%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : ALG369-1 : 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 : n003.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 03:41:28 EDT 2024 % Result : Unsatisfiable 1.32s 1.35s % Output : CNFRefutation 1.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ALG369-1 : TPTP v8.2.0. Released v4.1.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.34 % Computer : n003.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Wed Jun 19 16:23:54 EDT 2024 % 0.12/0.34 % CPUTime : % 0.19/0.56 start to proof:theBenchmark % 1.18/1.30 %------------------------------------------- % 1.18/1.30 % File :CSE---1.7 % 1.18/1.30 % Problem :theBenchmark % 1.18/1.30 % Transform :cnf % 1.18/1.30 % Format :tptp:raw % 1.18/1.30 % Command :java -jar mcs_scs.jar %d %s % 1.18/1.30 % 1.18/1.30 % Result :Theorem 0.520000s % 1.18/1.30 % Output :CNFRefutation 0.520000s % 1.18/1.30 %------------------------------------------- % 1.18/1.31 %------------------------------------------------------------------------------ % 1.18/1.31 % File : ALG369-1 : TPTP v8.2.0. Released v4.1.0. % 1.18/1.31 % Domain : General Algebra % 1.18/1.31 % Problem : Fundamental theorem of algebra 0356_50 % 1.18/1.31 % Version : Especial. % 1.18/1.31 % English : % 1.18/1.31 % 1.18/1.31 % Refs : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe % 1.18/1.31 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 1.18/1.31 % Source : [Nip10] % 1.18/1.31 % Names : Fundamental_Theorem_Algebra-0356_50 [Nip10] % 1.18/1.31 % 1.18/1.31 % Status : Unsatisfiable % 1.18/1.31 % Rating : 0.05 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.07 v6.4.0, 0.00 v5.5.0, 0.30 v5.3.0, 0.28 v5.2.0, 0.12 v5.1.0, 0.24 v5.0.0, 0.21 v4.1.0 % 1.18/1.31 % Syntax : Number of clauses : 626 ( 76 unt; 126 nHn; 451 RR) % 1.18/1.31 % Number of literals : 2013 ( 327 equ;1268 neg) % 1.18/1.31 % Maximal clause size : 6 ( 3 avg) % 1.18/1.31 % Maximal term depth : 4 ( 1 avg) % 1.18/1.31 % Number of predicates : 62 ( 61 usr; 1 prp; 0-3 aty) % 1.18/1.31 % Number of functors : 16 ( 16 usr; 3 con; 0-3 aty) % 1.18/1.31 % Number of variables : 1609 ( 46 sgn) % 1.18/1.31 % SPC : CNF_UNS_RFO_SEQ_NHN % 1.18/1.31 % 1.18/1.31 % Comments : % 1.18/1.31 %------------------------------------------------------------------------------ % 1.18/1.31 cnf(cls_linorder__not__less_0,axiom, % 1.18/1.31 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.31 | c_lessequals(V_y,V_x,T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_linorder__not__less_1,axiom, % 1.18/1.31 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.18/1.31 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_linorder__antisym__conv1_1,axiom, % 1.18/1.31 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_x,V_x,T_a) % 1.18/1.31 | c_lessequals(V_x,V_x,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_linorder__antisym__conv2_1,axiom, % 1.18/1.31 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.31 | ~ c_lessequals(V_x,V_x,T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_not__leE_0,axiom, % 1.18/1.31 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.18/1.31 | c_lessequals(V_y,V_x,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_less__le__not__le_1,axiom, % 1.18/1.31 ( ~ class_Orderings_Opreorder(T_a) % 1.18/1.31 | ~ c_lessequals(V_y,V_x,T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_order__less__le_2,axiom, % 1.18/1.31 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.18/1.31 | V_x = V_y % 1.18/1.31 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_order__le__less_0,axiom, % 1.18/1.31 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.31 | V_x = V_y % 1.18/1.31 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.18/1.31 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_order__le__neq__trans_0,axiom, % 1.18/1.31 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.31 | V_a = V_b % 1.18/1.31 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_order__neq__le__trans_0,axiom, % 1.18/1.31 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.31 | ~ c_lessequals(V_a,V_b,T_a) % 1.18/1.31 | V_a = V_b ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_linorder__antisym__conv1_0,axiom, % 1.18/1.31 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.31 | V_x = V_y % 1.18/1.31 | ~ c_lessequals(V_x,V_y,T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_linorder__antisym__conv2_0,axiom, % 1.18/1.31 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.31 | V_x = V_y % 1.18/1.31 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.18/1.31 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_xt1_I12_J_0,axiom, % 1.18/1.31 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.18/1.31 | ~ c_lessequals(V_b,V_a,T_a) % 1.18/1.31 | V_a = V_b ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_xt1_I11_J_0,axiom, % 1.18/1.31 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.18/1.31 | V_a = V_b % 1.18/1.31 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_mult__less__cancel__left__disj_3,axiom, % 1.18/1.31 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_mult__less__cancel__right__disj_3,axiom, % 1.18/1.31 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_abs__less__iff_0,axiom, % 1.18/1.31 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_less__le__not__le_2,axiom, % 1.18/1.31 ( ~ class_Orderings_Opreorder(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.18/1.31 | c_lessequals(V_y,V_x,T_a) % 1.18/1.31 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_add__strict__mono_0,axiom, % 1.18/1.31 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_order__le__less_1,axiom, % 1.18/1.31 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.31 | c_lessequals(V_x,V_y,T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_order__less__imp__le_0,axiom, % 1.18/1.31 ( ~ class_Orderings_Opreorder(T_a) % 1.18/1.31 | c_lessequals(V_x,V_y,T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_add__less__cancel__left_0,axiom, % 1.18/1.31 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_add__less__cancel__left_1,axiom, % 1.18/1.31 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_add__strict__left__mono_0,axiom, % 1.18/1.31 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_add__less__cancel__right_0,axiom, % 1.18/1.31 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_add__less__cancel__right_1,axiom, % 1.18/1.31 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_add__strict__right__mono_0,axiom, % 1.18/1.31 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_order__le__less__trans_0,axiom, % 1.18/1.31 ( ~ class_Orderings_Opreorder(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.18/1.31 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_order__less__le__trans_0,axiom, % 1.18/1.31 ( ~ class_Orderings_Opreorder(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.18/1.31 | ~ c_lessequals(V_y,V_z,T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_xt1_I8_J_0,axiom, % 1.18/1.31 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.18/1.31 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_xt1_I7_J_0,axiom, % 1.18/1.31 ( ~ class_Orderings_Oorder(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.18/1.31 | ~ c_lessequals(V_z,V_y,T_a) % 1.18/1.31 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_sum__squares__gt__zero__iff_1,axiom, % 1.18/1.31 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.31 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a) % 1.18/1.31 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.31 % 1.18/1.31 cnf(cls_sum__squares__gt__zero__iff_2,axiom, % 1.18/1.31 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.32 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a) % 1.18/1.32 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_mult__le__cancel__left__neg_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.32 | c_lessequals(V_b,V_a,T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_mult__le__cancel__left__neg_1,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.32 | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.32 | ~ c_lessequals(V_b,V_a,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_mult__le__cancel__left__pos_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.32 | c_lessequals(V_a,V_b,T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_mult__le__cancel__left__pos_1,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.32 | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.18/1.32 | ~ c_lessequals(V_a,V_b,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_mult__left__le__imp__le_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.32 | c_lessequals(V_a,V_b,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_mult__right__le__imp__le_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.32 | c_lessequals(V_a,V_b,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_add__strict__increasing2_0,axiom, % 1.18/1.32 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.18/1.32 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.18/1.32 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_mult__strict__mono_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.32 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_mult__left__less__imp__less_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 1.18/1.32 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_mult__right__less__imp__less_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 1.18/1.32 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_mult__less__imp__less__left_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.32 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_mult__less__imp__less__right_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.32 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_not__sum__squares__lt__zero_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_add__neg__nonpos_0,axiom, % 1.18/1.32 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.18/1.32 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.32 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_add__nonpos__neg_0,axiom, % 1.18/1.32 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.18/1.32 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.32 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_mult__strict__mono_H_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.32 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_sum__squares__gt__zero__iff_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_add__nonneg__pos_0,axiom, % 1.18/1.32 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.18/1.32 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_add__pos__nonneg_0,axiom, % 1.18/1.32 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.18/1.32 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_add__strict__increasing_0,axiom, % 1.18/1.32 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.18/1.32 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.18/1.32 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.18/1.32 | ~ c_lessequals(V_b,V_c,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_inverse__le__imp__le_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.32 | c_lessequals(V_b,V_a,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_le__imp__inverse__le_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.32 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.32 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_inverse__le__imp__le__neg_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.32 | c_lessequals(V_b,V_a,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_le__imp__inverse__le__neg_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.32 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.32 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_mult__le__less__imp__less_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.32 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.18/1.32 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_mult__less__le__imp__less_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.32 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.32 | ~ c_lessequals(V_c,V_d,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.32 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.32 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_comm__monoid__add_Omult__1_0,axiom, % 1.18/1.32 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.18/1.32 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_class__semiring_Oadd__0_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.32 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = V_x ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_class__ringb_Oadd__r0__iff_1,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.32 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.32 | V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_comm__monoid__add_Omult__1__right_0,axiom, % 1.18/1.32 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.18/1.32 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_linorder__not__le_0,axiom, % 1.18/1.32 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.32 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.18/1.32 | c_lessequals(V_x,V_y,T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_linorder__not__le_1,axiom, % 1.18/1.32 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.32 | ~ c_lessequals(V_x,V_y,T_a) % 1.18/1.32 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_mult__right__le__one__le_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.32 | c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_x,T_a) % 1.18/1.32 | ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_mult__left__le__one__le_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.32 | c_lessequals(c_HOL_Otimes__class_Otimes(V_y,V_x,T_a),V_x,T_a) % 1.18/1.32 | ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_right__inverse_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.32 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) % 1.18/1.32 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_left__inverse_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.32 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.18/1.32 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_field__inverse_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.32 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.18/1.32 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_inverse__le__1__iff_1,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.32 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.32 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.32 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_inverse__le__1__iff_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.32 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.32 | c_lessequals(c_HOL_Oone__class_Oone(T_a),V_x,T_a) % 1.18/1.32 | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_norm__sgn_0,axiom, % 1.18/1.32 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.18/1.32 | c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_add__frac__eq_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.32 | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) % 1.18/1.32 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.32 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_add__num__frac_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.32 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.32 | c_HOL_Oplus__class_Oplus(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a),V_y,T_a) % 1.18/1.32 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_add__frac__num_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.32 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.32 | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a),V_y,T_a) % 1.18/1.32 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_le__divide__eq_9,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.32 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.32 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.32 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.32 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_divide__le__eq_9,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.32 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.32 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.32 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.18/1.32 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_inverse__1_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.32 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_inverse__eq__1__iff_1,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.32 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.32 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_abs__one_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.32 | c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_mult__1__right_0,axiom, % 1.18/1.32 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.18/1.32 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_mult__1__left_0,axiom, % 1.18/1.32 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.18/1.32 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_mult__1_0,axiom, % 1.18/1.32 ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) % 1.18/1.32 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_class__semiring_Omul__1_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.32 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_x,T_a) = V_x ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.32 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_class__semiring_Osemiring__rules_I11_J_0,axiom, % 1.18/1.32 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.18/1.32 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 1.18/1.32 % 1.18/1.32 cnf(cls_sgn__one_0,axiom, % 1.18/1.33 ( ~ class_RealVector_Oreal__normed__algebra__1(T_a) % 1.18/1.33 | c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_inverse__eq__1__iff_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_HOL_Oinverse__class_Oinverse(V_x,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.18/1.33 | V_x = c_HOL_Oone__class_Oone(T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_norm__sgn_1,axiom, % 1.18/1.33 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.18/1.33 | c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(V_x,T_a),T_a) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) % 1.18/1.33 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_real__sgn__def_0,axiom, % 1.18/1.33 c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_INVERSE__ZERO_0,axiom, % 1.18/1.33 c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_inverse__divide_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_b,V_a,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_mult__frac__frac_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_z,V_w,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_y,V_w,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_abs__divide_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_mult__frac__num_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),V_y,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_add__divide__distrib_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.18/1.33 | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_divide_Oadd_0,axiom, % 1.18/1.33 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.18/1.33 | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_ya,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_ya,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_exp__ln_0,axiom, % 1.18/1.33 ( c_Transcendental_Oexp(c_Transcendental_Oln(V_x),tc_RealDef_Oreal) = V_x % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_exp__ln__iff_0,axiom, % 1.18/1.33 ( c_Transcendental_Oexp(c_Transcendental_Oln(V_x),tc_RealDef_Oreal) != V_x % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_exp__less__cancel_0,axiom, % 1.18/1.33 ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_Transcendental_Oexp(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_exp__less__mono_0,axiom, % 1.18/1.33 ( c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_Transcendental_Oexp(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_one__le__inverse__iff_2,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) % 1.18/1.33 | ~ c_lessequals(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_inverse__less__1__iff_1,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.18/1.33 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_one__le__inverse__iff_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.18/1.33 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_inverse__less__1__iff_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_x,T_a) % 1.18/1.33 | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_le__divide__eq_4,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_le__divide__eq_1,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.33 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_divide__le__eq_4,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_divide__le__eq_1,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.33 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_le__divide__eq_7,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.33 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_le__divide__eq_5,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.33 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_divide__le__eq_7,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.18/1.33 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_divide__le__eq_5,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.18/1.33 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.33 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_le__divide__eq_8,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.18/1.33 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_divide__le__eq_8,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.18/1.33 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_mult__imp__le__div__pos_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | c_lessequals(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.18/1.33 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_mult__imp__div__pos__le_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) % 1.18/1.33 | ~ c_lessequals(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_le__divide__eq_6,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.33 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_le__divide__eq_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.33 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_divide__le__eq_6,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.33 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_divide__le__eq_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.33 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_divide__left__mono__neg_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.18/1.33 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_divide__left__mono_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.18/1.33 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.33 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_mult__less__cancel__right__disj_2,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_mult__less__cancel__right__disj_1,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_mult__less__cancel__left__disj_2,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_mult__less__cancel__left__disj_1,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_zero__less__abs__iff_0,axiom, % 1.18/1.33 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.33 | ~ 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) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_abs__if_1,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oabs__if(T_a) % 1.18/1.33 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.18/1.33 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_abs__if__lattice_1,axiom, % 1.18/1.33 ( ~ class_Orderings_Olinorder(T_a) % 1.18/1.33 | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.18/1.33 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.18/1.33 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_abs__not__less__zero_0,axiom, % 1.18/1.33 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_negative__imp__inverse__negative_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_inverse__negative__iff__negative_1,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_inverse__negative__iff__negative_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_add__pos__pos_0,axiom, % 1.18/1.33 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_zero__less__abs__iff_1,axiom, % 1.18/1.33 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) % 1.18/1.33 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_less__imp__inverse__less__neg_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_inverse__less__imp__less__neg_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_less__imp__inverse__less_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_inverse__less__imp__less_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_inverse__positive__imp__positive_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.33 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_not__square__less__zero_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_Rational_Oordered__idom__class_Osgn__less_1,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_Rational_Oordered__idom__class_Osgn__less_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_mult__less__cancel__right__disj_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_mult__less__cancel__left__disj_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom, % 1.18/1.33 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom, % 1.18/1.33 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_inverse__negative__imp__negative_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_pos__add__strict_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_mult__pos__neg2_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_mult__pos__neg_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_mult__neg__pos_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_zero__less__mult__pos2_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_zero__less__mult__pos_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_mult__pos__pos_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_mult__neg__neg_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom, % 1.18/1.33 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom, % 1.18/1.33 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_even__less__0__iff_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_even__less__0__iff_1,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_Rational_Oordered__idom__class_Osgn__greater_1,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.33 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) % 1.18/1.33 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_add__0__left_0,axiom, % 1.18/1.33 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 1.18/1.33 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_monoid__add__class_Oadd__0__right_0,axiom, % 1.18/1.33 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 1.18/1.33 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_exp__not__eq__zero_0,axiom, % 1.18/1.33 ( ~ class_SEQ_Obanach(T_a) % 1.18/1.33 | ~ class_RealVector_Oreal__normed__field(T_a) % 1.18/1.33 | c_Transcendental_Oexp(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_sgn__zero__iff_0,axiom, % 1.18/1.33 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.18/1.33 | c_HOL_Osgn__class_Osgn(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.33 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_sgn__0__0_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.18/1.33 | c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.33 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_abs__eq__0_1,axiom, % 1.18/1.33 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.18/1.33 | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_double__eq__0__iff_1,axiom, % 1.18/1.33 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.33 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_class__ringb_Oadd__r0__iff_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.18/1.33 | ~ class_Int_Onumber__ring(T_a) % 1.18/1.33 | V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) % 1.18/1.33 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_double__eq__0__iff_0,axiom, % 1.18/1.33 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.18/1.33 | c_HOL_Oplus__class_Oplus(V_a,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.33 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_no__zero__divirors__neq0_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.18/1.33 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.33 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.33 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_no__zero__divisors_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.18/1.33 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.33 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.33 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_mult__eq__0__iff_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.18/1.33 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.33 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.33 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_nonzero__inverse__eq__imp__eq_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.33 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a) % 1.18/1.33 | V_a = V_b % 1.18/1.33 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.18/1.33 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_inverse__nonzero__iff__nonzero_1,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.18/1.33 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.18/1.33 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.18/1.33 % 1.18/1.33 cnf(cls_inverse__zero_0,axiom, % 1.18/1.33 ( ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.33 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.33 % 1.32/1.33 cnf(cls_nonzero__inverse__inverse__eq_0,axiom, % 1.32/1.33 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.32/1.33 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a % 1.32/1.33 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.33 % 1.32/1.33 cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom, % 1.32/1.33 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.33 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.33 % 1.32/1.33 cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom, % 1.32/1.33 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.33 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.33 % 1.32/1.33 cnf(cls_mult__left_Ozero_0,axiom, % 1.32/1.33 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.32/1.33 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.33 % 1.32/1.33 cnf(cls_mult_Ozero__left_0,axiom, % 1.32/1.33 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.32/1.33 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.33 % 1.32/1.33 cnf(cls_mult_Ozero__right_0,axiom, % 1.32/1.33 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.32/1.33 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.33 % 1.32/1.33 cnf(cls_mult__right_Ozero_0,axiom, % 1.32/1.33 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.32/1.33 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.33 % 1.32/1.33 cnf(cls_class__semiring_Omul__0_0,axiom, % 1.32/1.33 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.33 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.33 % 1.32/1.33 cnf(cls_mult__zero__left_0,axiom, % 1.32/1.33 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 1.32/1.33 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.33 % 1.32/1.33 cnf(cls_mult__zero__right_0,axiom, % 1.32/1.33 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 1.32/1.33 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.33 % 1.32/1.33 cnf(cls_mult__eq__0__iff_1,axiom, % 1.32/1.33 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.32/1.33 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.33 % 1.32/1.33 cnf(cls_mult__eq__0__iff_2,axiom, % 1.32/1.33 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.32/1.33 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.33 % 1.32/1.33 cnf(cls_sgn__zero_0,axiom, % 1.32/1.34 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.32/1.34 | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_sgn0_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Osgn__if(T_a) % 1.32/1.34 | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_sgn__0__0_1,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.32/1.34 | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_inverse__nonzero__iff__nonzero_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.34 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_inverse__zero__imp__zero_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.32/1.34 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.34 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_abs__eq__0_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.32/1.34 | c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.34 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_add__le__less__mono_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.32/1.34 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_add__less__le__mono_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_lessequals(V_c,V_d,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_exp__add_0,axiom, % 1.32/1.34 ( ~ class_SEQ_Obanach(T_a) % 1.32/1.34 | ~ class_RealVector_Oreal__normed__field(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_abs__inverse_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_inverse__nonpositive__iff__nonpositive_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_inverse__nonpositive__iff__nonpositive_1,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_sum__squares__le__zero__iff_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.34 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.34 | ~ 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_sum__squares__le__zero__iff_1,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.34 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.34 | ~ 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_combine__common__factor_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Osemiring(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_abs__triangle__ineq_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_add__cancel__21_1,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_class__semiring_Oadd__a_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_comm__monoid__add_Omult__assoc_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.34 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_class__semiring_Omul__c_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.34 | c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_add__nonneg__eq__0__iff_2,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_inverse__inverse__eq_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_norm__inverse_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | ~ class_RealVector_Oreal__normed__div__algebra(T_a) % 1.32/1.34 | c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Onorm__class_Onorm(V_a,T_a),tc_RealDef_Oreal) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_abs__mult__less_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_b,T_a),V_d,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_c,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_class__ringb_Onoteq__reduce_1,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.32/1.34 | ~ class_Int_Onumber__ring(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_class__ringb_Oadd__mul__solve_1,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.32/1.34 | ~ class_Int_Onumber__ring(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_abs__le__D1_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.32/1.34 | c_lessequals(V_a,V_b,T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_abs__le__mult_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Olordered__ring(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_of__real__eq__iff_0,axiom, % 1.32/1.34 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 1.32/1.34 | c_RealVector_Oof__real(V_x,T_a) != c_RealVector_Oof__real(V_y,T_a) % 1.32/1.34 | V_x = V_y ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_add__increasing_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.32/1.34 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.32/1.34 | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.32/1.34 | ~ c_lessequals(V_b,V_c,T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_add__increasing2_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.32/1.34 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.32/1.34 | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.32/1.34 | ~ c_lessequals(V_b,V_a,T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_sum__squares__ge__zero_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__sgn__abs_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.32/1.34 | c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_x,T_a),c_HOL_Oabs__class_Oabs(V_x,T_a),T_a) = V_x ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_add__nonneg__eq__0__iff_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.32/1.34 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.32/1.34 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_add__nonneg__eq__0__iff_1,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.32/1.34 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.32/1.34 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_sum__squares__le__zero__iff_2,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_abs__le__zero__iff_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.32/1.34 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_exp__of__real_0,axiom, % 1.32/1.34 ( ~ class_SEQ_Obanach(T_a) % 1.32/1.34 | ~ class_RealVector_Oreal__normed__field(T_a) % 1.32/1.34 | c_Transcendental_Oexp(c_RealVector_Oof__real(V_x,T_a),T_a) = c_RealVector_Oof__real(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_estimate__by__abs_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.32/1.34 | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_order__antisym_0,axiom, % 1.32/1.34 ( ~ class_Orderings_Oorder(T_a) % 1.32/1.34 | V_x = V_y % 1.32/1.34 | ~ c_lessequals(V_y,V_x,T_a) % 1.32/1.34 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_order__eq__iff_2,axiom, % 1.32/1.34 ( ~ class_Orderings_Oorder(T_a) % 1.32/1.34 | V_x = V_y % 1.32/1.34 | ~ c_lessequals(V_y,V_x,T_a) % 1.32/1.34 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_order__antisym__conv_0,axiom, % 1.32/1.34 ( ~ class_Orderings_Oorder(T_a) % 1.32/1.34 | V_x = V_y % 1.32/1.34 | ~ c_lessequals(V_x,V_y,T_a) % 1.32/1.34 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_abs__of__nonneg_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.32/1.34 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_add__left__mono_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_add__right__mono_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_add__le__cancel__left_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.32/1.34 | c_lessequals(V_a,V_b,T_a) % 1.32/1.34 | ~ 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_add__le__cancel__left_1,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_add__le__cancel__right_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.32/1.34 | c_lessequals(V_a,V_b,T_a) % 1.32/1.34 | ~ 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_add__le__cancel__right_1,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_abs__mult_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_abs__eq__mult_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_abs__eq__mult_1,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_abs__eq__mult_2,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.34 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_abs__eq__mult_3,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__left__idem_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 1.32/1.34 | 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__le__0__iff_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.34 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__le__0__iff_1,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.34 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.34 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__le__0__iff_2,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.34 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__le__0__iff_3,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.34 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.34 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_of__real__inverse_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | ~ class_RealVector_Oreal__div__algebra(T_a) % 1.32/1.34 | c_RealVector_Oof__real(c_HOL_Oinverse__class_Oinverse(V_x,tc_RealDef_Oreal),T_a) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(V_x,T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_exp__inj__iff_0,axiom, % 1.32/1.34 ( c_Transcendental_Oexp(V_x,tc_RealDef_Oreal) != c_Transcendental_Oexp(V_y,tc_RealDef_Oreal) % 1.32/1.34 | V_x = V_y ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__mono1_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Omult__mono1(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.34 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__left__mono_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.34 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_Rational_Oordered__idom__class_Osgn__greater_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_add__neg__neg_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_abs__of__pos_0,axiom, % 1.32/1.34 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.32/1.34 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_positive__imp__inverse__positive_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_inverse__positive__iff__positive_1,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_inverse__positive__iff__positive_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__strict__left__mono__comm_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__less__cancel__right__disj_5,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__less__cancel__right__disj_4,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__strict__right__mono_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__strict__right__mono__neg_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__less__cancel__left__disj_5,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__less__cancel__left__disj_4,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__strict__left__mono_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__strict__left__mono__neg_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__less__cancel__left__pos_1,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__less__cancel__left__pos_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.32/1.34 | ~ 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) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__less__cancel__left__neg_1,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.34 | 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) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__less__cancel__left__neg_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.32/1.34 | ~ 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) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_not__one__le__zero_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_zero__le__one_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.32/1.34 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_exp__zero_0,axiom, % 1.32/1.34 ( ~ class_SEQ_Obanach(T_a) % 1.32/1.34 | ~ class_RealVector_Oreal__normed__field(T_a) % 1.32/1.34 | c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_inverse__less__1__iff_2,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_x,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_one__less__inverse__iff_1,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_less__add__one_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_less__1__mult_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Otimes__class_Otimes(V_m,V_n,T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_n,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_m,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_norm__zero_0,axiom, % 1.32/1.34 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.32/1.34 | c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_of__real__eq__0__iff_0,axiom, % 1.32/1.34 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 1.32/1.34 | c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.34 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_of__real__0_0,axiom, % 1.32/1.34 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 1.32/1.34 | c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_of__real_Ozero_0,axiom, % 1.32/1.34 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.32/1.34 | ~ class_RealVector_Oreal__algebra__1(T_a) % 1.32/1.34 | c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_norm__eq__zero_0,axiom, % 1.32/1.34 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.32/1.34 | c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.32/1.34 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__eq__eq_4,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a),V_c,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_frac__eq__eq_1,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.34 | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) != c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) % 1.32/1.34 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.34 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.34 | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_frac__eq__eq_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.34 | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) != c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) % 1.32/1.34 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.34 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.34 | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) = c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_zero__le__divide__iff_5,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) % 1.32/1.34 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_zero__le__divide__iff_4,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_eq__divide__eq_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b % 1.32/1.34 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__eq__eq_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) % 1.32/1.34 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_eq__divide__eq_4,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a),V_c,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__le__0__iff_3,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.34 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__le__0__iff_2,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__le__0__iff_1,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.34 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__le__0__iff_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_nonzero__abs__divide_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) % 1.32/1.34 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__right__mono__neg_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),T_a) % 1.32/1.34 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__right__mono_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.34 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_eq__divide__imp_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.34 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.34 | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__eq__imp_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.34 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.34 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_eq__divide__eq_3,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) % 1.32/1.34 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__eq__eq_3,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a % 1.32/1.34 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__le__0__iff_5,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.34 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__le__0__iff_4,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_zero__le__divide__iff_3,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_zero__le__divide__iff_2,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_zero__le__divide__iff_1,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_zero__le__divide__iff_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__divide__mult__cancel__right_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) % 1.32/1.34 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_mult__divide__mult__cancel__left_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) % 1.32/1.34 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_inverse__eq__divide_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.34 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_class__fieldgb_Oinverse__divide_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.34 | ~ class_Int_Onumber__ring(T_a) % 1.32/1.34 | c_HOL_Oinverse__class_Oinverse(V_x,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_x,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_ln__less__cancel__iff_1,axiom, % 1.32/1.34 ( c_HOL_Oord__class_Oless(c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y),tc_RealDef_Oreal) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_ln__less__cancel__iff_0,axiom, % 1.32/1.34 ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y),tc_RealDef_Oreal) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_ln__inj__iff_0,axiom, % 1.32/1.34 ( c_Transcendental_Oln(V_x) != c_Transcendental_Oln(V_y) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.32/1.34 | V_x = V_y ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_ln__less__self_0,axiom, % 1.32/1.34 ( c_HOL_Oord__class_Oless(c_Transcendental_Oln(V_x),V_x,tc_RealDef_Oreal) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_not__exp__less__zero_0,axiom, % 1.32/1.34 ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_norm__not__less__zero_0,axiom, % 1.32/1.34 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.32/1.34 | ~ 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) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_exp__gt__zero_0,axiom, % 1.32/1.34 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_norm__one_0,axiom, % 1.32/1.34 ( ~ class_RealVector_Oreal__normed__algebra__1(T_a) % 1.32/1.34 | c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_of__real__1_0,axiom, % 1.32/1.34 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 1.32/1.34 | c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_exp__eq__one__iff_1,axiom, % 1.32/1.34 c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_ln__one_0,axiom, % 1.32/1.34 c_Transcendental_Oln(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_exp__eq__one__iff_0,axiom, % 1.32/1.34 ( c_Transcendental_Oexp(V_x,tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) % 1.32/1.34 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_of__real__divide_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | ~ class_RealVector_Oreal__field(T_a) % 1.32/1.34 | c_RealVector_Oof__real(c_HOL_Oinverse__class_Odivide(V_x,V_y,tc_RealDef_Oreal),T_a) = c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(V_x,T_a),c_RealVector_Oof__real(V_y,T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_norm__divide_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | ~ class_RealVector_Oreal__normed__field(T_a) % 1.32/1.34 | c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_RealVector_Onorm__class_Onorm(V_a,T_a),c_RealVector_Onorm__class_Onorm(V_b,T_a),tc_RealDef_Oreal) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_sgn__1__pos_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.32/1.34 | c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_sgn__pos_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.32/1.34 | c_HOL_Osgn__class_Osgn(V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_one__less__inverse__iff_2,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_zero__less__two_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_one__less__inverse__iff_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_sgn__if_1,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Osgn__if(T_a) % 1.32/1.34 | c_HOL_Osgn__class_Osgn(V_x,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.32/1.34 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__strict__left__mono__neg_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a) % 1.32/1.34 | ~ 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) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__strict__left__mono_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a) % 1.32/1.34 | ~ 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) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_frac__le_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_z,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_w,T_a),T_a) % 1.32/1.34 | ~ c_lessequals(V_w,V_z,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 1.32/1.34 | ~ c_lessequals(V_x,V_y,T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_less__divide__eq_7,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_less__divide__eq_5,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_less__divide__eq_4,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_less__divide__eq_1,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__less__eq_7,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__less__eq_5,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__less__eq_4,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__less__eq_1,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__nonpos__neg_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__nonneg__pos_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.32/1.34 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_less__divide__eq_9,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_less__divide__eq_8,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__less__eq_9,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_divide__less__eq_8,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.34 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.34 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.32/1.34 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.32/1.34 % 1.32/1.34 cnf(cls_frac__less_0,axiom, % 1.32/1.34 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_z,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_w,T_a),T_a) % 1.32/1.35 | ~ c_lessequals(V_w,V_z,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__nonpos__pos_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.32/1.35 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__nonneg__neg_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult__right__mono_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 1.32/1.35 | 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) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.35 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult__left__mono__neg_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.32/1.35 | 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) % 1.32/1.35 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult__right__mono__neg_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.32/1.35 | 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) % 1.32/1.35 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.32/1.35 | ~ class_Int_Onumber__ring(T_a) % 1.32/1.35 | 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) % 1.32/1.35 | V_c = V_d % 1.32/1.35 | V_r = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_sum__squares__eq__zero__iff_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.35 | 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) % 1.32/1.35 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_sum__squares__eq__zero__iff_1,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.35 | 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) % 1.32/1.35 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_inverse__unique_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.32/1.35 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.32/1.35 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult__idem_0,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 1.32/1.35 | c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = V_x ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_inverse__eq__iff__eq_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a) % 1.32/1.35 | V_a = V_b ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_split__mult__pos__le_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_split__mult__pos__le_1,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.32/1.35 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult__nonpos__nonpos_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.32/1.35 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__le__square_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__le__mult__iff_4,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__le__mult__iff_5,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.32/1.35 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult__nonneg__nonneg_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_class__semiring_Omul__a_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult__right_Oadd_0,axiom, % 1.32/1.35 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult_Oadd__right_0,axiom, % 1.32/1.35 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult__left_Oadd_0,axiom, % 1.32/1.35 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult_Oadd__left_0,axiom, % 1.32/1.35 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_class__semiring_Omul__d_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_comm__semiring__class_Odistrib_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ocomm__semiring(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__le__mult__iff_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.35 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__le__mult__iff_1,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.35 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__le__mult__iff_2,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.35 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__le__mult__iff_3,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.35 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult__mono_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 1.32/1.35 | 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) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.35 | ~ c_lessequals(V_c,V_d,T_a) % 1.32/1.35 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult__mono_H_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 1.32/1.35 | 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) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.35 | ~ c_lessequals(V_c,V_d,T_a) % 1.32/1.35 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_sgn__sgn_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.32/1.35 | c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) = c_HOL_Osgn__class_Osgn(V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_inverse__add_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.35 | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) % 1.32/1.35 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.35 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_division__ring__inverse__add_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.32/1.35 | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) % 1.32/1.35 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.35 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_abs__sgn_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.32/1.35 | c_HOL_Oabs__class_Oabs(V_k,T_a) = c_HOL_Otimes__class_Otimes(V_k,c_HOL_Osgn__class_Osgn(V_k,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_class__ringb_Oadd__cancel_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.32/1.35 | ~ class_Int_Onumber__ring(T_a) % 1.32/1.35 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) % 1.32/1.35 | V_y = V_z ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_add__imp__eq_0,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a) % 1.32/1.35 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) % 1.32/1.35 | V_b = V_c ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_add__left__cancel_0,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 1.32/1.35 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) % 1.32/1.35 | V_b = V_c ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_add__right__cancel_0,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 1.32/1.35 | c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) != c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) % 1.32/1.35 | V_b = V_c ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult__le__0__iff_4,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult__le__0__iff_5,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.35 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_split__mult__neg__le_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_split__mult__neg__le_1,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.35 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult__nonneg__nonpos_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult__nonpos__nonneg_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.35 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult__nonneg__nonpos2_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_inverse__mult__distrib_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_nonzero__inverse__mult__distrib_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.32/1.35 | c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.32/1.35 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.35 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_abs__le__zero__iff_1,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_ln__unique_0,axiom, % 1.32/1.35 c_Transcendental_Oln(c_Transcendental_Oexp(V_y,tc_RealDef_Oreal)) = V_y ). % 1.32/1.35 % 1.32/1.35 cnf(cls_exp__ln__eq_0,axiom, % 1.32/1.35 c_Transcendental_Oln(c_Transcendental_Oexp(V_u,tc_RealDef_Oreal)) = V_u ). % 1.32/1.35 % 1.32/1.35 cnf(cls_ln__exp_0,axiom, % 1.32/1.35 c_Transcendental_Oln(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal)) = V_x ). % 1.32/1.35 % 1.32/1.35 cnf(cls_nonzero__norm__inverse_0,axiom, % 1.32/1.35 ( ~ class_RealVector_Oreal__normed__div__algebra(T_a) % 1.32/1.35 | c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Onorm__class_Onorm(V_a,T_a),tc_RealDef_Oreal) % 1.32/1.35 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_nonzero__abs__inverse_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) % 1.32/1.35 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult__exp__exp_0,axiom, % 1.32/1.35 ( ~ class_SEQ_Obanach(T_a) % 1.32/1.35 | ~ class_RealVector_Oreal__normed__field(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_add__cancel__21_0,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.32/1.35 | 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) % 1.32/1.35 | c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) = V_u ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_add__nonneg__nonneg_0,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_add__mono_0,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 1.32/1.35 | 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) % 1.32/1.35 | ~ c_lessequals(V_c,V_d,T_a) % 1.32/1.35 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_inverse__nonnegative__iff__nonnegative_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_inverse__nonnegative__iff__nonnegative_1,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_sgn__of__real_0,axiom, % 1.32/1.35 ( ~ class_RealVector_Oreal__normed__algebra__1(T_a) % 1.32/1.35 | c_HOL_Osgn__class_Osgn(c_RealVector_Oof__real(V_r,T_a),T_a) = c_RealVector_Oof__real(c_HOL_Osgn__class_Osgn(V_r,tc_RealDef_Oreal),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_abs__idempotent_0,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.35 | c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_class__semiring_Oadd__c_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.35 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_y,V_x,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_comm__monoid__add_Omult__commute_0,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.32/1.35 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_inverse__le__1__iff_2,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_x,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_class__semiring_Osemiring__rules_I4_J_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.35 | c_HOL_Oplus__class_Oplus(V_m,V_m,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_abs__ge__self_0,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.32/1.35 | c_lessequals(V_a,c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_class__ringb_Onoteq__reduce_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.32/1.35 | ~ class_Int_Onumber__ring(T_a) % 1.32/1.35 | 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) % 1.32/1.35 | V_c = V_d % 1.32/1.35 | V_a = V_b ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_class__ringb_Oadd__mul__solve_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.32/1.35 | ~ class_Int_Onumber__ring(T_a) % 1.32/1.35 | 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) % 1.32/1.35 | V_y = V_z % 1.32/1.35 | V_w = V_x ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_abs__mult__self_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_class__semiring_Osemiring__rules_I2_J_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.35 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),V_m,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.32/1.35 | c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_abs__mult__pos_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.32/1.35 | 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) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_one__le__inverse__iff_1,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_lessequals(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_nonzero__of__real__inverse_0,axiom, % 1.32/1.35 ( ~ class_RealVector_Oreal__div__algebra(T_a) % 1.32/1.35 | c_RealVector_Oof__real(c_HOL_Oinverse__class_Oinverse(V_x,tc_RealDef_Oreal),T_a) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(V_x,T_a),T_a) % 1.32/1.35 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__inverse_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.35 | c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_class__fieldgb_Odivide__inverse_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.35 | ~ class_Int_Onumber__ring(T_a) % 1.32/1.35 | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.32/1.35 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_abs__add__abs_0,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_order__eq__refl_0,axiom, % 1.32/1.35 ( ~ class_Orderings_Opreorder(T_a) % 1.32/1.35 | c_lessequals(V_x,V_x,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_order__eq__iff_0,axiom, % 1.32/1.35 ( ~ class_Orderings_Oorder(T_a) % 1.32/1.35 | c_lessequals(V_x,V_x,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_le__add__right__mono_0,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.32/1.35 | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) % 1.32/1.35 | ~ c_lessequals(V_c,V_d,T_a) % 1.32/1.35 | ~ c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_order__trans_0,axiom, % 1.32/1.35 ( ~ class_Orderings_Opreorder(T_a) % 1.32/1.35 | c_lessequals(V_x,V_z,T_a) % 1.32/1.35 | ~ c_lessequals(V_y,V_z,T_a) % 1.32/1.35 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_add__nonpos__nonpos_0,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_xt1_I6_J_0,axiom, % 1.32/1.35 ( ~ class_Orderings_Oorder(T_a) % 1.32/1.35 | c_lessequals(V_z,V_x,T_a) % 1.32/1.35 | ~ c_lessequals(V_z,V_y,T_a) % 1.32/1.35 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_sum__squares__eq__zero__iff_2,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.32/1.35 | 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_sgn__mult_0,axiom, % 1.32/1.35 ( ~ class_RealVector_Oreal__normed__div__algebra(T_a) % 1.32/1.35 | c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_x,T_a),c_HOL_Osgn__class_Osgn(V_y,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_sgn__times_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.32/1.35 | c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Osgn__class_Osgn(V_b,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_abs__ge__zero_0,axiom, % 1.32/1.35 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_linorder__linear_0,axiom, % 1.32/1.35 ( ~ class_Orderings_Olinorder(T_a) % 1.32/1.35 | c_lessequals(V_y,V_x,T_a) % 1.32/1.35 | c_lessequals(V_x,V_y,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult__imp__less__div__pos_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_mult__imp__div__pos__less_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_less__divide__eq_6,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_less__divide__eq_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__less__eq_6,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__less__eq_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_abs__div__pos_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_x,T_a),V_y,T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_frac__less2_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_z,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_w,T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_w,V_z,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 1.32/1.35 | ~ c_lessequals(V_x,V_y,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_le__divide__eq_3,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.32/1.35 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_le__divide__eq_2,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.35 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__le__eq_3,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__le__eq_2,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_nonzero__inverse__eq__divide_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.35 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 1.32/1.35 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__le__0__1__iff_1,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__le__0__1__iff_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__le__divide__1__iff_1,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__le__divide__1__iff_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.35 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_less__half__sum_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_gt__half__sum_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),T_a),V_b,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__less__norm__iff_1,axiom, % 1.32/1.35 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.32/1.35 | 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) % 1.32/1.35 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__less__norm__iff_0,axiom, % 1.32/1.35 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.32/1.35 | ~ 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) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_nonzero__norm__divide_0,axiom, % 1.32/1.35 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.32/1.35 | c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_RealVector_Onorm__class_Onorm(V_a,T_a),c_RealVector_Onorm__class_Onorm(V_b,T_a),tc_RealDef_Oreal) % 1.32/1.35 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_real__sgn__pos_0,axiom, % 1.32/1.35 ( c_HOL_Osgn__class_Osgn(V_x,tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_real__inverse__gt__one_0,axiom, % 1.32/1.35 ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_exp__less__one__iff_1,axiom, % 1.32/1.35 ( c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_exp__less__one__iff_0,axiom, % 1.32/1.35 ( c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_ln__eq__zero__iff_1,axiom, % 1.32/1.35 ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.32/1.35 | c_Transcendental_Oln(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_ln__eq__zero__iff_0,axiom, % 1.32/1.35 ( c_Transcendental_Oln(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.32/1.35 | V_x = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_ln__less__zero__iff_0,axiom, % 1.32/1.35 ( c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_Transcendental_Oln(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_ln__less__zero_0,axiom, % 1.32/1.35 ( c_HOL_Oord__class_Oless(c_Transcendental_Oln(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_real__sgn__def_1,axiom, % 1.32/1.35 ( c_HOL_Osgn__class_Osgn(V_x,tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.32/1.35 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_ln__gt__zero_0,axiom, % 1.32/1.35 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x),tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_ln__gt__zero__imp__gt__one_0,axiom, % 1.32/1.35 ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x),tc_RealDef_Oreal) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_ln__gt__zero__iff_1,axiom, % 1.32/1.35 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x),tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_ln__gt__zero__iff_0,axiom, % 1.32/1.35 ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x),tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_one__less__exp__iff_0,axiom, % 1.32/1.35 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_exp__gt__one_0,axiom, % 1.32/1.35 ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_nonzero__of__real__divide_0,axiom, % 1.32/1.35 ( ~ class_RealVector_Oreal__field(T_a) % 1.32/1.35 | c_RealVector_Oof__real(c_HOL_Oinverse__class_Odivide(V_x,V_y,tc_RealDef_Oreal),T_a) = c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(V_x,T_a),c_RealVector_Oof__real(V_y,T_a),T_a) % 1.32/1.35 | V_y = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_xt1_I9_J_0,axiom, % 1.32/1.35 ( ~ class_Orderings_Oorder(T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_not__less__iff__gr__or__eq_1,axiom, % 1.32/1.35 ( ~ class_Orderings_Olinorder(T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_order__less__asym_0,axiom, % 1.32/1.35 ( ~ class_Orderings_Opreorder(T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_order__less__asym_H_0,axiom, % 1.32/1.35 ( ~ class_Orderings_Opreorder(T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_eq__divide__eq_2,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__less__0__iff_5,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__less__0__iff_4,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__pos__neg_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__neg__pos_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__less__divide__1__iff_1,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__less__divide__1__iff_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_that_0,axiom, % 1.32/1.35 ( v_thesis____ % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__less__one_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_one0_0,axiom, % 1.32/1.35 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_order__less__irrefl_0,axiom, % 1.32/1.35 ( ~ class_Orderings_Opreorder(T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_real__less__def_1,axiom, % 1.32/1.35 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_order__less__le_1,axiom, % 1.32/1.35 ( ~ class_Orderings_Oorder(T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_linorder__neq__iff_1,axiom, % 1.32/1.35 ( ~ class_Orderings_Olinorder(T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_not__one__less__zero_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__less__0__1__iff_1,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__less__0__1__iff_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__neq__one_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.32/1.35 | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_real__zero__not__eq__one_0,axiom, % 1.32/1.35 c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__self__if_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__1_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.35 | c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__strict__right__mono__neg_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__strict__right__mono_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__less__divide__iff_5,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__less__divide__iff_4,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__pos__pos_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__neg__neg_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_less__divide__eq_3,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_less__divide__eq_2,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__less__eq_3,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__less__eq_2,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_right__inverse__eq_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.35 | c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.32/1.35 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.35 | V_a = V_b ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_ep_0,axiom, % 1.32/1.35 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_e,tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__less__divide__iff_3,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__less__divide__iff_2,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__less__divide__iff_1,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_zero__less__divide__iff_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_linorder__neqE__ordered__idom_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.32/1.35 | V_x = V_y ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_not__less__iff__gr__or__eq_0,axiom, % 1.32/1.35 ( ~ class_Orderings_Olinorder(T_a) % 1.32/1.35 | V_x = V_y % 1.32/1.35 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_linorder__antisym__conv3_0,axiom, % 1.32/1.35 ( ~ class_Orderings_Olinorder(T_a) % 1.32/1.35 | V_x = V_y % 1.32/1.35 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_linorder__less__linear_0,axiom, % 1.32/1.35 ( ~ class_Orderings_Olinorder(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.32/1.35 | V_x = V_y % 1.32/1.35 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_linorder__neqE_0,axiom, % 1.32/1.35 ( ~ class_Orderings_Olinorder(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.32/1.35 | V_x = V_y ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_one__neq__zero_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.32/1.35 | c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_em0_0,axiom, % 1.32/1.35 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_xt1_I10_J_0,axiom, % 1.32/1.35 ( ~ class_Orderings_Oorder(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_order__less__trans_0,axiom, % 1.32/1.35 ( ~ class_Orderings_Opreorder(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_right__inverse__eq_1,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.35 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.32/1.35 | c_HOL_Oinverse__class_Odivide(V_x,V_x,T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__self_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.35 | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.32/1.35 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__self__if_1,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.32/1.35 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__zero__left_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.35 | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__eq__eq_1,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__zero_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide_Ozero_0,axiom, % 1.32/1.35 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.32/1.35 | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__less__0__iff_3,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__less__0__iff_2,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__less__0__iff_1,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_divide__less__0__iff_0,axiom, % 1.32/1.35 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.32/1.35 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.32/1.35 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.32/1.35 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_m_I1_J_0,axiom, % 1.32/1.35 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_CHAINED_2,axiom, % 1.32/1.35 c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_CHAINED_1,axiom, % 1.32/1.35 c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_CHAINED_0,axiom, % 1.32/1.35 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_e,v_m____),tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(cls_conjecture_0,negated_conjecture, % 1.32/1.35 ~ v_thesis____ ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom, % 1.32/1.35 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom, % 1.32/1.35 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict,axiom, % 1.32/1.35 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring,axiom, % 1.32/1.35 class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict,axiom, % 1.32/1.35 class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add,axiom, % 1.32/1.35 class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,axiom, % 1.32/1.35 class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs,axiom, % 1.32/1.35 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add,axiom, % 1.32/1.35 class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors,axiom, % 1.32/1.35 class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 1.32/1.35 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict,axiom, % 1.32/1.35 class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom, % 1.32/1.35 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,axiom, % 1.32/1.35 class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,axiom, % 1.32/1.35 class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add,axiom, % 1.32/1.35 class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring,axiom, % 1.32/1.35 class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs,axiom, % 1.32/1.35 class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom, % 1.32/1.35 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring,axiom, % 1.32/1.35 class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors,axiom, % 1.32/1.35 class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero,axiom, % 1.32/1.35 class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom,axiom, % 1.32/1.35 class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom, % 1.32/1.35 class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom, % 1.32/1.35 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult,axiom, % 1.32/1.35 class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom, % 1.32/1.35 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult,axiom, % 1.32/1.35 class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add,axiom, % 1.32/1.35 class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring,axiom, % 1.32/1.35 class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field,axiom, % 1.32/1.35 class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring,axiom, % 1.32/1.35 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring,axiom, % 1.32/1.35 class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring,axiom, % 1.32/1.35 class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom, % 1.32/1.35 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add,axiom, % 1.32/1.35 class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one,axiom, % 1.32/1.35 class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,axiom, % 1.32/1.35 class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__div__algebra,axiom, % 1.32/1.35 class_RealVector_Oreal__div__algebra(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1,axiom, % 1.32/1.35 class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1,axiom, % 1.32/1.35 class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,axiom, % 1.32/1.35 class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero,axiom, % 1.32/1.35 class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono,axiom, % 1.32/1.35 class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult,axiom, % 1.32/1.35 class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring,axiom, % 1.32/1.35 class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add,axiom, % 1.32/1.35 class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if,axiom, % 1.32/1.35 class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if,axiom, % 1.32/1.35 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__field,axiom, % 1.32/1.35 class_RealVector_Oreal__field(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ofield,axiom, % 1.32/1.35 class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oidom,axiom, % 1.32/1.35 class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom, % 1.32/1.35 class_Orderings_Opreorder(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom, % 1.32/1.35 class_Orderings_Olinorder(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Orderings_Oorder,axiom, % 1.32/1.35 class_Orderings_Oorder(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom, % 1.32/1.35 class_Int_Onumber__ring(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 cnf(clsarity_RealDef__Oreal__SEQ_Obanach,axiom, % 1.32/1.35 class_SEQ_Obanach(tc_RealDef_Oreal) ). % 1.32/1.35 % 1.32/1.35 %------------------------------------------------------------------------------ % 1.32/1.35 %------------------------------------------- % 1.32/1.35 % Proof found % 1.32/1.35 % SZS status Theorem for theBenchmark % 1.32/1.35 % SZS output start Proof % 1.32/1.35 %ClaNum:720(EqnAxiom:94) % 1.32/1.35 %VarNum:5028(SingletonVarNum:1388) % 1.32/1.35 %MaxLitNum:6 % 1.32/1.35 %MaxfuncDepth:3 % 1.32/1.35 %SharedTerms:83 % 1.32/1.35 %goalClause: 167 % 1.32/1.35 %singleGoalClaCount:1 % 1.32/1.35 [95]P1(a1) % 1.32/1.35 [96]P23(a1) % 1.32/1.35 [97]P24(a1) % 1.32/1.35 [98]P25(a1) % 1.32/1.35 [99]P26(a1) % 1.32/1.35 [100]P2(a1) % 1.32/1.35 [101]P3(a1) % 1.32/1.35 [102]P49(a1) % 1.32/1.35 [103]P4(a1) % 1.32/1.35 [104]P50(a1) % 1.32/1.35 [105]P22(a1) % 1.32/1.35 [106]P27(a1) % 1.32/1.35 [107]P28(a1) % 1.32/1.35 [108]P39(a1) % 1.32/1.35 [109]P5(a1) % 1.32/1.35 [110]P40(a1) % 1.32/1.35 [111]P42(a1) % 1.32/1.35 [112]P41(a1) % 1.32/1.35 [113]P29(a1) % 1.32/1.35 [114]P14(a1) % 1.32/1.35 [115]P15(a1) % 1.32/1.35 [116]P30(a1) % 1.32/1.35 [117]P35(a1) % 1.32/1.35 [118]P19(a1) % 1.32/1.35 [119]P37(a1) % 1.32/1.35 [120]P16(a1) % 1.32/1.35 [121]P17(a1) % 1.32/1.35 [122]P51(a1) % 1.32/1.35 [123]P18(a1) % 1.32/1.35 [124]P52(a1) % 1.32/1.35 [125]P43(a1) % 1.32/1.35 [126]P53(a1) % 1.32/1.35 [127]P31(a1) % 1.32/1.35 [128]P44(a1) % 1.32/1.35 [129]P58(a1) % 1.32/1.35 [130]P59(a1) % 1.32/1.35 [131]P8(a1) % 1.32/1.35 [132]P9(a1) % 1.32/1.35 [133]P36(a1) % 1.32/1.35 [134]P45(a1) % 1.32/1.35 [135]P32(a1) % 1.32/1.35 [136]P21(a1) % 1.32/1.35 [137]P54(a1) % 1.32/1.35 [138]P33(a1) % 1.32/1.35 [139]P46(a1) % 1.32/1.35 [140]P47(a1) % 1.32/1.35 [141]P48(a1) % 1.32/1.35 [142]P34(a1) % 1.32/1.35 [143]P55(a1) % 1.32/1.35 [144]P56(a1) % 1.32/1.35 [145]P10(a1) % 1.32/1.35 [146]P38(a1) % 1.32/1.35 [147]P57(a1) % 1.32/1.35 [148]P12(a1) % 1.32/1.35 [149]P13(a1) % 1.32/1.35 [150]P20(a1) % 1.32/1.35 [151]P60(a1) % 1.32/1.35 [167]~P61(a5000) % 1.32/1.35 [159]P6(f7(a1),a14,a1) % 1.32/1.35 [160]P6(f7(a1),a15,a1) % 1.32/1.35 [161]P6(f7(a1),f2(a1),a1) % 1.32/1.35 [162]P6(f7(a1),f16(a14,a15),a1) % 1.32/1.35 [163]P6(f16(a14,a15),f2(a1),a1) % 1.32/1.35 [165]P6(f7(a1),f4(a14,a15,a1),a1) % 1.32/1.35 [166]P6(f16(a14,a15),f4(a14,a15,a1),a1) % 1.32/1.35 [168]~E(f7(a1),f2(a1)) % 1.32/1.35 [152]E(f6(f2(a1)),f7(a1)) % 1.32/1.35 [153]E(f3(f7(a1),a1),f7(a1)) % 1.32/1.35 [154]E(f8(f7(a1),a1),f7(a1)) % 1.32/1.35 [155]E(f11(f7(a1),a1),f2(a1)) % 1.32/1.35 [169]~P6(x1691,x1691,a1) % 1.32/1.35 [164]P6(f7(a1),f11(x1641,a1),a1) % 1.32/1.35 [170]~P6(f11(x1701,a1),f7(a1),a1) % 1.32/1.35 [158]E(f6(f11(x1581,a1)),x1581) % 1.32/1.35 [172]~P60(x1721)+~E(f7(x1721),f2(x1721)) % 1.32/1.35 [173]E(x1731,f7(a1))+~E(f11(x1731,a1),f2(a1)) % 1.32/1.35 [241]~P51(x2411)+P7(f7(x2411),f2(x2411),x2411) % 1.32/1.35 [242]~P51(x2421)+P6(f7(x2421),f2(x2421),x2421) % 1.32/1.35 [278]~P6(f7(a1),x2781,a1)+E(f8(x2781,a1),f2(a1)) % 1.32/1.35 [288]~P51(x2881)+~P7(f2(x2881),f7(x2881),x2881) % 1.32/1.35 [289]~P51(x2891)+~P6(f2(x2891),f7(x2891),x2891) % 1.32/1.35 [314]P6(f6(x3141),x3141,a1)+~P6(f7(a1),x3141,a1) % 1.32/1.35 [327]~P6(f2(a1),x3271,a1)+P6(f7(a1),f6(x3271),a1) % 1.32/1.35 [330]~P6(f7(a1),x3301,a1)+P6(f2(a1),f11(x3301,a1),a1) % 1.32/1.35 [331]~P6(x3311,f7(a1),a1)+P6(f11(x3311,a1),f2(a1),a1) % 1.32/1.35 [348]P6(x3481,f7(a1),a1)+~P6(f11(x3481,a1),f2(a1),a1) % 1.32/1.35 [349]P6(f7(a1),x3491,a1)+~P6(f2(a1),f11(x3491,a1),a1) % 1.32/1.35 [174]~P32(x1741)+E(f12(f7(a1),x1741),f7(x1741)) % 1.32/1.35 [175]~P32(x1751)+E(f12(f2(a1),x1751),f2(x1751)) % 1.32/1.35 [176]~P29(x1761)+E(f13(f7(x1761),x1761),f7(a1)) % 1.32/1.35 [177]~P30(x1771)+E(f13(f2(x1771),x1771),f2(a1)) % 1.32/1.35 [178]~P19(x1781)+E(f5(f7(x1781),x1781),f7(x1781)) % 1.32/1.35 [179]~P26(x1791)+E(f5(f2(x1791),x1791),f2(x1791)) % 1.32/1.35 [180]~P41(x1801)+E(f3(f7(x1801),x1801),f7(x1801)) % 1.32/1.35 [181]~P40(x1811)+E(f3(f2(x1811),x1811),f2(x1811)) % 1.32/1.35 [182]~P26(x1821)+E(f8(f7(x1821),x1821),f7(x1821)) % 1.32/1.35 [183]~P29(x1831)+E(f8(f7(x1831),x1831),f7(x1831)) % 1.32/1.35 [184]~P58(x1841)+E(f8(f7(x1841),x1841),f7(x1841)) % 1.32/1.35 [185]~P30(x1851)+E(f8(f2(x1851),x1851),f2(x1851)) % 1.32/1.35 [244]~P17(x2441)+E(f9(f7(x2441),f7(x2441),x2441),f7(x2441)) % 1.32/1.35 [254]P6(f7(a1),x2541,a1)+~E(f11(f6(x2541),a1),x2541) % 1.32/1.35 [280]~P19(x2801)+P7(f5(f7(x2801),x2801),f7(x2801),x2801) % 1.32/1.35 [284]~P6(f7(a1),x2841,a1)+E(f11(f6(x2841),a1),x2841) % 1.32/1.35 [328]~P29(x3281)+~P6(f7(a1),f13(f7(x3281),x3281),a1) % 1.32/1.35 [329]~P19(x3291)+~P6(f7(x3291),f5(f7(x3291),x3291),x3291) % 1.32/1.35 [378]~P51(x3781)+P6(f7(x3781),f9(f2(x3781),f2(x3781),x3781),x3781) % 1.32/1.35 [209]~P29(x2091)+E(f13(f8(f7(x2091),x2091),x2091),f7(a1)) % 1.32/1.35 [451]~P25(x4511)+E(f9(f10(f7(x4511),f7(x4511),x4511),f10(f7(x4511),f7(x4511),x4511),x4511),f7(x4511)) % 1.32/1.35 [698]~P25(x6981)+P7(f9(f10(f7(x6981),f7(x6981),x6981),f10(f7(x6981),f7(x6981),x6981),x6981),f7(x6981),x6981) % 1.32/1.35 [720]~P25(x7201)+~P6(f7(x7201),f9(f10(f7(x7201),f7(x7201),x7201),f10(f7(x7201),f7(x7201),x7201),x7201),x7201) % 1.32/1.35 [207]~P23(x2072)+P7(x2071,x2071,x2072) % 1.32/1.35 [208]~P24(x2082)+P7(x2081,x2081,x2082) % 1.32/1.35 [264]~P6(x2642,x2642,x2641)+~P1(x2641) % 1.32/1.35 [265]~P6(x2652,x2652,x2651)+~P23(x2651) % 1.32/1.35 [266]~P6(x2662,x2662,x2661)+~P24(x2661) % 1.32/1.35 [196]E(x1961,x1962)+~E(f11(x1961,a1),f11(x1962,a1)) % 1.32/1.35 [210]~P11(x2102)+E(f10(x2101,x2101,x2102),x2101) % 1.32/1.35 [255]~P19(x2552)+P7(x2551,f5(x2551,x2552),x2552) % 1.32/1.35 [267]~P19(x2671)+P7(f7(x2671),f5(x2672,x2671),x2671) % 1.32/1.35 [311]~P29(x3111)+~P6(f13(x3112,x3111),f7(a1),a1) % 1.32/1.35 [313]~P19(x3131)+~P6(f5(x3132,x3131),f7(x3131),x3131) % 1.32/1.35 [333]~P25(x3331)+P7(f7(x3331),f10(x3332,x3332,x3331),x3331) % 1.32/1.35 [357]~P6(x3571,x3572,a1)+P6(f11(x3571,a1),f11(x3572,a1),a1) % 1.32/1.35 [382]P6(x3821,x3822,a1)+~P6(f11(x3821,a1),f11(x3822,a1),a1) % 1.32/1.35 [427]~P25(x4271)+~P6(f10(x4272,x4272,x4271),f7(x4271),x4271) % 1.32/1.35 [205]~P19(x2052)+E(f5(f5(x2051,x2052),x2052),f5(x2051,x2052)) % 1.32/1.35 [206]~P26(x2062)+E(f8(f8(x2061,x2062),x2062),f8(x2061,x2062)) % 1.32/1.35 [212]~P28(x2122)+E(f10(x2121,f2(x2122),x2122),x2121) % 1.32/1.35 [213]~P14(x2132)+E(f10(x2131,f2(x2132),x2132),x2131) % 1.32/1.35 [214]~P4(x2142)+E(f9(x2141,f7(x2142),x2142),x2141) % 1.32/1.35 [215]~P28(x2152)+E(f9(x2151,f7(x2152),x2152),x2151) % 1.32/1.35 [216]~P18(x2162)+E(f9(x2161,f7(x2162),x2162),x2161) % 1.32/1.35 [217]~P42(x2172)+E(f4(x2171,f2(x2172),x2172),x2171) % 1.32/1.35 [219]~P28(x2191)+E(f10(f2(x2191),x2192,x2191),x2192) % 1.32/1.35 [220]~P14(x2201)+E(f10(f2(x2201),x2202,x2201),x2202) % 1.32/1.35 [221]~P15(x2211)+E(f10(f2(x2211),x2212,x2211),x2212) % 1.32/1.35 [222]~P4(x2221)+E(f9(f7(x2221),x2222,x2221),x2222) % 1.32/1.35 [224]~P28(x2241)+E(f9(f7(x2241),x2242,x2241),x2242) % 1.32/1.35 [225]~P18(x2251)+E(f9(f7(x2251),x2252,x2251),x2252) % 1.32/1.35 [228]~P28(x2282)+E(f10(x2281,f7(x2282),x2282),f7(x2282)) % 1.32/1.35 [229]~P53(x2292)+E(f10(x2291,f7(x2292),x2292),f7(x2292)) % 1.32/1.35 [231]~P31(x2312)+E(f10(x2311,f7(x2312),x2312),f7(x2312)) % 1.32/1.35 [232]~P44(x2322)+E(f10(x2321,f7(x2322),x2322),f7(x2322)) % 1.32/1.35 [234]~P28(x2341)+E(f10(f7(x2341),x2342,x2341),f7(x2341)) % 1.32/1.35 [235]~P53(x2351)+E(f10(f7(x2351),x2352,x2351),f7(x2351)) % 1.32/1.35 [237]~P31(x2371)+E(f10(f7(x2371),x2372,x2371),f7(x2371)) % 1.32/1.35 [238]~P44(x2381)+E(f10(f7(x2381),x2382,x2381),f7(x2381)) % 1.32/1.35 [239]~P42(x2391)+E(f4(f7(x2391),x2392,x2391),f7(x2391)) % 1.32/1.35 [240]~P35(x2401)+E(f4(f7(x2401),x2402,x2401),f7(x2401)) % 1.32/1.35 [249]~P42(x2491)+E(f4(f2(x2491),x2492,x2491),f3(x2492,x2491)) % 1.32/1.35 [251]~P30(x2512)+E(f8(f12(x2511,x2512),x2512),f12(f8(x2511,a1),x2512)) % 1.32/1.35 [275]~P26(x2752)+E(f10(x2751,f8(x2751,x2752),x2752),f5(x2751,x2752)) % 1.32/1.35 [290]~P26(x2902)+E(f10(f8(x2901,x2902),f5(x2901,x2902),x2902),x2901) % 1.32/1.35 [332]~P26(x3322)+E(f10(f5(x3321,x3322),f5(x3321,x3322),x3322),f10(x3321,x3321,x3322)) % 1.32/1.35 [347]~P51(x3472)+P6(x3471,f9(x3471,f2(x3472),x3472),x3472) % 1.32/1.35 [420]~P28(x4202)+E(f9(x4201,x4201,x4202),f10(f9(f2(x4202),f2(x4202),x4202),x4201,x4202)) % 1.32/1.35 [293]~P28(x2933)+E(f10(x2931,x2932,x2933),f10(x2932,x2931,x2933)) % 1.32/1.35 [294]~P4(x2943)+E(f9(x2941,x2942,x2943),f9(x2942,x2941,x2943)) % 1.32/1.35 [296]~P28(x2963)+E(f9(x2961,x2962,x2963),f9(x2962,x2961,x2963)) % 1.32/1.35 [312]~P42(x3123)+E(f10(x3121,f3(x3122,x3123),x3123),f4(x3121,x3122,x3123)) % 1.32/1.35 [393]~P11(x3933)+E(f10(x3931,f10(x3931,x3932,x3933),x3933),f10(x3931,x3932,x3933)) % 1.32/1.35 [394]~P26(x3942)+E(f10(f5(x3941,x3942),f5(x3943,x3942),x3942),f5(f10(x3941,x3943,x3942),x3942)) % 1.32/1.35 [395]~P26(x3952)+E(f10(f8(x3951,x3952),f8(x3953,x3952),x3952),f8(f10(x3951,x3953,x3952),x3952)) % 1.32/1.35 [396]~P36(x3962)+E(f10(f8(x3961,x3962),f8(x3963,x3962),x3962),f8(f10(x3961,x3963,x3962),x3962)) % 1.32/1.35 [625]~P45(x6253)+P7(f5(f10(x6251,x6252,x6253),x6253),f10(f5(x6251,x6253),f5(x6252,x6253),x6253),x6253) % 1.32/1.35 [626]~P19(x6263)+P7(f5(f9(x6261,x6262,x6263),x6263),f9(f5(x6261,x6263),f5(x6262,x6263),x6263),x6263) % 1.32/1.35 [683]~P25(x6831)+P7(f7(x6831),f9(f10(x6832,x6832,x6831),f10(x6833,x6833,x6831),x6831),x6831) % 1.32/1.35 [716]~P25(x7161)+~P6(f9(f10(x7162,x7162,x7161),f10(x7163,x7163,x7161),x7161),f7(x7161),x7161) % 1.32/1.35 [474]~P19(x4742)+E(f5(f9(f5(x4741,x4742),f5(x4743,x4742),x4742),x4742),f9(f5(x4741,x4742),f5(x4743,x4742),x4742)) % 1.32/1.35 [475]~P28(x4753)+E(f9(x4751,f10(x4752,x4751,x4753),x4753),f10(f9(x4752,f2(x4753),x4753),x4751,x4753)) % 1.32/1.35 [476]~P28(x4763)+E(f9(f10(x4761,x4762,x4763),x4762,x4763),f10(f9(x4761,f2(x4763),x4763),x4762,x4763)) % 1.32/1.35 [452]~P28(x4524)+E(f10(x4521,f10(x4522,x4523,x4524),x4524),f10(x4522,f10(x4521,x4523,x4524),x4524)) % 1.32/1.35 [453]~P4(x4534)+E(f9(x4531,f9(x4532,x4533,x4534),x4534),f9(x4532,f9(x4531,x4533,x4534),x4534)) % 1.32/1.35 [454]~P28(x4544)+E(f9(x4541,f9(x4542,x4543,x4544),x4544),f9(x4542,f9(x4541,x4543,x4544),x4544)) % 1.32/1.35 [455]~P9(x4554)+E(f9(x4551,f9(x4552,x4553,x4554),x4554),f9(x4552,f9(x4551,x4553,x4554),x4554)) % 1.32/1.35 [460]~P28(x4603)+E(f10(f10(x4601,x4602,x4603),x4604,x4603),f10(x4601,f10(x4602,x4604,x4603),x4603)) % 1.32/1.35 [461]~P10(x4613)+E(f10(f10(x4611,x4612,x4613),x4614,x4613),f10(x4611,f10(x4612,x4614,x4613),x4613)) % 1.32/1.35 [462]~P4(x4623)+E(f9(f9(x4621,x4622,x4623),x4624,x4623),f9(x4621,f9(x4622,x4624,x4623),x4623)) % 1.32/1.35 [463]~P28(x4633)+E(f9(f9(x4631,x4632,x4633),x4634,x4633),f9(x4631,f9(x4632,x4634,x4633),x4633)) % 1.32/1.35 [464]~P8(x4643)+E(f9(f9(x4641,x4642,x4643),x4644,x4643),f9(x4641,f9(x4642,x4644,x4643),x4643)) % 1.32/1.35 [465]~P28(x4653)+E(f10(f10(x4651,x4652,x4653),x4654,x4653),f10(f10(x4651,x4654,x4653),x4652,x4653)) % 1.32/1.35 [466]~P28(x4663)+E(f9(f9(x4661,x4662,x4663),x4664,x4663),f9(f9(x4661,x4664,x4663),x4662,x4663)) % 1.32/1.35 [575]~P28(x5753)+E(f9(f10(x5751,x5752,x5753),f10(x5751,x5754,x5753),x5753),f10(x5751,f9(x5752,x5754,x5753),x5753)) % 1.32/1.35 [577]~P31(x5773)+E(f9(f10(x5771,x5772,x5773),f10(x5771,x5774,x5773),x5773),f10(x5771,f9(x5772,x5774,x5773),x5773)) % 1.32/1.35 [580]~P31(x5803)+E(f9(f10(x5801,x5802,x5803),f10(x5804,x5802,x5803),x5803),f10(f9(x5801,x5804,x5803),x5802,x5803)) % 1.32/1.35 [581]~P38(x5813)+E(f9(f10(x5811,x5812,x5813),f10(x5814,x5812,x5813),x5813),f10(f9(x5811,x5814,x5813),x5812,x5813)) % 1.32/1.35 [582]~P42(x5823)+E(f9(f4(x5821,x5822,x5823),f4(x5824,x5822,x5823),x5823),f4(f9(x5821,x5824,x5823),x5822,x5823)) % 1.32/1.35 [583]~P35(x5833)+E(f9(f4(x5831,x5832,x5833),f4(x5834,x5832,x5833),x5833),f4(f9(x5831,x5834,x5833),x5832,x5833)) % 1.32/1.35 [584]~P28(x5843)+E(f9(f10(x5841,x5842,x5843),f10(x5844,x5842,x5843),x5843),f10(f9(x5841,x5844,x5843),x5842,x5843)) % 1.32/1.35 [642]~P28(x6423)+E(f10(f10(x6421,x6422,x6423),f10(x6424,x6425,x6423),x6423),f10(f10(x6421,x6424,x6423),f10(x6422,x6425,x6423),x6423)) % 1.32/1.35 [643]~P28(x6433)+E(f9(f9(x6431,x6432,x6433),f9(x6434,x6435,x6433),x6433),f9(f9(x6431,x6434,x6433),f9(x6432,x6435,x6433),x6433)) % 1.32/1.35 [715]~P59(x7153)+E(f9(f10(x7151,x7152,x7153),f9(f10(x7154,x7152,x7153),x7155,x7153),x7153),f9(f10(f9(x7151,x7154,x7153),x7152,x7153),x7155,x7153)) % 1.32/1.35 [276]~E(f6(x2761),f7(a1))+E(x2761,f2(a1))+~P6(f7(a1),x2761,a1) % 1.32/1.35 [409]~P6(x4091,f2(a1),a1)+~P6(f7(a1),x4091,a1)+P6(f6(x4091),f7(a1),a1) % 1.32/1.35 [416]~P6(f7(a1),x4161,a1)+~P6(f6(x4161),f7(a1),a1)+P6(x4161,f2(a1),a1) % 1.32/1.35 [418]~P6(f7(a1),x4181,a1)+~P6(f7(a1),f6(x4181),a1)+P6(f2(a1),x4181,a1) % 1.32/1.35 [421]~P6(x4211,f2(a1),a1)+~P6(f7(a1),x4211,a1)+P6(f2(a1),f3(x4211,a1),a1) % 1.32/1.35 [188]~P42(x1881)+~P41(x1881)+E(f3(f2(x1881),x1881),f2(x1881)) % 1.32/1.35 [189]~P35(x1891)+~P52(x1891)+E(f11(f7(x1891),x1891),f2(x1891)) % 1.32/1.35 [358]~P22(x3581)+~P7(f7(x3581),f7(x3581),x3581)+E(f9(f7(x3581),f7(x3581),x3581),f7(x3581)) % 1.32/1.35 [190]~P29(x1902)+E(x1901,f7(x1902))+~E(f13(x1901,x1902),f7(a1)) % 1.32/1.35 [191]~P32(x1912)+~E(f12(x1911,x1912),f7(x1912))+E(x1911,f7(a1)) % 1.32/1.35 [192]~P19(x1922)+~E(f5(x1921,x1922),f7(x1922))+E(x1921,f7(x1922)) % 1.32/1.35 [193]~P40(x1932)+~E(f3(x1931,x1932),f7(x1932))+E(x1931,f7(x1932)) % 1.32/1.35 [194]~P26(x1942)+~E(f8(x1941,x1942),f7(x1942))+E(x1941,f7(x1942)) % 1.32/1.35 [195]~P29(x1952)+~E(f8(x1951,x1952),f7(x1952))+E(x1951,f7(x1952)) % 1.32/1.35 [197]~P35(x1972)+~P52(x1972)+~E(f11(x1971,x1972),f7(x1972)) % 1.32/1.35 [227]~P42(x2272)+E(f4(x2271,x2271,x2272),f2(x2272))+E(x2271,f7(x2272)) % 1.32/1.35 [250]~P37(x2502)+P6(x2501,f7(x2502),x2502)+E(f5(x2501,x2502),x2501) % 1.32/1.35 [269]~P29(x2692)+E(x2691,f7(x2692))+P6(f7(a1),f13(x2691,x2692),a1) % 1.32/1.35 [270]~P26(x2701)+P6(f7(x2701),x2702,x2701)+~E(f8(x2702,x2701),f2(x2701)) % 1.32/1.35 [274]~P19(x2742)+P6(f7(x2742),f5(x2741,x2742),x2742)+E(x2741,f7(x2742)) % 1.32/1.35 [279]~P17(x2792)+~E(f9(x2791,x2791,x2792),f7(x2792))+E(x2791,f7(x2792)) % 1.32/1.35 [302]~P19(x3022)+~P7(f7(x3022),x3021,x3022)+E(f5(x3021,x3022),x3021) % 1.32/1.35 [303]~P19(x3032)+~P6(f7(x3032),x3031,x3032)+E(f5(x3031,x3032),x3031) % 1.32/1.35 [309]~P26(x3092)+~P6(f7(x3092),x3091,x3092)+E(f8(x3091,x3092),f2(x3092)) % 1.32/1.35 [317]~P19(x3172)+~P7(f5(x3171,x3172),f7(x3172),x3172)+E(x3171,f7(x3172)) % 1.32/1.35 [363]~P27(x3631)+~P6(f7(x3631),x3632,x3631)+P6(f7(x3631),f3(x3632,x3631),x3631) % 1.32/1.35 [364]~P26(x3641)+~P6(f7(x3641),x3642,x3641)+P6(f7(x3641),f8(x3642,x3641),x3641) % 1.32/1.35 [365]~P27(x3652)+~P6(x3651,f7(x3652),x3652)+P6(f3(x3651,x3652),f7(x3652),x3652) % 1.32/1.35 [366]~P26(x3662)+~P6(x3661,f7(x3662),x3662)+P6(f8(x3661,x3662),f7(x3662),x3662) % 1.32/1.35 [380]~P26(x3802)+~P6(f8(x3801,x3802),f7(x3802),x3802)+P6(x3801,f7(x3802),x3802) % 1.32/1.35 [381]~P26(x3811)+~P6(f7(x3811),f8(x3812,x3811),x3811)+P6(f7(x3811),x3812,x3811) % 1.32/1.35 [422]~P17(x4221)+~P7(f7(x4221),x4222,x4221)+P7(f7(x4221),f9(x4222,x4222,x4221),x4221) % 1.32/1.35 [423]~P17(x4231)+~P6(f7(x4231),x4232,x4231)+P6(f7(x4231),f9(x4232,x4232,x4231),x4231) % 1.32/1.35 [424]~P17(x4242)+~P7(x4241,f7(x4242),x4242)+P7(f9(x4241,x4241,x4242),f7(x4242),x4242) % 1.32/1.35 [425]~P26(x4252)+~P6(x4251,f7(x4252),x4252)+P6(f9(x4251,x4251,x4252),f7(x4252),x4252) % 1.32/1.35 [426]~P17(x4262)+~P6(x4261,f7(x4262),x4262)+P6(f9(x4261,x4261,x4262),f7(x4262),x4262) % 1.32/1.35 [467]~P17(x4672)+~P7(f9(x4671,x4671,x4672),f7(x4672),x4672)+P7(x4671,f7(x4672),x4672) % 1.32/1.35 [468]~P26(x4682)+~P6(f9(x4681,x4681,x4682),f7(x4682),x4682)+P6(x4681,f7(x4682),x4682) % 1.32/1.35 [469]~P17(x4692)+~P6(f9(x4691,x4691,x4692),f7(x4692),x4692)+P6(x4691,f7(x4692),x4692) % 1.32/1.35 [470]~P17(x4701)+~P7(f7(x4701),f9(x4702,x4702,x4701),x4701)+P7(f7(x4701),x4702,x4701) % 1.32/1.35 [471]~P17(x4711)+~P6(f7(x4711),f9(x4712,x4712,x4711),x4711)+P6(f7(x4711),x4712,x4711) % 1.32/1.35 [200]~P40(x2002)+E(x2001,f7(x2002))+E(f3(f3(x2001,x2002),x2002),x2001) % 1.32/1.35 [202]~P29(x2022)+E(x2021,f7(x2022))+E(f13(f8(x2021,x2022),x2022),f2(a1)) % 1.32/1.35 [203]~P40(x2032)+~P41(x2032)+E(f3(f3(x2031,x2032),x2032),x2031) % 1.32/1.35 [243]~P39(x2432)+~P5(x2432)+E(f9(x2431,f7(x2432),x2432),x2431) % 1.32/1.35 [248]~P42(x2482)+~P41(x2482)+E(f4(x2481,f7(x2482),x2482),f7(x2482)) % 1.32/1.35 [256]~P33(x2562)+E(x2561,f7(a1))+E(f12(f3(x2561,a1),x2562),f3(f12(x2561,x2562),x2562)) % 1.32/1.35 [259]~P36(x2592)+E(x2591,f7(x2592))+E(f13(f3(x2591,x2592),x2592),f3(f13(x2591,x2592),a1)) % 1.32/1.35 [260]~P35(x2602)+~P52(x2602)+E(f11(f12(x2601,x2602),x2602),f12(f11(x2601,a1),x2602)) % 1.32/1.35 [261]~P41(x2612)+~P33(x2612)+E(f12(f3(x2611,a1),x2612),f3(f12(x2611,x2612),x2612)) % 1.32/1.35 [262]~P27(x2622)+E(x2621,f7(x2622))+E(f5(f3(x2621,x2622),x2622),f3(f5(x2621,x2622),x2622)) % 1.32/1.35 [263]~P41(x2632)+~P36(x2632)+E(f13(f3(x2631,x2632),x2632),f3(f13(x2631,x2632),a1)) % 1.32/1.35 [268]~P27(x2682)+~P41(x2682)+E(f5(f3(x2681,x2682),x2682),f3(f5(x2681,x2682),x2682)) % 1.32/1.35 [271]~P40(x2712)+E(x2711,f7(x2712))+E(f10(x2711,f3(x2711,x2712),x2712),f2(x2712)) % 1.32/1.35 [272]~P40(x2722)+E(x2721,f7(x2722))+E(f10(f3(x2721,x2722),x2721,x2722),f2(x2722)) % 1.32/1.35 [273]~P42(x2732)+E(x2731,f7(x2732))+E(f10(f3(x2731,x2732),x2731,x2732),f2(x2732)) % 1.32/1.35 [368]~P42(x3681)+~P41(x3681)+E(f4(f10(f7(x3681),x3682,x3681),x3682,x3681),f7(x3681)) % 1.32/1.35 [297]P7(x2972,x2971,x2973)+~P1(x2973)+P7(x2971,x2972,x2973) % 1.32/1.35 [300]P6(x3002,x3001,x3003)+~P1(x3003)+P7(x3001,x3002,x3003) % 1.32/1.35 [315]~P23(x3153)+~P6(x3151,x3152,x3153)+P7(x3151,x3152,x3153) % 1.32/1.35 [316]~P24(x3163)+~P6(x3161,x3162,x3163)+P7(x3161,x3162,x3163) % 1.32/1.35 [337]~P6(x3373,x3372,x3371)+~P1(x3371)+~P7(x3372,x3373,x3371) % 1.32/1.35 [339]~P6(x3393,x3392,x3391)+~P1(x3391)+~P6(x3392,x3393,x3391) % 1.32/1.35 [340]~P6(x3403,x3402,x3401)+~P23(x3401)+~P7(x3402,x3403,x3401) % 1.32/1.35 [342]~P6(x3423,x3422,x3421)+~P23(x3421)+~P6(x3422,x3423,x3421) % 1.32/1.35 [343]~P6(x3433,x3432,x3431)+~P24(x3431)+~P6(x3432,x3433,x3431) % 1.32/1.35 [201]~P32(x2013)+E(x2011,x2012)+~E(f12(x2011,x2013),f12(x2012,x2013)) % 1.32/1.35 [291]~P40(x2912)+~E(f10(x2911,x2913,x2912),f2(x2912))+E(f3(x2911,x2912),x2913) % 1.32/1.35 [360]~P19(x3603)+P7(x3601,x3602,x3603)+~P7(f5(x3601,x3603),x3602,x3603) % 1.32/1.35 [361]~P26(x3613)+P6(x3611,x3612,x3613)+~P6(f5(x3611,x3613),x3612,x3613) % 1.32/1.35 [335]~P42(x3352)+E(x3351,f7(x3352))+E(f4(f10(x3353,x3351,x3352),x3351,x3352),x3353) % 1.32/1.35 [362]~P42(x3623)+~P41(x3623)+E(f3(f4(x3621,x3622,x3623),x3623),f4(x3622,x3621,x3623)) % 1.32/1.35 [405]~P34(x4053)+E(x4051,f7(a1))+E(f4(f12(x4052,x4053),f12(x4051,x4053),x4053),f12(f4(x4052,x4051,a1),x4053)) % 1.32/1.35 [406]~P35(x4062)+E(x4061,f7(x4062))+E(f4(f13(x4063,x4062),f13(x4061,x4062),a1),f13(f4(x4063,x4061,x4062),x4062)) % 1.32/1.35 [407]~P41(x4072)+~P34(x4072)+E(f4(f12(x4071,x4072),f12(x4073,x4072),x4072),f12(f4(x4071,x4073,a1),x4072)) % 1.32/1.35 [408]~P27(x4082)+E(x4081,f7(x4082))+E(f4(f5(x4083,x4082),f5(x4081,x4082),x4082),f5(f4(x4083,x4081,x4082),x4082)) % 1.32/1.35 [411]~P41(x4112)+~P35(x4112)+E(f4(f13(x4111,x4112),f13(x4113,x4112),a1),f13(f4(x4111,x4113,x4112),x4112)) % 1.32/1.35 [412]~P27(x4122)+~P41(x4122)+E(f4(f5(x4121,x4122),f5(x4123,x4122),x4122),f5(f4(x4121,x4123,x4122),x4122)) % 1.32/1.35 [413]~P42(x4132)+~P41(x4132)+E(f10(f3(x4131,x4132),f3(x4133,x4132),x4132),f3(f10(x4131,x4133,x4132),x4132)) % 1.32/1.35 [415]~P35(x4152)+~P52(x4152)+E(f10(f11(x4151,x4152),f11(x4153,x4152),x4152),f11(f9(x4151,x4153,x4152),x4152)) % 1.32/1.35 [444]~P26(x4442)+~P7(f7(x4442),x4443,x4442)+E(f10(f5(x4441,x4442),x4443,x4442),f5(f10(x4441,x4443,x4442),x4442)) % 1.32/1.35 [585]~P25(x5852)+E(x5851,f7(x5852))+~E(f9(f10(x5853,x5853,x5852),f10(x5851,x5851,x5852),x5852),f7(x5852)) % 1.32/1.35 [586]~P25(x5862)+E(x5861,f7(x5862))+~E(f9(f10(x5861,x5861,x5862),f10(x5863,x5863,x5862),x5862),f7(x5862)) % 1.32/1.35 [684]~P25(x6842)+E(x6841,f7(x6842))+P6(f7(x6842),f9(f10(x6843,x6843,x6842),f10(x6841,x6841,x6842),x6842),x6842) % 1.32/1.35 [685]~P25(x6852)+E(x6851,f7(x6852))+P6(f7(x6852),f9(f10(x6851,x6851,x6852),f10(x6853,x6853,x6852),x6852),x6852) % 1.32/1.35 [717]~P25(x7172)+E(x7171,f7(x7172))+~P7(f9(f10(x7173,x7173,x7172),f10(x7171,x7171,x7172),x7172),f7(x7172),x7172) % 1.32/1.35 [718]~P25(x7182)+E(x7181,f7(x7182))+~P7(f9(f10(x7181,x7181,x7182),f10(x7183,x7183,x7182),x7182),f7(x7182),x7182) % 1.32/1.35 [703]~P27(x7033)+~P6(x7031,x7032,x7033)+P6(x7031,f4(f9(x7031,x7032,x7033),f9(f2(x7033),f2(x7033),x7033),x7033),x7033) % 1.32/1.35 [704]~P27(x7043)+~P6(x7041,x7042,x7043)+P6(f4(f9(x7041,x7042,x7043),f9(f2(x7043),f2(x7043),x7043),x7043),x7042,x7043) % 1.32/1.35 [344]~P12(x3444)+E(x3441,x3442)+~E(f9(x3443,x3441,x3444),f9(x3443,x3442,x3444)) % 1.32/1.35 [345]~P13(x3454)+E(x3451,x3452)+~E(f9(x3453,x3451,x3454),f9(x3453,x3452,x3454)) % 1.32/1.35 [346]~P13(x3464)+E(x3461,x3462)+~E(f9(x3461,x3463,x3464),f9(x3462,x3463,x3464)) % 1.32/1.35 [488]~P3(x4883)+~P7(x4881,x4884,x4883)+P7(f9(x4881,x4882,x4883),f9(x4884,x4882,x4883),x4883) % 1.32/1.35 [489]~P21(x4893)+~P7(x4891,x4894,x4893)+P7(f9(x4891,x4892,x4893),f9(x4894,x4892,x4893),x4893) % 1.32/1.35 [490]~P3(x4903)+~P7(x4902,x4904,x4903)+P7(f9(x4901,x4902,x4903),f9(x4901,x4904,x4903),x4903) % 1.32/1.35 [491]~P21(x4913)+~P7(x4912,x4914,x4913)+P7(f9(x4911,x4912,x4913),f9(x4911,x4914,x4913),x4913) % 1.32/1.35 [492]~P2(x4923)+~P6(x4921,x4924,x4923)+P6(f9(x4921,x4922,x4923),f9(x4924,x4922,x4923),x4923) % 1.32/1.35 [493]~P3(x4933)+~P6(x4931,x4934,x4933)+P6(f9(x4931,x4932,x4933),f9(x4934,x4932,x4933),x4933) % 1.32/1.35 [494]~P2(x4943)+~P6(x4942,x4944,x4943)+P6(f9(x4941,x4942,x4943),f9(x4941,x4944,x4943),x4943) % 1.32/1.35 [495]~P3(x4953)+~P6(x4952,x4954,x4953)+P6(f9(x4951,x4952,x4953),f9(x4951,x4954,x4953),x4953) % 1.32/1.35 [620]~P3(x6203)+P7(x6201,x6202,x6203)+~P7(f9(x6204,x6201,x6203),f9(x6204,x6202,x6203),x6203) % 1.32/1.35 [621]~P3(x6213)+P7(x6211,x6212,x6213)+~P7(f9(x6211,x6214,x6213),f9(x6212,x6214,x6213),x6213) % 1.32/1.35 [622]~P3(x6223)+P6(x6221,x6222,x6223)+~P6(f9(x6224,x6221,x6223),f9(x6224,x6222,x6223),x6223) % 1.32/1.35 [623]~P3(x6233)+P6(x6231,x6232,x6233)+~P6(f9(x6231,x6234,x6233),f9(x6232,x6234,x6233),x6233) % 1.32/1.35 [473]~P42(x4733)+~P41(x4733)+E(f10(f4(x4731,x4732,x4733),x4734,x4733),f4(f10(x4731,x4734,x4733),x4732,x4733)) % 1.32/1.35 [619]~P16(x6194)+~P7(f9(x6191,x6193,x6194),x6192,x6194)+P7(x6191,f9(x6192,f5(x6193,x6194),x6194),x6194) % 1.32/1.35 [649]~P39(x6493)+~P5(x6493)+E(f9(f10(x6491,x6492,x6493),f10(x6491,x6494,x6493),x6493),f9(f10(x6491,x6494,x6493),f10(x6491,x6492,x6493),x6493)) % 1.32/1.35 [567]~P9(x5673)+E(f9(x5671,x5672,x5673),x5674)+~E(f9(x5671,f9(x5675,x5672,x5673),x5673),f9(x5675,x5674,x5673)) % 1.32/1.35 [650]~P42(x6503)+~P41(x6503)+E(f10(f4(x6501,x6502,x6503),f4(x6504,x6505,x6503),x6503),f4(f10(x6501,x6504,x6503),f10(x6502,x6505,x6503),x6503)) % 1.32/1.35 [568]~P6(x5681,f4(a14,a15,a1),a1)+~P6(f7(a1),x5681,a1)+~P6(x5681,f2(a1),a1)+P61(a5000) % 1.32/1.35 [199]~P42(x1992)+~P41(x1992)+~E(f3(x1991,x1992),f2(x1992))+E(x1991,f2(x1992)) % 1.32/1.35 [258]~P1(x2582)+~P16(x2582)+P6(x2581,f7(x2582),x2582)+E(f5(x2581,x2582),x2581) % 1.32/1.35 [310]~P58(x3102)+~P6(f7(x3102),x3101,x3102)+E(f8(x3101,x3102),f2(x3102))+E(x3101,f7(x3102)) % 1.32/1.35 [369]E(x3691,x3692)+~E(f6(x3691),f6(x3692))+~P6(f7(a1),x3692,a1)+~P6(f7(a1),x3691,a1) % 1.32/1.35 [370]~P27(x3701)+~P41(x3701)+~P7(f7(x3701),x3702,x3701)+P7(f7(x3701),f3(x3702,x3701),x3701) % 1.32/1.35 [372]~P27(x3722)+~P41(x3722)+~P7(x3721,f7(x3722),x3722)+P7(f3(x3721,x3722),f7(x3722),x3722) % 1.32/1.35 [373]~P27(x3732)+~P41(x3732)+~P7(x3731,f7(x3732),x3732)+P7(f3(x3731,x3732),f2(x3732),x3732) % 1.32/1.35 [375]~P27(x3752)+~P41(x3752)+~P7(x3751,f7(x3752),x3752)+P6(f3(x3751,x3752),f2(x3752),x3752) % 1.32/1.35 [376]~P27(x3762)+~P41(x3762)+~P7(f2(x3762),x3761,x3762)+P7(f3(x3761,x3762),f2(x3762),x3762) % 1.32/1.35 [377]~P27(x3772)+~P41(x3772)+~P6(f2(x3772),x3771,x3772)+P6(f3(x3771,x3772),f2(x3772),x3772) % 1.32/1.35 [383]~P27(x3832)+~P6(f3(x3831,x3832),f7(x3832),x3832)+P6(x3831,f7(x3832),x3832)+E(x3831,f7(x3832)) % 1.32/1.35 [384]~P27(x3842)+~P6(f7(x3842),f3(x3841,x3842),x3842)+P6(f7(x3842),x3841,x3842)+E(x3841,f7(x3842)) % 1.32/1.35 [385]~P27(x3852)+~P41(x3852)+~P7(f2(x3852),f3(x3851,x3852),x3852)+P7(x3851,f2(x3852),x3852) % 1.32/1.35 [386]~P27(x3862)+~P41(x3862)+~P6(f2(x3862),f3(x3861,x3862),x3862)+P6(x3861,f2(x3862),x3862) % 1.32/1.35 [387]~P27(x3872)+~P41(x3872)+~P7(f3(x3871,x3872),f7(x3872),x3872)+P7(x3871,f7(x3872),x3872) % 1.32/1.35 [388]~P27(x3882)+~P41(x3882)+~P6(f3(x3881,x3882),f7(x3882),x3882)+P6(x3881,f7(x3882),x3882) % 1.32/1.35 [389]~P27(x3891)+~P41(x3891)+~P7(f7(x3891),f3(x3892,x3891),x3891)+P7(f7(x3891),x3892,x3891) % 1.32/1.35 [390]~P27(x3901)+~P41(x3901)+~P7(f2(x3901),f3(x3902,x3901),x3901)+P6(f7(x3901),x3902,x3901) % 1.32/1.35 [391]~P27(x3911)+~P41(x3911)+~P6(f7(x3911),f3(x3912,x3911),x3911)+P6(f7(x3911),x3912,x3911) % 1.32/1.35 [392]~P27(x3921)+~P41(x3921)+~P6(f2(x3921),f3(x3922,x3921),x3921)+P6(f7(x3921),x3922,x3921) % 1.32/1.35 [450]~P6(x4501,x4502,a1)+P6(f6(x4501),f6(x4502),a1)+~P6(f7(a1),x4502,a1)+~P6(f7(a1),x4501,a1) % 1.32/1.35 [472]P6(x4721,x4722,a1)+~P6(f6(x4721),f6(x4722),a1)+~P6(f7(a1),x4722,a1)+~P6(f7(a1),x4721,a1) % 1.32/1.35 [430]~P27(x4301)+~P41(x4301)+~P7(f7(x4301),x4302,x4301)+P7(f7(x4301),f4(f2(x4301),x4302,x4301),x4301) % 1.32/1.35 [431]~P27(x4311)+~P41(x4311)+~P6(f7(x4311),x4312,x4311)+P6(f7(x4311),f4(f2(x4311),x4312,x4311),x4311) % 1.32/1.35 [432]~P27(x4321)+~P41(x4321)+~P7(x4322,f7(x4321),x4321)+P7(f4(f2(x4321),x4322,x4321),f7(x4321),x4321) % 1.32/1.35 [433]~P27(x4331)+~P41(x4331)+~P6(x4332,f7(x4331),x4331)+P6(f4(f2(x4331),x4332,x4331),f7(x4331),x4331) % 1.32/1.35 [480]~P27(x4802)+~P41(x4802)+P7(x4801,f7(x4802),x4802)+~P7(f4(f2(x4802),x4801,x4802),f7(x4802),x4802) % 1.32/1.35 [481]~P27(x4812)+~P41(x4812)+P6(x4811,f7(x4812),x4812)+~P6(f4(f2(x4812),x4811,x4812),f7(x4812),x4812) % 1.32/1.35 [482]~P27(x4821)+~P41(x4821)+P7(f7(x4821),x4822,x4821)+~P7(f7(x4821),f4(f2(x4821),x4822,x4821),x4821) % 1.32/1.35 [483]~P27(x4831)+~P41(x4831)+P6(f7(x4831),x4832,x4831)+~P6(f7(x4831),f4(f2(x4831),x4832,x4831),x4831) % 1.32/1.35 [307]P6(x3071,x3072,x3073)+~P1(x3073)+E(x3071,x3072)+P6(x3072,x3071,x3073) % 1.32/1.35 [308]P6(x3081,x3082,x3083)+~P26(x3083)+E(x3081,x3082)+P6(x3082,x3081,x3083) % 1.32/1.35 [320]~P1(x3203)+~P7(x3201,x3202,x3203)+E(x3201,x3202)+P6(x3201,x3202,x3203) % 1.32/1.35 [326]~P24(x3263)+~P7(x3261,x3262,x3263)+E(x3261,x3262)+P6(x3261,x3262,x3263) % 1.32/1.35 [352]~P7(x3522,x3521,x3523)+~P7(x3521,x3522,x3523)+E(x3521,x3522)+~P24(x3523) % 1.32/1.35 [379]P6(x3792,x3791,x3793)+~P23(x3793)+~P7(x3792,x3791,x3793)+P7(x3791,x3792,x3793) % 1.32/1.35 [204]~P40(x2043)+~P41(x2043)+E(x2041,x2042)+~E(f3(x2041,x2043),f3(x2042,x2043)) % 1.32/1.35 [281]~P42(x2813)+E(x2811,x2812)+~E(f4(x2811,x2812,x2813),f2(x2813))+E(x2812,f7(x2813)) % 1.32/1.35 [282]~P39(x2822)+~P5(x2822)+~E(f9(x2823,x2821,x2822),x2823)+E(x2821,f7(x2822)) % 1.32/1.35 [286]~P43(x2862)+~E(f10(x2863,x2861,x2862),f7(x2862))+E(x2861,f7(x2862))+E(x2863,f7(x2862)) % 1.32/1.35 [287]~P53(x2872)+~E(f10(x2873,x2871,x2872),f7(x2872))+E(x2871,f7(x2872))+E(x2873,f7(x2872)) % 1.32/1.36 [436]~P27(x4362)+~P7(x4363,x4361,x4362)+~P6(x4361,f7(x4362),x4362)+P7(f3(x4361,x4362),f3(x4363,x4362),x4362) % 1.32/1.36 [437]~P27(x4372)+~P6(x4373,x4371,x4372)+~P6(x4371,f7(x4372),x4372)+P6(f3(x4371,x4372),f3(x4373,x4372),x4372) % 1.32/1.36 [438]~P27(x4382)+~P7(x4383,x4381,x4382)+~P6(f7(x4382),x4383,x4382)+P7(f3(x4381,x4382),f3(x4383,x4382),x4382) % 1.32/1.36 [439]~P27(x4392)+~P6(x4393,x4391,x4392)+~P6(f7(x4392),x4393,x4392)+P6(f3(x4391,x4392),f3(x4393,x4392),x4392) % 1.32/1.36 [446]~P27(x4463)+P7(x4461,x4462,x4463)+~P6(x4461,f7(x4463),x4463)+~P7(f3(x4462,x4463),f3(x4461,x4463),x4463) % 1.32/1.36 [447]~P27(x4473)+P6(x4471,x4472,x4473)+~P6(x4471,f7(x4473),x4473)+~P6(f3(x4472,x4473),f3(x4471,x4473),x4473) % 1.32/1.36 [448]~P27(x4483)+P7(x4481,x4482,x4483)+~P6(f7(x4483),x4482,x4483)+~P7(f3(x4482,x4483),f3(x4481,x4483),x4483) % 1.32/1.36 [449]~P27(x4493)+P6(x4491,x4492,x4493)+~P6(f7(x4493),x4492,x4493)+~P6(f3(x4492,x4493),f3(x4491,x4493),x4493) % 1.32/1.36 [496]~P25(x4961)+~P7(x4963,f7(x4961),x4961)+~P7(x4962,f7(x4961),x4961)+P7(f7(x4961),f10(x4962,x4963,x4961),x4961) % 1.32/1.36 [498]~P55(x4981)+~P7(x4983,f7(x4981),x4981)+~P7(x4982,f7(x4981),x4981)+P7(f7(x4981),f10(x4982,x4983,x4981),x4981) % 1.32/1.36 [499]~P27(x4991)+~P7(x4992,f7(x4991),x4991)+~P6(x4993,f7(x4991),x4991)+P7(f7(x4991),f4(x4992,x4993,x4991),x4991) % 1.32/1.36 [500]~P25(x5001)+~P6(x5003,f7(x5001),x5001)+~P6(x5002,f7(x5001),x5001)+P6(f7(x5001),f10(x5002,x5003,x5001),x5001) % 1.32/1.36 [501]~P27(x5011)+~P6(x5013,f7(x5011),x5011)+~P6(x5012,f7(x5011),x5011)+P6(f7(x5011),f4(x5012,x5013,x5011),x5011) % 1.32/1.36 [502]~P25(x5021)+~P7(f7(x5021),x5023,x5021)+~P7(f7(x5021),x5022,x5021)+P7(f7(x5021),f10(x5022,x5023,x5021),x5021) % 1.32/1.36 [503]~P55(x5031)+~P7(f7(x5031),x5033,x5031)+~P7(f7(x5031),x5032,x5031)+P7(f7(x5031),f10(x5032,x5033,x5031),x5031) % 1.32/1.36 [504]~P56(x5041)+~P7(f7(x5041),x5043,x5041)+~P7(f7(x5041),x5042,x5041)+P7(f7(x5041),f10(x5042,x5043,x5041),x5041) % 1.32/1.36 [505]~P22(x5051)+~P7(f7(x5051),x5053,x5051)+~P7(f7(x5051),x5052,x5051)+P7(f7(x5051),f9(x5052,x5053,x5051),x5051) % 1.32/1.36 [506]~P27(x5061)+~P7(f7(x5061),x5062,x5061)+~P6(f7(x5061),x5063,x5061)+P7(f7(x5061),f4(x5062,x5063,x5061),x5061) % 1.32/1.36 [507]~P49(x5071)+~P6(f7(x5071),x5073,x5071)+~P6(f7(x5071),x5072,x5071)+P6(f7(x5071),f10(x5072,x5073,x5071),x5071) % 1.32/1.36 [508]~P22(x5081)+~P7(f7(x5081),x5083,x5081)+~P6(f7(x5081),x5082,x5081)+P6(f7(x5081),f9(x5082,x5083,x5081),x5081) % 1.32/1.36 [509]~P22(x5091)+~P7(f7(x5091),x5092,x5091)+~P6(f7(x5091),x5093,x5091)+P6(f7(x5091),f9(x5092,x5093,x5091),x5091) % 1.32/1.36 [510]~P22(x5101)+~P6(f7(x5101),x5103,x5101)+~P6(f7(x5101),x5102,x5101)+P6(f7(x5101),f9(x5102,x5103,x5101),x5101) % 1.32/1.36 [511]~P27(x5111)+~P6(f7(x5111),x5113,x5111)+~P6(f7(x5111),x5112,x5111)+P6(f7(x5111),f4(x5112,x5113,x5111),x5111) % 1.32/1.36 [512]~P51(x5121)+~P6(f2(x5121),x5123,x5121)+~P6(f2(x5121),x5122,x5121)+P6(f2(x5121),f10(x5122,x5123,x5121),x5121) % 1.32/1.36 [513]~P22(x5133)+~P7(x5132,f7(x5133),x5133)+~P7(x5131,f7(x5133),x5133)+P7(f9(x5131,x5132,x5133),f7(x5133),x5133) % 1.32/1.36 [514]~P22(x5143)+~P7(x5142,f7(x5143),x5143)+~P6(x5141,f7(x5143),x5143)+P6(f9(x5141,x5142,x5143),f7(x5143),x5143) % 1.32/1.36 [515]~P22(x5153)+~P7(x5151,f7(x5153),x5153)+~P6(x5152,f7(x5153),x5153)+P6(f9(x5151,x5152,x5153),f7(x5153),x5153) % 1.32/1.36 [516]~P22(x5163)+~P6(x5162,f7(x5163),x5163)+~P6(x5161,f7(x5163),x5163)+P6(f9(x5161,x5162,x5163),f7(x5163),x5163) % 1.32/1.36 [517]~P25(x5173)+~P7(x5172,f7(x5173),x5173)+~P7(f7(x5173),x5171,x5173)+P7(f10(x5171,x5172,x5173),f7(x5173),x5173) % 1.32/1.36 [518]~P25(x5183)+~P7(x5181,f7(x5183),x5183)+~P7(f7(x5183),x5182,x5183)+P7(f10(x5181,x5182,x5183),f7(x5183),x5183) % 1.32/1.36 [520]~P56(x5203)+~P7(x5202,f7(x5203),x5203)+~P7(f7(x5203),x5201,x5203)+P7(f10(x5201,x5202,x5203),f7(x5203),x5203) % 1.32/1.36 [523]~P56(x5233)+~P7(x5231,f7(x5233),x5233)+~P7(f7(x5233),x5232,x5233)+P7(f10(x5231,x5232,x5233),f7(x5233),x5233) % 1.32/1.36 [524]~P27(x5243)+~P7(x5241,f7(x5243),x5243)+~P6(f7(x5243),x5242,x5243)+P7(f4(x5241,x5242,x5243),f7(x5243),x5243) % 1.32/1.36 [525]~P27(x5253)+~P6(x5252,f7(x5253),x5253)+~P7(f7(x5253),x5251,x5253)+P7(f4(x5251,x5252,x5253),f7(x5253),x5253) % 1.32/1.36 [526]~P49(x5263)+~P6(x5262,f7(x5263),x5263)+~P6(f7(x5263),x5261,x5263)+P6(f10(x5261,x5262,x5263),f7(x5263),x5263) % 1.32/1.36 [528]~P49(x5283)+~P6(x5281,f7(x5283),x5283)+~P6(f7(x5283),x5282,x5283)+P6(f10(x5281,x5282,x5283),f7(x5283),x5283) % 1.32/1.36 [529]~P27(x5293)+~P6(x5292,f7(x5293),x5293)+~P6(f7(x5293),x5291,x5293)+P6(f4(x5291,x5292,x5293),f7(x5293),x5293) % 1.32/1.36 [530]~P27(x5303)+~P6(x5301,f7(x5303),x5303)+~P6(f7(x5303),x5302,x5303)+P6(f4(x5301,x5302,x5303),f7(x5303),x5303) % 1.32/1.36 [539]~P25(x5392)+~P7(f10(x5393,x5391,x5392),f7(x5392),x5392)+P7(x5391,f7(x5392),x5392)+P7(x5393,f7(x5392),x5392) % 1.32/1.36 [540]~P25(x5402)+~P7(f7(x5402),f10(x5403,x5401,x5402),x5402)+P7(x5401,f7(x5402),x5402)+P7(f7(x5402),x5403,x5402) % 1.32/1.36 [541]~P25(x5412)+~P7(f7(x5412),f10(x5411,x5413,x5412),x5412)+P7(x5411,f7(x5412),x5412)+P7(f7(x5412),x5413,x5412) % 1.32/1.36 [542]~P25(x5422)+~P7(f7(x5422),f10(x5423,x5421,x5422),x5422)+P7(x5421,f7(x5422),x5422)+P7(f7(x5422),x5421,x5422) % 1.32/1.36 [543]~P25(x5432)+~P7(f7(x5432),f10(x5431,x5433,x5432),x5432)+P7(x5431,f7(x5432),x5432)+P7(f7(x5432),x5431,x5432) % 1.32/1.36 [544]~P25(x5442)+~P7(f10(x5443,x5441,x5442),f7(x5442),x5442)+P7(x5441,f7(x5442),x5442)+P7(f7(x5442),x5441,x5442) % 1.32/1.36 [545]~P25(x5452)+~P7(f10(x5451,x5453,x5452),f7(x5452),x5452)+P7(x5451,f7(x5452),x5452)+P7(f7(x5452),x5451,x5452) % 1.32/1.36 [546]~P25(x5461)+~P7(f10(x5462,x5463,x5461),f7(x5461),x5461)+P7(f7(x5461),x5462,x5461)+P7(f7(x5461),x5463,x5461) % 1.32/1.36 [573]~P49(x5731)+~P6(f7(x5731),f10(x5733,x5732,x5731),x5731)+P6(f7(x5731),x5732,x5731)+~P6(f7(x5731),x5733,x5731) % 1.32/1.36 [574]~P49(x5741)+~P6(f7(x5741),f10(x5742,x5743,x5741),x5741)+P6(f7(x5741),x5742,x5741)+~P6(f7(x5741),x5743,x5741) % 1.32/1.36 [355]~P42(x3552)+~P41(x3552)+E(x3551,f7(x3552))+E(f10(f4(x3553,x3551,x3552),x3551,x3552),x3553) % 1.32/1.36 [419]~P40(x4192)+E(x4191,f7(x4192))+E(x4193,f7(x4192))+E(f10(f3(x4191,x4192),f3(x4193,x4192),x4192),f3(f10(x4193,x4191,x4192),x4192)) % 1.32/1.36 [445]~P27(x4452)+~P41(x4452)+~P6(f7(x4452),x4453,x4452)+E(f4(f5(x4451,x4452),x4453,x4452),f5(f4(x4451,x4453,x4452),x4452)) % 1.32/1.36 [569]~P54(x5692)+~P7(x5693,f7(x5692),x5692)+~P7(x5691,f7(x5692),x5692)+E(f10(f5(x5691,x5692),f5(x5693,x5692),x5692),f5(f10(x5691,x5693,x5692),x5692)) % 1.32/1.36 [570]~P54(x5702)+~P7(x5703,f7(x5702),x5702)+~P7(f7(x5702),x5701,x5702)+E(f10(f5(x5701,x5702),f5(x5703,x5702),x5702),f5(f10(x5701,x5703,x5702),x5702)) % 1.32/1.36 [571]~P54(x5712)+~P7(x5711,f7(x5712),x5712)+~P7(f7(x5712),x5713,x5712)+E(f10(f5(x5711,x5712),f5(x5713,x5712),x5712),f5(f10(x5711,x5713,x5712),x5712)) % 1.32/1.36 [572]~P54(x5722)+~P7(f7(x5722),x5723,x5722)+~P7(f7(x5722),x5721,x5722)+E(f10(f5(x5721,x5722),f5(x5723,x5722),x5722),f5(f10(x5721,x5723,x5722),x5722)) % 1.32/1.36 [655]~P40(x6552)+E(x6551,f7(x6552))+E(x6553,f7(x6552))+E(f10(f10(f3(x6553,x6552),f9(x6553,x6551,x6552),x6552),f3(x6551,x6552),x6552),f9(f3(x6553,x6552),f3(x6551,x6552),x6552)) % 1.32/1.36 [656]~P42(x6562)+E(x6561,f7(x6562))+E(x6563,f7(x6562))+E(f10(f10(f9(x6563,x6561,x6562),f3(x6563,x6562),x6562),f3(x6561,x6562),x6562),f9(f3(x6563,x6562),f3(x6561,x6562),x6562)) % 1.32/1.36 [397]~P23(x3973)+~P7(x3971,x3974,x3973)+P7(x3971,x3972,x3973)+~P7(x3974,x3972,x3973) % 1.32/1.36 [398]~P24(x3983)+~P7(x3981,x3984,x3983)+P7(x3981,x3982,x3983)+~P7(x3984,x3982,x3983) % 1.32/1.36 [399]~P23(x3993)+~P6(x3991,x3994,x3993)+P6(x3991,x3992,x3993)+~P7(x3994,x3992,x3993) % 1.32/1.36 [400]~P23(x4003)+~P6(x4004,x4002,x4003)+P6(x4001,x4002,x4003)+~P7(x4001,x4004,x4003) % 1.32/1.36 [401]~P23(x4013)+~P6(x4011,x4014,x4013)+P6(x4011,x4012,x4013)+~P6(x4014,x4012,x4013) % 1.32/1.36 [402]~P24(x4023)+~P6(x4021,x4024,x4023)+P6(x4021,x4022,x4023)+~P7(x4024,x4022,x4023) % 1.32/1.36 [403]~P24(x4033)+~P6(x4034,x4032,x4033)+P6(x4031,x4032,x4033)+~P7(x4031,x4034,x4033) % 1.32/1.36 [404]~P24(x4043)+~P6(x4041,x4044,x4043)+P6(x4041,x4042,x4043)+~P6(x4044,x4042,x4043) % 1.32/1.36 [359]~P39(x3594)+~P5(x3594)+E(x3591,x3592)+~E(f9(x3593,x3591,x3594),f9(x3593,x3592,x3594)) % 1.32/1.36 [479]~P51(x4794)+~P6(x4791,x4793,x4794)+~P6(f7(x4794),x4792,x4794)+P6(x4791,f9(x4792,x4793,x4794),x4794) % 1.32/1.36 [597]~P55(x5973)+~P7(x5974,x5971,x5973)+~P7(x5972,f7(x5973),x5973)+P7(f10(x5971,x5972,x5973),f10(x5974,x5972,x5973),x5973) % 1.32/1.36 [598]~P25(x5983)+~P7(x5984,x5982,x5983)+~P6(x5981,f7(x5983),x5983)+P7(f10(x5981,x5982,x5983),f10(x5981,x5984,x5983),x5983) % 1.32/1.36 [599]~P55(x5993)+~P7(x5994,x5992,x5993)+~P7(x5991,f7(x5993),x5993)+P7(f10(x5991,x5992,x5993),f10(x5991,x5994,x5993),x5993) % 1.32/1.36 [601]~P25(x6013)+~P6(x6014,x6011,x6013)+~P6(x6012,f7(x6013),x6013)+P6(f10(x6011,x6012,x6013),f10(x6014,x6012,x6013),x6013) % 1.32/1.36 [604]~P25(x6043)+~P6(x6044,x6042,x6043)+~P6(x6041,f7(x6043),x6043)+P6(f10(x6041,x6042,x6043),f10(x6041,x6044,x6043),x6043) % 1.32/1.36 [605]~P27(x6053)+~P6(x6054,x6051,x6053)+~P6(x6052,f7(x6053),x6053)+P6(f4(x6051,x6052,x6053),f4(x6054,x6052,x6053),x6053) % 1.32/1.36 [606]~P47(x6063)+~P7(x6061,x6064,x6063)+~P7(f7(x6063),x6062,x6063)+P7(f10(x6061,x6062,x6063),f10(x6064,x6062,x6063),x6063) % 1.32/1.36 [607]~P25(x6073)+~P7(x6072,x6074,x6073)+~P6(f7(x6073),x6071,x6073)+P7(f10(x6071,x6072,x6073),f10(x6071,x6074,x6073),x6073) % 1.32/1.36 [608]~P46(x6083)+~P7(x6082,x6084,x6083)+~P7(f7(x6083),x6081,x6083)+P7(f10(x6081,x6082,x6083),f10(x6081,x6084,x6083),x6083) % 1.32/1.36 [609]~P47(x6093)+~P7(x6092,x6094,x6093)+~P7(f7(x6093),x6091,x6093)+P7(f10(x6091,x6092,x6093),f10(x6091,x6094,x6093),x6093) % 1.32/1.36 [610]~P25(x6103)+~P6(x6101,x6104,x6103)+~P6(f7(x6103),x6102,x6103)+P6(f10(x6101,x6102,x6103),f10(x6104,x6102,x6103),x6103) % 1.32/1.36 [611]~P49(x6113)+~P6(x6111,x6114,x6113)+~P6(f7(x6113),x6112,x6113)+P6(f10(x6111,x6112,x6113),f10(x6114,x6112,x6113),x6113) % 1.32/1.36 [613]~P25(x6133)+~P6(x6132,x6134,x6133)+~P6(f7(x6133),x6131,x6133)+P6(f10(x6131,x6132,x6133),f10(x6131,x6134,x6133),x6133) % 1.32/1.36 [614]~P49(x6143)+~P6(x6142,x6144,x6143)+~P6(f7(x6143),x6141,x6143)+P6(f10(x6141,x6142,x6143),f10(x6141,x6144,x6143),x6143) % 1.32/1.36 [615]~P48(x6153)+~P6(x6152,x6154,x6153)+~P6(f7(x6153),x6151,x6153)+P6(f10(x6151,x6152,x6153),f10(x6151,x6154,x6153),x6153) % 1.32/1.36 [616]~P27(x6163)+~P6(x6161,x6164,x6163)+~P6(f7(x6163),x6162,x6163)+P6(f4(x6161,x6162,x6163),f4(x6164,x6162,x6163),x6163) % 1.32/1.36 [627]~P27(x6274)+~P6(f7(x6274),x6273,x6274)+~P7(f10(x6271,x6273,x6274),x6272,x6274)+P7(x6271,f4(x6272,x6273,x6274),x6274) % 1.32/1.36 [628]~P27(x6284)+~P6(f7(x6284),x6283,x6284)+~P6(f10(x6281,x6283,x6284),x6282,x6284)+P6(x6281,f4(x6282,x6283,x6284),x6284) % 1.32/1.36 [629]~P27(x6293)+~P6(f7(x6293),x6292,x6293)+~P7(x6291,f10(x6294,x6292,x6293),x6293)+P7(f4(x6291,x6292,x6293),x6294,x6293) % 1.32/1.36 [630]~P27(x6303)+~P6(f7(x6303),x6302,x6303)+~P6(x6301,f10(x6304,x6302,x6303),x6303)+P6(f4(x6301,x6302,x6303),x6304,x6303) % 1.32/1.36 [640]P6(x6402,x6401,x6403)+~P25(x6403)+P6(x6401,x6402,x6403)+~P6(f10(x6404,x6401,x6403),f10(x6404,x6402,x6403),x6403) % 1.32/1.36 [641]P6(x6412,x6411,x6413)+~P25(x6413)+P6(x6411,x6412,x6413)+~P6(f10(x6411,x6414,x6413),f10(x6412,x6414,x6413),x6413) % 1.32/1.36 [644]~P25(x6443)+P6(x6441,x6442,x6443)+~P6(f10(x6441,x6444,x6443),f10(x6442,x6444,x6443),x6443)+P6(x6444,f7(x6443),x6443) % 1.32/1.36 [645]~P25(x6453)+P6(x6451,x6452,x6453)+~P6(f10(x6454,x6451,x6453),f10(x6454,x6452,x6453),x6453)+P6(x6454,f7(x6453),x6453) % 1.32/1.36 [646]~P25(x6463)+P6(x6461,x6462,x6463)+~P6(f10(x6464,x6462,x6463),f10(x6464,x6461,x6463),x6463)+P6(f7(x6463),x6464,x6463) % 1.32/1.36 [647]~P25(x6473)+P6(x6471,x6472,x6473)+~P6(f10(x6472,x6474,x6473),f10(x6471,x6474,x6473),x6473)+P6(f7(x6473),x6474,x6473) % 1.32/1.36 [651]~P25(x6512)+~P6(f10(x6513,x6511,x6512),f10(x6514,x6511,x6512),x6512)+P6(x6511,f7(x6512),x6512)+P6(f7(x6512),x6511,x6512) % 1.32/1.36 [652]~P25(x6522)+~P6(f10(x6521,x6523,x6522),f10(x6521,x6524,x6522),x6522)+P6(x6521,f7(x6522),x6522)+P6(f7(x6522),x6521,x6522) % 1.32/1.36 [657]~P25(x6573)+P7(x6571,x6572,x6573)+~P7(f10(x6574,x6572,x6573),f10(x6574,x6571,x6573),x6573)+~P6(x6574,f7(x6573),x6573) % 1.32/1.36 [658]~P25(x6583)+P6(x6581,x6582,x6583)+~P6(f10(x6584,x6582,x6583),f10(x6584,x6581,x6583),x6583)+~P6(x6584,f7(x6583),x6583) % 1.32/1.36 [659]~P25(x6593)+P7(x6591,x6592,x6593)+~P7(f10(x6594,x6591,x6593),f10(x6594,x6592,x6593),x6593)+~P6(f7(x6593),x6594,x6593) % 1.32/1.36 [660]~P49(x6603)+P7(x6601,x6602,x6603)+~P7(f10(x6604,x6601,x6603),f10(x6604,x6602,x6603),x6603)+~P6(f7(x6603),x6604,x6603) % 1.32/1.36 [661]~P49(x6613)+P7(x6611,x6612,x6613)+~P7(f10(x6611,x6614,x6613),f10(x6612,x6614,x6613),x6613)+~P6(f7(x6613),x6614,x6613) % 1.32/1.36 [662]~P25(x6623)+P6(x6621,x6622,x6623)+~P6(f10(x6624,x6621,x6623),f10(x6624,x6622,x6623),x6623)+~P6(f7(x6623),x6624,x6623) % 1.32/1.36 [663]~P49(x6633)+P6(x6631,x6632,x6633)+~P6(f10(x6634,x6631,x6633),f10(x6634,x6632,x6633),x6633)+~P7(f7(x6633),x6634,x6633) % 1.32/1.36 [664]~P49(x6643)+P6(x6641,x6642,x6643)+~P6(f10(x6641,x6644,x6643),f10(x6642,x6644,x6643),x6643)+~P7(f7(x6643),x6644,x6643) % 1.32/1.36 [665]~P50(x6653)+P6(x6651,x6652,x6653)+~P6(f10(x6654,x6651,x6653),f10(x6654,x6652,x6653),x6653)+~P7(f7(x6653),x6654,x6653) % 1.32/1.36 [666]~P50(x6663)+P6(x6661,x6662,x6663)+~P6(f10(x6661,x6664,x6663),f10(x6662,x6664,x6663),x6663)+~P7(f7(x6663),x6664,x6663) % 1.32/1.36 [477]~P42(x4772)+~P41(x4772)+E(x4771,f7(x4772))+E(f4(f10(x4773,x4771,x4772),f10(x4774,x4771,x4772),x4772),f4(x4773,x4774,x4772)) % 1.32/1.36 [478]~P42(x4782)+~P41(x4782)+E(x4781,f7(x4782))+E(f4(f10(x4781,x4783,x4782),f10(x4781,x4784,x4782),x4782),f4(x4783,x4784,x4782)) % 1.32/1.36 [653]~P42(x6532)+~P41(x6532)+E(x6531,f7(x6532))+E(f4(f9(x6533,f10(x6534,x6531,x6532),x6532),x6531,x6532),f9(x6534,f4(x6533,x6531,x6532),x6532)) % 1.32/1.36 [654]~P42(x6542)+~P41(x6542)+E(x6541,f7(x6542))+E(f4(f9(x6543,f10(x6544,x6541,x6542),x6542),x6541,x6542),f9(f4(x6543,x6541,x6542),x6544,x6542)) % 1.32/1.36 [587]~P21(x5873)+~P7(x5872,x5875,x5873)+~P7(x5871,x5874,x5873)+P7(f9(x5871,x5872,x5873),f9(x5874,x5875,x5873),x5873) % 1.32/1.36 [588]~P2(x5883)+~P7(x5882,x5885,x5883)+~P6(x5881,x5884,x5883)+P6(f9(x5881,x5882,x5883),f9(x5884,x5885,x5883),x5883) % 1.32/1.36 [589]~P2(x5893)+~P7(x5891,x5894,x5893)+~P6(x5892,x5895,x5893)+P6(f9(x5891,x5892,x5893),f9(x5894,x5895,x5893),x5893) % 1.32/1.36 [590]~P2(x5903)+~P6(x5902,x5905,x5903)+~P6(x5901,x5904,x5903)+P6(f9(x5901,x5902,x5903),f9(x5904,x5905,x5903),x5903) % 1.32/1.36 [624]~P20(x6244)+~P7(x6245,x6243,x6244)+~P7(x6241,f9(x6242,x6245,x6244),x6244)+P7(x6241,f9(x6242,x6243,x6244),x6244) % 1.32/1.36 [686]~P26(x6862)+~P6(f5(x6861,x6862),x6864,x6862)+~P6(f5(x6863,x6862),x6865,x6862)+P6(f10(f5(x6861,x6862),f5(x6863,x6862),x6862),f10(x6864,x6865,x6862),x6862) % 1.32/1.36 [719]~P42(x7192)+E(x7191,f7(x7192))+E(x7193,f7(x7192))+E(f4(f9(f10(x7194,x7191,x7192),f10(x7195,x7193,x7192),x7192),f10(x7193,x7191,x7192),x7192),f9(f4(x7194,x7193,x7192),f4(x7195,x7191,x7192),x7192)) % 1.32/1.36 [428]~P27(x4282)+~P41(x4282)+P7(f2(x4282),x4281,x4282)+~P7(f3(x4281,x4282),f2(x4282),x4282)+P7(x4281,f7(x4282),x4282) % 1.32/1.36 [429]~P27(x4292)+~P41(x4292)+P6(f2(x4292),x4291,x4292)+~P6(f3(x4291,x4292),f2(x4292),x4292)+P7(x4291,f7(x4292),x4292) % 1.32/1.36 [434]~P27(x4341)+~P41(x4341)+~P6(f7(x4341),x4342,x4341)+~P7(x4342,f2(x4341),x4341)+P7(f2(x4341),f3(x4342,x4341),x4341) % 1.32/1.36 [435]~P27(x4351)+~P41(x4351)+~P6(f7(x4351),x4352,x4351)+~P6(x4352,f2(x4351),x4351)+P6(f2(x4351),f3(x4352,x4351),x4351) % 1.32/1.36 [211]~P40(x2113)+E(x2111,x2112)+~E(f3(x2111,x2113),f3(x2112,x2113))+E(x2112,f7(x2113))+E(x2111,f7(x2113)) % 1.32/1.36 [440]~P22(x4402)+~P7(f7(x4402),x4401,x4402)+~P7(f7(x4402),x4403,x4402)+~E(f9(x4403,x4401,x4402),f7(x4402))+E(x4401,f7(x4402)) % 1.32/1.36 [441]~P22(x4412)+~P7(f7(x4412),x4413,x4412)+~P7(f7(x4412),x4411,x4412)+~E(f9(x4411,x4413,x4412),f7(x4412))+E(x4411,f7(x4412)) % 1.32/1.36 [531]~P27(x5311)+~P41(x5311)+~P7(x5313,f7(x5311),x5311)+~P7(x5312,f7(x5311),x5311)+P7(f7(x5311),f4(x5312,x5313,x5311),x5311) % 1.32/1.36 [533]~P27(x5331)+~P41(x5331)+~P7(f7(x5331),x5333,x5331)+~P7(f7(x5331),x5332,x5331)+P7(f7(x5331),f4(x5332,x5333,x5331),x5331) % 1.32/1.36 [535]~P27(x5353)+~P41(x5353)+~P7(x5352,f7(x5353),x5353)+~P7(f7(x5353),x5351,x5353)+P7(f4(x5351,x5352,x5353),f7(x5353),x5353) % 1.32/1.36 [536]~P27(x5363)+~P41(x5363)+~P7(x5361,f7(x5363),x5363)+~P7(f7(x5363),x5362,x5363)+P7(f4(x5361,x5362,x5363),f7(x5363),x5363) % 1.32/1.36 [551]~P27(x5512)+~P41(x5512)+~P7(f4(x5513,x5511,x5512),f7(x5512),x5512)+P7(x5511,f7(x5512),x5512)+P7(x5513,f7(x5512),x5512) % 1.32/1.36 [552]~P27(x5522)+~P41(x5522)+~P6(f4(x5523,x5521,x5522),f7(x5522),x5522)+P6(x5521,f7(x5522),x5522)+P6(x5523,f7(x5522),x5522) % 1.32/1.36 [553]~P27(x5532)+~P41(x5532)+~P7(f7(x5532),f4(x5533,x5531,x5532),x5532)+P7(x5531,f7(x5532),x5532)+P7(f7(x5532),x5533,x5532) % 1.32/1.36 [554]~P27(x5542)+~P41(x5542)+~P7(f7(x5542),f4(x5541,x5543,x5542),x5542)+P7(x5541,f7(x5542),x5542)+P7(f7(x5542),x5543,x5542) % 1.32/1.36 [555]~P27(x5552)+~P41(x5552)+~P7(f7(x5552),f4(x5553,x5551,x5552),x5552)+P7(x5551,f7(x5552),x5552)+P7(f7(x5552),x5551,x5552) % 1.32/1.36 [556]~P27(x5562)+~P41(x5562)+~P7(f7(x5562),f4(x5561,x5563,x5562),x5562)+P7(x5561,f7(x5562),x5562)+P7(f7(x5562),x5561,x5562) % 1.32/1.36 [557]~P27(x5572)+~P41(x5572)+~P6(f7(x5572),f4(x5573,x5571,x5572),x5572)+P6(x5571,f7(x5572),x5572)+P6(f7(x5572),x5573,x5572) % 1.32/1.36 [558]~P27(x5582)+~P41(x5582)+~P6(f7(x5582),f4(x5581,x5583,x5582),x5582)+P6(x5581,f7(x5582),x5582)+P6(f7(x5582),x5583,x5582) % 1.32/1.36 [559]~P27(x5592)+~P41(x5592)+~P6(f7(x5592),f4(x5593,x5591,x5592),x5592)+P6(x5591,f7(x5592),x5592)+P6(f7(x5592),x5591,x5592) % 1.32/1.36 [560]~P27(x5602)+~P41(x5602)+~P6(f7(x5602),f4(x5601,x5603,x5602),x5602)+P6(x5601,f7(x5602),x5602)+P6(f7(x5602),x5601,x5602) % 1.32/1.36 [561]~P27(x5612)+~P41(x5612)+~P7(f4(x5613,x5611,x5612),f7(x5612),x5612)+P7(x5611,f7(x5612),x5612)+P7(f7(x5612),x5611,x5612) % 1.32/1.36 [562]~P27(x5622)+~P41(x5622)+~P7(f4(x5621,x5623,x5622),f7(x5622),x5622)+P7(x5621,f7(x5622),x5622)+P7(f7(x5622),x5621,x5622) % 1.32/1.36 [563]~P27(x5632)+~P41(x5632)+~P6(f4(x5633,x5631,x5632),f7(x5632),x5632)+P6(x5631,f7(x5632),x5632)+P6(f7(x5632),x5631,x5632) % 1.32/1.36 [564]~P27(x5642)+~P41(x5642)+~P6(f4(x5641,x5643,x5642),f7(x5642),x5642)+P6(x5641,f7(x5642),x5642)+P6(f7(x5642),x5641,x5642) % 1.32/1.36 [565]~P27(x5651)+~P41(x5651)+~P7(f4(x5652,x5653,x5651),f7(x5651),x5651)+P7(f7(x5651),x5652,x5651)+P7(f7(x5651),x5653,x5651) % 1.32/1.36 [566]~P27(x5661)+~P41(x5661)+~P6(f4(x5662,x5663,x5661),f7(x5661),x5661)+P6(f7(x5661),x5662,x5661)+P6(f7(x5661),x5663,x5661) % 1.32/1.36 [595]~P26(x5953)+~P7(x5951,f2(x5953),x5953)+~P7(f7(x5953),x5952,x5953)+~P7(f7(x5953),x5951,x5953)+P7(f10(x5951,x5952,x5953),x5952,x5953) % 1.32/1.36 [596]~P26(x5963)+~P7(x5962,f2(x5963),x5963)+~P7(f7(x5963),x5962,x5963)+~P7(f7(x5963),x5961,x5963)+P7(f10(x5961,x5962,x5963),x5961,x5963) % 1.32/1.36 [484]~P3(x4844)+~P4(x4844)+~P7(x4841,x4843,x4844)+~P7(f7(x4844),x4842,x4844)+P7(x4841,f9(x4842,x4843,x4844),x4844) % 1.32/1.36 [485]~P3(x4854)+~P4(x4854)+~P7(x4851,x4852,x4854)+~P7(f7(x4854),x4853,x4854)+P7(x4851,f9(x4852,x4853,x4854),x4854) % 1.32/1.36 [486]~P3(x4864)+~P4(x4864)+~P7(x4861,x4863,x4864)+~P6(f7(x4864),x4862,x4864)+P6(x4861,f9(x4862,x4863,x4864),x4864) % 1.32/1.36 [487]~P3(x4874)+~P4(x4874)+~P6(x4871,x4873,x4874)+~P7(f7(x4874),x4872,x4874)+P6(x4871,f9(x4872,x4873,x4874),x4874) % 1.32/1.36 [617]~P27(x6173)+~P41(x6173)+~P7(x6174,x6171,x6173)+~P7(x6172,f7(x6173),x6173)+P7(f4(x6171,x6172,x6173),f4(x6174,x6172,x6173),x6173) % 1.32/1.36 [618]~P27(x6183)+~P41(x6183)+~P7(x6181,x6184,x6183)+~P7(f7(x6183),x6182,x6183)+P7(f4(x6181,x6182,x6183),f4(x6184,x6182,x6183),x6183) % 1.32/1.36 [631]~P27(x6314)+~P41(x6314)+~P6(f7(x6314),x6313,x6314)+~P7(f4(x6311,x6313,x6314),x6312,x6314)+P7(x6311,f10(x6312,x6313,x6314),x6314) % 1.32/1.36 [633]~P27(x6334)+~P41(x6334)+~P6(f7(x6334),x6333,x6334)+~P6(f4(x6331,x6333,x6334),x6332,x6334)+P6(x6331,f10(x6332,x6333,x6334),x6334) % 1.32/1.36 [635]~P27(x6353)+~P41(x6353)+~P6(f7(x6353),x6352,x6353)+~P7(x6351,f4(x6354,x6352,x6353),x6353)+P7(f10(x6351,x6352,x6353),x6354,x6353) % 1.32/1.36 [637]~P27(x6373)+~P41(x6373)+~P6(f7(x6373),x6372,x6373)+~P6(x6371,f4(x6374,x6372,x6373),x6373)+P6(f10(x6371,x6372,x6373),x6374,x6373) % 1.32/1.36 [699]~P27(x6993)+~P6(x6992,x6994,x6993)+~P6(x6991,f7(x6993),x6993)+~P6(f7(x6993),f10(x6992,x6994,x6993),x6993)+P6(f4(x6991,x6992,x6993),f4(x6991,x6994,x6993),x6993) % 1.32/1.36 [700]~P27(x7003)+~P7(x7004,x7002,x7003)+~P7(f7(x7003),x7001,x7003)+~P6(f7(x7003),f10(x7002,x7004,x7003),x7003)+P7(f4(x7001,x7002,x7003),f4(x7001,x7004,x7003),x7003) % 1.32/1.36 [701]~P27(x7013)+~P6(x7014,x7012,x7013)+~P6(f7(x7013),x7011,x7013)+~P6(f7(x7013),f10(x7012,x7014,x7013),x7013)+P6(f4(x7011,x7012,x7013),f4(x7011,x7014,x7013),x7013) % 1.32/1.36 [442]~P42(x4422)+~E(f4(x4424,x4423,x4422),f4(x4425,x4421,x4422))+E(f10(x4424,x4421,x4422),f10(x4425,x4423,x4422))+E(x4421,f7(x4422))+E(x4423,f7(x4422)) % 1.32/1.36 [443]~P42(x4432)+~E(f10(x4434,x4433,x4432),f10(x4435,x4431,x4432))+E(f4(x4434,x4431,x4432),f4(x4435,x4433,x4432))+E(x4431,f7(x4432))+E(x4433,f7(x4432)) % 1.32/1.36 [639]~P39(x6394)+~P5(x6394)+E(x6391,x6392)+E(x6393,f7(x6394))+~E(f9(x6395,f10(x6393,x6391,x6394),x6394),f9(x6395,f10(x6393,x6392,x6394),x6394)) % 1.32/1.36 [714]~P39(x7145)+~P5(x7145)+E(x7141,x7142)+E(x7143,x7144)+~E(f9(f10(x7143,x7141,x7145),f10(x7144,x7142,x7145),x7145),f9(f10(x7143,x7142,x7145),f10(x7144,x7141,x7145),x7145)) % 1.32/1.36 [547]~P27(x5472)+~P41(x5472)+P6(x5471,f7(x5472),x5472)+P6(f7(x5472),x5471,x5472)+~P7(x5473,f7(x5472),x5472)+P7(x5473,f4(x5474,x5471,x5472),x5472) % 1.32/1.36 [548]~P27(x5482)+~P41(x5482)+P6(x5481,f7(x5482),x5482)+P6(f7(x5482),x5481,x5482)+~P6(x5483,f7(x5482),x5482)+P6(x5483,f4(x5484,x5481,x5482),x5482) % 1.32/1.36 [549]~P27(x5492)+~P41(x5492)+P6(x5491,f7(x5492),x5492)+P6(f7(x5492),x5491,x5492)+~P7(f7(x5492),x5494,x5492)+P7(f4(x5493,x5491,x5492),x5494,x5492) % 1.32/1.36 [550]~P27(x5502)+~P41(x5502)+P6(x5501,f7(x5502),x5502)+P6(f7(x5502),x5501,x5502)+~P6(f7(x5502),x5504,x5502)+P6(f4(x5503,x5501,x5502),x5504,x5502) % 1.32/1.36 [591]~P27(x5912)+~P41(x5912)+P7(x5911,f7(x5912),x5912)+P6(f7(x5912),x5913,x5912)+~P7(x5911,f4(x5914,x5913,x5912),x5912)+P6(x5913,f7(x5912),x5912) % 1.32/1.36 [592]~P27(x5922)+~P41(x5922)+P6(x5921,f7(x5922),x5922)+P6(f7(x5922),x5921,x5922)+~P6(x5923,f4(x5924,x5921,x5922),x5922)+P6(x5923,f7(x5922),x5922) % 1.32/1.36 [593]~P27(x5932)+~P41(x5932)+P6(x5931,f7(x5932),x5932)+P6(f7(x5932),x5931,x5932)+~P7(f4(x5934,x5931,x5932),x5933,x5932)+P7(f7(x5932),x5933,x5932) % 1.32/1.36 [594]~P27(x5942)+~P41(x5942)+P6(x5941,f7(x5942),x5942)+P6(f7(x5942),x5941,x5942)+~P6(f4(x5944,x5941,x5942),x5943,x5942)+P6(f7(x5942),x5943,x5942) % 1.32/1.36 [667]~P27(x6672)+~P41(x6672)+~P7(f10(x6673,x6671,x6672),x6674,x6672)+P6(x6671,f7(x6672),x6672)+~P7(x6673,f7(x6672),x6672)+P7(x6673,f4(x6674,x6671,x6672),x6672) % 1.32/1.36 [668]~P27(x6682)+~P41(x6682)+~P6(f10(x6683,x6681,x6682),x6684,x6682)+P6(x6681,f7(x6682),x6682)+~P6(x6683,f7(x6682),x6682)+P6(x6683,f4(x6684,x6681,x6682),x6682) % 1.32/1.36 [669]~P27(x6692)+~P41(x6692)+~P7(x6693,f10(x6694,x6691,x6692),x6692)+P6(x6691,f7(x6692),x6692)+~P7(f7(x6692),x6694,x6692)+P7(f4(x6693,x6691,x6692),x6694,x6692) % 1.32/1.36 [670]~P27(x6702)+~P41(x6702)+~P6(x6703,f10(x6704,x6701,x6702),x6702)+P6(x6701,f7(x6702),x6702)+~P6(f7(x6702),x6704,x6702)+P6(f4(x6703,x6701,x6702),x6704,x6702) % 1.32/1.36 [671]~P27(x6711)+~P41(x6711)+~P7(x6714,f4(x6713,x6712,x6711),x6711)+~P6(x6712,f7(x6711),x6711)+P6(f7(x6711),x6712,x6711)+P7(x6713,f10(x6714,x6712,x6711),x6711) % 1.32/1.36 [672]~P27(x6721)+~P41(x6721)+~P7(x6724,f10(x6723,x6722,x6721),x6721)+~P7(x6723,f7(x6721),x6721)+P6(f7(x6721),x6722,x6721)+P7(x6723,f4(x6724,x6722,x6721),x6721) % 1.32/1.36 [673]~P27(x6731)+~P41(x6731)+~P7(x6734,f10(x6733,x6732,x6731),x6731)+~P6(x6732,f7(x6731),x6731)+P6(f7(x6731),x6732,x6731)+P7(x6733,f4(x6734,x6732,x6731),x6731) % 1.32/1.36 [674]~P27(x6741)+~P41(x6741)+~P6(x6744,f4(x6743,x6742,x6741),x6741)+~P6(x6742,f7(x6741),x6741)+P6(f7(x6741),x6742,x6741)+P6(x6743,f10(x6744,x6742,x6741),x6741) % 1.32/1.36 [675]~P27(x6751)+~P41(x6751)+~P6(x6754,f10(x6753,x6752,x6751),x6751)+~P6(x6752,f7(x6751),x6751)+P6(f7(x6751),x6752,x6751)+P6(x6753,f4(x6754,x6752,x6751),x6751) % 1.32/1.36 [676]~P27(x6761)+~P41(x6761)+~P6(x6764,f10(x6763,x6762,x6761),x6761)+~P6(x6763,f7(x6761),x6761)+P6(f7(x6761),x6762,x6761)+P6(x6763,f4(x6764,x6762,x6761),x6761) % 1.32/1.36 [677]~P27(x6771)+~P41(x6771)+~P7(f4(x6774,x6772,x6771),x6773,x6771)+~P6(x6772,f7(x6771),x6771)+P6(f7(x6771),x6772,x6771)+P7(f10(x6773,x6772,x6771),x6774,x6771) % 1.32/1.36 [678]~P27(x6781)+~P41(x6781)+~P7(f10(x6784,x6782,x6781),x6783,x6781)+~P6(x6782,f7(x6781),x6781)+P6(f7(x6781),x6782,x6781)+P7(f4(x6783,x6782,x6781),x6784,x6781) % 1.32/1.36 [679]~P27(x6791)+~P41(x6791)+~P6(f4(x6794,x6792,x6791),x6793,x6791)+~P6(x6792,f7(x6791),x6791)+P6(f7(x6791),x6792,x6791)+P6(f10(x6793,x6792,x6791),x6794,x6791) % 1.32/1.36 [680]~P27(x6801)+~P41(x6801)+~P6(f10(x6804,x6802,x6801),x6803,x6801)+~P6(x6802,f7(x6801),x6801)+P6(f7(x6801),x6802,x6801)+P6(f4(x6803,x6802,x6801),x6804,x6801) % 1.32/1.36 [681]~P27(x6811)+~P41(x6811)+~P7(f10(x6814,x6812,x6811),x6813,x6811)+~P7(f7(x6811),x6814,x6811)+P6(f7(x6811),x6812,x6811)+P7(f4(x6813,x6812,x6811),x6814,x6811) % 1.32/1.36 [682]~P27(x6821)+~P41(x6821)+~P6(f10(x6824,x6822,x6821),x6823,x6821)+~P6(f7(x6821),x6824,x6821)+P6(f7(x6821),x6822,x6821)+P6(f4(x6823,x6822,x6821),x6824,x6821) % 1.32/1.36 [702]~P27(x7023)+~P41(x7023)+~P7(x7022,x7024,x7023)+~P7(x7021,f7(x7023),x7023)+~P6(f7(x7023),f10(x7022,x7024,x7023),x7023)+P7(f4(x7021,x7022,x7023),f4(x7021,x7024,x7023),x7023) % 1.32/1.36 [705]~P27(x7054)+~P41(x7054)+~P7(x7051,f7(x7054),x7054)+~P7(x7052,f10(x7051,x7053,x7054),x7054)+~P7(f10(x7051,x7053,x7054),x7052,x7054)+P7(x7051,f4(x7052,x7053,x7054),x7054) % 1.32/1.36 [706]~P27(x7064)+~P41(x7064)+~P6(x7063,f7(x7064),x7064)+~P7(x7062,f10(x7061,x7063,x7064),x7064)+~P7(f10(x7061,x7063,x7064),x7062,x7064)+P7(x7061,f4(x7062,x7063,x7064),x7064) % 1.32/1.36 [707]~P27(x7074)+~P41(x7074)+~P6(x7073,f7(x7074),x7074)+~P6(x7072,f10(x7071,x7073,x7074),x7074)+~P6(f10(x7071,x7073,x7074),x7072,x7074)+P6(x7071,f4(x7072,x7073,x7074),x7074) % 1.32/1.36 [708]~P27(x7084)+~P41(x7084)+~P6(x7081,f7(x7084),x7084)+~P6(x7082,f10(x7081,x7083,x7084),x7084)+~P6(f10(x7081,x7083,x7084),x7082,x7084)+P6(x7081,f4(x7082,x7083,x7084),x7084) % 1.32/1.36 [709]~P27(x7093)+~P41(x7093)+~P6(x7092,f7(x7093),x7093)+~P7(x7091,f10(x7094,x7092,x7093),x7093)+~P7(f10(x7094,x7092,x7093),x7091,x7093)+P7(f4(x7091,x7092,x7093),x7094,x7093) % 1.32/1.36 [710]~P27(x7103)+~P41(x7103)+~P6(x7102,f7(x7103),x7103)+~P6(x7101,f10(x7104,x7102,x7103),x7103)+~P6(f10(x7104,x7102,x7103),x7101,x7103)+P6(f4(x7101,x7102,x7103),x7104,x7103) % 1.32/1.36 [711]~P27(x7113)+~P41(x7113)+~P7(f7(x7113),x7114,x7113)+~P7(x7111,f10(x7114,x7112,x7113),x7113)+~P7(f10(x7114,x7112,x7113),x7111,x7113)+P7(f4(x7111,x7112,x7113),x7114,x7113) % 1.32/1.36 [712]~P27(x7123)+~P41(x7123)+~P6(f7(x7123),x7124,x7123)+~P6(x7121,f10(x7124,x7122,x7123),x7123)+~P6(f10(x7124,x7122,x7123),x7121,x7123)+P6(f4(x7121,x7122,x7123),x7124,x7123) % 1.32/1.36 [687]~P57(x6873)+~P7(x6872,x6875,x6873)+~P7(x6871,x6874,x6873)+~P7(f7(x6873),x6874,x6873)+~P7(f7(x6873),x6872,x6873)+P7(f10(x6871,x6872,x6873),f10(x6874,x6875,x6873),x6873) % 1.32/1.36 [688]~P57(x6883)+~P7(x6882,x6885,x6883)+~P7(x6881,x6884,x6883)+~P7(f7(x6883),x6882,x6883)+~P7(f7(x6883),x6881,x6883)+P7(f10(x6881,x6882,x6883),f10(x6884,x6885,x6883),x6883) % 1.32/1.36 [689]~P27(x6893)+~P7(x6895,x6892,x6893)+~P7(x6891,x6894,x6893)+~P7(f7(x6893),x6891,x6893)+~P6(f7(x6893),x6895,x6893)+P7(f4(x6891,x6892,x6893),f4(x6894,x6895,x6893),x6893) % 1.32/1.36 [690]~P49(x6903)+~P7(x6902,x6905,x6903)+~P6(x6901,x6904,x6903)+~P7(f7(x6903),x6901,x6903)+~P6(f7(x6903),x6902,x6903)+P6(f10(x6901,x6902,x6903),f10(x6904,x6905,x6903),x6903) % 1.32/1.36 [691]~P49(x6913)+~P7(x6911,x6914,x6913)+~P6(x6912,x6915,x6913)+~P7(f7(x6913),x6912,x6913)+~P6(f7(x6913),x6911,x6913)+P6(f10(x6911,x6912,x6913),f10(x6914,x6915,x6913),x6913) % 1.32/1.36 [692]~P49(x6923)+~P6(x6922,x6925,x6923)+~P6(x6921,x6924,x6923)+~P7(f7(x6923),x6922,x6923)+~P7(f7(x6923),x6921,x6923)+P6(f10(x6921,x6922,x6923),f10(x6924,x6925,x6923),x6923) % 1.32/1.36 [693]~P49(x6933)+~P6(x6932,x6935,x6933)+~P6(x6931,x6934,x6933)+~P7(f7(x6933),x6932,x6933)+~P6(f7(x6933),x6934,x6933)+P6(f10(x6931,x6932,x6933),f10(x6934,x6935,x6933),x6933) % 1.32/1.36 [694]~P27(x6943)+~P7(x6945,x6942,x6943)+~P6(x6941,x6944,x6943)+~P7(f7(x6943),x6941,x6943)+~P6(f7(x6943),x6945,x6943)+P6(f4(x6941,x6942,x6943),f4(x6944,x6945,x6943),x6943) % 1.32/1.36 [695]~P27(x6953)+~P7(x6951,x6954,x6953)+~P6(x6955,x6952,x6953)+~P6(f7(x6953),x6955,x6953)+~P6(f7(x6953),x6951,x6953)+P6(f4(x6951,x6952,x6953),f4(x6954,x6955,x6953),x6953) % 1.32/1.36 %EqnAxiom % 1.32/1.36 [1]E(x11,x11) % 1.32/1.36 [2]E(x22,x21)+~E(x21,x22) % 1.32/1.36 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.32/1.36 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 1.32/1.36 [5]~E(x51,x52)+E(f6(x51),f6(x52)) % 1.32/1.36 [6]~E(x61,x62)+E(f7(x61),f7(x62)) % 1.32/1.36 [7]~E(x71,x72)+E(f10(x71,x73,x74),f10(x72,x73,x74)) % 1.32/1.36 [8]~E(x81,x82)+E(f10(x83,x81,x84),f10(x83,x82,x84)) % 1.32/1.36 [9]~E(x91,x92)+E(f10(x93,x94,x91),f10(x93,x94,x92)) % 1.32/1.36 [10]~E(x101,x102)+E(f3(x101,x103),f3(x102,x103)) % 1.32/1.36 [11]~E(x111,x112)+E(f3(x113,x111),f3(x113,x112)) % 1.32/1.36 [12]~E(x121,x122)+E(f9(x121,x123,x124),f9(x122,x123,x124)) % 1.32/1.36 [13]~E(x131,x132)+E(f9(x133,x131,x134),f9(x133,x132,x134)) % 1.32/1.36 [14]~E(x141,x142)+E(f9(x143,x144,x141),f9(x143,x144,x142)) % 1.32/1.36 [15]~E(x151,x152)+E(f4(x151,x153,x154),f4(x152,x153,x154)) % 1.32/1.36 [16]~E(x161,x162)+E(f4(x163,x161,x164),f4(x163,x162,x164)) % 1.32/1.36 [17]~E(x171,x172)+E(f4(x173,x174,x171),f4(x173,x174,x172)) % 1.32/1.36 [18]~E(x181,x182)+E(f8(x181,x183),f8(x182,x183)) % 1.32/1.36 [19]~E(x191,x192)+E(f8(x193,x191),f8(x193,x192)) % 1.32/1.36 [20]~E(x201,x202)+E(f11(x201,x203),f11(x202,x203)) % 1.32/1.36 [21]~E(x211,x212)+E(f11(x213,x211),f11(x213,x212)) % 1.32/1.36 [22]~E(x221,x222)+E(f5(x221,x223),f5(x222,x223)) % 1.32/1.36 [23]~E(x231,x232)+E(f5(x233,x231),f5(x233,x232)) % 1.32/1.36 [24]~E(x241,x242)+E(f13(x241,x243),f13(x242,x243)) % 1.32/1.36 [25]~E(x251,x252)+E(f13(x253,x251),f13(x253,x252)) % 1.32/1.36 [26]~E(x261,x262)+E(f12(x261,x263),f12(x262,x263)) % 1.32/1.36 [27]~E(x271,x272)+E(f12(x273,x271),f12(x273,x272)) % 1.32/1.36 [28]~E(x281,x282)+E(f16(x281,x283),f16(x282,x283)) % 1.32/1.36 [29]~E(x291,x292)+E(f16(x293,x291),f16(x293,x292)) % 1.32/1.36 [30]~P1(x301)+P1(x302)+~E(x301,x302) % 1.32/1.36 [31]~P23(x311)+P23(x312)+~E(x311,x312) % 1.32/1.36 [32]~P24(x321)+P24(x322)+~E(x321,x322) % 1.32/1.36 [33]~P25(x331)+P25(x332)+~E(x331,x332) % 1.32/1.36 [34]~P26(x341)+P26(x342)+~E(x341,x342) % 1.32/1.36 [35]~P2(x351)+P2(x352)+~E(x351,x352) % 1.32/1.36 [36]~P3(x361)+P3(x362)+~E(x361,x362) % 1.32/1.36 [37]~P49(x371)+P49(x372)+~E(x371,x372) % 1.32/1.36 [38]~P4(x381)+P4(x382)+~E(x381,x382) % 1.32/1.36 [39]~P50(x391)+P50(x392)+~E(x391,x392) % 1.32/1.36 [40]~P22(x401)+P22(x402)+~E(x401,x402) % 1.32/1.36 [41]~P27(x411)+P27(x412)+~E(x411,x412) % 1.32/1.36 [42]~P28(x421)+P28(x422)+~E(x421,x422) % 1.32/1.36 [43]~P39(x431)+P39(x432)+~E(x431,x432) % 1.32/1.36 [44]~P5(x441)+P5(x442)+~E(x441,x442) % 1.32/1.36 [45]~P40(x451)+P40(x452)+~E(x451,x452) % 1.32/1.36 [46]~P42(x461)+P42(x462)+~E(x461,x462) % 1.32/1.36 [47]~P41(x471)+P41(x472)+~E(x471,x472) % 1.32/1.36 [48]~P29(x481)+P29(x482)+~E(x481,x482) % 1.32/1.36 [49]~P14(x491)+P14(x492)+~E(x491,x492) % 1.32/1.36 [50]~P15(x501)+P15(x502)+~E(x501,x502) % 1.32/1.36 [51]~P30(x511)+P30(x512)+~E(x511,x512) % 1.32/1.36 [52]~P35(x521)+P35(x522)+~E(x521,x522) % 1.32/1.36 [53]~P19(x531)+P19(x532)+~E(x531,x532) % 1.32/1.36 [54]~P37(x541)+P37(x542)+~E(x541,x542) % 1.32/1.36 [55]~P16(x551)+P16(x552)+~E(x551,x552) % 1.32/1.36 [56]~P17(x561)+P17(x562)+~E(x561,x562) % 1.32/1.36 [57]~P51(x571)+P51(x572)+~E(x571,x572) % 1.32/1.36 [58]~P18(x581)+P18(x582)+~E(x581,x582) % 1.32/1.36 [59]~P52(x591)+P52(x592)+~E(x591,x592) % 1.32/1.36 [60]~P43(x601)+P43(x602)+~E(x601,x602) % 1.32/1.36 [61]~P53(x611)+P53(x612)+~E(x611,x612) % 1.32/1.36 [62]~P31(x621)+P31(x622)+~E(x621,x622) % 1.32/1.36 [63]~P44(x631)+P44(x632)+~E(x631,x632) % 1.32/1.36 [64]~P58(x641)+P58(x642)+~E(x641,x642) % 1.32/1.36 [65]~P59(x651)+P59(x652)+~E(x651,x652) % 1.32/1.36 [66]~P8(x661)+P8(x662)+~E(x661,x662) % 1.32/1.36 [67]~P9(x671)+P9(x672)+~E(x671,x672) % 1.32/1.36 [68]~P36(x681)+P36(x682)+~E(x681,x682) % 1.32/1.36 [69]~P45(x691)+P45(x692)+~E(x691,x692) % 1.32/1.36 [70]~P32(x701)+P32(x702)+~E(x701,x702) % 1.32/1.36 [71]~P21(x711)+P21(x712)+~E(x711,x712) % 1.32/1.36 [72]~P54(x721)+P54(x722)+~E(x721,x722) % 1.32/1.36 [73]~P33(x731)+P33(x732)+~E(x731,x732) % 1.32/1.36 [74]~P46(x741)+P46(x742)+~E(x741,x742) % 1.32/1.36 [75]~P47(x751)+P47(x752)+~E(x751,x752) % 1.32/1.36 [76]~P48(x761)+P48(x762)+~E(x761,x762) % 1.32/1.36 [77]~P34(x771)+P34(x772)+~E(x771,x772) % 1.32/1.36 [78]~P55(x781)+P55(x782)+~E(x781,x782) % 1.32/1.36 [79]~P56(x791)+P56(x792)+~E(x791,x792) % 1.32/1.36 [80]~P10(x801)+P10(x802)+~E(x801,x802) % 1.32/1.36 [81]~P38(x811)+P38(x812)+~E(x811,x812) % 1.32/1.36 [82]~P57(x821)+P57(x822)+~E(x821,x822) % 1.32/1.36 [83]~P12(x831)+P12(x832)+~E(x831,x832) % 1.32/1.36 [84]~P13(x841)+P13(x842)+~E(x841,x842) % 1.32/1.36 [85]~P20(x851)+P20(x852)+~E(x851,x852) % 1.32/1.36 [86]~P60(x861)+P60(x862)+~E(x861,x862) % 1.32/1.36 [87]P6(x872,x873,x874)+~E(x871,x872)+~P6(x871,x873,x874) % 1.32/1.36 [88]P6(x883,x882,x884)+~E(x881,x882)+~P6(x883,x881,x884) % 1.32/1.36 [89]P6(x893,x894,x892)+~E(x891,x892)+~P6(x893,x894,x891) % 1.32/1.36 [90]P7(x902,x903,x904)+~E(x901,x902)+~P7(x901,x903,x904) % 1.32/1.36 [91]P7(x913,x912,x914)+~E(x911,x912)+~P7(x913,x911,x914) % 1.32/1.36 [92]P7(x923,x924,x922)+~E(x921,x922)+~P7(x923,x924,x921) % 1.32/1.36 [93]~P11(x931)+P11(x932)+~E(x931,x932) % 1.32/1.36 [94]~P61(x941)+P61(x942)+~E(x941,x942) % 1.32/1.36 % 1.32/1.36 %------------------------------------------- % 1.32/1.36 cnf(737,plain, % 1.32/1.36 (E(x7371,f6(f11(x7371,a1)))), % 1.32/1.36 inference(scs_inference,[],[165,158,314,2])). % 1.32/1.36 cnf(739,plain, % 1.32/1.36 (E(f6(f11(x7391,a1)),x7391)), % 1.32/1.36 inference(rename_variables,[],[158])). % 1.32/1.36 cnf(743,plain, % 1.32/1.36 (~P6(x7431,x7431,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(746,plain, % 1.32/1.36 (~P6(x7461,x7461,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(749,plain, % 1.32/1.36 (~P6(x7491,x7491,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(754,plain, % 1.32/1.36 (~P6(x7541,x7541,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(759,plain, % 1.32/1.36 (~P6(x7591,x7591,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(761,plain, % 1.32/1.36 (~P6(x7611,x7611,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(779,plain, % 1.32/1.36 (~P6(x7791,x7791,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(782,plain, % 1.32/1.36 (~P6(x7821,x7821,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(785,plain, % 1.32/1.36 (~P6(x7851,x7851,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(788,plain, % 1.32/1.36 (~P6(x7881,x7881,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(791,plain, % 1.32/1.36 (~P6(x7911,x7911,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(798,plain, % 1.32/1.36 (~P6(x7981,x7981,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(801,plain, % 1.32/1.36 (~P6(x8011,x8011,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(804,plain, % 1.32/1.36 (~P6(x8041,x8041,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(807,plain, % 1.32/1.36 (~P6(x8071,x8071,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(810,plain, % 1.32/1.36 (~P6(x8101,x8101,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(821,plain, % 1.32/1.36 (~P6(x8211,x8211,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(824,plain, % 1.32/1.36 (~P6(x8241,x8241,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(851,plain, % 1.32/1.36 (~P6(x8511,x8511,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(854,plain, % 1.32/1.36 (~P6(x8541,x8541,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(857,plain, % 1.32/1.36 (~P6(x8571,x8571,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(860,plain, % 1.32/1.36 (~P6(x8601,x8601,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(863,plain, % 1.32/1.36 (~P6(x8631,x8631,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(866,plain, % 1.32/1.36 (~P6(x8661,x8661,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(869,plain, % 1.32/1.36 (~P6(x8691,x8691,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(872,plain, % 1.32/1.36 (~P6(x8721,x8721,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(875,plain, % 1.32/1.36 (~P6(x8751,x8751,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(880,plain, % 1.32/1.36 (~P6(x8801,x8801,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(897,plain, % 1.32/1.36 (~P6(x8971,x8971,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(900,plain, % 1.32/1.36 (~P6(x9001,x9001,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(903,plain, % 1.32/1.36 (~P6(x9031,x9031,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(906,plain, % 1.32/1.36 (~P6(x9061,x9061,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(909,plain, % 1.32/1.36 (~P6(x9091,x9091,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(912,plain, % 1.32/1.36 (~P6(x9121,x9121,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(919,plain, % 1.32/1.36 (~P6(x9191,x9191,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(931,plain, % 1.32/1.36 (E(f4(f4(a14,a15,a1),f4(a14,a15,a1),a1),f2(a1))), % 1.32/1.36 inference(scs_inference,[],[167,165,163,164,162,158,739,159,160,169,743,746,749,754,759,761,779,782,785,788,791,798,801,804,807,810,821,824,851,854,857,860,863,866,869,872,875,880,897,900,903,906,909,912,170,95,99,101,106,121,96,97,98,102,103,108,109,110,111,112,113,118,122,125,126,135,168,314,2,94,300,380,381,468,469,471,3,87,88,339,409,199,282,286,287,320,383,386,388,390,391,392,401,404,479,573,574,628,630,644,645,646,647,651,652,387,524,528,529,530,539,610,629,657,659,660,661,486,487,552,557,558,559,560,563,564,566,633,637,435,484,485,551,631,635,547,548,549,550,591,592,594,669,670,191,192,193,194,195,227])). % 1.32/1.36 cnf(949,plain, % 1.32/1.36 (~E(f4(x9491,f7(a1),a1),f4(a14,a15,a1))), % 1.32/1.36 inference(scs_inference,[],[167,165,163,164,162,158,739,159,160,169,743,746,749,754,759,761,779,782,785,788,791,798,801,804,807,810,821,824,851,854,857,860,863,866,869,872,875,880,897,900,903,906,909,912,170,95,99,101,106,121,96,97,98,102,103,108,109,110,111,112,113,118,122,125,126,135,168,314,2,94,300,380,381,468,469,471,3,87,88,339,409,199,282,286,287,320,383,386,388,390,391,392,401,404,479,573,574,628,630,644,645,646,647,651,652,387,524,528,529,530,539,610,629,657,659,660,661,486,487,552,557,558,559,560,563,564,566,633,637,435,484,485,551,631,635,547,548,549,550,591,592,594,669,670,191,192,193,194,195,227,274,276,279,291,317,315,316,467,90])). % 1.32/1.36 cnf(973,plain, % 1.32/1.36 (~P6(x9731,x9731,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(980,plain, % 1.32/1.36 (~P6(x9801,x9801,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(983,plain, % 1.32/1.36 (~P6(x9831,x9831,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(988,plain, % 1.32/1.36 (~P6(x9881,x9881,a1)), % 1.32/1.36 inference(rename_variables,[],[169])). % 1.32/1.36 cnf(995,plain, % 1.32/1.36 (P6(f7(a1),f4(a14,a15,a1),x9951)+~E(a1,x9951)), % 1.32/1.36 inference(scs_inference,[],[167,165,163,164,162,158,739,159,160,169,743,746,749,754,759,761,779,782,785,788,791,798,801,804,807,810,821,824,851,854,857,860,863,866,869,872,875,880,897,900,903,906,909,912,919,973,980,983,988,170,95,99,101,106,121,96,97,98,102,103,108,109,110,111,112,113,118,122,125,126,135,139,143,168,314,2,94,300,380,381,468,469,471,3,87,88,339,409,199,282,286,287,320,383,386,388,390,391,392,401,404,479,573,574,628,630,644,645,646,647,651,652,387,524,528,529,530,539,610,629,657,659,660,661,486,487,552,557,558,559,560,563,564,566,633,637,435,484,485,551,631,635,547,548,549,550,591,592,594,669,670,191,192,193,194,195,227,274,276,279,291,317,315,316,467,90,297,400,511,599,607,608,553,554,556,562,565,593,667,673,674,675,678,679,680,327,89])). % 1.32/1.36 cnf(1003,plain, % 1.32/1.36 (~P6(x10031,f4(a14,a15,a1),a1)+~P6(f7(a1),x10031,a1)+~P6(x10031,f2(a1),a1)), % 1.32/1.36 inference(scs_inference,[],[167,568])). % 1.32/1.36 cnf(1011,plain, % 1.32/1.36 ($false), % 1.32/1.36 inference(scs_inference,[],[164,162,737,931,166,163,949,995,16,314,2,1003]), % 1.32/1.36 ['proof']). % 1.32/1.36 % SZS output end Proof % 1.32/1.36 % Total time :0.520000s %------------------------------------------------------------------------------