%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : ALG387-1 : 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 : n029.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 03:41:34 EDT 2024 % Result : Unsatisfiable 1.21s 1.27s % Output : CNFRefutation 1.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : ALG387-1 : 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 % 0.12/0.33 % Computer : n029.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.33 % CPULimit : 300 % 0.18/0.33 % WCLimit : 300 % 0.18/0.33 % DateTime : Wed Jun 19 16:13:39 EDT 2024 % 0.18/0.33 % CPUTime : % 0.19/0.56 start to proof:theBenchmark % 1.12/1.21 %------------------------------------------- % 1.12/1.21 % File :CSE---1.7 % 1.12/1.21 % Problem :theBenchmark % 1.12/1.21 % Transform :cnf % 1.12/1.21 % Format :tptp:raw % 1.12/1.21 % Command :java -jar mcs_scs.jar %d %s % 1.12/1.21 % 1.12/1.21 % Result :Theorem 0.440000s % 1.12/1.21 % Output :CNFRefutation 0.440000s % 1.12/1.21 %------------------------------------------- % 1.12/1.21 %------------------------------------------------------------------------------ % 1.12/1.21 % File : ALG387-1 : TPTP v8.2.0. Released v4.1.0. % 1.12/1.21 % Domain : General Algebra % 1.12/1.21 % Problem : Fundamental theorem of algebra 0546_36 % 1.12/1.21 % Version : Especial. % 1.12/1.21 % English : % 1.12/1.21 % 1.12/1.21 % Refs : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe % 1.12/1.22 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 1.12/1.22 % Source : [Nip10] % 1.12/1.22 % Names : Fundamental_Theorem_Algebra-0546_36 [Nip10] % 1.12/1.22 % 1.12/1.22 % Status : Unsatisfiable % 1.12/1.22 % Rating : 0.20 v8.2.0, 0.24 v8.1.0, 0.26 v7.5.0, 0.21 v7.4.0, 0.24 v7.3.0, 0.25 v7.0.0, 0.33 v6.3.0, 0.27 v6.2.0, 0.40 v6.1.0, 0.36 v6.0.0, 0.40 v5.5.0, 0.75 v5.4.0, 0.80 v5.3.0, 0.83 v5.2.0, 0.75 v5.1.0, 0.76 v5.0.0, 0.71 v4.1.0 % 1.12/1.22 % Syntax : Number of clauses : 884 ( 147 unt; 67 nHn; 571 RR) % 1.12/1.22 % Number of literals : 2217 ( 417 equ;1288 neg) % 1.12/1.22 % Maximal clause size : 6 ( 2 avg) % 1.12/1.22 % Maximal term depth : 5 ( 1 avg) % 1.12/1.22 % Number of predicates : 72 ( 71 usr; 0 prp; 1-3 aty) % 1.12/1.22 % Number of functors : 39 ( 39 usr; 8 con; 0-3 aty) % 1.12/1.22 % Number of variables : 2227 ( 124 sgn) % 1.12/1.22 % SPC : CNF_UNS_RFO_SEQ_NHN % 1.12/1.22 % 1.12/1.22 % Comments : % 1.12/1.22 %------------------------------------------------------------------------------ % 1.12/1.22 cnf(cls_less__infI2_0,axiom, % 1.12/1.22 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.12/1.22 | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a) % 1.12/1.22 | ~ c_HOL_Oord__class_Oless(V_b,V_x,T_a) ) ). % 1.12/1.22 % 1.12/1.22 cnf(cls_abs__mult_0,axiom, % 1.12/1.22 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.12/1.22 | 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) ) ). % 1.12/1.22 % 1.12/1.22 cnf(cls_abs__eq__mult_0,axiom, % 1.12/1.22 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.12/1.22 | 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) % 1.12/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.12/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.12/1.22 % 1.12/1.22 cnf(cls_abs__eq__mult_1,axiom, % 1.12/1.22 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.12/1.22 | 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) % 1.12/1.22 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.12/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.12/1.22 % 1.12/1.22 cnf(cls_abs__eq__mult_2,axiom, % 1.12/1.22 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.12/1.22 | 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) % 1.12/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.12/1.22 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.12/1.22 % 1.12/1.22 cnf(cls_abs__eq__mult_3,axiom, % 1.12/1.22 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.12/1.22 | 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) % 1.12/1.22 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.12/1.22 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.12/1.22 % 1.12/1.22 cnf(cls_minus__mult__left_0,axiom, % 1.17/1.22 ( ~ class_Ring__and__Field_Oring(T_a) % 1.17/1.22 | 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) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_minus__mult__right_0,axiom, % 1.17/1.22 ( ~ class_Ring__and__Field_Oring(T_a) % 1.17/1.22 | 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) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_real__add__le__0__iff_1,axiom, % 1.17/1.22 ( c_lessequals(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.17/1.22 | ~ c_lessequals(V_y,c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_real__add__le__0__iff_0,axiom, % 1.17/1.22 ( c_lessequals(V_y,c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.17/1.22 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_le__eq__neg_0,axiom, % 1.17/1.22 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.17/1.22 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.22 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_le__eq__neg_1,axiom, % 1.17/1.22 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.17/1.22 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.17/1.22 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_mult__left__idem_0,axiom, % 1.17/1.22 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 1.17/1.22 | 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) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_eq__poly__code_I2_J_0,axiom, % 1.17/1.22 ( ~ class_HOL_Ozero(T_a) % 1.17/1.22 | ~ class_HOL_Oeq(T_a) % 1.17/1.22 | c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.22 | ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(V_b,V_q,T_a),tc_Polynomial_Opoly(T_a)) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_eq__poly__code_I2_J_1,axiom, % 1.17/1.22 ( ~ class_HOL_Ozero(T_a) % 1.17/1.22 | ~ class_HOL_Oeq(T_a) % 1.17/1.22 | c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,tc_Polynomial_Opoly(T_a)) % 1.17/1.22 | ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(V_b,V_q,T_a),tc_Polynomial_Opoly(T_a)) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_power__eq__0__iff_0,axiom, % 1.17/1.22 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.17/1.22 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.17/1.22 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.17/1.22 | ~ class_Power_Opower(T_a) % 1.17/1.22 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.22 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_field__power__not__zero_0,axiom, % 1.17/1.22 ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(T_a) % 1.17/1.22 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.22 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_neg__le__0__iff__le_0,axiom, % 1.17/1.22 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.17/1.22 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.17/1.22 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_neg__le__0__iff__le_1,axiom, % 1.17/1.22 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.17/1.22 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_zero__less__norm__iff_1,axiom, % 1.17/1.22 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.17/1.22 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal) % 1.17/1.22 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_abs__less__iff_2,axiom, % 1.17/1.22 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.17/1.22 | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 1.17/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.17/1.22 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_mult__le__0__iff_0,axiom, % 1.17/1.22 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.22 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.22 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.17/1.22 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_mult__le__0__iff_1,axiom, % 1.17/1.22 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.22 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.22 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.17/1.22 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_mult__le__0__iff_2,axiom, % 1.17/1.22 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.22 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.22 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.22 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_mult__le__0__iff_3,axiom, % 1.17/1.22 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.22 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.22 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.22 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_mult__neg__pos_0,axiom, % 1.17/1.22 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.17/1.22 | 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) % 1.17/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.22 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_mult__pos__neg_0,axiom, % 1.17/1.22 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.17/1.22 | 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) % 1.17/1.22 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_mult__pos__neg2_0,axiom, % 1.17/1.22 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.17/1.22 | 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) % 1.17/1.22 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_abs__le__interval__iff_0,axiom, % 1.17/1.22 ( c_lessequals(c_HOL_Ouminus__class_Ouminus(V_r,tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.17/1.22 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),V_r,tc_RealDef_Oreal) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_abs__le__D2_0,axiom, % 1.17/1.22 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.17/1.22 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.17/1.22 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_add__minus__cancel_0,axiom, % 1.17/1.22 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.22 | 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 ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_real__sqrt__ge__0__iff_1,axiom, % 1.17/1.22 ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) % 1.17/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_less__infI1_0,axiom, % 1.17/1.22 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.17/1.22 | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a) % 1.17/1.22 | ~ c_HOL_Oord__class_Oless(V_a,V_x,T_a) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_abs__of__nonneg_0,axiom, % 1.17/1.22 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.17/1.22 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.17/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_min__max_Osup__idem_0,axiom, % 1.17/1.22 ( ~ class_Orderings_Olinorder(T_a) % 1.17/1.22 | c_Orderings_Oord__class_Omax(V_x,V_x,T_a) = V_x ) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_arctan__zero__zero_0,axiom, % 1.17/1.22 c_Transcendental_Oarctan(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.17/1.22 % 1.17/1.22 cnf(cls_linorder__neqE__ordered__idom_0,axiom, % 1.17/1.22 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.17/1.22 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.17/1.22 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.17/1.22 | V_x = V_y ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_not__less__iff__gr__or__eq_0,axiom, % 1.17/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.17/1.23 | V_x = V_y % 1.17/1.23 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.17/1.23 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_linorder__antisym__conv3_0,axiom, % 1.17/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.17/1.23 | V_x = V_y % 1.17/1.23 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.17/1.23 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_linorder__less__linear_0,axiom, % 1.17/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.17/1.23 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.17/1.23 | V_x = V_y % 1.17/1.23 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_linorder__neqE_0,axiom, % 1.17/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.17/1.23 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.17/1.23 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.17/1.23 | V_x = V_y ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_compl__eq__compl__iff_0,axiom, % 1.17/1.23 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.17/1.23 | c_HOL_Ouminus__class_Ouminus(V_x,T_a) != c_HOL_Ouminus__class_Ouminus(V_y,T_a) % 1.17/1.23 | V_x = V_y ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_neg__equal__iff__equal_0,axiom, % 1.17/1.23 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.23 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(V_b,T_a) % 1.17/1.23 | V_a = V_b ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_real__sqrt__not__eq__zero_0,axiom, % 1.17/1.23 ( c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_estimate__by__abs_0,axiom, % 1.17/1.23 ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.17/1.23 | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) % 1.17/1.23 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_min__max_Oinf__idem_0,axiom, % 1.17/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.17/1.23 | c_Orderings_Oord__class_Omin(V_x,V_x,T_a) = V_x ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_not__exp__less__zero_0,axiom, % 1.17/1.23 ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_abs__le__zero__iff_0,axiom, % 1.17/1.23 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.17/1.23 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.23 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_norm__add__less_0,axiom, % 1.17/1.23 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.17/1.23 | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a),c_HOL_Oplus__class_Oplus(V_r,V_s,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_y,T_a),V_s,tc_RealDef_Oreal) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),V_r,tc_RealDef_Oreal) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_zero__less__norm__iff_0,axiom, % 1.17/1.23 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a),tc_RealDef_Oreal) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.23 | 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) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.23 | 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) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.23 | 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) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_neg__equal__0__iff__equal_0,axiom, % 1.17/1.23 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.23 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.23 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_sum__squares__le__zero__iff_2,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.23 | 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) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_add__nonpos__neg_0,axiom, % 1.17/1.23 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.17/1.23 | 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) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.23 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_add__neg__nonpos_0,axiom, % 1.17/1.23 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.17/1.23 | 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) % 1.17/1.23 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_neg__less__iff__less_1,axiom, % 1.17/1.23 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.17/1.23 | 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) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_neg__less__iff__less_0,axiom, % 1.17/1.23 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.17/1.23 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.17/1.23 | ~ 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) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_not__sum__squares__lt__zero_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.23 | ~ 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) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_inf__left__commute_0,axiom, % 1.17/1.23 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.17/1.23 | 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) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_inf__assoc_0,axiom, % 1.17/1.23 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.17/1.23 | 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) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_inf__sup__aci_I3_J_0,axiom, % 1.17/1.23 ( ~ class_Lattices_Olattice(T_a) % 1.17/1.23 | 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) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_inf__sup__aci_I2_J_0,axiom, % 1.17/1.23 ( ~ class_Lattices_Olattice(T_a) % 1.17/1.23 | 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) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_not__pos__poly__0_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.17/1.23 | ~ c_Polynomial_Opos__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_abs__less__iff_1,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.17/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_power__less__imp__less__base_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.23 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.17/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.23 | ~ 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) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_zero__less__mult__pos2_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.17/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.17/1.23 | ~ 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) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_zero__less__mult__pos_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.17/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.17/1.23 | ~ 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) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_mult__pos__pos_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.17/1.23 | 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) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_mult__neg__neg_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.23 | 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) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_real__mult__order_0,axiom, % 1.17/1.23 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom, % 1.17/1.23 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.17/1.23 | 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) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom, % 1.17/1.23 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.17/1.23 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.23 | ~ 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) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_even__less__0__iff_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.17/1.23 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.23 | ~ 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) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_even__less__0__iff_1,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.17/1.23 | 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) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_mult__eq__0__iff_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.17/1.23 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.23 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.23 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_no__zero__divisors_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.17/1.23 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.23 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.23 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_no__zero__divirors__neq0_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.17/1.23 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.23 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.23 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_offset__poly__eq__0__lemma_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) % 1.17/1.23 | c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_c,V_p,T_a),c_Polynomial_OpCons(V_a,V_p,T_a),tc_Polynomial_Opoly(T_a)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) % 1.17/1.23 | V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_add__nonneg__eq__0__iff_1,axiom, % 1.17/1.23 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.17/1.23 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.17/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.17/1.23 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_add__nonneg__eq__0__iff_0,axiom, % 1.17/1.23 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.17/1.23 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.17/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.17/1.23 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_double__eq__0__iff_0,axiom, % 1.17/1.23 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.17/1.23 | c_HOL_Oplus__class_Oplus(V_a,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.23 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_eq__iff__diff__eq__0_0,axiom, % 1.17/1.23 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.17/1.23 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_right__minus__eq_1,axiom, % 1.17/1.23 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.23 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_diff__0__right_0,axiom, % 1.17/1.23 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.23 | c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_diff__self_0,axiom, % 1.17/1.23 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.23 | c_HOL_Ominus__class_Ominus(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_class__ringb_Osubr0__iff_1,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.17/1.23 | ~ class_Int_Onumber__ring(T_a) % 1.17/1.23 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_abs__of__neg_0,axiom, % 1.17/1.23 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.17/1.23 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_abs__if_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oabs__if(T_a) % 1.17/1.23 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_abs__if__lattice_0,axiom, % 1.17/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.17/1.23 | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.17/1.23 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_real__abs__def_0,axiom, % 1.17/1.23 ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(V_r,tc_RealDef_Oreal) % 1.17/1.23 | ~ c_HOL_Oord__class_Oless(V_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_square__eq__iff_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.17/1.23 | c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) != c_HOL_Otimes__class_Otimes(V_b,V_b,T_a) % 1.17/1.23 | V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a) % 1.17/1.23 | V_a = V_b ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_mult__less__imp__less__right_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.17/1.23 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.17/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.23 | ~ 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) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_mult__less__imp__less__left_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.17/1.23 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.17/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.23 | ~ 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) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_mult__right__less__imp__less_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 1.17/1.23 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.17/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.23 | ~ 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) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_mult__left__less__imp__less_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 1.17/1.23 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.17/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.23 | ~ 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) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_class__ringb_Oadd__r0__iff_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.17/1.23 | ~ class_Int_Onumber__ring(T_a) % 1.17/1.23 | V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) % 1.17/1.23 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_real__add__minus__iff_0,axiom, % 1.17/1.23 ( c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_a,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.17/1.23 | V_x = V_a ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_abs__sum__triangle__ineq_0,axiom, % 1.17/1.23 c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_l,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(V_m,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_l,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(V_y,c_HOL_Ouminus__class_Ouminus(V_m,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_inf__bot__right_0,axiom, % 1.17/1.23 ( ~ class_Lattices_Obounded__lattice(T_a) % 1.17/1.23 | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Orderings_Obot__class_Obot(T_a),T_a) = c_Orderings_Obot__class_Obot(T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_inf__bot__left_0,axiom, % 1.17/1.23 ( ~ class_Lattices_Obounded__lattice(T_a) % 1.17/1.23 | c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) = c_Orderings_Obot__class_Obot(T_a) ) ). % 1.17/1.23 % 1.17/1.23 cnf(cls_sum__squares__ge__zero_0,axiom, % 1.17/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.23 | 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) ) ). % 1.17/1.24 % 1.17/1.24 cnf(cls_real__mult__self__sum__ge__zero_0,axiom, % 1.17/1.24 c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.17/1.24 % 1.17/1.24 cnf(cls_smult__add__left_0,axiom, % 1.17/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) % 1.17/1.24 | c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_p,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_a,V_p,T_a),c_Polynomial_Osmult(V_b,V_p,T_a),tc_Polynomial_Opoly(T_a)) ) ). % 1.17/1.24 % 1.17/1.24 cnf(cls_smult__add__right_0,axiom, % 1.17/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) % 1.17/1.24 | c_Polynomial_Osmult(V_a,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_a,V_p,T_a),c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a)) ) ). % 1.17/1.24 % 1.17/1.24 cnf(cls_le__add__iff2_1,axiom, % 1.17/1.24 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.17/1.24 | 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) % 1.17/1.24 | ~ 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_le__add__iff2_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.21/1.24 | 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) % 1.21/1.24 | ~ 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_le__add__iff1_1,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.21/1.24 | 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) % 1.21/1.24 | ~ 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_le__add__iff1_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.21/1.24 | 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) % 1.21/1.24 | ~ 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_eq__poly__code_I4_J_2,axiom, % 1.21/1.24 ( ~ class_HOL_Ozero(T_a) % 1.21/1.24 | ~ class_HOL_Oeq(T_a) % 1.21/1.24 | c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(V_a,V_p,T_a),c_Polynomial_OpCons(V_b,V_q,T_a),tc_Polynomial_Opoly(T_a)) % 1.21/1.24 | ~ c_HOL_Oeq__class_Oeq(V_p,V_q,tc_Polynomial_Opoly(T_a)) % 1.21/1.24 | ~ c_HOL_Oeq__class_Oeq(V_a,V_b,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_add__increasing2_0,axiom, % 1.21/1.24 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.21/1.24 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.21/1.24 | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.21/1.24 | ~ c_lessequals(V_b,V_a,T_a) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_add__increasing_0,axiom, % 1.21/1.24 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.21/1.24 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.21/1.24 | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.21/1.24 | ~ c_lessequals(V_b,V_c,T_a) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_min__max_Oinf__sup__distrib2_0,axiom, % 1.21/1.24 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_min__max_Oinf__sup__distrib1_0,axiom, % 1.21/1.24 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_norm__eq__zero_0,axiom, % 1.21/1.24 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.21/1.24 | c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.21/1.24 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_abs__minus__le__zero_0,axiom, % 1.21/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_eq__add__iff2_1,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oring(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_abs__le__mult_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Olordered__ring(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__strict__mono_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.21/1.24 | 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) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_max__less__iff__conj_2,axiom, % 1.21/1.24 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.24 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(V_x,V_z,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_norm__not__less__zero_0,axiom, % 1.21/1.24 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_abs__minus__add__cancel_0,axiom, % 1.21/1.24 c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(V_y,c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_neg__less__0__iff__less_1,axiom, % 1.21/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_neg__less__0__iff__less_0,axiom, % 1.21/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_min__less__iff__conj_2,axiom, % 1.21/1.24 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.24 | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_class__ringb_Oadd__mul__solve_1,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.24 | ~ class_Int_Onumber__ring(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_class__ringb_Onoteq__reduce_1,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.24 | ~ class_Int_Onumber__ring(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_arctan__minus_0,axiom, % 1.21/1.24 c_Transcendental_Oarctan(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Oarctan(V_x),tc_RealDef_Oreal) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_abs__triangle__ineq3_0,axiom, % 1.21/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_min__max_Oinf__left__idem_0,axiom, % 1.21/1.24 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_exp__ge__zero_0,axiom, % 1.21/1.24 c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_real__sqrt__ge__0__iff_0,axiom, % 1.21/1.24 ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_real__sqrt__ge__zero_0,axiom, % 1.21/1.24 ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x),tc_RealDef_Oreal) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_pos__add__strict_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.21/1.24 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_cnj_Oadd_0,axiom, % 1.21/1.24 c_Complex_Ocnj(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(c_Complex_Ocnj(V_x),c_Complex_Ocnj(V_y),tc_Complex_Ocomplex) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_real__sqrt__eq__iff_0,axiom, % 1.21/1.24 ( c_NthRoot_Osqrt(V_x) != c_NthRoot_Osqrt(V_y) % 1.21/1.24 | V_x = V_y ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_exp__inj__iff_0,axiom, % 1.21/1.24 ( c_Transcendental_Oexp(V_x,tc_RealDef_Oreal) != c_Transcendental_Oexp(V_y,tc_RealDef_Oreal) % 1.21/1.24 | V_x = V_y ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_eq__poly__code_I2_J_2,axiom, % 1.21/1.24 ( ~ class_HOL_Ozero(T_a) % 1.21/1.24 | ~ class_HOL_Oeq(T_a) % 1.21/1.24 | c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(V_b,V_q,T_a),tc_Polynomial_Opoly(T_a)) % 1.21/1.24 | ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,tc_Polynomial_Opoly(T_a)) % 1.21/1.24 | ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__mono1_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Omult__mono1(T_a) % 1.21/1.24 | 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) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.24 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__left__mono_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 1.21/1.24 | 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) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.24 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__right__mono_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 1.21/1.24 | 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) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.24 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__left__mono__neg_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.21/1.24 | 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) % 1.21/1.24 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.24 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__right__mono__neg_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.21/1.24 | 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) % 1.21/1.24 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.24 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.24 | ~ class_Int_Onumber__ring(T_a) % 1.21/1.24 | 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) % 1.21/1.24 | V_c = V_d % 1.21/1.24 | V_r = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_real__sum__squares__cancel_0,axiom, % 1.21/1.24 ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.21/1.24 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_real__sum__squares__cancel2_0,axiom, % 1.21/1.24 ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.21/1.24 | V_y = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_sum__squares__eq__zero__iff_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.24 | 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) % 1.21/1.24 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_sum__squares__eq__zero__iff_1,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.24 | 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) % 1.21/1.24 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_pos__poly__add_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.24 | c_Polynomial_Opos__poly(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) % 1.21/1.24 | ~ c_Polynomial_Opos__poly(V_q,T_a) % 1.21/1.24 | ~ c_Polynomial_Opos__poly(V_p,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_smult__pCons_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) % 1.21/1.24 | c_Polynomial_Osmult(V_a,c_Polynomial_OpCons(V_b,V_p,T_a),T_a) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_Polynomial_Osmult(V_a,V_p,T_a),T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__idem_0,axiom, % 1.21/1.24 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 1.21/1.24 | c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = V_x ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__strict__mono_H_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.21/1.24 | 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) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_less__eqI_1,axiom, % 1.21/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.24 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.21/1.24 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_less__eqI_0,axiom, % 1.21/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.24 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.21/1.24 | c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_class__semiring_Opwr__mul_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_power__mult__distrib_0,axiom, % 1.21/1.24 ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_min__max_Osup__inf__distrib1_0,axiom, % 1.21/1.24 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_min__max_Osup__inf__distrib2_0,axiom, % 1.21/1.24 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_split__mult__pos__le_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.21/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_split__mult__pos__le_1,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.21/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.21/1.24 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.24 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__nonpos__nonpos_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.21/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.21/1.24 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.24 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_zero__le__square_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_zero__le__mult__iff_4,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_zero__le__mult__iff_5,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.21/1.24 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.24 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__nonneg__nonneg_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.21/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_norm__mult__less_0,axiom, % 1.21/1.24 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.21/1.24 | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(V_r,V_s,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_y,T_a),V_s,tc_RealDef_Oreal) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),V_r,tc_RealDef_Oreal) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_real__0__less__add__iff_0,axiom, % 1.21/1.24 ( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_real__0__less__add__iff_1,axiom, % 1.21/1.24 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_Im_Oadd_0,axiom, % 1.21/1.24 c_Complex_OIm(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(c_Complex_OIm(V_x),c_Complex_OIm(V_y),tc_RealDef_Oreal) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_abs__triangle__ineq2_0,axiom, % 1.21/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom, % 1.21/1.24 ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_real__mult__assoc_0,axiom, % 1.21/1.24 c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_z1,V_z2,tc_RealDef_Oreal),V_z3,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_z1,c_HOL_Otimes__class_Otimes(V_z2,V_z3,tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_class__semiring_Omul__a_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__right_Oadd_0,axiom, % 1.21/1.24 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.21/1.24 | c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),c_HOL_Otimes__class_Otimes(V_xa,V_y,T_a),T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult_Oadd__right_0,axiom, % 1.21/1.24 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.21/1.24 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oplus__class_Oplus(V_b,V_b_H,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b_H,T_a),T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__left_Oadd_0,axiom, % 1.21/1.24 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.21/1.24 | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_ya,T_a),c_HOL_Otimes__class_Otimes(V_y,V_ya,T_a),T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult_Oadd__left_0,axiom, % 1.21/1.24 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.21/1.24 | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_real__add__mult__distrib_0,axiom, % 1.21/1.24 c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_z1,V_z2,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_z1,V_w,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_z2,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_class__semiring_Omul__d_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_comm__semiring__class_Odistrib_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom, % 1.21/1.24 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.24 | ~ 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom, % 1.21/1.24 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.24 | 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) % 1.21/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_abs__minus__commute_0,axiom, % 1.21/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_zero__le__mult__iff_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.24 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_zero__le__mult__iff_1,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.24 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_zero__le__mult__iff_2,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.24 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_zero__le__mult__iff_3,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.24 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_min__max_Osup__left__idem_0,axiom, % 1.21/1.24 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_neg__equal__zero_0,axiom, % 1.21/1.24 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.21/1.24 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != V_a % 1.21/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_synthetic__div__unique__lemma_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) % 1.21/1.24 | c_Polynomial_Osmult(V_c,V_p,T_a) != c_Polynomial_OpCons(V_a,V_p,T_a) % 1.21/1.24 | V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_sum__squares__gt__zero__iff_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.24 | ~ 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_eq__poly__def_1,axiom, % 1.21/1.24 ( ~ class_HOL_Ozero(T_a) % 1.21/1.24 | ~ class_HOL_Oeq(T_a) % 1.21/1.24 | c_HOL_Oeq__class_Oeq(V_x,V_x,tc_Polynomial_Opoly(T_a)) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_eq__class_Oeq__refl_0,axiom, % 1.21/1.24 ( ~ class_HOL_Oeq(T_a) % 1.21/1.24 | c_HOL_Oeq__class_Oeq(V_x,V_x,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult_Ominus__left_0,axiom, % 1.21/1.24 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.21/1.24 | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__left_Ominus_0,axiom, % 1.21/1.24 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.21/1.24 | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult_Ominus__right_0,axiom, % 1.21/1.24 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.21/1.24 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__right_Ominus_0,axiom, % 1.21/1.24 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.21/1.24 | c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_square__eq__iff_1,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_minus__mult__minus_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oring(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__mono_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 1.21/1.24 | 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) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.24 | ~ c_lessequals(V_c,V_d,T_a) % 1.21/1.24 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__mono_H_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 1.21/1.24 | 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) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.24 | ~ c_lessequals(V_c,V_d,T_a) % 1.21/1.24 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_max__add__distrib__left_0,axiom, % 1.21/1.24 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.21/1.24 | 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__less__cancel__left__disj_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.24 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.24 | ~ 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__less__cancel__left__disj_3,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.24 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.21/1.24 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.24 | ~ 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__less__cancel__right__disj_0,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.24 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.24 | ~ 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_mult__less__cancel__right__disj_3,axiom, % 1.21/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.24 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.21/1.24 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.24 | ~ 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) ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_min__max_Osup__inf__absorb_0,axiom, % 1.21/1.24 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.24 | c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) = V_x ) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_real__sqrt__mult__self__sum__ge__zero_0,axiom, % 1.21/1.24 c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ). % 1.21/1.24 % 1.21/1.24 cnf(cls_real__sqrt__zero_0,axiom, % 1.21/1.25 c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_min__max_Odistrib__inf__le_0,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_min__max_Osup__commute_0,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = c_Orderings_Oord__class_Omax(V_y,V_x,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_group__add__class_Odiff__0_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__sum__squares__cancel__a_0,axiom, % 1.21/1.25 ( c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.25 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__sum__squares__cancel__a_1,axiom, % 1.21/1.25 ( c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.25 | V_y = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_order__root_1,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.25 | c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_poly__0_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) % 1.21/1.25 | c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__diff__def_0,axiom, % 1.21/1.25 c_HOL_Ominus__class_Ominus(V_r,V_s,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(V_r,c_HOL_Ouminus__class_Ouminus(V_s,tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_diff__def_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_class__ring_Osub__add_0,axiom, % 1.21/1.25 ( ~ class_Int_Onumber__ring(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_diff__minus_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_ab__diff__minus_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_min__add__distrib__left_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_eq__poly__code_I1_J_0,axiom, % 1.21/1.25 ( ~ class_HOL_Ozero(T_a) % 1.21/1.25 | ~ class_HOL_Oeq(T_a) % 1.21/1.25 | c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_abs__le__interval__iff_2,axiom, % 1.21/1.25 ( c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),V_r,tc_RealDef_Oreal) % 1.21/1.25 | ~ c_lessequals(V_x,V_r,tc_RealDef_Oreal) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_r,tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_abs__mult__less_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_b,T_a),V_d,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_c,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_diff__add__cancel_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.25 | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_pcompose__0_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) % 1.21/1.25 | c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_cnj_Ozero_0,axiom, % 1.21/1.25 c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__sqrt__lt__0__iff_0,axiom, % 1.21/1.25 ( c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__sqrt__lt__0__iff_1,axiom, % 1.21/1.25 ( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_add__nonneg__eq__0__iff_2,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_class__semiring_Omul__c_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.25 | c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_double__eq__0__iff_1,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__mult__commute_0,axiom, % 1.21/1.25 c_HOL_Otimes__class_Otimes(V_z,V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,V_z,tc_RealDef_Oreal) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.25 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_xt1_I10_J_0,axiom, % 1.21/1.25 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_order__less__trans_0,axiom, % 1.21/1.25 ( ~ class_Orderings_Opreorder(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_abs__eq__0_1,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.25 | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_not__exp__le__zero_0,axiom, % 1.21/1.25 ~ c_lessequals(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_comm__monoid__add_Omult__assoc_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_class__semiring_Oadd__a_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_add__cancel__21_1,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_neg__0__equal__iff__equal_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.25 | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.21/1.25 | c_HOL_Ozero__class_Ozero(T_a) = V_a ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_Re_Ozero_0,axiom, % 1.21/1.25 c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_abs__triangle__ineq_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_norm__triangle__ineq3_0,axiom, % 1.21/1.25 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(V_a,T_a),c_RealVector_Onorm__class_Onorm(V_b,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_add__strict__increasing2_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.21/1.25 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_power__mono_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.25 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_eq__eqI_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.21/1.25 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.21/1.25 | V_x_H = V_y_H ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_eq__eqI_1,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.21/1.25 | c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) % 1.21/1.25 | V_xa = V_y ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_min__max_Oinf__sup__absorb_0,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) = V_x ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_power__less__zero__eq_1,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_diff__eq_0,axiom, % 1.21/1.25 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_power__le__zero__eq_3,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.25 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.25 | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | ~ c_lessequals(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__right__le__imp__le_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.21/1.25 | c_lessequals(V_a,V_b,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.25 | ~ 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__left__le__imp__le_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.21/1.25 | c_lessequals(V_a,V_b,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.25 | ~ 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__le__cancel__left__pos_1,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | ~ c_lessequals(V_a,V_b,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__le__cancel__left__pos_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.25 | c_lessequals(V_a,V_b,T_a) % 1.21/1.25 | ~ 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) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__le__cancel__left__neg_1,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | ~ c_lessequals(V_b,V_a,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__le__cancel__left__neg_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.25 | c_lessequals(V_b,V_a,T_a) % 1.21/1.25 | ~ 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) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__mult__le__cancel__iff2_1,axiom, % 1.21/1.25 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_z,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.25 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__mult__le__cancel__iff2_0,axiom, % 1.21/1.25 ( c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.21/1.25 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_z,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__mult__le__cancel__iff1_1,axiom, % 1.21/1.25 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.25 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__mult__le__cancel__iff1_0,axiom, % 1.21/1.25 ( c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.21/1.25 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult_Oprod__diff__prod_0,axiom, % 1.21/1.25 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.21/1.25 | c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_max__less__iff__conj_1,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_max__less__iff__conj_0,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_less__max__iff__disj_2,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_less__max__iff__disj_1,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_min__max_Oless__supI2_0,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_x,V_b,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_min__max_Oless__supI1_0,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_x,V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_inf__commute_0,axiom, % 1.21/1.25 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.21/1.25 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_inf__sup__aci_I1_J_0,axiom, % 1.21/1.25 ( ~ class_Lattices_Olattice(T_a) % 1.21/1.25 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_min__max_Oinf__commute_0,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = c_Orderings_Oord__class_Omin(V_y,V_x,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_combine__common__factor_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Osemiring(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_eq__neg__iff__add__eq__0_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_ab__left__minus_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_right__minus_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_left__minus_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__add__eq__0__iff_1,axiom, % 1.21/1.25 c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_add__neg__neg_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_eq__iff__diff__eq__0_1,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.21/1.25 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.25 | V_a = V_b ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_right__minus__eq_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.25 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.25 | V_a = V_b ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_class__ringb_Osubr0__iff_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.25 | ~ class_Int_Onumber__ring(T_a) % 1.21/1.25 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.25 | V_x = V_y ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_sum__squares__le__zero__iff_1,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.25 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.25 | ~ 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_sum__squares__le__zero__iff_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.25 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.25 | ~ 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__right_Odiff_0,axiom, % 1.21/1.25 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.21/1.25 | c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),c_HOL_Otimes__class_Otimes(V_xa,V_y,T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult_Odiff__right_0,axiom, % 1.21/1.25 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.21/1.25 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ominus__class_Ominus(V_b,V_b_H,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b_H,T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult_Odiff__left_0,axiom, % 1.21/1.25 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.21/1.25 | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__left_Odiff_0,axiom, % 1.21/1.25 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.21/1.25 | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_ya,T_a),c_HOL_Otimes__class_Otimes(V_y,V_ya,T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_Deriv_Oadd__diff__add_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.21/1.25 | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ominus__class_Ominus(V_c,V_d,T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_min__less__iff__disj_2,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_min__less__iff__disj_1,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_x,V_z,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_min__less__iff__conj_1,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_min__less__iff__conj_0,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_min__max_Oless__infI2_0,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_b,V_x,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_min__max_Oless__infI1_0,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_a,V_x,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__sqrt__mult_0,axiom, % 1.21/1.25 c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__sqrt__le__0__iff_0,axiom, % 1.21/1.25 ( c_lessequals(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.25 | ~ c_lessequals(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__sqrt__le__0__iff_1,axiom, % 1.21/1.25 ( c_lessequals(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.25 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_power__abs_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_abs__diff__less__iff_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_r,T_a),V_x,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_abs__of__pos_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.25 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_sum__squares__gt__zero__iff_2,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_sum__squares__gt__zero__iff_1,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__sum__square__gt__zero2_0,axiom, % 1.21/1.25 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.25 | V_y = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__sum__square__gt__zero_0,axiom, % 1.21/1.25 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.25 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_poly__smult_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) % 1.21/1.25 | c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__minus__mult__self__le_0,axiom, % 1.21/1.25 c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_u,V_u,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_pos__poly__pCons_3,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.25 | c_Polynomial_Opos__poly(c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_le__real__sqrt__sumsq_0,axiom, % 1.21/1.25 c_lessequals(V_x,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_add__cancel__end_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.21/1.25 | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != V_y % 1.21/1.25 | V_x = c_HOL_Ouminus__class_Ouminus(V_z,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_exp__add_0,axiom, % 1.21/1.25 ( ~ class_SEQ_Obanach(T_a) % 1.21/1.25 | ~ class_RealVector_Oreal__normed__field(T_a) % 1.21/1.25 | c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(V_x,T_a),c_Transcendental_Oexp(V_y,T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__sqrt__less__iff_0,axiom, % 1.21/1.25 ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__sqrt__less__iff_1,axiom, % 1.21/1.25 ( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_exp__not__eq__zero_0,axiom, % 1.21/1.25 ( ~ class_SEQ_Obanach(T_a) % 1.21/1.25 | ~ class_RealVector_Oreal__normed__field(T_a) % 1.21/1.25 | c_Transcendental_Oexp(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_abs__of__nonpos_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.25 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.21/1.25 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__strict__left__mono__comm_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_abs__leI_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.21/1.25 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_abs__le__iff_2,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.21/1.25 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_abs__minus__cancel_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__less__sum__gt__zero_0,axiom, % 1.21/1.25 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_S,c_HOL_Ouminus__class_Ouminus(V_W,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_W,V_S,tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__sum__gt__zero__less_0,axiom, % 1.21/1.25 ( c_HOL_Oord__class_Oless(V_W,V_S,tc_RealDef_Oreal) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_S,c_HOL_Ouminus__class_Ouminus(V_W,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_class__ringb_Oadd__cancel_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.25 | ~ class_Int_Onumber__ring(T_a) % 1.21/1.25 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) % 1.21/1.25 | V_y = V_z ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_add__imp__eq_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a) % 1.21/1.25 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) % 1.21/1.25 | V_b = V_c ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_add__left__cancel_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 1.21/1.25 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) % 1.21/1.25 | V_b = V_c ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_add__right__cancel_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 1.21/1.25 | c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) != c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) % 1.21/1.25 | V_b = V_c ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_poly__bound__exists_0,axiom, % 1.21/1.25 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(V_p,V_r),tc_RealDef_Oreal) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_not__square__less__zero_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.25 | ~ 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__le__0__iff_4,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__le__0__iff_5,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.25 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_split__mult__neg__le_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_split__mult__neg__le_1,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.25 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__nonneg__nonpos_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__nonpos__nonneg_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.25 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__nonneg__nonpos2_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_abs__le__zero__iff_1,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_add__nonneg__pos_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_add__pos__nonneg_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_exp__less__mono_0,axiom, % 1.21/1.25 ( c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_Transcendental_Oexp(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_exp__less__cancel_0,axiom, % 1.21/1.25 ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_Transcendental_Oexp(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_pCons__0__0_0,axiom, % 1.21/1.25 ( ~ class_HOL_Ozero(T_a) % 1.21/1.25 | c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__sqrt__gt__0__iff_1,axiom, % 1.21/1.25 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__sqrt__gt__0__iff_0,axiom, % 1.21/1.25 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__sqrt__gt__zero_0,axiom, % 1.21/1.25 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x),tc_RealDef_Oreal) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_min__max_Oinf__assoc_0,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_min__max_Oinf__left__commute_0,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_add__inf__distrib__left_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Olordered__ab__group__add__meet(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_add__inf__distrib__right_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Olordered__ab__group__add__meet(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_neg__0__le__iff__le_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.25 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_neg__0__le__iff__le_1,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.21/1.25 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_max__diff__distrib__left_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_smult__eq__0__iff_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.25 | c_Polynomial_Osmult(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) % 1.21/1.25 | V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) % 1.21/1.25 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__exp__exp_0,axiom, % 1.21/1.25 ( ~ class_SEQ_Obanach(T_a) % 1.21/1.25 | ~ class_RealVector_Oreal__normed__field(T_a) % 1.21/1.25 | c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(V_x,T_a),c_Transcendental_Oexp(V_y,T_a),T_a) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_add__cancel__21_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) = V_u ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__sqrt__eq__zero__cancel_0,axiom, % 1.21/1.25 ( c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.21/1.25 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_zero__le__power__abs_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_add__nonneg__nonneg_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_pos__poly__pCons_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.25 | V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) % 1.21/1.25 | c_Polynomial_Opos__poly(V_p,T_a) % 1.21/1.25 | ~ c_Polynomial_Opos__poly(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_rabs__ratiotest__lemma_0,axiom, % 1.21/1.25 ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.21/1.25 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_c,c_HOL_Oabs__class_Oabs(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.25 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_inf__0__imp__0_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_pos__poly__pCons_1,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.25 | c_Polynomial_Opos__poly(V_p,T_a) % 1.21/1.25 | ~ c_Polynomial_Opos__poly(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_abs__diff__triangle__ineq_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__sqrt__eq__0__iff_0,axiom, % 1.21/1.25 ( c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.21/1.25 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_add__strict__increasing_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.21/1.25 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.21/1.25 | ~ c_lessequals(V_b,V_c,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_arctan__monotone_0,axiom, % 1.21/1.25 ( c_HOL_Oord__class_Oless(c_Transcendental_Oarctan(V_x),c_Transcendental_Oarctan(V_y),tc_RealDef_Oreal) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_min__diff__distrib__left_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_compl__inf__bot_0,axiom, % 1.21/1.25 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_inf__compl__bot_0,axiom, % 1.21/1.25 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_zero__le__power__iff_1,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_zero__le__power_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_le__minus__self__iff_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.25 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_le__minus__self__iff_1,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.25 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.21/1.25 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_minus__le__self__iff_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_minus__le__self__iff_1,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_less__eq__neg__nonpos_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.21/1.25 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_less__eq__neg__nonpos_1,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.21/1.25 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.21/1.25 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_neg__less__eq__nonneg_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_neg__less__eq__nonneg_1,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) % 1.21/1.25 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_eq__add__iff1_1,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oring(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__add__less__0__iff_0,axiom, % 1.21/1.25 ( c_HOL_Oord__class_Oless(V_y,c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__add__less__0__iff_1,axiom, % 1.21/1.25 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_eq__poly__code_I4_J_0,axiom, % 1.21/1.25 ( ~ class_HOL_Ozero(T_a) % 1.21/1.25 | ~ class_HOL_Oeq(T_a) % 1.21/1.25 | c_HOL_Oeq__class_Oeq(V_a,V_b,T_a) % 1.21/1.25 | ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(V_a,V_p,T_a),c_Polynomial_OpCons(V_b,V_q,T_a),tc_Polynomial_Opoly(T_a)) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_abs__idempotent_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_eq__add__iff1_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oring(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | 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 ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_eq__add__iff2_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oring(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_zero__less__abs__iff_1,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) % 1.21/1.25 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_poly__add_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) % 1.21/1.25 | c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_complex__cnj__cnj_0,axiom, % 1.21/1.25 c_Complex_Ocnj(c_Complex_Ocnj(V_z)) = V_z ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__sqrt__power_0,axiom, % 1.21/1.25 c_NthRoot_Osqrt(c_Power_Opower__class_Opower(V_x,V_k,tc_RealDef_Oreal)) = c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),V_k,tc_RealDef_Oreal) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__sqrt__minus_0,axiom, % 1.21/1.25 c_NthRoot_Osqrt(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_NthRoot_Osqrt(V_x),tc_RealDef_Oreal) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_not__real__square__gt__zero_1,axiom, % 1.21/1.25 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.25 | c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_class__semiring_Oadd__c_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.25 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_y,V_x,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_comm__monoid__add_Omult__commute_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.21/1.25 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_norm__zero_0,axiom, % 1.21/1.25 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.21/1.25 | c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_pCons__eq__0__iff_0,axiom, % 1.21/1.25 ( ~ class_HOL_Ozero(T_a) % 1.21/1.25 | c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) % 1.21/1.25 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_norm__mult_0,axiom, % 1.21/1.25 ( ~ class_RealVector_Oreal__normed__div__algebra(T_a) % 1.21/1.25 | c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_RealVector_Onorm__class_Onorm(V_y,T_a),tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_power__commutes_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.21/1.25 | 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__mult__left__cancel_0,axiom, % 1.21/1.25 ( c_HOL_Otimes__class_Otimes(V_c,V_a,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_c,V_b,tc_RealDef_Oreal) % 1.21/1.25 | V_c = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.21/1.25 | V_a = V_b ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__mult__right__cancel_0,axiom, % 1.21/1.25 ( c_HOL_Otimes__class_Otimes(V_a,V_c,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_b,V_c,tc_RealDef_Oreal) % 1.21/1.25 | V_c = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.21/1.25 | V_a = V_b ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_abs__ge__minus__self_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.25 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_add__pCons_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.21/1.25 | c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(V_a,V_p,T_a),c_Polynomial_OpCons(V_b,V_q,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_less__add__iff1_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | ~ 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_less__add__iff1_1,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | ~ 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_less__add__iff2_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | ~ 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_less__add__iff2_1,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | ~ 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) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_zero__less__power_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_less__max__iff__disj_0,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_real__add__eq__0__iff_0,axiom, % 1.21/1.25 ( c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.21/1.25 | V_y = c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_minus__unique_0,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.25 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.25 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_eq__neg__iff__add__eq__0_1,axiom, % 1.21/1.25 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.25 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.25 | V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_abs__less__iff_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_min__less__iff__disj_0,axiom, % 1.21/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.21/1.25 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__less__cancel__right__disj_5,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__less__cancel__right__disj_4,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__strict__right__mono_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__strict__right__mono__neg_0,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__less__cancel__left__disj_5,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__less__cancel__left__disj_4,axiom, % 1.21/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.25 | 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) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.21/1.25 % 1.21/1.25 cnf(cls_mult__strict__left__mono_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.21/1.26 | 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) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_mult__strict__left__mono__neg_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.26 | 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) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_mult__less__cancel__left__pos_1,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.26 | 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) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_mult__less__cancel__left__pos_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.26 | ~ 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) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_mult__less__cancel__left__neg_1,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.26 | 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) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_mult__less__cancel__left__neg_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.21/1.26 | ~ 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) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__mult__less__mono2_0,axiom, % 1.21/1.26 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_z,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__mult__less__iff1_1,axiom, % 1.21/1.26 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__mult__less__iff1_0,axiom, % 1.21/1.26 ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Osup__left__commute_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Osup__assoc_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_diff__minus__eq__add_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.26 | 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_smult__smult_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) % 1.21/1.26 | c_Polynomial_Osmult(V_a,c_Polynomial_Osmult(V_b,V_p,T_a),T_a) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_p,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__0__le__add__iff_0,axiom, % 1.21/1.26 ( c_lessequals(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__0__le__add__iff_1,axiom, % 1.21/1.26 ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_exp__gt__zero_0,axiom, % 1.21/1.26 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__poly__code_I1_J_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.21/1.26 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,tc_Polynomial_Opoly(T_a)) = V_q ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__poly__code_I2_J_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.21/1.26 | c_HOL_Oplus__class_Oplus(V_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = V_p ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_monoid__add__class_Oadd__0__right_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 1.21/1.26 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__0__left_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 1.21/1.26 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_comm__monoid__add_Omult__1__right_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.21/1.26 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_class__ringb_Oadd__r0__iff_1,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.26 | ~ class_Int_Onumber__ring(T_a) % 1.21/1.26 | V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_class__semiring_Oadd__0_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.26 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = V_x ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_comm__monoid__add_Omult__1_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.21/1.26 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.26 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.26 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_synthetic__div__correct_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) % 1.21/1.26 | c_HOL_Oplus__class_Oplus(V_p,c_Polynomial_Osmult(V_c,c_Polynomial_Osynthetic__div(V_p,V_c,T_a),T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(c_Polynomial_Opoly(V_p,V_c,T_a),c_Polynomial_Osynthetic__div(V_p,V_c,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_id__apply_0,axiom, % 1.21/1.26 c_Fun_Oid(V_x,T_a) = V_x ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__diff__cancel_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.26 | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_abs__diff__less__iff_2,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_a,V_r,T_a),T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_r,T_a),V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_minus__equation__iff_1,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.26 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_equation__minus__iff_1,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.26 | V_a = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_equation__minus__iff_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.26 | V_b = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_double__compl_0,axiom, % 1.21/1.26 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.21/1.26 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = V_x ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_minus__minus_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.26 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_minus__diff__eq_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.21/1.26 | 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__less__le__mono_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.21/1.26 | 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) % 1.21/1.26 | ~ c_lessequals(V_c,V_d,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__le__less__mono_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.21/1.26 | 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) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.21/1.26 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_minus__less__iff_1,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_minus__less__iff_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_less__minus__iff_1,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_less__minus__iff_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_xt1_I7_J_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.21/1.26 | ~ c_lessequals(V_z,V_y,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_xt1_I8_J_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.21/1.26 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__add__right__mono_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.26 | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_c,V_d,T_a) % 1.21/1.26 | ~ c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_order__less__le__trans_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Opreorder(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.21/1.26 | ~ c_lessequals(V_y,V_z,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_order__le__less__trans_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Opreorder(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_order__less__imp__le_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Opreorder(T_a) % 1.21/1.26 | c_lessequals(V_x,V_y,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_order__le__less_1,axiom, % 1.21/1.26 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.26 | c_lessequals(V_x,V_y,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_less__le__not__le_2,axiom, % 1.21/1.26 ( ~ class_Orderings_Opreorder(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.21/1.26 | c_lessequals(V_y,V_x,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__sup__iff_1,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_y,V_z,T_a) % 1.21/1.26 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__sup__iff_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_x,V_z,T_a) % 1.21/1.26 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__max__iff__disj_2,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_z,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__max__iff__disj_1,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_z,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__supI2_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__supI1_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_a,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__supE_1,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_b,V_x,T_a) % 1.21/1.26 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__supE_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_a,V_x,T_a) % 1.21/1.26 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__le__iff__disj_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_y,V_z,T_a) % 1.21/1.26 | c_lessequals(V_x,V_z,T_a) % 1.21/1.26 | ~ c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_abs__ge__self_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.26 | c_lessequals(V_a,c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__inf__iff_1,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_x,V_z,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__inf__iff_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_x,V_y,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__le__iff__disj_2,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 1.21/1.26 | ~ c_lessequals(V_y,V_z,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__le__iff__disj_1,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_z,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__infI2_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 1.21/1.26 | ~ c_lessequals(V_b,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__infI1_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 1.21/1.26 | ~ c_lessequals(V_a,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__infE_1,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_x,V_b,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__infE_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_x,V_a,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__max__iff__disj_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_z,V_y,T_a) % 1.21/1.26 | c_lessequals(V_z,V_x,T_a) % 1.21/1.26 | ~ c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__mono_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 1.21/1.26 | 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) % 1.21/1.26 | ~ c_lessequals(V_c,V_d,T_a) % 1.21/1.26 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Osup__absorb1_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = V_x % 1.21/1.26 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__iff__sup_1,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) != V_y % 1.21/1.26 | c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__iff__sup_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = V_y % 1.21/1.26 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Oinf__absorb2_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = V_y % 1.21/1.26 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__iff__inf_1,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) != V_x % 1.21/1.26 | c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__iff__inf_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = V_x % 1.21/1.26 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__inf__iff_1,axiom, % 1.21/1.26 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.21/1.26 | c_lessequals(V_x,V_z,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__inf__iff_0,axiom, % 1.21/1.26 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.21/1.26 | c_lessequals(V_x,V_y,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__infI2_0,axiom, % 1.21/1.26 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.21/1.26 | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a) % 1.21/1.26 | ~ c_lessequals(V_b,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__infI1_0,axiom, % 1.21/1.26 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.21/1.26 | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a) % 1.21/1.26 | ~ c_lessequals(V_a,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__infE_1,axiom, % 1.21/1.26 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.21/1.26 | c_lessequals(V_x,V_b,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__infE_0,axiom, % 1.21/1.26 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.21/1.26 | c_lessequals(V_x,V_a,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_xt1_I11_J_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.21/1.26 | V_a = V_b % 1.21/1.26 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_xt1_I12_J_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.21/1.26 | ~ c_lessequals(V_b,V_a,T_a) % 1.21/1.26 | V_a = V_b ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_linorder__antisym__conv2_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | V_x = V_y % 1.21/1.26 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_linorder__antisym__conv1_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | V_x = V_y % 1.21/1.26 | ~ c_lessequals(V_x,V_y,T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_order__neq__le__trans_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.26 | ~ c_lessequals(V_a,V_b,T_a) % 1.21/1.26 | V_a = V_b ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_order__le__neq__trans_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.26 | V_a = V_b % 1.21/1.26 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_order__le__less_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.26 | V_x = V_y % 1.21/1.26 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_order__less__le_2,axiom, % 1.21/1.26 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.21/1.26 | V_x = V_y % 1.21/1.26 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__eqI_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.26 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.21/1.26 | c_lessequals(V_y_H,V_x_H,T_a) % 1.21/1.26 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__eqI_1,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.26 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.21/1.26 | c_lessequals(V_y,V_x,T_a) % 1.21/1.26 | ~ c_lessequals(V_y_H,V_x_H,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_inf__greatest_0,axiom, % 1.21/1.26 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.21/1.26 | c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_z,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__inf__iff_2,axiom, % 1.21/1.26 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.21/1.26 | c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_z,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_class__ringb_Onoteq__reduce_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.26 | ~ class_Int_Onumber__ring(T_a) % 1.21/1.26 | 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) % 1.21/1.26 | V_c = V_d % 1.21/1.26 | V_a = V_b ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_class__ringb_Oadd__mul__solve_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.26 | ~ class_Int_Onumber__ring(T_a) % 1.21/1.26 | 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) % 1.21/1.26 | V_y = V_z % 1.21/1.26 | V_w = V_x ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_abs__exp__cancel_0,axiom, % 1.21/1.26 c_HOL_Oabs__class_Oabs(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Oexp(V_x,tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_abs__mult__self_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.26 | 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_Im_Ozero_0,axiom, % 1.21/1.26 c_Complex_OIm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.26 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.26 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_mult__left_Ozero_0,axiom, % 1.21/1.26 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.21/1.26 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_mult_Ozero__left_0,axiom, % 1.21/1.26 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.21/1.26 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_mult_Ozero__right_0,axiom, % 1.21/1.26 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.21/1.26 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_mult__right_Ozero_0,axiom, % 1.21/1.26 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.21/1.26 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_class__semiring_Omul__0_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.26 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_mult__zero__left_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 1.21/1.26 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_mult__zero__right_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 1.21/1.26 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_mult__eq__0__iff_1,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.21/1.26 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_mult__eq__0__iff_2,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.21/1.26 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_abs__power__minus_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.26 | 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_eq__poly__code_I3_J_0,axiom, % 1.21/1.26 ( ~ class_HOL_Ozero(T_a) % 1.21/1.26 | ~ class_HOL_Oeq(T_a) % 1.21/1.26 | c_HOL_Oeq__class_Oeq(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.26 | ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(V_a,V_p,T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_eq__poly__code_I3_J_1,axiom, % 1.21/1.26 ( ~ class_HOL_Ozero(T_a) % 1.21/1.26 | ~ class_HOL_Oeq(T_a) % 1.21/1.26 | c_HOL_Oeq__class_Oeq(V_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) % 1.21/1.26 | ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(V_a,V_p,T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_abs__mult__pos_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.26 | 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) % 1.21/1.26 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_linorder__neq__iff_1,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_order__less__le_1,axiom, % 1.21/1.26 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__less__def_1,axiom, % 1.21/1.26 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_order__less__irrefl_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Opreorder(T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__pos__pos_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.21/1.26 | 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) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_eq__poly__code_I3_J_2,axiom, % 1.21/1.26 ( ~ class_HOL_Ozero(T_a) % 1.21/1.26 | ~ class_HOL_Oeq(T_a) % 1.21/1.26 | c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(V_a,V_p,T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) % 1.21/1.26 | ~ c_HOL_Oeq__class_Oeq(V_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) % 1.21/1.26 | ~ c_HOL_Oeq__class_Oeq(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__le__eq__diff_1,axiom, % 1.21/1.26 ( c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__le__eq__diff_0,axiom, % 1.21/1.26 ( c_lessequals(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__iff__diff__le__0_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.26 | c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__iff__diff__le__0_1,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.26 | c_lessequals(V_a,V_b,T_a) % 1.21/1.26 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__strict__mono_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.21/1.26 | 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) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__cancel__end_1,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.21/1.26 | 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 ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_minus__add__cancel_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.26 | 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 ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_complex__equality_0,axiom, % 1.21/1.26 ( c_Complex_OIm(V_x) != c_Complex_OIm(V_y) % 1.21/1.26 | c_Complex_ORe(V_x) != c_Complex_ORe(V_y) % 1.21/1.26 | V_x = V_y ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_eq__poly__def_0,axiom, % 1.21/1.26 ( ~ class_HOL_Ozero(T_a) % 1.21/1.26 | ~ class_HOL_Oeq(T_a) % 1.21/1.26 | V_p = V_q % 1.21/1.26 | ~ c_HOL_Oeq__class_Oeq(V_p,V_q,tc_Polynomial_Opoly(T_a)) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_eq__equals_0,axiom, % 1.21/1.26 ( ~ class_HOL_Oeq(T_a) % 1.21/1.26 | V_x = V_y % 1.21/1.26 | ~ c_HOL_Oeq__class_Oeq(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_less__iff__diff__less__0_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.26 | 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) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_less__iff__diff__less__0_1,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.26 | ~ 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_abs__not__less__zero_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_complex__Re__cnj_0,axiom, % 1.21/1.26 c_Complex_ORe(c_Complex_Ocnj(V_x)) = c_Complex_ORe(V_x) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_neg__0__equal__iff__equal_1,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.26 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_norm__diff__triangle__ineq_0,axiom, % 1.21/1.26 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.21/1.26 | c_lessequals(c_RealVector_Onorm__class_Onorm(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_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_a,V_c,T_a),T_a),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_b,V_d,T_a),T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_mult__le__less__imp__less_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.21/1.26 | 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) % 1.21/1.26 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.21/1.26 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_mult__less__le__imp__less_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.21/1.26 | 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) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.26 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.26 | ~ c_lessequals(V_c,V_d,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_complex__cnj__zero__iff_0,axiom, % 1.21/1.26 ( c_Complex_Ocnj(V_z) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) % 1.21/1.26 | V_z = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_complex__cnj__cancel__iff_0,axiom, % 1.21/1.26 ( c_Complex_Ocnj(V_x) != c_Complex_Ocnj(V_y) % 1.21/1.26 | V_x = V_y ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_synthetic__div__0_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) % 1.21/1.26 | c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_minus__mult__commute_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oring(T_a) % 1.21/1.26 | 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_abs__triangle__ineq4_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.26 | 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_minus__zero_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.26 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_neg__equal__zero_1,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.21/1.26 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_inf__sup__aci_I4_J_0,axiom, % 1.21/1.26 ( ~ class_Lattices_Olattice(T_a) % 1.21/1.26 | 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_inf__left__idem_0,axiom, % 1.21/1.26 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.21/1.26 | 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_synthetic__div__unique_1,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) % 1.21/1.26 | c_HOL_Oplus__class_Oplus(V_p,c_Polynomial_Osmult(V_c,V_q,T_a),tc_Polynomial_Opoly(T_a)) != c_Polynomial_OpCons(V_r,V_q,T_a) % 1.21/1.26 | V_q = c_Polynomial_Osynthetic__div(V_p,V_c,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_smult__eq__0__iff_2,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.26 | c_Polynomial_Osmult(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_smult__eq__0__iff_1,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.26 | c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(T_a),V_p,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_smult__0__right_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) % 1.21/1.26 | c_Polynomial_Osmult(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_smult__0__left_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) % 1.21/1.26 | c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(T_a),V_p,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.26 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.26 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.26 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__sqrt__abs2_0,axiom, % 1.21/1.26 c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal)) = c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__abs__def_1,axiom, % 1.21/1.26 ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r % 1.21/1.26 | c_HOL_Oord__class_Oless(V_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_abs__if__lattice_1,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.21/1.26 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.21/1.26 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_abs__if_1,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oabs__if(T_a) % 1.21/1.26 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.21/1.26 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_Lim_Ominus__diff__minus_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.21/1.26 | c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_abs__add__abs_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.26 | 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_abs__eq__0_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.26 | c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.26 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_inf__idem_0,axiom, % 1.21/1.26 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.21/1.26 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_x,T_a) = V_x ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_zero__less__abs__iff_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.26 | ~ 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_Re_Oadd_0,axiom, % 1.21/1.26 c_Complex_ORe(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(c_Complex_ORe(V_x),c_Complex_ORe(V_y),tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__less__cancel__left_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.26 | ~ 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__less__cancel__left_1,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.21/1.26 | 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) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__strict__left__mono_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.21/1.26 | 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) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__less__cancel__right_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.26 | ~ 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__less__cancel__right_1,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.21/1.26 | 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) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__strict__right__mono_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.21/1.26 | 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) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__nonpos__nonpos_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.21/1.26 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_norm__power_0,axiom, % 1.21/1.26 ( ~ class_RealVector_Oreal__normed__div__algebra(T_a) % 1.21/1.26 | c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(V_x,T_a),V_n,tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_norm__ratiotest__lemma_0,axiom, % 1.21/1.26 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.21/1.26 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.26 | ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Otimes__class_Otimes(V_c,c_RealVector_Onorm__class_Onorm(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__two__squares__add__zero__iff_2,axiom, % 1.21/1.26 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_sum__squares__eq__zero__iff_2,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.26 | 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_mult__less__cancel__left__disj_1,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.26 | ~ 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_mult__less__cancel__left__disj_2,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.26 | ~ 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_mult__less__cancel__right__disj_1,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.26 | ~ 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_mult__less__cancel__right__disj_2,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.26 | ~ 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_abs__diff__less__iff_1,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_a,V_r,T_a),T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_not__real__square__gt__zero_0,axiom, % 1.21/1.26 ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.21/1.26 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Odistrib__sup__le_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_neg__0__less__iff__less_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_neg__0__less__iff__less_1,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_complex__Im__cnj_0,axiom, % 1.21/1.26 c_Complex_OIm(c_Complex_Ocnj(V_x)) = c_HOL_Ouminus__class_Ouminus(c_Complex_OIm(V_x),tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_less__minus__self__iff_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_less__minus__self__iff_1,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_abs__ge__zero_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.26 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_minus__add_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.26 | 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_minus__add__distrib_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.21/1.26 | 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) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_order__less__asym_H_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Opreorder(T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_order__less__asym_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Opreorder(T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_not__less__iff__gr__or__eq_1,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_xt1_I9_J_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__infI_0,axiom, % 1.21/1.26 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.21/1.26 | c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_b,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_a,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_inf__le2_0,axiom, % 1.21/1.26 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.21/1.26 | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_inf__le1_0,axiom, % 1.21/1.26 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.21/1.26 | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_inf__sup__ord_I2_J_0,axiom, % 1.21/1.26 ( ~ class_Lattices_Olattice(T_a) % 1.21/1.26 | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_inf__sup__ord_I1_J_0,axiom, % 1.21/1.26 ( ~ class_Lattices_Olattice(T_a) % 1.21/1.26 | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__le__cancel__right_1,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.21/1.26 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__le__cancel__right_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.21/1.26 | c_lessequals(V_a,V_b,T_a) % 1.21/1.26 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__le__cancel__left_1,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.21/1.26 | c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__le__cancel__left_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.21/1.26 | c_lessequals(V_a,V_b,T_a) % 1.21/1.26 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__right__mono_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 1.21/1.26 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_add__left__mono_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 1.21/1.26 | c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_bot__least_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Obot(T_a) % 1.21/1.26 | c_lessequals(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__sup__iff_2,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) % 1.21/1.26 | ~ c_lessequals(V_y,V_z,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_z,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Osup__least_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(c_Orderings_Oord__class_Omax(V_y,V_z,T_a),V_x,T_a) % 1.21/1.26 | ~ c_lessequals(V_z,V_x,T_a) % 1.21/1.26 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__supI_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) % 1.21/1.26 | ~ c_lessequals(V_b,V_x,T_a) % 1.21/1.26 | ~ c_lessequals(V_a,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__maxI1_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__maxI2_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_y,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_neg__le__iff__le_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.26 | c_lessequals(V_a,V_b,T_a) % 1.21/1.26 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__imp__neg__le_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.26 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_abs__le__D1_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.26 | c_lessequals(V_a,V_b,T_a) % 1.21/1.26 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Oinf__greatest_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_z,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__inf__iff_2,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_z,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Ole__infI_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_b,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_a,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Oinf__le2_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_min__max_Oinf__le1_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_less__le__not__le_1,axiom, % 1.21/1.26 ( ~ class_Orderings_Opreorder(T_a) % 1.21/1.26 | ~ c_lessequals(V_y,V_x,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_not__leE_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.21/1.26 | c_lessequals(V_y,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_linorder__antisym__conv2_1,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_x,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_linorder__antisym__conv1_1,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_x,V_x,T_a) % 1.21/1.26 | c_lessequals(V_x,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_linorder__not__less_1,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.21/1.26 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_linorder__not__less_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_y,V_x,T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_linorder__not__le_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.21/1.26 | c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_linorder__not__le_1,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_y,T_a) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_inf__absorb2_0,axiom, % 1.21/1.26 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.21/1.26 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y % 1.21/1.26 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__iff__inf_1,axiom, % 1.21/1.26 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.21/1.26 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x % 1.21/1.26 | c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__iff__inf_0,axiom, % 1.21/1.26 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.21/1.26 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_x % 1.21/1.26 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_minus__le__iff_1,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.26 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.21/1.26 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_minus__le__iff_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.26 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) % 1.21/1.26 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__minus__iff_1,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.26 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_le__minus__iff_0,axiom, % 1.21/1.26 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.26 | c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.21/1.26 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__less__def_0,axiom, % 1.21/1.26 ( c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.21/1.26 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__sqrt__le__iff_0,axiom, % 1.21/1.26 ( c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__sqrt__le__iff_1,axiom, % 1.21/1.26 ( c_lessequals(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__less__def_2,axiom, % 1.21/1.26 ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.21/1.26 | V_x = V_y % 1.21/1.26 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__add__left__mono_0,axiom, % 1.21/1.26 ( c_lessequals(c_HOL_Oplus__class_Oplus(V_z,V_x,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_exp__le__cancel__iff_1,axiom, % 1.21/1.26 ( c_lessequals(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_Transcendental_Oexp(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_exp__le__cancel__iff_0,axiom, % 1.21/1.26 ( c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_Transcendental_Oexp(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_arctan__monotone_H_0,axiom, % 1.21/1.26 ( c_lessequals(c_Transcendental_Oarctan(V_x),c_Transcendental_Oarctan(V_y),tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_abs__le__interval__iff_1,axiom, % 1.21/1.26 ( c_lessequals(V_x,V_r,tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),V_r,tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_norm__triangle__ineq_0,axiom, % 1.21/1.26 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.21/1.26 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_RealVector_Onorm__class_Onorm(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_norm__triangle__ineq2_0,axiom, % 1.21/1.26 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.21/1.26 | c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(V_a,T_a),c_RealVector_Onorm__class_Onorm(V_b,T_a),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_norm__diff__ineq_0,axiom, % 1.21/1.26 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.21/1.26 | c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(V_a,T_a),c_RealVector_Onorm__class_Onorm(V_b,T_a),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_norm__triangle__ineq4_0,axiom, % 1.21/1.26 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.21/1.26 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(V_a,T_a),c_RealVector_Onorm__class_Onorm(V_b,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_norm__power__ineq_0,axiom, % 1.21/1.26 ( ~ class_RealVector_Oreal__normed__algebra__1(T_a) % 1.21/1.26 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(V_x,T_a),V_n,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_norm__mult__ineq_0,axiom, % 1.21/1.26 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.21/1.26 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_RealVector_Onorm__class_Onorm(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_norm__le__zero__iff_1,axiom, % 1.21/1.26 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.21/1.26 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_norm__le__zero__iff_0,axiom, % 1.21/1.26 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.21/1.26 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.26 | ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_norm__minus__cancel_0,axiom, % 1.21/1.26 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.21/1.26 | c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_abs__norm__cancel_0,axiom, % 1.21/1.26 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.21/1.26 | c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(V_a,T_a),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(V_a,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_norm__minus__commute_0,axiom, % 1.21/1.26 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.21/1.26 | c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_complex__mod__triangle__sub_0,axiom, % 1.21/1.26 c_lessequals(c_RealVector_Onorm__class_Onorm(V_w,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(V_w,V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_abs__Im__le__cmod_0,axiom, % 1.21/1.26 c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_OIm(V_x),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_abs__Re__le__cmod_0,axiom, % 1.21/1.26 c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(V_x),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_complex__mod__triangle__ineq2_0,axiom, % 1.21/1.26 c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(V_b,V_a,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(V_b,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_a,tc_Complex_Ocomplex),tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_pCons__eq__0__iff_1,axiom, % 1.21/1.26 ( ~ class_HOL_Ozero(T_a) % 1.21/1.26 | c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) % 1.21/1.26 | V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_eq__poly__code_I4_J_1,axiom, % 1.21/1.26 ( ~ class_HOL_Ozero(T_a) % 1.21/1.26 | ~ class_HOL_Oeq(T_a) % 1.21/1.26 | c_HOL_Oeq__class_Oeq(V_p,V_q,tc_Polynomial_Opoly(T_a)) % 1.21/1.26 | ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(V_a,V_p,T_a),c_Polynomial_OpCons(V_b,V_q,T_a),tc_Polynomial_Opoly(T_a)) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_pos__poly__pCons_2,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.26 | c_Polynomial_Opos__poly(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) % 1.21/1.26 | ~ c_Polynomial_Opos__poly(V_p,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_id__def_0,axiom, % 1.21/1.26 c_Fun_Oid(v_x,t_a) = v_x ). % 1.21/1.26 % 1.21/1.26 cnf(cls_complex__mod__cnj_0,axiom, % 1.21/1.26 c_RealVector_Onorm__class_Onorm(c_Complex_Ocnj(V_z),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_poly__pCons_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) % 1.21/1.26 | c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_synthetic__div__unique_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) % 1.21/1.26 | c_HOL_Oplus__class_Oplus(V_p,c_Polynomial_Osmult(V_c,V_q,T_a),tc_Polynomial_Opoly(T_a)) != c_Polynomial_OpCons(V_r,V_q,T_a) % 1.21/1.26 | V_r = c_Polynomial_Opoly(V_p,V_c,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_poly__pcompose_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) % 1.21/1.26 | c_Polynomial_Opoly(c_Polynomial_Opcompose(V_p,V_q,T_a),V_x,T_a) = c_Polynomial_Opoly(V_p,c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_cs0_0,axiom, % 1.21/1.26 v_cs____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_norm__ge__zero_0,axiom, % 1.21/1.26 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.21/1.26 | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_complex__mod__minus__le__complex__mod_0,axiom, % 1.21/1.26 c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_complex__Re__le__cmod_0,axiom, % 1.21/1.26 c_lessequals(c_Complex_ORe(V_x),c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_ath_0,axiom, % 1.21/1.26 ( c_lessequals(c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.26 | c_lessequals(V_r,c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_synthetic__div__pCons_0,axiom, % 1.21/1.26 ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) % 1.21/1.26 | c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(V_a,V_p,T_a),V_c,T_a) = c_Polynomial_OpCons(c_Polynomial_Opoly(V_p,V_c,T_a),c_Polynomial_Osynthetic__div(V_p,V_c,T_a),T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_poly__infinity_0,axiom, % 1.21/1.26 ( c_lessequals(V_d,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1(V_a,V_d,V_p),c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),tc_RealDef_Oreal) % 1.21/1.26 | V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_v_0,axiom, % 1.21/1.26 ( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),V_w,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_w,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_poly__minimum__modulus__disc_0,axiom, % 1.21/1.26 ( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(V_p,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1(V_p,V_r),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(V_p,V_w,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_w,tc_Complex_Ocomplex),V_r,tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_poly__bound__exists_1,axiom, % 1.21/1.26 ( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(V_p,V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(V_p,V_r),tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),V_r,tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_v0_0,axiom, % 1.21/1.26 ( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_r_0,axiom, % 1.21/1.26 ( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_pCons_0,axiom, % 1.21/1.26 c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,v_sko__local__XpCons__1(v_cs____),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,V_w,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_pCons_Ohyps_0,axiom, % 1.21/1.26 c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,v_sko__local__XpCons__Xhyps__1(v_cs____),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,V_w,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__le__linear_0,axiom, % 1.21/1.26 ( c_lessequals(V_w,V_z,tc_RealDef_Oreal) % 1.21/1.26 | c_lessequals(V_z,V_w,tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_linorder__linear_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.26 | c_lessequals(V_y,V_x,T_a) % 1.21/1.26 | c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_xt1_I6_J_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.26 | c_lessequals(V_z,V_x,T_a) % 1.21/1.26 | ~ c_lessequals(V_z,V_y,T_a) % 1.21/1.26 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_order__trans_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Opreorder(T_a) % 1.21/1.26 | c_lessequals(V_x,V_z,T_a) % 1.21/1.26 | ~ c_lessequals(V_y,V_z,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__le__refl_0,axiom, % 1.21/1.26 c_lessequals(V_w,V_w,tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__le__trans_0,axiom, % 1.21/1.26 ( c_lessequals(V_i,V_k,tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_order__eq__iff_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.26 | c_lessequals(V_x,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_order__eq__refl_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Opreorder(T_a) % 1.21/1.26 | c_lessequals(V_x,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_pCons__eq__iff_0,axiom, % 1.21/1.26 ( ~ class_HOL_Ozero(T_a) % 1.21/1.26 | c_Polynomial_OpCons(V_a,V_p,T_a) != c_Polynomial_OpCons(V_b,V_q,T_a) % 1.21/1.26 | V_a = V_b ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_pCons__eq__iff_1,axiom, % 1.21/1.26 ( ~ class_HOL_Ozero(T_a) % 1.21/1.26 | c_Polynomial_OpCons(V_a,V_p,T_a) != c_Polynomial_OpCons(V_b,V_q,T_a) % 1.21/1.26 | V_p = V_q ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_order__antisym__conv_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.26 | V_x = V_y % 1.21/1.26 | ~ c_lessequals(V_x,V_y,T_a) % 1.21/1.26 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_order__eq__iff_2,axiom, % 1.21/1.26 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.26 | V_x = V_y % 1.21/1.26 | ~ c_lessequals(V_y,V_x,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_order__antisym_0,axiom, % 1.21/1.26 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.26 | V_x = V_y % 1.21/1.26 | ~ c_lessequals(V_y,V_x,T_a) % 1.21/1.26 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_real__le__antisym_0,axiom, % 1.21/1.26 ( V_z = V_w % 1.21/1.26 | ~ c_lessequals(V_w,V_z,tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(V_z,V_w,tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_CHAINED_0,axiom, % 1.21/1.26 ( c_lessequals(c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.21/1.26 | c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_CHAINED_0_01,axiom, % 1.21/1.26 ( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),V_w,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_w,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_CHAINED_0_02,axiom, % 1.21/1.26 ( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) % 1.21/1.26 | ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ). % 1.21/1.26 % 1.21/1.26 cnf(cls_conjecture_0,negated_conjecture, % 1.21/1.26 ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),V_xa,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add,axiom, % 1.21/1.26 ( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) % 1.21/1.26 | ~ class_OrderedGroup_Ocancel__comm__monoid__add(T_1) ) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring,axiom, % 1.21/1.26 ( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(T_1)) % 1.21/1.26 | ~ class_Ring__and__Field_Ocomm__ring(T_1) ) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1,axiom, % 1.21/1.26 ( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) % 1.21/1.26 | ~ class_Ring__and__Field_Ocomm__ring__1(T_1) ) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add,axiom, % 1.21/1.26 class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring,axiom, % 1.21/1.26 class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,axiom, % 1.21/1.26 class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add,axiom, % 1.21/1.26 class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring,axiom, % 1.21/1.26 class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1,axiom, % 1.21/1.26 class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom, % 1.21/1.26 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom, % 1.21/1.26 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict,axiom, % 1.21/1.26 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring,axiom, % 1.21/1.26 class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__meet,axiom, % 1.21/1.26 class_OrderedGroup_Olordered__ab__group__add__meet(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors,axiom, % 1.21/1.26 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict,axiom, % 1.21/1.26 class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add,axiom, % 1.21/1.26 class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,axiom, % 1.21/1.26 class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs,axiom, % 1.21/1.26 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add,axiom, % 1.21/1.26 class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors,axiom, % 1.21/1.26 class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 1.21/1.26 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict,axiom, % 1.21/1.26 class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom, % 1.21/1.26 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,axiom, % 1.21/1.26 class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,axiom, % 1.21/1.26 class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add,axiom, % 1.21/1.26 class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add,axiom, % 1.21/1.26 class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring,axiom, % 1.21/1.26 class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs,axiom, % 1.21/1.26 class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom, % 1.21/1.26 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring,axiom, % 1.21/1.26 class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors,axiom, % 1.21/1.26 class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom,axiom, % 1.21/1.26 class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom, % 1.21/1.26 class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0,axiom, % 1.21/1.26 class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom, % 1.21/1.26 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult,axiom, % 1.21/1.26 class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom, % 1.21/1.26 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult,axiom, % 1.21/1.26 class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add,axiom, % 1.21/1.26 class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring,axiom, % 1.21/1.26 class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring,axiom, % 1.21/1.26 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring,axiom, % 1.21/1.26 class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom, % 1.21/1.26 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ). % 1.21/1.26 % 1.21/1.26 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add,axiom, % 1.21/1.27 class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one,axiom, % 1.21/1.27 class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,axiom, % 1.21/1.27 class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__Lattices_Olower__semilattice,axiom, % 1.21/1.27 class_Lattices_Olower__semilattice(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1,axiom, % 1.21/1.27 class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,axiom, % 1.21/1.27 class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero,axiom, % 1.21/1.27 class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono,axiom, % 1.21/1.27 class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult,axiom, % 1.21/1.27 class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring,axiom, % 1.21/1.27 class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add,axiom, % 1.21/1.27 class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom, % 1.21/1.27 class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if,axiom, % 1.21/1.27 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring,axiom, % 1.21/1.27 class_Ring__and__Field_Oring(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oidom,axiom, % 1.21/1.27 class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom, % 1.21/1.27 class_Orderings_Opreorder(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom, % 1.21/1.27 class_Orderings_Olinorder(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__Lattices_Olattice,axiom, % 1.21/1.27 class_Lattices_Olattice(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__Orderings_Oorder,axiom, % 1.21/1.27 class_Orderings_Oorder(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom, % 1.21/1.27 class_Int_Onumber__ring(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__Power_Opower,axiom, % 1.21/1.27 class_Power_Opower(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__SEQ_Obanach,axiom, % 1.21/1.27 class_SEQ_Obanach(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__HOL_Ozero,axiom, % 1.21/1.27 class_HOL_Ozero(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_RealDef__Oreal__HOL_Oeq,axiom, % 1.21/1.27 class_HOL_Oeq(tc_RealDef_Oreal) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors,axiom, % 1.21/1.27 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,axiom, % 1.21/1.27 class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 1.21/1.27 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom, % 1.21/1.27 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add,axiom, % 1.21/1.27 class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom, % 1.21/1.27 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,axiom, % 1.21/1.27 class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom, % 1.21/1.27 class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom, % 1.21/1.27 class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom, % 1.21/1.27 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,axiom, % 1.21/1.27 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom, % 1.21/1.27 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,axiom, % 1.21/1.27 class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add,axiom, % 1.21/1.27 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring,axiom, % 1.21/1.27 class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom, % 1.21/1.27 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,axiom, % 1.21/1.27 class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom, % 1.21/1.27 class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,axiom, % 1.21/1.27 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,axiom, % 1.21/1.27 class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom, % 1.21/1.27 class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring,axiom, % 1.21/1.27 class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add,axiom, % 1.21/1.27 class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom, % 1.21/1.27 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring,axiom, % 1.21/1.27 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom, % 1.21/1.27 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom, % 1.21/1.27 class_Int_Onumber__ring(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__Power_Opower,axiom, % 1.21/1.27 class_Power_Opower(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__SEQ_Obanach,axiom, % 1.21/1.27 class_SEQ_Obanach(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__HOL_Ozero,axiom, % 1.21/1.27 class_HOL_Ozero(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Complex__Ocomplex__HOL_Oeq,axiom, % 1.21/1.27 class_HOL_Oeq(tc_Complex_Ocomplex) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom, % 1.21/1.27 ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom, % 1.21/1.27 ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict,axiom, % 1.21/1.27 ( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring,axiom, % 1.21/1.27 ( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors,axiom, % 1.21/1.27 ( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oidom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict,axiom, % 1.21/1.27 ( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add,axiom, % 1.21/1.27 ( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs,axiom, % 1.21/1.27 ( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add,axiom, % 1.21/1.27 ( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors,axiom, % 1.21/1.27 ( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oidom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 1.21/1.27 ( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_OrderedGroup_Ocancel__comm__monoid__add(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict,axiom, % 1.21/1.27 ( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add,axiom, % 1.21/1.27 ( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add,axiom, % 1.21/1.27 ( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add,axiom, % 1.21/1.27 ( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_OrderedGroup_Ocancel__comm__monoid__add(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring,axiom, % 1.21/1.27 ( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring__abs,axiom, % 1.21/1.27 ( class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring,axiom, % 1.21/1.27 ( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors,axiom, % 1.21/1.27 ( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oidom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom,axiom, % 1.21/1.27 ( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1,axiom, % 1.21/1.27 ( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0,axiom, % 1.21/1.27 ( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult,axiom, % 1.21/1.27 ( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult,axiom, % 1.21/1.27 ( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add,axiom, % 1.21/1.27 ( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_OrderedGroup_Ocomm__monoid__add(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring,axiom, % 1.21/1.27 ( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring,axiom, % 1.21/1.27 ( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add,axiom, % 1.21/1.27 ( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_OrderedGroup_Ocomm__monoid__add(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one,axiom, % 1.21/1.27 ( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom,axiom, % 1.21/1.27 ( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1,axiom, % 1.21/1.27 ( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add,axiom, % 1.21/1.27 ( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_OrderedGroup_Oab__group__add(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero,axiom, % 1.21/1.27 ( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono,axiom, % 1.21/1.27 ( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult,axiom, % 1.21/1.27 ( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring,axiom, % 1.21/1.27 ( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add,axiom, % 1.21/1.27 ( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_OrderedGroup_Ocomm__monoid__add(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add,axiom, % 1.21/1.27 ( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_OrderedGroup_Oab__group__add(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if,axiom, % 1.21/1.27 ( class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring,axiom, % 1.21/1.27 ( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Ocomm__ring(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oidom,axiom, % 1.21/1.27 ( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oidom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Orderings_Opreorder,axiom, % 1.21/1.27 ( class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Orderings_Olinorder,axiom, % 1.21/1.27 ( class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Orderings_Oorder,axiom, % 1.21/1.27 ( class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Int_Onumber__ring,axiom, % 1.21/1.27 ( class_Int_Onumber__ring(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Ocomm__ring__1(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__Power_Opower,axiom, % 1.21/1.27 ( class_Power_Opower(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__HOL_Ozero,axiom, % 1.21/1.27 ( class_HOL_Ozero(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_HOL_Ozero(T_1) ) ). % 1.21/1.27 % 1.21/1.27 cnf(clsarity_Polynomial__Opoly__HOL_Oeq,axiom, % 1.21/1.27 ( class_HOL_Oeq(tc_Polynomial_Opoly(T_1)) % 1.21/1.27 | ~ class_HOL_Ozero(T_1) % 1.21/1.27 | ~ class_HOL_Oeq(T_1) ) ). % 1.21/1.27 % 1.21/1.27 %------------------------------------------------------------------------------ % 1.21/1.27 %------------------------------------------- % 1.21/1.27 % Proof found % 1.21/1.27 % SZS status Theorem for theBenchmark % 1.21/1.27 % SZS output start Proof % 1.21/1.27 %ClaNum:1026(EqnAxiom:144) % 1.21/1.27 %VarNum:5765(SingletonVarNum:1943) % 1.21/1.27 %MaxLitNum:6 % 1.21/1.27 %MaxfuncDepth:4 % 1.21/1.27 %SharedTerms:133 % 1.21/1.27 %goalClause: 289 % 1.21/1.27 %singleGoalClaCount:1 % 1.21/1.27 [145]P1(a1) % 1.21/1.27 [146]P12(a1) % 1.21/1.27 [147]P58(a1) % 1.21/1.27 [148]P65(a1) % 1.21/1.27 [149]P65(a2) % 1.21/1.27 [150]P13(a1) % 1.21/1.27 [151]P2(a1) % 1.21/1.27 [152]P2(a2) % 1.21/1.27 [153]P3(a1) % 1.21/1.27 [154]P3(a2) % 1.21/1.27 [155]P67(a1) % 1.21/1.27 [156]P67(a2) % 1.21/1.27 [157]P24(a1) % 1.21/1.27 [158]P24(a2) % 1.21/1.27 [159]P25(a1) % 1.21/1.27 [160]P25(a2) % 1.21/1.27 [161]P26(a1) % 1.21/1.27 [162]P26(a2) % 1.21/1.27 [163]P68(a1) % 1.21/1.27 [164]P68(a2) % 1.21/1.27 [165]P27(a1) % 1.21/1.27 [166]P42(a1) % 1.21/1.27 [167]P42(a2) % 1.21/1.27 [168]P59(a1) % 1.21/1.27 [169]P60(a1) % 1.21/1.27 [170]P33(a1) % 1.21/1.27 [171]P14(a1) % 1.21/1.27 [172]P14(a2) % 1.21/1.27 [173]P34(a1) % 1.21/1.27 [174]P28(a1) % 1.21/1.27 [175]P47(a1) % 1.21/1.27 [176]P47(a2) % 1.21/1.27 [177]P35(a1) % 1.21/1.27 [178]P8(a1) % 1.21/1.27 [179]P61(a1) % 1.21/1.27 [180]P69(a1) % 1.21/1.27 [181]P69(a2) % 1.21/1.27 [182]P48(a1) % 1.21/1.27 [183]P48(a2) % 1.21/1.27 [184]P15(a1) % 1.21/1.27 [185]P15(a2) % 1.21/1.27 [186]P53(a1) % 1.21/1.27 [187]P53(a2) % 1.21/1.27 [188]P9(a1) % 1.21/1.27 [189]P9(a2) % 1.21/1.27 [190]P49(a1) % 1.21/1.27 [191]P62(a1) % 1.21/1.27 [192]P63(a1) % 1.21/1.27 [193]P36(a1) % 1.21/1.27 [194]P16(a1) % 1.21/1.27 [195]P16(a2) % 1.21/1.27 [196]P54(a1) % 1.21/1.27 [197]P55(a1) % 1.21/1.27 [198]P56(a1) % 1.21/1.27 [199]P23(a1) % 1.21/1.27 [200]P23(a2) % 1.21/1.27 [201]P64(a1) % 1.21/1.27 [202]P43(a1) % 1.21/1.27 [203]P43(a2) % 1.21/1.27 [204]P17(a1) % 1.21/1.27 [205]P17(a2) % 1.21/1.27 [206]P50(a1) % 1.21/1.27 [207]P50(a2) % 1.21/1.27 [208]P29(a1) % 1.21/1.27 [209]P66(a1) % 1.21/1.27 [210]P40(a1) % 1.21/1.27 [211]P41(a1) % 1.21/1.27 [212]P18(a1) % 1.21/1.27 [213]P18(a2) % 1.21/1.27 [214]P70(a1) % 1.21/1.27 [215]P70(a2) % 1.21/1.27 [216]P71(a1) % 1.21/1.27 [217]P71(a2) % 1.21/1.27 [218]P44(a1) % 1.21/1.27 [219]P44(a2) % 1.21/1.27 [220]P57(a1) % 1.21/1.27 [221]P20(a1) % 1.21/1.27 [222]P20(a2) % 1.21/1.27 [223]P21(a1) % 1.21/1.27 [224]P21(a2) % 1.21/1.27 [225]P30(a1) % 1.21/1.27 [226]P45(a1) % 1.21/1.27 [227]P45(a2) % 1.21/1.27 [228]P31(a1) % 1.21/1.27 [229]P31(a2) % 1.21/1.27 [230]P32(a1) % 1.21/1.27 [231]P32(a2) % 1.21/1.27 [232]P38(a1) % 1.21/1.27 [233]P37(a1) % 1.21/1.27 [234]P46(a1) % 1.21/1.27 [235]P46(a2) % 1.21/1.27 [236]P22(a1) % 1.21/1.27 [237]P22(a2) % 1.21/1.27 [238]P51(a1) % 1.21/1.27 [239]P51(a2) % 1.21/1.27 [240]P52(a1) % 1.21/1.27 [241]P52(a2) % 1.21/1.27 [242]E(f12(f3(a1)),f3(a1)) % 1.21/1.27 [243]E(f14(f3(a1)),f3(a1)) % 1.21/1.27 [244]E(f4(f3(a2)),f3(a2)) % 1.21/1.27 [245]E(f5(f3(a2)),f3(a1)) % 1.21/1.27 [246]E(f6(f3(a2)),f3(a1)) % 1.21/1.27 [284]~E(f3(f27(a2)),a29) % 1.21/1.27 [288]~P5(f3(a1),f11(f3(a1),f3(a1),a1),a1) % 1.21/1.27 [271]E(f9(f11(f3(a1),f3(a1),a1),f11(f3(a1),f3(a1),a1),a1),f3(a1)) % 1.21/1.27 [254]P4(x2541,x2541,a1) % 1.21/1.27 [285]~P5(x2851,x2851,a1) % 1.21/1.27 [256]P5(f3(a1),f25(x2561,a1),a1) % 1.21/1.27 [257]P4(f3(a1),f25(x2571,a1),a1) % 1.21/1.27 [258]P4(f6(x2581),f15(x2581,a2),a1) % 1.21/1.27 [286]~P5(f25(x2861,a1),f3(a1),a1) % 1.21/1.27 [287]~P4(f25(x2871,a1),f3(a1),a1) % 1.21/1.27 [247]E(f4(f4(x2471)),x2471) % 1.21/1.27 [248]E(f6(f4(x2481)),f6(x2481)) % 1.21/1.27 [249]E(f7(f5(x2491),a1),f5(f4(x2491))) % 1.21/1.27 [250]E(f15(f4(x2501),a2),f15(x2501,a2)) % 1.21/1.27 [251]E(f12(f7(x2511,a1)),f7(f12(x2511),a1)) % 1.21/1.27 [252]E(f14(f7(x2521,a1)),f7(f14(x2521),a1)) % 1.21/1.27 [253]E(f8(f25(x2531,a1),a1),f25(x2531,a1)) % 1.21/1.27 [255]E(f9(x2551,f7(x2551,a1),a1),f3(a1)) % 1.21/1.27 [261]P4(f8(f5(x2611),a1),f15(x2611,a2),a1) % 1.21/1.27 [262]P4(f8(f6(x2621),a1),f15(x2621,a2),a1) % 1.21/1.27 [263]E(f12(f11(x2631,x2631,a1)),f8(x2631,a1)) % 1.21/1.27 [265]P4(f7(f15(x2651,a2),a1),f15(x2651,a2),a1) % 1.21/1.27 [276]P4(f15(f17(a29,f32(a29),a2),a2),f15(f17(a29,x2761,a2),a2),a1) % 1.21/1.27 [277]P4(f15(f17(a29,f35(a29),a2),a2),f15(f17(a29,x2771,a2),a2),a1) % 1.21/1.27 [289]~P4(f15(f17(f18(a30,a29,a2),x2891,a2),a2),f15(f17(f18(a30,a29,a2),f26(a36,x2891),a2),a2),a1) % 1.21/1.27 [259]P5(f3(a1),f28(x2591,x2592),a1) % 1.21/1.27 [260]E(f11(x2601,x2602,a1),f11(x2602,x2601,a1)) % 1.21/1.27 [264]E(f9(x2641,f7(x2642,a1),a1),f10(x2641,x2642,a1)) % 1.21/1.27 [266]E(f12(f16(x2661,x2662,a1)),f16(f12(x2661),x2662,a1)) % 1.21/1.27 [267]E(f11(f12(x2671),f12(x2672),a1),f12(f11(x2671,x2672,a1))) % 1.21/1.27 [268]E(f9(f4(x2681),f4(x2682),a2),f4(f9(x2681,x2682,a2))) % 1.21/1.27 [269]E(f9(f5(x2691),f5(x2692),a1),f5(f9(x2691,x2692,a2))) % 1.21/1.27 [270]E(f9(f6(x2701),f6(x2702),a1),f6(f9(x2701,x2702,a2))) % 1.21/1.27 [274]P4(f7(f11(x2741,x2741,a1),a1),f11(x2742,x2742,a1),a1) % 1.21/1.27 [278]P4(f3(a1),f9(f11(x2781,x2781,a1),f11(x2782,x2782,a1),a1),a1) % 1.21/1.27 [279]P4(f15(x2791,a2),f9(f15(f9(x2791,x2792,a2),a2),f15(x2792,a2),a1),a1) % 1.21/1.27 [280]P4(f10(f15(f9(x2801,x2802,a2),a2),f15(x2801,a2),a1),f15(x2802,a2),a1) % 1.21/1.27 [273]E(f8(f9(x2731,f7(x2732,a1),a1),a1),f8(f9(x2732,f7(x2731,a1),a1),a1)) % 1.21/1.27 [281]P4(x2811,f12(f9(f11(x2811,x2811,a1),f11(x2812,x2812,a1),a1)),a1) % 1.21/1.27 [282]P4(f3(a1),f12(f9(f11(x2821,x2821,a1),f11(x2822,x2822,a1),a1)),a1) % 1.21/1.27 [272]E(f11(f11(x2721,x2722,a1),x2723,a1),f11(x2721,f11(x2722,x2723,a1),a1)) % 1.21/1.27 [275]E(f9(f11(x2751,x2752,a1),f11(x2753,x2752,a1),a1),f11(f9(x2751,x2753,a1),x2752,a1)) % 1.21/1.27 [283]P4(f8(f9(f9(x2831,x2832,a1),f9(f7(x2833,a1),f7(x2834,a1),a1),a1),a1),f9(f8(f9(x2831,f7(x2833,a1),a1),a1),f8(f9(x2832,f7(x2834,a1),a1),a1),a1),a1) % 1.21/1.27 [290]~E(f12(x2901),f3(a1))+E(x2901,f3(a1)) % 1.21/1.27 [291]~E(f4(x2911),f3(a2))+E(x2911,f3(a2)) % 1.21/1.27 [294]~P12(x2941)+P12(f27(x2941)) % 1.21/1.27 [295]~P12(x2951)+P58(f27(x2951)) % 1.21/1.27 [296]~P51(x2961)+P65(f27(x2961)) % 1.21/1.27 [297]~P2(x2971)+P2(f27(x2971)) % 1.21/1.27 [298]~P47(x2981)+P67(f27(x2981)) % 1.21/1.27 [299]~P53(x2991)+P24(f27(x2991)) % 1.21/1.27 [300]~P48(x3001)+P25(f27(x3001)) % 1.21/1.27 [301]~P47(x3011)+P26(f27(x3011)) % 1.21/1.27 [302]~P53(x3021)+P68(f27(x3021)) % 1.21/1.27 [303]~P12(x3031)+P27(f27(x3031)) % 1.21/1.27 [304]~P12(x3041)+P59(f27(x3041)) % 1.21/1.27 [305]~P12(x3051)+P60(f27(x3051)) % 1.21/1.27 [306]~P12(x3061)+P33(f27(x3061)) % 1.21/1.27 [307]~P15(x3071)+P14(f27(x3071)) % 1.21/1.27 [308]~P12(x3081)+P34(f27(x3081)) % 1.21/1.27 [309]~P47(x3091)+P47(f27(x3091)) % 1.21/1.27 [310]~P12(x3101)+P35(f27(x3101)) % 1.21/1.27 [311]~P12(x3111)+P61(f27(x3111)) % 1.21/1.27 [312]~P53(x3121)+P69(f27(x3121)) % 1.21/1.27 [313]~P48(x3131)+P48(f27(x3131)) % 1.21/1.27 [314]~P15(x3141)+P15(f27(x3141)) % 1.21/1.27 [315]~P53(x3151)+P53(f27(x3151)) % 1.21/1.27 [316]~P52(x3161)+P9(f27(x3161)) % 1.21/1.27 [317]~P12(x3171)+P49(f27(x3171)) % 1.21/1.27 [318]~P12(x3181)+P62(f27(x3181)) % 1.21/1.27 [319]~P12(x3191)+P63(f27(x3191)) % 1.21/1.27 [320]~P12(x3201)+P36(f27(x3201)) % 1.21/1.27 [321]~P16(x3211)+P16(f27(x3211)) % 1.21/1.27 [322]~P12(x3221)+P55(f27(x3221)) % 1.21/1.27 [323]~P12(x3231)+P56(f27(x3231)) % 1.21/1.27 [324]~P47(x3241)+P23(f27(x3241)) % 1.21/1.27 [325]~P12(x3251)+P64(f27(x3251)) % 1.21/1.27 [326]~P48(x3261)+P17(f27(x3261)) % 1.21/1.27 [327]~P48(x3271)+P50(f27(x3271)) % 1.21/1.27 [328]~P12(x3281)+P29(f27(x3281)) % 1.21/1.27 [329]~P12(x3291)+P66(f27(x3291)) % 1.21/1.27 [330]~P12(x3301)+P40(f27(x3301)) % 1.21/1.27 [331]~P12(x3311)+P41(f27(x3311)) % 1.21/1.27 [332]~P16(x3321)+P18(f27(x3321)) % 1.21/1.27 [333]~P48(x3331)+P70(f27(x3331)) % 1.21/1.27 [334]~P12(x3341)+P57(f27(x3341)) % 1.21/1.27 [335]~P22(x3351)+P20(f27(x3351)) % 1.21/1.27 [336]~P22(x3361)+P21(f27(x3361)) % 1.21/1.27 [337]~P47(x3371)+P31(f27(x3371)) % 1.21/1.27 [338]~P16(x3381)+P32(f27(x3381)) % 1.21/1.27 [339]~P12(x3391)+P38(f27(x3391)) % 1.21/1.27 [340]~P12(x3401)+P37(f27(x3401)) % 1.21/1.27 [341]~P22(x3411)+P22(f27(x3411)) % 1.21/1.27 [342]~P51(x3421)+P51(f27(x3421)) % 1.21/1.27 [343]~P52(x3431)+P52(f27(x3431)) % 1.21/1.27 [389]E(f8(x3891,a1),x3891)+P5(x3891,f3(a1),a1) % 1.21/1.27 [436]~E(f12(x4361),f3(a1))+~P5(f3(a1),x4361,a1) % 1.21/1.27 [453]E(f8(x4531,a1),f7(x4531,a1))+~P5(x4531,f3(a1),a1) % 1.21/1.27 [524]~P5(x5241,f3(a1),a1)+P5(f12(x5241),f3(a1),a1) % 1.21/1.27 [525]~P4(x5251,f3(a1),a1)+P4(f12(x5251),f3(a1),a1) % 1.21/1.27 [527]~P5(f3(a1),x5271,a1)+P5(f3(a1),f12(x5271),a1) % 1.21/1.27 [529]~P4(f3(a1),x5291,a1)+P4(f3(a1),f12(x5291),a1) % 1.21/1.27 [531]~P5(f12(x5311),f3(a1),a1)+P5(x5311,f3(a1),a1) % 1.21/1.27 [532]~P4(f12(x5321),f3(a1),a1)+P4(x5321,f3(a1),a1) % 1.21/1.27 [533]~P5(f3(a1),f12(x5331),a1)+P5(f3(a1),x5331,a1) % 1.21/1.27 [534]~P4(f3(a1),f12(x5341),a1)+P4(f3(a1),x5341,a1) % 1.21/1.27 [539]E(x5391,f3(a1))+P5(f3(a1),f11(x5391,x5391,a1),a1) % 1.21/1.27 [346]~P42(x3461)+E(f15(f3(x3461),x3461),f3(a1)) % 1.21/1.27 [348]~P33(x3481)+E(f8(f3(x3481),x3481),f3(x3481)) % 1.21/1.27 [349]~P14(x3491)+E(f7(f3(x3491),x3491),f3(x3491)) % 1.21/1.27 [350]~P29(x3501)+E(f7(f3(x3501),x3501),f3(x3501)) % 1.21/1.27 [365]~P12(x3651)+~P7(f3(f27(x3651)),x3651) % 1.21/1.27 [408]~P13(x4081)+E(f9(f3(x4081),f3(x4081),x4081),f3(x4081)) % 1.21/1.27 [438]~P42(x4381)+P4(f15(f3(x4381),x4381),f3(a1),a1) % 1.21/1.27 [444]~P33(x4441)+P4(f8(f3(x4441),x4441),f3(x4441),x4441) % 1.21/1.27 [535]~P42(x5351)+~P5(f3(a1),f15(f3(x5351),x5351),a1) % 1.21/1.27 [538]~P33(x5381)+~P5(f3(x5381),f8(f3(x5381),x5381),x5381) % 1.21/1.27 [434]~P2(x4341)+E(f18(f3(x4341),f3(f27(x4341)),x4341),f3(f27(x4341))) % 1.21/1.27 [741]~P59(x7411)+E(f9(f11(f3(x7411),f3(x7411),x7411),f11(f3(x7411),f3(x7411),x7411),x7411),f3(x7411)) % 1.21/1.27 [992]~P59(x9921)+P4(f9(f11(f3(x9921),f3(x9921),x9921),f11(f3(x9921),f3(x9921),x9921),x9921),f3(x9921),x9921) % 1.21/1.27 [1010]~P59(x10101)+~P5(f3(x10101),f9(f11(f3(x10101),f3(x10101),x10101),f11(f3(x10101),f3(x10101),x10101),x10101),x10101) % 1.21/1.27 [1012]~P4(a31,f15(x10121,a2),a1)+P4(f15(f17(f18(a30,a29,a2),a37,a2),a2),f15(f17(f18(a30,a29,a2),x10121,a2),a2),a1) % 1.21/1.27 [1013]~P4(a31,f15(x10131,a2),a1)+P4(f15(f17(f18(a30,a29,a2),f3(a2),a2),a2),f15(f17(f18(a30,a29,a2),x10131,a2),a2),a1) % 1.21/1.27 [1015]~P4(f15(x10151,a2),f8(a31,a1),a1)+P4(f15(f17(f18(a30,a29,a2),a37,a2),a2),f15(f17(f18(a30,a29,a2),x10151,a2),a2),a1) % 1.21/1.27 [370]~P40(x3702)+P4(x3701,x3701,x3702) % 1.21/1.27 [371]~P41(x3712)+P4(x3711,x3711,x3712) % 1.21/1.27 [372]~P3(x3722)+P6(x3721,x3721,x3722) % 1.21/1.27 [428]~P5(x4282,x4282,x4281)+~P34(x4281) % 1.21/1.27 [429]~P5(x4292,x4292,x4291)+~P40(x4291) % 1.21/1.27 [430]~P5(x4302,x4302,x4301)+~P41(x4301) % 1.21/1.27 [445]P4(x4452,x4451,a1)+P4(x4451,x4452,a1) % 1.21/1.27 [487]~P5(x4871,x4872,a1)+P4(x4871,x4872,a1) % 1.21/1.27 [292]E(x2921,x2922)+~E(f12(x2921),f12(x2922)) % 1.21/1.27 [293]E(x2931,x2932)+~E(f4(x2931),f4(x2932)) % 1.21/1.27 [356]E(x3561,x3562)+~E(f25(x3561,a1),f25(x3562,a1)) % 1.21/1.27 [373]~P1(x3732)+E(f13(x3731,x3731,x3732),x3731) % 1.21/1.27 [374]~P19(x3742)+E(f11(x3741,x3741,x3742),x3741) % 1.21/1.27 [375]~P34(x3752)+E(f19(x3751,x3751,x3752),x3751) % 1.21/1.27 [376]~P34(x3762)+E(f21(x3761,x3761,x3762),x3761) % 1.21/1.27 [378]~P14(x3782)+E(f10(x3781,x3781,x3782),f3(x3782)) % 1.21/1.27 [379]~P15(x3792)+E(f10(x3791,x3791,x3792),f3(x3792)) % 1.21/1.27 [380]~P39(x3801)+P4(f20(x3801),x3802,x3801) % 1.21/1.27 [415]~P33(x4152)+P4(x4151,f8(x4151,x4152),x4152) % 1.21/1.27 [416]~P42(x4162)+P4(f3(a1),f15(x4161,x4162),a1) % 1.21/1.27 [431]~P33(x4311)+P4(f3(x4311),f8(x4312,x4311),x4311) % 1.21/1.27 [437]E(x4371,f7(x4372,a1))+~E(f9(x4372,x4371,a1),f3(a1)) % 1.21/1.27 [454]~P33(x4542)+P4(f7(x4541,x4542),f8(x4541,x4542),x4542) % 1.21/1.27 [486]~P42(x4861)+~P5(f15(x4862,x4861),f3(a1),a1) % 1.21/1.27 [497]~P33(x4971)+~P5(f8(x4972,x4971),f3(x4971),x4971) % 1.21/1.27 [509]~P5(x5091,x5092,a1)+P5(f12(x5091),f12(x5092),a1) % 1.21/1.27 [510]~P5(x5101,x5102,a1)+P5(f14(x5101),f14(x5102),a1) % 1.21/1.27 [511]~P4(x5111,x5112,a1)+P4(f12(x5111),f12(x5112),a1) % 1.21/1.27 [512]~P4(x5121,x5122,a1)+P4(f14(x5121),f14(x5122),a1) % 1.21/1.27 [536]P5(x5361,x5362,a1)+~P5(f12(x5361),f12(x5362),a1) % 1.21/1.27 [537]P4(x5371,x5372,a1)+~P4(f12(x5371),f12(x5372),a1) % 1.21/1.27 [560]P4(x5601,x5602,a1)+~P4(f8(x5601,a1),x5602,a1) % 1.21/1.27 [561]~P59(x5611)+P4(f3(x5611),f11(x5612,x5612,x5611),x5611) % 1.21/1.27 [562]P4(x5621,f15(x5622,a2),a1)+P4(f15(x5622,a2),f8(x5621,a1),a1) % 1.21/1.27 [582]~P5(x5821,x5822,a1)+P5(f25(x5821,a1),f25(x5822,a1),a1) % 1.21/1.27 [583]~P4(x5831,x5832,a1)+P4(f25(x5831,a1),f25(x5832,a1),a1) % 1.21/1.27 [606]~P4(f8(x6062,a1),x6061,a1)+P4(f7(x6061,a1),x6062,a1) % 1.21/1.27 [623]P5(x6231,x6232,a1)+~P5(f25(x6231,a1),f25(x6232,a1),a1) % 1.21/1.27 [624]P4(x6241,x6242,a1)+~P4(f25(x6241,a1),f25(x6242,a1),a1) % 1.21/1.27 [661]~P4(x6611,x6612,a1)+P4(f10(x6611,x6612,a1),f3(a1),a1) % 1.21/1.27 [697]~P59(x6971)+~P5(f11(x6972,x6972,x6971),f3(x6971),x6971) % 1.21/1.27 [700]~P5(f7(x7001,a1),x7002,a1)+P5(f3(a1),f9(x7001,x7002,a1),a1) % 1.21/1.27 [701]~P4(f7(x7011,a1),x7012,a1)+P4(f3(a1),f9(x7011,x7012,a1),a1) % 1.21/1.27 [702]~P5(x7022,f7(x7021,a1),a1)+P5(f9(x7021,x7022,a1),f3(a1),a1) % 1.21/1.27 [703]~P4(x7032,f7(x7031,a1),a1)+P4(f9(x7031,x7032,a1),f3(a1),a1) % 1.21/1.27 [714]P4(x7141,x7142,a1)+~P4(f10(x7141,x7142,a1),f3(a1),a1) % 1.21/1.27 [737]P5(x7371,f7(x7372,a1),a1)+~P5(f9(x7372,x7371,a1),f3(a1),a1) % 1.21/1.27 [738]P4(x7381,f7(x7382,a1),a1)+~P4(f9(x7382,x7381,a1),f3(a1),a1) % 1.21/1.27 [739]P5(f7(x7391,a1),x7392,a1)+~P5(f3(a1),f9(x7391,x7392,a1),a1) % 1.21/1.27 [740]P4(f7(x7401,a1),x7402,a1)+~P4(f3(a1),f9(x7401,x7402,a1),a1) % 1.21/1.27 [361]~P14(x3612)+E(f7(f7(x3611,x3612),x3612),x3611) % 1.21/1.27 [362]~P10(x3622)+E(f7(f7(x3621,x3622),x3622),x3621) % 1.21/1.27 [366]~P42(x3662)+E(f8(f15(x3661,x3662),a1),f15(x3661,x3662)) % 1.21/1.27 [367]~P33(x3672)+E(f8(f8(x3671,x3672),x3672),f8(x3671,x3672)) % 1.21/1.27 [368]~P33(x3682)+E(f8(f7(x3681,x3682),x3682),f8(x3681,x3682)) % 1.21/1.27 [369]~P42(x3692)+E(f15(f7(x3691,x3692),x3692),f15(x3691,x3692)) % 1.21/1.27 [381]~P47(x3812)+E(f9(x3811,f3(x3812),x3812),x3811) % 1.21/1.27 [382]~P16(x3822)+E(f9(x3821,f3(x3822),x3822),x3821) % 1.21/1.27 [383]~P32(x3832)+E(f9(x3831,f3(x3832),x3832),x3831) % 1.21/1.27 [384]~P14(x3842)+E(f10(x3841,f3(x3842),x3842),x3841) % 1.21/1.27 [386]~P47(x3861)+E(f9(f3(x3861),x3862,x3861),x3862) % 1.21/1.27 [387]~P16(x3871)+E(f9(f3(x3871),x3872,x3871),x3872) % 1.21/1.27 [388]~P32(x3881)+E(f9(f3(x3881),x3882,x3881),x3882) % 1.21/1.27 [390]~P11(x3902)+E(f13(x3901,f20(x3902),x3902),f20(x3902)) % 1.21/1.27 [391]~P25(x3912)+E(f11(x3911,f3(x3912),x3912),f3(x3912)) % 1.21/1.27 [392]~P47(x3922)+E(f11(x3921,f3(x3922),x3922),f3(x3922)) % 1.21/1.27 [393]~P69(x3932)+E(f11(x3931,f3(x3932),x3932),f3(x3932)) % 1.21/1.27 [395]~P43(x3952)+E(f11(x3951,f3(x3952),x3952),f3(x3952)) % 1.21/1.27 [396]~P11(x3961)+E(f13(f20(x3961),x3962,x3961),f20(x3961)) % 1.21/1.27 [397]~P25(x3971)+E(f11(f3(x3971),x3972,x3971),f3(x3971)) % 1.21/1.27 [399]~P47(x3991)+E(f11(f3(x3991),x3992,x3991),f3(x3991)) % 1.21/1.27 [400]~P69(x4001)+E(f11(f3(x4001),x4002,x4001),f3(x4001)) % 1.21/1.27 [402]~P43(x4021)+E(f11(f3(x4021),x4022,x4021),f3(x4021)) % 1.21/1.27 [406]~P48(x4061)+E(f23(f3(x4061),x4062,x4061),f3(f27(x4061))) % 1.21/1.27 [407]~P53(x4071)+E(f23(f3(x4071),x4072,x4071),f3(f27(x4071))) % 1.21/1.27 [409]~P14(x4091)+E(f10(f3(x4091),x4092,x4091),f7(x4092,x4091)) % 1.21/1.27 [413]~P16(x4132)+E(f9(x4131,f3(f27(x4132)),f27(x4132)),x4131) % 1.21/1.27 [414]~P16(x4141)+E(f9(f3(f27(x4141)),x4142,f27(x4141)),x4142) % 1.21/1.27 [422]~P10(x4222)+E(f13(x4221,f7(x4221,x4222),x4222),f20(x4222)) % 1.21/1.27 [423]~P14(x4232)+E(f9(x4231,f7(x4231,x4232),x4232),f3(x4232)) % 1.21/1.27 [424]~P10(x4242)+E(f13(f7(x4241,x4242),x4241,x4242),f20(x4242)) % 1.21/1.27 [426]~P14(x4262)+E(f9(f7(x4261,x4262),x4261,x4262),f3(x4262)) % 1.21/1.27 [427]~P15(x4272)+E(f9(f7(x4271,x4272),x4271,x4272),f3(x4272)) % 1.21/1.27 [480]E(x4801,x4802)+~E(f9(x4801,f7(x4802,a1),a1),f3(a1)) % 1.21/1.27 [499]~P33(x4992)+P4(f7(f8(x4991,x4992),x4992),f3(x4992),x4992) % 1.21/1.27 [541]~P12(x5412)+E(f11(f8(x5411,x5412),f8(x5411,x5412),x5412),f11(x5411,x5411,x5412)) % 1.21/1.27 [543]~P53(x5432)+E(f11(f7(x5431,x5432),f7(x5431,x5432),x5432),f11(x5431,x5431,x5432)) % 1.21/1.27 [687]E(x6871,f3(a1))+~E(f11(x6872,x6872,a1),f7(f11(x6871,x6871,a1),a1)) % 1.21/1.27 [688]E(x6881,f3(a1))+~E(f11(x6881,x6881,a1),f7(f11(x6882,x6882,a1),a1)) % 1.21/1.27 [705]~P5(x7052,x7051,a1)+P5(f3(a1),f9(x7051,f7(x7052,a1),a1),a1) % 1.21/1.27 [836]P5(x8361,x8362,a1)+~P5(f3(a1),f9(x8362,f7(x8361,a1),a1),a1) % 1.21/1.27 [850]E(x8501,f3(a1))+~E(f9(f11(x8502,x8502,a1),f11(x8501,x8501,a1),a1),f3(a1)) % 1.21/1.27 [851]E(x8511,f3(a1))+~E(f9(f11(x8511,x8511,a1),f11(x8512,x8512,a1),a1),f3(a1)) % 1.21/1.27 [962]E(x9621,f3(a1))+P5(f3(a1),f9(f11(x9622,x9622,a1),f11(x9621,x9621,a1),a1),a1) % 1.21/1.27 [963]E(x9631,f3(a1))+P5(f3(a1),f9(f11(x9631,x9631,a1),f11(x9632,x9632,a1),a1),a1) % 1.21/1.27 [411]~P48(x4111)+E(f17(f3(f27(x4111)),x4112,x4111),f3(x4111)) % 1.21/1.27 [412]~P53(x4121)+E(f17(f3(f27(x4121)),x4122,x4121),f3(x4121)) % 1.21/1.27 [417]~P48(x4172)+E(f23(x4171,f3(f27(x4172)),x4172),f3(f27(x4172))) % 1.21/1.27 [418]~P53(x4182)+E(f23(x4181,f3(f27(x4182)),x4182),f3(f27(x4182))) % 1.21/1.27 [419]~P48(x4191)+E(f22(f3(f27(x4191)),x4192,x4191),f3(f27(x4191))) % 1.21/1.27 [420]~P48(x4201)+E(f24(f3(f27(x4201)),x4202,x4201),f3(f27(x4201))) % 1.21/1.27 [458]~P1(x4583)+E(f13(x4581,x4582,x4583),f13(x4582,x4581,x4583)) % 1.21/1.27 [459]~P8(x4593)+E(f13(x4591,x4592,x4593),f13(x4592,x4591,x4593)) % 1.21/1.27 [461]~P47(x4613)+E(f11(x4611,x4612,x4613),f11(x4612,x4611,x4613)) % 1.21/1.27 [463]~P47(x4633)+E(f9(x4631,x4632,x4633),f9(x4632,x4631,x4633)) % 1.21/1.27 [464]~P16(x4643)+E(f9(x4641,x4642,x4643),f9(x4642,x4641,x4643)) % 1.21/1.27 [465]~P34(x4653)+E(f19(x4651,x4652,x4653),f19(x4652,x4651,x4653)) % 1.21/1.27 [466]~P34(x4663)+E(f21(x4661,x4662,x4663),f21(x4662,x4661,x4663)) % 1.21/1.27 [544]~P34(x5443)+P4(x5441,f19(x5442,x5441,x5443),x5443) % 1.21/1.27 [545]~P34(x5453)+P4(x5451,f19(x5451,x5452,x5453),x5453) % 1.21/1.27 [546]~P1(x5463)+P4(f13(x5461,x5462,x5463),x5462,x5463) % 1.21/1.27 [547]~P8(x5473)+P4(f13(x5471,x5472,x5473),x5472,x5473) % 1.21/1.27 [548]~P1(x5483)+P4(f13(x5481,x5482,x5483),x5481,x5483) % 1.21/1.27 [549]~P8(x5493)+P4(f13(x5491,x5492,x5493),x5491,x5493) % 1.21/1.27 [550]~P34(x5503)+P4(f21(x5501,x5502,x5503),x5502,x5503) % 1.21/1.27 [551]~P34(x5513)+P4(f21(x5511,x5512,x5513),x5511,x5513) % 1.21/1.27 [789]~P4(x7892,x7893,a1)+P4(f9(x7891,x7892,a1),f9(x7891,x7893,a1),a1) % 1.21/1.27 [491]~P10(x4913)+E(f13(x4911,f7(x4912,x4913),x4913),f10(x4911,x4912,x4913)) % 1.21/1.27 [492]~P14(x4923)+E(f9(x4921,f7(x4922,x4923),x4923),f10(x4921,x4922,x4923)) % 1.21/1.27 [494]~P15(x4943)+E(f9(x4941,f7(x4942,x4943),x4943),f10(x4941,x4942,x4943)) % 1.21/1.27 [495]~P9(x4953)+E(f9(x4951,f7(x4952,x4953),x4953),f10(x4951,x4952,x4953)) % 1.21/1.27 [496]~P14(x4963)+E(f10(x4961,f7(x4962,x4963),x4963),f9(x4961,x4962,x4963)) % 1.21/1.27 [540]~P65(x5402)+E(f11(f7(x5401,x5402),x5403,x5402),f11(x5401,f7(x5403,x5402),x5402)) % 1.21/1.27 [542]~P65(x5422)+E(f11(f7(x5421,x5422),f7(x5423,x5422),x5422),f11(x5421,x5423,x5422)) % 1.21/1.27 [552]~P34(x5523)+E(f19(x5521,f21(x5521,x5522,x5523),x5523),x5521) % 1.21/1.27 [553]~P34(x5533)+E(f21(x5531,f19(x5531,x5532,x5533),x5533),x5531) % 1.21/1.27 [554]~P14(x5543)+E(f9(f10(x5541,x5542,x5543),x5542,x5543),x5541) % 1.21/1.27 [555]~P14(x5553)+E(f10(f9(x5551,x5552,x5553),x5552,x5553),x5551) % 1.21/1.27 [581]~P15(x5813)+E(f7(f10(x5811,x5812,x5813),x5813),f10(x5812,x5811,x5813)) % 1.21/1.27 [604]~P15(x6042)+E(f9(f7(x6041,x6042),f9(x6043,x6041,x6042),x6042),x6043) % 1.21/1.27 [605]~P14(x6052)+E(f9(f7(x6051,x6052),f9(x6051,x6053,x6052),x6052),x6053) % 1.21/1.27 [615]~P45(x6153)+E(f15(f16(x6151,x6152,x6153),x6153),f16(f15(x6151,x6153),x6152,a1)) % 1.21/1.27 [616]~P65(x6163)+E(f11(x6161,f7(x6162,x6163),x6163),f7(f11(x6161,x6162,x6163),x6163)) % 1.21/1.27 [617]~P12(x6172)+E(f16(f8(x6171,x6172),x6173,x6172),f8(f16(x6171,x6173,x6172),x6172)) % 1.21/1.27 [618]~P65(x6182)+E(f11(f7(x6181,x6182),x6183,x6182),f7(f11(x6181,x6183,x6182),x6182)) % 1.21/1.27 [620]~P43(x6203)+E(f11(x6201,f7(x6202,x6203),x6203),f7(f11(x6201,x6202,x6203),x6203)) % 1.21/1.27 [622]~P43(x6222)+E(f11(f7(x6221,x6222),x6223,x6222),f7(f11(x6221,x6223,x6222),x6222)) % 1.21/1.27 [637]~P1(x6373)+E(f13(x6371,f13(x6371,x6372,x6373),x6373),f13(x6371,x6372,x6373)) % 1.21/1.27 [638]~P8(x6383)+E(f13(x6381,f13(x6381,x6382,x6383),x6383),f13(x6381,x6382,x6383)) % 1.21/1.27 [639]~P19(x6393)+E(f11(x6391,f11(x6391,x6392,x6393),x6393),f11(x6391,x6392,x6393)) % 1.21/1.27 [640]~P34(x6403)+E(f19(x6401,f19(x6401,x6402,x6403),x6403),f19(x6401,x6402,x6403)) % 1.21/1.27 [641]~P34(x6413)+E(f21(x6411,f21(x6411,x6412,x6413),x6413),f21(x6411,x6412,x6413)) % 1.21/1.27 [643]~P12(x6431)+P4(f3(x6431),f16(f8(x6432,x6431),x6433,x6431),x6431) % 1.21/1.27 [646]~P45(x6462)+E(f11(f15(x6461,x6462),f15(x6463,x6462),a1),f15(f11(x6461,x6463,x6462),x6462)) % 1.21/1.27 [647]~P12(x6472)+E(f11(f8(x6471,x6472),f8(x6473,x6472),x6472),f8(f11(x6471,x6473,x6472),x6472)) % 1.21/1.27 [648]~P14(x6482)+E(f9(f7(x6481,x6482),f7(x6483,x6482),x6482),f7(f9(x6483,x6481,x6482),x6482)) % 1.21/1.27 [649]~P15(x6492)+E(f9(f7(x6491,x6492),f7(x6493,x6492),x6492),f7(f9(x6491,x6493,x6492),x6492)) % 1.21/1.27 [650]~P15(x6502)+E(f10(f7(x6501,x6502),f7(x6503,x6502),x6502),f7(f10(x6501,x6503,x6502),x6502)) % 1.21/1.27 [662]~P33(x6623)+E(f8(f10(x6621,x6622,x6623),x6623),f8(f10(x6622,x6621,x6623),x6623)) % 1.21/1.27 [663]~P42(x6633)+E(f15(f10(x6631,x6632,x6633),x6633),f15(f10(x6632,x6631,x6633),x6633)) % 1.21/1.27 [759]~P31(x7593)+E(f11(f16(x7591,x7592,x7593),x7591,x7593),f11(x7591,f16(x7591,x7592,x7593),x7593)) % 1.21/1.27 [860]~P4(f15(x8602,a2),x8603,a1)+P4(f15(f17(x8601,x8602,a2),a2),f28(x8601,x8603),a1) % 1.21/1.27 [903]~P46(x9033)+P4(f15(f16(x9031,x9032,x9033),x9033),f16(f15(x9031,x9033),x9032,a1),a1) % 1.21/1.27 [933]~P43(x9333)+P4(f15(f11(x9331,x9332,x9333),x9333),f11(f15(x9331,x9333),f15(x9332,x9333),a1),a1) % 1.21/1.27 [934]~P42(x9343)+P4(f15(f9(x9341,x9342,x9343),x9343),f9(f15(x9341,x9343),f15(x9342,x9343),a1),a1) % 1.21/1.27 [935]~P42(x9353)+P4(f15(f10(x9351,x9352,x9353),x9353),f9(f15(x9351,x9353),f15(x9352,x9353),a1),a1) % 1.21/1.27 [936]~P42(x9362)+P4(f10(f15(x9361,x9362),f15(x9363,x9362),a1),f15(f9(x9361,x9363,x9362),x9362),a1) % 1.21/1.27 [937]~P42(x9372)+P4(f10(f15(x9371,x9372),f15(x9373,x9372),a1),f15(f10(x9371,x9373,x9372),x9372),a1) % 1.21/1.27 [939]~P54(x9393)+P4(f8(f11(x9391,x9392,x9393),x9393),f11(f8(x9391,x9393),f8(x9392,x9393),x9393),x9393) % 1.21/1.27 [940]~P33(x9403)+P4(f8(f9(x9401,x9402,x9403),x9403),f9(f8(x9401,x9403),f8(x9402,x9403),x9403),x9403) % 1.21/1.27 [941]~P33(x9413)+P4(f8(f10(x9411,x9412,x9413),x9413),f9(f8(x9411,x9413),f8(x9412,x9413),x9413),x9413) % 1.21/1.27 [942]~P33(x9422)+P4(f10(f8(x9421,x9422),f8(x9423,x9422),x9422),f8(f10(x9421,x9423,x9422),x9422),x9422) % 1.21/1.27 [975]~P59(x9751)+P4(f3(x9751),f9(f11(x9752,x9752,x9751),f11(x9753,x9753,x9751),x9751),x9751) % 1.21/1.27 [991]~P48(x9913)+E(f9(x9911,f23(x9912,f24(x9911,x9912,x9913),x9913),f27(x9913)),f18(f17(x9911,x9912,x9913),f24(x9911,x9912,x9913),x9913)) % 1.21/1.27 [1004]~P59(x10041)+~P5(f9(f11(x10042,x10042,x10041),f11(x10043,x10043,x10041),x10041),f3(x10041),x10041) % 1.21/1.27 [636]~P14(x6362)+E(f9(x6361,f9(f7(x6361,x6362),x6363,x6362),x6362),x6363) % 1.21/1.27 [708]~P12(x7082)+E(f8(f16(f7(x7081,x7082),x7083,x7082),x7082),f8(f16(x7081,x7083,x7082),x7082)) % 1.21/1.27 [777]~P33(x7772)+E(f8(f9(f8(x7771,x7772),f8(x7773,x7772),x7772),x7772),f9(f8(x7771,x7772),f8(x7773,x7772),x7772)) % 1.21/1.27 [993]~P4(f15(x9933,a2),x9932,a1)+P4(f15(f17(x9931,f33(x9931,x9932),a2),a2),f15(f17(x9931,x9933,a2),a2),a1) % 1.21/1.27 [994]~P42(x9942)+P4(f8(f10(f15(x9941,x9942),f15(x9943,x9942),a1),a1),f15(f10(x9941,x9943,x9942),x9942),a1) % 1.21/1.27 [995]~P33(x9952)+P4(f8(f10(f8(x9951,x9952),f8(x9953,x9952),x9952),x9952),f8(f10(x9951,x9953,x9952),x9952),x9952) % 1.21/1.27 [742]~P1(x7424)+E(f13(x7421,f13(x7422,x7423,x7424),x7424),f13(x7422,f13(x7421,x7423,x7424),x7424)) % 1.21/1.27 [743]~P8(x7434)+E(f13(x7431,f13(x7432,x7433,x7434),x7434),f13(x7432,f13(x7431,x7433,x7434),x7434)) % 1.21/1.27 [744]~P47(x7444)+E(f11(x7441,f11(x7442,x7443,x7444),x7444),f11(x7442,f11(x7441,x7443,x7444),x7444)) % 1.21/1.27 [745]~P47(x7454)+E(f9(x7451,f9(x7452,x7453,x7454),x7454),f9(x7452,f9(x7451,x7453,x7454),x7454)) % 1.21/1.27 [746]~P15(x7464)+E(f9(x7461,f9(x7462,x7463,x7464),x7464),f9(x7462,f9(x7461,x7463,x7464),x7464)) % 1.21/1.27 [747]~P16(x7474)+E(f9(x7471,f9(x7472,x7473,x7474),x7474),f9(x7472,f9(x7471,x7473,x7474),x7474)) % 1.21/1.27 [748]~P34(x7484)+E(f19(x7481,f19(x7482,x7483,x7484),x7484),f19(x7482,f19(x7481,x7483,x7484),x7484)) % 1.21/1.27 [749]~P34(x7494)+E(f21(x7491,f21(x7492,x7493,x7494),x7494),f21(x7492,f21(x7491,x7493,x7494),x7494)) % 1.21/1.27 [754]~P48(x7543)+E(f23(f11(x7541,x7542,x7543),x7544,x7543),f23(x7541,f23(x7542,x7544,x7543),x7543)) % 1.21/1.27 [755]~P1(x7553)+E(f13(f13(x7551,x7552,x7553),x7554,x7553),f13(x7551,f13(x7552,x7554,x7553),x7553)) % 1.21/1.27 [756]~P8(x7563)+E(f13(f13(x7561,x7562,x7563),x7564,x7563),f13(x7561,f13(x7562,x7564,x7563),x7563)) % 1.21/1.27 [757]~P47(x7573)+E(f11(f11(x7571,x7572,x7573),x7574,x7573),f11(x7571,f11(x7572,x7574,x7573),x7573)) % 1.21/1.27 [758]~P17(x7583)+E(f11(f11(x7581,x7582,x7583),x7584,x7583),f11(x7581,f11(x7582,x7584,x7583),x7583)) % 1.21/1.27 [760]~P47(x7603)+E(f9(f9(x7601,x7602,x7603),x7604,x7603),f9(x7601,f9(x7602,x7604,x7603),x7603)) % 1.21/1.27 [761]~P16(x7613)+E(f9(f9(x7611,x7612,x7613),x7614,x7613),f9(x7611,f9(x7612,x7614,x7613),x7613)) % 1.21/1.27 [762]~P18(x7623)+E(f9(f9(x7621,x7622,x7623),x7624,x7623),f9(x7621,f9(x7622,x7624,x7623),x7623)) % 1.21/1.27 [763]~P34(x7633)+E(f19(f19(x7631,x7632,x7633),x7634,x7633),f19(x7631,f19(x7632,x7634,x7633),x7633)) % 1.21/1.27 [764]~P34(x7643)+E(f21(f21(x7641,x7642,x7643),x7644,x7643),f21(x7641,f21(x7642,x7644,x7643),x7643)) % 1.21/1.27 [765]~P48(x7653)+E(f17(f23(x7651,x7652,x7653),x7654,x7653),f11(x7651,f17(x7652,x7654,x7653),x7653)) % 1.21/1.27 [766]~P48(x7663)+E(f17(f22(x7661,x7662,x7663),x7664,x7663),f17(x7661,f17(x7662,x7664,x7663),x7663)) % 1.21/1.27 [767]~P47(x7673)+E(f11(f11(x7671,x7672,x7673),x7674,x7673),f11(f11(x7671,x7674,x7673),x7672,x7673)) % 1.21/1.27 [768]~P47(x7683)+E(f9(f9(x7681,x7682,x7683),x7684,x7683),f9(f9(x7681,x7684,x7683),x7682,x7683)) % 1.21/1.27 [865]~P47(x8653)+E(f9(f11(x8651,x8652,x8653),f11(x8651,x8654,x8653),x8653),f11(x8651,f9(x8652,x8654,x8653),x8653)) % 1.21/1.27 [867]~P43(x8673)+E(f9(f11(x8671,x8672,x8673),f11(x8671,x8674,x8673),x8673),f11(x8671,f9(x8672,x8674,x8673),x8673)) % 1.21/1.27 [869]~P43(x8693)+E(f10(f11(x8691,x8692,x8693),f11(x8691,x8694,x8693),x8693),f11(x8691,f10(x8692,x8694,x8693),x8693)) % 1.21/1.27 [870]~P13(x8703)+E(f13(f9(x8701,x8702,x8703),f9(x8701,x8704,x8703),x8703),f9(x8701,f13(x8702,x8704,x8703),x8703)) % 1.21/1.27 [871]~P30(x8713)+E(f13(f9(x8711,x8712,x8713),f9(x8711,x8714,x8713),x8713),f9(x8711,f13(x8712,x8714,x8713),x8713)) % 1.21/1.27 [872]~P34(x8723)+E(f21(f19(x8721,x8722,x8723),f19(x8721,x8724,x8723),x8723),f19(x8721,f21(x8722,x8724,x8723),x8723)) % 1.21/1.27 [873]~P34(x8733)+E(f19(f21(x8731,x8732,x8733),f21(x8731,x8734,x8733),x8733),f21(x8731,f19(x8732,x8734,x8733),x8733)) % 1.21/1.27 [874]~P48(x8743)+E(f18(f11(x8741,x8742,x8743),f23(x8741,x8744,x8743),x8743),f23(x8741,f18(x8742,x8744,x8743),x8743)) % 1.21/1.27 [877]~P43(x8773)+E(f9(f11(x8771,x8772,x8773),f11(x8774,x8772,x8773),x8773),f11(f9(x8771,x8774,x8773),x8772,x8773)) % 1.21/1.27 [878]~P50(x8783)+E(f9(f11(x8781,x8782,x8783),f11(x8784,x8782,x8783),x8783),f11(f9(x8781,x8784,x8783),x8782,x8783)) % 1.21/1.27 [880]~P43(x8803)+E(f10(f11(x8801,x8802,x8803),f11(x8804,x8802,x8803),x8803),f11(f10(x8801,x8804,x8803),x8802,x8803)) % 1.21/1.27 [881]~P13(x8813)+E(f13(f9(x8811,x8812,x8813),f9(x8814,x8812,x8813),x8813),f9(f13(x8811,x8814,x8813),x8812,x8813)) % 1.21/1.27 [882]~P30(x8823)+E(f13(f9(x8821,x8822,x8823),f9(x8824,x8822,x8823),x8823),f9(f13(x8821,x8824,x8823),x8822,x8823)) % 1.21/1.27 [883]~P36(x8833)+E(f19(f9(x8831,x8832,x8833),f9(x8834,x8832,x8833),x8833),f9(f19(x8831,x8834,x8833),x8832,x8833)) % 1.21/1.27 [884]~P36(x8843)+E(f21(f9(x8841,x8842,x8843),f9(x8844,x8842,x8843),x8843),f9(f21(x8841,x8844,x8843),x8842,x8843)) % 1.21/1.27 [885]~P47(x8853)+E(f11(f16(x8851,x8852,x8853),f16(x8854,x8852,x8853),x8853),f16(f11(x8851,x8854,x8853),x8852,x8853)) % 1.21/1.27 [886]~P23(x8863)+E(f11(f16(x8861,x8862,x8863),f16(x8864,x8862,x8863),x8863),f16(f11(x8861,x8864,x8863),x8862,x8863)) % 1.21/1.27 [887]~P34(x8873)+E(f21(f19(x8871,x8872,x8873),f19(x8874,x8872,x8873),x8873),f19(f21(x8871,x8874,x8873),x8872,x8873)) % 1.21/1.27 [888]~P34(x8883)+E(f19(f21(x8881,x8882,x8883),f21(x8884,x8882,x8883),x8883),f21(f19(x8881,x8884,x8883),x8882,x8883)) % 1.21/1.27 [889]~P27(x8893)+E(f19(f10(x8891,x8892,x8893),f10(x8894,x8892,x8893),x8893),f10(f19(x8891,x8894,x8893),x8892,x8893)) % 1.21/1.27 [890]~P27(x8903)+E(f21(f10(x8901,x8902,x8903),f10(x8904,x8902,x8903),x8903),f10(f21(x8901,x8904,x8903),x8902,x8903)) % 1.21/1.27 [891]~P48(x8913)+E(f24(f18(x8911,x8912,x8913),x8914,x8913),f18(f17(x8912,x8914,x8913),f24(x8912,x8914,x8913),x8913)) % 1.21/1.27 [892]~P47(x8923)+E(f9(f11(x8921,x8922,x8923),f11(x8924,x8922,x8923),x8923),f11(f9(x8921,x8924,x8923),x8922,x8923)) % 1.21/1.27 [895]~P48(x8953)+E(f9(f23(x8951,x8952,x8953),f23(x8954,x8952,x8953),f27(x8953)),f23(f9(x8951,x8954,x8953),x8952,x8953)) % 1.21/1.27 [1002]~P34(x10024)+P4(f19(x10021,f21(x10022,x10023,x10024),x10024),f21(f19(x10021,x10022,x10024),f19(x10021,x10023,x10024),x10024),x10024) % 1.21/1.27 [1003]~P34(x10033)+P4(f19(f21(x10031,x10032,x10033),f21(x10031,x10034,x10033),x10033),f21(x10031,f19(x10032,x10034,x10033),x10033),x10033) % 1.21/1.27 [901]~P48(x9013)+E(f9(f17(x9011,x9012,x9013),f17(x9014,x9012,x9013),x9013),f17(f9(x9011,x9014,f27(x9013)),x9012,x9013)) % 1.21/1.27 [902]~P48(x9023)+E(f9(f23(x9021,x9022,x9023),f23(x9021,x9024,x9023),f27(x9023)),f23(x9021,f9(x9022,x9024,f27(x9023)),x9023)) % 1.21/1.27 [946]~P48(x9464)+E(f9(x9461,f11(x9462,f17(x9463,x9462,x9464),x9464),x9464),f17(f18(x9461,x9463,x9464),x9462,x9464)) % 1.21/1.27 [947]~P47(x9473)+E(f11(f11(x9471,x9472,x9473),f11(x9474,x9475,x9473),x9473),f11(f11(x9471,x9474,x9473),f11(x9472,x9475,x9473),x9473)) % 1.21/1.27 [948]~P47(x9483)+E(f9(f9(x9481,x9482,x9483),f9(x9484,x9485,x9483),x9483),f9(f9(x9481,x9484,x9483),f9(x9482,x9485,x9483),x9483)) % 1.21/1.27 [949]~P15(x9493)+E(f10(f9(x9491,x9492,x9493),f9(x9494,x9495,x9493),x9493),f9(f10(x9491,x9494,x9493),f10(x9492,x9495,x9493),x9493)) % 1.21/1.27 [961]~P16(x9613)+E(f18(f9(x9611,x9612,x9613),f9(x9614,x9615,f27(x9613)),x9613),f9(f18(x9611,x9614,x9613),f18(x9612,x9615,x9613),f27(x9613))) % 1.21/1.27 [999]~P70(x9993)+E(f9(f11(x9991,x9992,x9993),f9(f11(x9994,x9992,x9993),x9995,x9993),x9993),f9(f11(f9(x9991,x9994,x9993),x9992,x9993),x9995,x9993)) % 1.21/1.27 [1024]~P42(x10243)+P4(f15(f10(f9(x10241,x10242,x10243),f9(x10244,x10245,x10243),x10243),x10243),f9(f15(f10(x10241,x10244,x10243),x10243),f15(f10(x10242,x10245,x10243),x10243),a1),a1) % 1.21/1.27 [1025]~P33(x10253)+P4(f8(f10(f9(x10251,x10252,x10253),f9(x10254,x10255,x10253),x10253),x10253),f9(f8(f10(x10251,x10254,x10253),x10253),f8(f10(x10252,x10255,x10253),x10253),x10253),x10253) % 1.21/1.27 [1026]~P43(x10263)+E(f9(f9(f11(f10(x10261,x10262,x10263),f10(x10264,x10265,x10263),x10263),f11(f10(x10261,x10262,x10263),x10265,x10263),x10263),f11(x10262,f10(x10264,x10265,x10263),x10263),x10263),f10(f11(x10261,x10264,x10263),f11(x10262,x10265,x10263),x10263)) % 1.21/1.27 [1009]~P65(x10093)+E(f9(f11(x10091,x10092,x10093),f9(f11(f10(x10094,x10091,x10093),x10092,x10093),x10095,x10093),x10093),f9(f11(x10094,x10092,x10093),x10095,x10093)) % 1.21/1.27 [344]~P2(x3441)+~P3(x3441)+P3(f27(x3441)) % 1.21/1.27 [584]~P35(x5841)+~P4(f3(x5841),f3(x5841),x5841)+E(f9(f3(x5841),f3(x5841),x5841),f3(x5841)) % 1.21/1.27 [489]E(x4891,x4892)+P5(x4891,x4892,a1)+~P4(x4891,x4892,a1) % 1.21/1.27 [556]E(x5561,x5562)+~P4(x5562,x5561,a1)+~P4(x5561,x5562,a1) % 1.21/1.27 [345]E(x3451,x3452)+~E(f5(x3451),f5(x3452))+~E(f6(x3451),f6(x3452)) % 1.21/1.27 [351]~P29(x3512)+~E(f7(x3511,x3512),x3511)+E(x3511,f3(x3512)) % 1.21/1.27 [352]~P42(x3522)+E(x3521,f3(x3522))+~E(f15(x3521,x3522),f3(a1)) % 1.21/1.27 [353]~P33(x3532)+~E(f8(x3531,x3532),f3(x3532))+E(x3531,f3(x3532)) % 1.21/1.27 [354]~P14(x3542)+~E(f7(x3541,x3542),f3(x3542))+E(x3541,f3(x3542)) % 1.21/1.27 [355]~P14(x3551)+~E(f7(x3552,x3551),f3(x3551))+E(f3(x3551),x3552) % 1.21/1.27 [357]~P71(x3572)+~P44(x3572)+~E(f25(x3571,x3572),f3(x3572)) % 1.21/1.27 [403]~P53(x4032)+~P9(x4032)+E(f10(x4031,x4031,x4032),f3(x4032)) % 1.21/1.27 [404]~P2(x4042)+~P3(x4042)+P6(x4041,x4041,f27(x4042)) % 1.21/1.27 [410]~P49(x4102)+P5(x4101,f3(x4102),x4102)+E(f8(x4101,x4102),x4101) % 1.21/1.27 [432]~P42(x4322)+E(x4321,f3(x4322))+P5(f3(a1),f15(x4321,x4322),a1) % 1.21/1.27 [435]~P33(x4352)+P5(f3(x4352),f8(x4351,x4352),x4352)+E(x4351,f3(x4352)) % 1.21/1.27 [442]~P13(x4422)+~E(f9(x4421,x4421,x4422),f3(x4422))+E(x4421,f3(x4422)) % 1.21/1.27 [472]~P33(x4722)+~P5(f3(x4722),x4721,x4722)+E(f8(x4721,x4722),x4721) % 1.21/1.27 [473]~P33(x4732)+~P4(f3(x4732),x4731,x4732)+E(f8(x4731,x4732),x4731) % 1.21/1.27 [483]~P33(x4832)+~P5(x4831,f3(x4832),x4832)+E(f8(x4831,x4832),f7(x4831,x4832)) % 1.21/1.27 [484]~P33(x4842)+~P4(x4841,f3(x4842),x4842)+E(f8(x4841,x4842),f7(x4841,x4842)) % 1.21/1.27 [485]~P49(x4852)+~P5(x4851,f3(x4852),x4852)+E(f8(x4851,x4852),f7(x4851,x4852)) % 1.21/1.27 [490]~P42(x4902)+E(x4901,f3(x4902))+~P4(f15(x4901,x4902),f3(a1),a1) % 1.21/1.27 [508]~P33(x5082)+~P4(f8(x5081,x5082),f3(x5082),x5082)+E(x5081,f3(x5082)) % 1.21/1.27 [585]~P12(x5852)+~P5(x5851,f3(x5852),x5852)+P5(x5851,f7(x5851,x5852),x5852) % 1.21/1.27 [586]~P13(x5862)+~P4(x5861,f3(x5862),x5862)+P4(x5861,f7(x5861,x5862),x5862) % 1.21/1.27 [587]~P29(x5872)+~P4(x5871,f3(x5872),x5872)+P4(x5871,f7(x5871,x5872),x5872) % 1.21/1.27 [588]~P13(x5882)+~P4(f3(x5882),x5881,x5882)+P4(f7(x5881,x5882),x5881,x5882) % 1.21/1.27 [589]~P29(x5892)+~P4(f3(x5892),x5891,x5892)+P4(f7(x5891,x5892),x5891,x5892) % 1.21/1.27 [595]~P27(x5951)+~P5(x5952,f3(x5951),x5951)+P5(f3(x5951),f7(x5952,x5951),x5951) % 1.21/1.27 [596]~P27(x5961)+~P4(x5962,f3(x5961),x5961)+P4(f3(x5961),f7(x5962,x5961),x5961) % 1.21/1.27 [597]~P27(x5972)+~P5(f3(x5972),x5971,x5972)+P5(f7(x5971,x5972),f3(x5972),x5972) % 1.21/1.27 [598]~P27(x5982)+~P4(f3(x5982),x5981,x5982)+P4(f7(x5981,x5982),f3(x5982),x5982) % 1.21/1.27 [599]~P12(x5992)+~P5(x5991,f7(x5991,x5992),x5992)+P5(x5991,f3(x5992),x5992) % 1.21/1.27 [600]~P13(x6002)+~P4(x6001,f7(x6001,x6002),x6002)+P4(x6001,f3(x6002),x6002) % 1.21/1.27 [601]~P29(x6012)+~P4(x6011,f7(x6011,x6012),x6012)+P4(x6011,f3(x6012),x6012) % 1.21/1.27 [602]~P13(x6021)+~P4(f7(x6022,x6021),x6022,x6021)+P4(f3(x6021),x6022,x6021) % 1.21/1.27 [603]~P29(x6031)+~P4(f7(x6032,x6031),x6032,x6031)+P4(f3(x6031),x6032,x6031) % 1.21/1.27 [611]~P27(x6112)+~P5(f3(x6112),f7(x6111,x6112),x6112)+P5(x6111,f3(x6112),x6112) % 1.21/1.27 [612]~P27(x6122)+~P4(f3(x6122),f7(x6121,x6122),x6122)+P4(x6121,f3(x6122),x6122) % 1.21/1.27 [613]~P27(x6131)+~P5(f7(x6132,x6131),f3(x6131),x6131)+P5(f3(x6131),x6132,x6131) % 1.21/1.27 [614]~P27(x6141)+~P4(f7(x6142,x6141),f3(x6141),x6141)+P4(f3(x6141),x6142,x6141) % 1.21/1.27 [689]~P13(x6891)+~P5(f3(x6891),x6892,x6891)+P5(f3(x6891),f9(x6892,x6892,x6891),x6891) % 1.21/1.27 [691]~P13(x6911)+~P4(f3(x6911),x6912,x6911)+P4(f3(x6911),f9(x6912,x6912,x6911),x6911) % 1.21/1.27 [694]~P12(x6942)+~P5(x6941,f3(x6942),x6942)+P5(f9(x6941,x6941,x6942),f3(x6942),x6942) % 1.21/1.27 [695]~P13(x6952)+~P5(x6951,f3(x6952),x6952)+P5(f9(x6951,x6951,x6952),f3(x6952),x6952) % 1.21/1.27 [696]~P13(x6962)+~P4(x6961,f3(x6962),x6962)+P4(f9(x6961,x6961,x6962),f3(x6962),x6962) % 1.21/1.27 [704]~P4(x7041,x7042,a1)+~P4(f7(x7042,a1),x7041,a1)+P4(f8(x7041,a1),x7042,a1) % 1.21/1.27 [769]~P12(x7692)+~P5(f9(x7691,x7691,x7692),f3(x7692),x7692)+P5(x7691,f3(x7692),x7692) % 1.21/1.27 [771]~P13(x7712)+~P5(f9(x7711,x7711,x7712),f3(x7712),x7712)+P5(x7711,f3(x7712),x7712) % 1.21/1.27 [772]~P13(x7722)+~P4(f9(x7721,x7721,x7722),f3(x7722),x7722)+P4(x7721,f3(x7722),x7722) % 1.21/1.27 [773]~P13(x7731)+~P5(f3(x7731),f9(x7732,x7732,x7731),x7731)+P5(f3(x7731),x7732,x7731) % 1.21/1.27 [774]~P13(x7741)+~P4(f3(x7741),f9(x7742,x7742,x7741),x7741)+P4(f3(x7741),x7742,x7741) % 1.21/1.27 [776]~P5(f3(a1),x7762,a1)+~P5(f3(a1),x7761,a1)+P5(f3(a1),f11(x7761,x7762,a1),a1) % 1.21/1.27 [405]~P53(x4052)+~P9(x4052)+E(f9(x4051,f3(x4052),x4052),x4051) % 1.21/1.27 [498]~P13(x4982)+E(x4981,f3(x4982))+~E(f13(x4981,f7(x4981,x4982),x4982),f3(x4982)) % 1.21/1.27 [684]~P12(x6842)+~P5(f3(x6842),x6841,x6842)+P7(f18(x6841,f3(f27(x6842)),x6842),x6842) % 1.21/1.27 [433]~P6(x4331,x4332,x4333)+E(x4331,x4332)+~P3(x4333) % 1.21/1.27 [469]P4(x4692,x4691,x4693)+~P34(x4693)+P5(x4691,x4692,x4693) % 1.21/1.27 [471]P4(x4712,x4711,x4713)+~P34(x4713)+P4(x4711,x4712,x4713) % 1.21/1.27 [500]~P40(x5003)+~P5(x5001,x5002,x5003)+P4(x5001,x5002,x5003) % 1.21/1.27 [501]~P41(x5013)+~P5(x5011,x5012,x5013)+P4(x5011,x5012,x5013) % 1.21/1.27 [563]~P5(x5633,x5632,x5631)+~P34(x5631)+~P5(x5632,x5633,x5631) % 1.21/1.27 [565]~P4(x5653,x5652,x5651)+~P34(x5651)+~P5(x5652,x5653,x5651) % 1.21/1.27 [567]~P5(x5673,x5672,x5671)+~P40(x5671)+~P5(x5672,x5673,x5671) % 1.21/1.27 [569]~P5(x5693,x5692,x5691)+~P41(x5691)+~P5(x5692,x5693,x5691) % 1.21/1.27 [570]~P4(x5703,x5702,x5701)+~P41(x5701)+~P5(x5702,x5703,x5701) % 1.21/1.27 [635]~P4(x6351,x6353,a1)+P4(x6351,x6352,a1)+~P4(x6353,x6352,a1) % 1.21/1.27 [363]~P14(x3633)+E(x3631,x3632)+~E(f7(x3631,x3633),f7(x3632,x3633)) % 1.21/1.27 [364]~P10(x3643)+E(x3641,x3642)+~E(f7(x3641,x3643),f7(x3642,x3643)) % 1.21/1.27 [439]~P14(x4393)+E(x4391,x4392)+~E(f10(x4391,x4392,x4393),f3(x4393)) % 1.21/1.27 [440]~P15(x4403)+E(x4401,x4402)+~E(f10(x4401,x4402,x4403),f3(x4403)) % 1.21/1.27 [443]~P68(x4432)+~E(f16(x4431,x4433,x4432),f3(x4432))+E(x4431,f3(x4432)) % 1.21/1.27 [456]~P14(x4563)+~E(f9(x4561,x4562,x4563),f3(x4563))+E(x4561,f7(x4562,x4563)) % 1.21/1.27 [457]~P14(x4572)+~E(f9(x4571,x4573,x4572),f3(x4572))+E(f7(x4571,x4572),x4573) % 1.21/1.27 [502]~P1(x5023)+~P4(x5022,x5021,x5023)+E(f13(x5021,x5022,x5023),x5022) % 1.21/1.27 [503]~P1(x5033)+~P4(x5031,x5032,x5033)+E(f13(x5031,x5032,x5033),x5031) % 1.21/1.27 [504]~P34(x5043)+~P4(x5041,x5042,x5043)+E(f19(x5041,x5042,x5043),x5042) % 1.21/1.27 [505]~P34(x5053)+~P4(x5052,x5051,x5053)+E(f19(x5051,x5052,x5053),x5051) % 1.21/1.27 [506]~P34(x5063)+~P4(x5062,x5061,x5063)+E(f21(x5061,x5062,x5063),x5062) % 1.21/1.27 [507]~P34(x5073)+~P4(x5071,x5072,x5073)+E(f21(x5071,x5072,x5073),x5071) % 1.21/1.27 [513]~P1(x5133)+P4(x5131,x5132,x5133)+~E(f13(x5131,x5132,x5133),x5131) % 1.21/1.27 [514]~P34(x5143)+P4(x5141,x5142,x5143)+~E(f19(x5141,x5142,x5143),x5142) % 1.21/1.27 [515]~P34(x5153)+P4(x5151,x5152,x5153)+~E(f21(x5151,x5152,x5153),x5151) % 1.21/1.27 [530]~P12(x5303)+~P7(x5302,x5303)+P7(f18(x5301,x5302,x5303),x5303) % 1.21/1.27 [558]E(x5581,x5582)+~E(f11(x5583,x5581,a1),f11(x5583,x5582,a1))+E(x5583,f3(a1)) % 1.21/1.27 [559]E(x5591,x5592)+~E(f11(x5591,x5593,a1),f11(x5592,x5593,a1))+E(x5593,f3(a1)) % 1.21/1.27 [592]~P12(x5923)+P5(x5921,x5922,x5923)+~P5(f8(x5921,x5923),x5922,x5923) % 1.21/1.27 [593]~P33(x5933)+P4(x5931,x5932,x5933)+~P4(f8(x5931,x5933),x5932,x5933) % 1.21/1.27 [608]~P27(x6082)+~P5(x6083,x6081,x6082)+P5(f7(x6081,x6082),f7(x6083,x6082),x6082) % 1.21/1.27 [609]~P27(x6092)+~P4(x6093,x6091,x6092)+P4(f7(x6091,x6092),f7(x6093,x6092),x6092) % 1.21/1.27 [626]~P27(x6263)+~P5(x6262,f7(x6261,x6263),x6263)+P5(x6261,f7(x6262,x6263),x6263) % 1.21/1.27 [628]~P27(x6283)+~P4(x6282,f7(x6281,x6283),x6283)+P4(x6281,f7(x6282,x6283),x6283) % 1.21/1.27 [629]~P12(x6292)+~P5(f8(x6291,x6292),x6293,x6292)+P5(f7(x6291,x6292),x6293,x6292) % 1.21/1.27 [631]~P27(x6312)+~P5(f7(x6313,x6312),x6311,x6312)+P5(f7(x6311,x6312),x6313,x6312) % 1.21/1.27 [633]~P27(x6332)+~P4(f7(x6333,x6332),x6331,x6332)+P4(f7(x6331,x6332),x6333,x6332) % 1.21/1.27 [634]~P33(x6342)+~P4(f8(x6341,x6342),x6343,x6342)+P4(f7(x6341,x6342),x6343,x6342) % 1.21/1.27 [644]~P27(x6443)+P5(x6441,x6442,x6443)+~P5(f7(x6442,x6443),f7(x6441,x6443),x6443) % 1.21/1.27 [645]~P27(x6453)+P4(x6451,x6452,x6453)+~P4(f7(x6452,x6453),f7(x6451,x6453),x6453) % 1.21/1.27 [685]~P27(x6853)+~P5(x6851,x6852,x6853)+P5(f10(x6851,x6852,x6853),f3(x6853),x6853) % 1.21/1.27 [686]~P27(x6863)+~P4(x6861,x6862,x6863)+P4(f10(x6861,x6862,x6863),f3(x6863),x6863) % 1.21/1.27 [690]~P61(x6901)+~P5(f3(x6901),x6902,x6901)+P5(f3(x6901),f16(x6902,x6903,x6901),x6901) % 1.21/1.27 [692]~P12(x6921)+~P4(f3(x6921),x6922,x6921)+P4(f3(x6921),f16(x6922,x6923,x6921),x6921) % 1.21/1.27 [693]~P61(x6931)+~P4(f3(x6931),x6932,x6931)+P4(f3(x6931),f16(x6932,x6933,x6931),x6931) % 1.21/1.27 [712]~P13(x7123)+~P4(x7121,f7(x7122,x7123),x7123)+P4(f9(x7121,x7122,x7123),f3(x7123),x7123) % 1.21/1.27 [735]~P27(x7353)+P5(x7351,x7352,x7353)+~P5(f10(x7351,x7352,x7353),f3(x7353),x7353) % 1.21/1.27 [736]~P27(x7363)+P4(x7361,x7362,x7363)+~P4(f10(x7361,x7362,x7363),f3(x7363),x7363) % 1.21/1.27 [770]~P12(x7702)+~P5(f16(x7701,x7703,x7702),f3(x7702),x7702)+P5(x7701,f3(x7702),x7702) % 1.21/1.27 [791]~P13(x7913)+~P4(f9(x7911,x7912,x7913),f3(x7913),x7913)+P4(x7911,f7(x7912,x7913),x7913) % 1.21/1.27 [861]~P5(x8611,x8613,a1)+P5(f11(x8611,x8612,a1),f11(x8613,x8612,a1),a1)+~P5(f3(a1),x8612,a1) % 1.21/1.27 [862]~P5(x8622,x8623,a1)+P5(f11(x8621,x8622,a1),f11(x8621,x8623,a1),a1)+~P5(f3(a1),x8621,a1) % 1.21/1.27 [863]~P4(x8631,x8633,a1)+P4(f11(x8631,x8632,a1),f11(x8633,x8632,a1),a1)+~P5(f3(a1),x8632,a1) % 1.21/1.27 [864]~P4(x8642,x8643,a1)+P4(f11(x8641,x8642,a1),f11(x8641,x8643,a1),a1)+~P5(f3(a1),x8641,a1) % 1.21/1.27 [958]P5(x9581,x9582,a1)+~P5(f11(x9581,x9583,a1),f11(x9582,x9583,a1),a1)+~P5(f3(a1),x9583,a1) % 1.21/1.27 [959]P4(x9591,x9592,a1)+~P4(f11(x9593,x9591,a1),f11(x9593,x9592,a1),a1)+~P5(f3(a1),x9593,a1) % 1.21/1.27 [960]P4(x9601,x9602,a1)+~P4(f11(x9601,x9603,a1),f11(x9602,x9603,a1),a1)+~P5(f3(a1),x9603,a1) % 1.21/1.27 [455]~P2(x4552)+E(x4551,f3(x4552))+~E(f18(x4551,x4553,x4552),f3(f27(x4552))) % 1.21/1.27 [479]~P2(x4792)+~E(f18(x4793,x4791,x4792),f3(f27(x4792)))+E(x4791,f3(f27(x4792))) % 1.21/1.27 [660]~P71(x6602)+~P44(x6602)+E(f11(f25(x6601,x6602),f25(x6603,x6602),x6602),f25(f9(x6601,x6603,x6602),x6602)) % 1.21/1.27 [713]~P12(x7132)+~P4(f3(x7132),x7133,x7132)+E(f11(f8(x7131,x7132),x7133,x7132),f8(f11(x7131,x7133,x7132),x7132)) % 1.21/1.27 [893]~P59(x8932)+E(x8931,f3(x8932))+~E(f9(f11(x8933,x8933,x8932),f11(x8931,x8931,x8932),x8932),f3(x8932)) % 1.21/1.27 [894]~P59(x8942)+E(x8941,f3(x8942))+~E(f9(f11(x8941,x8941,x8942),f11(x8943,x8943,x8942),x8942),f3(x8942)) % 1.21/1.27 [896]E(x8961,f3(a1))+~P4(x8962,f3(a1),a1)+~P4(f8(x8961,a1),f11(x8962,f8(x8963,a1),a1),a1) % 1.21/1.27 [976]~P59(x9762)+E(x9761,f3(x9762))+P5(f3(x9762),f9(f11(x9763,x9763,x9762),f11(x9761,x9761,x9762),x9762),x9762) % 1.21/1.27 [977]~P59(x9772)+E(x9771,f3(x9772))+P5(f3(x9772),f9(f11(x9771,x9771,x9772),f11(x9773,x9773,x9772),x9772),x9772) % 1.21/1.27 [1005]~P59(x10052)+E(x10051,f3(x10052))+~P4(f9(f11(x10053,x10053,x10052),f11(x10051,x10051,x10052),x10052),f3(x10052),x10052) % 1.21/1.27 [1006]~P59(x10062)+E(x10061,f3(x10062))+~P4(f9(f11(x10061,x10061,x10062),f11(x10063,x10063,x10062),x10062),f3(x10062),x10062) % 1.21/1.27 [572]~P20(x5724)+E(x5721,x5722)+~E(f9(x5723,x5721,x5724),f9(x5723,x5722,x5724)) % 1.21/1.27 [573]~P21(x5734)+E(x5731,x5732)+~E(f9(x5733,x5731,x5734),f9(x5733,x5732,x5734)) % 1.21/1.27 [574]~P15(x5744)+E(x5741,x5742)+~E(f10(x5743,x5743,x5744),f10(x5741,x5742,x5744)) % 1.21/1.27 [575]~P21(x5754)+E(x5751,x5752)+~E(f9(x5751,x5753,x5754),f9(x5752,x5753,x5754)) % 1.21/1.27 [577]~P15(x5773)+E(x5771,x5772)+~E(f10(x5771,x5772,x5773),f10(x5774,x5774,x5773)) % 1.21/1.27 [665]~P34(x6654)+~P5(x6651,x6653,x6654)+P5(x6651,f19(x6652,x6653,x6654),x6654) % 1.21/1.27 [667]~P34(x6674)+~P5(x6671,x6672,x6674)+P5(x6671,f19(x6672,x6673,x6674),x6674) % 1.21/1.27 [669]~P34(x6694)+~P4(x6691,x6693,x6694)+P4(x6691,f19(x6692,x6693,x6694),x6694) % 1.21/1.27 [671]~P34(x6714)+~P4(x6711,x6712,x6714)+P4(x6711,f19(x6712,x6713,x6714),x6714) % 1.21/1.27 [672]~P1(x6723)+~P5(x6722,x6724,x6723)+P5(f13(x6721,x6722,x6723),x6724,x6723) % 1.21/1.27 [673]~P1(x6733)+~P5(x6731,x6734,x6733)+P5(f13(x6731,x6732,x6733),x6734,x6733) % 1.21/1.27 [675]~P34(x6753)+~P5(x6752,x6754,x6753)+P5(f21(x6751,x6752,x6753),x6754,x6753) % 1.21/1.27 [677]~P34(x6773)+~P5(x6771,x6774,x6773)+P5(f21(x6771,x6772,x6773),x6774,x6773) % 1.21/1.27 [678]~P1(x6783)+~P4(x6782,x6784,x6783)+P4(f13(x6781,x6782,x6783),x6784,x6783) % 1.21/1.27 [679]~P1(x6793)+~P4(x6791,x6794,x6793)+P4(f13(x6791,x6792,x6793),x6794,x6793) % 1.21/1.27 [681]~P34(x6813)+~P4(x6812,x6814,x6813)+P4(f21(x6811,x6812,x6813),x6814,x6813) % 1.21/1.27 [683]~P34(x6833)+~P4(x6831,x6834,x6833)+P4(f21(x6831,x6832,x6833),x6834,x6833) % 1.21/1.27 [715]~P34(x7153)+P5(x7151,x7152,x7153)+~P5(x7151,f21(x7154,x7152,x7153),x7153) % 1.21/1.27 [716]~P34(x7163)+P5(x7161,x7162,x7163)+~P5(x7161,f21(x7162,x7164,x7163),x7163) % 1.21/1.27 [718]~P1(x7183)+P4(x7181,x7182,x7183)+~P4(x7181,f13(x7184,x7182,x7183),x7183) % 1.21/1.27 [720]~P1(x7203)+P4(x7201,x7202,x7203)+~P4(x7201,f13(x7202,x7204,x7203),x7203) % 1.21/1.27 [722]~P34(x7223)+P4(x7221,x7222,x7223)+~P4(x7221,f21(x7224,x7222,x7223),x7223) % 1.21/1.27 [724]~P34(x7243)+P4(x7241,x7242,x7243)+~P4(x7241,f21(x7242,x7244,x7243),x7243) % 1.21/1.27 [725]~P34(x7253)+P5(x7251,x7252,x7253)+~P5(f19(x7254,x7251,x7253),x7252,x7253) % 1.21/1.27 [726]~P34(x7263)+P5(x7261,x7262,x7263)+~P5(f19(x7261,x7264,x7263),x7262,x7263) % 1.21/1.27 [728]~P34(x7283)+P4(x7281,x7282,x7283)+~P4(f19(x7284,x7281,x7283),x7282,x7283) % 1.21/1.27 [730]~P34(x7303)+P4(x7301,x7302,x7303)+~P4(f19(x7301,x7304,x7303),x7302,x7303) % 1.21/1.27 [796]~P36(x7963)+~P5(x7961,x7964,x7963)+P5(f9(x7961,x7962,x7963),f9(x7964,x7962,x7963),x7963) % 1.21/1.27 [797]~P38(x7973)+~P5(x7971,x7974,x7973)+P5(f9(x7971,x7972,x7973),f9(x7974,x7972,x7973),x7973) % 1.21/1.27 [798]~P36(x7983)+~P5(x7982,x7984,x7983)+P5(f9(x7981,x7982,x7983),f9(x7981,x7984,x7983),x7983) % 1.21/1.27 [799]~P38(x7993)+~P5(x7992,x7994,x7993)+P5(f9(x7991,x7992,x7993),f9(x7991,x7994,x7993),x7993) % 1.21/1.27 [800]~P36(x8003)+~P4(x8001,x8004,x8003)+P4(f9(x8001,x8002,x8003),f9(x8004,x8002,x8003),x8003) % 1.21/1.27 [801]~P37(x8013)+~P4(x8011,x8014,x8013)+P4(f9(x8011,x8012,x8013),f9(x8014,x8012,x8013),x8013) % 1.21/1.27 [802]~P36(x8023)+~P4(x8022,x8024,x8023)+P4(f9(x8021,x8022,x8023),f9(x8021,x8024,x8023),x8023) % 1.21/1.27 [803]~P37(x8033)+~P4(x8032,x8034,x8033)+P4(f9(x8031,x8032,x8033),f9(x8031,x8034,x8033),x8033) % 1.21/1.27 [927]~P36(x9273)+P5(x9271,x9272,x9273)+~P5(f9(x9274,x9271,x9273),f9(x9274,x9272,x9273),x9273) % 1.21/1.27 [928]~P36(x9283)+P5(x9281,x9282,x9283)+~P5(f9(x9281,x9284,x9283),f9(x9282,x9284,x9283),x9283) % 1.21/1.27 [929]~P36(x9293)+P4(x9291,x9292,x9293)+~P4(f9(x9294,x9291,x9293),f9(x9294,x9292,x9293),x9293) % 1.21/1.27 [930]~P36(x9303)+P4(x9301,x9302,x9303)+~P4(f9(x9301,x9304,x9303),f9(x9302,x9304,x9303),x9303) % 1.21/1.27 [594]~P48(x5942)+~E(f23(x5943,x5941,x5942),f18(x5944,x5941,x5942))+E(x5941,f3(f27(x5942))) % 1.21/1.27 [699]~P15(x6993)+E(x6991,f7(x6992,x6993))+~E(f9(x6991,f9(x6994,x6992,x6993),x6993),x6994) % 1.21/1.27 [923]~P48(x9232)+~E(f9(f23(x9233,x9231,x9232),f18(x9234,x9231,x9232),f27(x9232)),f3(f27(x9232)))+E(x9231,f3(f27(x9232))) % 1.21/1.27 [926]~P28(x9264)+~P4(f9(x9261,x9263,x9264),x9262,x9264)+P4(x9261,f9(x9262,f8(x9263,x9264),x9264),x9264) % 1.21/1.27 [955]~P53(x9553)+~P9(x9553)+E(f9(f11(x9551,x9552,x9553),f11(x9551,x9554,x9553),x9553),f9(f11(x9551,x9554,x9553),f11(x9551,x9552,x9553),x9553)) % 1.21/1.27 [978]~P12(x9784)+P5(x9781,f9(x9782,x9783,x9784),x9784)+~P5(f8(f10(x9781,x9782,x9784),x9784),x9783,x9784) % 1.21/1.27 [979]~P12(x9793)+P5(f10(x9791,x9792,x9793),x9794,x9793)+~P5(f8(f10(x9794,x9791,x9793),x9793),x9792,x9793) % 1.21/1.27 [1007]~P4(f34(x10073,x10072,x10071),f15(x10074,a2),a1)+E(x10071,f3(f27(a2)))+P4(x10072,f15(f17(f18(x10073,x10071,a2),x10074,a2),a2),a1) % 1.21/1.27 [571]~P2(x5714)+E(x5711,x5712)+~E(f18(x5713,x5711,x5714),f18(x5715,x5712,x5714)) % 1.21/1.27 [576]~P2(x5764)+E(x5761,x5762)+~E(f18(x5761,x5763,x5764),f18(x5762,x5765,x5764)) % 1.21/1.27 [847]~P15(x8473)+E(f9(x8471,x8472,x8473),x8474)+~E(f9(x8471,f9(x8475,x8472,x8473),x8473),f9(x8475,x8474,x8473)) % 1.21/1.27 [848]~P48(x8484)+E(x8481,f17(x8482,x8483,x8484))+~E(f9(x8482,f23(x8483,x8485,x8484),f27(x8484)),f18(x8481,x8485,x8484)) % 1.21/1.27 [849]~P48(x8494)+E(x8491,f24(x8492,x8493,x8494))+~E(f9(x8492,f23(x8493,x8491,x8494),f27(x8494)),f18(x8495,x8491,x8494)) % 1.21/1.27 [1000]~P65(x10004)+~E(f9(f11(x10003,x10005,x10004),x10001,x10004),f9(f11(x10002,x10005,x10004),x10006,x10004))+E(x10001,f9(f11(f10(x10002,x10003,x10004),x10005,x10004),x10006,x10004)) % 1.21/1.27 [1001]~P65(x10013)+~E(f9(f11(x10011,x10014,x10013),x10015,x10013),f9(f11(x10012,x10014,x10013),x10016,x10013))+E(f9(f11(f10(x10011,x10012,x10013),x10014,x10013),x10015,x10013),x10016) % 1.21/1.27 [1016]~P63(x10164)+~P5(f9(f11(x10163,x10165,x10164),x10161,x10164),f9(f11(x10162,x10165,x10164),x10166,x10164),x10164)+P5(x10161,f9(f11(f10(x10162,x10163,x10164),x10165,x10164),x10166,x10164),x10164) % 1.21/1.27 [1017]~P63(x10174)+~P4(f9(f11(x10173,x10175,x10174),x10171,x10174),f9(f11(x10172,x10175,x10174),x10176,x10174),x10174)+P4(x10171,f9(f11(f10(x10172,x10173,x10174),x10175,x10174),x10176,x10174),x10174) % 1.21/1.27 [1018]~P63(x10183)+~P5(f9(f11(x10181,x10184,x10183),x10185,x10183),f9(f11(x10182,x10184,x10183),x10186,x10183),x10183)+P5(f9(f11(f10(x10181,x10182,x10183),x10184,x10183),x10185,x10183),x10186,x10183) % 1.21/1.27 [1019]~P63(x10193)+~P4(f9(f11(x10191,x10194,x10193),x10195,x10193),f9(f11(x10192,x10194,x10193),x10196,x10193),x10193)+P4(f9(f11(f10(x10191,x10192,x10193),x10194,x10193),x10195,x10193),x10196,x10193) % 1.21/1.27 [1020]~P63(x10203)+P5(f9(f11(x10201,x10202,x10203),x10204,x10203),f9(f11(x10205,x10202,x10203),x10206,x10203),x10203)+~P5(x10204,f9(f11(f10(x10205,x10201,x10203),x10202,x10203),x10206,x10203),x10203) % 1.21/1.27 [1021]~P63(x10213)+P4(f9(f11(x10211,x10212,x10213),x10214,x10213),f9(f11(x10215,x10212,x10213),x10216,x10213),x10213)+~P4(x10214,f9(f11(f10(x10215,x10211,x10213),x10212,x10213),x10216,x10213),x10213) % 1.21/1.27 [1022]~P63(x10223)+P5(f9(f11(x10221,x10222,x10223),x10224,x10223),f9(f11(x10225,x10222,x10223),x10226,x10223),x10223)+~P5(f9(f11(f10(x10221,x10225,x10223),x10222,x10223),x10224,x10223),x10226,x10223) % 1.21/1.27 [1023]~P63(x10233)+P4(f9(f11(x10231,x10232,x10233),x10234,x10233),f9(f11(x10235,x10232,x10233),x10236,x10233),x10233)+~P4(f9(f11(f10(x10231,x10235,x10233),x10232,x10233),x10234,x10233),x10236,x10233) % 1.21/1.27 [421]~P34(x4212)+~P28(x4212)+P5(x4211,f3(x4212),x4212)+E(f8(x4211,x4212),x4211) % 1.21/1.27 [488]~P34(x4882)+~P28(x4882)+~P5(x4881,f3(x4882),x4882)+E(f8(x4881,x4882),f7(x4881,x4882)) % 1.21/1.27 [474]P5(x4741,x4742,x4743)+~P12(x4743)+E(x4741,x4742)+P5(x4742,x4741,x4743) % 1.21/1.27 [478]P5(x4781,x4782,x4783)+~P34(x4783)+E(x4781,x4782)+P5(x4782,x4781,x4783) % 1.21/1.27 [517]~P34(x5173)+~P4(x5171,x5172,x5173)+E(x5171,x5172)+P5(x5171,x5172,x5173) % 1.21/1.27 [523]~P40(x5233)+~P4(x5231,x5232,x5233)+E(x5231,x5232)+P5(x5231,x5232,x5233) % 1.21/1.27 [580]~P4(x5802,x5801,x5803)+~P4(x5801,x5802,x5803)+E(x5801,x5802)+~P40(x5803) % 1.21/1.27 [610]P4(x6102,x6101,x6103)+~P41(x6103)+~P4(x6101,x6102,x6103)+P5(x6101,x6102,x6103) % 1.21/1.27 [446]~P53(x4462)+~P9(x4462)+~E(f9(x4463,x4461,x4462),x4463)+E(x4461,f3(x4462)) % 1.21/1.27 [447]~P53(x4473)+~P9(x4473)+E(x4471,x4472)+~E(f10(x4471,x4472,x4473),f3(x4473)) % 1.21/1.27 [449]~P24(x4492)+~E(f11(x4493,x4491,x4492),f3(x4492))+E(x4491,f3(x4492))+E(x4493,f3(x4492)) % 1.21/1.27 [450]~P69(x4502)+~E(f11(x4503,x4501,x4502),f3(x4502))+E(x4501,f3(x4502))+E(x4503,f3(x4502)) % 1.21/1.27 [452]~P3(x4523)+E(x4521,x4522)+~P2(x4523)+~P6(x4521,x4522,f27(x4523)) % 1.21/1.27 [607]~P53(x6073)+E(x6071,x6072)+~E(f11(x6071,x6071,x6073),f11(x6072,x6072,x6073))+E(x6071,f7(x6072,x6073)) % 1.21/1.27 [698]~P12(x6982)+P7(x6981,x6982)+P5(f3(x6982),x6983,x6982)+~P7(f18(x6983,x6981,x6982),x6982) % 1.21/1.27 [709]~P12(x7092)+~P5(x7091,x7093,x7092)+~P5(f7(x7091,x7092),x7093,x7092)+P5(f8(x7091,x7092),x7093,x7092) % 1.21/1.27 [711]~P33(x7112)+~P4(x7111,x7113,x7112)+~P4(f7(x7111,x7112),x7113,x7112)+P4(f8(x7111,x7112),x7113,x7112) % 1.21/1.27 [775]~P12(x7752)+~P4(f16(x7751,x7753,x7752),f3(x7752),x7752)+P4(x7751,f3(x7752),x7752)+E(x7751,f3(x7752)) % 1.21/1.27 [804]~P59(x8041)+~P5(x8043,f3(x8041),x8041)+~P5(x8042,f3(x8041),x8041)+P5(f3(x8041),f11(x8042,x8043,x8041),x8041) % 1.21/1.27 [805]~P59(x8051)+~P4(x8053,f3(x8051),x8051)+~P4(x8052,f3(x8051),x8051)+P4(f3(x8051),f11(x8052,x8053,x8051),x8051) % 1.21/1.27 [807]~P63(x8071)+~P4(x8073,f3(x8071),x8071)+~P4(x8072,f3(x8071),x8071)+P4(f3(x8071),f11(x8072,x8073,x8071),x8071) % 1.21/1.27 [808]~P60(x8081)+~P5(f3(x8081),x8083,x8081)+~P5(f3(x8081),x8082,x8081)+P5(f3(x8081),f11(x8082,x8083,x8081),x8081) % 1.21/1.27 [809]~P35(x8091)+~P5(f3(x8091),x8093,x8091)+~P5(f3(x8091),x8092,x8091)+P5(f3(x8091),f9(x8092,x8093,x8091),x8091) % 1.21/1.27 [810]~P35(x8101)+~P5(f3(x8101),x8103,x8101)+~P4(f3(x8101),x8102,x8101)+P5(f3(x8101),f9(x8102,x8103,x8101),x8101) % 1.21/1.27 [811]~P35(x8111)+~P5(f3(x8111),x8112,x8111)+~P4(f3(x8111),x8113,x8111)+P5(f3(x8111),f9(x8112,x8113,x8111),x8111) % 1.21/1.27 [812]~P59(x8121)+~P4(f3(x8121),x8123,x8121)+~P4(f3(x8121),x8122,x8121)+P4(f3(x8121),f11(x8122,x8123,x8121),x8121) % 1.21/1.27 [813]~P63(x8131)+~P4(f3(x8131),x8133,x8131)+~P4(f3(x8131),x8132,x8131)+P4(f3(x8131),f11(x8132,x8133,x8131),x8131) % 1.21/1.27 [814]~P64(x8141)+~P4(f3(x8141),x8143,x8141)+~P4(f3(x8141),x8142,x8141)+P4(f3(x8141),f11(x8142,x8143,x8141),x8141) % 1.21/1.27 [815]~P35(x8151)+~P4(f3(x8151),x8153,x8151)+~P4(f3(x8151),x8152,x8151)+P4(f3(x8151),f9(x8152,x8153,x8151),x8151) % 1.21/1.27 [816]~P35(x8163)+~P5(x8162,f3(x8163),x8163)+~P5(x8161,f3(x8163),x8163)+P5(f9(x8161,x8162,x8163),f3(x8163),x8163) % 1.21/1.27 [817]~P35(x8173)+~P5(x8172,f3(x8173),x8173)+~P4(x8171,f3(x8173),x8173)+P5(f9(x8171,x8172,x8173),f3(x8173),x8173) % 1.21/1.27 [818]~P35(x8183)+~P5(x8181,f3(x8183),x8183)+~P4(x8182,f3(x8183),x8183)+P5(f9(x8181,x8182,x8183),f3(x8183),x8183) % 1.21/1.27 [819]~P35(x8193)+~P4(x8192,f3(x8193),x8193)+~P4(x8191,f3(x8193),x8193)+P4(f9(x8191,x8192,x8193),f3(x8193),x8193) % 1.21/1.27 [820]~P60(x8203)+~P5(x8202,f3(x8203),x8203)+~P5(f3(x8203),x8201,x8203)+P5(f11(x8201,x8202,x8203),f3(x8203),x8203) % 1.21/1.27 [822]~P60(x8223)+~P5(x8221,f3(x8223),x8223)+~P5(f3(x8223),x8222,x8223)+P5(f11(x8221,x8222,x8223),f3(x8223),x8223) % 1.21/1.27 [823]~P59(x8233)+~P4(x8232,f3(x8233),x8233)+~P4(f3(x8233),x8231,x8233)+P4(f11(x8231,x8232,x8233),f3(x8233),x8233) % 1.21/1.27 [824]~P59(x8243)+~P4(x8241,f3(x8243),x8243)+~P4(f3(x8243),x8242,x8243)+P4(f11(x8241,x8242,x8243),f3(x8243),x8243) % 1.21/1.27 [826]~P64(x8263)+~P4(x8262,f3(x8263),x8263)+~P4(f3(x8263),x8261,x8263)+P4(f11(x8261,x8262,x8263),f3(x8263),x8263) % 1.21/1.27 [829]~P64(x8293)+~P4(x8291,f3(x8293),x8293)+~P4(f3(x8293),x8292,x8293)+P4(f11(x8291,x8292,x8293),f3(x8293),x8293) % 1.21/1.27 [839]~P59(x8392)+~P4(f11(x8393,x8391,x8392),f3(x8392),x8392)+P4(x8391,f3(x8392),x8392)+P4(x8393,f3(x8392),x8392) % 1.21/1.27 [840]~P59(x8402)+~P4(f3(x8402),f11(x8403,x8401,x8402),x8402)+P4(x8401,f3(x8402),x8402)+P4(f3(x8402),x8403,x8402) % 1.21/1.27 [841]~P59(x8412)+~P4(f3(x8412),f11(x8411,x8413,x8412),x8412)+P4(x8411,f3(x8412),x8412)+P4(f3(x8412),x8413,x8412) % 1.21/1.27 [842]~P59(x8422)+~P4(f3(x8422),f11(x8423,x8421,x8422),x8422)+P4(x8421,f3(x8422),x8422)+P4(f3(x8422),x8421,x8422) % 1.21/1.27 [843]~P59(x8432)+~P4(f3(x8432),f11(x8431,x8433,x8432),x8432)+P4(x8431,f3(x8432),x8432)+P4(f3(x8432),x8431,x8432) % 1.21/1.27 [844]~P59(x8442)+~P4(f11(x8443,x8441,x8442),f3(x8442),x8442)+P4(x8441,f3(x8442),x8442)+P4(f3(x8442),x8441,x8442) % 1.21/1.27 [845]~P59(x8452)+~P4(f11(x8451,x8453,x8452),f3(x8452),x8452)+P4(x8451,f3(x8452),x8452)+P4(f3(x8452),x8451,x8452) % 1.21/1.27 [846]~P59(x8461)+~P4(f11(x8462,x8463,x8461),f3(x8461),x8461)+P4(f3(x8461),x8462,x8461)+P4(f3(x8461),x8463,x8461) % 1.21/1.27 [858]~P60(x8581)+~P5(f3(x8581),f11(x8583,x8582,x8581),x8581)+P5(f3(x8581),x8582,x8581)+~P5(f3(x8581),x8583,x8581) % 1.21/1.27 [859]~P60(x8591)+~P5(f3(x8591),f11(x8592,x8593,x8591),x8591)+P5(f3(x8591),x8592,x8591)+~P5(f3(x8591),x8593,x8591) % 1.21/1.27 [481]~P53(x4812)+E(x4811,f3(x4812))+~E(f23(x4811,x4813,x4812),f3(f27(x4812)))+E(x4813,f3(f27(x4812))) % 1.21/1.27 [590]~P12(x5903)+~P7(x5902,x5903)+~P7(x5901,x5903)+P7(f9(x5901,x5902,f27(x5903)),x5903) % 1.21/1.27 [642]P7(x6421,x6422)+~P12(x6422)+~P7(f18(x6423,x6421,x6422),x6422)+E(x6421,f3(f27(x6422))) % 1.21/1.27 [830]~P2(x8302)+~P3(x8302)+P6(x8301,f3(x8302),x8302)+~P6(f18(x8301,x8303,x8302),f3(f27(x8302)),f27(x8302)) % 1.21/1.27 [831]~P2(x8311)+~P3(x8311)+P6(f3(x8311),x8312,x8311)+~P6(f3(f27(x8311)),f18(x8312,x8313,x8311),f27(x8311)) % 1.21/1.27 [837]~P2(x8372)+~P3(x8372)+~P6(f18(x8373,x8371,x8372),f3(f27(x8372)),f27(x8372))+P6(x8371,f3(f27(x8372)),f27(x8372)) % 1.21/1.27 [838]~P2(x8381)+~P3(x8381)+~P6(f3(f27(x8381)),f18(x8383,x8382,x8381),f27(x8381))+P6(f3(f27(x8381)),x8382,f27(x8381)) % 1.21/1.27 [854]~P58(x8542)+~P4(x8543,f3(x8542),x8542)+~P4(x8541,f3(x8542),x8542)+E(f11(f8(x8541,x8542),f8(x8543,x8542),x8542),f8(f11(x8541,x8543,x8542),x8542)) % 1.21/1.27 [855]~P58(x8552)+~P4(x8553,f3(x8552),x8552)+~P4(f3(x8552),x8551,x8552)+E(f11(f8(x8551,x8552),f8(x8553,x8552),x8552),f8(f11(x8551,x8553,x8552),x8552)) % 1.21/1.27 [856]~P58(x8562)+~P4(x8561,f3(x8562),x8562)+~P4(f3(x8562),x8563,x8562)+E(f11(f8(x8561,x8562),f8(x8563,x8562),x8562),f8(f11(x8561,x8563,x8562),x8562)) % 1.21/1.27 [857]~P58(x8572)+~P4(f3(x8572),x8573,x8572)+~P4(f3(x8572),x8571,x8572)+E(f11(f8(x8571,x8572),f8(x8573,x8572),x8572),f8(f11(x8571,x8573,x8572),x8572)) % 1.21/1.27 [651]~P40(x6513)+~P5(x6511,x6514,x6513)+P5(x6511,x6512,x6513)+~P5(x6514,x6512,x6513) % 1.21/1.27 [652]~P40(x6523)+~P4(x6521,x6524,x6523)+P5(x6521,x6522,x6523)+~P5(x6524,x6522,x6523) % 1.21/1.27 [653]~P40(x6533)+~P4(x6534,x6532,x6533)+P5(x6531,x6532,x6533)+~P5(x6531,x6534,x6533) % 1.21/1.27 [654]~P41(x6543)+~P5(x6541,x6544,x6543)+P5(x6541,x6542,x6543)+~P5(x6544,x6542,x6543) % 1.21/1.27 [655]~P41(x6553)+~P4(x6551,x6554,x6553)+P5(x6551,x6552,x6553)+~P5(x6554,x6552,x6553) % 1.21/1.27 [656]~P41(x6563)+~P4(x6564,x6562,x6563)+P5(x6561,x6562,x6563)+~P5(x6561,x6564,x6563) % 1.21/1.27 [657]~P40(x6573)+~P4(x6571,x6574,x6573)+P4(x6571,x6572,x6573)+~P4(x6574,x6572,x6573) % 1.21/1.27 [658]~P41(x6583)+~P4(x6581,x6584,x6583)+P4(x6581,x6582,x6583)+~P4(x6584,x6582,x6583) % 1.21/1.27 [591]~P53(x5914)+~P9(x5914)+E(x5911,x5912)+~E(f9(x5913,x5911,x5914),f9(x5913,x5912,x5914)) % 1.21/1.27 [778]~P34(x7784)+~P5(x7781,x7783,x7784)+~P5(x7781,x7782,x7784)+P5(x7781,f21(x7782,x7783,x7784),x7784) % 1.21/1.27 [781]~P1(x7814)+~P4(x7811,x7813,x7814)+~P4(x7811,x7812,x7814)+P4(x7811,f13(x7812,x7813,x7814),x7814) % 1.21/1.27 [784]~P34(x7844)+~P4(x7841,x7843,x7844)+~P4(x7841,x7842,x7844)+P4(x7841,f21(x7842,x7843,x7844),x7844) % 1.21/1.27 [785]~P34(x7853)+~P5(x7852,x7854,x7853)+~P5(x7851,x7854,x7853)+P5(f19(x7851,x7852,x7853),x7854,x7853) % 1.21/1.27 [788]~P34(x7883)+~P4(x7882,x7884,x7883)+~P4(x7881,x7884,x7883)+P4(f19(x7881,x7882,x7883),x7884,x7883) % 1.21/1.27 [790]~P61(x7904)+~P5(x7901,x7903,x7904)+~P5(f3(x7904),x7902,x7904)+P5(x7901,f9(x7902,x7903,x7904),x7904) % 1.21/1.27 [832]~P34(x8323)+P5(x8321,x8322,x8323)+P5(x8321,x8324,x8323)+~P5(x8321,f19(x8322,x8324,x8323),x8323) % 1.21/1.27 [833]~P34(x8333)+P4(x8331,x8332,x8333)+P4(x8331,x8334,x8333)+~P4(x8331,f19(x8332,x8334,x8333),x8333) % 1.21/1.27 [834]~P34(x8343)+P5(x8341,x8342,x8343)+P5(x8344,x8342,x8343)+~P5(f21(x8341,x8344,x8343),x8342,x8343) % 1.21/1.27 [835]~P34(x8353)+P4(x8351,x8352,x8353)+P4(x8354,x8352,x8353)+~P4(f21(x8351,x8354,x8353),x8352,x8353) % 1.21/1.27 [905]~P59(x9053)+~P5(x9054,x9051,x9053)+~P5(x9052,f3(x9053),x9053)+P5(f11(x9051,x9052,x9053),f11(x9054,x9052,x9053),x9053) % 1.21/1.27 [908]~P59(x9083)+~P5(x9084,x9082,x9083)+~P5(x9081,f3(x9083),x9083)+P5(f11(x9081,x9082,x9083),f11(x9081,x9084,x9083),x9083) % 1.21/1.27 [909]~P63(x9093)+~P4(x9094,x9091,x9093)+~P4(x9092,f3(x9093),x9093)+P4(f11(x9091,x9092,x9093),f11(x9094,x9092,x9093),x9093) % 1.21/1.27 [910]~P59(x9103)+~P4(x9104,x9102,x9103)+~P5(x9101,f3(x9103),x9103)+P4(f11(x9101,x9102,x9103),f11(x9101,x9104,x9103),x9103) % 1.21/1.27 [911]~P63(x9113)+~P4(x9114,x9112,x9113)+~P4(x9111,f3(x9113),x9113)+P4(f11(x9111,x9112,x9113),f11(x9111,x9114,x9113),x9113) % 1.21/1.27 [912]~P59(x9123)+~P5(x9121,x9124,x9123)+~P5(f3(x9123),x9122,x9123)+P5(f11(x9121,x9122,x9123),f11(x9124,x9122,x9123),x9123) % 1.21/1.27 [913]~P60(x9133)+~P5(x9131,x9134,x9133)+~P5(f3(x9133),x9132,x9133)+P5(f11(x9131,x9132,x9133),f11(x9134,x9132,x9133),x9133) % 1.21/1.27 [915]~P59(x9153)+~P5(x9152,x9154,x9153)+~P5(f3(x9153),x9151,x9153)+P5(f11(x9151,x9152,x9153),f11(x9151,x9154,x9153),x9153) % 1.21/1.27 [916]~P60(x9163)+~P5(x9162,x9164,x9163)+~P5(f3(x9163),x9161,x9163)+P5(f11(x9161,x9162,x9163),f11(x9161,x9164,x9163),x9163) % 1.21/1.27 [917]~P57(x9173)+~P5(x9172,x9174,x9173)+~P5(f3(x9173),x9171,x9173)+P5(f11(x9171,x9172,x9173),f11(x9171,x9174,x9173),x9173) % 1.21/1.27 [918]~P56(x9183)+~P4(x9181,x9184,x9183)+~P4(f3(x9183),x9182,x9183)+P4(f11(x9181,x9182,x9183),f11(x9184,x9182,x9183),x9183) % 1.21/1.27 [919]~P59(x9193)+~P4(x9192,x9194,x9193)+~P5(f3(x9193),x9191,x9193)+P4(f11(x9191,x9192,x9193),f11(x9191,x9194,x9193),x9193) % 1.21/1.27 [920]~P55(x9203)+~P4(x9202,x9204,x9203)+~P4(f3(x9203),x9201,x9203)+P4(f11(x9201,x9202,x9203),f11(x9201,x9204,x9203),x9203) % 1.21/1.27 [921]~P56(x9213)+~P4(x9212,x9214,x9213)+~P4(f3(x9213),x9211,x9213)+P4(f11(x9211,x9212,x9213),f11(x9211,x9214,x9213),x9213) % 1.21/1.27 [922]~P61(x9223)+~P4(x9221,x9224,x9223)+~P4(f3(x9223),x9221,x9223)+P4(f16(x9221,x9222,x9223),f16(x9224,x9222,x9223),x9223) % 1.21/1.27 [944]P5(x9442,x9441,x9443)+~P59(x9443)+P5(x9441,x9442,x9443)+~P5(f11(x9444,x9441,x9443),f11(x9444,x9442,x9443),x9443) % 1.21/1.27 [945]P5(x9452,x9451,x9453)+~P59(x9453)+P5(x9451,x9452,x9453)+~P5(f11(x9451,x9454,x9453),f11(x9452,x9454,x9453),x9453) % 1.21/1.27 [950]~P59(x9503)+P5(x9501,x9502,x9503)+~P5(f11(x9501,x9504,x9503),f11(x9502,x9504,x9503),x9503)+P5(x9504,f3(x9503),x9503) % 1.21/1.27 [951]~P59(x9513)+P5(x9511,x9512,x9513)+~P5(f11(x9514,x9511,x9513),f11(x9514,x9512,x9513),x9513)+P5(x9514,f3(x9513),x9513) % 1.21/1.27 [952]~P59(x9523)+P5(x9521,x9522,x9523)+~P5(f11(x9524,x9522,x9523),f11(x9524,x9521,x9523),x9523)+P5(f3(x9523),x9524,x9523) % 1.21/1.27 [953]~P59(x9533)+P5(x9531,x9532,x9533)+~P5(f11(x9532,x9534,x9533),f11(x9531,x9534,x9533),x9533)+P5(f3(x9533),x9534,x9533) % 1.21/1.27 [956]~P59(x9562)+~P5(f11(x9563,x9561,x9562),f11(x9564,x9561,x9562),x9562)+P5(x9561,f3(x9562),x9562)+P5(f3(x9562),x9561,x9562) % 1.21/1.27 [957]~P59(x9572)+~P5(f11(x9571,x9573,x9572),f11(x9571,x9574,x9572),x9572)+P5(x9571,f3(x9572),x9572)+P5(f3(x9572),x9571,x9572) % 1.21/1.27 [964]~P59(x9643)+P5(x9641,x9642,x9643)+~P5(f11(x9644,x9642,x9643),f11(x9644,x9641,x9643),x9643)+~P5(x9644,f3(x9643),x9643) % 1.21/1.27 [965]~P59(x9653)+P4(x9651,x9652,x9653)+~P4(f11(x9654,x9652,x9653),f11(x9654,x9651,x9653),x9653)+~P5(x9654,f3(x9653),x9653) % 1.21/1.27 [966]~P59(x9663)+P5(x9661,x9662,x9663)+~P5(f11(x9664,x9661,x9663),f11(x9664,x9662,x9663),x9663)+~P5(f3(x9663),x9664,x9663) % 1.21/1.27 [967]~P60(x9673)+P5(x9671,x9672,x9673)+~P5(f11(x9674,x9671,x9673),f11(x9674,x9672,x9673),x9673)+~P4(f3(x9673),x9674,x9673) % 1.21/1.27 [968]~P60(x9683)+P5(x9681,x9682,x9683)+~P5(f11(x9681,x9684,x9683),f11(x9682,x9684,x9683),x9683)+~P4(f3(x9683),x9684,x9683) % 1.21/1.27 [969]~P61(x9693)+P5(x9691,x9692,x9693)+~P4(f3(x9693),x9692,x9693)+~P5(f16(x9691,x9694,x9693),f16(x9692,x9694,x9693),x9693) % 1.21/1.27 [970]~P62(x9703)+P5(x9701,x9702,x9703)+~P5(f11(x9704,x9701,x9703),f11(x9704,x9702,x9703),x9703)+~P4(f3(x9703),x9704,x9703) % 1.21/1.27 [971]~P62(x9713)+P5(x9711,x9712,x9713)+~P5(f11(x9711,x9714,x9713),f11(x9712,x9714,x9713),x9713)+~P4(f3(x9713),x9714,x9713) % 1.21/1.27 [972]~P59(x9723)+P4(x9721,x9722,x9723)+~P4(f11(x9724,x9721,x9723),f11(x9724,x9722,x9723),x9723)+~P5(f3(x9723),x9724,x9723) % 1.21/1.27 [973]~P60(x9733)+P4(x9731,x9732,x9733)+~P4(f11(x9734,x9731,x9733),f11(x9734,x9732,x9733),x9733)+~P5(f3(x9733),x9734,x9733) % 1.21/1.27 [974]~P60(x9743)+P4(x9741,x9742,x9743)+~P4(f11(x9741,x9744,x9743),f11(x9742,x9744,x9743),x9743)+~P5(f3(x9743),x9744,x9743) % 1.21/1.27 [924]~P42(x9242)+E(x9241,f3(x9242))+~P4(x9243,f3(a1),a1)+~P4(f15(x9241,x9242),f11(x9243,f15(x9244,x9242),a1),a1) % 1.21/1.27 [996]~P12(x9963)+~P5(x9961,f9(x9962,x9964,x9963),x9963)+~P5(f10(x9962,x9964,x9963),x9961,x9963)+P5(f8(f10(x9961,x9962,x9963),x9963),x9964,x9963) % 1.21/1.27 [731]~P27(x7313)+~P5(x7314,x7315,x7313)+P5(x7311,x7312,x7313)+~E(f10(x7314,x7315,x7313),f10(x7311,x7312,x7313)) % 1.21/1.27 [732]~P27(x7323)+~P5(x7324,x7325,x7323)+P5(x7321,x7322,x7323)+~E(f10(x7321,x7322,x7323),f10(x7324,x7325,x7323)) % 1.21/1.27 [733]~P27(x7333)+~P4(x7335,x7334,x7333)+P4(x7331,x7332,x7333)+~E(f10(x7334,x7335,x7333),f10(x7332,x7331,x7333)) % 1.21/1.27 [734]~P27(x7343)+~P4(x7345,x7344,x7343)+P4(x7341,x7342,x7343)+~E(f10(x7342,x7341,x7343),f10(x7344,x7345,x7343)) % 1.21/1.27 [897]~P38(x8973)+~P5(x8972,x8975,x8973)+~P5(x8971,x8974,x8973)+P5(f9(x8971,x8972,x8973),f9(x8974,x8975,x8973),x8973) % 1.21/1.27 [898]~P38(x8983)+~P5(x8982,x8985,x8983)+~P4(x8981,x8984,x8983)+P5(f9(x8981,x8982,x8983),f9(x8984,x8985,x8983),x8983) % 1.21/1.27 [899]~P38(x8993)+~P5(x8991,x8994,x8993)+~P4(x8992,x8995,x8993)+P5(f9(x8991,x8992,x8993),f9(x8994,x8995,x8993),x8993) % 1.21/1.27 [900]~P37(x9003)+~P4(x9002,x9005,x9003)+~P4(x9001,x9004,x9003)+P4(f9(x9001,x9002,x9003),f9(x9004,x9005,x9003),x9003) % 1.21/1.27 [931]~P2(x9313)+~P3(x9313)+P6(x9311,x9312,x9313)+~P6(f18(x9311,x9314,x9313),f18(x9312,x9315,x9313),f27(x9313)) % 1.21/1.27 [932]~P2(x9323)+~P3(x9323)+~P6(f18(x9324,x9321,x9323),f18(x9325,x9322,x9323),f27(x9323))+P6(x9321,x9322,f27(x9323)) % 1.21/1.27 [938]~P27(x9384)+~P4(x9385,x9383,x9384)+~P4(x9381,f9(x9382,x9385,x9384),x9384)+P4(x9381,f9(x9382,x9383,x9384),x9384) % 1.21/1.27 [980]~P12(x9802)+~P5(f8(x9801,x9802),x9804,x9802)+~P5(f8(x9803,x9802),x9805,x9802)+P5(f11(f8(x9801,x9802),f8(x9803,x9802),x9802),f11(x9804,x9805,x9802),x9802) % 1.21/1.27 [989]~P43(x9893)+~P5(f15(x9892,x9893),x9895,a1)+~P5(f15(x9891,x9893),x9894,a1)+P5(f15(f11(x9891,x9892,x9893),x9893),f11(x9894,x9895,a1),a1) % 1.21/1.27 [990]~P42(x9903)+~P5(f15(x9902,x9903),x9905,a1)+~P5(f15(x9901,x9903),x9904,a1)+P5(f15(f9(x9901,x9902,x9903),x9903),f9(x9904,x9905,a1),a1) % 1.21/1.27 [706]~P35(x7062)+~P4(f3(x7062),x7061,x7062)+~P4(f3(x7062),x7063,x7062)+~E(f9(x7063,x7061,x7062),f3(x7062))+E(x7061,f3(x7062)) % 1.21/1.27 [707]~P35(x7072)+~P4(f3(x7072),x7073,x7072)+~P4(f3(x7072),x7071,x7072)+~E(f9(x7071,x7073,x7072),f3(x7072))+E(x7071,f3(x7072)) % 1.21/1.27 [852]~P2(x8521)+~P3(x8521)+~P6(f3(x8521),x8522,x8521)+~P6(f3(f27(x8521)),x8523,f27(x8521))+P6(f3(f27(x8521)),f18(x8522,x8523,x8521),f27(x8521)) % 1.21/1.27 [853]~P2(x8533)+~P3(x8533)+~P6(x8531,f3(x8533),x8533)+~P6(x8532,f3(f27(x8533)),f27(x8533))+P6(f18(x8531,x8532,x8533),f3(f27(x8533)),f27(x8533)) % 1.21/1.27 [792]~P36(x7924)+~P16(x7924)+~P5(x7921,x7923,x7924)+~P4(f3(x7924),x7922,x7924)+P5(x7921,f9(x7922,x7923,x7924),x7924) % 1.21/1.27 [793]~P36(x7934)+~P16(x7934)+~P4(x7931,x7933,x7934)+~P5(f3(x7934),x7932,x7934)+P5(x7931,f9(x7932,x7933,x7934),x7934) % 1.21/1.27 [794]~P36(x7944)+~P16(x7944)+~P4(x7941,x7943,x7944)+~P4(f3(x7944),x7942,x7944)+P4(x7941,f9(x7942,x7943,x7944),x7944) % 1.21/1.27 [795]~P36(x7954)+~P16(x7954)+~P4(x7951,x7952,x7954)+~P4(f3(x7954),x7953,x7954)+P4(x7951,f9(x7952,x7953,x7954),x7954) % 1.21/1.27 [925]~P2(x9253)+~P3(x9253)+~P6(x9251,x9254,x9253)+~P6(x9252,x9255,f27(x9253))+P6(f18(x9251,x9252,x9253),f18(x9254,x9255,x9253),f27(x9253)) % 1.21/1.27 [943]~P53(x9434)+~P9(x9434)+E(x9431,x9432)+E(x9433,f3(x9434))+~E(f9(x9435,f11(x9433,x9431,x9434),x9434),f9(x9435,f11(x9433,x9432,x9434),x9434)) % 1.21/1.27 [998]~P53(x9985)+~P9(x9985)+E(x9981,x9982)+E(x9983,x9984)+~E(f9(f11(x9983,x9981,x9985),f11(x9984,x9982,x9985),x9985),f9(f11(x9983,x9982,x9985),f11(x9984,x9981,x9985),x9985)) % 1.21/1.27 [482]~P67(x4822)+~P24(x4822)+~P25(x4822)+~P26(x4822)+~E(f16(x4821,x4823,x4822),f3(x4822))+E(x4821,f3(x4822)) % 1.21/1.27 [981]~P60(x9813)+~P5(x9812,x9815,x9813)+~P5(x9811,x9814,x9813)+~P5(f3(x9813),x9814,x9813)+~P4(f3(x9813),x9812,x9813)+P5(f11(x9811,x9812,x9813),f11(x9814,x9815,x9813),x9813) % 1.21/1.27 [982]~P60(x9823)+~P5(x9822,x9825,x9823)+~P5(x9821,x9824,x9823)+~P4(f3(x9823),x9822,x9823)+~P4(f3(x9823),x9821,x9823)+P5(f11(x9821,x9822,x9823),f11(x9824,x9825,x9823),x9823) % 1.21/1.27 [983]~P60(x9833)+~P5(x9832,x9835,x9833)+~P4(x9831,x9834,x9833)+~P5(f3(x9833),x9831,x9833)+~P4(f3(x9833),x9832,x9833)+P5(f11(x9831,x9832,x9833),f11(x9834,x9835,x9833),x9833) % 1.21/1.27 [984]~P60(x9843)+~P5(x9841,x9844,x9843)+~P4(x9842,x9845,x9843)+~P5(f3(x9843),x9842,x9843)+~P4(f3(x9843),x9841,x9843)+P5(f11(x9841,x9842,x9843),f11(x9844,x9845,x9843),x9843) % 1.21/1.27 [985]~P66(x9853)+~P4(x9852,x9855,x9853)+~P4(x9851,x9854,x9853)+~P4(f3(x9853),x9854,x9853)+~P4(f3(x9853),x9852,x9853)+P4(f11(x9851,x9852,x9853),f11(x9854,x9855,x9853),x9853) % 1.21/1.27 [986]~P66(x9863)+~P4(x9862,x9865,x9863)+~P4(x9861,x9864,x9863)+~P4(f3(x9863),x9862,x9863)+~P4(f3(x9863),x9861,x9863)+P4(f11(x9861,x9862,x9863),f11(x9864,x9865,x9863),x9863) % 1.21/1.27 %EqnAxiom % 1.21/1.27 [1]E(x11,x11) % 1.21/1.27 [2]E(x22,x21)+~E(x21,x22) % 1.21/1.27 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.21/1.27 [4]~E(x41,x42)+E(f3(x41),f3(x42)) % 1.21/1.27 [5]~E(x51,x52)+E(f12(x51),f12(x52)) % 1.21/1.27 [6]~E(x61,x62)+E(f10(x61,x63,x64),f10(x62,x63,x64)) % 1.21/1.27 [7]~E(x71,x72)+E(f10(x73,x71,x74),f10(x73,x72,x74)) % 1.21/1.27 [8]~E(x81,x82)+E(f10(x83,x84,x81),f10(x83,x84,x82)) % 1.21/1.27 [9]~E(x91,x92)+E(f11(x91,x93,x94),f11(x92,x93,x94)) % 1.21/1.27 [10]~E(x101,x102)+E(f11(x103,x101,x104),f11(x103,x102,x104)) % 1.21/1.27 [11]~E(x111,x112)+E(f11(x113,x114,x111),f11(x113,x114,x112)) % 1.21/1.27 [12]~E(x121,x122)+E(f14(x121),f14(x122)) % 1.21/1.27 [13]~E(x131,x132)+E(f9(x131,x133,x134),f9(x132,x133,x134)) % 1.21/1.27 [14]~E(x141,x142)+E(f9(x143,x141,x144),f9(x143,x142,x144)) % 1.21/1.27 [15]~E(x151,x152)+E(f9(x153,x154,x151),f9(x153,x154,x152)) % 1.21/1.27 [16]~E(x161,x162)+E(f16(x161,x163,x164),f16(x162,x163,x164)) % 1.21/1.27 [17]~E(x171,x172)+E(f16(x173,x171,x174),f16(x173,x172,x174)) % 1.21/1.27 [18]~E(x181,x182)+E(f16(x183,x184,x181),f16(x183,x184,x182)) % 1.21/1.27 [19]~E(x191,x192)+E(f4(x191),f4(x192)) % 1.21/1.27 [20]~E(x201,x202)+E(f13(x201,x203,x204),f13(x202,x203,x204)) % 1.21/1.27 [21]~E(x211,x212)+E(f13(x213,x211,x214),f13(x213,x212,x214)) % 1.21/1.27 [22]~E(x221,x222)+E(f13(x223,x224,x221),f13(x223,x224,x222)) % 1.21/1.27 [23]~E(x231,x232)+E(f7(x231,x233),f7(x232,x233)) % 1.21/1.27 [24]~E(x241,x242)+E(f7(x243,x241),f7(x243,x242)) % 1.21/1.27 [25]~E(x251,x252)+E(f5(x251),f5(x252)) % 1.21/1.27 [26]~E(x261,x262)+E(f8(x261,x263),f8(x262,x263)) % 1.21/1.27 [27]~E(x271,x272)+E(f8(x273,x271),f8(x273,x272)) % 1.21/1.27 [28]~E(x281,x282)+E(f19(x281,x283,x284),f19(x282,x283,x284)) % 1.21/1.27 [29]~E(x291,x292)+E(f19(x293,x291,x294),f19(x293,x292,x294)) % 1.21/1.27 [30]~E(x301,x302)+E(f19(x303,x304,x301),f19(x303,x304,x302)) % 1.21/1.27 [31]~E(x311,x312)+E(f6(x311),f6(x312)) % 1.21/1.27 [32]~E(x321,x322)+E(f15(x321,x323),f15(x322,x323)) % 1.21/1.27 [33]~E(x331,x332)+E(f15(x333,x331),f15(x333,x332)) % 1.21/1.27 [34]~E(x341,x342)+E(f25(x341,x343),f25(x342,x343)) % 1.21/1.27 [35]~E(x351,x352)+E(f25(x353,x351),f25(x353,x352)) % 1.21/1.27 [36]~E(x361,x362)+E(f21(x361,x363,x364),f21(x362,x363,x364)) % 1.21/1.27 [37]~E(x371,x372)+E(f21(x373,x371,x374),f21(x373,x372,x374)) % 1.21/1.27 [38]~E(x381,x382)+E(f21(x383,x384,x381),f21(x383,x384,x382)) % 1.21/1.27 [39]~E(x391,x392)+E(f18(x391,x393,x394),f18(x392,x393,x394)) % 1.21/1.27 [40]~E(x401,x402)+E(f18(x403,x401,x404),f18(x403,x402,x404)) % 1.21/1.27 [41]~E(x411,x412)+E(f18(x413,x414,x411),f18(x413,x414,x412)) % 1.21/1.27 [42]~E(x421,x422)+E(f27(x421),f27(x422)) % 1.21/1.27 [43]~E(x431,x432)+E(f17(x431,x433,x434),f17(x432,x433,x434)) % 1.21/1.27 [44]~E(x441,x442)+E(f17(x443,x441,x444),f17(x443,x442,x444)) % 1.21/1.27 [45]~E(x451,x452)+E(f17(x453,x454,x451),f17(x453,x454,x452)) % 1.21/1.27 [46]~E(x461,x462)+E(f20(x461),f20(x462)) % 1.21/1.27 [47]~E(x471,x472)+E(f23(x471,x473,x474),f23(x472,x473,x474)) % 1.21/1.27 [48]~E(x481,x482)+E(f23(x483,x481,x484),f23(x483,x482,x484)) % 1.21/1.27 [49]~E(x491,x492)+E(f23(x493,x494,x491),f23(x493,x494,x492)) % 1.21/1.27 [50]~E(x501,x502)+E(f24(x501,x503,x504),f24(x502,x503,x504)) % 1.21/1.27 [51]~E(x511,x512)+E(f24(x513,x511,x514),f24(x513,x512,x514)) % 1.21/1.27 [52]~E(x521,x522)+E(f24(x523,x524,x521),f24(x523,x524,x522)) % 1.21/1.27 [53]~E(x531,x532)+E(f33(x531,x533),f33(x532,x533)) % 1.21/1.27 [54]~E(x541,x542)+E(f33(x543,x541),f33(x543,x542)) % 1.21/1.27 [55]~E(x551,x552)+E(f35(x551),f35(x552)) % 1.21/1.27 [56]~E(x561,x562)+E(f22(x561,x563,x564),f22(x562,x563,x564)) % 1.21/1.27 [57]~E(x571,x572)+E(f22(x573,x571,x574),f22(x573,x572,x574)) % 1.21/1.27 [58]~E(x581,x582)+E(f22(x583,x584,x581),f22(x583,x584,x582)) % 1.21/1.27 [59]~E(x591,x592)+E(f28(x591,x593),f28(x592,x593)) % 1.21/1.27 [60]~E(x601,x602)+E(f28(x603,x601),f28(x603,x602)) % 1.21/1.27 [61]~E(x611,x612)+E(f34(x611,x613,x614),f34(x612,x613,x614)) % 1.21/1.27 [62]~E(x621,x622)+E(f34(x623,x621,x624),f34(x623,x622,x624)) % 1.21/1.27 [63]~E(x631,x632)+E(f34(x633,x634,x631),f34(x633,x634,x632)) % 1.21/1.27 [64]~E(x641,x642)+E(f32(x641),f32(x642)) % 1.21/1.27 [65]~E(x651,x652)+E(f26(x651,x653),f26(x652,x653)) % 1.21/1.27 [66]~E(x661,x662)+E(f26(x663,x661),f26(x663,x662)) % 1.21/1.27 [67]~P1(x671)+P1(x672)+~E(x671,x672) % 1.21/1.27 [68]~P12(x681)+P12(x682)+~E(x681,x682) % 1.21/1.27 [69]~P58(x691)+P58(x692)+~E(x691,x692) % 1.21/1.27 [70]~P65(x701)+P65(x702)+~E(x701,x702) % 1.21/1.27 [71]~P42(x711)+P42(x712)+~E(x711,x712) % 1.21/1.27 [72]~P13(x721)+P13(x722)+~E(x721,x722) % 1.21/1.27 [73]~P2(x731)+P2(x732)+~E(x731,x732) % 1.21/1.27 [74]P4(x742,x743,x744)+~E(x741,x742)+~P4(x741,x743,x744) % 1.21/1.27 [75]P4(x753,x752,x754)+~E(x751,x752)+~P4(x753,x751,x754) % 1.21/1.27 [76]P4(x763,x764,x762)+~E(x761,x762)+~P4(x763,x764,x761) % 1.21/1.27 [77]~P3(x771)+P3(x772)+~E(x771,x772) % 1.21/1.27 [78]~P36(x781)+P36(x782)+~E(x781,x782) % 1.21/1.27 [79]~P67(x791)+P67(x792)+~E(x791,x792) % 1.21/1.27 [80]~P34(x801)+P34(x802)+~E(x801,x802) % 1.21/1.27 [81]~P24(x811)+P24(x812)+~E(x811,x812) % 1.21/1.27 [82]P5(x822,x823,x824)+~E(x821,x822)+~P5(x821,x823,x824) % 1.21/1.27 [83]P5(x833,x832,x834)+~E(x831,x832)+~P5(x833,x831,x834) % 1.21/1.27 [84]P5(x843,x844,x842)+~E(x841,x842)+~P5(x843,x844,x841) % 1.21/1.27 [85]~P25(x851)+P25(x852)+~E(x851,x852) % 1.21/1.27 [86]~P63(x861)+P63(x862)+~E(x861,x862) % 1.21/1.27 [87]~P26(x871)+P26(x872)+~E(x871,x872) % 1.21/1.27 [88]~P29(x881)+P29(x882)+~E(x881,x882) % 1.21/1.27 [89]~P68(x891)+P68(x892)+~E(x891,x892) % 1.21/1.27 [90]~P64(x901)+P64(x902)+~E(x901,x902) % 1.21/1.27 [91]~P27(x911)+P27(x912)+~E(x911,x912) % 1.21/1.27 [92]~P59(x921)+P59(x922)+~E(x921,x922) % 1.21/1.27 [93]~P35(x931)+P35(x932)+~E(x931,x932) % 1.21/1.27 [94]~P43(x941)+P43(x942)+~E(x941,x942) % 1.21/1.27 [95]~P60(x951)+P60(x952)+~E(x951,x952) % 1.21/1.27 [96]~P33(x961)+P33(x962)+~E(x961,x962) % 1.21/1.27 [97]~P14(x971)+P14(x972)+~E(x971,x972) % 1.21/1.27 [98]~P41(x981)+P41(x982)+~E(x981,x982) % 1.21/1.27 [99]~P38(x991)+P38(x992)+~E(x991,x992) % 1.21/1.27 [100]~P28(x1001)+P28(x1002)+~E(x1001,x1002) % 1.21/1.27 [101]~P47(x1011)+P47(x1012)+~E(x1011,x1012) % 1.21/1.27 [102]P6(x1022,x1023,x1024)+~E(x1021,x1022)+~P6(x1021,x1023,x1024) % 1.21/1.27 [103]P6(x1033,x1032,x1034)+~E(x1031,x1032)+~P6(x1033,x1031,x1034) % 1.21/1.27 [104]P6(x1043,x1044,x1042)+~E(x1041,x1042)+~P6(x1043,x1044,x1041) % 1.21/1.27 [105]P7(x1052,x1053)+~E(x1051,x1052)+~P7(x1051,x1053) % 1.21/1.27 [106]P7(x1063,x1062)+~E(x1061,x1062)+~P7(x1063,x1061) % 1.21/1.27 [107]~P8(x1071)+P8(x1072)+~E(x1071,x1072) % 1.21/1.27 [108]~P61(x1081)+P61(x1082)+~E(x1081,x1082) % 1.21/1.27 [109]~P69(x1091)+P69(x1092)+~E(x1091,x1092) % 1.21/1.27 [110]~P40(x1101)+P40(x1102)+~E(x1101,x1102) % 1.21/1.27 [111]~P48(x1111)+P48(x1112)+~E(x1111,x1112) % 1.21/1.27 [112]~P9(x1121)+P9(x1122)+~E(x1121,x1122) % 1.21/1.27 [113]~P15(x1131)+P15(x1132)+~E(x1131,x1132) % 1.21/1.27 [114]~P10(x1141)+P10(x1142)+~E(x1141,x1142) % 1.21/1.27 [115]~P53(x1151)+P53(x1152)+~E(x1151,x1152) % 1.21/1.27 [116]~P66(x1161)+P66(x1162)+~E(x1161,x1162) % 1.21/1.27 [117]~P50(x1171)+P50(x1172)+~E(x1171,x1172) % 1.21/1.27 [118]~P19(x1181)+P19(x1182)+~E(x1181,x1182) % 1.21/1.27 [119]~P49(x1191)+P49(x1192)+~E(x1191,x1192) % 1.21/1.27 [120]~P62(x1201)+P62(x1202)+~E(x1201,x1202) % 1.21/1.27 [121]~P37(x1211)+P37(x1212)+~E(x1211,x1212) % 1.21/1.27 [122]~P44(x1221)+P44(x1222)+~E(x1221,x1222) % 1.21/1.27 [123]~P16(x1231)+P16(x1232)+~E(x1231,x1232) % 1.21/1.27 [124]~P20(x1241)+P20(x1242)+~E(x1241,x1242) % 1.21/1.27 [125]~P54(x1251)+P54(x1252)+~E(x1251,x1252) % 1.21/1.27 [126]~P55(x1261)+P55(x1262)+~E(x1261,x1262) % 1.21/1.27 [127]~P56(x1271)+P56(x1272)+~E(x1271,x1272) % 1.21/1.27 [128]~P23(x1281)+P23(x1282)+~E(x1281,x1282) % 1.21/1.27 [129]~P45(x1291)+P45(x1292)+~E(x1291,x1292) % 1.21/1.27 [130]~P30(x1301)+P30(x1302)+~E(x1301,x1302) % 1.21/1.27 [131]~P32(x1311)+P32(x1312)+~E(x1311,x1312) % 1.21/1.27 [132]~P22(x1321)+P22(x1322)+~E(x1321,x1322) % 1.21/1.27 [133]~P17(x1331)+P17(x1332)+~E(x1331,x1332) % 1.21/1.27 [134]~P51(x1341)+P51(x1342)+~E(x1341,x1342) % 1.21/1.27 [135]~P52(x1351)+P52(x1352)+~E(x1351,x1352) % 1.21/1.27 [136]~P21(x1361)+P21(x1362)+~E(x1361,x1362) % 1.21/1.27 [137]~P71(x1371)+P71(x1372)+~E(x1371,x1372) % 1.21/1.27 [138]~P39(x1381)+P39(x1382)+~E(x1381,x1382) % 1.21/1.27 [139]~P46(x1391)+P46(x1392)+~E(x1391,x1392) % 1.21/1.27 [140]~P31(x1401)+P31(x1402)+~E(x1401,x1402) % 1.21/1.27 [141]~P18(x1411)+P18(x1412)+~E(x1411,x1412) % 1.21/1.27 [142]~P70(x1421)+P70(x1422)+~E(x1421,x1422) % 1.21/1.27 [143]~P57(x1431)+P57(x1432)+~E(x1431,x1432) % 1.21/1.27 [144]~P11(x1441)+P11(x1442)+~E(x1441,x1442) % 1.21/1.27 % 1.21/1.27 %------------------------------------------- % 1.21/1.27 cnf(1053,plain, % 1.21/1.27 (~P4(f15(f17(f18(a30,a29,a2),x10531,a2),a2),f15(f17(f18(a30,a29,a2),f26(a36,x10531),a2),a2),a1)), % 1.21/1.27 inference(rename_variables,[],[289])). % 1.21/1.27 cnf(1063,plain, % 1.21/1.27 (P4(x10631,x10631,a1)), % 1.21/1.27 inference(rename_variables,[],[254])). % 1.21/1.27 cnf(1066,plain, % 1.21/1.27 (~P4(f15(f17(f18(a30,a29,a2),x10661,a2),a2),f15(f17(f18(a30,a29,a2),f26(a36,x10661),a2),a2),a1)), % 1.21/1.27 inference(rename_variables,[],[289])). % 1.21/1.27 cnf(1069,plain, % 1.21/1.27 (~P4(f15(f17(f18(a30,a29,a2),x10691,a2),a2),f15(f17(f18(a30,a29,a2),f26(a36,x10691),a2),a2),a1)), % 1.21/1.27 inference(rename_variables,[],[289])). % 1.21/1.27 cnf(1072,plain, % 1.21/1.27 (~P4(f15(f17(f18(a30,a29,a2),x10721,a2),a2),f15(f17(f18(a30,a29,a2),f26(a36,x10721),a2),a2),a1)), % 1.21/1.27 inference(rename_variables,[],[289])). % 1.21/1.27 cnf(1075,plain, % 1.21/1.27 (~P5(x10751,x10751,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1082,plain, % 1.21/1.27 (~P5(x10821,x10821,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1087,plain, % 1.21/1.27 (~P5(x10871,x10871,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1097,plain, % 1.21/1.27 (P4(x10971,x10971,a1)), % 1.21/1.27 inference(rename_variables,[],[254])). % 1.21/1.27 cnf(1100,plain, % 1.21/1.27 (P4(x11001,x11001,a1)), % 1.21/1.27 inference(rename_variables,[],[254])). % 1.21/1.27 cnf(1103,plain, % 1.21/1.27 (P4(x11031,x11031,a1)), % 1.21/1.27 inference(rename_variables,[],[254])). % 1.21/1.27 cnf(1106,plain, % 1.21/1.27 (P4(x11061,x11061,a1)), % 1.21/1.27 inference(rename_variables,[],[254])). % 1.21/1.27 cnf(1109,plain, % 1.21/1.27 (P4(x11091,x11091,a1)), % 1.21/1.27 inference(rename_variables,[],[254])). % 1.21/1.27 cnf(1112,plain, % 1.21/1.27 (P4(x11121,x11121,a1)), % 1.21/1.27 inference(rename_variables,[],[254])). % 1.21/1.27 cnf(1117,plain, % 1.21/1.27 (P4(x11171,x11171,a1)), % 1.21/1.27 inference(rename_variables,[],[254])). % 1.21/1.27 cnf(1119,plain, % 1.21/1.27 (P4(x11191,x11191,a1)), % 1.21/1.27 inference(rename_variables,[],[254])). % 1.21/1.27 cnf(1144,plain, % 1.21/1.27 (~P5(x11441,x11441,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1155,plain, % 1.21/1.27 (~P5(x11551,x11551,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1160,plain, % 1.21/1.27 (~P5(x11601,x11601,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1165,plain, % 1.21/1.27 (~P5(x11651,x11651,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1168,plain, % 1.21/1.27 (~P5(x11681,x11681,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1175,plain, % 1.21/1.27 (~P5(x11751,x11751,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1178,plain, % 1.21/1.27 (~P5(x11781,x11781,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1181,plain, % 1.21/1.27 (~P5(x11811,x11811,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1184,plain, % 1.21/1.27 (~P5(x11841,x11841,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1187,plain, % 1.21/1.27 (~P5(x11871,x11871,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1190,plain, % 1.21/1.27 (~P5(x11901,x11901,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1193,plain, % 1.21/1.27 (P4(x11931,x11931,a1)), % 1.21/1.27 inference(rename_variables,[],[254])). % 1.21/1.27 cnf(1196,plain, % 1.21/1.27 (~P5(x11961,x11961,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1199,plain, % 1.21/1.27 (~P5(x11991,x11991,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1206,plain, % 1.21/1.27 (~P5(x12061,x12061,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1213,plain, % 1.21/1.27 (~P5(x12131,x12131,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1216,plain, % 1.21/1.27 (~P5(x12161,x12161,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1219,plain, % 1.21/1.27 (P4(x12191,x12191,a1)), % 1.21/1.27 inference(rename_variables,[],[254])). % 1.21/1.27 cnf(1222,plain, % 1.21/1.27 (P4(x12221,x12221,a1)), % 1.21/1.27 inference(rename_variables,[],[254])). % 1.21/1.27 cnf(1239,plain, % 1.21/1.27 (~P5(x12391,x12391,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1241,plain, % 1.21/1.27 (~P5(x12411,x12411,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1309,plain, % 1.21/1.27 (~P5(x13091,x13091,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1312,plain, % 1.21/1.27 (P4(x13121,x13121,a1)), % 1.21/1.27 inference(rename_variables,[],[254])). % 1.21/1.27 cnf(1317,plain, % 1.21/1.27 (~P5(x13171,x13171,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1328,plain, % 1.21/1.27 (~P5(x13281,x13281,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1331,plain, % 1.21/1.27 (~P5(x13311,x13311,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1334,plain, % 1.21/1.27 (P4(x13341,x13341,a1)), % 1.21/1.27 inference(rename_variables,[],[254])). % 1.21/1.27 cnf(1345,plain, % 1.21/1.27 (~P5(x13451,x13451,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1348,plain, % 1.21/1.27 (~P5(x13481,x13481,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1351,plain, % 1.21/1.27 (~P5(x13511,x13511,a1)), % 1.21/1.27 inference(rename_variables,[],[285])). % 1.21/1.27 cnf(1352,plain, % 1.21/1.27 (P4(x13521,x13521,a1)), % 1.21/1.27 inference(rename_variables,[],[254])). % 1.21/1.27 cnf(1358,plain, % 1.21/1.27 (P4(x13581,x13581,a1)), % 1.21/1.27 inference(rename_variables,[],[254])). % 1.21/1.27 cnf(1361,plain, % 1.21/1.27 (P4(x13611,x13611,a1)), % 1.21/1.27 inference(rename_variables,[],[254])). % 1.21/1.27 cnf(1368,plain, % 1.21/1.27 ($false), % 1.21/1.27 inference(scs_inference,[],[289,1053,1066,1069,1072,254,1063,1097,1100,1103,1106,1109,1112,1117,1119,1193,1219,1222,1312,1334,1352,1358,1361,285,1075,1082,1087,1144,1155,1160,1165,1168,1175,1178,1181,1184,1187,1190,1196,1199,1206,1213,1216,1239,1241,1309,1317,1328,1331,1345,1348,1351,259,257,286,287,145,165,170,173,193,210,211,265,261,288,281,260,146,147,148,150,151,153,155,157,159,161,163,166,168,169,171,174,175,177,178,179,180,182,184,186,188,190,191,192,194,196,197,198,199,201,202,204,206,208,209,212,214,216,218,220,221,223,225,226,228,230,232,233,234,236,238,240,247,267,284,271,1012,445,487,537,560,993,1013,1015,389,436,437,531,532,533,2,500,501,593,718,720,722,724,728,730,930,74,75,76,351,353,354,433,435,442,443,457,508,563,565,599,600,601,611,612,613,614,626,628,629,631,633,634,665,667,672,673,675,677,704,769,770,771,772,773,774,791,1016,1018,1021,1023,3,67,68,69,70,71,72,73,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,107,108,109,110,111,112,113,115,116,117,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,139,140,141,142,143,446,449,450,481,517,580,591,651,711,775,790,839,840,841,846,858,859,898,950,951,952,953,956,957,792,793,794,795,482,985,562]), % 1.21/1.27 ['proof']). % 1.21/1.27 % SZS output end Proof % 1.21/1.27 % Total time :0.440000s %------------------------------------------------------------------------------