%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : ALG384-1 : 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 : n016.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 03:41:33 EDT 2024 % Result : Unsatisfiable 1.14s 1.25s % Output : CNFRefutation 1.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : ALG384-1 : TPTP v8.2.0. Released v4.1.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.34 % Computer : n016.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 16:01:39 EDT 2024 % 0.12/0.34 % CPUTime : % 0.47/0.56 start to proof:theBenchmark % 1.14/1.20 %------------------------------------------- % 1.14/1.20 % File :CSE---1.7 % 1.14/1.20 % Problem :theBenchmark % 1.14/1.20 % Transform :cnf % 1.14/1.20 % Format :tptp:raw % 1.14/1.20 % Command :java -jar mcs_scs.jar %d %s % 1.14/1.20 % 1.14/1.20 % Result :Theorem 0.480000s % 1.14/1.20 % Output :CNFRefutation 0.480000s % 1.14/1.20 %------------------------------------------- % 1.14/1.21 %------------------------------------------------------------------------------ % 1.14/1.21 % File : ALG384-1 : TPTP v8.2.0. Released v4.1.0. % 1.14/1.21 % Domain : General Algebra % 1.14/1.21 % Problem : Fundamental theorem of algebra 0517_33 % 1.14/1.21 % Version : Especial. % 1.14/1.21 % English : % 1.14/1.21 % 1.14/1.21 % Refs : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe % 1.14/1.21 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 1.14/1.21 % Source : [Nip10] % 1.14/1.21 % Names : Fundamental_Theorem_Algebra-0517_33 [Nip10] % 1.14/1.21 % 1.14/1.21 % Status : Unsatisfiable % 1.14/1.21 % Rating : 0.05 v8.1.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.00 v6.1.0, 0.07 v6.0.0, 0.10 v5.5.0, 0.45 v5.4.0, 0.40 v5.3.0, 0.44 v5.2.0, 0.31 v5.1.0, 0.41 v5.0.0, 0.29 v4.1.0 % 1.14/1.21 % Syntax : Number of clauses : 574 ( 110 unt; 111 nHn; 412 RR) % 1.14/1.21 % Number of literals : 1714 ( 240 equ;1041 neg) % 1.14/1.21 % Maximal clause size : 6 ( 2 avg) % 1.14/1.21 % Maximal term depth : 4 ( 1 avg) % 1.14/1.21 % Number of predicates : 45 ( 44 usr; 0 prp; 1-3 aty) % 1.14/1.21 % Number of functors : 40 ( 40 usr; 8 con; 0-3 aty) % 1.14/1.21 % Number of variables : 1383 ( 92 sgn) % 1.14/1.21 % SPC : CNF_UNS_RFO_SEQ_NHN % 1.14/1.21 % 1.14/1.21 % Comments : % 1.14/1.21 %------------------------------------------------------------------------------ % 1.14/1.21 cnf(cls_real__norm__def_0,axiom, % 1.14/1.21 c_RealVector_Onorm__class_Onorm(V_r,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_scaleR__cancel__right_1,axiom, % 1.14/1.21 ( ~ class_RealVector_Oreal__vector(T_a) % 1.14/1.21 | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_abs__eq__0_0,axiom, % 1.14/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.14/1.21 | c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_inverse__zero__imp__zero_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.14/1.21 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_inverse__nonzero__iff__nonzero_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.14/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.21 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_sgn__0__0_1,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.14/1.21 | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_sgn0_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Osgn__if(T_a) % 1.14/1.21 | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_sgn__zero_0,axiom, % 1.14/1.21 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.21 | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_mult__eq__0__iff_2,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.14/1.21 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_mult__eq__0__iff_1,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.14/1.21 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_mult__zero__right_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 1.14/1.21 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_mult__zero__left_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 1.14/1.21 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_class__semiring_Omul__0_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.14/1.21 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_mult__right_Ozero_0,axiom, % 1.14/1.21 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.14/1.21 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_mult_Ozero__right_0,axiom, % 1.14/1.21 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.14/1.21 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_mult_Ozero__left_0,axiom, % 1.14/1.21 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.14/1.21 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_mult__left_Ozero_0,axiom, % 1.14/1.21 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.14/1.21 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.14/1.21 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.14/1.21 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_nonzero__inverse__inverse__eq_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.14/1.21 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a % 1.14/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_divide__self__if_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.21 | 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) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_inverse__zero_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.21 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_inverse__nonzero__iff__nonzero_1,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.14/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.21 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_nonzero__inverse__eq__imp__eq_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.14/1.21 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a) % 1.14/1.21 | V_a = V_b % 1.14/1.21 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_mult__eq__0__iff_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.14/1.21 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.21 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_no__zero__divisors_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.14/1.21 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.21 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_no__zero__divirors__neq0_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.14/1.21 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.21 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_abs__eq__0_1,axiom, % 1.14/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.14/1.21 | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_scaleR_Ozero__right_0,axiom, % 1.14/1.21 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.21 | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_scaleR__eq__0__iff_2,axiom, % 1.14/1.21 ( ~ class_RealVector_Oreal__vector(T_a) % 1.14/1.21 | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_divide__zero__left_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.21 | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_divide__eq__eq_1,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.21 | c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_divide__zero_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.21 | c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_divide_Ozero_0,axiom, % 1.14/1.21 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.14/1.21 | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_sgn__0__0_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.14/1.21 | c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_sgn__zero__iff_0,axiom, % 1.14/1.21 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.21 | c_HOL_Osgn__class_Osgn(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.21 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_exp__not__eq__zero_0,axiom, % 1.14/1.21 ( ~ class_SEQ_Obanach(T_a) % 1.14/1.21 | ~ class_RealVector_Oreal__normed__field(T_a) % 1.14/1.21 | c_Transcendental_Oexp(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_mult__less__le__imp__less_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.14/1.21 | 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) % 1.14/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.21 | ~ c_lessequals(V_c,V_d,T_a) % 1.14/1.21 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.14/1.21 % 1.14/1.21 cnf(cls_mult__le__less__imp__less_0,axiom, % 1.14/1.21 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.14/1.21 | 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) % 1.14/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.14/1.22 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_divide__strict__left__mono__neg_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | 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) % 1.14/1.22 | ~ 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) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_divide__strict__left__mono_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | 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) % 1.14/1.22 | ~ 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) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_frac__le_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | 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) % 1.14/1.22 | ~ c_lessequals(V_w,V_z,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 1.14/1.22 | ~ c_lessequals(V_x,V_y,T_a) % 1.14/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_less__divide__eq_7,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_less__divide__eq_5,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_less__divide__eq_4,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_less__divide__eq_1,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_divide__less__eq_7,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_divide__less__eq_5,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_divide__less__eq_4,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_divide__less__eq_1,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_le__imp__inverse__le__neg_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_inverse__le__imp__le__neg_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | c_lessequals(V_b,V_a,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_le__imp__inverse__le_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.22 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_inverse__le__imp__le_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | c_lessequals(V_b,V_a,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.22 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_divide__nonpos__neg_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_divide__nonneg__pos_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.14/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_less__divide__eq_9,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_less__divide__eq_8,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_divide__less__eq_9,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_divide__less__eq_8,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_frac__less_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | 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) % 1.14/1.22 | ~ c_lessequals(V_w,V_z,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.14/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_mult__strict__mono_H_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.14/1.22 | 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) % 1.14/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_divide__nonpos__pos_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.14/1.22 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_divide__nonneg__neg_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_mult__imp__less__div__pos_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_mult__imp__div__pos__less_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_less__divide__eq_6,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_less__divide__eq_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_divide__less__eq_6,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_divide__less__eq_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_abs__div__pos_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | 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) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_mult__less__imp__less__right_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.14/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.22 | ~ 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) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_mult__less__imp__less__left_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.14/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.22 | ~ 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) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_mult__right__less__imp__less_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.14/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.22 | ~ 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) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_mult__left__less__imp__less_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.14/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.22 | ~ 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) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_mult__strict__mono_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.14/1.22 | 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) % 1.14/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_frac__less2_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | 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) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_w,V_z,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 1.14/1.22 | ~ c_lessequals(V_x,V_y,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_mult__right__le__imp__le_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.14/1.22 | c_lessequals(V_a,V_b,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.22 | ~ 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) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_mult__left__le__imp__le_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.14/1.22 | c_lessequals(V_a,V_b,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.22 | ~ 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) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_mult__le__cancel__left__pos_1,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.22 | 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) % 1.14/1.22 | ~ c_lessequals(V_a,V_b,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_mult__le__cancel__left__pos_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.22 | c_lessequals(V_a,V_b,T_a) % 1.14/1.22 | ~ 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) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_mult__le__cancel__left__neg_1,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.22 | 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) % 1.14/1.22 | ~ c_lessequals(V_b,V_a,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_mult__le__cancel__left__neg_0,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.22 | c_lessequals(V_b,V_a,T_a) % 1.14/1.22 | ~ 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) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_le__divide__eq_3,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.14/1.22 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_le__divide__eq_2,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.22 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_divide__le__eq_3,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.14/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_divide__le__eq_2,axiom, % 1.14/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.22 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.22 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_xt1_I7_J_0,axiom, % 1.14/1.22 ( ~ class_Orderings_Oorder(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.14/1.22 | ~ c_lessequals(V_z,V_y,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_xt1_I8_J_0,axiom, % 1.14/1.22 ( ~ class_Orderings_Oorder(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.14/1.22 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_order__less__le__trans_0,axiom, % 1.14/1.22 ( ~ class_Orderings_Opreorder(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.14/1.22 | ~ c_lessequals(V_y,V_z,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_order__le__less__trans_0,axiom, % 1.14/1.22 ( ~ class_Orderings_Opreorder(T_a) % 1.14/1.22 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.14/1.22 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.14/1.22 % 1.14/1.22 cnf(cls_order__less__imp__le_0,axiom, % 1.14/1.22 ( ~ class_Orderings_Opreorder(T_a) % 1.14/1.22 | c_lessequals(V_x,V_y,T_a) % 1.14/1.22 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.14/1.22 % 1.14/1.23 cnf(cls_of__real_Opos__bounded_1,axiom, % 1.14/1.23 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.23 | ~ class_RealVector_Oreal__algebra__1(T_a) % 1.14/1.23 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(V_K,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xof__real__Xpos__bounded__1__1(V_vskULr,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_scaleR_Opos__bounded_1,axiom, % 1.14/1.23 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.23 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_a,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_b,T_a),tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__Xpos__bounded__1__1(V_vskULo,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_scaleR__left_Opos__bounded_1,axiom, % 1.14/1.23 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.23 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(V_K,V_x,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__left__Xpos__bounded__1__1(V_x,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_scaleR__cancel__right_0,axiom, % 1.14/1.23 ( ~ class_RealVector_Oreal__vector(T_a) % 1.14/1.23 | c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a) != c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a) % 1.14/1.23 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.23 | V_a = V_b ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_eq__divide__eq_2,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_divide__le__eq_9,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.14/1.23 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_le__divide__eq_9,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.14/1.23 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_of__nat__0__le__iff_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.14/1.23 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_zero__le__imp__of__nat_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.14/1.23 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_dist__le__zero__iff_0,axiom, % 1.14/1.23 ( ~ class_RealVector_Ometric__space(T_a) % 1.14/1.23 | V_x = V_y % 1.14/1.23 | ~ c_lessequals(c_RealVector_Odist__class_Odist(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__frac__num_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | 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) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__divide__mult__cancel__left_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | 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) % 1.14/1.23 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__divide__mult__cancel__right_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | 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) % 1.14/1.23 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_abs__divide_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | 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) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_abs__inverse_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | 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) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_real__sqrt__le__0__iff_1,axiom, % 1.14/1.23 ( c_lessequals(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.14/1.23 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_real__sqrt__le__0__iff_0,axiom, % 1.14/1.23 ( c_lessequals(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.14/1.23 | ~ c_lessequals(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_inverse__nonpositive__iff__nonpositive_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_inverse__nonpositive__iff__nonpositive_1,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_real__sqrt__mult_0,axiom, % 1.14/1.23 c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_real__of__nat__ge__zero_0,axiom, % 1.14/1.23 c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(V_n,tc_nat),tc_RealDef_Oreal) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_real__vector_Oscale__scale_0,axiom, % 1.14/1.23 ( ~ class_RealVector_Oreal__vector(T_a) % 1.14/1.23 | c_RealVector_OscaleR__class_OscaleR(V_a,c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Otimes__class_Otimes(V_a,V_b,tc_RealDef_Oreal),V_x,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_zero__le__divide__iff_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_zero__le__divide__iff_1,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_zero__le__divide__iff_2,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_zero__le__divide__iff_3,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_scaleR__conv__of__real_0,axiom, % 1.14/1.23 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 1.14/1.23 | c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(V_r,T_a),V_x,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_not__exp__le__zero_0,axiom, % 1.14/1.23 ~ c_lessequals(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__left_Opos__bounded_1,axiom, % 1.14/1.23 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.14/1.23 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_K,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.14/1.23 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_real__mult__commute_0,axiom, % 1.14/1.23 c_HOL_Otimes__class_Otimes(V_z,V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,V_z,tc_RealDef_Oreal) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_class__semiring_Omul__c_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.14/1.23 | c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_inverse__inverse__eq_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_abs__mult__less_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.14/1.23 | 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) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_b,T_a),V_d,T_a) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_c,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_exp__ge__zero_0,axiom, % 1.14/1.23 c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_divide__left__mono_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | 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) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.23 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_divide__left__mono__neg_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | 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) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.14/1.23 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_abs__le__interval__iff_1,axiom, % 1.14/1.23 ( c_lessequals(V_x,V_r,tc_RealDef_Oreal) % 1.14/1.23 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),V_r,tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_abs__le__D1_0,axiom, % 1.14/1.23 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.14/1.23 | c_lessequals(V_a,V_b,T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_abs__le__mult_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Olordered__ring(T_a) % 1.14/1.23 | 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) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_of__real__eq__iff_0,axiom, % 1.14/1.23 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 1.14/1.23 | c_RealVector_Oof__real(V_x,T_a) != c_RealVector_Oof__real(V_y,T_a) % 1.14/1.23 | V_x = V_y ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_divide__le__0__iff_4,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_divide__le__0__iff_5,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.23 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_norm__mult__ineq_0,axiom, % 1.14/1.23 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.14/1.23 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_RealVector_Onorm__class_Onorm(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__sgn__abs_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.14/1.23 | 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 ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_of__nat__eq__iff_0,axiom, % 1.14/1.23 ( ~ class_Nat_Osemiring__char__0(T_a) % 1.14/1.23 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) % 1.14/1.23 | V_m = V_n ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_divide__le__eq_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_divide__le__eq_6,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.23 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_le__divide__eq_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.23 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_le__divide__eq_6,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__imp__div__pos__le_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) % 1.14/1.23 | ~ c_lessequals(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__imp__le__div__pos_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | c_lessequals(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_divide_Opos__bounded_1,axiom, % 1.14/1.23 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.14/1.23 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(V_K,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__Xdivide__Xpos__bounded__1__1(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_real__of__nat__inject_0,axiom, % 1.14/1.23 ( c_RealDef_Oreal(V_n,tc_nat) != c_RealDef_Oreal(V_m,tc_nat) % 1.14/1.23 | V_n = V_m ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_divide__le__eq_8,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.14/1.23 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_le__divide__eq_8,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_dist__le__zero__iff_1,axiom, % 1.14/1.23 ( ~ class_RealVector_Ometric__space(T_a) % 1.14/1.23 | c_lessequals(c_RealVector_Odist__class_Odist(V_x,V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.14/1.23 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.14/1.23 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.14/1.23 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_ry,T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_abs__le__zero__iff_0,axiom, % 1.14/1.23 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.14/1.23 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_exp__of__real_0,axiom, % 1.14/1.23 ( ~ class_SEQ_Obanach(T_a) % 1.14/1.23 | ~ class_RealVector_Oreal__normed__field(T_a) % 1.14/1.23 | 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) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_divide__eq__eq_3,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a % 1.14/1.23 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_eq__divide__eq_3,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) % 1.14/1.23 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_divide__eq__imp_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.23 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.23 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_eq__divide__imp_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.23 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.23 | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_exp__le__cancel__iff_0,axiom, % 1.14/1.23 ( c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.14/1.23 | ~ c_lessequals(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_Transcendental_Oexp(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_exp__le__cancel__iff_1,axiom, % 1.14/1.23 ( c_lessequals(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_Transcendental_Oexp(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.14/1.23 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_real__le__antisym_0,axiom, % 1.14/1.23 ( V_z = V_w % 1.14/1.23 | ~ c_lessequals(V_w,V_z,tc_RealDef_Oreal) % 1.14/1.23 | ~ c_lessequals(V_z,V_w,tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_order__antisym_0,axiom, % 1.14/1.23 ( ~ class_Orderings_Oorder(T_a) % 1.14/1.23 | V_x = V_y % 1.14/1.23 | ~ c_lessequals(V_y,V_x,T_a) % 1.14/1.23 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_order__eq__iff_2,axiom, % 1.14/1.23 ( ~ class_Orderings_Oorder(T_a) % 1.14/1.23 | V_x = V_y % 1.14/1.23 | ~ c_lessequals(V_y,V_x,T_a) % 1.14/1.23 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_order__antisym__conv_0,axiom, % 1.14/1.23 ( ~ class_Orderings_Oorder(T_a) % 1.14/1.23 | V_x = V_y % 1.14/1.23 | ~ c_lessequals(V_x,V_y,T_a) % 1.14/1.23 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_abs__of__nonneg_0,axiom, % 1.14/1.23 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.14/1.23 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_abs__mult_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.14/1.23 | 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) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_abs__eq__mult_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.14/1.23 | 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) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_abs__eq__mult_1,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.14/1.23 | 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) % 1.14/1.23 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_abs__eq__mult_2,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.14/1.23 | 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) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.23 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_abs__eq__mult_3,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.14/1.23 | 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) % 1.14/1.23 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__frac__frac_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | 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) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__left__idem_0,axiom, % 1.14/1.23 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 1.14/1.23 | 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) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__le__0__iff_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.23 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__le__0__iff_1,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.23 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.23 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__le__0__iff_2,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.23 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__le__0__iff_3,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.23 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.23 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_real__sqrt__ge__0__iff_1,axiom, % 1.14/1.23 ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_real__sqrt__ge__0__iff_0,axiom, % 1.14/1.23 ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_real__sqrt__ge__zero_0,axiom, % 1.14/1.23 ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x),tc_RealDef_Oreal) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_real__sqrt__eq__iff_0,axiom, % 1.14/1.23 ( c_NthRoot_Osqrt(V_x) != c_NthRoot_Osqrt(V_y) % 1.14/1.23 | V_x = V_y ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_exp__inj__iff_0,axiom, % 1.14/1.23 ( c_Transcendental_Oexp(V_x,tc_RealDef_Oreal) != c_Transcendental_Oexp(V_y,tc_RealDef_Oreal) % 1.14/1.23 | V_x = V_y ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_inverse__divide_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | 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) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__mono1_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Omult__mono1(T_a) % 1.14/1.23 | 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) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.23 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__left__mono_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 1.14/1.23 | 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) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.23 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__right__mono_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 1.14/1.23 | 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) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.23 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__left__mono__neg_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.14/1.23 | 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) % 1.14/1.23 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__right__mono__neg_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.14/1.23 | 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) % 1.14/1.23 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_zero__le__dist_0,axiom, % 1.14/1.23 ( ~ class_RealVector_Ometric__space(T_a) % 1.14/1.23 | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(V_x,V_y,T_a),tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_abs__real__of__nat__cancel_0,axiom, % 1.14/1.23 c_HOL_Oabs__class_Oabs(c_RealDef_Oreal(V_x,tc_nat),tc_RealDef_Oreal) = c_RealDef_Oreal(V_x,tc_nat) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__idem_0,axiom, % 1.14/1.23 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 1.14/1.23 | c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = V_x ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_inverse__eq__iff__eq_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a) % 1.14/1.23 | V_a = V_b ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_of__real__mult_0,axiom, % 1.14/1.23 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 1.14/1.23 | c_RealVector_Oof__real(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),T_a) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(V_x,T_a),c_RealVector_Oof__real(V_y,T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_divide__right__mono_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | 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) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.23 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_divide__right__mono__neg_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.23 | 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) % 1.14/1.23 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.23 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_split__mult__pos__le_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.14/1.23 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_order__le__less_1,axiom, % 1.14/1.23 ( ~ class_Orderings_Oorder(T_a) % 1.14/1.23 | c_lessequals(V_x,V_y,T_a) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_less__le__not__le_2,axiom, % 1.14/1.23 ( ~ class_Orderings_Opreorder(T_a) % 1.14/1.23 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.14/1.23 | c_lessequals(V_y,V_x,T_a) % 1.14/1.23 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_abs__less__iff_0,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.14/1.23 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__less__cancel__right__disj_3,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.23 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.14/1.23 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_mult__less__cancel__left__disj_3,axiom, % 1.14/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.23 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.14/1.23 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_xt1_I11_J_0,axiom, % 1.14/1.23 ( ~ class_Orderings_Oorder(T_a) % 1.14/1.23 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.14/1.23 | V_a = V_b % 1.14/1.23 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_xt1_I12_J_0,axiom, % 1.14/1.23 ( ~ class_Orderings_Oorder(T_a) % 1.14/1.23 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.14/1.23 | ~ c_lessequals(V_b,V_a,T_a) % 1.14/1.23 | V_a = V_b ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_linorder__antisym__conv2_0,axiom, % 1.14/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.14/1.23 | V_x = V_y % 1.14/1.23 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.14/1.23 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_linorder__antisym__conv1_0,axiom, % 1.14/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.14/1.23 | V_x = V_y % 1.14/1.23 | ~ c_lessequals(V_x,V_y,T_a) % 1.14/1.23 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_order__neq__le__trans_0,axiom, % 1.14/1.23 ( ~ class_Orderings_Oorder(T_a) % 1.14/1.23 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.14/1.23 | ~ c_lessequals(V_a,V_b,T_a) % 1.14/1.23 | V_a = V_b ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_order__le__neq__trans_0,axiom, % 1.14/1.23 ( ~ class_Orderings_Oorder(T_a) % 1.14/1.23 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.14/1.23 | V_a = V_b % 1.14/1.23 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_order__le__less_0,axiom, % 1.14/1.23 ( ~ class_Orderings_Oorder(T_a) % 1.14/1.23 | V_x = V_y % 1.14/1.23 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.14/1.23 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_order__less__le_2,axiom, % 1.14/1.23 ( ~ class_Orderings_Oorder(T_a) % 1.14/1.23 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.14/1.23 | V_x = V_y % 1.14/1.23 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_less__le__not__le_1,axiom, % 1.14/1.23 ( ~ class_Orderings_Opreorder(T_a) % 1.14/1.23 | ~ c_lessequals(V_y,V_x,T_a) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_not__leE_0,axiom, % 1.14/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.14/1.23 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.14/1.23 | c_lessequals(V_y,V_x,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_linorder__antisym__conv2_1,axiom, % 1.14/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.14/1.23 | ~ c_lessequals(V_x,V_x,T_a) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_linorder__antisym__conv1_1,axiom, % 1.14/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.14/1.23 | c_HOL_Oord__class_Oless(V_x,V_x,T_a) % 1.14/1.23 | c_lessequals(V_x,V_x,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_linorder__not__less_1,axiom, % 1.14/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.14/1.23 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_linorder__not__less_0,axiom, % 1.14/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.14/1.23 | c_lessequals(V_y,V_x,T_a) % 1.14/1.23 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_linorder__not__le_0,axiom, % 1.14/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.14/1.23 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.14/1.23 | c_lessequals(V_x,V_y,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_linorder__not__le_1,axiom, % 1.14/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.14/1.23 | ~ c_lessequals(V_x,V_y,T_a) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_scaleR__cancel__left_0,axiom, % 1.14/1.23 ( ~ class_RealVector_Oreal__vector(T_a) % 1.14/1.23 | c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a) != c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a) % 1.14/1.23 | V_a = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.14/1.23 | V_x = V_y ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_scaleR__cancel__left_1,axiom, % 1.14/1.23 ( ~ class_RealVector_Oreal__vector(T_a) % 1.14/1.23 | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,T_a) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,T_a) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_real__mult__right__cancel_0,axiom, % 1.14/1.23 ( c_HOL_Otimes__class_Otimes(V_a,V_c,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_b,V_c,tc_RealDef_Oreal) % 1.14/1.23 | V_c = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.14/1.23 | V_a = V_b ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_real__mult__left__cancel_0,axiom, % 1.14/1.23 ( c_HOL_Otimes__class_Otimes(V_c,V_a,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_c,V_b,tc_RealDef_Oreal) % 1.14/1.23 | V_c = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.14/1.23 | V_a = V_b ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_real__sqrt__eq__0__iff_0,axiom, % 1.14/1.23 ( c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.14/1.23 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_pi__neq__zero_0,axiom, % 1.14/1.23 c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_real__sqrt__zero_0,axiom, % 1.14/1.23 c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_real__root__zero_0,axiom, % 1.14/1.23 c_NthRoot_Oroot(V_n,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_dist__self_0,axiom, % 1.14/1.23 ( ~ class_RealVector_Ometric__space(T_a) % 1.14/1.23 | c_RealVector_Odist__class_Odist(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_dist__eq__0__iff_0,axiom, % 1.14/1.23 ( ~ class_RealVector_Ometric__space(T_a) % 1.14/1.23 | c_RealVector_Odist__class_Odist(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.14/1.23 | V_x = V_y ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_ln__le__cancel__iff_1,axiom, % 1.14/1.23 ( c_lessequals(c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y),tc_RealDef_Oreal) % 1.14/1.23 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_ln__le__cancel__iff_0,axiom, % 1.14/1.23 ( c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.14/1.23 | ~ c_lessequals(c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y),tc_RealDef_Oreal) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.14/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_real__less__all__preal_0,axiom, % 1.14/1.23 ( c_HOL_Oord__class_Oless(V_y,c_RealDef_Oreal__of__preal(V_x),tc_RealDef_Oreal) % 1.14/1.23 | ~ c_lessequals(V_y,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.23 % 1.14/1.23 cnf(cls_exp__ln_0,axiom, % 1.14/1.23 ( c_Transcendental_Oexp(c_Transcendental_Oln(V_x),tc_RealDef_Oreal) = V_x % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_exp__ln__iff_0,axiom, % 1.14/1.24 ( c_Transcendental_Oexp(c_Transcendental_Oln(V_x),tc_RealDef_Oreal) != V_x % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_real__mult__le__cancel__iff2_1,axiom, % 1.14/1.24 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_z,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.14/1.24 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_real__mult__le__cancel__iff2_0,axiom, % 1.14/1.24 ( c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.14/1.24 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_z,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_real__mult__le__cancel__iff1_1,axiom, % 1.14/1.24 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.14/1.24 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_real__mult__le__cancel__iff1_0,axiom, % 1.14/1.24 ( c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.14/1.24 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_real__less__def_0,axiom, % 1.14/1.24 ( c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_exp__less__cancel_0,axiom, % 1.14/1.24 ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_Transcendental_Oexp(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_exp__less__mono_0,axiom, % 1.14/1.24 ( c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_Transcendental_Oexp(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_real__less__def_2,axiom, % 1.14/1.24 ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.14/1.24 | V_x = V_y % 1.14/1.24 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_real__sqrt__less__iff_0,axiom, % 1.14/1.24 ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_real__sqrt__less__iff_1,axiom, % 1.14/1.24 ( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_norm__mult__less_0,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(V_r,V_s,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_y,T_a),V_s,tc_RealDef_Oreal) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),V_r,tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_abs__norm__cancel_0,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.24 | c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(V_a,T_a),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_norm__ratiotest__lemma_0,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.24 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.24 | ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Otimes__class_Otimes(V_c,c_RealVector_Onorm__class_Onorm(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.14/1.24 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__less__cancel__right__disj_2,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__less__cancel__right__disj_1,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__less__cancel__left__disj_2,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__less__cancel__left__disj_1,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__less__0__iff_5,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__less__0__iff_4,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__pos__neg_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__neg__pos_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_zero__less__abs__iff_0,axiom, % 1.14/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.14/1.24 | ~ 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_abs__if_1,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oabs__if(T_a) % 1.14/1.24 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.14/1.24 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_abs__if__lattice_1,axiom, % 1.14/1.24 ( ~ class_Orderings_Olinorder(T_a) % 1.14/1.24 | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.14/1.24 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.14/1.24 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_abs__not__less__zero_0,axiom, % 1.14/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_negative__imp__inverse__negative_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_inverse__negative__iff__negative_1,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_inverse__negative__iff__negative_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_zero__less__abs__iff_1,axiom, % 1.14/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) % 1.14/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_less__imp__inverse__less__neg_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_inverse__less__imp__less__neg_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_less__imp__inverse__less_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_inverse__less__imp__less_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.24 | ~ 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_inverse__positive__imp__positive_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_not__square__less__zero_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.24 | ~ 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__strict__right__mono__neg_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__strict__right__mono_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_Rational_Oordered__idom__class_Osgn__less_1,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_Rational_Oordered__idom__class_Osgn__less_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_zero__less__divide__iff_5,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_zero__less__divide__iff_4,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__pos__pos_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__neg__neg_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__less__cancel__right__disj_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__less__cancel__left__disj_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_less__divide__eq_3,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_less__divide__eq_2,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__less__eq_3,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__less__eq_2,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_zero__less__divide__iff_3,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.24 | ~ 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_zero__less__divide__iff_2,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.24 | ~ 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_zero__less__divide__iff_1,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.24 | ~ 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_zero__less__divide__iff_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.24 | ~ 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_inverse__negative__imp__negative_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__pos__neg2_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__pos__neg_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__neg__pos_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_zero__less__mult__pos2_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.24 | ~ 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_zero__less__mult__pos_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.24 | ~ 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__pos__pos_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__neg__neg_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_Rational_Oordered__idom__class_Osgn__greater_1,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_Rational_Oordered__idom__class_Osgn__greater_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_abs__of__pos_0,axiom, % 1.14/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.14/1.24 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_split__mult__pos__le_1,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.14/1.24 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__nonpos__nonpos_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.14/1.24 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_zero__le__square_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_zero__le__mult__iff_4,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_zero__le__mult__iff_5,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.14/1.24 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__nonneg__nonneg_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom, % 1.14/1.24 ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a) % 1.14/1.24 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.14/1.24 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.14/1.24 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,V_rx,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.14/1.24 | c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ry,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.14/1.24 | c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_real__mult__assoc_0,axiom, % 1.14/1.24 c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_z1,V_z2,tc_RealDef_Oreal),V_z3,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_z1,c_HOL_Otimes__class_Otimes(V_z2,V_z3,tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_class__semiring_Omul__a_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.14/1.24 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_zero__le__mult__iff_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.24 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_zero__le__mult__iff_1,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.24 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_zero__le__mult__iff_2,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.24 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_zero__le__mult__iff_3,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.24 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__mono_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.24 | ~ c_lessequals(V_c,V_d,T_a) % 1.14/1.24 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__mono_H_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.24 | ~ c_lessequals(V_c,V_d,T_a) % 1.14/1.24 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_sgn__sgn_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.14/1.24 | 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_abs__sgn_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.14/1.24 | 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult_Opos__bounded_1,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.14/1.24 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_a,T_a),c_RealVector_Onorm__class_Onorm(V_b,T_a),tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(V_vskULn,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__right_Opos__bounded_1,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.14/1.24 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_K,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(V_x,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_abs__of__nat_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.14/1.24 | c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) = c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__le__0__iff_4,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__le__0__iff_5,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.24 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_split__mult__neg__le_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_split__mult__neg__le_1,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.24 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__nonneg__nonpos_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__nonpos__nonneg_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.24 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__nonneg__nonpos2_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_inverse__mult__distrib_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_nonzero__inverse__mult__distrib_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_abs__le__zero__iff_1,axiom, % 1.14/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.14/1.24 | 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_ln__unique_0,axiom, % 1.14/1.24 c_Transcendental_Oln(c_Transcendental_Oexp(V_y,tc_RealDef_Oreal)) = V_y ). % 1.14/1.24 % 1.14/1.24 cnf(cls_exp__ln__eq_0,axiom, % 1.14/1.24 c_Transcendental_Oln(c_Transcendental_Oexp(V_u,tc_RealDef_Oreal)) = V_u ). % 1.14/1.24 % 1.14/1.24 cnf(cls_ln__exp_0,axiom, % 1.14/1.24 c_Transcendental_Oln(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal)) = V_x ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__le__eq_5,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__le__eq_7,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_le__divide__eq_5,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.14/1.24 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_le__divide__eq_7,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.14/1.24 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_dist__commute_0,axiom, % 1.14/1.24 ( ~ class_RealVector_Ometric__space(T_a) % 1.14/1.24 | c_RealVector_Odist__class_Odist(V_x,V_y,T_a) = c_RealVector_Odist__class_Odist(V_y,V_x,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_scaleR__right_Opos__bounded_1,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.24 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(V_r,V_K,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1(V_vskULt,V_r,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult_OscaleR__left_0,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.14/1.24 | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(V_r,V_a,T_a),V_b,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__left_OscaleR_0,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.14/1.24 | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),V_y,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult_OscaleR__right_0,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.14/1.24 | c_HOL_Otimes__class_Otimes(V_a,c_RealVector_OscaleR__class_OscaleR(V_r,V_b,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__right_OscaleR_0,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.14/1.24 | c_HOL_Otimes__class_Otimes(V_xa,c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__scaleR__left_0,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__algebra(T_a) % 1.14/1.24 | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),V_y,T_a) = c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_mult__scaleR__right_0,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__algebra(T_a) % 1.14/1.24 | c_HOL_Otimes__class_Otimes(V_x,c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_norm__scaleR_0,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.24 | c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_nonzero__abs__inverse_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_nonzero__abs__divide_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_real__sqrt__eq__zero__cancel_0,axiom, % 1.14/1.24 ( c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.14/1.24 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_real__sqrt__le__iff_1,axiom, % 1.14/1.24 ( c_lessequals(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) % 1.14/1.24 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_real__sqrt__le__iff_0,axiom, % 1.14/1.24 ( c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.14/1.24 | ~ c_lessequals(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide_OscaleR_0,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.14/1.24 | c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),V_y,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_rabs__ratiotest__lemma_0,axiom, % 1.14/1.24 ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.14/1.24 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_c,c_HOL_Oabs__class_Oabs(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.14/1.24 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_inverse__nonnegative__iff__nonnegative_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_inverse__nonnegative__iff__nonnegative_1,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_norm__of__real_0,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__normed__algebra__1(T_a) % 1.14/1.24 | c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(V_r,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_abs__idempotent_0,axiom, % 1.14/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.14/1.24 | 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_scaleR_OscaleR__right_0,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.24 | c_RealVector_OscaleR__class_OscaleR(V_a,c_RealVector_OscaleR__class_OscaleR(V_r,V_b,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_scaleR__left__commute_0,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__vector(T_a) % 1.14/1.24 | c_RealVector_OscaleR__class_OscaleR(V_a,c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_b,c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_scaleR__right_OscaleR_0,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.24 | c_RealVector_OscaleR__class_OscaleR(V_ra,c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_RealVector_OscaleR__class_OscaleR(V_ra,V_x,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__le__0__iff_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__le__0__iff_1,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__le__0__iff_2,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__le__0__iff_3,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.24 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_norm__mult_0,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__normed__div__algebra(T_a) % 1.14/1.24 | c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_RealVector_Onorm__class_Onorm(V_y,T_a),tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_abs__ge__self_0,axiom, % 1.14/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.14/1.24 | c_lessequals(V_a,c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_eq__divide__eq_4,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_abs__exp__cancel_0,axiom, % 1.14/1.24 c_HOL_Oabs__class_Oabs(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Oexp(V_x,tc_RealDef_Oreal) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_abs__mult__self_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.14/1.24 | 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__eq__eq_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) % 1.14/1.24 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_eq__divide__eq_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b % 1.14/1.24 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_abs__mult__pos_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.14/1.24 | 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) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_zero__le__divide__iff_4,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_zero__le__divide__iff_5,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) % 1.14/1.24 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__inverse_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.24 | 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_class__fieldgb_Odivide__inverse_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.24 | ~ class_Int_Onumber__ring(T_a) % 1.14/1.24 | 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_real__sqrt__abs2_0,axiom, % 1.14/1.24 c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal)) = c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__le__eq_1,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__le__eq_4,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_le__divide__eq_1,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.24 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_le__divide__eq_4,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.24 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_pi__ge__zero_0,axiom, % 1.14/1.24 c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_order__eq__refl_0,axiom, % 1.14/1.24 ( ~ class_Orderings_Opreorder(T_a) % 1.14/1.24 | c_lessequals(V_x,V_x,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_order__eq__iff_0,axiom, % 1.14/1.24 ( ~ class_Orderings_Oorder(T_a) % 1.14/1.24 | c_lessequals(V_x,V_x,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_real__le__trans_0,axiom, % 1.14/1.24 ( c_lessequals(V_i,V_k,tc_RealDef_Oreal) % 1.14/1.24 | ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal) % 1.14/1.24 | ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_real__le__refl_0,axiom, % 1.14/1.24 c_lessequals(V_w,V_w,tc_RealDef_Oreal) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_order__trans_0,axiom, % 1.14/1.24 ( ~ class_Orderings_Opreorder(T_a) % 1.14/1.24 | c_lessequals(V_x,V_z,T_a) % 1.14/1.24 | ~ c_lessequals(V_y,V_z,T_a) % 1.14/1.24 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_xt1_I6_J_0,axiom, % 1.14/1.24 ( ~ class_Orderings_Oorder(T_a) % 1.14/1.24 | c_lessequals(V_z,V_x,T_a) % 1.14/1.24 | ~ c_lessequals(V_z,V_y,T_a) % 1.14/1.24 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_frac__eq__eq_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.24 | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) != c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) % 1.14/1.24 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.24 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.24 | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) = c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_frac__eq__eq_1,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.24 | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) != c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) % 1.14/1.24 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.24 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.24 | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_sgn__mult_0,axiom, % 1.14/1.24 ( ~ class_RealVector_Oreal__normed__div__algebra(T_a) % 1.14/1.24 | 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_sgn__times_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.14/1.24 | 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_abs__ge__zero_0,axiom, % 1.14/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.14/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_divide__eq__eq_4,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | 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) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_linorder__linear_0,axiom, % 1.14/1.24 ( ~ class_Orderings_Olinorder(T_a) % 1.14/1.24 | c_lessequals(V_y,V_x,T_a) % 1.14/1.24 | c_lessequals(V_x,V_y,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_real__le__linear_0,axiom, % 1.14/1.24 ( c_lessequals(V_w,V_z,tc_RealDef_Oreal) % 1.14/1.24 | c_lessequals(V_z,V_w,tc_RealDef_Oreal) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_positive__imp__inverse__positive_0,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.14/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.24 % 1.14/1.24 cnf(cls_inverse__positive__iff__positive_1,axiom, % 1.14/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_inverse__positive__iff__positive_0,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.25 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_of__nat__less__0__iff_0,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_divide__less__0__iff_3,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.25 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.25 | ~ 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) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_divide__less__0__iff_2,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.25 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.25 | ~ 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) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_divide__less__0__iff_1,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.25 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.25 | ~ 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) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_divide__less__0__iff_0,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.14/1.25 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.14/1.25 | ~ 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) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_mult__strict__left__mono__comm_0,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_mult__less__cancel__right__disj_5,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_mult__less__cancel__right__disj_4,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_mult__strict__right__mono_0,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_mult__strict__right__mono__neg_0,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_mult__less__cancel__left__disj_5,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_mult__less__cancel__left__disj_4,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_mult__strict__left__mono_0,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_mult__strict__left__mono__neg_0,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_mult__less__cancel__left__pos_1,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_mult__less__cancel__left__pos_0,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_mult__less__cancel__left__neg_1,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_mult__less__cancel__left__neg_0,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_scaleR__eq__0__iff_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__vector(T_a) % 1.14/1.25 | c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.25 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.25 | V_a = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_of__real__eq__0__iff_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 1.14/1.25 | c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.25 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_of__real__0_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 1.14/1.25 | c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_of__real_Ozero_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.25 | ~ class_RealVector_Oreal__algebra__1(T_a) % 1.14/1.25 | c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_scaleR_Ozero__left_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.25 | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_scaleR__eq__0__iff_1,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__vector(T_a) % 1.14/1.25 | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_real__less__all__real2_0,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(V_y,c_RealDef_Oreal__of__preal(V_x),tc_RealDef_Oreal) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_pi__gt__zero_0,axiom, % 1.14/1.25 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_not__real__square__gt__zero_0,axiom, % 1.14/1.25 ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_real__abs__def_1,axiom, % 1.14/1.25 ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r % 1.14/1.25 | c_HOL_Oord__class_Oless(V_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_mult__right_Opos__bounded_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(V_x,T_a),tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_Re_Opos__bounded_0,axiom, % 1.14/1.25 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__XRe__Xpos__bounded__1__1,tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_mult__left_Opos__bounded_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(V_y,T_a),tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_not__real__square__gt__zero_1,axiom, % 1.14/1.25 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_divide_Opos__bounded_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xdivide__Xpos__bounded__1__1(V_y,T_a),tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_real__of__preal__zero__less_0,axiom, % 1.14/1.25 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(V_m),tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_real__gt__zero__preal__Ex_1,axiom, % 1.14/1.25 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(V_xa),tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_scaleR__right_Opos__bounded_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1(V_vskULt,V_r,T_a),tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_lemma__tan__total_0,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1(V_y),tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_real__lbound__gt__zero_0,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(V_d1,V_d2),tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2,tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d1,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_realpow__pos__nth2_0,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osko__NthRoot__Xrealpow__pos__nth2__1__1(V_a,V_n),tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_a,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_lemma__interval_0,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Deriv_Osko__Deriv__Xlemma__interval__1__1(V_a,V_b,V_x),tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_x,V_b,tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_a,V_x,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_real__sqrt__gt__zero_0,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x),tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_real__sqrt__gt__0__iff_0,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_real__sqrt__gt__0__iff_1,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_ln__less__cancel__iff_1,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y),tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_ln__less__cancel__iff_0,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y),tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_poly__bound__exists_0,axiom, % 1.14/1.25 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(V_p,V_r),tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_ln__inj__iff_0,axiom, % 1.14/1.25 ( c_Transcendental_Oln(V_x) != c_Transcendental_Oln(V_y) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.14/1.25 | V_x = V_y ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_ln__less__self_0,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(c_Transcendental_Oln(V_x),V_x,tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_root__def_2,axiom, % 1.14/1.25 ( c_NthRoot_Oroot(V_n,V_x) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.14/1.25 | c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_scaleR_Opos__bounded_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__Xpos__bounded__1__1(V_vskULo,T_a),tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_lemma__interval__lt_0,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Deriv_Osko__Deriv__Xlemma__interval__lt__1__1(V_a,V_b,V_x),tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_x,V_b,tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_a,V_x,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_zero__less__dist__iff_1,axiom, % 1.14/1.25 ( ~ class_RealVector_Ometric__space(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(V_x,V_y,T_a),tc_RealDef_Oreal) % 1.14/1.25 | V_x = V_y ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_of__real_Opos__bounded_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.25 | ~ class_RealVector_Oreal__algebra__1(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xof__real__Xpos__bounded__1__1(V_vskULr,T_a),tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_dist__not__less__zero_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Ometric__space(T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_Im_Opos__bounded_0,axiom, % 1.14/1.25 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__XIm__Xpos__bounded__1__1,tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_real__sqrt__not__eq__zero_0,axiom, % 1.14/1.25 ( c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_not__exp__less__zero_0,axiom, % 1.14/1.25 ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_real__mult__order_0,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_real__lbound__gt__zero_2,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(V_d1,V_d2),V_d2,tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2,tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d1,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_real__lbound__gt__zero_1,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(V_d1,V_d2),V_d1,tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2,tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d1,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_zero__less__dist__iff_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Ometric__space(T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(V_x,V_x,T_a),tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_not__real__of__nat__less__zero_0,axiom, % 1.14/1.25 ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(V_n,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_real__sqrt__lt__0__iff_0,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_real__sqrt__lt__0__iff_1,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_pi__not__less__zero_0,axiom, % 1.14/1.25 ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_poly__cont_0,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__cont__1(V_e,V_p,V_z),tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_e,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_cnj_Opos__bounded_0,axiom, % 1.14/1.25 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__Xcnj__Xpos__bounded__1__1,tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_mult_Opos__bounded_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(V_vskULn,T_a),tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_real__mult__less__mono2_0,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_z,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_real__mult__less__iff1_1,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_real__mult__less__iff1_0,axiom, % 1.14/1.25 ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_exp__gt__zero_0,axiom, % 1.14/1.25 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_scaleR__left_Opos__bounded_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__left__Xpos__bounded__1__1(V_x,T_a),tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_norm__ge__zero_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.25 | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_norm__sgn_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.25 | 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) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_norm__le__zero__iff_1,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.25 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_norm__le__zero__iff_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.25 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.14/1.25 | ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_xt1_I9_J_0,axiom, % 1.14/1.25 ( ~ class_Orderings_Oorder(T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_not__less__iff__gr__or__eq_1,axiom, % 1.14/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_order__less__asym_0,axiom, % 1.14/1.25 ( ~ class_Orderings_Opreorder(T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_order__less__asym_H_0,axiom, % 1.14/1.25 ( ~ class_Orderings_Opreorder(T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_order__less__irrefl_0,axiom, % 1.14/1.25 ( ~ class_Orderings_Opreorder(T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_real__less__def_1,axiom, % 1.14/1.25 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_order__less__le_1,axiom, % 1.14/1.25 ( ~ class_Orderings_Oorder(T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_linorder__neq__iff_1,axiom, % 1.14/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_norm__zero_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.25 | c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_zero__less__norm__iff_1,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.25 | 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) % 1.14/1.25 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_linorder__neqE__ordered__idom_0,axiom, % 1.14/1.25 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.14/1.25 | V_x = V_y ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_not__less__iff__gr__or__eq_0,axiom, % 1.14/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.14/1.25 | V_x = V_y % 1.14/1.25 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_linorder__antisym__conv3_0,axiom, % 1.14/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.14/1.25 | V_x = V_y % 1.14/1.25 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_linorder__less__linear_0,axiom, % 1.14/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.14/1.25 | V_x = V_y % 1.14/1.25 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_linorder__neqE_0,axiom, % 1.14/1.25 ( ~ class_Orderings_Olinorder(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.14/1.25 | V_x = V_y ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_zero__less__norm__iff_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.25 | ~ 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) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_norm__eq__zero_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.25 | c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.14/1.25 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_norm__not__less__zero_0,axiom, % 1.14/1.25 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.14/1.25 | ~ 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) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_xt1_I10_J_0,axiom, % 1.14/1.25 ( ~ class_Orderings_Oorder(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_order__less__trans_0,axiom, % 1.14/1.25 ( ~ class_Orderings_Opreorder(T_a) % 1.14/1.25 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.14/1.25 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_CHAINED_0,axiom, % 1.14/1.25 v_c____ != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(cls_conjecture_0,negated_conjecture, % 1.14/1.25 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom, % 1.14/1.25 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,axiom, % 1.14/1.25 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom, % 1.14/1.25 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_nat__Ring__and__Field_Opordered__semiring,axiom, % 1.14/1.25 class_Ring__and__Field_Opordered__semiring(tc_nat) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_nat__Ring__and__Field_Oordered__semiring,axiom, % 1.14/1.25 class_Ring__and__Field_Oordered__semiring(tc_nat) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom, % 1.14/1.25 class_Ring__and__Field_Ono__zero__divisors(tc_nat) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom, % 1.14/1.25 class_Ring__and__Field_Oordered__semidom(tc_nat) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom, % 1.14/1.25 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom, % 1.14/1.25 class_OrderedGroup_Oab__semigroup__mult(tc_nat) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_nat__Ring__and__Field_Omult__mono1,axiom, % 1.14/1.25 class_Ring__and__Field_Omult__mono1(tc_nat) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom, % 1.14/1.25 class_Ring__and__Field_Omult__zero(tc_nat) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_nat__Ring__and__Field_Omult__mono,axiom, % 1.14/1.25 class_Ring__and__Field_Omult__mono(tc_nat) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom, % 1.14/1.25 class_Nat_Osemiring__char__0(tc_nat) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_nat__Orderings_Opreorder,axiom, % 1.14/1.25 class_Orderings_Opreorder(tc_nat) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_nat__Orderings_Olinorder,axiom, % 1.14/1.25 class_Orderings_Olinorder(tc_nat) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_nat__Orderings_Oorder,axiom, % 1.14/1.25 class_Orderings_Oorder(tc_nat) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict,axiom, % 1.14/1.25 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring,axiom, % 1.14/1.25 class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict,axiom, % 1.14/1.25 class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,axiom, % 1.14/1.25 class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs,axiom, % 1.14/1.25 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors,axiom, % 1.14/1.25 class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict,axiom, % 1.14/1.25 class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom, % 1.14/1.25 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring,axiom, % 1.14/1.25 class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs,axiom, % 1.14/1.25 class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom, % 1.14/1.25 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring,axiom, % 1.14/1.25 class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors,axiom, % 1.14/1.25 class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero,axiom, % 1.14/1.25 class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom,axiom, % 1.14/1.25 class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom, % 1.14/1.25 class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom, % 1.14/1.25 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult,axiom, % 1.14/1.25 class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom, % 1.14/1.25 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring,axiom, % 1.14/1.25 class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field,axiom, % 1.14/1.25 class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring,axiom, % 1.14/1.25 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring,axiom, % 1.14/1.25 class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom, % 1.14/1.25 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,axiom, % 1.14/1.25 class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1,axiom, % 1.14/1.25 class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1,axiom, % 1.14/1.25 class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero,axiom, % 1.14/1.25 class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono,axiom, % 1.14/1.25 class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__algebra,axiom, % 1.14/1.25 class_RealVector_Oreal__algebra(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__RealVector_Ometric__space,axiom, % 1.14/1.25 class_RealVector_Ometric__space(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__vector,axiom, % 1.14/1.25 class_RealVector_Oreal__vector(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if,axiom, % 1.14/1.25 class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if,axiom, % 1.14/1.25 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ofield,axiom, % 1.14/1.25 class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Nat_Osemiring__char__0,axiom, % 1.14/1.25 class_Nat_Osemiring__char__0(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom, % 1.14/1.25 class_Orderings_Opreorder(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom, % 1.14/1.25 class_Orderings_Olinorder(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Orderings_Oorder,axiom, % 1.14/1.25 class_Orderings_Oorder(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom, % 1.14/1.25 class_Int_Onumber__ring(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_RealDef__Oreal__SEQ_Obanach,axiom, % 1.14/1.25 class_SEQ_Obanach(tc_RealDef_Oreal) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,axiom, % 1.14/1.25 class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom, % 1.14/1.25 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom, % 1.14/1.25 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,axiom, % 1.14/1.25 class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom, % 1.14/1.25 class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom, % 1.14/1.25 class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom, % 1.14/1.25 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,axiom, % 1.14/1.25 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom, % 1.14/1.25 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring,axiom, % 1.14/1.25 class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom, % 1.14/1.25 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom, % 1.14/1.25 class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,axiom, % 1.14/1.25 class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__algebra,axiom, % 1.14/1.25 class_RealVector_Oreal__algebra(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__RealVector_Ometric__space,axiom, % 1.14/1.25 class_RealVector_Ometric__space(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__vector,axiom, % 1.14/1.25 class_RealVector_Oreal__vector(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom, % 1.14/1.25 class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__Nat_Osemiring__char__0,axiom, % 1.14/1.25 class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom, % 1.14/1.25 class_Int_Onumber__ring(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 cnf(clsarity_Complex__Ocomplex__SEQ_Obanach,axiom, % 1.14/1.25 class_SEQ_Obanach(tc_Complex_Ocomplex) ). % 1.14/1.25 % 1.14/1.25 %------------------------------------------------------------------------------ % 1.14/1.25 %------------------------------------------- % 1.14/1.25 % Proof found % 1.14/1.25 % SZS status Theorem for theBenchmark % 1.14/1.25 % SZS output start Proof % 1.14/1.25 %ClaNum:692(EqnAxiom:118) % 1.14/1.25 %VarNum:3978(SingletonVarNum:1195) % 1.14/1.25 %MaxLitNum:6 % 1.14/1.25 %MaxfuncDepth:3 % 1.14/1.25 %SharedTerms:101 % 1.14/1.25 %goalClause: 224 % 1.14/1.25 %singleGoalClaCount:1 % 1.14/1.25 [119]P1(a1) % 1.14/1.25 [120]P1(a2) % 1.14/1.25 [121]P2(a1) % 1.14/1.25 [122]P21(a1) % 1.14/1.25 [123]P21(a2) % 1.14/1.25 [124]P22(a1) % 1.14/1.25 [125]P22(a2) % 1.14/1.25 [126]P25(a1) % 1.14/1.25 [127]P34(a1) % 1.14/1.25 [128]P10(a1) % 1.14/1.25 [129]P10(a2) % 1.14/1.25 [130]P35(a1) % 1.14/1.25 [131]P35(a2) % 1.14/1.25 [132]P26(a1) % 1.14/1.25 [133]P26(a37) % 1.14/1.25 [134]P26(a2) % 1.14/1.25 [135]P23(a1) % 1.14/1.25 [136]P23(a37) % 1.14/1.25 [137]P23(a2) % 1.14/1.25 [138]P11(a1) % 1.14/1.25 [139]P11(a2) % 1.14/1.25 [140]P27(a1) % 1.14/1.25 [141]P27(a2) % 1.14/1.25 [142]P31(a1) % 1.14/1.25 [143]P31(a37) % 1.14/1.25 [144]P31(a2) % 1.14/1.25 [145]P18(a1) % 1.14/1.25 [146]P18(a2) % 1.14/1.25 [147]P44(a1) % 1.14/1.25 [148]P44(a2) % 1.14/1.25 [149]P36(a1) % 1.14/1.25 [150]P36(a37) % 1.14/1.25 [151]P32(a1) % 1.14/1.25 [152]P37(a1) % 1.14/1.25 [153]P37(a37) % 1.14/1.25 [154]P38(a1) % 1.14/1.25 [155]P12(a1) % 1.14/1.25 [156]P12(a37) % 1.14/1.25 [157]P14(a1) % 1.14/1.25 [158]P14(a37) % 1.14/1.25 [159]P15(a1) % 1.14/1.25 [160]P15(a2) % 1.14/1.25 [161]P39(a1) % 1.14/1.25 [162]P39(a37) % 1.14/1.25 [163]P16(a1) % 1.14/1.25 [164]P16(a2) % 1.14/1.25 [165]P28(a1) % 1.14/1.25 [166]P3(a1) % 1.14/1.25 [167]P3(a37) % 1.14/1.25 [168]P3(a2) % 1.14/1.25 [169]P40(a1) % 1.14/1.25 [170]P29(a1) % 1.14/1.25 [171]P29(a37) % 1.14/1.25 [172]P30(a1) % 1.14/1.25 [173]P30(a37) % 1.14/1.25 [174]P41(a1) % 1.14/1.25 [175]P13(a1) % 1.14/1.25 [176]P13(a37) % 1.14/1.25 [177]P24(a1) % 1.14/1.25 [178]P7(a1) % 1.14/1.25 [179]P42(a1) % 1.14/1.25 [180]P42(a37) % 1.14/1.25 [181]P8(a1) % 1.14/1.25 [182]P8(a37) % 1.14/1.25 [183]P8(a2) % 1.14/1.25 [184]P43(a1) % 1.14/1.25 [185]P43(a37) % 1.14/1.25 [186]P17(a1) % 1.14/1.25 [187]P17(a2) % 1.14/1.25 [188]P19(a1) % 1.14/1.25 [189]P19(a2) % 1.14/1.25 [190]P20(a1) % 1.14/1.25 [191]P20(a2) % 1.14/1.25 [192]P4(a1) % 1.14/1.25 [193]P4(a2) % 1.14/1.25 [194]P33(a1) % 1.14/1.25 [195]P33(a37) % 1.14/1.25 [205]P6(f3(a1),a35,a1) % 1.14/1.25 [206]P6(f3(a1),a5,a1) % 1.14/1.25 [207]P6(f3(a1),a6,a1) % 1.14/1.25 [208]P6(f3(a1),a7,a1) % 1.14/1.25 [209]P5(f3(a1),a35,a1) % 1.14/1.25 [220]~E(f3(a1),a35) % 1.14/1.25 [221]~E(f3(a2),a39) % 1.14/1.25 [223]~P6(a35,f3(a1),a1) % 1.14/1.25 [224]~P6(f3(a1),f18(a39,a2),a1) % 1.14/1.25 [196]E(f14(f3(a1)),f3(a1)) % 1.14/1.25 [228]~P6(f3(a1),f10(f3(a1),f3(a1),a1),a1) % 1.14/1.25 [204]P5(x2041,x2041,a1) % 1.14/1.25 [222]~P6(x2221,x2221,a1) % 1.14/1.25 [198]E(f18(x1981,a1),f4(x1981,a1)) % 1.14/1.25 [211]P6(f3(a1),f20(x2111),a1) % 1.14/1.25 [212]P6(f3(a1),f23(x2121,a1),a1) % 1.14/1.25 [213]P5(f3(a1),f23(x2131,a1),a1) % 1.14/1.25 [214]P5(f3(a1),f19(x2141,a37),a1) % 1.14/1.25 [225]~P6(f23(x2251,a1),f3(a1),a1) % 1.14/1.25 [226]~P6(f19(x2261,a37),f3(a1),a1) % 1.14/1.25 [227]~P5(f23(x2271,a1),f3(a1),a1) % 1.14/1.25 [197]E(f15(x1971,f3(a1)),f3(a1)) % 1.14/1.25 [201]E(f34(f23(x2011,a1)),x2011) % 1.14/1.25 [202]E(f4(f23(x2021,a1),a1),f23(x2021,a1)) % 1.14/1.25 [203]E(f4(f19(x2031,a37),a1),f19(x2031,a37)) % 1.14/1.25 [217]E(f14(f10(x2171,x2171,a1)),f4(x2171,a1)) % 1.14/1.25 [215]P6(f3(a1),f38(x2151,x2152),a1) % 1.14/1.25 [216]E(f10(x2161,x2162,a1),f10(x2162,x2161,a1)) % 1.14/1.25 [218]E(f10(f14(x2181),f14(x2182),a1),f14(f10(x2181,x2182,a1))) % 1.14/1.25 [219]E(f10(f10(x2191,x2192,a1),x2193,a1),f10(x2191,f10(x2192,x2193,a1),a1)) % 1.14/1.25 [229]~E(f14(x2291),f3(a1))+E(x2291,f3(a1)) % 1.14/1.25 [268]E(f4(x2681,a1),x2681)+P6(x2681,f3(a1),a1) % 1.14/1.25 [312]~E(f14(x3121),f3(a1))+~P6(f3(a1),x3121,a1) % 1.14/1.25 [352]P6(f34(x3521),x3521,a1)+~P6(f3(a1),x3521,a1) % 1.14/1.25 [367]~P6(x3671,f3(a1),a1)+P6(f14(x3671),f3(a1),a1) % 1.14/1.25 [368]~P5(x3681,f3(a1),a1)+P5(f14(x3681),f3(a1),a1) % 1.14/1.25 [370]~P6(f3(a1),x3701,a1)+P6(f3(a1),f14(x3701),a1) % 1.14/1.25 [371]~P6(f3(a1),x3711,a1)+P6(f3(a1),f36(x3711),a1) % 1.14/1.25 [373]~P5(f3(a1),x3731,a1)+P5(f3(a1),f14(x3731),a1) % 1.14/1.25 [374]~P6(f14(x3741),f3(a1),a1)+P6(x3741,f3(a1),a1) % 1.14/1.25 [375]~P5(f14(x3751),f3(a1),a1)+P5(x3751,f3(a1),a1) % 1.14/1.25 [376]~P6(f3(a1),f14(x3761),a1)+P6(f3(a1),x3761,a1) % 1.14/1.25 [377]~P5(f3(a1),f14(x3771),a1)+P5(f3(a1),x3771,a1) % 1.14/1.25 [382]E(x3821,f3(a1))+P6(f3(a1),f10(x3821,x3821,a1),a1) % 1.14/1.25 [231]~P15(x2311)+E(f24(f3(a1),x2311),f3(x2311)) % 1.14/1.25 [232]~P10(x2321)+E(f18(f3(x2321),x2321),f3(a1)) % 1.14/1.25 [233]~P2(x2331)+E(f4(f3(x2331),x2331),f3(x2331)) % 1.14/1.25 [234]~P22(x2341)+E(f11(f3(x2341),x2341),f3(x2341)) % 1.14/1.25 [235]~P25(x2351)+E(f13(f3(x2351),x2351),f3(x2351)) % 1.14/1.25 [236]~P34(x2361)+E(f13(f3(x2361),x2361),f3(x2361)) % 1.14/1.25 [237]~P10(x2371)+E(f13(f3(x2371),x2371),f3(x2371)) % 1.14/1.25 [289]P6(f3(a1),x2891,a1)+~E(f23(f34(x2891),a1),x2891) % 1.14/1.25 [314]~P10(x3141)+P5(f18(f3(x3141),x3141),f3(a1),a1) % 1.14/1.25 [316]~P2(x3161)+P5(f4(f3(x3161),x3161),f3(x3161),x3161) % 1.14/1.25 [318]~P6(f3(a1),x3181,a1)+E(f23(f34(x3181),a1),x3181) % 1.14/1.25 [378]~P10(x3781)+~P6(f3(a1),f18(f3(x3781),x3781),a1) % 1.14/1.25 [381]~P2(x3811)+~P6(f3(x3811),f4(f3(x3811),x3811),x3811) % 1.14/1.25 [262]~P10(x2621)+E(f18(f13(f3(x2621),x2621),x2621),f3(a1)) % 1.14/1.25 [260]~P12(x2602)+P5(x2601,x2601,x2602) % 1.14/1.25 [261]~P14(x2612)+P5(x2611,x2611,x2612) % 1.14/1.25 [301]~P6(x3012,x3012,x3011)+~P12(x3011) % 1.14/1.25 [302]~P6(x3022,x3022,x3021)+~P14(x3021) % 1.14/1.25 [303]~P6(x3032,x3032,x3031)+~P13(x3031) % 1.14/1.25 [317]P5(x3172,x3171,a1)+P5(x3171,x3172,a1) % 1.14/1.25 [344]~P6(x3441,x3442,a1)+P5(x3441,x3442,a1) % 1.14/1.25 [230]E(x2301,x2302)+~E(f14(x2301),f14(x2302)) % 1.14/1.25 [246]E(x2461,x2462)+~E(f23(x2461,a1),f23(x2462,a1)) % 1.14/1.25 [247]E(x2471,x2472)+~E(f19(x2471,a37),f19(x2472,a37)) % 1.14/1.25 [263]~P9(x2632)+E(f10(x2631,x2631,x2632),x2631) % 1.14/1.25 [264]~P16(x2642)+E(f21(x2641,x2641,x2642),f3(a1)) % 1.14/1.25 [290]~P2(x2902)+P5(x2901,f4(x2901,x2902),x2902) % 1.14/1.25 [291]~P10(x2912)+P6(f3(a1),f26(x2911,x2912),a1) % 1.14/1.25 [292]~P10(x2922)+P6(f3(a1),f32(x2921,x2922),a1) % 1.14/1.25 [293]~P11(x2932)+P6(f3(a1),f27(x2931,x2932),a1) % 1.14/1.25 [294]~P18(x2942)+P6(f3(a1),f28(x2941,x2942),a1) % 1.14/1.25 [295]~P11(x2952)+P6(f3(a1),f29(x2951,x2952),a1) % 1.14/1.25 [296]~P11(x2962)+P6(f3(a1),f30(x2961,x2962),a1) % 1.14/1.25 [297]~P10(x2972)+P5(f3(a1),f18(x2971,x2972),a1) % 1.14/1.25 [304]~P2(x3041)+P5(f3(x3041),f4(x3042,x3041),x3041) % 1.14/1.25 [306]~P39(x3061)+P5(f3(x3061),f16(x3062,x3061),x3061) % 1.14/1.25 [324]P6(x3241,f20(x3242),a1)+P6(f3(a1),x3241,a1) % 1.14/1.25 [343]~P10(x3431)+~P6(f18(x3432,x3431),f3(a1),a1) % 1.14/1.25 [349]~P2(x3491)+~P6(f4(x3492,x3491),f3(x3491),x3491) % 1.14/1.25 [350]~P39(x3501)+~P6(f16(x3502,x3501),f3(x3501),x3501) % 1.14/1.25 [351]P6(x3511,f20(x3512),a1)+~P5(x3511,f3(a1),a1) % 1.14/1.25 [357]~P6(x3571,x3572,a1)+P6(f14(x3571),f14(x3572),a1) % 1.14/1.25 [358]~P5(x3581,x3582,a1)+P5(f14(x3581),f14(x3582),a1) % 1.14/1.25 [379]P6(x3791,x3792,a1)+~P6(f14(x3791),f14(x3792),a1) % 1.14/1.25 [380]P5(x3801,x3802,a1)+~P5(f14(x3801),f14(x3802),a1) % 1.14/1.25 [387]~P16(x3872)+P5(f21(x3871,x3871,x3872),f3(a1),a1) % 1.14/1.25 [388]~P6(f3(a1),x3881,a1)+P6(f3(a1),f17(x3881,x3882),a1) % 1.14/1.25 [392]P5(x3921,x3922,a1)+~P5(f4(x3921,a1),x3922,a1) % 1.14/1.25 [393]~P38(x3931)+P5(f3(x3931),f10(x3932,x3932,x3931),x3931) % 1.14/1.25 [411]~P6(x4111,x4112,a1)+P6(f23(x4111,a1),f23(x4112,a1),a1) % 1.14/1.25 [412]~P5(x4121,x4122,a1)+P5(f23(x4121,a1),f23(x4122,a1),a1) % 1.14/1.25 [432]P6(x4321,x4322,a1)+~P6(f23(x4321,a1),f23(x4322,a1),a1) % 1.14/1.25 [433]P5(x4331,x4332,a1)+~P5(f23(x4331,a1),f23(x4332,a1),a1) % 1.14/1.25 [464]~P16(x4641)+~P6(f3(a1),f21(x4642,x4642,x4641),a1) % 1.14/1.25 [467]~P38(x4671)+~P6(f10(x4672,x4672,x4671),f3(x4671),x4671) % 1.14/1.25 [254]~P19(x2542)+E(f18(f24(x2541,x2542),x2542),f4(x2541,a1)) % 1.14/1.25 [255]~P10(x2552)+E(f4(f18(x2551,x2552),a1),f18(x2551,x2552)) % 1.14/1.25 [257]~P2(x2572)+E(f4(f4(x2571,x2572),x2572),f4(x2571,x2572)) % 1.14/1.25 [258]~P25(x2582)+E(f4(f16(x2581,x2582),x2582),f16(x2581,x2582)) % 1.14/1.25 [259]~P25(x2592)+E(f13(f13(x2591,x2592),x2592),f13(x2591,x2592)) % 1.14/1.25 [266]~P1(x2662)+E(f25(f3(a1),x2661,x2662),f3(x2662)) % 1.14/1.25 [267]~P10(x2672)+E(f25(f3(a1),x2671,x2672),f3(x2672)) % 1.14/1.25 [269]~P1(x2692)+E(f25(x2691,f3(x2692),x2692),f3(x2692)) % 1.14/1.25 [270]~P10(x2702)+E(f25(x2701,f3(x2702),x2702),f3(x2702)) % 1.14/1.25 [271]~P35(x2712)+E(f10(x2711,f3(x2712),x2712),f3(x2712)) % 1.14/1.25 [272]~P26(x2722)+E(f10(x2721,f3(x2722),x2722),f3(x2722)) % 1.14/1.25 [273]~P23(x2732)+E(f10(x2731,f3(x2732),x2732),f3(x2732)) % 1.14/1.25 [275]~P11(x2752)+E(f10(x2751,f3(x2752),x2752),f3(x2752)) % 1.14/1.25 [276]~P35(x2761)+E(f10(f3(x2761),x2762,x2761),f3(x2761)) % 1.14/1.25 [277]~P26(x2771)+E(f10(f3(x2771),x2772,x2771),f3(x2771)) % 1.14/1.25 [279]~P23(x2791)+E(f10(f3(x2791),x2792,x2791),f3(x2791)) % 1.14/1.25 [281]~P11(x2811)+E(f10(f3(x2811),x2812,x2811),f3(x2811)) % 1.14/1.25 [282]~P27(x2821)+E(f12(f3(x2821),x2822,x2821),f3(x2821)) % 1.14/1.25 [283]~P18(x2831)+E(f12(f3(x2831),x2832,x2831),f3(x2831)) % 1.14/1.25 [313]~P25(x3132)+E(f10(x3131,f13(x3131,x3132),x3132),f4(x3131,x3132)) % 1.14/1.25 [323]~P25(x3232)+E(f10(f13(x3231,x3232),f4(x3231,x3232),x3232),x3231) % 1.14/1.25 [383]~P25(x3832)+E(f10(f4(x3831,x3832),f4(x3831,x3832),x3832),f10(x3831,x3831,x3832)) % 1.14/1.25 [326]~P23(x3263)+E(f10(x3261,x3262,x3263),f10(x3262,x3261,x3263)) % 1.14/1.25 [327]~P16(x3273)+E(f21(x3271,x3272,x3273),f21(x3272,x3271,x3273)) % 1.14/1.25 [385]~P10(x3853)+P6(f3(a1),f33(x3851,x3852,x3853),a1) % 1.14/1.25 [386]~P16(x3863)+P5(f3(a1),f21(x3861,x3862,x3863),a1) % 1.14/1.25 [460]~P6(f3(a1),x4601,a1)+P6(f3(a1),f40(x4601,x4602,x4603),a1) % 1.14/1.25 [465]~P16(x4651)+~P6(f21(x4652,x4653,x4651),f3(a1),a1) % 1.14/1.25 [340]~P1(x3402)+E(f25(f3(a1),x3401,x3402),f25(f3(a1),x3403,x3402)) % 1.14/1.25 [341]~P1(x3412)+E(f25(x3411,f3(x3412),x3412),f25(x3413,f3(x3412),x3412)) % 1.14/1.25 [347]~P27(x3473)+E(f10(x3471,f11(x3472,x3473),x3473),f12(x3471,x3472,x3473)) % 1.14/1.25 [348]~P15(x3482)+E(f10(f24(x3481,x3482),x3483,x3482),f25(x3481,x3483,x3482)) % 1.14/1.25 [441]~P9(x4413)+E(f10(x4411,f10(x4411,x4412,x4413),x4413),f10(x4411,x4412,x4413)) % 1.14/1.25 [442]~P10(x4423)+E(f18(f25(x4421,x4422,x4423),x4423),f10(f4(x4421,a1),f18(x4422,x4423),a1)) % 1.14/1.25 [443]~P15(x4432)+E(f10(f24(x4431,x4432),f24(x4433,x4432),x4432),f24(f10(x4431,x4433,a1),x4432)) % 1.14/1.25 [444]~P20(x4442)+E(f10(f18(x4441,x4442),f18(x4443,x4442),a1),f18(f10(x4441,x4443,x4442),x4442)) % 1.14/1.25 [445]~P25(x4452)+E(f10(f4(x4451,x4452),f4(x4453,x4452),x4452),f4(f10(x4451,x4453,x4452),x4452)) % 1.14/1.25 [446]~P25(x4462)+E(f10(f13(x4461,x4462),f13(x4463,x4462),x4462),f13(f10(x4461,x4463,x4462),x4462)) % 1.14/1.25 [447]~P20(x4472)+E(f10(f13(x4471,x4472),f13(x4473,x4472),x4472),f13(f10(x4471,x4473,x4472),x4472)) % 1.14/1.25 [608]~P10(x6083)+P5(f18(f25(x6081,x6082,x6083),x6083),f10(f18(x6081,a1),f32(x6082,x6083),a1),a1) % 1.14/1.25 [609]~P11(x6093)+P5(f18(f10(x6091,x6092,x6093),x6093),f10(f18(x6092,x6093),f30(x6091,x6093),a1),a1) % 1.14/1.25 [610]~P11(x6103)+P5(f18(f10(x6101,x6102,x6103),x6103),f10(f18(x6101,x6103),f18(x6102,x6103),a1),a1) % 1.14/1.25 [611]~P11(x6113)+P5(f18(f10(x6111,x6112,x6113),x6113),f10(f18(x6111,x6113),f27(x6112,x6113),a1),a1) % 1.14/1.25 [612]~P18(x6123)+P5(f18(f12(x6121,x6122,x6123),x6123),f10(f18(x6121,x6123),f28(x6122,x6123),a1),a1) % 1.14/1.25 [613]~P28(x6133)+P5(f4(f10(x6131,x6132,x6133),x6133),f10(f4(x6131,x6133),f4(x6132,x6133),x6133),x6133) % 1.14/1.25 [480]~P1(x4804)+E(f25(x4801,f25(x4802,x4803,x4804),x4804),f25(f10(x4801,x4802,a1),x4803,x4804)) % 1.14/1.25 [483]~P1(x4834)+E(f25(x4831,f25(x4832,x4833,x4834),x4834),f25(x4832,f25(x4831,x4833,x4834),x4834)) % 1.14/1.25 [485]~P10(x4854)+E(f25(x4851,f25(x4852,x4853,x4854),x4854),f25(x4852,f25(x4851,x4853,x4854),x4854)) % 1.14/1.25 [487]~P11(x4874)+E(f25(x4871,f10(x4872,x4873,x4874),x4874),f10(x4872,f25(x4871,x4873,x4874),x4874)) % 1.14/1.25 [488]~P17(x4884)+E(f25(x4881,f10(x4882,x4883,x4884),x4884),f10(x4882,f25(x4881,x4883,x4884),x4884)) % 1.14/1.25 [489]~P23(x4894)+E(f10(x4891,f10(x4892,x4893,x4894),x4894),f10(x4892,f10(x4891,x4893,x4894),x4894)) % 1.14/1.25 [493]~P11(x4934)+E(f25(x4931,f10(x4932,x4933,x4934),x4934),f10(f25(x4931,x4932,x4934),x4933,x4934)) % 1.14/1.25 [494]~P17(x4944)+E(f25(x4941,f10(x4942,x4943,x4944),x4944),f10(f25(x4941,x4942,x4944),x4943,x4944)) % 1.14/1.25 [495]~P23(x4953)+E(f10(f10(x4951,x4952,x4953),x4954,x4953),f10(x4951,f10(x4952,x4954,x4953),x4953)) % 1.14/1.25 [496]~P8(x4963)+E(f10(f10(x4961,x4962,x4963),x4964,x4963),f10(x4961,f10(x4962,x4964,x4963),x4963)) % 1.14/1.25 [497]~P18(x4973)+E(f12(f25(x4971,x4972,x4973),x4974,x4973),f25(x4971,f12(x4972,x4974,x4973),x4973)) % 1.14/1.25 [498]~P23(x4983)+E(f10(f10(x4981,x4982,x4983),x4984,x4983),f10(f10(x4981,x4984,x4983),x4982,x4983)) % 1.14/1.25 [678]~P10(x6783)+P5(f18(f25(x6781,x6782,x6783),x6783),f10(f18(x6782,x6783),f33(x6784,x6781,x6783),a1),a1) % 1.14/1.25 [691]~P10(x6913)+P5(f18(f25(x6911,x6912,x6913),x6913),f10(f10(f18(x6911,a1),f18(x6912,x6913),a1),f26(x6914,x6913),a1),a1) % 1.14/1.25 [692]~P11(x6923)+P5(f18(f10(x6921,x6922,x6923),x6923),f10(f10(f18(x6921,x6923),f18(x6922,x6923),a1),f29(x6924,x6923),a1),a1) % 1.14/1.25 [628]~P23(x6283)+E(f10(f10(x6281,x6282,x6283),f10(x6284,x6285,x6283),x6283),f10(f10(x6281,x6284,x6283),f10(x6282,x6285,x6283),x6283)) % 1.14/1.25 [345]E(x3451,x3452)+P6(x3451,x3452,a1)+~P5(x3451,x3452,a1) % 1.14/1.25 [384]E(x3841,x3842)+~P5(x3842,x3841,a1)+~P5(x3841,x3842,a1) % 1.14/1.25 [240]~P10(x2402)+E(x2401,f3(x2402))+~E(f18(x2401,x2402),f3(a1)) % 1.14/1.25 [241]~P15(x2412)+~E(f24(x2411,x2412),f3(x2412))+E(x2411,f3(a1)) % 1.14/1.25 [242]~P2(x2422)+~E(f4(x2421,x2422),f3(x2422))+E(x2421,f3(x2422)) % 1.14/1.25 [243]~P21(x2432)+~E(f11(x2431,x2432),f3(x2432))+E(x2431,f3(x2432)) % 1.14/1.25 [244]~P25(x2442)+~E(f13(x2441,x2442),f3(x2442))+E(x2441,f3(x2442)) % 1.14/1.25 [245]~P10(x2452)+~E(f13(x2451,x2452),f3(x2452))+E(x2451,f3(x2452)) % 1.14/1.25 [248]~P18(x2482)+~P44(x2482)+~E(f23(x2481,x2482),f3(x2482)) % 1.14/1.25 [287]~P24(x2872)+P6(x2871,f3(x2872),x2872)+E(f4(x2871,x2872),x2871) % 1.14/1.25 [308]~P10(x3082)+E(x3081,f3(x3082))+P6(f3(a1),f18(x3081,x3082),a1) % 1.14/1.25 [309]~P10(x3092)+~P15(x3092)+P6(f3(a1),f31(x3091,x3092),a1) % 1.14/1.25 [311]~P2(x3112)+P6(f3(x3112),f4(x3111,x3112),x3112)+E(x3111,f3(x3112)) % 1.14/1.25 [333]~P2(x3332)+~P6(f3(x3332),x3331,x3332)+E(f4(x3331,x3332),x3331) % 1.14/1.25 [334]~P2(x3342)+~P5(f3(x3342),x3341,x3342)+E(f4(x3341,x3342),x3341) % 1.14/1.25 [342]E(f15(x3421,x3422),f3(a1))+P6(x3422,f3(a1),a1)+P6(f3(a1),x3422,a1) % 1.14/1.25 [346]~P10(x3462)+E(x3461,f3(x3462))+~P5(f18(x3461,x3462),f3(a1),a1) % 1.14/1.25 [355]~P2(x3552)+~P5(f4(x3551,x3552),f3(x3552),x3552)+E(x3551,f3(x3552)) % 1.14/1.25 [418]~P32(x4181)+~P6(f3(x4181),x4182,x4181)+P6(f3(x4181),f11(x4182,x4181),x4181) % 1.14/1.25 [419]~P25(x4191)+~P6(f3(x4191),x4192,x4191)+P6(f3(x4191),f13(x4192,x4191),x4191) % 1.14/1.25 [420]~P32(x4202)+~P6(x4201,f3(x4202),x4202)+P6(f11(x4201,x4202),f3(x4202),x4202) % 1.14/1.25 [421]~P25(x4212)+~P6(x4211,f3(x4212),x4212)+P6(f13(x4211,x4212),f3(x4212),x4212) % 1.14/1.25 [430]~P25(x4302)+~P6(f13(x4301,x4302),f3(x4302),x4302)+P6(x4301,f3(x4302),x4302) % 1.14/1.25 [431]~P25(x4311)+~P6(f3(x4311),f13(x4312,x4311),x4311)+P6(f3(x4311),x4312,x4311) % 1.14/1.25 [461]P6(f22(x4611,x4612),x4612,a1)+~P6(f3(a1),x4612,a1)+~P6(f3(a1),x4611,a1) % 1.14/1.25 [462]P6(f22(x4621,x4622),x4621,a1)+~P6(f3(a1),x4622,a1)+~P6(f3(a1),x4621,a1) % 1.14/1.25 [463]~P6(f3(a1),x4632,a1)+~P6(f3(a1),x4631,a1)+P6(f3(a1),f22(x4631,x4632),a1) % 1.14/1.25 [504]~P6(f3(a1),x5042,a1)+~P6(f3(a1),x5041,a1)+P6(f3(a1),f10(x5041,x5042,a1),a1) % 1.14/1.25 [250]~P21(x2502)+E(x2501,f3(x2502))+E(f11(f11(x2501,x2502),x2502),x2501) % 1.14/1.25 [253]~P21(x2532)+~P22(x2532)+E(f11(f11(x2531,x2532),x2532),x2531) % 1.14/1.25 [286]~P22(x2862)+~P27(x2862)+E(f12(x2861,f3(x2862),x2862),f3(x2862)) % 1.14/1.25 [299]~P18(x2992)+~P44(x2992)+E(f23(f24(x2991,x2992),x2992),f24(f23(x2991,a1),x2992)) % 1.14/1.25 [300]~P32(x3002)+E(x3001,f3(x3002))+E(f11(f4(x3001,x3002),x3002),f4(f11(x3001,x3002),x3002)) % 1.14/1.25 [307]~P22(x3072)+~P32(x3072)+E(f11(f4(x3071,x3072),x3072),f4(f11(x3071,x3072),x3072)) % 1.14/1.25 [423]~P22(x4231)+~P27(x4231)+E(f12(f10(f3(x4231),x4232,x4231),x4232,x4231),f3(x4231)) % 1.14/1.25 [330]P5(x3302,x3301,x3303)+~P13(x3303)+P6(x3301,x3302,x3303) % 1.14/1.25 [332]P5(x3322,x3321,x3323)+~P13(x3323)+P5(x3321,x3322,x3323) % 1.14/1.25 [353]~P12(x3533)+~P6(x3531,x3532,x3533)+P5(x3531,x3532,x3533) % 1.14/1.25 [354]~P14(x3543)+~P6(x3541,x3542,x3543)+P5(x3541,x3542,x3543) % 1.14/1.25 [396]~P6(x3963,x3962,x3961)+~P12(x3961)+~P6(x3962,x3963,x3961) % 1.14/1.25 [398]~P6(x3983,x3982,x3981)+~P14(x3981)+~P6(x3982,x3983,x3981) % 1.14/1.25 [399]~P5(x3993,x3992,x3991)+~P14(x3991)+~P6(x3992,x3993,x3991) % 1.14/1.25 [400]~P6(x4003,x4002,x4001)+~P13(x4001)+~P6(x4002,x4003,x4001) % 1.14/1.25 [402]~P5(x4023,x4022,x4021)+~P13(x4021)+~P6(x4022,x4023,x4021) % 1.14/1.25 [440]~P5(x4401,x4403,a1)+P5(x4401,x4402,a1)+~P5(x4403,x4402,a1) % 1.14/1.25 [251]~P15(x2513)+E(x2511,x2512)+~E(f24(x2511,x2513),f24(x2512,x2513)) % 1.14/1.25 [252]~P3(x2523)+E(x2521,x2522)+~E(f16(x2521,x2523),f16(x2522,x2523)) % 1.14/1.25 [310]~P16(x3103)+E(x3101,x3102)+~E(f21(x3101,x3102,x3103),f3(a1)) % 1.14/1.25 [389]E(x3891,x3892)+~E(f10(x3893,x3891,a1),f10(x3893,x3892,a1))+E(x3893,f3(a1)) % 1.14/1.25 [390]E(x3901,x3902)+~E(f10(x3901,x3903,a1),f10(x3902,x3903,a1))+E(x3903,f3(a1)) % 1.14/1.25 [391]~P16(x3913)+E(x3911,x3912)+P6(f3(a1),f21(x3911,x3912,x3913),a1) % 1.14/1.25 [415]~P25(x4153)+P6(x4151,x4152,x4153)+~P6(f4(x4151,x4153),x4152,x4153) % 1.14/1.25 [416]~P2(x4163)+P5(x4161,x4162,x4163)+~P5(f4(x4161,x4163),x4162,x4163) % 1.14/1.25 [466]E(x4661,x4662)+~P16(x4663)+~P5(f21(x4661,x4662,x4663),f3(a1),a1) % 1.14/1.25 [499]~P6(x4993,x4992,a1)+~P6(x4991,x4993,a1)+P6(f3(a1),f8(x4991,x4992,x4993),a1) % 1.14/1.25 [500]~P6(x5003,x5002,a1)+~P6(x5001,x5003,a1)+P6(f3(a1),f9(x5001,x5002,x5003),a1) % 1.14/1.25 [576]~P6(x5761,x5763,a1)+P6(f10(x5761,x5762,a1),f10(x5763,x5762,a1),a1)+~P6(f3(a1),x5762,a1) % 1.14/1.25 [577]~P6(x5772,x5773,a1)+P6(f10(x5771,x5772,a1),f10(x5771,x5773,a1),a1)+~P6(f3(a1),x5771,a1) % 1.14/1.25 [578]~P5(x5781,x5783,a1)+P5(f10(x5781,x5782,a1),f10(x5783,x5782,a1),a1)+~P6(f3(a1),x5782,a1) % 1.14/1.25 [579]~P5(x5792,x5793,a1)+P5(f10(x5791,x5792,a1),f10(x5791,x5793,a1),a1)+~P6(f3(a1),x5791,a1) % 1.14/1.25 [636]P6(x6361,x6362,a1)+~P6(f10(x6361,x6363,a1),f10(x6362,x6363,a1),a1)+~P6(f3(a1),x6363,a1) % 1.14/1.25 [637]P5(x6371,x6372,a1)+~P5(f10(x6373,x6371,a1),f10(x6373,x6372,a1),a1)+~P6(f3(a1),x6373,a1) % 1.14/1.25 [638]P5(x6381,x6382,a1)+~P5(f10(x6381,x6383,a1),f10(x6382,x6383,a1),a1)+~P6(f3(a1),x6383,a1) % 1.14/1.25 [395]~P27(x3952)+E(x3951,f3(x3952))+E(f12(f10(x3953,x3951,x3952),x3951,x3952),x3953) % 1.14/1.25 [417]~P22(x4173)+~P27(x4173)+E(f11(f12(x4171,x4172,x4173),x4173),f12(x4172,x4171,x4173)) % 1.14/1.25 [456]~P32(x4562)+E(x4561,f3(x4562))+E(f12(f4(x4563,x4562),f4(x4561,x4562),x4562),f4(f12(x4563,x4561,x4562),x4562)) % 1.14/1.25 [457]~P22(x4572)+~P32(x4572)+E(f12(f4(x4571,x4572),f4(x4573,x4572),x4572),f4(f12(x4571,x4573,x4572),x4572)) % 1.14/1.25 [458]~P22(x4582)+~P27(x4582)+E(f10(f11(x4581,x4582),f11(x4583,x4582),x4582),f11(f10(x4581,x4583,x4582),x4582)) % 1.14/1.25 [474]~P25(x4742)+~P5(f3(x4742),x4743,x4742)+E(f10(f4(x4741,x4742),x4743,x4742),f4(f10(x4741,x4743,x4742),x4742)) % 1.14/1.25 [507]~P10(x5072)+~P15(x5072)+P5(f18(f24(x5071,x5072),x5072),f10(f18(x5071,a1),f31(x5073,x5072),a1),a1) % 1.14/1.25 [580]E(x5801,f3(a1))+~P5(x5802,f3(a1),a1)+~P5(f4(x5801,a1),f10(x5802,f4(x5803,a1),a1),a1) % 1.14/1.25 [503]~P22(x5033)+~P27(x5033)+E(f12(f10(x5031,x5032,x5033),x5034,x5033),f10(f12(x5031,x5034,x5033),x5032,x5033)) % 1.14/1.25 [633]~P22(x6333)+~P27(x6333)+E(f12(f10(x6331,x6332,x6333),f10(x6334,x6335,x6333),x6333),f10(f12(x6331,x6334,x6333),f12(x6332,x6335,x6333),x6333)) % 1.14/1.25 [298]~P13(x2982)+~P7(x2982)+P6(x2981,f3(x2982),x2982)+E(f4(x2981,x2982),x2981) % 1.14/1.25 [424]E(x4241,x4242)+~E(f34(x4241),f34(x4242))+~P6(f3(a1),x4242,a1)+~P6(f3(a1),x4241,a1) % 1.14/1.25 [426]~P22(x4261)+~P32(x4261)+~P5(f3(x4261),x4262,x4261)+P5(f3(x4261),f11(x4262,x4261),x4261) % 1.14/1.25 [428]~P22(x4282)+~P32(x4282)+~P5(x4281,f3(x4282),x4282)+P5(f11(x4281,x4282),f3(x4282),x4282) % 1.14/1.25 [434]~P32(x4342)+~P6(f11(x4341,x4342),f3(x4342),x4342)+P6(x4341,f3(x4342),x4342)+E(x4341,f3(x4342)) % 1.14/1.25 [435]~P32(x4352)+~P6(f3(x4352),f11(x4351,x4352),x4352)+P6(f3(x4352),x4351,x4352)+E(x4351,f3(x4352)) % 1.14/1.25 [436]~P22(x4362)+~P32(x4362)+~P6(f11(x4361,x4362),f3(x4362),x4362)+P6(x4361,f3(x4362),x4362) % 1.14/1.25 [437]~P22(x4372)+~P32(x4372)+~P5(f11(x4371,x4372),f3(x4372),x4372)+P5(x4371,f3(x4372),x4372) % 1.14/1.25 [438]~P22(x4381)+~P32(x4381)+~P6(f3(x4381),f11(x4382,x4381),x4381)+P6(f3(x4381),x4382,x4381) % 1.14/1.25 [439]~P22(x4391)+~P32(x4391)+~P5(f3(x4391),f11(x4392,x4391),x4391)+P5(f3(x4391),x4392,x4391) % 1.14/1.25 [481]~P6(x4811,x4812,a1)+P6(f34(x4811),f34(x4812),a1)+~P6(f3(a1),x4812,a1)+~P6(f3(a1),x4811,a1) % 1.14/1.25 [482]~P5(x4821,x4822,a1)+P5(f34(x4821),f34(x4822),a1)+~P6(f3(a1),x4822,a1)+~P6(f3(a1),x4821,a1) % 1.14/1.25 [501]P6(x5011,x5012,a1)+~P6(f34(x5011),f34(x5012),a1)+~P6(f3(a1),x5012,a1)+~P6(f3(a1),x5011,a1) % 1.14/1.25 [502]P5(x5021,x5022,a1)+~P5(f34(x5021),f34(x5022),a1)+~P6(f3(a1),x5022,a1)+~P6(f3(a1),x5021,a1) % 1.14/1.25 [335]P6(x3351,x3352,x3353)+~P25(x3353)+E(x3351,x3352)+P6(x3352,x3351,x3353) % 1.14/1.25 [339]P6(x3391,x3392,x3393)+~P13(x3393)+E(x3391,x3392)+P6(x3392,x3391,x3393) % 1.14/1.25 [364]~P12(x3643)+~P5(x3641,x3642,x3643)+E(x3641,x3642)+P6(x3641,x3642,x3643) % 1.14/1.25 [366]~P13(x3663)+~P5(x3661,x3662,x3663)+E(x3661,x3662)+P6(x3661,x3662,x3663) % 1.14/1.25 [406]~P5(x4062,x4061,x4063)+~P5(x4061,x4062,x4063)+E(x4061,x4062)+~P12(x4063) % 1.14/1.25 [429]P5(x4292,x4291,x4293)+~P14(x4293)+~P5(x4291,x4292,x4293)+P6(x4291,x4292,x4293) % 1.14/1.25 [256]~P21(x2563)+~P22(x2563)+E(x2561,x2562)+~E(f11(x2561,x2563),f11(x2562,x2563)) % 1.14/1.25 [319]~P1(x3192)+~E(f25(x3193,x3191,x3192),f3(x3192))+E(x3191,f3(x3192))+E(x3193,f3(a1)) % 1.14/1.25 [320]~P35(x3202)+~E(f10(x3203,x3201,x3202),f3(x3202))+E(x3201,f3(x3202))+E(x3203,f3(x3202)) % 1.14/1.25 [322]~P31(x3222)+~E(f10(x3223,x3221,x3222),f3(x3222))+E(x3221,f3(x3222))+E(x3223,f3(x3222)) % 1.14/1.25 [468]~P32(x4682)+~P6(x4683,x4681,x4682)+~P6(x4681,f3(x4682),x4682)+P6(f11(x4681,x4682),f11(x4683,x4682),x4682) % 1.14/1.25 [469]~P32(x4692)+~P5(x4693,x4691,x4692)+~P6(x4691,f3(x4692),x4692)+P5(f11(x4691,x4692),f11(x4693,x4692),x4692) % 1.14/1.25 [470]~P32(x4702)+~P6(x4703,x4701,x4702)+~P6(f3(x4702),x4703,x4702)+P6(f11(x4701,x4702),f11(x4703,x4702),x4702) % 1.14/1.25 [471]~P32(x4712)+~P5(x4713,x4711,x4712)+~P6(f3(x4712),x4713,x4712)+P5(f11(x4711,x4712),f11(x4713,x4712),x4712) % 1.14/1.25 [476]~P32(x4763)+P6(x4761,x4762,x4763)+~P6(x4761,f3(x4763),x4763)+~P6(f11(x4762,x4763),f11(x4761,x4763),x4763) % 1.14/1.25 [477]~P32(x4773)+P5(x4771,x4772,x4773)+~P6(x4771,f3(x4773),x4773)+~P5(f11(x4772,x4773),f11(x4771,x4773),x4773) % 1.14/1.25 [478]~P32(x4783)+P6(x4781,x4782,x4783)+~P6(f3(x4783),x4782,x4783)+~P6(f11(x4782,x4783),f11(x4781,x4783),x4783) % 1.14/1.25 [479]~P32(x4793)+P5(x4791,x4792,x4793)+~P6(f3(x4793),x4792,x4793)+~P5(f11(x4792,x4793),f11(x4791,x4793),x4793) % 1.14/1.25 [508]~P38(x5081)+~P6(x5083,f3(x5081),x5081)+~P6(x5082,f3(x5081),x5081)+P6(f3(x5081),f10(x5082,x5083,x5081),x5081) % 1.14/1.25 [509]~P32(x5091)+~P6(x5093,f3(x5091),x5091)+~P6(x5092,f3(x5091),x5091)+P6(f3(x5091),f12(x5092,x5093,x5091),x5091) % 1.14/1.25 [510]~P38(x5101)+~P5(x5103,f3(x5101),x5101)+~P5(x5102,f3(x5101),x5101)+P5(f3(x5101),f10(x5102,x5103,x5101),x5101) % 1.14/1.25 [512]~P41(x5121)+~P5(x5123,f3(x5121),x5121)+~P5(x5122,f3(x5121),x5121)+P5(f3(x5121),f10(x5122,x5123,x5121),x5121) % 1.14/1.25 [513]~P32(x5131)+~P6(x5133,f3(x5131),x5131)+~P5(x5132,f3(x5131),x5131)+P5(f3(x5131),f12(x5132,x5133,x5131),x5131) % 1.14/1.25 [514]~P36(x5141)+~P6(f3(x5141),x5143,x5141)+~P6(f3(x5141),x5142,x5141)+P6(f3(x5141),f10(x5142,x5143,x5141),x5141) % 1.14/1.25 [515]~P32(x5151)+~P6(f3(x5151),x5153,x5151)+~P6(f3(x5151),x5152,x5151)+P6(f3(x5151),f12(x5152,x5153,x5151),x5151) % 1.14/1.25 [516]~P38(x5161)+~P5(f3(x5161),x5163,x5161)+~P5(f3(x5161),x5162,x5161)+P5(f3(x5161),f10(x5162,x5163,x5161),x5161) % 1.14/1.25 [517]~P41(x5171)+~P5(f3(x5171),x5173,x5171)+~P5(f3(x5171),x5172,x5171)+P5(f3(x5171),f10(x5172,x5173,x5171),x5171) % 1.14/1.25 [518]~P42(x5181)+~P5(f3(x5181),x5183,x5181)+~P5(f3(x5181),x5182,x5181)+P5(f3(x5181),f10(x5182,x5183,x5181),x5181) % 1.14/1.25 [519]~P32(x5191)+~P6(f3(x5191),x5193,x5191)+~P5(f3(x5191),x5192,x5191)+P5(f3(x5191),f12(x5192,x5193,x5191),x5191) % 1.14/1.25 [520]~P36(x5203)+~P6(x5202,f3(x5203),x5203)+~P6(f3(x5203),x5201,x5203)+P6(f10(x5201,x5202,x5203),f3(x5203),x5203) % 1.14/1.25 [522]~P36(x5223)+~P6(x5221,f3(x5223),x5223)+~P6(f3(x5223),x5222,x5223)+P6(f10(x5221,x5222,x5223),f3(x5223),x5223) % 1.14/1.25 [523]~P32(x5233)+~P6(x5232,f3(x5233),x5233)+~P6(f3(x5233),x5231,x5233)+P6(f12(x5231,x5232,x5233),f3(x5233),x5233) % 1.14/1.25 [524]~P32(x5243)+~P6(x5241,f3(x5243),x5243)+~P6(f3(x5243),x5242,x5243)+P6(f12(x5241,x5242,x5243),f3(x5243),x5243) % 1.14/1.25 [525]~P38(x5253)+~P5(x5252,f3(x5253),x5253)+~P5(f3(x5253),x5251,x5253)+P5(f10(x5251,x5252,x5253),f3(x5253),x5253) % 1.14/1.25 [526]~P38(x5263)+~P5(x5261,f3(x5263),x5263)+~P5(f3(x5263),x5262,x5263)+P5(f10(x5261,x5262,x5263),f3(x5263),x5263) % 1.14/1.25 [528]~P42(x5283)+~P5(x5282,f3(x5283),x5283)+~P5(f3(x5283),x5281,x5283)+P5(f10(x5281,x5282,x5283),f3(x5283),x5283) % 1.14/1.25 [531]~P42(x5313)+~P5(x5311,f3(x5313),x5313)+~P5(f3(x5313),x5312,x5313)+P5(f10(x5311,x5312,x5313),f3(x5313),x5313) % 1.14/1.25 [532]~P32(x5323)+~P6(x5322,f3(x5323),x5323)+~P5(f3(x5323),x5321,x5323)+P5(f12(x5321,x5322,x5323),f3(x5323),x5323) % 1.14/1.25 [533]~P32(x5333)+~P5(x5331,f3(x5333),x5333)+~P6(f3(x5333),x5332,x5333)+P5(f12(x5331,x5332,x5333),f3(x5333),x5333) % 1.14/1.25 [542]~P38(x5422)+~P5(f10(x5423,x5421,x5422),f3(x5422),x5422)+P5(x5421,f3(x5422),x5422)+P5(x5423,f3(x5422),x5422) % 1.14/1.25 [543]~P38(x5432)+~P5(f3(x5432),f10(x5433,x5431,x5432),x5432)+P5(x5431,f3(x5432),x5432)+P5(f3(x5432),x5433,x5432) % 1.14/1.25 [544]~P38(x5442)+~P5(f3(x5442),f10(x5441,x5443,x5442),x5442)+P5(x5441,f3(x5442),x5442)+P5(f3(x5442),x5443,x5442) % 1.14/1.25 [545]~P38(x5452)+~P5(f3(x5452),f10(x5453,x5451,x5452),x5452)+P5(x5451,f3(x5452),x5452)+P5(f3(x5452),x5451,x5452) % 1.14/1.25 [546]~P38(x5462)+~P5(f3(x5462),f10(x5461,x5463,x5462),x5462)+P5(x5461,f3(x5462),x5462)+P5(f3(x5462),x5461,x5462) % 1.14/1.25 [547]~P38(x5472)+~P5(f10(x5473,x5471,x5472),f3(x5472),x5472)+P5(x5471,f3(x5472),x5472)+P5(f3(x5472),x5471,x5472) % 1.14/1.25 [548]~P38(x5482)+~P5(f10(x5481,x5483,x5482),f3(x5482),x5482)+P5(x5481,f3(x5482),x5482)+P5(f3(x5482),x5481,x5482) % 1.14/1.25 [549]~P38(x5491)+~P5(f10(x5492,x5493,x5491),f3(x5491),x5491)+P5(f3(x5491),x5492,x5491)+P5(f3(x5491),x5493,x5491) % 1.14/1.25 [574]~P36(x5741)+~P6(f3(x5741),f10(x5743,x5742,x5741),x5741)+P6(f3(x5741),x5742,x5741)+~P6(f3(x5741),x5743,x5741) % 1.14/1.25 [575]~P36(x5751)+~P6(f3(x5751),f10(x5752,x5753,x5751),x5751)+P6(f3(x5751),x5752,x5751)+~P6(f3(x5751),x5753,x5751) % 1.14/1.25 [409]~P22(x4092)+~P27(x4092)+E(x4091,f3(x4092))+E(f10(f12(x4093,x4091,x4092),x4091,x4092),x4093) % 1.14/1.25 [459]~P21(x4592)+E(x4591,f3(x4592))+E(x4593,f3(x4592))+E(f10(f11(x4591,x4592),f11(x4593,x4592),x4592),f11(f10(x4593,x4591,x4592),x4592)) % 1.14/1.25 [475]~P22(x4752)+~P32(x4752)+~P6(f3(x4752),x4753,x4752)+E(f12(f4(x4751,x4752),x4753,x4752),f4(f12(x4751,x4753,x4752),x4752)) % 1.14/1.25 [570]~P40(x5702)+~P5(x5703,f3(x5702),x5702)+~P5(x5701,f3(x5702),x5702)+E(f10(f4(x5701,x5702),f4(x5703,x5702),x5702),f4(f10(x5701,x5703,x5702),x5702)) % 1.14/1.25 [571]~P40(x5712)+~P5(x5713,f3(x5712),x5712)+~P5(f3(x5712),x5711,x5712)+E(f10(f4(x5711,x5712),f4(x5713,x5712),x5712),f4(f10(x5711,x5713,x5712),x5712)) % 1.14/1.25 [572]~P40(x5722)+~P5(x5721,f3(x5722),x5722)+~P5(f3(x5722),x5723,x5722)+E(f10(f4(x5721,x5722),f4(x5723,x5722),x5722),f4(f10(x5721,x5723,x5722),x5722)) % 1.14/1.25 [573]~P40(x5732)+~P5(f3(x5732),x5733,x5732)+~P5(f3(x5732),x5731,x5732)+E(f10(f4(x5731,x5732),f4(x5733,x5732),x5732),f4(f10(x5731,x5733,x5732),x5732)) % 1.14/1.25 [448]~P12(x4483)+~P6(x4481,x4484,x4483)+P6(x4481,x4482,x4483)+~P6(x4484,x4482,x4483) % 1.14/1.25 [449]~P12(x4493)+~P5(x4491,x4494,x4493)+P6(x4491,x4492,x4493)+~P6(x4494,x4492,x4493) % 1.14/1.25 [450]~P12(x4503)+~P5(x4504,x4502,x4503)+P6(x4501,x4502,x4503)+~P6(x4501,x4504,x4503) % 1.14/1.25 [451]~P14(x4513)+~P6(x4511,x4514,x4513)+P6(x4511,x4512,x4513)+~P6(x4514,x4512,x4513) % 1.14/1.25 [452]~P14(x4523)+~P5(x4521,x4524,x4523)+P6(x4521,x4522,x4523)+~P6(x4524,x4522,x4523) % 1.14/1.25 [453]~P14(x4533)+~P5(x4534,x4532,x4533)+P6(x4531,x4532,x4533)+~P6(x4531,x4534,x4533) % 1.14/1.25 [454]~P12(x4543)+~P5(x4541,x4544,x4543)+P5(x4541,x4542,x4543)+~P5(x4544,x4542,x4543) % 1.14/1.25 [455]~P14(x4553)+~P5(x4551,x4554,x4553)+P5(x4551,x4552,x4553)+~P5(x4554,x4552,x4553) % 1.14/1.25 [413]~P1(x4134)+E(x4131,x4132)+~E(f25(x4133,x4131,x4134),f25(x4133,x4132,x4134))+E(x4133,f3(a1)) % 1.14/1.25 [414]~P1(x4144)+E(x4141,x4142)+~E(f25(x4141,x4143,x4144),f25(x4142,x4143,x4144))+E(x4143,f3(x4144)) % 1.14/1.25 [586]~P38(x5863)+~P6(x5864,x5861,x5863)+~P6(x5862,f3(x5863),x5863)+P6(f10(x5861,x5862,x5863),f10(x5864,x5862,x5863),x5863) % 1.14/1.25 [589]~P38(x5893)+~P6(x5894,x5892,x5893)+~P6(x5891,f3(x5893),x5893)+P6(f10(x5891,x5892,x5893),f10(x5891,x5894,x5893),x5893) % 1.14/1.25 [590]~P32(x5903)+~P6(x5904,x5901,x5903)+~P6(x5902,f3(x5903),x5903)+P6(f12(x5901,x5902,x5903),f12(x5904,x5902,x5903),x5903) % 1.14/1.25 [591]~P41(x5913)+~P5(x5914,x5911,x5913)+~P5(x5912,f3(x5913),x5913)+P5(f10(x5911,x5912,x5913),f10(x5914,x5912,x5913),x5913) % 1.14/1.25 [592]~P38(x5923)+~P5(x5924,x5922,x5923)+~P6(x5921,f3(x5923),x5923)+P5(f10(x5921,x5922,x5923),f10(x5921,x5924,x5923),x5923) % 1.14/1.25 [593]~P41(x5933)+~P5(x5934,x5932,x5933)+~P5(x5931,f3(x5933),x5933)+P5(f10(x5931,x5932,x5933),f10(x5931,x5934,x5933),x5933) % 1.14/1.25 [594]~P36(x5943)+~P6(x5941,x5944,x5943)+~P6(f3(x5943),x5942,x5943)+P6(f10(x5941,x5942,x5943),f10(x5944,x5942,x5943),x5943) % 1.14/1.25 [595]~P38(x5953)+~P6(x5951,x5954,x5953)+~P6(f3(x5953),x5952,x5953)+P6(f10(x5951,x5952,x5953),f10(x5954,x5952,x5953),x5953) % 1.14/1.25 [596]~P36(x5963)+~P6(x5962,x5964,x5963)+~P6(f3(x5963),x5961,x5963)+P6(f10(x5961,x5962,x5963),f10(x5961,x5964,x5963),x5963) % 1.14/1.25 [598]~P38(x5983)+~P6(x5982,x5984,x5983)+~P6(f3(x5983),x5981,x5983)+P6(f10(x5981,x5982,x5983),f10(x5981,x5984,x5983),x5983) % 1.14/1.25 [599]~P33(x5993)+~P6(x5992,x5994,x5993)+~P6(f3(x5993),x5991,x5993)+P6(f10(x5991,x5992,x5993),f10(x5991,x5994,x5993),x5993) % 1.14/1.25 [600]~P32(x6003)+~P6(x6001,x6004,x6003)+~P6(f3(x6003),x6002,x6003)+P6(f12(x6001,x6002,x6003),f12(x6004,x6002,x6003),x6003) % 1.14/1.25 [601]~P30(x6013)+~P5(x6011,x6014,x6013)+~P5(f3(x6013),x6012,x6013)+P5(f10(x6011,x6012,x6013),f10(x6014,x6012,x6013),x6013) % 1.14/1.25 [602]~P38(x6023)+~P5(x6022,x6024,x6023)+~P6(f3(x6023),x6021,x6023)+P5(f10(x6021,x6022,x6023),f10(x6021,x6024,x6023),x6023) % 1.14/1.25 [603]~P29(x6033)+~P5(x6032,x6034,x6033)+~P5(f3(x6033),x6031,x6033)+P5(f10(x6031,x6032,x6033),f10(x6031,x6034,x6033),x6033) % 1.14/1.25 [604]~P30(x6043)+~P5(x6042,x6044,x6043)+~P5(f3(x6043),x6041,x6043)+P5(f10(x6041,x6042,x6043),f10(x6041,x6044,x6043),x6043) % 1.14/1.25 [614]~P32(x6144)+~P6(f3(x6144),x6143,x6144)+~P6(f10(x6141,x6143,x6144),x6142,x6144)+P6(x6141,f12(x6142,x6143,x6144),x6144) % 1.14/1.25 [615]~P32(x6154)+~P6(f3(x6154),x6153,x6154)+~P5(f10(x6151,x6153,x6154),x6152,x6154)+P5(x6151,f12(x6152,x6153,x6154),x6154) % 1.14/1.25 [616]~P32(x6163)+~P6(f3(x6163),x6162,x6163)+~P6(x6161,f10(x6164,x6162,x6163),x6163)+P6(f12(x6161,x6162,x6163),x6164,x6163) % 1.14/1.25 [617]~P32(x6173)+~P6(f3(x6173),x6172,x6173)+~P5(x6171,f10(x6174,x6172,x6173),x6173)+P5(f12(x6171,x6172,x6173),x6174,x6173) % 1.14/1.25 [626]P6(x6262,x6261,x6263)+~P38(x6263)+P6(x6261,x6262,x6263)+~P6(f10(x6264,x6261,x6263),f10(x6264,x6262,x6263),x6263) % 1.14/1.25 [627]P6(x6272,x6271,x6273)+~P38(x6273)+P6(x6271,x6272,x6273)+~P6(f10(x6271,x6274,x6273),f10(x6272,x6274,x6273),x6273) % 1.14/1.25 [629]~P38(x6293)+P6(x6291,x6292,x6293)+~P6(f10(x6291,x6294,x6293),f10(x6292,x6294,x6293),x6293)+P6(x6294,f3(x6293),x6293) % 1.14/1.25 [630]~P38(x6303)+P6(x6301,x6302,x6303)+~P6(f10(x6304,x6301,x6303),f10(x6304,x6302,x6303),x6303)+P6(x6304,f3(x6303),x6303) % 1.14/1.25 [631]~P38(x6313)+P6(x6311,x6312,x6313)+~P6(f10(x6314,x6312,x6313),f10(x6314,x6311,x6313),x6313)+P6(f3(x6313),x6314,x6313) % 1.14/1.25 [632]~P38(x6323)+P6(x6321,x6322,x6323)+~P6(f10(x6322,x6324,x6323),f10(x6321,x6324,x6323),x6323)+P6(f3(x6323),x6324,x6323) % 1.14/1.25 [634]~P38(x6342)+~P6(f10(x6343,x6341,x6342),f10(x6344,x6341,x6342),x6342)+P6(x6341,f3(x6342),x6342)+P6(f3(x6342),x6341,x6342) % 1.14/1.25 [635]~P38(x6352)+~P6(f10(x6351,x6353,x6352),f10(x6351,x6354,x6352),x6352)+P6(x6351,f3(x6352),x6352)+P6(f3(x6352),x6351,x6352) % 1.14/1.25 [639]~P38(x6393)+P6(x6391,x6392,x6393)+~P6(f10(x6394,x6392,x6393),f10(x6394,x6391,x6393),x6393)+~P6(x6394,f3(x6393),x6393) % 1.14/1.25 [640]~P38(x6403)+P5(x6401,x6402,x6403)+~P5(f10(x6404,x6402,x6403),f10(x6404,x6401,x6403),x6403)+~P6(x6404,f3(x6403),x6403) % 1.14/1.25 [641]~P36(x6413)+P6(x6411,x6412,x6413)+~P6(f10(x6414,x6411,x6413),f10(x6414,x6412,x6413),x6413)+~P5(f3(x6413),x6414,x6413) % 1.14/1.25 [642]~P36(x6423)+P6(x6421,x6422,x6423)+~P6(f10(x6421,x6424,x6423),f10(x6422,x6424,x6423),x6423)+~P5(f3(x6423),x6424,x6423) % 1.14/1.25 [643]~P37(x6433)+P6(x6431,x6432,x6433)+~P6(f10(x6434,x6431,x6433),f10(x6434,x6432,x6433),x6433)+~P5(f3(x6433),x6434,x6433) % 1.14/1.25 [644]~P37(x6443)+P6(x6441,x6442,x6443)+~P6(f10(x6441,x6444,x6443),f10(x6442,x6444,x6443),x6443)+~P5(f3(x6443),x6444,x6443) % 1.14/1.25 [645]~P38(x6453)+P6(x6451,x6452,x6453)+~P6(f10(x6454,x6451,x6453),f10(x6454,x6452,x6453),x6453)+~P6(f3(x6453),x6454,x6453) % 1.14/1.25 [646]~P36(x6463)+P5(x6461,x6462,x6463)+~P5(f10(x6464,x6461,x6463),f10(x6464,x6462,x6463),x6463)+~P6(f3(x6463),x6464,x6463) % 1.14/1.25 [647]~P36(x6473)+P5(x6471,x6472,x6473)+~P5(f10(x6471,x6474,x6473),f10(x6472,x6474,x6473),x6473)+~P6(f3(x6473),x6474,x6473) % 1.14/1.25 [648]~P38(x6483)+P5(x6481,x6482,x6483)+~P5(f10(x6484,x6481,x6483),f10(x6484,x6482,x6483),x6483)+~P6(f3(x6483),x6484,x6483) % 1.14/1.25 [505]~P22(x5052)+~P27(x5052)+E(x5051,f3(x5052))+E(f12(f10(x5053,x5051,x5052),f10(x5054,x5051,x5052),x5052),f12(x5053,x5054,x5052)) % 1.14/1.25 [506]~P22(x5062)+~P27(x5062)+E(x5061,f3(x5062))+E(f12(f10(x5061,x5063,x5062),f10(x5061,x5064,x5062),x5062),f12(x5063,x5064,x5062)) % 1.14/1.25 [607]~P10(x6072)+E(x6071,f3(x6072))+~P5(x6073,f3(a1),a1)+~P5(f18(x6071,x6072),f10(x6073,f18(x6074,x6072),a1),a1) % 1.14/1.25 [665]~P25(x6652)+~P6(f4(x6651,x6652),x6654,x6652)+~P6(f4(x6653,x6652),x6655,x6652)+P6(f10(f4(x6651,x6652),f4(x6653,x6652),x6652),f10(x6654,x6655,x6652),x6652) % 1.14/1.25 [677]~P11(x6773)+~P6(f18(x6772,x6773),x6775,a1)+~P6(f18(x6771,x6773),x6774,a1)+P6(f18(f10(x6771,x6772,x6773),x6773),f10(x6774,x6775,a1),a1) % 1.14/1.25 [265]~P21(x2653)+E(x2651,x2652)+~E(f11(x2651,x2653),f11(x2652,x2653))+E(x2652,f3(x2653))+E(x2651,f3(x2653)) % 1.14/1.25 [535]~P22(x5351)+~P32(x5351)+~P5(x5353,f3(x5351),x5351)+~P5(x5352,f3(x5351),x5351)+P5(f3(x5351),f12(x5352,x5353,x5351),x5351) % 1.14/1.25 [537]~P22(x5371)+~P32(x5371)+~P5(f3(x5371),x5373,x5371)+~P5(f3(x5371),x5372,x5371)+P5(f3(x5371),f12(x5372,x5373,x5371),x5371) % 1.14/1.25 [540]~P22(x5403)+~P32(x5403)+~P5(x5402,f3(x5403),x5403)+~P5(f3(x5403),x5401,x5403)+P5(f12(x5401,x5402,x5403),f3(x5403),x5403) % 1.14/1.25 [541]~P22(x5413)+~P32(x5413)+~P5(x5411,f3(x5413),x5413)+~P5(f3(x5413),x5412,x5413)+P5(f12(x5411,x5412,x5413),f3(x5413),x5413) % 1.14/1.25 [554]~P22(x5542)+~P32(x5542)+~P6(f12(x5543,x5541,x5542),f3(x5542),x5542)+P6(x5541,f3(x5542),x5542)+P6(x5543,f3(x5542),x5542) % 1.14/1.25 [555]~P22(x5552)+~P32(x5552)+~P5(f12(x5553,x5551,x5552),f3(x5552),x5552)+P5(x5551,f3(x5552),x5552)+P5(x5553,f3(x5552),x5552) % 1.14/1.25 [556]~P22(x5562)+~P32(x5562)+~P6(f3(x5562),f12(x5563,x5561,x5562),x5562)+P6(x5561,f3(x5562),x5562)+P6(f3(x5562),x5563,x5562) % 1.14/1.25 [557]~P22(x5572)+~P32(x5572)+~P6(f3(x5572),f12(x5571,x5573,x5572),x5572)+P6(x5571,f3(x5572),x5572)+P6(f3(x5572),x5573,x5572) % 1.14/1.25 [558]~P22(x5582)+~P32(x5582)+~P6(f3(x5582),f12(x5583,x5581,x5582),x5582)+P6(x5581,f3(x5582),x5582)+P6(f3(x5582),x5581,x5582) % 1.14/1.25 [559]~P22(x5592)+~P32(x5592)+~P6(f3(x5592),f12(x5591,x5593,x5592),x5592)+P6(x5591,f3(x5592),x5592)+P6(f3(x5592),x5591,x5592) % 1.14/1.25 [560]~P22(x5602)+~P32(x5602)+~P5(f3(x5602),f12(x5603,x5601,x5602),x5602)+P5(x5601,f3(x5602),x5602)+P5(f3(x5602),x5603,x5602) % 1.14/1.25 [561]~P22(x5612)+~P32(x5612)+~P5(f3(x5612),f12(x5611,x5613,x5612),x5612)+P5(x5611,f3(x5612),x5612)+P5(f3(x5612),x5613,x5612) % 1.14/1.25 [562]~P22(x5622)+~P32(x5622)+~P5(f3(x5622),f12(x5623,x5621,x5622),x5622)+P5(x5621,f3(x5622),x5622)+P5(f3(x5622),x5621,x5622) % 1.14/1.25 [563]~P22(x5632)+~P32(x5632)+~P5(f3(x5632),f12(x5631,x5633,x5632),x5632)+P5(x5631,f3(x5632),x5632)+P5(f3(x5632),x5631,x5632) % 1.14/1.25 [564]~P22(x5642)+~P32(x5642)+~P6(f12(x5643,x5641,x5642),f3(x5642),x5642)+P6(x5641,f3(x5642),x5642)+P6(f3(x5642),x5641,x5642) % 1.14/1.25 [565]~P22(x5652)+~P32(x5652)+~P6(f12(x5651,x5653,x5652),f3(x5652),x5652)+P6(x5651,f3(x5652),x5652)+P6(f3(x5652),x5651,x5652) % 1.14/1.25 [566]~P22(x5662)+~P32(x5662)+~P5(f12(x5663,x5661,x5662),f3(x5662),x5662)+P5(x5661,f3(x5662),x5662)+P5(f3(x5662),x5661,x5662) % 1.14/1.25 [567]~P22(x5672)+~P32(x5672)+~P5(f12(x5671,x5673,x5672),f3(x5672),x5672)+P5(x5671,f3(x5672),x5672)+P5(f3(x5672),x5671,x5672) % 1.14/1.25 [568]~P22(x5681)+~P32(x5681)+~P6(f12(x5682,x5683,x5681),f3(x5681),x5681)+P6(f3(x5681),x5682,x5681)+P6(f3(x5681),x5683,x5681) % 1.14/1.25 [569]~P22(x5691)+~P32(x5691)+~P5(f12(x5692,x5693,x5691),f3(x5691),x5691)+P5(f3(x5691),x5692,x5691)+P5(f3(x5691),x5693,x5691) % 1.14/1.25 [605]~P22(x6053)+~P32(x6053)+~P5(x6054,x6051,x6053)+~P5(x6052,f3(x6053),x6053)+P5(f12(x6051,x6052,x6053),f12(x6054,x6052,x6053),x6053) % 1.14/1.25 [606]~P22(x6063)+~P32(x6063)+~P5(x6061,x6064,x6063)+~P5(f3(x6063),x6062,x6063)+P5(f12(x6061,x6062,x6063),f12(x6064,x6062,x6063),x6063) % 1.14/1.25 [618]~P22(x6184)+~P32(x6184)+~P6(f3(x6184),x6183,x6184)+~P6(f12(x6181,x6183,x6184),x6182,x6184)+P6(x6181,f10(x6182,x6183,x6184),x6184) % 1.14/1.25 [620]~P22(x6204)+~P32(x6204)+~P6(f3(x6204),x6203,x6204)+~P5(f12(x6201,x6203,x6204),x6202,x6204)+P5(x6201,f10(x6202,x6203,x6204),x6204) % 1.14/1.25 [622]~P22(x6223)+~P32(x6223)+~P6(f3(x6223),x6222,x6223)+~P6(x6221,f12(x6224,x6222,x6223),x6223)+P6(f10(x6221,x6222,x6223),x6224,x6223) % 1.14/1.25 [624]~P22(x6243)+~P32(x6243)+~P6(f3(x6243),x6242,x6243)+~P5(x6241,f12(x6244,x6242,x6243),x6243)+P5(f10(x6241,x6242,x6243),x6244,x6243) % 1.14/1.25 [679]~P32(x6793)+~P6(x6792,x6794,x6793)+~P6(x6791,f3(x6793),x6793)+~P6(f3(x6793),f10(x6792,x6794,x6793),x6793)+P6(f12(x6791,x6792,x6793),f12(x6791,x6794,x6793),x6793) % 1.14/1.25 [680]~P32(x6803)+~P6(x6804,x6802,x6803)+~P6(f3(x6803),x6801,x6803)+~P6(f3(x6803),f10(x6802,x6804,x6803),x6803)+P6(f12(x6801,x6802,x6803),f12(x6801,x6804,x6803),x6803) % 1.14/1.25 [681]~P32(x6813)+~P5(x6814,x6812,x6813)+~P5(f3(x6813),x6811,x6813)+~P6(f3(x6813),f10(x6812,x6814,x6813),x6813)+P5(f12(x6811,x6812,x6813),f12(x6811,x6814,x6813),x6813) % 1.14/1.25 [472]~P27(x4722)+~E(f12(x4724,x4723,x4722),f12(x4725,x4721,x4722))+E(f10(x4724,x4721,x4722),f10(x4725,x4723,x4722))+E(x4721,f3(x4722))+E(x4723,f3(x4722)) % 1.14/1.25 [473]~P27(x4732)+~E(f10(x4734,x4733,x4732),f10(x4735,x4731,x4732))+E(f12(x4734,x4731,x4732),f12(x4735,x4733,x4732))+E(x4731,f3(x4732))+E(x4733,f3(x4732)) % 1.14/1.25 [550]~P22(x5502)+~P32(x5502)+P6(x5501,f3(x5502),x5502)+P6(f3(x5502),x5501,x5502)+~P6(x5503,f3(x5502),x5502)+P6(x5503,f12(x5504,x5501,x5502),x5502) % 1.14/1.25 [551]~P22(x5512)+~P32(x5512)+P6(x5511,f3(x5512),x5512)+P6(f3(x5512),x5511,x5512)+~P5(x5513,f3(x5512),x5512)+P5(x5513,f12(x5514,x5511,x5512),x5512) % 1.14/1.25 [552]~P22(x5522)+~P32(x5522)+P6(x5521,f3(x5522),x5522)+P6(f3(x5522),x5521,x5522)+~P6(f3(x5522),x5524,x5522)+P6(f12(x5523,x5521,x5522),x5524,x5522) % 1.14/1.25 [553]~P22(x5532)+~P32(x5532)+P6(x5531,f3(x5532),x5532)+P6(f3(x5532),x5531,x5532)+~P5(f3(x5532),x5534,x5532)+P5(f12(x5533,x5531,x5532),x5534,x5532) % 1.14/1.25 [581]~P22(x5812)+~P32(x5812)+P6(x5811,f3(x5812),x5812)+P6(f3(x5812),x5811,x5812)+~P6(x5813,f12(x5814,x5811,x5812),x5812)+P6(x5813,f3(x5812),x5812) % 1.14/1.25 [582]~P22(x5822)+~P32(x5822)+P6(x5821,f3(x5822),x5822)+P6(f3(x5822),x5821,x5822)+~P5(x5823,f12(x5824,x5821,x5822),x5822)+P5(x5823,f3(x5822),x5822) % 1.14/1.25 [583]~P22(x5832)+~P32(x5832)+P6(x5831,f3(x5832),x5832)+P6(f3(x5832),x5831,x5832)+~P6(f12(x5834,x5831,x5832),x5833,x5832)+P6(f3(x5832),x5833,x5832) % 1.14/1.25 [584]~P22(x5842)+~P32(x5842)+P6(x5841,f3(x5842),x5842)+P6(f3(x5842),x5841,x5842)+~P5(f12(x5844,x5841,x5842),x5843,x5842)+P5(f3(x5842),x5843,x5842) % 1.14/1.25 [649]~P22(x6492)+~P32(x6492)+~P6(f10(x6493,x6491,x6492),x6494,x6492)+P6(x6491,f3(x6492),x6492)+~P6(x6493,f3(x6492),x6492)+P6(x6493,f12(x6494,x6491,x6492),x6492) % 1.14/1.25 [650]~P22(x6502)+~P32(x6502)+~P5(f10(x6503,x6501,x6502),x6504,x6502)+P6(x6501,f3(x6502),x6502)+~P5(x6503,f3(x6502),x6502)+P5(x6503,f12(x6504,x6501,x6502),x6502) % 1.14/1.25 [651]~P22(x6512)+~P32(x6512)+~P6(x6513,f10(x6514,x6511,x6512),x6512)+P6(x6511,f3(x6512),x6512)+~P6(f3(x6512),x6514,x6512)+P6(f12(x6513,x6511,x6512),x6514,x6512) % 1.14/1.25 [652]~P22(x6522)+~P32(x6522)+~P5(x6523,f10(x6524,x6521,x6522),x6522)+P6(x6521,f3(x6522),x6522)+~P5(f3(x6522),x6524,x6522)+P5(f12(x6523,x6521,x6522),x6524,x6522) % 1.14/1.25 [653]~P22(x6531)+~P32(x6531)+~P6(x6534,f12(x6533,x6532,x6531),x6531)+~P6(x6532,f3(x6531),x6531)+P6(f3(x6531),x6532,x6531)+P6(x6533,f10(x6534,x6532,x6531),x6531) % 1.14/1.25 [654]~P22(x6541)+~P32(x6541)+~P6(x6544,f10(x6543,x6542,x6541),x6541)+~P6(x6542,f3(x6541),x6541)+P6(f3(x6541),x6542,x6541)+P6(x6543,f12(x6544,x6542,x6541),x6541) % 1.14/1.25 [655]~P22(x6551)+~P32(x6551)+~P6(x6554,f10(x6553,x6552,x6551),x6551)+~P6(x6553,f3(x6551),x6551)+P6(f3(x6551),x6552,x6551)+P6(x6553,f12(x6554,x6552,x6551),x6551) % 1.14/1.25 [656]~P22(x6561)+~P32(x6561)+~P5(x6564,f12(x6563,x6562,x6561),x6561)+~P6(x6562,f3(x6561),x6561)+P6(f3(x6561),x6562,x6561)+P5(x6563,f10(x6564,x6562,x6561),x6561) % 1.14/1.25 [657]~P22(x6571)+~P32(x6571)+~P5(x6574,f10(x6573,x6572,x6571),x6571)+~P6(x6572,f3(x6571),x6571)+P6(f3(x6571),x6572,x6571)+P5(x6573,f12(x6574,x6572,x6571),x6571) % 1.14/1.25 [658]~P22(x6581)+~P32(x6581)+~P5(x6584,f10(x6583,x6582,x6581),x6581)+~P5(x6583,f3(x6581),x6581)+P6(f3(x6581),x6582,x6581)+P5(x6583,f12(x6584,x6582,x6581),x6581) % 1.14/1.25 [659]~P22(x6591)+~P32(x6591)+~P6(f12(x6594,x6592,x6591),x6593,x6591)+~P6(x6592,f3(x6591),x6591)+P6(f3(x6591),x6592,x6591)+P6(f10(x6593,x6592,x6591),x6594,x6591) % 1.14/1.25 [660]~P22(x6601)+~P32(x6601)+~P6(f10(x6604,x6602,x6601),x6603,x6601)+~P6(x6602,f3(x6601),x6601)+P6(f3(x6601),x6602,x6601)+P6(f12(x6603,x6602,x6601),x6604,x6601) % 1.14/1.25 [661]~P22(x6611)+~P32(x6611)+~P5(f12(x6614,x6612,x6611),x6613,x6611)+~P6(x6612,f3(x6611),x6611)+P6(f3(x6611),x6612,x6611)+P5(f10(x6613,x6612,x6611),x6614,x6611) % 1.14/1.25 [662]~P22(x6621)+~P32(x6621)+~P5(f10(x6624,x6622,x6621),x6623,x6621)+~P6(x6622,f3(x6621),x6621)+P6(f3(x6621),x6622,x6621)+P5(f12(x6623,x6622,x6621),x6624,x6621) % 1.14/1.25 [663]~P22(x6631)+~P32(x6631)+~P6(f10(x6634,x6632,x6631),x6633,x6631)+~P6(f3(x6631),x6634,x6631)+P6(f3(x6631),x6632,x6631)+P6(f12(x6633,x6632,x6631),x6634,x6631) % 1.14/1.25 [664]~P22(x6641)+~P32(x6641)+~P5(f10(x6644,x6642,x6641),x6643,x6641)+~P5(f3(x6641),x6644,x6641)+P6(f3(x6641),x6642,x6641)+P5(f12(x6643,x6642,x6641),x6644,x6641) % 1.14/1.25 [682]~P22(x6823)+~P32(x6823)+~P5(x6822,x6824,x6823)+~P5(x6821,f3(x6823),x6823)+~P6(f3(x6823),f10(x6822,x6824,x6823),x6823)+P5(f12(x6821,x6822,x6823),f12(x6821,x6824,x6823),x6823) % 1.14/1.25 [683]~P22(x6834)+~P32(x6834)+~P6(x6833,f3(x6834),x6834)+~P6(x6832,f10(x6831,x6833,x6834),x6834)+~P6(f10(x6831,x6833,x6834),x6832,x6834)+P6(x6831,f12(x6832,x6833,x6834),x6834) % 1.32/1.25 [684]~P22(x6844)+~P32(x6844)+~P6(x6841,f3(x6844),x6844)+~P6(x6842,f10(x6841,x6843,x6844),x6844)+~P6(f10(x6841,x6843,x6844),x6842,x6844)+P6(x6841,f12(x6842,x6843,x6844),x6844) % 1.32/1.25 [685]~P22(x6854)+~P32(x6854)+~P6(x6853,f3(x6854),x6854)+~P5(x6852,f10(x6851,x6853,x6854),x6854)+~P5(f10(x6851,x6853,x6854),x6852,x6854)+P5(x6851,f12(x6852,x6853,x6854),x6854) % 1.32/1.25 [686]~P22(x6864)+~P32(x6864)+~P5(x6861,f3(x6864),x6864)+~P5(x6862,f10(x6861,x6863,x6864),x6864)+~P5(f10(x6861,x6863,x6864),x6862,x6864)+P5(x6861,f12(x6862,x6863,x6864),x6864) % 1.32/1.25 [687]~P22(x6873)+~P32(x6873)+~P6(x6872,f3(x6873),x6873)+~P6(x6871,f10(x6874,x6872,x6873),x6873)+~P6(f10(x6874,x6872,x6873),x6871,x6873)+P6(f12(x6871,x6872,x6873),x6874,x6873) % 1.32/1.25 [688]~P22(x6883)+~P32(x6883)+~P6(x6882,f3(x6883),x6883)+~P5(x6881,f10(x6884,x6882,x6883),x6883)+~P5(f10(x6884,x6882,x6883),x6881,x6883)+P5(f12(x6881,x6882,x6883),x6884,x6883) % 1.32/1.25 [689]~P22(x6893)+~P32(x6893)+~P6(f3(x6893),x6894,x6893)+~P6(x6891,f10(x6894,x6892,x6893),x6893)+~P6(f10(x6894,x6892,x6893),x6891,x6893)+P6(f12(x6891,x6892,x6893),x6894,x6893) % 1.32/1.25 [690]~P22(x6903)+~P32(x6903)+~P5(f3(x6903),x6904,x6903)+~P5(x6901,f10(x6904,x6902,x6903),x6903)+~P5(f10(x6904,x6902,x6903),x6901,x6903)+P5(f12(x6901,x6902,x6903),x6904,x6903) % 1.32/1.25 [666]~P36(x6663)+~P6(x6662,x6665,x6663)+~P6(x6661,x6664,x6663)+~P6(f3(x6663),x6664,x6663)+~P5(f3(x6663),x6662,x6663)+P6(f10(x6661,x6662,x6663),f10(x6664,x6665,x6663),x6663) % 1.32/1.25 [667]~P36(x6673)+~P6(x6672,x6675,x6673)+~P6(x6671,x6674,x6673)+~P5(f3(x6673),x6672,x6673)+~P5(f3(x6673),x6671,x6673)+P6(f10(x6671,x6672,x6673),f10(x6674,x6675,x6673),x6673) % 1.32/1.25 [668]~P36(x6683)+~P6(x6682,x6685,x6683)+~P5(x6681,x6684,x6683)+~P6(f3(x6683),x6681,x6683)+~P5(f3(x6683),x6682,x6683)+P6(f10(x6681,x6682,x6683),f10(x6684,x6685,x6683),x6683) % 1.32/1.25 [669]~P36(x6693)+~P6(x6691,x6694,x6693)+~P5(x6692,x6695,x6693)+~P6(f3(x6693),x6692,x6693)+~P5(f3(x6693),x6691,x6693)+P6(f10(x6691,x6692,x6693),f10(x6694,x6695,x6693),x6693) % 1.32/1.25 [670]~P32(x6703)+~P6(x6705,x6702,x6703)+~P5(x6701,x6704,x6703)+~P6(f3(x6703),x6705,x6703)+~P6(f3(x6703),x6701,x6703)+P6(f12(x6701,x6702,x6703),f12(x6704,x6705,x6703),x6703) % 1.32/1.25 [671]~P32(x6713)+~P6(x6711,x6714,x6713)+~P5(x6715,x6712,x6713)+~P6(f3(x6713),x6715,x6713)+~P5(f3(x6713),x6711,x6713)+P6(f12(x6711,x6712,x6713),f12(x6714,x6715,x6713),x6713) % 1.32/1.25 [672]~P43(x6723)+~P5(x6722,x6725,x6723)+~P5(x6721,x6724,x6723)+~P5(f3(x6723),x6724,x6723)+~P5(f3(x6723),x6722,x6723)+P5(f10(x6721,x6722,x6723),f10(x6724,x6725,x6723),x6723) % 1.32/1.25 [673]~P43(x6733)+~P5(x6732,x6735,x6733)+~P5(x6731,x6734,x6733)+~P5(f3(x6733),x6732,x6733)+~P5(f3(x6733),x6731,x6733)+P5(f10(x6731,x6732,x6733),f10(x6734,x6735,x6733),x6733) % 1.32/1.25 [674]~P32(x6743)+~P5(x6745,x6742,x6743)+~P5(x6741,x6744,x6743)+~P6(f3(x6743),x6745,x6743)+~P5(f3(x6743),x6741,x6743)+P5(f12(x6741,x6742,x6743),f12(x6744,x6745,x6743),x6743) % 1.32/1.25 %EqnAxiom % 1.32/1.25 [1]E(x11,x11) % 1.32/1.25 [2]E(x22,x21)+~E(x21,x22) % 1.32/1.25 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.32/1.25 [4]~E(x41,x42)+E(f3(x41),f3(x42)) % 1.32/1.25 [5]~E(x51,x52)+E(f14(x51),f14(x52)) % 1.32/1.25 [6]~E(x61,x62)+E(f10(x61,x63,x64),f10(x62,x63,x64)) % 1.32/1.25 [7]~E(x71,x72)+E(f10(x73,x71,x74),f10(x73,x72,x74)) % 1.32/1.25 [8]~E(x81,x82)+E(f10(x83,x84,x81),f10(x83,x84,x82)) % 1.32/1.25 [9]~E(x91,x92)+E(f29(x91,x93),f29(x92,x93)) % 1.32/1.25 [10]~E(x101,x102)+E(f29(x103,x101),f29(x103,x102)) % 1.32/1.25 [11]~E(x111,x112)+E(f15(x111,x113),f15(x112,x113)) % 1.32/1.25 [12]~E(x121,x122)+E(f15(x123,x121),f15(x123,x122)) % 1.32/1.25 [13]~E(x131,x132)+E(f12(x131,x133,x134),f12(x132,x133,x134)) % 1.32/1.25 [14]~E(x141,x142)+E(f12(x143,x141,x144),f12(x143,x142,x144)) % 1.32/1.25 [15]~E(x151,x152)+E(f12(x153,x154,x151),f12(x153,x154,x152)) % 1.32/1.25 [16]~E(x161,x162)+E(f18(x161,x163),f18(x162,x163)) % 1.32/1.25 [17]~E(x171,x172)+E(f18(x173,x171),f18(x173,x172)) % 1.32/1.25 [18]~E(x181,x182)+E(f4(x181,x183),f4(x182,x183)) % 1.32/1.25 [19]~E(x191,x192)+E(f4(x193,x191),f4(x193,x192)) % 1.32/1.25 [20]~E(x201,x202)+E(f23(x201,x203),f23(x202,x203)) % 1.32/1.25 [21]~E(x211,x212)+E(f23(x213,x211),f23(x213,x212)) % 1.32/1.25 [22]~E(x221,x222)+E(f34(x221),f34(x222)) % 1.32/1.25 [23]~E(x231,x232)+E(f32(x231,x233),f32(x232,x233)) % 1.32/1.25 [24]~E(x241,x242)+E(f32(x243,x241),f32(x243,x242)) % 1.32/1.25 [25]~E(x251,x252)+E(f25(x251,x253,x254),f25(x252,x253,x254)) % 1.32/1.25 [26]~E(x261,x262)+E(f25(x263,x261,x264),f25(x263,x262,x264)) % 1.32/1.25 [27]~E(x271,x272)+E(f25(x273,x274,x271),f25(x273,x274,x272)) % 1.32/1.25 [28]~E(x281,x282)+E(f11(x281,x283),f11(x282,x283)) % 1.32/1.25 [29]~E(x291,x292)+E(f11(x293,x291),f11(x293,x292)) % 1.32/1.25 [30]~E(x301,x302)+E(f16(x301,x303),f16(x302,x303)) % 1.32/1.25 [31]~E(x311,x312)+E(f16(x313,x311),f16(x313,x312)) % 1.32/1.25 [32]~E(x321,x322)+E(f24(x321,x323),f24(x322,x323)) % 1.32/1.25 [33]~E(x331,x332)+E(f24(x333,x331),f24(x333,x332)) % 1.32/1.25 [34]~E(x341,x342)+E(f28(x341,x343),f28(x342,x343)) % 1.32/1.25 [35]~E(x351,x352)+E(f28(x353,x351),f28(x353,x352)) % 1.32/1.25 [36]~E(x361,x362)+E(f13(x361,x363),f13(x362,x363)) % 1.32/1.25 [37]~E(x371,x372)+E(f13(x373,x371),f13(x373,x372)) % 1.32/1.25 [38]~E(x381,x382)+E(f19(x381,x383),f19(x382,x383)) % 1.32/1.25 [39]~E(x391,x392)+E(f19(x393,x391),f19(x393,x392)) % 1.32/1.25 [40]~E(x401,x402)+E(f20(x401),f20(x402)) % 1.32/1.25 [41]~E(x411,x412)+E(f33(x411,x413,x414),f33(x412,x413,x414)) % 1.32/1.25 [42]~E(x421,x422)+E(f33(x423,x421,x424),f33(x423,x422,x424)) % 1.32/1.25 [43]~E(x431,x432)+E(f33(x433,x434,x431),f33(x433,x434,x432)) % 1.32/1.25 [44]~E(x441,x442)+E(f26(x441,x443),f26(x442,x443)) % 1.32/1.25 [45]~E(x451,x452)+E(f26(x453,x451),f26(x453,x452)) % 1.32/1.25 [46]~E(x461,x462)+E(f31(x461,x463),f31(x462,x463)) % 1.32/1.25 [47]~E(x471,x472)+E(f31(x473,x471),f31(x473,x472)) % 1.32/1.25 [48]~E(x481,x482)+E(f21(x481,x483,x484),f21(x482,x483,x484)) % 1.32/1.25 [49]~E(x491,x492)+E(f21(x493,x491,x494),f21(x493,x492,x494)) % 1.32/1.25 [50]~E(x501,x502)+E(f21(x503,x504,x501),f21(x503,x504,x502)) % 1.32/1.25 [51]~E(x511,x512)+E(f22(x511,x513),f22(x512,x513)) % 1.32/1.25 [52]~E(x521,x522)+E(f22(x523,x521),f22(x523,x522)) % 1.32/1.25 [53]~E(x531,x532)+E(f27(x531,x533),f27(x532,x533)) % 1.32/1.25 [54]~E(x541,x542)+E(f27(x543,x541),f27(x543,x542)) % 1.32/1.25 [55]~E(x551,x552)+E(f9(x551,x553,x554),f9(x552,x553,x554)) % 1.32/1.25 [56]~E(x561,x562)+E(f9(x563,x561,x564),f9(x563,x562,x564)) % 1.32/1.25 [57]~E(x571,x572)+E(f9(x573,x574,x571),f9(x573,x574,x572)) % 1.32/1.25 [58]~E(x581,x582)+E(f17(x581,x583),f17(x582,x583)) % 1.32/1.25 [59]~E(x591,x592)+E(f17(x593,x591),f17(x593,x592)) % 1.32/1.25 [60]~E(x601,x602)+E(f8(x601,x603,x604),f8(x602,x603,x604)) % 1.32/1.25 [61]~E(x611,x612)+E(f8(x613,x611,x614),f8(x613,x612,x614)) % 1.32/1.25 [62]~E(x621,x622)+E(f8(x623,x624,x621),f8(x623,x624,x622)) % 1.32/1.25 [63]~E(x631,x632)+E(f30(x631,x633),f30(x632,x633)) % 1.32/1.25 [64]~E(x641,x642)+E(f30(x643,x641),f30(x643,x642)) % 1.32/1.25 [65]~E(x651,x652)+E(f40(x651,x653,x654),f40(x652,x653,x654)) % 1.32/1.25 [66]~E(x661,x662)+E(f40(x663,x661,x664),f40(x663,x662,x664)) % 1.32/1.25 [67]~E(x671,x672)+E(f40(x673,x674,x671),f40(x673,x674,x672)) % 1.32/1.25 [68]~E(x681,x682)+E(f36(x681),f36(x682)) % 1.32/1.25 [69]~E(x691,x692)+E(f38(x691,x693),f38(x692,x693)) % 1.32/1.25 [70]~E(x701,x702)+E(f38(x703,x701),f38(x703,x702)) % 1.32/1.25 [71]~P1(x711)+P1(x712)+~E(x711,x712) % 1.32/1.25 [72]~P11(x721)+P11(x722)+~E(x721,x722) % 1.32/1.25 [73]~P2(x731)+P2(x732)+~E(x731,x732) % 1.32/1.25 [74]~P21(x741)+P21(x742)+~E(x741,x742) % 1.32/1.25 [75]P6(x752,x753,x754)+~E(x751,x752)+~P6(x751,x753,x754) % 1.32/1.25 [76]P6(x763,x762,x764)+~E(x761,x762)+~P6(x763,x761,x764) % 1.32/1.25 [77]P6(x773,x774,x772)+~E(x771,x772)+~P6(x773,x774,x771) % 1.32/1.25 [78]~P22(x781)+P22(x782)+~E(x781,x782) % 1.32/1.25 [79]P5(x792,x793,x794)+~E(x791,x792)+~P5(x791,x793,x794) % 1.32/1.25 [80]P5(x803,x802,x804)+~E(x801,x802)+~P5(x803,x801,x804) % 1.32/1.25 [81]P5(x813,x814,x812)+~E(x811,x812)+~P5(x813,x814,x811) % 1.32/1.25 [82]~P25(x821)+P25(x822)+~E(x821,x822) % 1.32/1.25 [83]~P34(x831)+P34(x832)+~E(x831,x832) % 1.32/1.25 [84]~P10(x841)+P10(x842)+~E(x841,x842) % 1.32/1.25 [85]~P32(x851)+P32(x852)+~E(x851,x852) % 1.32/1.25 [86]~P35(x861)+P35(x862)+~E(x861,x862) % 1.32/1.25 [87]~P39(x871)+P39(x872)+~E(x871,x872) % 1.32/1.25 [88]~P26(x881)+P26(x882)+~E(x881,x882) % 1.32/1.25 [89]~P14(x891)+P14(x892)+~E(x891,x892) % 1.32/1.25 [90]~P30(x901)+P30(x902)+~E(x901,x902) % 1.32/1.25 [91]~P23(x911)+P23(x912)+~E(x911,x912) % 1.32/1.25 [92]~P27(x921)+P27(x922)+~E(x921,x922) % 1.32/1.25 [93]~P38(x931)+P38(x932)+~E(x931,x932) % 1.32/1.25 [94]~P36(x941)+P36(x942)+~E(x941,x942) % 1.32/1.25 [95]~P13(x951)+P13(x952)+~E(x951,x952) % 1.32/1.25 [96]~P12(x961)+P12(x962)+~E(x961,x962) % 1.32/1.25 [97]~P31(x971)+P31(x972)+~E(x971,x972) % 1.32/1.25 [98]~P19(x981)+P19(x982)+~E(x981,x982) % 1.32/1.25 [99]~P42(x991)+P42(x992)+~E(x991,x992) % 1.32/1.25 [100]~P20(x1001)+P20(x1002)+~E(x1001,x1002) % 1.32/1.25 [101]~P18(x1011)+P18(x1012)+~E(x1011,x1012) % 1.32/1.25 [102]~P16(x1021)+P16(x1022)+~E(x1021,x1022) % 1.32/1.25 [103]~P44(x1031)+P44(x1032)+~E(x1031,x1032) % 1.32/1.25 [104]~P15(x1041)+P15(x1042)+~E(x1041,x1042) % 1.32/1.25 [105]~P8(x1051)+P8(x1052)+~E(x1051,x1052) % 1.32/1.25 [106]~P28(x1061)+P28(x1062)+~E(x1061,x1062) % 1.32/1.25 [107]~P41(x1071)+P41(x1072)+~E(x1071,x1072) % 1.32/1.25 [108]~P37(x1081)+P37(x1082)+~E(x1081,x1082) % 1.32/1.25 [109]~P17(x1091)+P17(x1092)+~E(x1091,x1092) % 1.32/1.25 [110]~P4(x1101)+P4(x1102)+~E(x1101,x1102) % 1.32/1.25 [111]~P40(x1111)+P40(x1112)+~E(x1111,x1112) % 1.32/1.25 [112]~P43(x1121)+P43(x1122)+~E(x1121,x1122) % 1.32/1.25 [113]~P33(x1131)+P33(x1132)+~E(x1131,x1132) % 1.32/1.25 [114]~P7(x1141)+P7(x1142)+~E(x1141,x1142) % 1.32/1.25 [115]~P29(x1151)+P29(x1152)+~E(x1151,x1152) % 1.32/1.25 [116]~P9(x1161)+P9(x1162)+~E(x1161,x1162) % 1.32/1.25 [117]~P3(x1171)+P3(x1172)+~E(x1171,x1172) % 1.32/1.25 [118]~P24(x1181)+P24(x1182)+~E(x1181,x1182) % 1.32/1.25 % 1.32/1.25 %------------------------------------------- % 1.32/1.25 cnf(707,plain, % 1.32/1.25 (~P6(f3(a1),f14(f18(a39,a2)),a1)), % 1.32/1.25 inference(scs_inference,[],[224,376])). % 1.32/1.25 cnf(718,plain, % 1.32/1.25 (~P6(x7181,x7181,a1)), % 1.32/1.25 inference(rename_variables,[],[222])). % 1.32/1.25 cnf(720,plain, % 1.32/1.25 (P6(f3(a1),f17(f20(x7201),x7202),a1)), % 1.32/1.25 inference(scs_inference,[],[224,222,211,156,376,324,301,312,352,374,388])). % 1.32/1.25 cnf(726,plain, % 1.32/1.25 (~P6(x7261,x7261,a1)), % 1.32/1.25 inference(rename_variables,[],[222])). % 1.32/1.25 cnf(731,plain, % 1.32/1.25 (P5(x7311,x7311,a1)), % 1.32/1.25 inference(rename_variables,[],[204])). % 1.32/1.25 cnf(733,plain, % 1.32/1.25 (E(a39,f3(a2))), % 1.32/1.25 inference(scs_inference,[],[224,222,718,204,198,211,227,129,156,376,324,301,312,352,374,388,460,2,268,375,392,308])). % 1.32/1.25 cnf(742,plain, % 1.32/1.25 (~P6(x7421,x7421,a1)), % 1.32/1.25 inference(rename_variables,[],[222])). % 1.32/1.25 cnf(760,plain, % 1.32/1.25 (~P5(f20(x7601),f3(a1),a1)), % 1.32/1.25 inference(scs_inference,[],[224,222,718,726,204,198,211,227,121,122,126,129,155,156,157,159,175,376,324,301,312,352,374,388,460,2,268,375,392,308,330,431,636,75,76,241,242,243,244,311,353,355,396,399])). % 1.32/1.25 cnf(763,plain, % 1.32/1.25 (~P6(x7631,x7631,a1)), % 1.32/1.25 inference(rename_variables,[],[222])). % 1.32/1.25 cnf(772,plain, % 1.32/1.25 (P5(x7721,x7721,a1)), % 1.32/1.25 inference(rename_variables,[],[204])). % 1.32/1.25 cnf(774,plain, % 1.32/1.25 (P5(x7741,x7741,a1)), % 1.32/1.25 inference(rename_variables,[],[204])). % 1.32/1.25 cnf(775,plain, % 1.32/1.25 (P5(x7751,f4(f4(x7751,a1),a1),a1)), % 1.32/1.25 inference(scs_inference,[],[224,222,718,726,742,204,731,772,198,211,215,227,121,122,126,129,155,156,157,159,175,201,376,324,301,312,352,374,388,460,2,268,375,392,308,330,431,636,75,76,241,242,243,244,311,353,355,396,399,430,461,462,3,79,80,416])). % 1.32/1.25 cnf(779,plain, % 1.32/1.25 (~P6(f38(x7791,x7792),f3(a1),a1)), % 1.32/1.25 inference(scs_inference,[],[224,222,718,726,742,763,204,731,772,198,211,215,227,121,122,124,126,129,151,155,156,157,159,175,201,376,324,301,312,352,374,388,460,2,268,375,392,308,330,431,636,75,76,241,242,243,244,311,353,355,396,399,430,461,462,3,79,80,416,438,448])). % 1.32/1.25 cnf(780,plain, % 1.32/1.25 (~P6(x7801,x7801,a1)), % 1.32/1.25 inference(rename_variables,[],[222])). % 1.32/1.25 cnf(783,plain, % 1.32/1.25 (~P6(x7831,x7831,a1)), % 1.32/1.25 inference(rename_variables,[],[222])). % 1.32/1.25 cnf(798,plain, % 1.32/1.25 (~P6(x7981,x7981,a1)), % 1.32/1.25 inference(rename_variables,[],[222])). % 1.32/1.25 cnf(801,plain, % 1.32/1.25 (~P6(x8011,x8011,a1)), % 1.32/1.25 inference(rename_variables,[],[222])). % 1.32/1.25 cnf(817,plain, % 1.32/1.25 (~E(f10(f23(x8171,a1),f23(x8171,a1),a1),f3(a1))), % 1.32/1.26 inference(scs_inference,[],[224,222,718,726,742,763,780,783,798,225,204,731,772,198,211,215,213,214,227,119,121,122,124,126,129,130,142,149,151,152,154,155,156,157,159,175,201,206,376,324,301,312,352,374,388,460,2,268,375,392,308,330,431,636,75,76,241,242,243,244,311,353,355,396,399,430,461,462,3,79,80,416,438,448,451,574,575,629,630,631,632,634,635,641,642,643,644,645,319,320,322])). % 1.32/1.26 cnf(828,plain, % 1.32/1.26 (~P6(x8281,x8281,a1)), % 1.32/1.26 inference(rename_variables,[],[222])). % 1.32/1.26 cnf(831,plain, % 1.32/1.26 (~P6(x8311,x8311,a1)), % 1.32/1.26 inference(rename_variables,[],[222])). % 1.32/1.26 cnf(834,plain, % 1.32/1.26 (~P6(x8341,x8341,a1)), % 1.32/1.26 inference(rename_variables,[],[222])). % 1.32/1.26 cnf(839,plain, % 1.32/1.26 (~P5(f23(x8391,a1),f3(a1),a1)), % 1.32/1.26 inference(rename_variables,[],[227])). % 1.32/1.26 cnf(844,plain, % 1.32/1.26 (~P6(x8441,x8441,a1)), % 1.32/1.26 inference(rename_variables,[],[222])). % 1.32/1.26 cnf(849,plain, % 1.32/1.26 (~P6(x8491,x8491,a1)), % 1.32/1.26 inference(rename_variables,[],[222])). % 1.32/1.26 cnf(852,plain, % 1.32/1.26 (~P6(x8521,x8521,a1)), % 1.32/1.26 inference(rename_variables,[],[222])). % 1.32/1.26 cnf(855,plain, % 1.32/1.26 (~P6(x8551,x8551,a1)), % 1.32/1.26 inference(rename_variables,[],[222])). % 1.32/1.26 cnf(858,plain, % 1.32/1.26 (~P6(x8581,x8581,a1)), % 1.32/1.26 inference(rename_variables,[],[222])). % 1.32/1.26 cnf(865,plain, % 1.32/1.26 (~P6(x8651,x8651,a1)), % 1.32/1.26 inference(rename_variables,[],[222])). % 1.32/1.26 cnf(866,plain, % 1.32/1.26 (P6(f3(a1),f20(x8661),a1)), % 1.32/1.26 inference(rename_variables,[],[211])). % 1.32/1.26 cnf(869,plain, % 1.32/1.26 (~P6(x8691,x8691,a1)), % 1.32/1.26 inference(rename_variables,[],[222])). % 1.32/1.26 cnf(874,plain, % 1.32/1.26 (~P5(f23(x8741,a1),f3(a1),a1)), % 1.32/1.26 inference(rename_variables,[],[227])). % 1.32/1.26 cnf(877,plain, % 1.32/1.26 (~P6(x8771,x8771,a1)), % 1.32/1.26 inference(rename_variables,[],[222])). % 1.32/1.26 cnf(880,plain, % 1.32/1.26 (~P6(x8801,x8801,a1)), % 1.32/1.26 inference(rename_variables,[],[222])). % 1.32/1.26 cnf(881,plain, % 1.32/1.26 (P5(x8811,x8811,a1)), % 1.32/1.26 inference(rename_variables,[],[204])). % 1.32/1.26 cnf(884,plain, % 1.32/1.26 (~P6(x8841,x8841,a1)), % 1.32/1.26 inference(rename_variables,[],[222])). % 1.32/1.26 cnf(887,plain, % 1.32/1.26 (~P6(x8871,x8871,a1)), % 1.32/1.26 inference(rename_variables,[],[222])). % 1.32/1.26 cnf(891,plain, % 1.32/1.26 (~P6(x8911,x8911,a1)), % 1.32/1.26 inference(rename_variables,[],[222])). % 1.32/1.26 cnf(893,plain, % 1.32/1.26 (~P5(f23(x8931,a1),f12(x8932,f3(a1),a1),a1)), % 1.32/1.26 inference(scs_inference,[],[224,222,718,726,742,763,780,783,798,801,828,831,834,844,849,852,855,858,865,869,877,880,884,887,891,225,220,204,731,772,774,881,198,211,866,215,212,213,214,227,839,874,119,121,122,124,126,129,130,139,142,149,151,152,154,155,156,157,159,175,201,206,209,376,324,301,312,352,374,388,460,2,268,375,392,308,330,431,636,75,76,241,242,243,244,311,353,355,396,399,430,461,462,3,79,80,416,438,448,451,574,575,629,630,631,632,634,635,641,642,643,644,645,319,320,322,406,413,414,434,436,614,616,677,437,542,556,557,558,559,564,565,568,554,618,622,624,555,550,551,552,553,581,582])). % 1.32/1.26 cnf(990,plain, % 1.32/1.26 ($false), % 1.32/1.26 inference(scs_inference,[],[707,733,779,893,817,760,720,221,775,374,392,312,375,229,376,460,344,324,388,268,352,317,2]), % 1.32/1.26 ['proof']). % 1.32/1.26 % SZS output end Proof % 1.32/1.26 % Total time :0.480000s %------------------------------------------------------------------------------