%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWV821-1 : TPTP v8.2.0. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/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 16:48:35 EDT 2024 % Result : Unsatisfiable 1.29s 1.20s % Output : CNFRefutation 1.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWV821-1 : TPTP v8.2.0. Released v4.1.0. % 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/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 17:18:54 EDT 2024 % 0.13/0.33 % CPUTime : % 0.20/0.55 start to proof:theBenchmark % 1.03/1.15 %------------------------------------------- % 1.03/1.15 % File :CSE---1.7 % 1.03/1.15 % Problem :theBenchmark % 1.03/1.15 % Transform :cnf % 1.03/1.15 % Format :tptp:raw % 1.03/1.15 % Command :java -jar mcs_scs.jar %d %s % 1.03/1.15 % 1.03/1.15 % Result :Theorem 0.110000s % 1.03/1.15 % Output :CNFRefutation 0.110000s % 1.03/1.15 %------------------------------------------- % 1.03/1.15 %------------------------------------------------------------------------------ % 1.03/1.15 % File : SWV821-1 : TPTP v8.2.0. Released v4.1.0. % 1.03/1.15 % Domain : Software Verification % 1.03/1.15 % Problem : Hoare logic with procedures 132_1 % 1.03/1.15 % Version : Especial. % 1.03/1.15 % English : Completeness is taken relative to completeness of the underlying % 1.03/1.15 % logic. Two versions of completeness proof: nested single recursion % 1.03/1.15 % and simultaneous recursion in call rule. % 1.03/1.15 % 1.03/1.15 % Refs : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe % 1.03/1.15 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 1.03/1.15 % Source : [Nip10] % 1.03/1.15 % Names : Hoare-132_1 [Nip10] % 1.03/1.15 % 1.03/1.15 % Status : Unsatisfiable % 1.03/1.15 % Rating : 0.10 v8.2.0, 0.14 v8.1.0, 0.11 v7.5.0, 0.16 v7.4.0, 0.18 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.13 v6.3.0, 0.09 v6.2.0, 0.20 v6.1.0, 0.21 v6.0.0, 0.30 v5.5.0, 0.55 v5.3.0, 0.56 v5.2.0, 0.50 v5.1.0, 0.59 v5.0.0, 0.50 v4.1.0 % 1.03/1.15 % Syntax : Number of clauses : 1307 ( 160 unt; 173 nHn; 776 RR) % 1.03/1.15 % Number of literals : 3695 ( 782 equ;2235 neg) % 1.03/1.15 % Maximal clause size : 6 ( 2 avg) % 1.03/1.15 % Maximal term depth : 6 ( 1 avg) % 1.03/1.15 % Number of predicates : 79 ( 78 usr; 0 prp; 1-4 aty) % 1.03/1.15 % Number of functors : 48 ( 48 usr; 12 con; 0-6 aty) % 1.03/1.15 % Number of variables : 3741 ( 248 sgn) % 1.03/1.15 % SPC : CNF_UNS_RFO_SEQ_NHN % 1.03/1.15 % 1.03/1.15 % Comments : % 1.03/1.15 %------------------------------------------------------------------------------ % 1.03/1.15 cnf(cls_less__add__Suc1_0,axiom, % 1.03/1.15 c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_i,V_m,tc_nat)),tc_nat) ). % 1.03/1.15 % 1.03/1.15 cnf(cls_eq__add__iff1_0,axiom, % 1.03/1.15 ( ~ class_Ring__and__Field_Oring(T_a) % 1.03/1.15 | 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) % 1.03/1.15 | 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 ) ). % 1.03/1.15 % 1.03/1.15 cnf(cls_eq__add__iff2_0,axiom, % 1.03/1.15 ( ~ class_Ring__and__Field_Oring(T_a) % 1.03/1.15 | 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) % 1.03/1.15 | 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) ) ). % 1.03/1.15 % 1.03/1.15 cnf(cls_nat__less__add__iff2_1,axiom, % 1.03/1.15 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) % 1.03/1.15 | ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) % 1.03/1.15 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.03/1.15 % 1.03/1.15 cnf(cls_nat__less__add__iff2_0,axiom, % 1.03/1.15 ( c_HOL_Oord__class_Oless(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) % 1.03/1.15 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) % 1.03/1.15 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.03/1.15 % 1.03/1.15 cnf(cls_nat__less__add__iff1_1,axiom, % 1.03/1.15 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) % 1.03/1.15 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat) % 1.03/1.15 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 1.03/1.15 % 1.03/1.15 cnf(cls_nat__less__add__iff1_0,axiom, % 1.03/1.15 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat) % 1.03/1.15 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) % 1.03/1.15 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 1.03/1.15 % 1.03/1.15 cnf(cls_eq__add__iff2_1,axiom, % 1.03/1.15 ( ~ class_Ring__and__Field_Oring(T_a) % 1.03/1.15 | 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) ) ). % 1.03/1.15 % 1.03/1.15 cnf(cls_le__imp__neg__le_0,axiom, % 1.03/1.15 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.03/1.15 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.03/1.15 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.03/1.15 % 1.03/1.15 cnf(cls_neg__le__iff__le_0,axiom, % 1.03/1.15 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.03/1.15 | c_lessequals(V_a,V_b,T_a) % 1.03/1.15 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.03/1.15 % 1.03/1.16 cnf(cls_abs__le__mult_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Olordered__ring(T_a) % 1.03/1.16 | 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) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_add__Suc_0,axiom, % 1.03/1.16 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)) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_add__Suc__right_0,axiom, % 1.03/1.16 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)) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_abs__idempotent_0,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.03/1.16 | 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) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_power__0__Suc_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 1.03/1.16 | ~ class_Power_Opower(T_a) % 1.03/1.16 | 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) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_one__le__power_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.03/1.16 | c_lessequals(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.03/1.16 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_abs__le__D1_0,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.03/1.16 | c_lessequals(V_a,V_b,T_a) % 1.03/1.16 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_mult__strict__mono_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.03/1.16 | 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) % 1.03/1.16 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.03/1.16 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.03/1.16 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.03/1.16 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_class__fieldgb_Oinverse__divide_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.03/1.16 | ~ class_Int_Onumber__ring(T_a) % 1.03/1.16 | 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) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_inverse__eq__divide_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.03/1.16 | 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) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_zmod__simps_I4_J_0,axiom, % 1.03/1.16 ( ~ class_Divides_Osemiring__div(T_a) % 1.03/1.16 | 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) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_dvd__mult__cancel__left_2,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.03/1.16 | 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) % 1.03/1.16 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_dvd__mult__cancel__right_2,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.03/1.16 | 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) % 1.03/1.16 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_divide__left__mono__neg_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.16 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.03/1.16 | 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) % 1.03/1.16 | ~ 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) % 1.03/1.16 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.03/1.16 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_divide__left__mono_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.16 | 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) % 1.03/1.16 | ~ 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) % 1.03/1.16 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.03/1.16 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_min__max_Oinf__le1_0,axiom, % 1.03/1.16 ( ~ class_Orderings_Olinorder(T_a) % 1.03/1.16 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_x,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_min__max_Oinf__le2_0,axiom, % 1.03/1.16 ( ~ class_Orderings_Olinorder(T_a) % 1.03/1.16 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_y,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_min__max_Ole__infI_0,axiom, % 1.03/1.16 ( ~ class_Orderings_Olinorder(T_a) % 1.03/1.16 | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) % 1.03/1.16 | ~ c_lessequals(V_x,V_b,T_a) % 1.03/1.16 | ~ c_lessequals(V_x,V_a,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_min__max_Ole__inf__iff_2,axiom, % 1.03/1.16 ( ~ class_Orderings_Olinorder(T_a) % 1.03/1.16 | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) % 1.03/1.16 | ~ c_lessequals(V_x,V_z,T_a) % 1.03/1.16 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_min__max_Oinf__greatest_0,axiom, % 1.03/1.16 ( ~ class_Orderings_Olinorder(T_a) % 1.03/1.16 | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) % 1.03/1.16 | ~ c_lessequals(V_x,V_z,T_a) % 1.03/1.16 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_eq__add__iff1_1,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Oring(T_a) % 1.03/1.16 | 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) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_le__minus__self__iff_0,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.03/1.16 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.03/1.16 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_le__minus__self__iff_1,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.03/1.16 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.03/1.16 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_minus__le__self__iff_0,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.03/1.16 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.03/1.16 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_minus__le__self__iff_1,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.03/1.16 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) % 1.03/1.16 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_less__eq__neg__nonpos_0,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.03/1.16 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.03/1.16 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_less__eq__neg__nonpos_1,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.03/1.16 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.03/1.16 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_neg__less__eq__nonneg_0,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.03/1.16 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.03/1.16 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_neg__less__eq__nonneg_1,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.03/1.16 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) % 1.03/1.16 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_zero__le__power_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.03/1.16 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.03/1.16 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_compl__inf__bot_0,axiom, % 1.03/1.16 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.03/1.16 | c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_x,T_a) = c_Orderings_Obot__class_Obot(T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_inf__compl__bot_0,axiom, % 1.03/1.16 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.03/1.16 | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_Orderings_Obot__class_Obot(T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_diff__is__0__eq_1,axiom, % 1.03/1.16 ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) % 1.03/1.16 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_diff__is__0__eq_0,axiom, % 1.03/1.16 ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.03/1.16 | c_lessequals(V_m,V_n,tc_nat) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_min__diff__distrib__left_0,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.03/1.16 | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(V_x,V_z,T_a),c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_max__less__iff__conj_2,axiom, % 1.03/1.16 ( ~ class_Orderings_Olinorder(T_a) % 1.03/1.16 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) % 1.03/1.16 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.03/1.16 | ~ c_HOL_Oord__class_Oless(V_x,V_z,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_diff__Suc__diff__eq2_0,axiom, % 1.03/1.16 ( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),V_m,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(V_j),c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),tc_nat) % 1.03/1.16 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_replicate__eq__replicate_0,axiom, % 1.03/1.16 ( c_List_Oreplicate(V_m,V_x,T_a) != c_List_Oreplicate(V_n,V_y,T_a) % 1.03/1.16 | V_m = V_n ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_class__semiring_Omul__1_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.03/1.16 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_x,T_a) = V_x ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_mult__1_0,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) % 1.03/1.16 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_mult__1__left_0,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.03/1.16 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_mult__1__right_0,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.03/1.16 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.03/1.16 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_class__semiring_Osemiring__rules_I11_J_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.03/1.16 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_add__strict__increasing_0,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.03/1.16 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.03/1.16 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.03/1.16 | ~ c_lessequals(V_b,V_c,T_a) % 1.03/1.16 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_dvdI_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Odvd(T_a) % 1.03/1.16 | c_Ring__and__Field_Odvd__class_Odvd(V_b,c_HOL_Otimes__class_Otimes(V_b,V_k,T_a),T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_dvd__triv__left_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.03/1.16 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_dvd__triv__right_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.03/1.16 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_abs__diff__triangle__ineq_0,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.03/1.16 | 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) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_abs__prts_0,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.03/1.16 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ominus__class_Ominus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a),T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_frac__less2_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.16 | 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) % 1.03/1.16 | ~ c_HOL_Oord__class_Oless(V_w,V_z,T_a) % 1.03/1.16 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 1.03/1.16 | ~ c_lessequals(V_x,V_y,T_a) % 1.03/1.16 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_power__one__over_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.03/1.16 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.03/1.16 | 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) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_add__is__1_4,axiom, % 1.03/1.16 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)) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_mod__mod__trivial_0,axiom, % 1.03/1.16 ( ~ class_Divides_Osemiring__div(T_a) % 1.03/1.16 | 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) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_less__add__Suc2_0,axiom, % 1.03/1.16 c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_i,tc_nat)),tc_nat) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_less__iff__Suc__add_1,axiom, % 1.03/1.16 c_HOL_Oord__class_Oless(V_m,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat)),tc_nat) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_le__diff__conv2_0,axiom, % 1.03/1.16 ( c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) % 1.03/1.16 | ~ c_lessequals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) % 1.03/1.16 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_le__diff__conv2_1,axiom, % 1.03/1.16 ( c_lessequals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) % 1.03/1.16 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) % 1.03/1.16 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_min__max_Ole__sup__iff_2,axiom, % 1.03/1.16 ( ~ class_Orderings_Olinorder(T_a) % 1.03/1.16 | c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) % 1.03/1.16 | ~ c_lessequals(V_y,V_z,T_a) % 1.03/1.16 | ~ c_lessequals(V_x,V_z,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_min__max_Osup__least_0,axiom, % 1.03/1.16 ( ~ class_Orderings_Olinorder(T_a) % 1.03/1.16 | c_lessequals(c_Orderings_Oord__class_Omax(V_y,V_z,T_a),V_x,T_a) % 1.03/1.16 | ~ c_lessequals(V_z,V_x,T_a) % 1.03/1.16 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_min__max_Ole__supI_0,axiom, % 1.03/1.16 ( ~ class_Orderings_Olinorder(T_a) % 1.03/1.16 | c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) % 1.03/1.16 | ~ c_lessequals(V_b,V_x,T_a) % 1.03/1.16 | ~ c_lessequals(V_a,V_x,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_le__maxI1_0,axiom, % 1.03/1.16 ( ~ class_Orderings_Olinorder(T_a) % 1.03/1.16 | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_le__maxI2_0,axiom, % 1.03/1.16 ( ~ class_Orderings_Olinorder(T_a) % 1.03/1.16 | c_lessequals(V_y,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_zero__less__abs__iff_1,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.03/1.16 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) % 1.03/1.16 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_bot__least_0,axiom, % 1.03/1.16 ( ~ class_Orderings_Obot(T_a) % 1.03/1.16 | c_lessequals(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_abs__minus__le__zero_0,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.03/1.16 | 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) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_com_Osimps_I3_J_1,axiom, % 1.03/1.16 ( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) % 1.03/1.16 | V_com2 = V_com2_H ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_com_Osimps_I3_J_0,axiom, % 1.03/1.16 ( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) % 1.03/1.16 | V_com1 = V_com1_H ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_min__max_Oinf__sup__distrib2_0,axiom, % 1.03/1.16 ( ~ class_Orderings_Olinorder(T_a) % 1.03/1.16 | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_y,V_z,T_a),V_x,T_a) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_y,V_x,T_a),c_Orderings_Oord__class_Omin(V_z,V_x,T_a),T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_min__max_Oinf__sup__distrib1_0,axiom, % 1.03/1.16 ( ~ class_Orderings_Olinorder(T_a) % 1.03/1.16 | c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),c_Orderings_Oord__class_Omin(V_x,V_z,T_a),T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_power__strict__decreasing_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.03/1.16 | 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) % 1.03/1.16 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 1.03/1.16 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.03/1.16 | ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_add__increasing_0,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.03/1.16 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.03/1.16 | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.03/1.16 | ~ c_lessequals(V_b,V_c,T_a) % 1.03/1.16 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_add__increasing2_0,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.03/1.16 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.03/1.16 | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.03/1.16 | ~ c_lessequals(V_b,V_a,T_a) % 1.03/1.16 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_le__imp__power__dvd_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.03/1.16 | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.03/1.16 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_Suc__leI_0,axiom, % 1.03/1.16 ( c_lessequals(c_Suc(V_m),V_n,tc_nat) % 1.03/1.16 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_Suc__le__eq_0,axiom, % 1.03/1.16 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.03/1.16 | ~ c_lessequals(c_Suc(V_m),V_n,tc_nat) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_less__eq__Suc__le_0,axiom, % 1.03/1.16 ( c_lessequals(c_Suc(V_n),V_m,tc_nat) % 1.03/1.16 | ~ c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_less__eq__Suc__le_1,axiom, % 1.03/1.16 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 1.03/1.16 | ~ c_lessequals(c_Suc(V_n),V_m,tc_nat) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_add__eq__inf__sup_0,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.03/1.16 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_le__zero__iff__zero__pprt_1,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.03/1.16 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.03/1.16 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_le__zero__iff__zero__pprt_0,axiom, % 1.03/1.16 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.03/1.16 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.03/1.16 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_termination__basic__simps_I1_J_0,axiom, % 1.03/1.16 ( c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) % 1.03/1.16 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_termination__basic__simps_I2_J_0,axiom, % 1.03/1.16 ( c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) % 1.03/1.16 | ~ c_HOL_Oord__class_Oless(V_x,V_z,tc_nat) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_add__lessD1_0,axiom, % 1.03/1.16 ( c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) % 1.03/1.16 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_trans__less__add1_0,axiom, % 1.03/1.16 ( c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat) % 1.03/1.16 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_trans__less__add2_0,axiom, % 1.03/1.16 ( c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat) % 1.03/1.16 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.03/1.16 % 1.03/1.16 cnf(cls_power__decreasing_0,axiom, % 1.03/1.16 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.03/1.17 | c_lessequals(c_Power_Opower__class_Opower(V_a,V_N,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.03/1.17 | ~ c_lessequals(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 1.03/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.03/1.17 | ~ c_lessequals(V_n,V_N,tc_nat) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_divide__le__0__iff_4,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.03/1.17 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.03/1.17 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.03/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_divide__le__0__iff_5,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.03/1.17 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.03/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.03/1.17 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_le__add__iff2_1,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.03/1.17 | 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) % 1.03/1.17 | ~ 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) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_le__add__iff2_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.03/1.17 | 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) % 1.03/1.17 | ~ 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) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_le__add__iff1_1,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.03/1.17 | 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) % 1.03/1.17 | ~ 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) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_le__add__iff1_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.03/1.17 | 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) % 1.03/1.17 | ~ 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) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_dvd__mod__imp__dvd_0,axiom, % 1.03/1.17 ( ~ class_Divides_Osemiring__div(T_a) % 1.03/1.17 | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) % 1.03/1.17 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) % 1.03/1.17 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_dvd__mod__iff_1,axiom, % 1.03/1.17 ( ~ class_Divides_Osemiring__div(T_a) % 1.03/1.17 | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) % 1.03/1.17 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) % 1.03/1.17 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_dvd__mod__iff_0,axiom, % 1.03/1.17 ( ~ class_Divides_Osemiring__div(T_a) % 1.03/1.17 | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) % 1.03/1.17 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) % 1.03/1.17 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_dvd__mod_0,axiom, % 1.03/1.17 ( ~ class_Divides_Osemiring__div(T_a) % 1.03/1.17 | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) % 1.03/1.17 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) % 1.03/1.17 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_Suc__diff__le_0,axiom, % 1.03/1.17 ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) % 1.03/1.17 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_zero__le__divide__1__iff_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.03/1.17 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.03/1.17 | ~ 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) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_zero__le__divide__1__iff_1,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.03/1.17 | 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) % 1.03/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_mult__ge__prts_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Olordered__ring(T_a) % 1.03/1.17 | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a1,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_b2,T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a2,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_b2,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a1,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_b1,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a2,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_b1,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.03/1.17 | ~ c_lessequals(V_b,V_b2,T_a) % 1.03/1.17 | ~ c_lessequals(V_b1,V_b,T_a) % 1.03/1.17 | ~ c_lessequals(V_a,V_a2,T_a) % 1.03/1.17 | ~ c_lessequals(V_a1,V_a,T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_sum__squares__ge__zero_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.03/1.17 | 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) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_inverse__le__1__iff_1,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.03/1.17 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.03/1.17 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_inf__bot__right_0,axiom, % 1.03/1.17 ( ~ class_Lattices_Obounded__lattice(T_a) % 1.03/1.17 | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Orderings_Obot__class_Obot(T_a),T_a) = c_Orderings_Obot__class_Obot(T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_inf__bot__left_0,axiom, % 1.03/1.17 ( ~ class_Lattices_Obounded__lattice(T_a) % 1.03/1.17 | c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) = c_Orderings_Obot__class_Obot(T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.03/1.17 | c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_comm__monoid__add_Omult__commute_0,axiom, % 1.03/1.17 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.03/1.17 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_nat__add__commute_0,axiom, % 1.03/1.17 c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_less__add__eq__less_0,axiom, % 1.03/1.17 ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) % 1.03/1.17 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat) % 1.03/1.17 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_class__semiring_Oadd__c_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.03/1.17 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_y,V_x,T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_divide__le__0__iff_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.03/1.17 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.03/1.17 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.03/1.17 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_divide__le__0__iff_1,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.03/1.17 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.03/1.17 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.03/1.17 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_divide__le__0__iff_2,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.03/1.17 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.03/1.17 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.03/1.17 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_divide__le__0__iff_3,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.03/1.17 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.03/1.17 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.03/1.17 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_mult__eq__1__iff_0,axiom, % 1.03/1.17 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.03/1.17 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_mult__eq__1__iff_1,axiom, % 1.03/1.17 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.03/1.17 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_mult__sgn__abs_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.03/1.17 | c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_x,T_a),c_HOL_Oabs__class_Oabs(V_x,T_a),T_a) = V_x ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_diff__less__mono2_0,axiom, % 1.03/1.17 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat) % 1.03/1.17 | ~ c_HOL_Oord__class_Oless(V_m,V_l,tc_nat) % 1.03/1.17 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_power__minus_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oring__1(T_a) % 1.03/1.17 | 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) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_dvd__power_1,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.03/1.17 | 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) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_le__imp__inverse__le__neg_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.17 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.03/1.17 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.03/1.17 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_inverse__le__imp__le__neg_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.17 | c_lessequals(V_b,V_a,T_a) % 1.03/1.17 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.03/1.17 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_inverse__le__imp__le_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.17 | c_lessequals(V_b,V_a,T_a) % 1.03/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.03/1.17 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_le__imp__inverse__le_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.17 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.03/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.03/1.17 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_of__nat__eq__iff_0,axiom, % 1.03/1.17 ( ~ class_Nat_Osemiring__char__0(T_a) % 1.03/1.17 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) % 1.03/1.17 | V_m = V_n ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_divide__le__eq_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.03/1.17 | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.03/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.03/1.17 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_divide__le__eq_6,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.03/1.17 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.03/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.03/1.17 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_le__divide__eq_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.03/1.17 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.03/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.03/1.17 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_le__divide__eq_6,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.03/1.17 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.03/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.03/1.17 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_mult__imp__div__pos__le_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.17 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) % 1.03/1.17 | ~ c_lessequals(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a) % 1.03/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_mult__imp__le__div__pos_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.03/1.17 | c_lessequals(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.03/1.17 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a) % 1.03/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_mult__less__imp__less__right_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.03/1.17 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.03/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.03/1.17 | ~ 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) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_mult__less__imp__less__left_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.03/1.17 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.03/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.03/1.17 | ~ 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) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_mult__right__less__imp__less_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 1.03/1.17 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.03/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.03/1.17 | ~ 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) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_mult__left__less__imp__less_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 1.03/1.17 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.03/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.03/1.17 | ~ 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) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_square__eq__iff_0,axiom, % 1.03/1.17 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.03/1.17 | c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) != c_HOL_Otimes__class_Otimes(V_b,V_b,T_a) % 1.03/1.17 | V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a) % 1.03/1.17 | V_a = V_b ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_abs__of__neg_0,axiom, % 1.03/1.17 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.03/1.17 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.03/1.17 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.03/1.17 % 1.03/1.17 cnf(cls_abs__if__lattice_0,axiom, % 1.03/1.17 ( ~ class_Orderings_Olinorder(T_a) % 1.03/1.17 | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.03/1.17 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.03/1.17 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.03/1.17 % 1.16/1.17 cnf(cls_abs__if_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Oabs__if(T_a) % 1.16/1.17 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_mod__minus__cong_0,axiom, % 1.16/1.17 ( ~ class_Divides_Oring__div(T_a) % 1.16/1.17 | c_Divides_Odiv__class_Omod(V_a,V_b,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_b,T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_nprt__le__zero_0,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.17 | c_lessequals(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_mod__mult__eq_0,axiom, % 1.16/1.17 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_dvd__diff_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.16/1.17 | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a) % 1.16/1.17 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,T_a) % 1.16/1.17 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_power__commutes_0,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_le__max__iff__disj_0,axiom, % 1.16/1.17 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.17 | c_lessequals(V_z,V_y,T_a) % 1.16/1.17 | c_lessequals(V_z,V_x,T_a) % 1.16/1.17 | ~ c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_class__semiring_Omul__pwr_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_nat__eq__add__iff1_1,axiom, % 1.16/1.17 ( ~ c_lessequals(V_j,V_i,tc_nat) % 1.16/1.17 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),tc_nat) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_min__max_Ole__inf__iff_1,axiom, % 1.16/1.17 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.17 | c_lessequals(V_x,V_z,T_a) % 1.16/1.17 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_min__max_Ole__inf__iff_0,axiom, % 1.16/1.17 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.17 | c_lessequals(V_x,V_y,T_a) % 1.16/1.17 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_min__le__iff__disj_2,axiom, % 1.16/1.17 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.17 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 1.16/1.17 | ~ c_lessequals(V_y,V_z,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_min__le__iff__disj_1,axiom, % 1.16/1.17 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.17 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 1.16/1.17 | ~ c_lessequals(V_x,V_z,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_min__max_Ole__infI2_0,axiom, % 1.16/1.17 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.17 | c_lessequals(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 1.16/1.17 | ~ c_lessequals(V_b,V_x,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_min__max_Ole__infI1_0,axiom, % 1.16/1.17 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.17 | c_lessequals(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 1.16/1.17 | ~ c_lessequals(V_a,V_x,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_min__max_Ole__infE_1,axiom, % 1.16/1.17 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.17 | c_lessequals(V_x,V_b,T_a) % 1.16/1.17 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_of__nat__le__iff_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.17 | c_lessequals(V_m,V_n,tc_nat) % 1.16/1.17 | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_of__nat__le__iff_1,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.17 | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) % 1.16/1.17 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_nonzero__minus__divide__right_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.17 | 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) % 1.16/1.17 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_divide__less__0__1__iff_1,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.17 | 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) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_divide__less__0__1__iff_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.17 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.17 | ~ 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_neg__less__0__iff__less_0,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.17 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_neg__less__0__iff__less_1,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.17 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_min__less__iff__conj_2,axiom, % 1.16/1.17 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.17 | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_natgb_Oadd__mul__solve_1,axiom, % 1.16/1.17 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) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_natgb_Onoteq__reduce_1,axiom, % 1.16/1.17 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) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_class__ringb_Onoteq__reduce_1,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.16/1.17 | ~ class_Int_Onumber__ring(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_class__ringb_Oadd__mul__solve_1,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.16/1.17 | ~ class_Int_Onumber__ring(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_max__Suc__Suc_0,axiom, % 1.16/1.17 c_Orderings_Oord__class_Omax(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(V_m,V_n,tc_nat)) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_less__Suc0_0,axiom, % 1.16/1.17 ( V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.17 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.17 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) % 1.16/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_abs__triangle__ineq3_0,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_min__max_Oinf__left__idem_0,axiom, % 1.16/1.17 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.17 | c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) = c_Orderings_Oord__class_Omin(V_x,V_y,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_inf__0__imp__0_0,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.17 | c_Lattices_Olower__semilattice__class_Oinf(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.17 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_sup__eq__if_0,axiom, % 1.16/1.17 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.17 | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.17 | c_Lattices_Oupper__semilattice__class_Osup(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_abs__mult__less_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.17 | 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) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_b,T_a),V_d,T_a) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_c,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_nat__diff__add__eq2_0,axiom, % 1.16/1.17 ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) % 1.16/1.17 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_nat__diff__add__eq1_0,axiom, % 1.16/1.17 ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat) % 1.16/1.17 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_diff__add__cancel_0,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.17 | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_inverse__nonnegative__iff__nonnegative_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.17 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_inverse__nonnegative__iff__nonnegative_1,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.17 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.16/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_inverse__inverse__eq_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.16/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.17 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_mult__le__cancel2_1,axiom, % 1.16/1.17 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) % 1.16/1.17 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_mult__le__cancel1_1,axiom, % 1.16/1.17 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 1.16/1.17 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_class__semiring_Opwr__pwr_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_power__Suc2_0,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_power__Suc_0,axiom, % 1.16/1.17 ( ~ class_Power_Opower(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_class__semiring_Opwr__Suc_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_class__semiring_Osemiring__rules_I35_J_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_add__le__mono_0,axiom, % 1.16/1.17 ( c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_l,tc_nat),tc_nat) % 1.16/1.17 | ~ c_lessequals(V_k,V_l,tc_nat) % 1.16/1.17 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_add__mono_0,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 1.16/1.17 | 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) % 1.16/1.17 | ~ c_lessequals(V_c,V_d,T_a) % 1.16/1.17 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_inf__sup__distrib1_0,axiom, % 1.16/1.17 ( ~ class_Lattices_Odistrib__lattice(T_a) % 1.16/1.17 | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_inf__sup__distrib2_0,axiom, % 1.16/1.17 ( ~ class_Lattices_Odistrib__lattice(T_a) % 1.16/1.17 | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),V_x,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_z,V_x,T_a),T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_less__Suc__eq__le_1,axiom, % 1.16/1.17 ( c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) % 1.16/1.17 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_less__Suc__eq__le_0,axiom, % 1.16/1.17 ( c_lessequals(V_m,V_n,tc_nat) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_le__less__Suc__eq_1,axiom, % 1.16/1.17 ( ~ c_lessequals(V_x,V_x,tc_nat) % 1.16/1.17 | c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_class__semiring_Omul__c_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.17 | c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_nat__mult__commute_0,axiom, % 1.16/1.17 c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) = c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_add__nonneg__eq__0__iff_2,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.16/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.17 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_diff__less__Suc_0,axiom, % 1.16/1.17 c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_Suc(V_m),tc_nat) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_mod__add__eq_0,axiom, % 1.16/1.17 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_add__sup__distrib__left_0,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Olordered__ab__group__add__join(T_a) % 1.16/1.17 | c_HOL_Oplus__class_Oplus(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_b,V_c,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_add__sup__distrib__right_0,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Olordered__ab__group__add__join(T_a) % 1.16/1.17 | c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_c,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.17 | c_HOL_Oplus__class_Oplus(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_b,V_c,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.17 | c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_c,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_add__nonneg__nonneg_0,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.16/1.17 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) % 1.16/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_zero__le__power__abs_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_inverse__less__imp__less_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.17 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.17 | ~ 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_less__imp__inverse__less_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.17 | 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) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_inverse__less__imp__less__neg_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.17 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.17 | ~ 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_less__imp__inverse__less__neg_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.17 | 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) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_nprt__neg_0,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.17 | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_x,T_a),T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_le__zero__iff__pprt__id_0,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.17 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) = V_a % 1.16/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_le__zero__iff__pprt__id_1,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.17 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) != V_a % 1.16/1.17 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_power__Suc__less__one_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.17 | 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) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_sup__idem_0,axiom, % 1.16/1.17 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.17 | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_x,T_a) = V_x ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_order__less__trans_0,axiom, % 1.16/1.17 ( ~ class_Orderings_Opreorder(T_a) % 1.16/1.17 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_xt1_I10_J_0,axiom, % 1.16/1.17 ( ~ class_Orderings_Oorder(T_a) % 1.16/1.17 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.16/1.17 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_sgn__if_2,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Osgn__if(T_a) % 1.16/1.17 | c_HOL_Osgn__class_Osgn(V_x,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a) % 1.16/1.17 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.16/1.17 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_min__max_Ole__iff__sup_0,axiom, % 1.16/1.17 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.17 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = V_y % 1.16/1.17 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_min__max_Ole__iff__sup_1,axiom, % 1.16/1.17 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.17 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) != V_y % 1.16/1.17 | c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_min__max_Osup__absorb1_0,axiom, % 1.16/1.17 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.17 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = V_x % 1.16/1.17 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_class__semiring_Oadd__a_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_add__cancel__21_1,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_nat__add__left__commute_0,axiom, % 1.16/1.17 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) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_nat__add__assoc_0,axiom, % 1.16/1.17 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) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_comm__monoid__add_Omult__assoc_0,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom, % 1.16/1.17 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom, % 1.16/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.17 | 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) ) ). % 1.16/1.17 % 1.16/1.17 cnf(cls_add__gr__0_0,axiom, % 1.16/1.18 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 1.16/1.18 | ~ 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_power__add_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_com_Osize_I12_J_0,axiom, % 1.16/1.18 c_Nat_Osize__class_Osize(c_Com_Ocom_OSemi(V_com1,V_com2),tc_Com_Ocom) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(V_com1,tc_Com_Ocom),c_Nat_Osize__class_Osize(V_com2,tc_Com_Ocom),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_one__le__mult__iff_1,axiom, % 1.16/1.18 ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) % 1.16/1.18 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_one__le__mult__iff_0,axiom, % 1.16/1.18 ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 1.16/1.18 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mult__le__prts_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Olordered__ring(T_a) % 1.16/1.18 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a2,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_b2,T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a1,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_b2,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a2,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_b1,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a1,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_b1,T_a),T_a),T_a),T_a) % 1.16/1.18 | ~ c_lessequals(V_b,V_b2,T_a) % 1.16/1.18 | ~ c_lessequals(V_b1,V_b,T_a) % 1.16/1.18 | ~ c_lessequals(V_a,V_a2,T_a) % 1.16/1.18 | ~ c_lessequals(V_a1,V_a,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_add__cancel__21_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) = V_u ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_abs__triangle__ineq_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_trans__le__add2_0,axiom, % 1.16/1.18 ( c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat) % 1.16/1.18 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_trans__le__add1_0,axiom, % 1.16/1.18 ( c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat) % 1.16/1.18 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_add__leE_1,axiom, % 1.16/1.18 ( c_lessequals(V_k,V_n,tc_nat) % 1.16/1.18 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),V_n,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_add__leE_0,axiom, % 1.16/1.18 ( c_lessequals(V_m,V_n,tc_nat) % 1.16/1.18 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),V_n,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_termination__basic__simps_I4_J_0,axiom, % 1.16/1.18 ( c_lessequals(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) % 1.16/1.18 | ~ c_lessequals(V_x,V_z,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_termination__basic__simps_I3_J_0,axiom, % 1.16/1.18 ( c_lessequals(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) % 1.16/1.18 | ~ c_lessequals(V_x,V_y,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mod__diff__left__eq_0,axiom, % 1.16/1.18 ( ~ class_Divides_Oring__div(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mod__diff__right__eq_0,axiom, % 1.16/1.18 ( ~ class_Divides_Oring__div(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inverse__positive__imp__positive_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.18 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nonzero__abs__divide_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_power__one_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.16/1.18 | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nonzero__abs__inverse_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__max_Ole__iff__inf_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = V_x % 1.16/1.18 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__max_Ole__infE_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_lessequals(V_x,V_a,T_a) % 1.16/1.18 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_sgn__greater_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_sgn__greater_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_divide__less__eq_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_divide__less__eq_4,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_divide__less__eq_5,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_divide__less__eq_7,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__divide__eq_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__divide__eq_4,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__divide__eq_5,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__divide__eq_7,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inverse__le__1__iff_2,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_class__semiring_Osemiring__rules_I4_J_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_add__nonneg__eq__0__iff_1,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.16/1.18 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.16/1.18 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_add__nonneg__eq__0__iff_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.16/1.18 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.16/1.18 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_Suc__inject_0,axiom, % 1.16/1.18 ( c_Suc(V_x) != c_Suc(V_y) % 1.16/1.18 | V_x = V_y ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nat_Oinject_0,axiom, % 1.16/1.18 ( c_Suc(V_nat) != c_Suc(V_nat_H) % 1.16/1.18 | V_nat = V_nat_H ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_abs__ge__minus__self_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.18 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_diff__divide__distrib_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_abs__ge__self_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.18 | c_lessequals(V_a,c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__add__iff2_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__add__iff2_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__add__iff1_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__add__iff1_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nat__eq__add__iff1_0,axiom, % 1.16/1.18 ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat) % 1.16/1.18 | ~ c_lessequals(V_j,V_i,tc_nat) % 1.16/1.18 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat) = V_n ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nat__eq__add__iff2_0,axiom, % 1.16/1.18 ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat) % 1.16/1.18 | ~ c_lessequals(V_i,V_j,tc_nat) % 1.16/1.18 | V_m = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__le__iff__disj_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_lessequals(V_y,V_z,T_a) % 1.16/1.18 | c_lessequals(V_x,V_z,T_a) % 1.16/1.18 | ~ c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nat__eq__add__iff2_1,axiom, % 1.16/1.18 ( ~ c_lessequals(V_i,V_j,tc_nat) % 1.16/1.18 | 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(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_eq__divide__eq_4,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mod__add__cong_0,axiom, % 1.16/1.18 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.18 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 1.16/1.18 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__Suc0_1,axiom, % 1.16/1.18 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_even__less__0__iff_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_even__less__0__iff_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_one__is__add_1,axiom, % 1.16/1.18 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) % 1.16/1.18 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.16/1.18 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_one__is__add_2,axiom, % 1.16/1.18 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) % 1.16/1.18 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 1.16/1.18 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_zero__less__mult__pos2_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.18 | ~ 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_zero__less__mult__pos_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.18 | ~ 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mult__pos__pos_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mult__neg__neg_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nat__0__less__mult__iff_2,axiom, % 1.16/1.18 ( 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) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_power__less__imp__less__base_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.18 | ~ 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__max_Ole__sup__iff_1,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_lessequals(V_y,V_z,T_a) % 1.16/1.18 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__max_Ole__sup__iff_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_lessequals(V_x,V_z,T_a) % 1.16/1.18 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__max__iff__disj_2,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 1.16/1.18 | ~ c_lessequals(V_z,V_y,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__max__iff__disj_1,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 1.16/1.18 | ~ c_lessequals(V_z,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__max_Ole__supI2_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 1.16/1.18 | ~ c_lessequals(V_x,V_b,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__max_Ole__supI1_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 1.16/1.18 | ~ c_lessequals(V_x,V_a,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__max_Ole__supE_1,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_lessequals(V_b,V_x,T_a) % 1.16/1.18 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__max_Ole__supE_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_lessequals(V_a,V_x,T_a) % 1.16/1.18 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__diff__conv_0,axiom, % 1.16/1.18 ( c_lessequals(V_j,c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),tc_nat) % 1.16/1.18 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__diff__conv_1,axiom, % 1.16/1.18 ( c_lessequals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) % 1.16/1.18 | ~ c_lessequals(V_j,c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_zero__less__power_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__max__iff__disj_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mult__Suc__right_0,axiom, % 1.16/1.18 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) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mult__Suc_0,axiom, % 1.16/1.18 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) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_eq__neg__iff__add__eq__0_1,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.18 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.18 | V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_minus__unique_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.18 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.18 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_abs__less__iff_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_not__one__less__zero_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_abs__less__iff_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inf__sup__aci_I2_J_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Olattice(T_a) % 1.16/1.18 | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inf__sup__aci_I3_J_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Olattice(T_a) % 1.16/1.18 | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inf__left__commute_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.18 | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inf__assoc_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.18 | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_sgn__if_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Osgn__if(T_a) % 1.16/1.18 | c_HOL_Osgn__class_Osgn(V_x,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.16/1.18 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_not__sum__squares__lt__zero_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.18 | ~ 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nat__le__add__iff1_0,axiom, % 1.16/1.18 ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat) % 1.16/1.18 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) % 1.16/1.18 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nat__le__add__iff1_1,axiom, % 1.16/1.18 ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) % 1.16/1.18 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat) % 1.16/1.18 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nat__le__add__iff2_0,axiom, % 1.16/1.18 ( c_lessequals(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) % 1.16/1.18 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) % 1.16/1.18 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nat__le__add__iff2_1,axiom, % 1.16/1.18 ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) % 1.16/1.18 | ~ c_lessequals(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) % 1.16/1.18 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_divide__le__eq_8,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.16/1.18 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__divide__eq_8,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_of__nat__mult_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__less__iff__disj_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_class__ringb_Oadd__mul__solve_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.16/1.18 | ~ class_Int_Onumber__ring(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | V_y = V_z % 1.16/1.18 | V_w = V_x ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_class__ringb_Onoteq__reduce_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.16/1.18 | ~ class_Int_Onumber__ring(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | V_c = V_d % 1.16/1.18 | V_a = V_b ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_natgb_Onoteq__reduce_0,axiom, % 1.16/1.18 ( 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) % 1.16/1.18 | V_c = V_d % 1.16/1.18 | V_a = V_b ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_natgb_Oadd__mul__solve_0,axiom, % 1.16/1.18 ( 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) % 1.16/1.18 | V_y = V_z % 1.16/1.18 | V_w = V_x ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_abs__div__pos_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_abs__mult__self_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_sup__bot__right_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Obounded__lattice(T_a) % 1.16/1.18 | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Orderings_Obot__class_Obot(T_a),T_a) = V_x ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_sup__bot__left_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Obounded__lattice(T_a) % 1.16/1.18 | c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) = V_x ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nat__size_0,axiom, % 1.16/1.18 c_Nat_Osize__class_Osize(V_n,tc_nat) = V_n ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nonzero__inverse__minus__eq_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nonzero__power__inverse_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_diff__Suc__Suc_0,axiom, % 1.16/1.18 c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_neg__less__iff__less_1,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_neg__less__iff__less_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.16/1.18 | ~ 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_add__nonpos__neg_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_add__neg__nonpos_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__SucE_0,axiom, % 1.16/1.18 ( V_m = V_n % 1.16/1.18 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__antisym_0,axiom, % 1.16/1.18 ( V_m = V_n % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_not__less__less__Suc__eq_0,axiom, % 1.16/1.18 ( V_n = V_m % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_sum__squares__le__zero__iff_2,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mod__mult__cong_0,axiom, % 1.16/1.18 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.18 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 1.16/1.18 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_diff__add__assoc_0,axiom, % 1.16/1.18 ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) % 1.16/1.18 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_diff__add__assoc2_0,axiom, % 1.16/1.18 ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) % 1.16/1.18 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_sup__0__imp__0_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.18 | c_Lattices_Oupper__semilattice__class_Osup(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.18 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__max_Ole__iff__inf_1,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) != V_x % 1.16/1.18 | c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__max_Oinf__absorb2_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = V_y % 1.16/1.18 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_max__diff__distrib__left_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.18 | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(V_x,V_z,T_a),c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_COMBI__def_0,axiom, % 1.16/1.18 c_COMBI(V_P,T_a) = V_P ). % 1.16/1.18 % 1.16/1.18 cnf(cls_COMBK__def_0,axiom, % 1.16/1.18 c_COMBK(V_P,V_Q,T_a,T_b) = V_P ). % 1.16/1.18 % 1.16/1.18 cnf(cls_not__leE_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.16/1.18 | c_lessequals(V_y,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_linorder__antisym__conv2_1,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | ~ c_lessequals(V_x,V_x,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_linorder__antisym__conv1_1,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_x,V_x,T_a) % 1.16/1.18 | c_lessequals(V_x,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_linorder__not__less_1,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.16/1.18 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_linorder__not__less_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_lessequals(V_y,V_x,T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_linorder__not__le_1,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | ~ c_lessequals(V_x,V_y,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_linorder__not__le_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.16/1.18 | c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__le__not__le_1,axiom, % 1.16/1.18 ( ~ class_Orderings_Opreorder(T_a) % 1.16/1.18 | ~ c_lessequals(V_y,V_x,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_neg__0__le__iff__le_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.18 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_neg__0__le__iff__le_1,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.18 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.16/1.18 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_add__inf__distrib__left_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Olordered__ab__group__add__meet(T_a) % 1.16/1.18 | c_HOL_Oplus__class_Oplus(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_b,V_c,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_add__inf__distrib__right_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Olordered__ab__group__add__meet(T_a) % 1.16/1.18 | c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_c,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.18 | c_HOL_Oplus__class_Oplus(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_b,V_c,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.18 | c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_c,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_divide__self__if_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.16/1.18 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_divide__self_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.18 | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.16/1.18 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_right__inverse__eq_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.18 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.18 | c_HOL_Oinverse__class_Odivide(V_x,V_x,T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mod__add__left__eq_0,axiom, % 1.16/1.18 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mod__add__right__eq_0,axiom, % 1.16/1.18 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_zero__le__divide__iff_3,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_zero__le__divide__iff_2,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_zero__le__divide__iff_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_zero__le__divide__iff_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__max_Oinf__assoc_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__max_Oinf__left__commute_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omin(V_y,c_Orderings_Oord__class_Omin(V_x,V_z,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_one__is__add_5,axiom, % 1.16/1.18 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) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_add__strict__increasing2_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.16/1.18 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_power__increasing_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.18 | c_lessequals(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_a,V_N,T_a),T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 1.16/1.18 | ~ c_lessequals(V_n,V_N,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_diff__le__mono2_0,axiom, % 1.16/1.18 ( c_lessequals(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat) % 1.16/1.18 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_diff__le__mono_0,axiom, % 1.16/1.18 ( c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_l,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_l,tc_nat),tc_nat) % 1.16/1.18 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__diff__iff_1,axiom, % 1.16/1.18 ( c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) % 1.16/1.18 | ~ c_lessequals(V_m,V_n,tc_nat) % 1.16/1.18 | ~ c_lessequals(V_k,V_n,tc_nat) % 1.16/1.18 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__diff__iff_0,axiom, % 1.16/1.18 ( c_lessequals(V_m,V_n,tc_nat) % 1.16/1.18 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) % 1.16/1.18 | ~ c_lessequals(V_k,V_n,tc_nat) % 1.16/1.18 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_diff__add__0_0,axiom, % 1.16/1.18 c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_diff__diff__left_0,axiom, % 1.16/1.18 c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(V_i,c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_power__mono_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.18 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_eq__eqI_1,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.16/1.18 | c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) % 1.16/1.18 | V_xa = V_y ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_eq__eqI_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.16/1.18 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.16/1.18 | V_x_H = V_y_H ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_eq__diff__iff_0,axiom, % 1.16/1.18 ( c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat) != c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat) % 1.16/1.18 | ~ c_lessequals(V_k,V_n,tc_nat) % 1.16/1.18 | ~ c_lessequals(V_k,V_m,tc_nat) % 1.16/1.18 | V_m = V_n ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__max_Oinf__sup__absorb_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) = V_x ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nat__mult__eq__cancel1_0,axiom, % 1.16/1.18 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.16/1.18 | V_m = V_n ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_one__is__add_3,axiom, % 1.16/1.18 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) % 1.16/1.18 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.16/1.18 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_one__is__add_0,axiom, % 1.16/1.18 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) % 1.16/1.18 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 1.16/1.18 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mult__less__cancel2_0,axiom, % 1.16/1.18 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.16/1.18 | ~ 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mult__less__cancel1_0,axiom, % 1.16/1.18 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.16/1.18 | ~ 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_of__nat__Suc_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inverse__le__1__iff_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_lessequals(c_HOL_Oone__class_Oone(T_a),V_x,T_a) % 1.16/1.18 | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_diff__eq_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.16/1.18 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_add__Suc__shift_0,axiom, % 1.16/1.18 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) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mult__le__cancel2_0,axiom, % 1.16/1.18 ( c_lessequals(V_m,V_n,tc_nat) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.16/1.18 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mult__le__cancel1_0,axiom, % 1.16/1.18 ( c_lessequals(V_m,V_n,tc_nat) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.16/1.18 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nat__mult__le__cancel1_0,axiom, % 1.16/1.18 ( c_lessequals(V_m,V_n,tc_nat) % 1.16/1.18 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nat__mult__le__cancel1_1,axiom, % 1.16/1.18 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 1.16/1.18 | ~ c_lessequals(V_m,V_n,tc_nat) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mult__le__cancel__left__neg_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.18 | c_lessequals(V_b,V_a,T_a) % 1.16/1.18 | ~ 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) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mult__le__cancel__left__neg_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ c_lessequals(V_b,V_a,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mult__le__cancel__left__pos_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.18 | c_lessequals(V_a,V_b,T_a) % 1.16/1.18 | ~ 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) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mult__le__cancel__left__pos_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ c_lessequals(V_a,V_b,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mult__left__le__imp__le_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.16/1.18 | c_lessequals(V_a,V_b,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.18 | ~ 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mult__right__le__imp__le_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.16/1.18 | c_lessequals(V_a,V_b,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.18 | ~ 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_one__less__mult_0,axiom, % 1.16/1.18 ( 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) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_evalc_OSemi_0,axiom, % 1.16/1.18 ( c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_s2) % 1.16/1.18 | ~ c_Natural_Oevalc(V_c1,V_s1,V_s2) % 1.16/1.18 | ~ c_Natural_Oevalc(V_c0,V_s0,V_s1) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__divide__eq_7,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.16/1.18 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__divide__eq_5,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.16/1.18 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_divide__le__eq_7,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_divide__le__eq_5,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_sup__assoc_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.18 | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_sup__left__commute_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.18 | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inf__sup__aci_I7_J_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Olattice(T_a) % 1.16/1.18 | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inf__sup__aci_I6_J_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Olattice(T_a) % 1.16/1.18 | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_minus__divide__divide_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_diff__cancel2_0,axiom, % 1.16/1.18 c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_diff__cancel_0,axiom, % 1.16/1.18 c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__iff__inf_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.18 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_x % 1.16/1.18 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__iff__inf_1,axiom, % 1.16/1.18 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.18 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x % 1.16/1.18 | c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inf__absorb2_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.18 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y % 1.16/1.18 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_zero__less__Suc_0,axiom, % 1.16/1.18 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_gr0__conv__Suc_1,axiom, % 1.16/1.18 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__supI_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.18 | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a) % 1.16/1.18 | ~ c_lessequals(V_b,V_x,T_a) % 1.16/1.18 | ~ c_lessequals(V_a,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_sup__ge1_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.18 | c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_sup__ge2_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.18 | c_lessequals(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_sup__least_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.18 | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),V_x,T_a) % 1.16/1.18 | ~ c_lessequals(V_z,V_x,T_a) % 1.16/1.18 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__sup__iff_2,axiom, % 1.16/1.18 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.18 | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) % 1.16/1.18 | ~ c_lessequals(V_y,V_z,T_a) % 1.16/1.18 | ~ c_lessequals(V_x,V_z,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inf__sup__ord_I4_J_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Olattice(T_a) % 1.16/1.18 | c_lessequals(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inf__sup__ord_I3_J_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Olattice(T_a) % 1.16/1.18 | c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_one__le__inverse__iff_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__max_Oless__supI1_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_a,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__max_Oless__supI2_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_b,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__max__iff__disj_1,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__max__iff__disj_2,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_max__less__iff__conj_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_max__less__iff__conj_1,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inf__commute_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.18 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inf__sup__aci_I1_J_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Olattice(T_a) % 1.16/1.18 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__max_Oinf__commute_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = c_Orderings_Oord__class_Omin(V_y,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_one__less__power_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_left__add__mult__distrib_0,axiom, % 1.16/1.18 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) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_add__frac__eq_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.18 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mult__eq__1__iff_2,axiom, % 1.16/1.18 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)) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_divide__eq__eq_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) % 1.16/1.18 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_eq__divide__eq_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b % 1.16/1.18 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_zero__le__one_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.18 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_abs__power__minus_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_abs__lattice_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.16/1.18 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_class__semiring_Osemiring__rules_I2_J_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_diff__diff__right_0,axiom, % 1.16/1.18 ( c_HOL_Ominus__class_Ominus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) % 1.16/1.18 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inverse__less__1__iff_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.16/1.18 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__imp__diff__less_0,axiom, % 1.16/1.18 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_zero__le__iff__zero__nprt_1,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.18 | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.18 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_zero__le__iff__zero__nprt_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.18 | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_abs__le__zero__iff_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.18 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nat_Osize_I4_J_0,axiom, % 1.16/1.18 c_Nat_Osize__class_Osize(c_Suc(V_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(V_nat,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mod__by__1_0,axiom, % 1.16/1.18 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.18 | c_Divides_Odiv__class_Omod(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_distrib__sup__le_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Olattice(T_a) % 1.16/1.18 | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_abs__mult__pos_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_divide__le__0__1__iff_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_divide__le__0__1__iff_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_one__le__inverse__iff_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_lessequals(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_dvd__abs__iff_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.18 | c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a) % 1.16/1.18 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_dvd__abs__iff_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.18 | c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) % 1.16/1.18 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_abs__dvd__iff_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.18 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a) % 1.16/1.18 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_abs__dvd__iff_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.18 | c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) % 1.16/1.18 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_one__is__add_4,axiom, % 1.16/1.18 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) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__le__not__le_2,axiom, % 1.16/1.18 ( ~ class_Orderings_Opreorder(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.16/1.18 | c_lessequals(V_y,V_x,T_a) % 1.16/1.18 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nat__less__le_1,axiom, % 1.16/1.18 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__not__refl_0,axiom, % 1.16/1.18 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_order__less__le_1,axiom, % 1.16/1.18 ( ~ class_Orderings_Oorder(T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_linorder__neq__iff_1,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_order__less__irrefl_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Opreorder(T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__imp__diff__is__add_1,axiom, % 1.16/1.18 ( ~ c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_k,V_i,tc_nat),tc_nat) % 1.16/1.18 | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k,V_i,tc_nat),V_i,tc_nat) = V_k ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_sup__inf__absorb_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Olattice(T_a) % 1.16/1.18 | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = V_x ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__max_Oinf__idem_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_Orderings_Oord__class_Omin(V_x,V_x,T_a) = V_x ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_eq__divide__imp_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.18 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.18 | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_divide__eq__imp_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.18 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.18 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_divide__eq__eq_3,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a % 1.16/1.18 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_eq__divide__eq_3,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) % 1.16/1.18 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_estimate__by__abs_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.16/1.18 | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_add__pos__pos_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__add1_0,axiom, % 1.16/1.18 c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__add2_0,axiom, % 1.16/1.18 c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__iff__add_1,axiom, % 1.16/1.18 c_lessequals(V_m,c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat),tc_nat) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nat__minus__add__max_0,axiom, % 1.16/1.18 c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),V_m,tc_nat) = c_Orderings_Oord__class_Omax(V_n,V_m,tc_nat) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_compl__eq__compl__iff_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.16/1.18 | c_HOL_Ouminus__class_Ouminus(V_x,T_a) != c_HOL_Ouminus__class_Ouminus(V_y,T_a) % 1.16/1.18 | V_x = V_y ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_neg__equal__iff__equal_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.18 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(V_b,T_a) % 1.16/1.18 | V_a = V_b ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_power__divide_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_not__one__le__zero_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_negative__imp__inverse__negative_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inverse__negative__iff__negative_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inverse__negative__iff__negative_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_power__gt1__lemma_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_evalc_OSkip_0,axiom, % 1.16/1.18 c_Natural_Oevalc(c_Com_Ocom_OSKIP,V_s,V_s) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_linorder__neqE__ordered__idom_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.16/1.18 | V_x = V_y ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_not__less__iff__gr__or__eq_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | V_x = V_y % 1.16/1.18 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__antisym_0,axiom, % 1.16/1.18 ( V_m = V_n % 1.16/1.18 | ~ c_lessequals(V_n,V_m,tc_nat) % 1.16/1.18 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nat__neq__iff_0,axiom, % 1.16/1.18 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.18 | V_m = V_n ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_com__det_0,axiom, % 1.16/1.18 ( V_u = V_t % 1.16/1.18 | ~ c_Natural_Oevalc(V_c,V_s,V_u) % 1.16/1.18 | ~ c_Natural_Oevalc(V_c,V_s,V_t) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_linorder__neqE__nat_0,axiom, % 1.16/1.18 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 1.16/1.18 | V_x = V_y ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_order__eq__iff_2,axiom, % 1.16/1.18 ( ~ class_Orderings_Oorder(T_a) % 1.16/1.18 | V_x = V_y % 1.16/1.18 | ~ c_lessequals(V_y,V_x,T_a) % 1.16/1.18 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_linorder__neqE_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.16/1.18 | V_x = V_y ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_order__antisym_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Oorder(T_a) % 1.16/1.18 | V_x = V_y % 1.16/1.18 | ~ c_lessequals(V_y,V_x,T_a) % 1.16/1.18 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_order__antisym__conv_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Oorder(T_a) % 1.16/1.18 | V_x = V_y % 1.16/1.18 | ~ c_lessequals(V_x,V_y,T_a) % 1.16/1.18 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_linorder__less__linear_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.16/1.18 | V_x = V_y % 1.16/1.18 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_linorder__antisym__conv3_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | V_x = V_y % 1.16/1.18 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_mod__diff__cong_0,axiom, % 1.16/1.18 ( ~ class_Divides_Oring__div(T_a) % 1.16/1.18 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 1.16/1.18 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 1.16/1.18 | 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) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__iff__diff__le__0_1,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.18 | c_lessequals(V_a,V_b,T_a) % 1.16/1.18 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__iff__diff__le__0_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.18 | c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.18 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_min__max_Osup__idem_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.18 | c_Orderings_Oord__class_Omax(V_x,V_x,T_a) = V_x ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_abs__of__nonneg_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.18 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.16/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_add__strict__mono_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.16/1.18 | 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) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inf__sup__absorb_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Olattice(T_a) % 1.16/1.18 | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = V_x ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_add__less__mono_0,axiom, % 1.16/1.18 ( 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) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__infI2_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_b,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_less__infI1_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.18 | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_a,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_termination__basic__simps_I5_J_0,axiom, % 1.16/1.18 ( c_lessequals(V_x,V_y,tc_nat) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_nat__less__le_0,axiom, % 1.16/1.18 ( c_lessequals(V_m,V_n,tc_nat) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_order__le__less_1,axiom, % 1.16/1.18 ( ~ class_Orderings_Oorder(T_a) % 1.16/1.18 | c_lessequals(V_x,V_y,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_order__less__imp__le_0,axiom, % 1.16/1.18 ( ~ class_Orderings_Opreorder(T_a) % 1.16/1.18 | c_lessequals(V_x,V_y,T_a) % 1.16/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_sup__absorb1_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.18 | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_x % 1.16/1.18 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__iff__sup_1,axiom, % 1.16/1.18 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.18 | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) != V_y % 1.16/1.18 | c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_le__iff__sup_0,axiom, % 1.16/1.18 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.18 | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y % 1.16/1.18 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_minus__add__cancel_0,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.18 | 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 ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_add__cancel__end_1,axiom, % 1.16/1.18 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.16/1.18 | 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 ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inverse__1_0,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.16/1.18 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_inverse__eq__1__iff_1,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.18 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.16/1.18 % 1.16/1.18 cnf(cls_one__less__inverse__iff_2,axiom, % 1.16/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_dvd__trans_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 1.16/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 1.16/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_dvd__refl_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__le__divide__iff_4,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__le__divide__iff_5,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_frac__le_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_lessequals(V_w,V_z,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 1.16/1.19 | ~ c_lessequals(V_x,V_y,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_power__gt1_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_com_Osize_I1_J_0,axiom, % 1.16/1.19 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_diff__Suc__diff__eq1_0,axiom, % 1.16/1.19 ( c_HOL_Ominus__class_Ominus(V_m,c_Suc(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),c_Suc(V_j),tc_nat) % 1.16/1.19 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_combine__common__factor_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Osemiring(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_distrib__inf__le_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Olattice(T_a) % 1.16/1.19 | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_diff__le__self_0,axiom, % 1.16/1.19 c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_left__minus_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_right__minus_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_ab__left__minus_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_eq__neg__iff__add__eq__0_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_nat__0__less__mult__iff_1,axiom, % 1.16/1.19 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_nat__0__less__mult__iff_0,axiom, % 1.16/1.19 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__neg__neg_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_power__strict__mono_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_sum__squares__le__zero__iff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_sum__squares__le__zero__iff_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_diff__mult__distrib2_0,axiom, % 1.16/1.19 c_HOL_Otimes__class_Otimes(V_k,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_diff__mult__distrib_0,axiom, % 1.16/1.19 c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_power__diff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_n,V_m,tc_nat) % 1.16/1.19 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_dvd__imp__mod__0_0,axiom, % 1.16/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.19 | c_Divides_Odiv__class_Omod(V_b,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_dvd__eq__mod__eq__0_1,axiom, % 1.16/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.19 | c_Divides_Odiv__class_Omod(V_b,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_min__max_Oless__infI1_0,axiom, % 1.16/1.19 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_min__max_Oless__infI2_0,axiom, % 1.16/1.19 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_b,V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_min__less__iff__conj_0,axiom, % 1.16/1.19 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_min__less__iff__conj_1,axiom, % 1.16/1.19 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_min__less__iff__disj_1,axiom, % 1.16/1.19 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_x,V_z,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_min__less__iff__disj_2,axiom, % 1.16/1.19 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_Nat_Odiff__diff__eq_0,axiom, % 1.16/1.19 ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) % 1.16/1.19 | ~ c_lessequals(V_k,V_n,tc_nat) % 1.16/1.19 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_diff__commute_0,axiom, % 1.16/1.19 c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_k,tc_nat),V_j,tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inverse__nonpositive__iff__nonpositive_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inverse__nonpositive__iff__nonpositive_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__nonneg__pos_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__pos__nonneg_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__le__zero__iff_1,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inverse__mult__distrib_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_nonzero__inverse__mult__distrib_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.19 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_diff__less__mono_0,axiom, % 1.16/1.19 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_c,tc_nat),c_HOL_Ominus__class_Ominus(V_b,V_c,tc_nat),tc_nat) % 1.16/1.19 | ~ c_lessequals(V_c,V_a,tc_nat) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__le__0__iff_4,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__le__0__iff_5,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_split__mult__neg__le_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_split__mult__neg__le_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__nonneg__nonpos_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__nonpos__nonneg_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__nonneg__nonpos2_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_not__square__less__zero_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_Suc__mult__less__cancel1_1,axiom, % 1.16/1.19 ( 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_Suc__mult__less__cancel1_0,axiom, % 1.16/1.19 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_Suc__lessI_0,axiom, % 1.16/1.19 ( c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) % 1.16/1.19 | c_Suc(V_m) = V_n % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_not__less__eq__eq_1,axiom, % 1.16/1.19 ( ~ c_lessequals(V_m,V_n,tc_nat) % 1.16/1.19 | ~ c_lessequals(c_Suc(V_n),V_m,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_not__less__eq__eq_0,axiom, % 1.16/1.19 ( c_lessequals(c_Suc(V_n),V_m,tc_nat) % 1.16/1.19 | c_lessequals(V_m,V_n,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_natgb_Oadd__cancel_0,axiom, % 1.16/1.19 ( c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat) != c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat) % 1.16/1.19 | V_y = V_z ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_nat__add__right__cancel_0,axiom, % 1.16/1.19 ( c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat) != c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat) % 1.16/1.19 | V_m = V_n ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_nat__add__left__cancel_0,axiom, % 1.16/1.19 ( c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) % 1.16/1.19 | V_m = V_n ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_class__ringb_Oadd__cancel_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.16/1.19 | ~ class_Int_Onumber__ring(T_a) % 1.16/1.19 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) % 1.16/1.19 | V_y = V_z ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__imp__eq_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a) % 1.16/1.19 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) % 1.16/1.19 | V_b = V_c ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__left__cancel_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 1.16/1.19 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) % 1.16/1.19 | V_b = V_c ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__right__cancel_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 1.16/1.19 | c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) != c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) % 1.16/1.19 | V_b = V_c ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__minus__cancel_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inverse__eq__1__iff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oinverse__class_Oinverse(V_x,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.16/1.19 | V_x = c_HOL_Oone__class_Oone(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inverse__less__1__iff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_x,T_a) % 1.16/1.19 | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__leI_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.16/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__le__iff_2,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.16/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__1_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_min__add__distrib__left_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.16/1.19 | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__add__diff_0,axiom, % 1.16/1.19 ( c_lessequals(V_m,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_k,tc_nat),tc_nat) % 1.16/1.19 | ~ c_lessequals(V_k,V_n,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__right__le__one__le_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_x,T_a) % 1.16/1.19 | ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__left__le__one__le_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Otimes__class_Otimes(V_y,V_x,T_a),V_x,T_a) % 1.16/1.19 | ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__nonpos__neg_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__nonneg__pos_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mod__diff__eq_0,axiom, % 1.16/1.19 ( ~ class_Divides_Oring__div(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_power__abs_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__of__nat_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_dvd__power__same_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_sup__eq__bot__eq1_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Obounded__lattice(T_a) % 1.16/1.19 | c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,T_a) != c_Orderings_Obot__class_Obot(T_a) % 1.16/1.19 | V_A = c_Orderings_Obot__class_Obot(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_sup__eq__bot__eq2_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Obounded__lattice(T_a) % 1.16/1.19 | c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,T_a) != c_Orderings_Obot__class_Obot(T_a) % 1.16/1.19 | V_B = c_Orderings_Obot__class_Obot(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__inverse_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__strict__right__mono_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__strict__right__mono__neg_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__divide_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__of__pos_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.19 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inverse__positive__iff__positive_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inverse__positive__iff__positive_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_positive__imp__inverse__positive_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mod__mult__left__eq_0,axiom, % 1.16/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mod__mult__right__eq_0,axiom, % 1.16/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__infE_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.19 | c_lessequals(V_x,V_a,T_a) % 1.16/1.19 | ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__infE_1,axiom, % 1.16/1.19 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.19 | c_lessequals(V_x,V_b,T_a) % 1.16/1.19 | ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__infI1_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.19 | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a) % 1.16/1.19 | ~ c_lessequals(V_a,V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__infI2_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.19 | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a) % 1.16/1.19 | ~ c_lessequals(V_b,V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__inf__iff_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.19 | c_lessequals(V_x,V_y,T_a) % 1.16/1.19 | ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__inf__iff_1,axiom, % 1.16/1.19 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.19 | c_lessequals(V_x,V_z,T_a) % 1.16/1.19 | ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__is__1_3,axiom, % 1.16/1.19 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.16/1.19 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.16/1.19 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__is__1_0,axiom, % 1.16/1.19 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.16/1.19 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 1.16/1.19 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_sgn__less_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_sgn__less_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_Suc__diff__diff_0,axiom, % 1.16/1.19 c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat),c_Suc(V_k),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_dvd__minus__iff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.16/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) % 1.16/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_dvd__minus__iff_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.16/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) % 1.16/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_minus__dvd__iff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.16/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) % 1.16/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_minus__dvd__iff_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.16/1.19 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) % 1.16/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_nonzero__minus__divide__divide_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_class__ring_Osub__add_0,axiom, % 1.16/1.19 ( ~ class_Int_Onumber__ring(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_diff__def_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_less__iff__diff__less__0_1,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_less__iff__diff__less__0_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__not__less__zero_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_of__nat__less__iff_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_of__nat__less__iff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_dvd__mult__cancel__right_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_dvd__mult__cancel__left_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_lessI_0,axiom, % 1.16/1.19 c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_less__Suc__eq_2,axiom, % 1.16/1.19 c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_less__trans__Suc_0,axiom, % 1.16/1.19 ( c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__le__cancel__right_1,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__le__cancel__right_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.16/1.19 | c_lessequals(V_a,V_b,T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__le__cancel__left_1,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__le__cancel__left_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.16/1.19 | c_lessequals(V_a,V_b,T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__right__mono_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__left__mono_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__le__mono1_0,axiom, % 1.16/1.19 ( c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat) % 1.16/1.19 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_nat__add__left__cancel__le_0,axiom, % 1.16/1.19 ( c_lessequals(V_m,V_n,tc_nat) % 1.16/1.19 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_nat__add__left__cancel__le_1,axiom, % 1.16/1.19 ( c_lessequals(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) % 1.16/1.19 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__eq__mult_3,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__eq__mult_2,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__eq__mult_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__eq__mult_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__mult_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__less__one_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__frac__frac_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_minus__mult__right_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oring(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_minus__mult__left_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oring(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__imp__diff__is__add_0,axiom, % 1.16/1.19 ( ~ c_lessequals(V_i,V_j,tc_nat) % 1.16/1.19 | V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__add__diff__inverse_0,axiom, % 1.16/1.19 ( c_HOL_Oplus__class_Oplus(V_n,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = V_m % 1.16/1.19 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__add__diff__inverse2_0,axiom, % 1.16/1.19 ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat) = V_m % 1.16/1.19 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__less__cancel1_1,axiom, % 1.16/1.19 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__less__cancel2_1,axiom, % 1.16/1.19 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__eq__neg_1,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.19 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__eq__neg_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__strict__left__mono__neg_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__strict__left__mono_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_less__add__one_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__diff__assoc_0,axiom, % 1.16/1.19 ( c_HOL_Oplus__class_Oplus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat) % 1.16/1.19 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__diff__assoc2_0,axiom, % 1.16/1.19 ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_k,tc_nat) % 1.16/1.19 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_drop__drop_0,axiom, % 1.16/1.19 c_List_Odrop(V_n,c_List_Odrop(V_m,V_xs,T_a),T_a) = c_List_Odrop(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_xs,T_a) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_power__le__imp__le__base_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | c_lessequals(V_a,V_b,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__left__idem_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_one__less__inverse__iff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_neg__le__0__iff__le_1,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_neg__le__0__iff__le_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_of__nat__0__less__iff_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_of__nat__0__less__iff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__less__le__imp__less_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | ~ c_lessequals(V_c,V_d,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__le__less__imp__less_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.16/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_one__dvd_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.19 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_power__inject__exp_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | c_Power_Opower__class_Opower(V_a,V_m,T_a) != c_Power_Opower__class_Opower(V_a,V_n,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 1.16/1.19 | V_m = V_n ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_power__0_0,axiom, % 1.16/1.19 ( ~ class_Power_Opower(T_a) % 1.16/1.19 | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_class__semiring_Opwr__0_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.19 | c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inf__sup__ord_I1_J_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Olattice(T_a) % 1.16/1.19 | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inf__sup__ord_I2_J_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Olattice(T_a) % 1.16/1.19 | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_y,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inf__greatest_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.19 | c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_x,V_z,T_a) % 1.16/1.19 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__inf__iff_2,axiom, % 1.16/1.19 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.19 | c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_x,V_z,T_a) % 1.16/1.19 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__infI_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.19 | c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_x,V_b,T_a) % 1.16/1.19 | ~ c_lessequals(V_x,V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inf__le2_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.19 | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_y,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inf__le1_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.19 | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_sgn__1__neg_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.19 | c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_sgn__neg_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.19 | c_HOL_Osgn__class_Osgn(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_class__semiring_Osemiring__rules_I27_J_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_class__semiring_Osemiring__rules_I28_J_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_com_Osimps_I13_J_0,axiom, % 1.16/1.19 c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ). % 1.16/1.19 % 1.16/1.19 cnf(cls_minus__mult__commute_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oring(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__less__iff_2,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mod__add__self2_0,axiom, % 1.16/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mod__add__self1_0,axiom, % 1.16/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__triangle__ineq4_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_dvd__power__le_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.19 | 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_m,T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_n,V_m,tc_nat) % 1.16/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__le__0__iff_3,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__le__0__iff_2,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__le__0__iff_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__le__0__iff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__pos__neg2_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__pos__neg_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__neg__pos_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__le__D2_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_Suc__leD_0,axiom, % 1.16/1.19 ( c_lessequals(V_m,V_n,tc_nat) % 1.16/1.19 | ~ c_lessequals(c_Suc(V_m),V_n,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__SucI_0,axiom, % 1.16/1.19 ( c_lessequals(V_m,c_Suc(V_n),tc_nat) % 1.16/1.19 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_n__less__m__mult__n_0,axiom, % 1.16/1.19 ( c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_n__less__n__mult__m_0,axiom, % 1.16/1.19 ( c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),tc_nat) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__minus__cancel_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.19 | 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 ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_sup__inf__distrib2_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Odistrib__lattice(T_a) % 1.16/1.19 | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),V_x,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_z,V_x,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_sup__inf__distrib1_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Odistrib__lattice(T_a) % 1.16/1.19 | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_class__fieldgb_Odivide__inverse_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | ~ class_Int_Onumber__ring(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__inverse_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_Suc__n__not__le__n_0,axiom, % 1.16/1.19 ~ c_lessequals(c_Suc(V_n),V_n,tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_dvd__mult__right_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 1.16/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_dvd__mult__left_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 1.16/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_dvd__mult2_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.16/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_dvd__mult_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.16/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_less__diff__iff_0,axiom, % 1.16/1.19 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) % 1.16/1.19 | ~ c_lessequals(V_k,V_n,tc_nat) % 1.16/1.19 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_less__diff__iff_1,axiom, % 1.16/1.19 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.19 | ~ c_lessequals(V_k,V_n,tc_nat) % 1.16/1.19 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_pos__add__strict_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inf__sup__aci_I4_J_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Olattice(T_a) % 1.16/1.19 | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inf__left__idem_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.19 | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__le__iff__nprt__id_1,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.19 | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a) != V_a % 1.16/1.19 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_diff__minus_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_ab__diff__minus_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_Suc__mult__le__cancel1_1,axiom, % 1.16/1.19 ( c_lessequals(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) % 1.16/1.19 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_Suc__mult__le__cancel1_0,axiom, % 1.16/1.19 ( c_lessequals(V_m,V_n,tc_nat) % 1.16/1.19 | ~ c_lessequals(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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_sum__squares__gt__zero__iff_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_sum__squares__gt__zero__iff_2,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__num__frac_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__frac__num_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inf__eq__neg__sup_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.19 | c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_sup__commute_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.19 | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inf__sup__aci_I5_J_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Olattice(T_a) % 1.16/1.19 | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_compl__inf_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.16/1.19 | c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(V_x,T_a),c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_neg__inf__eq__sup_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.19 | c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_of__nat__less__0__iff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__less__0__iff_3,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__less__0__iff_2,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__less__0__iff_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__less__0__iff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_less__half__sum_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_gt__half__sum_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_group__add__class_Odiff__0_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_min__max_Osup__commute_0,axiom, % 1.16/1.19 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.19 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = c_Orderings_Oord__class_Omax(V_y,V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_power__eq__imp__eq__base_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_Power_Opower__class_Opower(V_b,V_n,T_a) % 1.16/1.19 | V_a = V_b % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__cancel__end_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.16/1.19 | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != V_y % 1.16/1.19 | V_x = c_HOL_Ouminus__class_Ouminus(V_z,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__sgn_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.19 | c_HOL_Oabs__class_Oabs(V_k,T_a) = c_HOL_Otimes__class_Otimes(V_k,c_HOL_Osgn__class_Osgn(V_k,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__divide__mult__cancel__left_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__divide__mult__cancel__right_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_division__ring__inverse__add_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.19 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inverse__add_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.19 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_dvd__add_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) % 1.16/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 1.16/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__Suc__eq_2,axiom, % 1.16/1.19 c_lessequals(c_Suc(V_n),c_Suc(V_n),tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_one__less__inverse__iff_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_sup__left__idem_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.19 | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inf__sup__aci_I8_J_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Olattice(T_a) % 1.16/1.19 | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_drop__replicate_0,axiom, % 1.16/1.19 c_List_Odrop(V_i,c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(V_k,V_i,tc_nat),V_x,T_a) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_min__max_Odistrib__inf__le_0,axiom, % 1.16/1.19 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.19 | c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),c_Orderings_Oord__class_Omin(V_x,V_z,T_a),T_a),c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__le__pprt_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__less__divide__iff_5,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__less__divide__iff_4,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__pos__pos_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__neg__neg_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_compl__sup_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.16/1.19 | c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_x,T_a),c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_neg__sup__eq__inf_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.19 | c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_nat_Osize_I2_J_0,axiom, % 1.16/1.19 c_nat_Onat__size(c_Suc(V_nat)) = c_HOL_Oplus__class_Oplus(c_nat_Onat__size(V_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_min__max_Osup__inf__absorb_0,axiom, % 1.16/1.19 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.19 | c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) = V_x ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mod__minus__eq_0,axiom, % 1.16/1.19 ( ~ class_Divides_Oring__div(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__square_0,axiom, % 1.16/1.19 c_lessequals(V_m,c_HOL_Otimes__class_Otimes(V_m,V_m,tc_nat),tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_pprt__neg_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.19 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_x,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__less__cancel__left__disj_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__less__cancel__left__disj_3,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__less__cancel__right__disj_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__less__cancel__right__disj_3,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__frac__num_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_diff__diff__cancel_0,axiom, % 1.16/1.19 ( c_HOL_Ominus__class_Ominus(V_n,c_HOL_Ominus__class_Ominus(V_n,V_i,tc_nat),tc_nat) = V_i % 1.16/1.19 | ~ c_lessequals(V_i,V_n,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_power__Suc__less_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_com_Osize_I4_J_0,axiom, % 1.16/1.19 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(V_com1,V_com2)) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Com_Ocom_Ocom__size(V_com1),c_Com_Ocom_Ocom__size(V_com2),tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_min__Suc__Suc_0,axiom, % 1.16/1.19 c_Orderings_Oord__class_Omin(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(V_m,V_n,tc_nat)) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__SucE_0,axiom, % 1.16/1.19 ( V_m = c_Suc(V_n) % 1.16/1.19 | c_lessequals(V_m,V_n,tc_nat) % 1.16/1.19 | ~ c_lessequals(V_m,c_Suc(V_n),tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_not__less__less__Suc__eq_1,axiom, % 1.16/1.19 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_not__less__eq_1,axiom, % 1.16/1.19 ( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_not__less__eq_0,axiom, % 1.16/1.19 ( c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__of__nonpos_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.19 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.16/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__less__cancel2_2,axiom, % 1.16/1.19 ( 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__less__cancel1_2,axiom, % 1.16/1.19 ( 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__less__mono2_0,axiom, % 1.16/1.19 ( 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__less__mono1_0,axiom, % 1.16/1.19 ( 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_nat__mult__less__cancel1_0,axiom, % 1.16/1.19 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.19 | ~ 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_nat__mult__less__cancel1_1,axiom, % 1.16/1.19 ( 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__less__cancel__left__neg_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.16/1.19 | ~ 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__less__cancel__left__neg_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__less__cancel__left__pos_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.16/1.19 | ~ 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__less__cancel__left__pos_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__strict__left__mono__neg_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__strict__left__mono_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__less__cancel__left__disj_4,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__less__cancel__left__disj_5,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__strict__right__mono__neg_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__strict__right__mono_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__less__cancel__right__disj_4,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__less__cancel__right__disj_5,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__strict__left__mono__comm_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_less__divide__eq_9,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_less__divide__eq_8,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_less__divide__eq_3,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_less__divide__eq_2,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__less__eq_9,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__less__eq_8,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__less__eq_3,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__less__eq_2,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_max__add__distrib__left_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.16/1.19 | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_sgn__sgn_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.19 | c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) = c_HOL_Osgn__class_Osgn(V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_power__inject__base_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_a = V_b % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__le__mono_0,axiom, % 1.16/1.19 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_l,tc_nat),tc_nat) % 1.16/1.19 | ~ c_lessequals(V_k,V_l,tc_nat) % 1.16/1.19 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__cube_0,axiom, % 1.16/1.19 c_lessequals(V_m,c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_m,V_m,tc_nat),tc_nat),tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__mono_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ c_lessequals(V_c,V_d,T_a) % 1.16/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__mono_H_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | ~ c_lessequals(V_c,V_d,T_a) % 1.16/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_field__inverse_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_left__inverse_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_right__inverse_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__le__iff__nprt__id_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.19 | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a) = V_a % 1.16/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mod__mod__cancel_0,axiom, % 1.16/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_com_Osize_I9_J_0,axiom, % 1.16/1.19 c_Nat_Osize__class_Osize(c_Com_Ocom_OSKIP,tc_Com_Ocom) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__less__divide__1__iff_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__less__divide__1__iff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.19 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__if__lattice_1,axiom, % 1.16/1.19 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.19 | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.16/1.19 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__if_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oabs__if(T_a) % 1.16/1.19 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_power__strict__increasing__iff_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_power__strict__increasing__iff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 1.16/1.19 | ~ 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_power__strict__increasing_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_power__less__imp__less__exp_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.19 | ~ 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_not__add__less1_0,axiom, % 1.16/1.19 ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_i,tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_not__add__less2_0,axiom, % 1.16/1.19 ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_i,tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_nonzero__power__divide_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inverse__negative__imp__negative_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_of__nat__diff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oring__1(T_a) % 1.16/1.19 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_power__less__power__Suc_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inverse__divide_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__dvd__mono_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_d,T_a) % 1.16/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__right__mono__neg_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__left__mono__neg_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__right__mono_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__left__mono_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__mono1_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Omult__mono1(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_sup__eq__if_1,axiom, % 1.16/1.19 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.19 | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.19 | c_Lattices_Oupper__semilattice__class_Osup(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_prts_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.19 | V_a = c_HOL_Oplus__class_Oplus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.16/1.19 | ~ class_Int_Onumber__ring(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_c = V_d % 1.16/1.19 | V_r = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_natgb_Oadd__scale__eq__noteq_0,axiom, % 1.16/1.19 ( 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) % 1.16/1.19 | V_c = V_d % 1.16/1.19 | V_r = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_sum__squares__eq__zero__iff_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_sum__squares__eq__zero__iff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__add__abs_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_less__diff__conv_0,axiom, % 1.16/1.19 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_less__diff__conv_1,axiom, % 1.16/1.19 ( c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__le__eq_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__le__eq_4,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__divide__eq_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__divide__eq_4,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_Suc__n__not__n_0,axiom, % 1.16/1.19 c_Suc(V_n) != V_n ). % 1.16/1.19 % 1.16/1.19 cnf(cls_n__not__Suc__n_0,axiom, % 1.16/1.19 V_n != c_Suc(V_n) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inverse__unique_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.16/1.19 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.16/1.19 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__less__abs__iff_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inf__idem_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.16/1.19 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_x,T_a) = V_x ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__imp__less__div__pos_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__imp__div__pos__less_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__less__eq_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__less__eq_6,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_less__divide__eq_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_less__divide__eq_6,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__neg__pos_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__pos__neg_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__less__0__iff_4,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__less__0__iff_5,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__sup__iff_1,axiom, % 1.16/1.19 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.19 | c_lessequals(V_y,V_z,T_a) % 1.16/1.19 | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__sup__iff_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.19 | c_lessequals(V_x,V_z,T_a) % 1.16/1.19 | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__supI2_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.19 | c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_x,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__supI1_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.19 | c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_x,V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__supE_1,axiom, % 1.16/1.19 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.19 | c_lessequals(V_b,V_x,T_a) % 1.16/1.19 | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__supE_0,axiom, % 1.16/1.19 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.19 | c_lessequals(V_a,V_x,T_a) % 1.16/1.19 | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_dvd__power_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__strict__right__mono_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__less__cancel__right_1,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__less__cancel__right_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__strict__left__mono_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__less__cancel__left_1,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__less__cancel__left_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__less__mono1_0,axiom, % 1.16/1.19 ( 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_nat__add__left__cancel__less_0,axiom, % 1.16/1.19 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_nat__add__left__cancel__less_1,axiom, % 1.16/1.19 ( 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) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_one__le__mult__iff_2,axiom, % 1.16/1.19 ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) % 1.16/1.19 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) % 1.16/1.19 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_xt1_I6_J_0,axiom, % 1.16/1.19 ( ~ class_Orderings_Oorder(T_a) % 1.16/1.19 | c_lessequals(V_z,V_x,T_a) % 1.16/1.19 | ~ c_lessequals(V_z,V_y,T_a) % 1.16/1.19 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_xt1_I7_J_0,axiom, % 1.16/1.19 ( ~ class_Orderings_Oorder(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.16/1.19 | ~ c_lessequals(V_z,V_y,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_xt1_I8_J_0,axiom, % 1.16/1.19 ( ~ class_Orderings_Oorder(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.16/1.19 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__nonpos__nonpos_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_power__le__dvd_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.19 | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_b,T_a) % 1.16/1.19 | ~ c_lessequals(V_m,V_n,tc_nat) % 1.16/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_order__trans_0,axiom, % 1.16/1.19 ( ~ class_Orderings_Opreorder(T_a) % 1.16/1.19 | c_lessequals(V_x,V_z,T_a) % 1.16/1.19 | ~ c_lessequals(V_y,V_z,T_a) % 1.16/1.19 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__refl_0,axiom, % 1.16/1.19 c_lessequals(V_n,V_n,tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__trans_0,axiom, % 1.16/1.19 ( c_lessequals(V_i,V_k,tc_nat) % 1.16/1.19 | ~ c_lessequals(V_j,V_k,tc_nat) % 1.16/1.19 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_eq__imp__le_0,axiom, % 1.16/1.19 c_lessequals(V_x,V_x,tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_order__eq__iff_0,axiom, % 1.16/1.19 ( ~ class_Orderings_Oorder(T_a) % 1.16/1.19 | c_lessequals(V_x,V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_order__eq__refl_0,axiom, % 1.16/1.19 ( ~ class_Orderings_Opreorder(T_a) % 1.16/1.19 | c_lessequals(V_x,V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_order__le__less__trans_0,axiom, % 1.16/1.19 ( ~ class_Orderings_Opreorder(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.16/1.19 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_order__less__le__trans_0,axiom, % 1.16/1.19 ( ~ class_Orderings_Opreorder(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.16/1.19 | ~ c_lessequals(V_y,V_z,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__add__right__mono_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.19 | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_c,V_d,T_a) % 1.16/1.19 | ~ c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_inverse__less__1__iff_2,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_min__diff_0,axiom, % 1.16/1.19 c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(V_m,V_i,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_i,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(V_m,V_n,tc_nat),V_i,tc_nat) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__is__1_5,axiom, % 1.16/1.19 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)) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__less__divide__iff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__less__divide__iff_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__less__divide__iff_2,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__less__divide__iff_3,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__nonneg__neg_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__nonpos__pos_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.16/1.19 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__idem_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 1.16/1.19 | c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = V_x ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mod__mult__self2__is__0_0,axiom, % 1.16/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mod__mult__self1__is__0_0,axiom, % 1.16/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mult__strict__mono_H_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__less__Suc__eq_0,axiom, % 1.16/1.19 ( V_n = V_m % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 1.16/1.19 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_division__ring__inverse__diff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.19 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_square__eq__iff_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_min__max_Osup__assoc_0,axiom, % 1.16/1.19 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.19 | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_minus__mult__minus_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oring(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_min__max_Osup__left__commute_0,axiom, % 1.16/1.19 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.19 | c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omax(V_y,c_Orderings_Oord__class_Omax(V_x,V_z,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_diff__minus__eq__add_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__less__two_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mod__mult__self1_0,axiom, % 1.16/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_mod__mult__self2_0,axiom, % 1.16/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_diff__frac__eq_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.19 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_dvd__mult__cancel__left_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.16/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) % 1.16/1.19 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_dvd__mult__cancel__right_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.16/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) % 1.16/1.19 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_abs__one_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.19 | c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_of__nat__0__le__iff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__le__imp__of__nat_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_nonzero__inverse__eq__divide_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | 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) % 1.16/1.19 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_sum__squares__gt__zero__iff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | ~ 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__divide__eq_9,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__divide__eq_3,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_le__divide__eq_2,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__le__eq_9,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.16/1.19 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__le__eq_3,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_divide__le__eq_2,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_min__max_Osup__left__idem_0,axiom, % 1.16/1.19 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.19 | c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) = c_Orderings_Oord__class_Omax(V_x,V_y,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__le__mult__iff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__le__mult__iff_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__le__mult__iff_2,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_zero__le__mult__iff_3,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.19 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_id__apply_0,axiom, % 1.16/1.19 c_Fun_Oid(V_x,T_a) = V_x ). % 1.16/1.19 % 1.16/1.19 cnf(cls_diff__add__inverse2_0,axiom, % 1.16/1.19 c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_n,tc_nat) = V_m ). % 1.16/1.19 % 1.16/1.19 cnf(cls_diff__add__inverse_0,axiom, % 1.16/1.19 c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_n,tc_nat) = V_m ). % 1.16/1.19 % 1.16/1.19 cnf(cls_add__diff__cancel_0,axiom, % 1.16/1.19 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.19 | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_one__le__inverse__iff_2,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_power__le__imp__le__exp_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | c_lessequals(V_m,V_n,tc_nat) % 1.16/1.19 | ~ c_lessequals(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_power__increasing__iff_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | c_lessequals(V_x,V_y,tc_nat) % 1.16/1.19 | ~ c_lessequals(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_power__increasing__iff_1,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.19 | c_lessequals(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a) % 1.16/1.19 | ~ c_lessequals(V_x,V_y,tc_nat) % 1.16/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_minus__divide__right_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.19 % 1.16/1.19 cnf(cls_minus__divide__left_0,axiom, % 1.16/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.19 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_add__divide__distrib_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_less__1__mult_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.16/1.20 | 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) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_n,T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_m,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_abs__minus__commute_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_minus__minus_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.20 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_double__compl_0,axiom, % 1.16/1.20 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.16/1.20 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = V_x ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_equation__minus__iff_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.20 | V_b = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_equation__minus__iff_1,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.20 | V_a = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_minus__equation__iff_1,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.20 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_less__supI1_0,axiom, % 1.16/1.20 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_x,V_a,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_less__supI2_0,axiom, % 1.16/1.20 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_x,V_b,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_minus__diff__eq_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_add__le__less__mono_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.16/1.20 | 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) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.16/1.20 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_add__less__le__mono_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.16/1.20 | 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) % 1.16/1.20 | ~ c_lessequals(V_c,V_d,T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_less__Suc__eq__0__disj_3,axiom, % 1.16/1.20 ( c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_x,V_n,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_Suc__less__eq_0,axiom, % 1.16/1.20 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_Suc__mono_0,axiom, % 1.16/1.20 ( c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_evalc__elim__cases_I1_J_0,axiom, % 1.16/1.20 ( V_t = V_s % 1.16/1.20 | ~ c_Natural_Oevalc(c_Com_Ocom_OSKIP,V_s,V_t) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_add__gr__0_2,axiom, % 1.16/1.20 ( 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) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_add__gr__0_1,axiom, % 1.16/1.20 ( 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) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.16/1.20 | ~ 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.20 | 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) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_le__minus__iff_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.20 | c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.16/1.20 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_le__minus__iff_1,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.20 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.16/1.20 | ~ c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_minus__le__iff_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.20 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) % 1.16/1.20 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_minus__le__iff_1,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.20 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.16/1.20 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_less__minus__iff_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_less__minus__iff_1,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_minus__less__iff_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_minus__less__iff_1,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_eq__divide__eq_2,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.20 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_inverse__nonzero__iff__nonzero_1,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.16/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.20 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_inverse__zero_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.20 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_nonzero__inverse__eq__imp__eq_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.16/1.20 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a) % 1.16/1.20 | V_a = V_b % 1.16/1.20 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_abs__eq__0_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.20 | c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_minus__zero_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.20 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_neg__equal__zero_1,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.16/1.20 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_nprt__0_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.20 | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_inverse__nonzero__iff__nonzero_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.16/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.20 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_inverse__zero__imp__zero_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.16/1.20 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_power__eq__0__iff_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.16/1.20 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.16/1.20 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.16/1.20 | ~ class_Power_Opower(T_a) % 1.16/1.20 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_field__power__not__zero_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(T_a) % 1.16/1.20 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_neg__0__equal__iff__equal_1,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.20 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_sgn0_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Osgn__if(T_a) % 1.16/1.20 | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_sgn__0__0_1,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.20 | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_class__semiring_Omul__0_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.20 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mult__zero__left_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 1.16/1.20 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mult__zero__right_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 1.16/1.20 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mult__eq__0__iff_1,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.16/1.20 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mult__eq__0__iff_2,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.16/1.20 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.20 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.20 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_neg__equal__0__iff__equal_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.20 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_dvd__0__right_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.20 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_one__neq__zero_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.16/1.20 | c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_no__zero__divirors__neq0_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.16/1.20 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_no__zero__divisors_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.16/1.20 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mult__eq__0__iff_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.16/1.20 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_double__eq__0__iff_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.20 | c_HOL_Oplus__class_Oplus(V_a,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_class__ringb_Osubr0__iff_1,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.16/1.20 | ~ class_Int_Onumber__ring(T_a) % 1.16/1.20 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_diff__self_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.20 | c_HOL_Ominus__class_Ominus(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_diff__0__right_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.20 | c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_right__minus__eq_1,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.20 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mult__le__mono1_0,axiom, % 1.16/1.20 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_k,tc_nat),tc_nat) % 1.16/1.20 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mult__le__mono2_0,axiom, % 1.16/1.20 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_j,tc_nat),tc_nat) % 1.16/1.20 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mult__le__cancel1_2,axiom, % 1.16/1.20 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 1.16/1.20 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mult__le__cancel2_2,axiom, % 1.16/1.20 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) % 1.16/1.20 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_zero__less__diff_0,axiom, % 1.16/1.20 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_zero__less__diff_1,axiom, % 1.16/1.20 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_Suc__lessD_0,axiom, % 1.16/1.20 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_less__SucI_0,axiom, % 1.16/1.20 ( c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_inverse__eq__iff__eq_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.16/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.20 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a) % 1.16/1.20 | V_a = V_b ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_sum__squares__eq__zero__iff_2,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mult__less__cancel__right__disj_2,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.16/1.20 | ~ 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mult__less__cancel__right__disj_1,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.20 | ~ 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mult__less__cancel__left__disj_2,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.16/1.20 | ~ 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mult__less__cancel__left__disj_1,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.20 | ~ 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_Suc__mult__cancel1_0,axiom, % 1.16/1.20 ( 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) % 1.16/1.20 | V_m = V_n ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_Suc__pred_0,axiom, % 1.16/1.20 ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_of__nat__add_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_diff__less_0,axiom, % 1.16/1.20 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_min__max_Odistrib__sup__le_0,axiom, % 1.16/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.20 | c_lessequals(c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),c_Orderings_Oord__class_Omax(V_x,V_z,T_a),T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_sup__eq__neg__inf_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.20 | c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_le__eqI_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.20 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.16/1.20 | c_lessequals(V_y_H,V_x_H,T_a) % 1.16/1.20 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_le__eqI_1,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.20 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.16/1.20 | c_lessequals(V_y,V_x,T_a) % 1.16/1.20 | ~ c_lessequals(V_y_H,V_x_H,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_less__eqI_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.20 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_less__eqI_1,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.20 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_power__mult__distrib_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_class__semiring_Opwr__mul_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_zmod__simps_I1_J_0,axiom, % 1.16/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_zmod__simps_I2_J_0,axiom, % 1.16/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_neg__0__less__iff__less_1,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_neg__0__less__iff__less_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_add__diff__inverse_0,axiom, % 1.16/1.20 ( c_HOL_Oplus__class_Oplus(V_n,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = V_m % 1.16/1.20 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_diff__Suc__less_0,axiom, % 1.16/1.20 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_n,c_Suc(V_i),tc_nat),V_n,tc_nat) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_inf__period_I4_J_1,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Odvd(T_a) % 1.16/1.20 | ~ class_Ring__and__Field_Ocomm__ring(T_a) % 1.16/1.20 | c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a) % 1.16/1.20 | ~ 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) % 1.16/1.20 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_inf__period_I4_J_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Odvd(T_a) % 1.16/1.20 | ~ class_Ring__and__Field_Ocomm__ring(T_a) % 1.16/1.20 | 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) % 1.16/1.20 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a) % 1.16/1.20 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_frac__eq__eq_1,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.20 | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) != c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) % 1.16/1.20 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_frac__eq__eq_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.20 | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) != c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) % 1.16/1.20 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) = c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_add__is__1_1,axiom, % 1.16/1.20 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.16/1.20 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.16/1.20 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_add__is__1_2,axiom, % 1.16/1.20 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.16/1.20 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 1.16/1.20 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_min__max_Osup__inf__distrib2_0,axiom, % 1.16/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.20 | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_y,V_z,T_a),V_x,T_a) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_y,V_x,T_a),c_Orderings_Oord__class_Omax(V_z,V_x,T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_min__max_Osup__inf__distrib1_0,axiom, % 1.16/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.20 | c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),c_Orderings_Oord__class_Omax(V_x,V_z,T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_power__mult_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_xt1_I11_J_0,axiom, % 1.16/1.20 ( ~ class_Orderings_Oorder(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.16/1.20 | V_a = V_b % 1.16/1.20 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_xt1_I12_J_0,axiom, % 1.16/1.20 ( ~ class_Orderings_Oorder(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.16/1.20 | ~ c_lessequals(V_b,V_a,T_a) % 1.16/1.20 | V_a = V_b ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_nat__less__le_2,axiom, % 1.16/1.20 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.20 | V_m = V_n % 1.16/1.20 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_le__eq__less__or__eq_0,axiom, % 1.16/1.20 ( V_m = V_n % 1.16/1.20 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.20 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_le__neq__implies__less_0,axiom, % 1.16/1.20 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.16/1.20 | V_m = V_n % 1.16/1.20 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_order__le__less_0,axiom, % 1.16/1.20 ( ~ class_Orderings_Oorder(T_a) % 1.16/1.20 | V_x = V_y % 1.16/1.20 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.16/1.20 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_order__less__le_2,axiom, % 1.16/1.20 ( ~ class_Orderings_Oorder(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.16/1.20 | V_x = V_y % 1.16/1.20 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_order__le__neq__trans_0,axiom, % 1.16/1.20 ( ~ class_Orderings_Oorder(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.16/1.20 | V_a = V_b % 1.16/1.20 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_order__neq__le__trans_0,axiom, % 1.16/1.20 ( ~ class_Orderings_Oorder(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.16/1.20 | ~ c_lessequals(V_a,V_b,T_a) % 1.16/1.20 | V_a = V_b ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_linorder__antisym__conv1_0,axiom, % 1.16/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.20 | V_x = V_y % 1.16/1.20 | ~ c_lessequals(V_x,V_y,T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_linorder__antisym__conv2_0,axiom, % 1.16/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.20 | V_x = V_y % 1.16/1.20 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.16/1.20 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_divide__right__mono__neg_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.20 | 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) % 1.16/1.20 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.20 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_divide__right__mono_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.20 | 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) % 1.16/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.16/1.20 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_power__inverse_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.16/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_inverse__minus__eq_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.16/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_sgn__times_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.20 | c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Osgn__class_Osgn(V_b,T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mult__nonneg__nonneg_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.16/1.20 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.16/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_zero__le__mult__iff_5,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.20 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.16/1.20 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.20 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_zero__le__mult__iff_4,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.20 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.16/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_zero__le__square_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.16/1.20 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mult__nonpos__nonpos_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.16/1.20 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.16/1.20 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.20 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_split__mult__pos__le_1,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.16/1.20 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.16/1.20 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.20 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_split__mult__pos__le_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.16/1.20 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.16/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.16/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mod__mult__mult2_0,axiom, % 1.16/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mod__mult__mult1_0,axiom, % 1.16/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_less__minus__self__iff_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_less__minus__self__iff_1,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_right__inverse__eq_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.20 | c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.16/1.20 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_a = V_b ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_abs__ge__zero_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.20 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_class__ring_Oneg__mul_0,axiom, % 1.16/1.20 ( ~ class_Int_Onumber__ring(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_Suc__le__mono_0,axiom, % 1.16/1.20 ( c_lessequals(V_n,V_m,tc_nat) % 1.16/1.20 | ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_Suc__le__mono_1,axiom, % 1.16/1.20 ( c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) % 1.16/1.20 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_divide__eq__eq_4,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_sgn__1__pos_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.20 | c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.16/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_sgn__pos_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.20 | c_HOL_Osgn__class_Osgn(V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_abs__triangle__ineq2_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_nat__mult__assoc_0,axiom, % 1.16/1.20 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) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_class__semiring_Omul__a_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_comm__semiring__class_Odistrib_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_add__mult__distrib_0,axiom, % 1.16/1.20 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) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_add__mult__distrib2_0,axiom, % 1.16/1.20 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) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_class__semiring_Omul__d_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_dvd__if__abs__eq_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.20 | c_HOL_Oabs__class_Oabs(V_l,T_a) != c_HOL_Oabs__class_Oabs(V_k,T_a) % 1.16/1.20 | c_Ring__and__Field_Odvd__class_Odvd(V_l,V_k,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_minus__add__distrib_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_minus__add_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_com_Osimps_I12_J_0,axiom, % 1.16/1.20 c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_frac__less_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.16/1.20 | 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) % 1.16/1.20 | ~ c_lessequals(V_w,V_z,T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.16/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_xt1_I9_J_0,axiom, % 1.16/1.20 ( ~ class_Orderings_Oorder(T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_not__less__iff__gr__or__eq_1,axiom, % 1.16/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_nat__le__linear_0,axiom, % 1.16/1.20 ( c_lessequals(V_n,V_m,tc_nat) % 1.16/1.20 | c_lessequals(V_m,V_n,tc_nat) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_linorder__linear_0,axiom, % 1.16/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.16/1.20 | c_lessequals(V_y,V_x,T_a) % 1.16/1.20 | c_lessequals(V_x,V_y,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_order__less__asym_0,axiom, % 1.16/1.20 ( ~ class_Orderings_Opreorder(T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_order__less__asym_H_0,axiom, % 1.16/1.20 ( ~ class_Orderings_Opreorder(T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.16/1.20 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_eq__iff__diff__eq__0_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.16/1.20 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_class__ringb_Oadd__r0__iff_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.16/1.20 | ~ class_Int_Onumber__ring(T_a) % 1.16/1.20 | V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) % 1.16/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mod__self_0,axiom, % 1.16/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.20 | c_Divides_Odiv__class_Omod(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mod__by__0_0,axiom, % 1.16/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.20 | c_Divides_Odiv__class_Omod(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_pprt__0_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.20 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mod__0_0,axiom, % 1.16/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 1.16/1.20 | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_double__eq__0__iff_1,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_abs__eq__0_1,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.16/1.20 | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_neg__0__equal__iff__equal_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.20 | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.16/1.20 | c_HOL_Ozero__class_Ozero(T_a) = V_a ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_zero__neq__one_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.16/1.20 | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_nonzero__inverse__inverse__eq_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.16/1.20 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a % 1.16/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_dvd__0__left_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_class__ringb_Osubr0__iff_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.16/1.20 | ~ class_Int_Onumber__ring(T_a) % 1.16/1.20 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_x = V_y ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_right__minus__eq_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.16/1.20 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_a = V_b ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_eq__iff__diff__eq__0_1,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.16/1.20 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_a = V_b ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_divide__eq__eq_1,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.20 | c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_divide__zero_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.20 | c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_divide__zero__left_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.20 | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_divide__self__if_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.16/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_sgn__0__0_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.16/1.20 | c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.16/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_class__semiring_Oadd__0_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.20 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = V_x ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_comm__monoid__add_Omult__1_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.16/1.20 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_class__ringb_Oadd__r0__iff_1,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.16/1.20 | ~ class_Int_Onumber__ring(T_a) % 1.16/1.20 | V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_comm__monoid__add_Omult__1__right_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.16/1.20 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_add__0__left_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 1.16/1.20 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_monoid__add__class_Oadd__0__right_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 1.16/1.20 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.20 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.16/1.20 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_neg__equal__zero_0,axiom, % 1.16/1.20 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.16/1.20 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != V_a % 1.16/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_power__0__left_0,axiom, % 1.16/1.20 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 1.16/1.20 | ~ class_Power_Opower(T_a) % 1.16/1.20 | 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) ) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_nat_Osize_I3_J_0,axiom, % 1.16/1.20 c_Nat_Osize__class_Osize(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_le__0__eq_1,axiom, % 1.16/1.20 c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mult__cancel2_1,axiom, % 1.16/1.20 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) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_mult__cancel1_1,axiom, % 1.16/1.20 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) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_neq0__conv_1,axiom, % 1.16/1.20 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.16/1.20 % 1.16/1.20 cnf(cls_gr0I_0,axiom, % 1.29/1.20 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.29/1.20 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_Suc__neq__Zero_0,axiom, % 1.29/1.20 c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_nat_Osimps_I3_J_0,axiom, % 1.29/1.20 c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_diffs0__imp__equal_0,axiom, % 1.29/1.20 ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.29/1.20 | c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.29/1.20 | V_m = V_n ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_le__0__eq_0,axiom, % 1.29/1.20 ( V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 1.29/1.20 | ~ c_lessequals(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_mult__is__0_2,axiom, % 1.29/1.20 c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_mult__is__0_1,axiom, % 1.29/1.20 c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_mult__is__0_0,axiom, % 1.29/1.20 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.29/1.20 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 1.29/1.20 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_add__is__0_1,axiom, % 1.29/1.20 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.29/1.20 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_add__is__0_0,axiom, % 1.29/1.20 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.29/1.20 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_min__0R_0,axiom, % 1.29/1.20 c_Orderings_Oord__class_Omin(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_min__0L_0,axiom, % 1.29/1.20 c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_mult__cancel2_0,axiom, % 1.29/1.20 ( c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat) != c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat) % 1.29/1.20 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) % 1.29/1.20 | V_m = V_n ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_mult__cancel1_0,axiom, % 1.29/1.20 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) % 1.29/1.20 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) % 1.29/1.20 | V_m = V_n ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_nat__mult__eq__cancel__disj_0,axiom, % 1.29/1.20 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) % 1.29/1.20 | V_m = V_n % 1.29/1.20 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_minus__nat_Odiff__0_0,axiom, % 1.29/1.20 c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ). % 1.29/1.20 % 1.29/1.20 cnf(cls_diff__self__eq__0_0,axiom, % 1.29/1.20 c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_natgb_Oadd__r0__iff_0,axiom, % 1.29/1.20 ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) % 1.29/1.20 | V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_add__eq__self__zero_0,axiom, % 1.29/1.20 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != V_m % 1.29/1.20 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_Zero__neq__Suc_0,axiom, % 1.29/1.20 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_nat_Osimps_I2_J_0,axiom, % 1.29/1.20 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_nat__gcd_Osimps_0,axiom, % 1.29/1.20 c_Nitpick_Onat__gcd(V_x,c_HOL_Ozero__class_Ozero(tc_nat)) = V_x ). % 1.29/1.20 % 1.29/1.20 cnf(cls_nat_Osize_I1_J_0,axiom, % 1.29/1.20 c_nat_Onat__size(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_char__size_0,axiom, % 1.29/1.20 c_String_Ochar_Ochar__size(V_c) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_add__is__0_2,axiom, % 1.29/1.20 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) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_gr__implies__not0_0,axiom, % 1.29/1.20 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_not__less0_0,axiom, % 1.29/1.20 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_bot__nat__def_0,axiom, % 1.29/1.20 c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_drop__0_0,axiom, % 1.29/1.20 c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),V_xs,T_a) = V_xs ). % 1.29/1.20 % 1.29/1.20 cnf(cls_diff__0__eq__0_0,axiom, % 1.29/1.20 c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_le0_0,axiom, % 1.29/1.20 c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_size__char_0,axiom, % 1.29/1.20 c_Nat_Osize__class_Osize(V_c,tc_String_Ochar) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_replicate__eq__replicate_2,axiom, % 1.29/1.20 c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_max__0R_0,axiom, % 1.29/1.20 c_Orderings_Oord__class_Omax(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_n ). % 1.29/1.20 % 1.29/1.20 cnf(cls_max__0L_0,axiom, % 1.29/1.20 c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ). % 1.29/1.20 % 1.29/1.20 cnf(cls_replicate__eq__replicate_1,axiom, % 1.29/1.20 ( c_List_Oreplicate(V_m,V_x,T_a) != c_List_Oreplicate(V_n,V_y,T_a) % 1.29/1.20 | V_x = V_y % 1.29/1.20 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_natgb_Oadd__r0__iff_1,axiom, % 1.29/1.20 V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_plus__nat_Oadd__0_0,axiom, % 1.29/1.20 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ). % 1.29/1.20 % 1.29/1.20 cnf(cls_Nat_Oadd__0__right_0,axiom, % 1.29/1.20 c_HOL_Oplus__class_Oplus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ). % 1.29/1.20 % 1.29/1.20 cnf(cls_pprt__def__raw_0,axiom, % 1.29/1.20 ( ~ class_OrderedGroup_Olordered__ab__group__add(t_a) % 1.29/1.20 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(v_x,t_a) = c_Lattices_Oupper__semilattice__class_Osup(v_x,c_HOL_Ozero__class_Ozero(t_a),t_a) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_nprt__def__raw_0,axiom, % 1.29/1.20 ( ~ class_OrderedGroup_Olordered__ab__group__add(t_a) % 1.29/1.20 | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(v_x,t_a) = c_Lattices_Olower__semilattice__class_Oinf(v_x,c_HOL_Ozero__class_Ozero(t_a),t_a) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_id__def_0,axiom, % 1.29/1.20 c_Fun_Oid(v_x,t_a) = v_x ). % 1.29/1.20 % 1.29/1.20 cnf(cls_evaln__nonstrict_0,axiom, % 1.29/1.20 ( c_Natural_Oevaln(V_c,V_s,V_m,V_t) % 1.29/1.20 | ~ c_lessequals(V_n,V_m,tc_nat) % 1.29/1.20 | ~ c_Natural_Oevaln(V_c,V_s,V_n,V_t) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_evaln_OSkip_0,axiom, % 1.29/1.20 c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_evaln__Suc_0,axiom, % 1.29/1.20 ( c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H) % 1.29/1.20 | ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_evaln__max2_1,axiom, % 1.29/1.20 ( c_Natural_Oevaln(V_c2,V_s2,c_Natural_Osko__Natural__Xevaln__max2__1__1(V_c1,V_c2,V_s1,V_s2,V_t1,V_t2),V_t2) % 1.29/1.20 | ~ c_Natural_Oevaln(V_c2,V_s2,V_n2,V_t2) % 1.29/1.20 | ~ c_Natural_Oevaln(V_c1,V_s1,V_n1,V_t1) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_evaln__max2_0,axiom, % 1.29/1.20 ( c_Natural_Oevaln(V_c1,V_s1,c_Natural_Osko__Natural__Xevaln__max2__1__1(V_c1,V_c2,V_s1,V_s2,V_t1,V_t2),V_t1) % 1.29/1.20 | ~ c_Natural_Oevaln(V_c2,V_s2,V_n2,V_t2) % 1.29/1.20 | ~ c_Natural_Oevaln(V_c1,V_s1,V_n1,V_t1) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_evaln_OSemi_0,axiom, % 1.29/1.20 ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_n,V_s2) % 1.29/1.20 | ~ c_Natural_Oevaln(V_c1,V_s1,V_n,V_s2) % 1.29/1.20 | ~ c_Natural_Oevaln(V_c0,V_s0,V_n,V_s1) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_evaln__elim__cases_I1_J_0,axiom, % 1.29/1.20 ( V_t = V_s % 1.29/1.20 | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_evaln__evalc_0,axiom, % 1.29/1.20 ( c_Natural_Oevalc(V_c,V_s,V_t) % 1.29/1.20 | ~ c_Natural_Oevaln(V_c,V_s,V_n,V_t) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_eval__eq_1,axiom, % 1.29/1.20 ( c_Natural_Oevalc(V_c,V_s,V_t) % 1.29/1.20 | ~ c_Natural_Oevaln(V_c,V_s,V_x,V_t) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_evaln__elim__cases_I6_J_0,axiom, % 1.29/1.20 ( V_n = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1)) % 1.29/1.20 | ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_com_Osimps_I19_J_0,axiom, % 1.29/1.20 c_Com_Ocom_OBODY(V_pname_H) != c_Com_Ocom_OSKIP ). % 1.29/1.20 % 1.29/1.20 cnf(cls_com_Osimps_I49_J_0,axiom, % 1.29/1.20 c_Com_Ocom_OBODY(V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_com_Osimps_I48_J_0,axiom, % 1.29/1.20 c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OBODY(V_pname_H) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_com_Osimps_I18_J_0,axiom, % 1.29/1.20 c_Com_Ocom_OSKIP != c_Com_Ocom_OBODY(V_pname_H) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_COMBI__def__raw_0,axiom, % 1.29/1.20 c_COMBI(v_P,t_a) = v_P ). % 1.29/1.20 % 1.29/1.20 cnf(cls_power__eq__0__iff_2,axiom, % 1.29/1.20 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.29/1.20 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.29/1.20 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.29/1.20 | ~ class_Power_Opower(T_a) % 1.29/1.20 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.29/1.20 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_power__0__left_1,axiom, % 1.29/1.20 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 1.29/1.20 | ~ class_Power_Opower(T_a) % 1.29/1.20 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.29/1.20 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_power__eq__0__iff_1,axiom, % 1.29/1.20 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.29/1.20 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.29/1.20 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.29/1.20 | ~ class_Power_Opower(T_a) % 1.29/1.20 | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_of__nat__0_0,axiom, % 1.29/1.20 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.29/1.20 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_com_Osize_I15_J_0,axiom, % 1.29/1.20 c_Nat_Osize__class_Osize(c_Com_Ocom_OBODY(V_pname),tc_Com_Ocom) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_com_Osize_I7_J_0,axiom, % 1.29/1.20 c_Com_Ocom_Ocom__size(c_Com_Ocom_OBODY(V_pname)) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_COMBK__def__raw_0,axiom, % 1.29/1.20 c_COMBK(v_P,v_Q,t_a,t_b) = v_P ). % 1.29/1.20 % 1.29/1.20 cnf(cls_com_Osimps_I6_J_0,axiom, % 1.29/1.20 ( c_Com_Ocom_OBODY(V_pname) != c_Com_Ocom_OBODY(V_pname_H) % 1.29/1.20 | V_pname = V_pname_H ) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_conjecture_0,negated_conjecture, % 1.29/1.20 hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_conjecture_1,negated_conjecture, % 1.29/1.20 c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_HOL_Ozero__class_Ozero(tc_nat),v_xb) ). % 1.29/1.20 % 1.29/1.20 cnf(cls_conjecture_2,negated_conjecture, % 1.29/1.20 ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb)) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom, % 1.29/1.20 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom, % 1.29/1.20 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom, % 1.29/1.20 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,axiom, % 1.29/1.20 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom, % 1.29/1.20 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom, % 1.29/1.20 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom, % 1.29/1.20 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 1.29/1.20 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom, % 1.29/1.20 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Ring__and__Field_Opordered__semiring,axiom, % 1.29/1.20 class_Ring__and__Field_Opordered__semiring(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Ring__and__Field_Oordered__semiring,axiom, % 1.29/1.20 class_Ring__and__Field_Oordered__semiring(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom, % 1.29/1.20 class_Ring__and__Field_Ono__zero__divisors(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom, % 1.29/1.20 class_Ring__and__Field_Oordered__semidom(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom, % 1.29/1.20 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom, % 1.29/1.20 class_OrderedGroup_Oab__semigroup__mult(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom, % 1.29/1.20 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom, % 1.29/1.20 class_OrderedGroup_Oab__semigroup__add(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom, % 1.29/1.20 class_Ring__and__Field_Ocomm__semiring(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom, % 1.29/1.20 class_OrderedGroup_Ocomm__monoid__add(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom, % 1.29/1.20 class_Ring__and__Field_Ozero__neq__one(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Lattices_Oupper__semilattice,axiom, % 1.29/1.20 class_Lattices_Oupper__semilattice(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Lattices_Olower__semilattice,axiom, % 1.29/1.20 class_Lattices_Olower__semilattice(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom, % 1.29/1.20 class_Ring__and__Field_Osemiring__1(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom, % 1.29/1.20 class_Ring__and__Field_Osemiring__0(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Ring__and__Field_Omult__mono1,axiom, % 1.29/1.20 class_Ring__and__Field_Omult__mono1(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom, % 1.29/1.20 class_Ring__and__Field_Omult__zero(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Ring__and__Field_Omult__mono,axiom, % 1.29/1.20 class_Ring__and__Field_Omult__mono(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom, % 1.29/1.20 class_OrderedGroup_Omonoid__mult(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Lattices_Odistrib__lattice,axiom, % 1.29/1.20 class_Lattices_Odistrib__lattice(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom, % 1.29/1.20 class_Ring__and__Field_Osemiring(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom, % 1.29/1.20 class_OrderedGroup_Omonoid__add(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Divides_Osemiring__div,axiom, % 1.29/1.20 class_Divides_Osemiring__div(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom, % 1.29/1.20 class_Nat_Osemiring__char__0(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Ring__and__Field_Odvd,axiom, % 1.29/1.20 class_Ring__and__Field_Odvd(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Orderings_Opreorder,axiom, % 1.29/1.20 class_Orderings_Opreorder(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Orderings_Olinorder,axiom, % 1.29/1.20 class_Orderings_Olinorder(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Lattices_Olattice,axiom, % 1.29/1.20 class_Lattices_Olattice(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Orderings_Oorder,axiom, % 1.29/1.20 class_Orderings_Oorder(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Orderings_Obot,axiom, % 1.29/1.20 class_Orderings_Obot(tc_nat) ). % 1.29/1.20 % 1.29/1.20 cnf(clsarity_nat__Power_Opower,axiom, % 1.29/1.20 class_Power_Opower(tc_nat) ). % 1.29/1.20 % 1.29/1.20 %------------------------------------------------------------------------------ % 1.29/1.20 %------------------------------------------- % 1.29/1.20 % Proof found % 1.29/1.20 % SZS status Theorem for theBenchmark % 1.29/1.20 % SZS output start Proof % 1.29/1.20 %ClaNum:1467(EqnAxiom:167) % 1.29/1.20 %VarNum:10070(SingletonVarNum:3225) % 1.29/1.20 %MaxLitNum:6 % 1.29/1.20 %MaxfuncDepth:4 % 1.29/1.20 %SharedTerms:89 % 1.29/1.20 %goalClause: 242 276 318 % 1.29/1.20 %singleGoalClaCount:3 % 1.29/1.20 [168]P1(a1) % 1.29/1.20 [169]P2(a1) % 1.29/1.20 [170]P44(a1) % 1.29/1.20 [171]P64(a1) % 1.29/1.20 [172]P3(a1) % 1.29/1.20 [173]P10(a1) % 1.29/1.20 [174]P45(a1) % 1.29/1.20 [175]P11(a1) % 1.29/1.20 [176]P27(a1) % 1.29/1.20 [177]P34(a1) % 1.29/1.20 [178]P12(a1) % 1.29/1.20 [179]P50(a1) % 1.29/1.20 [180]P39(a1) % 1.29/1.20 [181]P13(a1) % 1.29/1.20 [182]P65(a1) % 1.29/1.20 [183]P35(a1) % 1.29/1.20 [184]P14(a1) % 1.29/1.20 [185]P40(a1) % 1.29/1.20 [186]P18(a1) % 1.29/1.20 [187]P42(a1) % 1.29/1.20 [188]P43(a1) % 1.29/1.20 [189]P21(a1) % 1.29/1.20 [190]P19(a1) % 1.29/1.20 [191]P20(a1) % 1.29/1.20 [192]P75(a1) % 1.29/1.20 [193]P41(a1) % 1.29/1.20 [194]P66(a1) % 1.29/1.20 [195]P67(a1) % 1.29/1.20 [196]P23(a1) % 1.29/1.20 [197]P26(a1) % 1.29/1.20 [198]P53(a1) % 1.29/1.20 [199]P68(a1) % 1.29/1.20 [200]P54(a1) % 1.29/1.20 [201]P58(a1) % 1.29/1.20 [202]P76(a1) % 1.29/1.20 [203]P59(a1) % 1.29/1.20 [204]P60(a1) % 1.29/1.20 [205]P24(a1) % 1.29/1.20 [206]P46(a1) % 1.29/1.20 [207]P28(a1) % 1.29/1.20 [208]E(f2(a1),f17(a1)) % 1.29/1.20 [209]E(f5(a3),f2(a1)) % 1.29/1.20 [213]E(f18(a3,a34),f2(a1)) % 1.29/1.20 [276]P7(f4(a40),a42,f2(a1),a43) % 1.29/1.20 [210]E(f29(f2(a1)),f2(a1)) % 1.29/1.20 [242]P78(f35(f35(a38,a39),a42)) % 1.29/1.20 [318]~P78(f35(f35(a41,a39),a43)) % 1.29/1.20 [249]E(f14(f32(f2(a1)),f32(f2(a1)),a1),f32(f2(a1))) % 1.29/1.20 [219]P4(x2191,x2191,a1) % 1.29/1.20 [220]P5(a3,x2201,x2201) % 1.29/1.20 [313]~P6(x3131,x3131,a1) % 1.29/1.20 [212]E(f18(x2121,a1),x2121) % 1.29/1.20 [214]E(f18(x2141,a37),f2(a1)) % 1.29/1.20 [221]E(f7(x2211,x2211,a1),f2(a1)) % 1.29/1.20 [222]P4(f2(a1),x2221,a1) % 1.29/1.20 [236]P6(x2361,f32(x2361),a1) % 1.29/1.20 [240]P6(f2(a1),f32(x2401),a1) % 1.29/1.20 [261]P4(x2611,f14(x2611,x2611,a1),a1) % 1.29/1.20 [301]~E(f4(x3011),a3) % 1.29/1.20 [303]~E(f32(x3031),x3031) % 1.29/1.20 [307]~E(f32(x3071),f2(a1)) % 1.29/1.20 [315]~P6(x3151,f2(a1),a1) % 1.29/1.20 [316]~P4(f32(x3161),x3161,a1) % 1.29/1.20 [211]E(f5(f4(x2111)),f2(a1)) % 1.29/1.20 [215]E(f24(x2151,f2(a1)),x2151) % 1.29/1.20 [217]E(f18(f4(x2171),a34),f2(a1)) % 1.29/1.20 [224]E(f12(x2241,f2(a1),a1),x2241) % 1.29/1.20 [225]E(f7(x2251,f2(a1),a1),x2251) % 1.29/1.20 [226]E(f30(x2261,f2(a1),a1),x2261) % 1.29/1.20 [227]E(f12(f2(a1),x2271,a1),x2271) % 1.29/1.20 [228]E(f30(f2(a1),x2281,a1),x2281) % 1.29/1.20 [230]E(f14(x2301,f2(a1),a1),f2(a1)) % 1.29/1.20 [231]E(f31(x2311,f2(a1),a1),f2(a1)) % 1.29/1.20 [232]E(f14(f2(a1),x2321,a1),f2(a1)) % 1.29/1.20 [233]E(f7(f2(a1),x2331,a1),f2(a1)) % 1.29/1.20 [234]E(f31(f2(a1),x2341,a1),f2(a1)) % 1.29/1.20 [291]P4(x2911,f14(x2911,f14(x2911,x2911,a1),a1),a1) % 1.29/1.20 [248]E(f12(f29(x2481),f32(f2(a1)),a1),f29(f32(x2481))) % 1.29/1.20 [252]E(f12(f18(x2521,a1),f32(f2(a1)),a1),f18(f32(x2521),a1)) % 1.29/1.20 [275]P7(a3,x2751,x2752,x2751) % 1.29/1.20 [250]E(f12(x2501,x2502,a1),f12(x2502,x2501,a1)) % 1.29/1.20 [251]E(f14(x2511,x2512,a1),f14(x2512,x2511,a1)) % 1.29/1.20 [258]P4(x2581,f12(x2582,x2581,a1),a1) % 1.29/1.20 [260]P4(x2601,f12(x2601,x2602,a1),a1) % 1.29/1.20 [262]P4(f7(x2621,x2622,a1),x2621,a1) % 1.29/1.20 [266]P6(f7(x2661,x2662,a1),f32(x2661),a1) % 1.29/1.20 [309]~E(f6(x3091,x3092),a3) % 1.29/1.20 [319]~P6(f12(x3191,x3192,a1),x3192,a1) % 1.29/1.20 [320]~P6(f12(x3201,x3202,a1),x3201,a1) % 1.29/1.20 [229]E(f19(f2(a1),x2291,x2292),x2291) % 1.29/1.20 [253]E(f14(x2531,f2(a1),a1),f14(x2532,f2(a1),a1)) % 1.29/1.20 [254]E(f14(f2(a1),x2541,a1),f14(f2(a1),x2542,a1)) % 1.29/1.20 [256]E(f12(f32(x2561),x2562,a1),f12(x2561,f32(x2562),a1)) % 1.29/1.20 [257]E(f7(f32(x2571),f32(x2572),a1),f7(x2571,x2572,a1)) % 1.29/1.20 [263]E(f7(f12(x2631,x2632,a1),x2632,a1),x2631) % 1.29/1.20 [264]E(f7(f12(x2641,x2642,a1),x2641,a1),x2642) % 1.29/1.20 [265]E(f7(x2651,f12(x2651,x2652,a1),a1),f2(a1)) % 1.29/1.20 [267]E(f32(f12(x2671,x2672,a1)),f12(x2671,f32(x2672),a1)) % 1.29/1.20 [268]E(f32(f12(x2681,x2682,a1)),f12(f32(x2681),x2682,a1)) % 1.29/1.20 [269]E(f31(f32(x2691),f32(x2692),a1),f32(f31(x2691,x2692,a1))) % 1.29/1.20 [270]E(f30(f32(x2701),f32(x2702),a1),f32(f30(x2701,x2702,a1))) % 1.29/1.20 [271]E(f12(f7(x2711,x2712,a1),x2712,a1),f30(x2711,x2712,a1)) % 1.29/1.20 [272]E(f12(x2721,f14(x2721,x2722,a1),a1),f14(x2721,f32(x2722),a1)) % 1.29/1.20 [273]E(f12(x2731,f14(x2732,x2731,a1),a1),f14(f32(x2732),x2731,a1)) % 1.29/1.20 [277]P6(x2771,f32(f12(x2772,x2771,a1)),a1) % 1.29/1.20 [279]P6(x2791,f32(f12(x2791,x2792,a1)),a1) % 1.29/1.20 [274]E(f12(f12(f5(x2741),f5(x2742),a1),f32(f2(a1)),a1),f5(f6(x2741,x2742))) % 1.29/1.20 [280]E(f12(f12(f18(x2801,a34),f18(x2802,a34),a1),f32(f2(a1)),a1),f18(f6(x2801,x2802),a34)) % 1.29/1.20 [310]~E(f4(x3101),f6(x3102,x3103)) % 1.29/1.20 [311]~E(f6(x3111,x3112),f4(x3113)) % 1.29/1.20 [255]E(f22(f2(a1),x2551,x2552),f22(f2(a1),x2553,x2552)) % 1.29/1.20 [281]E(f12(x2811,f12(x2812,x2813,a1),a1),f12(x2812,f12(x2811,x2813,a1),a1)) % 1.29/1.20 [282]E(f12(f12(x2821,x2822,a1),x2823,a1),f12(x2821,f12(x2822,x2823,a1),a1)) % 1.29/1.20 [283]E(f14(f14(x2831,x2832,a1),x2833,a1),f14(x2831,f14(x2832,x2833,a1),a1)) % 1.29/1.20 [284]E(f7(f7(x2841,x2842,a1),x2843,a1),f7(x2841,f12(x2842,x2843,a1),a1)) % 1.29/1.20 [285]E(f7(f7(x2851,x2852,a1),x2853,a1),f7(f7(x2851,x2853,a1),x2852,a1)) % 1.29/1.20 [286]E(f7(f12(x2861,x2862,a1),f12(x2863,x2862,a1),a1),f7(x2861,x2863,a1)) % 1.29/1.20 [287]E(f7(f12(x2871,x2872,a1),f12(x2871,x2873,a1),a1),f7(x2872,x2873,a1)) % 1.29/1.20 [290]E(f7(f7(f32(x2901),x2902,a1),f32(x2903),a1),f7(f7(x2901,x2902,a1),x2903,a1)) % 1.29/1.20 [292]E(f12(f14(x2921,x2922,a1),f14(x2921,x2923,a1),a1),f14(x2921,f12(x2922,x2923,a1),a1)) % 1.29/1.20 [293]E(f7(f14(x2931,x2932,a1),f14(x2931,x2933,a1),a1),f14(x2931,f7(x2932,x2933,a1),a1)) % 1.29/1.20 [294]E(f12(f14(x2941,x2942,a1),f14(x2943,x2942,a1),a1),f14(f12(x2941,x2943,a1),x2942,a1)) % 1.29/1.20 [295]E(f7(f14(x2951,x2952,a1),f14(x2953,x2952,a1),a1),f14(f7(x2951,x2953,a1),x2952,a1)) % 1.29/1.20 [296]E(f31(f7(x2961,x2962,a1),f7(x2963,x2962,a1),a1),f7(f31(x2961,x2963,a1),x2962,a1)) % 1.29/1.20 [288]E(f19(x2881,f22(x2882,x2883,x2884),x2884),f22(f7(x2882,x2881,a1),x2883,x2884)) % 1.29/1.20 [289]E(f19(x2891,f19(x2892,x2893,x2894),x2894),f19(f12(x2891,x2892,a1),x2893,x2894)) % 1.29/1.20 [299]E(f12(f14(x2991,x2992,a1),f12(f14(x2993,x2992,a1),x2994,a1),a1),f12(f14(f12(x2991,x2993,a1),x2992,a1),x2994,a1)) % 1.29/1.20 [402]~P30(a36)+E(f21(a39,f2(a36),a36),f27(a39,a36)) % 1.29/1.20 [403]~P30(a36)+E(f20(a39,f2(a36),a36),f28(a39,a36)) % 1.29/1.20 [325]~P76(x3251)+~E(f13(x3251),f2(x3251)) % 1.29/1.20 [360]E(x3601,f2(a1))+P6(f2(a1),x3601,a1) % 1.29/1.20 [420]~P44(x4201)+P6(f2(x4201),f13(x4201),x4201) % 1.29/1.20 [421]~P44(x4211)+P4(f2(x4211),f13(x4211),x4211) % 1.29/1.20 [454]E(x4541,f2(a1))+~P4(x4541,f2(a1),a1) % 1.29/1.20 [508]~P44(x5081)+~P6(f13(x5081),f2(x5081),x5081) % 1.29/1.20 [509]~P44(x5091)+~P4(f13(x5091),f2(x5091),x5091) % 1.29/1.20 [326]~P75(x3261)+E(f23(f2(a1),x3261),f2(x3261)) % 1.29/1.20 [328]~P36(x3281)+E(f16(f2(x3281),x3281),f2(x3281)) % 1.29/1.20 [329]~P29(x3291)+E(f16(f2(x3291),x3291),f2(x3291)) % 1.29/1.20 [330]~P37(x3301)+E(f8(f2(x3301),x3301),f2(x3301)) % 1.29/1.20 [331]~P61(x3311)+E(f8(f13(x3311),x3311),f13(x3311)) % 1.29/1.20 [332]~P51(x3321)+E(f10(f2(x3321),x3321),f2(x3321)) % 1.29/1.20 [333]~P52(x3331)+E(f10(f13(x3331),x3331),f13(x3331)) % 1.29/1.20 [334]~P30(x3341)+E(f27(f2(x3341),x3341),f2(x3341)) % 1.29/1.20 [335]~P30(x3351)+E(f28(f2(x3351),x3351),f2(x3351)) % 1.29/1.20 [336]~P61(x3361)+E(f15(f2(x3361),x3361),f2(x3361)) % 1.29/1.20 [337]~P77(x3371)+E(f15(f2(x3371),x3371),f2(x3371)) % 1.29/1.20 [423]~P30(x4231)+E(f12(f2(x4231),f2(x4231),x4231),f2(x4231)) % 1.29/1.20 [488]~P37(x4881)+P4(f8(f2(x4881),x4881),f2(x4881),x4881) % 1.29/1.20 [491]E(x4911,f2(a1))+~P6(x4911,f32(f2(a1)),a1) % 1.29/1.20 [626]~P37(x6261)+~P6(f2(x6261),f8(f2(x6261),x6261),x6261) % 1.29/1.20 [744]~P44(x7441)+P6(f2(x7441),f12(f13(x7441),f13(x7441),x7441),x7441) % 1.29/1.20 [968]~P63(x9681)+E(f12(f14(f2(x9681),f2(x9681),x9681),f14(f2(x9681),f2(x9681),x9681),x9681),f2(x9681)) % 1.29/1.20 [1398]~P63(x13981)+P4(f12(f14(f2(x13981),f2(x13981),x13981),f14(f2(x13981),f2(x13981),x13981),x13981),f2(x13981),x13981) % 1.29/1.20 [1440]~P63(x14401)+~P6(f2(x14401),f12(f14(f2(x14401),f2(x14401),x14401),f14(f2(x14401),f2(x14401),x14401),x14401),x14401) % 1.29/1.20 [787]~P6(f2(a1),x7871,a1)+E(f32(f7(x7871,f32(f2(a1)),a1)),x7871) % 1.29/1.20 [366]~P42(x3662)+P4(x3661,x3661,x3662) % 1.29/1.20 [367]~P43(x3672)+P4(x3671,x3671,x3672) % 1.29/1.20 [368]~P45(x3682)+P8(x3681,x3681,x3682) % 1.29/1.20 [435]E(x4351,x4352)+~P5(a3,x4352,x4351) % 1.29/1.20 [457]~P6(x4572,x4572,x4571)+~P10(x4571) % 1.29/1.20 [458]~P6(x4582,x4582,x4581)+~P42(x4581) % 1.29/1.20 [459]~P6(x4592,x4592,x4591)+~P43(x4591) % 1.29/1.20 [490]P4(x4902,x4901,a1)+P4(x4901,x4902,a1) % 1.29/1.20 [558]~P6(x5581,x5582,a1)+P4(x5581,x5582,a1) % 1.29/1.20 [322]E(x3221,x3222)+~E(f32(x3221),f32(x3222)) % 1.29/1.20 [323]E(x3231,x3232)+~E(f4(x3231),f4(x3232)) % 1.29/1.20 [369]~P25(x3692)+E(f14(x3691,x3691,x3692),x3691) % 1.29/1.20 [370]~P10(x3702)+E(f31(x3701,x3701,x3702),x3701) % 1.29/1.20 [371]~P20(x3712)+E(f20(x3711,x3711,x3712),x3711) % 1.29/1.20 [372]~P10(x3722)+E(f30(x3721,x3721,x3722),x3721) % 1.29/1.20 [373]~P18(x3732)+E(f21(x3731,x3731,x3732),x3731) % 1.29/1.20 [376]~P29(x3762)+E(f7(x3761,x3761,x3762),f2(x3762)) % 1.29/1.20 [377]~P22(x3772)+E(f7(x3771,x3771,x3772),f2(x3772)) % 1.29/1.20 [378]~P3(x3782)+E(f9(x3781,x3781,x3782),f2(x3782)) % 1.29/1.20 [379]~P45(x3792)+P8(x3791,f2(x3792),x3792) % 1.29/1.20 [380]~P39(x3801)+P4(f17(x3801),x3802,x3801) % 1.29/1.20 [381]~P45(x3811)+P8(f13(x3811),x3812,x3811) % 1.29/1.20 [439]~P37(x4392)+P4(x4391,f8(x4391,x4392),x4392) % 1.29/1.20 [441]~E(f12(x4412,x4411,a1),x4412)+E(x4411,f2(a1)) % 1.29/1.20 [444]E(x4441,f2(a1))+~E(f12(x4442,x4441,a1),f2(a1)) % 1.29/1.20 [445]E(x4451,f2(a1))+~E(f12(x4451,x4452,a1),f2(a1)) % 1.29/1.20 [460]~P37(x4601)+P4(f2(x4601),f8(x4602,x4601),x4601) % 1.29/1.20 [461]~P30(x4611)+P4(f2(x4611),f27(x4612,x4611),x4611) % 1.29/1.20 [463]~P44(x4631)+P4(f2(x4631),f23(x4632,x4631),x4631) % 1.29/1.20 [464]~P30(x4642)+P4(f28(x4641,x4642),f2(x4642),x4642) % 1.29/1.20 [510]P6(x5101,x5102,a1)+P6(x5102,f32(x5101),a1) % 1.29/1.20 [512]P4(x5121,x5122,a1)+P4(f32(x5122),x5121,a1) % 1.29/1.20 [513]~P37(x5132)+P4(f16(x5131,x5132),f8(x5131,x5132),x5132) % 1.29/1.20 [561]~P4(x5611,x5612,a1)+E(f7(x5611,x5612,a1),f2(a1)) % 1.29/1.20 [565]P4(x5651,x5652,a1)+~E(f7(x5651,x5652,a1),f2(a1)) % 1.29/1.20 [573]~P6(x5731,x5732,a1)+P6(x5731,f32(x5732),a1) % 1.29/1.20 [574]~P4(x5741,x5742,a1)+P6(x5741,f32(x5742),a1) % 1.29/1.20 [576]~P4(x5761,x5762,a1)+P4(x5761,f32(x5762),a1) % 1.29/1.20 [578]~P6(x5781,x5782,a1)+P4(f32(x5781),x5782,a1) % 1.29/1.20 [579]~P37(x5791)+~P6(f8(x5792,x5791),f2(x5791),x5791) % 1.29/1.20 [580]~P44(x5801)+~P6(f23(x5802,x5801),f2(x5801),x5801) % 1.29/1.20 [584]P4(x5841,x5842,a1)+~P6(x5841,f32(x5842),a1) % 1.29/1.20 [585]P6(x5851,x5852,a1)+~P6(f32(x5851),x5852,a1) % 1.29/1.20 [587]P6(x5871,x5872,a1)+~P4(f32(x5871),x5872,a1) % 1.29/1.20 [588]P4(x5881,x5882,a1)+~P4(f32(x5881),x5882,a1) % 1.29/1.20 [606]~P6(x6061,x6062,a1)+P6(f32(x6061),f32(x6062),a1) % 1.29/1.20 [607]~P4(x6071,x6072,a1)+P4(f32(x6071),f32(x6072),a1) % 1.29/1.20 [623]P6(x6231,x6232,a1)+~P6(f32(x6231),f32(x6232),a1) % 1.29/1.20 [624]P4(x6241,x6242,a1)+~P4(f32(x6241),f32(x6242),a1) % 1.29/1.20 [668]~P63(x6681)+P4(f2(x6681),f14(x6682,x6682,x6681),x6681) % 1.29/1.20 [673]~P6(x6731,x6732,a1)+~P6(x6732,f32(x6731),a1) % 1.29/1.20 [674]~P4(x6741,x6742,a1)+~P4(f32(x6742),x6741,a1) % 1.29/1.20 [845]~P6(x8452,x8451,a1)+P6(f2(a1),f7(x8451,x8452,a1),a1) % 1.29/1.20 [892]~P63(x8921)+~P6(f14(x8922,x8922,x8921),f2(x8921),x8921) % 1.29/1.20 [926]P6(x9261,x9262,a1)+~P6(f2(a1),f7(x9262,x9261,a1),a1) % 1.29/1.20 [927]P6(f2(a1),x9271,a1)+~P6(f2(a1),f14(x9272,x9271,a1),a1) % 1.29/1.20 [928]P6(f2(a1),x9281,a1)+~P6(f2(a1),f14(x9281,x9282,a1),a1) % 1.29/1.20 [350]~P15(x3502)+E(f16(f16(x3501,x3502),x3502),x3501) % 1.29/1.20 [352]~P29(x3522)+E(f16(f16(x3521,x3522),x3522),x3521) % 1.29/1.20 [362]~P37(x3622)+E(f8(f16(x3621,x3622),x3622),f8(x3621,x3622)) % 1.29/1.20 [363]~P37(x3632)+E(f8(f8(x3631,x3632),x3632),f8(x3631,x3632)) % 1.29/1.20 [364]~P61(x3642)+E(f8(f23(x3641,x3642),x3642),f23(x3641,x3642)) % 1.29/1.20 [365]~P61(x3652)+E(f15(f15(x3651,x3652),x3652),f15(x3651,x3652)) % 1.29/1.20 [382]~P45(x3822)+E(f12(x3821,f2(x3822),x3822),x3821) % 1.29/1.20 [383]~P12(x3832)+E(f12(x3831,f2(x3832),x3832),x3831) % 1.29/1.20 [384]~P28(x3842)+E(f12(x3841,f2(x3842),x3842),x3841) % 1.29/1.20 [385]~P45(x3852)+E(f14(x3851,f13(x3852),x3852),x3851) % 1.29/1.20 [386]~P27(x3862)+E(f14(x3861,f13(x3862),x3862),x3861) % 1.29/1.20 [387]~P29(x3872)+E(f7(x3871,f2(x3872),x3872),x3871) % 1.29/1.20 [388]~P55(x3882)+E(f11(x3881,f13(x3882),x3882),x3881) % 1.29/1.20 [389]~P3(x3892)+E(f9(x3891,f2(x3892),x3892),x3891) % 1.29/1.20 [390]~P17(x3902)+E(f21(x3901,f17(x3902),x3902),x3901) % 1.29/1.20 [392]~P45(x3921)+E(f12(f2(x3921),x3922,x3921),x3922) % 1.29/1.20 [393]~P12(x3931)+E(f12(f2(x3931),x3932,x3931),x3932) % 1.29/1.20 [394]~P28(x3941)+E(f12(f2(x3941),x3942,x3941),x3942) % 1.29/1.20 [396]~P45(x3961)+E(f14(f13(x3961),x3962,x3961),x3962) % 1.29/1.20 [397]~P11(x3971)+E(f14(f13(x3971),x3972,x3971),x3972) % 1.29/1.20 [398]~P27(x3981)+E(f14(f13(x3981),x3982,x3981),x3982) % 1.29/1.20 [399]~P17(x3991)+E(f21(f17(x3991),x3992,x3991),x3992) % 1.29/1.20 [400]~P2(x4002)+E(f33(x4001,f2(a1),x4002),f13(x4002)) % 1.29/1.20 [401]~P45(x4012)+E(f33(x4011,f2(a1),x4012),f13(x4012)) % 1.29/1.20 [406]~P45(x4062)+E(f14(x4061,f2(x4062),x4062),f2(x4062)) % 1.29/1.20 [407]~P60(x4072)+E(f14(x4071,f2(x4072),x4072),f2(x4072)) % 1.29/1.20 [408]~P71(x4082)+E(f14(x4081,f2(x4082),x4082),f2(x4082)) % 1.29/1.20 [409]~P3(x4092)+E(f9(x4091,f13(x4092),x4092),f2(x4092)) % 1.29/1.20 [410]~P17(x4102)+E(f20(x4101,f17(x4102),x4102),f17(x4102)) % 1.29/1.20 [412]~P45(x4121)+E(f14(f2(x4121),x4122,x4121),f2(x4121)) % 1.29/1.20 [413]~P60(x4131)+E(f14(f2(x4131),x4132,x4131),f2(x4131)) % 1.29/1.20 [414]~P71(x4141)+E(f14(f2(x4141),x4142,x4141),f2(x4141)) % 1.29/1.20 [415]~P27(x4151)+E(f33(f13(x4151),x4152,x4151),f13(x4151)) % 1.29/1.20 [416]~P55(x4161)+E(f11(f2(x4161),x4162,x4161),f2(x4161)) % 1.29/1.20 [417]~P3(x4171)+E(f9(f2(x4171),x4172,x4171),f2(x4171)) % 1.29/1.20 [418]~P17(x4181)+E(f20(f17(x4181),x4182,x4181),f17(x4181)) % 1.29/1.20 [428]~P55(x4281)+E(f11(f13(x4281),x4282,x4281),f10(x4282,x4281)) % 1.29/1.20 [429]~P29(x4291)+E(f7(f2(x4291),x4292,x4291),f16(x4292,x4291)) % 1.29/1.20 [436]~P30(x4362)+E(f27(f16(x4361,x4362),x4362),f16(f28(x4361,x4362),x4362)) % 1.29/1.20 [437]~P30(x4372)+E(f28(f16(x4371,x4372),x4372),f16(f27(x4371,x4372),x4372)) % 1.29/1.20 [446]~P29(x4462)+E(f12(x4461,f16(x4461,x4462),x4462),f2(x4462)) % 1.29/1.20 [447]~P15(x4472)+E(f20(x4471,f16(x4471,x4472),x4472),f17(x4472)) % 1.29/1.20 [449]~P29(x4492)+E(f12(f16(x4491,x4492),x4491,x4492),f2(x4492)) % 1.29/1.20 [450]~P22(x4502)+E(f12(f16(x4501,x4502),x4501,x4502),f2(x4502)) % 1.29/1.20 [451]~P15(x4512)+E(f20(f16(x4511,x4512),x4511,x4512),f17(x4512)) % 1.29/1.20 [476]~P61(x4762)+E(f14(x4761,f15(x4761,x4762),x4762),f8(x4761,x4762)) % 1.29/1.20 [477]~P31(x4772)+E(f21(x4771,f16(x4771,x4772),x4772),f8(x4771,x4772)) % 1.29/1.20 [482]E(x4821,f32(f2(a1)))+~E(f14(x4822,x4821,a1),f32(f2(a1))) % 1.29/1.20 [483]E(x4831,f32(f2(a1)))+~E(f14(x4831,x4832,a1),f32(f2(a1))) % 1.29/1.20 [515]~P75(x5151)+E(f12(f13(x5151),f23(x5152,x5151),x5151),f23(f32(x5152),x5151)) % 1.29/1.20 [516]~P30(x5162)+E(f12(f27(x5161,x5162),f28(x5161,x5162),x5162),x5161) % 1.29/1.20 [517]~P61(x5172)+E(f14(f15(x5171,x5172),f8(x5171,x5172),x5172),x5171) % 1.29/1.20 [553]~P31(x5532)+E(f7(f27(x5531,x5532),f28(x5531,x5532),x5532),f8(x5531,x5532)) % 1.29/1.20 [583]~P37(x5832)+P4(f16(f8(x5831,x5832),x5832),f2(x5832),x5832) % 1.29/1.20 [629]~P56(x6292)+E(f14(f16(x6291,x6292),f16(x6291,x6292),x6292),f14(x6291,x6291,x6292)) % 1.29/1.20 [630]~P61(x6302)+E(f14(f8(x6301,x6302),f8(x6301,x6302),x6302),f14(x6301,x6301,x6302)) % 1.29/1.20 [690]~P44(x6902)+P6(x6901,f12(x6901,f13(x6902),x6902),x6902) % 1.29/1.20 [762]P6(x7622,x7621,a1)+E(f12(x7621,f7(x7622,x7621,a1),a1),x7622) % 1.29/1.20 [842]~P4(x8421,x8422,a1)+E(f12(x8421,f7(x8422,x8421,a1),a1),x8422) % 1.29/1.20 [843]~P4(x8432,x8431,a1)+E(f7(x8431,f7(x8431,x8432,a1),a1),x8432) % 1.29/1.20 [844]~P4(x8442,x8441,a1)+E(f12(f7(x8441,x8442,a1),x8442,a1),x8441) % 1.29/1.20 [851]~P4(x8512,x8511,a1)+E(f32(f7(x8511,x8512,a1)),f7(f32(x8511),x8512,a1)) % 1.29/1.20 [881]~P6(f2(a1),x8811,a1)+P6(f7(x8811,f32(x8812),a1),x8811,a1) % 1.29/1.20 [998]P4(f32(f2(a1)),x9981,a1)+~P4(f32(f2(a1)),f14(x9982,x9981,a1),a1) % 1.29/1.20 [999]P4(f32(f2(a1)),x9991,a1)+~P4(f32(f2(a1)),f14(x9991,x9992,a1),a1) % 1.29/1.20 [514]~P16(x5141)+E(f14(f16(f13(x5141),x5141),x5142,x5141),f16(x5142,x5141)) % 1.29/1.20 [847]~P45(x8472)+E(f12(x8471,x8471,x8472),f14(f12(f13(x8472),f13(x8472),x8472),x8471,x8472)) % 1.29/1.20 [1123]E(x11231,x11232)+~P7(a3,x11232,x11233,x11231) % 1.29/1.20 [522]~P45(x5223)+E(f12(x5221,x5222,x5223),f12(x5222,x5221,x5223)) % 1.29/1.20 [523]~P12(x5233)+E(f12(x5231,x5232,x5233),f12(x5232,x5231,x5233)) % 1.29/1.20 [525]~P45(x5253)+E(f14(x5251,x5252,x5253),f14(x5252,x5251,x5253)) % 1.29/1.20 [526]~P10(x5263)+E(f31(x5261,x5262,x5263),f31(x5262,x5261,x5263)) % 1.29/1.20 [527]~P19(x5273)+E(f20(x5271,x5272,x5273),f20(x5272,x5271,x5273)) % 1.29/1.20 [528]~P20(x5283)+E(f20(x5281,x5282,x5283),f20(x5282,x5281,x5283)) % 1.29/1.20 [529]~P10(x5293)+E(f30(x5291,x5292,x5293),f30(x5292,x5291,x5293)) % 1.29/1.20 [530]~P18(x5303)+E(f21(x5301,x5302,x5303),f21(x5302,x5301,x5303)) % 1.29/1.20 [531]~P19(x5313)+E(f21(x5311,x5312,x5313),f21(x5312,x5311,x5313)) % 1.29/1.20 [632]E(x6321,x6322)+~E(f12(x6323,x6321,a1),f12(x6323,x6322,a1)) % 1.29/1.20 [633]E(x6331,x6332)+~E(f12(x6331,x6333,a1),f12(x6332,x6333,a1)) % 1.29/1.20 [634]~P10(x6343)+P4(x6341,f30(x6342,x6341,x6343),x6343) % 1.29/1.20 [635]~P10(x6353)+P4(x6351,f30(x6351,x6352,x6353),x6353) % 1.29/1.20 [636]~P18(x6363)+P4(x6361,f21(x6362,x6361,x6363),x6363) % 1.29/1.20 [637]~P19(x6373)+P4(x6371,f21(x6372,x6371,x6373),x6373) % 1.29/1.20 [638]~P18(x6383)+P4(x6381,f21(x6381,x6382,x6383),x6383) % 1.29/1.20 [639]~P19(x6393)+P4(x6391,f21(x6391,x6392,x6393),x6393) % 1.29/1.20 [640]~P45(x6403)+P8(x6401,f14(x6402,x6401,x6403),x6403) % 1.29/1.20 [641]~P45(x6413)+P8(x6411,f14(x6411,x6412,x6413),x6413) % 1.29/1.20 [642]~P50(x6423)+P8(x6421,f14(x6421,x6422,x6423),x6423) % 1.29/1.20 [643]~P10(x6433)+P4(f31(x6431,x6432,x6433),x6432,x6433) % 1.29/1.20 [644]~P10(x6443)+P4(f31(x6441,x6442,x6443),x6441,x6443) % 1.29/1.20 [645]~P19(x6453)+P4(f20(x6451,x6452,x6453),x6452,x6453) % 1.29/1.20 [646]~P20(x6463)+P4(f20(x6461,x6462,x6463),x6462,x6463) % 1.29/1.20 [647]~P19(x6473)+P4(f20(x6471,x6472,x6473),x6471,x6473) % 1.29/1.20 [648]~P20(x6483)+P4(f20(x6481,x6482,x6483),x6481,x6483) % 1.29/1.20 [831]~P6(x8311,x8313,a1)+P6(x8311,f12(x8312,x8313,a1),a1) % 1.29/1.20 [833]~P6(x8331,x8332,a1)+P6(x8331,f12(x8332,x8333,a1),a1) % 1.29/1.20 [835]~P4(x8351,x8353,a1)+P4(x8351,f12(x8352,x8353,a1),a1) % 1.29/1.20 [837]~P4(x8371,x8372,a1)+P4(x8371,f12(x8372,x8373,a1),a1) % 1.29/1.20 [838]~P6(x8381,x8383,a1)+P6(f7(x8381,x8382,a1),x8383,a1) % 1.29/1.20 [916]P6(x9161,x9162,a1)+~P6(f12(x9161,x9163,a1),x9162,a1) % 1.29/1.20 [917]P4(x9171,x9172,a1)+~P4(f12(x9173,x9171,a1),x9172,a1) % 1.29/1.20 [918]P4(x9181,x9182,a1)+~P4(f12(x9181,x9183,a1),x9182,a1) % 1.29/1.20 [954]P4(f14(x9542,x9541,a1),f14(x9543,x9541,a1),a1)+P6(f2(a1),x9541,a1) % 1.29/1.20 [955]P4(f14(x9551,x9552,a1),f14(x9551,x9553,a1),a1)+P6(f2(a1),x9551,a1) % 1.29/1.20 [1033]~P6(x10331,x10333,a1)+P6(f12(x10331,x10332,a1),f12(x10333,x10332,a1),a1) % 1.29/1.20 [1034]~P6(x10342,x10343,a1)+P6(f12(x10341,x10342,a1),f12(x10341,x10343,a1),a1) % 1.29/1.20 [1035]~P4(x10351,x10353,a1)+P4(f12(x10351,x10352,a1),f12(x10353,x10352,a1),a1) % 1.29/1.20 [1036]~P4(x10362,x10363,a1)+P4(f12(x10361,x10362,a1),f12(x10361,x10363,a1),a1) % 1.29/1.20 [1038]~P4(x10381,x10383,a1)+P4(f14(x10381,x10382,a1),f14(x10383,x10382,a1),a1) % 1.29/1.20 [1040]~P4(x10402,x10403,a1)+P4(f14(x10401,x10402,a1),f14(x10401,x10403,a1),a1) % 1.29/1.20 [1041]~P4(x10411,x10413,a1)+P4(f7(x10411,x10412,a1),f7(x10413,x10412,a1),a1) % 1.29/1.20 [1042]~P4(x10423,x10422,a1)+P4(f7(x10421,x10422,a1),f7(x10421,x10423,a1),a1) % 1.29/1.20 [1161]~P6(f12(x11611,x11613,a1),x11612,a1)+P6(x11611,f7(x11612,x11613,a1),a1) % 1.29/1.20 [1162]~P4(f7(x11621,x11623,a1),x11622,a1)+P4(x11621,f12(x11622,x11623,a1),a1) % 1.29/1.20 [1163]~P6(x11631,f7(x11633,x11632,a1),a1)+P6(f12(x11631,x11632,a1),x11633,a1) % 1.29/1.20 [1164]~P4(x11641,f12(x11643,x11642,a1),a1)+P4(f7(x11641,x11642,a1),x11643,a1) % 1.29/1.20 [1263]P6(x12631,x12632,a1)+~P6(f12(x12633,x12631,a1),f12(x12633,x12632,a1),a1) % 1.29/1.20 [1264]P6(x12641,x12642,a1)+~P6(f14(x12643,x12641,a1),f14(x12643,x12642,a1),a1) % 1.29/1.20 [1265]P6(x12651,x12652,a1)+~P6(f14(x12651,x12653,a1),f14(x12652,x12653,a1),a1) % 1.29/1.20 [1266]P4(x12661,x12662,a1)+~P4(f12(x12663,x12661,a1),f12(x12663,x12662,a1),a1) % 1.29/1.20 [1269]~P6(f14(x12692,x12691,a1),f14(x12693,x12691,a1),a1)+P6(f2(a1),x12691,a1) % 1.29/1.20 [1270]~P6(f14(x12701,x12702,a1),f14(x12701,x12703,a1),a1)+P6(f2(a1),x12701,a1) % 1.29/1.20 [566]~P16(x5663)+E(f12(x5661,f16(x5662,x5663),x5663),f7(x5661,x5662,x5663)) % 1.29/1.20 [567]~P29(x5673)+E(f12(x5671,f16(x5672,x5673),x5673),f7(x5671,x5672,x5673)) % 1.29/1.20 [569]~P22(x5693)+E(f12(x5691,f16(x5692,x5693),x5693),f7(x5691,x5692,x5693)) % 1.29/1.20 [570]~P15(x5703)+E(f20(x5701,f16(x5702,x5703),x5703),f7(x5701,x5702,x5703)) % 1.29/1.20 [571]~P55(x5713)+E(f14(x5711,f10(x5712,x5713),x5713),f11(x5711,x5712,x5713)) % 1.29/1.20 [572]~P29(x5723)+E(f7(x5721,f16(x5722,x5723),x5723),f12(x5721,x5722,x5723)) % 1.29/1.20 [627]~P73(x6272)+E(f14(f16(x6271,x6272),x6273,x6272),f14(x6271,f16(x6273,x6272),x6272)) % 1.29/1.20 [628]~P73(x6282)+E(f14(f16(x6281,x6282),f16(x6283,x6282),x6282),f14(x6281,x6283,x6282)) % 1.29/1.20 [649]~P10(x6493)+E(f31(x6491,f30(x6491,x6492,x6493),x6493),x6491) % 1.29/1.20 [650]~P19(x6503)+E(f20(x6501,f21(x6501,x6502,x6503),x6503),x6501) % 1.29/1.20 [651]~P10(x6513)+E(f30(x6511,f31(x6511,x6512,x6513),x6513),x6511) % 1.29/1.20 [652]~P19(x6523)+E(f21(x6521,f20(x6521,x6522,x6523),x6523),x6521) % 1.29/1.20 [653]~P29(x6533)+E(f12(f7(x6531,x6532,x6533),x6532,x6533),x6531) % 1.29/1.20 [654]~P29(x6543)+E(f7(f12(x6541,x6542,x6543),x6542,x6543),x6541) % 1.29/1.20 [656]~P3(x6563)+E(f9(f14(x6561,x6562,x6563),x6562,x6563),f2(x6563)) % 1.29/1.20 [657]~P3(x6573)+E(f9(f14(x6571,x6572,x6573),x6571,x6573),f2(x6573)) % 1.29/1.20 [698]~P22(x6983)+E(f16(f7(x6981,x6982,x6983),x6983),f7(x6982,x6981,x6983)) % 1.29/1.20 [707]E(x7071,x7072)+~E(f14(f32(x7073),x7071,a1),f14(f32(x7073),x7072,a1)) % 1.29/1.20 [731]~P22(x7312)+E(f12(f16(x7311,x7312),f12(x7313,x7311,x7312),x7312),x7313) % 1.29/1.20 [732]~P29(x7322)+E(f12(f16(x7321,x7322),f12(x7321,x7323,x7322),x7322),x7323) % 1.29/1.20 [756]~P73(x7563)+E(f14(x7561,f16(x7562,x7563),x7563),f16(f14(x7561,x7562,x7563),x7563)) % 1.29/1.20 [757]~P73(x7572)+E(f14(f16(x7571,x7572),x7573,x7572),f16(f14(x7571,x7573,x7572),x7572)) % 1.29/1.20 [758]~P55(x7582)+E(f11(f16(x7581,x7582),x7583,x7582),f16(f11(x7581,x7583,x7582),x7582)) % 1.29/1.20 [759]~P61(x7592)+E(f33(f8(x7591,x7592),x7593,x7592),f8(f33(x7591,x7593,x7592),x7592)) % 1.29/1.20 [788]~P25(x7883)+E(f14(x7881,f14(x7881,x7882,x7883),x7883),f14(x7881,x7882,x7883)) % 1.29/1.20 [789]~P10(x7893)+E(f31(x7891,f31(x7891,x7892,x7893),x7893),f31(x7891,x7892,x7893)) % 1.29/1.20 [790]~P19(x7903)+E(f20(x7901,f20(x7901,x7902,x7903),x7903),f20(x7901,x7902,x7903)) % 1.29/1.20 [791]~P20(x7913)+E(f20(x7911,f20(x7911,x7912,x7913),x7913),f20(x7911,x7912,x7913)) % 1.29/1.20 [792]~P10(x7923)+E(f30(x7921,f30(x7921,x7922,x7923),x7923),f30(x7921,x7922,x7923)) % 1.29/1.20 [793]~P18(x7933)+E(f21(x7931,f21(x7931,x7932,x7933),x7933),f21(x7931,x7932,x7933)) % 1.29/1.20 [794]~P19(x7943)+E(f21(x7941,f21(x7941,x7942,x7943),x7943),f21(x7941,x7942,x7943)) % 1.29/1.20 [795]~P3(x7953)+E(f9(f12(x7951,x7952,x7953),x7952,x7953),f9(x7951,x7952,x7953)) % 1.29/1.20 [796]~P3(x7963)+E(f9(f12(x7961,x7962,x7963),x7961,x7963),f9(x7962,x7961,x7963)) % 1.29/1.20 [797]~P3(x7973)+E(f9(f9(x7971,x7972,x7973),x7972,x7973),f9(x7971,x7972,x7973)) % 1.29/1.20 [798]~P61(x7981)+P4(f2(x7981),f33(f8(x7982,x7981),x7983,x7981),x7981) % 1.29/1.20 [802]~P2(x8023)+E(f14(x8021,f33(x8021,x8022,x8023),x8023),f33(x8021,f32(x8022),x8023)) % 1.29/1.20 [805]~P27(x8053)+E(f14(f33(x8051,x8052,x8053),x8051,x8053),f33(x8051,f32(x8052),x8053)) % 1.29/1.20 [806]~P45(x8063)+E(f14(x8061,f33(x8061,x8062,x8063),x8063),f33(x8061,f32(x8062),x8063)) % 1.29/1.20 [807]~P45(x8073)+E(f14(f33(x8071,x8072,x8073),x8071,x8073),f33(x8071,f32(x8072),x8073)) % 1.29/1.20 [810]~P75(x8102)+E(f12(f23(x8101,x8102),f23(x8103,x8102),x8102),f23(f12(x8101,x8103,a1),x8102)) % 1.29/1.20 [811]~P75(x8112)+E(f14(f23(x8111,x8112),f23(x8113,x8112),x8112),f23(f14(x8111,x8113,a1),x8112)) % 1.29/1.20 [812]~P29(x8122)+E(f12(f16(x8121,x8122),f16(x8123,x8122),x8122),f16(f12(x8123,x8121,x8122),x8122)) % 1.29/1.20 [813]~P22(x8132)+E(f12(f16(x8131,x8132),f16(x8133,x8132),x8132),f16(f12(x8131,x8133,x8132),x8132)) % 1.29/1.20 [814]~P30(x8142)+E(f21(f16(x8141,x8142),f16(x8143,x8142),x8142),f16(f20(x8141,x8143,x8142),x8142)) % 1.29/1.20 [815]~P15(x8152)+E(f21(f16(x8151,x8152),f16(x8153,x8152),x8152),f16(f20(x8151,x8153,x8152),x8152)) % 1.29/1.20 [816]~P30(x8162)+E(f20(f16(x8161,x8162),f16(x8163,x8162),x8162),f16(f21(x8161,x8163,x8162),x8162)) % 1.29/1.20 [817]~P15(x8172)+E(f20(f16(x8171,x8172),f16(x8173,x8172),x8172),f16(f21(x8171,x8173,x8172),x8172)) % 1.29/1.20 [818]~P61(x8182)+E(f14(f8(x8181,x8182),f8(x8183,x8182),x8182),f8(f14(x8181,x8183,x8182),x8182)) % 1.29/1.20 [819]~P61(x8192)+E(f14(f15(x8191,x8192),f15(x8193,x8192),x8192),f15(f14(x8191,x8193,x8192),x8192)) % 1.29/1.20 [850]~P37(x8503)+E(f8(f7(x8501,x8502,x8503),x8503),f8(f7(x8502,x8501,x8503),x8503)) % 1.29/1.20 [914]~P56(x9142)+P8(f14(x9141,f2(x9142),x9142),f14(x9143,f2(x9142),x9142),x9142) % 1.29/1.20 [915]~P56(x9151)+P8(f14(f2(x9151),x9152,x9151),f14(f2(x9151),x9153,x9151),x9151) % 1.29/1.20 [969]~P30(x9693)+E(f12(f21(x9691,x9692,x9693),f20(x9691,x9692,x9693),x9693),f12(x9691,x9692,x9693)) % 1.29/1.20 [989]~P27(x9893)+E(f14(f33(x9891,x9892,x9893),x9891,x9893),f14(x9891,f33(x9891,x9892,x9893),x9893)) % 1.29/1.20 [1105]~P6(x11052,x11053,a1)+P6(f14(f32(x11051),x11052,a1),f14(f32(x11051),x11053,a1),a1) % 1.29/1.20 [1138]~P4(x11382,x11383,a1)+E(f7(f12(x11381,x11382,a1),x11383,a1),f7(x11381,f7(x11383,x11382,a1),a1)) % 1.29/1.20 [1139]~P4(x11393,x11392,a1)+E(f7(f12(x11391,x11392,a1),x11393,a1),f12(x11391,f7(x11392,x11393,a1),a1)) % 1.29/1.20 [1141]~P4(x11413,x11411,a1)+E(f7(f12(x11411,x11412,a1),x11413,a1),f12(f7(x11411,x11413,a1),x11412,a1)) % 1.29/1.20 [1177]~P74(x11771)+E(f14(f33(f16(f13(x11771),x11771),x11772,x11771),f33(x11773,x11772,x11771),x11771),f33(f16(x11773,x11771),x11772,x11771)) % 1.29/1.20 [1230]~P4(x12303,x12302,a1)+P4(x12301,f7(f12(x12302,x12301,a1),x12303,a1),a1) % 1.29/1.20 [1284]P4(x12841,x12842,a1)+~P4(f14(f32(x12843),x12841,a1),f14(f32(x12843),x12842,a1),a1) % 1.29/1.20 [1287]~P37(x12873)+P4(f8(f12(x12871,x12872,x12873),x12873),f12(f8(x12871,x12873),f8(x12872,x12873),x12873),x12873) % 1.29/1.20 [1288]~P57(x12883)+P4(f8(f14(x12881,x12882,x12883),x12883),f14(f8(x12881,x12883),f8(x12882,x12883),x12883),x12883) % 1.29/1.20 [1289]~P37(x12893)+P4(f8(f7(x12891,x12892,x12893),x12893),f12(f8(x12891,x12893),f8(x12892,x12893),x12893),x12893) % 1.29/1.20 [1290]~P37(x12902)+P4(f7(f8(x12901,x12902),f8(x12903,x12902),x12902),f8(f7(x12901,x12903,x12902),x12902),x12902) % 1.29/1.20 [1375]~P63(x13751)+P4(f2(x13751),f12(f14(x13752,x13752,x13751),f14(x13753,x13753,x13751),x13751),x13751) % 1.29/1.20 [1432]~P63(x14321)+~P6(f12(f14(x14322,x14322,x14321),f14(x14323,x14323,x14321),x14321),f2(x14321),x14321) % 1.29/1.20 [786]~P29(x7862)+E(f12(x7861,f12(f16(x7861,x7862),x7863,x7862),x7862),x7863) % 1.29/1.20 [898]~P30(x8982)+E(f16(f21(f16(x8981,x8982),f16(x8983,x8982),x8982),x8982),f20(x8981,x8983,x8982)) % 1.29/1.20 [899]~P30(x8992)+E(f16(f20(f16(x8991,x8992),f16(x8993,x8992),x8992),x8992),f21(x8991,x8993,x8992)) % 1.29/1.20 [919]~P61(x9192)+E(f8(f33(f16(x9191,x9192),x9193,x9192),x9192),f8(f33(x9191,x9193,x9192),x9192)) % 1.29/1.20 [1009]~P37(x10092)+E(f8(f12(f8(x10091,x10092),f8(x10093,x10092),x10092),x10092),f12(f8(x10091,x10092),f8(x10093,x10092),x10092)) % 1.29/1.20 [1029]~P45(x10293)+E(f12(x10291,f14(x10292,x10291,x10293),x10293),f14(f12(x10292,f13(x10293),x10293),x10291,x10293)) % 1.29/1.20 [1030]~P45(x10303)+E(f12(f14(x10301,x10302,x10303),x10302,x10303),f14(f12(x10301,f13(x10303),x10303),x10302,x10303)) % 1.29/1.20 [1122]~P9(x11223)+E(f9(f16(f9(x11221,x11222,x11223),x11223),x11222,x11223),f9(f16(x11221,x11223),x11222,x11223)) % 1.29/1.20 [1293]~P4(x12932,x12933,a1)+E(f7(f12(x12931,x12932,a1),f32(x12933),a1),f7(x12931,f32(f7(x12933,x12932,a1)),a1)) % 1.29/1.20 [1294]~P4(x12942,x12941,a1)+E(f7(f32(f7(x12941,x12942,a1)),x12943,a1),f7(f32(x12941),f12(x12942,x12943,a1),a1)) % 1.29/1.20 [1406]~P37(x14062)+P4(f8(f7(f8(x14061,x14062),f8(x14063,x14062),x14062),x14062),f8(f7(x14061,x14063,x14062),x14062),x14062) % 1.29/1.20 [1223]P5(x12231,x12232,x12233)+~P7(x12231,x12232,x12234,x12233) % 1.29/1.20 [346]E(x3461,x3462)+~E(f6(x3463,x3461),f6(x3464,x3462)) % 1.29/1.20 [347]E(x3471,x3472)+~E(f6(x3471,x3473),f6(x3472,x3474)) % 1.29/1.20 [1391]~P7(x13911,x13912,x13913,x13914)+P7(x13911,x13912,f32(x13913),x13914) % 1.29/1.20 [966]~P45(x9663)+E(f33(f33(x9661,x9662,x9663),x9664,x9663),f33(x9661,f14(x9662,x9664,a1),x9663)) % 1.29/1.20 [967]~P27(x9673)+E(f33(f33(x9671,x9672,x9673),x9674,x9673),f33(x9671,f14(x9672,x9674,a1),x9673)) % 1.29/1.20 [970]~P45(x9704)+E(f12(x9701,f12(x9702,x9703,x9704),x9704),f12(x9702,f12(x9701,x9703,x9704),x9704)) % 1.29/1.20 [971]~P12(x9714)+E(f12(x9711,f12(x9712,x9713,x9714),x9714),f12(x9712,f12(x9711,x9713,x9714),x9714)) % 1.29/1.20 [972]~P22(x9724)+E(f12(x9721,f12(x9722,x9723,x9724),x9724),f12(x9722,f12(x9721,x9723,x9724),x9724)) % 1.29/1.20 [973]~P45(x9734)+E(f14(x9731,f14(x9732,x9733,x9734),x9734),f14(x9732,f14(x9731,x9733,x9734),x9734)) % 1.29/1.20 [974]~P10(x9744)+E(f31(x9741,f31(x9742,x9743,x9744),x9744),f31(x9742,f31(x9741,x9743,x9744),x9744)) % 1.29/1.20 [975]~P19(x9754)+E(f20(x9751,f20(x9752,x9753,x9754),x9754),f20(x9752,f20(x9751,x9753,x9754),x9754)) % 1.29/1.20 [976]~P20(x9764)+E(f20(x9761,f20(x9762,x9763,x9764),x9764),f20(x9762,f20(x9761,x9763,x9764),x9764)) % 1.29/1.20 [977]~P10(x9774)+E(f30(x9771,f30(x9772,x9773,x9774),x9774),f30(x9772,f30(x9771,x9773,x9774),x9774)) % 1.29/1.20 [978]~P18(x9784)+E(f21(x9781,f21(x9782,x9783,x9784),x9784),f21(x9782,f21(x9781,x9783,x9784),x9784)) % 1.29/1.20 [979]~P19(x9794)+E(f21(x9791,f21(x9792,x9793,x9794),x9794),f21(x9792,f21(x9791,x9793,x9794),x9794)) % 1.29/1.20 [984]~P45(x9843)+E(f12(f12(x9841,x9842,x9843),x9844,x9843),f12(x9841,f12(x9842,x9844,x9843),x9843)) % 1.29/1.20 [985]~P12(x9853)+E(f12(f12(x9851,x9852,x9853),x9854,x9853),f12(x9851,f12(x9852,x9854,x9853),x9853)) % 1.29/1.20 [986]~P21(x9863)+E(f12(f12(x9861,x9862,x9863),x9864,x9863),f12(x9861,f12(x9862,x9864,x9863),x9863)) % 1.29/1.20 [987]~P45(x9873)+E(f14(f14(x9871,x9872,x9873),x9874,x9873),f14(x9871,f14(x9872,x9874,x9873),x9873)) % 1.29/1.20 [988]~P24(x9883)+E(f14(f14(x9881,x9882,x9883),x9884,x9883),f14(x9881,f14(x9882,x9884,x9883),x9883)) % 1.29/1.20 [990]~P10(x9903)+E(f31(f31(x9901,x9902,x9903),x9904,x9903),f31(x9901,f31(x9902,x9904,x9903),x9903)) % 1.29/1.20 [991]~P19(x9913)+E(f20(f20(x9911,x9912,x9913),x9914,x9913),f20(x9911,f20(x9912,x9914,x9913),x9913)) % 1.29/1.20 [992]~P20(x9923)+E(f20(f20(x9921,x9922,x9923),x9924,x9923),f20(x9921,f20(x9922,x9924,x9923),x9923)) % 1.29/1.20 [993]~P10(x9933)+E(f30(f30(x9931,x9932,x9933),x9934,x9933),f30(x9931,f30(x9932,x9934,x9933),x9933)) % 1.29/1.20 [994]~P18(x9943)+E(f21(f21(x9941,x9942,x9943),x9944,x9943),f21(x9941,f21(x9942,x9944,x9943),x9943)) % 1.29/1.20 [995]~P19(x9953)+E(f21(f21(x9951,x9952,x9953),x9954,x9953),f21(x9951,f21(x9952,x9954,x9953),x9953)) % 1.29/1.20 [996]~P45(x9963)+E(f12(f12(x9961,x9962,x9963),x9964,x9963),f12(f12(x9961,x9964,x9963),x9962,x9963)) % 1.29/1.20 [997]~P45(x9973)+E(f14(f14(x9971,x9972,x9973),x9974,x9973),f14(f14(x9971,x9974,x9973),x9972,x9973)) % 1.29/1.20 [1184]~P27(x11843)+E(f14(f33(x11841,x11842,x11843),f33(x11841,x11844,x11843),x11843),f33(x11841,f12(x11842,x11844,a1),x11843)) % 1.29/1.20 [1185]~P45(x11853)+E(f14(f33(x11851,x11852,x11853),f33(x11851,x11854,x11853),x11853),f33(x11851,f12(x11852,x11854,a1),x11853)) % 1.29/1.20 [1188]~P30(x11883)+E(f20(f12(x11881,x11882,x11883),f12(x11881,x11884,x11883),x11883),f12(x11881,f20(x11882,x11884,x11883),x11883)) % 1.29/1.20 [1189]~P32(x11893)+E(f20(f12(x11891,x11892,x11893),f12(x11891,x11894,x11893),x11893),f12(x11891,f20(x11892,x11894,x11893),x11893)) % 1.29/1.20 [1190]~P30(x11903)+E(f21(f12(x11901,x11902,x11903),f12(x11901,x11904,x11903),x11903),f12(x11901,f21(x11902,x11904,x11903),x11903)) % 1.29/1.20 [1191]~P33(x11913)+E(f21(f12(x11911,x11912,x11913),f12(x11911,x11914,x11913),x11913),f12(x11911,f21(x11912,x11914,x11913),x11913)) % 1.29/1.20 [1192]~P45(x11923)+E(f12(f14(x11921,x11922,x11923),f14(x11921,x11924,x11923),x11923),f14(x11921,f12(x11922,x11924,x11923),x11923)) % 1.29/1.20 [1193]~P10(x11933)+E(f30(f31(x11931,x11932,x11933),f31(x11931,x11934,x11933),x11933),f31(x11931,f30(x11932,x11934,x11933),x11933)) % 1.29/1.20 [1194]~P14(x11943)+E(f21(f20(x11941,x11942,x11943),f20(x11941,x11944,x11943),x11943),f20(x11941,f21(x11942,x11944,x11943),x11943)) % 1.29/1.20 [1195]~P10(x11953)+E(f31(f30(x11951,x11952,x11953),f30(x11951,x11954,x11953),x11953),f30(x11951,f31(x11952,x11954,x11953),x11953)) % 1.29/1.20 [1196]~P14(x11963)+E(f20(f21(x11961,x11962,x11963),f21(x11961,x11964,x11963),x11963),f21(x11961,f20(x11962,x11964,x11963),x11963)) % 1.29/1.20 [1197]~P34(x11973)+E(f31(f12(x11971,x11972,x11973),f12(x11974,x11972,x11973),x11973),f12(f31(x11971,x11974,x11973),x11972,x11973)) % 1.29/1.20 [1198]~P30(x11983)+E(f20(f12(x11981,x11982,x11983),f12(x11984,x11982,x11983),x11983),f12(f20(x11981,x11984,x11983),x11982,x11983)) % 1.29/1.20 [1199]~P32(x11993)+E(f20(f12(x11991,x11992,x11993),f12(x11994,x11992,x11993),x11993),f12(f20(x11991,x11994,x11993),x11992,x11993)) % 1.29/1.20 [1200]~P34(x12003)+E(f30(f12(x12001,x12002,x12003),f12(x12004,x12002,x12003),x12003),f12(f30(x12001,x12004,x12003),x12002,x12003)) % 1.29/1.20 [1201]~P30(x12013)+E(f21(f12(x12011,x12012,x12013),f12(x12014,x12012,x12013),x12013),f12(f21(x12011,x12014,x12013),x12012,x12013)) % 1.29/1.20 [1202]~P33(x12023)+E(f21(f12(x12021,x12022,x12023),f12(x12024,x12022,x12023),x12023),f12(f21(x12021,x12024,x12023),x12022,x12023)) % 1.29/1.20 [1204]~P46(x12043)+E(f12(f14(x12041,x12042,x12043),f14(x12044,x12042,x12043),x12043),f14(f12(x12041,x12044,x12043),x12042,x12043)) % 1.29/1.20 [1205]~P38(x12053)+E(f31(f7(x12051,x12052,x12053),f7(x12054,x12052,x12053),x12053),f7(f31(x12051,x12054,x12053),x12052,x12053)) % 1.29/1.20 [1206]~P38(x12063)+E(f30(f7(x12061,x12062,x12063),f7(x12064,x12062,x12063),x12063),f7(f30(x12061,x12064,x12063),x12062,x12063)) % 1.29/1.20 [1207]~P45(x12073)+E(f14(f33(x12071,x12072,x12073),f33(x12074,x12072,x12073),x12073),f33(f14(x12071,x12074,x12073),x12072,x12073)) % 1.29/1.20 [1208]~P11(x12083)+E(f14(f33(x12081,x12082,x12083),f33(x12084,x12082,x12083),x12083),f33(f14(x12081,x12084,x12083),x12082,x12083)) % 1.29/1.20 [1209]~P55(x12093)+E(f12(f11(x12091,x12092,x12093),f11(x12094,x12092,x12093),x12093),f11(f12(x12091,x12094,x12093),x12092,x12093)) % 1.29/1.20 [1210]~P55(x12103)+E(f7(f11(x12101,x12102,x12103),f11(x12104,x12102,x12103),x12103),f11(f7(x12101,x12104,x12103),x12102,x12103)) % 1.29/1.20 [1211]~P10(x12113)+E(f30(f31(x12111,x12112,x12113),f31(x12114,x12112,x12113),x12113),f31(f30(x12111,x12114,x12113),x12112,x12113)) % 1.29/1.20 [1212]~P14(x12123)+E(f21(f20(x12121,x12122,x12123),f20(x12124,x12122,x12123),x12123),f20(f21(x12121,x12124,x12123),x12122,x12123)) % 1.29/1.20 [1213]~P10(x12133)+E(f31(f30(x12131,x12132,x12133),f30(x12134,x12132,x12133),x12133),f30(f31(x12131,x12134,x12133),x12132,x12133)) % 1.29/1.20 [1214]~P14(x12143)+E(f20(f21(x12141,x12142,x12143),f21(x12144,x12142,x12143),x12143),f21(f20(x12141,x12144,x12143),x12142,x12143)) % 1.29/1.20 [1215]~P3(x12153)+E(f9(f14(x12151,x12152,x12153),f14(x12151,x12154,x12153),x12153),f14(x12151,f9(x12152,x12154,x12153),x12153)) % 1.29/1.20 [1216]~P45(x12163)+E(f12(f14(x12161,x12162,x12163),f14(x12164,x12162,x12163),x12163),f14(f12(x12161,x12164,x12163),x12162,x12163)) % 1.29/1.20 [1217]~P3(x12173)+E(f9(f14(x12171,x12172,x12173),f14(x12174,x12172,x12173),x12173),f14(f9(x12171,x12174,x12173),x12172,x12173)) % 1.29/1.20 [1425]~P7(f4(x14251),x14253,x14252,x14254)+E(f32(f25(x14251,x14252,x14253,x14254)),x14252) % 1.29/1.20 [1426]~P10(x14264)+P4(f30(x14261,f31(x14262,x14263,x14264),x14264),f31(f30(x14261,x14262,x14264),f30(x14261,x14263,x14264),x14264),x14264) % 1.29/1.20 [1427]~P19(x14274)+P4(f21(x14271,f20(x14272,x14273,x14274),x14274),f20(f21(x14271,x14272,x14274),f21(x14271,x14273,x14274),x14274),x14274) % 1.29/1.20 [1428]~P10(x14283)+P4(f30(f31(x14281,x14282,x14283),f31(x14281,x14284,x14283),x14283),f31(x14281,f30(x14282,x14284,x14283),x14283),x14283) % 1.29/1.20 [1429]~P19(x14293)+P4(f21(f20(x14291,x14292,x14293),f20(x14291,x14294,x14293),x14293),f20(x14291,f21(x14292,x14294,x14293),x14293),x14293) % 1.29/1.20 [1186]~P3(x11864)+E(f9(f12(x11861,f14(x11862,x11863,x11864),x11864),x11863,x11864),f9(x11861,x11863,x11864)) % 1.29/1.20 [1187]~P3(x11874)+E(f9(f12(x11871,f14(x11872,x11873,x11874),x11874),x11872,x11874),f9(x11871,x11872,x11874)) % 1.29/1.20 [1312]~P3(x13124)+E(f9(f14(x13121,f9(x13122,x13123,x13124),x13124),x13123,x13124),f9(f14(x13121,x13122,x13124),x13123,x13124)) % 1.29/1.20 [1313]~P9(x13134)+E(f9(f7(x13131,f9(x13132,x13133,x13134),x13134),x13133,x13134),f9(f7(x13131,x13132,x13134),x13133,x13134)) % 1.29/1.20 [1316]~P9(x13163)+E(f9(f7(f9(x13161,x13162,x13163),x13164,x13163),x13162,x13163),f9(f7(x13161,x13164,x13163),x13162,x13163)) % 1.29/1.20 [1317]~P3(x13174)+E(f9(f12(x13171,f9(x13172,x13173,x13174),x13174),x13173,x13174),f9(f12(x13171,x13172,x13174),x13173,x13174)) % 1.29/1.20 [1318]~P3(x13183)+E(f9(f12(f9(x13181,x13182,x13183),x13184,x13183),x13182,x13183),f9(f12(x13181,x13184,x13183),x13182,x13183)) % 1.29/1.20 [1319]~P3(x13193)+E(f9(f14(f9(x13191,x13192,x13193),x13194,x13193),x13192,x13193),f9(f14(x13191,x13194,x13193),x13192,x13193)) % 1.29/1.20 [1407]~P3(x14073)+E(f9(f12(f9(x14071,x14072,x14073),f9(x14074,x14072,x14073),x14073),x14072,x14073),f9(f12(x14071,x14074,x14073),x14072,x14073)) % 1.29/1.20 [1408]~P3(x14083)+E(f9(f14(f9(x14081,x14082,x14083),f9(x14084,x14082,x14083),x14083),x14082,x14083),f9(f14(x14081,x14084,x14083),x14082,x14083)) % 1.29/1.20 [1409]~P9(x14093)+E(f9(f7(f9(x14091,x14092,x14093),f9(x14094,x14092,x14093),x14093),x14092,x14093),f9(f7(x14091,x14094,x14093),x14092,x14093)) % 1.29/1.20 [1442]~P4(x14421,x14423,a1)+E(f12(f14(x14421,x14422,a1),f12(f14(f7(x14423,x14421,a1),x14422,a1),x14424,a1),a1),f12(f14(x14423,x14422,a1),x14424,a1)) % 1.29/1.20 [662]E(x6621,x6622)+~E(f22(x6621,x6623,x6624),f22(x6622,x6625,x6624)) % 1.29/1.20 [1320]~P45(x13203)+E(f12(f12(x13201,x13202,x13203),f12(x13204,x13205,x13203),x13203),f12(f12(x13201,x13204,x13203),f12(x13202,x13205,x13203),x13203)) % 1.29/1.20 [1321]~P45(x13213)+E(f14(f14(x13211,x13212,x13213),f14(x13214,x13215,x13213),x13213),f14(f14(x13211,x13214,x13213),f14(x13212,x13215,x13213),x13213)) % 1.29/1.20 [1422]~P66(x14223)+E(f12(f14(x14221,x14222,x14223),f12(f14(x14224,x14222,x14223),x14225,x14223),x14223),f12(f14(f12(x14221,x14224,x14223),x14222,x14223),x14225,x14223)) % 1.29/1.20 [1463]~P37(x14633)+P4(f8(f7(f12(x14631,x14632,x14633),f12(x14634,x14635,x14633),x14633),x14633),f12(f8(f7(x14631,x14634,x14633),x14633),f8(f7(x14632,x14635,x14633),x14633),x14633),x14633) % 1.29/1.20 [1439]~P73(x14393)+E(f12(f14(x14391,x14392,x14393),f12(f14(f7(x14394,x14391,x14393),x14392,x14393),x14395,x14393),x14393),f12(f14(x14394,x14392,x14393),x14395,x14393)) % 1.29/1.20 [1445]~P4(x14451,x14454,a1)+E(f7(f12(f14(x14451,x14452,a1),x14453,a1),f12(f14(x14454,x14452,a1),x14455,a1),a1),f7(x14453,f12(f14(f7(x14454,x14451,a1),x14452,a1),x14455,a1),a1)) % 1.29/1.20 [1446]~P4(x14464,x14461,a1)+E(f7(f12(f14(x14461,x14462,a1),x14463,a1),f12(f14(x14464,x14462,a1),x14465,a1),a1),f7(f12(f14(f7(x14461,x14464,a1),x14462,a1),x14463,a1),x14465,a1)) % 1.29/1.20 [340]~P55(x3401)+~P51(x3401)+E(f10(f13(x3401),x3401),f13(x3401)) % 1.29/1.20 [700]~P40(x7001)+~P4(f2(x7001),f2(x7001),x7001)+E(f12(f2(x7001),f2(x7001),x7001),f2(x7001)) % 1.29/1.20 [502]E(x5021,x5022)+P6(x5022,x5021,a1)+P6(x5021,x5022,a1) % 1.29/1.20 [564]E(x5641,x5642)+P6(x5641,x5642,a1)+~P4(x5641,x5642,a1) % 1.29/1.20 [655]E(x6551,x6552)+~P4(x6552,x6551,a1)+~P4(x6551,x6552,a1) % 1.29/1.20 [338]~P36(x3382)+~E(f16(x3381,x3382),x3381)+E(x3381,f2(x3382)) % 1.29/1.20 [341]~P29(x3412)+~E(f16(x3411,x3412),f2(x3412))+E(x3411,f2(x3412)) % 1.29/1.20 [342]~P37(x3422)+~E(f8(x3421,x3422),f2(x3422))+E(x3421,f2(x3422)) % 1.29/1.20 [343]~P52(x3432)+~E(f10(x3431,x3432),f2(x3432))+E(x3431,f2(x3432)) % 1.29/1.20 [344]~P61(x3442)+~E(f15(x3441,x3442),f2(x3442))+E(x3441,f2(x3442)) % 1.29/1.20 [345]~P29(x3451)+~E(f16(x3452,x3451),f2(x3451))+E(f2(x3451),x3452) % 1.29/1.20 [405]~P55(x4052)+E(f11(x4051,x4051,x4052),f13(x4052))+E(x4051,f2(x4052)) % 1.29/1.20 [419]~P16(x4192)+~P56(x4192)+E(f7(x4191,x4191,x4192),f2(x4192)) % 1.29/1.20 [432]~P47(x4322)+P6(x4321,f2(x4322),x4322)+E(f8(x4321,x4322),x4321) % 1.29/1.20 [452]~P30(x4522)+P4(x4521,f2(x4522),x4522)+~E(f28(x4521,x4522),x4521) % 1.29/1.20 [453]~P30(x4531)+P4(f2(x4531),x4532,x4531)+~E(f27(x4532,x4531),x4532) % 1.29/1.20 [467]E(x4671,f2(a1))+E(x4672,f2(a1))+~E(f14(x4672,x4671,a1),f2(a1)) % 1.29/1.20 [468]~P30(x4682)+P4(x4681,f2(x4682),x4682)+~E(f27(x4681,x4682),f2(x4682)) % 1.29/1.20 [469]~P61(x4691)+P6(f2(x4691),x4692,x4691)+~E(f15(x4692,x4691),f13(x4691)) % 1.29/1.20 [470]~P30(x4701)+P4(f2(x4701),x4702,x4701)+~E(f28(x4702,x4701),f2(x4701)) % 1.29/1.20 [475]~P37(x4752)+P6(f2(x4752),f8(x4751,x4752),x4752)+E(x4751,f2(x4752)) % 1.29/1.20 [485]~P30(x4852)+~E(f12(x4851,x4851,x4852),f2(x4852))+E(x4851,f2(x4852)) % 1.29/1.20 [499]~P45(x4992)+~P8(f2(x4992),x4991,x4992)+E(x4991,f2(x4992)) % 1.29/1.20 [537]~P30(x5372)+~P4(x5371,f2(x5372),x5372)+E(f28(x5371,x5372),x5371) % 1.29/1.20 [538]~P37(x5382)+~P6(f2(x5382),x5381,x5382)+E(f8(x5381,x5382),x5381) % 1.29/1.20 [539]~P37(x5392)+~P4(f2(x5392),x5391,x5392)+E(f8(x5391,x5392),x5391) % 1.29/1.20 [540]~P30(x5402)+~P4(f2(x5402),x5401,x5402)+E(f27(x5401,x5402),x5401) % 1.29/1.20 [546]~P30(x5462)+~P4(x5461,f2(x5462),x5462)+E(f27(x5461,x5462),f2(x5462)) % 1.29/1.20 [547]~P30(x5472)+~P4(f2(x5472),x5471,x5472)+E(f28(x5471,x5472),f2(x5472)) % 1.29/1.20 [548]~P61(x5482)+~P6(f2(x5482),x5481,x5482)+E(f15(x5481,x5482),f13(x5482)) % 1.29/1.20 [554]~P37(x5542)+~P6(x5541,f2(x5542),x5542)+E(f8(x5541,x5542),f16(x5541,x5542)) % 1.29/1.20 [555]~P37(x5552)+~P4(x5551,f2(x5552),x5552)+E(f8(x5551,x5552),f16(x5551,x5552)) % 1.29/1.20 [556]~P47(x5562)+~P6(x5561,f2(x5562),x5562)+E(f8(x5561,x5562),f16(x5561,x5562)) % 1.29/1.20 [591]~P6(x5911,x5912,a1)+E(f32(x5911),x5912)+P6(f32(x5911),x5912,a1) % 1.29/1.20 [592]E(x5921,x5922)+P6(x5922,x5921,a1)+~P6(x5922,f32(x5921),a1) % 1.29/1.20 [594]E(x5941,x5942)+P6(x5941,x5942,a1)+~P6(x5941,f32(x5942),a1) % 1.29/1.20 [603]~P37(x6032)+~P4(f8(x6031,x6032),f2(x6032),x6032)+E(x6031,f2(x6032)) % 1.29/1.20 [620]P4(x6201,x6202,a1)+E(x6201,f32(x6202))+~P4(x6201,f32(x6202),a1) % 1.29/1.20 [672]E(x6721,x6722)+~E(f7(x6722,x6721,a1),f2(a1))+~E(f7(x6721,x6722,a1),f2(a1)) % 1.29/1.20 [676]E(x6761,x6762)+~P4(x6762,x6761,a1)+~P6(x6761,f32(x6762),a1) % 1.29/1.20 [699]~P44(x6991)+P6(f2(x6991),f23(x6992,x6991),x6991)+~P6(f2(a1),x6992,a1) % 1.29/1.20 [701]~P61(x7012)+~P6(x7011,f2(x7012),x7012)+P6(x7011,f16(x7011,x7012),x7012) % 1.29/1.20 [702]~P30(x7022)+~P4(x7021,f2(x7022),x7022)+P4(x7021,f16(x7021,x7022),x7022) % 1.29/1.20 [703]~P36(x7032)+~P4(x7031,f2(x7032),x7032)+P4(x7031,f16(x7031,x7032),x7032) % 1.29/1.20 [704]~P30(x7042)+~P4(f2(x7042),x7041,x7042)+P4(f16(x7041,x7042),x7041,x7042) % 1.29/1.20 [705]~P36(x7052)+~P4(f2(x7052),x7051,x7052)+P4(f16(x7051,x7052),x7051,x7052) % 1.29/1.20 [716]~P38(x7161)+~P6(x7162,f2(x7161),x7161)+P6(f2(x7161),f16(x7162,x7161),x7161) % 1.29/1.20 [717]~P38(x7171)+~P4(x7172,f2(x7171),x7171)+P4(f2(x7171),f16(x7172,x7171),x7171) % 1.29/1.20 [718]~P62(x7181)+~P6(f2(x7181),x7182,x7181)+P6(f2(x7181),f10(x7182,x7181),x7181) % 1.29/1.20 [719]~P61(x7191)+~P6(f2(x7191),x7192,x7191)+P6(f2(x7191),f15(x7192,x7191),x7191) % 1.29/1.20 [720]~P62(x7202)+~P6(x7201,f2(x7202),x7202)+P6(f10(x7201,x7202),f2(x7202),x7202) % 1.29/1.20 [721]~P61(x7212)+~P6(x7211,f2(x7212),x7212)+P6(f15(x7211,x7212),f2(x7212),x7212) % 1.29/1.20 [722]~P38(x7222)+~P6(f2(x7222),x7221,x7222)+P6(f16(x7221,x7222),f2(x7222),x7222) % 1.29/1.20 [723]~P38(x7232)+~P4(f2(x7232),x7231,x7232)+P4(f16(x7231,x7232),f2(x7232),x7232) % 1.29/1.20 [726]~P61(x7262)+~P6(x7261,f16(x7261,x7262),x7262)+P6(x7261,f2(x7262),x7262) % 1.29/1.20 [727]~P30(x7272)+~P4(x7271,f16(x7271,x7272),x7272)+P4(x7271,f2(x7272),x7272) % 1.29/1.20 [728]~P36(x7282)+~P4(x7281,f16(x7281,x7282),x7282)+P4(x7281,f2(x7282),x7282) % 1.29/1.20 [729]~P30(x7291)+~P4(f16(x7292,x7291),x7292,x7291)+P4(f2(x7291),x7292,x7291) % 1.29/1.20 [730]~P36(x7301)+~P4(f16(x7302,x7301),x7302,x7301)+P4(f2(x7301),x7302,x7301) % 1.29/1.20 [747]~P44(x7472)+~P6(f2(x7472),f23(x7471,x7472),x7472)+P6(f2(a1),x7471,a1) % 1.29/1.20 [749]~P38(x7492)+~P6(f2(x7492),f16(x7491,x7492),x7492)+P6(x7491,f2(x7492),x7492) % 1.29/1.20 [750]~P38(x7502)+~P4(f2(x7502),f16(x7501,x7502),x7502)+P4(x7501,f2(x7502),x7502) % 1.29/1.20 [751]~P61(x7512)+~P6(f15(x7511,x7512),f2(x7512),x7512)+P6(x7511,f2(x7512),x7512) % 1.29/1.20 [752]~P61(x7521)+~P6(f2(x7521),f15(x7522,x7521),x7521)+P6(f2(x7521),x7522,x7521) % 1.29/1.20 [753]~P38(x7531)+~P6(f16(x7532,x7531),f2(x7531),x7531)+P6(f2(x7531),x7532,x7531) % 1.29/1.20 [754]~P38(x7541)+~P4(f16(x7542,x7541),f2(x7541),x7541)+P4(f2(x7541),x7542,x7541) % 1.29/1.20 [884]~P30(x8841)+~P6(f2(x8841),x8842,x8841)+P6(f2(x8841),f12(x8842,x8842,x8841),x8841) % 1.29/1.20 [886]~P30(x8861)+~P4(f2(x8861),x8862,x8861)+P4(f2(x8861),f12(x8862,x8862,x8861),x8861) % 1.29/1.20 [889]~P30(x8892)+~P6(x8891,f2(x8892),x8892)+P6(f12(x8891,x8891,x8892),f2(x8892),x8892) % 1.29/1.20 [890]~P61(x8902)+~P6(x8901,f2(x8902),x8902)+P6(f12(x8901,x8901,x8902),f2(x8902),x8902) % 1.29/1.20 [891]~P30(x8912)+~P4(x8911,f2(x8912),x8912)+P4(f12(x8911,x8911,x8912),f2(x8912),x8912) % 1.29/1.20 [1000]~P30(x10002)+~P6(f12(x10001,x10001,x10002),f2(x10002),x10002)+P6(x10001,f2(x10002),x10002) % 1.29/1.20 [1001]~P61(x10012)+~P6(f12(x10011,x10011,x10012),f2(x10012),x10012)+P6(x10011,f2(x10012),x10012) % 1.29/1.20 [1002]~P30(x10022)+~P4(f12(x10021,x10021,x10022),f2(x10022),x10022)+P4(x10021,f2(x10022),x10022) % 1.29/1.20 [1003]~P30(x10031)+~P6(f2(x10031),f12(x10032,x10032,x10031),x10031)+P6(f2(x10031),x10032,x10031) % 1.29/1.20 [1004]~P30(x10041)+~P4(f2(x10041),f12(x10042,x10042,x10041),x10041)+P4(f2(x10041),x10042,x10041) % 1.29/1.20 [1005]P6(f7(x10051,x10052,a1),x10051,a1)+~P6(f2(a1),x10052,a1)+~P6(f2(a1),x10051,a1) % 1.29/1.20 [1008]~P6(f2(a1),x10082,a1)+~P6(f2(a1),x10081,a1)+P6(f2(a1),f14(x10081,x10082,a1),a1) % 1.29/1.20 [1069]P6(f2(a1),x10691,a1)+P6(f2(a1),x10692,a1)+~P6(f2(a1),f12(x10691,x10692,a1),a1) % 1.29/1.20 [355]~P52(x3552)+E(x3551,f2(x3552))+E(f10(f10(x3551,x3552),x3552),x3551) % 1.29/1.20 [359]~P51(x3592)+~P52(x3592)+E(f10(f10(x3591,x3592),x3592),x3591) % 1.29/1.20 [422]~P16(x4222)+~P56(x4222)+E(f12(x4221,f2(x4222),x4222),x4221) % 1.29/1.20 [427]~P55(x4272)+~P51(x4272)+E(f11(x4271,f2(x4272),x4272),f2(x4272)) % 1.29/1.20 [433]~P1(x4331)+~P2(x4331)+E(f33(f2(x4331),f32(x4332),x4331),f2(x4331)) % 1.29/1.20 [455]~P52(x4552)+E(x4551,f2(x4552))+E(f10(f16(x4551,x4552),x4552),f16(f10(x4551,x4552),x4552)) % 1.29/1.20 [456]~P62(x4562)+E(x4561,f2(x4562))+E(f10(f8(x4561,x4562),x4562),f8(f10(x4561,x4562),x4562)) % 1.29/1.20 [465]~P51(x4652)+~P52(x4652)+E(f10(f16(x4651,x4652),x4652),f16(f10(x4651,x4652),x4652)) % 1.29/1.20 [466]~P62(x4662)+~P51(x4662)+E(f10(f8(x4661,x4662),x4662),f8(f10(x4661,x4662),x4662)) % 1.29/1.20 [471]~P52(x4712)+E(x4711,f2(x4712))+E(f14(x4711,f10(x4711,x4712),x4712),f13(x4712)) % 1.29/1.20 [472]~P55(x4722)+E(x4721,f2(x4722))+E(f14(f10(x4721,x4722),x4721,x4722),f13(x4722)) % 1.29/1.20 [473]~P52(x4732)+E(x4731,f2(x4732))+E(f14(f10(x4731,x4732),x4731,x4732),f13(x4732)) % 1.29/1.20 [481]E(x4811,f2(a1))+E(x4812,f2(a1))+~E(f12(x4812,x4811,a1),f32(f2(a1))) % 1.29/1.20 [494]E(x4941,f2(a1))+E(x4941,f32(f2(a1)))+~E(f12(x4942,x4941,a1),f32(f2(a1))) % 1.29/1.20 [495]E(x4951,f2(a1))+E(x4951,f32(f2(a1)))+~E(f12(x4951,x4952,a1),f32(f2(a1))) % 1.29/1.20 [507]E(x5071,f32(f2(a1)))+E(x5072,f32(f2(a1)))+~E(f12(x5072,x5071,a1),f32(f2(a1))) % 1.29/1.20 [549]~P61(x5492)+P6(x5491,f2(x5492),x5492)+~E(f15(x5491,x5492),f16(f13(x5492),x5492)) % 1.29/1.20 [559]~P61(x5592)+~P6(x5591,f2(x5592),x5592)+E(f15(x5591,x5592),f16(f13(x5592),x5592)) % 1.29/1.20 [581]~P30(x5812)+E(x5811,f2(x5812))+~E(f20(x5811,f16(x5811,x5812),x5812),f2(x5812)) % 1.29/1.20 [582]~P30(x5822)+E(x5821,f2(x5822))+~E(f21(x5821,f16(x5821,x5822),x5822),f2(x5822)) % 1.29/1.20 [1067]P6(x10671,f14(x10672,x10671,a1),a1)+~P6(f32(f2(a1)),x10672,a1)+~P6(f32(f2(a1)),x10671,a1) % 1.29/1.20 [1068]P6(x10681,f14(x10681,x10682,a1),a1)+~P6(f32(f2(a1)),x10682,a1)+~P6(f32(f2(a1)),x10681,a1) % 1.29/1.20 [1119]~P6(f32(f2(a1)),x11192,a1)+~P6(f32(f2(a1)),x11191,a1)+P6(f32(f2(a1)),f14(x11191,x11192,a1),a1) % 1.29/1.20 [1120]~P4(f32(f2(a1)),x11202,a1)+~P4(f32(f2(a1)),x11201,a1)+P4(f32(f2(a1)),f14(x11201,x11202,a1),a1) % 1.29/1.20 [725]~P55(x7251)+~P51(x7251)+E(f11(f14(f2(x7251),x7252,x7251),x7252,x7251),f2(x7251)) % 1.29/1.20 [534]P4(x5342,x5341,x5343)+~P10(x5343)+P6(x5341,x5342,x5343) % 1.29/1.20 [536]P4(x5362,x5361,x5363)+~P10(x5363)+P4(x5361,x5362,x5363) % 1.29/1.20 [589]~P42(x5893)+~P6(x5891,x5892,x5893)+P4(x5891,x5892,x5893) % 1.29/1.20 [590]~P43(x5903)+~P6(x5901,x5902,x5903)+P4(x5901,x5902,x5903) % 1.29/1.20 [677]~P6(x6773,x6772,x6771)+~P10(x6771)+~P6(x6772,x6773,x6771) % 1.29/1.20 [679]~P4(x6793,x6792,x6791)+~P10(x6791)+~P6(x6792,x6793,x6791) % 1.29/1.20 [682]~P6(x6823,x6822,x6821)+~P42(x6821)+~P6(x6822,x6823,x6821) % 1.29/1.20 [683]~P4(x6833,x6832,x6831)+~P42(x6831)+~P6(x6832,x6833,x6831) % 1.29/1.20 [684]~P6(x6843,x6842,x6841)+~P43(x6841)+~P6(x6842,x6843,x6841) % 1.29/1.20 [785]~P4(x7851,x7853,a1)+P4(x7851,x7852,a1)+~P4(x7853,x7852,a1) % 1.29/1.20 [356]~P15(x3563)+E(x3561,x3562)+~E(f16(x3561,x3563),f16(x3562,x3563)) % 1.29/1.20 [357]~P29(x3573)+E(x3571,x3572)+~E(f16(x3571,x3573),f16(x3572,x3573)) % 1.29/1.20 [358]~P13(x3583)+E(x3581,x3582)+~E(f23(x3581,x3583),f23(x3582,x3583)) % 1.29/1.20 [478]~P29(x4783)+E(x4781,x4782)+~E(f7(x4781,x4782,x4783),f2(x4783)) % 1.29/1.20 [479]~P22(x4793)+E(x4791,x4792)+~E(f7(x4791,x4792,x4793),f2(x4793)) % 1.29/1.20 [484]~P17(x4842)+~E(f21(x4843,x4841,x4842),f17(x4842))+E(x4841,f17(x4842)) % 1.29/1.20 [486]~P72(x4862)+~E(f33(x4861,x4863,x4862),f2(x4862))+E(x4861,f2(x4862)) % 1.29/1.20 [487]~P17(x4872)+~E(f21(x4871,x4873,x4872),f17(x4872))+E(x4871,f17(x4872)) % 1.29/1.20 [489]~P61(x4893)+P8(x4891,x4892,x4893)+~E(f8(x4891,x4893),f8(x4892,x4893)) % 1.29/1.20 [518]~P29(x5183)+~E(f12(x5181,x5182,x5183),f2(x5183))+E(x5181,f16(x5182,x5183)) % 1.29/1.20 [519]~P29(x5192)+~E(f12(x5191,x5193,x5192),f2(x5192))+E(f16(x5191,x5192),x5193) % 1.29/1.20 [520]~P52(x5202)+~E(f14(x5201,x5203,x5202),f13(x5202))+E(f10(x5201,x5202),x5203) % 1.29/1.20 [595]~P10(x5953)+~P4(x5952,x5951,x5953)+E(f31(x5951,x5952,x5953),x5952) % 1.29/1.20 [596]~P10(x5963)+~P4(x5961,x5962,x5963)+E(f31(x5961,x5962,x5963),x5961) % 1.29/1.20 [597]~P20(x5973)+~P4(x5972,x5971,x5973)+E(f20(x5971,x5972,x5973),x5972) % 1.29/1.20 [598]~P20(x5983)+~P4(x5981,x5982,x5983)+E(f20(x5981,x5982,x5983),x5981) % 1.29/1.20 [599]~P10(x5993)+~P4(x5991,x5992,x5993)+E(f30(x5991,x5992,x5993),x5992) % 1.29/1.20 [600]~P10(x6003)+~P4(x6002,x6001,x6003)+E(f30(x6001,x6002,x6003),x6001) % 1.29/1.20 [601]~P18(x6013)+~P4(x6011,x6012,x6013)+E(f21(x6011,x6012,x6013),x6012) % 1.29/1.20 [602]~P18(x6023)+~P4(x6022,x6021,x6023)+E(f21(x6021,x6022,x6023),x6021) % 1.29/1.20 [608]~P10(x6083)+P4(x6081,x6082,x6083)+~E(f31(x6081,x6082,x6083),x6081) % 1.29/1.20 [609]~P20(x6093)+P4(x6091,x6092,x6093)+~E(f20(x6091,x6092,x6093),x6091) % 1.29/1.20 [610]~P10(x6103)+P4(x6101,x6102,x6103)+~E(f30(x6101,x6102,x6103),x6102) % 1.29/1.20 [611]~P18(x6113)+P4(x6111,x6112,x6113)+~E(f21(x6111,x6112,x6113),x6112) % 1.29/1.20 [621]~P3(x6213)+~P8(x6212,x6211,x6213)+E(f9(x6211,x6212,x6213),f2(x6213)) % 1.29/1.20 [622]~P3(x6223)+P8(x6221,x6222,x6223)+~E(f9(x6222,x6221,x6223),f2(x6223)) % 1.29/1.20 [659]E(x6591,x6592)+~E(f14(x6593,x6591,a1),f14(x6593,x6592,a1))+E(x6593,f2(a1)) % 1.29/1.20 [660]E(x6601,x6602)+~E(f14(x6601,x6603,a1),f14(x6602,x6603,a1))+E(x6603,f2(a1)) % 1.29/1.20 [663]~P48(x6633)+~P8(x6631,x6632,x6633)+P8(x6631,f16(x6632,x6633),x6633) % 1.29/1.20 [664]~P61(x6643)+~P8(x6641,x6642,x6643)+P8(x6641,f8(x6642,x6643),x6643) % 1.29/1.20 [665]~P48(x6652)+~P8(x6651,x6653,x6652)+P8(f16(x6651,x6652),x6653,x6652) % 1.29/1.20 [666]~P61(x6662)+~P8(x6661,x6663,x6662)+P8(f8(x6661,x6662),x6663,x6662) % 1.29/1.20 [709]~P61(x7093)+P8(x7091,x7092,x7093)+~P8(x7091,f8(x7092,x7093),x7093) % 1.29/1.20 [710]~P48(x7103)+P8(x7101,x7102,x7103)+~P8(x7101,f16(x7102,x7103),x7103) % 1.29/1.20 [711]~P61(x7113)+P6(x7111,x7112,x7113)+~P6(f8(x7111,x7113),x7112,x7113) % 1.29/1.20 [712]~P37(x7123)+P4(x7121,x7122,x7123)+~P4(f8(x7121,x7123),x7122,x7123) % 1.29/1.20 [713]~P61(x7133)+P8(x7131,x7132,x7133)+~P8(f8(x7131,x7133),x7132,x7133) % 1.29/1.20 [714]~P48(x7143)+P8(x7141,x7142,x7143)+~P8(f16(x7141,x7143),x7142,x7143) % 1.29/1.20 [742]~P44(x7422)+~P6(x7421,x7423,a1)+P6(f23(x7421,x7422),f23(x7423,x7422),x7422) % 1.29/1.20 [743]~P44(x7432)+~P4(x7431,x7433,a1)+P4(f23(x7431,x7432),f23(x7433,x7432),x7432) % 1.29/1.20 [745]~P38(x7452)+~P6(x7453,x7451,x7452)+P6(f16(x7451,x7452),f16(x7453,x7452),x7452) % 1.29/1.20 [746]~P38(x7462)+~P4(x7463,x7461,x7462)+P4(f16(x7461,x7462),f16(x7463,x7462),x7462) % 1.29/1.20 [774]~P38(x7743)+~P6(x7742,f16(x7741,x7743),x7743)+P6(x7741,f16(x7742,x7743),x7743) % 1.29/1.20 [776]~P38(x7763)+~P4(x7762,f16(x7761,x7763),x7763)+P4(x7761,f16(x7762,x7763),x7763) % 1.29/1.20 [778]~P38(x7782)+~P6(f16(x7783,x7782),x7781,x7782)+P6(f16(x7781,x7782),x7783,x7782) % 1.29/1.20 [779]~P61(x7792)+~P6(f8(x7791,x7792),x7793,x7792)+P6(f16(x7791,x7792),x7793,x7792) % 1.29/1.20 [781]~P38(x7812)+~P4(f16(x7813,x7812),x7811,x7812)+P4(f16(x7811,x7812),x7813,x7812) % 1.29/1.20 [782]~P37(x7822)+~P4(f8(x7821,x7822),x7823,x7822)+P4(f16(x7821,x7822),x7823,x7822) % 1.29/1.20 [799]~P6(x7991,x7993,a1)+~P6(x7993,x7992,a1)+P6(f32(x7991),x7992,a1) % 1.29/1.20 [800]~P44(x8003)+~P6(f23(x8001,x8003),f23(x8002,x8003),x8003)+P6(x8001,x8002,a1) % 1.29/1.20 [801]~P44(x8013)+~P4(f23(x8011,x8013),f23(x8012,x8013),x8013)+P4(x8011,x8012,a1) % 1.29/1.20 [808]~P38(x8083)+P6(x8081,x8082,x8083)+~P6(f16(x8082,x8083),f16(x8081,x8083),x8083) % 1.29/1.20 [809]~P38(x8093)+P4(x8091,x8092,x8093)+~P4(f16(x8092,x8093),f16(x8091,x8093),x8093) % 1.29/1.20 [879]E(x8791,x8792)+~E(f14(x8793,x8791,a1),f14(x8793,x8792,a1))+~P6(f2(a1),x8793,a1) % 1.29/1.20 [880]~P45(x8803)+P8(x8801,f33(x8801,x8802,x8803),x8803)+~P6(f2(a1),x8802,a1) % 1.29/1.20 [882]~P38(x8823)+~P6(x8821,x8822,x8823)+P6(f7(x8821,x8822,x8823),f2(x8823),x8823) % 1.29/1.20 [883]~P38(x8833)+~P4(x8831,x8832,x8833)+P4(f7(x8831,x8832,x8833),f2(x8833),x8833) % 1.29/1.20 [885]~P44(x8851)+~P6(f2(x8851),x8852,x8851)+P6(f2(x8851),f33(x8852,x8853,x8851),x8851) % 1.29/1.20 [887]~P44(x8871)+~P4(f2(x8871),x8872,x8871)+P4(f2(x8871),f33(x8872,x8873,x8871),x8871) % 1.29/1.20 [888]~P44(x8881)+~P4(f13(x8881),x8882,x8881)+P4(f13(x8881),f33(x8882,x8883,x8881),x8881) % 1.29/1.20 [923]~P30(x9233)+~P4(x9231,f16(x9232,x9233),x9233)+P4(f12(x9231,x9232,x9233),f2(x9233),x9233) % 1.29/1.20 [960]~P38(x9603)+P6(x9601,x9602,x9603)+~P6(f7(x9601,x9602,x9603),f2(x9603),x9603) % 1.29/1.20 [961]~P38(x9613)+P4(x9611,x9612,x9613)+~P4(f7(x9611,x9612,x9613),f2(x9613),x9613) % 1.29/1.20 [1044]~P30(x10443)+~P4(f12(x10441,x10442,x10443),f2(x10443),x10443)+P4(x10441,f16(x10442,x10443),x10443) % 1.29/1.20 [1173]~P6(x11731,x11733,a1)+~P4(x11732,x11731,a1)+P6(f7(x11731,x11732,a1),f7(x11733,x11732,a1),a1) % 1.29/1.20 [1174]~P6(x11743,x11742,a1)+~P6(x11743,x11741,a1)+P6(f7(x11741,x11742,a1),f7(x11741,x11743,a1),a1) % 1.29/1.20 [1179]~P6(x11791,x11793,a1)+P6(f14(x11791,x11792,a1),f14(x11793,x11792,a1),a1)+~P6(f2(a1),x11792,a1) % 1.29/1.20 [1182]~P6(x11822,x11823,a1)+P6(f14(x11821,x11822,a1),f14(x11821,x11823,a1),a1)+~P6(f2(a1),x11821,a1) % 1.29/1.20 [1278]~P4(x12783,x12782,a1)+~P4(f12(x12781,x12783,a1),x12782,a1)+P4(x12781,f7(x12782,x12783,a1),a1) % 1.29/1.20 [1279]~P4(x12792,x12793,a1)+~P4(x12791,f7(x12793,x12792,a1),a1)+P4(f12(x12791,x12792,a1),x12793,a1) % 1.29/1.20 [1336]P4(x13361,x13362,a1)+~P4(f14(x13363,x13361,a1),f14(x13363,x13362,a1),a1)+~P6(f2(a1),x13363,a1) % 1.29/1.20 [1337]P4(x13371,x13372,a1)+~P4(f14(x13371,x13373,a1),f14(x13372,x13373,a1),a1)+~P6(f2(a1),x13373,a1) % 1.29/1.20 [661]~P55(x6612)+E(x6611,f2(x6612))+E(f11(f16(x6613,x6612),f16(x6611,x6612),x6612),f11(x6613,x6611,x6612)) % 1.29/1.20 [670]~P55(x6702)+E(x6701,f2(x6702))+E(f11(f14(x6703,x6701,x6702),x6701,x6702),x6703) % 1.29/1.20 [671]~P55(x6712)+~P51(x6712)+E(f11(f16(x6711,x6712),f16(x6713,x6712),x6712),f11(x6711,x6713,x6712)) % 1.29/1.20 [715]~P55(x7153)+~P51(x7153)+E(f10(f11(x7151,x7152,x7153),x7153),f11(x7152,x7151,x7153)) % 1.29/1.20 [771]~P55(x7712)+E(x7711,f2(x7712))+E(f11(x7713,f16(x7711,x7712),x7712),f16(f11(x7713,x7711,x7712),x7712)) % 1.29/1.20 [772]~P52(x7722)+E(x7721,f2(x7722))+E(f33(f10(x7721,x7722),x7723,x7722),f10(f33(x7721,x7723,x7722),x7722)) % 1.29/1.20 [783]~P55(x7833)+~P51(x7833)+E(f11(x7831,f16(x7832,x7833),x7833),f16(f11(x7831,x7832,x7833),x7833)) % 1.29/1.20 [784]~P51(x7842)+~P52(x7842)+E(f33(f10(x7841,x7842),x7843,x7842),f10(f33(x7841,x7843,x7842),x7842)) % 1.29/1.20 [829]~P62(x8292)+E(x8291,f2(x8292))+E(f11(f8(x8293,x8292),f8(x8291,x8292),x8292),f8(f11(x8293,x8291,x8292),x8292)) % 1.29/1.20 [839]~P62(x8392)+~P51(x8392)+E(f11(f8(x8391,x8392),f8(x8393,x8392),x8392),f8(f11(x8391,x8393,x8392),x8392)) % 1.29/1.20 [840]~P55(x8402)+~P51(x8402)+E(f14(f10(x8401,x8402),f10(x8403,x8402),x8402),f10(f14(x8401,x8403,x8402),x8402)) % 1.29/1.20 [897]~P44(x8971)+~P6(f13(x8971),x8972,x8971)+P6(f13(x8971),f33(x8972,f32(x8973),x8971),x8971) % 1.29/1.20 [925]~P61(x9252)+~P4(f2(x9252),x9253,x9252)+E(f14(f8(x9251,x9252),x9253,x9252),f8(f14(x9251,x9253,x9252),x9252)) % 1.29/1.20 [931]~P74(x9312)+~P4(x9313,x9311,a1)+E(f7(f23(x9311,x9312),f23(x9313,x9312),x9312),f23(f7(x9311,x9313,a1),x9312)) % 1.29/1.20 [1218]~P63(x12182)+E(x12181,f2(x12182))+~E(f12(f14(x12183,x12183,x12182),f14(x12181,x12181,x12182),x12182),f2(x12182)) % 1.29/1.20 [1219]~P63(x12192)+E(x12191,f2(x12192))+~E(f12(f14(x12191,x12191,x12192),f14(x12193,x12193,x12192),x12192),f2(x12192)) % 1.29/1.20 [1272]~P4(x12722,x12723,a1)+~P4(x12722,x12721,a1)+E(f7(f7(x12721,x12722,a1),f7(x12723,x12722,a1),a1),f7(x12721,x12723,a1)) % 1.29/1.20 [1277]~P44(x12771)+~P6(f13(x12771),x12772,x12771)+P6(f13(x12771),f14(x12772,f33(x12772,x12773,x12771),x12771),x12771) % 1.29/1.20 [1358]~P44(x13583)+~P6(f13(x13583),x13581,x13583)+P6(f33(x13581,x13582,x13583),f14(x13581,f33(x13581,x13582,x13583),x13583),x13583) % 1.29/1.20 [1376]~P63(x13762)+E(x13761,f2(x13762))+P6(f2(x13762),f12(f14(x13763,x13763,x13762),f14(x13761,x13761,x13762),x13762),x13762) % 1.29/1.20 [1377]~P63(x13772)+E(x13771,f2(x13772))+P6(f2(x13772),f12(f14(x13771,x13771,x13772),f14(x13773,x13773,x13772),x13772),x13772) % 1.29/1.20 [1433]~P63(x14332)+E(x14331,f2(x14332))+~P4(f12(f14(x14333,x14333,x14332),f14(x14331,x14331,x14332),x14332),f2(x14332),x14332) % 1.29/1.20 [1434]~P63(x14342)+E(x14341,f2(x14342))+~P4(f12(f14(x14341,x14341,x14342),f14(x14343,x14343,x14342),x14342),f2(x14342),x14342) % 1.29/1.20 [1045]~P55(x10451)+~P51(x10451)+E(f33(f11(f13(x10451),x10452,x10451),x10453,x10451),f11(f13(x10451),f33(x10452,x10453,x10451),x10451)) % 1.29/1.20 [1404]~P62(x14043)+~P6(x14041,x14042,x14043)+P6(x14041,f11(f12(x14041,x14042,x14043),f12(f13(x14043),f13(x14043),x14043),x14043),x14043) % 1.29/1.20 [1405]~P62(x14053)+~P6(x14051,x14052,x14053)+P6(f11(f12(x14051,x14052,x14053),f12(f13(x14053),f13(x14053),x14053),x14053),x14052,x14053) % 1.29/1.20 [667]~P5(x6673,x6674,x6671)+E(x6671,x6672)+~P5(x6673,x6674,x6672) % 1.29/1.20 [685]~P23(x6854)+E(x6851,x6852)+~E(f12(x6853,x6851,x6854),f12(x6853,x6852,x6854)) % 1.29/1.20 [686]~P26(x6864)+E(x6861,x6862)+~E(f12(x6863,x6861,x6864),f12(x6863,x6862,x6864)) % 1.29/1.20 [687]~P22(x6874)+E(x6871,x6872)+~E(f7(x6873,x6873,x6874),f7(x6871,x6872,x6874)) % 1.29/1.20 [688]~P26(x6884)+E(x6881,x6882)+~E(f12(x6881,x6883,x6884),f12(x6882,x6883,x6884)) % 1.29/1.20 [689]~P22(x6893)+E(x6891,x6892)+~E(f7(x6891,x6892,x6893),f7(x6894,x6894,x6893)) % 1.29/1.20 [854]~P10(x8544)+~P6(x8541,x8543,x8544)+P6(x8541,f30(x8542,x8543,x8544),x8544) % 1.29/1.20 [856]~P10(x8564)+~P6(x8561,x8562,x8564)+P6(x8561,f30(x8562,x8563,x8564),x8564) % 1.29/1.20 [857]~P18(x8574)+~P6(x8571,x8573,x8574)+P6(x8571,f21(x8572,x8573,x8574),x8574) % 1.29/1.20 [858]~P18(x8584)+~P6(x8581,x8582,x8584)+P6(x8581,f21(x8582,x8583,x8584),x8584) % 1.29/1.20 [860]~P10(x8604)+~P4(x8601,x8603,x8604)+P4(x8601,f30(x8602,x8603,x8604),x8604) % 1.29/1.20 [862]~P10(x8624)+~P4(x8621,x8622,x8624)+P4(x8621,f30(x8622,x8623,x8624),x8624) % 1.29/1.20 [863]~P18(x8634)+~P4(x8631,x8633,x8634)+P4(x8631,f21(x8632,x8633,x8634),x8634) % 1.29/1.20 [864]~P18(x8644)+~P4(x8641,x8642,x8644)+P4(x8641,f21(x8642,x8643,x8644),x8644) % 1.29/1.20 [865]~P45(x8654)+~P8(x8651,x8653,x8654)+P8(x8651,f14(x8652,x8653,x8654),x8654) % 1.29/1.20 [866]~P45(x8664)+~P8(x8661,x8662,x8664)+P8(x8661,f14(x8662,x8663,x8664),x8664) % 1.29/1.20 [868]~P10(x8683)+~P6(x8682,x8684,x8683)+P6(f31(x8681,x8682,x8683),x8684,x8683) % 1.29/1.20 [870]~P10(x8703)+~P6(x8701,x8704,x8703)+P6(f31(x8701,x8702,x8703),x8704,x8703) % 1.29/1.20 [871]~P20(x8713)+~P6(x8712,x8714,x8713)+P6(f20(x8711,x8712,x8713),x8714,x8713) % 1.29/1.20 [872]~P20(x8723)+~P6(x8721,x8724,x8723)+P6(f20(x8721,x8722,x8723),x8724,x8723) % 1.29/1.20 [874]~P10(x8743)+~P4(x8742,x8744,x8743)+P4(f31(x8741,x8742,x8743),x8744,x8743) % 1.29/1.20 [876]~P10(x8763)+~P4(x8761,x8764,x8763)+P4(f31(x8761,x8762,x8763),x8764,x8763) % 1.29/1.20 [877]~P20(x8773)+~P4(x8772,x8774,x8773)+P4(f20(x8771,x8772,x8773),x8774,x8773) % 1.29/1.20 [878]~P20(x8783)+~P4(x8781,x8784,x8783)+P4(f20(x8781,x8782,x8783),x8784,x8783) % 1.29/1.20 [924]~P6(x9244,x9243,a1)+P6(x9241,x9242,a1)+~E(f12(x9241,x9243,a1),f12(x9244,x9242,a1)) % 1.29/1.20 [932]~P10(x9323)+P6(x9321,x9322,x9323)+~P6(x9321,f31(x9324,x9322,x9323),x9323) % 1.29/1.20 [933]~P10(x9333)+P6(x9331,x9332,x9333)+~P6(x9331,f31(x9332,x9334,x9333),x9333) % 1.29/1.20 [935]~P10(x9353)+P4(x9351,x9352,x9353)+~P4(x9351,f31(x9354,x9352,x9353),x9353) % 1.29/1.20 [937]~P10(x9373)+P4(x9371,x9372,x9373)+~P4(x9371,f31(x9372,x9374,x9373),x9373) % 1.29/1.20 [939]~P20(x9393)+P4(x9391,x9392,x9393)+~P4(x9391,f20(x9394,x9392,x9393),x9393) % 1.29/1.20 [941]~P20(x9413)+P4(x9411,x9412,x9413)+~P4(x9411,f20(x9412,x9414,x9413),x9413) % 1.29/1.20 [942]~P10(x9423)+P6(x9421,x9422,x9423)+~P6(f30(x9424,x9421,x9423),x9422,x9423) % 1.29/1.20 [943]~P10(x9433)+P6(x9431,x9432,x9433)+~P6(f30(x9431,x9434,x9433),x9432,x9433) % 1.29/1.20 [945]~P10(x9453)+P4(x9451,x9452,x9453)+~P4(f30(x9454,x9451,x9453),x9452,x9453) % 1.29/1.20 [947]~P10(x9473)+P4(x9471,x9472,x9473)+~P4(f30(x9471,x9474,x9473),x9472,x9473) % 1.29/1.20 [949]~P18(x9493)+P4(x9491,x9492,x9493)+~P4(f21(x9494,x9491,x9493),x9492,x9493) % 1.29/1.20 [951]~P18(x9513)+P4(x9511,x9512,x9513)+~P4(f21(x9511,x9514,x9513),x9512,x9513) % 1.29/1.20 [952]~P45(x9523)+P8(x9521,x9522,x9523)+~P8(f14(x9524,x9521,x9523),x9522,x9523) % 1.29/1.20 [953]~P45(x9533)+P8(x9531,x9532,x9533)+~P8(f14(x9531,x9534,x9533),x9532,x9533) % 1.29/1.20 [1054]~P45(x10543)+~P4(x10542,x10544,a1)+P8(f33(x10541,x10542,x10543),f33(x10541,x10544,x10543),x10543) % 1.29/1.20 [1056]~P34(x10563)+~P6(x10561,x10564,x10563)+P6(f12(x10561,x10562,x10563),f12(x10564,x10562,x10563),x10563) % 1.29/1.20 [1057]~P41(x10573)+~P6(x10571,x10574,x10573)+P6(f12(x10571,x10572,x10573),f12(x10574,x10572,x10573),x10573) % 1.29/1.20 [1058]~P34(x10583)+~P6(x10582,x10584,x10583)+P6(f12(x10581,x10582,x10583),f12(x10581,x10584,x10583),x10583) % 1.29/1.20 [1059]~P41(x10593)+~P6(x10592,x10594,x10593)+P6(f12(x10591,x10592,x10593),f12(x10591,x10594,x10593),x10593) % 1.29/1.20 [1060]~P34(x10603)+~P4(x10601,x10604,x10603)+P4(f12(x10601,x10602,x10603),f12(x10604,x10602,x10603),x10603) % 1.29/1.20 [1061]~P35(x10613)+~P4(x10611,x10614,x10613)+P4(f12(x10611,x10612,x10613),f12(x10614,x10612,x10613),x10613) % 1.29/1.20 [1062]~P34(x10623)+~P4(x10622,x10624,x10623)+P4(f12(x10621,x10622,x10623),f12(x10621,x10624,x10623),x10623) % 1.29/1.20 [1063]~P35(x10633)+~P4(x10632,x10634,x10633)+P4(f12(x10631,x10632,x10633),f12(x10631,x10634,x10633),x10633) % 1.29/1.20 [1064]~P56(x10643)+~P8(x10641,x10644,x10643)+P8(f14(x10641,x10642,x10643),f14(x10644,x10642,x10643),x10643) % 1.29/1.20 [1065]~P56(x10653)+~P8(x10652,x10654,x10653)+P8(f14(x10651,x10652,x10653),f14(x10651,x10654,x10653),x10653) % 1.29/1.20 [1066]~P45(x10663)+~P8(x10661,x10664,x10663)+P8(f33(x10661,x10662,x10663),f33(x10664,x10662,x10663),x10663) % 1.29/1.20 [1172]~P6(x11722,x11724,a1)+~P6(x11721,x11723,a1)+P6(f12(x11721,x11722,a1),f12(x11723,x11724,a1),a1) % 1.29/1.20 [1175]~P4(x11752,x11754,a1)+~P4(x11751,x11753,a1)+P4(f12(x11751,x11752,a1),f12(x11753,x11754,a1),a1) % 1.29/1.20 [1176]~P4(x11762,x11764,a1)+~P4(x11761,x11763,a1)+P4(f14(x11761,x11762,a1),f14(x11763,x11764,a1),a1) % 1.29/1.20 [1273]~P34(x12733)+P6(x12731,x12732,x12733)+~P6(f12(x12734,x12731,x12733),f12(x12734,x12732,x12733),x12733) % 1.29/1.20 [1274]~P34(x12743)+P6(x12741,x12742,x12743)+~P6(f12(x12741,x12744,x12743),f12(x12742,x12744,x12743),x12743) % 1.29/1.20 [1275]~P34(x12753)+P4(x12751,x12752,x12753)+~P4(f12(x12754,x12751,x12753),f12(x12754,x12752,x12753),x12753) % 1.29/1.20 [1276]~P34(x12763)+P4(x12761,x12762,x12763)+~P4(f12(x12761,x12764,x12763),f12(x12762,x12764,x12763),x12763) % 1.29/1.20 [896]~P22(x8963)+E(x8961,f16(x8962,x8963))+~E(f12(x8961,f12(x8964,x8962,x8963),x8963),x8964) % 1.29/1.20 [929]~P3(x9293)+~P8(x9294,x9292,x9293)+E(f9(f9(x9291,x9292,x9293),x9294,x9293),f9(x9291,x9294,x9293)) % 1.29/1.20 [1007]~P55(x10073)+~P51(x10073)+E(f11(f14(x10071,x10072,x10073),x10074,x10073),f14(f11(x10071,x10074,x10073),x10072,x10073)) % 1.29/1.20 [1010]~P9(x10102)+~E(f9(x10101,x10103,x10102),f9(x10104,x10103,x10102))+E(f9(f16(x10101,x10102),x10103,x10102),f9(f16(x10104,x10102),x10103,x10102)) % 1.29/1.20 [1220]~P55(x12202)+E(x12201,f2(x12202))+E(f11(f33(x12203,x12204,x12202),f33(x12201,x12204,x12202),x12202),f33(f11(x12203,x12201,x12202),x12204,x12202)) % 1.29/1.20 [1221]~P55(x12213)+~P51(x12213)+E(f11(f33(x12211,x12212,x12213),f33(x12214,x12212,x12213),x12213),f33(f11(x12211,x12214,x12213),x12212,x12213)) % 1.29/1.20 [1271]~P31(x12714)+~P4(f12(x12711,x12713,x12714),x12712,x12714)+P4(x12711,f12(x12712,f8(x12713,x12714),x12714),x12714) % 1.29/1.20 [1282]E(x12821,x12822)+E(x12823,f2(a1))+~E(f12(x12824,f14(x12823,x12821,a1),a1),f12(x12824,f14(x12823,x12822,a1),a1)) % 1.29/1.20 [1328]~P16(x13283)+~P56(x13283)+E(f12(f14(x13281,x13282,x13283),f14(x13281,x13284,x13283),x13283),f12(f14(x13281,x13284,x13283),f14(x13281,x13282,x13283),x13283)) % 1.29/1.20 [1419]E(x14191,x14192)+E(x14193,x14194)+~E(f12(f14(x14193,x14191,a1),f14(x14194,x14192,a1),a1),f12(f14(x14193,x14192,a1),f14(x14194,x14191,a1),a1)) % 1.29/1.20 [1399]~P7(x13991,x13992,x13995,x13994)+P7(x13991,x13992,x13993,x13994)+~P4(x13995,x13993,a1) % 1.29/1.20 [675]E(x6751,x6752)+~E(f22(x6753,x6751,x6754),f22(x6755,x6752,x6754))+E(x6753,f2(a1)) % 1.29/1.20 [852]~P5(x8521,x8523,x8525)+~P5(x8522,x8525,x8524)+P5(f6(x8521,x8522),x8523,x8524) % 1.29/1.20 [1158]~P22(x11583)+E(f12(x11581,x11582,x11583),x11584)+~E(f12(x11581,f12(x11585,x11582,x11583),x11583),f12(x11585,x11584,x11583)) % 1.29/1.20 [1329]~P55(x13293)+~P51(x13293)+E(f11(f14(x13291,x13292,x13293),f14(x13294,x13295,x13293),x13293),f14(f11(x13291,x13294,x13293),f11(x13292,x13295,x13293),x13293)) % 1.29/1.20 [1430]~P4(x14303,x14302,a1)+~E(f12(f14(x14303,x14304,a1),x14301,a1),f12(f14(x14302,x14304,a1),x14305,a1))+E(x14301,f12(f14(f7(x14302,x14303,a1),x14304,a1),x14305,a1)) % 1.29/1.20 [1431]~P4(x14312,x14311,a1)+~E(f12(f14(x14311,x14313,a1),x14314,a1),f12(f14(x14312,x14313,a1),x14315,a1))+E(f12(f14(f7(x14311,x14312,a1),x14313,a1),x14314,a1),x14315) % 1.29/1.20 [1451]~P4(x14513,x14512,a1)+~P6(f12(f14(x14513,x14514,a1),x14511,a1),f12(f14(x14512,x14514,a1),x14515,a1),a1)+P6(x14511,f12(f14(f7(x14512,x14513,a1),x14514,a1),x14515,a1),a1) % 1.29/1.20 [1452]~P4(x14523,x14522,a1)+~P4(f12(f14(x14523,x14524,a1),x14521,a1),f12(f14(x14522,x14524,a1),x14525,a1),a1)+P4(x14521,f12(f14(f7(x14522,x14523,a1),x14524,a1),x14525,a1),a1) % 1.29/1.20 [1453]~P4(x14532,x14531,a1)+~P6(f12(f14(x14531,x14533,a1),x14534,a1),f12(f14(x14532,x14533,a1),x14535,a1),a1)+P6(f12(f14(f7(x14531,x14532,a1),x14533,a1),x14534,a1),x14535,a1) % 1.29/1.20 [1454]~P4(x14542,x14541,a1)+~P4(f12(f14(x14541,x14543,a1),x14544,a1),f12(f14(x14542,x14543,a1),x14545,a1),a1)+P4(f12(f14(f7(x14541,x14542,a1),x14543,a1),x14544,a1),x14545,a1) % 1.29/1.20 [1459]~P4(x14591,x14594,a1)+P6(f12(f14(x14591,x14592,a1),x14593,a1),f12(f14(x14594,x14592,a1),x14595,a1),a1)+~P6(x14593,f12(f14(f7(x14594,x14591,a1),x14592,a1),x14595,a1),a1) % 1.29/1.20 [1460]~P4(x14601,x14604,a1)+P4(f12(f14(x14601,x14602,a1),x14603,a1),f12(f14(x14604,x14602,a1),x14605,a1),a1)+~P4(x14603,f12(f14(f7(x14604,x14601,a1),x14602,a1),x14605,a1),a1) % 1.29/1.20 [1461]~P4(x14614,x14611,a1)+P6(f12(f14(x14611,x14612,a1),x14613,a1),f12(f14(x14614,x14612,a1),x14615,a1),a1)+~P6(f12(f14(f7(x14611,x14614,a1),x14612,a1),x14613,a1),x14615,a1) % 1.29/1.20 [1462]~P4(x14624,x14621,a1)+P4(f12(f14(x14621,x14622,a1),x14623,a1),f12(f14(x14624,x14622,a1),x14625,a1),a1)+~P4(f12(f14(f7(x14621,x14624,a1),x14622,a1),x14623,a1),x14625,a1) % 1.29/1.20 [1437]~P7(x14371,x14373,x14374,x14376)+~P7(x14372,x14376,x14374,x14375)+P7(f6(x14371,x14372),x14373,x14374,x14375) % 1.29/1.20 [1423]~P73(x14234)+~E(f12(f14(x14233,x14235,x14234),x14231,x14234),f12(f14(x14232,x14235,x14234),x14236,x14234))+E(x14231,f12(f14(f7(x14232,x14233,x14234),x14235,x14234),x14236,x14234)) % 1.29/1.20 [1424]~P73(x14243)+~E(f12(f14(x14241,x14244,x14243),x14245,x14243),f12(f14(x14242,x14244,x14243),x14246,x14243))+E(f12(f14(f7(x14241,x14242,x14243),x14244,x14243),x14245,x14243),x14246) % 1.29/1.20 [1447]~P69(x14474)+~P6(f12(f14(x14473,x14475,x14474),x14471,x14474),f12(f14(x14472,x14475,x14474),x14476,x14474),x14474)+P6(x14471,f12(f14(f7(x14472,x14473,x14474),x14475,x14474),x14476,x14474),x14474) % 1.29/1.20 [1448]~P69(x14484)+~P4(f12(f14(x14483,x14485,x14484),x14481,x14484),f12(f14(x14482,x14485,x14484),x14486,x14484),x14484)+P4(x14481,f12(f14(f7(x14482,x14483,x14484),x14485,x14484),x14486,x14484),x14484) % 1.29/1.20 [1449]~P69(x14493)+~P6(f12(f14(x14491,x14494,x14493),x14495,x14493),f12(f14(x14492,x14494,x14493),x14496,x14493),x14493)+P6(f12(f14(f7(x14491,x14492,x14493),x14494,x14493),x14495,x14493),x14496,x14493) % 1.29/1.20 [1450]~P69(x14503)+~P4(f12(f14(x14501,x14504,x14503),x14505,x14503),f12(f14(x14502,x14504,x14503),x14506,x14503),x14503)+P4(f12(f14(f7(x14501,x14502,x14503),x14504,x14503),x14505,x14503),x14506,x14503) % 1.29/1.20 [1455]~P69(x14553)+P6(f12(f14(x14551,x14552,x14553),x14554,x14553),f12(f14(x14555,x14552,x14553),x14556,x14553),x14553)+~P6(x14554,f12(f14(f7(x14555,x14551,x14553),x14552,x14553),x14556,x14553),x14553) % 1.29/1.20 [1456]~P69(x14563)+P4(f12(f14(x14561,x14562,x14563),x14564,x14563),f12(f14(x14565,x14562,x14563),x14566,x14563),x14563)+~P4(x14564,f12(f14(f7(x14565,x14561,x14563),x14562,x14563),x14566,x14563),x14563) % 1.29/1.20 [1457]~P69(x14573)+P6(f12(f14(x14571,x14572,x14573),x14574,x14573),f12(f14(x14575,x14572,x14573),x14576,x14573),x14573)+~P6(f12(f14(f7(x14571,x14575,x14573),x14572,x14573),x14574,x14573),x14576,x14573) % 1.29/1.20 [1458]~P69(x14583)+P4(f12(f14(x14581,x14582,x14583),x14584,x14583),f12(f14(x14585,x14582,x14583),x14586,x14583),x14583)+~P4(f12(f14(f7(x14581,x14585,x14583),x14582,x14583),x14584,x14583),x14586,x14583) % 1.29/1.20 [1466]~P7(x14663,x14664,x14667,x14665)+~P7(x14661,x14662,x14668,x14666)+P7(x14661,x14662,f26(x14663,x14661,x14664,x14662,x14665,x14666),x14666) % 1.29/1.20 [1467]~P7(x14673,x14674,x14677,x14676)+~P7(x14671,x14672,x14678,x14675)+P7(x14671,x14672,f26(x14671,x14673,x14672,x14674,x14675,x14676),x14675) % 1.29/1.20 [354]~P55(x3542)+~P51(x3542)+~E(f10(x3541,x3542),f13(x3542))+E(x3541,f13(x3542)) % 1.29/1.20 [443]~P10(x4432)+~P31(x4432)+P6(x4431,f2(x4432),x4432)+E(f8(x4431,x4432),x4431) % 1.29/1.20 [552]~P77(x5522)+~P6(f2(x5522),x5521,x5522)+E(f15(x5521,x5522),f13(x5522))+E(x5521,f2(x5522)) % 1.29/1.20 [560]~P10(x5602)+~P31(x5602)+~P6(x5601,f2(x5602),x5602)+E(f8(x5601,x5602),f16(x5601,x5602)) % 1.29/1.20 [735]~P62(x7351)+~P51(x7351)+~P4(f2(x7351),x7352,x7351)+P4(f2(x7351),f10(x7352,x7351),x7351) % 1.29/1.20 [737]~P62(x7372)+~P51(x7372)+~P4(x7371,f2(x7372),x7372)+P6(f10(x7371,x7372),f13(x7372),x7372) % 1.29/1.20 [738]~P62(x7382)+~P51(x7382)+~P4(x7381,f2(x7382),x7382)+P4(f10(x7381,x7382),f2(x7382),x7382) % 1.29/1.20 [739]~P62(x7392)+~P51(x7392)+~P4(x7391,f2(x7392),x7392)+P4(f10(x7391,x7392),f13(x7392),x7392) % 1.29/1.20 [740]~P62(x7402)+~P51(x7402)+~P6(f13(x7402),x7401,x7402)+P6(f10(x7401,x7402),f13(x7402),x7402) % 1.29/1.20 [741]~P62(x7412)+~P51(x7412)+~P4(f13(x7412),x7411,x7412)+P4(f10(x7411,x7412),f13(x7412),x7412) % 1.29/1.20 [760]~P62(x7602)+~P6(f10(x7601,x7602),f2(x7602),x7602)+P6(x7601,f2(x7602),x7602)+E(x7601,f2(x7602)) % 1.29/1.20 [761]~P62(x7612)+~P6(f2(x7612),f10(x7611,x7612),x7612)+P6(f2(x7612),x7611,x7612)+E(x7611,f2(x7612)) % 1.29/1.20 [763]~P62(x7632)+~P51(x7632)+~P6(f13(x7632),f10(x7631,x7632),x7632)+P6(x7631,f13(x7632),x7632) % 1.29/1.20 [764]~P62(x7642)+~P51(x7642)+~P4(f13(x7642),f10(x7641,x7642),x7642)+P4(x7641,f13(x7642),x7642) % 1.29/1.20 [765]~P62(x7652)+~P51(x7652)+~P6(f10(x7651,x7652),f2(x7652),x7652)+P6(x7651,f2(x7652),x7652) % 1.29/1.20 [766]~P62(x7662)+~P51(x7662)+~P4(f10(x7661,x7662),f2(x7662),x7662)+P4(x7661,f2(x7662),x7662) % 1.29/1.20 [767]~P62(x7671)+~P51(x7671)+~P6(f2(x7671),f10(x7672,x7671),x7671)+P6(f2(x7671),x7672,x7671) % 1.29/1.20 [768]~P62(x7681)+~P51(x7681)+~P6(f13(x7681),f10(x7682,x7681),x7681)+P6(f2(x7681),x7682,x7681) % 1.29/1.20 [769]~P62(x7691)+~P51(x7691)+~P4(f13(x7691),f10(x7692,x7691),x7691)+P6(f2(x7691),x7692,x7691) % 1.29/1.20 [770]~P62(x7701)+~P51(x7701)+~P4(f2(x7701),f10(x7702,x7701),x7701)+P4(f2(x7701),x7702,x7701) % 1.29/1.20 [431]~P1(x4312)+~P2(x4312)+E(x4311,f2(a1))+E(f33(f2(x4312),x4311,x4312),f2(x4312)) % 1.29/1.20 [498]~P77(x4982)+P6(f2(x4982),x4981,x4982)+E(x4981,f2(x4982))+E(f15(x4981,x4982),f16(f13(x4982),x4982)) % 1.29/1.20 [625]~P10(x6252)+~P30(x6252)+P6(x6251,f2(x6252),x6252)+E(f21(x6251,f16(x6251,x6252),x6252),x6251) % 1.29/1.20 [755]~P10(x7552)+~P30(x7552)+~P6(x7551,f2(x7552),x7552)+E(f21(x7551,f16(x7551,x7552),x7552),f16(x7551,x7552)) % 1.29/1.20 [900]~P62(x9001)+~P51(x9001)+~P6(f2(x9001),x9002,x9001)+P6(f2(x9001),f11(f13(x9001),x9002,x9001),x9001) % 1.29/1.20 [901]~P62(x9011)+~P51(x9011)+~P4(f2(x9011),x9012,x9011)+P4(f2(x9011),f11(f13(x9011),x9012,x9011),x9011) % 1.29/1.20 [902]~P62(x9021)+~P51(x9021)+~P6(x9022,f2(x9021),x9021)+P6(f11(f13(x9021),x9022,x9021),f2(x9021),x9021) % 1.29/1.20 [903]~P62(x9031)+~P51(x9031)+~P4(x9032,f2(x9031),x9031)+P4(f11(f13(x9031),x9032,x9031),f2(x9031),x9031) % 1.29/1.20 [1046]~P62(x10462)+~P51(x10462)+P6(x10461,f2(x10462),x10462)+~P6(f11(f13(x10462),x10461,x10462),f2(x10462),x10462) % 1.29/1.20 [1047]~P62(x10472)+~P51(x10472)+P4(x10471,f2(x10472),x10472)+~P4(f11(f13(x10472),x10471,x10472),f2(x10472),x10472) % 1.29/1.20 [1048]~P62(x10481)+~P51(x10481)+P6(f2(x10481),x10482,x10481)+~P6(f2(x10481),f11(f13(x10481),x10482,x10481),x10481) % 1.29/1.20 [1049]~P62(x10491)+~P51(x10491)+P4(f2(x10491),x10492,x10491)+~P4(f2(x10491),f11(f13(x10491),x10492,x10491),x10491) % 1.29/1.20 [544]P6(x5441,x5442,x5443)+~P10(x5443)+E(x5441,x5442)+P6(x5442,x5441,x5443) % 1.29/1.20 [545]P6(x5451,x5452,x5453)+~P61(x5453)+E(x5451,x5452)+P6(x5452,x5451,x5453) % 1.29/1.20 [613]~P10(x6133)+~P4(x6131,x6132,x6133)+E(x6131,x6132)+P6(x6131,x6132,x6133) % 1.29/1.20 [619]~P43(x6193)+~P4(x6191,x6192,x6193)+E(x6191,x6192)+P6(x6191,x6192,x6193) % 1.29/1.20 [693]~P4(x6932,x6931,x6933)+~P4(x6931,x6932,x6933)+E(x6931,x6932)+~P43(x6933) % 1.29/1.20 [748]P4(x7482,x7481,x7483)+~P42(x7483)+~P4(x7481,x7482,x7483)+P6(x7481,x7482,x7483) % 1.29/1.20 [361]~P51(x3613)+~P52(x3613)+E(x3611,x3612)+~E(f10(x3611,x3613),f10(x3612,x3613)) % 1.29/1.20 [496]~P55(x4963)+E(x4961,x4962)+~E(f11(x4961,x4962,x4963),f13(x4963))+E(x4962,f2(x4963)) % 1.29/1.20 [497]~P16(x4972)+~P56(x4972)+~E(f12(x4973,x4971,x4972),x4973)+E(x4971,f2(x4972)) % 1.29/1.20 [500]~P16(x5003)+~P56(x5003)+E(x5001,x5002)+~E(f7(x5001,x5002,x5003),f2(x5003)) % 1.29/1.20 [504]~P59(x5042)+~E(f14(x5043,x5041,x5042),f2(x5042))+E(x5041,f2(x5042))+E(x5043,f2(x5042)) % 1.29/1.20 [505]~P71(x5052)+~E(f14(x5053,x5051,x5052),f2(x5052))+E(x5051,f2(x5052))+E(x5053,f2(x5052)) % 1.29/1.20 [733]~P56(x7333)+E(x7331,x7332)+~E(f14(x7331,x7331,x7333),f14(x7332,x7332,x7333))+E(x7331,f16(x7332,x7333)) % 1.29/1.20 [906]~P62(x9062)+~P6(x9063,x9061,x9062)+~P6(x9061,f2(x9062),x9062)+P6(f10(x9061,x9062),f10(x9063,x9062),x9062) % 1.29/1.20 [907]~P62(x9072)+~P4(x9073,x9071,x9072)+~P6(x9071,f2(x9072),x9072)+P4(f10(x9071,x9072),f10(x9073,x9072),x9072) % 1.29/1.20 [908]~P62(x9082)+~P6(x9083,x9081,x9082)+~P6(f2(x9082),x9083,x9082)+P6(f10(x9081,x9082),f10(x9083,x9082),x9082) % 1.29/1.20 [909]~P62(x9092)+~P4(x9093,x9091,x9092)+~P6(f2(x9092),x9093,x9092)+P4(f10(x9091,x9092),f10(x9093,x9092),x9092) % 1.29/1.20 [920]~P61(x9202)+~P6(x9201,x9203,x9202)+~P6(f16(x9201,x9202),x9203,x9202)+P6(f8(x9201,x9202),x9203,x9202) % 1.29/1.20 [922]~P37(x9222)+~P4(x9221,x9223,x9222)+~P4(f16(x9221,x9222),x9223,x9222)+P4(f8(x9221,x9222),x9223,x9222) % 1.29/1.20 [962]~P62(x9623)+P6(x9621,x9622,x9623)+~P6(x9621,f2(x9623),x9623)+~P6(f10(x9622,x9623),f10(x9621,x9623),x9623) % 1.29/1.21 [963]~P62(x9633)+P4(x9631,x9632,x9633)+~P6(x9631,f2(x9633),x9633)+~P4(f10(x9632,x9633),f10(x9631,x9633),x9633) % 1.29/1.21 [964]~P62(x9643)+P6(x9641,x9642,x9643)+~P6(f2(x9643),x9642,x9643)+~P6(f10(x9642,x9643),f10(x9641,x9643),x9643) % 1.29/1.21 [965]~P62(x9653)+P4(x9651,x9652,x9653)+~P6(f2(x9653),x9652,x9653)+~P4(f10(x9652,x9653),f10(x9651,x9653),x9653) % 1.29/1.21 [1006]E(x10061,x10062)+~P4(x10063,x10062,a1)+~P4(x10063,x10061,a1)+~E(f7(x10061,x10063,a1),f7(x10062,x10063,a1)) % 1.29/1.21 [1055]~P44(x10551)+~P6(f13(x10551),x10552,x10551)+P6(f13(x10551),f33(x10552,x10553,x10551),x10551)+~P6(f2(a1),x10553,a1) % 1.29/1.21 [1070]~P63(x10701)+~P6(x10703,f2(x10701),x10701)+~P6(x10702,f2(x10701),x10701)+P6(f2(x10701),f14(x10702,x10703,x10701),x10701) % 1.29/1.21 [1071]~P62(x10711)+~P6(x10713,f2(x10711),x10711)+~P6(x10712,f2(x10711),x10711)+P6(f2(x10711),f11(x10712,x10713,x10711),x10711) % 1.29/1.21 [1073]~P69(x10731)+~P4(x10733,f2(x10731),x10731)+~P4(x10732,f2(x10731),x10731)+P4(f2(x10731),f14(x10732,x10733,x10731),x10731) % 1.29/1.21 [1074]~P63(x10741)+~P4(x10743,f2(x10741),x10741)+~P4(x10742,f2(x10741),x10741)+P4(f2(x10741),f14(x10742,x10743,x10741),x10741) % 1.29/1.21 [1075]~P62(x10751)+~P6(x10753,f2(x10751),x10751)+~P4(x10752,f2(x10751),x10751)+P4(f2(x10751),f11(x10752,x10753,x10751),x10751) % 1.29/1.21 [1076]~P40(x10761)+~P6(f2(x10761),x10763,x10761)+~P6(f2(x10761),x10762,x10761)+P6(f2(x10761),f12(x10762,x10763,x10761),x10761) % 1.29/1.21 [1077]~P40(x10771)+~P6(f2(x10771),x10773,x10771)+~P4(f2(x10771),x10772,x10771)+P6(f2(x10771),f12(x10772,x10773,x10771),x10771) % 1.29/1.21 [1078]~P40(x10781)+~P6(f2(x10781),x10782,x10781)+~P4(f2(x10781),x10783,x10781)+P6(f2(x10781),f12(x10782,x10783,x10781),x10781) % 1.29/1.21 [1079]~P64(x10791)+~P6(f2(x10791),x10793,x10791)+~P6(f2(x10791),x10792,x10791)+P6(f2(x10791),f14(x10792,x10793,x10791),x10791) % 1.29/1.21 [1080]~P62(x10801)+~P6(f2(x10801),x10803,x10801)+~P6(f2(x10801),x10802,x10801)+P6(f2(x10801),f11(x10802,x10803,x10801),x10801) % 1.29/1.21 [1081]~P44(x10811)+~P6(f13(x10811),x10813,x10811)+~P6(f13(x10811),x10812,x10811)+P6(f13(x10811),f14(x10812,x10813,x10811),x10811) % 1.29/1.21 [1082]~P40(x10821)+~P4(f2(x10821),x10823,x10821)+~P4(f2(x10821),x10822,x10821)+P4(f2(x10821),f12(x10822,x10823,x10821),x10821) % 1.29/1.21 [1083]~P69(x10831)+~P4(f2(x10831),x10833,x10831)+~P4(f2(x10831),x10832,x10831)+P4(f2(x10831),f14(x10832,x10833,x10831),x10831) % 1.29/1.21 [1084]~P63(x10841)+~P4(f2(x10841),x10843,x10841)+~P4(f2(x10841),x10842,x10841)+P4(f2(x10841),f14(x10842,x10843,x10841),x10841) % 1.29/1.21 [1085]~P67(x10851)+~P4(f2(x10851),x10853,x10851)+~P4(f2(x10851),x10852,x10851)+P4(f2(x10851),f14(x10852,x10853,x10851),x10851) % 1.29/1.21 [1086]~P62(x10861)+~P6(f2(x10861),x10863,x10861)+~P4(f2(x10861),x10862,x10861)+P4(f2(x10861),f11(x10862,x10863,x10861),x10861) % 1.29/1.21 [1087]~P40(x10873)+~P6(x10872,f2(x10873),x10873)+~P6(x10871,f2(x10873),x10873)+P6(f12(x10871,x10872,x10873),f2(x10873),x10873) % 1.29/1.21 [1088]~P40(x10883)+~P6(x10882,f2(x10883),x10883)+~P4(x10881,f2(x10883),x10883)+P6(f12(x10881,x10882,x10883),f2(x10883),x10883) % 1.29/1.21 [1089]~P40(x10893)+~P6(x10891,f2(x10893),x10893)+~P4(x10892,f2(x10893),x10893)+P6(f12(x10891,x10892,x10893),f2(x10893),x10893) % 1.29/1.21 [1090]~P40(x10903)+~P4(x10902,f2(x10903),x10903)+~P4(x10901,f2(x10903),x10903)+P4(f12(x10901,x10902,x10903),f2(x10903),x10903) % 1.29/1.21 [1091]~P64(x10913)+~P6(x10912,f2(x10913),x10913)+~P6(f2(x10913),x10911,x10913)+P6(f14(x10911,x10912,x10913),f2(x10913),x10913) % 1.29/1.21 [1093]~P64(x10933)+~P6(x10931,f2(x10933),x10933)+~P6(f2(x10933),x10932,x10933)+P6(f14(x10931,x10932,x10933),f2(x10933),x10933) % 1.29/1.21 [1094]~P62(x10943)+~P6(x10942,f2(x10943),x10943)+~P6(f2(x10943),x10941,x10943)+P6(f11(x10941,x10942,x10943),f2(x10943),x10943) % 1.29/1.21 [1095]~P62(x10953)+~P6(x10951,f2(x10953),x10953)+~P6(f2(x10953),x10952,x10953)+P6(f11(x10951,x10952,x10953),f2(x10953),x10953) % 1.29/1.21 [1096]~P63(x10963)+~P4(x10962,f2(x10963),x10963)+~P4(f2(x10963),x10961,x10963)+P4(f14(x10961,x10962,x10963),f2(x10963),x10963) % 1.29/1.21 [1097]~P63(x10973)+~P4(x10971,f2(x10973),x10973)+~P4(f2(x10973),x10972,x10973)+P4(f14(x10971,x10972,x10973),f2(x10973),x10973) % 1.29/1.21 [1099]~P67(x10993)+~P4(x10992,f2(x10993),x10993)+~P4(f2(x10993),x10991,x10993)+P4(f14(x10991,x10992,x10993),f2(x10993),x10993) % 1.29/1.21 [1102]~P67(x11023)+~P4(x11021,f2(x11023),x11023)+~P4(f2(x11023),x11022,x11023)+P4(f14(x11021,x11022,x11023),f2(x11023),x11023) % 1.29/1.21 [1103]~P62(x11033)+~P6(x11032,f2(x11033),x11033)+~P4(f2(x11033),x11031,x11033)+P4(f11(x11031,x11032,x11033),f2(x11033),x11033) % 1.29/1.21 [1104]~P62(x11043)+~P4(x11041,f2(x11043),x11043)+~P6(f2(x11043),x11042,x11043)+P4(f11(x11041,x11042,x11043),f2(x11043),x11043) % 1.29/1.21 [1125]~P63(x11252)+~P4(f14(x11253,x11251,x11252),f2(x11252),x11252)+P4(x11251,f2(x11252),x11252)+P4(x11253,f2(x11252),x11252) % 1.29/1.21 [1126]~P63(x11262)+~P4(f2(x11262),f14(x11263,x11261,x11262),x11262)+P4(x11261,f2(x11262),x11262)+P4(f2(x11262),x11263,x11262) % 1.29/1.21 [1127]~P63(x11272)+~P4(f2(x11272),f14(x11271,x11273,x11272),x11272)+P4(x11271,f2(x11272),x11272)+P4(f2(x11272),x11273,x11272) % 1.29/1.21 [1128]~P63(x11282)+~P4(f2(x11282),f14(x11283,x11281,x11282),x11282)+P4(x11281,f2(x11282),x11282)+P4(f2(x11282),x11281,x11282) % 1.29/1.21 [1129]~P63(x11292)+~P4(f2(x11292),f14(x11291,x11293,x11292),x11292)+P4(x11291,f2(x11292),x11292)+P4(f2(x11292),x11291,x11292) % 1.29/1.21 [1130]~P63(x11302)+~P4(f14(x11303,x11301,x11302),f2(x11302),x11302)+P4(x11301,f2(x11302),x11302)+P4(f2(x11302),x11301,x11302) % 1.29/1.21 [1131]~P63(x11312)+~P4(f14(x11311,x11313,x11312),f2(x11312),x11312)+P4(x11311,f2(x11312),x11312)+P4(f2(x11312),x11311,x11312) % 1.29/1.21 [1132]~P63(x11321)+~P4(f14(x11322,x11323,x11321),f2(x11321),x11321)+P4(f2(x11321),x11322,x11321)+P4(f2(x11321),x11323,x11321) % 1.29/1.21 [1170]~P64(x11701)+~P6(f2(x11701),f14(x11703,x11702,x11701),x11701)+P6(f2(x11701),x11702,x11701)+~P6(f2(x11701),x11703,x11701) % 1.29/1.21 [1171]~P64(x11711)+~P6(f2(x11711),f14(x11712,x11713,x11711),x11711)+P6(f2(x11711),x11712,x11711)+~P6(f2(x11711),x11713,x11711) % 1.29/1.21 [1379]~P4(x13793,x13791,a1)+P6(x13791,x13792,a1)+~P4(x13793,x13792,a1)+~P6(f7(x13791,x13793,a1),f7(x13792,x13793,a1),a1) % 1.29/1.21 [1380]~P4(x13803,x13801,a1)+P4(x13801,x13802,a1)+~P4(x13803,x13802,a1)+~P4(f7(x13801,x13803,a1),f7(x13802,x13803,a1),a1) % 1.29/1.21 [696]~P55(x6962)+~P51(x6962)+E(x6961,f2(x6962))+E(f14(f11(x6963,x6961,x6962),x6961,x6962),x6963) % 1.29/1.21 [846]~P52(x8462)+E(x8461,f2(x8462))+E(x8463,f2(x8462))+E(f14(f10(x8461,x8462),f10(x8463,x8462),x8462),f10(f14(x8463,x8461,x8462),x8462)) % 1.29/1.21 [930]~P62(x9302)+~P51(x9302)+~P6(f2(x9302),x9303,x9302)+E(f11(f8(x9301,x9302),x9303,x9302),f8(f11(x9301,x9303,x9302),x9302)) % 1.29/1.21 [1121]~P44(x11213)+~P6(x11211,f13(x11213),x11213)+~P6(f2(x11213),x11211,x11213)+P6(f33(x11211,f32(x11212),x11213),f13(x11213),x11213) % 1.29/1.21 [1166]~P70(x11662)+~P4(x11663,f2(x11662),x11662)+~P4(x11661,f2(x11662),x11662)+E(f14(f8(x11661,x11662),f8(x11663,x11662),x11662),f8(f14(x11661,x11663,x11662),x11662)) % 1.29/1.21 [1167]~P70(x11672)+~P4(x11673,f2(x11672),x11672)+~P4(f2(x11672),x11671,x11672)+E(f14(f8(x11671,x11672),f8(x11673,x11672),x11672),f8(f14(x11671,x11673,x11672),x11672)) % 1.29/1.21 [1168]~P70(x11682)+~P4(x11681,f2(x11682),x11682)+~P4(f2(x11682),x11683,x11682)+E(f14(f8(x11681,x11682),f8(x11683,x11682),x11682),f8(f14(x11681,x11683,x11682),x11682)) % 1.29/1.21 [1169]~P70(x11692)+~P4(f2(x11692),x11693,x11692)+~P4(f2(x11692),x11691,x11692)+E(f14(f8(x11691,x11692),f8(x11693,x11692),x11692),f8(f14(x11691,x11693,x11692),x11692)) % 1.29/1.21 [1340]~P52(x13402)+E(x13401,f2(x13402))+E(x13403,f2(x13402))+E(f14(f14(f10(x13403,x13402),f12(x13403,x13401,x13402),x13402),f10(x13401,x13402),x13402),f12(f10(x13403,x13402),f10(x13401,x13402),x13402)) % 1.29/1.21 [1341]~P52(x13412)+E(x13411,f2(x13412))+E(x13413,f2(x13412))+E(f14(f14(f10(x13413,x13412),f7(x13411,x13413,x13412),x13412),f10(x13411,x13412),x13412),f7(f10(x13413,x13412),f10(x13411,x13412),x13412)) % 1.29/1.21 [1342]~P55(x13422)+E(x13421,f2(x13422))+E(x13423,f2(x13422))+E(f14(f14(f12(x13423,x13421,x13422),f10(x13423,x13422),x13422),f10(x13421,x13422),x13422),f12(f10(x13423,x13422),f10(x13421,x13422),x13422)) % 1.29/1.21 [1397]~P44(x13973)+~P6(x13971,f13(x13973),x13973)+~P6(f2(x13973),x13971,x13973)+P6(f14(x13971,f33(x13971,x13972,x13973),x13973),f33(x13971,x13972,x13973),x13973) % 1.29/1.21 [820]~P42(x8203)+~P6(x8201,x8204,x8203)+P6(x8201,x8202,x8203)+~P6(x8204,x8202,x8203) % 1.29/1.21 [821]~P42(x8213)+~P4(x8211,x8214,x8213)+P6(x8211,x8212,x8213)+~P6(x8214,x8212,x8213) % 1.29/1.21 [822]~P42(x8223)+~P4(x8224,x8222,x8223)+P6(x8221,x8222,x8223)+~P6(x8221,x8224,x8223) % 1.29/1.21 [823]~P43(x8233)+~P6(x8231,x8234,x8233)+P6(x8231,x8232,x8233)+~P6(x8234,x8232,x8233) % 1.29/1.21 [824]~P43(x8243)+~P4(x8241,x8244,x8243)+P6(x8241,x8242,x8243)+~P6(x8244,x8242,x8243) % 1.29/1.21 [825]~P43(x8253)+~P4(x8254,x8252,x8253)+P6(x8251,x8252,x8253)+~P6(x8251,x8254,x8253) % 1.29/1.21 [826]~P42(x8263)+~P4(x8261,x8264,x8263)+P4(x8261,x8262,x8263)+~P4(x8264,x8262,x8263) % 1.29/1.21 [827]~P43(x8273)+~P4(x8271,x8274,x8273)+P4(x8271,x8272,x8273)+~P4(x8274,x8272,x8273) % 1.29/1.21 [828]~P45(x8283)+~P8(x8281,x8284,x8283)+P8(x8281,x8282,x8283)+~P8(x8284,x8282,x8283) % 1.29/1.21 [708]~P16(x7084)+~P56(x7084)+E(x7081,x7082)+~E(f12(x7083,x7081,x7084),f12(x7083,x7082,x7084)) % 1.29/1.21 [895]~P44(x8954)+E(x8951,x8952)+~P6(f13(x8954),x8953,x8954)+~E(f33(x8953,x8951,x8954),f33(x8953,x8952,x8954)) % 1.29/1.21 [1011]~P10(x10114)+~P6(x10111,x10113,x10114)+~P6(x10111,x10112,x10114)+P6(x10111,f31(x10112,x10113,x10114),x10114) % 1.29/1.21 [1014]~P10(x10144)+~P4(x10141,x10143,x10144)+~P4(x10141,x10142,x10144)+P4(x10141,f31(x10142,x10143,x10144),x10144) % 1.29/1.21 [1017]~P20(x10174)+~P4(x10171,x10173,x10174)+~P4(x10171,x10172,x10174)+P4(x10171,f20(x10172,x10173,x10174),x10174) % 1.29/1.21 [1018]~P45(x10184)+~P8(x10181,x10183,x10184)+~P8(x10181,x10182,x10184)+P8(x10181,f12(x10182,x10183,x10184),x10184) % 1.29/1.21 [1019]~P48(x10194)+~P8(x10191,x10193,x10194)+~P8(x10191,x10192,x10194)+P8(x10191,f7(x10192,x10193,x10194),x10194) % 1.29/1.21 [1021]~P3(x10214)+~P8(x10211,x10213,x10214)+~P8(x10211,x10212,x10214)+P8(x10211,f9(x10212,x10213,x10214),x10214) % 1.29/1.21 [1022]~P10(x10223)+~P6(x10222,x10224,x10223)+~P6(x10221,x10224,x10223)+P6(f30(x10221,x10222,x10223),x10224,x10223) % 1.29/1.21 [1025]~P10(x10253)+~P4(x10252,x10254,x10253)+~P4(x10251,x10254,x10253)+P4(f30(x10251,x10252,x10253),x10254,x10253) % 1.29/1.21 [1028]~P18(x10283)+~P4(x10282,x10284,x10283)+~P4(x10281,x10284,x10283)+P4(f21(x10281,x10282,x10283),x10284,x10283) % 1.29/1.21 [1043]~P44(x10434)+~P6(x10431,x10433,x10434)+~P6(f2(x10434),x10432,x10434)+P6(x10431,f12(x10432,x10433,x10434),x10434) % 1.29/1.21 [1107]~P10(x11073)+P6(x11071,x11072,x11073)+P6(x11071,x11074,x11073)+~P6(x11071,f30(x11072,x11074,x11073),x11073) % 1.29/1.21 [1108]~P10(x11083)+P4(x11081,x11082,x11083)+P4(x11081,x11084,x11083)+~P4(x11081,f30(x11082,x11084,x11083),x11083) % 1.29/1.21 [1109]~P10(x11093)+P6(x11091,x11092,x11093)+P6(x11094,x11092,x11093)+~P6(f31(x11091,x11094,x11093),x11092,x11093) % 1.29/1.21 [1110]~P10(x11103)+P4(x11101,x11102,x11103)+P4(x11104,x11102,x11103)+~P4(f31(x11101,x11104,x11103),x11102,x11103) % 1.29/1.21 [1160]~P3(x11603)+P8(x11601,x11602,x11603)+~P8(x11601,x11604,x11603)+~P8(x11601,f9(x11602,x11604,x11603),x11603) % 1.29/1.21 [1236]~P44(x12363)+~P6(x12362,x12364,a1)+~P6(f13(x12363),x12361,x12363)+P6(f33(x12361,x12362,x12363),f33(x12361,x12364,x12363),x12363) % 1.29/1.21 [1237]~P44(x12373)+~P4(x12372,x12374,a1)+~P6(f13(x12373),x12371,x12373)+P4(f33(x12371,x12372,x12373),f33(x12371,x12374,x12373),x12373) % 1.29/1.21 [1238]~P44(x12383)+~P4(x12382,x12384,a1)+~P4(f13(x12383),x12381,x12383)+P4(f33(x12381,x12382,x12383),f33(x12381,x12384,x12383),x12383) % 1.29/1.21 [1242]~P63(x12423)+~P6(x12424,x12421,x12423)+~P6(x12422,f2(x12423),x12423)+P6(f14(x12421,x12422,x12423),f14(x12424,x12422,x12423),x12423) % 1.29/1.21 [1245]~P63(x12453)+~P6(x12454,x12452,x12453)+~P6(x12451,f2(x12453),x12453)+P6(f14(x12451,x12452,x12453),f14(x12451,x12454,x12453),x12453) % 1.29/1.21 [1246]~P62(x12463)+~P6(x12464,x12461,x12463)+~P6(x12462,f2(x12463),x12463)+P6(f11(x12461,x12462,x12463),f11(x12464,x12462,x12463),x12463) % 1.29/1.21 [1247]~P69(x12473)+~P4(x12474,x12471,x12473)+~P4(x12472,f2(x12473),x12473)+P4(f14(x12471,x12472,x12473),f14(x12474,x12472,x12473),x12473) % 1.29/1.21 [1248]~P69(x12483)+~P4(x12484,x12482,x12483)+~P4(x12481,f2(x12483),x12483)+P4(f14(x12481,x12482,x12483),f14(x12481,x12484,x12483),x12483) % 1.29/1.21 [1249]~P63(x12493)+~P4(x12494,x12492,x12493)+~P6(x12491,f2(x12493),x12493)+P4(f14(x12491,x12492,x12493),f14(x12491,x12494,x12493),x12493) % 1.29/1.21 [1250]~P64(x12503)+~P6(x12501,x12504,x12503)+~P6(f2(x12503),x12502,x12503)+P6(f14(x12501,x12502,x12503),f14(x12504,x12502,x12503),x12503) % 1.29/1.21 [1251]~P63(x12513)+~P6(x12511,x12514,x12513)+~P6(f2(x12513),x12512,x12513)+P6(f14(x12511,x12512,x12513),f14(x12514,x12512,x12513),x12513) % 1.29/1.21 [1252]~P64(x12523)+~P6(x12522,x12524,x12523)+~P6(f2(x12523),x12521,x12523)+P6(f14(x12521,x12522,x12523),f14(x12521,x12524,x12523),x12523) % 1.29/1.21 [1254]~P63(x12543)+~P6(x12542,x12544,x12543)+~P6(f2(x12543),x12541,x12543)+P6(f14(x12541,x12542,x12543),f14(x12541,x12544,x12543),x12543) % 1.29/1.21 [1255]~P53(x12553)+~P6(x12552,x12554,x12553)+~P6(f2(x12553),x12551,x12553)+P6(f14(x12551,x12552,x12553),f14(x12551,x12554,x12553),x12553) % 1.29/1.21 [1256]~P62(x12563)+~P6(x12561,x12564,x12563)+~P6(f2(x12563),x12562,x12563)+P6(f11(x12561,x12562,x12563),f11(x12564,x12562,x12563),x12563) % 1.29/1.21 [1257]~P54(x12573)+~P4(x12571,x12574,x12573)+~P4(f2(x12573),x12572,x12573)+P4(f14(x12571,x12572,x12573),f14(x12574,x12572,x12573),x12573) % 1.29/1.21 [1258]~P63(x12583)+~P4(x12582,x12584,x12583)+~P6(f2(x12583),x12581,x12583)+P4(f14(x12581,x12582,x12583),f14(x12581,x12584,x12583),x12583) % 1.29/1.21 [1259]~P54(x12593)+~P4(x12592,x12594,x12593)+~P4(f2(x12593),x12591,x12593)+P4(f14(x12591,x12592,x12593),f14(x12591,x12594,x12593),x12593) % 1.29/1.21 [1260]~P58(x12603)+~P4(x12602,x12604,x12603)+~P4(f2(x12603),x12601,x12603)+P4(f14(x12601,x12602,x12603),f14(x12601,x12604,x12603),x12603) % 1.29/1.21 [1261]~P44(x12613)+~P4(x12611,x12614,x12613)+~P4(f2(x12613),x12611,x12613)+P4(f33(x12611,x12612,x12613),f33(x12614,x12612,x12613),x12613) % 1.29/1.21 [1280]~P56(x12802)+P8(x12803,x12804,x12802)+~P8(f14(x12801,x12803,x12802),f14(x12801,x12804,x12802),x12802)+E(x12801,f2(x12802)) % 1.29/1.21 [1281]~P56(x12812)+P8(x12813,x12814,x12812)+~P8(f14(x12813,x12811,x12812),f14(x12814,x12811,x12812),x12812)+E(x12811,f2(x12812)) % 1.29/1.21 [1295]~P62(x12954)+~P6(f2(x12954),x12953,x12954)+~P6(f14(x12951,x12953,x12954),x12952,x12954)+P6(x12951,f11(x12952,x12953,x12954),x12954) % 1.29/1.21 [1296]~P62(x12964)+~P6(f2(x12964),x12963,x12964)+~P4(f14(x12961,x12963,x12964),x12962,x12964)+P4(x12961,f11(x12962,x12963,x12964),x12964) % 1.29/1.21 [1297]~P62(x12973)+~P6(f2(x12973),x12972,x12973)+~P6(x12971,f14(x12974,x12972,x12973),x12973)+P6(f11(x12971,x12972,x12973),x12974,x12973) % 1.29/1.21 [1298]~P62(x12983)+~P6(f2(x12983),x12982,x12983)+~P4(x12981,f14(x12984,x12982,x12983),x12983)+P4(f11(x12981,x12982,x12983),x12984,x12983) % 1.29/1.21 [1309]P6(x13092,x13091,x13093)+~P63(x13093)+P6(x13091,x13092,x13093)+~P6(f14(x13094,x13091,x13093),f14(x13094,x13092,x13093),x13093) % 1.29/1.21 [1310]P6(x13102,x13101,x13103)+~P63(x13103)+P6(x13101,x13102,x13103)+~P6(f14(x13101,x13104,x13103),f14(x13102,x13104,x13103),x13103) % 1.29/1.21 [1322]~P63(x13223)+P6(x13221,x13222,x13223)+~P6(f14(x13221,x13224,x13223),f14(x13222,x13224,x13223),x13223)+P6(x13224,f2(x13223),x13223) % 1.29/1.21 [1323]~P63(x13233)+P6(x13231,x13232,x13233)+~P6(f14(x13234,x13231,x13233),f14(x13234,x13232,x13233),x13233)+P6(x13234,f2(x13233),x13233) % 1.29/1.21 [1324]~P63(x13243)+P6(x13241,x13242,x13243)+~P6(f14(x13244,x13242,x13243),f14(x13244,x13241,x13243),x13243)+P6(f2(x13243),x13244,x13243) % 1.29/1.21 [1325]~P63(x13253)+P6(x13251,x13252,x13253)+~P6(f14(x13252,x13254,x13253),f14(x13251,x13254,x13253),x13253)+P6(f2(x13253),x13254,x13253) % 1.29/1.21 [1330]~P63(x13302)+~P6(f14(x13303,x13301,x13302),f14(x13304,x13301,x13302),x13302)+P6(x13301,f2(x13302),x13302)+P6(f2(x13302),x13301,x13302) % 1.29/1.21 [1331]~P63(x13312)+~P6(f14(x13311,x13313,x13312),f14(x13311,x13314,x13312),x13312)+P6(x13311,f2(x13312),x13312)+P6(f2(x13312),x13311,x13312) % 1.29/1.21 [1344]~P44(x13443)+~P6(f33(x13444,x13441,x13443),f33(x13444,x13442,x13443),x13443)+P6(x13441,x13442,a1)+~P6(f13(x13443),x13444,x13443) % 1.29/1.21 [1346]~P44(x13463)+~P4(f33(x13464,x13461,x13463),f33(x13464,x13462,x13463),x13463)+P4(x13461,x13462,a1)+~P6(f13(x13463),x13464,x13463) % 1.29/1.21 [1347]~P63(x13473)+P6(x13471,x13472,x13473)+~P6(f14(x13474,x13472,x13473),f14(x13474,x13471,x13473),x13473)+~P6(x13474,f2(x13473),x13473) % 1.29/1.21 [1348]~P63(x13483)+P4(x13481,x13482,x13483)+~P4(f14(x13484,x13482,x13483),f14(x13484,x13481,x13483),x13483)+~P6(x13484,f2(x13483),x13483) % 1.29/1.21 [1349]~P44(x13493)+P6(x13491,x13492,x13493)+~P4(f2(x13493),x13492,x13493)+~P6(f33(x13491,x13494,x13493),f33(x13492,x13494,x13493),x13493) % 1.29/1.21 [1350]~P64(x13503)+P6(x13501,x13502,x13503)+~P6(f14(x13504,x13501,x13503),f14(x13504,x13502,x13503),x13503)+~P4(f2(x13503),x13504,x13503) % 1.29/1.21 [1351]~P64(x13513)+P6(x13511,x13512,x13513)+~P6(f14(x13511,x13514,x13513),f14(x13512,x13514,x13513),x13513)+~P4(f2(x13513),x13514,x13513) % 1.29/1.21 [1352]~P63(x13523)+P6(x13521,x13522,x13523)+~P6(f14(x13524,x13521,x13523),f14(x13524,x13522,x13523),x13523)+~P6(f2(x13523),x13524,x13523) % 1.29/1.21 [1353]~P65(x13533)+P6(x13531,x13532,x13533)+~P6(f14(x13534,x13531,x13533),f14(x13534,x13532,x13533),x13533)+~P4(f2(x13533),x13534,x13533) % 1.29/1.21 [1354]~P65(x13543)+P6(x13541,x13542,x13543)+~P6(f14(x13541,x13544,x13543),f14(x13542,x13544,x13543),x13543)+~P4(f2(x13543),x13544,x13543) % 1.29/1.21 [1355]~P64(x13553)+P4(x13551,x13552,x13553)+~P4(f14(x13554,x13551,x13553),f14(x13554,x13552,x13553),x13553)+~P6(f2(x13553),x13554,x13553) % 1.29/1.21 [1356]~P64(x13563)+P4(x13561,x13562,x13563)+~P4(f14(x13561,x13564,x13563),f14(x13562,x13564,x13563),x13563)+~P6(f2(x13563),x13564,x13563) % 1.29/1.21 [1357]~P63(x13573)+P4(x13571,x13572,x13573)+~P4(f14(x13574,x13571,x13573),f14(x13574,x13572,x13573),x13573)+~P6(f2(x13573),x13574,x13573) % 1.29/1.21 [1031]~P55(x10312)+~P51(x10312)+E(x10311,f2(x10312))+E(f11(f14(x10313,x10311,x10312),f14(x10314,x10311,x10312),x10312),f11(x10313,x10314,x10312)) % 1.29/1.21 [1032]~P55(x10322)+~P51(x10322)+E(x10321,f2(x10322))+E(f11(f14(x10321,x10323,x10322),f14(x10321,x10324,x10322),x10322),f11(x10323,x10324,x10322)) % 1.29/1.21 [1299]~P55(x12992)+~P4(x12994,x12993,a1)+E(x12991,f2(x12992))+E(f11(f33(x12991,x12993,x12992),f33(x12991,x12994,x12992),x12992),f33(x12991,f7(x12993,x12994,a1),x12992)) % 1.29/1.21 [1378]~P44(x13783)+P4(x13781,x13782,x13783)+~P4(f2(x13783),x13782,x13783)+~P4(f33(x13781,f32(x13784),x13783),f33(x13782,f32(x13784),x13783),x13783) % 1.29/1.21 [1338]~P55(x13382)+~P51(x13382)+E(x13381,f2(x13382))+E(f11(f12(x13383,f14(x13384,x13381,x13382),x13382),x13381,x13382),f12(x13384,f11(x13383,x13381,x13382),x13382)) % 1.29/1.21 [1339]~P55(x13392)+~P51(x13392)+E(x13391,f2(x13392))+E(f11(f12(x13393,f14(x13394,x13391,x13392),x13392),x13391,x13392),f12(f11(x13393,x13391,x13392),x13394,x13392)) % 1.29/1.21 [956]~P38(x9563)+~P6(x9564,x9565,x9563)+P6(x9561,x9562,x9563)+~E(f7(x9564,x9565,x9563),f7(x9561,x9562,x9563)) % 1.29/1.21 [957]~P38(x9573)+~P6(x9574,x9575,x9573)+P6(x9571,x9572,x9573)+~E(f7(x9571,x9572,x9573),f7(x9574,x9575,x9573)) % 1.29/1.21 [958]~P38(x9583)+~P4(x9585,x9584,x9583)+P4(x9581,x9582,x9583)+~E(f7(x9584,x9585,x9583),f7(x9582,x9581,x9583)) % 1.29/1.21 [959]~P38(x9593)+~P4(x9595,x9594,x9593)+P4(x9591,x9592,x9593)+~E(f7(x9592,x9591,x9593),f7(x9594,x9595,x9593)) % 1.29/1.21 [1224]~P45(x12243)+~P8(x12241,x12244,x12243)+~P4(x12242,x12245,a1)+P8(f33(x12241,x12242,x12243),f33(x12244,x12245,x12243),x12243) % 1.29/1.21 [1225]~P41(x12253)+~P6(x12252,x12255,x12253)+~P6(x12251,x12254,x12253)+P6(f12(x12251,x12252,x12253),f12(x12254,x12255,x12253),x12253) % 1.29/1.21 [1226]~P41(x12263)+~P6(x12262,x12265,x12263)+~P4(x12261,x12264,x12263)+P6(f12(x12261,x12262,x12263),f12(x12264,x12265,x12263),x12263) % 1.29/1.21 [1227]~P41(x12273)+~P6(x12271,x12274,x12273)+~P4(x12272,x12275,x12273)+P6(f12(x12271,x12272,x12273),f12(x12274,x12275,x12273),x12273) % 1.29/1.21 [1228]~P35(x12283)+~P4(x12282,x12285,x12283)+~P4(x12281,x12284,x12283)+P4(f12(x12281,x12282,x12283),f12(x12284,x12285,x12283),x12283) % 1.29/1.21 [1229]~P45(x12293)+~P8(x12292,x12295,x12293)+~P8(x12291,x12294,x12293)+P8(f14(x12291,x12292,x12293),f14(x12294,x12295,x12293),x12293) % 1.29/1.21 [1285]~P45(x12853)+~P8(f33(x12851,x12855,x12853),x12854,x12853)+P8(f33(x12851,x12852,x12853),x12854,x12853)+~P4(x12852,x12855,a1) % 1.29/1.21 [1286]~P38(x12864)+~P4(x12865,x12863,x12864)+~P4(x12861,f12(x12862,x12865,x12864),x12864)+P4(x12861,f12(x12862,x12863,x12864),x12864) % 1.29/1.21 [1381]~P61(x13812)+~P6(f8(x13811,x13812),x13814,x13812)+~P6(f8(x13813,x13812),x13815,x13812)+P6(f14(f8(x13811,x13812),f8(x13813,x13812),x13812),f14(x13814,x13815,x13812),x13812) % 1.29/1.21 [1435]~P55(x14352)+E(x14351,f2(x14352))+E(x14353,f2(x14352))+E(f11(f12(f14(x14354,x14351,x14352),f14(x14355,x14353,x14352),x14352),f14(x14353,x14351,x14352),x14352),f12(f11(x14354,x14353,x14352),f11(x14355,x14351,x14352),x14352)) % 1.29/1.21 [1436]~P55(x14362)+E(x14361,f2(x14362))+E(x14363,f2(x14362))+E(f11(f7(f14(x14364,x14361,x14362),f14(x14365,x14363,x14362),x14362),f14(x14363,x14361,x14362),x14362),f7(f11(x14364,x14363,x14362),f11(x14365,x14361,x14362),x14362)) % 1.29/1.21 [1394]~P3(x13943)+~E(f9(x13941,x13944,x13943),f9(x13945,x13944,x13943))+~E(f9(x13942,x13944,x13943),f9(x13946,x13944,x13943))+E(f9(f12(x13941,x13942,x13943),x13944,x13943),f9(f12(x13945,x13946,x13943),x13944,x13943)) % 1.29/1.21 [1395]~P3(x13953)+~E(f9(x13951,x13954,x13953),f9(x13955,x13954,x13953))+~E(f9(x13952,x13954,x13953),f9(x13956,x13954,x13953))+E(f9(f14(x13951,x13952,x13953),x13954,x13953),f9(f14(x13955,x13956,x13953),x13954,x13953)) % 1.29/1.21 [1396]~P9(x13963)+~E(f9(x13961,x13964,x13963),f9(x13965,x13964,x13963))+~E(f9(x13962,x13964,x13963),f9(x13966,x13964,x13963))+E(f9(f7(x13961,x13962,x13963),x13964,x13963),f9(f7(x13965,x13966,x13963),x13964,x13963)) % 1.29/1.21 [893]~P62(x8932)+~P51(x8932)+P6(f13(x8932),x8931,x8932)+~P6(f10(x8931,x8932),f13(x8932),x8932)+P4(x8931,f2(x8932),x8932) % 1.29/1.21 [894]~P62(x8942)+~P51(x8942)+P4(f13(x8942),x8941,x8942)+~P4(f10(x8941,x8942),f13(x8942),x8942)+P4(x8941,f2(x8942),x8942) % 1.29/1.21 [904]~P62(x9041)+~P51(x9041)+~P6(f2(x9041),x9042,x9041)+~P6(x9042,f13(x9041),x9041)+P6(f13(x9041),f10(x9042,x9041),x9041) % 1.29/1.21 [905]~P62(x9051)+~P51(x9051)+~P6(f2(x9051),x9052,x9051)+~P4(x9052,f13(x9051),x9051)+P4(f13(x9051),f10(x9052,x9051),x9051) % 1.29/1.21 [550]~P2(x5502)+~P76(x5502)+~P59(x5502)+~P60(x5502)+~E(f33(x5501,f2(a1),x5502),f2(x5502)) % 1.29/1.21 [374]~P52(x3743)+E(x3741,x3742)+~E(f10(x3741,x3743),f10(x3742,x3743))+E(x3742,f2(x3743))+E(x3741,f2(x3743)) % 1.29/1.21 [910]~P40(x9102)+~P4(f2(x9102),x9101,x9102)+~P4(f2(x9102),x9103,x9102)+~E(f12(x9103,x9101,x9102),f2(x9102))+E(x9101,f2(x9102)) % 1.29/1.21 [911]~P40(x9112)+~P4(f2(x9112),x9113,x9112)+~P4(f2(x9112),x9111,x9112)+~E(f12(x9111,x9113,x9112),f2(x9112))+E(x9111,f2(x9112)) % 1.29/1.21 [1112]~P62(x11121)+~P51(x11121)+~P4(x11123,f2(x11121),x11121)+~P4(x11122,f2(x11121),x11121)+P4(f2(x11121),f11(x11122,x11123,x11121),x11121) % 1.29/1.21 [1114]~P62(x11141)+~P51(x11141)+~P4(f2(x11141),x11143,x11141)+~P4(f2(x11141),x11142,x11141)+P4(f2(x11141),f11(x11142,x11143,x11141),x11141) % 1.29/1.21 [1117]~P62(x11173)+~P51(x11173)+~P4(x11172,f2(x11173),x11173)+~P4(f2(x11173),x11171,x11173)+P4(f11(x11171,x11172,x11173),f2(x11173),x11173) % 1.29/1.21 [1118]~P62(x11183)+~P51(x11183)+~P4(x11181,f2(x11183),x11183)+~P4(f2(x11183),x11182,x11183)+P4(f11(x11181,x11182,x11183),f2(x11183),x11183) % 1.29/1.21 [1142]~P62(x11422)+~P51(x11422)+~P6(f11(x11423,x11421,x11422),f2(x11422),x11422)+P6(x11421,f2(x11422),x11422)+P6(x11423,f2(x11422),x11422) % 1.29/1.21 [1143]~P62(x11432)+~P51(x11432)+~P4(f11(x11433,x11431,x11432),f2(x11432),x11432)+P4(x11431,f2(x11432),x11432)+P4(x11433,f2(x11432),x11432) % 1.29/1.21 [1144]~P62(x11442)+~P51(x11442)+~P6(f2(x11442),f11(x11443,x11441,x11442),x11442)+P6(x11441,f2(x11442),x11442)+P6(f2(x11442),x11443,x11442) % 1.29/1.21 [1145]~P62(x11452)+~P51(x11452)+~P6(f2(x11452),f11(x11451,x11453,x11452),x11452)+P6(x11451,f2(x11452),x11452)+P6(f2(x11452),x11453,x11452) % 1.29/1.21 [1146]~P62(x11462)+~P51(x11462)+~P6(f2(x11462),f11(x11463,x11461,x11462),x11462)+P6(x11461,f2(x11462),x11462)+P6(f2(x11462),x11461,x11462) % 1.29/1.21 [1147]~P62(x11472)+~P51(x11472)+~P6(f2(x11472),f11(x11471,x11473,x11472),x11472)+P6(x11471,f2(x11472),x11472)+P6(f2(x11472),x11471,x11472) % 1.29/1.21 [1148]~P62(x11482)+~P51(x11482)+~P4(f2(x11482),f11(x11483,x11481,x11482),x11482)+P4(x11481,f2(x11482),x11482)+P4(f2(x11482),x11483,x11482) % 1.29/1.21 [1149]~P62(x11492)+~P51(x11492)+~P4(f2(x11492),f11(x11491,x11493,x11492),x11492)+P4(x11491,f2(x11492),x11492)+P4(f2(x11492),x11493,x11492) % 1.29/1.21 [1150]~P62(x11502)+~P51(x11502)+~P4(f2(x11502),f11(x11503,x11501,x11502),x11502)+P4(x11501,f2(x11502),x11502)+P4(f2(x11502),x11501,x11502) % 1.29/1.21 [1151]~P62(x11512)+~P51(x11512)+~P4(f2(x11512),f11(x11511,x11513,x11512),x11512)+P4(x11511,f2(x11512),x11512)+P4(f2(x11512),x11511,x11512) % 1.29/1.21 [1152]~P62(x11522)+~P51(x11522)+~P6(f11(x11523,x11521,x11522),f2(x11522),x11522)+P6(x11521,f2(x11522),x11522)+P6(f2(x11522),x11521,x11522) % 1.29/1.21 [1153]~P62(x11532)+~P51(x11532)+~P6(f11(x11531,x11533,x11532),f2(x11532),x11532)+P6(x11531,f2(x11532),x11532)+P6(f2(x11532),x11531,x11532) % 1.29/1.21 [1154]~P62(x11542)+~P51(x11542)+~P4(f11(x11543,x11541,x11542),f2(x11542),x11542)+P4(x11541,f2(x11542),x11542)+P4(f2(x11542),x11541,x11542) % 1.29/1.21 [1155]~P62(x11552)+~P51(x11552)+~P4(f11(x11551,x11553,x11552),f2(x11552),x11552)+P4(x11551,f2(x11552),x11552)+P4(f2(x11552),x11551,x11552) % 1.29/1.21 [1156]~P62(x11561)+~P51(x11561)+~P6(f11(x11562,x11563,x11561),f2(x11561),x11561)+P6(f2(x11561),x11562,x11561)+P6(f2(x11561),x11563,x11561) % 1.29/1.21 [1157]~P62(x11571)+~P51(x11571)+~P4(f11(x11572,x11573,x11571),f2(x11571),x11571)+P4(f2(x11571),x11572,x11571)+P4(f2(x11571),x11573,x11571) % 1.29/1.21 [1239]~P61(x12393)+~P4(x12391,f13(x12393),x12393)+~P4(f2(x12393),x12392,x12393)+~P4(f2(x12393),x12391,x12393)+P4(f14(x12391,x12392,x12393),x12392,x12393) % 1.29/1.21 [1240]~P61(x12403)+~P4(x12402,f13(x12403),x12403)+~P4(f2(x12403),x12402,x12403)+~P4(f2(x12403),x12401,x12403)+P4(f14(x12401,x12402,x12403),x12401,x12403) % 1.29/1.21 [1050]~P34(x10504)+~P12(x10504)+~P6(x10501,x10503,x10504)+~P4(f2(x10504),x10502,x10504)+P6(x10501,f12(x10502,x10503,x10504),x10504) % 1.29/1.21 [1051]~P34(x10514)+~P12(x10514)+~P4(x10511,x10513,x10514)+~P6(f2(x10514),x10512,x10514)+P6(x10511,f12(x10512,x10513,x10514),x10514) % 1.29/1.21 [1052]~P34(x10524)+~P12(x10524)+~P4(x10521,x10523,x10524)+~P4(f2(x10524),x10522,x10524)+P4(x10521,f12(x10522,x10523,x10524),x10524) % 1.29/1.21 [1053]~P34(x10534)+~P12(x10534)+~P4(x10531,x10532,x10534)+~P4(f2(x10534),x10533,x10534)+P4(x10531,f12(x10532,x10533,x10534),x10534) % 1.29/1.21 [1267]~P62(x12673)+~P51(x12673)+~P4(x12674,x12671,x12673)+~P4(x12672,f2(x12673),x12673)+P4(f11(x12671,x12672,x12673),f11(x12674,x12672,x12673),x12673) % 1.29/1.21 [1268]~P62(x12683)+~P51(x12683)+~P4(x12681,x12684,x12683)+~P4(f2(x12683),x12682,x12683)+P4(f11(x12681,x12682,x12683),f11(x12684,x12682,x12683),x12683) % 1.29/1.21 [1300]~P62(x13004)+~P51(x13004)+~P6(f2(x13004),x13003,x13004)+~P6(f11(x13001,x13003,x13004),x13002,x13004)+P6(x13001,f14(x13002,x13003,x13004),x13004) % 1.29/1.21 [1302]~P62(x13024)+~P51(x13024)+~P6(f2(x13024),x13023,x13024)+~P4(f11(x13021,x13023,x13024),x13022,x13024)+P4(x13021,f14(x13022,x13023,x13024),x13024) % 1.29/1.21 [1304]~P62(x13043)+~P51(x13043)+~P6(f2(x13043),x13042,x13043)+~P6(x13041,f11(x13044,x13042,x13043),x13043)+P6(f14(x13041,x13042,x13043),x13044,x13043) % 1.29/1.21 [1306]~P62(x13063)+~P51(x13063)+~P6(f2(x13063),x13062,x13063)+~P4(x13061,f11(x13064,x13062,x13063),x13063)+P4(f14(x13061,x13062,x13063),x13064,x13063) % 1.29/1.21 [1326]~P44(x13263)+~P6(x13261,x13264,x13263)+~P4(f2(x13263),x13261,x13263)+P6(f33(x13261,x13262,x13263),f33(x13264,x13262,x13263),x13263)+~P6(f2(a1),x13262,a1) % 1.29/1.21 [1332]~P44(x13323)+~P6(x13324,x13322,a1)+~P6(x13321,f13(x13323),x13323)+~P6(f2(x13323),x13321,x13323)+P6(f33(x13321,x13322,x13323),f33(x13321,x13324,x13323),x13323) % 1.29/1.21 [1333]~P44(x13333)+~P4(x13334,x13332,a1)+~P4(x13331,f13(x13333),x13333)+~P4(f2(x13333),x13331,x13333)+P4(f33(x13331,x13332,x13333),f33(x13331,x13334,x13333),x13333) % 1.29/1.21 [1400]~P62(x14003)+~P6(x14002,x14004,x14003)+~P6(x14001,f2(x14003),x14003)+~P6(f2(x14003),f14(x14002,x14004,x14003),x14003)+P6(f11(x14001,x14002,x14003),f11(x14001,x14004,x14003),x14003) % 1.29/1.21 [1401]~P62(x14013)+~P6(x14014,x14012,x14013)+~P6(f2(x14013),x14011,x14013)+~P6(f2(x14013),f14(x14012,x14014,x14013),x14013)+P6(f11(x14011,x14012,x14013),f11(x14011,x14014,x14013),x14013) % 1.29/1.21 [1402]~P62(x14023)+~P4(x14024,x14022,x14023)+~P4(f2(x14023),x14021,x14023)+~P6(f2(x14023),f14(x14022,x14024,x14023),x14023)+P4(f11(x14021,x14022,x14023),f11(x14021,x14024,x14023),x14023) % 1.29/1.21 [1124]~P44(x11244)+E(x11241,x11242)+~P4(f2(x11244),x11242,x11244)+~P4(f2(x11244),x11241,x11244)+~E(f33(x11241,f32(x11243),x11244),f33(x11242,f32(x11243),x11244)) % 1.29/1.21 [912]~P55(x9122)+~E(f11(x9124,x9123,x9122),f11(x9125,x9121,x9122))+E(f14(x9124,x9121,x9122),f14(x9125,x9123,x9122))+E(x9121,f2(x9122))+E(x9123,f2(x9122)) % 1.29/1.21 [913]~P55(x9132)+~E(f14(x9134,x9133,x9132),f14(x9135,x9131,x9132))+E(f11(x9134,x9131,x9132),f11(x9135,x9133,x9132))+E(x9131,f2(x9132))+E(x9133,f2(x9132)) % 1.29/1.21 [1308]~P16(x13084)+~P56(x13084)+E(x13081,x13082)+E(x13083,f2(x13084))+~E(f12(x13085,f14(x13083,x13081,x13084),x13084),f12(x13085,f14(x13083,x13082,x13084),x13084)) % 1.29/1.21 [1421]~P16(x14215)+~P56(x14215)+E(x14211,x14212)+E(x14213,x14214)+~E(f12(f14(x14213,x14211,x14215),f14(x14214,x14212,x14215),x14215),f12(f14(x14213,x14212,x14215),f14(x14214,x14211,x14215),x14215)) % 1.29/1.21 [1443]~P50(x14435)+~P49(x14435)+~P8(x14431,x14434,x14435)+~P8(x14431,f12(x14432,x14436,x14435),x14435)+P8(x14431,f12(f7(x14432,f14(x14433,x14434,x14435),x14435),x14436,x14435),x14435) % 1.29/1.21 [1444]~P50(x14444)+~P49(x14444)+~P8(x14441,x14445,x14444)+P8(x14441,f12(x14442,x14443,x14444),x14444)+~P8(x14441,f12(f7(x14442,f14(x14446,x14445,x14444),x14444),x14443,x14444),x14444) % 1.29/1.21 [474]~P2(x4742)+~P76(x4742)+~P59(x4742)+~P60(x4742)+E(x4741,f2(a1))+E(f33(f2(x4742),x4741,x4742),f2(x4742)) % 1.29/1.21 [551]~P2(x5512)+~P76(x5512)+~P59(x5512)+~P60(x5512)+~E(f33(x5511,x5513,x5512),f2(x5512))+E(x5511,f2(x5512)) % 1.29/1.21 [1133]~P62(x11332)+~P51(x11332)+P6(x11331,f2(x11332),x11332)+P6(f2(x11332),x11331,x11332)+~P6(x11333,f2(x11332),x11332)+P6(x11333,f11(x11334,x11331,x11332),x11332) % 1.29/1.21 [1134]~P62(x11342)+~P51(x11342)+P6(x11341,f2(x11342),x11342)+P6(f2(x11342),x11341,x11342)+~P4(x11343,f2(x11342),x11342)+P4(x11343,f11(x11344,x11341,x11342),x11342) % 1.29/1.21 [1135]~P62(x11352)+~P51(x11352)+P6(x11351,f2(x11352),x11352)+P6(f2(x11352),x11351,x11352)+~P6(f2(x11352),x11354,x11352)+P6(f11(x11353,x11351,x11352),x11354,x11352) % 1.29/1.21 [1136]~P62(x11362)+~P51(x11362)+P6(x11361,f2(x11362),x11362)+P6(f2(x11362),x11361,x11362)+~P4(f2(x11362),x11364,x11362)+P4(f11(x11363,x11361,x11362),x11364,x11362) % 1.29/1.21 [1231]~P62(x12312)+~P51(x12312)+P6(x12311,f2(x12312),x12312)+P6(f2(x12312),x12311,x12312)+~P6(x12313,f11(x12314,x12311,x12312),x12312)+P6(x12313,f2(x12312),x12312) % 1.29/1.21 [1232]~P62(x12322)+~P51(x12322)+P6(x12321,f2(x12322),x12322)+P6(f2(x12322),x12321,x12322)+~P4(x12323,f11(x12324,x12321,x12322),x12322)+P4(x12323,f2(x12322),x12322) % 1.29/1.21 [1233]~P62(x12332)+~P51(x12332)+P6(x12331,f2(x12332),x12332)+P6(f2(x12332),x12331,x12332)+~P6(f11(x12334,x12331,x12332),x12333,x12332)+P6(f2(x12332),x12333,x12332) % 1.29/1.21 [1234]~P62(x12342)+~P51(x12342)+P6(x12341,f2(x12342),x12342)+P6(f2(x12342),x12341,x12342)+~P4(f11(x12344,x12341,x12342),x12343,x12342)+P4(f2(x12342),x12343,x12342) % 1.29/1.21 [1262]~P44(x12624)+E(x12621,x12622)+~P4(f2(x12624),x12622,x12624)+~P4(f2(x12624),x12621,x12624)+~E(f33(x12621,x12623,x12624),f33(x12622,x12623,x12624))+~P6(f2(a1),x12623,a1) % 1.29/1.21 [1359]~P62(x13592)+~P51(x13592)+~P6(f14(x13593,x13591,x13592),x13594,x13592)+P6(x13591,f2(x13592),x13592)+~P6(x13593,f2(x13592),x13592)+P6(x13593,f11(x13594,x13591,x13592),x13592) % 1.29/1.21 [1360]~P62(x13602)+~P51(x13602)+~P4(f14(x13603,x13601,x13602),x13604,x13602)+P6(x13601,f2(x13602),x13602)+~P4(x13603,f2(x13602),x13602)+P4(x13603,f11(x13604,x13601,x13602),x13602) % 1.29/1.21 [1361]~P62(x13612)+~P51(x13612)+~P6(x13613,f14(x13614,x13611,x13612),x13612)+P6(x13611,f2(x13612),x13612)+~P6(f2(x13612),x13614,x13612)+P6(f11(x13613,x13611,x13612),x13614,x13612) % 1.29/1.21 [1362]~P62(x13622)+~P51(x13622)+~P4(x13623,f14(x13624,x13621,x13622),x13622)+P6(x13621,f2(x13622),x13622)+~P4(f2(x13622),x13624,x13622)+P4(f11(x13623,x13621,x13622),x13624,x13622) % 1.29/1.21 [1363]~P62(x13631)+~P51(x13631)+~P6(x13634,f11(x13633,x13632,x13631),x13631)+~P6(x13632,f2(x13631),x13631)+P6(f2(x13631),x13632,x13631)+P6(x13633,f14(x13634,x13632,x13631),x13631) % 1.29/1.21 [1364]~P62(x13641)+~P51(x13641)+~P6(x13644,f14(x13643,x13642,x13641),x13641)+~P6(x13642,f2(x13641),x13641)+P6(f2(x13641),x13642,x13641)+P6(x13643,f11(x13644,x13642,x13641),x13641) % 1.29/1.21 [1365]~P62(x13651)+~P51(x13651)+~P6(x13654,f14(x13653,x13652,x13651),x13651)+~P6(x13653,f2(x13651),x13651)+P6(f2(x13651),x13652,x13651)+P6(x13653,f11(x13654,x13652,x13651),x13651) % 1.29/1.21 [1366]~P62(x13661)+~P51(x13661)+~P4(x13664,f11(x13663,x13662,x13661),x13661)+~P6(x13662,f2(x13661),x13661)+P6(f2(x13661),x13662,x13661)+P4(x13663,f14(x13664,x13662,x13661),x13661) % 1.29/1.21 [1367]~P62(x13671)+~P51(x13671)+~P4(x13674,f14(x13673,x13672,x13671),x13671)+~P6(x13672,f2(x13671),x13671)+P6(f2(x13671),x13672,x13671)+P4(x13673,f11(x13674,x13672,x13671),x13671) % 1.29/1.21 [1368]~P62(x13681)+~P51(x13681)+~P4(x13684,f14(x13683,x13682,x13681),x13681)+~P4(x13683,f2(x13681),x13681)+P6(f2(x13681),x13682,x13681)+P4(x13683,f11(x13684,x13682,x13681),x13681) % 1.29/1.21 [1369]~P62(x13691)+~P51(x13691)+~P6(f11(x13694,x13692,x13691),x13693,x13691)+~P6(x13692,f2(x13691),x13691)+P6(f2(x13691),x13692,x13691)+P6(f14(x13693,x13692,x13691),x13694,x13691) % 1.29/1.21 [1370]~P62(x13701)+~P51(x13701)+~P6(f14(x13704,x13702,x13701),x13703,x13701)+~P6(x13702,f2(x13701),x13701)+P6(f2(x13701),x13702,x13701)+P6(f11(x13703,x13702,x13701),x13704,x13701) % 1.29/1.21 [1371]~P62(x13711)+~P51(x13711)+~P4(f11(x13714,x13712,x13711),x13713,x13711)+~P6(x13712,f2(x13711),x13711)+P6(f2(x13711),x13712,x13711)+P4(f14(x13713,x13712,x13711),x13714,x13711) % 1.29/1.21 [1372]~P62(x13721)+~P51(x13721)+~P4(f14(x13724,x13722,x13721),x13723,x13721)+~P6(x13722,f2(x13721),x13721)+P6(f2(x13721),x13722,x13721)+P4(f11(x13723,x13722,x13721),x13724,x13721) % 1.29/1.21 [1373]~P62(x13731)+~P51(x13731)+~P6(f14(x13734,x13732,x13731),x13733,x13731)+~P6(f2(x13731),x13734,x13731)+P6(f2(x13731),x13732,x13731)+P6(f11(x13733,x13732,x13731),x13734,x13731) % 1.29/1.21 [1374]~P62(x13741)+~P51(x13741)+~P4(f14(x13744,x13742,x13741),x13743,x13741)+~P4(f2(x13741),x13744,x13741)+P6(f2(x13741),x13742,x13741)+P4(f11(x13743,x13742,x13741),x13744,x13741) % 1.29/1.21 [1403]~P62(x14033)+~P51(x14033)+~P4(x14032,x14034,x14033)+~P4(x14031,f2(x14033),x14033)+~P6(f2(x14033),f14(x14032,x14034,x14033),x14033)+P4(f11(x14031,x14032,x14033),f11(x14031,x14034,x14033),x14033) % 1.29/1.21 [1410]~P62(x14104)+~P51(x14104)+~P6(x14103,f2(x14104),x14104)+~P6(x14102,f14(x14101,x14103,x14104),x14104)+~P6(f14(x14101,x14103,x14104),x14102,x14104)+P6(x14101,f11(x14102,x14103,x14104),x14104) % 1.29/1.21 [1411]~P62(x14114)+~P51(x14114)+~P6(x14111,f2(x14114),x14114)+~P6(x14112,f14(x14111,x14113,x14114),x14114)+~P6(f14(x14111,x14113,x14114),x14112,x14114)+P6(x14111,f11(x14112,x14113,x14114),x14114) % 1.29/1.21 [1412]~P62(x14124)+~P51(x14124)+~P6(x14123,f2(x14124),x14124)+~P4(x14122,f14(x14121,x14123,x14124),x14124)+~P4(f14(x14121,x14123,x14124),x14122,x14124)+P4(x14121,f11(x14122,x14123,x14124),x14124) % 1.29/1.21 [1413]~P62(x14134)+~P51(x14134)+~P4(x14131,f2(x14134),x14134)+~P4(x14132,f14(x14131,x14133,x14134),x14134)+~P4(f14(x14131,x14133,x14134),x14132,x14134)+P4(x14131,f11(x14132,x14133,x14134),x14134) % 1.29/1.21 [1414]~P62(x14143)+~P51(x14143)+~P6(x14142,f2(x14143),x14143)+~P6(x14141,f14(x14144,x14142,x14143),x14143)+~P6(f14(x14144,x14142,x14143),x14141,x14143)+P6(f11(x14141,x14142,x14143),x14144,x14143) % 1.29/1.21 [1415]~P62(x14153)+~P51(x14153)+~P6(x14152,f2(x14153),x14153)+~P4(x14151,f14(x14154,x14152,x14153),x14153)+~P4(f14(x14154,x14152,x14153),x14151,x14153)+P4(f11(x14151,x14152,x14153),x14154,x14153) % 1.29/1.21 [1416]~P62(x14163)+~P51(x14163)+~P6(f2(x14163),x14164,x14163)+~P6(x14161,f14(x14164,x14162,x14163),x14163)+~P6(f14(x14164,x14162,x14163),x14161,x14163)+P6(f11(x14161,x14162,x14163),x14164,x14163) % 1.29/1.21 [1417]~P62(x14173)+~P51(x14173)+~P4(f2(x14173),x14174,x14173)+~P4(x14171,f14(x14174,x14172,x14173),x14173)+~P4(f14(x14174,x14172,x14173),x14171,x14173)+P4(f11(x14171,x14172,x14173),x14174,x14173) % 1.29/1.21 [1382]~P64(x13823)+~P6(x13822,x13825,x13823)+~P6(x13821,x13824,x13823)+~P6(f2(x13823),x13824,x13823)+~P4(f2(x13823),x13822,x13823)+P6(f14(x13821,x13822,x13823),f14(x13824,x13825,x13823),x13823) % 1.29/1.21 [1383]~P64(x13833)+~P6(x13832,x13835,x13833)+~P6(x13831,x13834,x13833)+~P4(f2(x13833),x13832,x13833)+~P4(f2(x13833),x13831,x13833)+P6(f14(x13831,x13832,x13833),f14(x13834,x13835,x13833),x13833) % 1.29/1.21 [1384]~P64(x13843)+~P6(x13842,x13845,x13843)+~P4(x13841,x13844,x13843)+~P6(f2(x13843),x13841,x13843)+~P4(f2(x13843),x13842,x13843)+P6(f14(x13841,x13842,x13843),f14(x13844,x13845,x13843),x13843) % 1.29/1.21 [1385]~P64(x13853)+~P6(x13851,x13854,x13853)+~P4(x13852,x13855,x13853)+~P6(f2(x13853),x13852,x13853)+~P4(f2(x13853),x13851,x13853)+P6(f14(x13851,x13852,x13853),f14(x13854,x13855,x13853),x13853) % 1.29/1.21 [1386]~P62(x13863)+~P6(x13865,x13862,x13863)+~P4(x13861,x13864,x13863)+~P6(f2(x13863),x13865,x13863)+~P6(f2(x13863),x13861,x13863)+P6(f11(x13861,x13862,x13863),f11(x13864,x13865,x13863),x13863) % 1.29/1.21 [1387]~P62(x13873)+~P6(x13871,x13874,x13873)+~P4(x13875,x13872,x13873)+~P6(f2(x13873),x13875,x13873)+~P4(f2(x13873),x13871,x13873)+P6(f11(x13871,x13872,x13873),f11(x13874,x13875,x13873),x13873) % 1.29/1.21 [1388]~P68(x13883)+~P4(x13882,x13885,x13883)+~P4(x13881,x13884,x13883)+~P4(f2(x13883),x13884,x13883)+~P4(f2(x13883),x13882,x13883)+P4(f14(x13881,x13882,x13883),f14(x13884,x13885,x13883),x13883) % 1.29/1.21 [1389]~P68(x13893)+~P4(x13892,x13895,x13893)+~P4(x13891,x13894,x13893)+~P4(f2(x13893),x13892,x13893)+~P4(f2(x13893),x13891,x13893)+P4(f14(x13891,x13892,x13893),f14(x13894,x13895,x13893),x13893) % 1.29/1.21 [1390]~P62(x13903)+~P4(x13905,x13902,x13903)+~P4(x13901,x13904,x13903)+~P6(f2(x13903),x13905,x13903)+~P4(f2(x13903),x13901,x13903)+P4(f11(x13901,x13902,x13903),f11(x13904,x13905,x13903),x13903) % 1.29/1.21 [1464]~P57(x14643)+~P4(x14647,x14642,x14643)+~P4(x14646,x14641,x14643)+~P4(x14642,x14645,x14643)+~P4(x14641,x14644,x14643)+P4(f14(x14641,x14642,x14643),f12(f12(f12(f14(f27(x14644,x14643),f27(x14645,x14643),x14643),f14(f27(x14646,x14643),f28(x14645,x14643),x14643),x14643),f14(f28(x14644,x14643),f27(x14647,x14643),x14643),x14643),f14(f28(x14646,x14643),f28(x14647,x14643),x14643),x14643),x14643) % 1.29/1.21 [1465]~P57(x14652)+~P4(x14657,x14653,x14652)+~P4(x14656,x14654,x14652)+~P4(x14655,x14657,x14652)+~P4(x14651,x14656,x14652)+P4(f12(f12(f12(f14(f28(x14651,x14652),f27(x14653,x14652),x14652),f14(f28(x14654,x14652),f28(x14653,x14652),x14652),x14652),f14(f27(x14651,x14652),f27(x14655,x14652),x14652),x14652),f14(f27(x14654,x14652),f28(x14655,x14652),x14652),x14652),f14(x14656,x14657,x14652),x14652) % 1.29/1.21 %EqnAxiom % 1.29/1.21 [1]E(x11,x11) % 1.29/1.21 [2]E(x22,x21)+~E(x21,x22) % 1.29/1.21 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.29/1.21 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 1.29/1.21 [5]~E(x51,x52)+E(f17(x51),f17(x52)) % 1.29/1.21 [6]~E(x61,x62)+E(f5(x61),f5(x62)) % 1.29/1.21 [7]~E(x71,x72)+E(f26(x71,x73,x74,x75,x76,x77),f26(x72,x73,x74,x75,x76,x77)) % 1.29/1.21 [8]~E(x81,x82)+E(f26(x83,x81,x84,x85,x86,x87),f26(x83,x82,x84,x85,x86,x87)) % 1.29/1.21 [9]~E(x91,x92)+E(f26(x93,x94,x91,x95,x96,x97),f26(x93,x94,x92,x95,x96,x97)) % 1.29/1.21 [10]~E(x101,x102)+E(f26(x103,x104,x105,x101,x106,x107),f26(x103,x104,x105,x102,x106,x107)) % 1.29/1.21 [11]~E(x111,x112)+E(f26(x113,x114,x115,x116,x111,x117),f26(x113,x114,x115,x116,x112,x117)) % 1.29/1.21 [12]~E(x121,x122)+E(f26(x123,x124,x125,x126,x127,x121),f26(x123,x124,x125,x126,x127,x122)) % 1.29/1.21 [13]~E(x131,x132)+E(f14(x131,x133,x134),f14(x132,x133,x134)) % 1.29/1.21 [14]~E(x141,x142)+E(f14(x143,x141,x144),f14(x143,x142,x144)) % 1.29/1.21 [15]~E(x151,x152)+E(f14(x153,x154,x151),f14(x153,x154,x152)) % 1.29/1.21 [16]~E(x161,x162)+E(f29(x161),f29(x162)) % 1.29/1.21 [17]~E(x171,x172)+E(f12(x171,x173,x174),f12(x172,x173,x174)) % 1.29/1.21 [18]~E(x181,x182)+E(f12(x183,x181,x184),f12(x183,x182,x184)) % 1.29/1.21 [19]~E(x191,x192)+E(f12(x193,x194,x191),f12(x193,x194,x192)) % 1.29/1.21 [20]~E(x201,x202)+E(f4(x201),f4(x202)) % 1.29/1.21 [21]~E(x211,x212)+E(f11(x211,x213,x214),f11(x212,x213,x214)) % 1.29/1.21 [22]~E(x221,x222)+E(f11(x223,x221,x224),f11(x223,x222,x224)) % 1.29/1.21 [23]~E(x231,x232)+E(f11(x233,x234,x231),f11(x233,x234,x232)) % 1.29/1.21 [24]~E(x241,x242)+E(f13(x241),f13(x242)) % 1.29/1.21 [25]~E(x251,x252)+E(f18(x251,x253),f18(x252,x253)) % 1.29/1.21 [26]~E(x261,x262)+E(f18(x263,x261),f18(x263,x262)) % 1.29/1.21 [27]~E(x271,x272)+E(f9(x271,x273,x274),f9(x272,x273,x274)) % 1.29/1.21 [28]~E(x281,x282)+E(f9(x283,x281,x284),f9(x283,x282,x284)) % 1.29/1.21 [29]~E(x291,x292)+E(f9(x293,x294,x291),f9(x293,x294,x292)) % 1.29/1.21 [30]~E(x301,x302)+E(f33(x301,x303,x304),f33(x302,x303,x304)) % 1.29/1.21 [31]~E(x311,x312)+E(f33(x313,x311,x314),f33(x313,x312,x314)) % 1.29/1.21 [32]~E(x321,x322)+E(f33(x323,x324,x321),f33(x323,x324,x322)) % 1.29/1.21 [33]~E(x331,x332)+E(f7(x331,x333,x334),f7(x332,x333,x334)) % 1.29/1.21 [34]~E(x341,x342)+E(f7(x343,x341,x344),f7(x343,x342,x344)) % 1.29/1.21 [35]~E(x351,x352)+E(f7(x353,x354,x351),f7(x353,x354,x352)) % 1.29/1.21 [36]~E(x361,x362)+E(f28(x361,x363),f28(x362,x363)) % 1.29/1.21 [37]~E(x371,x372)+E(f28(x373,x371),f28(x373,x372)) % 1.29/1.21 [38]~E(x381,x382)+E(f27(x381,x383),f27(x382,x383)) % 1.29/1.21 [39]~E(x391,x392)+E(f27(x393,x391),f27(x393,x392)) % 1.29/1.21 [40]~E(x401,x402)+E(f24(x401,x403),f24(x402,x403)) % 1.29/1.21 [41]~E(x411,x412)+E(f24(x413,x411),f24(x413,x412)) % 1.29/1.21 [42]~E(x421,x422)+E(f15(x421,x423),f15(x422,x423)) % 1.29/1.21 [43]~E(x431,x432)+E(f15(x433,x431),f15(x433,x432)) % 1.29/1.21 [44]~E(x441,x442)+E(f8(x441,x443),f8(x442,x443)) % 1.29/1.21 [45]~E(x451,x452)+E(f8(x453,x451),f8(x453,x452)) % 1.29/1.21 [46]~E(x461,x462)+E(f10(x461,x463),f10(x462,x463)) % 1.29/1.21 [47]~E(x471,x472)+E(f10(x473,x471),f10(x473,x472)) % 1.29/1.21 [48]~E(x481,x482)+E(f21(x481,x483,x484),f21(x482,x483,x484)) % 1.29/1.21 [49]~E(x491,x492)+E(f21(x493,x491,x494),f21(x493,x492,x494)) % 1.29/1.21 [50]~E(x501,x502)+E(f21(x503,x504,x501),f21(x503,x504,x502)) % 1.29/1.21 [51]~E(x511,x512)+E(f16(x511,x513),f16(x512,x513)) % 1.29/1.21 [52]~E(x521,x522)+E(f16(x523,x521),f16(x523,x522)) % 1.29/1.21 [53]~E(x531,x532)+E(f30(x531,x533,x534),f30(x532,x533,x534)) % 1.29/1.21 [54]~E(x541,x542)+E(f30(x543,x541,x544),f30(x543,x542,x544)) % 1.29/1.21 [55]~E(x551,x552)+E(f30(x553,x554,x551),f30(x553,x554,x552)) % 1.29/1.21 [56]~E(x561,x562)+E(f31(x561,x563,x564),f31(x562,x563,x564)) % 1.29/1.21 [57]~E(x571,x572)+E(f31(x573,x571,x574),f31(x573,x572,x574)) % 1.29/1.21 [58]~E(x581,x582)+E(f31(x583,x584,x581),f31(x583,x584,x582)) % 1.29/1.21 [59]~E(x591,x592)+E(f6(x591,x593),f6(x592,x593)) % 1.29/1.21 [60]~E(x601,x602)+E(f6(x603,x601),f6(x603,x602)) % 1.29/1.21 [61]~E(x611,x612)+E(f32(x611),f32(x612)) % 1.29/1.21 [62]~E(x621,x622)+E(f20(x621,x623,x624),f20(x622,x623,x624)) % 1.29/1.21 [63]~E(x631,x632)+E(f20(x633,x631,x634),f20(x633,x632,x634)) % 1.29/1.21 [64]~E(x641,x642)+E(f20(x643,x644,x641),f20(x643,x644,x642)) % 1.29/1.21 [65]~E(x651,x652)+E(f23(x651,x653),f23(x652,x653)) % 1.29/1.21 [66]~E(x661,x662)+E(f23(x663,x661),f23(x663,x662)) % 1.29/1.21 [67]~E(x671,x672)+E(f19(x671,x673,x674),f19(x672,x673,x674)) % 1.29/1.21 [68]~E(x681,x682)+E(f19(x683,x681,x684),f19(x683,x682,x684)) % 1.29/1.21 [69]~E(x691,x692)+E(f19(x693,x694,x691),f19(x693,x694,x692)) % 1.29/1.21 [70]~E(x701,x702)+E(f25(x701,x703,x704,x705),f25(x702,x703,x704,x705)) % 1.29/1.21 [71]~E(x711,x712)+E(f25(x713,x711,x714,x715),f25(x713,x712,x714,x715)) % 1.29/1.21 [72]~E(x721,x722)+E(f25(x723,x724,x721,x725),f25(x723,x724,x722,x725)) % 1.29/1.21 [73]~E(x731,x732)+E(f25(x733,x734,x735,x731),f25(x733,x734,x735,x732)) % 1.29/1.21 [74]~E(x741,x742)+E(f22(x741,x743,x744),f22(x742,x743,x744)) % 1.29/1.21 [75]~E(x751,x752)+E(f22(x753,x751,x754),f22(x753,x752,x754)) % 1.29/1.21 [76]~E(x761,x762)+E(f22(x763,x764,x761),f22(x763,x764,x762)) % 1.29/1.21 [77]~E(x771,x772)+E(f35(x771,x773),f35(x772,x773)) % 1.29/1.21 [78]~E(x781,x782)+E(f35(x783,x781),f35(x783,x782)) % 1.29/1.21 [79]~P1(x791)+P1(x792)+~E(x791,x792) % 1.29/1.21 [80]~P2(x801)+P2(x802)+~E(x801,x802) % 1.29/1.21 [81]~P44(x811)+P44(x812)+~E(x811,x812) % 1.29/1.21 [82]~P64(x821)+P64(x822)+~E(x821,x822) % 1.29/1.21 [83]~P3(x831)+P3(x832)+~E(x831,x832) % 1.29/1.21 [84]~P10(x841)+P10(x842)+~E(x841,x842) % 1.29/1.21 [85]~P45(x851)+P45(x852)+~E(x851,x852) % 1.29/1.21 [86]~P11(x861)+P11(x862)+~E(x861,x862) % 1.29/1.21 [87]~P27(x871)+P27(x872)+~E(x871,x872) % 1.29/1.21 [88]~P34(x881)+P34(x882)+~E(x881,x882) % 1.29/1.21 [89]~P12(x891)+P12(x892)+~E(x891,x892) % 1.29/1.21 [90]~P50(x901)+P50(x902)+~E(x901,x902) % 1.29/1.21 [91]~P39(x911)+P39(x912)+~E(x911,x912) % 1.29/1.21 [92]~P13(x921)+P13(x922)+~E(x921,x922) % 1.29/1.21 [93]~P65(x931)+P65(x932)+~E(x931,x932) % 1.29/1.21 [94]~P35(x941)+P35(x942)+~E(x941,x942) % 1.29/1.21 [95]~P14(x951)+P14(x952)+~E(x951,x952) % 1.29/1.21 [96]~P40(x961)+P40(x962)+~E(x961,x962) % 1.29/1.21 [97]~P18(x971)+P18(x972)+~E(x971,x972) % 1.29/1.21 [98]~P42(x981)+P42(x982)+~E(x981,x982) % 1.29/1.21 [99]~P43(x991)+P43(x992)+~E(x991,x992) % 1.29/1.21 [100]~P21(x1001)+P21(x1002)+~E(x1001,x1002) % 1.29/1.21 [101]~P19(x1011)+P19(x1012)+~E(x1011,x1012) % 1.29/1.21 [102]~P20(x1021)+P20(x1022)+~E(x1021,x1022) % 1.29/1.21 [103]~P75(x1031)+P75(x1032)+~E(x1031,x1032) % 1.29/1.21 [104]~P41(x1041)+P41(x1042)+~E(x1041,x1042) % 1.29/1.21 [105]~P66(x1051)+P66(x1052)+~E(x1051,x1052) % 1.29/1.21 [106]~P67(x1061)+P67(x1062)+~E(x1061,x1062) % 1.29/1.21 [107]~P23(x1071)+P23(x1072)+~E(x1071,x1072) % 1.29/1.21 [108]~P26(x1081)+P26(x1082)+~E(x1081,x1082) % 1.29/1.21 [109]~P53(x1091)+P53(x1092)+~E(x1091,x1092) % 1.29/1.21 [110]~P68(x1101)+P68(x1102)+~E(x1101,x1102) % 1.29/1.21 [111]~P54(x1111)+P54(x1112)+~E(x1111,x1112) % 1.29/1.21 [112]~P58(x1121)+P58(x1122)+~E(x1121,x1122) % 1.29/1.21 [113]~P76(x1131)+P76(x1132)+~E(x1131,x1132) % 1.29/1.21 [114]~P59(x1141)+P59(x1142)+~E(x1141,x1142) % 1.29/1.21 [115]~P60(x1151)+P60(x1152)+~E(x1151,x1152) % 1.29/1.21 [116]~P24(x1161)+P24(x1162)+~E(x1161,x1162) % 1.29/1.21 [117]~P46(x1171)+P46(x1172)+~E(x1171,x1172) % 1.29/1.21 [118]~P28(x1181)+P28(x1182)+~E(x1181,x1182) % 1.29/1.21 [119]P4(x1192,x1193,x1194)+~E(x1191,x1192)+~P4(x1191,x1193,x1194) % 1.29/1.21 [120]P4(x1203,x1202,x1204)+~E(x1201,x1202)+~P4(x1203,x1201,x1204) % 1.29/1.21 [121]P4(x1213,x1214,x1212)+~E(x1211,x1212)+~P4(x1213,x1214,x1211) % 1.29/1.21 [122]P6(x1222,x1223,x1224)+~E(x1221,x1222)+~P6(x1221,x1223,x1224) % 1.29/1.21 [123]P6(x1233,x1232,x1234)+~E(x1231,x1232)+~P6(x1233,x1231,x1234) % 1.29/1.21 [124]P6(x1243,x1244,x1242)+~E(x1241,x1242)+~P6(x1243,x1244,x1241) % 1.29/1.21 [125]P5(x1252,x1253,x1254)+~E(x1251,x1252)+~P5(x1251,x1253,x1254) % 1.29/1.21 [126]P5(x1263,x1262,x1264)+~E(x1261,x1262)+~P5(x1263,x1261,x1264) % 1.29/1.21 [127]P5(x1273,x1274,x1272)+~E(x1271,x1272)+~P5(x1273,x1274,x1271) % 1.29/1.21 [128]~P51(x1281)+P51(x1282)+~E(x1281,x1282) % 1.29/1.21 [129]~P69(x1291)+P69(x1292)+~E(x1291,x1292) % 1.29/1.21 [130]~P62(x1301)+P62(x1302)+~E(x1301,x1302) % 1.29/1.21 [131]~P61(x1311)+P61(x1312)+~E(x1311,x1312) % 1.29/1.21 [132]~P63(x1321)+P63(x1322)+~E(x1321,x1322) % 1.29/1.21 [133]P8(x1332,x1333,x1334)+~E(x1331,x1332)+~P8(x1331,x1333,x1334) % 1.29/1.21 [134]P8(x1343,x1342,x1344)+~E(x1341,x1342)+~P8(x1343,x1341,x1344) % 1.29/1.21 [135]P8(x1353,x1354,x1352)+~E(x1351,x1352)+~P8(x1353,x1354,x1351) % 1.29/1.21 [136]~P55(x1361)+P55(x1362)+~E(x1361,x1362) % 1.29/1.21 [137]~P78(x1371)+P78(x1372)+~E(x1371,x1372) % 1.29/1.21 [138]~P48(x1381)+P48(x1382)+~E(x1381,x1382) % 1.29/1.21 [139]~P38(x1391)+P38(x1392)+~E(x1391,x1392) % 1.29/1.21 [140]~P31(x1401)+P31(x1402)+~E(x1401,x1402) % 1.29/1.21 [141]~P49(x1411)+P49(x1412)+~E(x1411,x1412) % 1.29/1.21 [142]~P77(x1421)+P77(x1422)+~E(x1421,x1422) % 1.29/1.21 [143]~P52(x1431)+P52(x1432)+~E(x1431,x1432) % 1.29/1.21 [144]~P30(x1441)+P30(x1442)+~E(x1441,x1442) % 1.29/1.21 [145]P7(x1452,x1453,x1454,x1455)+~E(x1451,x1452)+~P7(x1451,x1453,x1454,x1455) % 1.29/1.21 [146]P7(x1463,x1462,x1464,x1465)+~E(x1461,x1462)+~P7(x1463,x1461,x1464,x1465) % 1.29/1.21 [147]P7(x1473,x1474,x1472,x1475)+~E(x1471,x1472)+~P7(x1473,x1474,x1471,x1475) % 1.29/1.21 [148]P7(x1483,x1484,x1485,x1482)+~E(x1481,x1482)+~P7(x1483,x1484,x1485,x1481) % 1.29/1.21 [149]~P29(x1491)+P29(x1492)+~E(x1491,x1492) % 1.29/1.21 [150]~P22(x1501)+P22(x1502)+~E(x1501,x1502) % 1.29/1.21 [151]~P37(x1511)+P37(x1512)+~E(x1511,x1512) % 1.29/1.21 [152]~P73(x1521)+P73(x1522)+~E(x1521,x1522) % 1.29/1.21 [153]~P71(x1531)+P71(x1532)+~E(x1531,x1532) % 1.29/1.21 [154]~P9(x1541)+P9(x1542)+~E(x1541,x1542) % 1.29/1.21 [155]~P56(x1551)+P56(x1552)+~E(x1551,x1552) % 1.29/1.21 [156]~P16(x1561)+P16(x1562)+~E(x1561,x1562) % 1.29/1.21 [157]~P15(x1571)+P15(x1572)+~E(x1571,x1572) % 1.29/1.21 [158]~P36(x1581)+P36(x1582)+~E(x1581,x1582) % 1.29/1.21 [159]~P70(x1591)+P70(x1592)+~E(x1591,x1592) % 1.29/1.21 [160]~P57(x1601)+P57(x1602)+~E(x1601,x1602) % 1.29/1.21 [161]~P47(x1611)+P47(x1612)+~E(x1611,x1612) % 1.29/1.21 [162]~P17(x1621)+P17(x1622)+~E(x1621,x1622) % 1.29/1.21 [163]~P74(x1631)+P74(x1632)+~E(x1631,x1632) % 1.29/1.21 [164]~P33(x1641)+P33(x1642)+~E(x1641,x1642) % 1.29/1.21 [165]~P32(x1651)+P32(x1652)+~E(x1651,x1652) % 1.29/1.21 [166]~P25(x1661)+P25(x1662)+~E(x1661,x1662) % 1.29/1.21 [167]~P72(x1671)+P72(x1672)+~E(x1671,x1672) % 1.29/1.21 % 1.29/1.21 %------------------------------------------- % 1.29/1.21 cnf(1513,plain, % 1.29/1.21 ($false), % 1.29/1.21 inference(scs_inference,[],[276,307,1425]), % 1.29/1.21 ['proof']). % 1.29/1.21 % SZS output end Proof % 1.29/1.21 % Total time :0.110000s %------------------------------------------------------------------------------