30(f30(a24,a1),a1),x2891)),f30(a24,f2(x2891)))
% 4.22/4.19 [290]E(f3(f30(f30(f30(a24,a1),a1),x2901)),f32(a25,f3(x2901)))
% 4.22/4.19 [291]E(f2(f30(x2911,f30(f30(a24,a1),a1))),f30(f2(x2911),a24))
% 4.22/4.19 [292]E(f3(f30(x2921,f30(f30(a24,a1),a1))),f32(f3(x2921),a25))
% 4.22/4.19 [314]E(f40(x3141,x3141),f31(x3141,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [315]E(f41(x3151,x3151),f34(x3151,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [316]E(f42(x3161,x3161),f35(x3161,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [318]E(f40(x3181,f2(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f30(x3181,x3181))
% 4.22/4.19 [319]E(f31(x3191,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f40(x3191,x3191))
% 4.22/4.19 [320]E(f34(x3201,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f41(x3201,x3201))
% 4.22/4.19 [322]E(f41(x3221,f3(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f32(x3221,x3221))
% 4.22/4.19 [323]E(f35(x3231,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f42(x3231,x3231))
% 4.22/4.19 [325]E(f42(x3251,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f33(x3251,x3251))
% 4.22/4.19 [327]E(f40(f2(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3271),f30(x3271,x3271))
% 4.22/4.19 [329]E(f41(f3(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3291),f32(x3291,x3291))
% 4.22/4.19 [331]E(f42(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3311),f33(x3311,x3311))
% 4.22/4.19 [338]E(f31(x3381,f23(f30(f30(a24,f30(f30(a24,a1),a1)),f30(f30(a24,a1),a1)))),f40(f40(x3381,x3381),x3381))
% 4.22/4.19 [339]E(f34(x3391,f23(f30(f30(a24,f30(f30(a24,a1),a1)),f30(f30(a24,a1),a1)))),f41(f41(x3391,x3391),x3391))
% 4.22/4.19 [340]E(f35(x3401,f23(f30(f30(a24,f30(f30(a24,a1),a1)),f30(f30(a24,a1),a1)))),f42(f42(x3401,x3401),x3401))
% 4.22/4.19 [341]P5(a27,f31(x3411,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [342]P7(a43,f34(x3421,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [343]P7(a25,f34(f3(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3431))
% 4.22/4.19 [344]P5(x3441,f31(x3441,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [411]~P6(f31(x4111,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a27)
% 4.22/4.19 [412]~P12(f34(x4121,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a43)
% 4.22/4.19 [345]E(f31(f2(a4),f42(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3451)),a24)
% 4.22/4.19 [346]E(f34(f3(a4),f42(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3461)),a25)
% 4.22/4.19 [353]E(f40(x3531,f31(x3531,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),f31(x3531,f23(f30(f30(a24,f30(f30(a24,a1),a1)),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [359]E(f31(f31(x3591,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x3591,f23(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))))
% 4.22/4.19 [362]E(f41(f3(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x3621,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),f34(f41(f3(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3621),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [155]P9(x1551,x1552,a24)
% 4.22/4.19 [157]P9(x1571,x1571,x1572)
% 4.22/4.19 [143]E(f30(x1431,x1432),f30(x1432,x1431))
% 4.22/4.19 [145]E(f40(x1451,x1452),f40(x1452,x1451))
% 4.22/4.19 [146]E(f32(x1461,x1462),f32(x1462,x1461))
% 4.22/4.19 [148]E(f41(x1481,x1482),f41(x1482,x1481))
% 4.22/4.19 [149]E(f33(x1491,x1492),f33(x1492,x1491))
% 4.22/4.19 [150]E(f42(x1501,x1502),f42(x1502,x1501))
% 4.22/4.19 [158]E(f20(f2(x1581),f2(x1582)),f2(f20(x1581,x1582)))
% 4.22/4.19 [164]E(f30(f2(x1641),f2(x1642)),f2(f30(x1641,x1642)))
% 4.22/4.19 [166]E(f40(f2(x1661),f2(x1662)),f2(f40(x1661,x1662)))
% 4.22/4.19 [167]E(f32(f3(x1671),f3(x1672)),f3(f30(x1671,x1672)))
% 4.22/4.19 [168]E(f41(f3(x1681),f3(x1682)),f3(f40(x1681,x1682)))
% 4.22/4.19 [181]E(f30(x1811,f40(x1812,x1811)),f40(f30(x1812,a24),x1811))
% 4.22/4.19 [182]E(f32(x1821,f41(x1822,x1821)),f41(f32(x1822,a25),x1821))
% 4.22/4.19 [183]E(f33(x1831,f42(x1832,x1831)),f42(f33(x1832,a26),x1831))
% 4.22/4.19 [184]E(f30(f40(x1841,x1842),x1842),f40(f30(x1841,a24),x1842))
% 4.22/4.19 [185]E(f32(f41(x1851,x1852),x1852),f41(f32(x1851,a25),x1852))
% 4.22/4.19 [186]E(f33(f42(x1861,x1862),x1862),f42(f33(x1861,a26),x1862))
% 4.22/4.19 [263]E(f20(f30(x2631,x2631),f30(x2632,x2632)),f30(f20(x2631,x2632),f20(x2631,x2632)))
% 4.22/4.19 [277]P5(a27,f30(f40(x2771,x2771),f40(x2772,x2772)))
% 4.22/4.19 [278]P7(a43,f32(f41(x2781,x2781),f41(x2782,x2782)))
% 4.22/4.19 [296]E(f20(f30(f30(a24,x2961),x2961),f30(x2962,x2962)),f30(f30(a24,f20(x2961,x2962)),f20(x2961,x2962)))
% 4.22/4.19 [297]E(f30(f30(f30(a24,x2971),x2971),f30(x2972,x2972)),f30(f30(a24,f30(x2971,x2972)),f30(x2971,x2972)))
% 4.22/4.19 [408]~E(f30(f30(a24,x4081),x4081),f30(x4082,x4082))
% 4.22/4.19 [409]~P6(f30(f40(x4091,x4091),f40(x4092,x4092)),a27)
% 4.22/4.19 [410]~P12(f32(f41(x4101,x4101),f41(x4102,x4102)),a43)
% 4.22/4.19 [294]E(f20(f30(f30(a24,x2941),x2941),f30(f30(a24,x2942),x2942)),f30(f20(x2941,x2942),f20(x2941,x2942)))
% 4.22/4.19 [295]E(f30(f30(x2951,x2951),f30(f30(a24,x2952),x2952)),f30(f30(a24,f30(x2951,x2952)),f30(x2951,x2952)))
% 4.22/4.19 [298]E(f30(f30(f40(x2981,x2982),f40(x2981,x2982)),x2982),f40(f30(f30(a24,x2981),x2981),x2982))
% 4.22/4.19 [347]E(f31(x3471,f42(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3472)),f40(f31(x3471,x3472),f31(x3471,x3472)))
% 4.22/4.19 [348]E(f34(x3481,f42(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3482)),f41(f34(x3481,x3482),f34(x3481,x3482)))
% 4.22/4.19 [349]E(f35(x3491,f42(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3492)),f42(f35(x3491,x3492),f35(x3491,x3492)))
% 4.22/4.19 [350]E(f31(f31(x3501,x3502),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x3501,f42(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3502)))
% 4.22/4.19 [351]E(f34(f34(x3511,x3512),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x3511,f42(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3512)))
% 4.22/4.19 [352]E(f35(f35(x3521,x3522),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f35(x3521,f42(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3522)))
% 4.22/4.19 [355]P5(a27,f31(x3551,f42(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3552)))
% 4.22/4.19 [356]P7(a43,f34(x3561,f42(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3562)))
% 4.22/4.19 [357]E(f40(f30(x3571,x3572),f20(x3571,x3572)),f20(f31(x3571,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x3572,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))))
% 4.22/4.19 [358]E(f21(f35(x3581,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f35(x3582,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),f42(f33(x3581,x3582),f21(x3581,x3582)))
% 4.22/4.19 [360]P5(a27,f30(f31(x3601,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x3602,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))))
% 4.22/4.19 [361]P7(a43,f32(f34(x3611,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x3612,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))))
% 4.22/4.19 [367]E(f30(f20(f31(x3671,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f40(f40(f2(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3671),x3672)),f31(x3672,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),f31(f20(x3671,x3672),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [368]E(f30(f30(f31(x3681,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f40(f40(f2(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3681),x3682)),f31(x3682,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),f31(f30(x3681,x3682),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [390]E(f20(f30(f20(f31(x3901,f23(f30(f30(a24,f30(f30(a24,a1),a1)),f30(f30(a24,a1),a1)))),f40(f40(f2(f30(f30(a24,f30(f30(a24,a1),a1)),f30(f30(a24,a1),a1))),f31(x3901,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),x3902)),f40(f40(f2(f30(f30(a24,f30(f30(a24,a1),a1)),f30(f30(a24,a1),a1))),x3901),f31(x3902,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))),f31(x3902,f23(f30(f30(a24,f30(f30(a24,a1),a1)),f30(f30(a24,a1),a1))))),f31(f20(x3901,x3902),f23(f30(f30(a24,f30(f30(a24,a1),a1)),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [391]E(f30(f30(f30(f31(x3911,f23(f30(f30(a24,f30(f30(a24,a1),a1)),f30(f30(a24,a1),a1)))),f40(f40(f2(f30(f30(a24,f30(f30(a24,a1),a1)),f30(f30(a24,a1),a1))),f31(x3911,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),x3912)),f40(f40(f2(f30(f30(a24,f30(f30(a24,a1),a1)),f30(f30(a24,a1),a1))),x3911),f31(x3912,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))),f31(x3912,f23(f30(f30(a24,f30(f30(a24,a1),a1)),f30(f30(a24,a1),a1))))),f31(f30(x3911,x3912),f23(f30(f30(a24,f30(f30(a24,a1),a1)),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [413]~P6(f30(f31(x4131,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x4132,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),a27)
% 4.22/4.19 [414]~P12(f32(f34(x4141,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x4142,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),a43)
% 4.22/4.19 [363]E(f30(f30(f31(x3631,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x3632,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),f40(f40(f2(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3631),x3632)),f31(f30(x3631,x3632),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [365]E(f32(f32(f34(x3651,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x3652,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),f41(f41(f3(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3651),x3652)),f34(f32(x3651,x3652),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [366]E(f33(f33(f35(x3661,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f35(x3662,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),f42(f42(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x3661),x3662)),f35(f33(x3661,x3662),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [415]~E(f30(f31(x4151,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x4152,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))
% 4.22/4.19 [256]P9(f40(x2561,x2562),f40(x2563,x2562),x2562)
% 4.22/4.19 [188]E(f30(x1881,f30(x1882,x1883)),f30(x1882,f30(x1881,x1883)))
% 4.22/4.19 [189]E(f40(x1891,f40(x1892,x1893)),f40(x1892,f40(x1891,x1893)))
% 4.22/4.19 [190]E(f32(x1901,f32(x1902,x1903)),f32(x1902,f32(x1901,x1903)))
% 4.22/4.19 [191]E(f41(x1911,f41(x1912,x1913)),f41(x1912,f41(x1911,x1913)))
% 4.22/4.19 [192]E(f33(x1921,f33(x1922,x1923)),f33(x1922,f33(x1921,x1923)))
% 4.22/4.19 [193]E(f42(x1931,f42(x1932,x1933)),f42(x1932,f42(x1931,x1933)))
% 4.22/4.19 [204]E(f30(f30(x2041,x2042),x2043),f30(x2041,f30(x2042,x2043)))
% 4.22/4.19 [206]E(f40(f40(x2061,x2062),x2063),f40(x2061,f40(x2062,x2063)))
% 4.22/4.19 [209]E(f31(f31(x2091,x2092),x2093),f31(x2091,f42(x2092,x2093)))
% 4.22/4.19 [210]E(f32(f32(x2101,x2102),x2103),f32(x2101,f32(x2102,x2103)))
% 4.22/4.19 [211]E(f34(f34(x2111,x2112),x2113),f34(x2111,f42(x2112,x2113)))
% 4.22/4.19 [214]E(f41(f41(x2141,x2142),x2143),f41(x2141,f41(x2142,x2143)))
% 4.22/4.19 [215]E(f33(f33(x2151,x2152),x2153),f33(x2151,f33(x2152,x2153)))
% 4.22/4.19 [216]E(f35(f35(x2161,x2162),x2163),f35(x2161,f42(x2162,x2163)))
% 4.22/4.19 [218]E(f42(f42(x2181,x2182),x2183),f42(x2181,f42(x2182,x2183)))
% 4.22/4.19 [219]E(f30(f30(x2191,x2192),x2193),f30(f30(x2191,x2193),x2192))
% 4.22/4.19 [220]E(f40(f40(x2201,x2202),x2203),f40(f40(x2201,x2203),x2202))
% 4.22/4.19 [221]E(f32(f32(x2211,x2212),x2213),f32(f32(x2211,x2213),x2212))
% 4.22/4.19 [222]E(f41(f41(x2221,x2222),x2223),f41(f41(x2221,x2223),x2222))
% 4.22/4.19 [223]E(f33(f33(x2231,x2232),x2233),f33(f33(x2231,x2233),x2232))
% 4.22/4.19 [224]E(f42(f42(x2241,x2242),x2243),f42(f42(x2241,x2243),x2242))
% 4.22/4.19 [228]E(f20(f40(x2281,x2282),f40(x2281,x2283)),f40(x2281,f20(x2282,x2283)))
% 4.22/4.19 [230]E(f30(f40(x2301,x2302),f40(x2301,x2303)),f40(x2301,f30(x2302,x2303)))
% 4.22/4.19 [234]E(f32(f41(x2341,x2342),f41(x2341,x2343)),f41(x2341,f32(x2342,x2343)))
% 4.22/4.19 [236]E(f33(f42(x2361,x2362),f42(x2361,x2363)),f42(x2361,f33(x2362,x2363)))
% 4.22/4.19 [237]E(f20(f40(x2371,x2372),f40(x2373,x2372)),f40(f20(x2371,x2373),x2372))
% 4.22/4.19 [242]E(f40(f31(x2421,x2422),f31(x2423,x2422)),f31(f40(x2421,x2423),x2422))
% 4.22/4.19 [244]E(f41(f34(x2441,x2442),f34(x2443,x2442)),f34(f41(x2441,x2443),x2442))
% 4.22/4.19 [248]E(f42(f35(x2481,x2482),f35(x2483,x2482)),f35(f42(x2481,x2483),x2482))
% 4.22/4.19 [250]E(f40(f31(x2501,x2502),f31(x2501,x2503)),f31(x2501,f33(x2502,x2503)))
% 4.22/4.19 [251]E(f41(f34(x2511,x2512),f34(x2511,x2513)),f34(x2511,f33(x2512,x2513)))
% 4.22/4.19 [252]E(f42(f35(x2521,x2522),f35(x2521,x2523)),f35(x2521,f33(x2522,x2523)))
% 4.22/4.19 [253]E(f30(f40(x2531,x2532),f40(x2533,x2532)),f40(f30(x2531,x2533),x2532))
% 4.22/4.19 [254]E(f32(f41(x2541,x2542),f41(x2543,x2542)),f41(f32(x2541,x2543),x2542))
% 4.22/4.19 [255]E(f33(f42(x2551,x2552),f42(x2553,x2552)),f42(f33(x2551,x2553),x2552))
% 4.22/4.19 [257]E(f30(f2(x2571),f30(f2(x2572),x2573)),f30(f2(f30(x2571,x2572)),x2573))
% 4.22/4.19 [258]E(f40(f2(x2581),f40(f2(x2582),x2583)),f40(f2(f40(x2581,x2582)),x2583))
% 4.22/4.19 [259]E(f32(f3(x2591),f32(f3(x2592),x2593)),f32(f3(f30(x2591,x2592)),x2593))
% 4.22/4.19 [260]E(f41(f3(x2601),f41(f3(x2602),x2603)),f41(f3(f40(x2601,x2602)),x2603))
% 4.22/4.19 [264]E(f30(f30(x2641,x2642),f30(x2643,x2644)),f30(f30(x2641,x2643),f30(x2642,x2644)))
% 4.22/4.19 [266]E(f40(f40(x2661,x2662),f40(x2663,x2664)),f40(f40(x2661,x2663),f40(x2662,x2664)))
% 4.22/4.19 [267]E(f32(f32(x2671,x2672),f32(x2673,x2674)),f32(f32(x2671,x2673),f32(x2672,x2674)))
% 4.22/4.19 [268]E(f41(f41(x2681,x2682),f41(x2683,x2684)),f41(f41(x2681,x2683),f41(x2682,x2684)))
% 4.22/4.19 [269]E(f33(f33(x2691,x2692),f33(x2693,x2694)),f33(f33(x2691,x2693),f33(x2692,x2694)))
% 4.22/4.19 [270]E(f42(f42(x2701,x2702),f42(x2703,x2704)),f42(f42(x2701,x2703),f42(x2702,x2704)))
% 4.22/4.19 [335]E(f39(f36(f30(f40(x3351,x3352),f40(x3353,x3354)),f20(f40(x3351,x3354),f40(x3353,x3352)))),f40(f39(f36(x3351,x3353)),f39(f36(x3352,x3354))))
% 4.22/4.19 [336]E(f30(f40(f20(x3361,f40(x3362,x3363)),x3364),f40(f20(x3365,f40(x3362,x3366)),x3367)),f20(f30(f40(x3361,x3364),f40(x3365,x3367)),f40(x3362,f30(f40(x3363,x3364),f40(x3366,x3367)))))
% 4.22/4.19 [416]P1(a7)+~E(a37,a24)
% 4.22/4.19 [417]~E(a37,a24)+P1(a11)
% 4.22/4.19 [455]P1(a12)+~P6(a24,a37)
% 4.22/4.19 [456]~P6(a24,a37)+P1(a13)
% 4.22/4.19 [1000]~E(a37,a24)+E(f30(f31(a7,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(a11,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))
% 4.22/4.19 [1001]~P6(a24,a37)+E(f30(f31(a12,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(a13,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))
% 4.22/4.19 [499]~P6(a27,x4991)+P5(a24,x4991)
% 4.22/4.19 [500]~P5(a24,x5001)+P6(a27,x5001)
% 4.22/4.19 [418]~P1(x4181)+E(f2(x4181),x4181)
% 4.22/4.19 [419]E(x4191,a44)+E(f31(a27,x4191),a27)
% 4.22/4.19 [420]E(x4201,a44)+E(f34(a43,x4201),a43)
% 4.22/4.19 [421]E(x4211,a44)+E(f35(a44,x4211),a44)
% 4.22/4.19 [422]~E(x4221,a44)+E(f31(a27,x4221),a24)
% 4.22/4.19 [423]~E(x4231,a44)+E(f34(a43,x4231),a25)
% 4.22/4.19 [425]~E(x4251,a43)+E(f32(x4251,x4251),a43)
% 4.22/4.19 [432]~P1(x4321)+P1(f2(x4321))
% 4.22/4.19 [441]P5(x4411,a1)+~E(f23(x4411),a44)
% 4.22/4.19 [442]~P1(x4421)+E(f20(x4421,a1),x4421)
% 4.22/4.19 [444]~P1(x4441)+E(f30(x4441,a27),x4441)
% 4.22/4.19 [445]~P1(x4451)+E(f30(x4451,a1),x4451)
% 4.22/4.19 [447]~P1(x4471)+E(f40(x4471,a24),x4471)
% 4.22/4.19 [449]~P1(x4491)+E(f31(x4491,a26),x4491)
% 4.22/4.19 [451]~P1(x4511)+E(f30(a27,x4511),x4511)
% 4.22/4.19 [452]~P1(x4521)+E(f30(a1,x4521),x4521)
% 4.22/4.19 [454]~P1(x4541)+E(f40(a24,x4541),x4541)
% 4.22/4.19 [465]E(x4651,a43)+~E(f32(x4651,x4651),a43)
% 4.22/4.19 [471]~P5(x4711,a1)+E(f23(x4711),a44)
% 4.22/4.19 [509]~P1(x5091)+P1(f30(x5091,x5091))
% 4.22/4.19 [513]~P5(a1,x5131)+P5(a27,f2(x5131))
% 4.22/4.19 [514]~P6(a1,x5141)+P6(a27,f2(x5141))
% 4.22/4.19 [515]~P5(a1,x5151)+P7(a43,f3(x5151))
% 4.22/4.19 [516]~P6(a1,x5161)+P12(a43,f3(x5161))
% 4.22/4.19 [517]~P6(a1,x5171)+P10(a44,f23(x5171))
% 4.22/4.19 [518]~P5(x5181,a1)+P5(f2(x5181),a27)
% 4.22/4.19 [519]~P6(x5191,a1)+P6(f2(x5191),a27)
% 4.22/4.19 [520]~P5(x5201,a1)+P7(f3(x5201),a43)
% 4.22/4.19 [521]~P6(x5211,a1)+P12(f3(x5211),a43)
% 4.22/4.19 [529]E(x5291,a43)+P12(a43,f41(x5291,x5291))
% 4.22/4.19 [544]P5(x5441,a1)+~P5(f2(x5441),a27)
% 4.22/4.19 [545]P5(x5451,a1)+~P7(f3(x5451),a43)
% 4.22/4.19 [546]P6(x5461,a1)+~P6(f2(x5461),a27)
% 4.22/4.19 [547]P6(x5471,a1)+~P12(f3(x5471),a43)
% 4.22/4.19 [548]P5(a1,x5481)+~P5(a27,f2(x5481))
% 4.22/4.19 [549]P5(a1,x5491)+~P7(a43,f3(x5491))
% 4.22/4.19 [550]P6(a1,x5501)+~P6(a27,f2(x5501))
% 4.22/4.19 [551]P6(a1,x5511)+~P12(a43,f3(x5511))
% 4.22/4.19 [552]P6(a1,x5521)+~P10(a44,f23(x5521))
% 4.22/4.19 [589]~P5(a27,x5891)+P6(a27,f30(a24,x5891))
% 4.22/4.19 [604]~P6(a4,x6041)+P5(a4,f30(x6041,x6041))
% 4.22/4.19 [605]~P5(a1,x6051)+P5(a1,f30(x6051,x6051))
% 4.22/4.19 [607]~P6(a4,x6071)+P6(a4,f30(x6071,x6071))
% 4.22/4.19 [608]~P6(a1,x6081)+P6(a1,f30(x6081,x6081))
% 4.22/4.19 [617]~P5(x6171,a4)+P5(f30(x6171,x6171),a4)
% 4.22/4.19 [618]~P5(x6181,a1)+P5(f30(x6181,x6181),a1)
% 4.22/4.19 [620]~P6(x6201,a27)+P6(f30(x6201,x6201),a27)
% 4.22/4.19 [621]~P5(x6211,a4)+P6(f30(x6211,x6211),a4)
% 4.22/4.19 [622]~P6(x6221,a1)+P6(f30(x6221,x6221),a1)
% 4.22/4.19 [623]~P12(x6231,a43)+P12(f32(x6231,x6231),a43)
% 4.22/4.19 [637]~E(x6371,a43)+~P12(a43,f41(x6371,x6371))
% 4.22/4.19 [657]P5(x6571,a4)+~P5(f30(x6571,x6571),a4)
% 4.22/4.19 [658]P5(x6581,a4)+~P6(f30(x6581,x6581),a4)
% 4.22/4.19 [659]P5(x6591,a1)+~P5(f30(x6591,x6591),a1)
% 4.22/4.19 [661]P6(x6611,a27)+~P6(f30(x6611,x6611),a27)
% 4.22/4.19 [662]P6(x6621,a1)+~P6(f30(x6621,x6621),a1)
% 4.22/4.19 [663]P12(x6631,a43)+~P12(f32(x6631,x6631),a43)
% 4.22/4.19 [664]P5(a1,x6641)+~P5(a1,f30(x6641,x6641))
% 4.22/4.19 [665]P6(a4,x6651)+~P5(a4,f30(x6651,x6651))
% 4.22/4.19 [666]P6(a4,x6661)+~P6(a4,f30(x6661,x6661))
% 4.22/4.19 [667]P6(a1,x6671)+~P6(a1,f30(x6671,x6671))
% 4.22/4.19 [477]~P1(x4771)+E(f30(x4771,f2(a1)),x4771)
% 4.22/4.19 [478]~P1(x4781)+E(f30(f2(a1),x4781),x4781)
% 4.22/4.19 [508]E(f31(f2(a4),x5081),f2(a4))+E(f31(f2(a4),x5081),a24)
% 4.22/4.19 [688]~P1(x6881)+P1(f30(f30(a24,x6881),x6881))
% 4.22/4.19 [734]~P5(a4,x7341)+P5(a4,f30(f30(a24,x7341),x7341))
% 4.22/4.19 [735]~P5(a1,x7351)+P5(a1,f30(f30(a24,x7351),x7351))
% 4.22/4.19 [736]~P6(a4,x7361)+P6(a4,f30(f30(a24,x7361),x7361))
% 4.22/4.19 [737]~P5(a1,x7371)+P6(a1,f30(f30(a24,x7371),x7371))
% 4.22/4.19 [738]~P5(x7381,a4)+P5(f30(f30(a24,x7381),x7381),a4)
% 4.22/4.19 [739]~P6(x7391,a1)+P5(f30(f30(a24,x7391),x7391),a1)
% 4.22/4.19 [741]~P6(x7411,a27)+P6(f30(f30(a24,x7411),x7411),a27)
% 4.22/4.19 [742]~P6(x7421,a4)+P6(f30(f30(a24,x7421),x7421),a4)
% 4.22/4.19 [743]~P6(x7431,a1)+P6(f30(f30(a24,x7431),x7431),a1)
% 4.22/4.19 [749]~P5(f2(x7491),a24)+P5(x7491,f30(f30(a24,a1),a1))
% 4.22/4.19 [750]~P7(f3(x7501),a25)+P5(x7501,f30(f30(a24,a1),a1))
% 4.22/4.19 [751]~P6(f2(x7511),a24)+P6(x7511,f30(f30(a24,a1),a1))
% 4.22/4.19 [752]~P12(f3(x7521),a25)+P6(x7521,f30(f30(a24,a1),a1))
% 4.22/4.19 [753]~P5(a24,f2(x7531))+P5(f30(f30(a24,a1),a1),x7531)
% 4.22/4.19 [754]~P7(a25,f3(x7541))+P5(f30(f30(a24,a1),a1),x7541)
% 4.22/4.19 [755]~P6(a24,f2(x7551))+P6(f30(f30(a24,a1),a1),x7551)
% 4.22/4.19 [756]~P12(a25,f3(x7561))+P6(f30(f30(a24,a1),a1),x7561)
% 4.22/4.19 [857]~P5(f30(f30(a24,a1),a1),x8571)+P5(a24,f2(x8571))
% 4.22/4.19 [858]~P6(f30(f30(a24,a1),a1),x8581)+P6(a24,f2(x8581))
% 4.22/4.19 [859]~P5(f30(f30(a24,a1),a1),x8591)+P7(a25,f3(x8591))
% 4.22/4.19 [860]~P6(f30(f30(a24,a1),a1),x8601)+P12(a25,f3(x8601))
% 4.22/4.19 [861]~P5(x8611,f30(f30(a24,a1),a1))+P5(f2(x8611),a24)
% 4.22/4.19 [862]~P6(x8621,f30(f30(a24,a1),a1))+P6(f2(x8621),a24)
% 4.22/4.19 [863]~P5(x8631,f30(f30(a24,a1),a1))+P7(f3(x8631),a25)
% 4.22/4.19 [864]~P6(x8641,f30(f30(a24,a1),a1))+P12(f3(x8641),a25)
% 4.22/4.19 [870]P5(x8701,a4)+~P5(f30(f30(a24,x8701),x8701),a4)
% 4.22/4.19 [872]P6(x8721,a27)+~P6(f30(f30(a24,x8721),x8721),a27)
% 4.22/4.19 [873]P6(x8731,a4)+~P6(f30(f30(a24,x8731),x8731),a4)
% 4.22/4.19 [874]P6(x8741,a1)+~P5(f30(f30(a24,x8741),x8741),a1)
% 4.22/4.19 [875]P6(x8751,a1)+~P6(f30(f30(a24,x8751),x8751),a1)
% 4.22/4.19 [876]P5(a4,x8761)+~P5(a4,f30(f30(a24,x8761),x8761))
% 4.22/4.19 [877]P5(a1,x8771)+~P5(a1,f30(f30(a24,x8771),x8771))
% 4.22/4.19 [878]P5(a1,x8781)+~P6(a1,f30(f30(a24,x8781),x8781))
% 4.22/4.19 [879]P6(a4,x8791)+~P6(a4,f30(f30(a24,x8791),x8791))
% 4.22/4.19 [881]~P1(x8811)+E(f40(x8811,f2(f30(f30(a24,a1),a1))),x8811)
% 4.22/4.19 [882]~P1(x8821)+E(f40(f2(f30(f30(a24,a1),a1)),x8821),x8821)
% 4.22/4.19 [962]~P9(a24,f2(a4),x9621)+~P6(f2(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x9621)
% 4.22/4.19 [957]~E(x9571,a43)+E(f34(x9571,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a43)
% 4.22/4.19 [965]E(x9651,a43)+P12(a43,f34(x9651,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [969]~E(x9691,a43)+~P12(a43,f34(x9691,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [1008]E(f19(f2(a4),f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),x10081),a24)),a24)+~P14(f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),x10081),a24))
% 4.22/4.19 [433]~E(x4331,x4332)+P7(x4331,x4332)
% 4.22/4.19 [435]~E(x4351,x4352)+P3(x4351,x4352)
% 4.22/4.19 [484]~P12(x4841,x4842)+~E(x4841,x4842)
% 4.22/4.19 [488]P5(x4882,x4881)+P5(x4881,x4882)
% 4.22/4.19 [489]P7(x4892,x4891)+P7(x4891,x4892)
% 4.22/4.19 [507]~P12(x5071,x5072)+P7(x5071,x5072)
% 4.22/4.19 [675]~P2(x6752,x6751)+P9(x6751,a27,x6752)
% 4.22/4.19 [725]P2(x7251,x7252)+~P9(x7252,a27,x7251)
% 4.22/4.19 [427]~E(x4272,a44)+E(f35(x4271,x4272),a26)
% 4.22/4.19 [428]~E(x4281,a26)+E(f35(x4281,x4282),a26)
% 4.22/4.19 [429]~E(x4291,a44)+E(f42(x4291,x4292),a44)
% 4.22/4.19 [430]~E(x4302,a43)+E(f32(x4301,x4302),x4301)
% 4.22/4.19 [431]~E(x4312,a44)+E(f33(x4311,x4312),x4311)
% 4.22/4.19 [463]E(x4631,a26)+~E(f42(x4632,x4631),a26)
% 4.22/4.19 [464]E(x4641,a26)+~E(f42(x4641,x4642),a26)
% 4.22/4.19 [467]E(x4671,a43)+~E(f34(x4671,x4672),a43)
% 4.22/4.19 [469]E(x4691,a44)+~E(f35(x4691,x4692),a44)
% 4.22/4.19 [472]~E(x4721,a44)+~E(f34(x4722,x4721),a43)
% 4.22/4.19 [474]~E(x4741,a44)+~E(f35(x4742,x4741),a44)
% 4.22/4.19 [475]~E(f32(x4752,x4751),x4752)+E(x4751,a43)
% 4.22/4.19 [476]~E(f33(x4762,x4761),x4762)+E(x4761,a44)
% 4.22/4.19 [510]~P1(x5101)+P1(f31(x5101,x5102))
% 4.22/4.19 [535]~E(x5352,a44)+P10(a44,f35(x5351,x5352))
% 4.22/4.19 [540]~E(x5401,a24)+P2(x5401,f31(x5401,x5402))
% 4.22/4.19 [541]~E(x5411,a26)+P3(x5411,f35(x5411,x5412))
% 4.22/4.19 [542]~E(x5421,a25)+P4(x5421,f34(x5421,x5422))
% 4.22/4.19 [564]~P5(x5641,a1)+P8(f23(x5641),f23(x5642))
% 4.22/4.19 [570]~P5(x5701,x5702)+P5(f2(x5701),f2(x5702))
% 4.22/4.19 [572]~P6(x5721,x5722)+P6(f2(x5721),f2(x5722))
% 4.22/4.19 [573]~P5(x5731,x5732)+P7(f3(x5731),f3(x5732))
% 4.22/4.19 [574]~P6(x5741,x5742)+P12(f3(x5741),f3(x5742))
% 4.22/4.19 [575]~P5(x5751,x5752)+P8(f23(x5751),f23(x5752))
% 4.22/4.19 [581]~P11(x5811,x5812)+P1(f8(x5811,x5812))
% 4.22/4.19 [582]P5(f2(x5821),f2(x5822))+P6(f2(x5822),f2(x5821))
% 4.22/4.19 [583]P7(f3(x5831),f3(x5832))+P12(f3(x5832),f3(x5831))
% 4.22/4.19 [584]P8(f23(x5841),f23(x5842))+P10(f23(x5842),f23(x5841))
% 4.22/4.19 [591]P5(x5911,x5912)+~P5(f2(x5911),f2(x5912))
% 4.22/4.19 [592]P5(x5921,x5922)+~P7(f3(x5921),f3(x5922))
% 4.22/4.19 [594]P6(x5941,x5942)+~P6(f2(x5941),f2(x5942))
% 4.22/4.19 [595]P6(x5951,x5952)+~P12(f3(x5951),f3(x5952))
% 4.22/4.19 [596]P6(x5961,x5962)+~P10(f23(x5961),f23(x5962))
% 4.22/4.19 [601]~P5(a24,x6011)+P5(a24,f31(x6011,x6012))
% 4.22/4.19 [603]~P5(a27,x6031)+P5(a27,f31(x6031,x6032))
% 4.22/4.19 [606]~P6(a27,x6061)+P6(a27,f31(x6061,x6062))
% 4.22/4.19 [609]~P7(a25,x6091)+P7(a25,f34(x6091,x6092))
% 4.22/4.19 [610]~P7(a43,x6101)+P7(a43,f34(x6101,x6102))
% 4.22/4.19 [611]~P12(a43,x6111)+P12(a43,f34(x6111,x6112))
% 4.22/4.19 [612]~P8(a26,x6121)+P8(a26,f35(x6121,x6122))
% 4.22/4.19 [613]~P8(a44,x6131)+P8(a44,f35(x6131,x6132))
% 4.22/4.19 [616]~P10(a44,x6161)+P10(a44,f35(x6161,x6162))
% 4.22/4.19 [626]~P6(x6261,x6262)+P5(x6261,f20(x6262,a24))
% 4.22/4.19 [627]~P5(x6271,x6272)+P6(x6271,f30(x6272,a24))
% 4.22/4.19 [629]~P6(x6291,x6292)+P5(f30(x6291,a24),x6292)
% 4.22/4.19 [630]~P10(a44,x6302)+P2(x6301,f31(x6301,x6302))
% 4.22/4.19 [631]~P10(a44,x6312)+P3(x6311,f35(x6311,x6312))
% 4.22/4.19 [632]~P10(a44,x6322)+P4(x6321,f34(x6321,x6322))
% 4.22/4.19 [634]~P6(x6341,x6342)+P6(f20(x6341,x6342),a27)
% 4.22/4.19 [635]~P7(x6351,x6352)+P7(f22(x6351,x6352),a43)
% 4.22/4.19 [654]P5(x6541,x6542)+~P6(x6541,f30(x6542,a24))
% 4.22/4.19 [655]P6(x6551,x6552)+~P5(x6551,f20(x6552,a24))
% 4.22/4.19 [656]P6(x6561,x6562)+~P5(f30(x6561,a24),x6562)
% 4.22/4.19 [670]P6(x6701,x6702)+~P6(f20(x6701,x6702),a27)
% 4.22/4.19 [671]P7(x6711,x6712)+~P7(f22(x6711,x6712),a43)
% 4.22/4.19 [690]~P5(f2(x6901),f2(x6902))+~P6(f2(x6902),f2(x6901))
% 4.22/4.19 [691]~P7(f3(x6911),f3(x6912))+~P12(f3(x6912),f3(x6911))
% 4.22/4.19 [692]~P8(f23(x6921),f23(x6922))+~P10(f23(x6922),f23(x6921))
% 4.22/4.19 [698]~P5(x6981,x6982)+P5(f30(x6981,x6981),f30(x6982,x6982))
% 4.22/4.19 [701]~P6(x7011,x7012)+P6(f30(x7011,x7011),f30(x7012,x7012))
% 4.22/4.19 [723]~P9(x7231,a27,x7232)+E(f19(x7231,x7232),a27)
% 4.22/4.19 [790]P5(x7901,x7902)+~P5(f30(x7901,x7901),f30(x7902,x7902))
% 4.22/4.19 [792]P6(x7921,x7922)+~P6(f30(x7921,x7921),f30(x7922,x7922))
% 4.22/4.19 [563]~P6(x5631,a1)+E(f42(f23(x5631),f23(x5632)),a44)
% 4.22/4.19 [577]~P6(x5771,a1)+E(f33(f23(x5771),f23(x5772)),f23(x5772))
% 4.22/4.19 [647]P6(x6471,a1)+E(f42(f23(x6471),f23(x6472)),f23(f40(x6471,x6472)))
% 4.22/4.19 [746]E(x7461,a43)+~E(f32(f41(x7462,x7462),f41(x7461,x7461)),a43)
% 4.22/4.19 [748]E(x7481,a43)+~E(f32(f41(x7481,x7481),f41(x7482,x7482)),a43)
% 4.22/4.19 [779]~P6(a24,x7791)+P6(a24,f40(x7791,f31(x7791,x7792)))
% 4.22/4.19 [780]~P12(a25,x7801)+P12(a25,f41(x7801,f34(x7801,x7802)))
% 4.22/4.19 [781]~P10(a26,x7811)+P10(a26,f42(x7811,f35(x7811,x7812)))
% 4.22/4.19 [821]~P5(x8211,x8212)+P5(f30(x8211,x8211),f30(f30(a24,x8212),x8212))
% 4.22/4.19 [823]~P5(x8231,x8232)+P6(f30(x8231,x8231),f30(f30(a24,x8232),x8232))
% 4.22/4.19 [825]~P6(x8251,x8252)+P5(f30(f30(a24,x8251),x8251),f30(x8252,x8252))
% 4.22/4.19 [827]~P6(x8271,x8272)+P6(f30(f30(a24,x8271),x8271),f30(x8272,x8272))
% 4.22/4.19 [834]~P6(a24,x8341)+P6(f31(x8341,x8342),f40(x8341,f31(x8341,x8342)))
% 4.22/4.19 [835]~P12(a25,x8351)+P12(f34(x8351,x8352),f41(x8351,f34(x8351,x8352)))
% 4.22/4.19 [836]~P10(a26,x8361)+P10(f35(x8361,x8362),f42(x8361,f35(x8361,x8362)))
% 4.22/4.19 [868]E(x8681,a43)+P12(a43,f32(f41(x8682,x8682),f41(x8681,x8681)))
% 4.22/4.19 [869]E(x8691,a43)+P12(a43,f32(f41(x8691,x8691),f41(x8692,x8692)))
% 4.22/4.19 [897]~P5(x8971,x8972)+P5(f30(f30(a24,x8971),x8971),f30(f30(a24,x8972),x8972))
% 4.22/4.19 [899]~P6(x8991,x8992)+P6(f30(f30(a24,x8991),x8991),f30(f30(a24,x8992),x8992))
% 4.22/4.19 [902]P5(x9021,x9022)+~P5(f30(x9021,x9021),f30(f30(a24,x9022),x9022))
% 4.22/4.19 [904]P5(x9041,x9042)+~P6(f30(x9041,x9041),f30(f30(a24,x9042),x9042))
% 4.22/4.19 [906]P6(x9061,x9062)+~P5(f30(f30(a24,x9061),x9061),f30(x9062,x9062))
% 4.22/4.19 [908]P6(x9081,x9082)+~P6(f30(f30(a24,x9081),x9081),f30(x9082,x9082))
% 4.22/4.19 [922]E(x9221,a43)+~P7(f32(f41(x9222,x9222),f41(x9221,x9221)),a43)
% 4.22/4.19 [923]E(x9231,a43)+~P7(f32(f41(x9231,x9231),f41(x9232,x9232)),a43)
% 4.22/4.19 [933]~P9(x9331,f20(x9332,a24),x9332)+P9(f40(x9331,f20(x9332,a24)),a24,x9332)
% 4.22/4.19 [938]P5(x9381,x9382)+~P5(f30(f30(a24,x9381),x9381),f30(f30(a24,x9382),x9382))
% 4.22/4.19 [940]P6(x9401,x9402)+~P6(f30(f30(a24,x9401),x9401),f30(f30(a24,x9402),x9402))
% 4.22/4.19 [941]P9(x9411,f20(x9412,a24),x9412)+~P9(f40(x9411,f20(x9412,a24)),a24,x9412)
% 4.22/4.19 [730]E(x7301,a44)+E(f42(x7302,f35(x7302,f21(x7301,a26))),f35(x7302,x7301))
% 4.22/4.19 [731]E(x7311,a44)+E(f33(x7312,f42(f21(x7311,a26),x7312)),f42(x7311,x7312))
% 4.22/4.19 [968]~P11(x9681,x9682)+P9(f31(f8(x9681,x9682),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),x9682,x9681)
% 4.22/4.19 [980]E(x9801,a43)+~E(f32(f34(x9802,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x9801,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),a43)
% 4.22/4.19 [982]E(x9821,a43)+~E(f32(f34(x9821,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x9822,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),a43)
% 4.22/4.19 [991]E(x9911,a43)+~P7(f34(x9911,f42(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x9912)),a43)
% 4.22/4.19 [994]E(x9941,a43)+P12(a43,f32(f34(x9942,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x9941,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))))
% 4.22/4.19 [995]E(x9951,a43)+P12(a43,f32(f34(x9951,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x9952,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))))
% 4.22/4.19 [1002]E(x10021,a43)+~P7(f32(f34(x10022,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x10021,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),a43)
% 4.22/4.19 [1003]E(x10031,a43)+~P7(f32(f34(x10031,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x10032,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),a43)
% 4.22/4.19 [866]~P9(x8662,x8661,x8663)+P9(x8661,x8662,x8663)
% 4.22/4.19 [646]~E(x6462,a44)+P3(f42(x6461,x6462),f42(x6463,x6462))
% 4.22/4.19 [696]~P5(x6962,x6963)+P5(f30(x6961,x6962),f30(x6961,x6963))
% 4.22/4.19 [699]~P6(x6991,x6993)+P6(f30(x6991,x6992),f30(x6993,x6992))
% 4.22/4.19 [702]~P7(x7022,x7023)+P7(f32(x7021,x7022),f32(x7021,x7023))
% 4.22/4.19 [703]~P8(x7032,x7033)+P2(f31(x7031,x7032),f31(x7031,x7033))
% 4.22/4.19 [704]~P2(x7041,x7043)+P2(f31(x7041,x7042),f31(x7043,x7042))
% 4.22/4.19 [705]~P8(x7052,x7053)+P3(f35(x7051,x7052),f35(x7051,x7053))
% 4.22/4.19 [707]~P3(x7071,x7073)+P3(f35(x7071,x7072),f35(x7073,x7072))
% 4.22/4.19 [708]~P3(x7082,x7083)+P3(f42(x7081,x7082),f42(x7081,x7083))
% 4.22/4.19 [710]~P3(x7101,x7103)+P3(f42(x7101,x7102),f42(x7103,x7102))
% 4.22/4.19 [711]~P8(x7112,x7113)+P4(f34(x7111,x7112),f34(x7111,x7113))
% 4.22/4.19 [712]~P4(x7121,x7123)+P4(f34(x7121,x7122),f34(x7123,x7122))
% 4.22/4.19 [787]P9(x7871,x7872,x7873)+~P2(x7873,f20(x7871,x7872))
% 4.22/4.19 [800]~P9(x8002,x8003,x8001)+P2(x8001,f20(x8002,x8003))
% 4.22/4.19 [786]~P2(x7861,x7862)+P2(x7861,f30(x7862,f40(x7861,x7863)))
% 4.22/4.19 [889]P2(x8891,x8892)+~P2(x8891,f30(x8892,f40(x8891,x8893)))
% 4.22/4.19 [677]~P6(x6771,a1)+E(f42(f23(x6771),f42(f23(x6772),x6773)),a44)
% 4.22/4.19 [867]P6(x8671,a1)+E(f42(f23(x8671),f42(f23(x8672),x8673)),f42(f23(f40(x8671,x8672)),x8673))
% 4.22/4.19 [909]~P9(x9091,x9093,x9094)+P9(f30(x9091,x9092),f30(x9093,x9092),x9094)
% 4.22/4.19 [910]~P9(x9102,x9103,x9104)+P9(f40(x9101,x9102),f40(x9101,x9103),x9104)
% 4.22/4.19 [911]~P9(x9111,x9113,x9114)+P9(f40(x9111,x9112),f40(x9113,x9112),x9114)
% 4.22/4.19 [912]~P9(x9121,x9123,x9124)+P9(f31(x9121,x9122),f31(x9123,x9122),x9124)
% 4.22/4.19 [829]~E(x8291,x8293)+E(f32(f41(x8291,x8292),f41(x8293,x8294)),f32(f41(x8291,x8294),f41(x8293,x8292)))
% 4.22/4.19 [831]~E(x8311,x8313)+E(f33(f42(x8311,x8312),f42(x8313,x8314)),f33(f42(x8311,x8314),f42(x8313,x8312)))
% 4.22/4.19 [934]~P9(f31(x9341,x9342),a24,x9344)+P9(f31(x9341,f42(x9342,x9343)),a24,x9344)
% 4.22/4.19 [485]~P1(x4851)+~P14(x4851)+P6(a24,x4851)
% 4.22/4.19 [460]~P1(x4601)+~E(a1,x4601)+E(f30(x4601,x4601),a1)
% 4.22/4.19 [461]~P1(x4611)+~E(x4611,a27)+E(f30(x4611,x4611),a27)
% 4.22/4.19 [462]~P1(x4621)+~E(x4621,a1)+E(f30(x4621,x4621),a1)
% 4.22/4.19 [492]~P1(x4921)+E(x4921,a27)+~E(f30(x4921,x4921),a27)
% 4.22/4.19 [495]~P1(x4951)+E(x4951,a1)+~E(f30(x4951,x4951),a1)
% 4.22/4.19 [496]~P1(x4961)+E(a1,x4961)+~E(f30(x4961,x4961),a1)
% 4.22/4.19 [561]~P1(x5611)+~E(a4,x5611)+E(f30(f30(a24,x5611),x5611),a4)
% 4.22/4.19 [562]~P1(x5621)+~E(x5621,a4)+E(f30(f30(a24,x5621),x5621),a4)
% 4.22/4.19 [643]~P1(x6431)+E(x6431,a4)+~E(f30(f30(a24,x6431),x6431),a4)
% 4.22/4.19 [644]~P1(x6441)+E(a4,x6441)+~E(f30(f30(a24,x6441),x6441),a4)
% 4.22/4.19 [958]~P1(x9581)+~E(x9581,a27)+E(f31(x9581,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a27)
% 4.22/4.19 [966]~P1(x9661)+E(x9661,a27)+P6(a27,f31(x9661,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [970]~P1(x9701)+~E(x9701,a27)+~P6(a27,f31(x9701,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [511]~P3(x5112,x5111)+P8(x5112,x5111)+E(x5111,a44)
% 4.22/4.19 [524]P12(x5241,x5242)+~P7(x5241,x5242)+E(x5241,x5242)
% 4.22/4.19 [525]P10(x5251,x5252)+~P8(x5251,x5252)+E(x5251,x5252)
% 4.22/4.19 [565]~P7(x5652,x5651)+~P7(x5651,x5652)+E(x5651,x5652)
% 4.22/4.19 [566]~P3(x5662,x5661)+~P3(x5661,x5662)+E(x5661,x5662)
% 4.22/4.19 [576]~P2(x5761,x5762)+P5(x5761,x5762)+P5(x5762,a27)
% 4.22/4.19 [597]~P2(x5971,x5972)+P5(x5971,x5972)+~P6(a27,x5972)
% 4.22/4.19 [639]~P2(x6392,x6391)+~P6(x6391,x6392)+~P6(a27,x6391)
% 4.22/4.19 [804]~P6(x8041,x8042)+~P9(x8041,a27,x8042)+~P6(a27,x8041)
% 4.22/4.19 [436]~E(x4362,a43)+E(x4361,a44)+E(f34(x4362,x4361),a43)
% 4.22/4.19 [438]~E(x4382,a44)+E(x4381,a44)+E(f35(x4382,x4381),a44)
% 4.22/4.19 [439]~E(x4392,a26)+~E(x4391,a26)+E(f42(x4391,x4392),a26)
% 4.22/4.19 [480]E(x4801,a44)+E(x4802,a26)+~E(f35(x4802,x4801),a26)
% 4.22/4.19 [494]~P1(x4941)+E(x4941,a27)+~E(f31(x4941,x4942),a27)
% 4.22/4.19 [498]~P1(x4982)+~E(x4981,a44)+~E(f31(x4982,x4981),a27)
% 4.22/4.19 [553]~P1(x5532)+~P1(x5531)+P1(f20(x5531,x5532))
% 4.22/4.19 [554]~P1(x5542)+~P1(x5541)+P1(f30(x5541,x5542))
% 4.22/4.19 [555]~P1(x5552)+~P1(x5551)+P1(f40(x5551,x5552))
% 4.22/4.19 [556]~P1(x5562)+~P1(x5561)+P1(f19(x5561,x5562))
% 4.22/4.19 [557]~P13(x5572)+~P13(x5571)+P13(f40(x5571,x5572))
% 4.22/4.19 [648]P5(x6481,x6482)+P5(x6481,a1)+~P8(f23(x6481),f23(x6482))
% 4.22/4.19 [649]~P6(x6491,x6492)+~P6(a1,x6492)+P10(f23(x6491),f23(x6492))
% 4.22/4.19 [673]E(x6731,a44)+P10(a44,x6732)+~P10(a44,f35(x6732,x6731))
% 4.22/4.19 [676]~P6(x6762,x6761)+~P10(f23(x6762),f23(x6761))+P6(a1,x6761)
% 4.22/4.19 [679]~P5(a27,x6792)+~P5(a27,x6791)+P5(a27,f30(x6791,x6792))
% 4.22/4.19 [680]~P5(a27,x6802)+~P5(a27,x6801)+P5(a27,f40(x6801,x6802))
% 4.22/4.19 [681]~P6(a24,x6811)+~P10(a44,x6812)+P6(a24,f31(x6811,x6812))
% 4.22/4.19 [682]~P12(a25,x6821)+~P10(a44,x6822)+P12(a25,f34(x6821,x6822))
% 4.22/4.19 [683]~P12(a43,x6832)+~P12(a43,x6831)+P12(a43,f41(x6831,x6832))
% 4.22/4.19 [684]~P12(a43,x6841)+~P10(a44,x6842)+P12(a43,f10(x6841,x6842))
% 4.22/4.19 [685]~P10(a26,x6851)+~P10(a44,x6852)+P10(a26,f35(x6851,x6852))
% 4.22/4.19 [693]P11(x6932,x6931)+P9(x6931,a27,x6932)+E(f19(x6931,x6932),f2(a4))
% 4.22/4.19 [714]~P11(x7142,x7141)+P9(x7141,a27,x7142)+E(f19(x7141,x7142),a24)
% 4.22/4.19 [715]P6(a27,x7151)+~P6(a27,x7152)+~P6(a27,f40(x7152,x7151))
% 4.22/4.19 [638]P6(x6381,a1)+~P6(x6382,a1)+E(f33(f23(x6381),f23(x6382)),f23(x6381))
% 4.22/4.19 [651]~E(x6512,a43)+~E(x6511,a43)+E(f32(f41(x6511,x6511),f41(x6512,x6512)),a43)
% 4.22/4.19 [686]~P12(a43,x6861)+~P10(a44,x6862)+E(f34(f10(x6861,x6862),x6862),x6861)
% 4.22/4.19 [687]P6(x6871,a1)+P6(x6872,a1)+E(f33(f23(x6871),f23(x6872)),f23(f30(x6871,x6872)))
% 4.22/4.19 [720]~P5(a1,x7202)+~P5(a1,x7201)+E(f33(f23(x7201),f23(x7202)),f23(f30(x7201,x7202)))
% 4.22/4.19 [721]~P5(a1,x7212)+~P5(a1,x7211)+E(f42(f23(x7211),f23(x7212)),f23(f40(x7211,x7212)))
% 4.22/4.19 [880]~E(x8802,a43)+~E(x8801,a43)+P7(f32(f41(x8801,x8801),f41(x8802,x8802)),a43)
% 4.22/4.19 [886]~P6(x8861,a24)+~P6(a27,x8861)+P6(f40(x8861,f31(x8861,x8862)),f31(x8861,x8862))
% 4.22/4.19 [887]~P12(x8871,a25)+~P12(a43,x8871)+P12(f41(x8871,f34(x8871,x8872)),f34(x8871,x8872))
% 4.22/4.19 [888]~P10(x8881,a26)+~P10(a44,x8881)+P10(f42(x8881,f35(x8881,x8882)),f35(x8881,x8882))
% 4.22/4.19 [925]~E(x9251,a43)+~E(x9252,a43)+~P12(a43,f32(f41(x9252,x9252),f41(x9251,x9251)))
% 4.22/4.19 [963]~P9(x9631,a24,x9632)+~P9(x9631,f2(a4),x9632)+~P6(f2(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x9632)
% 4.22/4.19 [985]P5(x9851,x9852)+~P5(a27,x9852)+~P5(f31(x9851,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x9852,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [987]P7(x9871,x9872)+~P7(a43,x9872)+~P7(f34(x9871,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x9872,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [989]P8(x9891,x9892)+~P8(a44,x9892)+~P8(f35(x9891,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f35(x9892,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [977]~E(x9772,a43)+~E(x9771,a43)+E(f32(f34(x9771,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x9772,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),a43)
% 4.22/4.19 [992]~P1(x9921)+E(x9921,a27)+~P5(f31(x9921,f42(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x9922)),a27)
% 4.22/4.19 [996]~E(x9962,a43)+~E(x9961,a43)+P7(f32(f34(x9961,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x9962,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),a43)
% 4.22/4.19 [1004]~E(x10041,a43)+~E(x10042,a43)+~P12(a43,f32(f34(x10042,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x10041,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))))
% 4.22/4.19 [624]~P5(x6241,x6243)+P5(x6241,x6242)+~P5(x6243,x6242)
% 4.22/4.19 [625]~P7(x6251,x6253)+P7(x6251,x6252)+~P7(x6253,x6252)
% 4.22/4.19 [559]~P1(x5591)+~E(f20(x5591,x5593),x5592)+E(x5591,f30(x5592,x5593))
% 4.22/4.19 [567]E(x5671,x5672)+~E(f41(x5673,x5671),f41(x5673,x5672))+E(x5673,a43)
% 4.22/4.19 [568]E(x5681,x5682)+~E(f41(x5681,x5683),f41(x5682,x5683))+E(x5683,a43)
% 4.22/4.19 [640]E(x6401,x6402)+~P6(a24,x6403)+~E(f31(x6403,x6401),f31(x6403,x6402))
% 4.22/4.19 [641]E(x6411,x6412)+~P12(a25,x6413)+~E(f34(x6413,x6411),f34(x6413,x6412))
% 4.22/4.19 [642]E(x6421,x6422)+~P10(a26,x6423)+~E(f35(x6423,x6421),f35(x6423,x6422))
% 4.22/4.19 [678]P3(x6782,x6783)+~P3(f35(x6782,x6781),x6783)+E(x6781,a44)
% 4.22/4.19 [689]~P2(x6891,x6892)+~P10(a44,x6893)+P2(x6891,f31(x6892,x6893))
% 4.22/4.19 [694]~P14(x6941)+P2(x6941,x6942)+~P2(x6941,f31(x6942,x6943))
% 4.22/4.19 [728]P2(x7281,x7282)+~P2(x7281,x7283)+~P2(x7281,f20(x7282,x7283))
% 4.22/4.19 [729]P3(x7291,x7292)+~P3(x7291,x7293)+~P3(x7291,f33(x7293,x7292))
% 4.22/4.19 [759]~P8(x7592,x7593)+~P5(a24,x7591)+P5(f31(x7591,x7592),f31(x7591,x7593))
% 4.22/4.19 [760]~P8(x7602,x7603)+~P6(a24,x7601)+P5(f31(x7601,x7602),f31(x7601,x7603))
% 4.22/4.19 [761]~P5(x7611,x7613)+~P5(a27,x7611)+P5(f31(x7611,x7612),f31(x7613,x7612))
% 4.22/4.19 [762]~P6(x7622,x7623)+~P6(a27,x7621)+P6(f40(x7621,x7622),f40(x7621,x7623))
% 4.22/4.19 [764]~P10(x7642,x7643)+~P6(a24,x7641)+P6(f31(x7641,x7642),f31(x7641,x7643))
% 4.22/4.19 [765]~P8(x7652,x7653)+~P7(a25,x7651)+P7(f34(x7651,x7652),f34(x7651,x7653))
% 4.22/4.19 [766]~P8(x7662,x7663)+~P12(a25,x7661)+P7(f34(x7661,x7662),f34(x7661,x7663))
% 4.22/4.19 [767]~P7(x7671,x7673)+~P7(a43,x7671)+P7(f34(x7671,x7672),f34(x7673,x7672))
% 4.22/4.19 [768]~P7(x7682,x7683)+~P12(a43,x7681)+P7(f41(x7681,x7682),f41(x7681,x7683))
% 4.22/4.19 [769]~P7(x7691,x7693)+~P12(a43,x7692)+P7(f41(x7691,x7692),f41(x7693,x7692))
% 4.22/4.19 [771]~P10(x7712,x7713)+~P12(a25,x7711)+P12(f34(x7711,x7712),f34(x7711,x7713))
% 4.22/4.19 [772]~P12(x7721,x7723)+~P12(a43,x7722)+P12(f41(x7721,x7722),f41(x7723,x7722))
% 4.22/4.19 [773]~P12(x7732,x7733)+~P12(a43,x7731)+P12(f41(x7731,x7732),f41(x7731,x7733))
% 4.22/4.19 [774]~P8(x7742,x7743)+~P8(a26,x7741)+P8(f35(x7741,x7742),f35(x7741,x7743))
% 4.22/4.19 [775]~P8(x7752,x7753)+~P10(a26,x7751)+P8(f35(x7751,x7752),f35(x7751,x7753))
% 4.22/4.19 [776]~P8(x7761,x7763)+~P8(a44,x7761)+P8(f35(x7761,x7762),f35(x7763,x7762))
% 4.22/4.19 [778]~P10(x7782,x7783)+~P10(a26,x7781)+P10(f35(x7781,x7782),f35(x7781,x7783))
% 4.22/4.19 [796]P3(x7962,x7963)+~P3(f35(x7962,x7961),f35(x7963,x7961))+E(x7961,a44)
% 4.22/4.19 [797]P3(x7972,x7973)+~P3(f42(x7972,x7971),f42(x7973,x7971))+E(x7971,a44)
% 4.22/4.19 [837]P6(x8371,x8372)+~P5(a27,x8372)+~P6(f31(x8371,x8373),f31(x8372,x8373))
% 4.22/4.19 [838]P7(x8381,x8382)+~P7(f41(x8383,x8381),f41(x8383,x8382))+~P12(a43,x8383)
% 4.22/4.19 [839]P7(x8391,x8392)+~P7(f41(x8391,x8393),f41(x8392,x8393))+~P12(a43,x8393)
% 4.22/4.19 [840]P12(x8401,x8402)+~P7(a43,x8402)+~P12(f34(x8401,x8403),f34(x8402,x8403))
% 4.22/4.19 [841]P12(x8411,x8412)+~P12(f41(x8411,x8413),f41(x8412,x8413))+~P12(a43,x8413)
% 4.22/4.19 [843]P8(x8431,x8432)+~P5(f31(x8433,x8431),f31(x8433,x8432))+~P6(a24,x8433)
% 4.22/4.19 [845]P8(x8451,x8452)+~P7(f34(x8453,x8451),f34(x8453,x8452))+~P12(a25,x8453)
% 4.22/4.19 [847]P8(x8471,x8472)+~P8(f35(x8473,x8471),f35(x8473,x8472))+~P10(a26,x8473)
% 4.22/4.19 [848]P8(x8481,x8482)+~P3(f35(x8483,x8481),f35(x8483,x8482))+~P10(a26,x8483)
% 4.22/4.19 [850]P10(x8501,x8502)+~P6(f31(x8503,x8501),f31(x8503,x8502))+~P6(a24,x8503)
% 4.22/4.19 [852]P10(x8521,x8522)+~P12(f34(x8523,x8521),f34(x8523,x8522))+~P12(a25,x8523)
% 4.22/4.19 [854]P10(x8541,x8542)+~P10(f35(x8543,x8541),f35(x8543,x8542))+~P10(a26,x8543)
% 4.22/4.19 [855]P10(x8551,x8552)+~P10(f35(x8553,x8551),f35(x8553,x8552))+~P10(a44,x8553)
% 4.22/4.19 [856]P10(x8561,x8562)+~P8(a44,x8562)+~P10(f35(x8561,x8563),f35(x8562,x8563))
% 4.22/4.19 [916]~P1(x9162)+~P9(x9161,x9162,x9163)+P1(f9(x9161,x9162,x9163))
% 4.22/4.19 [953]~P1(x9533)+~P9(x9531,x9533,x9532)+E(f30(x9531,f40(x9532,f9(x9531,x9533,x9532))),x9533)
% 4.22/4.19 [964]~P9(f31(f2(a4),x9641),f31(f2(a4),x9642),x9643)+E(f31(f2(a4),x9641),f31(f2(a4),x9642))+~P6(f2(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x9643)
% 4.22/4.19 [974]P11(x9741,x9742)+~P1(x9743)+~P9(f31(x9743,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),x9742,x9741)
% 4.22/4.19 [975]~P2(x9752,x9753)+P9(x9751,a27,x9752)+~P9(f31(x9753,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),x9751,x9752)
% 4.22/4.19 [924]~P9(x9241,x9244,x9243)+P9(x9241,x9242,x9243)+~P9(x9244,x9242,x9243)
% 4.22/4.19 [782]~P5(x7822,x7824)+~P6(x7821,x7823)+P6(f30(x7821,x7822),f30(x7823,x7824))
% 4.22/4.19 [783]~P8(x7832,x7834)+~P2(x7831,x7833)+P2(f31(x7831,x7832),f31(x7833,x7834))
% 4.22/4.19 [784]~P8(x7842,x7844)+~P3(x7841,x7843)+P3(f35(x7841,x7842),f35(x7843,x7844))
% 4.22/4.19 [785]~P8(x7852,x7854)+~P4(x7851,x7853)+P4(f34(x7851,x7852),f34(x7853,x7854))
% 4.22/4.19 [801]~P8(x8012,x8014)+~P2(f31(x8011,x8014),x8013)+P2(f31(x8011,x8012),x8013)
% 4.22/4.19 [802]~P8(x8022,x8024)+~P3(f35(x8021,x8024),x8023)+P3(f35(x8021,x8022),x8023)
% 4.22/4.19 [803]~P8(x8032,x8034)+~P4(f34(x8031,x8034),x8033)+P4(f34(x8031,x8032),x8033)
% 4.22/4.19 [920]E(x9201,x9202)+E(x9203,x9204)+~E(f32(f41(x9203,x9201),f41(x9204,x9202)),f32(f41(x9203,x9202),f41(x9204,x9201)))
% 4.22/4.19 [921]E(x9211,x9212)+E(x9213,x9214)+~E(f33(f42(x9213,x9211),f42(x9214,x9212)),f33(f42(x9213,x9212),f42(x9214,x9211)))
% 4.22/4.19 [942]~P9(x9422,x9424,x9425)+~P9(x9421,x9423,x9425)+P9(f20(x9421,x9422),f20(x9423,x9424),x9425)
% 4.22/4.19 [943]~P9(x9432,x9434,x9435)+~P9(x9431,x9433,x9435)+P9(f30(x9431,x9432),f30(x9433,x9434),x9435)
% 4.22/4.19 [944]~P9(x9442,x9444,x9445)+~P9(x9441,x9443,x9445)+P9(f40(x9441,x9442),f40(x9443,x9444),x9445)
% 4.22/4.19 [947]~P9(x9472,x9475,x9474)+~P9(x9471,f40(x9475,x9473),x9474)+P9(x9471,f40(x9472,x9473),x9474)
% 4.22/4.19 [948]~P9(x9485,x9482,x9484)+~P9(x9481,f40(x9485,x9483),x9484)+P9(x9481,f40(x9482,x9483),x9484)
% 4.22/4.19 [949]~P9(x9493,x9495,x9494)+~P9(x9491,f40(x9492,x9495),x9494)+P9(x9491,f40(x9492,x9493),x9494)
% 4.22/4.19 [950]~P9(x9505,x9503,x9504)+~P9(x9501,f40(x9502,x9505),x9504)+P9(x9501,f40(x9502,x9503),x9504)
% 4.22/4.19 [945]~P2(x9451,x9454)+~P2(x9451,f30(x9452,x9455))+P2(x9451,f30(f30(x9452,f40(x9453,x9454)),x9455))
% 4.22/4.19 [956]~P2(x9561,x9564)+P2(x9561,f30(x9562,x9563))+~P2(x9561,f30(f30(x9562,f40(x9565,x9564)),x9563))
% 4.22/4.19 [512]~P1(x5121)+P14(x5121)+~P6(a24,x5121)+~E(f17(x5121),a24)
% 4.22/4.19 [530]~P1(x5301)+P14(x5301)+~E(f17(x5301),x5301)+~P6(a24,x5301)
% 4.22/4.19 [543]~P1(x5431)+P14(x5431)+~P6(a24,x5431)+P1(f17(x5431))
% 4.22/4.19 [578]~P1(x5781)+P14(x5781)+~P6(a24,x5781)+P5(a27,f17(x5781))
% 4.22/4.19 [580]~P1(x5801)+P14(x5801)+P2(f17(x5801),x5801)+~P6(a24,x5801)
% 4.22/4.19 [531]~P1(x5312)+~P1(x5311)+~P6(x5311,x5312)+~E(x5311,x5312)
% 4.22/4.19 [579]~P1(x5792)+~P1(x5791)+~P6(x5791,x5792)+P5(x5791,x5792)
% 4.22/4.19 [652]~E(x6521,x6522)+~P1(x6522)+~P1(x6521)+P9(x6521,x6522,a27)
% 4.22/4.19 [727]~P1(x7272)+~P1(x7271)+E(x7271,x7272)+~P9(x7271,x7272,a27)
% 4.22/4.19 [479]~P1(x4792)+~E(x4792,a27)+E(x4791,a44)+E(f31(x4792,x4791),a27)
% 4.22/4.19 [490]~P1(x4902)+~P1(x4901)+E(x4901,x4902)+~E(f2(x4901),f2(x4902))
% 4.22/4.19 [491]~P1(x4912)+~P1(x4911)+E(x4911,x4912)+~E(f3(x4911),f3(x4912))
% 4.22/4.19 [497]~P1(x4971)+~P1(x4972)+~E(x4972,a27)+E(f30(x4971,x4972),x4971)
% 4.22/4.19 [505]~P1(x5051)+E(x5051,a24)+E(x5051,f2(a4))+~E(f40(x5051,x5052),a24)
% 4.22/4.19 [528]~P1(x5281)+~P1(x5282)+~E(f30(x5282,x5281),x5282)+E(x5281,a27)
% 4.22/4.19 [588]~E(x5881,x5882)+~P1(x5882)+~P1(x5881)+P6(x5881,f30(x5882,a24))
% 4.22/4.19 [633]~P1(x6332)+~P1(x6331)+E(x6331,x6332)+~E(f30(x6331,x6331),f30(x6332,x6332))
% 4.22/4.19 [669]~P1(x6692)+~P1(x6691)+~P6(x6691,x6692)+P6(x6691,f30(x6692,a24))
% 4.22/4.19 [794]~P1(x7942)+~P1(x7941)+E(x7941,a27)+~E(f30(f40(x7942,x7942),f40(x7941,x7941)),a27)
% 4.22/4.19 [795]~P1(x7952)+~P1(x7951)+E(x7951,a27)+~E(f30(f40(x7951,x7951),f40(x7952,x7952)),a27)
% 4.22/4.19 [816]~P1(x8162)+~P1(x8161)+E(x8161,x8162)+~E(f30(f30(a24,x8161),x8161),f30(f30(a24,x8162),x8162))
% 4.22/4.19 [884]~P1(x8842)+~P1(x8841)+E(x8841,a27)+P6(a27,f30(f40(x8842,x8842),f40(x8841,x8841)))
% 4.22/4.19 [885]~P1(x8852)+~P1(x8851)+E(x8851,a27)+P6(a27,f30(f40(x8851,x8851),f40(x8852,x8852)))
% 4.22/4.19 [928]~P1(x9281)+~P1(x9282)+E(x9281,a27)+~P5(f30(f40(x9282,x9282),f40(x9281,x9281)),a27)
% 4.22/4.19 [929]~P1(x9291)+~P1(x9292)+E(x9291,a27)+~P5(f30(f40(x9291,x9291),f40(x9292,x9292)),a27)
% 4.22/4.19 [967]~P3(x9671,x9672)+E(x9671,x9672)+E(x9672,a44)+P8(f42(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x9671),x9672)
% 4.22/4.19 [971]E(x9711,x9712)+~P7(a43,x9712)+~P7(a43,x9711)+~E(f34(x9711,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x9712,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [972]E(x9721,x9722)+~P8(a44,x9722)+~P8(a44,x9721)+~E(f35(x9721,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f35(x9722,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [983]~P1(x9832)+~P1(x9831)+E(x9831,a27)+~E(f30(f31(x9832,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x9831,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),a27)
% 4.22/4.19 [984]~P1(x9842)+~P1(x9841)+E(x9841,a27)+~E(f30(f31(x9841,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x9842,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),a27)
% 4.22/4.19 [997]~P1(x9972)+~P1(x9971)+E(x9971,a27)+P6(a27,f30(f31(x9972,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x9971,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))))
% 4.22/4.19 [998]~P1(x9982)+~P1(x9981)+E(x9981,a27)+P6(a27,f30(f31(x9981,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x9982,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))))
% 4.22/4.19 [1005]~P1(x10051)+~P1(x10052)+E(x10051,a27)+~P5(f30(f31(x10052,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x10051,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),a27)
% 4.22/4.19 [1006]~P1(x10061)+~P1(x10062)+E(x10061,a27)+~P5(f30(f31(x10061,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x10062,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),a27)
% 4.22/4.19 [726]~P14(x7261)+P2(x7261,x7262)+P2(x7261,x7263)+~P2(x7261,f40(x7263,x7262))
% 4.22/4.19 [805]~P1(x8051)+P2(x8052,x8053)+~P2(f40(x8051,x8052),f40(x8051,x8053))+E(x8051,a27)
% 4.22/4.19 [806]~P8(x8063,x8062)+~P5(x8061,a24)+~P5(a27,x8061)+P5(f31(x8061,x8062),f31(x8061,x8063))
% 4.22/4.19 [807]~P10(x8073,x8072)+~P6(x8071,a24)+~P6(a27,x8071)+P6(f31(x8071,x8072),f31(x8071,x8073))
% 4.22/4.19 [808]~P8(x8083,x8082)+~P7(x8081,a25)+~P7(a43,x8081)+P7(f34(x8081,x8082),f34(x8081,x8083))
% 4.22/4.19 [809]~P10(x8093,x8092)+~P12(x8091,a25)+~P12(a43,x8091)+P12(f34(x8091,x8092),f34(x8091,x8093))
% 4.22/4.19 [810]~P8(x8103,x8102)+~P8(x8101,a26)+~P8(a44,x8101)+P8(f35(x8101,x8102),f35(x8101,x8103))
% 4.22/4.19 [811]~P10(x8113,x8112)+~P10(x8111,a26)+~P10(a44,x8111)+P10(f35(x8111,x8112),f35(x8111,x8113))
% 4.22/4.19 [812]~P6(x8121,x8123)+~P5(a27,x8121)+~P10(a44,x8122)+P6(f31(x8121,x8122),f31(x8123,x8122))
% 4.22/4.19 [813]~P12(x8131,x8133)+~P7(a43,x8131)+~P10(a44,x8132)+P12(f34(x8131,x8132),f34(x8133,x8132))
% 4.22/4.19 [814]~P10(x8141,x8143)+~P8(a44,x8141)+~P10(a44,x8142)+P10(f35(x8141,x8142),f35(x8143,x8142))
% 4.22/4.19 [927]~P14(x9272)+P9(x9271,a27,x9272)+P9(x9273,a27,x9272)+~P9(f40(x9273,x9271),a27,x9272)
% 4.22/4.19 [788]~P5(a27,x7882)+~P6(a27,x7883)+P5(x7881,a24)+~E(f30(x7882,f40(x7883,x7881)),x7883)
% 4.22/4.19 [798]~P6(x7982,x7983)+~P6(a27,x7983)+P5(a24,x7981)+~E(f30(x7982,f40(x7983,x7981)),x7983)
% 4.22/4.19 [913]P5(x9131,a27)+~P5(a27,x9132)+~P6(a27,x9133)+~P6(f30(f40(x9133,x9131),x9132),a27)
% 4.22/4.19 [915]~P6(x9152,x9153)+~P6(a27,x9153)+P5(a27,x9151)+~P5(a27,f30(f40(x9153,x9151),x9152))
% 4.22/4.19 [893]~P14(x8931)+P2(x8931,x8932)+~P2(f31(x8931,x8933),f40(x8934,x8932))+P2(f31(x8931,x8933),x8934)
% 4.22/4.19 [894]~P14(x8941)+P2(x8941,x8942)+~P2(f31(x8941,x8943),f40(x8942,x8944))+P2(f31(x8941,x8943),x8944)
% 4.22/4.19 [815]~P10(x8154,x8153)+~P3(x8153,x8151)+~P10(a44,x8154)+~E(x8151,f33(f42(x8152,x8153),x8154))
% 4.22/4.19 [819]~P1(x8192)+~P1(x8194)+P9(x8191,x8192,x8193)+~E(x8192,f30(x8191,f40(x8193,x8194)))
% 4.22/4.19 [926]~P9(x9265,x9262,x9263)+~P9(x9261,x9264,x9263)+P9(x9261,x9262,x9263)+~E(x9264,x9265)
% 4.22/4.19 [817]E(x8171,x8172)+~E(x8174,x8175)+E(x8173,a43)+~E(f32(x8174,f41(x8173,x8171)),f32(x8175,f41(x8173,x8172)))
% 4.22/4.19 [818]E(x8181,x8182)+~E(x8184,x8185)+E(x8183,a44)+~E(f33(x8184,f42(x8183,x8181)),f33(x8185,f42(x8183,x8182)))
% 4.22/4.19 [961]~P1(x9611)+E(x9611,a27)+~P5(a27,x9611)+E(x9611,a24)+~P6(x9611,f2(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))
% 4.22/4.19 [993]~P1(x9931)+~P14(x9931)+E(x9931,f2(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))+E(x9931,f2(f30(f30(a24,f30(f30(a24,a1),a1)),f30(f30(a24,a1),a1))))+P5(f2(f30(f30(a24,f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),x9931)
% 4.22/4.19 [1010]~P1(x10101)+~P5(a27,x10101)+E(x10101,a14)+~P9(a28,x10101,f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))+~P6(x10101,f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))
% 4.22/4.19 [558]P6(x5582,x5581)+P6(x5581,x5582)+~P1(x5582)+~P1(x5581)+E(x5581,x5582)
% 4.22/4.19 [586]P6(x5861,x5862)+~P1(x5862)+~P1(x5861)+~P5(x5861,x5862)+E(x5861,x5862)
% 4.22/4.19 [636]~P1(x6362)+~P1(x6361)+~P5(x6362,x6361)+~P5(x6361,x6362)+E(x6361,x6362)
% 4.22/4.19 [833]~P1(x8331)+~P6(x8331,x8332)+~P9(x8331,a27,x8332)+~P5(a27,x8331)+E(x8331,a27)
% 4.22/4.19 [501]~P1(x5012)+~P1(x5011)+~E(x5012,a24)+~E(x5011,a24)+E(f40(x5011,x5012),a24)
% 4.22/4.19 [532]~P1(x5322)+~P1(x5321)+~E(x5322,f2(a4))+~E(x5321,f2(a4))+E(f40(x5321,x5322),a24)
% 4.22/4.19 [536]~P1(x5361)+~P1(x5362)+E(x5361,a24)+E(x5362,f2(a4))+~E(f40(x5361,x5362),a24)
% 4.22/4.19 [537]~P1(x5371)+~P1(x5372)+E(x5371,a24)+E(x5372,f2(a4))+~E(f40(x5372,x5371),a24)
% 4.22/4.19 [538]~P1(x5382)+~P1(x5381)+E(x5381,a24)+E(x5381,f2(a4))+~E(f40(x5382,x5381),a24)
% 4.22/4.19 [599]~P1(x5992)+~P1(x5991)+~P6(a27,x5992)+E(x5991,a24)+~E(f40(x5992,x5991),a24)
% 4.22/4.19 [600]~P1(x6002)+~P1(x6001)+~P6(a27,x6001)+E(x6001,a24)+~E(f40(x6001,x6002),a24)
% 4.22/4.19 [713]P6(x7131,x7132)+~P1(x7132)+~P1(x7131)+E(x7131,x7132)+~P6(x7131,f30(x7132,a24))
% 4.22/4.19 [732]~P1(x7321)+~P6(x7321,x7322)+~P6(a27,x7321)+P6(x7321,f20(x7322,a24))+E(x7321,f20(x7322,a24))
% 4.22/4.19 [946]~P14(x9462)+P9(x9461,a24,x9462)+P9(x9461,f20(x9462,a24),x9462)+~P6(a27,x9461)+~P9(f40(x9461,x9461),a24,x9462)
% 4.22/4.19 [695]~P1(x6952)+~P1(x6951)+~E(x6952,a27)+~E(x6951,a27)+E(f30(f40(x6951,x6951),f40(x6952,x6952)),a27)
% 4.22/4.19 [890]~P1(x8902)+~P1(x8901)+~E(x8902,a27)+~E(x8901,a27)+P5(f30(f40(x8901,x8901),f40(x8902,x8902)),a27)
% 4.22/4.19 [932]~P1(x9321)+~P1(x9322)+~E(x9321,a27)+~E(x9322,a27)+~P6(a27,f30(f40(x9322,x9322),f40(x9321,x9321)))
% 4.22/4.19 [978]~P1(x9782)+~P1(x9781)+~E(x9782,a27)+~E(x9781,a27)+E(f30(f31(x9781,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x9782,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),a27)
% 4.22/4.19 [999]~P1(x9992)+~P1(x9991)+~E(x9992,a27)+~E(x9991,a27)+P5(f30(f31(x9991,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x9992,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),a27)
% 4.22/4.19 [1007]~P1(x10071)+~P1(x10072)+~E(x10071,a27)+~E(x10072,a27)+~P6(a27,f30(f31(x10072,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x10071,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))))
% 4.22/4.19 [895]~P9(x8952,x8951,x8953)+~P6(x8951,x8952)+~P6(x8952,x8953)+~P6(a27,x8951)+~P6(a27,x8952)
% 4.22/4.19 [757]E(x7571,x7572)+~P7(a43,x7572)+~P7(a43,x7571)+~P10(a44,x7573)+~E(f34(x7571,x7573),f34(x7572,x7573))
% 4.22/4.19 [758]E(x7581,x7582)+~P8(a44,x7582)+~P8(a44,x7581)+~P10(a44,x7583)+~E(f35(x7581,x7583),f35(x7582,x7583))
% 4.22/4.19 [951]P5(x9511,x9512)+~P6(x9513,x9514)+~P6(x9513,x9515)+~P5(x9514,a27)+~P5(f30(f40(x9513,x9512),x9515),f30(f40(x9513,x9511),x9514))
% 4.22/4.19 [952]P5(x9521,x9522)+~P6(x9523,x9524)+~P6(x9525,x9524)+~P5(a27,x9525)+~P5(f30(f40(x9524,x9521),x9525),f30(f40(x9524,x9522),x9523))
% 4.22/4.19 [973]~P1(x9732)+~P1(x9731)+E(x9731,x9732)+~P5(a27,x9732)+~P5(a27,x9731)+~E(f31(x9731,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x9732,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))
% 4.22/4.19 [892]~E(x8921,x8923)+~P1(x8924)+~P1(x8922)+~P1(x8923)+~P1(x8921)+E(f30(f40(x8921,x8922),f40(x8923,x8924)),f30(f40(x8921,x8924),f40(x8923,x8922)))
% 4.22/4.19 [645]~P1(x6452)+~P1(x6451)+~P14(x6452)+~P2(x6451,x6452)+E(x6451,x6452)+E(x6451,a24)+~P5(a27,x6451)
% 4.22/4.19 [733]~P1(x7332)+~P1(x7331)+~P2(x7332,x7331)+~P2(x7331,x7332)+E(x7331,x7332)+~P5(a27,x7332)+~P5(a27,x7331)
% 4.22/4.19 [914]~P1(x9141)+~P14(x9142)+~P6(x9141,x9142)+~P6(a27,x9141)+E(x9141,a24)+E(x9141,f20(x9142,a24))+~P9(f40(x9141,x9141),a24,x9142)
% 4.22/4.19 [799]~P1(x7992)+~P1(x7991)+E(x7991,x7992)+~P5(a27,x7992)+~P5(a27,x7991)+~P10(a44,x7993)+~E(f31(x7991,x7993),f31(x7992,x7993))
% 4.22/4.19 [931]~P1(x9312)+~P1(x9314)+~P1(x9311)+~P1(x9313)+E(x9311,x9312)+E(x9313,x9314)+~E(f30(f40(x9313,x9311),f40(x9314,x9312)),f30(f40(x9313,x9312),f40(x9314,x9311)))
% 4.22/4.19 [883]~P1(x8833)+~P1(x8832)+~P1(x8831)+E(x8831,x8832)+~E(x8834,x8835)+E(x8833,a27)+~E(f30(x8834,f40(x8833,x8831)),f30(x8835,f40(x8833,x8832)))
% 4.22/4.19 [954]~P5(x9545,x9543)+~P6(x9546,x9545)+P5(x9541,x9542)+~P5(a27,x9544)+~P6(a27,x9545)+~E(f30(f40(x9543,x9541),x9544),f30(f40(x9545,x9542),x9546))+~P5(a27,f30(f40(x9545,x9542),x9546))
% 4.22/4.19 [955]~P5(x9555,x9553)+~P6(x9554,x9553)+P5(x9551,x9552)+~P5(a27,x9556)+~P6(a27,x9555)+~E(f30(f40(x9553,x9552),x9554),f30(f40(x9555,x9551),x9556))+~P6(f30(f40(x9555,x9551),x9556),a27)
% 4.22/4.19 [900]~P1(x9002)+~P1(x9001)+~P6(x9001,x9003)+~P9(x9002,x9001,x9003)+E(x9001,x9002)+~P6(x9002,x9003)+~P5(a27,x9002)+~P5(a27,x9001)
% 4.22/4.19 [917]~P1(x9172)+~P1(x9171)+~P6(x9171,x9173)+~P9(x9172,x9171,x9173)+E(x9171,x9172)+~P6(x9172,x9173)+~P6(a27,x9173)+~P6(a27,x9172)+~P6(a27,x9171)
% 4.22/4.19 %EqnAxiom
% 4.22/4.19 [1]E(x11,x11)
% 4.22/4.19 [2]E(x22,x21)+~E(x21,x22)
% 4.22/4.19 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 4.22/4.19 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 4.22/4.19 [5]~E(x51,x52)+E(f30(x51,x53),f30(x52,x53))
% 4.22/4.19 [6]~E(x61,x62)+E(f30(x63,x61),f30(x63,x62))
% 4.22/4.19 [7]~E(x71,x72)+E(f3(x71),f3(x72))
% 4.22/4.19 [8]~E(x81,x82)+E(f23(x81),f23(x82))
% 4.22/4.19 [9]~E(x91,x92)+E(f40(x91,x93),f40(x92,x93))
% 4.22/4.19 [10]~E(x101,x102)+E(f40(x103,x101),f40(x103,x102))
% 4.22/4.19 [11]~E(x111,x112)+E(f31(x111,x113),f31(x112,x113))
% 4.22/4.19 [12]~E(x121,x122)+E(f31(x123,x121),f31(x123,x122))
% 4.22/4.19 [13]~E(x131,x132)+E(f34(x131,x133),f34(x132,x133))
% 4.22/4.19 [14]~E(x141,x142)+E(f34(x143,x141),f34(x143,x142))
% 4.22/4.19 [15]~E(x151,x152)+E(f33(x151,x153),f33(x152,x153))
% 4.22/4.19 [16]~E(x161,x162)+E(f33(x163,x161),f33(x163,x162))
% 4.22/4.19 [17]~E(x171,x172)+E(f35(x171,x173),f35(x172,x173))
% 4.22/4.19 [18]~E(x181,x182)+E(f35(x183,x181),f35(x183,x182))
% 4.22/4.19 [19]~E(x191,x192)+E(f41(x191,x193),f41(x192,x193))
% 4.22/4.19 [20]~E(x201,x202)+E(f41(x203,x201),f41(x203,x202))
% 4.22/4.19 [21]~E(x211,x212)+E(f38(x211),f38(x212))
% 4.22/4.19 [22]~E(x221,x222)+E(f39(x221),f39(x222))
% 4.22/4.19 [23]~E(x231,x232)+E(f21(x231,x233),f21(x232,x233))
% 4.22/4.19 [24]~E(x241,x242)+E(f21(x243,x241),f21(x243,x242))
% 4.22/4.19 [25]~E(x251,x252)+E(f42(x251,x253),f42(x252,x253))
% 4.22/4.19 [26]~E(x261,x262)+E(f42(x263,x261),f42(x263,x262))
% 4.22/4.19 [27]~E(x271,x272)+E(f32(x271,x273),f32(x272,x273))
% 4.22/4.19 [28]~E(x281,x282)+E(f32(x283,x281),f32(x283,x282))
% 4.22/4.19 [29]~E(x291,x292)+E(f20(x291,x293),f20(x292,x293))
% 4.22/4.19 [30]~E(x301,x302)+E(f20(x303,x301),f20(x303,x302))
% 4.22/4.19 [31]~E(x311,x312)+E(f17(x311),f17(x312))
% 4.22/4.19 [32]~E(x321,x322)+E(f19(x321,x323),f19(x322,x323))
% 4.22/4.19 [33]~E(x331,x332)+E(f19(x333,x331),f19(x333,x332))
% 4.22/4.19 [34]~E(x341,x342)+E(f36(x341,x343),f36(x342,x343))
% 4.22/4.19 [35]~E(x351,x352)+E(f36(x353,x351),f36(x353,x352))
% 4.22/4.19 [36]~E(x361,x362)+E(f22(x361,x363),f22(x362,x363))
% 4.22/4.19 [37]~E(x371,x372)+E(f22(x373,x371),f22(x373,x372))
% 4.22/4.19 [38]~E(x381,x382)+E(f10(x381,x383),f10(x382,x383))
% 4.22/4.19 [39]~E(x391,x392)+E(f10(x393,x391),f10(x393,x392))
% 4.22/4.19 [40]~E(x401,x402)+E(f9(x401,x403,x404),f9(x402,x403,x404))
% 4.22/4.19 [41]~E(x411,x412)+E(f9(x413,x411,x414),f9(x413,x412,x414))
% 4.22/4.19 [42]~E(x421,x422)+E(f9(x423,x424,x421),f9(x423,x424,x422))
% 4.22/4.19 [43]~E(x431,x432)+E(f8(x431,x433),f8(x432,x433))
% 4.22/4.19 [44]~E(x441,x442)+E(f8(x443,x441),f8(x443,x442))
% 4.22/4.19 [45]~P1(x451)+P1(x452)+~E(x451,x452)
% 4.22/4.19 [46]P9(x462,x463,x464)+~E(x461,x462)+~P9(x461,x463,x464)
% 4.22/4.19 [47]P9(x473,x472,x474)+~E(x471,x472)+~P9(x473,x471,x474)
% 4.22/4.19 [48]P9(x483,x484,x482)+~E(x481,x482)+~P9(x483,x484,x481)
% 4.22/4.19 [49]P6(x492,x493)+~E(x491,x492)+~P6(x491,x493)
% 4.22/4.19 [50]P6(x503,x502)+~E(x501,x502)+~P6(x503,x501)
% 4.22/4.19 [51]P5(x512,x513)+~E(x511,x512)+~P5(x511,x513)
% 4.22/4.19 [52]P5(x523,x522)+~E(x521,x522)+~P5(x523,x521)
% 4.22/4.19 [53]P11(x532,x533)+~E(x531,x532)+~P11(x531,x533)
% 4.22/4.19 [54]P11(x543,x542)+~E(x541,x542)+~P11(x543,x541)
% 4.22/4.19 [55]~P14(x551)+P14(x552)+~E(x551,x552)
% 4.22/4.19 [56]P7(x562,x563)+~E(x561,x562)+~P7(x561,x563)
% 4.22/4.19 [57]P7(x573,x572)+~E(x571,x572)+~P7(x573,x571)
% 4.22/4.19 [58]P2(x582,x583)+~E(x581,x582)+~P2(x581,x583)
% 4.22/4.19 [59]P2(x593,x592)+~E(x591,x592)+~P2(x593,x591)
% 4.22/4.19 [60]P12(x602,x603)+~E(x601,x602)+~P12(x601,x603)
% 4.22/4.19 [61]P12(x613,x612)+~E(x611,x612)+~P12(x613,x611)
% 4.22/4.19 [62]P8(x622,x623)+~E(x621,x622)+~P8(x621,x623)
% 4.22/4.19 [63]P8(x633,x632)+~E(x631,x632)+~P8(x633,x631)
% 4.22/4.19 [64]P3(x642,x643)+~E(x641,x642)+~P3(x641,x643)
% 4.22/4.19 [65]P3(x653,x652)+~E(x651,x652)+~P3(x653,x651)
% 4.22/4.19 [66]P10(x662,x663)+~E(x661,x662)+~P10(x661,x663)
% 4.22/4.19 [67]P10(x673,x672)+~E(x671,x672)+~P10(x673,x671)
% 4.22/4.19 [68]~P13(x681)+P13(x682)+~E(x681,x682)
% 4.22/4.19 [69]P4(x692,x693)+~E(x691,x692)+~P4(x691,x693)
% 4.22/4.19 [70]P4(x703,x702)+~E(x701,x702)+~P4(x703,x701)
% 4.22/4.19
% 4.22/4.19 %-------------------------------------------
% 4.22/4.20 cnf(1012,plain,
% 4.22/4.20 (P2(x10121,a27)),
% 4.22/4.20 inference(scs_inference,[],[157,71,2,725])).
% 4.22/4.20 cnf(1013,plain,
% 4.22/4.20 (P9(x10131,x10131,x10132)),
% 4.22/4.20 inference(rename_variables,[],[157])).
% 4.22/4.20 cnf(1015,plain,
% 4.22/4.20 (~P12(a1,a27)),
% 4.22/4.20 inference(scs_inference,[],[157,71,2,725,484])).
% 4.22/4.20 cnf(1017,plain,
% 4.22/4.20 (~P6(a24,a37)),
% 4.22/4.20 inference(scs_inference,[],[415,157,71,2,725,484,1001])).
% 4.22/4.20 cnf(1018,plain,
% 4.22/4.20 (~E(f30(f31(x10181,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x10182,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))),
% 4.22/4.20 inference(rename_variables,[],[415])).
% 4.22/4.20 cnf(1019,plain,
% 4.22/4.20 (~E(a37,a24)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,157,71,2,725,484,1001,1000])).
% 4.22/4.20 cnf(1020,plain,
% 4.22/4.20 (~E(f30(f31(x10201,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x10202,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24))),
% 4.22/4.20 inference(rename_variables,[],[415])).
% 4.22/4.20 cnf(1021,plain,
% 4.22/4.20 (P6(x10211,f30(x10211,a24))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,157,71,2,725,484,1001,1000,656])).
% 4.22/4.20 cnf(1022,plain,
% 4.22/4.20 (P5(x10221,x10221)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1024,plain,
% 4.22/4.20 (P6(f20(x10241,a24),x10241)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,157,71,2,725,484,1001,1000,656,655])).
% 4.22/4.20 cnf(1025,plain,
% 4.22/4.20 (P5(x10251,x10251)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1029,plain,
% 4.22/4.20 (P8(f23(a1),f23(x10291))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,157,71,374,2,725,484,1001,1000,656,655,654,564])).
% 4.22/4.20 cnf(1030,plain,
% 4.22/4.20 (P5(x10301,x10301)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1038,plain,
% 4.22/4.20 (~E(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),a44)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,157,71,395,313,312,311,374,2,725,484,1001,1000,656,655,654,564,552,548,475,474])).
% 4.22/4.20 cnf(1041,plain,
% 4.22/4.20 (E(f34(x10411,a26),x10411)),
% 4.22/4.20 inference(rename_variables,[],[127])).
% 4.22/4.20 cnf(1045,plain,
% 4.22/4.20 (~E(x10451,f30(a24,x10451))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,157,71,395,313,312,311,374,127,408,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6])).
% 4.22/4.20 cnf(1046,plain,
% 4.22/4.20 (~E(f30(f30(a24,x10461),x10461),f30(x10462,x10462))),
% 4.22/4.20 inference(rename_variables,[],[408])).
% 4.22/4.20 cnf(1047,plain,
% 4.22/4.20 (~E(f30(a24,x10471),x10471)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,157,71,395,313,312,311,374,127,408,1046,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5])).
% 4.22/4.20 cnf(1053,plain,
% 4.22/4.20 (~P12(f41(x10531,x10531),a43)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,157,71,395,313,312,311,374,127,408,1046,410,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623])).
% 4.22/4.20 cnf(1054,plain,
% 4.22/4.20 (~P12(f32(f41(x10541,x10541),f41(x10542,x10542)),a43)),
% 4.22/4.20 inference(rename_variables,[],[410])).
% 4.22/4.20 cnf(1059,plain,
% 4.22/4.20 (~P5(f30(f30(a24,a1),a1),a1)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,157,71,395,313,312,311,374,127,408,1046,409,410,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618])).
% 4.22/4.20 cnf(1061,plain,
% 4.22/4.20 (~P10(f23(x10611),f23(a1))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,157,71,395,313,312,311,374,127,408,1046,409,410,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692])).
% 4.22/4.20 cnf(1063,plain,
% 4.22/4.20 (~P12(f3(x10631),f3(x10631))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,139,157,71,395,313,312,311,374,127,408,1046,409,410,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691])).
% 4.22/4.20 cnf(1064,plain,
% 4.22/4.20 (P7(x10641,x10641)),
% 4.22/4.20 inference(rename_variables,[],[139])).
% 4.22/4.20 cnf(1067,plain,
% 4.22/4.20 (P5(x10671,x10671)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1069,plain,
% 4.22/4.20 (P13(f39(f36(a29,a24)))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,1030,139,157,71,395,313,312,311,374,389,377,127,408,1046,409,410,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68])).
% 4.22/4.20 cnf(1072,plain,
% 4.22/4.20 (P8(a44,f23(a1))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,1030,139,157,71,395,79,313,312,304,311,374,389,377,127,408,1046,409,410,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62])).
% 4.22/4.20 cnf(1075,plain,
% 4.22/4.20 (P7(x10751,x10751)),
% 4.22/4.20 inference(rename_variables,[],[139])).
% 4.22/4.20 cnf(1077,plain,
% 4.22/4.20 (P7(x10771,x10771)),
% 4.22/4.20 inference(rename_variables,[],[139])).
% 4.22/4.20 cnf(1078,plain,
% 4.22/4.20 (P14(f30(a24,a24))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,1030,139,1064,1075,157,71,395,79,313,312,305,304,300,311,374,389,377,386,127,143,408,1046,409,410,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55])).
% 4.22/4.20 cnf(1080,plain,
% 4.22/4.20 (P5(x10801,x10801)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1082,plain,
% 4.22/4.20 (~E(a27,a4)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,1030,1067,139,1064,1075,157,71,98,107,395,397,398,79,313,312,305,304,300,311,374,389,377,386,127,143,408,1046,409,410,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50])).
% 4.22/4.20 cnf(1083,plain,
% 4.22/4.20 (P6(a1,a24)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,1030,1067,139,1064,1075,157,71,98,106,107,395,397,398,79,313,312,305,304,300,311,374,389,377,386,127,143,408,1046,409,410,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49])).
% 4.22/4.20 cnf(1085,plain,
% 4.22/4.20 (P9(x10851,a27,x10851)),
% 4.22/4.20 inference(rename_variables,[],[156])).
% 4.22/4.20 cnf(1087,plain,
% 4.22/4.20 (P9(x10871,x10871,x10872)),
% 4.22/4.20 inference(rename_variables,[],[157])).
% 4.22/4.20 cnf(1089,plain,
% 4.22/4.20 (P9(x10891,x10891,x10892)),
% 4.22/4.20 inference(rename_variables,[],[157])).
% 4.22/4.20 cnf(1090,plain,
% 4.22/4.20 (P1(f40(f39(f36(x10901,x10902)),f39(f36(x10903,x10904))))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,1030,1067,139,1064,1075,157,1013,1087,156,71,98,106,107,395,397,398,79,313,312,305,304,300,311,374,389,377,386,127,95,143,408,1046,409,410,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45])).
% 4.22/4.20 cnf(1092,plain,
% 4.22/4.20 (~E(a24,a1)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,1030,1067,139,1064,1075,157,1013,1087,156,71,98,106,107,392,395,397,398,79,313,312,305,304,300,311,374,389,377,386,127,95,143,408,1046,409,410,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3])).
% 4.22/4.20 cnf(1093,plain,
% 4.22/4.20 (~P6(a24,a24)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,1030,1067,139,1064,1075,157,1013,1087,156,1085,71,98,106,107,392,395,397,398,79,313,312,305,304,300,311,374,389,377,386,127,95,143,408,1046,409,410,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804])).
% 4.22/4.20 cnf(1094,plain,
% 4.22/4.20 (P9(x10941,a27,x10941)),
% 4.22/4.20 inference(rename_variables,[],[156])).
% 4.22/4.20 cnf(1098,plain,
% 4.22/4.20 (~P14(a37)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,1030,1067,139,1064,1075,157,1013,1087,156,1085,71,89,98,106,107,392,395,397,398,79,313,312,305,304,300,311,374,389,377,386,127,95,143,408,1046,409,410,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485])).
% 4.22/4.20 cnf(1101,plain,
% 4.22/4.20 (P9(x11011,x11011,x11012)),
% 4.22/4.20 inference(rename_variables,[],[157])).
% 4.22/4.20 cnf(1103,plain,
% 4.22/4.20 (P11(x11031,f31(a24,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,1030,1067,139,1064,1075,157,1013,1087,1089,1101,156,1085,71,82,89,98,106,107,392,395,397,398,79,313,312,305,304,300,311,374,389,377,386,127,95,143,408,1046,409,410,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974])).
% 4.22/4.20 cnf(1104,plain,
% 4.22/4.20 (P9(x11041,x11041,x11042)),
% 4.22/4.20 inference(rename_variables,[],[157])).
% 4.22/4.20 cnf(1106,plain,
% 4.22/4.20 (~P10(f35(f23(a1),x11061),f35(f23(a1),x11061))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,1030,1067,139,1064,1075,157,1013,1087,1089,1101,156,1085,71,82,89,98,106,107,392,395,397,398,79,313,312,305,304,300,311,374,389,377,386,127,95,143,408,1046,409,410,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856])).
% 4.22/4.20 cnf(1111,plain,
% 4.22/4.20 (P5(x11111,x11111)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1123,plain,
% 4.22/4.20 (P8(x11231,x11231)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,1030,1067,1080,1111,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,71,82,89,98,106,107,392,395,397,398,399,79,313,312,305,304,300,311,374,389,377,386,127,95,143,408,1046,409,410,1054,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843])).
% 4.22/4.20 cnf(1124,plain,
% 4.22/4.20 (P5(x11241,x11241)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1130,plain,
% 4.22/4.20 (~E(a27,a24)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,1030,1067,1080,1111,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,71,82,83,84,89,98,106,107,392,395,397,398,399,79,313,312,305,304,300,311,374,389,377,386,127,95,143,408,1046,409,410,1054,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531])).
% 4.22/4.20 cnf(1134,plain,
% 4.22/4.20 (P10(f35(a44,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f35(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,138,1022,1025,1030,1067,1080,1111,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,71,82,83,84,85,89,98,106,107,392,395,397,398,399,79,313,312,305,304,300,311,374,389,377,386,127,95,143,408,1046,409,410,1054,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814])).
% 4.22/4.20 cnf(1137,plain,
% 4.22/4.20 (P5(x11371,x11371)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1142,plain,
% 4.22/4.20 (~E(f41(a25,f30(f40(f2(f30(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)),f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),a5),a24)),f41(a25,f30(f31(x11421,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(x11422,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,71,82,83,84,85,89,98,106,107,392,395,397,398,399,79,313,312,305,304,300,311,374,389,377,386,127,95,143,146,149,408,1046,409,410,1054,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817])).
% 4.22/4.20 cnf(1145,plain,
% 4.22/4.20 (~P5(a37,a24)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,71,82,83,84,85,89,97,98,106,107,392,395,397,398,399,79,313,312,305,304,300,311,374,389,377,386,127,95,143,146,149,408,1046,409,410,1054,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636])).
% 4.22/4.20 cnf(1147,plain,
% 4.22/4.20 (E(a15,a14)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,71,82,83,84,85,89,92,97,98,102,106,107,392,395,397,398,399,79,313,312,305,304,300,311,380,374,389,377,386,127,95,143,146,149,408,1046,409,410,1054,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010])).
% 4.22/4.20 cnf(1153,plain,
% 4.22/4.20 (P6(a27,a37)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,1094,71,82,83,84,85,89,92,97,98,102,106,107,392,395,397,398,399,79,313,312,305,304,300,311,380,374,389,377,386,127,95,143,146,149,408,1046,409,410,1054,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500])).
% 4.22/4.20 cnf(1161,plain,
% 4.22/4.20 (~P6(f2(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),a24)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,106,107,392,395,397,398,399,77,79,313,312,305,304,300,311,380,374,370,389,377,386,127,95,143,146,149,408,1046,409,410,1054,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962])).
% 4.22/4.20 cnf(1177,plain,
% 4.22/4.20 (~P12(a43,f34(f3(a1),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,106,107,392,395,397,398,399,77,79,81,313,312,305,304,300,311,380,374,370,389,377,386,127,95,143,146,149,408,1046,409,410,1054,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969])).
% 4.22/4.20 cnf(1191,plain,
% 4.22/4.20 (P3(x11911,f35(x11911,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,106,107,108,392,395,397,398,399,77,79,81,313,312,305,304,300,311,380,374,370,389,377,386,127,95,143,146,149,408,1046,409,410,1054,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631])).
% 4.22/4.20 cnf(1193,plain,
% 4.22/4.20 (P2(x11931,f31(x11931,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,106,107,108,392,395,397,398,399,77,79,81,313,312,305,304,300,311,380,374,370,389,377,386,127,95,143,146,149,408,1046,409,410,1054,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630])).
% 4.22/4.20 cnf(1199,plain,
% 4.22/4.20 (P5(a27,f20(a24,a24))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,106,107,108,392,395,397,398,399,77,79,81,313,312,305,304,300,311,380,374,370,389,377,386,127,95,143,146,149,408,1046,409,410,1054,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626])).
% 4.22/4.20 cnf(1201,plain,
% 4.22/4.20 (P10(a44,f35(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),x12011))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,106,107,108,392,395,397,398,399,77,79,81,313,312,305,304,300,311,380,374,370,389,377,386,127,95,143,146,149,408,1046,409,410,1054,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616])).
% 4.22/4.20 cnf(1203,plain,
% 4.22/4.20 (P8(a44,f35(f23(a1),x12031))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,106,107,108,392,395,397,398,399,77,79,81,313,312,305,304,300,311,380,374,370,389,377,386,127,95,143,146,149,408,1046,409,410,1054,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613])).
% 4.22/4.20 cnf(1205,plain,
% 4.22/4.20 (P12(a43,f34(f32(f34(a25,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x12051,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),x12052))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,106,107,108,392,395,397,398,399,77,79,81,313,312,305,304,300,311,380,374,370,389,377,386,127,95,143,146,149,408,1046,409,410,1054,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611])).
% 4.22/4.20 cnf(1214,plain,
% 4.22/4.20 (P5(x12141,x12141)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1217,plain,
% 4.22/4.20 (P5(x12171,x12171)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1220,plain,
% 4.22/4.20 (P5(x12201,x12201)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1238,plain,
% 4.22/4.20 (~P5(f2(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),a27)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,106,107,108,392,395,397,398,399,401,77,79,81,313,312,305,304,300,311,380,374,370,389,377,386,127,95,143,146,149,408,1046,409,410,1054,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544])).
% 4.22/4.20 cnf(1248,plain,
% 4.22/4.20 (P12(f3(a4),a43)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,311,380,374,370,389,377,386,127,95,143,146,149,408,1046,409,410,1054,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521])).
% 4.22/4.20 cnf(1251,plain,
% 4.22/4.20 (P5(x12511,x12511)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1256,plain,
% 4.22/4.20 (P5(x12561,x12561)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1260,plain,
% 4.22/4.20 (P12(a43,f3(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,311,380,374,370,389,377,386,127,95,143,146,149,408,1046,409,410,1054,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516])).
% 4.22/4.20 cnf(1262,plain,
% 4.22/4.20 (P7(a43,f3(a1))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,311,380,374,370,389,377,386,127,95,143,146,149,408,1046,409,410,1054,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515])).
% 4.22/4.20 cnf(1263,plain,
% 4.22/4.20 (P5(x12631,x12631)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1269,plain,
% 4.22/4.20 (P1(f31(a24,x12691))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,311,380,374,370,389,377,386,127,95,143,146,149,408,1046,409,410,1054,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510])).
% 4.22/4.20 cnf(1277,plain,
% 4.22/4.20 (~E(f35(f32(a44,a25),x12771),a44)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,311,380,374,370,389,377,386,127,95,143,146,149,408,1046,409,410,1054,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469])).
% 4.22/4.20 cnf(1285,plain,
% 4.22/4.20 (E(f40(a24,a24),a24)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,311,380,374,370,389,377,386,127,95,143,146,149,408,1046,409,410,1054,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454])).
% 4.22/4.20 cnf(1329,plain,
% 4.22/4.20 (P7(f3(a1),a25)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,389,377,386,127,95,143,146,149,408,1046,409,410,1054,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863])).
% 4.22/4.20 cnf(1416,plain,
% 4.22/4.20 (P2(x14161,f20(x14162,x14162))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,127,95,143,146,149,408,1046,409,410,1054,344,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800])).
% 4.22/4.20 cnf(1424,plain,
% 4.22/4.20 (~E(f32(f41(x14241,x14241),f41(a25,a25)),a43)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,127,95,143,146,149,408,1046,409,410,1054,344,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746])).
% 4.22/4.20 cnf(1430,plain,
% 4.22/4.20 (P5(f30(f30(a24,a4),a4),a1)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,127,95,143,146,149,408,1046,409,410,1054,344,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739])).
% 4.22/4.20 cnf(1446,plain,
% 4.22/4.20 (P4(f34(x14461,x14462),f34(f34(x14461,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),x14462))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,127,95,143,146,149,408,1046,409,410,1054,344,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712])).
% 4.22/4.20 cnf(1468,plain,
% 4.22/4.20 (P1(f30(f30(a24,a24),a24))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,127,95,143,146,149,408,1046,278,409,410,1054,344,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688])).
% 4.22/4.20 cnf(1476,plain,
% 4.22/4.20 (~P5(a4,f30(a4,a4))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,127,95,143,146,149,408,1046,278,409,410,1054,344,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665])).
% 4.22/4.20 cnf(1480,plain,
% 4.22/4.20 (~P6(f30(a1,a1),a1)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,127,95,143,146,149,408,1046,278,409,410,1054,344,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662])).
% 4.22/4.20 cnf(1516,plain,
% 4.22/4.20 (~P7(f3(a1),f3(a4))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,127,95,143,146,149,408,1046,278,409,410,1054,344,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592])).
% 4.22/4.20 cnf(1518,plain,
% 4.22/4.20 (~P5(f2(a1),f2(a4))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,127,95,143,146,149,408,1046,278,409,410,1054,344,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591])).
% 4.22/4.20 cnf(1524,plain,
% 4.22/4.20 (P12(f3(a27),f3(a24))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,127,95,143,146,149,408,1046,278,409,410,1054,344,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574])).
% 4.22/4.20 cnf(1528,plain,
% 4.22/4.20 (P6(f2(a27),f2(a24))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,127,95,143,146,149,408,1046,278,409,410,1054,344,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572])).
% 4.22/4.20 cnf(1534,plain,
% 4.22/4.20 (P1(f30(a24,a24))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,127,95,143,146,149,408,1046,278,409,410,1054,344,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509])).
% 4.22/4.20 cnf(1542,plain,
% 4.22/4.20 (~P6(f30(f30(a24,a4),a4),f30(f30(a24,a4),a4))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,127,95,143,146,149,408,1046,278,409,410,1054,344,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940])).
% 4.22/4.20 cnf(1544,plain,
% 4.22/4.20 (~P5(f30(f30(a24,a1),a1),f30(f30(a24,a4),a4))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,127,95,143,146,149,408,1046,278,409,410,1054,344,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938])).
% 4.22/4.20 cnf(1578,plain,
% 4.22/4.20 (P7(f3(a27),f3(a1))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,127,95,143,146,149,408,1046,278,409,410,1054,344,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583])).
% 4.22/4.20 cnf(1601,plain,
% 4.22/4.20 (P7(f32(f34(f3(a1),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(f3(a1),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),a43)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,95,143,146,149,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996])).
% 4.22/4.20 cnf(1607,plain,
% 4.22/4.20 (~P6(a27,f31(a1,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,95,143,146,149,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970])).
% 4.22/4.20 cnf(1614,plain,
% 4.22/4.20 (~P2(f30(a24,a24),f20(a24,a27))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,95,143,146,149,405,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728])).
% 4.22/4.20 cnf(1620,plain,
% 4.22/4.20 (P12(a43,f10(f32(f34(a25,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x16201,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,95,143,146,149,405,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728,715,689,684])).
% 4.22/4.20 cnf(1622,plain,
% 4.22/4.20 (P12(a43,f41(f32(f34(a25,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x16221,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),f32(f34(a25,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x16221,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,95,143,146,149,405,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728,715,689,684,683])).
% 4.22/4.20 cnf(1624,plain,
% 4.22/4.20 (P6(a24,f31(f30(a24,a24),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,95,143,146,149,405,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728,715,689,684,683,681])).
% 4.22/4.20 cnf(1628,plain,
% 4.22/4.20 (P5(a27,f30(a24,a24))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,95,143,146,149,405,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728,715,689,684,683,681,680,679])).
% 4.22/4.20 cnf(1636,plain,
% 4.22/4.20 (P1(f40(a24,a24))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,95,143,146,149,405,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728,715,689,684,683,681,680,679,678,557,556,555])).
% 4.22/4.20 cnf(1638,plain,
% 4.22/4.20 (P1(f30(a27,a27))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,95,143,146,149,405,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728,715,689,684,683,681,680,679,678,557,556,555,554])).
% 4.22/4.20 cnf(1640,plain,
% 4.22/4.20 (P1(f20(a24,a24))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,95,143,146,149,405,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728,715,689,684,683,681,680,679,678,557,556,555,554,553])).
% 4.22/4.20 cnf(1644,plain,
% 4.22/4.20 (~E(f31(a24,x16441),a27)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,95,143,146,149,405,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728,715,689,684,683,681,680,679,678,557,556,555,554,553,498,494])).
% 4.22/4.20 cnf(1654,plain,
% 4.22/4.20 (~P8(f35(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f35(f23(a1),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,95,143,146,149,405,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728,715,689,684,683,681,680,679,678,557,556,555,554,553,498,494,480,439,438,436,989])).
% 4.22/4.20 cnf(1656,plain,
% 4.22/4.20 (~P7(f34(f32(f34(a25,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x16561,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(a43,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,95,143,146,149,405,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728,715,689,684,683,681,680,679,678,557,556,555,554,553,498,494,480,439,438,436,989,987])).
% 4.22/4.20 cnf(1658,plain,
% 4.22/4.20 (~P5(f31(a37,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f31(a24,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,95,143,146,149,405,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728,715,689,684,683,681,680,679,678,557,556,555,554,553,498,494,480,439,438,436,989,987,985])).
% 4.22/4.20 cnf(1678,plain,
% 4.22/4.20 (P3(x16781,f35(f35(x16781,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f32(a44,a25)))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,95,143,146,149,405,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728,715,689,684,683,681,680,679,678,557,556,555,554,553,498,494,480,439,438,436,989,987,985,686,676,638,944,943,942,925,916,880,796])).
% 4.22/4.20 cnf(1688,plain,
% 4.22/4.20 (P12(f41(f32(f34(a25,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x16881,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),a43),f41(f32(f34(a25,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x16881,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),f32(f34(a25,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f34(x16881,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,95,143,146,149,405,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728,715,689,684,683,681,680,679,678,557,556,555,554,553,498,494,480,439,438,436,989,987,985,686,676,638,944,943,942,925,916,880,796,785,784,783,782,773])).
% 4.22/4.20 cnf(1702,plain,
% 4.22/4.20 (E(f32(f41(f3(a1),f3(a1)),f41(f3(a1),f3(a1))),a43)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,95,143,146,149,405,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728,715,689,684,683,681,680,679,678,557,556,555,554,553,498,494,480,439,438,436,989,987,985,686,676,638,944,943,942,925,916,880,796,785,784,783,782,773,772,764,762,721,720,687,651])).
% 4.22/4.20 cnf(1706,plain,
% 4.22/4.20 (~E(f30(f30(a24,f30(a24,a24)),f30(a24,a24)),a4)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,394,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,403,95,143,146,149,405,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728,715,689,684,683,681,680,679,678,557,556,555,554,553,498,494,480,439,438,436,989,987,985,686,676,638,944,943,942,925,916,880,796,785,784,783,782,773,772,764,762,721,720,687,651,644,643])).
% 4.22/4.20 cnf(1713,plain,
% 4.22/4.20 (~E(f30(f30(f30(a24,a24),a24),f30(f30(a24,a24),a24)),a1)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,394,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,403,95,143,146,149,405,406,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728,715,689,684,683,681,680,679,678,557,556,555,554,553,498,494,480,439,438,436,989,987,985,686,676,638,944,943,942,925,916,880,796,785,784,783,782,773,772,764,762,721,720,687,651,644,643,640,496,495])).
% 4.22/4.20 cnf(1716,plain,
% 4.22/4.20 (~E(f30(a24,a24),a27)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,394,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,403,95,143,146,149,405,406,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728,715,689,684,683,681,680,679,678,557,556,555,554,553,498,494,480,439,438,436,989,987,985,686,676,638,944,943,942,925,916,880,796,785,784,783,782,773,772,764,762,721,720,687,651,644,643,640,496,495,492])).
% 4.22/4.20 cnf(1718,plain,
% 4.22/4.20 (E(f30(a27,a27),a1)),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,394,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,403,95,143,146,149,405,406,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728,715,689,684,683,681,680,679,678,557,556,555,554,553,498,494,480,439,438,436,989,987,985,686,676,638,944,943,942,925,916,880,796,785,784,783,782,773,772,764,762,721,720,687,651,644,643,640,496,495,492,462])).
% 4.22/4.20 cnf(1722,plain,
% 4.22/4.20 (~P2(f30(a24,a24),f30(f30(a24,f40(x17221,a27)),f40(f30(a24,a24),x17222)))),
% 4.22/4.20 inference(scs_inference,[],[415,1018,1020,138,1022,1025,1030,1067,1080,1111,1124,1137,1214,1217,1220,1251,1256,1263,139,1064,1075,1077,157,1013,1087,1089,1101,1104,156,1085,1094,155,71,82,83,84,85,89,92,97,98,102,104,106,107,108,392,394,395,397,398,399,401,77,79,81,178,176,174,313,312,305,304,300,309,311,380,374,370,376,389,377,386,125,127,1041,403,95,143,146,149,405,406,408,1046,278,409,410,1054,344,342,343,335,2,725,484,1001,1000,656,655,654,564,552,548,475,474,472,471,6,5,667,664,623,620,618,692,691,690,68,67,63,62,59,57,56,55,52,51,50,49,48,47,46,45,3,804,639,485,975,974,856,840,837,776,649,648,855,850,843,559,579,531,497,814,812,818,817,636,1010,866,675,500,499,435,433,962,1003,1002,995,994,991,982,980,969,965,957,882,881,677,632,631,630,629,627,626,616,613,611,610,609,606,603,601,589,577,563,551,550,549,547,546,545,544,542,541,540,535,521,520,519,518,517,516,515,514,513,510,478,477,476,469,467,464,463,454,452,451,449,447,445,444,442,441,432,431,430,429,428,427,423,422,421,420,419,418,864,863,862,861,859,857,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,4,968,923,922,912,911,910,909,889,879,878,877,875,874,873,872,870,869,868,867,800,786,779,748,746,743,741,739,737,736,735,734,731,730,723,712,711,710,708,707,705,704,703,702,699,696,688,671,670,666,665,663,662,661,659,658,657,647,646,637,635,634,622,608,607,605,604,596,595,594,592,591,581,575,574,573,572,570,529,509,465,425,834,940,938,908,906,904,902,899,897,831,829,827,825,823,821,792,790,701,698,583,582,66,61,60,58,924,625,624,597,565,694,1004,996,992,977,970,966,958,728,715,689,684,683,681,680,679,678,557,556,555,554,553,498,494,480,439,438,436,989,987,985,686,676,638,944,943,942,925,916,880,796,785,784,783,782,773,772,764,762,721,720,687,651,644,643,640,496,495,492,462,461,956])).
% 4.22/4.20 cnf(1855,plain,
% 4.22/4.20 (P8(x18551,x18551)),
% 4.22/4.20 inference(rename_variables,[],[1123])).
% 4.22/4.20 cnf(1858,plain,
% 4.22/4.20 (P6(x18581,f30(x18581,a24))),
% 4.22/4.20 inference(rename_variables,[],[1021])).
% 4.22/4.20 cnf(1861,plain,
% 4.22/4.20 (P6(x18611,f30(x18611,a24))),
% 4.22/4.20 inference(rename_variables,[],[1021])).
% 4.22/4.20 cnf(1868,plain,
% 4.22/4.20 (P6(f20(x18681,a24),x18681)),
% 4.22/4.20 inference(rename_variables,[],[1024])).
% 4.22/4.20 cnf(1871,plain,
% 4.22/4.20 (P5(x18711,x18711)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1874,plain,
% 4.22/4.20 (P5(x18741,x18741)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1877,plain,
% 4.22/4.20 (P5(x18771,x18771)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1880,plain,
% 4.22/4.20 (P9(x18801,x18801,x18802)),
% 4.22/4.20 inference(rename_variables,[],[157])).
% 4.22/4.20 cnf(1886,plain,
% 4.22/4.20 (P6(x18861,f30(x18861,a24))),
% 4.22/4.20 inference(rename_variables,[],[1021])).
% 4.22/4.20 cnf(1887,plain,
% 4.22/4.20 (P9(x18871,x18871,x18872)),
% 4.22/4.20 inference(rename_variables,[],[157])).
% 4.22/4.20 cnf(1889,plain,
% 4.22/4.20 (P12(a25,f34(f3(f30(f30(f30(a24,a1),a1),a24)),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))),
% 4.22/4.20 inference(scs_inference,[],[138,1871,1874,157,1880,143,376,313,1123,1021,1858,1861,1024,1476,612,860,858,876,780,742,738,621,617,933,835,53,963,682])).
% 4.22/4.20 cnf(1892,plain,
% 4.22/4.20 (P9(x18921,x18921,x18922)),
% 4.22/4.20 inference(rename_variables,[],[157])).
% 4.22/4.20 cnf(1895,plain,
% 4.22/4.20 (P9(x18951,x18951,x18952)),
% 4.22/4.20 inference(rename_variables,[],[157])).
% 4.22/4.20 cnf(1899,plain,
% 4.22/4.20 (P9(x18991,x18991,x18992)),
% 4.22/4.20 inference(rename_variables,[],[157])).
% 4.22/4.20 cnf(1906,plain,
% 4.22/4.20 (P4(f34(x19061,x19062),f34(f34(x19061,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),x19062))),
% 4.22/4.20 inference(rename_variables,[],[1446])).
% 4.22/4.20 cnf(1909,plain,
% 4.22/4.20 (P3(x19091,f35(f35(x19091,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))),f32(a44,a25)))),
% 4.22/4.20 inference(rename_variables,[],[1678])).
% 4.22/4.20 cnf(1912,plain,
% 4.22/4.20 (P8(x19121,x19121)),
% 4.22/4.20 inference(rename_variables,[],[1123])).
% 4.22/4.20 cnf(1919,plain,
% 4.22/4.20 (P7(x19191,x19191)),
% 4.22/4.20 inference(rename_variables,[],[139])).
% 4.22/4.20 cnf(1922,plain,
% 4.22/4.20 (P6(x19221,f30(x19221,a24))),
% 4.22/4.20 inference(rename_variables,[],[1021])).
% 4.22/4.20 cnf(1925,plain,
% 4.22/4.20 (P5(x19251,x19251)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1941,plain,
% 4.22/4.20 (P5(x19411,x19411)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1948,plain,
% 4.22/4.20 (P7(x19481,x19481)),
% 4.22/4.20 inference(rename_variables,[],[139])).
% 4.22/4.20 cnf(1955,plain,
% 4.22/4.20 (P6(x19551,f30(x19551,a24))),
% 4.22/4.20 inference(rename_variables,[],[1021])).
% 4.22/4.20 cnf(1960,plain,
% 4.22/4.20 (P5(x19601,x19601)),
% 4.22/4.20 inference(rename_variables,[],[138])).
% 4.22/4.20 cnf(1972,plain,
% 4.22/4.20 (~P9(a24,a27,f30(a24,a24))),
% 4.22/4.20 inference(scs_inference,[],[415,91,100,101,379,373,372,256,356,138,1871,1874,1877,1925,1941,139,1919,157,1880,1887,1892,1895,92,370,143,376,98,397,83,313,395,392,82,1123,1855,1416,1446,1678,1534,1722,1640,1656,1654,1106,1021,1858,1861,1886,1922,1024,1047,1029,1614,1468,1161,1012,1628,1716,1713,1706,1199,1476,1147,1153,612,860,858,876,780,742,738,621,617,933,835,53,963,682,950,949,947,852,845,803,802,774,771,766,765,760,759,641,561,460,652,588,961,973,733,787,767,568,567,895,952,761,725,489,654,548,862,800])).
% 4.22/4.20 cnf(1988,plain,
% 4.22/4.20 (P8(f32(a44,a25),f35(f32(a44,a25),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))),
% 4.22/4.21 inference(scs_inference,[],[415,91,100,101,400,379,373,372,256,356,138,1871,1874,1877,1925,1941,139,1919,157,1880,1887,1892,1895,92,370,143,376,98,107,397,83,313,395,392,82,1063,1123,1855,1416,1446,1678,1534,1191,1542,1722,1640,1656,1654,1106,1021,1858,1861,1886,1922,1024,1047,1029,1614,1468,1161,1012,1628,1716,1713,1277,1706,1199,1476,1248,1147,1153,612,860,858,876,780,742,738,621,617,933,835,53,963,682,950,949,947,852,845,803,802,774,771,766,765,760,759,641,561,460,652,588,961,973,733,787,767,568,567,895,952,761,725,489,654,548,862,800,786,699,667,623,620,574,639,511])).
% 4.22/4.21 cnf(1989,plain,
% 4.22/4.21 (~E(f35(f32(a44,a25),x19891),a44)),
% 4.22/4.21 inference(rename_variables,[],[1277])).
% 4.22/4.21 cnf(1990,plain,
% 4.22/4.21 (P3(x19901,f35(x19901,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))),
% 4.22/4.21 inference(rename_variables,[],[1191])).
% 4.22/4.21 cnf(2021,plain,
% 4.22/4.21 (P6(x20211,f30(x20211,a24))),
% 4.22/4.21 inference(rename_variables,[],[1021])).
% 4.22/4.21 cnf(2028,plain,
% 4.22/4.21 (E(f31(a24,x20281),a24)),
% 4.22/4.21 inference(rename_variables,[],[120])).
% 4.22/4.21 cnf(2057,plain,
% 4.22/4.21 (P5(x20571,x20571)),
% 4.22/4.21 inference(rename_variables,[],[138])).
% 4.22/4.21 cnf(2060,plain,
% 4.22/4.21 (~E(f32(f41(x20601,x20601),f41(a25,a25)),a43)),
% 4.22/4.21 inference(rename_variables,[],[1424])).
% 4.22/4.21 cnf(2065,plain,
% 4.22/4.21 (E(f33(x20651,a44),x20651)),
% 4.22/4.21 inference(rename_variables,[],[129])).
% 4.22/4.21 cnf(2070,plain,
% 4.22/4.21 (P5(x20701,f31(x20701,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))),
% 4.22/4.21 inference(rename_variables,[],[344])).
% 4.22/4.21 cnf(2089,plain,
% 4.22/4.21 (E(f33(x20891,a44),x20891)),
% 4.22/4.21 inference(rename_variables,[],[129])).
% 4.22/4.21 cnf(2096,plain,
% 4.22/4.21 (P5(a27,f31(x20961,f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1)))))),
% 4.22/4.21 inference(rename_variables,[],[341])).
% 4.22/4.21 cnf(2124,plain,
% 4.22/4.21 (P11(x21241,a24)),
% 4.22/4.21 inference(scs_inference,[],[415,86,88,91,100,101,400,396,379,378,373,372,371,256,341,356,96,369,387,129,2065,2089,131,113,120,2028,121,216,138,1871,1874,1877,1925,1941,1960,139,1919,157,1880,1887,1892,1895,92,370,403,143,376,344,2070,84,89,98,107,386,397,83,313,395,392,82,1063,1123,1855,1912,1416,1446,1906,1678,1909,1534,1191,1542,1722,1636,1640,1656,1654,1134,1106,1021,1858,1861,1886,1922,1955,2021,1024,1047,1078,1688,1103,1658,1019,1029,1069,1269,1614,1468,1430,1161,1012,1518,1524,1528,1628,1716,1622,1205,1424,1713,1238,1702,1277,1706,1199,1177,1476,1480,1607,1248,1015,1082,1098,1130,1147,1153,612,860,858,876,780,742,738,621,617,933,835,53,963,682,950,949,947,852,845,803,802,774,771,766,765,760,759,641,561,460,652,588,961,973,733,787,767,568,567,895,952,761,725,489,654,548,862,800,786,699,667,623,620,574,639,511,992,966,728,715,689,680,557,556,553,494,785,783,772,643,640,945,921,531,726,1006,998,913,805,795,600,866,500,484,656,601,471,618,425,582,498,764,721,720,687,461,497,636,1010,611,472,684,555,985,507,655,606,552,6,5,664,465,691,690,70,69,67,65,64,60,59,55,54])).
% 4.22/4.21 cnf(2126,plain,
% 4.22/4.21 (E(f42(x21261,a26),x21261)),
% 4.22/4.21 inference(rename_variables,[],[132])).
% 4.22/4.21 cnf(2128,plain,
% 4.22/4.21 (E(f42(x21281,a26),x21281)),
% 4.22/4.21 inference(rename_variables,[],[132])).
% 4.22/4.21 cnf(2145,plain,
% 4.22/4.21 (P6(f20(x21451,a24),x21451)),
% 4.22/4.21 inference(rename_variables,[],[1024])).
% 4.22/4.21 cnf(2204,plain,
% 4.22/4.21 (~E(f35(x22041,f42(a44,a26)),a44)),
% 4.22/4.21 inference(scs_inference,[],[415,86,88,91,100,101,400,396,379,378,373,372,371,256,341,2096,411,356,96,369,387,129,2065,2089,131,132,2126,2128,113,120,2028,121,216,228,138,1871,1874,1877,1925,1941,1960,139,1919,157,1880,1887,1892,1895,92,370,403,143,376,344,2070,84,89,98,107,386,397,83,313,395,392,82,1063,1123,1855,1912,1416,1090,1446,1906,1678,1909,1544,1534,1191,1193,1542,1722,1636,1640,1038,1656,1654,1134,1106,1021,1858,1861,1886,1922,1955,2021,1024,1868,1047,1078,1688,1103,1658,1019,1029,1069,1269,1614,1468,1430,1161,1012,1145,1518,1524,1528,1628,1716,1622,1205,1424,1713,1238,1702,1277,1706,1199,1203,1177,1476,1480,1607,1248,1015,1082,1092,1098,1130,1147,1153,612,860,858,876,780,742,738,621,617,933,835,53,963,682,950,949,947,852,845,803,802,774,771,766,765,760,759,641,561,460,652,588,961,973,733,787,767,568,567,895,952,761,725,489,654,548,862,800,786,699,667,623,620,574,639,511,992,966,728,715,689,680,557,556,553,494,785,783,772,643,640,945,921,531,726,1006,998,913,805,795,600,866,500,484,656,601,471,618,425,582,498,764,721,720,687,461,497,636,1010,611,472,684,555,985,507,655,606,552,6,5,664,465,691,690,70,69,67,65,64,60,59,55,54,52,49,624,975,694,683,679,554,989,676,944,943,942,916,784,782,773,762,495,492,956,559,920,1005,997,984,983,819,788,929,928,885,884,818,817,794,433,476,474])).
% 4.22/4.21 cnf(2205,plain,
% 4.22/4.21 (E(f42(x22051,a26),x22051)),
% 4.22/4.21 inference(rename_variables,[],[132])).
% 4.22/4.21 cnf(2212,plain,
% 4.22/4.21 (E(f33(x22121,a44),x22121)),
% 4.22/4.21 inference(rename_variables,[],[129])).
% 4.22/4.21 cnf(2221,plain,
% 4.22/4.21 (E(f32(a43,x22211),x22211)),
% 4.22/4.21 inference(rename_variables,[],[133])).
% 4.22/4.21 cnf(2224,plain,
% 4.22/4.21 (P6(f20(x22241,a24),x22241)),
% 4.22/4.21 inference(rename_variables,[],[1024])).
% 4.22/4.21 cnf(2230,plain,
% 4.22/4.21 (~P6(a37,a24)),
% 4.22/4.21 inference(scs_inference,[],[415,86,88,91,100,101,400,396,379,378,373,372,371,256,341,2096,411,356,96,369,387,129,2065,2089,2212,131,132,2126,2128,2205,133,113,120,2028,121,216,228,138,1871,1874,1877,1925,1941,1960,139,1919,157,1880,1887,1892,1895,92,370,403,143,376,344,2070,84,89,401,98,107,386,397,83,313,395,392,82,1063,1123,1855,1912,1416,1090,1446,1906,1678,1909,1544,1534,1191,1193,1542,1722,1636,1638,1640,1038,1656,1654,1134,1106,1021,1858,1861,1886,1922,1955,2021,1024,1868,2145,1047,1078,1688,1103,1658,1019,1029,1069,1269,1614,1468,1430,1718,1161,1012,1053,1145,1516,1518,1524,1528,1578,1628,1716,1622,1205,1201,1424,1713,1238,1702,1277,1989,1706,1199,1203,1177,1476,1480,1607,1248,1015,1082,1092,1098,1130,1147,1153,612,860,858,876,780,742,738,621,617,933,835,53,963,682,950,949,947,852,845,803,802,774,771,766,765,760,759,641,561,460,652,588,961,973,733,787,767,568,567,895,952,761,725,489,654,548,862,800,786,699,667,623,620,574,639,511,992,966,728,715,689,680,557,556,553,494,785,783,772,643,640,945,921,531,726,1006,998,913,805,795,600,866,500,484,656,601,471,618,425,582,498,764,721,720,687,461,497,636,1010,611,472,684,555,985,507,655,606,552,6,5,664,465,691,690,70,69,67,65,64,60,59,55,54,52,49,624,975,694,683,679,554,989,676,944,943,942,916,784,782,773,762,495,492,956,559,920,1005,997,984,983,819,788,929,928,885,884,818,817,794,433,476,474,592,583,66,51,48,524,681,438,638,462,953,579])).
% 4.22/4.21 cnf(2236,plain,
% 4.22/4.21 (~P5(f30(x22361,a24),x22361)),
% 4.22/4.21 inference(scs_inference,[],[415,86,88,91,100,101,400,396,379,378,373,372,371,256,341,2096,411,356,96,369,387,129,2065,2089,2212,131,132,2126,2128,2205,133,113,120,2028,121,216,228,138,1871,1874,1877,1925,1941,1960,139,1919,157,1880,1887,1892,1895,92,370,403,143,376,344,2070,84,89,401,98,107,386,97,397,83,313,395,392,82,1063,1123,1855,1912,1416,1090,1446,1906,1678,1909,1544,1534,1191,1193,1542,1722,1636,1638,1640,1038,1656,1654,1134,1106,1021,1858,1861,1886,1922,1955,2021,1024,1868,2145,1047,1078,1688,1103,1658,1017,1019,1029,1069,1269,1614,1468,1430,1718,1161,1012,1053,1145,1516,1518,1524,1528,1578,1628,1716,1622,1205,1201,1424,1713,1238,1702,1277,1989,1706,1199,1203,1177,1476,1480,1607,1248,1015,1082,1092,1098,1130,1147,1153,612,860,858,876,780,742,738,621,617,933,835,53,963,682,950,949,947,852,845,803,802,774,771,766,765,760,759,641,561,460,652,588,961,973,733,787,767,568,567,895,952,761,725,489,654,548,862,800,786,699,667,623,620,574,639,511,992,966,728,715,689,680,557,556,553,494,785,783,772,643,640,945,921,531,726,1006,998,913,805,795,600,866,500,484,656,601,471,618,425,582,498,764,721,720,687,461,497,636,1010,611,472,684,555,985,507,655,606,552,6,5,664,465,691,690,70,69,67,65,64,60,59,55,54,52,49,624,975,694,683,679,554,989,676,944,943,942,916,784,782,773,762,495,492,956,559,920,1005,997,984,983,819,788,929,928,885,884,818,817,794,433,476,474,592,583,66,51,48,524,681,438,638,462,953,579,528,586,627])).
% 4.22/4.21 cnf(2256,plain,
% 4.22/4.21 (E(f30(x22561,x22561),f40(f30(a24,a24),x22561))),
% 4.22/4.21 inference(rename_variables,[],[152])).
% 4.22/4.21 cnf(2271,plain,
% 4.22/4.21 (P7(x22711,x22711)),
% 4.22/4.21 inference(rename_variables,[],[139])).
% 4.22/4.21 cnf(2298,plain,
% 4.22/4.21 (P9(x22981,x22981,x22982)),
% 4.22/4.21 inference(rename_variables,[],[157])).
% 4.22/4.21 cnf(2329,plain,
% 4.22/4.21 (~P10(f35(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),f35(f23(a1),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))),f35(f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))),f35(f23(a1),f23(f30(f30(f30(a24,a1),a1),f30(f30(a24,a1),a1))))))),
% 4.22/4.21 inference(scs_inference,[],[415,86,88,91,100,101,400,396,379,378,373,372,371,256,341,2096,411,356,361,96,302,369,375,387,381,129,2065,2089,2212,131,132,2126,2128,2205,133,2221,136,137,109,113,120,2028,121,140,141,152,2256,216,228,412,138,1871,1874,1877,1925,1941,1960,2057,139,1919,1948,2271,157,1880,1887,1892,1895,1899,2298,92,370,403,342,143,155,376,389,344,2070,84,278,89,401,98,107,386,85,97,397,83,313,395,392,106,82,71,1063,1123,1855,1912,1416,1090,1446,1906,1678,1909,1544,1534,1191,1990,1193,1542,1722,1636,1638,1640,1038,1656,1654,1134,1106,1021,1858,1861,1886,1922,1955,2021,1024,1868,2145,2224,1047,1078,1093,1688,1103,1658,1017,1019,1029,1059,1069,1269,1614,1142,1468,1430,1718,1161,1012,1053,1145,1516,1518,1524,1528,1578,1628,1716,1622,1205,1201,1620,1424,2060,1260,1713,1601,1238,1702,1277,1989,1706,1199,1203,1177,1476,1480,1607,1072,1248,1015,1082,1083,1092,1098,1130,1147,1153,612,860,858,876,780,742,738,621,617,933,835,53,963,682,950,949,947,852,845,803,802,774,771,766,765,760,759,641,561,460,652,588,961,973,733,787,767,568,567,895,952,761,725,489,654,548,862,800,786,699,667,623,620,574,639,511,992,966,728,715,689,680,557,556,553,494,785,783,772,643,640,945,921,531,726,1006,998,913,805,795,600,866,500,484,656,601,471,618,425,582,498,764,721,720,687,461,497,636,1010,611,472,684,555,985,507,655,606,552,6,5,664,465,691,690,70,69,67,65,64,60,59,55,54,52,49,624,975,694,683,679,554,989,676,944,943,942,916,784,782,773,762,495,492,956,559,920,1005,997,984,983,819,788,929,928,885,884,818,817,794,433,476,474,592,583,66,51,48,524,681,438,638,462,953,579,528,586,627,20,565,987,488,68,63,62,61,57,56,50,47,46,3,2,58,45,841,778,927,971,915,713,752,750,749,813,833,558,637,625,576,485,974,856,776,649,648,496,926,798,812,1007,479,978,804,678,837,855])).
% 4.22/4.21 cnf(2355,plain,
% 4.22/4.21 (P10(f23(f30(f30(a24,a4),a4)),f23(f30(f30(a24,a1),a1)))),
% 4.22/4.21 inference(scs_inference,[],[415,86,88,91,100,101,400,396,379,378,373,372,371,256,341,2096,411,356,361,96,302,369,375,387,381,129,2065,2089,2212,131,132,2126,2128,2205,133,2221,136,137,109,113,120,2028,121,140,141,152,2256,216,228,412,138,1871,1874,1877,1925,1941,1960,2057,139,1919,1948,2271,157,1880,1887,1892,1895,1899,2298,92,370,403,342,143,155,376,389,344,2070,84,278,89,401,98,107,386,85,97,397,83,313,395,392,106,82,71,1063,1123,1855,1912,1416,1090,1446,1906,1678,1909,1544,1534,1191,1990,1193,1542,1722,1636,1638,1640,1038,1656,1654,1134,1106,1021,1858,1861,1886,1922,1955,2021,1024,1868,2145,2224,1047,1078,1093,1688,1103,1658,1017,1019,1029,1059,1061,1069,1269,1614,1142,1468,1430,1718,1161,1285,1012,1053,1145,1516,1518,1524,1528,1578,1628,1716,1622,1205,1201,1620,1424,2060,1260,1713,1601,1238,1702,1277,1989,1706,1199,1203,1177,1476,1480,1607,1072,1248,1015,1082,1083,1092,1098,1130,1147,1153,612,860,858,876,780,742,738,621,617,933,835,53,963,682,950,949,947,852,845,803,802,774,771,766,765,760,759,641,561,460,652,588,961,973,733,787,767,568,567,895,952,761,725,489,654,548,862,800,786,699,667,623,620,574,639,511,992,966,728,715,689,680,557,556,553,494,785,783,772,643,640,945,921,531,726,1006,998,913,805,795,600,866,500,484,656,601,471,618,425,582,498,764,721,720,687,461,497,636,1010,611,472,684,555,985,507,655,606,552,6,5,664,465,691,690,70,69,67,65,64,60,59,55,54,52,49,624,975,694,683,679,554,989,676,944,943,942,916,784,782,773,762,495,492,956,559,920,1005,997,984,983,819,788,929,928,885,884,818,817,794,433,476,474,592,583,66,51,48,524,681,438,638,462,953,579,528,586,627,20,565,987,488,68,63,62,61,57,56,50,47,46,3,2,58,45,841,778,927,971,915,713,752,750,749,813,833,558,637,625,576,485,974,856,776,649,648,496,926,798,812,1007,479,978,804,678,837,855,850,843,999,599,932,890,577,692,840,814,501,695,584])).
% 4.22/4.21 cnf(2423,plain,
% 4.22/4.21 ($false),
% 4.22/4.21 inference(scs_inference,[],[71,1012,371,411,100,98,89,397,85,83,313,392,82,1988,2329,2355,1045,2236,1972,1624,2124,2230,1889,2204,1262,1329,1644,1123,1416,1021,1047,1269,1628,1017,1203,1019,1716,1534,758,645,808,852,714,588,713,799,833,952,596,597,558]),
% 4.22/4.21 ['proof']).
% 4.22/4.21 % SZS output end Proof
% 4.22/4.21 % Total time :3.260000s
%------------------------------------------------------------------------------