%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWV633-1 : TPTP v8.2.0. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n028.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 : Mon Jun 24 16:48:05 EDT 2024 % Result : Unsatisfiable 1.37s 1.31s % Output : CNFRefutation 1.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWV633-1 : TPTP v8.2.0. Released v4.1.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.33 % Computer : n028.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Thu Jun 20 17:35:09 EDT 2024 % 0.13/0.33 % CPUTime : % 0.20/0.56 start to proof:theBenchmark % 1.18/1.25 %------------------------------------------- % 1.18/1.25 % File :CSE---1.7 % 1.18/1.25 % Problem :theBenchmark % 1.18/1.25 % Transform :cnf % 1.18/1.25 % Format :tptp:raw % 1.18/1.25 % Command :java -jar mcs_scs.jar %d %s % 1.18/1.25 % 1.18/1.25 % Result :Theorem 0.130000s % 1.18/1.25 % Output :CNFRefutation 0.130000s % 1.18/1.25 %------------------------------------------- % 1.18/1.25 %------------------------------------------------------------------------------ % 1.18/1.25 % File : SWV633-1 : TPTP v8.2.0. Released v4.1.0. % 1.18/1.25 % Domain : Software Verification % 1.18/1.25 % Problem : Fast Fourier Transform 242_5 % 1.18/1.25 % Version : Especial. % 1.18/1.25 % English : Formalization of a functional implementation of the FFT algorithm % 1.18/1.25 % over the complex numbers, and its inverse. Both are shown % 1.18/1.25 % equivalent to the usual definitions of these operations through % 1.18/1.25 % Vandermonde matrices. They are also shown to be inverse to each % 1.18/1.25 % other, more precisely, that composition of the inverse and the % 1.18/1.25 % transformation yield the identity up to a scalar. % 1.18/1.25 % 1.18/1.25 % Refs : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe % 1.18/1.25 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 1.18/1.25 % Source : [Nip10] % 1.18/1.25 % Names : FFT-242_5 [Nip10] % 1.18/1.25 % 1.18/1.25 % Status : Unsatisfiable % 1.18/1.25 % Rating : 0.10 v8.1.0, 0.05 v7.5.0, 0.11 v7.4.0, 0.18 v7.3.0, 0.17 v7.1.0, 0.08 v7.0.0, 0.27 v6.4.0, 0.20 v6.3.0, 0.09 v6.2.0, 0.30 v6.1.0, 0.43 v6.0.0, 0.30 v5.5.0, 0.55 v5.4.0, 0.60 v5.3.0, 0.61 v5.2.0, 0.56 v5.1.0, 0.53 v5.0.0, 0.50 v4.1.0 % 1.18/1.25 % Syntax : Number of clauses : 1484 ( 262 unt; 279 nHn; 947 RR) % 1.18/1.25 % Number of literals : 4436 ( 911 equ;2688 neg) % 1.18/1.25 % Maximal clause size : 7 ( 2 avg) % 1.18/1.25 % Maximal term depth : 7 ( 1 avg) % 1.18/1.25 % Number of predicates : 74 ( 73 usr; 0 prp; 1-3 aty) % 1.18/1.25 % Number of functors : 28 ( 28 usr; 9 con; 0-3 aty) % 1.18/1.25 % Number of variables : 3761 ( 225 sgn) % 1.18/1.25 % SPC : CNF_UNS_RFO_SEQ_NHN % 1.18/1.25 % 1.18/1.25 % Comments : % 1.18/1.25 %------------------------------------------------------------------------------ % 1.18/1.25 cnf(cls_dvd__trans_0,axiom, % 1.18/1.25 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.25 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 1.18/1.25 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 1.18/1.25 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.18/1.25 % 1.18/1.25 cnf(cls_power__mono__even_0,axiom, % 1.18/1.25 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.25 | c_lessequals(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a) % 1.18/1.25 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x,T_a),c_HOL_Oabs__class_Oabs(V_y,T_a),T_a) % 1.18/1.25 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.18/1.25 % 1.18/1.25 cnf(cls_nat__mult__dvd__cancel__disj_1,axiom, % 1.18/1.25 c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),tc_nat) ). % 1.18/1.25 % 1.18/1.25 cnf(cls_dvd__mult__cancel__left_1,axiom, % 1.18/1.25 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.25 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a) ) ). % 1.18/1.25 % 1.18/1.25 cnf(cls_dvd__mult__cancel__right_1,axiom, % 1.18/1.25 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.25 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) ) ). % 1.18/1.25 % 1.18/1.25 cnf(cls_less__trans__Suc_0,axiom, % 1.18/1.25 ( c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat) % 1.18/1.25 | ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) % 1.18/1.26 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_less__Suc__eq_2,axiom, % 1.18/1.26 c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_lessI_0,axiom, % 1.18/1.26 c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_add__left__mono_0,axiom, % 1.18/1.26 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 1.18/1.26 | c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) % 1.18/1.26 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_add__right__mono_0,axiom, % 1.18/1.26 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 1.18/1.26 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) % 1.18/1.26 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_add__le__cancel__left_0,axiom, % 1.18/1.26 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.18/1.26 | c_lessequals(V_a,V_b,T_a) % 1.18/1.26 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_add__le__cancel__left_1,axiom, % 1.18/1.26 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.18/1.26 | c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) % 1.18/1.26 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_add__le__cancel__right_0,axiom, % 1.18/1.26 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.18/1.26 | c_lessequals(V_a,V_b,T_a) % 1.18/1.26 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_add__le__cancel__right_1,axiom, % 1.18/1.26 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.18/1.26 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) % 1.18/1.26 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_abs__eq__mult_0,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.18/1.26 | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) % 1.18/1.26 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.26 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_abs__eq__mult_1,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.18/1.26 | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) % 1.18/1.26 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.26 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_abs__eq__mult_2,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.18/1.26 | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) % 1.18/1.26 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.26 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_abs__eq__mult_3,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.18/1.26 | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) % 1.18/1.26 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.26 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_div__mult1__eq_0,axiom, % 1.18/1.26 c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,tc_nat),V_c,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat),tc_nat),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat),tc_nat),V_c,tc_nat),tc_nat) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_le__eq__neg_0,axiom, % 1.18/1.26 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.26 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.26 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_le__eq__neg_1,axiom, % 1.18/1.26 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.26 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.18/1.26 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_less__add__one_0,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.26 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_divide__le__eq__number__of_9,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.26 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.26 | ~ class_Int_Onumber(T_a) % 1.18/1.26 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.26 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.26 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) % 1.18/1.26 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_divide__le__eq__number__of_3,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.26 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.26 | ~ class_Int_Onumber(T_a) % 1.18/1.26 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.26 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.26 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.26 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_divide__le__eq__number__of_2,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.26 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.26 | ~ class_Int_Onumber(T_a) % 1.18/1.26 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.26 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.26 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.26 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_one__less__inverse__iff_0,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.26 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.26 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.18/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_div__mult__div__if__dvd_0,axiom, % 1.18/1.26 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.26 | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),c_Divides_Odiv__class_Odiv(V_w,V_z,T_a),T_a) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_x,V_w,T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) % 1.18/1.26 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_w,T_a) % 1.18/1.26 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_neg__le__0__iff__le_0,axiom, % 1.18/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.26 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.26 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_neg__le__0__iff__le_1,axiom, % 1.18/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.26 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.26 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_gcd__lcm__complete__lattice__nat_Obot__least_0,axiom, % 1.18/1.26 c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),V_x,tc_nat) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_one__dvd_0,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.26 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_power__0_0,axiom, % 1.18/1.26 ( ~ class_Power_Opower(T_a) % 1.18/1.26 | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_class__semiring_Opwr__0_0,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.26 | c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_nat__mult__div__cancel1_0,axiom, % 1.18/1.26 ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat) % 1.18/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_divide__le__eq__number__of1_2,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.26 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.26 | ~ class_Int_Onumber(T_a) % 1.18/1.26 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.26 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.26 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.26 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_divide__le__eq__number__of1_3,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.26 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.26 | ~ class_Int_Onumber(T_a) % 1.18/1.26 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) % 1.18/1.26 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.26 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.26 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_le__divide__eq__number__of1_2,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.26 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.26 | ~ class_Int_Onumber(T_a) % 1.18/1.26 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.26 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.26 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.26 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_le__divide__eq__number__of1_3,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.26 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.26 | ~ class_Int_Onumber(T_a) % 1.18/1.26 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.26 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.26 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.26 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_power__eq__0__iff_2,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.18/1.26 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.18/1.26 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.18/1.26 | ~ class_Power_Opower(T_a) % 1.18/1.26 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.26 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_power__0__left_1,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 1.18/1.26 | ~ class_Power_Opower(T_a) % 1.18/1.26 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.26 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_even__nat__equiv__def_1,axiom, % 1.18/1.26 ( c_Divides_Odiv__class_Omod(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.26 | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_even__nat__equiv__def_0,axiom, % 1.18/1.26 ( c_Divides_Odiv__class_Omod(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.26 | ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_nat__mult__div__cancel__disj_0,axiom, % 1.18/1.26 c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_div__mult__mult1__if_0,axiom, % 1.18/1.26 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.26 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_abs__less__iff_2,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.26 | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 1.18/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.18/1.26 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_mod__add__self1_0,axiom, % 1.18/1.26 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.26 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_b,V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_mod__add__self2_0,axiom, % 1.18/1.26 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.26 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_mult__le__0__iff_0,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.26 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.26 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.26 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_mult__le__0__iff_1,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.26 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.26 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.26 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_mult__le__0__iff_2,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.26 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.26 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.26 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_mult__le__0__iff_3,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.26 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.26 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.26 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_dvd__refl_0,axiom, % 1.18/1.26 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.26 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_a,T_a) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_dvd_Oeq__iff_0,axiom, % 1.18/1.26 c_Ring__and__Field_Odvd__class_Odvd(V_x,V_x,tc_nat) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_dvd__pos__nat_0,axiom, % 1.18/1.26 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 1.18/1.26 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) % 1.18/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_dvd_Oless__trans_0,axiom, % 1.18/1.26 ( c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat) % 1.18/1.26 | c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat) % 1.18/1.26 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat) % 1.18/1.26 | c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat) % 1.18/1.26 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 1.18/1.26 % 1.18/1.26 cnf(cls_dvd_Oorder__trans_0,axiom, % 1.18/1.26 ( c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat) % 1.18/1.27 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat) % 1.18/1.27 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_abs__of__nonneg_0,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.27 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.18/1.27 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_linorder__neqE__ordered__idom_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.18/1.27 | V_x = V_y ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_not__less__iff__gr__or__eq_0,axiom, % 1.18/1.27 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.27 | V_x = V_y % 1.18/1.27 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_linorder__antisym__conv3_0,axiom, % 1.18/1.27 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.27 | V_x = V_y % 1.18/1.27 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_linorder__less__linear_0,axiom, % 1.18/1.27 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.18/1.27 | V_x = V_y % 1.18/1.27 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_order__antisym__conv_0,axiom, % 1.18/1.27 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.27 | V_x = V_y % 1.18/1.27 | ~ c_lessequals(V_x,V_y,T_a) % 1.18/1.27 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_dvd_Oeq__iff_2,axiom, % 1.18/1.27 ( V_x = V_y % 1.18/1.27 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat) % 1.18/1.27 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_dvd_Oantisym_0,axiom, % 1.18/1.27 ( V_x = V_y % 1.18/1.27 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat) % 1.18/1.27 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_dvd_Oless__le_0,axiom, % 1.18/1.27 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat) % 1.18/1.27 | V_x = V_y % 1.18/1.27 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_dvd__antisym_0,axiom, % 1.18/1.27 ( V_m = V_n % 1.18/1.27 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_n,V_m,tc_nat) % 1.18/1.27 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_nat__neq__iff_0,axiom, % 1.18/1.27 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.18/1.27 | V_m = V_n ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_dvd_Oantisym__conv_0,axiom, % 1.18/1.27 ( V_x = V_y % 1.18/1.27 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) % 1.18/1.27 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_dvd_Ole__neq__trans_0,axiom, % 1.18/1.27 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_a,tc_nat) % 1.18/1.27 | V_a = V_b % 1.18/1.27 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,tc_nat) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_dvd_Oneq__le__trans_0,axiom, % 1.18/1.27 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_a,tc_nat) % 1.18/1.27 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,tc_nat) % 1.18/1.27 | V_a = V_b ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_linorder__neqE__nat_0,axiom, % 1.18/1.27 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 1.18/1.27 | V_x = V_y ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_order__eq__iff_2,axiom, % 1.18/1.27 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.27 | V_x = V_y % 1.18/1.27 | ~ c_lessequals(V_y,V_x,T_a) % 1.18/1.27 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_linorder__neqE_0,axiom, % 1.18/1.27 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.18/1.27 | V_x = V_y ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_order__antisym_0,axiom, % 1.18/1.27 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.27 | V_x = V_y % 1.18/1.27 | ~ c_lessequals(V_y,V_x,T_a) % 1.18/1.27 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_compl__eq__compl__iff_0,axiom, % 1.18/1.27 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.18/1.27 | c_HOL_Ouminus__class_Ouminus(V_x,T_a) != c_HOL_Ouminus__class_Ouminus(V_y,T_a) % 1.18/1.27 | V_x = V_y ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_neg__equal__iff__equal_0,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.27 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(V_b,T_a) % 1.18/1.27 | V_a = V_b ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_eq__divide__imp_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.27 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.27 | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_divide__eq__imp_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.27 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.27 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_estimate__by__abs_0,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.18/1.27 | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_eq__divide__eq_3,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) % 1.18/1.27 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_divide__eq__eq_3,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a % 1.18/1.27 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mod__if_0,axiom, % 1.18/1.27 ( c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = V_m % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_divide__le__0__1__iff_1,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_divide__le__0__1__iff_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_divide__eq__eq__number__of_1,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | ~ class_Int_Onumber(T_a) % 1.18/1.27 | c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) != c_Int_Onumber__class_Onumber__of(V_w,T_a) % 1.18/1.27 | c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_divide__eq__eq__number__of_2,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | ~ class_Int_Onumber(T_a) % 1.18/1.27 | c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.27 | c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_Int_Onumber__class_Onumber__of(V_w,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_abs__le__zero__iff_0,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.27 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_inverse__less__1__iff_1,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.27 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_neg__equal__0__iff__equal_0,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.27 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.27 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_sum__squares__le__zero__iff_2,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.27 | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_div__mult__self2__is__id_0,axiom, % 1.18/1.27 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.27 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = V_a % 1.18/1.27 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_div__mult__self1__is__id_0,axiom, % 1.18/1.27 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.27 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = V_a % 1.18/1.27 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_add__nonpos__neg_0,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_add__neg__nonpos_0,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_neg__less__iff__less_1,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_neg__less__iff__less_0,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_abs__div__pos_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_x,T_a),V_y,T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_le__divide__eq_8,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_divide__le__eq_8,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.18/1.27 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_dvd__1__iff__1_1,axiom, % 1.18/1.27 c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_not__sum__squares__lt__zero_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_one__neq__zero_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.18/1.27 | c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_abs__less__iff_1,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__Suc__right_0,axiom, % 1.18/1.27 c_HOL_Otimes__class_Otimes(V_m,c_Suc(V_n),tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__Suc_0,axiom, % 1.18/1.27 c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_power__less__imp__less__base_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_zero__less__mult__pos2_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_zero__less__mult__pos_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__pos__pos_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__neg__neg_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_nat__0__less__mult__iff_2,axiom, % 1.18/1.27 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_even__less__0__iff_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_even__less__0__iff_1,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_even__nat__equiv__def2_1,axiom, % 1.18/1.27 c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),V_xa,tc_nat),tc_nat) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_diff__divide__distrib_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.27 | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_divide_Odiff_0,axiom, % 1.18/1.27 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.18/1.27 | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(V_x,V_ya,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_ya,T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_number__of__is__id_0,axiom, % 1.18/1.27 c_Int_Onumber__class_Onumber__of(V_k,tc_Int_Oint) = V_k ). % 1.18/1.27 % 1.18/1.27 cnf(cls_div__by__0_0,axiom, % 1.18/1.27 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.27 | c_Divides_Odiv__class_Odiv(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_div__0_0,axiom, % 1.18/1.27 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.27 | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_add__nonneg__eq__0__iff_1,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.18/1.27 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.18/1.27 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_add__nonneg__eq__0__iff_0,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.18/1.27 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.18/1.27 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_add__is__0_0,axiom, % 1.18/1.27 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.27 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_add__is__0_1,axiom, % 1.18/1.27 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.27 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_double__eq__0__iff_0,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.27 | c_HOL_Oplus__class_Oplus(V_a,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.27 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_eq__divide__eq__number__of_1,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | ~ class_Int_Onumber(T_a) % 1.18/1.27 | c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_eq__divide__eq__number__of_2,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | ~ class_Int_Onumber(T_a) % 1.18/1.27 | c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.27 | c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_eq__divide__eq__number__of1_2,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | ~ class_Int_Onumber(T_a) % 1.18/1.27 | c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.27 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_dvd__diff_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.18/1.27 | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a) % 1.18/1.27 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,T_a) % 1.18/1.27 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_eq__iff__diff__eq__0_0,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.18/1.27 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_right__minus__eq_1,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.27 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_diff__0__right_0,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.27 | c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_diff__self_0,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.27 | c_HOL_Ominus__class_Ominus(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_class__ringb_Osubr0__iff_1,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.27 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.27 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_abs__of__neg_0,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.27 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_abs__if_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oabs__if(T_a) % 1.18/1.27 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_abs__if__lattice_0,axiom, % 1.18/1.27 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.27 | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.18/1.27 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__less__imp__less__right_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__less__imp__less__left_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__right__less__imp__less_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__left__less__imp__less_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_div__if_0,axiom, % 1.18/1.27 ( c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__imp__le__div__pos_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | c_lessequals(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__imp__div__pos__le_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) % 1.18/1.27 | ~ c_lessequals(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_le__divide__eq_6,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_le__divide__eq_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.27 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_divide__le__eq_6,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.27 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_divide__le__eq_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_class__ringb_Oadd__r0__iff_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.27 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.27 | V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) % 1.18/1.27 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_natgb_Oadd__r0__iff_0,axiom, % 1.18/1.27 ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) % 1.18/1.27 | V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__neg__pos_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__pos__neg_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__pos__neg2_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_abs__le__D2_0,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.27 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_add__minus__cancel_0,axiom, % 1.18/1.27 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.27 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a),T_a) = V_b ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_pos__add__strict_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mod__mult2__eq_0,axiom, % 1.18/1.27 c_Divides_Odiv__class_Omod(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat),tc_nat),c_Divides_Odiv__class_Omod(V_a,V_b,tc_nat),tc_nat) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_DERIV__inverse__lemma_0,axiom, % 1.18/1.27 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.18/1.27 | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a),V_h,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_h,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a),T_a) % 1.18/1.27 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.27 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_inverse__negative__imp__negative_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_inverse__divide_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_b,V_a,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mod__lemma_0,axiom, % 1.18/1.27 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Omod(V_q,V_c,tc_nat),tc_nat),V_r,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_r,V_b,tc_nat) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_c,tc_nat) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__mono1_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Omult__mono1(T_a) % 1.18/1.27 | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.27 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__left__mono_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 1.18/1.27 | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.27 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__right__mono_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 1.18/1.27 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.18/1.27 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.27 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__left__mono__neg_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.18/1.27 | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.27 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__right__mono__neg_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.18/1.27 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.18/1.27 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_natgb_Oadd__scale__eq__noteq_0,axiom, % 1.18/1.27 ( c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_c,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_d,tc_nat),tc_nat) % 1.18/1.27 | V_c = V_d % 1.18/1.27 | V_r = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.27 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.27 | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_c,T_a),T_a) != c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_d,T_a),T_a) % 1.18/1.27 | V_c = V_d % 1.18/1.27 | V_r = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_sum__squares__eq__zero__iff_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.27 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.27 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_sum__squares__eq__zero__iff_1,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.27 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.27 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_n__not__Suc__n_0,axiom, % 1.18/1.27 V_n != c_Suc(V_n) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_Suc__n__not__n_0,axiom, % 1.18/1.27 c_Suc(V_n) != V_n ). % 1.18/1.27 % 1.18/1.27 cnf(cls_inverse__unique_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.27 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.18/1.27 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_power__le__zero__eq_4,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.27 | c_lessequals(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) % 1.18/1.27 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_power__less__zero__eq_2,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_power__0__left__number__of_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 1.18/1.27 | ~ class_Power_Opower(T_a) % 1.18/1.27 | c_Int_Onumber__class_Onumber__of(V_w,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.27 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_divide__less__eq_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_divide__less__eq_6,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_less__divide__eq_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_less__divide__eq_6,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__imp__div__pos__less_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_mult__imp__less__div__pos_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_abs__minus__one_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.27 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.27 | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_zero__less__divide__iff_0,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_zero__less__divide__iff_1,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_zero__less__divide__iff_2,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.27 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.18/1.27 % 1.18/1.27 cnf(cls_zero__less__divide__iff_3,axiom, % 1.18/1.27 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.27 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__nonneg__neg_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__nonpos__pos_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.18/1.28 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_neg__one__even__power_0,axiom, % 1.18/1.28 ( ~ class_Int_Onumber__ring(T_a) % 1.18/1.28 | c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),V_x,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.18/1.28 | ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_dvd__mult__cancel2_0,axiom, % 1.18/1.28 ( V_n = c_HOL_Oone__class_Oone(tc_nat) % 1.18/1.28 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),V_m,tc_nat) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_dvd__mult__cancel1_0,axiom, % 1.18/1.28 ( V_n = c_HOL_Oone__class_Oone(tc_nat) % 1.18/1.28 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_m,tc_nat) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_power__le__zero__eq_1,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.28 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.28 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) % 1.18/1.28 | ~ c_lessequals(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_mult__strict__mono_H_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_nat__dvd__1__iff__1_0,axiom, % 1.18/1.28 ( V_m = c_HOL_Oone__class_Oone(tc_nat) % 1.18/1.28 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_power__mono__odd_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.28 | c_lessequals(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_x,V_y,T_a) % 1.18/1.28 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_less__SucI_0,axiom, % 1.18/1.28 ( c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_Suc__lessD_0,axiom, % 1.18/1.28 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_inverse__eq__iff__eq_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a) % 1.18/1.28 | V_a = V_b ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_nonzero__inverse__eq__imp__eq_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.28 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a) % 1.18/1.28 | V_a = V_b % 1.18/1.28 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.28 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_inverse__nonzero__iff__nonzero_1,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_inverse__zero_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_less__divide__eq__number__of_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_less__divide__eq__number__of_6,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_le__divide__eq__number__of_6,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_le__divide__eq__number__of_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.28 | ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_le__divide__eq__number__of_7,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_le__divide__eq__number__of_5,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_of__nat__add_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.18/1.28 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),T_a) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__less__power__eq__number__of_3,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.28 | c_Int_Onumber__class_Onumber__of(V_w,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_less__eqI_1,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.28 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_less__eqI_0,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.28 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_le__eqI_1,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.28 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.18/1.28 | c_lessequals(V_y,V_x,T_a) % 1.18/1.28 | ~ c_lessequals(V_y_H,V_x_H,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_le__eqI_0,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.28 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.18/1.28 | c_lessequals(V_y_H,V_x_H,T_a) % 1.18/1.28 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zmod__simps_I2_J_0,axiom, % 1.18/1.28 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.28 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zmod__simps_I1_J_0,axiom, % 1.18/1.28 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.28 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_inf__period_I4_J_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Odvd(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Ocomm__ring(T_a) % 1.18/1.28 | c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_x,c_HOL_Otimes__class_Otimes(V_k,V_D,T_a),T_a),V_t,T_a),T_a) % 1.18/1.28 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a) % 1.18/1.28 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_inf__period_I4_J_1,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Odvd(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Ocomm__ring(T_a) % 1.18/1.28 | c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a) % 1.18/1.28 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_x,c_HOL_Otimes__class_Otimes(V_k,V_D,T_a),T_a),V_t,T_a),T_a) % 1.18/1.28 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_add__is__1_2,axiom, % 1.18/1.28 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.18/1.28 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.28 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_add__is__1_1,axiom, % 1.18/1.28 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.18/1.28 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.18/1.28 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_mod__div__decomp_0,axiom, % 1.18/1.28 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.28 | V_a = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_mod__div__equality_0,axiom, % 1.18/1.28 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.28 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) = V_a ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_mod__div__equality2_0,axiom, % 1.18/1.28 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.28 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) = V_a ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_order__less__le_2,axiom, % 1.18/1.28 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.18/1.28 | V_x = V_y % 1.18/1.28 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_order__le__less_0,axiom, % 1.18/1.28 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.28 | V_x = V_y % 1.18/1.28 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.18/1.28 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_order__le__neq__trans_0,axiom, % 1.18/1.28 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.28 | V_a = V_b % 1.18/1.28 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_order__neq__le__trans_0,axiom, % 1.18/1.28 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.28 | ~ c_lessequals(V_a,V_b,T_a) % 1.18/1.28 | V_a = V_b ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_linorder__antisym__conv1_0,axiom, % 1.18/1.28 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.28 | V_x = V_y % 1.18/1.28 | ~ c_lessequals(V_x,V_y,T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_linorder__antisym__conv2_0,axiom, % 1.18/1.28 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.28 | V_x = V_y % 1.18/1.28 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.18/1.28 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_xt1_I12_J_0,axiom, % 1.18/1.28 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.18/1.28 | ~ c_lessequals(V_b,V_a,T_a) % 1.18/1.28 | V_a = V_b ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_xt1_I11_J_0,axiom, % 1.18/1.28 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.18/1.28 | V_a = V_b % 1.18/1.28 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__right__mono_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.28 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__right__mono__neg_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_inverse__minus__eq_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_split__mult__pos__le_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_split__mult__pos__le_1,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_mult__nonpos__nonpos_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__le__square_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__le__mult__iff_4,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__le__mult__iff_5,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_mult__nonneg__nonneg_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_right__inverse__eq_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.28 | c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.18/1.28 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.28 | V_a = V_b ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_class__ring_Oneg__mul_0,axiom, % 1.18/1.28 ( ~ class_Int_Onumber__ring(T_a) % 1.18/1.28 | c_HOL_Ouminus__class_Ouminus(V_x,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),V_x,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_power__less__zero__eq__number__of_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.28 | ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_abs__triangle__ineq2_0,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_dvd__div__neg_0,axiom, % 1.18/1.28 ( ~ class_Divides_Oring__div(T_a) % 1.18/1.28 | c_Divides_Odiv__class_Odiv(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),T_a) % 1.18/1.28 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_dvd__neg__div_0,axiom, % 1.18/1.28 ( ~ class_Divides_Oring__div(T_a) % 1.18/1.28 | c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),T_a) % 1.18/1.28 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__less__power__eq_1,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.28 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a),T_a) % 1.18/1.28 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__le__eq__number__of1_7,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_le__divide__eq__number__of1_7,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_add__eq__self__zero_0,axiom, % 1.18/1.28 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != V_m % 1.18/1.28 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_of__nat__eq__iff_0,axiom, % 1.18/1.28 ( ~ class_Nat_Osemiring__char__0(T_a) % 1.18/1.28 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) % 1.18/1.28 | V_m = V_n ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_int__int__eq_0,axiom, % 1.18/1.28 ( c_Nat_Osemiring__1__class_Oof__nat(V_m,tc_Int_Oint) != c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Int_Oint) % 1.18/1.28 | V_m = V_n ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_Nat__Transfer_Otransfer__int__nat__relations_I1_J_0,axiom, % 1.18/1.28 ( c_Nat_Osemiring__1__class_Oof__nat(V_x,tc_Int_Oint) != c_Nat_Osemiring__1__class_Oof__nat(V_y,tc_Int_Oint) % 1.18/1.28 | V_x = V_y ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_dvd__power_1,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.28 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_le__divide__eq__number__of_8,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__le__power__eq__number__of_2,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.18/1.28 | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__le__power__eq__number__of_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.18/1.28 | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_mult__eq__1__iff_0,axiom, % 1.18/1.28 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.18/1.28 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_mult__eq__1__iff_1,axiom, % 1.18/1.28 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.18/1.28 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_inverse__le__1__iff_1,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_sum__squares__ge__zero_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__le__divide__1__iff_1,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__le__divide__1__iff_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_dvd__mod__imp__dvd_0,axiom, % 1.18/1.28 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.28 | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) % 1.18/1.28 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) % 1.18/1.28 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_dvd__mod__iff_1,axiom, % 1.18/1.28 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.28 | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) % 1.18/1.28 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) % 1.18/1.28 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_dvd__mod__iff_0,axiom, % 1.18/1.28 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.28 | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) % 1.18/1.28 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) % 1.18/1.28 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_dvd__mod_0,axiom, % 1.18/1.28 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.28 | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) % 1.18/1.28 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) % 1.18/1.28 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_le__add__iff2_1,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_le__add__iff2_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.18/1.28 | c_lessequals(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_le__add__iff1_1,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_le__add__iff1_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__le__0__iff_5,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.28 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__le__0__iff_4,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_termination__basic__simps_I1_J_0,axiom, % 1.18/1.28 ( c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_termination__basic__simps_I2_J_0,axiom, % 1.18/1.28 ( c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_x,V_z,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_add__lessD1_0,axiom, % 1.18/1.28 ( c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_trans__less__add1_0,axiom, % 1.18/1.28 ( c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_trans__less__add2_0,axiom, % 1.18/1.28 ( c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_add__increasing2_0,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.18/1.28 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.18/1.28 | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_b,V_a,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_add__increasing_0,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.18/1.28 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.18/1.28 | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_b,V_c,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_abs__minus__le__zero_0,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_less__add__Suc1_0,axiom, % 1.18/1.28 c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_i,V_m,tc_nat)),tc_nat) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_less__add__Suc2_0,axiom, % 1.18/1.28 c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_i,tc_nat)),tc_nat) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_less__iff__Suc__add_1,axiom, % 1.18/1.28 c_HOL_Oord__class_Oless(V_m,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat)),tc_nat) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_even__nat__div__two__times__two_0,axiom, % 1.18/1.28 ( c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_Divides_Odiv__class_Odiv(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat),tc_nat) = V_x % 1.18/1.28 | ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_power__less__zero__eq_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.28 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_eq__add__iff2_1,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oring(T_a) % 1.18/1.28 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_nat_Osimps_I2_J_0,axiom, % 1.18/1.28 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_Zero__neq__Suc_0,axiom, % 1.18/1.28 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_div__add_0,axiom, % 1.18/1.28 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.28 | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_x,V_z,T_a),c_Divides_Odiv__class_Odiv(V_y,V_z,T_a),T_a) % 1.18/1.28 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,T_a) % 1.18/1.28 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_neg__le__iff__le_0,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.28 | c_lessequals(V_a,V_b,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_le__imp__neg__le_0,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_abs__le__mult_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Olordered__ring(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_power__0__Suc_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 1.18/1.28 | ~ class_Power_Opower(T_a) % 1.18/1.28 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Suc(V_n),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_abs__le__D1_0,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.28 | c_lessequals(V_a,V_b,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_mult__strict__mono_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_inverse__eq__divide_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.28 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_class__fieldgb_Oinverse__divide_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.28 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.28 | c_HOL_Oinverse__class_Oinverse(V_x,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_x,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__less__eq__number__of_4,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__less__eq__number__of_1,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_less__divide__eq__number__of1_9,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__less__eq__number__of1_9,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__less__eq__number__of_8,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__left__mono__neg_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__left__mono_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.28 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__less__power__eq_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.18/1.28 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) % 1.18/1.28 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_frac__less2_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_z,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_w,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_w,V_z,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 1.18/1.28 | ~ c_lessequals(V_x,V_y,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_add__is__1_4,axiom, % 1.18/1.28 c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_power__one__over_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_Suc__eq__plus1__left_0,axiom, % 1.18/1.28 c_Suc(V_n) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_Suc__eq__plus1_0,axiom, % 1.18/1.28 c_Suc(V_n) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_nonzero__minus__divide__right_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.28 | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.18/1.28 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_abs__number__of_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.28 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.28 | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(V_x,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_x,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_neg__less__0__iff__less_1,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_neg__less__0__iff__less_0,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_mod__0_0,axiom, % 1.18/1.28 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.28 | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_dvd__mult__cancel1_1,axiom, % 1.18/1.28 ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 1.18/1.28 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_m,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_dvd__mult__cancel2_1,axiom, % 1.18/1.28 ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 1.18/1.28 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),V_m,tc_nat),V_m,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_less__Suc0_0,axiom, % 1.18/1.28 ( V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_power__le__zero__eq__number__of_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.28 | c_Int_Onumber__class_Onumber__of(V_w,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.28 | ~ c_lessequals(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_abs__triangle__ineq3_0,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_abs__mult__less_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(V_c,V_d,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_b,T_a),V_d,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_c,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_less__divide__eq__number__of1_7,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__less__eq__number__of1_7,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_diff__add__cancel_0,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.28 | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_mod__Suc_1,axiom, % 1.18/1.28 ( c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) % 1.18/1.28 | c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) = V_n ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_inverse__inverse__eq_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_less__divide__eq__number__of1_8,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__less__eq__number__of1_8,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_add__nonneg__eq__0__iff_2,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_add__is__0_2,axiom, % 1.18/1.28 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_double__eq__0__iff_1,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.28 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_mod__add__eq_0,axiom, % 1.18/1.28 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.28 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__le__eq__number__of_1,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__le__eq__number__of_4,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__less__power__eq_2,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.28 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a),T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_xt1_I10_J_0,axiom, % 1.18/1.28 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_order__less__trans_0,axiom, % 1.18/1.28 ( ~ class_Orderings_Opreorder(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_power__less__zero__eq__number__of_2,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_abs__eq__0_1,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.28 | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.18/1.28 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_comm__monoid__add_Omult__assoc_0,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.18/1.28 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_class__semiring_Oadd__a_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.28 | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_nat__add__assoc_0,axiom, % 1.18/1.28 c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_nat__add__left__commute_0,axiom, % 1.18/1.28 c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat),tc_nat) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_add__cancel__21_1,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.18/1.28 | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a) % 1.18/1.28 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.28 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_d,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.28 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_frac__less_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_z,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_w,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_w,V_z,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_add__gr__0_2,axiom, % 1.18/1.28 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_add__gr__0_1,axiom, % 1.18/1.28 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_abs__minus__commute_0,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.28 | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_minus__divide__right_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_minus__divide__left_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.28 | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__le__eq__number__of_6,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.28 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__le__eq__number__of_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | ~ class_Int_Onumber(T_a) % 1.18/1.28 | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_one__le__inverse__iff_2,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_odd__1__nat_0,axiom, % 1.18/1.28 ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oone__class_Oone(tc_nat),tc_nat) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__le__mult__iff_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.28 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__le__mult__iff_1,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.28 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__le__mult__iff_2,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.28 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__le__mult__iff_3,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.28 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_div__1_0,axiom, % 1.18/1.28 c_Divides_Odiv__class_Odiv(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = V_m ). % 1.18/1.28 % 1.18/1.28 cnf(cls_neg__equal__zero_0,axiom, % 1.18/1.28 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.18/1.28 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != V_a % 1.18/1.28 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__less__power__eq_3,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_sum__squares__gt__zero__iff_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_nonzero__inverse__eq__divide_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.28 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 1.18/1.28 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_div__add__self1_0,axiom, % 1.18/1.28 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.28 | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_b,V_a,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.28 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_div__add__self2_0,axiom, % 1.18/1.28 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.28 | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.28 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_abs__one_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.28 | c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_split__div__lemma_2,axiom, % 1.18/1.28 ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_m,c_HOL_Otimes__class_Otimes(V_n,c_Suc(c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)),tc_nat),tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__less__power__eq_5,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.18/1.28 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_diff__frac__eq_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.28 | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) % 1.18/1.28 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.28 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_zero__less__two_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_field__inverse_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.28 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.18/1.28 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_left__inverse_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.28 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.18/1.28 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_right__inverse_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.28 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) % 1.18/1.28 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_mult__mono_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.28 | ~ c_lessequals(V_c,V_d,T_a) % 1.18/1.28 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_mult__mono_H_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 1.18/1.28 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.28 | ~ c_lessequals(V_c,V_d,T_a) % 1.18/1.28 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_root1_0,axiom, % 1.18/1.28 c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_div__mult__mult1_0,axiom, % 1.18/1.28 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.28 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_Divides_Odiv__class_Odiv(V_a,V_b,T_a) % 1.18/1.28 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_div__mult__mult2_0,axiom, % 1.18/1.28 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.28 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_Divides_Odiv__class_Odiv(V_a,V_b,T_a) % 1.18/1.28 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_nat__mult__div__cancel__disj_1,axiom, % 1.18/1.28 ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat) % 1.18/1.28 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_power__inject__base_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.28 | c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) != c_Power_Opower__class_Opower(V_b,c_Suc(V_n),T_a) % 1.18/1.28 | V_a = V_b % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.28 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_div__add1__eq_0,axiom, % 1.18/1.28 c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,V_b,tc_nat),V_c,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_a,V_c,tc_nat),c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat),tc_nat),c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,tc_nat),c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat),tc_nat),V_c,tc_nat),tc_nat) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__less__eq_2,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__less__eq_3,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__less__eq_8,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_divide__less__eq_9,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_less__divide__eq_2,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_less__divide__eq_3,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_less__divide__eq_8,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_less__divide__eq_9,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_even__sum__nat_3,axiom, % 1.18/1.28 ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat),tc_nat) % 1.18/1.28 | c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat) % 1.18/1.28 | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_even__sum__nat_2,axiom, % 1.18/1.28 ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat),tc_nat) % 1.18/1.28 | ~ c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat) % 1.18/1.28 | ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_even__sum__nat_1,axiom, % 1.18/1.28 ( ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) % 1.18/1.28 | c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat) % 1.18/1.28 | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat),tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_even__sum__nat_0,axiom, % 1.18/1.28 ( ~ c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat) % 1.18/1.28 | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) % 1.18/1.28 | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat),tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_even__add_3,axiom, % 1.18/1.28 ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) % 1.18/1.28 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) % 1.18/1.28 | ~ c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_even__add_2,axiom, % 1.18/1.28 ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) % 1.18/1.28 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) % 1.18/1.28 | c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_even__add_1,axiom, % 1.18/1.28 ( c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat) % 1.18/1.28 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) % 1.18/1.28 | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_even__add_0,axiom, % 1.18/1.28 ( c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) % 1.18/1.28 | ~ c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat) % 1.18/1.28 | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_odd__add_3,axiom, % 1.18/1.28 ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) % 1.18/1.28 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) % 1.18/1.28 | ~ c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_odd__add_2,axiom, % 1.18/1.28 ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) % 1.18/1.28 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) % 1.18/1.28 | c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_odd__add_1,axiom, % 1.18/1.28 ( c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat) % 1.18/1.28 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) % 1.18/1.28 | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_odd__add_0,axiom, % 1.18/1.28 ( ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) % 1.18/1.28 | ~ c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat) % 1.18/1.28 | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_not__less__less__Suc__eq_1,axiom, % 1.18/1.28 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_not__less__eq_1,axiom, % 1.18/1.28 ( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_not__less__eq_0,axiom, % 1.18/1.28 ( c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_odd__nat__plus__one__div__two_0,axiom, % 1.18/1.28 ( c_Divides_Odiv__class_Odiv(c_Suc(V_x),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_Suc(c_Divides_Odiv__class_Odiv(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)) % 1.18/1.28 | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_power__Suc__less_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.28 % 1.18/1.28 cnf(cls_mult__less__cancel__left__disj_0,axiom, % 1.18/1.28 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.28 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__less__cancel__right__disj_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mod__minus__eq_0,axiom, % 1.18/1.29 ( ~ class_Divides_Oring__div(T_a) % 1.18/1.29 | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__neg__neg_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__pos__pos_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_zero__less__divide__iff_4,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_zero__less__divide__iff_5,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_one__less__inverse__iff_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_dvd__add_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.29 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_inverse__add_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.29 | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) % 1.18/1.29 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.29 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_division__ring__inverse__add_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.29 | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) % 1.18/1.29 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.29 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_odd__nat__equiv__def_1,axiom, % 1.18/1.29 ( c_Divides_Odiv__class_Omod(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.18/1.29 | ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_odd__nat__equiv__def_0,axiom, % 1.18/1.29 ( c_Divides_Odiv__class_Omod(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.18/1.29 | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_group__add__class_Odiff__0_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.29 | c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_gt__half__sum_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),T_a),V_b,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_less__half__sum_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_add__frac__num_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a),V_y,T_a) % 1.18/1.29 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_add__num__frac_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oplus__class_Oplus(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a),V_y,T_a) % 1.18/1.29 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.29 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_Deriv_Oinverse__diff__inverse_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.29 | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a),T_a) % 1.18/1.29 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.29 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_diff__def_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.18/1.29 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_class__ring_Osub__add_0,axiom, % 1.18/1.29 ( ~ class_Int_Onumber__ring(T_a) % 1.18/1.29 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_diff__minus_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.29 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_ab__diff__minus_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.18/1.29 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_nonzero__minus__divide__divide_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.29 | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) % 1.18/1.29 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_div__dvd__div_0,axiom, % 1.18/1.29 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.29 | c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a) % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_div__dvd__div_1,axiom, % 1.18/1.29 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.29 | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a) % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_dvd__minus__iff_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.18/1.29 | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_dvd__minus__iff_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.18/1.29 | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_minus__dvd__iff_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.18/1.29 | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_minus__dvd__iff_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.18/1.29 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__strict__right__mono_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__strict__right__mono__neg_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_abs__of__nat_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.29 | c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) = c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mod__diff__eq_0,axiom, % 1.18/1.29 ( ~ class_Divides_Oring__div(T_a) % 1.18/1.29 | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__nonneg__pos_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.29 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.29 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_add__gr__0_0,axiom, % 1.18/1.29 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_neg__0__equal__iff__equal_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.29 | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.18/1.29 | c_HOL_Ozero__class_Ozero(T_a) = V_a ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_power__eq__0__iff_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.18/1.29 | ~ class_Power_Opower(T_a) % 1.18/1.29 | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_dvd__1__left_0,axiom, % 1.18/1.29 c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_k,tc_nat) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_abs__triangle__ineq_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_odd__nat__equiv__def2_1,axiom, % 1.18/1.29 ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),V_xa,tc_nat)),tc_nat) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_less__le__not__le_1,axiom, % 1.18/1.29 ( ~ class_Orderings_Opreorder(T_a) % 1.18/1.29 | ~ c_lessequals(V_y,V_x,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_not__leE_0,axiom, % 1.18/1.29 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.18/1.29 | c_lessequals(V_y,V_x,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_linorder__antisym__conv2_1,axiom, % 1.18/1.29 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.29 | ~ c_lessequals(V_x,V_x,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_linorder__antisym__conv1_1,axiom, % 1.18/1.29 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_x,V_x,T_a) % 1.18/1.29 | c_lessequals(V_x,V_x,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_linorder__not__less_1,axiom, % 1.18/1.29 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.18/1.29 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_linorder__not__less_0,axiom, % 1.18/1.29 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.29 | c_lessequals(V_y,V_x,T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_linorder__not__le_0,axiom, % 1.18/1.29 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.18/1.29 | c_lessequals(V_x,V_y,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_linorder__not__le_1,axiom, % 1.18/1.29 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.29 | ~ c_lessequals(V_x,V_y,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_right__inverse__eq_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.29 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.29 | c_HOL_Oinverse__class_Odivide(V_x,V_x,T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__self_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.29 | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.18/1.29 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__self__if_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.18/1.29 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mod__add__right__eq_0,axiom, % 1.18/1.29 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.29 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mod__add__left__eq_0,axiom, % 1.18/1.29 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.29 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_zero__le__divide__iff_3,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_zero__le__divide__iff_2,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_zero__le__divide__iff_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_zero__le__divide__iff_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_add__strict__increasing2_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.18/1.29 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_power__mono_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.29 | c_lessequals(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.29 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_eq__eqI_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.18/1.29 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.18/1.29 | V_x_H = V_y_H ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_eq__eqI_1,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.18/1.29 | c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) % 1.18/1.29 | V_xa = V_y ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_nat__mult__eq__cancel1_0,axiom, % 1.18/1.29 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.18/1.29 | V_m = V_n ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__less__cancel1_0,axiom, % 1.18/1.29 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__less__cancel2_0,axiom, % 1.18/1.29 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_inverse__le__1__iff_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Oone__class_Oone(T_a),V_x,T_a) % 1.18/1.29 | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_power__le__zero__eq_5,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.29 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) % 1.18/1.29 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.29 | c_lessequals(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_power__less__zero__eq_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_power__le__zero__eq_3,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.29 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.29 | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__right__le__imp__le_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.29 | c_lessequals(V_a,V_b,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__left__le__imp__le_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.29 | c_lessequals(V_a,V_b,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__le__cancel__left__pos_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.29 | ~ c_lessequals(V_a,V_b,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__le__cancel__left__pos_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | c_lessequals(V_a,V_b,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__le__cancel__left__neg_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.29 | ~ c_lessequals(V_b,V_a,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__le__cancel__left__neg_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | c_lessequals(V_b,V_a,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_nat__lt__two__imp__zero__or__one_0,axiom, % 1.18/1.29 ( V_x = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.18/1.29 | V_x = c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_minus__divide__divide_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide_Ominus_0,axiom, % 1.18/1.29 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.18/1.29 | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult_Oprod__diff__prod_0,axiom, % 1.18/1.29 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.18/1.29 | c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_zero__le__power__eq_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) % 1.18/1.29 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_zero__le__power__iff_2,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.18/1.29 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_zero__le__even__power_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) % 1.18/1.29 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_gr0__conv__Suc_1,axiom, % 1.18/1.29 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_zero__less__Suc_0,axiom, % 1.18/1.29 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_arith__simps_I31_J_0,axiom, % 1.18/1.29 ( ~ class_Int_Onumber__ring(T_a) % 1.18/1.29 | c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_one__le__inverse__iff_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_one__less__power_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_eq__neg__iff__add__eq__0_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.29 | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_ab__left__minus_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.18/1.29 | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_right__minus_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.29 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_left__minus_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.29 | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_nat__0__less__mult__iff_0,axiom, % 1.18/1.29 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_nat__0__less__mult__iff_1,axiom, % 1.18/1.29 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_add__neg__neg_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_power__strict__mono_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_eq__iff__diff__eq__0_1,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.18/1.29 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.29 | V_a = V_b ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_right__minus__eq_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.29 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.29 | V_a = V_b ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_class__ringb_Osubr0__iff_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.29 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.29 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.29 | V_x = V_y ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_sum__squares__le__zero__iff_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_sum__squares__le__zero__iff_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_Deriv_Oadd__diff__add_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.18/1.29 | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ominus__class_Ominus(V_c,V_d,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__zero__left_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.29 | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__eq__eq_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__zero_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide_Ozero_0,axiom, % 1.18/1.29 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.18/1.29 | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_power__le__zero__eq__number__of_4,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.29 | c_lessequals(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat) % 1.18/1.29 | c_Int_Onumber__class_Onumber__of(V_w,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_inverse__nonpositive__iff__nonpositive_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_inverse__nonpositive__iff__nonpositive_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_dvd__div__mult_0,axiom, % 1.18/1.29 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.29 | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_c,T_a) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),V_a,T_a) % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_Suc__mult__less__cancel1_0,axiom, % 1.18/1.29 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_Suc__mult__less__cancel1_1,axiom, % 1.18/1.29 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_Suc__lessI_0,axiom, % 1.18/1.29 ( c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) % 1.18/1.29 | c_Suc(V_m) = V_n % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_power__even__abs_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.29 | c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_x,T_a),V_n,T_a) = c_Power_Opower__class_Opower(V_x,V_n,T_a) % 1.18/1.29 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_odd__pos_0,axiom, % 1.18/1.29 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.18/1.29 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_power__le__zero__eq__number__of_2,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.29 | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat) % 1.18/1.29 | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_nat__dvd__1__iff__1_1,axiom, % 1.18/1.29 c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_nonzero__number__of__Min_0,axiom, % 1.18/1.29 ( ~ class_Int_Onumber__ring(T_a) % 1.18/1.29 | ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_inverse__eq__1__iff_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oinverse__class_Oinverse(V_x,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.18/1.29 | V_x = c_HOL_Oone__class_Oone(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_inverse__less__1__iff_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_x,T_a) % 1.18/1.29 | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mod__Suc_0,axiom, % 1.18/1.29 ( c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) != V_n % 1.18/1.29 | c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_less__divide__eq__number__of1_6,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_less__divide__eq__number__of1_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__less__eq__number__of1_6,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__less__eq__number__of1_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_abs__diff__less__iff_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_r,T_a),V_x,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_abs__inverse_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_abs__divide_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_abs__of__pos_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.29 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_positive__imp__inverse__positive_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_inverse__positive__iff__positive_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_inverse__positive__iff__positive_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_add__is__1_0,axiom, % 1.18/1.29 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.18/1.29 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.29 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_add__is__1_3,axiom, % 1.18/1.29 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.18/1.29 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.18/1.29 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__nonpos__neg_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__left__le__one__le_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Otimes__class_Otimes(V_y,V_x,T_a),V_x,T_a) % 1.18/1.29 | ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__right__le__one__le_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_x,T_a) % 1.18/1.29 | ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__1_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.29 | c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__self__if_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_abs__leI_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.18/1.29 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_abs__le__iff_2,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.18/1.29 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_root0_0,axiom, % 1.18/1.29 c_FFT__Mirabelle_Oroot(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_abs__minus__cancel_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.29 | c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_nat__add__right__cancel_0,axiom, % 1.18/1.29 ( c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat) != c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat) % 1.18/1.29 | V_m = V_n ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_nat__add__left__cancel_0,axiom, % 1.18/1.29 ( c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) % 1.18/1.29 | V_m = V_n ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_natgb_Oadd__cancel_0,axiom, % 1.18/1.29 ( c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat) != c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat) % 1.18/1.29 | V_y = V_z ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_class__ringb_Oadd__cancel_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.29 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.29 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) % 1.18/1.29 | V_y = V_z ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_add__imp__eq_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a) % 1.18/1.29 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) % 1.18/1.29 | V_b = V_c ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_add__left__cancel_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 1.18/1.29 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) % 1.18/1.29 | V_b = V_c ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_add__right__cancel_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 1.18/1.29 | c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) != c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) % 1.18/1.29 | V_b = V_c ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_minus__one__even__power_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.18/1.29 | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),V_x,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.18/1.29 | ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_not__square__less__zero_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__le__0__iff_4,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__le__0__iff_5,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.29 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_split__mult__neg__le_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_split__mult__neg__le_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.29 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__nonneg__nonpos_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__nonpos__nonneg_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.29 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__nonneg__nonpos2_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_nonzero__inverse__mult__distrib_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.29 | c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.18/1.29 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.29 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_abs__le__zero__iff_1,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_add__nonneg__pos_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_add__pos__nonneg_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_dvd__imp__mod__0_0,axiom, % 1.18/1.29 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.29 | c_Divides_Odiv__class_Omod(V_b,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_dvd__eq__mod__eq__0_1,axiom, % 1.18/1.29 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.29 | c_Divides_Odiv__class_Omod(V_b,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.29 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_dvd__0__left_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.29 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_nonzero__inverse__inverse__eq_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.29 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a % 1.18/1.29 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_of__nat__0_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.18/1.29 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_zero__less__power__eq_4,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) % 1.18/1.29 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.29 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__less__eq__number__of_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__less__eq__number__of_6,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__le__eq__number__of1_8,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) % 1.18/1.29 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_le__divide__eq__number__of1_8,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__le__eq_5,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__le__eq_7,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_le__divide__eq_5,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.29 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_le__divide__eq_7,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.29 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_one__less__mult_0,axiom, % 1.18/1.29 ( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_add__Suc__shift_0,axiom, % 1.18/1.29 c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_of__nat__Suc_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.18/1.29 | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(V_m),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_one__is__add_3,axiom, % 1.18/1.29 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) % 1.18/1.29 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.18/1.29 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_one__is__add_0,axiom, % 1.18/1.29 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) % 1.18/1.29 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.29 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_zero__neq__one_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.18/1.29 | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_of__nat__1_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.18/1.29 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_one__is__add_5,axiom, % 1.18/1.29 c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_dvd_Oless__trans_1,axiom, % 1.18/1.29 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat) % 1.18/1.29 | c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat) % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat) % 1.18/1.29 | c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat) % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_neg__0__le__iff__le_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.29 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_neg__0__le__iff__le_1,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.18/1.29 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mod__less__divisor_0,axiom, % 1.18/1.29 ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_n,tc_nat) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__less__eq__number__of1_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__less__eq__number__of1_4,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_less__divide__eq__number__of1_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_less__divide__eq__number__of1_4,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_nonzero__abs__inverse_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) % 1.18/1.29 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_nonzero__abs__divide_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) % 1.18/1.29 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_inverse__positive__imp__positive_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.29 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mod__diff__left__eq_0,axiom, % 1.18/1.29 ( ~ class_Divides_Oring__div(T_a) % 1.18/1.29 | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mod__diff__right__eq_0,axiom, % 1.18/1.29 ( ~ class_Divides_Oring__div(T_a) % 1.18/1.29 | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__less__eq__number__of1_2,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__less__eq__number__of1_3,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_less__divide__eq__number__of1_2,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_less__divide__eq__number__of1_3,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_zero__le__power__eq__number__of_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),T_a) % 1.18/1.29 | ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_add__cancel__21_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.18/1.29 | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != c_HOL_Oplus__class_Oplus(V_y,V_u,T_a) % 1.18/1.29 | c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) = V_u ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_odd__nat__div__two__times__two__plus__one_0,axiom, % 1.18/1.29 ( c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_Divides_Odiv__class_Odiv(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat),tc_nat)) = V_x % 1.18/1.29 | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_gr__implies__not0_0,axiom, % 1.18/1.29 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_not__less0_0,axiom, % 1.18/1.29 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_nat__number__of__Min_0,axiom, % 1.18/1.29 c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_power__Suc__less__one_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_inverse__less__imp__less_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_less__imp__inverse__less_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_inverse__less__imp__less__neg_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_less__imp__inverse__less__neg_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_zero__le__power__abs_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_a,T_a),V_n,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_add__nonneg__nonneg_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_add__mono_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) % 1.18/1.29 | ~ c_lessequals(V_c,V_d,T_a) % 1.18/1.29 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_inverse__nonnegative__iff__nonnegative_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_inverse__nonnegative__iff__nonnegative_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_div__Suc_0,axiom, % 1.18/1.29 c_Divides_Odiv__class_Odiv(c_Suc(V_a),V_c,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_a,V_c,tc_nat),c_Divides_Odiv__class_Odiv(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_c,tc_nat),tc_nat),c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,tc_nat),c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_c,tc_nat),tc_nat),V_c,tc_nat),tc_nat) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_power__0__left_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 1.18/1.29 | ~ class_Power_Opower(T_a) % 1.18/1.29 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_power__le__zero__eq__number__of_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.29 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.29 | ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat) % 1.18/1.29 | ~ c_lessequals(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__less__0__1__iff_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__less__0__1__iff_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_DERIV__mult__lemma_0,axiom, % 1.18/1.29 ( ~ class_RealVector_Oreal__field(T_a) % 1.18/1.29 | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_c,V_d,T_a),T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_b,V_d,T_a),V_h,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_a,V_c,T_a),V_h,T_a),V_d,T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mod__mod__trivial_0,axiom, % 1.18/1.29 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.29 | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_div__self_0,axiom, % 1.18/1.29 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.29 | c_Divides_Odiv__class_Odiv(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.18/1.29 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_abs__diff__triangle__ineq_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_c,T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_b,V_d,T_a),T_a),T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_add__strict__increasing_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.18/1.29 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.18/1.29 | ~ c_lessequals(V_b,V_c,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_div__mult__self__is__m_0,axiom, % 1.18/1.29 ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_n,tc_nat) = V_m % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_div__mult__self1__is__m_0,axiom, % 1.18/1.29 ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),V_n,tc_nat) = V_m % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_zero__le__power__iff_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_zero__le__power_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_div__less_0,axiom, % 1.18/1.29 ( c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_sum__squares__gt__zero__iff_2,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a) % 1.18/1.29 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_sum__squares__gt__zero__iff_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a) % 1.18/1.29 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_of__nat__less__0__iff_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__less__0__iff_3,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__less__0__iff_2,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__less__0__iff_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__less__0__iff_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_power__eq__imp__eq__base_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.29 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_Power_Opower__class_Opower(V_b,V_n,T_a) % 1.18/1.29 | V_a = V_b % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_add__cancel__end_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.18/1.29 | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != V_y % 1.18/1.29 | V_x = c_HOL_Ouminus__class_Ouminus(V_z,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__divide__mult__cancel__right_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) % 1.18/1.29 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__divide__mult__cancel__left_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) % 1.18/1.29 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_even__Suc_0,axiom, % 1.18/1.29 ( ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) % 1.18/1.29 | ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(V_x),tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_even__Suc_1,axiom, % 1.18/1.29 ( c_Parity_Oeven__odd__class_Oeven(c_Suc(V_x),tc_nat) % 1.18/1.29 | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_dvd__1__iff__1_0,axiom, % 1.18/1.29 ( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_abs__power__minus__one_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.29 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.29 | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),V_n,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_le__divide__eq__number__of1_6,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_le__divide__eq__number__of1_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.29 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__le__eq__number__of1_6,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.29 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_divide__le__eq__number__of1_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.29 | ~ class_Int_Onumber(T_a) % 1.18/1.29 | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.29 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_dvd__mult__div__cancel_0,axiom, % 1.18/1.29 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.29 | c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),T_a) = V_b % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_dvd__div__mult__self_0,axiom, % 1.18/1.29 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.29 | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_a,T_a) = V_b % 1.18/1.29 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_abs__of__nonpos_0,axiom, % 1.18/1.29 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.29 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.18/1.29 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__strict__left__mono__comm_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__less__cancel__right__disj_5,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__less__cancel__right__disj_4,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__strict__right__mono_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__strict__right__mono__neg_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__less__cancel__left__disj_5,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__less__cancel__left__disj_4,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__strict__left__mono_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__strict__left__mono__neg_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__less__cancel__left__pos_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__less__cancel__left__pos_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__less__cancel__left__neg_1,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_mult__less__cancel__left__neg_0,axiom, % 1.18/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.29 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.29 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.29 % 1.18/1.29 cnf(cls_nat__mult__less__cancel1_1,axiom, % 1.18/1.30 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_nat__mult__less__cancel1_0,axiom, % 1.18/1.30 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__less__mono1_0,axiom, % 1.18/1.30 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_k,tc_nat),tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__less__mono2_0,axiom, % 1.18/1.30 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_j,tc_nat),tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__less__cancel1_2,axiom, % 1.18/1.30 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__less__cancel2_2,axiom, % 1.18/1.30 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_diff__minus__eq__add_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.30 | c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mod__mult__self2_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mod__mult__self1_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mod__mult__self3_0,axiom, % 1.18/1.30 c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),V_m,tc_nat),V_n,tc_nat) = c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_power__le__zero__eq__number__of_5,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.30 | ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat) % 1.18/1.30 | c_Int_Onumber__class_Onumber__of(V_w,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.30 | c_lessequals(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_dvd__mult__cancel__right_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.30 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) % 1.18/1.30 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_dvd__mult__cancel__left_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.30 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) % 1.18/1.30 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_nat__mult__dvd__cancel__disj_0,axiom, % 1.18/1.30 ( c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) % 1.18/1.30 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_zero__le__imp__of__nat_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_of__nat__0__le__iff_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_monoid__add__class_Oadd__0__right_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_add__0__left_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_comm__monoid__add_Omult__1__right_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__ringb_Oadd__r0__iff_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.30 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.30 | V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__semiring_Oadd__0_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = V_x ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_comm__monoid__add_Omult__1_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_natgb_Oadd__r0__iff_1,axiom, % 1.18/1.30 V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_Nat_Oadd__0__right_0,axiom, % 1.18/1.30 c_HOL_Oplus__class_Oplus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ). % 1.18/1.30 % 1.18/1.30 cnf(cls_plus__nat_Oadd__0_0,axiom, % 1.18/1.30 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_le__divide__eq_9,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.30 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_le__divide__eq_3,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.30 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_le__divide__eq_2,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.30 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__le__eq_9,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.18/1.30 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__le__eq_3,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__le__eq_2,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_add__diff__cancel_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.30 | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_add__divide__distrib_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide_Oadd_0,axiom, % 1.18/1.30 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.18/1.30 | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_ya,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_ya,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_abs__diff__less__iff_2,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_a,V_r,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_r,T_a),V_x,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__1__mult_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Otimes__class_Otimes(V_m,V_n,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_n,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_m,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_minus__equation__iff_1,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.30 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_equation__minus__iff_1,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.30 | V_a = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_equation__minus__iff_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.30 | V_b = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_double__compl_0,axiom, % 1.18/1.30 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.18/1.30 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = V_x ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_minus__minus_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.30 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_div__by__1_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_Divides_Odiv__class_Odiv(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_minus__diff__eq_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.18/1.30 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_add__less__le__mono_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) % 1.18/1.30 | ~ c_lessequals(V_c,V_d,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_add__le__less__mono_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.18/1.30 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_Suc__mono_0,axiom, % 1.18/1.30 ( c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_Suc__less__eq_0,axiom, % 1.18/1.30 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__Suc__eq__0__disj_3,axiom, % 1.18/1.30 ( c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_x,V_n,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_minus__less__iff_1,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_minus__less__iff_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__minus__iff_1,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__minus__iff_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_minus__le__iff_1,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_minus__le__iff_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_le__minus__iff_1,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.30 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.18/1.30 | ~ c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_le__minus__iff_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.30 | c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.18/1.30 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_dvd_Ole__less__trans_1,axiom, % 1.18/1.30 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat) % 1.18/1.30 | c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_dvd_Oless__le__trans_1,axiom, % 1.18/1.30 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat) % 1.18/1.30 | c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_lemma__not__even__div2_0,axiom, % 1.18/1.30 ( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Suc(c_Divides_Odiv__class_Odiv(V_n,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)) % 1.18/1.30 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_Suc__n__div__2__gt__zero_0,axiom, % 1.18/1.30 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mod__mult__mult2_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mod__mult__mult1_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_c,c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_le__minus__self__iff_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.30 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_le__minus__self__iff_1,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.30 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.18/1.30 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_minus__le__self__iff_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_minus__le__self__iff_1,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__eq__neg__nonpos_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.18/1.30 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__eq__neg__nonpos_1,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.18/1.30 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.18/1.30 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_neg__less__eq__nonneg_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_neg__less__eq__nonneg_1,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_eq__add__iff1_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oring(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_neg__power__if_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.18/1.30 | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_n,T_a) = c_Power_Opower__class_Opower(V_x,V_n,T_a) % 1.18/1.30 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__le__eq__number__of_8,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) % 1.18/1.30 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_one__le__power_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_abs__idempotent_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.30 | c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_add__Suc_0,axiom, % 1.18/1.30 c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_add__Suc__right_0,axiom, % 1.18/1.30 c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_eq__add__iff1_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oring(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) = V_d ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_eq__add__iff2_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oring(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a) % 1.18/1.30 | V_c = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_div__mod__equality_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_div__mod__equality2_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_zero__less__abs__iff_1,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) % 1.18/1.30 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__le__eq__number__of1_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__le__eq__number__of1_4,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_le__divide__eq__number__of1_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.30 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_le__divide__eq__number__of1_4,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_power__strict__decreasing_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_N,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_number__of__Min_0,axiom, % 1.18/1.30 ( ~ class_Int_Onumber__ring(T_a) % 1.18/1.30 | c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__less__eq__number__of_5,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__less__eq__number__of_7,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__less__eq__number__of1_5,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__divide__eq__number__of1_5,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_Suc__times__mod__eq_0,axiom, % 1.18/1.30 ( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)),V_k,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),V_k,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__less__eq__number__of_2,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__less__eq__number__of_3,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__less__eq__number__of_9,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_complex__i__not__one_0,axiom, % 1.18/1.30 c_Complex_Oii != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mod__by__0_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mod__self_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__add__eq__less_0,axiom, % 1.18/1.30 ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_nat__add__commute_0,axiom, % 1.18/1.30 c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__semiring_Oadd__c_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_y,V_x,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_comm__monoid__add_Omult__commute_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__le__0__iff_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__le__0__iff_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.30 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__le__0__iff_2,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__le__0__iff_3,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.30 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_inverse__le__imp__le_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | c_lessequals(V_b,V_a,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_le__imp__inverse__le_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.30 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_inverse__le__imp__le__neg_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | c_lessequals(V_b,V_a,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_le__imp__inverse__le__neg_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mod__div__trivial_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mod__minus__cong_0,axiom, % 1.18/1.30 ( ~ class_Divides_Oring__div(T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(V_a,V_b,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_b,T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a_H,T_a),V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_eq__number__of__Pls__Min_0,axiom, % 1.18/1.30 c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_div__mult__self1_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(V_c,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a) % 1.18/1.30 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_div__mult__self2_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(V_c,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a) % 1.18/1.30 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__less__eq_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__less__eq_4,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__less__eq_5,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__less__eq_7,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__divide__eq_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__divide__eq_4,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__divide__eq_5,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__divide__eq_7,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_inverse__le__1__iff_2,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_x,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__semiring_Osemiring__rules_I4_J_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(V_m,V_m,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_nat_Oinject_0,axiom, % 1.18/1.30 ( c_Suc(V_nat) != c_Suc(V_nat_H) % 1.18/1.30 | V_nat = V_nat_H ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_Suc__inject_0,axiom, % 1.18/1.30 ( c_Suc(V_x) != c_Suc(V_y) % 1.18/1.30 | V_x = V_y ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_abs__ge__minus__self_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__divide__eq__number__of_5,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__divide__eq__number__of_7,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_One__nat__def_0,axiom, % 1.18/1.30 c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_abs__ge__self_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.30 | c_lessequals(V_a,c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__divide__eq__number__of_2,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__divide__eq__number__of_3,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__divide__eq__number__of_9,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__add__iff1_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__add__iff1_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__add__iff2_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__add__iff2_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_eq__divide__eq_4,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mod__add__cong_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a_H,V_b_H,T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__Suc0_1,axiom, % 1.18/1.30 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_one__is__add_2,axiom, % 1.18/1.30 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) % 1.18/1.30 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.30 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_one__is__add_1,axiom, % 1.18/1.30 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) % 1.18/1.30 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.18/1.30 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_zero__less__power_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_even__zero__nat_0,axiom, % 1.18/1.30 c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_minus__unique_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.30 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_eq__neg__iff__add__eq__0_1,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.30 | V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_div__power_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),V_n,T_a) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_not__one__less__zero_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_abs__less__iff_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mod__mult__self4_0,axiom, % 1.18/1.30 c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),V_m,tc_nat)),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_nonzero__power__inverse_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.30 | c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) % 1.18/1.30 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_nonzero__inverse__minus__eq_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.30 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.18/1.30 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__divide__eq__number__of_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__divide__eq__number__of_4,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_not__less__less__Suc__eq_0,axiom, % 1.18/1.30 ( V_n = V_m % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__antisym_0,axiom, % 1.18/1.30 ( V_m = V_n % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__SucE_0,axiom, % 1.18/1.30 ( V_m = V_n % 1.18/1.30 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__eq__self__implies__10_0,axiom, % 1.18/1.30 ( V_m != c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) % 1.18/1.30 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.30 | V_n = c_HOL_Oone__class_Oone(tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__dvd__mono_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_d,T_a) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_minus__mult__commute_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oring(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__eq__0__iff_2,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__eq__0__iff_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__zero__right_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__zero__left_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__semiring_Omul__0_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__right_Ozero_0,axiom, % 1.18/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult_Ozero__right_0,axiom, % 1.18/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult_Ozero__left_0,axiom, % 1.18/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__left_Ozero_0,axiom, % 1.18/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mod__mult__cong_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a_H,V_b_H,T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_abs__mult__self_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__ringb_Oadd__mul__solve_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.30 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) % 1.18/1.30 | V_y = V_z % 1.18/1.30 | V_w = V_x ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__ringb_Onoteq__reduce_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.30 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_d,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.18/1.30 | V_c = V_d % 1.18/1.30 | V_a = V_b ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mod__mult__eq_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_dvd__mult__cancel__right_2,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.30 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_dvd__mult__cancel__left_2,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.30 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_inverse__mult__distrib_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__less__cancel__right__disj_3,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__less__cancel__left__disj_3,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_minus__mult__minus_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oring(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_square__eq__iff_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_b,V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__right_Ominus_0,axiom, % 1.18/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult_Ominus__right_0,axiom, % 1.18/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__left_Ominus_0,axiom, % 1.18/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult_Ominus__left_0,axiom, % 1.18/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_comm__semiring__class_Odistrib_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__semiring_Omul__d_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult_Oadd__left_0,axiom, % 1.18/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__left_Oadd_0,axiom, % 1.18/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_ya,T_a),c_HOL_Otimes__class_Otimes(V_y,V_ya,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult_Oadd__right_0,axiom, % 1.18/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oplus__class_Oplus(V_b,V_b_H,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b_H,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__right_Oadd_0,axiom, % 1.18/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),c_HOL_Otimes__class_Otimes(V_xa,V_y,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_dvd__mult__right_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_dvd__mult__left_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_dvd__mult2_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_dvd__mult_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_minus__mult__right_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oring(T_a) % 1.18/1.30 | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_minus__mult__left_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oring(T_a) % 1.18/1.30 | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__frac__frac_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_z,V_w,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_y,V_w,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_abs__mult_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.30 | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__eq__0__iff_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.30 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.30 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_no__zero__divisors_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.30 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.30 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_no__zero__divirors__neq0_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.30 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.30 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_square__eq__iff_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) != c_HOL_Otimes__class_Otimes(V_b,V_b,T_a) % 1.18/1.30 | V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a) % 1.18/1.30 | V_a = V_b ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_zmod__simps_I4_J_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__1__right_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__1__left_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__1_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__semiring_Omul__1_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_x,T_a) = V_x ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__semiring_Osemiring__rules_I11_J_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_dvd__triv__right_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_dvd__triv__left_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_dvdI_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Odvd(T_a) % 1.18/1.30 | c_Ring__and__Field_Odvd__class_Odvd(V_b,c_HOL_Otimes__class_Otimes(V_b,V_k,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__ringb_Oadd__mul__solve_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.30 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__ringb_Onoteq__reduce_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.30 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_combine__common__factor_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Osemiring(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__right_Odiff_0,axiom, % 1.18/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),c_HOL_Otimes__class_Otimes(V_xa,V_y,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult_Odiff__right_0,axiom, % 1.18/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ominus__class_Ominus(V_b,V_b_H,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b_H,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult_Odiff__left_0,axiom, % 1.18/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__left_Odiff_0,axiom, % 1.18/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_ya,T_a),c_HOL_Otimes__class_Otimes(V_y,V_ya,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mod__mult__right__eq_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mod__mult__left__eq_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__frac__num_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),V_y,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__eq__eq__number__of_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a) != c_Int_Onumber__class_Onumber__of(V_w,T_a) % 1.18/1.30 | V_b = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a) % 1.18/1.30 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__eq__eq__number__of1_4,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__eq__eq__number__of_3,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_c,T_a) = c_Int_Onumber__class_Onumber__of(V_w,T_a) % 1.18/1.30 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_eq__divide__eq__number__of1_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) = V_b % 1.18/1.30 | c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__eq__eq__number__of1_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.30 | c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_eq__divide__eq__number__of_3,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_c,T_a) % 1.18/1.30 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__eq__eq__number__of_4,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.30 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_c,T_a) = c_Int_Onumber__class_Onumber__of(V_w,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_eq__divide__eq__number__of_4,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.30 | c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_eq__divide__eq__number__of_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a) = V_b % 1.18/1.30 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_eq__divide__eq__number__of1_3,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.18/1.30 | c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__eq__eq__number__of1_3,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) = V_a % 1.18/1.30 | c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_eq__divide__eq__number__of1_4,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__minus1_0,axiom, % 1.18/1.30 ( ~ class_Int_Onumber__ring(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),V_z,T_a) = c_HOL_Ouminus__class_Ouminus(V_z,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__minus1__right_0,axiom, % 1.18/1.30 ( ~ class_Int_Onumber__ring(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(V_z,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_number__of__Bit1_0,axiom, % 1.18/1.30 ( ~ class_Int_Onumber__ring(T_a) % 1.18/1.30 | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(V_w),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__Numeral0_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.30 | c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_number__of__Bit0_0,axiom, % 1.18/1.30 ( ~ class_Int_Onumber__ring(T_a) % 1.18/1.30 | c_Int_Onumber__class_Onumber__of(c_Int_OBit0(V_w),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_power__minus_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oring__1(T_a) % 1.18/1.30 | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_n,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),V_n,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_power__less__power__Suc_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_power__gt1__lemma_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_neg__one__odd__power_0,axiom, % 1.18/1.30 ( ~ class_Int_Onumber__ring(T_a) % 1.18/1.30 | c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),V_x,T_a) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a) % 1.18/1.30 | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_half_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a),T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_Bit1__Min_0,axiom, % 1.18/1.30 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 1.18/1.30 % 1.18/1.30 cnf(cls_rel__simps_I47_J_0,axiom, % 1.18/1.30 ( c_Int_OBit1(V_k) != c_Int_OMin % 1.18/1.30 | V_k = c_Int_OMin ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_rel__simps_I43_J_0,axiom, % 1.18/1.30 ( c_Int_OMin != c_Int_OBit1(V_l) % 1.18/1.30 | c_Int_OMin = V_l ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_rel__simps_I43_J_1,axiom, % 1.18/1.30 c_Int_OMin = c_Int_OBit1(c_Int_OMin) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_rel__simps_I37_J_0,axiom, % 1.18/1.30 c_Int_OPls != c_Int_OMin ). % 1.18/1.30 % 1.18/1.30 cnf(cls_rel__simps_I40_J_0,axiom, % 1.18/1.30 c_Int_OMin != c_Int_OPls ). % 1.18/1.30 % 1.18/1.30 cnf(cls_rel__simps_I42_J_0,axiom, % 1.18/1.30 c_Int_OMin != c_Int_OBit0(V_l) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_rel__simps_I45_J_0,axiom, % 1.18/1.30 c_Int_OBit0(V_k) != c_Int_OMin ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mod2__gr__0_0,axiom, % 1.18/1.30 ( c_Divides_Odiv__class_Omod(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Omod(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_gcd__lcm__complete__lattice__nat_Otop__greatest_0,axiom, % 1.18/1.30 c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_dvd__0__right_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__divide__eq__number__of_8,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_le__divide__eq__number__of_4,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_le__divide__eq__number__of_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber(T_a) % 1.18/1.30 | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.30 | ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_add__frac__eq_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) % 1.18/1.30 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.30 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mult__eq__1__iff_2,axiom, % 1.18/1.30 c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_zero__less__power__eq__number__of_2,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.30 | c_Int_Onumber__class_Onumber__of(V_w,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__eq__eq_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) % 1.18/1.30 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_eq__divide__eq_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b % 1.18/1.30 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_zero__le__one_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_abs__power__minus_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.30 | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_n,T_a),T_a) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__semiring_Osemiring__rules_I2_J_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),V_m,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mod__1_0,axiom, % 1.18/1.30 c_Divides_Odiv__class_Omod(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_iszero__def_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.18/1.30 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.30 | ~ c_Int_Oiszero(V_z,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mod__by__1_0,axiom, % 1.18/1.30 ( ~ class_Divides_Osemiring__div(T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_abs__mult__pos_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_y,T_a),V_x,T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_y,V_x,T_a),T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_dvd__reduce_1,axiom, % 1.18/1.30 ( c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_dvd__reduce_0,axiom, % 1.18/1.30 ( c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_one__le__inverse__iff_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_lessequals(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_abs__dvd__iff_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.30 | c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_abs__dvd__iff_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.30 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_dvd__abs__iff_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.30 | c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_dvd__abs__iff_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.30 | c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a) % 1.18/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_one__is__add_4,axiom, % 1.18/1.30 c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_order__less__le_1,axiom, % 1.18/1.30 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__not__refl_0,axiom, % 1.18/1.30 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_nat__less__le_1,axiom, % 1.18/1.30 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_linorder__neq__iff_1,axiom, % 1.18/1.30 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_order__less__irrefl_0,axiom, % 1.18/1.30 ( ~ class_Orderings_Opreorder(T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__le__not__le_2,axiom, % 1.18/1.30 ( ~ class_Orderings_Opreorder(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.18/1.30 | c_lessequals(V_y,V_x,T_a) % 1.18/1.30 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_abs__number__of_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.30 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.30 | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(V_x,T_a),T_a) = c_Int_Onumber__class_Onumber__of(V_x,T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_x,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_add__pos__pos_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_not__one__le__zero_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_inverse__negative__iff__negative_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_inverse__negative__iff__negative_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_negative__imp__inverse__negative_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_divide__minus1_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.30 | c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(V_x,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_mod__diff__cong_0,axiom, % 1.18/1.30 ( ~ class_Divides_Oring__div(T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 1.18/1.30 | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a_H,V_b_H,T_a),V_c,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_nat__dvd__not__less_0,axiom, % 1.18/1.30 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_n,V_m,tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_le__iff__diff__le__0_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_le__iff__diff__le__0_1,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.30 | c_lessequals(V_a,V_b,T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_add__less__mono_0,axiom, % 1.18/1.30 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_l,tc_nat),tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_add__strict__mono_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_order__le__less_1,axiom, % 1.18/1.30 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.30 | c_lessequals(V_x,V_y,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_order__less__imp__le_0,axiom, % 1.18/1.30 ( ~ class_Orderings_Opreorder(T_a) % 1.18/1.30 | c_lessequals(V_x,V_y,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_add__cancel__end_1,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_z,T_a),c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = V_y ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_minus__add__cancel_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.18/1.30 | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) = V_b ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_inverse__eq__1__iff_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_one__less__inverse__iff_2,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_inverse__1_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.30 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_zero__le__divide__iff_4,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_zero__le__divide__iff_5,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) % 1.18/1.30 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_Suc__neq__Zero_0,axiom, % 1.18/1.30 c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_nat_Osimps_I3_J_0,axiom, % 1.18/1.30 c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_frac__le_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.30 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_z,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_w,T_a),T_a) % 1.18/1.30 | ~ c_lessequals(V_w,V_z,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 1.18/1.30 | ~ c_lessequals(V_x,V_y,T_a) % 1.18/1.30 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_power__gt1_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__iff__diff__less__0_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_less__iff__diff__less__0_1,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_abs__not__less__zero_0,axiom, % 1.18/1.30 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_of__nat__less__iff_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_of__nat__less__iff_1,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) % 1.18/1.30 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_power__le__zero__eq_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.30 | ~ c_lessequals(c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_power__le__zero__eq_2,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.30 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) % 1.18/1.30 | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.30 | ~ c_lessequals(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.30 % 1.18/1.30 cnf(cls_zero__less__one_0,axiom, % 1.18/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_divide__strict__left__mono_0,axiom, % 1.37/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_divide__strict__left__mono__neg_0,axiom, % 1.37/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_dvd__mult__cancel_0,axiom, % 1.37/1.30 ( c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.37/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_nat__mult__dvd__cancel1_0,axiom, % 1.37/1.30 ( c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) % 1.37/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_nat__mult__dvd__cancel1_1,axiom, % 1.37/1.30 ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 1.37/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_zero__less__power__eq__number__of_0,axiom, % 1.37/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.37/1.30 | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat) % 1.37/1.30 | c_Int_Onumber__class_Onumber__of(V_w,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),T_a) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_neg__0__equal__iff__equal_1,axiom, % 1.37/1.30 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.37/1.30 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_div__less__dividend_0,axiom, % 1.37/1.30 ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat),V_m,tc_nat) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_power__le__imp__le__base_0,axiom, % 1.37/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.37/1.30 | c_lessequals(V_a,V_b,T_a) % 1.37/1.30 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.37/1.30 | ~ c_lessequals(c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),c_Power_Opower__class_Opower(V_b,c_Suc(V_n),T_a),T_a) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_nat__mod__eq__iff_1,axiom, % 1.37/1.30 ( c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_n,V_xa,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(V_y,c_HOL_Otimes__class_Otimes(V_n,V_xb,tc_nat),tc_nat) % 1.37/1.30 | c_Divides_Odiv__class_Omod(V_x,V_n,tc_nat) = c_Divides_Odiv__class_Omod(V_y,V_n,tc_nat) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_of__nat__0__less__iff_0,axiom, % 1.37/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.37/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_of__nat__0__less__iff_1,axiom, % 1.37/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.37/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_inverse__nonzero__iff__nonzero_0,axiom, % 1.37/1.30 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.37/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.30 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.30 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_inverse__zero__imp__zero_0,axiom, % 1.37/1.30 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.37/1.30 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.30 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_mult__le__less__imp__less_0,axiom, % 1.37/1.30 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.37/1.30 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.37/1.30 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.37/1.30 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_mult__less__le__imp__less_0,axiom, % 1.37/1.30 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.37/1.30 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.37/1.30 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.37/1.30 | ~ c_lessequals(V_c,V_d,T_a) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_power__inject__exp_0,axiom, % 1.37/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.37/1.30 | c_Power_Opower__class_Opower(V_a,V_m,T_a) != c_Power_Opower__class_Opower(V_a,V_n,T_a) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 1.37/1.30 | V_m = V_n ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_le__number__of__eq__not__less_0,axiom, % 1.37/1.30 ( ~ class_Orderings_Olinorder(T_a) % 1.37/1.30 | ~ class_Int_Onumber(T_a) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a) % 1.37/1.30 | ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_le__number__of__eq__not__less_1,axiom, % 1.37/1.30 ( ~ class_Orderings_Olinorder(T_a) % 1.37/1.30 | ~ class_Int_Onumber(T_a) % 1.37/1.30 | c_lessequals(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.37/1.30 | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_dvd__eq__mod__eq__0__number__of_0,axiom, % 1.37/1.30 ( ~ class_Int_Onumber(T_a) % 1.37/1.30 | ~ class_Divides_Osemiring__div(T_a) % 1.37/1.30 | c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(V_y,T_a),c_Int_Onumber__class_Onumber__of(V_x,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.30 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(V_x,T_a),c_Int_Onumber__class_Onumber__of(V_y,T_a),T_a) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_dvd__eq__mod__eq__0__number__of_1,axiom, % 1.37/1.30 ( ~ class_Int_Onumber(T_a) % 1.37/1.30 | ~ class_Divides_Osemiring__div(T_a) % 1.37/1.30 | c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(V_y,T_a),c_Int_Onumber__class_Onumber__of(V_x,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.30 | c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(V_x,T_a),c_Int_Onumber__class_Onumber__of(V_y,T_a),T_a) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_zero__less__power__eq__number__of_5,axiom, % 1.37/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),T_a) % 1.37/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.37/1.30 | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_gr0I_0,axiom, % 1.37/1.30 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.37/1.30 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.37/1.30 % 1.37/1.30 cnf(cls_divide__eq__eq__number__of1_1,axiom, % 1.37/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | ~ class_Int_Onumber(T_a) % 1.37/1.31 | c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_neq0__conv_1,axiom, % 1.37/1.31 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_abs__triangle__ineq4_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.37/1.31 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_neg__power__if_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_n,T_a) = c_HOL_Ouminus__class_Ouminus(c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) % 1.37/1.31 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_minus__one__odd__power_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),V_x,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a) % 1.37/1.31 | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_n__less__n__mult__m_0,axiom, % 1.37/1.31 ( c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),tc_nat) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_n__less__m__mult__n_0,axiom, % 1.37/1.31 ( c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_minus__zero_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.37/1.31 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_neg__equal__zero_1,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.37/1.31 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_divide__inverse_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.37/1.31 | c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__fieldgb_Odivide__inverse_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.37/1.31 | ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mod2__gr__0_1,axiom, % 1.37/1.31 ( c_Divides_Odiv__class_Omod(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Oone__class_Oone(tc_nat) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Omod(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_div__2__gt__zero_0,axiom, % 1.37/1.31 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Odiv(V_n,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_lemma__even__div2_0,axiom, % 1.37/1.31 ( c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(V_n,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) % 1.37/1.31 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_Suc__mod__eq__add3__mod__number__of_0,axiom, % 1.37/1.31 c_Divides_Odiv__class_Omod(c_Suc(c_Suc(c_Suc(V_m))),c_Int_Onumber__class_Onumber__of(V_v,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_m,tc_nat),c_Int_Onumber__class_Onumber__of(V_v,tc_nat),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_Suc__div__eq__add3__div__number__of_0,axiom, % 1.37/1.31 c_Divides_Odiv__class_Odiv(c_Suc(c_Suc(c_Suc(V_m))),c_Int_Onumber__class_Onumber__of(V_v,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_m,tc_nat),c_Int_Onumber__class_Onumber__of(V_v,tc_nat),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mod__Suc__eq__mod__add3_0,axiom, % 1.37/1.31 c_Divides_Odiv__class_Omod(V_m,c_Suc(c_Suc(c_Suc(V_n))),tc_nat) = c_Divides_Odiv__class_Omod(V_m,c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_Suc__mod__eq__add3__mod_0,axiom, % 1.37/1.31 c_Divides_Odiv__class_Omod(c_Suc(c_Suc(c_Suc(V_m))),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_m,tc_nat),V_n,tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_div__Suc__eq__div__add3_0,axiom, % 1.37/1.31 c_Divides_Odiv__class_Odiv(V_m,c_Suc(c_Suc(c_Suc(V_n))),tc_nat) = c_Divides_Odiv__class_Odiv(V_m,c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_Suc__div__eq__add3__div_0,axiom, % 1.37/1.31 c_Divides_Odiv__class_Odiv(c_Suc(c_Suc(c_Suc(V_m))),V_n,tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_m,tc_nat),V_n,tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__one__right_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Osemiring__rules_I33_J_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(V_x,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_x ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__one_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__inverse_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_field__power__not__zero_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__eq__0__iff_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.37/1.31 | ~ class_Power_Opower(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__divide_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__abs_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_a,T_a),V_n,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_dvd__power__same_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a) % 1.37/1.31 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__even__abs__number__of_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_x,T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a) = c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a) % 1.37/1.31 | ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__eq__0__iff__number__of_2,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.37/1.31 | ~ class_Power_Opower(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | c_Int_Onumber__class_Onumber__of(V_w,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__0__left__number__of_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 1.37/1.31 | ~ class_Power_Opower(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | c_Int_Onumber__class_Onumber__of(V_w,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__le__zero__eq__number__of_3,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_lessequals(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__eq__0__iff__number__of_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.37/1.31 | ~ class_Power_Opower(T_a) % 1.37/1.31 | c_Int_Onumber__class_Onumber__of(V_w,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.37/1.31 | c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__less__zero__eq__number__of_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__1__eq__mult__iff_0,axiom, % 1.37/1.31 ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) % 1.37/1.31 | V_m = c_HOL_Oone__class_Oone(tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__1__eq__mult__iff_1,axiom, % 1.37/1.31 ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) % 1.37/1.31 | V_n = c_HOL_Oone__class_Oone(tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_even__product__nat_0,axiom, % 1.37/1.31 ( c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat) % 1.37/1.31 | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) % 1.37/1.31 | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_div__mult2__eq_0,axiom, % 1.37/1.31 c_Divides_Odiv__class_Odiv(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mult__is__0_1,axiom, % 1.37/1.31 c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mult__is__0_2,axiom, % 1.37/1.31 c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_natgb_Oadd__mul__solve_0,axiom, % 1.37/1.31 ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_y,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_z,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat) % 1.37/1.31 | V_y = V_z % 1.37/1.31 | V_w = V_x ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_natgb_Onoteq__reduce_0,axiom, % 1.37/1.31 ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_d,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_d,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) % 1.37/1.31 | V_c = V_d % 1.37/1.31 | V_a = V_b ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__mult__eq__cancel__disj_0,axiom, % 1.37/1.31 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) % 1.37/1.31 | V_m = V_n % 1.37/1.31 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mult__cancel1_0,axiom, % 1.37/1.31 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) % 1.37/1.31 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) % 1.37/1.31 | V_m = V_n ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mult__cancel2_0,axiom, % 1.37/1.31 ( c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat) != c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat) % 1.37/1.31 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) % 1.37/1.31 | V_m = V_n ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_even__product__nat_1,axiom, % 1.37/1.31 ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat) % 1.37/1.31 | ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_even__product__nat_2,axiom, % 1.37/1.31 ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat) % 1.37/1.31 | ~ c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__mult__dvd__cancel__disj_2,axiom, % 1.37/1.31 ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 1.37/1.31 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_add__mult__distrib_0,axiom, % 1.37/1.31 c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_add__mult__distrib2_0,axiom, % 1.37/1.31 c_HOL_Otimes__class_Otimes(V_k,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_Suc__mult__cancel1_0,axiom, % 1.37/1.31 ( c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat) % 1.37/1.31 | V_m = V_n ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mult__cancel1_1,axiom, % 1.37/1.31 c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mult__cancel2_1,axiom, % 1.37/1.31 c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mult__less__cancel1_1,axiom, % 1.37/1.31 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mult__less__cancel2_1,axiom, % 1.37/1.31 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mult__is__0_0,axiom, % 1.37/1.31 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.37/1.31 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 1.37/1.31 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__1__eq__mult__iff_2,axiom, % 1.37/1.31 c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__mult__1_0,axiom, % 1.37/1.31 c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) = V_n ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__mult__1__right_0,axiom, % 1.37/1.31 c_HOL_Otimes__class_Otimes(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = V_n ). % 1.37/1.31 % 1.37/1.31 cnf(cls_natgb_Oadd__mul__solve_1,axiom, % 1.37/1.31 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_natgb_Onoteq__reduce_1,axiom, % 1.37/1.31 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__mult__eq__1__iff_0,axiom, % 1.37/1.31 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) % 1.37/1.31 | V_m = c_HOL_Oone__class_Oone(tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__mult__eq__1__iff_1,axiom, % 1.37/1.31 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) % 1.37/1.31 | V_n = c_HOL_Oone__class_Oone(tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_left__add__mult__distrib_0,axiom, % 1.37/1.31 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_k,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_u,tc_nat),V_k,tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__mult__eq__1__iff_2,axiom, % 1.37/1.31 c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mod__mult__distrib_0,axiom, % 1.37/1.31 c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_k,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mod__mult__distrib2_0,axiom, % 1.37/1.31 c_HOL_Otimes__class_Otimes(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_half__gt__zero_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_r,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a),T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_r,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_half__gt__zero__iff_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_r,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_r,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_less__2__cases_0,axiom, % 1.37/1.31 ( V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.37/1.31 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_n,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mod__exhaust__less__4_0,axiom, % 1.37/1.31 ( c_Divides_Odiv__class_Omod(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) % 1.37/1.31 | c_Divides_Odiv__class_Omod(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) % 1.37/1.31 | c_Divides_Odiv__class_Omod(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat) % 1.37/1.31 | c_Divides_Odiv__class_Omod(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_double__number__of__Bit0_0,axiom, % 1.37/1.31 ( ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(V_w),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_numeral__1__eq__Suc__0_0,axiom, % 1.37/1.31 c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_numeral__3__eq__3_0,axiom, % 1.37/1.31 c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Suc(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_Suc3__eq__add__3_0,axiom, % 1.37/1.31 c_Suc(c_Suc(c_Suc(V_n))) = c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_transfer__int__nat__numerals_I4_J_0,axiom, % 1.37/1.31 c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power2__less__imp__less_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_sum__power2__le__zero__iff_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_sum__power2__le__zero__iff_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_sum__power2__le__zero__iff_2,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_lessequals(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_sum__power2__gt__zero__iff_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_sum__power2__gt__zero__iff_2,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),T_a) % 1.37/1.31 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_sum__power2__gt__zero__iff_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),T_a) % 1.37/1.31 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_sum__power2__ge__zero_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_not__sum__power2__lt__zero_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_root__cancel_0,axiom, % 1.37/1.31 ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_left__distrib__number__of_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Osemiring(T_a) % 1.37/1.31 | ~ class_Int_Onumber(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a),c_HOL_Otimes__class_Otimes(V_b,c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_left__diff__distrib__number__of_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oring(T_a) % 1.37/1.31 | ~ class_Int_Onumber(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a),c_HOL_Otimes__class_Otimes(V_b,c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_right__diff__distrib__number__of_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oring(T_a) % 1.37/1.31 | ~ class_Int_Onumber(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_HOL_Ominus__class_Ominus(V_b,V_c,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_v,T_a),V_b,T_a),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_v,T_a),V_c,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_right__distrib__number__of_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Osemiring(T_a) % 1.37/1.31 | ~ class_Int_Onumber(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_v,T_a),V_b,T_a),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_v,T_a),V_c,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_iszero__number__of__Bit1_0,axiom, % 1.37/1.31 ( ~ class_Int_Oring__char__0(T_a) % 1.37/1.31 | ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(V_w),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_comp__arith_I112_J_0,axiom, % 1.37/1.31 ( ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_HOL_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_number__of__Pls_0,axiom, % 1.37/1.31 ( ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_iszero__number__of__Pls_0,axiom, % 1.37/1.31 ( ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_add__numeral__0_0,axiom, % 1.37/1.31 ( ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a),V_a,T_a) = V_a ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_add__numeral__0__right_0,axiom, % 1.37/1.31 ( ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_HOL_Oplus__class_Oplus(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a),T_a) = V_a ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_iszero__number__of__Bit0_0,axiom, % 1.37/1.31 ( ~ class_Int_Oring__char__0(T_a) % 1.37/1.31 | ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.37/1.31 | ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(V_w),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_iszero__number__of__Bit0_1,axiom, % 1.37/1.31 ( ~ class_Int_Oring__char__0(T_a) % 1.37/1.31 | ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(V_w),T_a),T_a) % 1.37/1.31 | ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Osemiring__rules_I28_J_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_q,T_a),V_x,T_a) = c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Osemiring__rules_I27_J_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Omul__pwr_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_nat),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Opwr__Suc_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(V_x,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__Suc2_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_a,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__Suc_0,axiom, % 1.37/1.31 ( ~ class_Power_Opower(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Osemiring__rules_I35_J_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a) = c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__add_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(V_a,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_one__add__one__is__two_0,axiom, % 1.37/1.31 ( ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_of__nat__mult_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.37/1.31 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_numeral__2__eq__2_0,axiom, % 1.37/1.31 c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_div2__Suc__Suc_0,axiom, % 1.37/1.31 c_Divides_Odiv__class_Odiv(c_Suc(c_Suc(V_m)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Suc(c_Divides_Odiv__class_Odiv(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_iszero__0_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.37/1.31 | c_Int_Oiszero(c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mod__mod__cancel_0,axiom, % 1.37/1.31 ( ~ class_Divides_Osemiring__div(T_a) % 1.37/1.31 | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(V_a,V_c,T_a) % 1.37/1.31 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_b,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_zero__less__divide__1__iff_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_zero__less__divide__1__iff_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_even__nat__plus__one__div__two_0,axiom, % 1.37/1.31 ( c_Divides_Odiv__class_Odiv(c_Suc(V_x),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_Divides_Odiv__class_Odiv(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) % 1.37/1.31 | ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_inverse__eq__divide__number__of_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.37/1.31 | ~ class_Int_Onumber(T_a) % 1.37/1.31 | c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.37/1.31 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.37/1.31 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_abs__if__lattice_1,axiom, % 1.37/1.31 ( ~ class_Orderings_Olinorder(T_a) % 1.37/1.31 | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.37/1.31 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.37/1.31 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_abs__if_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oabs__if(T_a) % 1.37/1.31 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.37/1.31 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__less__imp__less__exp_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__strict__increasing_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_a,V_N,T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__strict__increasing__iff_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__strict__increasing__iff_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_le__divide__eq__number__of_9,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | ~ class_Int_Onumber(T_a) % 1.37/1.31 | c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.37/1.31 | ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_le__divide__eq__number__of_3,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | ~ class_Int_Onumber(T_a) % 1.37/1.31 | c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.37/1.31 | ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_le__divide__eq__number__of_2,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | ~ class_Int_Onumber(T_a) % 1.37/1.31 | c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.37/1.31 | ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_not__add__less2_0,axiom, % 1.37/1.31 ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_i,tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_not__add__less1_0,axiom, % 1.37/1.31 ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_i,tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_Lim_Ominus__diff__minus_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.37/1.31 | c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nonzero__power__divide_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) % 1.37/1.31 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_abs__add__abs_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.37/1.31 | c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_divide__le__eq_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_divide__le__eq_4,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_le__divide__eq_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.37/1.31 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_le__divide__eq_4,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_divide__le__eq__number__of1_5,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | ~ class_Int_Onumber(T_a) % 1.37/1.31 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_le__divide__eq__number__of1_5,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | ~ class_Int_Onumber(T_a) % 1.37/1.31 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.37/1.31 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mod__Suc__eq__Suc__mod_0,axiom, % 1.37/1.31 c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)),V_n,tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_abs__eq__0_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.37/1.31 | c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_zero__less__abs__iff_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_divide__neg__pos_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_divide__pos__neg_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_divide__less__0__iff_4,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_divide__less__0__iff_5,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_dvd__power_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_add__less__mono1_0,axiom, % 1.37/1.31 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__add__left__cancel__less_0,axiom, % 1.37/1.31 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__add__left__cancel__less_1,axiom, % 1.37/1.31 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_add__less__cancel__left_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_add__less__cancel__left_1,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_add__strict__left__mono_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_add__less__cancel__right_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_add__less__cancel__right_1,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_add__strict__right__mono_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_order__eq__refl_0,axiom, % 1.37/1.31 ( ~ class_Orderings_Opreorder(T_a) % 1.37/1.31 | c_lessequals(V_x,V_x,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_order__eq__iff_0,axiom, % 1.37/1.31 ( ~ class_Orderings_Oorder(T_a) % 1.37/1.31 | c_lessequals(V_x,V_x,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_order__le__less__trans_0,axiom, % 1.37/1.31 ( ~ class_Orderings_Opreorder(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.37/1.31 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_order__less__le__trans_0,axiom, % 1.37/1.31 ( ~ class_Orderings_Opreorder(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.37/1.31 | ~ c_lessequals(V_y,V_z,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_le__add__right__mono_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.37/1.31 | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) % 1.37/1.31 | ~ c_lessequals(V_c,V_d,T_a) % 1.37/1.31 | ~ c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_order__trans_0,axiom, % 1.37/1.31 ( ~ class_Orderings_Opreorder(T_a) % 1.37/1.31 | c_lessequals(V_x,V_z,T_a) % 1.37/1.31 | ~ c_lessequals(V_y,V_z,T_a) % 1.37/1.31 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_add__nonpos__nonpos_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.37/1.31 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_xt1_I8_J_0,axiom, % 1.37/1.31 ( ~ class_Orderings_Oorder(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.37/1.31 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_xt1_I7_J_0,axiom, % 1.37/1.31 ( ~ class_Orderings_Oorder(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.37/1.31 | ~ c_lessequals(V_z,V_y,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_xt1_I6_J_0,axiom, % 1.37/1.31 ( ~ class_Orderings_Oorder(T_a) % 1.37/1.31 | c_lessequals(V_z,V_x,T_a) % 1.37/1.31 | ~ c_lessequals(V_z,V_y,T_a) % 1.37/1.31 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_inverse__less__1__iff_2,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_x,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_add__is__1_5,axiom, % 1.37/1.31 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_divide__le__eq__number__of_7,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | ~ class_Int_Onumber(T_a) % 1.37/1.31 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_divide__le__eq__number__of_5,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | ~ class_Int_Onumber(T_a) % 1.37/1.31 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mod__eq__0__iff_1,axiom, % 1.37/1.31 c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_d,V_x,tc_nat),V_d,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mod__mult__self1__is__0_0,axiom, % 1.37/1.31 ( ~ class_Divides_Osemiring__div(T_a) % 1.37/1.31 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mod__mult__self2__is__0_0,axiom, % 1.37/1.31 ( ~ class_Divides_Osemiring__div(T_a) % 1.37/1.31 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_divide__le__eq__number__of1_9,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | ~ class_Int_Onumber(T_a) % 1.37/1.31 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) % 1.37/1.31 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_le__divide__eq__number__of1_9,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | ~ class_Int_Onumber(T_a) % 1.37/1.31 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.37/1.31 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_division__ring__inverse__diff_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.37/1.31 | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) % 1.37/1.31 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_semiring__div__class_Omod__div__equality_H_0,axiom, % 1.37/1.31 ( ~ class_Divides_Osemiring__div(T_a) % 1.37/1.31 | c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),T_a) = V_a ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_sum__squares__eq__zero__iff_2,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.37/1.31 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_minus1__divide_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),V_x,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_x,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mult__less__cancel__left__disj_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mult__less__cancel__left__disj_2,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mult__less__cancel__right__disj_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mult__less__cancel__right__disj_2,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_abs__diff__less__iff_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_a,V_r,T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_zero__less__power__eq__number__of_4,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),T_a) % 1.37/1.31 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_not__iszero__1_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.37/1.31 | ~ c_Int_Oiszero(c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_zero__less__power__eq__number__of_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_Int_Onumber__class_Onumber__of(V_w,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),T_a) % 1.37/1.31 | ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_eq__divide__eq_2,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_zero__le__power__iff_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) % 1.37/1.31 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_zero__le__odd__power_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.37/1.31 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_zero__le__odd__power_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) % 1.37/1.31 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_zero__le__power__eq_2,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.37/1.31 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_zero__le__power__eq_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.37/1.31 | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) % 1.37/1.31 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_neg__0__less__iff__less_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_neg__0__less__iff__less_1,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_frac__eq__eq_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.37/1.31 | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) != c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) % 1.37/1.31 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) = c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_frac__eq__eq_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) != c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) % 1.37/1.31 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_less__minus__self__iff_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_less__minus__self__iff_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_abs__ge__zero_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.37/1.31 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_divide__eq__eq_4,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.37/1.31 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a),V_c,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_dvd__if__abs__eq_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_HOL_Oabs__class_Oabs(V_l,T_a) != c_HOL_Oabs__class_Oabs(V_k,T_a) % 1.37/1.31 | c_Ring__and__Field_Odvd__class_Odvd(V_l,V_k,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_minus__add_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.37/1.31 | c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_minus__add__distrib_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.37/1.31 | c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_order__less__asym_0,axiom, % 1.37/1.31 ( ~ class_Orderings_Opreorder(T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_linorder__linear_0,axiom, % 1.37/1.31 ( ~ class_Orderings_Olinorder(T_a) % 1.37/1.31 | c_lessequals(V_y,V_x,T_a) % 1.37/1.31 | c_lessequals(V_x,V_y,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_dvd_Oless__le__trans_0,axiom, % 1.37/1.31 ( c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat) % 1.37/1.31 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat) % 1.37/1.31 | c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat) % 1.37/1.31 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_dvd_Ole__less__trans_0,axiom, % 1.37/1.31 ( c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat) % 1.37/1.31 | c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat) % 1.37/1.31 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat) % 1.37/1.31 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_order__less__asym_H_0,axiom, % 1.37/1.31 ( ~ class_Orderings_Opreorder(T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_not__less__iff__gr__or__eq_1,axiom, % 1.37/1.31 ( ~ class_Orderings_Olinorder(T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_xt1_I9_J_0,axiom, % 1.37/1.31 ( ~ class_Orderings_Oorder(T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_add__self__div__2_0,axiom, % 1.37/1.31 c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_m,V_m,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = V_m ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__even__iff__2__dvd_0,axiom, % 1.37/1.31 ( c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_x,tc_nat) % 1.37/1.31 | ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__even__iff__2__dvd_1,axiom, % 1.37/1.31 ( c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) % 1.37/1.31 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_x,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__1__add__1_0,axiom, % 1.37/1.31 c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_add__2__eq__Suc_0,axiom, % 1.37/1.31 c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat) = c_Suc(c_Suc(V_n)) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_add__2__eq__Suc_H_0,axiom, % 1.37/1.31 c_HOL_Oplus__class_Oplus(V_n,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Suc(c_Suc(V_n)) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_transfer__int__nat__numerals_I3_J_0,axiom, % 1.37/1.31 c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_pos2_0,axiom, % 1.37/1.31 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mod2__Suc__Suc_0,axiom, % 1.37/1.31 c_Divides_Odiv__class_Omod(c_Suc(c_Suc(V_m)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_comp__arith_I115_J_0,axiom, % 1.37/1.31 c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_even__even__mod__4__iff_1,axiom, % 1.37/1.31 ( c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) % 1.37/1.31 | ~ c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(V_n,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_even__even__mod__4__iff_0,axiom, % 1.37/1.31 ( c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(V_n,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat) % 1.37/1.31 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_comp__arith_I113_J_0,axiom, % 1.37/1.31 c_HOL_Ozero__class_Ozero(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__number__of__Pls_0,axiom, % 1.37/1.31 c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__minus1__odd_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat)),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_odd__power__less__zero_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat)),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_odd__0__le__power__imp__0__le_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat)),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__eq__0__iff__number__of_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.37/1.31 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.37/1.31 | ~ class_Power_Opower(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_sum__power2__eq__zero__iff_2,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power2__less__0_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_zero__less__power2_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power2__le__imp__le_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.37/1.31 | c_lessequals(V_x,V_y,T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.37/1.31 | ~ c_lessequals(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_sum__power2__eq__zero__iff_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_sum__power2__eq__zero__iff_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_zero__le__power2_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power2__eq__imp__eq_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) != c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) % 1.37/1.31 | V_x = V_y % 1.37/1.31 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.37/1.31 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_zero__less__power2_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a) % 1.37/1.31 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_odd__Suc__mult__two__ex_1,axiom, % 1.37/1.31 ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_x,tc_nat)),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_even__mult__two__ex_0,axiom, % 1.37/1.31 ( V_n = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1(V_n),tc_nat) % 1.37/1.31 | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_root__unity_0,axiom, % 1.37/1.31 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_inverse__numeral__1_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.37/1.31 | ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a),T_a) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_divide__Numeral1_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.37/1.31 | ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a),T_a) = V_x ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_divide__numeral__1_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.37/1.31 | ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_HOL_Oinverse__class_Odivide(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a),T_a) = V_a ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_numeral__1__eq__1_0,axiom, % 1.37/1.31 ( ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_comp__arith_I110_J_0,axiom, % 1.37/1.31 ( ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_HOL_Oone__class_Oone(T_a) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_not__iszero__Numeral1_0,axiom, % 1.37/1.31 ( ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__numeral__1__eq__1_0,axiom, % 1.37/1.31 c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_Numeral1__eq1__nat_0,axiom, % 1.37/1.31 c_HOL_Oone__class_Oone(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__minus1__even_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_zero__le__even__power_H_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_even__power__le__0__imp__0_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | ~ c_lessequals(c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_k,tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power2__diff_0,axiom, % 1.37/1.31 ( ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a),V_x,T_a),V_y,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__m1__odd_0,axiom, % 1.37/1.31 ( ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat)),T_a) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__m1__even_0,axiom, % 1.37/1.31 ( ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mult__2_0,axiom, % 1.37/1.31 ( ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a),V_z,T_a) = c_HOL_Oplus__class_Oplus(V_z,V_z,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mult__2__right_0,axiom, % 1.37/1.31 ( ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a),T_a) = c_HOL_Oplus__class_Oplus(V_z,V_z,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_zero__eq__power2_1,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_zero__power2_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_zero__eq__power2_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.37/1.31 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power2__abs_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_a,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_one__power2_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power2__minus_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_abs__power2_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.37/1.31 | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a) = c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_even__mult__two__ex_1,axiom, % 1.37/1.31 c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_x,tc_nat),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__mult__2__right_0,axiom, % 1.37/1.31 c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__mult__2_0,axiom, % 1.37/1.31 c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_root4_0,axiom, % 1.37/1.31 c_FFT__Mirabelle_Oroot(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)) = c_Complex_Oii ). % 1.37/1.31 % 1.37/1.31 cnf(cls_comm__ring__1__class_Opower__minus__even_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power2__sum_0,axiom, % 1.37/1.31 ( ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a),V_x,T_a),V_y,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Osemiring__rules_I37_J_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(V_x,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat)),T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__odd__eq_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(V_a,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat)),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__mult_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Osemiring__rules_I29_J_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_Bit0__Pls_0,axiom, % 1.37/1.31 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__commutes_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_a,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_rel__simps_I39_J_0,axiom, % 1.37/1.31 c_Int_OPls != c_Int_OBit1(V_l) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power2__eq__square__number__of_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.37/1.31 | ~ class_Int_Onumber(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_rel__simps_I46_J_0,axiom, % 1.37/1.31 c_Int_OBit1(V_k) != c_Int_OPls ). % 1.37/1.31 % 1.37/1.31 cnf(cls_rel__simps_I44_J_0,axiom, % 1.37/1.31 ( c_Int_OBit0(V_k) != c_Int_OPls % 1.37/1.31 | V_k = c_Int_OPls ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_rel__simps_I48_J_0,axiom, % 1.37/1.31 ( c_Int_OBit0(V_k) != c_Int_OBit0(V_l) % 1.37/1.31 | V_k = V_l ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__even__eq_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_rel__simps_I50_J_0,axiom, % 1.37/1.31 c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_rel__simps_I38_J_1,axiom, % 1.37/1.31 c_Int_OPls = c_Int_OBit0(c_Int_OPls) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Omul__a_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__mult__assoc_0,axiom, % 1.37/1.31 c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ry,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,V_rx,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power2__eq__square_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power__mult__distrib_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_n,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Opwr__mul_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_q,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_q,T_a),c_Power_Opower__class_Opower(V_y,V_q,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mult__idem_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = V_x ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mult__left__idem_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_ry,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mult__numeral__1_0,axiom, % 1.37/1.31 ( ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a),V_a,T_a) = V_a ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_mult__numeral__1__right_0,axiom, % 1.37/1.31 ( ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a),T_a) = V_a ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_rel__simps_I38_J_0,axiom, % 1.37/1.31 ( c_Int_OPls != c_Int_OBit0(V_l) % 1.37/1.31 | c_Int_OPls = V_l ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_rel__simps_I51_J_0,axiom, % 1.37/1.31 ( c_Int_OBit1(V_k) != c_Int_OBit1(V_l) % 1.37/1.31 | V_k = V_l ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Opwr__pwr_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_x,V_p,T_a),V_q,T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Otimes__class_Otimes(V_p,V_q,tc_nat),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Omul__c_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_nat__mult__commute_0,axiom, % 1.37/1.31 c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) = c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_power3__eq__cube_0,axiom, % 1.37/1.31 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),V_a,T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_eq__number__of_0,axiom, % 1.37/1.31 ( ~ class_Int_Oring__char__0(T_a) % 1.37/1.31 | ~ class_Int_Onumber__ring(T_a) % 1.37/1.31 | c_Int_Onumber__class_Onumber__of(V_x,T_a) != c_Int_Onumber__class_Onumber__of(V_y,T_a) % 1.37/1.31 | V_x = V_y ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_class__semiring_Osemiring__rules_I36_J_0,axiom, % 1.37/1.31 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.37/1.31 | c_Power_Opower__class_Opower(V_x,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) ) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_rel__simps_I49_J_0,axiom, % 1.37/1.31 c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 1.37/1.31 % 1.37/1.31 cnf(cls_conjecture_0,negated_conjecture, % 1.37/1.31 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom, % 1.37/1.31 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom, % 1.37/1.31 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom, % 1.37/1.31 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,axiom, % 1.37/1.31 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom, % 1.37/1.31 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom, % 1.37/1.31 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom, % 1.37/1.31 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 1.37/1.31 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom, % 1.37/1.31 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Ring__and__Field_Opordered__semiring,axiom, % 1.37/1.31 class_Ring__and__Field_Opordered__semiring(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Ring__and__Field_Oordered__semiring,axiom, % 1.37/1.31 class_Ring__and__Field_Oordered__semiring(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom, % 1.37/1.31 class_Ring__and__Field_Ono__zero__divisors(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom, % 1.37/1.31 class_Ring__and__Field_Oordered__semidom(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom, % 1.37/1.31 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom, % 1.37/1.31 class_OrderedGroup_Oab__semigroup__mult(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom, % 1.37/1.31 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom, % 1.37/1.31 class_OrderedGroup_Oab__semigroup__add(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom, % 1.37/1.31 class_Ring__and__Field_Ocomm__semiring(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom, % 1.37/1.31 class_OrderedGroup_Ocomm__monoid__add(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom, % 1.37/1.31 class_Ring__and__Field_Ozero__neq__one(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom, % 1.37/1.31 class_Ring__and__Field_Osemiring__1(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom, % 1.37/1.31 class_Ring__and__Field_Osemiring__0(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Ring__and__Field_Omult__mono1,axiom, % 1.37/1.31 class_Ring__and__Field_Omult__mono1(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom, % 1.37/1.31 class_Ring__and__Field_Omult__zero(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Ring__and__Field_Omult__mono,axiom, % 1.37/1.31 class_Ring__and__Field_Omult__mono(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom, % 1.37/1.31 class_OrderedGroup_Omonoid__mult(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom, % 1.37/1.31 class_Ring__and__Field_Osemiring(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom, % 1.37/1.31 class_OrderedGroup_Omonoid__add(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Divides_Osemiring__div,axiom, % 1.37/1.31 class_Divides_Osemiring__div(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom, % 1.37/1.31 class_Nat_Osemiring__char__0(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Ring__and__Field_Odvd,axiom, % 1.37/1.31 class_Ring__and__Field_Odvd(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Orderings_Opreorder,axiom, % 1.37/1.31 class_Orderings_Opreorder(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Orderings_Olinorder,axiom, % 1.37/1.31 class_Orderings_Olinorder(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Orderings_Oorder,axiom, % 1.37/1.31 class_Orderings_Oorder(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Power_Opower,axiom, % 1.37/1.31 class_Power_Opower(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_nat__Int_Onumber,axiom, % 1.37/1.31 class_Int_Onumber(tc_nat) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom, % 1.37/1.31 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom, % 1.37/1.31 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict,axiom, % 1.37/1.31 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring,axiom, % 1.37/1.31 class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors,axiom, % 1.37/1.31 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict,axiom, % 1.37/1.31 class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add,axiom, % 1.37/1.31 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs,axiom, % 1.37/1.31 class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs,axiom, % 1.37/1.31 class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add,axiom, % 1.37/1.31 class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors,axiom, % 1.37/1.31 class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 1.37/1.31 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict,axiom, % 1.37/1.31 class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add,axiom, % 1.37/1.31 class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add,axiom, % 1.37/1.31 class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add,axiom, % 1.37/1.31 class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add,axiom, % 1.37/1.31 class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring,axiom, % 1.37/1.31 class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs,axiom, % 1.37/1.31 class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring,axiom, % 1.37/1.31 class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors,axiom, % 1.37/1.31 class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom,axiom, % 1.37/1.31 class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1,axiom, % 1.37/1.31 class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult,axiom, % 1.37/1.31 class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult,axiom, % 1.37/1.31 class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add,axiom, % 1.37/1.31 class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__ring,axiom, % 1.37/1.31 class_Ring__and__Field_Opordered__ring(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Olordered__ring,axiom, % 1.37/1.31 class_Ring__and__Field_Olordered__ring(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring,axiom, % 1.37/1.31 class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add,axiom, % 1.37/1.31 class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one,axiom, % 1.37/1.31 class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__idom,axiom, % 1.37/1.31 class_Ring__and__Field_Oordered__idom(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1,axiom, % 1.37/1.31 class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Osemiring__1,axiom, % 1.37/1.31 class_Ring__and__Field_Osemiring__1(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Osemiring__0,axiom, % 1.37/1.31 class_Ring__and__Field_Osemiring__0(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Omult__mono1,axiom, % 1.37/1.31 class_Ring__and__Field_Omult__mono1(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__OrderedGroup_Oab__group__add,axiom, % 1.37/1.31 class_OrderedGroup_Oab__group__add(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Omult__zero,axiom, % 1.37/1.31 class_Ring__and__Field_Omult__zero(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Omult__mono,axiom, % 1.37/1.31 class_Ring__and__Field_Omult__mono(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__ring,axiom, % 1.37/1.31 class_Ring__and__Field_Ocomm__ring(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__OrderedGroup_Omonoid__mult,axiom, % 1.37/1.31 class_OrderedGroup_Omonoid__mult(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Osemiring,axiom, % 1.37/1.31 class_Ring__and__Field_Osemiring(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__OrderedGroup_Omonoid__add,axiom, % 1.37/1.31 class_OrderedGroup_Omonoid__add(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__OrderedGroup_Ogroup__add,axiom, % 1.37/1.31 class_OrderedGroup_Ogroup__add(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Oring__1,axiom, % 1.37/1.31 class_Ring__and__Field_Oring__1(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Oabs__if,axiom, % 1.37/1.31 class_Ring__and__Field_Oabs__if(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Divides_Osemiring__div,axiom, % 1.37/1.31 class_Divides_Osemiring__div(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Oring,axiom, % 1.37/1.31 class_Ring__and__Field_Oring(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Oidom,axiom, % 1.37/1.31 class_Ring__and__Field_Oidom(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Nat_Osemiring__char__0,axiom, % 1.37/1.31 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Ring__and__Field_Odvd,axiom, % 1.37/1.31 class_Ring__and__Field_Odvd(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Orderings_Opreorder,axiom, % 1.37/1.31 class_Orderings_Opreorder(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Orderings_Olinorder,axiom, % 1.37/1.31 class_Orderings_Olinorder(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Divides_Oring__div,axiom, % 1.37/1.31 class_Divides_Oring__div(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Orderings_Oorder,axiom, % 1.37/1.31 class_Orderings_Oorder(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Int_Oring__char__0,axiom, % 1.37/1.31 class_Int_Oring__char__0(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Int_Onumber__ring,axiom, % 1.37/1.31 class_Int_Onumber__ring(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Power_Opower,axiom, % 1.37/1.31 class_Power_Opower(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Int__Oint__Int_Onumber,axiom, % 1.37/1.31 class_Int_Onumber(tc_Int_Oint) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors,axiom, % 1.37/1.31 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,axiom, % 1.37/1.31 class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 1.37/1.31 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add,axiom, % 1.37/1.31 class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,axiom, % 1.37/1.31 class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom, % 1.37/1.31 class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom, % 1.37/1.31 class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom, % 1.37/1.31 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,axiom, % 1.37/1.31 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,axiom, % 1.37/1.31 class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add,axiom, % 1.37/1.31 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring,axiom, % 1.37/1.31 class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring,axiom, % 1.37/1.31 class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom, % 1.37/1.31 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,axiom, % 1.37/1.31 class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom, % 1.37/1.31 class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,axiom, % 1.37/1.31 class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1,axiom, % 1.37/1.31 class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0,axiom, % 1.37/1.31 class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,axiom, % 1.37/1.31 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,axiom, % 1.37/1.31 class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring,axiom, % 1.37/1.31 class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom, % 1.37/1.31 class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring,axiom, % 1.37/1.31 class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add,axiom, % 1.37/1.31 class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom, % 1.37/1.31 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1,axiom, % 1.37/1.31 class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__field,axiom, % 1.37/1.31 class_RealVector_Oreal__field(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom, % 1.37/1.31 class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring,axiom, % 1.37/1.31 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom, % 1.37/1.31 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Nat_Osemiring__char__0,axiom, % 1.37/1.31 class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odvd,axiom, % 1.37/1.31 class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Int_Oring__char__0,axiom, % 1.37/1.31 class_Int_Oring__char__0(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom, % 1.37/1.31 class_Int_Onumber__ring(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Power_Opower,axiom, % 1.37/1.31 class_Power_Opower(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 cnf(clsarity_Complex__Ocomplex__Int_Onumber,axiom, % 1.37/1.31 class_Int_Onumber(tc_Complex_Ocomplex) ). % 1.37/1.31 % 1.37/1.31 %------------------------------------------------------------------------------ % 1.37/1.31 %------------------------------------------- % 1.37/1.31 % Proof found % 1.37/1.31 % SZS status Theorem for theBenchmark % 1.37/1.31 % SZS output start Proof % 1.37/1.31 %ClaNum:1604(EqnAxiom:121) % 1.37/1.31 %VarNum:9524(SingletonVarNum:2877) % 1.37/1.31 %MaxLitNum:6 % 1.37/1.32 %MaxfuncDepth:6 % 1.37/1.32 %SharedTerms:213 % 1.37/1.32 %goalClause: 382 % 1.37/1.32 %singleGoalClaCount:1 % 1.37/1.32 [126]P1(a18) % 1.37/1.32 [127]P1(a19) % 1.37/1.32 [128]P1(a20) % 1.37/1.32 [129]P45(a19) % 1.37/1.32 [130]P46(a19) % 1.37/1.32 [131]P46(a20) % 1.37/1.32 [132]P2(a18) % 1.37/1.32 [133]P2(a19) % 1.37/1.32 [134]P31(a18) % 1.37/1.32 [135]P31(a19) % 1.37/1.32 [136]P58(a19) % 1.37/1.32 [137]P3(a19) % 1.37/1.32 [138]P59(a18) % 1.37/1.32 [139]P59(a19) % 1.37/1.32 [140]P47(a20) % 1.37/1.32 [141]P4(a18) % 1.37/1.32 [142]P4(a19) % 1.37/1.32 [143]P4(a20) % 1.37/1.32 [144]P5(a18) % 1.37/1.32 [145]P5(a19) % 1.37/1.32 [146]P25(a19) % 1.37/1.32 [147]P32(a18) % 1.37/1.32 [148]P32(a19) % 1.37/1.32 [149]P32(a20) % 1.37/1.32 [150]P65(a18) % 1.37/1.32 [151]P65(a19) % 1.37/1.32 [152]P65(a20) % 1.37/1.32 [153]P51(a18) % 1.37/1.32 [154]P51(a19) % 1.37/1.32 [155]P51(a20) % 1.37/1.32 [156]P52(a18) % 1.37/1.32 [157]P52(a19) % 1.37/1.32 [158]P52(a20) % 1.37/1.32 [159]P66(a18) % 1.37/1.32 [160]P66(a19) % 1.37/1.32 [161]P66(a20) % 1.37/1.32 [162]P60(a19) % 1.37/1.32 [163]P30(a19) % 1.37/1.32 [164]P33(a18) % 1.37/1.32 [165]P33(a19) % 1.37/1.32 [166]P36(a18) % 1.37/1.32 [167]P36(a19) % 1.37/1.32 [168]P12(a19) % 1.37/1.32 [169]P12(a20) % 1.37/1.32 [170]P48(a20) % 1.37/1.32 [171]P26(a19) % 1.37/1.32 [172]P34(a18) % 1.37/1.32 [173]P34(a19) % 1.37/1.32 [174]P61(a18) % 1.37/1.32 [175]P61(a19) % 1.37/1.32 [176]P38(a20) % 1.37/1.32 [177]P41(a19) % 1.37/1.32 [178]P41(a20) % 1.37/1.32 [179]P13(a19) % 1.37/1.32 [180]P13(a20) % 1.37/1.32 [181]P14(a19) % 1.37/1.32 [182]P14(a20) % 1.37/1.32 [183]P42(a19) % 1.37/1.32 [184]P62(a18) % 1.37/1.32 [185]P62(a19) % 1.37/1.32 [186]P53(a18) % 1.37/1.32 [187]P53(a19) % 1.37/1.32 [188]P54(a18) % 1.37/1.32 [189]P54(a19) % 1.37/1.32 [190]P63(a19) % 1.37/1.32 [191]P49(a20) % 1.37/1.32 [192]P73(a18) % 1.37/1.32 [193]P73(a19) % 1.37/1.32 [194]P73(a20) % 1.37/1.32 [195]P50(a18) % 1.37/1.32 [196]P50(a19) % 1.37/1.32 [197]P50(a20) % 1.37/1.32 [198]P43(a19) % 1.37/1.32 [199]P43(a20) % 1.37/1.32 [200]P64(a18) % 1.37/1.32 [201]P64(a19) % 1.37/1.32 [202]P6(a19) % 1.37/1.32 [203]P15(a18) % 1.37/1.32 [204]P15(a19) % 1.37/1.32 [205]P15(a20) % 1.37/1.32 [206]P18(a18) % 1.37/1.32 [207]P18(a19) % 1.37/1.32 [208]P18(a20) % 1.37/1.32 [209]P67(a19) % 1.37/1.32 [210]P67(a20) % 1.37/1.32 [211]P55(a19) % 1.37/1.32 [212]P37(a18) % 1.37/1.32 [213]P37(a19) % 1.37/1.32 [214]P19(a18) % 1.37/1.32 [215]P19(a19) % 1.37/1.32 [216]P19(a20) % 1.37/1.32 [217]P27(a19) % 1.37/1.32 [218]P68(a18) % 1.37/1.32 [219]P68(a19) % 1.37/1.32 [220]P39(a20) % 1.37/1.32 [221]P28(a18) % 1.37/1.32 [222]P28(a19) % 1.37/1.32 [223]P28(a20) % 1.37/1.32 [224]P20(a18) % 1.37/1.32 [225]P20(a19) % 1.37/1.32 [226]P20(a20) % 1.37/1.32 [227]P23(a18) % 1.37/1.32 [228]P23(a19) % 1.37/1.32 [229]P23(a20) % 1.37/1.32 [230]P40(a20) % 1.37/1.32 [231]P56(a18) % 1.37/1.32 [232]P56(a19) % 1.37/1.32 [233]P29(a18) % 1.37/1.32 [234]P29(a19) % 1.37/1.32 [235]P29(a20) % 1.37/1.32 [236]P35(a18) % 1.37/1.32 [237]P35(a19) % 1.37/1.32 [238]P69(a19) % 1.37/1.32 [239]P69(a20) % 1.37/1.32 [240]P44(a18) % 1.37/1.32 [241]P44(a19) % 1.37/1.32 [242]P44(a20) % 1.37/1.32 [243]P24(a18) % 1.37/1.32 [244]P24(a19) % 1.37/1.32 [245]P24(a20) % 1.37/1.32 [246]P72(a18) % 1.37/1.32 [247]P72(a19) % 1.37/1.32 [248]P72(a20) % 1.37/1.32 [249]P70(a19) % 1.37/1.32 [250]P70(a20) % 1.37/1.32 [251]P71(a19) % 1.37/1.32 [252]P71(a20) % 1.37/1.32 [253]P16(a19) % 1.37/1.32 [254]P16(a20) % 1.37/1.32 [255]P21(a18) % 1.37/1.32 [256]P21(a19) % 1.37/1.32 [257]P21(a20) % 1.37/1.32 [357]~E(a17,a1) % 1.37/1.32 [124]E(f2(a1),a1) % 1.37/1.32 [125]E(f3(a17),a17) % 1.37/1.32 [262]E(f21(a1,a18),f4(a18)) % 1.37/1.32 [263]E(f21(a17,a18),f4(a18)) % 1.37/1.32 [264]P7(f4(a18),a18) % 1.37/1.32 [358]~E(f9(a20),a6) % 1.37/1.32 [365]~P7(f9(a18),a18) % 1.37/1.32 [366]~E(f21(a17,a19),f21(a1,a19)) % 1.37/1.32 [258]E(f5(f4(a18)),f9(a20)) % 1.37/1.32 [259]E(f5(f9(a18)),f9(a20)) % 1.37/1.32 [266]E(f21(f2(a17),a18),f9(a18)) % 1.37/1.32 [283]E(f14(f4(a18),f9(a18),a18),f21(f2(a17),a18)) % 1.37/1.32 [284]E(f14(f9(a18),f9(a18),a18),f21(f3(f2(a17)),a18)) % 1.37/1.32 [288]P8(f4(a18),f21(f3(f2(a17)),a18),a18) % 1.37/1.32 [306]E(f14(f14(f4(a18),f9(a18),a18),f9(a18),a18),f21(f3(f2(a17)),a18)) % 1.37/1.32 [327]E(f15(f14(f4(a18),f9(a18),a18),f14(f4(a18),f9(a18),a18),a18),f14(f4(a18),f9(a18),a18)) % 1.37/1.32 [336]E(f14(f14(f14(f4(a18),f9(a18),a18),f9(a18),a18),f9(a18),a18),f21(f2(f2(a17)),a18)) % 1.37/1.32 [285]E(f23(f21(f2(f2(a17)),a18),a19),f21(f2(f2(a17)),a19)) % 1.37/1.32 [286]E(f23(f21(f3(f2(a17)),a18),a19),f21(f3(f2(a17)),a19)) % 1.37/1.32 [287]E(f5(f21(f3(f3(f2(a17))),a18)),a6) % 1.37/1.32 [382]~E(f22(f5(f15(f21(f3(f2(a17)),a18),a25,a18)),f15(f21(f3(f2(a17)),a18),f15(a26,a27,a18),a18),a20),f22(f5(f15(f21(f3(f2(a17)),a18),a25,a18)),f15(a26,f15(f21(f3(f2(a17)),a18),a27,a18),a18),a20)) % 1.37/1.32 [267]P10(x2671,x2671,a18) % 1.37/1.32 [368]~P8(x3681,x3681,a18) % 1.37/1.32 [260]E(f21(x2601,a19),x2601) % 1.37/1.32 [268]P10(x2681,f4(a18),a18) % 1.37/1.32 [269]P10(f9(a18),x2691,a18) % 1.37/1.32 [361]~E(f2(x3611),a17) % 1.37/1.32 [362]~E(f3(x3621),a1) % 1.37/1.32 [370]~P8(x3701,f4(a18),a18) % 1.37/1.32 [271]E(f15(x2711,f9(a18),a18),x2711) % 1.37/1.32 [272]E(f14(x2721,f4(a18),a18),x2721) % 1.37/1.32 [273]E(f15(f9(a18),x2731,a18),x2731) % 1.37/1.32 [274]E(f14(f4(a18),x2741,a18),x2741) % 1.37/1.32 [275]E(f15(x2751,f4(a18),a18),f4(a18)) % 1.37/1.32 [276]E(f15(f4(a18),x2761,a18),f4(a18)) % 1.37/1.32 [278]E(f22(f5(x2781),x2781,a20),f9(a20)) % 1.37/1.32 [298]P8(x2981,f14(x2981,f9(a18),a18),a18) % 1.37/1.32 [300]P8(f4(a18),f14(x3001,f9(a18),a18),a18) % 1.37/1.32 [301]P10(f14(f4(a18),f9(a18),a18),x3011,a18) % 1.37/1.32 [372]~E(f14(x3721,f9(a18),a18),x3721) % 1.37/1.32 [376]~E(f14(x3761,f9(a18),a18),f4(a18)) % 1.37/1.32 [380]~P7(f14(f15(f21(f3(f2(a17)),a18),x3801,a18),f9(a18),a18),a18) % 1.37/1.32 [381]~P7(f14(f15(f14(f14(f4(a18),f9(a18),a18),f9(a18),a18),x3811,a18),f9(a18),a18),a18) % 1.37/1.32 [302]E(f8(x3021,f14(f4(a18),f9(a18),a18),a18),x3021) % 1.37/1.32 [303]E(f7(x3031,f14(f4(a18),f9(a18),a18),a18),f4(a18)) % 1.37/1.32 [343]P7(f15(f14(f14(f4(a18),f9(a18),a18),f9(a18),a18),x3431,a18),a18) % 1.37/1.32 [294]E(f15(x2941,f21(f3(f2(a17)),a18),a18),f14(x2941,x2941,a18)) % 1.37/1.32 [295]E(f15(f21(f3(f2(a17)),a18),x2951,a18),f14(x2951,x2951,a18)) % 1.37/1.32 [307]E(f8(f14(x3071,x3071,a18),f21(f3(f2(a17)),a18),a18),x3071) % 1.37/1.32 [308]P7(f15(f21(f3(f2(a17)),a18),x3081,a18),a18) % 1.37/1.32 [313]E(f14(f14(x3131,f9(a18),a18),f9(a18),a18),f14(x3131,f21(f3(f2(a17)),a18),a18)) % 1.37/1.32 [314]E(f14(f14(x3141,f9(a18),a18),f9(a18),a18),f14(f21(f3(f2(a17)),a18),x3141,a18)) % 1.37/1.32 [337]E(f14(f14(f14(x3371,f9(a18),a18),f9(a18),a18),f9(a18),a18),f14(f21(f2(f2(a17)),a18),x3371,a18)) % 1.37/1.32 [340]E(f7(f14(f14(x3401,f9(a18),a18),f9(a18),a18),f21(f3(f2(a17)),a18),a18),f7(x3401,f21(f3(f2(a17)),a18),a18)) % 1.37/1.32 [342]E(f8(f14(f14(x3421,f9(a18),a18),f9(a18),a18),f21(f3(f2(a17)),a18),a18),f14(f8(x3421,f21(f3(f2(a17)),a18),a18),f9(a18),a18)) % 1.37/1.32 [289]E(f15(x2891,x2892,a18),f15(x2892,x2891,a18)) % 1.37/1.32 [290]E(f14(x2901,x2902,a18),f14(x2902,x2901,a18)) % 1.37/1.32 [364]~E(f3(x3641),f2(x3642)) % 1.37/1.32 [378]~P8(f14(x3781,x3782,a18),x3782,a18) % 1.37/1.32 [379]~P8(f14(x3791,x3792,a18),x3791,a18) % 1.37/1.32 [291]E(f15(x2911,f4(a18),a18),f15(x2912,f4(a18),a18)) % 1.37/1.32 [293]E(f15(f4(a18),x2931,a18),f15(f4(a18),x2932,a18)) % 1.37/1.32 [296]E(f7(f15(x2961,x2962,a18),x2961,a18),f4(a18)) % 1.37/1.32 [315]P10(f15(f4(a18),x3151,a18),f15(f4(a18),x3152,a18),a18) % 1.37/1.32 [328]P8(x3281,f14(f14(x3282,x3281,a18),f9(a18),a18),a18) % 1.37/1.32 [330]P8(x3301,f14(f14(x3301,x3302,a18),f9(a18),a18),a18) % 1.37/1.32 [316]E(f8(f15(f4(a18),x3161,a18),f15(f4(a18),x3162,a18),a18),f4(a18)) % 1.37/1.32 [322]E(f15(x3221,f14(x3222,f9(a18),a18),a18),f14(x3221,f15(x3221,x3222,a18),a18)) % 1.37/1.32 [323]E(f15(f14(x3231,f9(a18),a18),x3232,a18),f14(x3232,f15(x3231,x3232,a18),a18)) % 1.37/1.32 [325]E(f14(f14(x3251,f9(a18),a18),x3252,a18),f14(f14(x3251,x3252,a18),f9(a18),a18)) % 1.37/1.32 [326]E(f14(f14(x3261,f9(a18),a18),x3262,a18),f14(x3261,f14(x3262,f9(a18),a18),a18)) % 1.37/1.32 [341]E(f7(f14(f7(x3411,x3412,a18),f9(a18),a18),x3412,a18),f7(f14(x3411,f9(a18),a18),x3412,a18)) % 1.37/1.32 [347]E(f8(x3471,f14(f14(f14(x3472,f9(a18),a18),f9(a18),a18),f9(a18),a18),a18),f8(x3471,f14(f21(f2(f2(a17)),a18),x3472,a18),a18)) % 1.37/1.32 [348]E(f7(x3481,f14(f14(f14(x3482,f9(a18),a18),f9(a18),a18),f9(a18),a18),a18),f7(x3481,f14(f21(f2(f2(a17)),a18),x3482,a18),a18)) % 1.37/1.32 [349]E(f8(f14(f14(f14(x3491,f9(a18),a18),f9(a18),a18),f9(a18),a18),x3492,a18),f8(f14(f21(f2(f2(a17)),a18),x3491,a18),x3492,a18)) % 1.37/1.32 [350]E(f7(f14(f14(f14(x3501,f9(a18),a18),f9(a18),a18),f9(a18),a18),x3502,a18),f7(f14(f21(f2(f2(a17)),a18),x3501,a18),x3502,a18)) % 1.37/1.32 [355]E(f14(f14(f8(x3551,x3552,a18),f8(f14(f4(a18),f9(a18),a18),x3552,a18),a18),f8(f14(f7(x3551,x3552,a18),f7(f14(f4(a18),f9(a18),a18),x3552,a18),a18),x3552,a18),a18),f8(f14(x3551,f9(a18),a18),x3552,a18)) % 1.37/1.32 [318]E(f14(x3181,f14(x3182,x3183,a18),a18),f14(x3182,f14(x3181,x3183,a18),a18)) % 1.37/1.32 [319]E(f8(f8(x3191,x3192,a18),x3193,a18),f8(x3191,f15(x3192,x3193,a18),a18)) % 1.37/1.32 [320]E(f15(f15(x3201,x3202,a18),x3203,a18),f15(x3201,f15(x3202,x3203,a18),a18)) % 1.37/1.32 [321]E(f14(f14(x3211,x3212,a18),x3213,a18),f14(x3211,f14(x3212,x3213,a18),a18)) % 1.37/1.32 [332]E(f14(f15(x3321,x3322,a18),f15(x3321,x3323,a18),a18),f15(x3321,f14(x3322,x3323,a18),a18)) % 1.37/1.32 [333]E(f7(f15(x3331,x3332,a18),f15(x3331,x3333,a18),a18),f15(x3331,f7(x3332,x3333,a18),a18)) % 1.37/1.32 [334]E(f14(f15(x3341,x3342,a18),f15(x3343,x3342,a18),a18),f15(f14(x3341,x3343,a18),x3342,a18)) % 1.37/1.32 [335]E(f7(f15(x3351,x3352,a18),f15(x3353,x3352,a18),a18),f15(f7(x3351,x3353,a18),x3352,a18)) % 1.37/1.32 [346]E(f14(f15(x3461,f7(f8(x3462,x3461,a18),x3463,a18),a18),f7(x3462,x3461,a18),a18),f7(x3462,f15(x3461,x3463,a18),a18)) % 1.37/1.32 [331]E(f7(f14(f15(x3311,x3312,a18),x3313,a18),x3312,a18),f7(x3313,x3312,a18)) % 1.37/1.32 [345]E(f7(f14(f14(f15(x3451,x3452,a18),x3453,a18),f9(a18),a18),x3452,a18),f7(f14(x3453,f9(a18),a18),x3452,a18)) % 1.37/1.32 [353]E(f14(f15(x3531,f8(x3532,x3533,a18),a18),f8(f15(x3531,f7(x3532,x3533,a18),a18),x3533,a18),a18),f8(f15(x3531,x3532,a18),x3533,a18)) % 1.37/1.32 [354]E(f14(f14(f8(x3541,x3542,a18),f8(x3543,x3542,a18),a18),f8(f14(f7(x3541,x3542,a18),f7(x3543,x3542,a18),a18),x3542,a18),a18),f8(f14(x3541,x3543,a18),x3542,a18)) % 1.37/1.32 [344]E(f14(f15(x3441,x3442,a18),f14(f15(x3443,x3442,a18),x3444,a18),a18),f14(f15(f14(x3441,x3443,a18),x3442,a18),x3444,a18)) % 1.37/1.32 [383]E(x3831,a1)+~E(f2(x3831),a1) % 1.37/1.32 [384]E(x3841,a17)+~E(f3(x3841),a17) % 1.37/1.32 [385]E(a1,x3851)+~E(f2(x3851),a1) % 1.37/1.32 [386]E(a17,x3861)+~E(f3(x3861),a17) % 1.37/1.32 [390]~P65(x3901)+~E(f9(x3901),f4(x3901)) % 1.37/1.32 [392]~P14(x3921)+E(f21(a17,x3921),f4(x3921)) % 1.37/1.32 [393]~P73(x3931)+P9(f4(x3931),x3931) % 1.37/1.32 [409]~P73(x4091)+~P9(f9(x4091),x4091) % 1.37/1.32 [418]~P14(x4181)+P9(f21(a17,x4181),x4181) % 1.37/1.32 [432]E(x4321,f4(a18))+P8(f4(a18),x4321,a18) % 1.37/1.32 [449]~P14(x4491)+~P9(f21(a1,x4491),x4491) % 1.37/1.32 [471]P7(x4711,a18)+P8(f4(a18),x4711,a18) % 1.37/1.32 [494]~P59(x4941)+P11(f4(x4941),f9(x4941),x4941) % 1.37/1.32 [495]~P59(x4951)+P8(f4(x4951),f9(x4951),x4951) % 1.37/1.32 [528]E(x5281,f9(a18))+~P10(x5281,f9(a18),a18) % 1.37/1.32 [572]~P59(x5721)+~P11(f9(x5721),f4(x5721),x5721) % 1.37/1.32 [573]~P59(x5731)+~P8(f9(x5731),f4(x5731),x5731) % 1.37/1.32 [395]~P14(x3951)+E(f21(f2(a17),x3951),f9(x3951)) % 1.37/1.32 [396]~P73(x3961)+E(f23(f4(a18),x3961),f4(x3961)) % 1.37/1.32 [397]~P73(x3971)+E(f23(f9(a18),x3971),f9(x3971)) % 1.37/1.32 [399]~P30(x3991)+E(f10(f4(x3991),x3991),f4(x3991)) % 1.37/1.32 [400]~P45(x4001)+E(f10(f9(x4001),x4001),f9(x4001)) % 1.37/1.32 [401]~P12(x4011)+E(f16(f4(x4011),x4011),f4(x4011)) % 1.37/1.32 [402]~P27(x4021)+E(f16(f4(x4021),x4021),f4(x4021)) % 1.37/1.32 [403]~P47(x4031)+E(f11(f4(x4031),x4031),f4(x4031)) % 1.37/1.32 [404]~P49(x4041)+E(f11(f9(x4041),x4041),f9(x4041)) % 1.37/1.32 [411]~P14(x4111)+E(f16(f9(x4111),x4111),f21(a1,x4111)) % 1.37/1.32 [498]~P3(x4981)+E(f14(f4(x4981),f4(x4981),x4981),f4(x4981)) % 1.37/1.32 [503]~P14(x5031)+~P9(f21(f2(a17),x5031),x5031) % 1.37/1.32 [559]~P30(x5591)+P11(f10(f4(x5591),x5591),f4(x5591),x5591) % 1.37/1.32 [608]~P7(x6081,a18)+E(f15(f21(f3(f2(a17)),a18),f24(x6081),a18),x6081) % 1.37/1.32 [617]P7(x6171,a18)+P7(f14(x6171,f9(a18),a18),a18) % 1.37/1.32 [660]~P30(x6601)+~P8(f4(x6601),f10(f4(x6601),x6601),x6601) % 1.37/1.32 [776]~P59(x7761)+P8(f4(x7761),f14(f9(x7761),f9(x7761),x7761),x7761) % 1.37/1.32 [808]~P7(x8081,a18)+~P7(f14(x8081,f9(a18),a18),a18) % 1.37/1.32 [895]~P8(f4(a18),x8951,a18)+P10(f15(x8951,f9(a18),a18),x8951,a18) % 1.37/1.32 [896]~P8(f4(a18),x8961,a18)+P10(f15(f9(a18),x8961,a18),x8961,a18) % 1.37/1.32 [909]E(x9091,f4(a18))+~P8(x9091,f14(f4(a18),f9(a18),a18),a18) % 1.37/1.32 [1011]~P10(x10111,f14(f4(a18),f9(a18),a18),a18)+E(x10111,f14(f4(a18),f9(a18),a18)) % 1.37/1.32 [1603]P7(x16031,a18)+E(f14(f15(f14(f14(f4(a18),f9(a18),a18),f9(a18),a18),f8(x16031,f14(f14(f4(a18),f9(a18),a18),f9(a18),a18),a18),a18),f9(a18),a18),x16031) % 1.37/1.32 [551]~P14(x5511)+E(f14(f9(x5511),f9(x5511),x5511),f21(f3(f2(a17)),x5511)) % 1.37/1.32 [601]~P7(x6011,a18)+P10(f21(f3(f2(a17)),a18),x6011,a18) % 1.37/1.32 [684]P7(x6841,a18)+~P10(f21(f3(f2(a17)),a18),x6841,a18) % 1.37/1.32 [1015]~P60(x10151)+E(f14(f15(f4(x10151),f4(x10151),x10151),f15(f4(x10151),f4(x10151),x10151),x10151),f4(x10151)) % 1.37/1.32 [1194]~P7(x11941,a18)+E(f7(x11941,f14(f14(f4(a18),f9(a18),a18),f9(a18),a18),a18),f4(a18)) % 1.37/1.32 [1290]P7(x12901,a18)+E(f7(x12901,f14(f14(f4(a18),f9(a18),a18),f9(a18),a18),a18),f14(f4(a18),f9(a18),a18)) % 1.37/1.32 [1441]P7(x14411,a18)+~E(f7(x14411,f14(f14(f4(a18),f9(a18),a18),f9(a18),a18),a18),f4(a18)) % 1.37/1.32 [1469]~P60(x14691)+P11(f14(f15(f4(x14691),f4(x14691),x14691),f15(f4(x14691),f4(x14691),x14691),x14691),f4(x14691),x14691) % 1.37/1.32 [1490]~P7(x14901,a18)+~E(f7(x14901,f14(f14(f4(a18),f9(a18),a18),f9(a18),a18),a18),f14(f4(a18),f9(a18),a18)) % 1.37/1.32 [1543]~P7(x15431,a18)+E(f8(f14(x15431,f9(a18),a18),f14(f14(f4(a18),f9(a18),a18),f9(a18),a18),a18),f8(x15431,f14(f14(f4(a18),f9(a18),a18),f9(a18),a18),a18)) % 1.37/1.32 [1576]~P60(x15761)+~P8(f4(x15761),f14(f15(f4(x15761),f4(x15761),x15761),f15(f4(x15761),f4(x15761),x15761),x15761),x15761) % 1.37/1.32 [1583]P7(x15831,a18)+E(f8(f14(x15831,f9(a18),a18),f14(f14(f4(a18),f9(a18),a18),f9(a18),a18),a18),f14(f8(x15831,f14(f14(f4(a18),f9(a18),a18),f9(a18),a18),a18),f9(a18),a18)) % 1.37/1.32 [593]~P45(x5931)+E(f22(f4(x5931),f21(f3(f2(a17)),a18),x5931),f4(x5931)) % 1.37/1.32 [594]~P73(x5941)+E(f22(f4(x5941),f21(f3(f2(a17)),a18),x5941),f4(x5941)) % 1.37/1.32 [595]~P73(x5951)+E(f22(f9(x5951),f21(f3(f2(a17)),a18),x5951),f9(x5951)) % 1.37/1.32 [1032]~P7(x10321,a18)+E(f8(f14(x10321,f9(a18),a18),f21(f3(f2(a17)),a18),a18),f8(x10321,f21(f3(f2(a17)),a18),a18)) % 1.37/1.32 [1067]~P8(f9(a18),x10671,a18)+P8(f4(a18),f8(x10671,f21(f3(f2(a17)),a18),a18),a18) % 1.37/1.32 [1193]P8(f4(a18),f7(x11931,f21(f3(f2(a17)),a18),a18),a18)+~E(f7(x11931,f21(f3(f2(a17)),a18),a18),f9(a18)) % 1.37/1.32 [1236]~P45(x12361)+~P8(f4(x12361),f22(f4(x12361),f21(f3(f2(a17)),a18),x12361),x12361) % 1.37/1.32 [1298]P7(x12981,a18)+E(f8(f14(x12981,f9(a18),a18),f21(f3(f2(a17)),a18),a18),f14(f8(x12981,f21(f3(f2(a17)),a18),a18),f9(a18),a18)) % 1.37/1.32 [1315]~P8(f4(a18),f7(x13151,f21(f3(f2(a17)),a18),a18),a18)+E(f7(x13151,f21(f3(f2(a17)),a18),a18),f9(a18)) % 1.37/1.32 [1382]~P8(f4(a18),x13821,a18)+P8(f4(a18),f8(f14(x13821,f9(a18),a18),f21(f3(f2(a17)),a18),a18),a18) % 1.37/1.32 [1580]~P7(x15801,a18)+E(f15(f14(f14(f4(a18),f9(a18),a18),f9(a18),a18),f8(x15801,f14(f14(f4(a18),f9(a18),a18),f9(a18),a18),a18),a18),x15801) % 1.37/1.32 [985]~P7(x9851,a18)+P7(f7(x9851,f21(f3(f3(f2(a17))),a18),a18),a18) % 1.37/1.32 [1279]P7(x12791,a18)+~P7(f7(x12791,f21(f3(f3(f2(a17))),a18),a18),a18) % 1.37/1.32 [1313]~P45(x13131)+E(f14(f22(f4(x13131),f21(f3(f2(a17)),a18),x13131),f22(f4(x13131),f21(f3(f2(a17)),a18),x13131),x13131),f4(x13131)) % 1.37/1.32 [1564]~P45(x15641)+P11(f14(f22(f4(x15641),f21(f3(f2(a17)),a18),x15641),f22(f4(x15641),f21(f3(f2(a17)),a18),x15641),x15641),f4(x15641),x15641) % 1.37/1.32 [1588]~P45(x15881)+~P8(f4(x15881),f14(f22(f4(x15881),f21(f3(f2(a17)),a18),x15881),f22(f4(x15881),f21(f3(f2(a17)),a18),x15881),x15881),x15881) % 1.37/1.32 [438]~P1(x4382)+P10(x4381,x4381,x4382) % 1.37/1.32 [439]~P36(x4392)+P11(x4391,x4391,x4392) % 1.37/1.32 [440]~P37(x4402)+P11(x4401,x4401,x4402) % 1.37/1.32 [532]~P8(x5322,x5322,x5321)+~P33(x5321) % 1.37/1.32 [533]~P8(x5332,x5332,x5331)+~P36(x5331) % 1.37/1.32 [534]~P8(x5342,x5342,x5341)+~P37(x5341) % 1.37/1.32 [387]E(x3871,x3872)+~E(f2(x3871),f2(x3872)) % 1.37/1.32 [388]E(x3881,x3882)+~E(f3(x3881),f3(x3882)) % 1.37/1.32 [417]E(x4171,x4172)+~E(f23(x4171,a19),f23(x4172,a19)) % 1.37/1.32 [441]~P22(x4412)+E(f15(x4411,x4411,x4412),x4411) % 1.37/1.32 [443]~P5(x4432)+E(f7(x4431,x4431,x4432),f4(x4432)) % 1.37/1.32 [445]~P12(x4452)+E(f13(x4451,x4451,x4452),f4(x4452)) % 1.37/1.32 [446]~P13(x4462)+E(f13(x4461,x4461,x4462),f4(x4462)) % 1.37/1.32 [450]~P1(x4502)+P10(x4501,f4(x4502),x4502) % 1.37/1.32 [451]~P1(x4511)+P10(f9(x4511),x4512,x4511) % 1.37/1.32 [513]~P30(x5132)+P11(x5131,f10(x5131,x5132),x5132) % 1.37/1.32 [515]~E(f14(x5152,x5151,a18),x5152)+E(x5151,f4(a18)) % 1.37/1.32 [520]E(x5201,f4(a18))+~E(f14(x5202,x5201,a18),f4(a18)) % 1.37/1.32 [521]E(x5211,f9(a18))+~E(f15(x5212,x5211,a18),f9(a18)) % 1.37/1.32 [522]E(x5221,f4(a18))+~E(f14(x5221,x5222,a18),f4(a18)) % 1.37/1.32 [523]E(x5231,f9(a18))+~E(f15(x5231,x5232,a18),f9(a18)) % 1.37/1.32 [535]~P30(x5351)+P11(f4(x5351),f10(x5352,x5351),x5351) % 1.37/1.32 [537]~P59(x5371)+P11(f4(x5371),f23(x5372,x5371),x5371) % 1.37/1.32 [575]~P30(x5752)+P11(f16(x5751,x5752),f10(x5751,x5752),x5752) % 1.37/1.32 [618]~P7(x6182,a18)+P7(f15(x6181,x6182,a18),a18) % 1.37/1.32 [619]~P7(x6191,a18)+P7(f15(x6191,x6192,a18),a18) % 1.37/1.32 [621]~P8(x6211,x6212,a18)+E(f7(x6211,x6212,a18),x6211) % 1.37/1.32 [623]~P8(x6231,x6232,a18)+E(f8(x6231,x6232,a18),f4(a18)) % 1.37/1.32 [634]~P59(x6341)+~P8(f23(x6342,x6341),f4(x6341),x6341) % 1.37/1.32 [635]~P30(x6351)+~P8(f10(x6352,x6351),f4(x6351),x6351) % 1.37/1.32 [696]~P60(x6961)+P11(f4(x6961),f15(x6962,x6962,x6961),x6961) % 1.37/1.32 [876]~P10(x8761,x8762,a18)+P10(x8761,f14(x8762,x8761,a18),a18) % 1.37/1.32 [886]P8(f7(x8861,x8862,a18),x8862,a18)+~P8(f4(a18),x8862,a18) % 1.37/1.32 [920]~P60(x9201)+~P8(f15(x9202,x9202,x9201),f4(x9201),x9201) % 1.37/1.32 [971]P10(x9711,x9712,a18)+~P10(x9711,f14(x9712,x9711,a18),a18) % 1.37/1.32 [988]P8(f4(a18),x9881,a18)+~P8(f4(a18),f15(x9882,x9881,a18),a18) % 1.37/1.32 [989]P8(f4(a18),x9891,a18)+~P8(f4(a18),f15(x9891,x9892,a18),a18) % 1.37/1.32 [421]~P17(x4212)+E(f16(f16(x4211,x4212),x4212),x4211) % 1.37/1.32 [423]~P12(x4232)+E(f16(f16(x4231,x4232),x4232),x4231) % 1.37/1.32 [435]~P30(x4352)+E(f10(f10(x4351,x4352),x4352),f10(x4351,x4352)) % 1.37/1.32 [436]~P30(x4362)+E(f10(f16(x4361,x4362),x4362),f10(x4361,x4362)) % 1.37/1.32 [437]~P45(x4372)+E(f10(f23(x4371,x4372),x4372),f23(x4371,x4372)) % 1.37/1.32 [447]~P1(x4472)+E(f22(x4471,f9(a18),x4472),x4471) % 1.37/1.32 [448]~P28(x4482)+E(f22(x4481,f9(a18),x4482),x4481) % 1.37/1.32 [452]~P1(x4522)+E(f15(x4521,f9(x4522),x4522),x4521) % 1.37/1.32 [453]~P28(x4532)+E(f15(x4531,f9(x4532),x4532),x4531) % 1.37/1.32 [454]~P1(x4542)+E(f14(x4541,f4(x4542),x4542),x4541) % 1.37/1.32 [455]~P18(x4552)+E(f14(x4551,f4(x4552),x4552),x4551) % 1.37/1.32 [456]~P29(x4562)+E(f14(x4561,f4(x4562),x4562),x4561) % 1.37/1.32 [457]~P5(x4572)+E(f8(x4571,f9(x4572),x4572),x4571) % 1.37/1.32 [458]~P5(x4582)+E(f7(x4581,f4(x4582),x4582),x4581) % 1.37/1.32 [459]~P48(x4592)+E(f12(x4591,f9(x4592),x4592),x4591) % 1.37/1.32 [460]~P12(x4602)+E(f13(x4601,f4(x4602),x4602),x4601) % 1.37/1.32 [462]~P1(x4621)+E(f15(f9(x4621),x4622,x4621),x4622) % 1.37/1.32 [463]~P28(x4631)+E(f15(f9(x4631),x4632,x4631),x4632) % 1.37/1.32 [464]~P24(x4641)+E(f15(f9(x4641),x4642,x4641),x4642) % 1.37/1.32 [466]~P1(x4661)+E(f14(f4(x4661),x4662,x4661),x4662) % 1.37/1.32 [467]~P18(x4671)+E(f14(f4(x4671),x4672,x4671),x4672) % 1.37/1.32 [468]~P29(x4681)+E(f14(f4(x4681),x4682,x4681),x4682) % 1.37/1.32 [469]~P1(x4692)+E(f22(x4691,f4(a18),x4692),f9(x4692)) % 1.37/1.32 [470]~P32(x4702)+E(f22(x4701,f4(a18),x4702),f9(x4702)) % 1.37/1.32 [475]~P1(x4752)+E(f15(x4751,f4(x4752),x4752),f4(x4752)) % 1.37/1.32 [476]~P52(x4762)+E(f15(x4761,f4(x4762),x4762),f4(x4762)) % 1.37/1.32 [478]~P39(x4782)+E(f15(x4781,f4(x4782),x4782),f4(x4782)) % 1.37/1.32 [479]~P69(x4792)+E(f15(x4791,f4(x4792),x4792),f4(x4792)) % 1.37/1.32 [480]~P5(x4802)+E(f8(x4801,f4(x4802),x4802),f4(x4802)) % 1.37/1.32 [481]~P5(x4812)+E(f7(x4811,f9(x4812),x4812),f4(x4812)) % 1.37/1.32 [482]~P28(x4821)+E(f22(f9(x4821),x4822,x4821),f9(x4821)) % 1.37/1.32 [484]~P1(x4841)+E(f15(f4(x4841),x4842,x4841),f4(x4841)) % 1.37/1.32 [485]~P52(x4851)+E(f15(f4(x4851),x4852,x4851),f4(x4851)) % 1.37/1.32 [487]~P39(x4871)+E(f15(f4(x4871),x4872,x4871),f4(x4871)) % 1.37/1.32 [488]~P69(x4881)+E(f15(f4(x4881),x4882,x4881),f4(x4881)) % 1.37/1.32 [489]~P5(x4891)+E(f8(f4(x4891),x4892,x4891),f4(x4891)) % 1.37/1.32 [490]~P5(x4901)+E(f7(f4(x4901),x4902,x4901),f4(x4901)) % 1.37/1.32 [491]~P48(x4911)+E(f12(f4(x4911),x4912,x4911),f4(x4911)) % 1.37/1.32 [492]~P38(x4921)+E(f12(f4(x4921),x4922,x4921),f4(x4921)) % 1.37/1.32 [504]~P48(x5041)+E(f12(f9(x5041),x5042,x5041),f11(x5042,x5041)) % 1.37/1.32 [505]~P12(x5051)+E(f13(f4(x5051),x5052,x5051),f16(x5052,x5051)) % 1.37/1.32 [510]~P14(x5102)+E(f14(x5101,f21(a17,x5102),x5102),x5101) % 1.37/1.32 [511]~P14(x5111)+E(f14(f21(a17,x5111),x5112,x5111),x5112) % 1.37/1.32 [524]~P12(x5242)+E(f14(x5241,f16(x5241,x5242),x5242),f4(x5242)) % 1.37/1.32 [526]~P12(x5262)+E(f14(f16(x5261,x5262),x5261,x5262),f4(x5262)) % 1.37/1.32 [527]~P13(x5272)+E(f14(f16(x5271,x5272),x5271,x5272),f4(x5272)) % 1.37/1.32 [548]~P14(x5482)+E(f15(x5481,f21(a1,x5482),x5482),f16(x5481,x5482)) % 1.37/1.32 [549]~P14(x5491)+E(f15(f21(a1,x5491),x5492,x5491),f16(x5492,x5491)) % 1.37/1.32 [636]~P30(x6362)+P11(f16(f10(x6361,x6362),x6362),f4(x6362),x6362) % 1.37/1.32 [666]~P45(x6662)+E(f15(f10(x6661,x6662),f10(x6661,x6662),x6662),f15(x6661,x6661,x6662)) % 1.37/1.32 [668]~P46(x6682)+E(f15(f16(x6681,x6682),f16(x6681,x6682),x6682),f15(x6681,x6681,x6682)) % 1.37/1.32 [719]~P59(x7192)+P8(x7191,f14(x7191,f9(x7192),x7192),x7192) % 1.37/1.32 [720]~P45(x7201)+P8(f4(x7201),f22(x7202,f4(a18),x7201),x7201) % 1.37/1.32 [825]P8(x8251,x8252,a18)+P8(x8252,f14(x8251,f9(a18),a18),a18) % 1.37/1.32 [866]E(x8661,f14(f4(a18),f9(a18),a18))+~E(f15(x8662,x8661,a18),f14(f4(a18),f9(a18),a18)) % 1.37/1.32 [867]E(x8671,f14(f4(a18),f9(a18),a18))+~E(f15(x8671,x8672,a18),f14(f4(a18),f9(a18),a18)) % 1.37/1.32 [870]~P14(x8701)+E(f15(f14(f9(x8701),f9(x8701),x8701),f21(x8702,x8701),x8701),f21(f3(x8702),x8701)) % 1.37/1.32 [887]~P8(f4(a18),x8872,a18)+E(f8(f15(x8871,x8872,a18),x8872,a18),x8871) % 1.37/1.32 [888]~P8(f4(a18),x8881,a18)+E(f8(f15(x8881,x8882,a18),x8881,a18),x8882) % 1.37/1.32 [933]~P14(x9331)+E(f14(f14(f9(x9331),f21(x9332,x9331),x9331),f21(x9332,x9331),x9331),f21(f2(x9332),x9331)) % 1.37/1.32 [934]~P14(x9341)+E(f14(f14(f4(x9341),f21(x9342,x9341),x9341),f21(x9342,x9341),x9341),f21(f3(x9342),x9341)) % 1.37/1.32 [939]~P45(x9391)+~P11(f22(x9392,f4(a18),x9391),f4(x9391),x9391) % 1.37/1.32 [1056]~P8(x10561,x10562,a18)+~P8(x10562,f14(x10561,f9(a18),a18),a18) % 1.37/1.32 [1299]P8(x12991,x12992,a18)+~P8(f14(x12991,f9(a18),a18),f14(x12992,f9(a18),a18),a18) % 1.37/1.32 [540]~P14(x5402)+E(f15(x5401,f21(f2(a17),x5402),x5402),x5401) % 1.37/1.32 [541]~P14(x5411)+E(f15(f21(f2(a17),x5411),x5412,x5411),x5412) % 1.37/1.32 [576]~P14(x5761)+E(f15(f16(f9(x5761),x5761),x5762,x5761),f16(x5762,x5761)) % 1.37/1.32 [833]~P73(x8331)+E(f14(f9(x8331),f23(x8332,x8331),x8331),f23(f14(x8332,f9(a18),a18),x8331)) % 1.37/1.32 [890]~P1(x8902)+E(f14(x8901,x8901,x8902),f15(f14(f9(x8902),f9(x8902),x8902),x8901,x8902)) % 1.37/1.32 [1195]~E(f14(f7(x11951,x11952,a18),f9(a18),a18),x11952)+E(f7(f14(x11951,f9(a18),a18),x11952,a18),f4(a18)) % 1.37/1.32 [1281]~P8(f9(a18),x12811,a18)+E(f7(f14(f15(x12811,x12812,a18),f9(a18),a18),x12811,a18),f9(a18)) % 1.37/1.32 [1300]E(f14(f7(x13001,x13002,a18),f9(a18),a18),x13002)+E(f7(f14(x13001,f9(a18),a18),x13002,a18),f14(f7(x13001,x13002,a18),f9(a18),a18)) % 1.37/1.32 [1429]~P14(x14291)+E(f22(f21(a1,x14291),f14(f15(f21(f3(f2(a17)),a18),x14292,a18),f9(a18),a18),x14291),f21(a1,x14291)) % 1.37/1.32 [1437]~P41(x14371)+E(f22(f16(f9(x14371),x14371),f14(f15(f21(f3(f2(a17)),a18),x14372,a18),f9(a18),a18),x14371),f16(f9(x14371),x14371)) % 1.37/1.32 [1539]~P8(f4(a18),x15392,a18)+P8(x15391,f15(x15392,f14(f8(x15391,x15392,a18),f9(a18),a18),a18),a18) % 1.37/1.32 [661]~P1(x6612)+E(f15(x6611,x6611,x6612),f22(x6611,f21(f3(f2(a17)),a18),x6612)) % 1.37/1.32 [662]~P28(x6622)+E(f22(x6621,f21(f3(f2(a17)),a18),x6622),f15(x6621,x6621,x6622)) % 1.37/1.32 [663]~P14(x6632)+E(f15(x6631,f21(f3(f2(a17)),x6632),x6632),f14(x6631,x6631,x6632)) % 1.37/1.32 [664]~P14(x6641)+E(f15(f21(f3(f2(a17)),x6641),x6642,x6641),f14(x6642,x6642,x6641)) % 1.37/1.32 [868]~P45(x8682)+E(f22(f10(x8681,x8682),f21(f3(f2(a17)),a18),x8682),f22(x8681,f21(f3(f2(a17)),a18),x8682)) % 1.37/1.32 [869]~P41(x8692)+E(f22(f16(x8691,x8692),f21(f3(f2(a17)),a18),x8692),f22(x8691,f21(f3(f2(a17)),a18),x8692)) % 1.37/1.32 [908]~P45(x9081)+P11(f4(x9081),f22(x9082,f21(f3(f2(a17)),a18),x9081),x9081) % 1.37/1.32 [910]~P28(x9102)+E(f22(x9101,f21(f2(f2(a17)),a18),x9102),f15(f15(x9101,x9101,x9102),x9101,x9102)) % 1.37/1.32 [1196]~P45(x11961)+~P8(f22(x11962,f21(f3(f2(a17)),a18),x11961),f4(x11961),x11961) % 1.37/1.32 [945]~P14(x9451)+E(f22(f21(a1,x9451),f15(f21(f3(f2(a17)),a18),x9452,a18),x9451),f9(x9451)) % 1.37/1.32 [979]~P41(x9791)+E(f22(f16(f9(x9791),x9791),f15(f21(f3(f2(a17)),a18),x9792,a18),x9791),f9(x9791)) % 1.37/1.32 [1004]~P45(x10042)+E(f10(f22(x10041,f21(f3(f2(a17)),a18),x10042),x10042),f22(x10041,f21(f3(f2(a17)),a18),x10042)) % 1.37/1.32 [581]~P1(x5813)+E(f15(x5811,x5812,x5813),f15(x5812,x5811,x5813)) % 1.37/1.32 [583]~P1(x5833)+E(f14(x5831,x5832,x5833),f14(x5832,x5831,x5833)) % 1.37/1.32 [584]~P18(x5843)+E(f14(x5841,x5842,x5843),f14(x5842,x5841,x5843)) % 1.37/1.32 [670]E(x6701,x6702)+~E(f14(x6703,x6701,a18),f14(x6703,x6702,a18)) % 1.37/1.32 [671]E(x6711,x6712)+~E(f14(x6711,x6713,a18),f14(x6712,x6713,a18)) % 1.37/1.32 [672]~P1(x6723)+P10(x6721,f15(x6722,x6721,x6723),x6723) % 1.37/1.32 [673]~P1(x6733)+P10(x6731,f15(x6731,x6732,x6733),x6733) % 1.37/1.32 [674]~P50(x6743)+P10(x6741,f15(x6741,x6742,x6743),x6743) % 1.37/1.32 [878]~P8(x8781,x8783,a18)+P8(x8781,f14(x8782,x8783,a18),a18) % 1.37/1.32 [880]~P8(x8801,x8802,a18)+P8(x8801,f14(x8802,x8803,a18),a18) % 1.37/1.32 [972]P8(x9721,x9722,a18)+~P8(f14(x9721,x9723,a18),x9722,a18) % 1.37/1.32 [1068]~P10(x10682,x10683,a18)+P10(f15(x10681,x10682,a18),f15(x10681,x10683,a18),a18) % 1.37/1.32 [1069]~P8(x10691,x10693,a18)+P8(f14(x10691,x10692,a18),f14(x10693,x10692,a18),a18) % 1.37/1.32 [1070]~P8(x10702,x10703,a18)+P8(f14(x10701,x10702,a18),f14(x10701,x10703,a18),a18) % 1.37/1.32 [1282]P8(x12821,x12822,a18)+~P8(f15(x12823,x12821,a18),f15(x12823,x12822,a18),a18) % 1.37/1.32 [1283]P8(x12831,x12832,a18)+~P8(f15(x12831,x12833,a18),f15(x12832,x12833,a18),a18) % 1.37/1.32 [1284]P8(x12841,x12842,a18)+~P8(f14(x12843,x12841,a18),f14(x12843,x12842,a18),a18) % 1.37/1.32 [1288]~P8(f15(x12882,x12881,a18),f15(x12883,x12881,a18),a18)+P8(f4(a18),x12881,a18) % 1.37/1.32 [1289]~P8(f15(x12891,x12892,a18),f15(x12891,x12893,a18),a18)+P8(f4(a18),x12891,a18) % 1.37/1.32 [625]~P48(x6253)+E(f15(x6251,f11(x6252,x6253),x6253),f12(x6251,x6252,x6253)) % 1.37/1.32 [626]~P12(x6263)+E(f14(x6261,f16(x6262,x6263),x6263),f13(x6261,x6262,x6263)) % 1.37/1.32 [628]~P13(x6283)+E(f14(x6281,f16(x6282,x6283),x6283),f13(x6281,x6282,x6283)) % 1.37/1.32 [629]~P14(x6293)+E(f14(x6291,f16(x6292,x6293),x6293),f13(x6291,x6292,x6293)) % 1.37/1.32 [630]~P12(x6303)+E(f13(x6301,f16(x6302,x6303),x6303),f14(x6301,x6302,x6303)) % 1.37/1.32 [665]~P67(x6652)+E(f15(f16(x6651,x6652),x6653,x6652),f15(x6651,f16(x6653,x6652),x6652)) % 1.37/1.32 [667]~P67(x6672)+E(f15(f16(x6671,x6672),f16(x6673,x6672),x6672),f15(x6671,x6673,x6672)) % 1.37/1.32 [675]~P12(x6753)+E(f14(f13(x6751,x6752,x6753),x6752,x6753),x6751) % 1.37/1.32 [676]~P12(x6763)+E(f13(f14(x6761,x6762,x6763),x6762,x6763),x6761) % 1.37/1.32 [685]~P5(x6853)+E(f8(f7(x6851,x6852,x6853),x6852,x6853),f4(x6853)) % 1.37/1.32 [686]~P5(x6863)+E(f7(f15(x6861,x6862,x6863),x6862,x6863),f4(x6863)) % 1.37/1.32 [687]~P5(x6873)+E(f7(f15(x6871,x6872,x6873),x6871,x6873),f4(x6873)) % 1.37/1.32 [728]~P13(x7283)+E(f16(f13(x7281,x7282,x7283),x7283),f13(x7282,x7281,x7283)) % 1.37/1.32 [764]~P13(x7642)+E(f14(f16(x7641,x7642),f14(x7643,x7641,x7642),x7642),x7643) % 1.37/1.32 [765]~P12(x7652)+E(f14(f16(x7651,x7652),f14(x7651,x7653,x7652),x7652),x7653) % 1.37/1.32 [787]~P67(x7873)+E(f15(x7871,f16(x7872,x7873),x7873),f16(f15(x7871,x7872,x7873),x7873)) % 1.37/1.32 [788]~P45(x7882)+E(f22(f10(x7881,x7882),x7883,x7882),f10(f22(x7881,x7883,x7882),x7882)) % 1.37/1.32 [789]~P67(x7892)+E(f15(f16(x7891,x7892),x7893,x7892),f16(f15(x7891,x7893,x7892),x7892)) % 1.37/1.32 [790]~P48(x7902)+E(f12(f16(x7901,x7902),x7903,x7902),f16(f12(x7901,x7903,x7902),x7902)) % 1.37/1.32 [792]~P39(x7923)+E(f15(x7921,f16(x7922,x7923),x7923),f16(f15(x7921,x7922,x7923),x7923)) % 1.37/1.32 [794]~P39(x7942)+E(f15(f16(x7941,x7942),x7943,x7942),f16(f15(x7941,x7943,x7942),x7942)) % 1.37/1.32 [795]~P38(x7952)+E(f12(f16(x7951,x7952),x7953,x7952),f16(f12(x7951,x7953,x7952),x7952)) % 1.37/1.32 [838]~P22(x8383)+E(f15(x8381,f15(x8381,x8382,x8383),x8383),f15(x8381,x8382,x8383)) % 1.37/1.32 [839]~P5(x8393)+E(f7(f14(x8391,x8392,x8393),x8392,x8393),f7(x8391,x8392,x8393)) % 1.37/1.32 [840]~P5(x8403)+E(f7(f14(x8401,x8402,x8403),x8401,x8403),f7(x8402,x8401,x8403)) % 1.37/1.32 [841]~P5(x8413)+E(f7(f7(x8411,x8412,x8413),x8412,x8413),f7(x8411,x8412,x8413)) % 1.37/1.32 [842]~P45(x8421)+P11(f4(x8421),f22(f10(x8422,x8421),x8423,x8421),x8421) % 1.37/1.32 [850]~P73(x8502)+E(f15(f23(x8501,x8502),f23(x8503,x8502),x8502),f23(f15(x8501,x8503,a18),x8502)) % 1.37/1.32 [851]~P73(x8512)+E(f14(f23(x8511,x8512),f23(x8513,x8512),x8512),f23(f14(x8511,x8513,a18),x8512)) % 1.37/1.32 [853]~P45(x8532)+E(f15(f10(x8531,x8532),f10(x8533,x8532),x8532),f10(f15(x8531,x8533,x8532),x8532)) % 1.37/1.32 [854]~P12(x8542)+E(f14(f16(x8541,x8542),f16(x8543,x8542),x8542),f16(f14(x8543,x8541,x8542),x8542)) % 1.37/1.32 [855]~P13(x8552)+E(f14(f16(x8551,x8552),f16(x8553,x8552),x8552),f16(f14(x8551,x8553,x8552),x8552)) % 1.37/1.32 [856]~P13(x8562)+E(f13(f16(x8561,x8562),f16(x8563,x8562),x8562),f16(f13(x8561,x8563,x8562),x8562)) % 1.37/1.32 [894]~P30(x8943)+E(f10(f13(x8941,x8942,x8943),x8943),f10(f13(x8942,x8941,x8943),x8943)) % 1.37/1.32 [969]~P46(x9692)+P10(f15(x9691,f4(x9692),x9692),f15(x9693,f4(x9692),x9692),x9692) % 1.37/1.32 [970]~P46(x9701)+P10(f15(f4(x9701),x9702,x9701),f15(f4(x9701),x9703,x9701),x9701) % 1.37/1.32 [999]E(x9991,f4(a18))+E(f8(f15(x9991,x9992,a18),f15(x9991,x9993,a18),a18),f8(x9992,x9993,a18)) % 1.37/1.32 [1024]~P28(x10243)+E(f15(f22(x10241,x10242,x10243),x10241,x10243),f15(x10241,f22(x10241,x10242,x10243),x10243)) % 1.37/1.32 [1186]~P8(f4(a18),x11861,a18)+E(f8(f15(x11861,x11862,a18),f15(x11861,x11863,a18),a18),f8(x11862,x11863,a18)) % 1.37/1.32 [1204]~P70(x12041)+E(f15(f22(f16(f9(x12041),x12041),x12042,x12041),f22(x12043,x12042,x12041),x12041),f22(f16(x12043,x12041),x12042,x12041)) % 1.37/1.32 [1310]~P5(x13103)+E(f14(f15(x13101,f8(x13102,x13101,x13103),x13103),f7(x13102,x13101,x13103),x13103),x13102) % 1.37/1.32 [1311]~P5(x13113)+E(f14(f15(f8(x13111,x13112,x13113),x13112,x13113),f7(x13111,x13112,x13113),x13113),x13111) % 1.37/1.32 [1322]~P55(x13223)+P11(f10(f15(x13221,x13222,x13223),x13223),f15(f10(x13221,x13223),f10(x13222,x13223),x13223),x13223) % 1.37/1.32 [1323]~P30(x13233)+P11(f10(f14(x13231,x13232,x13233),x13233),f14(f10(x13231,x13233),f10(x13232,x13233),x13233),x13233) % 1.37/1.32 [1324]~P30(x13243)+P11(f10(f13(x13241,x13242,x13243),x13243),f14(f10(x13241,x13243),f10(x13242,x13243),x13243),x13243) % 1.37/1.32 [1325]~P30(x13252)+P11(f13(f10(x13251,x13252),f10(x13253,x13252),x13252),f10(f13(x13251,x13253,x13252),x13252),x13252) % 1.37/1.32 [1327]~P8(f4(a18),x13271,a18)+E(f22(f5(f15(x13271,x13272,a18)),f15(x13271,x13273,a18),a20),f22(f5(x13272),x13273,a20)) % 1.37/1.32 [1427]~P60(x14271)+P11(f4(x14271),f14(f15(x14272,x14272,x14271),f15(x14273,x14273,x14271),x14271),x14271) % 1.37/1.32 [1544]~P60(x15441)+~P8(f14(f15(x15442,x15442,x15441),f15(x15443,x15443,x15441),x15441),f4(x15441),x15441) % 1.37/1.32 [835]~P12(x8352)+E(f14(x8351,f14(f16(x8351,x8352),x8353,x8352),x8352),x8353) % 1.37/1.32 [973]~P45(x9732)+E(f10(f22(f16(x9731,x9732),x9733,x9732),x9732),f10(f22(x9731,x9733,x9732),x9732)) % 1.37/1.32 [980]~P5(x9801)+E(f8(f15(f4(x9801),x9802,x9801),f15(f4(x9801),x9803,x9801),x9801),f4(x9801)) % 1.37/1.32 [1040]~P1(x10403)+E(f15(x10401,f22(x10401,x10402,x10403),x10403),f22(x10401,f14(x10402,f9(a18),a18),x10403)) % 1.37/1.32 [1041]~P1(x10413)+E(f15(f22(x10411,x10412,x10413),x10411,x10413),f22(x10411,f14(x10412,f9(a18),a18),x10413)) % 1.37/1.32 [1043]~P1(x10433)+E(f22(x10431,f14(x10432,f9(a18),a18),x10433),f15(x10431,f22(x10431,x10432,x10433),x10433)) % 1.37/1.32 [1044]~P32(x10443)+E(f22(x10441,f14(x10442,f9(a18),a18),x10443),f15(x10441,f22(x10441,x10442,x10443),x10443)) % 1.37/1.32 [1045]~P28(x10453)+E(f22(x10451,f14(x10452,f9(a18),a18),x10453),f15(f22(x10451,x10452,x10453),x10451,x10453)) % 1.37/1.32 [1052]~P30(x10522)+E(f10(f14(f10(x10521,x10522),f10(x10523,x10522),x10522),x10522),f14(f10(x10521,x10522),f10(x10523,x10522),x10522)) % 1.37/1.32 [1063]~P1(x10633)+E(f14(x10631,f15(x10632,x10631,x10633),x10633),f15(f14(x10632,f9(x10633),x10633),x10631,x10633)) % 1.37/1.32 [1064]~P1(x10643)+E(f14(f15(x10641,x10642,x10643),x10642,x10643),f15(f14(x10641,f9(x10643),x10643),x10642,x10643)) % 1.37/1.32 [1154]~P6(x11543)+E(f7(f16(f7(x11541,x11542,x11543),x11543),x11542,x11543),f7(f16(x11541,x11543),x11542,x11543)) % 1.37/1.32 [1309]~P5(x13093)+E(f14(f7(x13091,x13092,x13093),f15(f8(x13091,x13092,x13093),x13092,x13093),x13093),x13091) % 1.37/1.32 [1326]E(x13261,x13262)+~E(f15(f14(x13263,f9(a18),a18),x13261,a18),f15(f14(x13263,f9(a18),a18),x13262,a18)) % 1.37/1.32 [1501]~P30(x15012)+P11(f10(f13(f10(x15011,x15012),f10(x15013,x15012),x15012),x15012),f10(f13(x15011,x15013,x15012),x15012),x15012) % 1.37/1.32 [1521]~P8(x15212,x15213,a18)+P8(f15(f14(x15211,f9(a18),a18),x15212,a18),f15(f14(x15211,f9(a18),a18),x15213,a18),a18) % 1.37/1.32 [1578]~P1(x15783)+E(f22(x15781,f14(f15(f21(f3(f2(a17)),a18),x15782,a18),f9(a18),a18),x15783),f15(x15781,f15(f22(x15781,x15782,x15783),f22(x15781,x15782,x15783),x15783),x15783)) % 1.37/1.32 [1296]~P28(x12963)+E(f22(f22(x12961,x12962,x12963),f21(f3(f2(a17)),a18),x12963),f22(x12961,f15(f21(f3(f2(a17)),a18),x12962,a18),x12963)) % 1.37/1.32 [1346]~P1(x13463)+E(f22(x13461,f15(f21(f3(f2(a17)),a18),x13462,a18),x13463),f15(f22(x13461,x13462,x13463),f22(x13461,x13462,x13463),x13463)) % 1.37/1.32 [1349]~P41(x13492)+E(f22(f16(x13491,x13492),f15(f21(f3(f2(a17)),a18),x13493,a18),x13492),f22(x13491,f15(f21(f3(f2(a17)),a18),x13493,a18),x13492)) % 1.37/1.32 [1383]~P45(x13831)+P11(f4(x13831),f22(x13832,f15(f21(f3(f2(a17)),a18),x13833,a18),x13831),x13831) % 1.37/1.32 [1551]~P45(x15511)+P11(f4(x15511),f14(f22(x15512,f21(f3(f2(a17)),a18),x15511),f22(x15513,f21(f3(f2(a17)),a18),x15511),x15511),x15511) % 1.37/1.32 [1565]~P28(x15653)+E(f22(x15651,f14(f15(f21(f3(f2(a17)),a18),x15652,a18),f9(a18),a18),x15653),f15(x15651,f22(f22(x15651,x15652,x15653),f21(f3(f2(a17)),a18),x15653),x15653)) % 1.37/1.32 [1585]~P45(x15851)+~P8(f14(f22(x15852,f21(f3(f2(a17)),a18),x15851),f22(x15853,f21(f3(f2(a17)),a18),x15851),x15851),f4(x15851),x15851) % 1.37/1.32 [1589]~P14(x15892)+E(f14(f14(f22(x15891,f21(f3(f2(a17)),a18),x15892),f22(x15893,f21(f3(f2(a17)),a18),x15892),x15892),f15(f15(f21(f3(f2(a17)),x15892),x15891,x15892),x15893,x15892),x15892),f22(f14(x15891,x15893,x15892),f21(f3(f2(a17)),a18),x15892)) % 1.37/1.32 [1590]~P14(x15902)+E(f13(f14(f22(x15901,f21(f3(f2(a17)),a18),x15902),f22(x15903,f21(f3(f2(a17)),a18),x15902),x15902),f15(f15(f21(f3(f2(a17)),x15902),x15901,x15902),x15903,x15902),x15902),f22(f13(x15901,x15903,x15902),f21(f3(f2(a17)),a18),x15902)) % 1.37/1.32 [1012]~P1(x10123)+E(f22(f22(x10121,x10122,x10123),x10124,x10123),f22(x10121,f15(x10122,x10124,a18),x10123)) % 1.37/1.32 [1013]~P28(x10133)+E(f22(f22(x10131,x10132,x10133),x10134,x10133),f22(x10131,f15(x10132,x10134,a18),x10133)) % 1.37/1.32 [1016]~P1(x10164)+E(f15(x10161,f15(x10162,x10163,x10164),x10164),f15(x10162,f15(x10161,x10163,x10164),x10164)) % 1.37/1.32 [1017]~P1(x10174)+E(f14(x10171,f14(x10172,x10173,x10174),x10174),f14(x10172,f14(x10171,x10173,x10174),x10174)) % 1.37/1.32 [1018]~P13(x10184)+E(f14(x10181,f14(x10182,x10183,x10184),x10184),f14(x10182,f14(x10181,x10183,x10184),x10184)) % 1.37/1.32 [1019]~P18(x10194)+E(f14(x10191,f14(x10192,x10193,x10194),x10194),f14(x10192,f14(x10191,x10193,x10194),x10194)) % 1.37/1.32 [1025]~P1(x10253)+E(f15(f15(x10251,x10252,x10253),x10254,x10253),f15(x10251,f15(x10252,x10254,x10253),x10253)) % 1.37/1.32 [1026]~P21(x10263)+E(f15(f15(x10261,x10262,x10263),x10264,x10263),f15(x10261,f15(x10262,x10264,x10263),x10263)) % 1.37/1.32 [1027]~P1(x10273)+E(f14(f14(x10271,x10272,x10273),x10274,x10273),f14(x10271,f14(x10272,x10274,x10273),x10273)) % 1.37/1.32 [1028]~P18(x10283)+E(f14(f14(x10281,x10282,x10283),x10284,x10283),f14(x10281,f14(x10282,x10284,x10283),x10283)) % 1.37/1.32 [1029]~P19(x10293)+E(f14(f14(x10291,x10292,x10293),x10294,x10293),f14(x10291,f14(x10292,x10294,x10293),x10293)) % 1.37/1.32 [1030]~P1(x10303)+E(f15(f15(x10301,x10302,x10303),x10304,x10303),f15(f15(x10301,x10304,x10303),x10302,x10303)) % 1.37/1.32 [1031]~P1(x10313)+E(f14(f14(x10311,x10312,x10313),x10314,x10313),f14(f14(x10311,x10314,x10313),x10312,x10313)) % 1.37/1.32 [1211]~P28(x12113)+E(f15(f22(x12111,x12112,x12113),f22(x12111,x12114,x12113),x12113),f22(x12111,f14(x12112,x12114,a18),x12113)) % 1.37/1.32 [1212]~P1(x12123)+E(f15(f22(x12121,x12122,x12123),f22(x12121,x12124,x12123),x12123),f22(x12121,f14(x12122,x12124,a18),x12123)) % 1.37/1.32 [1216]~P1(x12163)+E(f14(f15(x12161,x12162,x12163),f15(x12161,x12164,x12163),x12163),f15(x12161,f14(x12162,x12164,x12163),x12163)) % 1.37/1.32 [1218]~P39(x12183)+E(f14(f15(x12181,x12182,x12183),f15(x12181,x12184,x12183),x12183),f15(x12181,f14(x12182,x12184,x12183),x12183)) % 1.37/1.32 [1220]~P39(x12203)+E(f13(f15(x12201,x12202,x12203),f15(x12201,x12204,x12203),x12203),f15(x12201,f13(x12202,x12204,x12203),x12203)) % 1.37/1.32 [1221]~P1(x12213)+E(f15(f22(x12211,x12212,x12213),f22(x12214,x12212,x12213),x12213),f22(f15(x12211,x12214,x12213),x12212,x12213)) % 1.37/1.32 [1222]~P24(x12223)+E(f15(f22(x12221,x12222,x12223),f22(x12224,x12222,x12223),x12223),f22(f15(x12221,x12224,x12223),x12222,x12223)) % 1.37/1.32 [1225]~P39(x12253)+E(f14(f15(x12251,x12252,x12253),f15(x12254,x12252,x12253),x12253),f15(f14(x12251,x12254,x12253),x12252,x12253)) % 1.37/1.32 [1226]~P44(x12263)+E(f14(f15(x12261,x12262,x12263),f15(x12264,x12262,x12263),x12263),f15(f14(x12261,x12264,x12263),x12262,x12263)) % 1.37/1.32 [1228]~P39(x12283)+E(f13(f15(x12281,x12282,x12283),f15(x12284,x12282,x12283),x12283),f15(f13(x12281,x12284,x12283),x12282,x12283)) % 1.37/1.32 [1229]~P48(x12293)+E(f14(f12(x12291,x12292,x12293),f12(x12294,x12292,x12293),x12293),f12(f14(x12291,x12294,x12293),x12292,x12293)) % 1.37/1.32 [1230]~P38(x12303)+E(f14(f12(x12301,x12302,x12303),f12(x12304,x12302,x12303),x12303),f12(f14(x12301,x12304,x12303),x12302,x12303)) % 1.37/1.32 [1231]~P48(x12313)+E(f13(f12(x12311,x12312,x12313),f12(x12314,x12312,x12313),x12313),f12(f13(x12311,x12314,x12313),x12312,x12313)) % 1.37/1.32 [1232]~P38(x12323)+E(f13(f12(x12321,x12322,x12323),f12(x12324,x12322,x12323),x12323),f12(f13(x12321,x12324,x12323),x12322,x12323)) % 1.37/1.32 [1233]~P5(x12333)+E(f7(f15(x12331,x12332,x12333),f15(x12331,x12334,x12333),x12333),f15(x12331,f7(x12332,x12334,x12333),x12333)) % 1.37/1.32 [1234]~P1(x12343)+E(f14(f15(x12341,x12342,x12343),f15(x12344,x12342,x12343),x12343),f15(f14(x12341,x12344,x12343),x12342,x12343)) % 1.37/1.32 [1235]~P5(x12353)+E(f7(f15(x12351,x12352,x12353),f15(x12354,x12352,x12353),x12353),f15(f7(x12351,x12354,x12353),x12352,x12353)) % 1.37/1.32 [1214]~P5(x12144)+E(f7(f14(x12141,f15(x12142,x12143,x12144),x12144),x12143,x12144),f7(x12141,x12143,x12144)) % 1.37/1.32 [1215]~P5(x12154)+E(f7(f14(x12151,f15(x12152,x12153,x12154),x12154),x12152,x12154),f7(x12151,x12152,x12154)) % 1.37/1.32 [1352]~P5(x13524)+E(f7(f15(x13521,f7(x13522,x13523,x13524),x13524),x13523,x13524),f7(f15(x13521,x13522,x13524),x13523,x13524)) % 1.37/1.32 [1354]~P6(x13544)+E(f7(f13(x13541,f7(x13542,x13543,x13544),x13544),x13543,x13544),f7(f13(x13541,x13542,x13544),x13543,x13544)) % 1.37/1.32 [1357]~P6(x13573)+E(f7(f13(f7(x13571,x13572,x13573),x13574,x13573),x13572,x13573),f7(f13(x13571,x13574,x13573),x13572,x13573)) % 1.37/1.32 [1358]~P5(x13584)+E(f7(f14(x13581,f7(x13582,x13583,x13584),x13584),x13583,x13584),f7(f14(x13581,x13582,x13584),x13583,x13584)) % 1.37/1.32 [1359]~P5(x13593)+E(f7(f15(f7(x13591,x13592,x13593),x13594,x13593),x13592,x13593),f7(f15(x13591,x13594,x13593),x13592,x13593)) % 1.37/1.32 [1360]~P5(x13603)+E(f7(f14(f7(x13601,x13602,x13603),x13604,x13603),x13602,x13603),f7(f14(x13601,x13604,x13603),x13602,x13603)) % 1.37/1.32 [1510]~P5(x15103)+E(f7(f15(f7(x15101,x15102,x15103),f7(x15104,x15102,x15103),x15103),x15102,x15103),f7(f15(x15101,x15104,x15103),x15102,x15103)) % 1.37/1.32 [1511]~P5(x15113)+E(f7(f14(f7(x15111,x15112,x15113),f7(x15114,x15112,x15113),x15113),x15112,x15113),f7(f14(x15111,x15114,x15113),x15112,x15113)) % 1.37/1.32 [1512]~P6(x15123)+E(f7(f13(f7(x15121,x15122,x15123),f7(x15124,x15122,x15123),x15123),x15122,x15123),f7(f13(x15121,x15124,x15123),x15122,x15123)) % 1.37/1.32 [1572]~P5(x15723)+E(f14(f14(f15(x15721,f8(x15722,x15721,x15723),x15723),f7(x15722,x15721,x15723),x15723),x15724,x15723),f14(x15722,x15724,x15723)) % 1.37/1.32 [1573]~P5(x15733)+E(f14(f14(f15(f8(x15731,x15732,x15733),x15732,x15733),f7(x15731,x15732,x15733),x15733),x15734,x15733),f14(x15731,x15734,x15733)) % 1.37/1.32 [1361]~P1(x13613)+E(f15(f15(x13611,x13612,x13613),f15(x13614,x13615,x13613),x13613),f15(f15(x13611,x13614,x13613),f15(x13612,x13615,x13613),x13613)) % 1.37/1.32 [1362]~P1(x13623)+E(f14(f14(x13621,x13622,x13623),f14(x13624,x13625,x13623),x13623),f14(f14(x13621,x13624,x13623),f14(x13622,x13625,x13623),x13623)) % 1.37/1.32 [1363]~P13(x13633)+E(f13(f14(x13631,x13632,x13633),f14(x13634,x13635,x13633),x13633),f14(f13(x13631,x13634,x13633),f13(x13632,x13635,x13633),x13633)) % 1.37/1.32 [1426]E(f7(x14261,x14262,a18),f7(x14263,x14262,a18))+~E(f14(x14261,f15(x14262,x14264,a18),a18),f14(x14263,f15(x14262,x14265,a18),a18)) % 1.37/1.32 [1536]~P72(x15363)+E(f14(f15(x15361,x15362,x15363),f14(f15(x15364,x15362,x15363),x15365,x15363),x15363),f14(f15(f14(x15361,x15364,x15363),x15362,x15363),x15365,x15363)) % 1.37/1.32 [1602]~P30(x16023)+P11(f10(f13(f14(x16021,x16022,x16023),f14(x16024,x16025,x16023),x16023),x16023),f14(f10(f13(x16021,x16024,x16023),x16023),f10(f13(x16022,x16025,x16023),x16023),x16023),x16023) % 1.37/1.32 [1604]~P39(x16043)+E(f14(f14(f15(f13(x16041,x16042,x16043),f13(x16044,x16045,x16043),x16043),f15(f13(x16041,x16042,x16043),x16045,x16043),x16043),f15(x16042,f13(x16044,x16045,x16043),x16043),x16043),f13(f15(x16041,x16044,x16043),f15(x16042,x16045,x16043),x16043)) % 1.37/1.32 [1575]~P67(x15753)+E(f14(f15(x15751,x15752,x15753),f14(f15(f13(x15754,x15751,x15753),x15752,x15753),x15755,x15753),x15753),f14(f15(x15754,x15752,x15753),x15755,x15753)) % 1.37/1.32 [1601]~P40(x16014)+E(f14(f15(x16011,f12(f13(x16012,x16013,x16014),x16015,x16014),x16014),f15(f12(f13(x16011,x16016,x16014),x16015,x16014),x16013,x16014),x16014),f12(f13(f15(x16011,x16012,x16014),f15(x16016,x16013,x16014),x16014),x16015,x16014)) % 1.37/1.32 [408]~P47(x4081)+~P48(x4081)+E(f11(f9(x4081),x4081),f9(x4081)) % 1.37/1.32 [431]~P45(x4311)+~P14(x4311)+E(f10(f21(a1,x4311),x4311),f9(x4311)) % 1.37/1.32 [730]~P34(x7301)+~P11(f4(x7301),f4(x7301),x7301)+E(f14(f4(x7301),f4(x7301),x7301),f4(x7301)) % 1.37/1.32 [1462]E(x14621,f4(a18))+E(x14621,f14(f4(a18),f9(a18),a18))+~P8(x14621,f14(f14(f4(a18),f9(a18),a18),f9(a18),a18),a18) % 1.37/1.32 [497]~P48(x4971)+~P14(x4971)+E(f11(f21(f2(a17),x4971),x4971),f21(f2(a17),x4971)) % 1.37/1.32 [837]E(x8371,f4(a18))+E(x8371,f14(f4(a18),f9(a18),a18))+~P8(x8371,f21(f3(f2(a17)),a18),a18) % 1.37/1.32 [566]E(x5661,x5662)+P8(x5662,x5661,a18)+P8(x5661,x5662,a18) % 1.37/1.32 [683]E(x6831,x6832)+~P10(x6832,x6831,a18)+~P10(x6831,x6832,a18) % 1.37/1.32 [405]~P73(x4052)+~P9(x4051,x4052)+E(x4051,f4(x4052)) % 1.37/1.32 [406]~P27(x4062)+~E(f16(x4061,x4062),x4061)+E(x4061,f4(x4062)) % 1.37/1.32 [412]~P30(x4122)+~E(f10(x4121,x4122),f4(x4122))+E(x4121,f4(x4122)) % 1.37/1.32 [413]~P12(x4132)+~E(f16(x4131,x4132),f4(x4132))+E(x4131,f4(x4132)) % 1.37/1.32 [414]~P49(x4142)+~E(f11(x4141,x4142),f4(x4142))+E(x4141,f4(x4142)) % 1.37/1.32 [415]~P12(x4151)+~E(f16(x4152,x4151),f4(x4151))+E(f4(x4151),x4152) % 1.37/1.32 [472]~P5(x4722)+E(f8(x4721,x4721,x4722),f9(x4722))+E(x4721,f4(x4722)) % 1.37/1.32 [474]~P48(x4742)+E(f12(x4741,x4741,x4742),f9(x4742))+E(x4741,f4(x4742)) % 1.37/1.32 [493]~P46(x4932)+~P14(x4932)+E(f13(x4931,x4931,x4932),f4(x4932)) % 1.37/1.32 [508]~P42(x5082)+P8(x5081,f4(x5082),x5082)+E(f10(x5081,x5082),x5081) % 1.37/1.32 [531]~E(f15(x5312,x5311,a18),x5312)+E(x5311,f9(a18))+E(x5312,f4(a18)) % 1.37/1.32 [542]E(x5421,f4(a18))+E(x5422,f4(a18))+~E(f15(x5422,x5421,a18),f4(a18)) % 1.37/1.32 [550]~P30(x5502)+P8(f4(x5502),f10(x5501,x5502),x5502)+E(x5501,f4(x5502)) % 1.37/1.32 [558]~P3(x5582)+~E(f14(x5581,x5581,x5582),f4(x5582))+E(x5581,f4(x5582)) % 1.37/1.32 [563]~P1(x5632)+~P10(f4(x5632),x5631,x5632)+E(x5631,f4(x5632)) % 1.37/1.32 [591]~P30(x5912)+~P11(f4(x5912),x5911,x5912)+E(f10(x5911,x5912),x5911) % 1.37/1.32 [592]~P30(x5922)+~P8(f4(x5922),x5921,x5922)+E(f10(x5921,x5922),x5921) % 1.37/1.32 [610]~P30(x6102)+~P11(x6101,f4(x6102),x6102)+E(f10(x6101,x6102),f16(x6101,x6102)) % 1.37/1.32 [611]~P30(x6112)+~P8(x6111,f4(x6112),x6112)+E(f10(x6111,x6112),f16(x6111,x6112)) % 1.37/1.32 [612]~P42(x6122)+~P8(x6121,f4(x6122),x6122)+E(f10(x6121,x6122),f16(x6121,x6122)) % 1.37/1.32 [633]P7(x6331,a18)+P7(x6332,a18)+P7(f14(x6332,x6331,a18),a18) % 1.37/1.32 [639]~P30(x6392)+~P11(f10(x6391,x6392),f4(x6392),x6392)+E(x6391,f4(x6392)) % 1.37/1.32 [656]~P7(x6562,a18)+~P7(x6561,a18)+P7(f14(x6561,x6562,a18),a18) % 1.37/1.32 [729]~P59(x7291)+P8(f4(x7291),f23(x7292,x7291),x7291)+~P8(f4(a18),x7292,a18) % 1.37/1.32 [733]~P3(x7332)+~P11(x7331,f4(x7332),x7332)+P11(x7331,f16(x7331,x7332),x7332) % 1.37/1.32 [734]~P27(x7342)+~P11(x7341,f4(x7342),x7342)+P11(x7341,f16(x7341,x7342),x7342) % 1.37/1.32 [735]~P45(x7352)+~P8(x7351,f4(x7352),x7352)+P8(x7351,f16(x7351,x7352),x7352) % 1.37/1.32 [736]~P3(x7362)+~P11(f4(x7362),x7361,x7362)+P11(f16(x7361,x7362),x7361,x7362) % 1.37/1.32 [737]~P27(x7372)+~P11(f4(x7372),x7371,x7372)+P11(f16(x7371,x7372),x7371,x7372) % 1.37/1.32 [749]~P25(x7491)+~P11(x7492,f4(x7491),x7491)+P11(f4(x7491),f16(x7492,x7491),x7491) % 1.37/1.32 [750]~P25(x7501)+~P8(x7502,f4(x7501),x7501)+P8(f4(x7501),f16(x7502,x7501),x7501) % 1.37/1.32 [751]~P57(x7511)+~P8(f4(x7511),x7512,x7511)+P8(f4(x7511),f11(x7512,x7511),x7511) % 1.37/1.32 [752]~P57(x7522)+~P8(x7521,f4(x7522),x7522)+P8(f11(x7521,x7522),f4(x7522),x7522) % 1.37/1.32 [753]~P25(x7532)+~P11(f4(x7532),x7531,x7532)+P11(f16(x7531,x7532),f4(x7532),x7532) % 1.37/1.32 [754]~P25(x7542)+~P8(f4(x7542),x7541,x7542)+P8(f16(x7541,x7542),f4(x7542),x7542) % 1.37/1.32 [757]~P3(x7572)+~P11(x7571,f16(x7571,x7572),x7572)+P11(x7571,f4(x7572),x7572) % 1.37/1.32 [758]~P27(x7582)+~P11(x7581,f16(x7581,x7582),x7582)+P11(x7581,f4(x7582),x7582) % 1.37/1.32 [759]~P45(x7592)+~P8(x7591,f16(x7591,x7592),x7592)+P8(x7591,f4(x7592),x7592) % 1.37/1.32 [760]~P3(x7601)+~P11(f16(x7602,x7601),x7602,x7601)+P11(f4(x7601),x7602,x7601) % 1.37/1.32 [761]~P27(x7611)+~P11(f16(x7612,x7611),x7612,x7611)+P11(f4(x7611),x7612,x7611) % 1.37/1.32 [779]~P59(x7792)+~P8(f4(x7792),f23(x7791,x7792),x7792)+P8(f4(a18),x7791,a18) % 1.37/1.32 [783]~P25(x7832)+~P11(f4(x7832),f16(x7831,x7832),x7832)+P11(x7831,f4(x7832),x7832) % 1.37/1.32 [784]~P25(x7842)+~P8(f4(x7842),f16(x7841,x7842),x7842)+P8(x7841,f4(x7842),x7842) % 1.37/1.32 [785]~P25(x7851)+~P11(f16(x7852,x7851),f4(x7851),x7851)+P11(f4(x7851),x7852,x7851) % 1.37/1.32 [786]~P25(x7861)+~P8(f16(x7862,x7861),f4(x7861),x7861)+P8(f4(x7861),x7862,x7861) % 1.37/1.32 [796]P7(x7961,a18)+P7(x7962,a18)+~P7(f15(x7961,x7962,a18),a18) % 1.37/1.32 [830]P7(x8301,a18)+~P7(x8302,a18)+~P7(f14(x8302,x8301,a18),a18) % 1.37/1.32 [832]P7(x8321,a18)+~P7(x8322,a18)+~P7(f14(x8321,x8322,a18),a18) % 1.37/1.32 [846]~P10(x8461,x8462,a18)+~P8(f4(a18),x8462,a18)+P8(f4(a18),x8461,a18) % 1.37/1.32 [903]~P8(x9032,x9031,a18)+~P10(x9031,x9032,a18)+~P8(f4(a18),x9032,a18) % 1.37/1.32 [913]~P3(x9131)+~P11(f4(x9131),x9132,x9131)+P11(f4(x9131),f14(x9132,x9132,x9131),x9131) % 1.37/1.32 [916]~P3(x9161)+~P8(f4(x9161),x9162,x9161)+P8(f4(x9161),f14(x9162,x9162,x9161),x9161) % 1.37/1.32 [917]~P3(x9172)+~P11(x9171,f4(x9172),x9172)+P11(f14(x9171,x9171,x9172),f4(x9172),x9172) % 1.37/1.32 [918]~P45(x9182)+~P8(x9181,f4(x9182),x9182)+P8(f14(x9181,x9181,x9182),f4(x9182),x9182) % 1.37/1.32 [919]~P3(x9192)+~P8(x9191,f4(x9192),x9192)+P8(f14(x9191,x9191,x9192),f4(x9192),x9192) % 1.37/1.32 [1034]~P3(x10342)+~P11(f14(x10341,x10341,x10342),f4(x10342),x10342)+P11(x10341,f4(x10342),x10342) % 1.37/1.32 [1036]~P45(x10362)+~P8(f14(x10361,x10361,x10362),f4(x10362),x10362)+P8(x10361,f4(x10362),x10362) % 1.37/1.32 [1037]~P3(x10372)+~P8(f14(x10371,x10371,x10372),f4(x10372),x10372)+P8(x10371,f4(x10372),x10372) % 1.37/1.32 [1038]~P3(x10381)+~P11(f4(x10381),f14(x10382,x10382,x10381),x10381)+P11(f4(x10381),x10382,x10381) % 1.37/1.32 [1039]~P3(x10391)+~P8(f4(x10391),f14(x10392,x10392,x10391),x10391)+P8(f4(x10391),x10392,x10391) % 1.37/1.32 [1046]P8(f8(x10461,x10462,a18),x10461,a18)+~P8(f4(a18),x10461,a18)+~P8(f9(a18),x10462,a18) % 1.37/1.32 [1051]~P8(f4(a18),x10512,a18)+~P8(f4(a18),x10511,a18)+P8(f4(a18),f15(x10511,x10512,a18),a18) % 1.37/1.32 [1053]~P10(f15(x10532,x10531,a18),x10532,a18)+E(x10531,f9(a18))+~P8(f4(a18),x10532,a18) % 1.37/1.32 [1054]~P10(f15(x10541,x10542,a18),x10542,a18)+E(x10541,f9(a18))+~P8(f4(a18),x10542,a18) % 1.37/1.32 [1107]P8(f4(a18),x11071,a18)+P8(f4(a18),x11072,a18)+~P8(f4(a18),f14(x11071,x11072,a18),a18) % 1.37/1.32 [426]~P49(x4262)+E(x4261,f4(x4262))+E(f11(f11(x4261,x4262),x4262),x4261) % 1.37/1.32 [430]~P47(x4302)+~P49(x4302)+E(f11(f11(x4301,x4302),x4302),x4301) % 1.37/1.32 [496]~P46(x4962)+~P14(x4962)+E(f14(x4961,f4(x4962),x4962),x4961) % 1.37/1.32 [502]~P47(x5022)+~P48(x5022)+E(f12(x5021,f4(x5022),x5022),f4(x5022)) % 1.37/1.32 [529]~P57(x5292)+E(x5291,f4(x5292))+E(f11(f10(x5291,x5292),x5292),f10(f11(x5291,x5292),x5292)) % 1.37/1.32 [530]~P49(x5302)+E(x5301,f4(x5302))+E(f11(f16(x5301,x5302),x5302),f16(f11(x5301,x5302),x5302)) % 1.37/1.32 [538]~P57(x5382)+~P47(x5382)+E(f11(f10(x5381,x5382),x5382),f10(f11(x5381,x5382),x5382)) % 1.37/1.32 [539]~P47(x5392)+~P49(x5392)+E(f11(f16(x5391,x5392),x5392),f16(f11(x5391,x5392),x5392)) % 1.37/1.32 [543]~P16(x5431)+~P14(x5431)+~P9(f21(f2(x5432),x5431),x5431) % 1.37/1.32 [544]~P49(x5442)+E(x5441,f4(x5442))+E(f15(x5441,f11(x5441,x5442),x5442),f9(x5442)) % 1.37/1.32 [545]~P48(x5452)+E(x5451,f4(x5452))+E(f15(f11(x5451,x5452),x5451,x5452),f9(x5452)) % 1.37/1.32 [546]~P49(x5462)+E(x5461,f4(x5462))+E(f15(f11(x5461,x5462),x5461,x5462),f9(x5462)) % 1.37/1.32 [567]~P14(x5671)+~P7(x5672,a18)+E(f22(f21(a1,x5671),x5672,x5671),f9(x5671)) % 1.37/1.32 [568]~P14(x5681)+P7(x5682,a18)+E(f22(f21(a1,x5681),x5682,x5681),f21(a1,x5681)) % 1.37/1.32 [731]E(x7311,f4(a18))+E(x7312,f4(a18))+~E(f14(x7312,x7311,a18),f14(f4(a18),f9(a18),a18)) % 1.37/1.32 [732]E(x7321,f4(a18))+E(x7322,f4(a18))+~E(f14(f4(a18),f9(a18),a18),f14(x7322,x7321,a18)) % 1.37/1.32 [872]E(x8721,f4(a18))+E(x8721,f14(f4(a18),f9(a18),a18))+~E(f14(x8722,x8721,a18),f14(f4(a18),f9(a18),a18)) % 1.37/1.32 [873]E(x8731,f4(a18))+E(x8731,f14(f4(a18),f9(a18),a18))+~E(f14(x8731,x8732,a18),f14(f4(a18),f9(a18),a18)) % 1.37/1.32 [874]E(x8741,f4(a18))+E(x8741,f14(f4(a18),f9(a18),a18))+~E(f14(f4(a18),f9(a18),a18),f14(x8742,x8741,a18)) % 1.37/1.32 [875]E(x8751,f4(a18))+E(x8751,f14(f4(a18),f9(a18),a18))+~E(f14(f4(a18),f9(a18),a18),f14(x8751,x8752,a18)) % 1.37/1.32 [965]E(x9651,f14(f4(a18),f9(a18),a18))+E(x9652,f14(f4(a18),f9(a18),a18))+~E(f14(x9652,x9651,a18),f14(f4(a18),f9(a18),a18)) % 1.37/1.32 [966]E(x9661,f14(f4(a18),f9(a18),a18))+E(x9662,f14(f4(a18),f9(a18),a18))+~E(f14(f4(a18),f9(a18),a18),f14(x9662,x9661,a18)) % 1.37/1.32 [982]~P8(x9821,x9822,a18)+P8(f14(x9821,f9(a18),a18),x9822,a18)+E(f14(x9821,f9(a18),a18),x9822) % 1.37/1.32 [993]E(x9931,x9932)+P8(x9932,x9931,a18)+~P8(x9932,f14(x9931,f9(a18),a18),a18) % 1.37/1.32 [995]E(x9951,x9952)+P8(x9951,x9952,a18)+~P8(x9951,f14(x9952,f9(a18),a18),a18) % 1.37/1.32 [1467]P8(x14671,f15(x14672,x14671,a18),a18)+~P8(f14(f4(a18),f9(a18),a18),x14672,a18)+~P8(f14(f4(a18),f9(a18),a18),x14671,a18) % 1.37/1.32 [1468]P8(x14681,f15(x14681,x14682,a18),a18)+~P8(f14(f4(a18),f9(a18),a18),x14682,a18)+~P8(f14(f4(a18),f9(a18),a18),x14681,a18) % 1.37/1.32 [1530]~P8(f14(f4(a18),f9(a18),a18),x15302,a18)+~P8(f14(f4(a18),f9(a18),a18),x15301,a18)+P8(f14(f4(a18),f9(a18),a18),f15(x15301,x15302,a18),a18) % 1.37/1.32 [555]~P48(x5552)+~P14(x5552)+E(f12(x5551,f21(f2(a17),x5552),x5552),x5551) % 1.37/1.32 [602]~P41(x6021)+~P7(x6022,a18)+E(f22(f16(f9(x6021),x6021),x6022,x6021),f9(x6021)) % 1.37/1.32 [614]~P41(x6141)+P7(x6142,a18)+E(f22(f16(f9(x6141),x6141),x6142,x6141),f16(f9(x6141),x6141)) % 1.37/1.32 [738]~P45(x7381)+~P14(x7381)+E(f10(f22(f21(a1,x7381),x7382,x7381),x7381),f9(x7381)) % 1.37/1.32 [741]~P32(x7411)+~P66(x7411)+E(f22(f4(x7411),f14(x7412,f9(a18),a18),x7411),f4(x7411)) % 1.37/1.32 [756]~P47(x7561)+~P48(x7561)+E(f12(f15(f4(x7561),x7562,x7561),x7562,x7561),f4(x7561)) % 1.37/1.32 [704]~P45(x7042)+E(x7041,f4(x7042))+~E(f22(x7041,f21(f3(f2(a17)),a18),x7042),f4(x7042)) % 1.37/1.32 [925]~P45(x9252)+E(x9251,f4(x9252))+P8(f4(x9252),f22(x9251,f21(f3(f2(a17)),a18),x9252),x9252) % 1.37/1.32 [585]P11(x5852,x5851,x5853)+~P33(x5853)+P11(x5851,x5852,x5853) % 1.37/1.32 [588]P8(x5882,x5881,x5883)+~P33(x5883)+P11(x5881,x5882,x5883) % 1.37/1.32 [637]~P36(x6373)+~P8(x6371,x6372,x6373)+P11(x6371,x6372,x6373) % 1.37/1.32 [638]~P37(x6383)+~P8(x6381,x6382,x6383)+P11(x6381,x6382,x6383) % 1.37/1.32 [706]~P8(x7063,x7062,x7061)+~P33(x7061)+~P11(x7062,x7063,x7061) % 1.37/1.32 [708]~P8(x7083,x7082,x7081)+~P33(x7081)+~P8(x7082,x7083,x7081) % 1.37/1.32 [709]~P8(x7093,x7092,x7091)+~P36(x7091)+~P8(x7092,x7093,x7091) % 1.37/1.32 [710]~P8(x7103,x7102,x7101)+~P37(x7101)+~P11(x7102,x7103,x7101) % 1.37/1.32 [712]~P8(x7123,x7122,x7121)+~P37(x7121)+~P8(x7122,x7123,x7121) % 1.37/1.32 [834]~P10(x8341,x8343,a18)+P10(x8341,x8342,a18)+~P10(x8343,x8342,a18) % 1.37/1.32 [427]~P17(x4273)+E(x4271,x4272)+~E(f16(x4271,x4273),f16(x4272,x4273)) % 1.37/1.32 [428]~P12(x4283)+E(x4281,x4282)+~E(f16(x4281,x4283),f16(x4282,x4283)) % 1.37/1.32 [429]~P15(x4293)+E(x4291,x4292)+~E(f23(x4291,x4293),f23(x4292,x4293)) % 1.37/1.32 [552]~P12(x5523)+E(x5521,x5522)+~E(f13(x5521,x5522,x5523),f4(x5523)) % 1.37/1.32 [553]~P13(x5533)+E(x5531,x5532)+~E(f13(x5531,x5532,x5533),f4(x5533)) % 1.37/1.32 [557]~P71(x5572)+~E(f22(x5571,x5573,x5572),f4(x5572))+E(x5571,f4(x5572)) % 1.37/1.32 [560]~P45(x5603)+P10(x5601,x5602,x5603)+~E(f10(x5601,x5603),f10(x5602,x5603)) % 1.37/1.32 [577]~P12(x5773)+~E(f14(x5771,x5772,x5773),f4(x5773))+E(x5771,f16(x5772,x5773)) % 1.37/1.32 [578]~P12(x5782)+~E(f14(x5781,x5783,x5782),f4(x5782))+E(f16(x5781,x5782),x5783) % 1.37/1.32 [579]~P49(x5792)+~E(f15(x5791,x5793,x5792),f9(x5792))+E(f11(x5791,x5792),x5793) % 1.37/1.32 [649]~P5(x6493)+~P10(x6492,x6491,x6493)+E(f7(x6491,x6492,x6493),f4(x6493)) % 1.37/1.32 [650]~P5(x6503)+P10(x6501,x6502,x6503)+~E(f7(x6502,x6501,x6503),f4(x6503)) % 1.37/1.32 [689]E(x6891,x6892)+~E(f15(x6893,x6891,a18),f15(x6893,x6892,a18))+E(x6893,f4(a18)) % 1.37/1.32 [690]E(x6901,x6902)+~E(f15(x6901,x6903,a18),f15(x6902,x6903,a18))+E(x6903,f4(a18)) % 1.37/1.32 [692]~P45(x6923)+~P10(x6921,x6922,x6923)+P10(x6921,f10(x6922,x6923),x6923) % 1.37/1.32 [693]~P41(x6933)+~P10(x6931,x6932,x6933)+P10(x6931,f16(x6932,x6933),x6933) % 1.37/1.32 [694]~P45(x6942)+~P10(x6941,x6943,x6942)+P10(f10(x6941,x6942),x6943,x6942) % 1.37/1.32 [695]~P41(x6952)+~P10(x6951,x6953,x6952)+P10(f16(x6951,x6952),x6953,x6952) % 1.37/1.32 [742]~P45(x7423)+P10(x7421,x7422,x7423)+~P10(x7421,f10(x7422,x7423),x7423) % 1.37/1.32 [743]~P41(x7433)+P10(x7431,x7432,x7433)+~P10(x7431,f16(x7432,x7433),x7433) % 1.37/1.32 [744]~P45(x7443)+P10(x7441,x7442,x7443)+~P10(f10(x7441,x7443),x7442,x7443) % 1.37/1.32 [745]~P41(x7453)+P10(x7451,x7452,x7453)+~P10(f16(x7451,x7453),x7452,x7453) % 1.37/1.32 [746]~P30(x7463)+P11(x7461,x7462,x7463)+~P11(f10(x7461,x7463),x7462,x7463) % 1.37/1.32 [747]~P45(x7473)+P8(x7471,x7472,x7473)+~P8(f10(x7471,x7473),x7472,x7473) % 1.37/1.32 [763]~P45(x7631)+P11(f4(x7631),f22(x7632,x7633,x7631),x7631)+~P7(x7633,a18) % 1.37/1.32 [775]~P59(x7752)+~P8(x7751,x7753,a18)+P8(f23(x7751,x7752),f23(x7753,x7752),x7752) % 1.37/1.32 [777]~P25(x7772)+~P11(x7773,x7771,x7772)+P11(f16(x7771,x7772),f16(x7773,x7772),x7772) % 1.37/1.32 [778]~P25(x7782)+~P8(x7783,x7781,x7782)+P8(f16(x7781,x7782),f16(x7783,x7782),x7782) % 1.37/1.32 [812]~P25(x8123)+~P11(x8122,f16(x8121,x8123),x8123)+P11(x8121,f16(x8122,x8123),x8123) % 1.37/1.32 [814]~P25(x8143)+~P8(x8142,f16(x8141,x8143),x8143)+P8(x8141,f16(x8142,x8143),x8143) % 1.37/1.32 [816]~P25(x8162)+~P11(f16(x8163,x8162),x8161,x8162)+P11(f16(x8161,x8162),x8163,x8162) % 1.37/1.32 [817]~P30(x8172)+~P11(f10(x8171,x8172),x8173,x8172)+P11(f16(x8171,x8172),x8173,x8172) % 1.37/1.32 [818]~P45(x8182)+~P8(f10(x8181,x8182),x8183,x8182)+P8(f16(x8181,x8182),x8183,x8182) % 1.37/1.32 [820]~P25(x8202)+~P8(f16(x8203,x8202),x8201,x8202)+P8(f16(x8201,x8202),x8203,x8202) % 1.37/1.32 [845]~P59(x8453)+~P8(f23(x8451,x8453),f23(x8452,x8453),x8453)+P8(x8451,x8452,a18) % 1.37/1.32 [847]~P25(x8473)+P11(x8471,x8472,x8473)+~P11(f16(x8472,x8473),f16(x8471,x8473),x8473) % 1.37/1.32 [848]~P25(x8483)+P8(x8481,x8482,x8483)+~P8(f16(x8482,x8483),f16(x8481,x8483),x8483) % 1.37/1.32 [904]E(x9041,x9042)+~E(f15(x9043,x9041,a18),f15(x9043,x9042,a18))+~P8(f4(a18),x9043,a18) % 1.37/1.32 [905]~P1(x9053)+P10(x9051,f22(x9051,x9052,x9053),x9053)+~P8(f4(a18),x9052,a18) % 1.37/1.32 [906]~P25(x9063)+~P11(x9061,x9062,x9063)+P11(f13(x9061,x9062,x9063),f4(x9063),x9063) % 1.37/1.32 [907]~P25(x9073)+~P8(x9071,x9072,x9073)+P8(f13(x9071,x9072,x9073),f4(x9073),x9073) % 1.37/1.32 [911]~P45(x9111)+~P11(f4(x9111),x9112,x9111)+P11(f4(x9111),f22(x9112,x9113,x9111),x9111) % 1.37/1.32 [912]~P59(x9121)+~P11(f4(x9121),x9122,x9121)+P11(f4(x9121),f22(x9122,x9123,x9121),x9121) % 1.37/1.32 [914]~P59(x9141)+~P11(f9(x9141),x9142,x9141)+P11(f9(x9141),f22(x9142,x9143,x9141),x9141) % 1.37/1.32 [915]~P59(x9151)+~P8(f4(x9151),x9152,x9151)+P8(f4(x9151),f22(x9152,x9153,x9151),x9151) % 1.37/1.32 [951]~P45(x9511)+~P8(f22(x9513,x9512,x9511),f4(x9511),x9511)+~P7(x9512,a18) % 1.37/1.32 [977]~P3(x9773)+~P11(x9771,f16(x9772,x9773),x9773)+P11(f14(x9771,x9772,x9773),f4(x9773),x9773) % 1.37/1.32 [1005]~P25(x10053)+P11(x10051,x10052,x10053)+~P11(f13(x10051,x10052,x10053),f4(x10053),x10053) % 1.37/1.32 [1006]~P25(x10063)+P8(x10061,x10062,x10063)+~P8(f13(x10061,x10062,x10063),f4(x10063),x10063) % 1.37/1.32 [1035]~P45(x10352)+~P8(f22(x10351,x10353,x10352),f4(x10352),x10352)+P8(x10351,f4(x10352),x10352) % 1.37/1.32 [1078]~P3(x10783)+~P11(f14(x10781,x10782,x10783),f4(x10783),x10783)+P11(x10781,f16(x10782,x10783),x10783) % 1.37/1.32 [1207]~P8(x12071,x12073,a18)+P8(f15(x12071,x12072,a18),f15(x12073,x12072,a18),a18)+~P8(f4(a18),x12072,a18) % 1.37/1.32 [1210]~P8(x12102,x12103,a18)+P8(f15(x12101,x12102,a18),f15(x12101,x12103,a18),a18)+~P8(f4(a18),x12101,a18) % 1.37/1.32 [1291]P10(x12912,x12913,a18)+E(x12911,f4(a18))+~P10(f15(x12911,x12912,a18),f15(x12911,x12913,a18),a18) % 1.37/1.32 [1378]P10(x13781,x13782,a18)+~P10(f15(x13783,x13781,a18),f15(x13783,x13782,a18),a18)+~P8(f4(a18),x13783,a18) % 1.37/1.32 [658]~P45(x6582)+~P7(x6583,a18)+E(f22(f10(x6581,x6582),x6583,x6582),f22(x6581,x6583,x6582)) % 1.37/1.32 [659]~P41(x6592)+~P7(x6593,a18)+E(f22(f16(x6591,x6592),x6593,x6592),f22(x6591,x6593,x6592)) % 1.37/1.32 [691]~P48(x6912)+E(x6911,f4(x6912))+E(f12(f16(x6913,x6912),f16(x6911,x6912),x6912),f12(x6913,x6911,x6912)) % 1.37/1.32 [698]~P5(x6982)+E(x6981,f4(x6982))+E(f8(f15(x6983,x6981,x6982),x6981,x6982),x6983) % 1.37/1.32 [699]~P5(x6992)+E(x6991,f4(x6992))+E(f8(f15(x6991,x6993,x6992),x6991,x6992),x6993) % 1.37/1.32 [700]~P48(x7002)+E(x7001,f4(x7002))+E(f12(f15(x7003,x7001,x7002),x7001,x7002),x7003) % 1.37/1.32 [701]~P47(x7012)+~P48(x7012)+E(f12(f16(x7011,x7012),f16(x7013,x7012),x7012),f12(x7011,x7013,x7012)) % 1.37/1.32 [748]~P47(x7483)+~P48(x7483)+E(f11(f12(x7481,x7482,x7483),x7483),f12(x7482,x7481,x7483)) % 1.37/1.32 [809]~P48(x8092)+E(x8091,f4(x8092))+E(f12(x8093,f16(x8091,x8092),x8092),f16(f12(x8093,x8091,x8092),x8092)) % 1.37/1.32 [810]~P49(x8102)+E(x8101,f4(x8102))+E(f22(f11(x8101,x8102),x8103,x8102),f11(f22(x8101,x8103,x8102),x8102)) % 1.37/1.32 [821]~P47(x8213)+~P48(x8213)+E(f12(x8211,f16(x8212,x8213),x8213),f16(f12(x8211,x8212,x8213),x8213)) % 1.37/1.32 [822]~P47(x8222)+~P49(x8222)+E(f22(f11(x8221,x8222),x8223,x8222),f11(f22(x8221,x8223,x8222),x8222)) % 1.37/1.32 [836]~P41(x8362)+P7(x8363,a18)+E(f22(f16(x8361,x8362),x8363,x8362),f16(f22(x8361,x8363,x8362),x8362)) % 1.37/1.32 [871]~P57(x8712)+E(x8711,f4(x8712))+E(f12(f10(x8713,x8712),f10(x8711,x8712),x8712),f10(f12(x8713,x8711,x8712),x8712)) % 1.37/1.32 [881]~P57(x8812)+~P47(x8812)+E(f12(f10(x8811,x8812),f10(x8813,x8812),x8812),f10(f12(x8811,x8813,x8812),x8812)) % 1.37/1.32 [882]~P47(x8822)+~P48(x8822)+E(f15(f11(x8821,x8822),f11(x8823,x8822),x8822),f11(f15(x8821,x8823,x8822),x8822)) % 1.37/1.32 [884]~P45(x8841)+P8(f4(x8841),f22(x8842,f21(x8843,a18),x8841),x8841)+~E(f21(x8843,a18),f4(a18)) % 1.37/1.32 [901]~P5(x9013)+~P10(x9011,x9012,x9013)+E(f15(x9011,f8(x9012,x9011,x9013),x9013),x9012) % 1.37/1.32 [902]~P5(x9023)+~P10(x9022,x9021,x9023)+E(f15(f8(x9021,x9022,x9023),x9022,x9023),x9021) % 1.37/1.32 [955]~P6(x9553)+~P10(x9552,x9551,x9553)+E(f8(x9551,f16(x9552,x9553),x9553),f16(f8(x9551,x9552,x9553),x9553)) % 1.37/1.32 [956]~P6(x9562)+~P10(x9563,x9561,x9562)+E(f8(f16(x9561,x9562),x9563,x9562),f16(f8(x9561,x9563,x9562),x9562)) % 1.37/1.32 [983]~P45(x9832)+~P11(f4(x9832),x9833,x9832)+E(f15(f10(x9831,x9832),x9833,x9832),f10(f15(x9831,x9833,x9832),x9832)) % 1.37/1.32 [1033]~P8(x10331,x10333,a18)+~P8(x10333,x10332,a18)+P8(f14(x10331,f9(a18),a18),x10332,a18) % 1.37/1.32 [1057]~P5(x10572)+E(x10571,f4(x10572))+E(f8(f14(x10573,x10571,x10572),x10571,x10572),f14(f8(x10573,x10571,x10572),f9(x10572),x10572)) % 1.37/1.32 [1058]~P5(x10582)+E(x10581,f4(x10582))+E(f8(f14(x10581,x10583,x10582),x10581,x10582),f14(f8(x10583,x10581,x10582),f9(x10582),x10582)) % 1.37/1.32 [1143]~P45(x11432)+~P11(f22(x11433,f21(x11431,a18),x11432),f4(x11432),x11432)+~E(f21(x11431,a18),f4(a18)) % 1.37/1.32 [1239]~P60(x12392)+E(x12391,f4(x12392))+~E(f14(f15(x12393,x12393,x12392),f15(x12391,x12391,x12392),x12392),f4(x12392)) % 1.37/1.32 [1240]~P60(x12402)+E(x12401,f4(x12402))+~E(f14(f15(x12401,x12401,x12402),f15(x12403,x12403,x12402),x12402),f4(x12402)) % 1.37/1.32 [1305]~P59(x13051)+~P8(f9(x13051),x13052,x13051)+P8(f9(x13051),f15(x13052,f22(x13052,x13053,x13051),x13051),x13051) % 1.37/1.32 [1404]~P59(x14043)+~P8(f9(x14043),x14041,x14043)+P8(f22(x14041,x14042,x14043),f15(x14041,f22(x14041,x14042,x14043),x14043),x14043) % 1.37/1.32 [1430]~P60(x14302)+E(x14301,f4(x14302))+P8(f4(x14302),f14(f15(x14303,x14303,x14302),f15(x14301,x14301,x14302),x14302),x14302) % 1.37/1.32 [1431]~P60(x14312)+E(x14311,f4(x14312))+P8(f4(x14312),f14(f15(x14311,x14311,x14312),f15(x14313,x14313,x14312),x14312),x14312) % 1.37/1.32 [1545]~P60(x15452)+E(x15451,f4(x15452))+~P11(f14(f15(x15453,x15453,x15452),f15(x15451,x15451,x15452),x15452),f4(x15452),x15452) % 1.37/1.32 [1546]~P60(x15462)+E(x15461,f4(x15462))+~P11(f14(f15(x15461,x15461,x15462),f15(x15463,x15463,x15462),x15462),f4(x15462),x15462) % 1.37/1.32 [1082]~P47(x10821)+~P48(x10821)+E(f12(f9(x10821),f22(x10822,x10823,x10821),x10821),f22(f12(f9(x10821),x10822,x10821),x10823,x10821)) % 1.37/1.32 [1312]~P59(x13121)+~P8(f9(x13121),x13122,x13121)+P8(f9(x13121),f22(x13122,f14(x13123,f9(a18),a18),x13121),x13121) % 1.37/1.32 [1488]~P57(x14883)+~P8(x14881,x14882,x14883)+P8(x14881,f12(f14(x14881,x14882,x14883),f14(f9(x14883),f9(x14883),x14883),x14883),x14883) % 1.37/1.32 [1489]~P57(x14893)+~P8(x14891,x14892,x14893)+P8(f12(f14(x14891,x14892,x14893),f14(f9(x14893),f9(x14893),x14893),x14893),x14892,x14893) % 1.37/1.32 [1582]~P45(x15823)+~P8(x15821,f4(x15823),x15823)+P8(f22(x15821,f14(f15(f21(f3(f2(a17)),a18),x15822,a18),f9(a18),a18),x15823),f4(x15823),x15823) % 1.37/1.32 [1595]~P45(x15951)+P11(f4(x15951),x15952,x15951)+~P11(f4(x15951),f22(x15952,f14(f15(f21(f3(f2(a17)),a18),x15953,a18),f9(a18),a18),x15951),x15951) % 1.37/1.32 [1491]~P45(x14912)+E(x14911,f4(x14912))+~E(f14(f22(x14913,f21(f3(f2(a17)),a18),x14912),f22(x14911,f21(f3(f2(a17)),a18),x14912),x14912),f4(x14912)) % 1.37/1.32 [1492]~P45(x14922)+E(x14921,f4(x14922))+~E(f14(f22(x14921,f21(f3(f2(a17)),a18),x14922),f22(x14923,f21(f3(f2(a17)),a18),x14922),x14922),f4(x14922)) % 1.37/1.32 [1542]~P45(x15422)+E(x15421,f4(x15422))+~P11(f22(x15421,f15(f21(f3(f2(a17)),a18),x15423,a18),x15422),f4(x15422),x15422) % 1.37/1.32 [1554]~P45(x15542)+E(x15541,f4(x15542))+P8(f4(x15542),f14(f22(x15543,f21(f3(f2(a17)),a18),x15542),f22(x15541,f21(f3(f2(a17)),a18),x15542),x15542),x15542) % 1.37/1.32 [1555]~P45(x15552)+E(x15551,f4(x15552))+P8(f4(x15552),f14(f22(x15551,f21(f3(f2(a17)),a18),x15552),f22(x15553,f21(f3(f2(a17)),a18),x15552),x15552),x15552) % 1.37/1.32 [1586]~P45(x15862)+E(x15861,f4(x15862))+~P11(f14(f22(x15863,f21(f3(f2(a17)),a18),x15862),f22(x15861,f21(f3(f2(a17)),a18),x15862),x15862),f4(x15862),x15862) % 1.37/1.32 [1587]~P45(x15872)+E(x15871,f4(x15872))+~P11(f14(f22(x15871,f21(f3(f2(a17)),a18),x15872),f22(x15873,f21(f3(f2(a17)),a18),x15872),x15872),f4(x15872),x15872) % 1.37/1.32 [713]~P20(x7134)+E(x7131,x7132)+~E(f14(x7133,x7131,x7134),f14(x7133,x7132,x7134)) % 1.37/1.32 [714]~P23(x7144)+E(x7141,x7142)+~E(f14(x7143,x7141,x7144),f14(x7143,x7142,x7144)) % 1.37/1.32 [715]~P13(x7154)+E(x7151,x7152)+~E(f13(x7153,x7153,x7154),f13(x7151,x7152,x7154)) % 1.37/1.32 [716]~P23(x7164)+E(x7161,x7162)+~E(f14(x7161,x7163,x7164),f14(x7162,x7163,x7164)) % 1.37/1.32 [717]~P13(x7173)+E(x7171,x7172)+~E(f13(x7171,x7172,x7173),f13(x7174,x7174,x7173)) % 1.37/1.32 [899]~P1(x8994)+~P10(x8991,x8993,x8994)+P10(x8991,f15(x8992,x8993,x8994),x8994) % 1.37/1.32 [900]~P1(x9004)+~P10(x9001,x9002,x9004)+P10(x9001,f15(x9002,x9003,x9004),x9004) % 1.37/1.32 [981]~P8(x9814,x9813,a18)+P8(x9811,x9812,a18)+~E(f14(x9811,x9813,a18),f14(x9814,x9812,a18)) % 1.37/1.32 [997]~P1(x9973)+P10(x9971,x9972,x9973)+~P10(f15(x9974,x9971,x9973),x9972,x9973) % 1.37/1.32 [998]~P1(x9983)+P10(x9981,x9982,x9983)+~P10(f15(x9981,x9984,x9983),x9982,x9983) % 1.37/1.32 [1096]~P1(x10963)+~P10(x10961,x10964,x10963)+P10(f22(x10961,x10962,x10963),f22(x10964,x10962,x10963),x10963) % 1.37/1.32 [1097]~P46(x10973)+~P10(x10971,x10974,x10973)+P10(f15(x10971,x10972,x10973),f15(x10974,x10972,x10973),x10973) % 1.37/1.32 [1098]~P46(x10983)+~P10(x10982,x10984,x10983)+P10(f15(x10981,x10982,x10983),f15(x10981,x10984,x10983),x10983) % 1.37/1.32 [1099]~P2(x10993)+~P11(x10991,x10994,x10993)+P11(f14(x10991,x10992,x10993),f14(x10994,x10992,x10993),x10993) % 1.37/1.32 [1100]~P31(x11003)+~P11(x11001,x11004,x11003)+P11(f14(x11001,x11002,x11003),f14(x11004,x11002,x11003),x11003) % 1.37/1.32 [1101]~P2(x11013)+~P11(x11012,x11014,x11013)+P11(f14(x11011,x11012,x11013),f14(x11011,x11014,x11013),x11013) % 1.37/1.32 [1102]~P31(x11023)+~P11(x11022,x11024,x11023)+P11(f14(x11021,x11022,x11023),f14(x11021,x11024,x11023),x11023) % 1.37/1.32 [1103]~P31(x11033)+~P8(x11031,x11034,x11033)+P8(f14(x11031,x11032,x11033),f14(x11034,x11032,x11033),x11033) % 1.37/1.32 [1104]~P35(x11043)+~P8(x11041,x11044,x11043)+P8(f14(x11041,x11042,x11043),f14(x11044,x11042,x11043),x11043) % 1.37/1.32 [1105]~P31(x11053)+~P8(x11052,x11054,x11053)+P8(f14(x11051,x11052,x11053),f14(x11051,x11054,x11053),x11053) % 1.37/1.32 [1106]~P35(x11063)+~P8(x11062,x11064,x11063)+P8(f14(x11061,x11062,x11063),f14(x11061,x11064,x11063),x11063) % 1.37/1.32 [1203]~P8(x12032,x12034,a18)+~P8(x12031,x12033,a18)+P8(f14(x12031,x12032,a18),f14(x12033,x12034,a18),a18) % 1.37/1.32 [1301]~P31(x13013)+P11(x13011,x13012,x13013)+~P11(f14(x13014,x13011,x13013),f14(x13014,x13012,x13013),x13013) % 1.37/1.32 [1302]~P31(x13023)+P11(x13021,x13022,x13023)+~P11(f14(x13021,x13024,x13023),f14(x13022,x13024,x13023),x13023) % 1.37/1.32 [1303]~P31(x13033)+P8(x13031,x13032,x13033)+~P8(f14(x13034,x13031,x13033),f14(x13034,x13032,x13033),x13033) % 1.37/1.32 [1304]~P31(x13043)+P8(x13041,x13042,x13043)+~P8(f14(x13041,x13044,x13043),f14(x13042,x13044,x13043),x13043) % 1.37/1.32 [932]~P13(x9323)+E(x9321,f16(x9322,x9323))+~E(f14(x9321,f14(x9324,x9322,x9323),x9323),x9324) % 1.37/1.32 [990]~P5(x9903)+~P10(x9904,x9902,x9903)+E(f7(f7(x9901,x9902,x9903),x9904,x9903),f7(x9901,x9904,x9903)) % 1.37/1.32 [1047]~P5(x10472)+E(x10471,f4(x10472))+E(f8(f15(x10473,x10471,x10472),f15(x10474,x10471,x10472),x10472),f8(x10473,x10474,x10472)) % 1.37/1.32 [1048]~P5(x10482)+E(x10481,f4(x10482))+E(f8(f15(x10481,x10483,x10482),f15(x10481,x10484,x10482),x10482),f8(x10483,x10484,x10482)) % 1.37/1.32 [1049]~P47(x10493)+~P48(x10493)+E(f12(f15(x10491,x10492,x10493),x10494,x10493),f15(f12(x10491,x10494,x10493),x10492,x10493)) % 1.37/1.32 [1055]~P6(x10552)+~E(f7(x10551,x10553,x10552),f7(x10554,x10553,x10552))+E(f7(f16(x10551,x10552),x10553,x10552),f7(f16(x10554,x10552),x10553,x10552)) % 1.37/1.32 [1192]~P5(x11923)+~P10(x11924,x11921,x11923)+E(f8(f15(x11921,x11922,x11923),x11924,x11923),f15(f8(x11921,x11924,x11923),x11922,x11923)) % 1.37/1.32 [1241]~P48(x12412)+E(x12411,f4(x12412))+E(f12(f22(x12413,x12414,x12412),f22(x12411,x12414,x12412),x12412),f22(f12(x12413,x12411,x12412),x12414,x12412)) % 1.37/1.32 [1242]~P47(x12423)+~P48(x12423)+E(f12(f22(x12421,x12422,x12423),f22(x12424,x12422,x12423),x12423),f22(f12(x12421,x12424,x12423),x12422,x12423)) % 1.37/1.32 [1297]~P26(x12974)+~P11(f14(x12971,x12973,x12974),x12972,x12974)+P11(x12971,f14(x12972,f10(x12973,x12974),x12974),x12974) % 1.37/1.32 [1314]E(x13141,x13142)+E(x13143,f4(a18))+~E(f14(x13144,f15(x13143,x13141,a18),a18),f14(x13144,f15(x13143,x13142,a18),a18)) % 1.37/1.32 [1333]~P5(x13333)+~P10(x13334,x13331,x13333)+E(f8(f22(x13331,x13332,x13333),f22(x13334,x13332,x13333),x13333),f22(f8(x13331,x13334,x13333),x13332,x13333)) % 1.37/1.32 [1372]~P46(x13723)+~P14(x13723)+E(f14(f15(x13721,x13722,x13723),f15(x13721,x13724,x13723),x13723),f14(f15(x13721,x13724,x13723),f15(x13721,x13722,x13723),x13723)) % 1.37/1.32 [1438]~P45(x14384)+P8(x14381,f14(x14382,x14383,x14384),x14384)+~P8(f10(f13(x14381,x14382,x14384),x14384),x14383,x14384) % 1.37/1.32 [1439]~P45(x14393)+P8(f13(x14391,x14392,x14393),x14394,x14393)+~P8(f10(f13(x14394,x14391,x14393),x14393),x14392,x14393) % 1.37/1.32 [1533]E(x15331,x15332)+E(x15333,x15334)+~E(f14(f15(x15333,x15331,a18),f15(x15334,x15332,a18),a18),f14(f15(x15333,x15332,a18),f15(x15334,x15331,a18),a18)) % 1.37/1.32 [1369]~P5(x13692)+E(x13691,f4(x13692))+E(f8(f14(x13693,f15(x13694,x13691,x13692),x13692),x13691,x13692),f14(x13694,f8(x13693,x13691,x13692),x13692)) % 1.37/1.32 [1370]~P5(x13702)+E(x13701,f4(x13702))+E(f8(f14(x13703,f15(x13701,x13704,x13702),x13702),x13701,x13702),f14(x13704,f8(x13703,x13701,x13702),x13702)) % 1.37/1.32 [1384]~P4(x13842)+~P72(x13842)+E(f14(f15(f21(x13841,x13842),x13843,x13842),f15(f21(x13841,x13842),x13844,x13842),x13842),f15(f21(x13841,x13842),f14(x13843,x13844,x13842),x13842)) % 1.37/1.32 [1385]~P4(x13852)+~P67(x13852)+E(f13(f15(f21(x13851,x13852),x13853,x13852),f15(f21(x13851,x13852),x13854,x13852),x13852),f15(f21(x13851,x13852),f13(x13853,x13854,x13852),x13852)) % 1.37/1.32 [1386]~P4(x13863)+~P72(x13863)+E(f14(f15(x13861,f21(x13862,x13863),x13863),f15(x13864,f21(x13862,x13863),x13863),x13863),f15(f14(x13861,x13864,x13863),f21(x13862,x13863),x13863)) % 1.37/1.32 [1387]~P4(x13873)+~P67(x13873)+E(f13(f15(x13871,f21(x13872,x13873),x13873),f15(x13874,f21(x13872,x13873),x13873),x13873),f15(f13(x13871,x13874,x13873),f21(x13872,x13873),x13873)) % 1.37/1.32 [1571]~P8(x15714,x15711,a18)+~P8(f4(a18),x15713,a18)+P8(f14(f15(x15711,f7(x15712,x15713,a18),a18),x15714,a18),f15(x15711,x15713,a18),a18) % 1.37/1.32 [1185]~P13(x11853)+E(f14(x11851,x11852,x11853),x11854)+~E(f14(x11851,f14(x11855,x11852,x11853),x11853),f14(x11855,x11854,x11853)) % 1.37/1.32 [1373]~P47(x13733)+~P48(x13733)+E(f12(f15(x13731,x13732,x13733),f15(x13734,x13735,x13733),x13733),f15(f12(x13731,x13734,x13733),f12(x13732,x13735,x13733),x13733)) % 1.37/1.32 [1540]~P67(x15404)+~E(f14(f15(x15403,x15405,x15404),x15401,x15404),f14(f15(x15402,x15405,x15404),x15406,x15404))+E(x15401,f14(f15(f13(x15402,x15403,x15404),x15405,x15404),x15406,x15404)) % 1.37/1.32 [1541]~P67(x15413)+~E(f14(f15(x15411,x15414,x15413),x15415,x15413),f14(f15(x15412,x15414,x15413),x15416,x15413))+E(f14(f15(f13(x15411,x15412,x15413),x15414,x15413),x15415,x15413),x15416) % 1.37/1.32 [1591]~P63(x15914)+~P11(f14(f15(x15913,x15915,x15914),x15911,x15914),f14(f15(x15912,x15915,x15914),x15916,x15914),x15914)+P11(x15911,f14(f15(f13(x15912,x15913,x15914),x15915,x15914),x15916,x15914),x15914) % 1.37/1.32 [1592]~P63(x15924)+~P8(f14(f15(x15923,x15925,x15924),x15921,x15924),f14(f15(x15922,x15925,x15924),x15926,x15924),x15924)+P8(x15921,f14(f15(f13(x15922,x15923,x15924),x15925,x15924),x15926,x15924),x15924) % 1.37/1.32 [1593]~P63(x15933)+~P11(f14(f15(x15931,x15934,x15933),x15935,x15933),f14(f15(x15932,x15934,x15933),x15936,x15933),x15933)+P11(f14(f15(f13(x15931,x15932,x15933),x15934,x15933),x15935,x15933),x15936,x15933) % 1.37/1.32 [1594]~P63(x15943)+~P8(f14(f15(x15941,x15944,x15943),x15945,x15943),f14(f15(x15942,x15944,x15943),x15946,x15943),x15943)+P8(f14(f15(f13(x15941,x15942,x15943),x15944,x15943),x15945,x15943),x15946,x15943) % 1.37/1.32 [1596]~P63(x15963)+P11(f14(f15(x15961,x15962,x15963),x15964,x15963),f14(f15(x15965,x15962,x15963),x15966,x15963),x15963)+~P11(x15964,f14(f15(f13(x15965,x15961,x15963),x15962,x15963),x15966,x15963),x15963) % 1.37/1.32 [1597]~P63(x15973)+P8(f14(f15(x15971,x15972,x15973),x15974,x15973),f14(f15(x15975,x15972,x15973),x15976,x15973),x15973)+~P8(x15974,f14(f15(f13(x15975,x15971,x15973),x15972,x15973),x15976,x15973),x15973) % 1.37/1.32 [1598]~P63(x15983)+P11(f14(f15(x15981,x15982,x15983),x15984,x15983),f14(f15(x15985,x15982,x15983),x15986,x15983),x15983)+~P11(f14(f15(f13(x15981,x15985,x15983),x15982,x15983),x15984,x15983),x15986,x15983) % 1.37/1.32 [1599]~P63(x15993)+P8(f14(f15(x15991,x15992,x15993),x15994,x15993),f14(f15(x15995,x15992,x15993),x15996,x15993),x15993)+~P8(f14(f15(f13(x15991,x15995,x15993),x15992,x15993),x15994,x15993),x15996,x15993) % 1.37/1.32 [978]~P57(x9781)+~P47(x9781)+~P14(x9781)+P8(f4(x9781),f12(f9(x9781),f21(f3(f2(a17)),x9781),x9781),x9781) % 1.37/1.32 [1428]E(f7(x14281,f21(f3(f3(f2(a17))),a18),a18),f21(f3(f2(a17)),a18))+E(f7(x14281,f21(f3(f3(f2(a17))),a18),a18),f21(f2(f2(a17)),a18))+E(f7(x14281,f21(f3(f3(f2(a17))),a18),a18),f9(a18))+E(f7(x14281,f21(f3(f3(f2(a17))),a18),a18),f4(a18)) % 1.37/1.32 [425]~P47(x4252)+~P48(x4252)+~E(f11(x4251,x4252),f9(x4252))+E(x4251,f9(x4252)) % 1.37/1.32 [517]~P33(x5172)+~P26(x5172)+P8(x5171,f4(x5172),x5172)+E(f10(x5171,x5172),x5171) % 1.37/1.32 [622]~P33(x6222)+~P26(x6222)+~P8(x6221,f4(x6222),x6222)+E(f10(x6221,x6222),f16(x6221,x6222)) % 1.37/1.32 [767]~P57(x7671)+~P47(x7671)+~P11(f4(x7671),x7672,x7671)+P11(f4(x7671),f11(x7672,x7671),x7671) % 1.37/1.32 [769]~P57(x7692)+~P47(x7692)+~P11(x7691,f4(x7692),x7692)+P11(f11(x7691,x7692),f4(x7692),x7692) % 1.37/1.32 [770]~P57(x7702)+~P47(x7702)+~P11(x7701,f4(x7702),x7702)+P11(f11(x7701,x7702),f9(x7702),x7702) % 1.37/1.32 [772]~P57(x7722)+~P47(x7722)+~P11(x7721,f4(x7722),x7722)+P8(f11(x7721,x7722),f9(x7722),x7722) % 1.37/1.32 [773]~P57(x7732)+~P47(x7732)+~P11(f9(x7732),x7731,x7732)+P11(f11(x7731,x7732),f9(x7732),x7732) % 1.37/1.32 [774]~P57(x7742)+~P47(x7742)+~P8(f9(x7742),x7741,x7742)+P8(f11(x7741,x7742),f9(x7742),x7742) % 1.37/1.32 [797]~P57(x7972)+~P8(f11(x7971,x7972),f4(x7972),x7972)+P8(x7971,f4(x7972),x7972)+E(x7971,f4(x7972)) % 1.37/1.32 [798]~P57(x7982)+~P8(f4(x7982),f11(x7981,x7982),x7982)+P8(f4(x7982),x7981,x7982)+E(x7981,f4(x7982)) % 1.37/1.32 [800]~P57(x8002)+~P47(x8002)+~P11(f9(x8002),f11(x8001,x8002),x8002)+P11(x8001,f9(x8002),x8002) % 1.37/1.32 [801]~P57(x8012)+~P47(x8012)+~P8(f9(x8012),f11(x8011,x8012),x8012)+P8(x8011,f9(x8012),x8012) % 1.37/1.32 [802]~P57(x8022)+~P47(x8022)+~P11(f11(x8021,x8022),f4(x8022),x8022)+P11(x8021,f4(x8022),x8022) % 1.37/1.32 [803]~P57(x8032)+~P47(x8032)+~P8(f11(x8031,x8032),f4(x8032),x8032)+P8(x8031,f4(x8032),x8032) % 1.37/1.32 [804]~P57(x8041)+~P47(x8041)+~P11(f4(x8041),f11(x8042,x8041),x8041)+P11(f4(x8041),x8042,x8041) % 1.37/1.32 [805]~P57(x8051)+~P47(x8051)+~P11(f9(x8051),f11(x8052,x8051),x8051)+P8(f4(x8051),x8052,x8051) % 1.37/1.32 [806]~P57(x8061)+~P47(x8061)+~P8(f4(x8061),f11(x8062,x8061),x8061)+P8(f4(x8061),x8062,x8061) % 1.37/1.32 [807]~P57(x8071)+~P47(x8071)+~P8(f9(x8071),f11(x8072,x8071),x8071)+P8(f4(x8071),x8072,x8071) % 1.37/1.32 [507]~P32(x5072)+~P66(x5072)+E(x5071,f4(a18))+E(f22(f4(x5072),x5071,x5072),f4(x5072)) % 1.37/1.32 [556]~P47(x5562)+~P48(x5562)+~P14(x5562)+E(f12(x5561,f21(a17,x5562),x5562),f4(x5562)) % 1.37/1.32 [574]~P47(x5742)+~P48(x5742)+~P14(x5742)+E(f12(x5741,f21(a1,x5742),x5742),f16(x5741,x5742)) % 1.37/1.32 [606]~P32(x6061)+~P66(x6061)+~E(f21(x6062,a18),f4(a18))+E(f22(f4(x6061),f21(x6062,a18),x6061),f9(x6061)) % 1.37/1.32 [609]~P14(x6092)+~P16(x6092)+~P9(f21(x6091,x6092),x6092)+P9(f21(f3(x6091),x6092),x6092) % 1.37/1.32 [620]~P14(x6202)+~P16(x6202)+P9(f21(x6201,x6202),x6202)+~P9(f21(f3(x6201),x6202),x6202) % 1.37/1.32 [651]~P45(x6512)+~P14(x6512)+P8(f21(x6511,x6512),f4(x6512),x6512)+E(f10(f21(x6511,x6512),x6512),f21(x6511,x6512)) % 1.37/1.32 [799]~P45(x7992)+~P7(x7991,a18)+P11(f22(f4(x7992),x7991,x7992),f4(x7992),x7992)+E(x7991,f4(a18)) % 1.37/1.32 [849]~P45(x8492)+~P14(x8492)+~P8(f21(x8491,x8492),f4(x8492),x8492)+E(f10(f21(x8491,x8492),x8492),f16(f21(x8491,x8492),x8492)) % 1.37/1.32 [947]~P57(x9471)+~P47(x9471)+~P11(f4(x9471),x9472,x9471)+P11(f4(x9471),f12(f9(x9471),x9472,x9471),x9471) % 1.37/1.32 [948]~P57(x9481)+~P47(x9481)+~P8(f4(x9481),x9482,x9481)+P8(f4(x9481),f12(f9(x9481),x9482,x9481),x9481) % 1.37/1.32 [949]~P57(x9491)+~P47(x9491)+~P11(x9492,f4(x9491),x9491)+P11(f12(f9(x9491),x9492,x9491),f4(x9491),x9491) % 1.37/1.32 [950]~P57(x9501)+~P47(x9501)+~P8(x9502,f4(x9501),x9501)+P8(f12(f9(x9501),x9502,x9501),f4(x9501),x9501) % 1.37/1.32 [996]~P45(x9962)+~P7(x9961,a18)+~P8(f4(x9962),f22(f4(x9962),x9961,x9962),x9962)+E(x9961,f4(a18)) % 1.37/1.32 [1085]~P57(x10852)+~P47(x10852)+P11(x10851,f4(x10852),x10852)+~P11(f12(f9(x10852),x10851,x10852),f4(x10852),x10852) % 1.37/1.32 [1086]~P57(x10862)+~P47(x10862)+P8(x10861,f4(x10862),x10862)+~P8(f12(f9(x10862),x10861,x10862),f4(x10862),x10862) % 1.37/1.32 [1087]~P57(x10871)+~P47(x10871)+P11(f4(x10871),x10872,x10871)+~P11(f4(x10871),f12(f9(x10871),x10872,x10871),x10871) % 1.37/1.32 [1088]~P57(x10881)+~P47(x10881)+P8(f4(x10881),x10882,x10881)+~P8(f4(x10881),f12(f9(x10881),x10882,x10881),x10881) % 1.37/1.32 [1095]~P45(x10952)+P8(f4(x10952),f4(x10952),x10952)+~P8(f4(x10952),f22(f4(x10952),x10951,x10952),x10952)+E(x10951,f4(a18)) % 1.37/1.32 [852]~P47(x8521)+~P48(x8521)+~P14(x8521)+E(f16(f12(f9(x8521),x8522,x8521),x8521),f12(f21(a1,x8521),x8522,x8521)) % 1.37/1.32 [596]P8(x5961,x5962,x5963)+~P45(x5963)+E(x5961,x5962)+P8(x5962,x5961,x5963) % 1.37/1.32 [600]P8(x6001,x6002,x6003)+~P33(x6003)+E(x6001,x6002)+P8(x6002,x6001,x6003) % 1.37/1.32 [642]~P33(x6423)+~P11(x6421,x6422,x6423)+E(x6421,x6422)+P8(x6421,x6422,x6423) % 1.37/1.32 [648]~P36(x6483)+~P11(x6481,x6482,x6483)+E(x6481,x6482)+P8(x6481,x6482,x6483) % 1.37/1.32 [723]~P11(x7232,x7231,x7233)+~P11(x7231,x7232,x7233)+E(x7231,x7232)+~P36(x7233) % 1.37/1.32 [782]P8(x7822,x7821,x7823)+~P37(x7823)+~P11(x7822,x7821,x7823)+P11(x7821,x7822,x7823) % 1.37/1.32 [433]~P14(x4333)+~P16(x4333)+E(x4331,x4332)+~E(f21(x4331,x4333),f21(x4332,x4333)) % 1.37/1.32 [434]~P47(x4343)+~P49(x4343)+E(x4341,x4342)+~E(f11(x4341,x4343),f11(x4342,x4343)) % 1.37/1.32 [561]~P48(x5613)+E(x5611,x5612)+~E(f12(x5611,x5612,x5613),f9(x5613))+E(x5612,f4(x5613)) % 1.37/1.32 [562]~P46(x5622)+~P14(x5622)+~E(f14(x5623,x5621,x5622),x5623)+E(x5621,f4(x5622)) % 1.37/1.32 [564]~P46(x5643)+~P14(x5643)+E(x5641,x5642)+~E(f13(x5641,x5642,x5643),f4(x5643)) % 1.37/1.32 [570]~P51(x5702)+~E(f15(x5703,x5701,x5702),f4(x5702))+E(x5701,f4(x5702))+E(x5703,f4(x5702)) % 1.37/1.32 [571]~P69(x5712)+~E(f15(x5713,x5711,x5712),f4(x5712))+E(x5711,f4(x5712))+E(x5713,f4(x5712)) % 1.37/1.32 [766]~P46(x7663)+E(x7661,x7662)+~E(f15(x7661,x7661,x7663),f15(x7662,x7662,x7663))+E(x7661,f16(x7662,x7663)) % 1.37/1.32 [780]~P45(x7802)+P8(f4(x7802),f22(x7801,x7803,x7802),x7802)+~P7(x7803,a18)+E(x7801,f4(x7802)) % 1.37/1.32 [781]~P60(x7811)+~P28(x7811)+P11(f4(x7811),f22(x7812,x7813,x7811),x7811)+~P7(x7813,a18) % 1.37/1.32 [943]~P45(x9432)+P8(f4(x9432),f22(x9433,x9431,x9432),x9432)+~P8(f4(x9432),x9433,x9432)+P7(x9431,a18) % 1.37/1.32 [944]~P45(x9443)+~P8(x9442,f4(x9443),x9443)+P8(f22(x9442,x9441,x9443),f4(x9443),x9443)+P7(x9441,a18) % 1.37/1.32 [958]~P57(x9582)+~P11(x9583,x9581,x9582)+~P8(x9581,f4(x9582),x9582)+P11(f11(x9581,x9582),f11(x9583,x9582),x9582) % 1.37/1.32 [959]~P57(x9592)+~P8(x9593,x9591,x9592)+~P8(x9591,f4(x9592),x9592)+P8(f11(x9591,x9592),f11(x9593,x9592),x9592) % 1.37/1.32 [960]~P57(x9602)+~P11(x9603,x9601,x9602)+~P8(f4(x9602),x9603,x9602)+P11(f11(x9601,x9602),f11(x9603,x9602),x9602) % 1.37/1.32 [961]~P57(x9612)+~P8(x9613,x9611,x9612)+~P8(f4(x9612),x9613,x9612)+P8(f11(x9611,x9612),f11(x9613,x9612),x9612) % 1.37/1.32 [962]~P45(x9622)+~P11(f22(x9621,x9623,x9622),f4(x9622),x9622)+E(x9621,f4(x9622))+~P7(x9623,a18) % 1.37/1.32 [975]~P30(x9752)+~P11(x9751,x9753,x9752)+~P11(f16(x9751,x9752),x9753,x9752)+P11(f10(x9751,x9752),x9753,x9752) % 1.37/1.32 [976]~P45(x9762)+~P8(x9761,x9763,x9762)+~P8(f16(x9761,x9762),x9763,x9762)+P8(f10(x9761,x9762),x9763,x9762) % 1.37/1.32 [1007]~P57(x10073)+P11(x10071,x10072,x10073)+~P8(x10071,f4(x10073),x10073)+~P11(f11(x10072,x10073),f11(x10071,x10073),x10073) % 1.37/1.32 [1008]~P57(x10083)+P8(x10081,x10082,x10083)+~P8(x10081,f4(x10083),x10083)+~P8(f11(x10082,x10083),f11(x10081,x10083),x10083) % 1.37/1.32 [1009]~P57(x10093)+P11(x10091,x10092,x10093)+~P8(f4(x10093),x10092,x10093)+~P11(f11(x10092,x10093),f11(x10091,x10093),x10093) % 1.37/1.32 [1010]~P57(x10103)+P8(x10101,x10102,x10103)+~P8(f4(x10103),x10102,x10103)+~P8(f11(x10102,x10103),f11(x10101,x10103),x10103) % 1.37/1.32 [1050]~P45(x10502)+~P11(f22(x10501,x10503,x10502),f4(x10502),x10502)+P11(x10501,f4(x10502),x10502)+E(x10501,f4(x10502)) % 1.37/1.32 [1071]~P45(x10713)+~P11(f22(x10712,x10711,x10713),f4(x10713),x10713)+P11(x10712,f4(x10713),x10713)+P7(x10711,a18) % 1.37/1.32 [1074]~P45(x10742)+~P11(f4(x10742),f22(x10743,x10741,x10742),x10742)+P11(f4(x10742),x10743,x10742)+P7(x10741,a18) % 1.37/1.32 [1094]~P59(x10941)+~P8(f9(x10941),x10942,x10941)+P8(f9(x10941),f22(x10942,x10943,x10941),x10941)+~P8(f4(a18),x10943,a18) % 1.37/1.32 [1108]~P60(x11081)+~P11(x11083,f4(x11081),x11081)+~P11(x11082,f4(x11081),x11081)+P11(f4(x11081),f15(x11082,x11083,x11081),x11081) % 1.37/1.32 [1110]~P63(x11101)+~P11(x11103,f4(x11101),x11101)+~P11(x11102,f4(x11101),x11101)+P11(f4(x11101),f15(x11102,x11103,x11101),x11101) % 1.37/1.32 [1111]~P57(x11111)+~P11(x11112,f4(x11111),x11111)+~P8(x11113,f4(x11111),x11111)+P11(f4(x11111),f12(x11112,x11113,x11111),x11111) % 1.37/1.32 [1112]~P60(x11121)+~P8(x11123,f4(x11121),x11121)+~P8(x11122,f4(x11121),x11121)+P8(f4(x11121),f15(x11122,x11123,x11121),x11121) % 1.37/1.32 [1113]~P57(x11131)+~P8(x11133,f4(x11131),x11131)+~P8(x11132,f4(x11131),x11131)+P8(f4(x11131),f12(x11132,x11133,x11131),x11131) % 1.37/1.32 [1114]~P60(x11141)+~P11(f4(x11141),x11143,x11141)+~P11(f4(x11141),x11142,x11141)+P11(f4(x11141),f15(x11142,x11143,x11141),x11141) % 1.37/1.32 [1115]~P63(x11151)+~P11(f4(x11151),x11153,x11151)+~P11(f4(x11151),x11152,x11151)+P11(f4(x11151),f15(x11152,x11153,x11151),x11151) % 1.37/1.32 [1116]~P64(x11161)+~P11(f4(x11161),x11163,x11161)+~P11(f4(x11161),x11162,x11161)+P11(f4(x11161),f15(x11162,x11163,x11161),x11161) % 1.37/1.32 [1117]~P34(x11171)+~P11(f4(x11171),x11173,x11171)+~P11(f4(x11171),x11172,x11171)+P11(f4(x11171),f14(x11172,x11173,x11171),x11171) % 1.37/1.32 [1118]~P57(x11181)+~P11(f4(x11181),x11182,x11181)+~P8(f4(x11181),x11183,x11181)+P11(f4(x11181),f12(x11182,x11183,x11181),x11181) % 1.37/1.32 [1119]~P61(x11191)+~P8(f4(x11191),x11193,x11191)+~P8(f4(x11191),x11192,x11191)+P8(f4(x11191),f15(x11192,x11193,x11191),x11191) % 1.37/1.32 [1120]~P34(x11201)+~P11(f4(x11201),x11203,x11201)+~P8(f4(x11201),x11202,x11201)+P8(f4(x11201),f14(x11202,x11203,x11201),x11201) % 1.37/1.32 [1121]~P34(x11211)+~P11(f4(x11211),x11212,x11211)+~P8(f4(x11211),x11213,x11211)+P8(f4(x11211),f14(x11212,x11213,x11211),x11211) % 1.37/1.32 [1122]~P34(x11221)+~P8(f4(x11221),x11223,x11221)+~P8(f4(x11221),x11222,x11221)+P8(f4(x11221),f14(x11222,x11223,x11221),x11221) % 1.37/1.32 [1123]~P57(x11231)+~P8(f4(x11231),x11233,x11231)+~P8(f4(x11231),x11232,x11231)+P8(f4(x11231),f12(x11232,x11233,x11231),x11231) % 1.37/1.32 [1124]~P59(x11241)+~P8(f9(x11241),x11243,x11241)+~P8(f9(x11241),x11242,x11241)+P8(f9(x11241),f15(x11242,x11243,x11241),x11241) % 1.37/1.32 [1125]~P34(x11253)+~P11(x11252,f4(x11253),x11253)+~P11(x11251,f4(x11253),x11253)+P11(f14(x11251,x11252,x11253),f4(x11253),x11253) % 1.37/1.32 [1126]~P34(x11263)+~P11(x11262,f4(x11263),x11263)+~P8(x11261,f4(x11263),x11263)+P8(f14(x11261,x11262,x11263),f4(x11263),x11263) % 1.37/1.32 [1127]~P34(x11273)+~P11(x11271,f4(x11273),x11273)+~P8(x11272,f4(x11273),x11273)+P8(f14(x11271,x11272,x11273),f4(x11273),x11273) % 1.37/1.32 [1128]~P34(x11283)+~P8(x11282,f4(x11283),x11283)+~P8(x11281,f4(x11283),x11283)+P8(f14(x11281,x11282,x11283),f4(x11283),x11283) % 1.37/1.32 [1129]~P60(x11293)+~P11(x11292,f4(x11293),x11293)+~P11(f4(x11293),x11291,x11293)+P11(f15(x11291,x11292,x11293),f4(x11293),x11293) % 1.37/1.32 [1130]~P60(x11303)+~P11(x11301,f4(x11303),x11303)+~P11(f4(x11303),x11302,x11303)+P11(f15(x11301,x11302,x11303),f4(x11303),x11303) % 1.37/1.32 [1132]~P64(x11323)+~P11(x11322,f4(x11323),x11323)+~P11(f4(x11323),x11321,x11323)+P11(f15(x11321,x11322,x11323),f4(x11323),x11323) % 1.37/1.32 [1135]~P64(x11353)+~P11(x11351,f4(x11353),x11353)+~P11(f4(x11353),x11352,x11353)+P11(f15(x11351,x11352,x11353),f4(x11353),x11353) % 1.37/1.32 [1136]~P57(x11363)+~P11(x11361,f4(x11363),x11363)+~P8(f4(x11363),x11362,x11363)+P11(f12(x11361,x11362,x11363),f4(x11363),x11363) % 1.37/1.32 [1137]~P57(x11373)+~P8(x11372,f4(x11373),x11373)+~P11(f4(x11373),x11371,x11373)+P11(f12(x11371,x11372,x11373),f4(x11373),x11373) % 1.37/1.32 [1138]~P61(x11383)+~P8(x11382,f4(x11383),x11383)+~P8(f4(x11383),x11381,x11383)+P8(f15(x11381,x11382,x11383),f4(x11383),x11383) % 1.37/1.32 [1140]~P61(x11403)+~P8(x11401,f4(x11403),x11403)+~P8(f4(x11403),x11402,x11403)+P8(f15(x11401,x11402,x11403),f4(x11403),x11403) % 1.37/1.32 [1141]~P57(x11413)+~P8(x11412,f4(x11413),x11413)+~P8(f4(x11413),x11411,x11413)+P8(f12(x11411,x11412,x11413),f4(x11413),x11413) % 1.37/1.32 [1142]~P57(x11423)+~P8(x11421,f4(x11423),x11423)+~P8(f4(x11423),x11422,x11423)+P8(f12(x11421,x11422,x11423),f4(x11423),x11423) % 1.37/1.32 [1156]~P60(x11562)+~P11(f15(x11563,x11561,x11562),f4(x11562),x11562)+P11(x11561,f4(x11562),x11562)+P11(x11563,f4(x11562),x11562) % 1.37/1.32 [1157]~P60(x11572)+~P11(f4(x11572),f15(x11573,x11571,x11572),x11572)+P11(x11571,f4(x11572),x11572)+P11(f4(x11572),x11573,x11572) % 1.37/1.32 [1158]~P60(x11582)+~P11(f4(x11582),f15(x11581,x11583,x11582),x11582)+P11(x11581,f4(x11582),x11582)+P11(f4(x11582),x11583,x11582) % 1.37/1.32 [1159]~P60(x11592)+~P11(f4(x11592),f15(x11593,x11591,x11592),x11592)+P11(x11591,f4(x11592),x11592)+P11(f4(x11592),x11591,x11592) % 1.37/1.32 [1160]~P60(x11602)+~P11(f4(x11602),f15(x11601,x11603,x11602),x11602)+P11(x11601,f4(x11602),x11602)+P11(f4(x11602),x11601,x11602) % 1.37/1.32 [1161]~P60(x11612)+~P11(f15(x11613,x11611,x11612),f4(x11612),x11612)+P11(x11611,f4(x11612),x11612)+P11(f4(x11612),x11611,x11612) % 1.37/1.32 [1162]~P60(x11622)+~P11(f15(x11621,x11623,x11622),f4(x11622),x11622)+P11(x11621,f4(x11622),x11622)+P11(f4(x11622),x11621,x11622) % 1.37/1.32 [1163]~P60(x11631)+~P11(f15(x11632,x11633,x11631),f4(x11631),x11631)+P11(f4(x11631),x11632,x11631)+P11(f4(x11631),x11633,x11631) % 1.37/1.32 [1201]~P61(x12011)+~P8(f4(x12011),f15(x12013,x12012,x12011),x12011)+P8(f4(x12011),x12012,x12011)+~P8(f4(x12011),x12013,x12011) % 1.37/1.32 [1202]~P61(x12021)+~P8(f4(x12021),f15(x12022,x12023,x12021),x12021)+P8(f4(x12021),x12022,x12021)+~P8(f4(x12021),x12023,x12021) % 1.37/1.32 [726]~P47(x7262)+~P48(x7262)+E(x7261,f4(x7262))+E(f15(f12(x7263,x7261,x7262),x7261,x7262),x7263) % 1.37/1.32 [885]~P49(x8852)+E(x8851,f4(x8852))+E(x8853,f4(x8852))+E(f15(f11(x8851,x8852),f11(x8853,x8852),x8852),f11(f15(x8853,x8851,x8852),x8852)) % 1.37/1.32 [992]~P57(x9922)+~P47(x9922)+~P8(f4(x9922),x9923,x9922)+E(f12(f10(x9921,x9922),x9923,x9922),f10(f12(x9921,x9923,x9922),x9922)) % 1.37/1.32 [1197]~P58(x11972)+~P11(x11973,f4(x11972),x11972)+~P11(x11971,f4(x11972),x11972)+E(f15(f10(x11971,x11972),f10(x11973,x11972),x11972),f10(f15(x11971,x11973,x11972),x11972)) % 1.37/1.32 [1198]~P58(x11982)+~P11(x11983,f4(x11982),x11982)+~P11(f4(x11982),x11981,x11982)+E(f15(f10(x11981,x11982),f10(x11983,x11982),x11982),f10(f15(x11981,x11983,x11982),x11982)) % 1.37/1.32 [1199]~P58(x11992)+~P11(x11991,f4(x11992),x11992)+~P11(f4(x11992),x11993,x11992)+E(f15(f10(x11991,x11992),f10(x11993,x11992),x11992),f10(f15(x11991,x11993,x11992),x11992)) % 1.37/1.32 [1200]~P58(x12002)+~P11(f4(x12002),x12003,x12002)+~P11(f4(x12002),x12001,x12002)+E(f15(f10(x12001,x12002),f10(x12003,x12002),x12002),f10(f15(x12001,x12003,x12002),x12002)) % 1.37/1.32 [1388]~P49(x13882)+E(x13881,f4(x13882))+E(x13883,f4(x13882))+E(f15(f15(f11(x13883,x13882),f14(x13883,x13881,x13882),x13882),f11(x13881,x13882),x13882),f14(f11(x13883,x13882),f11(x13881,x13882),x13882)) % 1.37/1.32 [1389]~P49(x13892)+E(x13891,f4(x13892))+E(x13893,f4(x13892))+E(f15(f15(f11(x13893,x13892),f13(x13891,x13893,x13892),x13892),f11(x13891,x13892),x13892),f13(f11(x13893,x13892),f11(x13891,x13892),x13892)) % 1.37/1.32 [1390]~P48(x13902)+E(x13901,f4(x13902))+E(x13903,f4(x13902))+E(f15(f15(f14(x13903,x13901,x13902),f11(x13903,x13902),x13902),f11(x13901,x13902),x13902),f14(f11(x13903,x13902),f11(x13901,x13902),x13902)) % 1.37/1.32 [1461]~P59(x14613)+~P8(x14611,f9(x14613),x14613)+~P8(f4(x14613),x14611,x14613)+P8(f15(x14611,f22(x14611,x14612,x14613),x14613),f22(x14611,x14612,x14613),x14613) % 1.37/1.32 [1405]~P59(x14053)+~P8(x14051,f9(x14053),x14053)+~P8(f4(x14053),x14051,x14053)+P8(f22(x14051,f14(x14052,f9(a18),a18),x14053),f9(x14053),x14053) % 1.37/1.32 [1566]~P49(x15662)+E(x15661,f4(x15662))+E(x15663,f4(x15662))+E(f16(f15(f15(f11(x15663,x15662),f13(x15663,x15661,x15662),x15662),f11(x15661,x15662),x15662),x15662),f13(f11(x15663,x15662),f11(x15661,x15662),x15662)) % 1.37/1.32 [1537]~P59(x15373)+P11(x15371,x15372,x15373)+~P11(f4(x15373),x15372,x15373)+~P11(f22(x15371,f21(f3(f2(a17)),a18),x15373),f22(x15372,f21(f3(f2(a17)),a18),x15373),x15373) % 1.37/1.32 [857]~P1(x8573)+~P10(x8571,x8574,x8573)+P10(x8571,x8572,x8573)+~P10(x8574,x8572,x8573) % 1.37/1.32 [858]~P36(x8583)+~P11(x8581,x8584,x8583)+P11(x8581,x8582,x8583)+~P11(x8584,x8582,x8583) % 1.37/1.32 [859]~P37(x8593)+~P11(x8591,x8594,x8593)+P11(x8591,x8592,x8593)+~P11(x8594,x8592,x8593) % 1.37/1.32 [860]~P36(x8603)+~P8(x8601,x8604,x8603)+P8(x8601,x8602,x8603)+~P11(x8604,x8602,x8603) % 1.37/1.32 [861]~P36(x8613)+~P8(x8614,x8612,x8613)+P8(x8611,x8612,x8613)+~P11(x8611,x8614,x8613) % 1.37/1.32 [862]~P36(x8623)+~P8(x8621,x8624,x8623)+P8(x8621,x8622,x8623)+~P8(x8624,x8622,x8623) % 1.37/1.32 [863]~P37(x8633)+~P8(x8631,x8634,x8633)+P8(x8631,x8632,x8633)+~P11(x8634,x8632,x8633) % 1.37/1.32 [864]~P37(x8643)+~P8(x8644,x8642,x8643)+P8(x8641,x8642,x8643)+~P11(x8641,x8644,x8643) % 1.37/1.32 [865]~P37(x8653)+~P8(x8651,x8654,x8653)+P8(x8651,x8652,x8653)+~P8(x8654,x8652,x8653) % 1.37/1.32 [740]~P46(x7404)+~P14(x7404)+E(x7401,x7402)+~E(f14(x7403,x7401,x7404),f14(x7403,x7402,x7404)) % 1.37/1.32 [926]~P59(x9264)+E(x9261,x9262)+~P8(f9(x9264),x9263,x9264)+~E(f22(x9263,x9261,x9264),f22(x9263,x9262,x9264)) % 1.37/1.32 [1059]~P1(x10594)+~P10(x10591,x10593,x10594)+~P10(x10591,x10592,x10594)+P10(x10591,f14(x10592,x10593,x10594),x10594) % 1.37/1.32 [1061]~P5(x10614)+~P10(x10611,x10613,x10614)+~P10(x10611,x10612,x10614)+P10(x10611,f7(x10612,x10613,x10614),x10614) % 1.37/1.32 [1062]~P41(x10624)+~P10(x10621,x10623,x10624)+~P10(x10621,x10622,x10624)+P10(x10621,f13(x10622,x10623,x10624),x10624) % 1.37/1.32 [1077]~P59(x10774)+~P8(x10771,x10773,x10774)+~P8(f4(x10774),x10772,x10774)+P8(x10771,f14(x10772,x10773,x10774),x10774) % 1.37/1.32 [1153]~P45(x11533)+~P11(x11532,x11534,x11533)+P11(f22(x11532,x11531,x11533),f22(x11534,x11531,x11533),x11533)+P7(x11531,a18) % 1.37/1.32 [1188]~P5(x11883)+P10(x11881,x11882,x11883)+~P10(x11881,x11884,x11883)+~P10(x11881,f7(x11882,x11884,x11883),x11883) % 1.37/1.32 [1255]~P59(x12553)+~P8(x12552,x12554,a18)+~P8(f9(x12553),x12551,x12553)+P8(f22(x12551,x12552,x12553),f22(x12551,x12554,x12553),x12553) % 1.37/1.32 [1258]~P63(x12583)+~P11(x12584,x12581,x12583)+~P11(x12582,f4(x12583),x12583)+P11(f15(x12581,x12582,x12583),f15(x12584,x12582,x12583),x12583) % 1.37/1.32 [1259]~P60(x12593)+~P11(x12594,x12592,x12593)+~P8(x12591,f4(x12593),x12593)+P11(f15(x12591,x12592,x12593),f15(x12591,x12594,x12593),x12593) % 1.37/1.32 [1260]~P63(x12603)+~P11(x12604,x12602,x12603)+~P11(x12601,f4(x12603),x12603)+P11(f15(x12601,x12602,x12603),f15(x12601,x12604,x12603),x12603) % 1.37/1.32 [1262]~P60(x12623)+~P8(x12624,x12621,x12623)+~P8(x12622,f4(x12623),x12623)+P8(f15(x12621,x12622,x12623),f15(x12624,x12622,x12623),x12623) % 1.37/1.32 [1265]~P60(x12653)+~P8(x12654,x12652,x12653)+~P8(x12651,f4(x12653),x12653)+P8(f15(x12651,x12652,x12653),f15(x12651,x12654,x12653),x12653) % 1.37/1.32 [1266]~P57(x12663)+~P8(x12664,x12661,x12663)+~P8(x12662,f4(x12663),x12663)+P8(f12(x12661,x12662,x12663),f12(x12664,x12662,x12663),x12663) % 1.37/1.32 [1267]~P59(x12673)+~P11(x12671,x12674,x12673)+~P11(f4(x12673),x12671,x12673)+P11(f22(x12671,x12672,x12673),f22(x12674,x12672,x12673),x12673) % 1.37/1.32 [1268]~P54(x12683)+~P11(x12681,x12684,x12683)+~P11(f4(x12683),x12682,x12683)+P11(f15(x12681,x12682,x12683),f15(x12684,x12682,x12683),x12683) % 1.37/1.32 [1269]~P60(x12693)+~P11(x12692,x12694,x12693)+~P8(f4(x12693),x12691,x12693)+P11(f15(x12691,x12692,x12693),f15(x12691,x12694,x12693),x12693) % 1.37/1.32 [1270]~P53(x12703)+~P11(x12702,x12704,x12703)+~P11(f4(x12703),x12701,x12703)+P11(f15(x12701,x12702,x12703),f15(x12701,x12704,x12703),x12703) % 1.37/1.32 [1271]~P54(x12713)+~P11(x12712,x12714,x12713)+~P11(f4(x12713),x12711,x12713)+P11(f15(x12711,x12712,x12713),f15(x12711,x12714,x12713),x12713) % 1.37/1.32 [1272]~P60(x12723)+~P8(x12721,x12724,x12723)+~P8(f4(x12723),x12722,x12723)+P8(f15(x12721,x12722,x12723),f15(x12724,x12722,x12723),x12723) % 1.37/1.32 [1273]~P61(x12733)+~P8(x12731,x12734,x12733)+~P8(f4(x12733),x12732,x12733)+P8(f15(x12731,x12732,x12733),f15(x12734,x12732,x12733),x12733) % 1.37/1.32 [1275]~P60(x12753)+~P8(x12752,x12754,x12753)+~P8(f4(x12753),x12751,x12753)+P8(f15(x12751,x12752,x12753),f15(x12751,x12754,x12753),x12753) % 1.37/1.32 [1276]~P61(x12763)+~P8(x12762,x12764,x12763)+~P8(f4(x12763),x12761,x12763)+P8(f15(x12761,x12762,x12763),f15(x12761,x12764,x12763),x12763) % 1.37/1.32 [1277]~P56(x12773)+~P8(x12772,x12774,x12773)+~P8(f4(x12773),x12771,x12773)+P8(f15(x12771,x12772,x12773),f15(x12771,x12774,x12773),x12773) % 1.37/1.32 [1278]~P57(x12783)+~P8(x12781,x12784,x12783)+~P8(f4(x12783),x12782,x12783)+P8(f12(x12781,x12782,x12783),f12(x12784,x12782,x12783),x12783) % 1.37/1.32 [1285]~P45(x12853)+~P11(f10(x12851,x12853),f10(x12854,x12853),x12853)+P11(f22(x12851,x12852,x12853),f22(x12854,x12852,x12853),x12853)+~P7(x12852,a18) % 1.37/1.32 [1306]~P46(x13062)+P10(x13063,x13064,x13062)+~P10(f15(x13061,x13063,x13062),f15(x13061,x13064,x13062),x13062)+E(x13061,f4(x13062)) % 1.37/1.32 [1307]~P46(x13072)+P10(x13073,x13074,x13072)+~P10(f15(x13073,x13071,x13072),f15(x13074,x13071,x13072),x13072)+E(x13071,f4(x13072)) % 1.37/1.32 [1328]~P57(x13284)+~P8(f4(x13284),x13283,x13284)+~P11(f15(x13281,x13283,x13284),x13282,x13284)+P11(x13281,f12(x13282,x13283,x13284),x13284) % 1.37/1.32 [1329]~P57(x13294)+~P8(f4(x13294),x13293,x13294)+~P8(f15(x13291,x13293,x13294),x13292,x13294)+P8(x13291,f12(x13292,x13293,x13294),x13294) % 1.37/1.32 [1330]~P57(x13303)+~P8(f4(x13303),x13302,x13303)+~P11(x13301,f15(x13304,x13302,x13303),x13303)+P11(f12(x13301,x13302,x13303),x13304,x13303) % 1.37/1.32 [1331]~P57(x13313)+~P8(f4(x13313),x13312,x13313)+~P8(x13311,f15(x13314,x13312,x13313),x13313)+P8(f12(x13311,x13312,x13313),x13314,x13313) % 1.37/1.32 [1350]P8(x13502,x13501,x13503)+~P60(x13503)+P8(x13501,x13502,x13503)+~P8(f15(x13504,x13501,x13503),f15(x13504,x13502,x13503),x13503) % 1.37/1.32 [1351]P8(x13512,x13511,x13513)+~P60(x13513)+P8(x13511,x13512,x13513)+~P8(f15(x13511,x13514,x13513),f15(x13512,x13514,x13513),x13513) % 1.37/1.32 [1364]~P60(x13643)+P8(x13641,x13642,x13643)+~P8(f15(x13641,x13644,x13643),f15(x13642,x13644,x13643),x13643)+P8(x13644,f4(x13643),x13643) % 1.37/1.32 [1365]~P60(x13653)+P8(x13651,x13652,x13653)+~P8(f15(x13654,x13651,x13653),f15(x13654,x13652,x13653),x13653)+P8(x13654,f4(x13653),x13653) % 1.37/1.32 [1366]~P60(x13663)+P8(x13661,x13662,x13663)+~P8(f15(x13664,x13662,x13663),f15(x13664,x13661,x13663),x13663)+P8(f4(x13663),x13664,x13663) % 1.37/1.32 [1367]~P60(x13673)+P8(x13671,x13672,x13673)+~P8(f15(x13672,x13674,x13673),f15(x13671,x13674,x13673),x13673)+P8(f4(x13673),x13674,x13673) % 1.37/1.32 [1374]~P60(x13742)+~P8(f15(x13743,x13741,x13742),f15(x13744,x13741,x13742),x13742)+P8(x13741,f4(x13742),x13742)+P8(f4(x13742),x13741,x13742) % 1.37/1.32 [1375]~P60(x13752)+~P8(f15(x13751,x13753,x13752),f15(x13751,x13754,x13752),x13752)+P8(x13751,f4(x13752),x13752)+P8(f4(x13752),x13751,x13752) % 1.37/1.32 [1392]~P59(x13923)+~P8(f22(x13924,x13921,x13923),f22(x13924,x13922,x13923),x13923)+P8(x13921,x13922,a18)+~P8(f9(x13923),x13924,x13923) % 1.37/1.32 [1393]~P60(x13933)+P11(x13931,x13932,x13933)+~P11(f15(x13934,x13932,x13933),f15(x13934,x13931,x13933),x13933)+~P8(x13934,f4(x13933),x13933) % 1.37/1.32 [1394]~P60(x13943)+P8(x13941,x13942,x13943)+~P8(f15(x13944,x13942,x13943),f15(x13944,x13941,x13943),x13943)+~P8(x13944,f4(x13943),x13943) % 1.37/1.32 [1395]~P60(x13953)+P11(x13951,x13952,x13953)+~P11(f15(x13954,x13951,x13953),f15(x13954,x13952,x13953),x13953)+~P8(f4(x13953),x13954,x13953) % 1.37/1.32 [1396]~P61(x13963)+P11(x13961,x13962,x13963)+~P11(f15(x13964,x13961,x13963),f15(x13964,x13962,x13963),x13963)+~P8(f4(x13963),x13964,x13963) % 1.37/1.32 [1397]~P61(x13973)+P11(x13971,x13972,x13973)+~P11(f15(x13971,x13974,x13973),f15(x13972,x13974,x13973),x13973)+~P8(f4(x13973),x13974,x13973) % 1.37/1.32 [1398]~P59(x13983)+P8(x13981,x13982,x13983)+~P11(f4(x13983),x13982,x13983)+~P8(f22(x13981,x13984,x13983),f22(x13982,x13984,x13983),x13983) % 1.37/1.32 [1399]~P60(x13993)+P8(x13991,x13992,x13993)+~P8(f15(x13994,x13991,x13993),f15(x13994,x13992,x13993),x13993)+~P8(f4(x13993),x13994,x13993) % 1.37/1.32 [1400]~P61(x14003)+P8(x14001,x14002,x14003)+~P8(f15(x14004,x14001,x14003),f15(x14004,x14002,x14003),x14003)+~P11(f4(x14003),x14004,x14003) % 1.37/1.32 [1401]~P61(x14013)+P8(x14011,x14012,x14013)+~P8(f15(x14011,x14014,x14013),f15(x14012,x14014,x14013),x14013)+~P11(f4(x14013),x14014,x14013) % 1.37/1.32 [1402]~P62(x14023)+P8(x14021,x14022,x14023)+~P8(f15(x14024,x14021,x14023),f15(x14024,x14022,x14023),x14023)+~P11(f4(x14023),x14024,x14023) % 1.37/1.32 [1403]~P62(x14033)+P8(x14031,x14032,x14033)+~P8(f15(x14031,x14034,x14033),f15(x14032,x14034,x14033),x14033)+~P11(f4(x14033),x14034,x14033) % 1.37/1.32 [1065]~P47(x10652)+~P48(x10652)+E(x10651,f4(x10652))+E(f12(f15(x10653,x10651,x10652),f15(x10654,x10651,x10652),x10652),f12(x10653,x10654,x10652)) % 1.37/1.32 [1066]~P47(x10662)+~P48(x10662)+E(x10661,f4(x10662))+E(f12(f15(x10661,x10663,x10662),f15(x10661,x10664,x10662),x10662),f12(x10663,x10664,x10662)) % 1.37/1.32 [1432]~P5(x14323)+~P10(x14322,x14324,x14323)+~P10(x14322,x14321,x14323)+E(f14(f8(x14321,x14322,x14323),f8(x14324,x14322,x14323),x14323),f8(f14(x14321,x14324,x14323),x14322,x14323)) % 1.37/1.32 [1531]~P45(x15313)+~P8(x15311,f14(x15312,x15314,x15313),x15313)+~P8(f13(x15312,x15314,x15313),x15311,x15313)+P8(f10(f13(x15311,x15312,x15313),x15313),x15314,x15313) % 1.37/1.32 [1380]~P47(x13802)+~P48(x13802)+E(x13801,f4(x13802))+E(f12(f14(x13803,f15(x13804,x13801,x13802),x13802),x13801,x13802),f14(x13804,f12(x13803,x13801,x13802),x13802)) % 1.37/1.32 [1381]~P47(x13812)+~P48(x13812)+E(x13811,f4(x13812))+E(f12(f14(x13813,f15(x13814,x13811,x13812),x13812),x13811,x13812),f14(f12(x13813,x13811,x13812),x13814,x13812)) % 1.37/1.32 [1581]~P59(x15813)+P11(x15811,x15812,x15813)+~P11(f4(x15813),x15812,x15813)+~P11(f22(x15811,f14(x15814,f9(a18),a18),x15813),f22(x15812,f14(x15814,f9(a18),a18),x15813),x15813) % 1.37/1.32 [1600]~P38(x16002)+E(x16001,f4(x16002))+E(x16003,f4(x16002))+E(f16(f15(f15(f11(x16003,x16002),f12(f13(x16003,x16001,x16002),x16004,x16002),x16002),f11(x16001,x16002),x16002),x16002),f12(f13(f11(x16003,x16002),f11(x16001,x16002),x16002),x16004,x16002)) % 1.37/1.32 [1000]~P25(x10003)+~P11(x10005,x10004,x10003)+P11(x10001,x10002,x10003)+~E(f13(x10004,x10005,x10003),f13(x10002,x10001,x10003)) % 1.37/1.32 [1001]~P25(x10013)+~P11(x10015,x10014,x10013)+P11(x10011,x10012,x10013)+~E(f13(x10012,x10011,x10013),f13(x10014,x10015,x10013)) % 1.37/1.32 [1002]~P25(x10023)+~P8(x10024,x10025,x10023)+P8(x10021,x10022,x10023)+~E(f13(x10024,x10025,x10023),f13(x10021,x10022,x10023)) % 1.37/1.32 [1003]~P25(x10033)+~P8(x10034,x10035,x10033)+P8(x10031,x10032,x10033)+~E(f13(x10031,x10032,x10033),f13(x10034,x10035,x10033)) % 1.37/1.32 [1244]~P1(x12443)+~P10(x12442,x12445,x12443)+~P10(x12441,x12444,x12443)+P10(f15(x12441,x12442,x12443),f15(x12444,x12445,x12443),x12443) % 1.37/1.32 [1245]~P2(x12453)+~P11(x12452,x12455,x12453)+~P11(x12451,x12454,x12453)+P11(f14(x12451,x12452,x12453),f14(x12454,x12455,x12453),x12453) % 1.37/1.32 [1246]~P35(x12463)+~P11(x12462,x12465,x12463)+~P8(x12461,x12464,x12463)+P8(f14(x12461,x12462,x12463),f14(x12464,x12465,x12463),x12463) % 1.37/1.32 [1247]~P35(x12473)+~P11(x12471,x12474,x12473)+~P8(x12472,x12475,x12473)+P8(f14(x12471,x12472,x12473),f14(x12474,x12475,x12473),x12473) % 1.37/1.32 [1248]~P35(x12483)+~P8(x12482,x12485,x12483)+~P8(x12481,x12484,x12483)+P8(f14(x12481,x12482,x12483),f14(x12484,x12485,x12483),x12483) % 1.37/1.32 [1321]~P25(x13214)+~P11(x13215,x13213,x13214)+~P11(x13211,f14(x13212,x13215,x13214),x13214)+P11(x13211,f14(x13212,x13213,x13214),x13214) % 1.37/1.32 [1440]~P45(x14402)+~P8(f10(x14401,x14402),x14404,x14402)+~P8(f10(x14403,x14402),x14405,x14402)+P8(f15(f10(x14401,x14402),f10(x14403,x14402),x14402),f15(x14404,x14405,x14402),x14402) % 1.37/1.32 [1482]~P5(x14823)+~P10(x14825,x14822,x14823)+~P10(x14824,x14821,x14823)+E(f8(f15(x14821,x14822,x14823),f15(x14824,x14825,x14823),x14823),f15(f8(x14821,x14824,x14823),f8(x14822,x14825,x14823),x14823)) % 1.37/1.32 [1552]~P48(x15522)+E(x15521,f4(x15522))+E(x15523,f4(x15522))+E(f12(f14(f15(x15524,x15521,x15522),f15(x15525,x15523,x15522),x15522),f15(x15523,x15521,x15522),x15522),f14(f12(x15524,x15523,x15522),f12(x15525,x15521,x15522),x15522)) % 1.37/1.32 [1553]~P48(x15532)+E(x15531,f4(x15532))+E(x15533,f4(x15532))+E(f12(f13(f15(x15534,x15531,x15532),f15(x15535,x15533,x15532),x15532),f15(x15533,x15531,x15532),x15532),f13(f12(x15534,x15533,x15532),f12(x15535,x15531,x15532),x15532)) % 1.37/1.32 [1458]~P5(x14583)+~E(f7(x14581,x14584,x14583),f7(x14585,x14584,x14583))+~E(f7(x14582,x14584,x14583),f7(x14586,x14584,x14583))+E(f7(f15(x14581,x14582,x14583),x14584,x14583),f7(f15(x14585,x14586,x14583),x14584,x14583)) % 1.37/1.32 [1459]~P5(x14593)+~E(f7(x14591,x14594,x14593),f7(x14595,x14594,x14593))+~E(f7(x14592,x14594,x14593),f7(x14596,x14594,x14593))+E(f7(f14(x14591,x14592,x14593),x14594,x14593),f7(f14(x14595,x14596,x14593),x14594,x14593)) % 1.37/1.32 [1460]~P6(x14603)+~E(f7(x14601,x14604,x14603),f7(x14605,x14604,x14603))+~E(f7(x14602,x14604,x14603),f7(x14606,x14604,x14603))+E(f7(f13(x14601,x14602,x14603),x14604,x14603),f7(f13(x14605,x14606,x14603),x14604,x14603)) % 1.37/1.32 [921]~P57(x9212)+~P47(x9212)+P11(f9(x9212),x9211,x9212)+~P11(f11(x9211,x9212),f9(x9212),x9212)+P11(x9211,f4(x9212),x9212) % 1.37/1.32 [922]~P57(x9222)+~P47(x9222)+P8(f9(x9222),x9221,x9222)+~P8(f11(x9221,x9222),f9(x9222),x9222)+P11(x9221,f4(x9222),x9222) % 1.37/1.32 [953]~P57(x9531)+~P47(x9531)+~P8(f4(x9531),x9532,x9531)+~P11(x9532,f9(x9531),x9531)+P11(f9(x9531),f11(x9532,x9531),x9531) % 1.37/1.32 [954]~P57(x9541)+~P47(x9541)+~P8(f4(x9541),x9542,x9541)+~P8(x9542,f9(x9541),x9541)+P8(f9(x9541),f11(x9542,x9541),x9541) % 1.37/1.32 [605]~P32(x6052)+~P65(x6052)+~P51(x6052)+~P52(x6052)+~E(f22(x6051,f4(a18),x6052),f4(x6052)) % 1.37/1.32 [1155]~P57(x11551)+~P47(x11551)+~P14(x11551)+~P8(f4(x11551),x11552,x11551)+P8(f4(x11551),f12(x11552,f21(f3(f2(a17)),x11551),x11551),x11551) % 1.37/1.32 [1316]~P57(x13161)+~P47(x13161)+~P14(x13161)+P8(f4(x13161),x13162,x13161)+~P8(f4(x13161),f12(x13162,f21(f3(f2(a17)),x13161),x13161),x13161) % 1.37/1.32 [442]~P49(x4423)+E(x4421,x4422)+~E(f11(x4421,x4423),f11(x4422,x4423))+E(x4422,f4(x4423))+E(x4421,f4(x4423)) % 1.37/1.32 [946]~P45(x9463)+~P11(x9462,f4(x9463),x9463)+P11(f22(x9462,x9461,x9463),f4(x9463),x9463)+P7(x9461,a18)+E(x9461,f4(a18)) % 1.37/1.32 [963]~P34(x9632)+~P11(f4(x9632),x9631,x9632)+~P11(f4(x9632),x9633,x9632)+~E(f14(x9633,x9631,x9632),f4(x9632))+E(x9631,f4(x9632)) % 1.37/1.32 [964]~P34(x9642)+~P11(f4(x9642),x9643,x9642)+~P11(f4(x9642),x9641,x9642)+~E(f14(x9641,x9643,x9642),f4(x9642))+E(x9641,f4(x9642)) % 1.37/1.32 [1075]~P45(x10752)+~P8(f4(x10752),f22(x10753,x10751,x10752),x10752)+P8(f4(x10752),x10753,x10752)+P7(x10751,a18)+E(x10751,f4(a18)) % 1.37/1.32 [1145]~P57(x11451)+~P47(x11451)+~P11(x11453,f4(x11451),x11451)+~P11(x11452,f4(x11451),x11451)+P11(f4(x11451),f12(x11452,x11453,x11451),x11451) % 1.37/1.32 [1147]~P57(x11471)+~P47(x11471)+~P11(f4(x11471),x11473,x11471)+~P11(f4(x11471),x11472,x11471)+P11(f4(x11471),f12(x11472,x11473,x11471),x11471) % 1.37/1.32 [1149]~P57(x11493)+~P47(x11493)+~P11(x11492,f4(x11493),x11493)+~P11(f4(x11493),x11491,x11493)+P11(f12(x11491,x11492,x11493),f4(x11493),x11493) % 1.37/1.32 [1150]~P57(x11503)+~P47(x11503)+~P11(x11501,f4(x11503),x11503)+~P11(f4(x11503),x11502,x11503)+P11(f12(x11501,x11502,x11503),f4(x11503),x11503) % 1.37/1.32 [1169]~P57(x11692)+~P47(x11692)+~P11(f12(x11693,x11691,x11692),f4(x11692),x11692)+P11(x11691,f4(x11692),x11692)+P11(x11693,f4(x11692),x11692) % 1.37/1.32 [1170]~P57(x11702)+~P47(x11702)+~P8(f12(x11703,x11701,x11702),f4(x11702),x11702)+P8(x11701,f4(x11702),x11702)+P8(x11703,f4(x11702),x11702) % 1.37/1.32 [1171]~P57(x11712)+~P47(x11712)+~P11(f4(x11712),f12(x11713,x11711,x11712),x11712)+P11(x11711,f4(x11712),x11712)+P11(f4(x11712),x11713,x11712) % 1.37/1.32 [1172]~P57(x11722)+~P47(x11722)+~P11(f4(x11722),f12(x11721,x11723,x11722),x11722)+P11(x11721,f4(x11722),x11722)+P11(f4(x11722),x11723,x11722) % 1.37/1.32 [1173]~P57(x11732)+~P47(x11732)+~P11(f4(x11732),f12(x11733,x11731,x11732),x11732)+P11(x11731,f4(x11732),x11732)+P11(f4(x11732),x11731,x11732) % 1.37/1.32 [1174]~P57(x11742)+~P47(x11742)+~P11(f4(x11742),f12(x11741,x11743,x11742),x11742)+P11(x11741,f4(x11742),x11742)+P11(f4(x11742),x11741,x11742) % 1.37/1.32 [1175]~P57(x11752)+~P47(x11752)+~P8(f4(x11752),f12(x11753,x11751,x11752),x11752)+P8(x11751,f4(x11752),x11752)+P8(f4(x11752),x11753,x11752) % 1.37/1.32 [1176]~P57(x11762)+~P47(x11762)+~P8(f4(x11762),f12(x11761,x11763,x11762),x11762)+P8(x11761,f4(x11762),x11762)+P8(f4(x11762),x11763,x11762) % 1.37/1.32 [1177]~P57(x11772)+~P47(x11772)+~P8(f4(x11772),f12(x11773,x11771,x11772),x11772)+P8(x11771,f4(x11772),x11772)+P8(f4(x11772),x11771,x11772) % 1.37/1.32 [1178]~P57(x11782)+~P47(x11782)+~P8(f4(x11782),f12(x11781,x11783,x11782),x11782)+P8(x11781,f4(x11782),x11782)+P8(f4(x11782),x11781,x11782) % 1.37/1.32 [1179]~P57(x11792)+~P47(x11792)+~P11(f12(x11793,x11791,x11792),f4(x11792),x11792)+P11(x11791,f4(x11792),x11792)+P11(f4(x11792),x11791,x11792) % 1.37/1.32 [1180]~P57(x11802)+~P47(x11802)+~P11(f12(x11801,x11803,x11802),f4(x11802),x11802)+P11(x11801,f4(x11802),x11802)+P11(f4(x11802),x11801,x11802) % 1.37/1.32 [1181]~P57(x11812)+~P47(x11812)+~P8(f12(x11813,x11811,x11812),f4(x11812),x11812)+P8(x11811,f4(x11812),x11812)+P8(f4(x11812),x11811,x11812) % 1.37/1.32 [1182]~P57(x11822)+~P47(x11822)+~P8(f12(x11821,x11823,x11822),f4(x11822),x11822)+P8(x11821,f4(x11822),x11822)+P8(f4(x11822),x11821,x11822) % 1.37/1.32 [1183]~P57(x11831)+~P47(x11831)+~P11(f12(x11832,x11833,x11831),f4(x11831),x11831)+P11(f4(x11831),x11832,x11831)+P11(f4(x11831),x11833,x11831) % 1.37/1.32 [1184]~P57(x11841)+~P47(x11841)+~P8(f12(x11842,x11843,x11841),f4(x11841),x11841)+P8(f4(x11841),x11842,x11841)+P8(f4(x11841),x11843,x11841) % 1.37/1.32 [1256]~P45(x12563)+~P11(x12561,f9(x12563),x12563)+~P11(f4(x12563),x12562,x12563)+~P11(f4(x12563),x12561,x12563)+P11(f15(x12561,x12562,x12563),x12562,x12563) % 1.37/1.32 [1257]~P45(x12573)+~P11(x12572,f9(x12573),x12573)+~P11(f4(x12573),x12572,x12573)+~P11(f4(x12573),x12571,x12573)+P11(f15(x12571,x12572,x12573),x12571,x12573) % 1.37/1.32 [603]~P47(x6032)+~P4(x6032)+~P48(x6032)+~E(f21(x6031,x6032),f4(x6032))+E(f21(x6031,x6032),f12(x6033,f4(x6032),x6032)) % 1.37/1.32 [604]~P47(x6042)+~P4(x6042)+~P48(x6042)+~E(f21(x6043,x6042),f4(x6042))+E(f12(x6041,f4(x6042),x6042),f21(x6043,x6042)) % 1.37/1.32 [616]~P47(x6163)+~P4(x6163)+~P48(x6163)+~E(f21(x6162,x6163),f4(x6163))+E(f12(x6161,f21(x6162,x6163),x6163),f4(x6163)) % 1.37/1.32 [652]~P47(x6522)+~P4(x6522)+~P48(x6522)+E(f21(x6521,x6522),f4(x6522))+~E(f21(x6521,x6522),f12(x6523,f4(x6522),x6522)) % 1.37/1.32 [653]~P47(x6532)+~P4(x6532)+~P48(x6532)+E(f21(x6531,x6532),f4(x6532))+~E(f12(x6533,f4(x6532),x6532),f21(x6531,x6532)) % 1.37/1.32 [931]~P47(x9312)+~P4(x9312)+~P48(x9312)+~E(f21(x9311,x9312),f4(x9312))+E(f12(f15(f21(x9311,x9312),x9313,x9312),x9313,x9312),f21(x9311,x9312)) % 1.37/1.32 [1332]~P59(x13323)+E(x13321,x13322)+~P11(f4(x13323),x13322,x13323)+~P11(f4(x13323),x13321,x13323)+~E(f22(x13321,f21(f3(f2(a17)),a18),x13323),f22(x13322,f21(f3(f2(a17)),a18),x13323)) % 1.37/1.32 [1089]~P31(x10894)+~P18(x10894)+~P11(x10891,x10893,x10894)+~P11(f4(x10894),x10892,x10894)+P11(x10891,f14(x10892,x10893,x10894),x10894) % 1.37/1.32 [1090]~P31(x10904)+~P18(x10904)+~P11(x10901,x10902,x10904)+~P11(f4(x10904),x10903,x10904)+P11(x10901,f14(x10902,x10903,x10904),x10904) % 1.37/1.32 [1091]~P31(x10914)+~P18(x10914)+~P11(x10911,x10913,x10914)+~P8(f4(x10914),x10912,x10914)+P8(x10911,f14(x10912,x10913,x10914),x10914) % 1.37/1.32 [1092]~P31(x10924)+~P18(x10924)+~P8(x10921,x10923,x10924)+~P11(f4(x10924),x10922,x10924)+P8(x10921,f14(x10922,x10923,x10924),x10924) % 1.37/1.32 [1286]~P57(x12863)+~P47(x12863)+~P11(x12864,x12861,x12863)+~P11(x12862,f4(x12863),x12863)+P11(f12(x12861,x12862,x12863),f12(x12864,x12862,x12863),x12863) % 1.37/1.32 [1287]~P57(x12873)+~P47(x12873)+~P11(x12871,x12874,x12873)+~P11(f4(x12873),x12872,x12873)+P11(f12(x12871,x12872,x12873),f12(x12874,x12872,x12873),x12873) % 1.37/1.32 [1338]~P57(x13384)+~P47(x13384)+~P8(f4(x13384),x13383,x13384)+~P11(f12(x13381,x13383,x13384),x13382,x13384)+P11(x13381,f15(x13382,x13383,x13384),x13384) % 1.37/1.32 [1340]~P57(x13404)+~P47(x13404)+~P8(f4(x13404),x13403,x13404)+~P8(f12(x13401,x13403,x13404),x13402,x13404)+P8(x13401,f15(x13402,x13403,x13404),x13404) % 1.37/1.32 [1342]~P57(x13423)+~P47(x13423)+~P8(f4(x13423),x13422,x13423)+~P11(x13421,f12(x13424,x13422,x13423),x13423)+P11(f15(x13421,x13422,x13423),x13424,x13423) % 1.37/1.32 [1344]~P57(x13443)+~P47(x13443)+~P8(f4(x13443),x13442,x13443)+~P8(x13441,f12(x13444,x13442,x13443),x13443)+P8(f15(x13441,x13442,x13443),x13444,x13443) % 1.37/1.32 [1348]~P5(x13483)+~P10(x13482,x13484,x13483)+~P10(x13482,x13481,x13483)+~P10(x13481,x13484,x13483)+P10(f8(x13481,x13482,x13483),f8(x13484,x13482,x13483),x13483) % 1.37/1.32 [1368]~P59(x13683)+~P8(x13681,x13684,x13683)+~P11(f4(x13683),x13681,x13683)+P8(f22(x13681,x13682,x13683),f22(x13684,x13682,x13683),x13683)+~P8(f4(a18),x13682,a18) % 1.37/1.32 [1376]~P59(x13763)+~P8(x13764,x13762,a18)+~P8(x13761,f9(x13763),x13763)+~P8(f4(x13763),x13761,x13763)+P8(f22(x13761,x13762,x13763),f22(x13761,x13764,x13763),x13763) % 1.37/1.32 [1457]~P5(x14573)+~P10(x14574,x14571,x14573)+P10(x14571,x14572,x14573)+~P10(x14574,x14572,x14573)+~P10(f8(x14571,x14574,x14573),f8(x14572,x14574,x14573),x14573) % 1.37/1.32 [1484]~P57(x14843)+~P8(x14842,x14844,x14843)+~P8(x14841,f4(x14843),x14843)+~P8(f4(x14843),f15(x14842,x14844,x14843),x14843)+P8(f12(x14841,x14842,x14843),f12(x14841,x14844,x14843),x14843) % 1.37/1.32 [1485]~P57(x14853)+~P11(x14854,x14852,x14853)+~P11(f4(x14853),x14851,x14853)+~P8(f4(x14853),f15(x14852,x14854,x14853),x14853)+P11(f12(x14851,x14852,x14853),f12(x14851,x14854,x14853),x14853) % 1.37/1.32 [1486]~P57(x14863)+~P8(x14864,x14862,x14863)+~P8(f4(x14863),x14861,x14863)+~P8(f4(x14863),f15(x14862,x14864,x14863),x14863)+P8(f12(x14861,x14862,x14863),f12(x14861,x14864,x14863),x14863) % 1.37/1.32 [1483]~P59(x14834)+E(x14831,x14832)+~P11(f4(x14834),x14832,x14834)+~P11(f4(x14834),x14831,x14834)+~E(f22(x14831,f14(x14833,f9(a18),a18),x14834),f22(x14832,f14(x14833,f9(a18),a18),x14834)) % 1.37/1.32 [967]~P48(x9672)+~E(f12(x9674,x9673,x9672),f12(x9675,x9671,x9672))+E(f15(x9674,x9671,x9672),f15(x9675,x9673,x9672))+E(x9671,f4(x9672))+E(x9673,f4(x9672)) % 1.37/1.32 [968]~P48(x9682)+~E(f15(x9684,x9683,x9682),f15(x9685,x9681,x9682))+E(f12(x9684,x9681,x9682),f12(x9685,x9683,x9682))+E(x9681,f4(x9682))+E(x9683,f4(x9682)) % 1.37/1.32 [1347]~P46(x13474)+~P14(x13474)+E(x13471,x13472)+E(x13473,f4(x13474))+~E(f14(x13475,f15(x13473,x13471,x13474),x13474),f14(x13475,f15(x13473,x13472,x13474),x13474)) % 1.37/1.32 [1535]~P46(x15355)+~P14(x15355)+E(x15351,x15352)+E(x15353,x15354)+~E(f14(f15(x15353,x15351,x15355),f15(x15354,x15352,x15355),x15355),f14(f15(x15353,x15352,x15355),f15(x15354,x15351,x15355),x15355)) % 1.37/1.32 [1579]~P50(x15795)+~P43(x15795)+~P10(x15791,x15794,x15795)+~P10(x15791,f14(x15792,x15796,x15795),x15795)+P10(x15791,f14(f13(x15792,f15(x15793,x15794,x15795),x15795),x15796,x15795),x15795) % 1.37/1.32 [1584]~P50(x15844)+~P43(x15844)+~P10(x15841,x15845,x15844)+P10(x15841,f14(x15842,x15843,x15844),x15844)+~P10(x15841,f14(f13(x15842,f15(x15846,x15845,x15844),x15844),x15843,x15844),x15844) % 1.37/1.32 [547]~P32(x5472)+~P65(x5472)+~P51(x5472)+~P52(x5472)+E(x5471,f4(a18))+E(f22(f4(x5472),x5471,x5472),f4(x5472)) % 1.37/1.32 [607]~P32(x6072)+~P65(x6072)+~P51(x6072)+~P52(x6072)+~E(f22(x6071,x6073,x6072),f4(x6072))+E(x6071,f4(x6072)) % 1.37/1.32 [718]~P32(x7183)+~P65(x7183)+~P51(x7183)+~P52(x7183)+~E(f21(x7181,a18),f4(a18))+~E(f22(x7182,f21(x7181,a18),x7183),f4(x7183)) % 1.37/1.32 [1164]~P57(x11642)+~P47(x11642)+P8(x11641,f4(x11642),x11642)+P8(f4(x11642),x11641,x11642)+~P11(x11643,f4(x11642),x11642)+P11(x11643,f12(x11644,x11641,x11642),x11642) % 1.37/1.32 [1165]~P57(x11652)+~P47(x11652)+P8(x11651,f4(x11652),x11652)+P8(f4(x11652),x11651,x11652)+~P8(x11653,f4(x11652),x11652)+P8(x11653,f12(x11654,x11651,x11652),x11652) % 1.37/1.32 [1166]~P57(x11662)+~P47(x11662)+P8(x11661,f4(x11662),x11662)+P8(f4(x11662),x11661,x11662)+~P11(f4(x11662),x11664,x11662)+P11(f12(x11663,x11661,x11662),x11664,x11662) % 1.37/1.32 [1167]~P57(x11672)+~P47(x11672)+P8(x11671,f4(x11672),x11672)+P8(f4(x11672),x11671,x11672)+~P8(f4(x11672),x11674,x11672)+P8(f12(x11673,x11671,x11672),x11674,x11672) % 1.37/1.32 [1249]~P57(x12492)+~P47(x12492)+P11(x12491,f4(x12492),x12492)+P8(f4(x12492),x12493,x12492)+~P11(x12491,f12(x12494,x12493,x12492),x12492)+P8(x12493,f4(x12492),x12492) % 1.37/1.32 [1250]~P57(x12502)+~P47(x12502)+P8(x12501,f4(x12502),x12502)+P8(f4(x12502),x12501,x12502)+~P8(x12503,f12(x12504,x12501,x12502),x12502)+P8(x12503,f4(x12502),x12502) % 1.37/1.32 [1251]~P57(x12512)+~P47(x12512)+P8(x12511,f4(x12512),x12512)+P8(f4(x12512),x12511,x12512)+~P11(f12(x12514,x12511,x12512),x12513,x12512)+P11(f4(x12512),x12513,x12512) % 1.37/1.32 [1252]~P57(x12522)+~P47(x12522)+P8(x12521,f4(x12522),x12522)+P8(f4(x12522),x12521,x12522)+~P8(f12(x12524,x12521,x12522),x12523,x12522)+P8(f4(x12522),x12523,x12522) % 1.37/1.32 [1280]~P59(x12804)+E(x12801,x12802)+~P11(f4(x12804),x12802,x12804)+~P11(f4(x12804),x12801,x12804)+~E(f22(x12801,x12803,x12804),f22(x12802,x12803,x12804))+~P8(f4(a18),x12803,a18) % 1.37/1.32 [1406]~P57(x14062)+~P47(x14062)+~P11(f15(x14063,x14061,x14062),x14064,x14062)+P8(x14061,f4(x14062),x14062)+~P11(x14063,f4(x14062),x14062)+P11(x14063,f12(x14064,x14061,x14062),x14062) % 1.37/1.32 [1407]~P57(x14072)+~P47(x14072)+~P8(f15(x14073,x14071,x14072),x14074,x14072)+P8(x14071,f4(x14072),x14072)+~P8(x14073,f4(x14072),x14072)+P8(x14073,f12(x14074,x14071,x14072),x14072) % 1.37/1.32 [1408]~P57(x14082)+~P47(x14082)+~P11(x14083,f15(x14084,x14081,x14082),x14082)+P8(x14081,f4(x14082),x14082)+~P11(f4(x14082),x14084,x14082)+P11(f12(x14083,x14081,x14082),x14084,x14082) % 1.37/1.32 [1409]~P57(x14092)+~P47(x14092)+~P8(x14093,f15(x14094,x14091,x14092),x14092)+P8(x14091,f4(x14092),x14092)+~P8(f4(x14092),x14094,x14092)+P8(f12(x14093,x14091,x14092),x14094,x14092) % 1.37/1.32 [1410]~P57(x14101)+~P47(x14101)+~P11(x14104,f12(x14103,x14102,x14101),x14101)+~P8(x14102,f4(x14101),x14101)+P8(f4(x14101),x14102,x14101)+P11(x14103,f15(x14104,x14102,x14101),x14101) % 1.37/1.32 [1411]~P57(x14111)+~P47(x14111)+~P11(x14114,f15(x14113,x14112,x14111),x14111)+~P11(x14113,f4(x14111),x14111)+P8(f4(x14111),x14112,x14111)+P11(x14113,f12(x14114,x14112,x14111),x14111) % 1.37/1.32 [1412]~P57(x14121)+~P47(x14121)+~P11(x14124,f15(x14123,x14122,x14121),x14121)+~P8(x14122,f4(x14121),x14121)+P8(f4(x14121),x14122,x14121)+P11(x14123,f12(x14124,x14122,x14121),x14121) % 1.37/1.32 [1413]~P57(x14131)+~P47(x14131)+~P8(x14134,f12(x14133,x14132,x14131),x14131)+~P8(x14132,f4(x14131),x14131)+P8(f4(x14131),x14132,x14131)+P8(x14133,f15(x14134,x14132,x14131),x14131) % 1.37/1.32 [1414]~P57(x14141)+~P47(x14141)+~P8(x14144,f15(x14143,x14142,x14141),x14141)+~P8(x14142,f4(x14141),x14141)+P8(f4(x14141),x14142,x14141)+P8(x14143,f12(x14144,x14142,x14141),x14141) % 1.37/1.32 [1415]~P57(x14151)+~P47(x14151)+~P8(x14154,f15(x14153,x14152,x14151),x14151)+~P8(x14153,f4(x14151),x14151)+P8(f4(x14151),x14152,x14151)+P8(x14153,f12(x14154,x14152,x14151),x14151) % 1.37/1.32 [1416]~P57(x14161)+~P47(x14161)+~P11(f12(x14164,x14162,x14161),x14163,x14161)+~P8(x14162,f4(x14161),x14161)+P8(f4(x14161),x14162,x14161)+P11(f15(x14163,x14162,x14161),x14164,x14161) % 1.37/1.32 [1417]~P57(x14171)+~P47(x14171)+~P11(f15(x14174,x14172,x14171),x14173,x14171)+~P8(x14172,f4(x14171),x14171)+P8(f4(x14171),x14172,x14171)+P11(f12(x14173,x14172,x14171),x14174,x14171) % 1.37/1.32 [1418]~P57(x14181)+~P47(x14181)+~P8(f12(x14184,x14182,x14181),x14183,x14181)+~P8(x14182,f4(x14181),x14181)+P8(f4(x14181),x14182,x14181)+P8(f15(x14183,x14182,x14181),x14184,x14181) % 1.37/1.32 [1419]~P57(x14191)+~P47(x14191)+~P8(f15(x14194,x14192,x14191),x14193,x14191)+~P8(x14192,f4(x14191),x14191)+P8(f4(x14191),x14192,x14191)+P8(f12(x14193,x14192,x14191),x14194,x14191) % 1.37/1.32 [1420]~P57(x14201)+~P47(x14201)+~P11(f15(x14204,x14202,x14201),x14203,x14201)+~P11(f4(x14201),x14204,x14201)+P8(f4(x14201),x14202,x14201)+P11(f12(x14203,x14202,x14201),x14204,x14201) % 1.37/1.32 [1421]~P57(x14211)+~P47(x14211)+~P8(f15(x14214,x14212,x14211),x14213,x14211)+~P8(f4(x14211),x14214,x14211)+P8(f4(x14211),x14212,x14211)+P8(f12(x14213,x14212,x14211),x14214,x14211) % 1.37/1.32 [1487]~P57(x14873)+~P47(x14873)+~P11(x14872,x14874,x14873)+~P11(x14871,f4(x14873),x14873)+~P8(f4(x14873),f15(x14872,x14874,x14873),x14873)+P11(f12(x14871,x14872,x14873),f12(x14871,x14874,x14873),x14873) % 1.37/1.32 [1513]~P57(x15134)+~P47(x15134)+~P11(x15131,f4(x15134),x15134)+~P11(x15132,f15(x15131,x15133,x15134),x15134)+~P11(f15(x15131,x15133,x15134),x15132,x15134)+P11(x15131,f12(x15132,x15133,x15134),x15134) % 1.37/1.32 [1514]~P57(x15144)+~P47(x15144)+~P8(x15143,f4(x15144),x15144)+~P11(x15142,f15(x15141,x15143,x15144),x15144)+~P11(f15(x15141,x15143,x15144),x15142,x15144)+P11(x15141,f12(x15142,x15143,x15144),x15144) % 1.37/1.32 [1515]~P57(x15154)+~P47(x15154)+~P8(x15153,f4(x15154),x15154)+~P8(x15152,f15(x15151,x15153,x15154),x15154)+~P8(f15(x15151,x15153,x15154),x15152,x15154)+P8(x15151,f12(x15152,x15153,x15154),x15154) % 1.37/1.32 [1516]~P57(x15164)+~P47(x15164)+~P8(x15161,f4(x15164),x15164)+~P8(x15162,f15(x15161,x15163,x15164),x15164)+~P8(f15(x15161,x15163,x15164),x15162,x15164)+P8(x15161,f12(x15162,x15163,x15164),x15164) % 1.37/1.32 [1517]~P57(x15173)+~P47(x15173)+~P8(x15172,f4(x15173),x15173)+~P11(x15171,f15(x15174,x15172,x15173),x15173)+~P11(f15(x15174,x15172,x15173),x15171,x15173)+P11(f12(x15171,x15172,x15173),x15174,x15173) % 1.37/1.32 [1518]~P57(x15183)+~P47(x15183)+~P8(x15182,f4(x15183),x15183)+~P8(x15181,f15(x15184,x15182,x15183),x15183)+~P8(f15(x15184,x15182,x15183),x15181,x15183)+P8(f12(x15181,x15182,x15183),x15184,x15183) % 1.37/1.32 [1519]~P57(x15193)+~P47(x15193)+~P11(f4(x15193),x15194,x15193)+~P11(x15191,f15(x15194,x15192,x15193),x15193)+~P11(f15(x15194,x15192,x15193),x15191,x15193)+P11(f12(x15191,x15192,x15193),x15194,x15193) % 1.37/1.32 [1520]~P57(x15203)+~P47(x15203)+~P8(f4(x15203),x15204,x15203)+~P8(x15201,f15(x15204,x15202,x15203),x15203)+~P8(f15(x15204,x15202,x15203),x15201,x15203)+P8(f12(x15201,x15202,x15203),x15204,x15203) % 1.37/1.32 [823]~P47(x8232)+~P4(x8232)+~P48(x8232)+~E(f12(x8233,x8231,x8232),f21(x8234,x8232))+E(x8231,f4(x8232))+E(x8233,f15(f21(x8234,x8232),x8231,x8232)) % 1.37/1.32 [824]~P47(x8242)+~P4(x8242)+~P48(x8242)+~E(f21(x8243,x8242),f12(x8244,x8241,x8242))+E(x8241,f4(x8242))+E(f15(f21(x8243,x8242),x8241,x8242),x8244) % 1.37/1.32 [1442]~P68(x14423)+~P11(x14422,x14425,x14423)+~P11(x14421,x14424,x14423)+~P11(f4(x14423),x14424,x14423)+~P11(f4(x14423),x14422,x14423)+P11(f15(x14421,x14422,x14423),f15(x14424,x14425,x14423),x14423) % 1.37/1.32 [1443]~P68(x14433)+~P11(x14432,x14435,x14433)+~P11(x14431,x14434,x14433)+~P11(f4(x14433),x14432,x14433)+~P11(f4(x14433),x14431,x14433)+P11(f15(x14431,x14432,x14433),f15(x14434,x14435,x14433),x14433) % 1.37/1.32 [1444]~P57(x14443)+~P11(x14445,x14442,x14443)+~P11(x14441,x14444,x14443)+~P11(f4(x14443),x14441,x14443)+~P8(f4(x14443),x14445,x14443)+P11(f12(x14441,x14442,x14443),f12(x14444,x14445,x14443),x14443) % 1.37/1.32 [1445]~P61(x14453)+~P11(x14452,x14455,x14453)+~P8(x14451,x14454,x14453)+~P11(f4(x14453),x14451,x14453)+~P8(f4(x14453),x14452,x14453)+P8(f15(x14451,x14452,x14453),f15(x14454,x14455,x14453),x14453) % 1.37/1.32 [1446]~P61(x14463)+~P11(x14461,x14464,x14463)+~P8(x14462,x14465,x14463)+~P11(f4(x14463),x14462,x14463)+~P8(f4(x14463),x14461,x14463)+P8(f15(x14461,x14462,x14463),f15(x14464,x14465,x14463),x14463) % 1.37/1.32 [1447]~P61(x14473)+~P8(x14472,x14475,x14473)+~P8(x14471,x14474,x14473)+~P11(f4(x14473),x14472,x14473)+~P11(f4(x14473),x14471,x14473)+P8(f15(x14471,x14472,x14473),f15(x14474,x14475,x14473),x14473) % 1.37/1.32 [1448]~P61(x14483)+~P8(x14482,x14485,x14483)+~P8(x14481,x14484,x14483)+~P11(f4(x14483),x14482,x14483)+~P8(f4(x14483),x14484,x14483)+P8(f15(x14481,x14482,x14483),f15(x14484,x14485,x14483),x14483) % 1.37/1.32 [1449]~P57(x14493)+~P11(x14495,x14492,x14493)+~P8(x14491,x14494,x14493)+~P11(f4(x14493),x14491,x14493)+~P8(f4(x14493),x14495,x14493)+P8(f12(x14491,x14492,x14493),f12(x14494,x14495,x14493),x14493) % 1.37/1.32 [1450]~P57(x14503)+~P11(x14501,x14504,x14503)+~P8(x14505,x14502,x14503)+~P8(f4(x14503),x14505,x14503)+~P8(f4(x14503),x14501,x14503)+P8(f12(x14501,x14502,x14503),f12(x14504,x14505,x14503),x14503) % 1.37/1.32 %EqnAxiom % 1.37/1.32 [1]E(x11,x11) % 1.37/1.32 [2]E(x22,x21)+~E(x21,x22) % 1.37/1.32 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.37/1.32 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 1.37/1.32 [5]~E(x51,x52)+E(f3(x51),f3(x52)) % 1.37/1.32 [6]~E(x61,x62)+E(f13(x61,x63,x64),f13(x62,x63,x64)) % 1.37/1.32 [7]~E(x71,x72)+E(f13(x73,x71,x74),f13(x73,x72,x74)) % 1.37/1.32 [8]~E(x81,x82)+E(f13(x83,x84,x81),f13(x83,x84,x82)) % 1.37/1.32 [9]~E(x91,x92)+E(f22(x91,x93,x94),f22(x92,x93,x94)) % 1.37/1.32 [10]~E(x101,x102)+E(f22(x103,x101,x104),f22(x103,x102,x104)) % 1.37/1.32 [11]~E(x111,x112)+E(f22(x113,x114,x111),f22(x113,x114,x112)) % 1.37/1.32 [12]~E(x121,x122)+E(f4(x121),f4(x122)) % 1.37/1.32 [13]~E(x131,x132)+E(f5(x131),f5(x132)) % 1.37/1.32 [14]~E(x141,x142)+E(f9(x141),f9(x142)) % 1.37/1.32 [15]~E(x151,x152)+E(f15(x151,x153,x154),f15(x152,x153,x154)) % 1.37/1.32 [16]~E(x161,x162)+E(f15(x163,x161,x164),f15(x163,x162,x164)) % 1.37/1.32 [17]~E(x171,x172)+E(f15(x173,x174,x171),f15(x173,x174,x172)) % 1.37/1.32 [18]~E(x181,x182)+E(f12(x181,x183,x184),f12(x182,x183,x184)) % 1.37/1.32 [19]~E(x191,x192)+E(f12(x193,x191,x194),f12(x193,x192,x194)) % 1.37/1.32 [20]~E(x201,x202)+E(f12(x203,x204,x201),f12(x203,x204,x202)) % 1.37/1.32 [21]~E(x211,x212)+E(f21(x211,x213),f21(x212,x213)) % 1.37/1.32 [22]~E(x221,x222)+E(f21(x223,x221),f21(x223,x222)) % 1.37/1.32 [23]~E(x231,x232)+E(f8(x231,x233,x234),f8(x232,x233,x234)) % 1.37/1.32 [24]~E(x241,x242)+E(f8(x243,x241,x244),f8(x243,x242,x244)) % 1.37/1.32 [25]~E(x251,x252)+E(f8(x253,x254,x251),f8(x253,x254,x252)) % 1.37/1.32 [26]~E(x261,x262)+E(f16(x261,x263),f16(x262,x263)) % 1.37/1.32 [27]~E(x271,x272)+E(f16(x273,x271),f16(x273,x272)) % 1.37/1.32 [28]~E(x281,x282)+E(f14(x281,x283,x284),f14(x282,x283,x284)) % 1.37/1.32 [29]~E(x291,x292)+E(f14(x293,x291,x294),f14(x293,x292,x294)) % 1.37/1.32 [30]~E(x301,x302)+E(f14(x303,x304,x301),f14(x303,x304,x302)) % 1.37/1.32 [31]~E(x311,x312)+E(f11(x311,x313),f11(x312,x313)) % 1.37/1.32 [32]~E(x321,x322)+E(f11(x323,x321),f11(x323,x322)) % 1.37/1.32 [33]~E(x331,x332)+E(f7(x331,x333,x334),f7(x332,x333,x334)) % 1.37/1.32 [34]~E(x341,x342)+E(f7(x343,x341,x344),f7(x343,x342,x344)) % 1.37/1.32 [35]~E(x351,x352)+E(f7(x353,x354,x351),f7(x353,x354,x352)) % 1.37/1.32 [36]~E(x361,x362)+E(f23(x361,x363),f23(x362,x363)) % 1.37/1.32 [37]~E(x371,x372)+E(f23(x373,x371),f23(x373,x372)) % 1.37/1.32 [38]~E(x381,x382)+E(f10(x381,x383),f10(x382,x383)) % 1.37/1.32 [39]~E(x391,x392)+E(f10(x393,x391),f10(x393,x392)) % 1.37/1.32 [40]~E(x401,x402)+E(f24(x401),f24(x402)) % 1.37/1.32 [41]~P1(x411)+P1(x412)+~E(x411,x412) % 1.37/1.32 [42]~P39(x421)+P39(x422)+~E(x421,x422) % 1.37/1.32 [43]P7(x432,x433)+~E(x431,x432)+~P7(x431,x433) % 1.37/1.32 [44]P7(x443,x442)+~E(x441,x442)+~P7(x443,x441) % 1.37/1.32 [45]~P45(x451)+P45(x452)+~E(x451,x452) % 1.37/1.32 [46]~P46(x461)+P46(x462)+~E(x461,x462) % 1.37/1.32 [47]P8(x472,x473,x474)+~E(x471,x472)+~P8(x471,x473,x474) % 1.37/1.32 [48]P8(x483,x482,x484)+~E(x481,x482)+~P8(x483,x481,x484) % 1.37/1.32 [49]P8(x493,x494,x492)+~E(x491,x492)+~P8(x493,x494,x491) % 1.37/1.32 [50]~P2(x501)+P2(x502)+~E(x501,x502) % 1.37/1.32 [51]~P60(x511)+P60(x512)+~E(x511,x512) % 1.37/1.32 [52]~P31(x521)+P31(x522)+~E(x521,x522) % 1.37/1.32 [53]~P57(x531)+P57(x532)+~E(x531,x532) % 1.37/1.32 [54]~P58(x541)+P58(x542)+~E(x541,x542) % 1.37/1.32 [55]~P3(x551)+P3(x552)+~E(x551,x552) % 1.37/1.32 [56]~P59(x561)+P59(x562)+~E(x561,x562) % 1.37/1.32 [57]~P47(x571)+P47(x572)+~E(x571,x572) % 1.37/1.32 [58]P11(x582,x583,x584)+~E(x581,x582)+~P11(x581,x583,x584) % 1.37/1.32 [59]P11(x593,x592,x594)+~E(x591,x592)+~P11(x593,x591,x594) % 1.37/1.32 [60]P11(x603,x604,x602)+~E(x601,x602)+~P11(x603,x604,x601) % 1.37/1.32 [61]~P4(x611)+P4(x612)+~E(x611,x612) % 1.37/1.32 [62]~P73(x621)+P73(x622)+~E(x621,x622) % 1.37/1.32 [63]P10(x632,x633,x634)+~E(x631,x632)+~P10(x631,x633,x634) % 1.37/1.32 [64]P10(x643,x642,x644)+~E(x641,x642)+~P10(x643,x641,x644) % 1.37/1.32 [65]P10(x653,x654,x652)+~E(x651,x652)+~P10(x653,x654,x651) % 1.37/1.32 [66]~P5(x661)+P5(x662)+~E(x661,x662) % 1.37/1.32 [67]~P36(x671)+P36(x672)+~E(x671,x672) % 1.37/1.32 [68]~P25(x681)+P25(x682)+~E(x681,x682) % 1.37/1.32 [69]~P32(x691)+P32(x692)+~E(x691,x692) % 1.37/1.32 [70]~P65(x701)+P65(x702)+~E(x701,x702) % 1.37/1.32 [71]~P51(x711)+P51(x712)+~E(x711,x712) % 1.37/1.32 [72]~P14(x721)+P14(x722)+~E(x721,x722) % 1.37/1.32 [73]~P28(x731)+P28(x732)+~E(x731,x732) % 1.37/1.32 [74]~P41(x741)+P41(x742)+~E(x741,x742) % 1.37/1.32 [75]~P27(x751)+P27(x752)+~E(x751,x752) % 1.37/1.32 [76]~P63(x761)+P63(x762)+~E(x761,x762) % 1.37/1.32 [77]~P37(x771)+P37(x772)+~E(x771,x772) % 1.37/1.32 [78]~P52(x781)+P52(x782)+~E(x781,x782) % 1.37/1.32 [79]~P64(x791)+P64(x792)+~E(x791,x792) % 1.37/1.32 [80]~P54(x801)+P54(x802)+~E(x801,x802) % 1.37/1.32 [81]~P66(x811)+P66(x812)+~E(x811,x812) % 1.37/1.32 [82]~P33(x821)+P33(x822)+~E(x821,x822) % 1.37/1.32 [83]~P43(x831)+P43(x832)+~E(x831,x832) % 1.37/1.32 [84]~P70(x841)+P70(x842)+~E(x841,x842) % 1.37/1.32 [85]~P30(x851)+P30(x852)+~E(x851,x852) % 1.37/1.32 [86]~P61(x861)+P61(x862)+~E(x861,x862) % 1.37/1.32 [87]~P49(x871)+P49(x872)+~E(x871,x872) % 1.37/1.32 [88]~P48(x881)+P48(x882)+~E(x881,x882) % 1.37/1.32 [89]~P13(x891)+P13(x892)+~E(x891,x892) % 1.37/1.32 [90]~P12(x901)+P12(x902)+~E(x901,x902) % 1.37/1.32 [91]~P34(x911)+P34(x912)+~E(x911,x912) % 1.37/1.32 [92]~P67(x921)+P67(x922)+~E(x921,x922) % 1.37/1.32 [93]~P26(x931)+P26(x932)+~E(x931,x932) % 1.37/1.32 [94]~P38(x941)+P38(x942)+~E(x941,x942) % 1.37/1.32 [95]P9(x952,x953)+~E(x951,x952)+~P9(x951,x953) % 1.37/1.32 [96]P9(x963,x962)+~E(x961,x962)+~P9(x963,x961) % 1.37/1.32 [97]~P62(x971)+P62(x972)+~E(x971,x972) % 1.37/1.32 [98]~P6(x981)+P6(x982)+~E(x981,x982) % 1.37/1.32 [99]~P18(x991)+P18(x992)+~E(x991,x992) % 1.37/1.32 [100]~P17(x1001)+P17(x1002)+~E(x1001,x1002) % 1.37/1.32 [101]~P69(x1011)+P69(x1012)+~E(x1011,x1012) % 1.37/1.32 [102]~P23(x1021)+P23(x1022)+~E(x1021,x1022) % 1.37/1.32 [103]~P29(x1031)+P29(x1032)+~E(x1031,x1032) % 1.37/1.32 [104]~P35(x1041)+P35(x1042)+~E(x1041,x1042) % 1.37/1.32 [105]~P72(x1051)+P72(x1052)+~E(x1051,x1052) % 1.37/1.32 [106]~P42(x1061)+P42(x1062)+~E(x1061,x1062) % 1.37/1.32 [107]~P50(x1071)+P50(x1072)+~E(x1071,x1072) % 1.37/1.32 [108]~P20(x1081)+P20(x1082)+~E(x1081,x1082) % 1.37/1.32 [109]~P53(x1091)+P53(x1092)+~E(x1091,x1092) % 1.37/1.32 [110]~P56(x1101)+P56(x1102)+~E(x1101,x1102) % 1.37/1.32 [111]~P22(x1111)+P22(x1112)+~E(x1111,x1112) % 1.37/1.32 [112]~P16(x1121)+P16(x1122)+~E(x1121,x1122) % 1.37/1.32 [113]~P21(x1131)+P21(x1132)+~E(x1131,x1132) % 1.37/1.32 [114]~P19(x1141)+P19(x1142)+~E(x1141,x1142) % 1.37/1.32 [115]~P71(x1151)+P71(x1152)+~E(x1151,x1152) % 1.37/1.32 [116]~P68(x1161)+P68(x1162)+~E(x1161,x1162) % 1.37/1.32 [117]~P24(x1171)+P24(x1172)+~E(x1171,x1172) % 1.37/1.32 [118]~P44(x1181)+P44(x1182)+~E(x1181,x1182) % 1.37/1.32 [119]~P40(x1191)+P40(x1192)+~E(x1191,x1192) % 1.37/1.32 [120]~P55(x1201)+P55(x1202)+~E(x1201,x1202) % 1.37/1.32 [121]~P15(x1211)+P15(x1212)+~E(x1211,x1212) % 1.37/1.32 % 1.37/1.32 %------------------------------------------- % 1.37/1.32 cnf(1661,plain, % 1.37/1.32 (~E(f14(x16611,f9(a18),a18),x16611)), % 1.37/1.32 inference(rename_variables,[],[372])). % 1.37/1.32 cnf(1670,plain, % 1.37/1.32 (~E(f14(x16701,f9(a18),a18),f4(a18))), % 1.37/1.32 inference(rename_variables,[],[376])). % 1.37/1.32 cnf(1681,plain, % 1.37/1.32 (~P8(f14(x16811,x16812,a18),x16812,a18)), % 1.37/1.32 inference(rename_variables,[],[378])). % 1.37/1.32 cnf(1684,plain, % 1.37/1.32 (~P8(f14(x16841,x16842,a18),x16842,a18)), % 1.37/1.32 inference(rename_variables,[],[378])). % 1.37/1.32 cnf(1698,plain, % 1.37/1.32 ($false), % 1.37/1.32 inference(scs_inference,[],[382,372,1661,376,1670,267,260,290,378,1681,1684,126,165,298,328,271,337,671,2,10,515,866,1426,526,527,532,684,825,878,880,886,972,1011,1016]), % 1.37/1.32 ['proof']). % 1.37/1.32 % SZS output end Proof % 1.37/1.32 % Total time :0.130000s %------------------------------------------------------------------------------