%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWV594-1 : 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 : n019.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Jun 24 16:47:58 EDT 2024 % Result : Unsatisfiable 1.75s 1.87s % Output : CNFRefutation 1.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.10 % Problem : SWV594-1 : TPTP v8.2.0. Released v4.1.0. % 0.03/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.09/0.30 % Computer : n019.cluster.edu % 0.09/0.30 % Model : x86_64 x86_64 % 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.30 % Memory : 8042.1875MB % 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.30 % CPULimit : 300 % 0.09/0.30 % WCLimit : 300 % 0.09/0.30 % DateTime : Thu Jun 20 21:06:24 EDT 2024 % 0.09/0.30 % CPUTime : % 0.15/0.53 start to proof:theBenchmark % 1.74/1.81 %------------------------------------------- % 1.74/1.81 % File :CSE---1.7 % 1.74/1.81 % Problem :theBenchmark % 1.74/1.81 % Transform :cnf % 1.74/1.81 % Format :tptp:raw % 1.74/1.81 % Command :java -jar mcs_scs.jar %d %s % 1.74/1.81 % 1.74/1.81 % Result :Theorem 0.810000s % 1.74/1.81 % Output :CNFRefutation 0.810000s % 1.74/1.81 %------------------------------------------- % 1.74/1.82 %------------------------------------------------------------------------------ % 1.74/1.82 % File : SWV594-1 : TPTP v8.2.0. Released v4.1.0. % 1.74/1.82 % Domain : Software Verification % 1.74/1.82 % Problem : Fast Fourier Transform 127_27 % 1.74/1.82 % Version : Especial. % 1.74/1.82 % English : Formalization of a functional implementation of the FFT algorithm % 1.74/1.82 % over the complex numbers, and its inverse. Both are shown % 1.74/1.82 % equivalent to the usual definitions of these operations through % 1.74/1.82 % Vandermonde matrices. They are also shown to be inverse to each % 1.74/1.82 % other, more precisely, that composition of the inverse and the % 1.74/1.82 % transformation yield the identity up to a scalar. % 1.74/1.82 % 1.74/1.82 % Refs : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe % 1.74/1.82 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 1.74/1.82 % Source : [Nip10] % 1.74/1.82 % Names : FFT-127_27 [Nip10] % 1.74/1.82 % 1.74/1.82 % Status : Unsatisfiable % 1.74/1.82 % Rating : 0.10 v8.1.0, 0.05 v7.5.0, 0.11 v7.4.0, 0.12 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.20 v6.3.0, 0.09 v6.2.0, 0.20 v6.1.0, 0.21 v6.0.0, 0.20 v5.5.0, 0.40 v5.3.0, 0.33 v5.2.0, 0.38 v5.1.0, 0.47 v5.0.0, 0.36 v4.1.0 % 1.74/1.82 % Syntax : Number of clauses : 1205 ( 163 unt; 162 nHn; 737 RR) % 1.74/1.82 % Number of literals : 3400 ( 728 equ;2038 neg) % 1.74/1.82 % Maximal clause size : 6 ( 2 avg) % 1.74/1.82 % Maximal term depth : 6 ( 1 avg) % 1.74/1.82 % Number of predicates : 85 ( 84 usr; 0 prp; 1-3 aty) % 1.74/1.82 % Number of functors : 35 ( 35 usr; 5 con; 0-3 aty) % 1.74/1.82 % Number of variables : 3169 ( 140 sgn) % 1.74/1.82 % SPC : CNF_UNS_RFO_SEQ_NHN % 1.74/1.82 % 1.74/1.82 % Comments : % 1.74/1.82 %------------------------------------------------------------------------------ % 1.74/1.82 cnf(cls_mod__div__equality_0,axiom, % 1.74/1.82 ( ~ class_Divides_Osemiring__div(T_a) % 1.74/1.82 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) = V_a ) ). % 1.74/1.82 % 1.74/1.82 cnf(cls_mod__div__decomp_0,axiom, % 1.74/1.82 ( ~ class_Divides_Osemiring__div(T_a) % 1.74/1.82 | V_a = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) ) ). % 1.74/1.82 % 1.74/1.82 cnf(cls_inf__period_I4_J_1,axiom, % 1.74/1.82 ( ~ class_Ring__and__Field_Odvd(T_a) % 1.74/1.82 | ~ class_Ring__and__Field_Ocomm__ring(T_a) % 1.74/1.82 | c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a) % 1.74/1.82 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_x,c_HOL_Otimes__class_Otimes(V_k,V_D,T_a),T_a),V_t,T_a),T_a) % 1.74/1.82 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a) ) ). % 1.74/1.82 % 1.74/1.82 cnf(cls_inf__period_I4_J_0,axiom, % 1.74/1.82 ( ~ class_Ring__and__Field_Odvd(T_a) % 1.74/1.82 | ~ class_Ring__and__Field_Ocomm__ring(T_a) % 1.74/1.82 | c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_x,c_HOL_Otimes__class_Otimes(V_k,V_D,T_a),T_a),V_t,T_a),T_a) % 1.74/1.82 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a) % 1.74/1.82 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a) ) ). % 1.74/1.82 % 1.74/1.82 cnf(cls_zmod__simps_I1_J_0,axiom, % 1.74/1.82 ( ~ class_Divides_Osemiring__div(T_a) % 1.74/1.82 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ). % 1.74/1.82 % 1.74/1.82 cnf(cls_zmod__simps_I2_J_0,axiom, % 1.74/1.82 ( ~ class_Divides_Osemiring__div(T_a) % 1.74/1.82 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ). % 1.74/1.82 % 1.74/1.82 cnf(cls_power__mult__distrib_0,axiom, % 1.74/1.82 ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) % 1.74/1.82 | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_n,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ). % 1.74/1.82 % 1.74/1.82 cnf(cls_class__semiring_Opwr__mul_0,axiom, % 1.74/1.82 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.74/1.82 | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_q,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_q,T_a),c_Power_Opower__class_Opower(V_y,V_q,T_a),T_a) ) ). % 1.74/1.82 % 1.74/1.82 cnf(cls_le__eqI_0,axiom, % 1.74/1.82 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.74/1.82 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.74/1.82 | c_lessequals(V_y_H,V_x_H,T_a) % 1.74/1.82 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.74/1.82 % 1.74/1.82 cnf(cls_le__eqI_1,axiom, % 1.74/1.82 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.74/1.82 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.74/1.82 | c_lessequals(V_y,V_x,T_a) % 1.74/1.82 | ~ c_lessequals(V_y_H,V_x_H,T_a) ) ). % 1.74/1.82 % 1.74/1.82 cnf(cls_less__eqI_0,axiom, % 1.74/1.82 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.74/1.82 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.74/1.82 | c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) % 1.74/1.82 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.74/1.82 % 1.74/1.82 cnf(cls_less__eqI_1,axiom, % 1.74/1.82 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.74/1.82 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.74/1.82 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.74/1.82 | ~ c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) ) ). % 1.74/1.82 % 1.74/1.82 cnf(cls_of__real__mult_0,axiom, % 1.74/1.82 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 1.74/1.82 | 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) ) ). % 1.74/1.82 % 1.74/1.82 cnf(cls_inverse__eq__iff__eq_0,axiom, % 1.74/1.82 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.74/1.82 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.74/1.82 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a) % 1.74/1.82 | V_a = V_b ) ). % 1.74/1.82 % 1.74/1.82 cnf(cls_mult__strict__mono_H_0,axiom, % 1.74/1.82 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.75/1.82 | 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) % 1.75/1.82 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.82 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.82 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.75/1.82 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_sgn__div__norm_0,axiom, % 1.75/1.82 ( ~ class_RealVector_Osgn__div__norm(T_a) % 1.75/1.82 | c_HOL_Osgn__class_Osgn(V_x,T_a) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Oinverse__class_Oinverse(c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal),V_x,T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_mult__idem_0,axiom, % 1.75/1.82 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 1.75/1.82 | c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = V_x ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_divide__nonpos__pos_0,axiom, % 1.75/1.82 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.82 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.82 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.75/1.82 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_divide__nonneg__neg_0,axiom, % 1.75/1.82 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.82 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.82 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.82 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_zero__less__divide__iff_3,axiom, % 1.75/1.82 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.82 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.82 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.82 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.82 | ~ 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) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_zero__less__divide__iff_2,axiom, % 1.75/1.82 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.82 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.82 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.82 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.82 | ~ 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) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_zero__less__divide__iff_1,axiom, % 1.75/1.82 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.82 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.82 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.82 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.82 | ~ 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) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_zero__less__divide__iff_0,axiom, % 1.75/1.82 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.82 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.82 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.82 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.82 | ~ 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) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_zero__le__dist_0,axiom, % 1.75/1.82 ( ~ class_RealVector_Ometric__space(T_a) % 1.75/1.82 | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(V_x,V_y,T_a),tc_RealDef_Oreal) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_le__sup__iff_1,axiom, % 1.75/1.82 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.82 | c_lessequals(V_y,V_z,T_a) % 1.75/1.82 | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_le__sup__iff_0,axiom, % 1.75/1.82 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.82 | c_lessequals(V_x,V_z,T_a) % 1.75/1.82 | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_le__supI2_0,axiom, % 1.75/1.82 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.82 | c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a) % 1.75/1.82 | ~ c_lessequals(V_x,V_b,T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_le__supI1_0,axiom, % 1.75/1.82 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.82 | c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a) % 1.75/1.82 | ~ c_lessequals(V_x,V_a,T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_le__supE_1,axiom, % 1.75/1.82 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.82 | c_lessequals(V_b,V_x,T_a) % 1.75/1.82 | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_le__supE_0,axiom, % 1.75/1.82 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.82 | c_lessequals(V_a,V_x,T_a) % 1.75/1.82 | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_mult__imp__less__div__pos_0,axiom, % 1.75/1.82 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.82 | c_HOL_Oord__class_Oless(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.75/1.82 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a) % 1.75/1.82 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_mult__imp__div__pos__less_0,axiom, % 1.75/1.82 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.82 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) % 1.75/1.82 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a) % 1.75/1.82 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_less__divide__eq_6,axiom, % 1.75/1.82 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.82 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.82 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.75/1.82 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.82 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_less__divide__eq_0,axiom, % 1.75/1.82 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.82 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.82 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.75/1.82 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.82 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_divide__less__eq_6,axiom, % 1.75/1.82 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.82 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.82 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.75/1.82 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.82 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_divide__less__eq_0,axiom, % 1.75/1.82 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.82 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.82 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.75/1.82 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.82 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_inverse__unique_0,axiom, % 1.75/1.82 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.75/1.82 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.75/1.82 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_real__vector_Oscale__one_0,axiom, % 1.75/1.82 ( ~ class_RealVector_Oreal__vector(T_a) % 1.75/1.82 | c_RealVector_OscaleR__class_OscaleR(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,T_a) = V_x ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_sum__squares__eq__zero__iff_1,axiom, % 1.75/1.82 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.82 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.82 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_sum__squares__eq__zero__iff_0,axiom, % 1.75/1.82 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.82 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.82 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom, % 1.75/1.82 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.75/1.82 | ~ class_Int_Onumber__ring(T_a) % 1.75/1.82 | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_c,T_a),T_a) != c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_d,T_a),T_a) % 1.75/1.82 | V_c = V_d % 1.75/1.82 | V_r = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_prts_0,axiom, % 1.75/1.82 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.82 | V_a = c_HOL_Oplus__class_Oplus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a),T_a) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_ge__one__powr__ge__zero_0,axiom, % 1.75/1.82 ( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Log_Opowr(V_x,V_a),tc_RealDef_Oreal) % 1.75/1.82 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_a,tc_RealDef_Oreal) % 1.75/1.82 | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.82 % 1.75/1.82 cnf(cls_sup__eq__if_1,axiom, % 1.75/1.83 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.83 | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.83 | c_Lattices_Oupper__semilattice__class_Osup(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a % 1.75/1.83 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__right__mono__neg_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.75/1.83 | 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) % 1.75/1.83 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.83 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__left__mono__neg_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.75/1.83 | 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) % 1.75/1.83 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.83 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__right__mono_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 1.75/1.83 | 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) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.83 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__left__mono_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 1.75/1.83 | 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) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.83 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__mono1_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Omult__mono1(T_a) % 1.75/1.83 | 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) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.83 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_inverse__divide_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.83 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.83 | 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) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_power__less__power__Suc_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.75/1.83 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),T_a) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_inverse__negative__imp__negative_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.83 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.83 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_DERIV__inverse__lemma_0,axiom, % 1.75/1.83 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.75/1.83 | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a),V_h,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_h,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a),T_a) % 1.75/1.83 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.83 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_norm__sgn_1,axiom, % 1.75/1.83 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.83 | c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(V_x,T_a),T_a) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) % 1.75/1.83 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_real__sqrt__eq__iff_0,axiom, % 1.75/1.83 ( c_NthRoot_Osqrt(V_x) != c_NthRoot_Osqrt(V_y) % 1.75/1.83 | V_x = V_y ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_pos__add__strict_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.75/1.83 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_of__real__inverse_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.83 | ~ class_RealVector_Oreal__div__algebra(T_a) % 1.75/1.83 | c_RealVector_Oof__real(c_HOL_Oinverse__class_Oinverse(V_x,tc_RealDef_Oreal),T_a) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(V_x,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_dvd__mult__right_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.83 | c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 1.75/1.83 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_dvd__mult__left_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.83 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 1.75/1.83 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_dvd__mult2_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.83 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.75/1.83 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_dvd__mult_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.83 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.75/1.83 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_real__sqrt__ge__zero_0,axiom, % 1.75/1.83 ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x),tc_RealDef_Oreal) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_real__sqrt__ge__0__iff_0,axiom, % 1.75/1.83 ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_real__sqrt__ge__0__iff_1,axiom, % 1.75/1.83 ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_sup__inf__distrib2_0,axiom, % 1.75/1.83 ( ~ class_Lattices_Odistrib__lattice(T_a) % 1.75/1.83 | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),V_x,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_z,V_x,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_sup__inf__distrib1_0,axiom, % 1.75/1.83 ( ~ class_Lattices_Odistrib__lattice(T_a) % 1.75/1.83 | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_add__minus__cancel_0,axiom, % 1.75/1.83 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.83 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a),T_a) = V_b ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_abs__le__D2_0,axiom, % 1.75/1.83 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.83 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.75/1.83 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_cos__le__one_0,axiom, % 1.75/1.83 c_lessequals(c_Transcendental_Ocos(V_x),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__pos__neg2_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.75/1.83 | 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) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__pos__neg_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.75/1.83 | 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) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__neg__pos_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.75/1.83 | 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) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__le__0__iff_3,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.83 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.83 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.83 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__le__0__iff_2,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.83 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.83 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.83 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__le__0__iff_1,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.83 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.83 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.83 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__le__0__iff_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.83 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.83 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.83 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_zero__less__dist__iff_1,axiom, % 1.75/1.83 ( ~ class_RealVector_Ometric__space(T_a) % 1.75/1.83 | 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) % 1.75/1.83 | V_x = V_y ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mod__add__self2_0,axiom, % 1.75/1.83 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.83 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mod__add__self1_0,axiom, % 1.75/1.83 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.83 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_b,V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_abs__less__iff_2,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.83 | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_div__mult__mult1__if_0,axiom, % 1.75/1.83 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.83 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_inf__greatest_0,axiom, % 1.75/1.83 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.83 | c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) % 1.75/1.83 | ~ c_lessequals(V_x,V_z,T_a) % 1.75/1.83 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_le__inf__iff_2,axiom, % 1.75/1.83 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.83 | c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) % 1.75/1.83 | ~ c_lessequals(V_x,V_z,T_a) % 1.75/1.83 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_le__infI_0,axiom, % 1.75/1.83 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.83 | c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) % 1.75/1.83 | ~ c_lessequals(V_x,V_b,T_a) % 1.75/1.83 | ~ c_lessequals(V_x,V_a,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_inf__le2_0,axiom, % 1.75/1.83 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.83 | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_y,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_inf__le1_0,axiom, % 1.75/1.83 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.83 | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_x,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_inf__sup__ord_I2_J_0,axiom, % 1.75/1.83 ( ~ class_Lattices_Olattice(T_a) % 1.75/1.83 | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_y,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_inf__sup__ord_I1_J_0,axiom, % 1.75/1.83 ( ~ class_Lattices_Olattice(T_a) % 1.75/1.83 | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_x,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_one__dvd_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.83 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mod__div__equality2_0,axiom, % 1.75/1.83 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.83 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) = V_a ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_order__less__le_2,axiom, % 1.75/1.83 ( ~ class_Orderings_Oorder(T_a) % 1.75/1.83 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.75/1.83 | V_x = V_y % 1.75/1.83 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_order__le__less_0,axiom, % 1.75/1.83 ( ~ class_Orderings_Oorder(T_a) % 1.75/1.83 | V_x = V_y % 1.75/1.83 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.75/1.83 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_real__less__def_2,axiom, % 1.75/1.83 ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.75/1.83 | V_x = V_y % 1.75/1.83 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_order__le__neq__trans_0,axiom, % 1.75/1.83 ( ~ class_Orderings_Oorder(T_a) % 1.75/1.83 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.83 | V_a = V_b % 1.75/1.83 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_order__neq__le__trans_0,axiom, % 1.75/1.83 ( ~ class_Orderings_Oorder(T_a) % 1.75/1.83 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.83 | ~ c_lessequals(V_a,V_b,T_a) % 1.75/1.83 | V_a = V_b ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_linorder__antisym__conv1_0,axiom, % 1.75/1.83 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.83 | V_x = V_y % 1.75/1.83 | ~ c_lessequals(V_x,V_y,T_a) % 1.75/1.83 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_linorder__antisym__conv2_0,axiom, % 1.75/1.83 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.83 | V_x = V_y % 1.75/1.83 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.75/1.83 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_xt1_I12_J_0,axiom, % 1.75/1.83 ( ~ class_Orderings_Oorder(T_a) % 1.75/1.83 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.75/1.83 | ~ c_lessequals(V_b,V_a,T_a) % 1.75/1.83 | V_a = V_b ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_xt1_I11_J_0,axiom, % 1.75/1.83 ( ~ class_Orderings_Oorder(T_a) % 1.75/1.83 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.75/1.83 | V_a = V_b % 1.75/1.83 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_divide__right__mono_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.83 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.83 | 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) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.83 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_divide__right__mono__neg_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.83 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.83 | 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) % 1.75/1.83 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.83 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_power__inverse_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.75/1.83 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.83 | c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_inverse__minus__eq_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.75/1.83 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.83 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_split__mult__pos__le_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.75/1.83 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_split__mult__pos__le_1,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.75/1.83 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.75/1.83 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.83 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__nonpos__nonpos_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.75/1.83 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.75/1.83 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.83 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_zero__le__square_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.83 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_zero__le__mult__iff_4,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.83 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_zero__le__mult__iff_5,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.83 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.75/1.83 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.83 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__nonneg__nonneg_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.75/1.83 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_norm__mult__less_0,axiom, % 1.75/1.83 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.83 | 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) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_y,T_a),V_s,tc_RealDef_Oreal) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),V_r,tc_RealDef_Oreal) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_right__inverse__eq_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.83 | c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.75/1.83 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.83 | V_a = V_b ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_class__ring_Oneg__mul_0,axiom, % 1.75/1.83 ( ~ class_Int_Onumber__ring(T_a) % 1.75/1.83 | c_HOL_Ouminus__class_Ouminus(V_x,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),V_x,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_of__real__def_0,axiom, % 1.75/1.83 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 1.75/1.83 | c_RealVector_Oof__real(V_r,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_abs__triangle__ineq2_0,axiom, % 1.75/1.83 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.83 | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_dvd__div__neg_0,axiom, % 1.75/1.83 ( ~ class_Divides_Oring__div(T_a) % 1.75/1.83 | c_Divides_Odiv__class_Odiv(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),T_a) % 1.75/1.83 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_dvd__neg__div_0,axiom, % 1.75/1.83 ( ~ class_Divides_Oring__div(T_a) % 1.75/1.83 | c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),T_a) % 1.75/1.83 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom, % 1.75/1.83 ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a) % 1.75/1.83 | 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) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.83 | 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) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.83 | 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) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.83 | 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) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.83 | 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) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_real__mult__assoc_0,axiom, % 1.75/1.83 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) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_class__semiring_Omul__a_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.83 | 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) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.83 | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__right_Oadd_0,axiom, % 1.75/1.83 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.83 | c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),c_HOL_Otimes__class_Otimes(V_xa,V_y,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult_Oadd__right_0,axiom, % 1.75/1.83 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.83 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oplus__class_Oplus(V_b,V_b_H,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b_H,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__left_Oadd_0,axiom, % 1.75/1.83 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.83 | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_ya,T_a),c_HOL_Otimes__class_Otimes(V_y,V_ya,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult_Oadd__left_0,axiom, % 1.75/1.83 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.83 | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_class__semiring_Omul__d_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.83 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_comm__semiring__class_Odistrib_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ocomm__semiring(T_a) % 1.75/1.83 | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_frac__less_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.83 | 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) % 1.75/1.83 | ~ c_lessequals(V_w,V_z,T_a) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_tan__minus_0,axiom, % 1.75/1.83 c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(V_x),tc_RealDef_Oreal) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom, % 1.75/1.83 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.83 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom, % 1.75/1.83 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.83 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_less__supI1_0,axiom, % 1.75/1.83 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.83 | c_HOL_Oord__class_Oless(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(V_x,V_a,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_less__supI2_0,axiom, % 1.75/1.83 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.83 | c_HOL_Oord__class_Oless(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(V_x,V_b,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_abs__minus__commute_0,axiom, % 1.75/1.83 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.83 | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_minus__divide__right_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.83 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.83 | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_minus__divide__left_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.83 | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_one__le__inverse__iff_2,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.83 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.83 | c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) % 1.75/1.83 | ~ c_lessequals(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_zero__le__mult__iff_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.83 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.83 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_zero__le__mult__iff_1,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.83 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.83 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_zero__le__mult__iff_2,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.83 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.83 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_zero__le__mult__iff_3,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.83 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.83 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_sin__le__one_0,axiom, % 1.75/1.83 c_lessequals(c_Transcendental_Osin(V_x),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_sum__squares__gt__zero__iff_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.83 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_nonzero__inverse__eq__divide_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.83 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 1.75/1.83 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_div__add__self1_0,axiom, % 1.75/1.83 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.83 | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_b,V_a,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.75/1.83 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_div__add__self2_0,axiom, % 1.75/1.83 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.83 | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.75/1.83 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_abs__one_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.83 | c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.83 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_diff__frac__eq_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.83 | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) % 1.75/1.83 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.83 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_zero__less__two_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.75/1.83 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult_Ominus__left_0,axiom, % 1.75/1.83 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.83 | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__left_Ominus_0,axiom, % 1.75/1.83 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.83 | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult_Ominus__right_0,axiom, % 1.75/1.83 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.83 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__right_Ominus_0,axiom, % 1.75/1.83 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.83 | c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_square__eq__iff_1,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.75/1.83 | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_b,V_b,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_minus__mult__minus_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Oring(T_a) % 1.75/1.83 | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_real__mult__inverse__left_0,axiom, % 1.75/1.83 ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_x,tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) % 1.75/1.83 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_field__inverse_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.83 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.75/1.83 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_left__inverse_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.75/1.83 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.75/1.83 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_right__inverse_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.75/1.83 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) % 1.75/1.83 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__mono_0,axiom, % 1.75/1.83 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 1.75/1.83 | 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) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.83 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.83 | ~ c_lessequals(V_c,V_d,T_a) % 1.75/1.83 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.83 % 1.75/1.83 cnf(cls_mult__mono_H_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 1.75/1.84 | 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) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.84 | ~ c_lessequals(V_c,V_d,T_a) % 1.75/1.84 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_div__mult__mult1_0,axiom, % 1.75/1.84 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.84 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_Divides_Odiv__class_Odiv(V_a,V_b,T_a) % 1.75/1.84 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_div__mult__mult2_0,axiom, % 1.75/1.84 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.84 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_Divides_Odiv__class_Odiv(V_a,V_b,T_a) % 1.75/1.84 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_sgn__sgn_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.84 | 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_norm__ge__zero_0,axiom, % 1.75/1.84 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__less__eq_2,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__less__eq_3,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__less__eq_8,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__less__eq_9,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_less__divide__eq_2,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_less__divide__eq_3,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_less__divide__eq_8,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_less__divide__eq_9,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_of__real__minus_0,axiom, % 1.75/1.84 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 1.75/1.84 | c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(V_x,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_of__real_Ominus_0,axiom, % 1.75/1.84 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.84 | ~ class_RealVector_Oreal__algebra__1(T_a) % 1.75/1.84 | c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(V_x,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_power__Suc__less_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__less__cancel__left__disj_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.84 | ~ 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__less__cancel__left__disj_3,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.84 | ~ 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__less__cancel__right__disj_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.84 | ~ 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__less__cancel__right__disj_3,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.84 | ~ 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_pprt__neg_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.84 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_x,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mod__minus__eq_0,axiom, % 1.75/1.84 ( ~ class_Divides_Oring__div(T_a) % 1.75/1.84 | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_NthRoot_Oroot__def_2,axiom, % 1.75/1.84 ( c_NthRoot_Oroot(V_n,V_x) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_compl__sup_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.75/1.84 | c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_x,T_a),c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_real__mult__is__one_0,axiom, % 1.75/1.84 ( c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) % 1.75/1.84 | V_x = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.84 | V_x = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_neg__le__0__iff__le_1,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_neg__le__0__iff__le_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_div__mult__div__if__dvd_0,axiom, % 1.75/1.84 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.84 | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),c_Divides_Odiv__class_Odiv(V_w,V_z,T_a),T_a) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_x,V_w,T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_w,T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_one__less__inverse__iff_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__left__idem_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 1.75/1.84 | 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_less__add__one_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_le__eq__neg_1,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.84 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_le__eq__neg_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_minus__mult__right_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oring(T_a) % 1.75/1.84 | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_minus__mult__left_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oring(T_a) % 1.75/1.84 | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_sgn__minus_0,axiom, % 1.75/1.84 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.84 | c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(V_x,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_dist__not__less__zero_0,axiom, % 1.75/1.84 ( ~ class_RealVector_Ometric__space(T_a) % 1.75/1.84 | ~ 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__frac__frac_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_abs__eq__mult_3,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.75/1.84 | 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) % 1.75/1.84 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_abs__eq__mult_2,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.75/1.84 | 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) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.84 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_abs__eq__mult_1,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.75/1.84 | 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) % 1.75/1.84 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_abs__eq__mult_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.75/1.84 | 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) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_abs__mult_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.84 | 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_add__le__cancel__right_1,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_add__le__cancel__right_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.75/1.84 | c_lessequals(V_a,V_b,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_add__le__cancel__left_1,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_add__le__cancel__left_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.75/1.84 | c_lessequals(V_a,V_b,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_add__right__mono_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_add__left__mono_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_dvd__mult__cancel__right_1,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.75/1.84 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_dvd__mult__cancel__left_1,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.75/1.84 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_dvd__trans_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.84 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_dvd__refl_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.84 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_scaleR__right_Odiff_0,axiom, % 1.75/1.84 ( ~ class_RealVector_Oreal__vector(T_a) % 1.75/1.84 | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_scaleR_Odiff__right_0,axiom, % 1.75/1.84 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.84 | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ominus__class_Ominus(V_b,V_b_H,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),c_RealVector_OscaleR__class_OscaleR(V_a,V_b_H,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_less__infI2_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_b,V_x,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_less__infI1_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_a,V_x,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_inf__sup__absorb_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Olattice(T_a) % 1.75/1.84 | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = V_x ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_abs__of__nonneg_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.84 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_linorder__neqE__ordered__idom_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.75/1.84 | V_x = V_y ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_not__less__iff__gr__or__eq_0,axiom, % 1.75/1.84 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.84 | V_x = V_y % 1.75/1.84 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_linorder__antisym__conv3_0,axiom, % 1.75/1.84 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.84 | V_x = V_y % 1.75/1.84 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_linorder__less__linear_0,axiom, % 1.75/1.84 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.75/1.84 | V_x = V_y % 1.75/1.84 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_order__antisym__conv_0,axiom, % 1.75/1.84 ( ~ class_Orderings_Oorder(T_a) % 1.75/1.84 | V_x = V_y % 1.75/1.84 | ~ c_lessequals(V_x,V_y,T_a) % 1.75/1.84 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_order__eq__iff_2,axiom, % 1.75/1.84 ( ~ class_Orderings_Oorder(T_a) % 1.75/1.84 | V_x = V_y % 1.75/1.84 | ~ c_lessequals(V_y,V_x,T_a) % 1.75/1.84 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_linorder__neqE_0,axiom, % 1.75/1.84 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.75/1.84 | V_x = V_y ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_order__antisym_0,axiom, % 1.75/1.84 ( ~ class_Orderings_Oorder(T_a) % 1.75/1.84 | V_x = V_y % 1.75/1.84 | ~ c_lessequals(V_y,V_x,T_a) % 1.75/1.84 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_real__le__antisym_0,axiom, % 1.75/1.84 ( V_z = V_w % 1.75/1.84 | ~ c_lessequals(V_w,V_z,tc_RealDef_Oreal) % 1.75/1.84 | ~ c_lessequals(V_z,V_w,tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_power__gt1__lemma_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_power__divide_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_compl__eq__compl__iff_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.75/1.84 | c_HOL_Ouminus__class_Ouminus(V_x,T_a) != c_HOL_Ouminus__class_Ouminus(V_y,T_a) % 1.75/1.84 | V_x = V_y ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_neg__equal__iff__equal_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.84 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(V_b,T_a) % 1.75/1.84 | V_a = V_b ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_cos__monotone__minus__pi__0_H_0,axiom, % 1.75/1.84 ( c_lessequals(c_Transcendental_Ocos(V_y),c_Transcendental_Ocos(V_x),tc_RealDef_Oreal) % 1.75/1.84 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.84 | ~ c_lessequals(V_y,V_x,tc_RealDef_Oreal) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_real__sqrt__not__eq__zero_0,axiom, % 1.75/1.84 ( c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_eq__divide__imp_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.84 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.84 | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__eq__imp_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.84 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.84 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_estimate__by__abs_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.75/1.84 | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_eq__divide__eq_3,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) % 1.75/1.84 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__eq__eq_3,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a % 1.75/1.84 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__le__0__1__iff_1,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__le__0__1__iff_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_distrib__sup__le_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Olattice(T_a) % 1.75/1.84 | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_abs__le__zero__iff_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.84 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_cos__monotone__0__pi_H_0,axiom, % 1.75/1.84 ( c_lessequals(c_Transcendental_Ocos(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal) % 1.75/1.84 | ~ c_lessequals(V_x,c_Transcendental_Opi,tc_RealDef_Oreal) % 1.75/1.84 | ~ c_lessequals(V_y,V_x,tc_RealDef_Oreal) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_zero__le__iff__zero__nprt_1,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.84 | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_zero__le__iff__zero__nprt_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.84 | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_inverse__less__1__iff_1,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_abs__lattice_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.75/1.84 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.84 | 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.84 | 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.84 | 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_dist__le__zero__iff_1,axiom, % 1.75/1.84 ( ~ class_RealVector_Ometric__space(T_a) % 1.75/1.84 | c_lessequals(c_RealVector_Odist__class_Odist(V_x,V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_sup__0__imp__0_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.84 | c_Lattices_Oupper__semilattice__class_Osup(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.84 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_sum__squares__le__zero__iff_2,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_div__mult__self2__is__id_0,axiom, % 1.75/1.84 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.84 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = V_a % 1.75/1.84 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_div__mult__self1__is__id_0,axiom, % 1.75/1.84 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.84 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = V_a % 1.75/1.84 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_add__nonpos__neg_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_add__neg__nonpos_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_neg__less__iff__less_1,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_neg__less__iff__less_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_nonzero__inverse__scaleR__distrib_0,axiom, % 1.75/1.84 ( ~ class_RealVector_Oreal__div__algebra(T_a) % 1.75/1.84 | c_HOL_Oinverse__class_Oinverse(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Oinverse__class_Oinverse(V_a,tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) % 1.75/1.84 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.84 | V_a = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_inverse__scaleR__distrib_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | ~ class_RealVector_Oreal__div__algebra(T_a) % 1.75/1.84 | c_HOL_Oinverse__class_Oinverse(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Oinverse__class_Oinverse(V_a,tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_abs__div__pos_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | 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) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_le__divide__eq_8,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__le__eq_8,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.75/1.84 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_not__sum__squares__lt__zero_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_sgn__if_1,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Osgn__if(T_a) % 1.75/1.84 | c_HOL_Osgn__class_Osgn(V_x,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.75/1.84 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_real__sgn__def_1,axiom, % 1.75/1.84 ( c_HOL_Osgn__class_Osgn(V_x,tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.75/1.84 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_inf__left__commute_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.84 | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_inf__assoc_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.84 | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_inf__sup__aci_I3_J_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Olattice(T_a) % 1.75/1.84 | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_inf__sup__aci_I2_J_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Olattice(T_a) % 1.75/1.84 | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_abs__less__iff_1,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_power__less__imp__less__base_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_zero__less__mult__pos2_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.84 | ~ 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_zero__less__mult__pos_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.84 | ~ 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__pos__pos_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.75/1.84 | 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) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__neg__neg_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.84 | 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) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_real__mult__order_0,axiom, % 1.75/1.84 ( 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) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_even__less__0__iff_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_even__less__0__iff_1,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_powr__minus_0,axiom, % 1.75/1.84 c_Log_Opowr(V_x,c_HOL_Ouminus__class_Ouminus(V_a,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Oinverse(c_Log_Opowr(V_x,V_a),tc_RealDef_Oreal) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_neg__sup__eq__inf_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.84 | c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__neg__neg_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | 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) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__pos__pos_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | 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) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_zero__less__divide__iff_4,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | 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) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_zero__less__divide__iff_5,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | 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) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_zero__le__pprt_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_of__real__1_0,axiom, % 1.75/1.84 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 1.75/1.84 | c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_real__sqrt__le__1__iff_1,axiom, % 1.75/1.84 ( c_lessequals(c_NthRoot_Osqrt(V_x),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.84 | ~ c_lessequals(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_real__sqrt__le__1__iff_0,axiom, % 1.75/1.84 ( c_lessequals(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.84 | ~ c_lessequals(c_NthRoot_Osqrt(V_x),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_one__less__inverse__iff_1,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_dvd__add_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.84 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_inverse__add_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.84 | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) % 1.75/1.84 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.84 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_division__ring__inverse__add_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.75/1.84 | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) % 1.75/1.84 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.84 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_abs__sgn_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.84 | 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_group__add__class_Odiff__0_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.84 | c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_gt__half__sum_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),T_a),V_b,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_less__half__sum_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_cos__arctan__not__zero_0,axiom, % 1.75/1.84 c_Transcendental_Ocos(c_Transcendental_Oarctan(V_x)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_add__frac__num_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a),V_y,T_a) % 1.75/1.84 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_add__num__frac_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_HOL_Oplus__class_Oplus(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a),V_y,T_a) % 1.75/1.84 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_real__sum__squares__cancel__a_0,axiom, % 1.75/1.84 ( c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.84 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_real__sum__squares__cancel__a_1,axiom, % 1.75/1.84 ( c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.84 | V_y = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.84 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_Deriv_Oinverse__diff__inverse_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.75/1.84 | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a),T_a) % 1.75/1.84 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.84 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_diff__def_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.75/1.84 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_class__ring_Osub__add_0,axiom, % 1.75/1.84 ( ~ class_Int_Onumber__ring(T_a) % 1.75/1.84 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_diff__minus_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.84 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_ab__diff__minus_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.75/1.84 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_nonzero__minus__divide__divide_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.84 | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) % 1.75/1.84 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_div__dvd__div_0,axiom, % 1.75/1.84 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.84 | c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_div__dvd__div_1,axiom, % 1.75/1.84 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.84 | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_dvd__minus__iff_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.75/1.84 | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_dvd__minus__iff_1,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.75/1.84 | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_minus__dvd__iff_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.75/1.84 | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_minus__dvd__iff_1,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.75/1.84 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_Rational_Oordered__idom__class_Osgn__less_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_Rational_Oordered__idom__class_Osgn__less_1,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_le__infE_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.84 | c_lessequals(V_x,V_a,T_a) % 1.75/1.84 | ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_le__infE_1,axiom, % 1.75/1.84 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.84 | c_lessequals(V_x,V_b,T_a) % 1.75/1.84 | ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_le__infI1_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.84 | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a) % 1.75/1.84 | ~ c_lessequals(V_a,V_x,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_le__infI2_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.84 | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a) % 1.75/1.84 | ~ c_lessequals(V_b,V_x,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_le__inf__iff_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.84 | c_lessequals(V_x,V_y,T_a) % 1.75/1.84 | ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_le__inf__iff_1,axiom, % 1.75/1.84 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.84 | c_lessequals(V_x,V_z,T_a) % 1.75/1.84 | ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__strict__right__mono_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | 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) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__strict__right__mono__neg_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | 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) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mod__diff__eq_0,axiom, % 1.75/1.84 ( ~ class_Divides_Oring__div(T_a) % 1.75/1.84 | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__nonneg__pos_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__nonpos__neg_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__left__le__one__le_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Otimes__class_Otimes(V_y,V_x,T_a),V_x,T_a) % 1.75/1.84 | ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__right__le__one__le_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_x,T_a) % 1.75/1.84 | ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_powr__mono_0,axiom, % 1.75/1.84 ( c_lessequals(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_x,V_b),tc_RealDef_Oreal) % 1.75/1.84 | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.75/1.84 | ~ c_lessequals(V_a,V_b,tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__1_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.84 | c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_abs__leI_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.75/1.84 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_abs__le__iff_2,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.75/1.84 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_abs__minus__cancel_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.84 | c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_class__ringb_Oadd__cancel_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.75/1.84 | ~ class_Int_Onumber__ring(T_a) % 1.75/1.84 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) % 1.75/1.84 | V_y = V_z ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_add__imp__eq_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a) % 1.75/1.84 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) % 1.75/1.84 | V_b = V_c ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_add__left__cancel_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 1.75/1.84 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) % 1.75/1.84 | V_b = V_c ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_add__right__cancel_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 1.75/1.84 | c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) != c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) % 1.75/1.84 | V_b = V_c ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_powr__gt__zero_0,axiom, % 1.75/1.84 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Log_Opowr(V_x,V_a),tc_RealDef_Oreal) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_not__square__less__zero_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.84 | ~ 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__le__0__iff_4,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__le__0__iff_5,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.84 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_split__mult__neg__le_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_split__mult__neg__le_1,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.84 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__nonneg__nonpos_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__nonpos__nonneg_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.84 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__nonneg__nonpos2_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_inverse__mult__distrib_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_nonzero__inverse__mult__distrib_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.75/1.84 | 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) % 1.75/1.84 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.84 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_abs__le__zero__iff_1,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.84 | 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_cos__monotone__minus__pi__0_0,axiom, % 1.75/1.84 ( c_HOL_Oord__class_Oless(c_Transcendental_Ocos(V_y),c_Transcendental_Ocos(V_x),tc_RealDef_Oreal) % 1.75/1.84 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_y,V_x,tc_RealDef_Oreal) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_add__nonneg__pos_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_add__pos__nonneg_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_cos__monotone__0__pi_0,axiom, % 1.75/1.84 ( c_HOL_Oord__class_Oless(c_Transcendental_Ocos(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal) % 1.75/1.84 | ~ c_lessequals(V_x,c_Transcendental_Opi,tc_RealDef_Oreal) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_y,V_x,tc_RealDef_Oreal) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_dvd__imp__mod__0_0,axiom, % 1.75/1.84 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.84 | c_Divides_Odiv__class_Omod(V_b,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_dvd__eq__mod__eq__0_1,axiom, % 1.75/1.84 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.84 | c_Divides_Odiv__class_Omod(V_b,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.84 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_nonzero__norm__inverse_0,axiom, % 1.75/1.84 ( ~ class_RealVector_Oreal__normed__div__algebra(T_a) % 1.75/1.84 | c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Onorm__class_Onorm(V_a,T_a),tc_RealDef_Oreal) % 1.75/1.84 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_distrib__inf__le_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Olattice(T_a) % 1.75/1.84 | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_inf__sup__ord_I3_J_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Olattice(T_a) % 1.75/1.84 | c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_inf__sup__ord_I4_J_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Olattice(T_a) % 1.75/1.84 | c_lessequals(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_le__supI_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.84 | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a) % 1.75/1.84 | ~ c_lessequals(V_b,V_x,T_a) % 1.75/1.84 | ~ c_lessequals(V_a,V_x,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_sup__ge1_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.84 | c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_sup__ge2_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.84 | c_lessequals(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_sup__least_0,axiom, % 1.75/1.84 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.84 | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),V_x,T_a) % 1.75/1.84 | ~ c_lessequals(V_z,V_x,T_a) % 1.75/1.84 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_le__sup__iff_2,axiom, % 1.75/1.84 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.84 | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) % 1.75/1.84 | ~ c_lessequals(V_y,V_z,T_a) % 1.75/1.84 | ~ c_lessequals(V_x,V_z,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_norm__one_0,axiom, % 1.75/1.84 ( ~ class_RealVector_Oreal__normed__algebra__1(T_a) % 1.75/1.84 | c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__le__eq_5,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__le__eq_7,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_le__divide__eq_5,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_le__divide__eq_7,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_cos__zero_0,axiom, % 1.75/1.84 c_Transcendental_Ocos(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_real__sqrt__gt__0__iff_1,axiom, % 1.75/1.84 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_real__sqrt__gt__0__iff_0,axiom, % 1.75/1.84 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_real__sqrt__gt__zero_0,axiom, % 1.75/1.84 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x),tc_RealDef_Oreal) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_dist__commute_0,axiom, % 1.75/1.84 ( ~ class_RealVector_Ometric__space(T_a) % 1.75/1.84 | c_RealVector_Odist__class_Odist(V_x,V_y,T_a) = c_RealVector_Odist__class_Odist(V_y,V_x,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.84 | c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_c,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.84 | c_HOL_Oplus__class_Oplus(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_b,V_c,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_add__inf__distrib__left_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Olordered__ab__group__add__meet(T_a) % 1.75/1.84 | c_HOL_Oplus__class_Oplus(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_b,V_c,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_add__inf__distrib__right_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Olordered__ab__group__add__meet(T_a) % 1.75/1.84 | c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_c,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_diff__divide__distrib_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.84 | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide_Odiff_0,axiom, % 1.75/1.84 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.75/1.84 | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(V_x,V_ya,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_ya,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_add__nonneg__eq__0__iff_1,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.75/1.84 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.75/1.84 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_add__nonneg__eq__0__iff_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.75/1.84 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.75/1.84 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_Rational_Oordered__idom__class_Osgn__greater_1,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_Rational_Oordered__idom__class_Osgn__greater_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_powr__mono2_0,axiom, % 1.75/1.84 ( c_lessequals(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_y,V_a),tc_RealDef_Oreal) % 1.75/1.84 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_a,tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_dvd__diff_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.75/1.84 | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_abs__of__neg_0,axiom, % 1.75/1.84 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.84 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_abs__if_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oabs__if(T_a) % 1.75/1.84 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_abs__if__lattice_0,axiom, % 1.75/1.84 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.84 | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.75/1.84 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_square__eq__iff_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.75/1.84 | c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) != c_HOL_Otimes__class_Otimes(V_b,V_b,T_a) % 1.75/1.84 | V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a) % 1.75/1.84 | V_a = V_b ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__less__imp__less__right_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.84 | ~ 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__less__imp__less__left_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.84 | ~ 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__right__less__imp__less_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.84 | ~ 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__left__less__imp__less_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 1.75/1.84 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.84 | ~ 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__imp__le__div__pos_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | c_lessequals(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__imp__div__pos__le_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) % 1.75/1.84 | ~ c_lessequals(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_le__divide__eq_6,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_le__divide__eq_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.84 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__le__eq_6,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.84 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_divide__le__eq_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.75/1.84 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_dvd__power_1,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.84 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_real__sqrt__eq__1__iff_0,axiom, % 1.75/1.84 ( c_NthRoot_Osqrt(V_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) % 1.75/1.84 | V_x = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_mult__sgn__abs_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.84 | 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 ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_inverse__le__1__iff_1,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.75/1.84 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_norm__mult__ineq_0,axiom, % 1.75/1.84 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.84 | 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_sum__squares__ge__zero_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_arctan__monotone_H_0,axiom, % 1.75/1.84 ( c_lessequals(c_Transcendental_Oarctan(V_x),c_Transcendental_Oarctan(V_y),tc_RealDef_Oreal) % 1.75/1.84 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_zero__le__divide__1__iff_1,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_zero__le__divide__1__iff_0,axiom, % 1.75/1.84 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.84 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.84 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.84 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_zero__less__dist__iff_0,axiom, % 1.75/1.84 ( ~ class_RealVector_Ometric__space(T_a) % 1.75/1.84 | ~ 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) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_dvd__mod__imp__dvd_0,axiom, % 1.75/1.84 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.84 | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) ) ). % 1.75/1.84 % 1.75/1.84 cnf(cls_dvd__mod__iff_1,axiom, % 1.75/1.84 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.84 | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) % 1.75/1.84 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) % 1.75/1.85 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_dvd__mod__iff_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) % 1.75/1.85 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) % 1.75/1.85 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_dvd__mod_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) % 1.75/1.85 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) % 1.75/1.85 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_le__add__iff2_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_le__add__iff2_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.75/1.85 | c_lessequals(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_le__add__iff1_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_le__add__iff1_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__le__0__iff_5,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.85 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__le__0__iff_4,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_powr__powr__swap_0,axiom, % 1.75/1.85 c_Log_Opowr(c_Log_Opowr(V_x,V_a),V_b) = c_Log_Opowr(c_Log_Opowr(V_x,V_b),V_a) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_add__eq__inf__sup_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_add__increasing2_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.75/1.85 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.75/1.85 | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_b,V_a,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_add__increasing_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.75/1.85 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.75/1.85 | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_b,V_c,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_scaleR__minus__right_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__vector(T_a) % 1.75/1.85 | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_scaleR_Ominus__right_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.85 | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_scaleR__minus__left_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__vector(T_a) % 1.75/1.85 | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(V_a,tc_RealDef_Oreal),V_x,T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_scaleR__left_Ominus_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__vector(T_a) % 1.75/1.85 | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),V_xa,T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_x,V_xa,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_scaleR_Ominus__left_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.85 | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(V_a,tc_RealDef_Oreal),V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__minus__le__zero_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_of__real__eq__iff_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 1.75/1.85 | c_RealVector_Oof__real(V_x,T_a) != c_RealVector_Oof__real(V_y,T_a) % 1.75/1.85 | V_x = V_y ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_eq__add__iff2_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oring(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_div__add_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_x,V_z,T_a),c_Divides_Odiv__class_Odiv(V_y,V_z,T_a),T_a) % 1.75/1.85 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,T_a) % 1.75/1.85 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_neg__le__iff__le_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.85 | c_lessequals(V_a,V_b,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_le__imp__neg__le_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__le__mult_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Olordered__ring(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__le__D1_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.85 | c_lessequals(V_a,V_b,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__strict__mono_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__eq__divide_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.85 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__fieldgb_Oinverse__divide_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.85 | ~ class_Int_Onumber__ring(T_a) % 1.75/1.85 | c_HOL_Oinverse__class_Oinverse(V_x,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_zmod__simps_I4_J_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__left__mono__neg_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ 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) % 1.75/1.85 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__left__mono_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ 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) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.85 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_exp__diff_0,axiom, % 1.75/1.85 ( ~ class_SEQ_Obanach(T_a) % 1.75/1.85 | ~ class_RealVector_Oreal__normed__field(T_a) % 1.75/1.85 | c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(V_x,T_a),c_Transcendental_Oexp(V_y,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_norm__not__less__zero_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.85 | ~ 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__1__right_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.75/1.85 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__1__left_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.75/1.85 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__1_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) % 1.75/1.85 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__semiring_Omul__1_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.85 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_x,T_a) = V_x ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__mult__1_0,axiom, % 1.75/1.85 c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) = V_z ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.85 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__semiring_Osemiring__rules_I11_J_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.85 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_dvd__triv__right_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.85 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_dvd__triv__left_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.85 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_dvdI_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Odvd(T_a) % 1.75/1.85 | c_Ring__and__Field_Odvd__class_Odvd(V_b,c_HOL_Otimes__class_Otimes(V_b,V_k,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__prts_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.75/1.85 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ominus__class_Ominus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_arctan_2,axiom, % 1.75/1.85 c_Transcendental_Otan(c_Transcendental_Oarctan(V_y)) = V_y ). % 1.75/1.85 % 1.75/1.85 cnf(cls_frac__less2_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_w,V_z,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 1.75/1.85 | ~ c_lessequals(V_x,V_y,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_power__one__over_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_nonzero__minus__divide__right_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.85 | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.75/1.85 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_neg__less__0__iff__less_1,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_neg__less__0__iff__less_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__ringb_Oadd__mul__solve_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.75/1.85 | ~ class_Int_Onumber__ring(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__ringb_Onoteq__reduce_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.75/1.85 | ~ class_Int_Onumber__ring(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_arctan__minus_0,axiom, % 1.75/1.85 c_Transcendental_Oarctan(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Oarctan(V_x),tc_RealDef_Oreal) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__triangle__ineq3_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__mult__less_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_b,T_a),V_d,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_norm__inverse_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | ~ class_RealVector_Oreal__normed__div__algebra(T_a) % 1.75/1.85 | c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Onorm__class_Onorm(V_a,T_a),tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_diff__add__cancel_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__inverse__eq_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__sqrt__lt__0__iff_0,axiom, % 1.75/1.85 ( c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__sqrt__lt__0__iff_1,axiom, % 1.75/1.85 ( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inf__sup__distrib2_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Odistrib__lattice(T_a) % 1.75/1.85 | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),V_x,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_z,V_x,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inf__sup__distrib1_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Odistrib__lattice(T_a) % 1.75/1.85 | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_add__nonneg__eq__0__iff_2,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__semiring_Omul__c_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.85 | c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__mult__commute_0,axiom, % 1.75/1.85 c_HOL_Otimes__class_Otimes(V_z,V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,V_z,tc_RealDef_Oreal) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.85 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_neg__0__le__iff__le_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.85 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_neg__0__le__iff__le_1,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult_OscaleR__left_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__left_OscaleR_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult_OscaleR__right_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__right_OscaleR_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__scaleR__left_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__algebra(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__scaleR__right_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__algebra(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_nonzero__abs__inverse_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_power__one_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.75/1.85 | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_nonzero__abs__divide_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__positive__imp__positive_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mod__diff__left__eq_0,axiom, % 1.75/1.85 ( ~ class_Divides_Oring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mod__diff__right__eq_0,axiom, % 1.75/1.85 ( ~ class_Divides_Oring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__exp__exp_0,axiom, % 1.75/1.85 ( ~ class_SEQ_Obanach(T_a) % 1.75/1.85 | ~ class_RealVector_Oreal__normed__field(T_a) % 1.75/1.85 | c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(V_x,T_a),c_Transcendental_Oexp(V_y,T_a),T_a) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_add__cancel__21_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != c_HOL_Oplus__class_Oplus(V_y,V_u,T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) = V_u ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__le__prts_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Olordered__ring(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a2,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_b2,T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a1,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_b2,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a2,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_b1,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a1,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_b1,T_a),T_a),T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_b,V_b2,T_a) % 1.75/1.85 | ~ c_lessequals(V_b1,V_b,T_a) % 1.75/1.85 | ~ c_lessequals(V_a,V_a2,T_a) % 1.75/1.85 | ~ c_lessequals(V_a1,V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__sgn__def_2,axiom, % 1.75/1.85 ( c_HOL_Osgn__class_Osgn(V_x,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.75/1.85 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_sgn__if_2,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Osgn__if(T_a) % 1.75/1.85 | c_HOL_Osgn__class_Osgn(V_x,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.75/1.85 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__sqrt__eq__zero__cancel_0,axiom, % 1.75/1.85 ( c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.75/1.85 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_nprt__neg_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.85 | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_x,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_le__zero__iff__pprt__id_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.85 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) = V_a % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_le__zero__iff__pprt__id_1,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.85 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) != V_a % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__less__imp__less_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | ~ 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_less__imp__inverse__less_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__less__imp__less__neg_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_less__imp__inverse__less__neg_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_zero__le__power__abs_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_a,T_a),V_n,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_add__nonneg__nonneg_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__sqrt__le__iff_1,axiom, % 1.75/1.85 ( c_lessequals(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__sqrt__le__iff_0,axiom, % 1.75/1.85 ( c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_lessequals(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_exp__zero_0,axiom, % 1.75/1.85 ( ~ class_SEQ_Obanach(T_a) % 1.75/1.85 | ~ class_RealVector_Oreal__normed__field(T_a) % 1.75/1.85 | c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide_OscaleR_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_add__mono_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_c,V_d,T_a) % 1.75/1.85 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_powr__less__cancel__iff_1,axiom, % 1.75/1.85 ( c_HOL_Oord__class_Oless(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_x,V_b),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,V_b,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_powr__less__cancel__iff_0,axiom, % 1.75/1.85 ( c_HOL_Oord__class_Oless(V_a,V_b,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_x,V_b),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_powr__less__cancel_0,axiom, % 1.75/1.85 ( c_HOL_Oord__class_Oless(V_a,V_b,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_x,V_b),tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_powr__less__mono_0,axiom, % 1.75/1.85 ( c_HOL_Oord__class_Oless(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_x,V_b),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,V_b,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__nonnegative__iff__nonnegative_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__nonnegative__iff__nonnegative_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_sup__eq__if_0,axiom, % 1.75/1.85 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.85 | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.85 | c_Lattices_Oupper__semilattice__class_Osup(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inf__0__imp__0_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.85 | c_Lattices_Olower__semilattice__class_Oinf(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.85 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_powr__le__cancel__iff_1,axiom, % 1.75/1.85 ( c_lessequals(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_x,V_b),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_lessequals(V_a,V_b,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_powr__le__cancel__iff_0,axiom, % 1.75/1.85 ( c_lessequals(V_a,V_b,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_lessequals(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_x,V_b),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__less__0__1__iff_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__less__0__1__iff_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_DERIV__mult__lemma_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__field(T_a) % 1.75/1.85 | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_c,V_d,T_a),T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_b,V_d,T_a),V_h,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_a,V_c,T_a),V_h,T_a),V_d,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mod__mod__trivial_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_div__self_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Odiv(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.75/1.85 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__diff__triangle__ineq_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_c,T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_b,V_d,T_a),T_a),T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_add__strict__increasing_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.75/1.85 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_b,V_c,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_powr__mult_0,axiom, % 1.75/1.85 ( c_Log_Opowr(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),V_a) = c_HOL_Otimes__class_Otimes(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_y,V_a),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_powr__one__gt__zero__iff_1,axiom, % 1.75/1.85 ( c_Log_Opowr(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = V_x % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_powr__one__gt__zero__iff_0,axiom, % 1.75/1.85 ( c_Log_Opowr(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) != V_x % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_arctan__monotone_0,axiom, % 1.75/1.85 ( c_HOL_Oord__class_Oless(c_Transcendental_Oarctan(V_x),c_Transcendental_Oarctan(V_y),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_zero__le__power__iff_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_zero__le__power_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_le__minus__self__iff_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.85 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_le__minus__self__iff_1,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.85 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_minus__le__self__iff_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_minus__le__self__iff_1,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_less__eq__neg__nonpos_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.75/1.85 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_less__eq__neg__nonpos_1,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.75/1.85 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_neg__less__eq__nonneg_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_neg__less__eq__nonneg_1,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_eq__add__iff1_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oring(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_sgn__of__real_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__algebra__1(T_a) % 1.75/1.85 | c_HOL_Osgn__class_Osgn(c_RealVector_Oof__real(V_r,T_a),T_a) = c_RealVector_Oof__real(c_HOL_Osgn__class_Osgn(V_r,tc_RealDef_Oreal),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_dvd__mult__cancel__left_2,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.75/1.85 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.75/1.85 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_dvd__mult__cancel__right_2,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.75/1.85 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.75/1.85 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_one__le__power_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__idempotent_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_eq__add__iff1_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oring(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) = V_d ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_eq__add__iff2_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oring(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a) % 1.75/1.85 | V_c = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_div__mod__equality_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_div__mod__equality2_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_zero__less__abs__iff_1,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) % 1.75/1.85 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_norm__minus__cancel_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.85 | c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__sqrt__minus_0,axiom, % 1.75/1.85 c_NthRoot_Osqrt(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_NthRoot_Osqrt(V_x),tc_RealDef_Oreal) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_le__zero__iff__zero__pprt_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.85 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.85 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_le__zero__iff__zero__pprt_1,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.85 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.85 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_scaleR_OscaleR__right_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_scaleR__left__commute_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__vector(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_scaleR__right_OscaleR_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_not__real__square__gt__zero_1,axiom, % 1.75/1.85 ~ 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) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__ge__prts_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Olordered__ring(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a1,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_b2,T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a2,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_b2,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a1,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_b1,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a2,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_b1,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_b,V_b2,T_a) % 1.75/1.85 | ~ c_lessequals(V_b1,V_b,T_a) % 1.75/1.85 | ~ c_lessequals(V_a,V_a2,T_a) % 1.75/1.85 | ~ c_lessequals(V_a1,V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__semiring_Oadd__c_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_y,V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_comm__monoid__add_Omult__commute_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__le__0__iff_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__le__0__iff_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__le__0__iff_2,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__le__0__iff_3,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.85 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_power__minus_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oring__1(T_a) % 1.75/1.85 | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_n,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),V_n,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__le__imp__le_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | c_lessequals(V_b,V_a,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_le__imp__inverse__le_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__le__imp__le__neg_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | c_lessequals(V_b,V_a,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_le__imp__inverse__le__neg_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__mult__inverse__cancel_0,axiom, % 1.75/1.85 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_x,tc_RealDef_Oreal),V_y,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_x1,tc_RealDef_Oreal),V_u,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_x1,V_y,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_u,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mod__add__eq_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_add__sup__distrib__right_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add__join(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_c,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_add__sup__distrib__left_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add__join(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_b,V_c,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_b,V_c,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_c,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_sup__idem_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.85 | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_x,T_a) = V_x ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_xt1_I10_J_0,axiom, % 1.75/1.85 ( ~ class_Orderings_Oorder(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_order__less__trans_0,axiom, % 1.75/1.85 ( ~ class_Orderings_Opreorder(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_comm__monoid__add_Omult__assoc_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__semiring_Oadd__a_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_add__cancel__21_1,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_d,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_scaleR__conv__of__real_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__triangle__ineq_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_pi__not__less__zero_0,axiom, % 1.75/1.85 ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_less__le__not__le_1,axiom, % 1.75/1.85 ( ~ class_Orderings_Opreorder(T_a) % 1.75/1.85 | ~ c_lessequals(V_y,V_x,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_not__leE_0,axiom, % 1.75/1.85 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.75/1.85 | c_lessequals(V_y,V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_linorder__antisym__conv2_1,axiom, % 1.75/1.85 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.85 | ~ c_lessequals(V_x,V_x,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_linorder__antisym__conv1_1,axiom, % 1.75/1.85 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_x,V_x,T_a) % 1.75/1.85 | c_lessequals(V_x,V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_linorder__not__less_1,axiom, % 1.75/1.85 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.75/1.85 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_linorder__not__less_0,axiom, % 1.75/1.85 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.85 | c_lessequals(V_y,V_x,T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_linorder__not__le_0,axiom, % 1.75/1.85 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.75/1.85 | c_lessequals(V_x,V_y,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_linorder__not__le_1,axiom, % 1.75/1.85 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.85 | ~ c_lessequals(V_x,V_y,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_right__inverse__eq_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.85 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.85 | c_HOL_Oinverse__class_Odivide(V_x,V_x,T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__self_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.85 | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.75/1.85 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__self__if_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.75/1.85 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mod__add__right__eq_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mod__add__left__eq_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_zero__le__divide__iff_3,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_zero__le__divide__iff_2,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_zero__le__divide__iff_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_zero__le__divide__iff_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_add__strict__increasing2_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.75/1.85 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_power__mono_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.75/1.85 | c_lessequals(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_eq__eqI_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.75/1.85 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.75/1.85 | V_x_H = V_y_H ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_eq__eqI_1,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.75/1.85 | c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) % 1.75/1.85 | V_xa = V_y ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__le__1__iff_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Oone__class_Oone(T_a),V_x,T_a) % 1.75/1.85 | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_power__less__zero__eq_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_diff__eq_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.75/1.85 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_power__le__zero__eq_3,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.85 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.85 | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__right__le__imp__le_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.75/1.85 | c_lessequals(V_a,V_b,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.85 | ~ 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__left__le__imp__le_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.75/1.85 | c_lessequals(V_a,V_b,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.85 | ~ 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__le__cancel__left__pos_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ c_lessequals(V_a,V_b,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__le__cancel__left__pos_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.85 | c_lessequals(V_a,V_b,T_a) % 1.75/1.85 | ~ 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) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__le__cancel__left__neg_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ c_lessequals(V_b,V_a,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__le__cancel__left__neg_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.85 | c_lessequals(V_b,V_a,T_a) % 1.75/1.85 | ~ 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) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__mult__le__cancel__iff2_1,axiom, % 1.75/1.85 ( 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) % 1.75/1.85 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__mult__le__cancel__iff2_0,axiom, % 1.75/1.85 ( c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.75/1.85 | ~ 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) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__mult__le__cancel__iff1_1,axiom, % 1.75/1.85 ( 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) % 1.75/1.85 | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__mult__le__cancel__iff1_0,axiom, % 1.75/1.85 ( c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.75/1.85 | ~ 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) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_sup__left__commute_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.85 | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_sup__assoc_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.85 | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inf__sup__aci_I7_J_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Olattice(T_a) % 1.75/1.85 | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inf__sup__aci_I6_J_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Olattice(T_a) % 1.75/1.85 | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_minus__divide__divide_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide_Ominus_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.75/1.85 | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult_Oprod__diff__prod_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.85 | c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__vector_Oscale__scale_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__vector(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inf__absorb2_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.85 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y % 1.75/1.85 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_le__iff__inf_1,axiom, % 1.75/1.85 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.85 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x % 1.75/1.85 | c_lessequals(V_x,V_y,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_le__iff__inf_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.85 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_x % 1.75/1.85 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__sqrt__gt__1__iff_0,axiom, % 1.75/1.85 ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__sqrt__gt__1__iff_1,axiom, % 1.75/1.85 ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_one__le__inverse__iff_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inf__commute_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.85 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inf__sup__aci_I1_J_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Olattice(T_a) % 1.75/1.85 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_combine__common__factor_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Osemiring(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_eq__neg__iff__add__eq__0_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_ab__left__minus_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_right__minus_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_left__minus_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_add__neg__neg_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_sum__squares__le__zero__iff_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.85 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_sum__squares__le__zero__iff_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.85 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__right_Odiff_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.85 | c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),c_HOL_Otimes__class_Otimes(V_xa,V_y,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult_Odiff__right_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.85 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ominus__class_Ominus(V_b,V_b_H,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b_H,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult_Odiff__left_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.85 | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__left_Odiff_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.85 | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_ya,T_a),c_HOL_Otimes__class_Otimes(V_y,V_ya,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_Deriv_Oadd__diff__add_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.75/1.85 | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ominus__class_Ominus(V_c,V_d,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_sgn__one_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__algebra__1(T_a) % 1.75/1.85 | c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__sqrt__mult_0,axiom, % 1.75/1.85 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) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__nonpositive__iff__nonpositive_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__nonpositive__iff__nonpositive_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_dvd__div__mult_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_c,T_a) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),V_a,T_a) % 1.75/1.85 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__sqrt__le__0__iff_0,axiom, % 1.75/1.85 ( c_lessequals(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_lessequals(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__sqrt__le__0__iff_1,axiom, % 1.75/1.85 ( c_lessequals(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__eq__1__iff_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oinverse__class_Oinverse(V_x,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.75/1.85 | V_x = c_HOL_Oone__class_Oone(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__less__1__iff_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_x,T_a) % 1.75/1.85 | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_powr__less__mono2_0,axiom, % 1.75/1.85 ( c_HOL_Oord__class_Oless(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_y,V_a),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_a,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_powr__less__mono2__neg_0,axiom, % 1.75/1.85 ( c_HOL_Oord__class_Oless(c_Log_Opowr(V_y,V_a),c_Log_Opowr(V_x,V_a),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_power__abs_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.85 | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_a,T_a),V_n,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_dvd__power__same_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.85 | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a) % 1.75/1.85 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__diff__less__iff_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_r,T_a),V_x,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__inverse_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__divide_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__mult__inverse__cancel2_0,axiom, % 1.75/1.85 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_y,c_HOL_Oinverse__class_Oinverse(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_u,c_HOL_Oinverse__class_Oinverse(V_x1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_x1,V_y,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_u,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mod__div__trivial_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mod__minus__cong_0,axiom, % 1.75/1.85 ( ~ class_Divides_Oring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(V_a,V_b,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_b,T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a_H,T_a),V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_norm__mult_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__div__algebra(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_nprt__le__zero_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.85 | c_lessequals(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mod__mult__eq_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_power__commutes_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.75/1.85 | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_a,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_powr__zero__eq__one_0,axiom, % 1.75/1.85 c_Log_Opowr(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_div__mult__self1_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(V_c,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a) % 1.75/1.85 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_div__mult__self2_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(V_c,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a) % 1.75/1.85 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__less__eq_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__less__eq_4,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__less__eq_5,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__less__eq_7,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_less__divide__eq_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_less__divide__eq_4,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_less__divide__eq_5,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_less__divide__eq_7,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__le__1__iff_2,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__semiring_Osemiring__rules_I4_J_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(V_m,V_m,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__ge__minus__self_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__ge__self_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.85 | c_lessequals(V_a,c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_less__add__iff1_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_less__add__iff1_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_less__add__iff2_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_less__add__iff2_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_eq__divide__eq_4,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mod__add__cong_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a_H,V_b_H,T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_zero__less__power_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_minus__unique_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.85 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_eq__neg__iff__add__eq__0_1,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.85 | V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_div__power_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),V_n,T_a) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a) % 1.75/1.85 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_not__one__less__zero_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__less__iff_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__ringb_Onoteq__reduce_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.75/1.85 | ~ class_Int_Onumber__ring(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_d,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.75/1.85 | V_c = V_d % 1.75/1.85 | V_a = V_b ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__ringb_Oadd__mul__solve_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.75/1.85 | ~ class_Int_Onumber__ring(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) % 1.75/1.85 | V_y = V_z % 1.75/1.85 | V_w = V_x ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__mult__self_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_nonzero__power__inverse_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.75/1.85 | c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) % 1.75/1.85 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_nonzero__inverse__minus__eq_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.75/1.85 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.75/1.85 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mod__mult__cong_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a_H,V_b_H,T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__sqrt__ge__1__iff_1,axiom, % 1.75/1.85 ( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__sqrt__ge__1__iff_0,axiom, % 1.75/1.85 ( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__sqrt__ge__one_0,axiom, % 1.75/1.85 ( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_add__frac__eq_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) % 1.75/1.85 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.85 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__eq__eq_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) % 1.75/1.85 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_eq__divide__eq_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b % 1.75/1.85 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_zero__le__one_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__power__minus_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.85 | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_n,T_a),T_a) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_powr__powr_0,axiom, % 1.75/1.85 c_Log_Opowr(c_Log_Opowr(V_x,V_a),V_b) = c_Log_Opowr(V_x,c_HOL_Otimes__class_Otimes(V_a,V_b,tc_RealDef_Oreal)) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__semiring_Osemiring__rules_I2_J_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),V_m,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_Bseq__inverse__lemma_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__div__algebra(T_a) % 1.75/1.85 | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_r,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_r,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_lessequals(V_r,c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__sqrt__lt__1__iff_1,axiom, % 1.75/1.85 ( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__sqrt__lt__1__iff_0,axiom, % 1.75/1.85 ( c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mod__by__1_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__mult__pos_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_one__le__inverse__iff_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_lessequals(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__dvd__iff_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.85 | c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) % 1.75/1.85 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__dvd__iff_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.85 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a) % 1.75/1.85 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_dvd__abs__iff_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.85 | c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) % 1.75/1.85 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_dvd__abs__iff_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.85 | c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a) % 1.75/1.85 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_linorder__neq__iff_1,axiom, % 1.75/1.85 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_order__less__le_1,axiom, % 1.75/1.85 ( ~ class_Orderings_Oorder(T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__less__def_1,axiom, % 1.75/1.85 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_order__less__irrefl_0,axiom, % 1.75/1.85 ( ~ class_Orderings_Opreorder(T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_less__le__not__le_2,axiom, % 1.75/1.85 ( ~ class_Orderings_Opreorder(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.75/1.85 | c_lessequals(V_y,V_x,T_a) % 1.75/1.85 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_sup__inf__absorb_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Olattice(T_a) % 1.75/1.85 | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = V_x ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_add__pos__pos_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_not__one__le__zero_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__negative__iff__negative_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__negative__iff__negative_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_negative__imp__inverse__negative_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mod__diff__cong_0,axiom, % 1.75/1.85 ( ~ class_Divides_Oring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a_H,V_b_H,T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_le__iff__diff__le__0_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_le__iff__diff__le__0_1,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.85 | c_lessequals(V_a,V_b,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_add__strict__mono_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_order__le__less_1,axiom, % 1.75/1.85 ( ~ class_Orderings_Oorder(T_a) % 1.75/1.85 | c_lessequals(V_x,V_y,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__less__def_0,axiom, % 1.75/1.85 ( c_lessequals(V_x,V_y,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_order__less__imp__le_0,axiom, % 1.75/1.85 ( ~ class_Orderings_Opreorder(T_a) % 1.75/1.85 | c_lessequals(V_x,V_y,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_le__iff__sup_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.85 | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y % 1.75/1.85 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_le__iff__sup_1,axiom, % 1.75/1.85 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.85 | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) != V_y % 1.75/1.85 | c_lessequals(V_x,V_y,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_sup__absorb1_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.85 | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_x % 1.75/1.85 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_add__cancel__end_1,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_z,T_a),c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = V_y ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_minus__add__cancel_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) = V_b ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__inverse__gt__one_0,axiom, % 1.75/1.85 ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__eq__1__iff_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_one__less__inverse__iff_2,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__1_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.75/1.85 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_zero__le__divide__iff_4,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_zero__le__divide__iff_5,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_nonzero__of__real__inverse_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__div__algebra(T_a) % 1.75/1.85 | c_RealVector_Oof__real(c_HOL_Oinverse__class_Oinverse(V_x,tc_RealDef_Oreal),T_a) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(V_x,T_a),T_a) % 1.75/1.85 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_frac__le_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ c_lessequals(V_w,V_z,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 1.75/1.85 | ~ c_lessequals(V_x,V_y,T_a) % 1.75/1.85 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_cos__minus_0,axiom, % 1.75/1.85 c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal)) = c_Transcendental_Ocos(V_x) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_less__iff__diff__less__0_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_less__iff__diff__less__0_1,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__not__less__zero_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_zero__less__one_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__strict__left__mono_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ 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) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__strict__left__mono__neg_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ 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) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_powr__ge__pzero_0,axiom, % 1.75/1.85 c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Log_Opowr(V_x,V_y),tc_RealDef_Oreal) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__of__pos_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.85 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_positive__imp__inverse__positive_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__positive__iff__positive_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inverse__positive__iff__positive_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mod__mult__right__eq_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mod__mult__left__eq_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_sum__squares__gt__zero__iff_2,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a) % 1.75/1.85 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_sum__squares__gt__zero__iff_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a) % 1.75/1.85 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_scaleR__right_Oadd_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__vector(T_a) % 1.75/1.85 | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_scaleR_Oadd__right_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.85 | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Oplus__class_Oplus(V_b,V_b_H,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),c_RealVector_OscaleR__class_OscaleR(V_a,V_b_H,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inf__eq__neg__sup_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.85 | c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_sup__commute_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.85 | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inf__sup__aci_I5_J_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Olattice(T_a) % 1.75/1.85 | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_neg__inf__eq__sup_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.85 | c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_compl__inf_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.75/1.85 | c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(V_x,T_a),c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__less__0__iff_3,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__less__0__iff_2,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__less__0__iff_1,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | ~ 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_divide__less__0__iff_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.85 | ~ 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__minus__mult__self__le_0,axiom, % 1.75/1.85 c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_u,V_u,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_add__cancel__end_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.75/1.85 | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != V_y % 1.75/1.85 | V_x = c_HOL_Ouminus__class_Ouminus(V_z,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__divide__mult__cancel__right_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__divide__mult__cancel__left_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_sup__left__idem_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Oupper__semilattice(T_a) % 1.75/1.85 | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_inf__sup__aci_I8_J_0,axiom, % 1.75/1.85 ( ~ class_Lattices_Olattice(T_a) % 1.75/1.85 | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_exp__add_0,axiom, % 1.75/1.85 ( ~ class_SEQ_Obanach(T_a) % 1.75/1.85 | ~ class_RealVector_Oreal__normed__field(T_a) % 1.75/1.85 | c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(V_x,T_a),c_Transcendental_Oexp(V_y,T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__sqrt__less__iff_0,axiom, % 1.75/1.85 ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__sqrt__less__iff_1,axiom, % 1.75/1.85 ( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__frac__num_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.85 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.85 | 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) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_real__mult__is__one_1,axiom, % 1.75/1.85 c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_dvd__mult__div__cancel_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),T_a) = V_b % 1.75/1.85 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_dvd__div__mult__self_0,axiom, % 1.75/1.85 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.85 | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_a,T_a) = V_b % 1.75/1.85 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_dist__le__zero__iff_0,axiom, % 1.75/1.85 ( ~ class_RealVector_Ometric__space(T_a) % 1.75/1.85 | V_x = V_y % 1.75/1.85 | ~ c_lessequals(c_RealVector_Odist__class_Odist(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_abs__of__nonpos_0,axiom, % 1.75/1.85 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.85 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.75/1.85 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__strict__left__mono__comm_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__less__cancel__right__disj_5,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__less__cancel__right__disj_4,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__strict__right__mono_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__strict__right__mono__neg_0,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__less__cancel__left__disj_5,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__less__cancel__left__disj_4,axiom, % 1.75/1.85 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.85 | 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) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.85 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.75/1.85 % 1.75/1.85 cnf(cls_mult__strict__left__mono_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.75/1.86 | 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) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult__strict__left__mono__neg_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.86 | 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) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult__less__cancel__left__pos_1,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.86 | 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) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult__less__cancel__left__pos_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.86 | ~ 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) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult__less__cancel__left__neg_1,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.86 | 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) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult__less__cancel__left__neg_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.75/1.86 | ~ 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) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_real__mult__less__mono2_0,axiom, % 1.75/1.86 ( 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) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_real__mult__less__iff1_1,axiom, % 1.75/1.86 ( 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) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_real__mult__less__iff1_0,axiom, % 1.75/1.86 ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) % 1.75/1.86 | ~ 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) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_norm__minus__commute_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.86 | c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_diff__minus__eq__add_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.86 | c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mod__mult__self2_0,axiom, % 1.75/1.86 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.86 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mod__mult__self1_0,axiom, % 1.75/1.86 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.86 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_dvd__mult__cancel__right_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.75/1.86 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) % 1.75/1.86 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_dvd__mult__cancel__left_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.75/1.86 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) % 1.75/1.86 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_le__divide__eq_9,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.75/1.86 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.75/1.86 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_le__divide__eq_3,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.75/1.86 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_le__divide__eq_2,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.86 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_divide__le__eq_9,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.75/1.86 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.86 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.75/1.86 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_divide__le__eq_3,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.75/1.86 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_divide__le__eq_2,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.86 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_id__apply_0,axiom, % 1.75/1.86 c_Fun_Oid(V_x,T_a) = V_x ). % 1.75/1.86 % 1.75/1.86 cnf(cls_add__diff__cancel_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.86 | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_add__divide__distrib_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.86 | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_divide_Oadd_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.75/1.86 | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_ya,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_ya,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_abs__diff__less__iff_2,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_a,V_r,T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_r,T_a),V_x,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_less__1__mult_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Otimes__class_Otimes(V_m,V_n,T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_n,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_m,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_minus__equation__iff_1,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.86 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_equation__minus__iff_1,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.86 | V_a = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_equation__minus__iff_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.86 | V_b = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_double__compl_0,axiom, % 1.75/1.86 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.75/1.86 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = V_x ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_minus__minus_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.86 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_div__by__1_0,axiom, % 1.75/1.86 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.86 | c_Divides_Odiv__class_Odiv(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_minus__diff__eq_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.75/1.86 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_add__less__le__mono_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) % 1.75/1.86 | ~ c_lessequals(V_c,V_d,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_add__le__less__mono_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.75/1.86 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_minus__less__iff_1,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_minus__less__iff_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_less__minus__iff_1,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_less__minus__iff_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_minus__le__iff_1,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.86 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.75/1.86 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_minus__le__iff_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.86 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) % 1.75/1.86 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_le__minus__iff_1,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.86 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.75/1.86 | ~ c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_le__minus__iff_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.86 | c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.75/1.86 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_eq__divide__eq_2,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_scaleR__cancel__right_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__vector(T_a) % 1.75/1.86 | c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a) != c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a) % 1.75/1.86 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_a = V_b ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_scaleR__cancel__right_1,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__vector(T_a) % 1.75/1.86 | 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) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_abs__eq__0_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.86 | c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_neg__equal__zero_1,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.75/1.86 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_minus__zero_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.86 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_inverse__zero__imp__zero_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.75/1.86 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_inverse__nonzero__iff__nonzero_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_neg__0__equal__iff__equal_1,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.86 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_sgn__0__0_1,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.86 | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_sgn0_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Osgn__if(T_a) % 1.75/1.86 | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_sgn__zero_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.86 | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult__eq__0__iff_2,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.75/1.86 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult__eq__0__iff_1,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.75/1.86 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult__zero__right_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 1.75/1.86 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult__le__less__imp__less_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.75/1.86 | 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) % 1.75/1.86 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.75/1.86 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult__less__le__imp__less_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.75/1.86 | 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) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.86 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.75/1.86 | ~ c_lessequals(V_c,V_d,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_power__inject__exp_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.75/1.86 | c_Power_Opower__class_Opower(V_a,V_m,T_a) != c_Power_Opower__class_Opower(V_a,V_n,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 1.75/1.86 | V_m = V_n ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_sgn__neg_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.86 | c_HOL_Osgn__class_Osgn(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_sgn__1__neg_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.86 | c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_minus__mult__commute_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oring(T_a) % 1.75/1.86 | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_abs__triangle__ineq4_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.86 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_sgn__scaleR_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.86 | c_HOL_Osgn__class_Osgn(c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Osgn__class_Osgn(V_r,tc_RealDef_Oreal),c_HOL_Osgn__class_Osgn(V_x,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_real__sqrt__one_0,axiom, % 1.75/1.86 c_NthRoot_Osqrt(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_divide__inverse_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.86 | 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) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_class__fieldgb_Odivide__inverse_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.86 | ~ class_Int_Onumber__ring(T_a) % 1.75/1.86 | 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) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_inf__sup__aci_I4_J_0,axiom, % 1.75/1.86 ( ~ class_Lattices_Olattice(T_a) % 1.75/1.86 | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_inf__left__idem_0,axiom, % 1.75/1.86 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.86 | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_zero__le__iff__nprt__id_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.86 | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a) = V_a % 1.75/1.86 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_zero__le__iff__nprt__id_1,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.86 | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a) != V_a % 1.75/1.86 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mod__mod__cancel_0,axiom, % 1.75/1.86 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.86 | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(V_a,V_c,T_a) % 1.75/1.86 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_b,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_zero__less__divide__1__iff_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_zero__less__divide__1__iff_1,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_tan__pi_0,axiom, % 1.75/1.86 c_Transcendental_Otan(c_Transcendental_Opi) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.86 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.86 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_abs__if__lattice_1,axiom, % 1.75/1.86 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.86 | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.75/1.86 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.75/1.86 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_abs__if_1,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oabs__if(T_a) % 1.75/1.86 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.75/1.86 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_Lim_Ominus__diff__minus_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.75/1.86 | c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_nonzero__power__divide_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.86 | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) % 1.75/1.86 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult__dvd__mono_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.86 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.75/1.86 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_d,T_a) % 1.75/1.86 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_abs__add__abs_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.86 | c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_divide__le__eq_1,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.86 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_divide__le__eq_4,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_le__divide__eq_1,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.86 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_le__divide__eq_4,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_inf__idem_0,axiom, % 1.75/1.86 ( ~ class_Lattices_Olower__semilattice(T_a) % 1.75/1.86 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_x,T_a) = V_x ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_zero__less__abs__iff_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.86 | ~ 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) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_pi__ge__zero_0,axiom, % 1.75/1.86 c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_divide__neg__pos_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.86 | 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) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_divide__pos__neg_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.86 | 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) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_divide__less__0__iff_4,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | 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) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_divide__less__0__iff_5,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | 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) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_add__less__cancel__left_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_add__less__cancel__left_1,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_add__strict__left__mono_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_add__less__cancel__right_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_add__less__cancel__right_1,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_add__strict__right__mono_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_order__eq__refl_0,axiom, % 1.75/1.86 ( ~ class_Orderings_Opreorder(T_a) % 1.75/1.86 | c_lessequals(V_x,V_x,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_order__eq__iff_0,axiom, % 1.75/1.86 ( ~ class_Orderings_Oorder(T_a) % 1.75/1.86 | c_lessequals(V_x,V_x,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_real__le__trans_0,axiom, % 1.75/1.86 ( c_lessequals(V_i,V_k,tc_RealDef_Oreal) % 1.75/1.86 | ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal) % 1.75/1.86 | ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_real__le__refl_0,axiom, % 1.75/1.86 c_lessequals(V_w,V_w,tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_order__le__less__trans_0,axiom, % 1.75/1.86 ( ~ class_Orderings_Opreorder(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.75/1.86 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_order__less__le__trans_0,axiom, % 1.75/1.86 ( ~ class_Orderings_Opreorder(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.75/1.86 | ~ c_lessequals(V_y,V_z,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_le__add__right__mono_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.86 | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) % 1.75/1.86 | ~ c_lessequals(V_c,V_d,T_a) % 1.75/1.86 | ~ c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_order__trans_0,axiom, % 1.75/1.86 ( ~ class_Orderings_Opreorder(T_a) % 1.75/1.86 | c_lessequals(V_x,V_z,T_a) % 1.75/1.86 | ~ c_lessequals(V_y,V_z,T_a) % 1.75/1.86 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_add__nonpos__nonpos_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.75/1.86 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_xt1_I8_J_0,axiom, % 1.75/1.86 ( ~ class_Orderings_Oorder(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.75/1.86 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_xt1_I7_J_0,axiom, % 1.75/1.86 ( ~ class_Orderings_Oorder(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.75/1.86 | ~ c_lessequals(V_z,V_y,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_xt1_I6_J_0,axiom, % 1.75/1.86 ( ~ class_Orderings_Oorder(T_a) % 1.75/1.86 | c_lessequals(V_z,V_x,T_a) % 1.75/1.86 | ~ c_lessequals(V_z,V_y,T_a) % 1.75/1.86 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_inverse__less__1__iff_2,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_x,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mod__mult__self1__is__0_0,axiom, % 1.75/1.86 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.86 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mod__mult__self2__is__0_0,axiom, % 1.75/1.86 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.86 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_exp__minus_0,axiom, % 1.75/1.86 ( ~ class_SEQ_Obanach(T_a) % 1.75/1.86 | ~ class_RealVector_Oreal__normed__field(T_a) % 1.75/1.86 | c_Transcendental_Oexp(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Oexp(V_x,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_division__ring__inverse__diff_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.75/1.86 | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) % 1.75/1.86 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_powr__one__eq__one_0,axiom, % 1.75/1.86 c_Log_Opowr(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_a) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_semiring__div__class_Omod__div__equality_H_0,axiom, % 1.75/1.86 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.86 | c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),T_a) = V_a ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_norm__ratiotest__lemma_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.86 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | ~ 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) % 1.75/1.86 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_sum__squares__eq__zero__iff_2,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.86 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult__less__cancel__left__disj_1,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.86 | ~ 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) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult__less__cancel__left__disj_2,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.86 | ~ 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) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult__less__cancel__right__disj_1,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.75/1.86 | ~ 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) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult__less__cancel__right__disj_2,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.86 | ~ 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) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_abs__diff__less__iff_1,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_a,V_r,T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_real__mult__is__one_2,axiom, % 1.75/1.86 c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_not__real__square__gt__zero_0,axiom, % 1.75/1.86 ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.75/1.86 | 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) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_sup__eq__neg__inf_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.86 | c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_neg__0__less__iff__less_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_neg__0__less__iff__less_1,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_pi__gt__zero_0,axiom, % 1.75/1.86 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_frac__eq__eq_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.86 | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) != c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) % 1.75/1.86 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) = c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_frac__eq__eq_1,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.86 | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) != c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) % 1.75/1.86 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_sgn__mult_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__div__algebra(T_a) % 1.75/1.86 | 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) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_sgn__times_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.86 | 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) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_dist__norm_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Odist__norm(T_a) % 1.75/1.86 | c_RealVector_Odist__class_Odist(V_x,V_y,T_a) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mod__mult__mult1_0,axiom, % 1.75/1.86 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.86 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_c,c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mod__mult__mult2_0,axiom, % 1.75/1.86 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.86 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_less__minus__self__iff_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_less__minus__self__iff_1,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_abs__ge__zero_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.86 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_divide__eq__eq_4,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | 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) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_real__sgn__pos_0,axiom, % 1.75/1.86 ( c_HOL_Osgn__class_Osgn(V_x,tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_sgn__pos_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.86 | c_HOL_Osgn__class_Osgn(V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_sgn__1__pos_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.86 | c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.75/1.86 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_real__sqrt__inverse_0,axiom, % 1.75/1.86 c_NthRoot_Osqrt(c_HOL_Oinverse__class_Oinverse(V_x,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Oinverse(c_NthRoot_Osqrt(V_x),tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_dvd__if__abs__eq_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.86 | c_HOL_Oabs__class_Oabs(V_l,T_a) != c_HOL_Oabs__class_Oabs(V_k,T_a) % 1.75/1.86 | c_Ring__and__Field_Odvd__class_Odvd(V_l,V_k,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_minus__add_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.86 | c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_minus__add__distrib_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.75/1.86 | c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_order__less__asym_H_0,axiom, % 1.75/1.86 ( ~ class_Orderings_Opreorder(T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_order__less__asym_0,axiom, % 1.75/1.86 ( ~ class_Orderings_Opreorder(T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_linorder__linear_0,axiom, % 1.75/1.86 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.86 | c_lessequals(V_y,V_x,T_a) % 1.75/1.86 | c_lessequals(V_x,V_y,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_real__le__linear_0,axiom, % 1.75/1.86 ( c_lessequals(V_w,V_z,tc_RealDef_Oreal) % 1.75/1.86 | c_lessequals(V_z,V_w,tc_RealDef_Oreal) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_not__less__iff__gr__or__eq_1,axiom, % 1.75/1.86 ( ~ class_Orderings_Olinorder(T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_xt1_I9_J_0,axiom, % 1.75/1.86 ( ~ class_Orderings_Oorder(T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult__zero__left_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 1.75/1.86 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_class__semiring_Omul__0_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.86 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult__right_Ozero_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.86 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult_Ozero__right_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.86 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult_Ozero__left_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.86 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult__left_Ozero_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.75/1.86 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.86 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.86 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_dvd__0__right_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.86 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mod__self_0,axiom, % 1.75/1.86 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.86 | c_Divides_Odiv__class_Omod(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mod__by__0_0,axiom, % 1.75/1.86 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.86 | c_Divides_Odiv__class_Omod(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_zero__neq__one_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.75/1.86 | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_nonzero__inverse__inverse__eq_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.75/1.86 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a % 1.75/1.86 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_dvd__0__left_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.86 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_divide__self__if_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | 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) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_neg__equal__zero_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.75/1.86 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != V_a % 1.75/1.86 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_inverse__zero_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_inverse__nonzero__iff__nonzero_1,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_nonzero__inverse__eq__imp__eq_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.75/1.86 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a) % 1.75/1.86 | V_a = V_b % 1.75/1.86 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_nprt__0_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.86 | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_field__power__not__zero_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(T_a) % 1.75/1.86 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_power__eq__0__iff_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.75/1.86 | ~ class_Power_Opower(T_a) % 1.75/1.86 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_neg__equal__0__iff__equal_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.86 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_one__neq__zero_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.75/1.86 | c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mult__eq__0__iff_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.75/1.86 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_no__zero__divisors_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.75/1.86 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_no__zero__divirors__neq0_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.75/1.86 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_div__by__0_0,axiom, % 1.75/1.86 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.86 | c_Divides_Odiv__class_Odiv(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_div__0_0,axiom, % 1.75/1.86 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.86 | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_double__eq__0__iff_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.86 | c_HOL_Oplus__class_Oplus(V_a,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_eq__iff__diff__eq__0_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.75/1.86 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_right__minus__eq_1,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.86 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_diff__0__right_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.86 | c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_diff__self_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.86 | c_HOL_Ominus__class_Ominus(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_class__ringb_Osubr0__iff_1,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.75/1.86 | ~ class_Int_Onumber__ring(T_a) % 1.75/1.86 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_class__ringb_Oadd__r0__iff_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.75/1.86 | ~ class_Int_Onumber__ring(T_a) % 1.75/1.86 | V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) % 1.75/1.86 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_pprt__0_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.86 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_mod__0_0,axiom, % 1.75/1.86 ( ~ class_Divides_Osemiring__div(T_a) % 1.75/1.86 | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_double__eq__0__iff_1,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.75/1.86 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_abs__eq__0_1,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.75/1.86 | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_neg__0__equal__iff__equal_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.86 | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.75/1.86 | c_HOL_Ozero__class_Ozero(T_a) = V_a ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_scaleR_Ozero__right_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.86 | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_scaleR__eq__0__iff_2,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__vector(T_a) % 1.75/1.86 | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_eq__iff__diff__eq__0_1,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.75/1.86 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_a = V_b ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_right__minus__eq_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.75/1.86 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_a = V_b ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_class__ringb_Osubr0__iff_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.75/1.86 | ~ class_Int_Onumber__ring(T_a) % 1.75/1.86 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_x = V_y ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_divide__zero__left_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.86 | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_divide__eq__eq_1,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_divide__zero_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.75/1.86 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.75/1.86 | c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_divide_Ozero_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.75/1.86 | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_sgn__0__0_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.75/1.86 | c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_sgn__zero__iff_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.86 | c_HOL_Osgn__class_Osgn(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_exp__not__eq__zero_0,axiom, % 1.75/1.86 ( ~ class_SEQ_Obanach(T_a) % 1.75/1.86 | ~ class_RealVector_Oreal__normed__field(T_a) % 1.75/1.86 | c_Transcendental_Oexp(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_monoid__add__class_Oadd__0__right_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 1.75/1.86 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_add__0__left_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 1.75/1.86 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_comm__monoid__add_Omult__1__right_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.75/1.86 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_class__ringb_Oadd__r0__iff_1,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.75/1.86 | ~ class_Int_Onumber__ring(T_a) % 1.75/1.86 | V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_class__semiring_Oadd__0_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.86 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = V_x ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_comm__monoid__add_Omult__1_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.75/1.86 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.86 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom, % 1.75/1.86 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.75/1.86 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_norm__sgn_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.86 | 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) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_zero__less__norm__iff_1,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.86 | 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) % 1.75/1.86 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_zero__less__norm__iff_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.86 | ~ 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) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_norm__le__zero__iff_1,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.86 | 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) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_norm__le__zero__iff_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.86 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_scaleR__cancel__left_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__vector(T_a) % 1.75/1.86 | c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a) != c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a) % 1.75/1.86 | V_a = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.75/1.86 | V_x = V_y ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_scaleR__cancel__left_1,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__vector(T_a) % 1.75/1.86 | 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) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_real__sgn__def_0,axiom, % 1.75/1.86 c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_powr__not__zero_0,axiom, % 1.75/1.86 c_Log_Opowr(V_x,V_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_real__mult__right__cancel_0,axiom, % 1.75/1.86 ( c_HOL_Otimes__class_Otimes(V_a,V_c,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_b,V_c,tc_RealDef_Oreal) % 1.75/1.86 | V_c = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.75/1.86 | V_a = V_b ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_real__mult__left__cancel_0,axiom, % 1.75/1.86 ( c_HOL_Otimes__class_Otimes(V_c,V_a,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_c,V_b,tc_RealDef_Oreal) % 1.75/1.86 | V_c = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.75/1.86 | V_a = V_b ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_tan__zero_0,axiom, % 1.75/1.86 c_Transcendental_Otan(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_real__sqrt__eq__0__iff_0,axiom, % 1.75/1.86 ( c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.75/1.86 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_pi__neq__zero_0,axiom, % 1.75/1.86 c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_real__zero__not__eq__one_0,axiom, % 1.75/1.86 c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_real__sqrt__zero_0,axiom, % 1.75/1.86 c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_INVERSE__ZERO_0,axiom, % 1.75/1.86 c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_arctan__zero__zero_0,axiom, % 1.75/1.86 c_Transcendental_Oarctan(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_real__root__zero_0,axiom, % 1.75/1.86 c_NthRoot_Oroot(V_n,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_dist__self_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Ometric__space(T_a) % 1.75/1.86 | c_RealVector_Odist__class_Odist(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_dist__eq__0__iff_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Ometric__space(T_a) % 1.75/1.86 | c_RealVector_Odist__class_Odist(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.75/1.86 | V_x = V_y ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_pprt__def__raw_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Olordered__ab__group__add(t_a) % 1.75/1.86 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(v_x,t_a) = c_Lattices_Oupper__semilattice__class_Osup(v_x,c_HOL_Ozero__class_Ozero(t_a),t_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_nprt__def__raw_0,axiom, % 1.75/1.86 ( ~ class_OrderedGroup_Olordered__ab__group__add(t_a) % 1.75/1.86 | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(v_x,t_a) = c_Lattices_Olower__semilattice__class_Oinf(v_x,c_HOL_Ozero__class_Ozero(t_a),t_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_sin__gt__zero__pi_0,axiom, % 1.75/1.86 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(V_x),tc_RealDef_Oreal) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(V_x,c_Transcendental_Opi,tc_RealDef_Oreal) % 1.75/1.86 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_cos__one__sin__zero_0,axiom, % 1.75/1.86 ( c_Transcendental_Ocos(V_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) % 1.75/1.86 | c_Transcendental_Osin(V_x) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_sin__ge__zero_0,axiom, % 1.75/1.86 ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(V_x),tc_RealDef_Oreal) % 1.75/1.86 | ~ c_lessequals(V_x,c_Transcendental_Opi,tc_RealDef_Oreal) % 1.75/1.86 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_sin__minus_0,axiom, % 1.75/1.86 c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_id__def_0,axiom, % 1.75/1.86 c_Fun_Oid(v_x,t_a) = v_x ). % 1.75/1.86 % 1.75/1.86 cnf(cls_norm__zero_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.86 | c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_scaleR__eq__0__iff_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__vector(T_a) % 1.75/1.86 | c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_a = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_of__real__eq__0__iff_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 1.75/1.86 | c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.75/1.86 | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_of__real__0_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__algebra__1(T_a) % 1.75/1.86 | c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_of__real_Ozero_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.86 | ~ class_RealVector_Oreal__algebra__1(T_a) % 1.75/1.86 | c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_norm__eq__zero_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.86 | c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) % 1.75/1.86 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_scaleR_Ozero__left_0,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.75/1.86 | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_scaleR__eq__0__iff_1,axiom, % 1.75/1.86 ( ~ class_RealVector_Oreal__vector(T_a) % 1.75/1.86 | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_sin__pi_0,axiom, % 1.75/1.86 c_Transcendental_Osin(c_Transcendental_Opi) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_0_0,axiom, % 1.75/1.86 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_sin__zero_0,axiom, % 1.75/1.86 c_Transcendental_Osin(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_CHAINED_0,axiom, % 1.75/1.86 c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_CHAINED_0_01,axiom, % 1.75/1.86 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(cls_conjecture_0,negated_conjecture, % 1.75/1.86 c_Transcendental_Osin(v_x) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom, % 1.75/1.86 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom, % 1.75/1.86 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom, % 1.75/1.86 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,axiom, % 1.75/1.86 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom, % 1.75/1.86 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom, % 1.75/1.86 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom, % 1.75/1.86 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 1.75/1.86 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom, % 1.75/1.86 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Ring__and__Field_Opordered__semiring,axiom, % 1.75/1.86 class_Ring__and__Field_Opordered__semiring(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Ring__and__Field_Oordered__semiring,axiom, % 1.75/1.86 class_Ring__and__Field_Oordered__semiring(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom, % 1.75/1.86 class_Ring__and__Field_Ono__zero__divisors(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom, % 1.75/1.86 class_Ring__and__Field_Oordered__semidom(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom, % 1.75/1.86 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom, % 1.75/1.86 class_OrderedGroup_Oab__semigroup__mult(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom, % 1.75/1.86 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom, % 1.75/1.86 class_OrderedGroup_Oab__semigroup__add(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom, % 1.75/1.86 class_Ring__and__Field_Ocomm__semiring(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom, % 1.75/1.86 class_OrderedGroup_Ocomm__monoid__add(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom, % 1.75/1.86 class_Ring__and__Field_Ozero__neq__one(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Lattices_Oupper__semilattice,axiom, % 1.75/1.86 class_Lattices_Oupper__semilattice(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Lattices_Olower__semilattice,axiom, % 1.75/1.86 class_Lattices_Olower__semilattice(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Ring__and__Field_Omult__mono1,axiom, % 1.75/1.86 class_Ring__and__Field_Omult__mono1(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom, % 1.75/1.86 class_Ring__and__Field_Omult__zero(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Ring__and__Field_Omult__mono,axiom, % 1.75/1.86 class_Ring__and__Field_Omult__mono(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom, % 1.75/1.86 class_OrderedGroup_Omonoid__mult(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Lattices_Odistrib__lattice,axiom, % 1.75/1.86 class_Lattices_Odistrib__lattice(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom, % 1.75/1.86 class_Ring__and__Field_Osemiring(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom, % 1.75/1.86 class_OrderedGroup_Omonoid__add(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Divides_Osemiring__div,axiom, % 1.75/1.86 class_Divides_Osemiring__div(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Ring__and__Field_Odvd,axiom, % 1.75/1.86 class_Ring__and__Field_Odvd(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Orderings_Opreorder,axiom, % 1.75/1.86 class_Orderings_Opreorder(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Orderings_Olinorder,axiom, % 1.75/1.86 class_Orderings_Olinorder(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Lattices_Olattice,axiom, % 1.75/1.86 class_Lattices_Olattice(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Orderings_Oorder,axiom, % 1.75/1.86 class_Orderings_Oorder(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_nat__Power_Opower,axiom, % 1.75/1.86 class_Power_Opower(tc_nat) ). % 1.75/1.86 % 1.75/1.86 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom, % 1.75/1.86 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom, % 1.75/1.87 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict,axiom, % 1.75/1.87 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring,axiom, % 1.75/1.87 class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__meet,axiom, % 1.75/1.87 class_OrderedGroup_Olordered__ab__group__add__meet(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__join,axiom, % 1.75/1.87 class_OrderedGroup_Olordered__ab__group__add__join(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors,axiom, % 1.75/1.87 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict,axiom, % 1.75/1.87 class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add,axiom, % 1.75/1.87 class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,axiom, % 1.75/1.87 class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs,axiom, % 1.75/1.87 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add,axiom, % 1.75/1.87 class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors,axiom, % 1.75/1.87 class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 1.75/1.87 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict,axiom, % 1.75/1.87 class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom, % 1.75/1.87 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,axiom, % 1.75/1.87 class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,axiom, % 1.75/1.87 class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add,axiom, % 1.75/1.87 class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add,axiom, % 1.75/1.87 class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring,axiom, % 1.75/1.87 class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs,axiom, % 1.75/1.87 class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom, % 1.75/1.87 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring,axiom, % 1.75/1.87 class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors,axiom, % 1.75/1.87 class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero,axiom, % 1.75/1.87 class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom,axiom, % 1.75/1.87 class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom, % 1.75/1.87 class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom, % 1.75/1.87 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult,axiom, % 1.75/1.87 class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom, % 1.75/1.87 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult,axiom, % 1.75/1.87 class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add,axiom, % 1.75/1.87 class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring,axiom, % 1.75/1.87 class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field,axiom, % 1.75/1.87 class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring,axiom, % 1.75/1.87 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring,axiom, % 1.75/1.87 class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring,axiom, % 1.75/1.87 class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom, % 1.75/1.87 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add,axiom, % 1.75/1.87 class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one,axiom, % 1.75/1.87 class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,axiom, % 1.75/1.87 class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__div__algebra,axiom, % 1.75/1.87 class_RealVector_Oreal__div__algebra(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1,axiom, % 1.75/1.87 class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Lattices_Oupper__semilattice,axiom, % 1.75/1.87 class_Lattices_Oupper__semilattice(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Lattices_Olower__semilattice,axiom, % 1.75/1.87 class_Lattices_Olower__semilattice(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1,axiom, % 1.75/1.87 class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1,axiom, % 1.75/1.87 class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,axiom, % 1.75/1.87 class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero,axiom, % 1.75/1.87 class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono,axiom, % 1.75/1.87 class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring,axiom, % 1.75/1.87 class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult,axiom, % 1.75/1.87 class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Lattices_Odistrib__lattice,axiom, % 1.75/1.87 class_Lattices_Odistrib__lattice(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring,axiom, % 1.75/1.87 class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__RealVector_Osgn__div__norm,axiom, % 1.75/1.87 class_RealVector_Osgn__div__norm(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__algebra,axiom, % 1.75/1.87 class_RealVector_Oreal__algebra(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__RealVector_Ometric__space,axiom, % 1.75/1.87 class_RealVector_Ometric__space(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add,axiom, % 1.75/1.87 class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__vector,axiom, % 1.75/1.87 class_RealVector_Oreal__vector(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom, % 1.75/1.87 class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if,axiom, % 1.75/1.87 class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1,axiom, % 1.75/1.87 class_Ring__and__Field_Oring__1(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if,axiom, % 1.75/1.87 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__field,axiom, % 1.75/1.87 class_RealVector_Oreal__field(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ofield,axiom, % 1.75/1.87 class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__RealVector_Odist__norm,axiom, % 1.75/1.87 class_RealVector_Odist__norm(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring,axiom, % 1.75/1.87 class_Ring__and__Field_Oring(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oidom,axiom, % 1.75/1.87 class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odvd,axiom, % 1.75/1.87 class_Ring__and__Field_Odvd(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom, % 1.75/1.87 class_Orderings_Opreorder(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom, % 1.75/1.87 class_Orderings_Olinorder(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Lattices_Olattice,axiom, % 1.75/1.87 class_Lattices_Olattice(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Orderings_Oorder,axiom, % 1.75/1.87 class_Orderings_Oorder(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom, % 1.75/1.87 class_Int_Onumber__ring(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__Power_Opower,axiom, % 1.75/1.87 class_Power_Opower(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 cnf(clsarity_RealDef__Oreal__SEQ_Obanach,axiom, % 1.75/1.87 class_SEQ_Obanach(tc_RealDef_Oreal) ). % 1.75/1.87 % 1.75/1.87 %------------------------------------------------------------------------------ % 1.75/1.87 %------------------------------------------- % 1.75/1.87 % Proof found % 1.75/1.87 % SZS status Theorem for theBenchmark % 1.75/1.87 % SZS output start Proof % 1.75/1.87 %ClaNum:1358(EqnAxiom:155) % 1.75/1.87 %VarNum:9372(SingletonVarNum:2818) % 1.75/1.87 %MaxLitNum:6 % 1.75/1.87 %MaxfuncDepth:4 % 1.75/1.87 %SharedTerms:158 % 1.75/1.87 %goalClause: 271 % 1.75/1.87 %singleGoalClaCount:1 % 1.75/1.87 [156]P1(a1) % 1.75/1.87 [157]P6(a2) % 1.75/1.87 [158]P6(a1) % 1.75/1.87 [159]P7(a2) % 1.75/1.87 [160]P8(a2) % 1.75/1.87 [161]P8(a1) % 1.75/1.87 [162]P54(a2) % 1.75/1.87 [163]P54(a1) % 1.75/1.87 [164]P22(a2) % 1.75/1.87 [165]P31(a2) % 1.75/1.87 [166]P57(a2) % 1.75/1.87 [167]P58(a2) % 1.75/1.87 [168]P59(a2) % 1.75/1.87 [169]P59(a1) % 1.75/1.87 [170]P44(a2) % 1.75/1.87 [171]P60(a2) % 1.75/1.87 [172]P32(a2) % 1.75/1.87 [173]P9(a2) % 1.75/1.87 [174]P9(a1) % 1.75/1.87 [175]P45(a2) % 1.75/1.87 [176]P69(a2) % 1.75/1.87 [177]P61(a2) % 1.75/1.87 [178]P10(a2) % 1.75/1.87 [179]P23(a2) % 1.75/1.87 [180]P33(a2) % 1.75/1.87 [181]P33(a1) % 1.75/1.87 [182]P73(a2) % 1.75/1.87 [183]P63(a2) % 1.75/1.87 [184]P63(a1) % 1.75/1.87 [185]P65(a2) % 1.75/1.87 [186]P65(a1) % 1.75/1.87 [187]P62(a2) % 1.75/1.87 [188]P71(a2) % 1.75/1.87 [189]P71(a1) % 1.75/1.87 [190]P46(a2) % 1.75/1.87 [191]P52(a2) % 1.75/1.87 [192]P47(a2) % 1.75/1.87 [193]P11(a2) % 1.75/1.87 [194]P11(a1) % 1.75/1.87 [195]P24(a2) % 1.75/1.87 [196]P34(a2) % 1.75/1.87 [197]P70(a2) % 1.75/1.87 [198]P13(a2) % 1.75/1.87 [199]P13(a1) % 1.75/1.87 [200]P14(a2) % 1.75/1.87 [201]P14(a1) % 1.75/1.87 [202]P39(a2) % 1.75/1.87 [203]P39(a1) % 1.75/1.87 [204]P74(a2) % 1.75/1.87 [205]P74(a1) % 1.75/1.87 [206]P48(a2) % 1.75/1.87 [207]P15(a2) % 1.75/1.87 [208]P15(a1) % 1.75/1.87 [209]P55(a2) % 1.75/1.87 [210]P55(a1) % 1.75/1.87 [211]P75(a2) % 1.75/1.87 [212]P76(a2) % 1.75/1.87 [213]P76(a1) % 1.75/1.87 [214]P77(a2) % 1.75/1.87 [215]P35(a2) % 1.75/1.87 [216]P35(a1) % 1.75/1.87 [217]P36(a2) % 1.75/1.87 [218]P36(a1) % 1.75/1.87 [219]P25(a2) % 1.75/1.87 [220]P37(a2) % 1.75/1.87 [221]P37(a1) % 1.75/1.87 [222]P78(a2) % 1.75/1.87 [223]P16(a2) % 1.75/1.87 [224]P56(a2) % 1.75/1.87 [225]P19(a2) % 1.75/1.87 [226]P19(a1) % 1.75/1.87 [227]P20(a2) % 1.75/1.87 [228]P20(a1) % 1.75/1.87 [229]P50(a2) % 1.75/1.87 [230]P51(a2) % 1.75/1.87 [231]P26(a2) % 1.75/1.87 [232]P53(a2) % 1.75/1.87 [233]P72(a2) % 1.75/1.87 [234]P72(a1) % 1.75/1.87 [235]P21(a2) % 1.75/1.87 [236]P21(a1) % 1.75/1.87 [237]P64(a2) % 1.75/1.87 [238]P83(a2) % 1.75/1.87 [239]P28(a2) % 1.75/1.87 [240]P28(a1) % 1.75/1.87 [241]P43(a2) % 1.75/1.87 [242]P49(a2) % 1.75/1.87 [243]P30(a2) % 1.75/1.87 [244]P79(a2) % 1.75/1.87 [245]P27(a2) % 1.75/1.87 [246]P40(a2) % 1.75/1.87 [247]P40(a1) % 1.75/1.87 [248]P17(a2) % 1.75/1.87 [249]P17(a1) % 1.75/1.87 [250]P80(a2) % 1.75/1.87 [251]P80(a1) % 1.75/1.87 [252]P38(a2) % 1.75/1.87 [253]P38(a1) % 1.75/1.87 [254]P66(a2) % 1.75/1.87 [255]P66(a1) % 1.75/1.87 [256]P81(a2) % 1.75/1.87 [257]P67(a2) % 1.75/1.87 [258]P67(a1) % 1.75/1.87 [259]P41(a2) % 1.75/1.87 [260]P84(a2) % 1.75/1.87 [261]P84(a1) % 1.75/1.87 [262]P82(a2) % 1.75/1.87 [263]P68(a2) % 1.75/1.87 [264]P68(a1) % 1.75/1.87 [265]P42(a2) % 1.75/1.87 [266]P42(a1) % 1.75/1.87 [267]P29(a2) % 1.75/1.87 [268]P29(a1) % 1.75/1.87 [290]P2(a34,a15,a2) % 1.75/1.87 [269]E(f3(a2),f31(a15)) % 1.75/1.87 [270]E(f32(a15),f3(a2)) % 1.75/1.87 [271]E(f32(a34),f3(a2)) % 1.75/1.87 [292]P3(f3(a2),a15,a2) % 1.75/1.87 [293]P2(f3(a2),a15,a2) % 1.75/1.87 [295]P2(f3(a2),a34,a2) % 1.75/1.87 [310]~E(f3(a2),a15) % 1.75/1.87 [311]~E(f4(a2),f3(a2)) % 1.75/1.87 [315]~P2(a15,f3(a2),a2) % 1.75/1.87 [272]E(f16(f3(a2)),f3(a2)) % 1.75/1.87 [273]E(f16(f4(a2)),f4(a2)) % 1.75/1.87 [274]E(f21(f3(a2)),f4(a2)) % 1.75/1.87 [275]E(f31(f3(a2)),f3(a2)) % 1.75/1.87 [276]E(f32(f3(a2)),f3(a2)) % 1.75/1.87 [277]E(f22(f3(a2)),f3(a2)) % 1.75/1.87 [279]E(f5(f3(a2),a2),f3(a2)) % 1.75/1.87 [280]E(f11(f3(a2),a2),f3(a2)) % 1.75/1.87 [316]~P2(f3(a2),f14(f3(a2),f3(a2),a2),a2) % 1.75/1.87 [305]E(f14(f13(f4(a2),a2),f13(f4(a2),a2),a2),f4(a2)) % 1.75/1.87 [291]P3(x2911,x2911,a2) % 1.75/1.87 [314]~P2(x3141,x3141,a2) % 1.75/1.87 [298]P3(f21(x2981),f4(a2),a2) % 1.75/1.87 [299]P3(f32(x2991),f4(a2),a2) % 1.75/1.87 [278]E(f31(f22(x2781)),x2781) % 1.75/1.87 [281]E(f17(x2811,f3(a2)),f4(a2)) % 1.75/1.87 [282]E(f20(x2821,f3(a2)),f3(a2)) % 1.75/1.87 [283]E(f17(f4(a2),x2831),f4(a2)) % 1.75/1.87 [284]E(f21(f13(x2841,a2)),f21(x2841)) % 1.75/1.87 [285]E(f16(f5(x2851,a2)),f5(f16(x2851),a2)) % 1.75/1.87 [286]E(f16(f13(x2861,a2)),f13(f16(x2861),a2)) % 1.75/1.87 [287]E(f31(f13(x2871,a2)),f13(f31(x2871),a2)) % 1.75/1.87 [288]E(f32(f13(x2881,a2)),f13(f32(x2881),a2)) % 1.75/1.87 [289]E(f22(f13(x2891,a2)),f13(f22(x2891),a2)) % 1.75/1.87 [296]E(f14(f4(a2),x2961,a2),x2961) % 1.75/1.87 [312]~E(f21(f22(x3121)),f3(a2)) % 1.75/1.87 [302]P3(f3(a2),f17(x3021,x3022),a2) % 1.75/1.87 [303]P2(f3(a2),f17(x3031,x3032),a2) % 1.75/1.87 [304]E(f14(x3041,x3042,a2),f14(x3042,x3041,a2)) % 1.75/1.87 [313]~E(f17(x3131,x3132),f3(a2)) % 1.75/1.87 [300]E(f5(f17(x3001,x3002),a2),f17(x3001,f13(x3002,a2))) % 1.75/1.87 [307]E(f14(f16(x3071),f16(x3072),a2),f16(f14(x3071,x3072,a2))) % 1.75/1.87 [309]P3(f13(f14(x3091,x3091,a2),a2),f14(x3092,x3092,a2),a2) % 1.75/1.87 [301]E(f17(f17(x3011,x3012),x3013),f17(f17(x3011,x3013),x3012)) % 1.75/1.87 [306]E(f17(x3061,f14(x3062,x3063,a2)),f17(f17(x3061,x3062),x3063)) % 1.75/1.87 [308]E(f14(f14(x3081,x3082,a2),x3083,a2),f14(x3081,f14(x3082,x3083,a2),a2)) % 1.75/1.87 [407]~P23(a33)+E(f18(a34,f3(a33),a33),f25(a34,a33)) % 1.75/1.87 [408]~P23(a33)+E(f19(a34,f3(a33),a33),f26(a34,a33)) % 1.75/1.87 [317]~E(f16(x3171),f3(a2))+E(x3171,f3(a2)) % 1.75/1.87 [318]~E(f16(x3181),f4(a2))+E(x3181,f4(a2)) % 1.75/1.87 [320]~E(f21(x3201),f4(a2))+E(f32(x3201),f3(a2)) % 1.75/1.87 [322]~P84(x3221)+~E(f4(x3221),f3(x3221)) % 1.75/1.87 [433]~P71(x4331)+P3(f3(x4331),f4(x4331),x4331) % 1.75/1.87 [434]~P71(x4341)+P2(f3(x4341),f4(x4341),x4341) % 1.75/1.87 [490]~E(f16(x4901),f3(a2))+~P2(f3(a2),x4901,a2) % 1.75/1.87 [497]~P2(f3(a2),x4971,a2)+E(f11(x4971,a2),f4(a2)) % 1.75/1.87 [515]~P71(x5151)+~P3(f4(x5151),f3(x5151),x5151) % 1.75/1.87 [516]~P71(x5161)+~P2(f4(x5161),f3(x5161),x5161) % 1.75/1.87 [602]~P3(x6021,f3(a2),a2)+P3(f16(x6021),f3(a2),a2) % 1.75/1.87 [603]~P3(x6031,f4(a2),a2)+P3(f16(x6031),f4(a2),a2) % 1.75/1.87 [604]~P2(x6041,f3(a2),a2)+P2(f16(x6041),f3(a2),a2) % 1.75/1.87 [605]~P2(x6051,f4(a2),a2)+P2(f16(x6051),f4(a2),a2) % 1.75/1.87 [607]~P3(f3(a2),x6071,a2)+P3(f3(a2),f16(x6071),a2) % 1.75/1.87 [609]~P3(f4(a2),x6091,a2)+P3(f4(a2),f16(x6091),a2) % 1.75/1.87 [611]~P2(f3(a2),x6111,a2)+P2(f3(a2),f16(x6111),a2) % 1.75/1.87 [612]~P2(f4(a2),x6121,a2)+P2(f4(a2),f16(x6121),a2) % 1.75/1.87 [615]~P3(f16(x6151),f3(a2),a2)+P3(x6151,f3(a2),a2) % 1.75/1.87 [616]~P3(f16(x6161),f4(a2),a2)+P3(x6161,f4(a2),a2) % 1.75/1.87 [617]~P2(f16(x6171),f3(a2),a2)+P2(x6171,f3(a2),a2) % 1.75/1.87 [618]~P2(f16(x6181),f4(a2),a2)+P2(x6181,f4(a2),a2) % 1.75/1.87 [619]~P3(f3(a2),f16(x6191),a2)+P3(f3(a2),x6191,a2) % 1.75/1.87 [620]~P3(f4(a2),f16(x6201),a2)+P3(f4(a2),x6201,a2) % 1.75/1.87 [621]~P2(f3(a2),f16(x6211),a2)+P2(f3(a2),x6211,a2) % 1.75/1.87 [622]~P2(f4(a2),f16(x6221),a2)+P2(f4(a2),x6221,a2) % 1.75/1.87 [628]E(x6281,f3(a2))+P2(f3(a2),f14(x6281,x6281,a2),a2) % 1.75/1.87 [323]~P31(x3231)+E(f23(f3(a2),x3231),f3(x3231)) % 1.75/1.87 [324]~P31(x3241)+E(f23(f4(a2),x3241),f4(x3241)) % 1.75/1.87 [325]~P52(x3251)+E(f24(f3(x3251),x3251),f3(a2)) % 1.75/1.87 [326]~P51(x3261)+E(f24(f4(x3261),x3261),f4(a2)) % 1.75/1.87 [328]~P58(x3281)+E(f5(f3(x3281),x3281),f3(x3281)) % 1.75/1.87 [329]~P57(x3291)+E(f5(f4(x3291),x3291),f4(x3291)) % 1.75/1.87 [330]~P52(x3301)+E(f11(f3(x3301),x3301),f3(x3301)) % 1.75/1.87 [331]~P70(x3311)+E(f11(f3(x3311),x3311),f3(x3311)) % 1.75/1.87 [332]~P78(x3321)+E(f11(f3(x3321),x3321),f3(x3321)) % 1.75/1.87 [333]~P51(x3331)+E(f11(f4(x3331),x3331),f4(x3331)) % 1.75/1.87 [334]~P23(x3341)+E(f25(f3(x3341),x3341),f3(x3341)) % 1.75/1.87 [335]~P23(x3351)+E(f26(f3(x3351),x3351),f3(x3351)) % 1.75/1.87 [336]~P24(x3361)+E(f13(f3(x3361),x3361),f3(x3361)) % 1.75/1.87 [337]~P30(x3371)+E(f13(f3(x3371),x3371),f3(x3371)) % 1.75/1.87 [338]~P34(x3381)+E(f6(f3(x3381),x3381),f3(x3381)) % 1.75/1.87 [339]~P70(x3391)+E(f6(f4(x3391),x3391),f4(x3391)) % 1.75/1.87 [436]~P23(x4361)+E(f12(f3(x4361),f3(x4361),x4361),f3(x4361)) % 1.75/1.87 [444]E(x4441,f3(a2))+E(f14(f5(x4441,a2),x4441,a2),f4(a2)) % 1.75/1.87 [448]P2(f3(a2),x4481,a2)+~E(f17(x4481,f4(a2)),x4481) % 1.75/1.87 [493]~P52(x4931)+P3(f24(f3(x4931),x4931),f3(a2),a2) % 1.75/1.87 [500]~P34(x5001)+P3(f6(f3(x5001),x5001),f3(x5001),x5001) % 1.75/1.87 [503]~P2(f3(a2),x5031,a2)+E(f17(x5031,f4(a2)),x5031) % 1.75/1.87 [623]~P52(x6231)+~P2(f3(a2),f24(f3(x6231),x6231),a2) % 1.75/1.87 [627]~P34(x6271)+~P2(f3(x6271),f6(f3(x6271),x6271),x6271) % 1.75/1.87 [734]~P71(x7341)+P2(f3(x7341),f12(f4(x7341),f4(x7341),x7341),x7341) % 1.75/1.87 [375]~P52(x3751)+E(f24(f11(f3(x3751),x3751),x3751),f3(a2)) % 1.75/1.87 [926]~P69(x9261)+E(f12(f14(f3(x9261),f3(x9261),x9261),f14(f3(x9261),f3(x9261),x9261),x9261),f3(x9261)) % 1.75/1.87 [1302]~P69(x13021)+P3(f12(f14(f3(x13021),f3(x13021),x13021),f14(f3(x13021),f3(x13021),x13021),x13021),f3(x13021),x13021) % 1.75/1.87 [1342]~P69(x13421)+~P2(f3(x13421),f12(f14(f3(x13421),f3(x13421),x13421),f14(f3(x13421),f3(x13421),x13421),x13421),x13421) % 1.75/1.87 [372]~P54(x3722)+P4(x3721,x3721,x3722) % 1.75/1.87 [373]~P39(x3732)+P3(x3731,x3731,x3732) % 1.75/1.87 [374]~P40(x3742)+P3(x3741,x3741,x3742) % 1.75/1.87 [472]~P2(x4722,x4722,x4721)+~P33(x4721) % 1.75/1.87 [473]~P2(x4732,x4732,x4731)+~P39(x4731) % 1.75/1.87 [474]~P2(x4742,x4742,x4741)+~P40(x4741) % 1.75/1.87 [502]P3(x5022,x5021,a2)+P3(x5021,x5022,a2) % 1.75/1.87 [562]~P2(x5621,x5622,a2)+P3(x5621,x5622,a2) % 1.75/1.87 [319]E(x3191,x3192)+~E(f16(x3191),f16(x3192)) % 1.75/1.87 [376]~P18(x3762)+E(f14(x3761,x3761,x3762),x3761) % 1.75/1.87 [377]~P9(x3772)+E(f18(x3771,x3771,x3772),x3771) % 1.75/1.87 [378]~P13(x3782)+E(f19(x3781,x3781,x3782),x3781) % 1.75/1.87 [379]~P32(x3792)+E(f27(x3791,x3791,x3792),f3(a2)) % 1.75/1.87 [381]~P1(x3812)+E(f7(x3811,x3811,x3812),f3(x3812)) % 1.75/1.87 [383]~P24(x3832)+E(f10(x3831,x3831,x3832),f3(x3832)) % 1.75/1.87 [384]~P16(x3842)+E(f10(x3841,x3841,x3842),f3(x3842)) % 1.75/1.87 [386]~P54(x3862)+P4(x3861,f3(x3862),x3862) % 1.75/1.87 [387]~P54(x3871)+P4(f4(x3871),x3872,x3871) % 1.75/1.87 [454]~P34(x4542)+P3(x4541,f6(x4541,x4542),x4542) % 1.75/1.87 [458]~P52(x4582)+P3(f3(a2),f24(x4581,x4582),a2) % 1.75/1.87 [475]~P23(x4751)+P3(f3(x4751),f25(x4752,x4751),x4751) % 1.75/1.87 [476]~P34(x4761)+P3(f3(x4761),f6(x4762,x4761),x4761) % 1.75/1.87 [477]~P23(x4772)+P3(f26(x4771,x4772),f3(x4772),x4772) % 1.75/1.87 [517]~P34(x5172)+P3(f13(x5171,x5172),f6(x5171,x5172),x5172) % 1.75/1.87 [561]~P52(x5611)+~P2(f24(x5612,x5611),f3(a2),a2) % 1.75/1.87 [575]~P34(x5751)+~P2(f6(x5752,x5751),f3(x5751),x5751) % 1.75/1.87 [587]~P3(x5871,x5872,a2)+P3(f16(x5871),f16(x5872),a2) % 1.75/1.87 [588]~P3(x5881,x5882,a2)+P3(f22(x5881),f22(x5882),a2) % 1.75/1.87 [589]~P2(x5891,x5892,a2)+P2(f16(x5891),f16(x5892),a2) % 1.75/1.87 [590]~P2(x5901,x5902,a2)+P2(f22(x5901),f22(x5902),a2) % 1.75/1.87 [624]P3(x6241,x6242,a2)+~P3(f16(x6241),f16(x6242),a2) % 1.75/1.87 [625]P2(x6251,x6252,a2)+~P2(f16(x6251),f16(x6252),a2) % 1.75/1.87 [650]~P32(x6502)+P3(f27(x6501,x6501,x6502),f3(a2),a2) % 1.75/1.87 [662]~P69(x6621)+P3(f3(x6621),f14(x6622,x6622,x6621),x6621) % 1.75/1.87 [848]~P32(x8481)+~P2(f3(a2),f27(x8482,x8482,x8481),a2) % 1.75/1.87 [862]~P69(x8621)+~P2(f14(x8622,x8622,x8621),f3(x8621),x8621) % 1.75/1.87 [357]~P24(x3572)+E(f13(f13(x3571,x3572),x3572),x3571) % 1.75/1.87 [358]~P12(x3582)+E(f13(f13(x3581,x3582),x3582),x3581) % 1.75/1.87 [368]~P70(x3682)+E(f11(f11(x3681,x3682),x3682),f11(x3681,x3682)) % 1.75/1.87 [369]~P52(x3692)+E(f24(f13(x3691,x3692),x3692),f24(x3691,x3692)) % 1.75/1.87 [370]~P34(x3702)+E(f6(f13(x3701,x3702),x3702),f6(x3701,x3702)) % 1.75/1.87 [371]~P34(x3712)+E(f6(f6(x3711,x3712),x3712),f6(x3711,x3712)) % 1.75/1.87 [385]~P45(x3852)+E(f29(f4(a2),x3851,x3852),x3851) % 1.75/1.87 [388]~P1(x3882)+E(f8(x3881,f4(x3882),x3882),x3881) % 1.75/1.87 [389]~P54(x3892)+E(f14(x3891,f4(x3892),x3892),x3891) % 1.75/1.87 [390]~P28(x3902)+E(f14(x3901,f4(x3902),x3902),x3901) % 1.75/1.87 [391]~P1(x3912)+E(f7(x3911,f3(x3912),x3912),x3911) % 1.75/1.87 [392]~P54(x3922)+E(f12(x3921,f3(x3922),x3922),x3921) % 1.75/1.87 [393]~P21(x3932)+E(f12(x3931,f3(x3932),x3932),x3931) % 1.75/1.87 [394]~P29(x3942)+E(f12(x3941,f3(x3942),x3942),x3941) % 1.75/1.87 [395]~P24(x3952)+E(f10(x3951,f3(x3952),x3952),x3951) % 1.75/1.87 [396]~P62(x3962)+E(f9(x3961,f4(x3962),x3962),x3961) % 1.75/1.87 [397]~P8(x3971)+E(f14(f4(x3971),x3972,x3971),x3972) % 1.75/1.87 [399]~P54(x3991)+E(f14(f4(x3991),x3992,x3991),x3992) % 1.75/1.87 [400]~P28(x4001)+E(f14(f4(x4001),x4002,x4001),x4002) % 1.75/1.87 [402]~P54(x4021)+E(f12(f3(x4021),x4022,x4021),x4022) % 1.75/1.87 [403]~P21(x4031)+E(f12(f3(x4031),x4032,x4031),x4032) % 1.75/1.87 [404]~P29(x4041)+E(f12(f3(x4041),x4042,x4041),x4042) % 1.75/1.87 [405]~P45(x4052)+E(f29(f3(a2),x4051,x4052),f3(x4052)) % 1.75/1.87 [406]~P52(x4062)+E(f29(f3(a2),x4061,x4062),f3(x4062)) % 1.75/1.87 [412]~P1(x4122)+E(f8(x4121,f3(x4122),x4122),f3(x4122)) % 1.75/1.87 [413]~P54(x4132)+E(f14(x4131,f3(x4132),x4132),f3(x4132)) % 1.75/1.87 [415]~P48(x4152)+E(f14(x4151,f3(x4152),x4152),f3(x4152)) % 1.75/1.87 [416]~P81(x4162)+E(f14(x4161,f3(x4162),x4162),f3(x4162)) % 1.75/1.87 [417]~P67(x4172)+E(f14(x4171,f3(x4172),x4172),f3(x4172)) % 1.75/1.87 [418]~P1(x4182)+E(f7(x4181,f4(x4182),x4182),f3(x4182)) % 1.75/1.87 [419]~P45(x4192)+E(f29(x4191,f3(x4192),x4192),f3(x4192)) % 1.75/1.87 [420]~P52(x4202)+E(f29(x4201,f3(x4202),x4202),f3(x4202)) % 1.75/1.87 [421]~P1(x4211)+E(f8(f3(x4211),x4212,x4211),f3(x4211)) % 1.75/1.87 [423]~P54(x4231)+E(f14(f3(x4231),x4232,x4231),f3(x4231)) % 1.75/1.87 [425]~P48(x4251)+E(f14(f3(x4251),x4252,x4251),f3(x4251)) % 1.75/1.87 [426]~P81(x4261)+E(f14(f3(x4261),x4262,x4261),f3(x4261)) % 1.75/1.87 [427]~P67(x4271)+E(f14(f3(x4271),x4272,x4271),f3(x4271)) % 1.75/1.87 [428]~P1(x4281)+E(f7(f3(x4281),x4282,x4281),f3(x4281)) % 1.75/1.87 [429]~P28(x4291)+E(f28(f4(x4291),x4292,x4291),f4(x4291)) % 1.75/1.87 [430]~P62(x4301)+E(f9(f3(x4301),x4302,x4301),f3(x4301)) % 1.75/1.87 [431]~P46(x4311)+E(f9(f3(x4311),x4312,x4311),f3(x4311)) % 1.75/1.87 [441]~P31(x4412)+E(f29(x4411,f4(x4412),x4412),f23(x4411,x4412)) % 1.75/1.87 [442]~P62(x4421)+E(f9(f4(x4421),x4422,x4421),f5(x4422,x4421)) % 1.75/1.87 [443]~P24(x4431)+E(f10(f3(x4431),x4432,x4431),f13(x4432,x4431)) % 1.75/1.87 [446]~P51(x4462)+E(f11(f23(x4461,x4462),x4462),f23(f11(x4461,a2),x4462)) % 1.75/1.87 [447]~P31(x4472)+E(f23(f13(x4471,a2),x4472),f13(f23(x4471,x4472),x4472)) % 1.75/1.87 [450]~P52(x4502)+E(f11(f13(x4501,x4502),x4502),f13(f11(x4501,x4502),x4502)) % 1.75/1.87 [451]~P23(x4512)+E(f26(f13(x4511,x4512),x4512),f13(f25(x4511,x4512),x4512)) % 1.75/1.87 [452]~P23(x4522)+E(f25(f13(x4521,x4522),x4522),f13(f26(x4521,x4522),x4522)) % 1.75/1.87 [463]~P24(x4632)+E(f12(x4631,f13(x4631,x4632),x4632),f3(x4632)) % 1.75/1.87 [465]~P24(x4652)+E(f12(f13(x4651,x4652),x4651,x4652),f3(x4652)) % 1.75/1.87 [466]~P16(x4662)+E(f12(f13(x4661,x4662),x4661,x4662),f3(x4662)) % 1.75/1.87 [491]~P70(x4912)+E(f14(x4911,f11(x4911,x4912),x4912),f6(x4911,x4912)) % 1.75/1.87 [492]~P25(x4922)+E(f18(x4921,f13(x4921,x4922),x4922),f6(x4921,x4922)) % 1.75/1.87 [519]~P23(x5192)+E(f12(f25(x5191,x5192),f26(x5191,x5192),x5192),x5191) % 1.75/1.87 [520]~P70(x5202)+E(f14(f11(x5201,x5202),f6(x5201,x5202),x5202),x5201) % 1.75/1.87 [555]~P25(x5552)+E(f10(f25(x5551,x5552),f26(x5551,x5552),x5552),f6(x5551,x5552)) % 1.75/1.87 [578]~P34(x5782)+P3(f13(f6(x5781,x5782),x5782),f3(x5782),x5782) % 1.75/1.87 [631]~P61(x6312)+E(f14(f13(x6311,x6312),f13(x6311,x6312),x6312),f14(x6311,x6311,x6312)) % 1.75/1.87 [632]~P70(x6322)+E(f14(f6(x6321,x6322),f6(x6321,x6322),x6322),f14(x6321,x6321,x6322)) % 1.75/1.87 [681]~P71(x6812)+P2(x6811,f12(x6811,f4(x6812),x6812),x6812) % 1.75/1.87 [851]E(x8511,f3(a2))+~E(f14(x8512,x8512,a2),f13(f14(x8511,x8511,a2),a2)) % 1.75/1.87 [852]E(x8521,f3(a2))+~E(f14(x8521,x8521,a2),f13(f14(x8522,x8522,a2),a2)) % 1.75/1.87 [518]~P10(x5181)+E(f14(f13(f4(x5181),x5181),x5182,x5181),f13(x5182,x5181)) % 1.75/1.87 [593]~P44(x5932)+E(f29(f5(f24(x5931,x5932),a2),x5931,x5932),f11(x5931,x5932)) % 1.75/1.87 [829]~P54(x8292)+E(f12(x8291,x8291,x8292),f14(f12(f4(x8292),f4(x8292),x8292),x8291,x8292)) % 1.75/1.87 [525]~P54(x5253)+E(f14(x5251,x5252,x5253),f14(x5252,x5251,x5253)) % 1.75/1.87 [527]~P54(x5273)+E(f12(x5271,x5272,x5273),f12(x5272,x5271,x5273)) % 1.75/1.87 [528]~P21(x5283)+E(f12(x5281,x5282,x5283),f12(x5282,x5281,x5283)) % 1.75/1.87 [529]~P32(x5293)+E(f27(x5291,x5292,x5293),f27(x5292,x5291,x5293)) % 1.75/1.87 [530]~P9(x5303)+E(f18(x5301,x5302,x5303),f18(x5302,x5301,x5303)) % 1.75/1.87 [531]~P14(x5313)+E(f18(x5311,x5312,x5313),f18(x5312,x5311,x5313)) % 1.75/1.87 [532]~P13(x5323)+E(f19(x5321,x5322,x5323),f19(x5322,x5321,x5323)) % 1.75/1.87 [533]~P14(x5333)+E(f19(x5331,x5332,x5333),f19(x5332,x5331,x5333)) % 1.75/1.87 [633]~P54(x6333)+P4(x6331,f14(x6332,x6331,x6333),x6333) % 1.75/1.87 [634]~P6(x6343)+P4(x6341,f14(x6341,x6342,x6343),x6343) % 1.75/1.87 [635]~P54(x6353)+P4(x6351,f14(x6351,x6352,x6353),x6353) % 1.75/1.87 [636]~P9(x6363)+P3(x6361,f18(x6362,x6361,x6363),x6363) % 1.75/1.87 [637]~P14(x6373)+P3(x6371,f18(x6372,x6371,x6373),x6373) % 1.75/1.87 [638]~P9(x6383)+P3(x6381,f18(x6381,x6382,x6383),x6383) % 1.75/1.87 [639]~P14(x6393)+P3(x6391,f18(x6391,x6392,x6393),x6393) % 1.75/1.87 [640]~P13(x6403)+P3(f19(x6401,x6402,x6403),x6402,x6403) % 1.75/1.87 [641]~P14(x6413)+P3(f19(x6411,x6412,x6413),x6412,x6413) % 1.75/1.87 [642]~P13(x6423)+P3(f19(x6421,x6422,x6423),x6421,x6423) % 1.75/1.87 [643]~P14(x6433)+P3(f19(x6431,x6432,x6433),x6431,x6433) % 1.75/1.87 [649]~P32(x6493)+P3(f3(a2),f27(x6491,x6492,x6493),a2) % 1.75/1.87 [849]~P32(x8491)+~P2(f27(x8492,x8493,x8491),f3(a2),a2) % 1.75/1.87 [552]~P45(x5522)+E(f29(f3(a2),x5521,x5522),f29(f3(a2),x5523,x5522)) % 1.75/1.87 [556]~P45(x5562)+E(f29(x5561,f3(x5562),x5562),f29(x5563,f3(x5562),x5562)) % 1.75/1.87 [567]~P10(x5673)+E(f12(x5671,f13(x5672,x5673),x5673),f10(x5671,x5672,x5673)) % 1.75/1.87 [568]~P24(x5683)+E(f12(x5681,f13(x5682,x5683),x5683),f10(x5681,x5682,x5683)) % 1.75/1.87 [570]~P16(x5703)+E(f12(x5701,f13(x5702,x5703),x5703),f10(x5701,x5702,x5703)) % 1.75/1.87 [571]~P12(x5713)+E(f19(x5711,f13(x5712,x5713),x5713),f10(x5711,x5712,x5713)) % 1.75/1.87 [572]~P62(x5723)+E(f14(x5721,f5(x5722,x5723),x5723),f9(x5721,x5722,x5723)) % 1.75/1.87 [573]~P31(x5732)+E(f14(f23(x5731,x5732),x5733,x5732),f29(x5731,x5733,x5732)) % 1.75/1.87 [574]~P24(x5743)+E(f10(x5741,f13(x5742,x5743),x5743),f12(x5741,x5742,x5743)) % 1.75/1.87 [629]~P75(x6292)+E(f14(f13(x6291,x6292),x6293,x6292),f14(x6291,f13(x6293,x6292),x6292)) % 1.75/1.87 [630]~P75(x6302)+E(f14(f13(x6301,x6302),f13(x6303,x6302),x6302),f14(x6301,x6303,x6302)) % 1.75/1.87 [644]~P14(x6443)+E(f18(x6441,f19(x6441,x6442,x6443),x6443),x6441) % 1.75/1.87 [645]~P14(x6453)+E(f19(x6451,f18(x6451,x6452,x6453),x6453),x6451) % 1.75/1.87 [646]~P24(x6463)+E(f12(f10(x6461,x6462,x6463),x6462,x6463),x6461) % 1.75/1.87 [647]~P24(x6473)+E(f10(f12(x6471,x6472,x6473),x6472,x6473),x6471) % 1.75/1.87 [651]~P1(x6513)+E(f8(f7(x6511,x6512,x6513),x6512,x6513),f3(x6513)) % 1.75/1.87 [652]~P1(x6523)+E(f7(f14(x6521,x6522,x6523),x6522,x6523),f3(x6523)) % 1.75/1.87 [653]~P1(x6533)+E(f7(f14(x6531,x6532,x6533),x6531,x6533),f3(x6533)) % 1.75/1.87 [689]~P41(x6893)+E(f24(f10(x6891,x6892,x6893),x6893),f27(x6891,x6892,x6893)) % 1.75/1.87 [690]~P16(x6903)+E(f13(f10(x6901,x6902,x6903),x6903),f10(x6902,x6901,x6903)) % 1.75/1.87 [723]~P16(x7232)+E(f12(f13(x7231,x7232),f12(x7233,x7231,x7232),x7232),x7233) % 1.75/1.87 [724]~P24(x7242)+E(f12(f13(x7241,x7242),f12(x7241,x7243,x7242),x7242),x7243) % 1.75/1.87 [746]~P45(x7463)+E(f29(f13(x7461,a2),x7462,x7463),f13(f29(x7461,x7462,x7463),x7463)) % 1.75/1.87 [747]~P52(x7473)+E(f29(f13(x7471,a2),x7472,x7473),f13(f29(x7471,x7472,x7473),x7473)) % 1.75/1.87 [748]~P75(x7483)+E(f14(x7481,f13(x7482,x7483),x7483),f13(f14(x7481,x7482,x7483),x7483)) % 1.75/1.87 [749]~P75(x7492)+E(f14(f13(x7491,x7492),x7493,x7492),f13(f14(x7491,x7493,x7492),x7492)) % 1.75/1.87 [750]~P62(x7502)+E(f9(f13(x7501,x7502),x7503,x7502),f13(f9(x7501,x7503,x7502),x7502)) % 1.75/1.87 [751]~P70(x7512)+E(f28(f6(x7511,x7512),x7513,x7512),f6(f28(x7511,x7513,x7512),x7512)) % 1.75/1.87 [753]~P48(x7533)+E(f14(x7531,f13(x7532,x7533),x7533),f13(f14(x7531,x7532,x7533),x7533)) % 1.75/1.87 [754]~P45(x7543)+E(f29(x7541,f13(x7542,x7543),x7543),f13(f29(x7541,x7542,x7543),x7543)) % 1.75/1.87 [755]~P52(x7553)+E(f29(x7551,f13(x7552,x7553),x7553),f13(f29(x7551,x7552,x7553),x7553)) % 1.75/1.87 [757]~P48(x7572)+E(f14(f13(x7571,x7572),x7573,x7572),f13(f14(x7571,x7573,x7572),x7572)) % 1.75/1.87 [758]~P46(x7582)+E(f9(f13(x7581,x7582),x7583,x7582),f13(f9(x7581,x7583,x7582),x7582)) % 1.75/1.87 [785]~P18(x7853)+E(f14(x7851,f14(x7851,x7852,x7853),x7853),f14(x7851,x7852,x7853)) % 1.75/1.87 [786]~P9(x7863)+E(f18(x7861,f18(x7861,x7862,x7863),x7863),f18(x7861,x7862,x7863)) % 1.75/1.87 [787]~P14(x7873)+E(f18(x7871,f18(x7871,x7872,x7873),x7873),f18(x7871,x7872,x7873)) % 1.75/1.87 [788]~P13(x7883)+E(f19(x7881,f19(x7881,x7882,x7883),x7883),f19(x7881,x7882,x7883)) % 1.75/1.87 [789]~P14(x7893)+E(f19(x7891,f19(x7891,x7892,x7893),x7893),f19(x7891,x7892,x7893)) % 1.75/1.87 [790]~P1(x7903)+E(f7(f7(x7901,x7902,x7903),x7902,x7903),f7(x7901,x7902,x7903)) % 1.75/1.87 [791]~P1(x7913)+E(f7(f12(x7911,x7912,x7913),x7912,x7913),f7(x7911,x7912,x7913)) % 1.75/1.87 [792]~P1(x7923)+E(f7(f12(x7921,x7922,x7923),x7921,x7923),f7(x7922,x7921,x7923)) % 1.75/1.87 [793]~P70(x7931)+P3(f3(x7931),f28(f6(x7932,x7931),x7933,x7931),x7931) % 1.75/1.87 [796]~P52(x7963)+E(f29(f11(x7961,a2),f11(x7962,x7963),x7963),f11(f29(x7961,x7962,x7963),x7963)) % 1.75/1.87 [797]~P31(x7972)+E(f14(f23(x7971,x7972),f23(x7973,x7972),x7972),f23(f14(x7971,x7973,a2),x7972)) % 1.75/1.87 [800]~P50(x8002)+E(f14(f24(x8001,x8002),f24(x8003,x8002),a2),f24(f14(x8001,x8003,x8002),x8002)) % 1.75/1.87 [801]~P70(x8012)+E(f14(f11(x8011,x8012),f11(x8013,x8012),x8012),f11(f14(x8011,x8013,x8012),x8012)) % 1.75/1.87 [802]~P50(x8022)+E(f14(f11(x8021,x8022),f11(x8023,x8022),x8022),f11(f14(x8021,x8023,x8022),x8022)) % 1.75/1.87 [803]~P24(x8032)+E(f12(f13(x8031,x8032),f13(x8033,x8032),x8032),f13(f12(x8033,x8031,x8032),x8032)) % 1.75/1.87 [804]~P16(x8042)+E(f12(f13(x8041,x8042),f13(x8043,x8042),x8042),f13(f12(x8041,x8043,x8042),x8042)) % 1.75/1.87 [805]~P23(x8052)+E(f19(f13(x8051,x8052),f13(x8053,x8052),x8052),f13(f18(x8051,x8053,x8052),x8052)) % 1.75/1.87 [806]~P12(x8062)+E(f19(f13(x8061,x8062),f13(x8063,x8062),x8062),f13(f18(x8061,x8063,x8062),x8062)) % 1.75/1.87 [807]~P23(x8072)+E(f18(f13(x8071,x8072),f13(x8073,x8072),x8072),f13(f19(x8071,x8073,x8072),x8072)) % 1.75/1.87 [808]~P12(x8082)+E(f18(f13(x8081,x8082),f13(x8083,x8082),x8082),f13(f19(x8081,x8083,x8082),x8082)) % 1.75/1.87 [809]~P70(x8092)+E(f14(f6(x8091,x8092),f6(x8093,x8092),x8092),f6(f14(x8091,x8093,x8092),x8092)) % 1.75/1.87 [810]~P16(x8102)+E(f10(f13(x8101,x8102),f13(x8103,x8102),x8102),f13(f10(x8101,x8103,x8102),x8102)) % 1.75/1.87 [830]~P52(x8303)+E(f24(f10(x8301,x8302,x8303),x8303),f24(f10(x8302,x8301,x8303),x8303)) % 1.75/1.87 [831]~P34(x8313)+E(f6(f10(x8311,x8312,x8313),x8313),f6(f10(x8312,x8311,x8313),x8313)) % 1.75/1.87 [889]~P61(x8892)+P4(f14(x8891,f3(x8892),x8892),f14(x8893,f3(x8892),x8892),x8892) % 1.75/1.87 [890]~P61(x8901)+P4(f14(f3(x8901),x8902,x8901),f14(f3(x8901),x8903,x8901),x8901) % 1.75/1.87 [927]~P23(x9273)+E(f12(f18(x9271,x9272,x9273),f19(x9271,x9272,x9273),x9273),f12(x9271,x9272,x9273)) % 1.75/1.87 [948]~P28(x9483)+E(f14(f28(x9481,x9482,x9483),x9481,x9483),f14(x9481,f28(x9481,x9482,x9483),x9483)) % 1.75/1.87 [1102]~P79(x11021)+E(f14(f28(f13(f4(x11021),x11021),x11022,x11021),f28(x11023,x11022,x11021),x11021),f28(f13(x11023,x11021),x11022,x11021)) % 1.75/1.87 [1194]~P1(x11943)+E(f12(f14(x11941,f8(x11942,x11941,x11943),x11943),f7(x11942,x11941,x11943),x11943),x11942) % 1.75/1.87 [1195]~P1(x11953)+E(f12(f14(f8(x11951,x11952,x11953),x11952,x11953),f7(x11951,x11952,x11953),x11953),x11951) % 1.75/1.87 [1196]~P48(x11963)+P3(f24(f14(x11961,x11962,x11963),x11963),f14(f24(x11961,x11963),f24(x11962,x11963),a2),a2) % 1.75/1.87 [1198]~P64(x11983)+P3(f6(f14(x11981,x11982,x11983),x11983),f14(f6(x11981,x11983),f6(x11982,x11983),x11983),x11983) % 1.75/1.87 [1199]~P34(x11993)+P3(f6(f12(x11991,x11992,x11993),x11993),f12(f6(x11991,x11993),f6(x11992,x11993),x11993),x11993) % 1.75/1.87 [1200]~P34(x12003)+P3(f6(f10(x12001,x12002,x12003),x12003),f12(f6(x12001,x12003),f6(x12002,x12003),x12003),x12003) % 1.75/1.87 [1201]~P34(x12012)+P3(f10(f6(x12011,x12012),f6(x12013,x12012),x12012),f6(f10(x12011,x12013,x12012),x12012),x12012) % 1.75/1.87 [1278]~P69(x12781)+P3(f3(x12781),f12(f14(x12782,x12782,x12781),f14(x12783,x12783,x12781),x12781),x12781) % 1.75/1.87 [1332]~P69(x13321)+~P2(f12(f14(x13322,x13322,x13321),f14(x13323,x13323,x13321),x13321),f3(x13321),x13321) % 1.75/1.87 [784]~P24(x7842)+E(f12(x7841,f12(f13(x7841,x7842),x7843,x7842),x7842),x7843) % 1.75/1.87 [871]~P23(x8712)+E(f13(f19(f13(x8711,x8712),f13(x8713,x8712),x8712),x8712),f18(x8711,x8713,x8712)) % 1.75/1.87 [872]~P23(x8722)+E(f13(f18(f13(x8721,x8722),f13(x8723,x8722),x8722),x8722),f19(x8721,x8723,x8722)) % 1.75/1.87 [891]~P70(x8912)+E(f6(f28(f13(x8911,x8912),x8913,x8912),x8912),f6(f28(x8911,x8913,x8912),x8912)) % 1.75/1.87 [896]~P1(x8961)+E(f8(f14(f3(x8961),x8962,x8961),f14(f3(x8961),x8963,x8961),x8961),f3(x8961)) % 1.75/1.87 [973]~P34(x9732)+E(f6(f12(f6(x9731,x9732),f6(x9733,x9732),x9732),x9732),f12(f6(x9731,x9732),f6(x9733,x9732),x9732)) % 1.75/1.87 [987]~P54(x9873)+E(f12(x9871,f14(x9872,x9871,x9873),x9873),f14(f12(x9872,f4(x9873),x9873),x9871,x9873)) % 1.75/1.87 [988]~P54(x9883)+E(f12(f14(x9881,x9882,x9883),x9882,x9883),f14(f12(x9881,f4(x9883),x9883),x9882,x9883)) % 1.75/1.87 [1062]~P5(x10623)+E(f7(f13(f7(x10621,x10622,x10623),x10623),x10622,x10623),f7(f13(x10621,x10623),x10622,x10623)) % 1.75/1.87 [1193]~P1(x11933)+E(f12(f7(x11931,x11932,x11933),f14(f8(x11931,x11932,x11933),x11932,x11933),x11933),x11931) % 1.75/1.87 [1310]~P34(x13102)+P3(f6(f10(f6(x13101,x13102),f6(x13103,x13102),x13102),x13102),f6(f10(x13101,x13103,x13102),x13102),x13102) % 1.75/1.87 [925]~P45(x9254)+E(f29(x9251,f29(x9252,x9253,x9254),x9254),f29(f14(x9251,x9252,a2),x9253,x9254)) % 1.75/1.87 [928]~P54(x9284)+E(f14(x9281,f14(x9282,x9283,x9284),x9284),f14(x9282,f14(x9281,x9283,x9284),x9284)) % 1.75/1.87 [929]~P54(x9294)+E(f12(x9291,f12(x9292,x9293,x9294),x9294),f12(x9292,f12(x9291,x9293,x9294),x9294)) % 1.75/1.87 [930]~P16(x9304)+E(f12(x9301,f12(x9302,x9303,x9304),x9304),f12(x9302,f12(x9301,x9303,x9304),x9304)) % 1.75/1.87 [931]~P21(x9314)+E(f12(x9311,f12(x9312,x9313,x9314),x9314),f12(x9312,f12(x9311,x9313,x9314),x9314)) % 1.75/1.87 [933]~P48(x9334)+E(f29(x9331,f14(x9332,x9333,x9334),x9334),f14(x9332,f29(x9331,x9333,x9334),x9334)) % 1.75/1.87 [934]~P43(x9344)+E(f29(x9341,f14(x9342,x9343,x9344),x9344),f14(x9342,f29(x9341,x9343,x9344),x9344)) % 1.75/1.87 [935]~P45(x9354)+E(f29(x9351,f29(x9352,x9353,x9354),x9354),f29(x9352,f29(x9351,x9353,x9354),x9354)) % 1.75/1.87 [937]~P52(x9374)+E(f29(x9371,f29(x9372,x9373,x9374),x9374),f29(x9372,f29(x9371,x9373,x9374),x9374)) % 1.75/1.87 [938]~P9(x9384)+E(f18(x9381,f18(x9382,x9383,x9384),x9384),f18(x9382,f18(x9381,x9383,x9384),x9384)) % 1.75/1.87 [939]~P14(x9394)+E(f18(x9391,f18(x9392,x9393,x9394),x9394),f18(x9392,f18(x9391,x9393,x9394),x9394)) % 1.75/1.87 [940]~P13(x9404)+E(f19(x9401,f19(x9402,x9403,x9404),x9404),f19(x9402,f19(x9401,x9403,x9404),x9404)) % 1.75/1.87 [941]~P14(x9414)+E(f19(x9411,f19(x9412,x9413,x9414),x9414),f19(x9412,f19(x9411,x9413,x9414),x9414)) % 1.75/1.87 [946]~P54(x9463)+E(f14(f14(x9461,x9462,x9463),x9464,x9463),f14(x9461,f14(x9462,x9464,x9463),x9463)) % 1.75/1.87 [947]~P15(x9473)+E(f14(f14(x9471,x9472,x9473),x9474,x9473),f14(x9471,f14(x9472,x9474,x9473),x9473)) % 1.75/1.87 [950]~P48(x9504)+E(f29(x9501,f14(x9502,x9503,x9504),x9504),f14(f29(x9501,x9502,x9504),x9503,x9504)) % 1.75/1.87 [951]~P43(x9514)+E(f29(x9511,f14(x9512,x9513,x9514),x9514),f14(f29(x9511,x9512,x9514),x9513,x9514)) % 1.75/1.87 [952]~P54(x9523)+E(f12(f12(x9521,x9522,x9523),x9524,x9523),f12(x9521,f12(x9522,x9524,x9523),x9523)) % 1.75/1.87 [953]~P21(x9533)+E(f12(f12(x9531,x9532,x9533),x9534,x9533),f12(x9531,f12(x9532,x9534,x9533),x9533)) % 1.75/1.87 [954]~P17(x9543)+E(f12(f12(x9541,x9542,x9543),x9544,x9543),f12(x9541,f12(x9542,x9544,x9543),x9543)) % 1.75/1.87 [955]~P46(x9554)+E(f29(x9551,f9(x9552,x9553,x9554),x9554),f9(f29(x9551,x9552,x9554),x9553,x9554)) % 1.75/1.87 [956]~P9(x9563)+E(f18(f18(x9561,x9562,x9563),x9564,x9563),f18(x9561,f18(x9562,x9564,x9563),x9563)) % 1.75/1.87 [957]~P14(x9573)+E(f18(f18(x9571,x9572,x9573),x9574,x9573),f18(x9571,f18(x9572,x9574,x9573),x9573)) % 1.75/1.87 [958]~P13(x9583)+E(f19(f19(x9581,x9582,x9583),x9584,x9583),f19(x9581,f19(x9582,x9584,x9583),x9583)) % 1.75/1.87 [959]~P14(x9593)+E(f19(f19(x9591,x9592,x9593),x9594,x9593),f19(x9591,f19(x9592,x9594,x9593),x9593)) % 1.75/1.87 [960]~P54(x9603)+E(f14(f14(x9601,x9602,x9603),x9604,x9603),f14(f14(x9601,x9604,x9603),x9602,x9603)) % 1.75/1.87 [961]~P54(x9613)+E(f12(f12(x9611,x9612,x9613),x9614,x9613),f12(f12(x9611,x9614,x9613),x9612,x9613)) % 1.75/1.87 [1109]~P54(x11093)+E(f12(f14(x11091,x11092,x11093),f14(x11091,x11094,x11093),x11093),f14(x11091,f12(x11092,x11094,x11093),x11093)) % 1.75/1.87 [1111]~P48(x11113)+E(f12(f14(x11111,x11112,x11113),f14(x11111,x11114,x11113),x11113),f14(x11111,f12(x11112,x11114,x11113),x11113)) % 1.75/1.87 [1113]~P48(x11133)+E(f10(f14(x11131,x11132,x11133),f14(x11131,x11134,x11133),x11133),f14(x11131,f10(x11132,x11134,x11133),x11133)) % 1.75/1.87 [1114]~P23(x11143)+E(f18(f12(x11141,x11142,x11143),f12(x11141,x11144,x11143),x11143),f12(x11141,f18(x11142,x11144,x11143),x11143)) % 1.75/1.87 [1115]~P27(x11153)+E(f18(f12(x11151,x11152,x11153),f12(x11151,x11154,x11153),x11153),f12(x11151,f18(x11152,x11154,x11153),x11153)) % 1.75/1.87 [1116]~P23(x11163)+E(f19(f12(x11161,x11162,x11163),f12(x11161,x11164,x11163),x11163),f12(x11161,f19(x11162,x11164,x11163),x11163)) % 1.75/1.87 [1117]~P26(x11173)+E(f19(f12(x11171,x11172,x11173),f12(x11171,x11174,x11173),x11173),f12(x11171,f19(x11172,x11174,x11173),x11173)) % 1.75/1.87 [1118]~P45(x11183)+E(f12(f29(x11181,x11182,x11183),f29(x11181,x11184,x11183),x11183),f29(x11181,f12(x11182,x11184,x11183),x11183)) % 1.75/1.87 [1119]~P52(x11193)+E(f12(f29(x11191,x11192,x11193),f29(x11191,x11194,x11193),x11193),f29(x11191,f12(x11192,x11194,x11193),x11193)) % 1.75/1.87 [1120]~P45(x11203)+E(f10(f29(x11201,x11202,x11203),f29(x11201,x11204,x11203),x11203),f29(x11201,f10(x11202,x11204,x11203),x11203)) % 1.75/1.87 [1121]~P52(x11213)+E(f10(f29(x11211,x11212,x11213),f29(x11211,x11214,x11213),x11213),f29(x11211,f10(x11212,x11214,x11213),x11213)) % 1.75/1.87 [1122]~P11(x11223)+E(f19(f18(x11221,x11222,x11223),f18(x11221,x11224,x11223),x11223),f18(x11221,f19(x11222,x11224,x11223),x11223)) % 1.75/1.87 [1123]~P11(x11233)+E(f18(f19(x11231,x11232,x11233),f19(x11231,x11234,x11233),x11233),f19(x11231,f18(x11232,x11234,x11233),x11233)) % 1.75/1.87 [1126]~P48(x11263)+E(f12(f14(x11261,x11262,x11263),f14(x11264,x11262,x11263),x11263),f14(f12(x11261,x11264,x11263),x11262,x11263)) % 1.75/1.87 [1127]~P55(x11273)+E(f12(f14(x11271,x11272,x11273),f14(x11274,x11272,x11273),x11273),f14(f12(x11271,x11274,x11273),x11272,x11273)) % 1.75/1.87 [1129]~P48(x11293)+E(f10(f14(x11291,x11292,x11293),f14(x11294,x11292,x11293),x11293),f14(f10(x11291,x11294,x11293),x11292,x11293)) % 1.75/1.87 [1130]~P23(x11303)+E(f18(f12(x11301,x11302,x11303),f12(x11304,x11302,x11303),x11303),f12(f18(x11301,x11304,x11303),x11302,x11303)) % 1.75/1.87 [1131]~P27(x11313)+E(f18(f12(x11311,x11312,x11313),f12(x11314,x11312,x11313),x11313),f12(f18(x11311,x11314,x11313),x11312,x11313)) % 1.75/1.87 [1132]~P23(x11323)+E(f19(f12(x11321,x11322,x11323),f12(x11324,x11322,x11323),x11323),f12(f19(x11321,x11324,x11323),x11322,x11323)) % 1.75/1.87 [1133]~P26(x11333)+E(f19(f12(x11331,x11332,x11333),f12(x11334,x11332,x11333),x11333),f12(f19(x11331,x11334,x11333),x11332,x11333)) % 1.75/1.87 [1134]~P8(x11343)+E(f14(f28(x11341,x11342,x11343),f28(x11344,x11342,x11343),x11343),f28(f14(x11341,x11344,x11343),x11342,x11343)) % 1.75/1.87 [1135]~P54(x11353)+E(f14(f28(x11351,x11352,x11353),f28(x11354,x11352,x11353),x11353),f28(f14(x11351,x11354,x11353),x11352,x11353)) % 1.75/1.87 [1136]~P62(x11363)+E(f12(f9(x11361,x11362,x11363),f9(x11364,x11362,x11363),x11363),f9(f12(x11361,x11364,x11363),x11362,x11363)) % 1.75/1.87 [1137]~P46(x11373)+E(f12(f9(x11371,x11372,x11373),f9(x11374,x11372,x11373),x11373),f9(f12(x11371,x11374,x11373),x11372,x11373)) % 1.75/1.87 [1138]~P62(x11383)+E(f10(f9(x11381,x11382,x11383),f9(x11384,x11382,x11383),x11383),f9(f10(x11381,x11384,x11383),x11382,x11383)) % 1.75/1.87 [1139]~P46(x11393)+E(f10(f9(x11391,x11392,x11393),f9(x11394,x11392,x11393),x11393),f9(f10(x11391,x11394,x11393),x11392,x11393)) % 1.75/1.87 [1140]~P11(x11403)+E(f19(f18(x11401,x11402,x11403),f18(x11404,x11402,x11403),x11403),f18(f19(x11401,x11404,x11403),x11402,x11403)) % 1.75/1.87 [1141]~P11(x11413)+E(f18(f19(x11411,x11412,x11413),f19(x11414,x11412,x11413),x11413),f19(f18(x11411,x11414,x11413),x11412,x11413)) % 1.75/1.87 [1142]~P1(x11423)+E(f7(f14(x11421,x11422,x11423),f14(x11421,x11424,x11423),x11423),f14(x11421,f7(x11422,x11424,x11423),x11423)) % 1.75/1.87 [1143]~P1(x11433)+E(f7(f14(x11431,x11432,x11433),f14(x11434,x11432,x11433),x11433),f14(f7(x11431,x11434,x11433),x11432,x11433)) % 1.75/1.87 [1144]~P54(x11443)+E(f12(f14(x11441,x11442,x11443),f14(x11444,x11442,x11443),x11443),f14(f12(x11441,x11444,x11443),x11442,x11443)) % 1.75/1.87 [1328]~P14(x13284)+P3(f18(x13281,f19(x13282,x13283,x13284),x13284),f19(f18(x13281,x13282,x13284),f18(x13281,x13283,x13284),x13284),x13284) % 1.75/1.87 [1329]~P14(x13293)+P3(f18(f19(x13291,x13292,x13293),f19(x13291,x13294,x13293),x13293),f19(x13291,f18(x13292,x13294,x13293),x13293),x13293) % 1.75/1.87 [1107]~P1(x11074)+E(f7(f12(x11071,f14(x11072,x11073,x11074),x11074),x11073,x11074),f7(x11071,x11073,x11074)) % 1.75/1.87 [1108]~P1(x11084)+E(f7(f12(x11081,f14(x11082,x11083,x11084),x11084),x11082,x11084),f7(x11081,x11082,x11084)) % 1.75/1.87 [1219]~P1(x12194)+E(f7(f14(x12191,f7(x12192,x12193,x12194),x12194),x12193,x12194),f7(f14(x12191,x12192,x12194),x12193,x12194)) % 1.75/1.87 [1221]~P5(x12214)+E(f7(f10(x12211,f7(x12212,x12213,x12214),x12214),x12213,x12214),f7(f10(x12211,x12212,x12214),x12213,x12214)) % 1.75/1.87 [1224]~P5(x12243)+E(f7(f10(f7(x12241,x12242,x12243),x12244,x12243),x12242,x12243),f7(f10(x12241,x12244,x12243),x12242,x12243)) % 1.75/1.87 [1225]~P1(x12254)+E(f7(f12(x12251,f7(x12252,x12253,x12254),x12254),x12253,x12254),f7(f12(x12251,x12252,x12254),x12253,x12254)) % 1.75/1.87 [1226]~P1(x12263)+E(f7(f14(f7(x12261,x12262,x12263),x12264,x12263),x12262,x12263),f7(f14(x12261,x12264,x12263),x12262,x12263)) % 1.75/1.87 [1227]~P1(x12273)+E(f7(f12(f7(x12271,x12272,x12273),x12274,x12273),x12272,x12273),f7(f12(x12271,x12274,x12273),x12272,x12273)) % 1.75/1.87 [1311]~P1(x13113)+E(f7(f14(f7(x13111,x13112,x13113),f7(x13114,x13112,x13113),x13113),x13112,x13113),f7(f14(x13111,x13114,x13113),x13112,x13113)) % 1.75/1.87 [1312]~P1(x13123)+E(f7(f12(f7(x13121,x13122,x13123),f7(x13124,x13122,x13123),x13123),x13122,x13123),f7(f12(x13121,x13124,x13123),x13122,x13123)) % 1.75/1.87 [1313]~P5(x13133)+E(f7(f10(f7(x13131,x13132,x13133),f7(x13134,x13132,x13133),x13133),x13132,x13133),f7(f10(x13131,x13134,x13133),x13132,x13133)) % 1.75/1.87 [1338]~P1(x13383)+E(f12(f12(f14(x13381,f8(x13382,x13381,x13383),x13383),f7(x13382,x13381,x13383),x13383),x13384,x13383),f12(x13382,x13384,x13383)) % 1.75/1.87 [1339]~P1(x13393)+E(f12(f12(f14(f8(x13391,x13392,x13393),x13392,x13393),f7(x13391,x13392,x13393),x13393),x13394,x13393),f12(x13391,x13394,x13393)) % 1.75/1.87 [1228]~P54(x12283)+E(f14(f14(x12281,x12282,x12283),f14(x12284,x12285,x12283),x12283),f14(f14(x12281,x12284,x12283),f14(x12282,x12285,x12283),x12283)) % 1.75/1.87 [1229]~P54(x12293)+E(f12(f12(x12291,x12292,x12293),f12(x12294,x12295,x12293),x12293),f12(f12(x12291,x12294,x12293),f12(x12292,x12295,x12293),x12293)) % 1.75/1.87 [1230]~P16(x12303)+E(f12(f10(x12301,x12302,x12303),f10(x12304,x12305,x12303),x12303),f10(f12(x12301,x12304,x12303),f12(x12302,x12305,x12303),x12303)) % 1.75/1.87 [1325]~P80(x13253)+E(f12(f14(x13251,x13252,x13253),f12(f14(x13254,x13252,x13253),x13255,x13253),x13253),f12(f14(f12(x13251,x13254,x13253),x13252,x13253),x13255,x13253)) % 1.75/1.87 [1355]~P34(x13553)+P3(f6(f10(f12(x13551,x13552,x13553),f12(x13554,x13555,x13553),x13553),x13553),f12(f6(f10(x13551,x13554,x13553),x13553),f6(f10(x13552,x13555,x13553),x13553),x13553),x13553) % 1.75/1.87 [1356]~P48(x13563)+E(f12(f12(f14(f10(x13561,x13562,x13563),f10(x13564,x13565,x13563),x13563),f14(f10(x13561,x13562,x13563),x13565,x13563),x13563),f14(x13562,f10(x13564,x13565,x13563),x13563),x13563),f10(f14(x13561,x13564,x13563),f14(x13562,x13565,x13563),x13563)) % 1.75/1.87 [1341]~P75(x13413)+E(f12(f14(x13411,x13412,x13413),f12(f14(f10(x13414,x13411,x13413),x13412,x13413),x13415,x13413),x13413),f12(f14(x13414,x13412,x13413),x13415,x13413)) % 1.75/1.87 [1354]~P49(x13544)+E(f12(f14(x13541,f9(f10(x13542,x13543,x13544),x13545,x13544),x13544),f14(f9(f10(x13541,x13546,x13544),x13545,x13544),x13543,x13544),x13544),f9(f10(f14(x13541,x13542,x13544),f14(x13546,x13543,x13544),x13544),x13545,x13544)) % 1.75/1.87 [798]~P3(x7981,a15,a2)+~P3(f3(a2),x7981,a2)+P3(f3(a2),f32(x7981),a2) % 1.75/1.87 [799]~P2(x7991,a15,a2)+~P2(f3(a2),x7991,a2)+P2(f3(a2),f32(x7991),a2) % 1.75/1.87 [844]~P2(x8441,f4(a2),a2)+~P2(f3(a2),x8441,a2)+P2(f4(a2),f5(x8441,a2),a2) % 1.75/1.87 [343]~P58(x3431)+~P62(x3431)+E(f5(f4(x3431),x3431),f4(x3431)) % 1.75/1.87 [344]~P46(x3441)+~P83(x3441)+E(f30(f3(x3441),x3441),f4(x3441)) % 1.75/1.87 [456]E(x4561,f3(a2))+P2(f3(a2),x4561,a2)+E(f11(x4561,a2),f13(f4(a2),a2)) % 1.75/1.87 [508]E(x5081,f4(a2))+~E(f14(x5081,x5081,a2),f4(a2))+E(x5081,f13(f4(a2),a2)) % 1.75/1.87 [691]~P37(x6911)+~P3(f3(x6911),f3(x6911),x6911)+E(f12(f3(x6911),f3(x6911),x6911),f3(x6911)) % 1.75/1.87 [565]E(x5651,x5652)+P2(x5651,x5652,a2)+~P3(x5651,x5652,a2) % 1.75/1.87 [648]E(x6481,x6482)+~P3(x6482,x6481,a2)+~P3(x6481,x6482,a2) % 1.75/1.87 [341]~P30(x3412)+~E(f13(x3411,x3412),x3411)+E(x3411,f3(x3412)) % 1.75/1.87 [345]~P52(x3452)+E(x3451,f3(x3452))+~E(f24(x3451,x3452),f3(a2)) % 1.75/1.87 [346]~P31(x3462)+~E(f23(x3461,x3462),f3(x3462))+E(x3461,f3(a2)) % 1.75/1.87 [347]~P57(x3472)+~E(f5(x3471,x3472),f3(x3472))+E(x3471,f3(x3472)) % 1.75/1.87 [348]~P52(x3482)+~E(f11(x3481,x3482),f3(x3482))+E(x3481,f3(x3482)) % 1.75/1.87 [349]~P70(x3492)+~E(f11(x3491,x3492),f3(x3492))+E(x3491,f3(x3492)) % 1.75/1.87 [350]~P24(x3502)+~E(f13(x3501,x3502),f3(x3502))+E(x3501,f3(x3502)) % 1.75/1.87 [351]~P34(x3512)+~E(f6(x3511,x3512),f3(x3512))+E(x3511,f3(x3512)) % 1.75/1.87 [352]~P24(x3521)+~E(f13(x3522,x3521),f3(x3521))+E(f3(x3521),x3522) % 1.75/1.87 [353]~P46(x3532)+~P83(x3532)+~E(f30(x3531,x3532),f3(x3532)) % 1.75/1.87 [409]~P1(x4092)+E(f8(x4091,x4091,x4092),f4(x4092))+E(x4091,f3(x4092)) % 1.75/1.87 [411]~P62(x4112)+E(f9(x4111,x4111,x4112),f4(x4112))+E(x4111,f3(x4112)) % 1.75/1.87 [432]~P61(x4322)+~P10(x4322)+E(f10(x4321,x4321,x4322),f3(x4322)) % 1.75/1.87 [445]~P53(x4452)+P2(x4451,f3(x4452),x4452)+E(f6(x4451,x4452),x4451) % 1.75/1.87 [467]~P23(x4672)+P3(x4671,f3(x4672),x4672)+~E(f26(x4671,x4672),x4671) % 1.75/1.87 [468]~P23(x4681)+P3(f3(x4681),x4682,x4681)+~E(f25(x4682,x4681),x4682) % 1.75/1.87 [481]~P52(x4812)+E(x4811,f3(x4812))+P2(f3(a2),f24(x4811,x4812),a2) % 1.75/1.87 [482]~P23(x4822)+P3(x4821,f3(x4822),x4822)+~E(f25(x4821,x4822),f3(x4822)) % 1.75/1.87 [483]~P23(x4831)+P3(f3(x4831),x4832,x4831)+~E(f26(x4832,x4831),f3(x4831)) % 1.75/1.87 [484]~P70(x4841)+P2(f3(x4841),x4842,x4841)+~E(f11(x4842,x4841),f4(x4841)) % 1.75/1.87 [489]~P34(x4892)+P2(f3(x4892),f6(x4891,x4892),x4892)+E(x4891,f3(x4892)) % 1.75/1.87 [498]~P23(x4982)+~E(f12(x4981,x4981,x4982),f3(x4982))+E(x4981,f3(x4982)) % 1.75/1.87 [509]~P54(x5092)+~P4(f3(x5092),x5091,x5092)+E(x5091,f3(x5092)) % 1.75/1.87 [539]~P23(x5392)+~P3(x5391,f3(x5392),x5392)+E(f26(x5391,x5392),x5391) % 1.75/1.87 [540]~P23(x5402)+~P3(f3(x5402),x5401,x5402)+E(f25(x5401,x5402),x5401) % 1.75/1.87 [541]~P34(x5412)+~P3(f3(x5412),x5411,x5412)+E(f6(x5411,x5412),x5411) % 1.75/1.87 [542]~P34(x5422)+~P2(f3(x5422),x5421,x5422)+E(f6(x5421,x5422),x5421) % 1.75/1.87 [548]~P23(x5482)+~P3(x5481,f3(x5482),x5482)+E(f25(x5481,x5482),f3(x5482)) % 1.75/1.87 [549]~P70(x5492)+~P2(f3(x5492),x5491,x5492)+E(f11(x5491,x5492),f4(x5492)) % 1.75/1.87 [550]~P23(x5502)+~P3(f3(x5502),x5501,x5502)+E(f26(x5501,x5502),f3(x5502)) % 1.75/1.87 [557]E(f20(x5571,x5572),f3(a2))+P2(x5572,f3(a2),a2)+P2(f3(a2),x5572,a2) % 1.75/1.87 [558]~P34(x5582)+~P3(x5581,f3(x5582),x5582)+E(f6(x5581,x5582),f13(x5581,x5582)) % 1.75/1.87 [559]~P34(x5592)+~P2(x5591,f3(x5592),x5592)+E(f6(x5591,x5592),f13(x5591,x5592)) % 1.75/1.87 [560]~P53(x5602)+~P2(x5601,f3(x5602),x5602)+E(f6(x5601,x5602),f13(x5601,x5602)) % 1.75/1.87 [566]~P52(x5662)+E(x5661,f3(x5662))+~P3(f24(x5661,x5662),f3(a2),a2) % 1.75/1.87 [585]~P34(x5852)+~P3(f6(x5851,x5852),f3(x5852),x5852)+E(x5851,f3(x5852)) % 1.75/1.87 [692]~P23(x6922)+~P3(x6921,f3(x6922),x6922)+P3(x6921,f13(x6921,x6922),x6922) % 1.75/1.87 [693]~P30(x6932)+~P3(x6931,f3(x6932),x6932)+P3(x6931,f13(x6931,x6932),x6932) % 1.75/1.87 [694]~P70(x6942)+~P2(x6941,f3(x6942),x6942)+P2(x6941,f13(x6941,x6942),x6942) % 1.75/1.87 [695]~P23(x6952)+~P3(f3(x6952),x6951,x6952)+P3(f13(x6951,x6952),x6951,x6952) % 1.75/1.87 [696]~P30(x6962)+~P3(f3(x6962),x6961,x6962)+P3(f13(x6961,x6962),x6961,x6962) % 1.75/1.87 [708]~P22(x7081)+~P3(x7082,f3(x7081),x7081)+P3(f3(x7081),f13(x7082,x7081),x7081) % 1.75/1.87 [709]~P22(x7091)+~P2(x7092,f3(x7091),x7091)+P2(f3(x7091),f13(x7092,x7091),x7091) % 1.75/1.87 [710]~P60(x7101)+~P2(f3(x7101),x7102,x7101)+P2(f3(x7101),f5(x7102,x7101),x7101) % 1.75/1.87 [711]~P70(x7111)+~P2(f3(x7111),x7112,x7111)+P2(f3(x7111),f11(x7112,x7111),x7111) % 1.75/1.87 [712]~P60(x7122)+~P2(x7121,f3(x7122),x7122)+P2(f5(x7121,x7122),f3(x7122),x7122) % 1.75/1.87 [713]~P70(x7132)+~P2(x7131,f3(x7132),x7132)+P2(f11(x7131,x7132),f3(x7132),x7132) % 1.75/1.87 [714]~P22(x7142)+~P3(f3(x7142),x7141,x7142)+P3(f13(x7141,x7142),f3(x7142),x7142) % 1.75/1.87 [715]~P22(x7152)+~P2(f3(x7152),x7151,x7152)+P2(f13(x7151,x7152),f3(x7152),x7152) % 1.75/1.87 [718]~P23(x7182)+~P3(x7181,f13(x7181,x7182),x7182)+P3(x7181,f3(x7182),x7182) % 1.75/1.87 [719]~P30(x7192)+~P3(x7191,f13(x7191,x7192),x7192)+P3(x7191,f3(x7192),x7192) % 1.75/1.87 [720]~P70(x7202)+~P2(x7201,f13(x7201,x7202),x7202)+P2(x7201,f3(x7202),x7202) % 1.75/1.87 [721]~P23(x7211)+~P3(f13(x7212,x7211),x7212,x7211)+P3(f3(x7211),x7212,x7211) % 1.75/1.87 [722]~P30(x7221)+~P3(f13(x7222,x7221),x7222,x7221)+P3(f3(x7221),x7222,x7221) % 1.75/1.87 [738]~P22(x7382)+~P3(f3(x7382),f13(x7381,x7382),x7382)+P3(x7381,f3(x7382),x7382) % 1.75/1.87 [739]~P22(x7392)+~P2(f3(x7392),f13(x7391,x7392),x7392)+P2(x7391,f3(x7392),x7392) % 1.75/1.87 [740]~P70(x7402)+~P2(f11(x7401,x7402),f3(x7402),x7402)+P2(x7401,f3(x7402),x7402) % 1.75/1.87 [741]~P70(x7411)+~P2(f3(x7411),f11(x7412,x7411),x7411)+P2(f3(x7411),x7412,x7411) % 1.75/1.87 [742]~P22(x7421)+~P3(f13(x7422,x7421),f3(x7421),x7421)+P3(f3(x7421),x7422,x7421) % 1.75/1.87 [743]~P22(x7431)+~P2(f13(x7432,x7431),f3(x7431),x7431)+P2(f3(x7431),x7432,x7431) % 1.75/1.87 [845]~P3(f3(a2),x8452,a2)+~P3(f4(a2),x8451,a2)+P3(f4(a2),f17(x8451,x8452),a2) % 1.75/1.87 [853]~P23(x8531)+~P3(f3(x8531),x8532,x8531)+P3(f3(x8531),f12(x8532,x8532,x8531),x8531) % 1.75/1.87 [857]~P23(x8571)+~P2(f3(x8571),x8572,x8571)+P2(f3(x8571),f12(x8572,x8572,x8571),x8571) % 1.75/1.87 [859]~P23(x8592)+~P3(x8591,f3(x8592),x8592)+P3(f12(x8591,x8591,x8592),f3(x8592),x8592) % 1.75/1.87 [860]~P23(x8602)+~P2(x8601,f3(x8602),x8602)+P2(f12(x8601,x8601,x8602),f3(x8602),x8602) % 1.75/1.87 [861]~P70(x8612)+~P2(x8611,f3(x8612),x8612)+P2(f12(x8611,x8611,x8612),f3(x8612),x8612) % 1.75/1.87 [962]~P23(x9622)+~P3(f12(x9621,x9621,x9622),f3(x9622),x9622)+P3(x9621,f3(x9622),x9622) % 1.75/1.87 [963]~P23(x9632)+~P2(f12(x9631,x9631,x9632),f3(x9632),x9632)+P2(x9631,f3(x9632),x9632) % 1.75/1.87 [964]~P70(x9642)+~P2(f12(x9641,x9641,x9642),f3(x9642),x9642)+P2(x9641,f3(x9642),x9642) % 1.75/1.87 [966]~P23(x9661)+~P3(f3(x9661),f12(x9662,x9662,x9661),x9661)+P3(f3(x9661),x9662,x9661) % 1.75/1.87 [967]~P23(x9671)+~P2(f3(x9671),f12(x9672,x9672,x9671),x9671)+P2(f3(x9671),x9672,x9671) % 1.75/1.87 [972]~P2(f3(a2),x9722,a2)+~P2(f3(a2),x9721,a2)+P2(f3(a2),f14(x9721,x9722,a2),a2) % 1.75/1.87 [361]~P57(x3612)+E(x3611,f3(x3612))+E(f5(f5(x3611,x3612),x3612),x3611) % 1.75/1.87 [365]~P52(x3652)+E(x3651,f3(x3652))+E(f24(f11(x3651,x3652),x3652),f4(a2)) % 1.75/1.87 [366]~P57(x3662)+~P58(x3662)+E(f5(f5(x3661,x3662),x3662),x3661) % 1.75/1.87 [435]~P61(x4352)+~P10(x4352)+E(f12(x4351,f3(x4352),x4352),x4351) % 1.75/1.87 [440]~P58(x4402)+~P62(x4402)+E(f9(x4401,f3(x4402),x4402),f3(x4402)) % 1.75/1.87 [455]~P47(x4552)+E(x4551,f3(a2))+E(f23(f5(x4551,a2),x4552),f5(f23(x4551,x4552),x4552)) % 1.75/1.87 [460]~P50(x4602)+E(x4601,f3(x4602))+E(f24(f5(x4601,x4602),x4602),f5(f24(x4601,x4602),a2)) % 1.75/1.87 [461]~P58(x4612)+~P47(x4612)+E(f23(f5(x4611,a2),x4612),f5(f23(x4611,x4612),x4612)) % 1.75/1.87 [469]~P57(x4692)+E(x4691,f3(x4692))+E(f5(f13(x4691,x4692),x4692),f13(f5(x4691,x4692),x4692)) % 1.75/1.87 [470]~P60(x4702)+E(x4701,f3(x4702))+E(f6(f5(x4701,x4702),x4702),f5(f6(x4701,x4702),x4702)) % 1.75/1.87 [471]~P58(x4712)+~P50(x4712)+E(f24(f5(x4711,x4712),x4712),f5(f24(x4711,x4712),a2)) % 1.75/1.87 [478]~P57(x4782)+~P58(x4782)+E(f5(f13(x4781,x4782),x4782),f13(f5(x4781,x4782),x4782)) % 1.75/1.87 [479]~P58(x4792)+~P60(x4792)+E(f6(f5(x4791,x4792),x4792),f5(f6(x4791,x4792),x4792)) % 1.75/1.87 [480]~P46(x4802)+~P83(x4802)+E(f30(f13(x4801,x4802),x4802),f5(f30(x4801,x4802),x4802)) % 1.75/1.87 [485]~P57(x4852)+E(x4851,f3(x4852))+E(f14(x4851,f5(x4851,x4852),x4852),f4(x4852)) % 1.75/1.87 [486]~P57(x4862)+E(x4861,f3(x4862))+E(f14(f5(x4861,x4862),x4861,x4862),f4(x4862)) % 1.75/1.87 [487]~P62(x4872)+E(x4871,f3(x4872))+E(f14(f5(x4871,x4872),x4871,x4872),f4(x4872)) % 1.75/1.87 [551]~P70(x5512)+P2(x5511,f3(x5512),x5512)+~E(f11(x5511,x5512),f13(f4(x5512),x5512)) % 1.75/1.87 [563]~P70(x5632)+~P2(x5631,f3(x5632),x5632)+E(f11(x5631,x5632),f13(f4(x5632),x5632)) % 1.75/1.87 [576]~P23(x5762)+E(x5761,f3(x5762))+~E(f18(x5761,f13(x5761,x5762),x5762),f3(x5762)) % 1.75/1.87 [577]~P23(x5772)+E(x5771,f3(x5772))+~E(f19(x5771,f13(x5771,x5772),x5772),f3(x5772)) % 1.75/1.87 [717]~P58(x7171)+~P62(x7171)+E(f9(f14(f3(x7171),x7172,x7171),x7172,x7171),f3(x7171)) % 1.75/1.87 [534]P3(x5342,x5341,x5343)+~P33(x5343)+P3(x5341,x5342,x5343) % 1.75/1.87 [537]P2(x5372,x5371,x5373)+~P33(x5373)+P3(x5371,x5372,x5373) % 1.75/1.87 [579]~P39(x5793)+~P2(x5791,x5792,x5793)+P3(x5791,x5792,x5793) % 1.75/1.87 [580]~P40(x5803)+~P2(x5801,x5802,x5803)+P3(x5801,x5802,x5803) % 1.75/1.87 [669]~P2(x6693,x6692,x6691)+~P33(x6691)+~P3(x6692,x6693,x6691) % 1.75/1.87 [671]~P2(x6713,x6712,x6711)+~P33(x6711)+~P2(x6712,x6713,x6711) % 1.75/1.87 [672]~P2(x6723,x6722,x6721)+~P39(x6721)+~P2(x6722,x6723,x6721) % 1.75/1.87 [673]~P2(x6733,x6732,x6731)+~P40(x6731)+~P3(x6732,x6733,x6731) % 1.75/1.87 [675]~P2(x6753,x6752,x6751)+~P40(x6751)+~P2(x6752,x6753,x6751) % 1.75/1.87 [783]~P3(x7831,x7833,a2)+P3(x7831,x7832,a2)+~P3(x7833,x7832,a2) % 1.75/1.87 [362]~P31(x3623)+E(x3621,x3622)+~E(f23(x3621,x3623),f23(x3622,x3623)) % 1.75/1.87 [363]~P24(x3633)+E(x3631,x3632)+~E(f13(x3631,x3633),f13(x3632,x3633)) % 1.75/1.87 [364]~P12(x3643)+E(x3641,x3642)+~E(f13(x3641,x3643),f13(x3642,x3643)) % 1.75/1.87 [488]~P32(x4883)+E(x4881,x4882)+~E(f27(x4881,x4882,x4883),f3(a2)) % 1.75/1.87 [494]~P24(x4943)+E(x4941,x4942)+~E(f10(x4941,x4942,x4943),f3(x4943)) % 1.75/1.87 [495]~P16(x4953)+E(x4951,x4952)+~E(f10(x4951,x4952,x4953),f3(x4953)) % 1.75/1.87 [499]~P82(x4992)+~E(f28(x4991,x4993,x4992),f3(x4992))+E(x4991,f3(x4992)) % 1.75/1.87 [501]~P70(x5013)+P4(x5011,x5012,x5013)+~E(f6(x5011,x5013),f6(x5012,x5013)) % 1.75/1.87 [521]~P24(x5213)+~E(f12(x5211,x5212,x5213),f3(x5213))+E(x5211,f13(x5212,x5213)) % 1.75/1.87 [522]~P57(x5222)+~E(f14(x5221,x5223,x5222),f4(x5222))+E(f5(x5221,x5222),x5223) % 1.75/1.87 [523]~P24(x5232)+~E(f12(x5231,x5233,x5232),f3(x5232))+E(f13(x5231,x5232),x5233) % 1.75/1.87 [581]~P9(x5813)+~P3(x5811,x5812,x5813)+E(f18(x5811,x5812,x5813),x5812) % 1.75/1.87 [582]~P9(x5823)+~P3(x5822,x5821,x5823)+E(f18(x5821,x5822,x5823),x5821) % 1.75/1.87 [583]~P13(x5833)+~P3(x5832,x5831,x5833)+E(f19(x5831,x5832,x5833),x5832) % 1.75/1.87 [584]~P13(x5843)+~P3(x5841,x5842,x5843)+E(f19(x5841,x5842,x5843),x5841) % 1.75/1.87 [591]~P9(x5913)+P3(x5911,x5912,x5913)+~E(f18(x5911,x5912,x5913),x5912) % 1.75/1.87 [592]~P13(x5923)+P3(x5921,x5922,x5923)+~E(f19(x5921,x5922,x5923),x5921) % 1.75/1.87 [613]~P1(x6133)+~P4(x6132,x6131,x6133)+E(f7(x6131,x6132,x6133),f3(x6133)) % 1.75/1.87 [614]~P1(x6143)+P4(x6141,x6142,x6143)+~E(f7(x6142,x6141,x6143),f3(x6143)) % 1.75/1.87 [654]E(x6541,x6542)+~E(f14(x6543,x6541,a2),f14(x6543,x6542,a2))+E(x6543,f3(a2)) % 1.75/1.87 [655]E(x6551,x6552)+~E(f14(x6551,x6553,a2),f14(x6552,x6553,a2))+E(x6553,f3(a2)) % 1.75/1.87 [656]~P32(x6563)+E(x6561,x6562)+P2(f3(a2),f27(x6561,x6562,x6563),a2) % 1.75/1.87 [658]~P56(x6583)+~P4(x6581,x6582,x6583)+P4(x6581,f13(x6582,x6583),x6583) % 1.75/1.87 [659]~P70(x6593)+~P4(x6591,x6592,x6593)+P4(x6591,f6(x6592,x6593),x6593) % 1.75/1.87 [660]~P56(x6602)+~P4(x6601,x6603,x6602)+P4(f13(x6601,x6602),x6603,x6602) % 1.75/1.87 [661]~P70(x6612)+~P4(x6611,x6613,x6612)+P4(f6(x6611,x6612),x6613,x6612) % 1.75/1.87 [701]~P70(x7013)+P4(x7011,x7012,x7013)+~P4(x7011,f6(x7012,x7013),x7013) % 1.75/1.87 [702]~P56(x7023)+P4(x7021,x7022,x7023)+~P4(x7021,f13(x7022,x7023),x7023) % 1.75/1.87 [703]~P70(x7033)+P4(x7031,x7032,x7033)+~P4(f6(x7031,x7033),x7032,x7033) % 1.75/1.87 [704]~P56(x7043)+P4(x7041,x7042,x7043)+~P4(f13(x7041,x7043),x7042,x7043) % 1.75/1.87 [705]~P34(x7053)+P3(x7051,x7052,x7053)+~P3(f6(x7051,x7053),x7052,x7053) % 1.75/1.87 [706]~P70(x7063)+P2(x7061,x7062,x7063)+~P2(f6(x7061,x7063),x7062,x7063) % 1.75/1.87 [735]~P22(x7352)+~P3(x7353,x7351,x7352)+P3(f13(x7351,x7352),f13(x7353,x7352),x7352) % 1.75/1.87 [736]~P22(x7362)+~P2(x7363,x7361,x7362)+P2(f13(x7361,x7362),f13(x7363,x7362),x7362) % 1.75/1.87 [772]~P22(x7723)+~P3(x7722,f13(x7721,x7723),x7723)+P3(x7721,f13(x7722,x7723),x7723) % 1.75/1.87 [774]~P22(x7743)+~P2(x7742,f13(x7741,x7743),x7743)+P2(x7741,f13(x7742,x7743),x7743) % 1.75/1.87 [776]~P22(x7762)+~P3(f13(x7763,x7762),x7761,x7762)+P3(f13(x7761,x7762),x7763,x7762) % 1.75/1.87 [777]~P34(x7772)+~P3(f6(x7771,x7772),x7773,x7772)+P3(f13(x7771,x7772),x7773,x7772) % 1.75/1.87 [779]~P22(x7792)+~P2(f13(x7793,x7792),x7791,x7792)+P2(f13(x7791,x7792),x7793,x7792) % 1.75/1.87 [780]~P70(x7802)+~P2(f6(x7801,x7802),x7803,x7802)+P2(f13(x7801,x7802),x7803,x7802) % 1.75/1.87 [794]~P22(x7943)+P3(x7941,x7942,x7943)+~P3(f13(x7942,x7943),f13(x7941,x7943),x7943) % 1.75/1.87 [795]~P22(x7953)+P2(x7951,x7952,x7953)+~P2(f13(x7952,x7953),f13(x7951,x7953),x7953) % 1.75/1.87 [846]~P22(x8463)+~P3(x8461,x8462,x8463)+P3(f10(x8461,x8462,x8463),f3(x8463),x8463) % 1.75/1.87 [847]~P22(x8473)+~P2(x8471,x8472,x8473)+P2(f10(x8471,x8472,x8473),f3(x8473),x8473) % 1.75/1.87 [850]E(x8501,x8502)+~P32(x8503)+~P3(f27(x8501,x8502,x8503),f3(a2),a2) % 1.75/1.87 [854]~P71(x8541)+~P3(f3(x8541),x8542,x8541)+P3(f3(x8541),f28(x8542,x8543,x8541),x8541) % 1.75/1.87 [855]~P70(x8551)+~P3(f3(x8551),x8552,x8551)+P3(f3(x8551),f28(x8552,x8553,x8551),x8551) % 1.75/1.87 [856]~P71(x8561)+~P3(f4(x8561),x8562,x8561)+P3(f4(x8561),f28(x8562,x8563,x8561),x8561) % 1.75/1.87 [858]~P71(x8581)+~P2(f3(x8581),x8582,x8581)+P2(f3(x8581),f28(x8582,x8583,x8581),x8581) % 1.75/1.87 [867]~P3(x8672,x8673,a2)+P3(f17(x8671,x8672),f17(x8671,x8673),a2)+~P3(f4(a2),x8671,a2) % 1.75/1.87 [868]~P3(x8682,x8683,a2)+P3(f17(x8681,x8682),f17(x8681,x8683),a2)+~P2(f4(a2),x8681,a2) % 1.75/1.87 [870]~P2(x8702,x8703,a2)+P2(f17(x8701,x8702),f17(x8701,x8703),a2)+~P2(f4(a2),x8701,a2) % 1.75/1.87 [895]~P23(x8953)+~P3(x8951,f13(x8952,x8953),x8953)+P3(f12(x8951,x8952,x8953),f3(x8953),x8953) % 1.75/1.87 [898]P3(x8981,x8982,a2)+~P3(f17(x8983,x8981),f17(x8983,x8982),a2)+~P2(f4(a2),x8983,a2) % 1.75/1.87 [900]P2(x9001,x9002,a2)+~P2(f17(x9003,x9001),f17(x9003,x9002),a2)+~P2(f4(a2),x9003,a2) % 1.75/1.87 [919]~P22(x9193)+P3(x9191,x9192,x9193)+~P3(f10(x9191,x9192,x9193),f3(x9193),x9193) % 1.75/1.87 [920]~P22(x9203)+P2(x9201,x9202,x9203)+~P2(f10(x9201,x9202,x9203),f3(x9203),x9203) % 1.75/1.87 [965]~P70(x9652)+~P2(f28(x9651,x9653,x9652),f3(x9652),x9652)+P2(x9651,f3(x9652),x9652) % 1.75/1.87 [992]~P23(x9923)+~P3(f12(x9921,x9922,x9923),f3(x9923),x9923)+P3(x9921,f13(x9922,x9923),x9923) % 1.75/1.87 [1103]~P3(x11031,x11033,a2)+P3(f14(x11031,x11032,a2),f14(x11033,x11032,a2),a2)+~P2(f3(a2),x11032,a2) % 1.75/1.87 [1104]~P3(x11042,x11043,a2)+P3(f14(x11041,x11042,a2),f14(x11041,x11043,a2),a2)+~P2(f3(a2),x11041,a2) % 1.75/1.87 [1105]~P2(x11051,x11053,a2)+P2(f14(x11051,x11052,a2),f14(x11053,x11052,a2),a2)+~P2(f3(a2),x11052,a2) % 1.75/1.87 [1106]~P2(x11062,x11063,a2)+P2(f14(x11061,x11062,a2),f14(x11061,x11063,a2),a2)+~P2(f3(a2),x11061,a2) % 1.75/1.87 [1242]P3(x12421,x12422,a2)+~P3(f14(x12423,x12421,a2),f14(x12423,x12422,a2),a2)+~P2(f3(a2),x12423,a2) % 1.75/1.87 [1243]P3(x12431,x12432,a2)+~P3(f14(x12431,x12433,a2),f14(x12432,x12433,a2),a2)+~P2(f3(a2),x12433,a2) % 1.75/1.87 [1244]P2(x12441,x12442,a2)+~P2(f14(x12441,x12443,a2),f14(x12442,x12443,a2),a2)+~P2(f3(a2),x12443,a2) % 1.75/1.87 [657]~P62(x6572)+E(x6571,f3(x6572))+E(f9(f13(x6573,x6572),f13(x6571,x6572),x6572),f9(x6573,x6571,x6572)) % 1.75/1.87 [664]~P1(x6642)+E(x6641,f3(x6642))+E(f8(f14(x6643,x6641,x6642),x6641,x6642),x6643) % 1.75/1.87 [665]~P1(x6652)+E(x6651,f3(x6652))+E(f8(f14(x6651,x6653,x6652),x6651,x6652),x6653) % 1.75/1.87 [666]~P62(x6662)+E(x6661,f3(x6662))+E(f9(f14(x6663,x6661,x6662),x6661,x6662),x6663) % 1.75/1.87 [667]~P58(x6672)+~P62(x6672)+E(f9(f13(x6671,x6672),f13(x6673,x6672),x6672),f9(x6671,x6673,x6672)) % 1.75/1.87 [707]~P58(x7073)+~P62(x7073)+E(f5(f9(x7071,x7072,x7073),x7073),f9(x7072,x7071,x7073)) % 1.75/1.87 [769]~P62(x7692)+E(x7691,f3(x7692))+E(f9(x7693,f13(x7691,x7692),x7692),f13(f9(x7693,x7691,x7692),x7692)) % 1.75/1.87 [770]~P57(x7702)+E(x7701,f3(x7702))+E(f28(f5(x7701,x7702),x7703,x7702),f5(f28(x7701,x7703,x7702),x7702)) % 1.75/1.87 [781]~P58(x7813)+~P62(x7813)+E(f9(x7811,f13(x7812,x7813),x7813),f13(f9(x7811,x7812,x7813),x7813)) % 1.75/1.87 [782]~P57(x7822)+~P58(x7822)+E(f28(f5(x7821,x7822),x7823,x7822),f5(f28(x7821,x7823,x7822),x7822)) % 1.75/1.87 [820]~P58(x8203)+~P47(x8203)+E(f29(f5(x8201,a2),f5(x8202,x8203),x8203),f5(f29(x8201,x8202,x8203),x8203)) % 1.75/1.87 [821]~P60(x8212)+E(x8211,f3(x8212))+E(f9(f6(x8213,x8212),f6(x8211,x8212),x8212),f6(f9(x8213,x8211,x8212),x8212)) % 1.75/1.87 [823]~P58(x8232)+~P62(x8232)+E(f14(f5(x8231,x8232),f5(x8233,x8232),x8232),f5(f14(x8231,x8233,x8232),x8232)) % 1.75/1.87 [824]~P58(x8242)+~P60(x8242)+E(f9(f6(x8241,x8242),f6(x8243,x8242),x8242),f6(f9(x8241,x8243,x8242),x8242)) % 1.75/1.87 [826]~P46(x8262)+~P83(x8262)+E(f9(f30(x8261,x8262),f30(x8263,x8262),x8262),f30(f10(x8261,x8263,x8262),x8262)) % 1.75/1.87 [827]~P46(x8272)+~P83(x8272)+E(f14(f30(x8271,x8272),f30(x8273,x8272),x8272),f30(f12(x8271,x8273,x8272),x8272)) % 1.75/1.87 [842]~P1(x8423)+~P4(x8421,x8422,x8423)+E(f14(x8421,f8(x8422,x8421,x8423),x8423),x8422) % 1.75/1.87 [843]~P1(x8433)+~P4(x8432,x8431,x8433)+E(f14(f8(x8431,x8432,x8433),x8432,x8433),x8431) % 1.75/1.87 [879]~P5(x8793)+~P4(x8792,x8791,x8793)+E(f8(x8791,f13(x8792,x8793),x8793),f13(f8(x8791,x8792,x8793),x8793)) % 1.75/1.87 [880]~P5(x8802)+~P4(x8803,x8801,x8802)+E(f8(f13(x8801,x8802),x8803,x8802),f13(f8(x8801,x8803,x8802),x8802)) % 1.75/1.87 [897]~P70(x8972)+~P3(f3(x8972),x8973,x8972)+E(f14(f6(x8971,x8972),x8973,x8972),f6(f14(x8971,x8973,x8972),x8972)) % 1.75/1.87 [975]~P1(x9752)+E(x9751,f3(x9752))+E(f8(f12(x9753,x9751,x9752),x9751,x9752),f12(f8(x9753,x9751,x9752),f4(x9752),x9752)) % 1.75/1.87 [976]~P1(x9762)+E(x9761,f3(x9762))+E(f8(f12(x9761,x9763,x9762),x9761,x9762),f12(f8(x9763,x9761,x9762),f4(x9762),x9762)) % 1.75/1.87 [1075]~P2(f3(a2),x10753,a2)+~P2(f3(a2),x10751,a2)+E(f14(f17(x10751,x10752),f17(x10753,x10752),a2),f17(f14(x10751,x10753,a2),x10752)) % 1.75/1.87 [1145]~P69(x11452)+E(x11451,f3(x11452))+~E(f12(f14(x11453,x11453,x11452),f14(x11451,x11451,x11452),x11452),f3(x11452)) % 1.75/1.87 [1146]~P69(x11462)+E(x11461,f3(x11462))+~E(f12(f14(x11461,x11461,x11462),f14(x11463,x11463,x11462),x11462),f3(x11462)) % 1.75/1.87 [1189]~P71(x11891)+~P2(f4(x11891),x11892,x11891)+P2(f4(x11891),f14(x11892,f28(x11892,x11893,x11891),x11891),x11891) % 1.75/1.87 [1261]~P71(x12613)+~P2(f4(x12613),x12611,x12613)+P2(f28(x12611,x12612,x12613),f14(x12611,f28(x12611,x12612,x12613),x12613),x12613) % 1.75/1.87 [1279]~P69(x12792)+E(x12791,f3(x12792))+P2(f3(x12792),f12(f14(x12793,x12793,x12792),f14(x12791,x12791,x12792),x12792),x12792) % 1.75/1.87 [1280]~P69(x12802)+E(x12801,f3(x12802))+P2(f3(x12802),f12(f14(x12801,x12801,x12802),f14(x12803,x12803,x12802),x12802),x12802) % 1.75/1.87 [1333]~P69(x13332)+E(x13331,f3(x13332))+~P3(f12(f14(x13333,x13333,x13332),f14(x13331,x13331,x13332),x13332),f3(x13332),x13332) % 1.75/1.87 [1334]~P69(x13342)+E(x13341,f3(x13342))+~P3(f12(f14(x13341,x13341,x13342),f14(x13343,x13343,x13342),x13342),f3(x13342),x13342) % 1.75/1.87 [995]~P58(x9951)+~P62(x9951)+E(f28(f9(f4(x9951),x9952,x9951),x9953,x9951),f9(f4(x9951),f28(x9952,x9953,x9951),x9951)) % 1.75/1.87 [1308]~P60(x13083)+~P2(x13081,x13082,x13083)+P2(x13081,f9(f12(x13081,x13082,x13083),f12(f4(x13083),f4(x13083),x13083),x13083),x13083) % 1.75/1.87 [1309]~P60(x13093)+~P2(x13091,x13092,x13093)+P2(f9(f12(x13091,x13092,x13093),f12(f4(x13093),f4(x13093),x13093),x13093),x13092,x13093) % 1.75/1.87 [676]~P19(x6764)+E(x6761,x6762)+~E(f12(x6763,x6761,x6764),f12(x6763,x6762,x6764)) % 1.75/1.87 [677]~P20(x6774)+E(x6771,x6772)+~E(f12(x6773,x6771,x6774),f12(x6773,x6772,x6774)) % 1.75/1.87 [678]~P16(x6784)+E(x6781,x6782)+~E(f10(x6783,x6783,x6784),f10(x6781,x6782,x6784)) % 1.75/1.87 [679]~P20(x6794)+E(x6791,x6792)+~E(f12(x6791,x6793,x6794),f12(x6792,x6793,x6794)) % 1.75/1.87 [680]~P16(x6803)+E(x6801,x6802)+~E(f10(x6801,x6802,x6803),f10(x6804,x6804,x6803)) % 1.75/1.87 [832]~P54(x8324)+~P4(x8321,x8323,x8324)+P4(x8321,f14(x8322,x8323,x8324),x8324) % 1.75/1.87 [833]~P54(x8334)+~P4(x8331,x8332,x8334)+P4(x8331,f14(x8332,x8333,x8334),x8334) % 1.75/1.87 [834]~P9(x8344)+~P3(x8341,x8343,x8344)+P3(x8341,f18(x8342,x8343,x8344),x8344) % 1.75/1.87 [835]~P9(x8354)+~P3(x8351,x8352,x8354)+P3(x8351,f18(x8352,x8353,x8354),x8354) % 1.75/1.87 [836]~P9(x8364)+~P2(x8361,x8363,x8364)+P2(x8361,f18(x8362,x8363,x8364),x8364) % 1.75/1.87 [837]~P9(x8374)+~P2(x8371,x8372,x8374)+P2(x8371,f18(x8372,x8373,x8374),x8374) % 1.75/1.87 [838]~P13(x8383)+~P3(x8382,x8384,x8383)+P3(f19(x8381,x8382,x8383),x8384,x8383) % 1.75/1.87 [839]~P13(x8393)+~P3(x8391,x8394,x8393)+P3(f19(x8391,x8392,x8393),x8394,x8393) % 1.75/1.87 [840]~P13(x8403)+~P2(x8402,x8404,x8403)+P2(f19(x8401,x8402,x8403),x8404,x8403) % 1.75/1.87 [841]~P13(x8413)+~P2(x8411,x8414,x8413)+P2(f19(x8411,x8412,x8413),x8414,x8413) % 1.75/1.87 [904]~P13(x9043)+P3(x9041,x9042,x9043)+~P3(x9041,f19(x9044,x9042,x9043),x9043) % 1.75/1.87 [906]~P13(x9063)+P3(x9061,x9062,x9063)+~P3(x9061,f19(x9062,x9064,x9063),x9063) % 1.75/1.87 [907]~P54(x9073)+P4(x9071,x9072,x9073)+~P4(f14(x9074,x9071,x9073),x9072,x9073) % 1.75/1.87 [908]~P54(x9083)+P4(x9081,x9082,x9083)+~P4(f14(x9081,x9084,x9083),x9082,x9083) % 1.75/1.87 [910]~P9(x9103)+P3(x9101,x9102,x9103)+~P3(f18(x9104,x9101,x9103),x9102,x9103) % 1.75/1.87 [912]~P9(x9123)+P3(x9121,x9122,x9123)+~P3(f18(x9121,x9124,x9123),x9122,x9123) % 1.75/1.87 [1004]~P61(x10043)+~P4(x10041,x10044,x10043)+P4(f14(x10041,x10042,x10043),f14(x10044,x10042,x10043),x10043) % 1.75/1.87 [1005]~P61(x10053)+~P4(x10052,x10054,x10053)+P4(f14(x10051,x10052,x10053),f14(x10051,x10054,x10053),x10053) % 1.75/1.87 [1006]~P54(x10063)+~P4(x10061,x10064,x10063)+P4(f28(x10061,x10062,x10063),f28(x10064,x10062,x10063),x10063) % 1.75/1.87 [1007]~P35(x10073)+~P3(x10071,x10074,x10073)+P3(f12(x10071,x10072,x10073),f12(x10074,x10072,x10073),x10073) % 1.75/1.87 [1008]~P36(x10083)+~P3(x10081,x10084,x10083)+P3(f12(x10081,x10082,x10083),f12(x10084,x10082,x10083),x10083) % 1.75/1.87 [1009]~P35(x10093)+~P3(x10092,x10094,x10093)+P3(f12(x10091,x10092,x10093),f12(x10091,x10094,x10093),x10093) % 1.75/1.87 [1010]~P36(x10103)+~P3(x10102,x10104,x10103)+P3(f12(x10101,x10102,x10103),f12(x10101,x10104,x10103),x10103) % 1.75/1.87 [1011]~P35(x10113)+~P2(x10111,x10114,x10113)+P2(f12(x10111,x10112,x10113),f12(x10114,x10112,x10113),x10113) % 1.75/1.87 [1012]~P38(x10123)+~P2(x10121,x10124,x10123)+P2(f12(x10121,x10122,x10123),f12(x10124,x10122,x10123),x10123) % 1.75/1.87 [1013]~P35(x10133)+~P2(x10132,x10134,x10133)+P2(f12(x10131,x10132,x10133),f12(x10131,x10134,x10133),x10133) % 1.75/1.87 [1014]~P38(x10143)+~P2(x10142,x10144,x10143)+P2(f12(x10141,x10142,x10143),f12(x10141,x10144,x10143),x10143) % 1.75/1.87 [1185]~P35(x11853)+P3(x11851,x11852,x11853)+~P3(f12(x11854,x11851,x11853),f12(x11854,x11852,x11853),x11853) % 1.75/1.87 [1186]~P35(x11863)+P3(x11861,x11862,x11863)+~P3(f12(x11861,x11864,x11863),f12(x11862,x11864,x11863),x11863) % 1.75/1.87 [1187]~P35(x11873)+P2(x11871,x11872,x11873)+~P2(f12(x11874,x11871,x11873),f12(x11874,x11872,x11873),x11873) % 1.75/1.87 [1188]~P35(x11883)+P2(x11881,x11882,x11883)+~P2(f12(x11881,x11884,x11883),f12(x11882,x11884,x11883),x11883) % 1.75/1.87 [866]~P16(x8663)+E(x8661,f13(x8662,x8663))+~E(f12(x8661,f12(x8664,x8662,x8663),x8663),x8664) % 1.75/1.87 [901]~P1(x9013)+~P4(x9014,x9012,x9013)+E(f7(f7(x9011,x9012,x9013),x9014,x9013),f7(x9011,x9014,x9013)) % 1.75/1.87 [968]~P1(x9682)+E(x9681,f3(x9682))+E(f8(f14(x9683,x9681,x9682),f14(x9684,x9681,x9682),x9682),f8(x9683,x9684,x9682)) % 1.75/1.87 [969]~P1(x9692)+E(x9691,f3(x9692))+E(f8(f14(x9691,x9693,x9692),f14(x9691,x9694,x9692),x9692),f8(x9693,x9694,x9692)) % 1.75/1.87 [970]~P58(x9703)+~P62(x9703)+E(f9(f14(x9701,x9702,x9703),x9704,x9703),f14(f9(x9701,x9704,x9703),x9702,x9703)) % 1.75/1.87 [974]~P5(x9742)+~E(f7(x9741,x9743,x9742),f7(x9744,x9743,x9742))+E(f7(f13(x9741,x9742),x9743,x9742),f7(f13(x9744,x9742),x9743,x9742)) % 1.75/1.87 [1095]~P1(x10953)+~P4(x10954,x10951,x10953)+E(f8(f14(x10951,x10952,x10953),x10954,x10953),f14(f8(x10951,x10954,x10953),x10952,x10953)) % 1.75/1.87 [1147]~P62(x11472)+E(x11471,f3(x11472))+E(f9(f28(x11473,x11474,x11472),f28(x11471,x11474,x11472),x11472),f28(f9(x11473,x11471,x11472),x11474,x11472)) % 1.75/1.87 [1148]~P58(x11483)+~P62(x11483)+E(f9(f28(x11481,x11482,x11483),f28(x11484,x11482,x11483),x11483),f28(f9(x11481,x11484,x11483),x11482,x11483)) % 1.75/1.87 [1184]~P25(x11844)+~P3(f12(x11841,x11843,x11844),x11842,x11844)+P3(x11841,f12(x11842,f6(x11843,x11844),x11844),x11844) % 1.75/1.87 [1206]~P1(x12063)+~P4(x12064,x12061,x12063)+E(f8(f28(x12061,x12062,x12063),f28(x12064,x12062,x12063),x12063),f28(f8(x12061,x12064,x12063),x12062,x12063)) % 1.75/1.87 [1238]~P61(x12383)+~P10(x12383)+E(f12(f14(x12381,x12382,x12383),f14(x12381,x12384,x12383),x12383),f12(f14(x12381,x12384,x12383),f14(x12381,x12382,x12383),x12383)) % 1.75/1.87 [1282]~P70(x12824)+P2(x12821,f12(x12822,x12823,x12824),x12824)+~P2(f6(f10(x12821,x12822,x12824),x12824),x12823,x12824) % 1.75/1.87 [1283]~P70(x12833)+P2(f10(x12831,x12832,x12833),x12834,x12833)+~P2(f6(f10(x12834,x12831,x12833),x12833),x12832,x12833) % 1.75/1.87 [1235]~P1(x12352)+E(x12351,f3(x12352))+E(f8(f12(x12353,f14(x12354,x12351,x12352),x12352),x12351,x12352),f12(x12354,f8(x12353,x12351,x12352),x12352)) % 1.75/1.87 [1236]~P1(x12362)+E(x12361,f3(x12362))+E(f8(f12(x12363,f14(x12361,x12364,x12362),x12362),x12361,x12362),f12(x12364,f8(x12363,x12361,x12362),x12362)) % 1.75/1.87 [1092]~P16(x10923)+E(f12(x10921,x10922,x10923),x10924)+~E(f12(x10921,f12(x10925,x10922,x10923),x10923),f12(x10925,x10924,x10923)) % 1.75/1.87 [1239]~P58(x12393)+~P62(x12393)+E(f9(f14(x12391,x12392,x12393),f14(x12394,x12395,x12393),x12393),f14(f9(x12391,x12394,x12393),f9(x12392,x12395,x12393),x12393)) % 1.75/1.87 [1326]~P75(x13264)+~E(f12(f14(x13263,x13265,x13264),x13261,x13264),f12(f14(x13262,x13265,x13264),x13266,x13264))+E(x13261,f12(f14(f10(x13262,x13263,x13264),x13265,x13264),x13266,x13264)) % 1.75/1.87 [1327]~P75(x13273)+~E(f12(f14(x13271,x13274,x13273),x13275,x13273),f12(f14(x13272,x13274,x13273),x13276,x13273))+E(f12(f14(f10(x13271,x13272,x13273),x13274,x13273),x13275,x13273),x13276) % 1.75/1.87 [1345]~P73(x13454)+~P3(f12(f14(x13453,x13455,x13454),x13451,x13454),f12(f14(x13452,x13455,x13454),x13456,x13454),x13454)+P3(x13451,f12(f14(f10(x13452,x13453,x13454),x13455,x13454),x13456,x13454),x13454) % 1.75/1.87 [1346]~P73(x13464)+~P2(f12(f14(x13463,x13465,x13464),x13461,x13464),f12(f14(x13462,x13465,x13464),x13466,x13464),x13464)+P2(x13461,f12(f14(f10(x13462,x13463,x13464),x13465,x13464),x13466,x13464),x13464) % 1.75/1.87 [1347]~P73(x13473)+~P3(f12(f14(x13471,x13474,x13473),x13475,x13473),f12(f14(x13472,x13474,x13473),x13476,x13473),x13473)+P3(f12(f14(f10(x13471,x13472,x13473),x13474,x13473),x13475,x13473),x13476,x13473) % 1.75/1.87 [1348]~P73(x13483)+~P2(f12(f14(x13481,x13484,x13483),x13485,x13483),f12(f14(x13482,x13484,x13483),x13486,x13483),x13483)+P2(f12(f14(f10(x13481,x13482,x13483),x13484,x13483),x13485,x13483),x13486,x13483) % 1.75/1.87 [1349]~P73(x13493)+P3(f12(f14(x13491,x13492,x13493),x13494,x13493),f12(f14(x13495,x13492,x13493),x13496,x13493),x13493)+~P3(x13494,f12(f14(f10(x13495,x13491,x13493),x13492,x13493),x13496,x13493),x13493) % 1.75/1.87 [1350]~P73(x13503)+P2(f12(f14(x13501,x13502,x13503),x13504,x13503),f12(f14(x13505,x13502,x13503),x13506,x13503),x13503)+~P2(x13504,f12(f14(f10(x13505,x13501,x13503),x13502,x13503),x13506,x13503),x13503) % 1.75/1.87 [1351]~P73(x13513)+P3(f12(f14(x13511,x13512,x13513),x13514,x13513),f12(f14(x13515,x13512,x13513),x13516,x13513),x13513)+~P3(f12(f14(f10(x13511,x13515,x13513),x13512,x13513),x13514,x13513),x13516,x13513) % 1.75/1.87 [1352]~P73(x13523)+P2(f12(f14(x13521,x13522,x13523),x13524,x13523),f12(f14(x13525,x13522,x13523),x13526,x13523),x13523)+~P2(f12(f14(f10(x13521,x13525,x13523),x13522,x13523),x13524,x13523),x13526,x13523) % 1.75/1.87 [360]~P58(x3602)+~P62(x3602)+~E(f5(x3601,x3602),f4(x3602))+E(x3601,f4(x3602)) % 1.75/1.87 [459]~P33(x4592)+~P25(x4592)+P2(x4591,f3(x4592),x4592)+E(f6(x4591,x4592),x4591) % 1.75/1.87 [554]~P78(x5542)+~P2(f3(x5542),x5541,x5542)+E(f11(x5541,x5542),f4(x5542))+E(x5541,f3(x5542)) % 1.75/1.87 [564]~P33(x5642)+~P25(x5642)+~P2(x5641,f3(x5642),x5642)+E(f6(x5641,x5642),f13(x5641,x5642)) % 1.75/1.87 [726]~P58(x7261)+~P60(x7261)+~P3(f3(x7261),x7262,x7261)+P3(f3(x7261),f5(x7262,x7261),x7261) % 1.75/1.87 [728]~P58(x7282)+~P60(x7282)+~P3(x7281,f3(x7282),x7282)+P3(f5(x7281,x7282),f3(x7282),x7282) % 1.75/1.87 [729]~P58(x7292)+~P60(x7292)+~P3(x7291,f3(x7292),x7292)+P3(f5(x7291,x7292),f4(x7292),x7292) % 1.75/1.87 [731]~P58(x7312)+~P60(x7312)+~P3(x7311,f3(x7312),x7312)+P2(f5(x7311,x7312),f4(x7312),x7312) % 1.75/1.87 [732]~P58(x7322)+~P60(x7322)+~P3(f4(x7322),x7321,x7322)+P3(f5(x7321,x7322),f4(x7322),x7322) % 1.75/1.87 [733]~P58(x7332)+~P60(x7332)+~P2(f4(x7332),x7331,x7332)+P2(f5(x7331,x7332),f4(x7332),x7332) % 1.75/1.87 [759]~P60(x7592)+~P2(f5(x7591,x7592),f3(x7592),x7592)+P2(x7591,f3(x7592),x7592)+E(x7591,f3(x7592)) % 1.75/1.87 [760]~P60(x7602)+~P2(f3(x7602),f5(x7601,x7602),x7602)+P2(f3(x7602),x7601,x7602)+E(x7601,f3(x7602)) % 1.75/1.87 [761]~P58(x7612)+~P60(x7612)+~P3(f4(x7612),f5(x7611,x7612),x7612)+P3(x7611,f4(x7612),x7612) % 1.75/1.87 [762]~P58(x7622)+~P60(x7622)+~P2(f4(x7622),f5(x7621,x7622),x7622)+P2(x7621,f4(x7622),x7622) % 1.75/1.87 [763]~P58(x7632)+~P60(x7632)+~P3(f5(x7631,x7632),f3(x7632),x7632)+P3(x7631,f3(x7632),x7632) % 1.75/1.87 [764]~P58(x7642)+~P60(x7642)+~P2(f5(x7641,x7642),f3(x7642),x7642)+P2(x7641,f3(x7642),x7642) % 1.75/1.87 [765]~P58(x7651)+~P60(x7651)+~P3(f3(x7651),f5(x7652,x7651),x7651)+P3(f3(x7651),x7652,x7651) % 1.75/1.87 [766]~P58(x7661)+~P60(x7661)+~P3(f4(x7661),f5(x7662,x7661),x7661)+P2(f3(x7661),x7662,x7661) % 1.75/1.87 [767]~P58(x7671)+~P60(x7671)+~P2(f3(x7671),f5(x7672,x7671),x7671)+P2(f3(x7671),x7672,x7671) % 1.75/1.87 [768]~P58(x7681)+~P60(x7681)+~P2(f4(x7681),f5(x7682,x7681),x7681)+P2(f3(x7681),x7682,x7681) % 1.75/1.87 [913]~P3(x9132,x9131,a2)+~P3(x9131,a15,a2)+P3(f21(x9131),f21(x9132),a2)+~P3(f3(a2),x9132,a2) % 1.75/1.87 [914]~P2(x9142,x9141,a2)+~P3(x9141,a15,a2)+P2(f21(x9141),f21(x9142),a2)+~P3(f3(a2),x9142,a2) % 1.75/1.87 [993]~P3(x9931,x9932,a2)+P3(f21(x9931),f21(x9932),a2)+~P3(x9932,f3(a2),a2)+~P3(f13(a15,a2),x9931,a2) % 1.75/1.87 [994]~P2(x9941,x9942,a2)+P2(f21(x9941),f21(x9942),a2)+~P3(f13(a15,a2),x9941,a2)+~P3(x9942,f3(a2),a2) % 1.75/1.87 [507]~P78(x5072)+P2(f3(x5072),x5071,x5072)+E(x5071,f3(x5072))+E(f11(x5071,x5072),f13(f4(x5072),x5072)) % 1.75/1.87 [626]~P23(x6262)+~P33(x6262)+P2(x6261,f3(x6262),x6262)+E(f18(x6261,f13(x6261,x6262),x6262),x6261) % 1.75/1.87 [744]~P23(x7442)+~P33(x7442)+~P2(x7441,f3(x7442),x7442)+E(f18(x7441,f13(x7441,x7442),x7442),f13(x7441,x7442)) % 1.75/1.87 [873]~P58(x8731)+~P60(x8731)+~P3(f3(x8731),x8732,x8731)+P3(f3(x8731),f9(f4(x8731),x8732,x8731),x8731) % 1.75/1.87 [874]~P58(x8741)+~P60(x8741)+~P2(f3(x8741),x8742,x8741)+P2(f3(x8741),f9(f4(x8741),x8742,x8741),x8741) % 1.75/1.87 [875]~P58(x8751)+~P60(x8751)+~P3(x8752,f3(x8751),x8751)+P3(f9(f4(x8751),x8752,x8751),f3(x8751),x8751) % 1.75/1.87 [876]~P58(x8761)+~P60(x8761)+~P2(x8762,f3(x8761),x8761)+P2(f9(f4(x8761),x8762,x8761),f3(x8761),x8761) % 1.75/1.87 [996]~P58(x9962)+~P60(x9962)+P3(x9961,f3(x9962),x9962)+~P3(f9(f4(x9962),x9961,x9962),f3(x9962),x9962) % 1.75/1.87 [997]~P58(x9972)+~P60(x9972)+P2(x9971,f3(x9972),x9972)+~P2(f9(f4(x9972),x9971,x9972),f3(x9972),x9972) % 1.75/1.87 [998]~P58(x9981)+~P60(x9981)+P3(f3(x9981),x9982,x9981)+~P3(f3(x9981),f9(f4(x9981),x9982,x9981),x9981) % 1.75/1.87 [999]~P58(x9991)+~P60(x9991)+P2(f3(x9991),x9992,x9991)+~P2(f3(x9991),f9(f4(x9991),x9992,x9991),x9991) % 1.75/1.87 [546]P2(x5461,x5462,x5463)+~P33(x5463)+E(x5461,x5462)+P2(x5462,x5461,x5463) % 1.75/1.87 [547]P2(x5471,x5472,x5473)+~P70(x5473)+E(x5471,x5472)+P2(x5472,x5471,x5473) % 1.75/1.87 [595]~P33(x5953)+~P3(x5951,x5952,x5953)+E(x5951,x5952)+P2(x5951,x5952,x5953) % 1.75/1.87 [601]~P39(x6013)+~P3(x6011,x6012,x6013)+E(x6011,x6012)+P2(x6011,x6012,x6013) % 1.75/1.87 [684]~P3(x6842,x6841,x6843)+~P3(x6841,x6842,x6843)+E(x6841,x6842)+~P39(x6843) % 1.75/1.87 [737]P2(x7372,x7371,x7373)+~P40(x7373)+~P3(x7372,x7371,x7373)+P3(x7371,x7372,x7373) % 1.75/1.87 [367]~P57(x3673)+~P58(x3673)+E(x3671,x3672)+~E(f5(x3671,x3673),f5(x3672,x3673)) % 1.75/1.87 [504]~P62(x5043)+E(x5041,x5042)+~E(f9(x5041,x5042,x5043),f4(x5043))+E(x5042,f3(x5043)) % 1.75/1.87 [505]~P61(x5052)+~P10(x5052)+~E(f12(x5053,x5051,x5052),x5053)+E(x5051,f3(x5052)) % 1.75/1.87 [510]~P45(x5102)+~E(f29(x5103,x5101,x5102),f3(x5102))+E(x5101,f3(x5102))+E(x5103,f3(a2)) % 1.75/1.87 [511]~P61(x5113)+~P10(x5113)+E(x5111,x5112)+~E(f10(x5111,x5112,x5113),f3(x5113)) % 1.75/1.87 [512]~P81(x5122)+~E(f14(x5123,x5121,x5122),f3(x5122))+E(x5121,f3(x5122))+E(x5123,f3(x5122)) % 1.75/1.87 [514]~P68(x5142)+~E(f14(x5143,x5141,x5142),f3(x5142))+E(x5141,f3(x5142))+E(x5143,f3(x5142)) % 1.75/1.87 [725]~P61(x7253)+E(x7251,x7252)+~E(f14(x7251,x7251,x7253),f14(x7252,x7252,x7253))+E(x7251,f13(x7252,x7253)) % 1.75/1.87 [881]~P60(x8812)+~P3(x8813,x8811,x8812)+~P2(x8811,f3(x8812),x8812)+P3(f5(x8811,x8812),f5(x8813,x8812),x8812) % 1.75/1.87 [882]~P60(x8822)+~P2(x8823,x8821,x8822)+~P2(x8821,f3(x8822),x8822)+P2(f5(x8821,x8822),f5(x8823,x8822),x8822) % 1.75/1.87 [883]~P60(x8832)+~P3(x8833,x8831,x8832)+~P2(f3(x8832),x8833,x8832)+P3(f5(x8831,x8832),f5(x8833,x8832),x8832) % 1.75/1.87 [884]~P60(x8842)+~P2(x8843,x8841,x8842)+~P2(f3(x8842),x8843,x8842)+P2(f5(x8841,x8842),f5(x8843,x8842),x8842) % 1.75/1.87 [893]~P34(x8932)+~P3(x8931,x8933,x8932)+~P3(f13(x8931,x8932),x8933,x8932)+P3(f6(x8931,x8932),x8933,x8932) % 1.75/1.87 [894]~P70(x8942)+~P2(x8941,x8943,x8942)+~P2(f13(x8941,x8942),x8943,x8942)+P2(f6(x8941,x8942),x8943,x8942) % 1.75/1.87 [921]~P60(x9213)+P3(x9211,x9212,x9213)+~P2(x9211,f3(x9213),x9213)+~P3(f5(x9212,x9213),f5(x9211,x9213),x9213) % 1.75/1.87 [922]~P60(x9223)+P2(x9221,x9222,x9223)+~P2(x9221,f3(x9223),x9223)+~P2(f5(x9222,x9223),f5(x9221,x9223),x9223) % 1.75/1.87 [923]~P60(x9233)+P3(x9231,x9232,x9233)+~P2(f3(x9233),x9232,x9233)+~P3(f5(x9232,x9233),f5(x9231,x9233),x9233) % 1.75/1.87 [924]~P60(x9243)+P2(x9241,x9242,x9243)+~P2(f3(x9243),x9242,x9243)+~P2(f5(x9242,x9243),f5(x9241,x9243),x9243) % 1.75/1.87 [971]~P70(x9712)+~P3(f28(x9711,x9713,x9712),f3(x9712),x9712)+P3(x9711,f3(x9712),x9712)+E(x9711,f3(x9712)) % 1.75/1.87 [1015]~P2(x10153,x10151,a2)+P2(f17(x10151,x10152),f17(x10153,x10152),a2)+~P2(x10152,f3(a2),a2)+~P2(f3(a2),x10153,a2) % 1.75/1.87 [1016]~P3(x10161,x10163,a2)+P3(f17(x10161,x10162),f17(x10163,x10162),a2)+~P3(f3(a2),x10162,a2)+~P2(f3(a2),x10161,a2) % 1.75/1.87 [1017]~P2(x10171,x10173,a2)+P2(f17(x10171,x10172),f17(x10173,x10172),a2)+~P2(f3(a2),x10172,a2)+~P2(f3(a2),x10171,a2) % 1.75/1.87 [1018]~P69(x10181)+~P3(x10183,f3(x10181),x10181)+~P3(x10182,f3(x10181),x10181)+P3(f3(x10181),f14(x10182,x10183,x10181),x10181) % 1.75/1.87 [1020]~P73(x10201)+~P3(x10203,f3(x10201),x10201)+~P3(x10202,f3(x10201),x10201)+P3(f3(x10201),f14(x10202,x10203,x10201),x10201) % 1.75/1.87 [1021]~P60(x10211)+~P3(x10212,f3(x10211),x10211)+~P2(x10213,f3(x10211),x10211)+P3(f3(x10211),f9(x10212,x10213,x10211),x10211) % 1.75/1.87 [1022]~P69(x10221)+~P2(x10223,f3(x10221),x10221)+~P2(x10222,f3(x10221),x10221)+P2(f3(x10221),f14(x10222,x10223,x10221),x10221) % 1.75/1.87 [1023]~P60(x10231)+~P2(x10233,f3(x10231),x10231)+~P2(x10232,f3(x10231),x10231)+P2(f3(x10231),f9(x10232,x10233,x10231),x10231) % 1.75/1.87 [1024]~P69(x10241)+~P3(f3(x10241),x10243,x10241)+~P3(f3(x10241),x10242,x10241)+P3(f3(x10241),f14(x10242,x10243,x10241),x10241) % 1.75/1.87 [1025]~P73(x10251)+~P3(f3(x10251),x10253,x10251)+~P3(f3(x10251),x10252,x10251)+P3(f3(x10251),f14(x10252,x10253,x10251),x10251) % 1.75/1.87 [1026]~P74(x10261)+~P3(f3(x10261),x10263,x10261)+~P3(f3(x10261),x10262,x10261)+P3(f3(x10261),f14(x10262,x10263,x10261),x10261) % 1.75/1.87 [1027]~P37(x10271)+~P3(f3(x10271),x10273,x10271)+~P3(f3(x10271),x10272,x10271)+P3(f3(x10271),f12(x10272,x10273,x10271),x10271) % 1.75/1.87 [1028]~P60(x10281)+~P3(f3(x10281),x10282,x10281)+~P2(f3(x10281),x10283,x10281)+P3(f3(x10281),f9(x10282,x10283,x10281),x10281) % 1.75/1.87 [1029]~P59(x10291)+~P2(f3(x10291),x10293,x10291)+~P2(f3(x10291),x10292,x10291)+P2(f3(x10291),f14(x10292,x10293,x10291),x10291) % 1.75/1.87 [1030]~P37(x10301)+~P3(f3(x10301),x10303,x10301)+~P2(f3(x10301),x10302,x10301)+P2(f3(x10301),f12(x10302,x10303,x10301),x10301) % 1.75/1.87 [1031]~P37(x10311)+~P3(f3(x10311),x10312,x10311)+~P2(f3(x10311),x10313,x10311)+P2(f3(x10311),f12(x10312,x10313,x10311),x10311) % 1.75/1.87 [1032]~P37(x10321)+~P2(f3(x10321),x10323,x10321)+~P2(f3(x10321),x10322,x10321)+P2(f3(x10321),f12(x10322,x10323,x10321),x10321) % 1.75/1.87 [1033]~P60(x10331)+~P2(f3(x10331),x10333,x10331)+~P2(f3(x10331),x10332,x10331)+P2(f3(x10331),f9(x10332,x10333,x10331),x10331) % 1.75/1.87 [1034]~P71(x10341)+~P2(f4(x10341),x10343,x10341)+~P2(f4(x10341),x10342,x10341)+P2(f4(x10341),f14(x10342,x10343,x10341),x10341) % 1.75/1.87 [1035]~P37(x10353)+~P3(x10352,f3(x10353),x10353)+~P3(x10351,f3(x10353),x10353)+P3(f12(x10351,x10352,x10353),f3(x10353),x10353) % 1.75/1.87 [1036]~P37(x10363)+~P3(x10362,f3(x10363),x10363)+~P2(x10361,f3(x10363),x10363)+P2(f12(x10361,x10362,x10363),f3(x10363),x10363) % 1.75/1.87 [1037]~P37(x10373)+~P3(x10371,f3(x10373),x10373)+~P2(x10372,f3(x10373),x10373)+P2(f12(x10371,x10372,x10373),f3(x10373),x10373) % 1.75/1.87 [1038]~P37(x10383)+~P2(x10382,f3(x10383),x10383)+~P2(x10381,f3(x10383),x10383)+P2(f12(x10381,x10382,x10383),f3(x10383),x10383) % 1.75/1.87 [1039]~P69(x10393)+~P3(x10392,f3(x10393),x10393)+~P3(f3(x10393),x10391,x10393)+P3(f14(x10391,x10392,x10393),f3(x10393),x10393) % 1.75/1.87 [1040]~P69(x10403)+~P3(x10401,f3(x10403),x10403)+~P3(f3(x10403),x10402,x10403)+P3(f14(x10401,x10402,x10403),f3(x10403),x10403) % 1.75/1.87 [1042]~P74(x10423)+~P3(x10422,f3(x10423),x10423)+~P3(f3(x10423),x10421,x10423)+P3(f14(x10421,x10422,x10423),f3(x10423),x10423) % 1.75/1.87 [1045]~P74(x10453)+~P3(x10451,f3(x10453),x10453)+~P3(f3(x10453),x10452,x10453)+P3(f14(x10451,x10452,x10453),f3(x10453),x10453) % 1.75/1.87 [1046]~P60(x10463)+~P3(x10461,f3(x10463),x10463)+~P2(f3(x10463),x10462,x10463)+P3(f9(x10461,x10462,x10463),f3(x10463),x10463) % 1.75/1.87 [1047]~P60(x10473)+~P2(x10472,f3(x10473),x10473)+~P3(f3(x10473),x10471,x10473)+P3(f9(x10471,x10472,x10473),f3(x10473),x10473) % 1.75/1.87 [1048]~P59(x10483)+~P2(x10482,f3(x10483),x10483)+~P2(f3(x10483),x10481,x10483)+P2(f14(x10481,x10482,x10483),f3(x10483),x10483) % 1.75/1.87 [1050]~P59(x10503)+~P2(x10501,f3(x10503),x10503)+~P2(f3(x10503),x10502,x10503)+P2(f14(x10501,x10502,x10503),f3(x10503),x10503) % 1.75/1.87 [1051]~P60(x10513)+~P2(x10512,f3(x10513),x10513)+~P2(f3(x10513),x10511,x10513)+P2(f9(x10511,x10512,x10513),f3(x10513),x10513) % 1.75/1.87 [1052]~P60(x10523)+~P2(x10521,f3(x10523),x10523)+~P2(f3(x10523),x10522,x10523)+P2(f9(x10521,x10522,x10523),f3(x10523),x10523) % 1.75/1.87 [1063]~P69(x10632)+~P3(f14(x10633,x10631,x10632),f3(x10632),x10632)+P3(x10631,f3(x10632),x10632)+P3(x10633,f3(x10632),x10632) % 1.75/1.87 [1064]~P69(x10642)+~P3(f3(x10642),f14(x10643,x10641,x10642),x10642)+P3(x10641,f3(x10642),x10642)+P3(f3(x10642),x10643,x10642) % 1.75/1.87 [1065]~P69(x10652)+~P3(f3(x10652),f14(x10651,x10653,x10652),x10652)+P3(x10651,f3(x10652),x10652)+P3(f3(x10652),x10653,x10652) % 1.75/1.87 [1066]~P69(x10662)+~P3(f3(x10662),f14(x10663,x10661,x10662),x10662)+P3(x10661,f3(x10662),x10662)+P3(f3(x10662),x10661,x10662) % 1.75/1.87 [1067]~P69(x10672)+~P3(f3(x10672),f14(x10671,x10673,x10672),x10672)+P3(x10671,f3(x10672),x10672)+P3(f3(x10672),x10671,x10672) % 1.75/1.87 [1068]~P69(x10682)+~P3(f14(x10683,x10681,x10682),f3(x10682),x10682)+P3(x10681,f3(x10682),x10682)+P3(f3(x10682),x10681,x10682) % 1.75/1.87 [1069]~P69(x10692)+~P3(f14(x10691,x10693,x10692),f3(x10692),x10692)+P3(x10691,f3(x10692),x10692)+P3(f3(x10692),x10691,x10692) % 1.75/1.87 [1070]~P69(x10701)+~P3(f14(x10702,x10703,x10701),f3(x10701),x10701)+P3(f3(x10701),x10702,x10701)+P3(f3(x10701),x10703,x10701) % 1.75/1.87 [1100]~P59(x11001)+~P2(f3(x11001),f14(x11003,x11002,x11001),x11001)+P2(f3(x11001),x11002,x11001)+~P2(f3(x11001),x11003,x11001) % 1.75/1.87 [1101]~P59(x11011)+~P2(f3(x11011),f14(x11012,x11013,x11011),x11011)+P2(f3(x11011),x11012,x11011)+~P2(f3(x11011),x11013,x11011) % 1.75/1.87 [687]~P58(x6872)+~P62(x6872)+E(x6871,f3(x6872))+E(f14(f9(x6873,x6871,x6872),x6871,x6872),x6873) % 1.75/1.87 [822]~P47(x8222)+E(x8221,f3(x8222))+E(x8223,f3(a2))+E(f29(f5(x8223,a2),f5(x8221,x8222),x8222),f5(f29(x8223,x8221,x8222),x8222)) % 1.75/1.87 [828]~P57(x8282)+E(x8281,f3(x8282))+E(x8283,f3(x8282))+E(f14(f5(x8281,x8282),f5(x8283,x8282),x8282),f5(f14(x8283,x8281,x8282),x8282)) % 1.75/1.87 [902]~P58(x9022)+~P60(x9022)+~P2(f3(x9022),x9023,x9022)+E(f9(f6(x9021,x9022),x9023,x9022),f6(f9(x9021,x9023,x9022),x9022)) % 1.75/1.87 [1061]~P50(x10612)+~P3(x10613,f24(x10611,x10612),a2)+~P2(f3(a2),x10613,a2)+P3(f24(f5(x10611,x10612),x10612),f5(x10613,a2),a2) % 1.75/1.87 [1096]~P77(x10962)+~P3(x10963,f3(x10962),x10962)+~P3(x10961,f3(x10962),x10962)+E(f14(f6(x10961,x10962),f6(x10963,x10962),x10962),f6(f14(x10961,x10963,x10962),x10962)) % 1.75/1.87 [1097]~P77(x10972)+~P3(x10973,f3(x10972),x10972)+~P3(f3(x10972),x10971,x10972)+E(f14(f6(x10971,x10972),f6(x10973,x10972),x10972),f6(f14(x10971,x10973,x10972),x10972)) % 1.75/1.87 [1098]~P77(x10982)+~P3(x10981,f3(x10982),x10982)+~P3(f3(x10982),x10983,x10982)+E(f14(f6(x10981,x10982),f6(x10983,x10982),x10982),f6(f14(x10981,x10983,x10982),x10982)) % 1.75/1.87 [1099]~P77(x10992)+~P3(f3(x10992),x10993,x10992)+~P3(f3(x10992),x10991,x10992)+E(f14(f6(x10991,x10992),f6(x10993,x10992),x10992),f6(f14(x10991,x10993,x10992),x10992)) % 1.75/1.87 [1247]~P57(x12472)+E(x12471,f3(x12472))+E(x12473,f3(x12472))+E(f14(f14(f5(x12473,x12472),f12(x12473,x12471,x12472),x12472),f5(x12471,x12472),x12472),f12(f5(x12473,x12472),f5(x12471,x12472),x12472)) % 1.75/1.87 [1248]~P57(x12482)+E(x12481,f3(x12482))+E(x12483,f3(x12482))+E(f14(f14(f5(x12483,x12482),f10(x12481,x12483,x12482),x12482),f5(x12481,x12482),x12482),f10(f5(x12483,x12482),f5(x12481,x12482),x12482)) % 1.75/1.87 [1249]~P62(x12492)+E(x12491,f3(x12492))+E(x12493,f3(x12492))+E(f14(f14(f12(x12493,x12491,x12492),f5(x12493,x12492),x12492),f5(x12491,x12492),x12492),f12(f5(x12493,x12492),f5(x12491,x12492),x12492)) % 1.75/1.87 [1301]~P71(x13013)+~P2(x13011,f4(x13013),x13013)+~P2(f3(x13013),x13011,x13013)+P2(f14(x13011,f28(x13011,x13012,x13013),x13013),f28(x13011,x13012,x13013),x13013) % 1.75/1.87 [1337]~P57(x13372)+E(x13371,f3(x13372))+E(x13373,f3(x13372))+E(f13(f14(f14(f5(x13373,x13372),f10(x13373,x13371,x13372),x13372),f5(x13371,x13372),x13372),x13372),f10(f5(x13373,x13372),f5(x13371,x13372),x13372)) % 1.75/1.87 [811]~P54(x8113)+~P4(x8111,x8114,x8113)+P4(x8111,x8112,x8113)+~P4(x8114,x8112,x8113) % 1.75/1.87 [812]~P39(x8123)+~P3(x8121,x8124,x8123)+P3(x8121,x8122,x8123)+~P3(x8124,x8122,x8123) % 1.75/1.87 [813]~P40(x8133)+~P3(x8131,x8134,x8133)+P3(x8131,x8132,x8133)+~P3(x8134,x8132,x8133) % 1.75/1.87 [814]~P39(x8143)+~P2(x8141,x8144,x8143)+P2(x8141,x8142,x8143)+~P3(x8144,x8142,x8143) % 1.75/1.87 [815]~P39(x8153)+~P2(x8154,x8152,x8153)+P2(x8151,x8152,x8153)+~P3(x8151,x8154,x8153) % 1.75/1.87 [816]~P39(x8163)+~P2(x8161,x8164,x8163)+P2(x8161,x8162,x8163)+~P2(x8164,x8162,x8163) % 1.75/1.87 [817]~P40(x8173)+~P2(x8171,x8174,x8173)+P2(x8171,x8172,x8173)+~P3(x8174,x8172,x8173) % 1.75/1.87 [818]~P40(x8183)+~P2(x8184,x8182,x8183)+P2(x8181,x8182,x8183)+~P3(x8181,x8184,x8183) % 1.75/1.87 [819]~P40(x8193)+~P2(x8191,x8194,x8193)+P2(x8191,x8192,x8193)+~P2(x8194,x8192,x8193) % 1.75/1.87 [697]~P45(x6974)+E(x6971,x6972)+~E(f29(x6973,x6971,x6974),f29(x6973,x6972,x6974))+E(x6973,f3(a2)) % 1.75/1.87 [698]~P45(x6984)+E(x6981,x6982)+~E(f29(x6981,x6983,x6984),f29(x6982,x6983,x6984))+E(x6983,f3(x6984)) % 1.75/1.87 [700]~P61(x7004)+~P10(x7004)+E(x7001,x7002)+~E(f12(x7003,x7001,x7004),f12(x7003,x7002,x7004)) % 1.75/1.87 [865]~P71(x8654)+E(x8651,x8652)+~P2(f4(x8654),x8653,x8654)+~E(f28(x8653,x8651,x8654),f28(x8653,x8652,x8654)) % 1.75/1.87 [978]~P1(x9784)+~P4(x9781,x9783,x9784)+~P4(x9781,x9782,x9784)+P4(x9781,f7(x9782,x9783,x9784),x9784) % 1.75/1.87 [979]~P54(x9794)+~P4(x9791,x9793,x9794)+~P4(x9791,x9792,x9794)+P4(x9791,f12(x9792,x9793,x9794),x9794) % 1.75/1.87 [980]~P56(x9804)+~P4(x9801,x9803,x9804)+~P4(x9801,x9802,x9804)+P4(x9801,f10(x9802,x9803,x9804),x9804) % 1.75/1.87 [983]~P13(x9834)+~P3(x9831,x9833,x9834)+~P3(x9831,x9832,x9834)+P3(x9831,f19(x9832,x9833,x9834),x9834) % 1.75/1.87 [986]~P9(x9863)+~P3(x9862,x9864,x9863)+~P3(x9861,x9864,x9863)+P3(f18(x9861,x9862,x9863),x9864,x9863) % 1.75/1.87 [991]~P71(x9914)+~P2(x9911,x9913,x9914)+~P2(f3(x9914),x9912,x9914)+P2(x9911,f12(x9912,x9913,x9914),x9914) % 1.75/1.87 [1094]~P1(x10943)+P4(x10941,x10942,x10943)+~P4(x10941,x10944,x10943)+~P4(x10941,f7(x10942,x10944,x10943),x10943) % 1.75/1.87 [1160]~P73(x11603)+~P3(x11604,x11601,x11603)+~P3(x11602,f3(x11603),x11603)+P3(f14(x11601,x11602,x11603),f14(x11604,x11602,x11603),x11603) % 1.75/1.87 [1161]~P69(x11613)+~P3(x11614,x11612,x11613)+~P2(x11611,f3(x11613),x11613)+P3(f14(x11611,x11612,x11613),f14(x11611,x11614,x11613),x11613) % 1.75/1.87 [1162]~P73(x11623)+~P3(x11624,x11622,x11623)+~P3(x11621,f3(x11623),x11623)+P3(f14(x11621,x11622,x11623),f14(x11621,x11624,x11623),x11623) % 1.75/1.87 [1164]~P69(x11643)+~P2(x11644,x11641,x11643)+~P2(x11642,f3(x11643),x11643)+P2(f14(x11641,x11642,x11643),f14(x11644,x11642,x11643),x11643) % 1.75/1.87 [1167]~P69(x11673)+~P2(x11674,x11672,x11673)+~P2(x11671,f3(x11673),x11673)+P2(f14(x11671,x11672,x11673),f14(x11671,x11674,x11673),x11673) % 1.75/1.87 [1168]~P60(x11683)+~P2(x11684,x11681,x11683)+~P2(x11682,f3(x11683),x11683)+P2(f9(x11681,x11682,x11683),f9(x11684,x11682,x11683),x11683) % 1.75/1.87 [1169]~P63(x11693)+~P3(x11691,x11694,x11693)+~P3(f3(x11693),x11692,x11693)+P3(f14(x11691,x11692,x11693),f14(x11694,x11692,x11693),x11693) % 1.75/1.87 [1170]~P69(x11703)+~P3(x11702,x11704,x11703)+~P2(f3(x11703),x11701,x11703)+P3(f14(x11701,x11702,x11703),f14(x11701,x11704,x11703),x11703) % 1.75/1.87 [1171]~P63(x11713)+~P3(x11712,x11714,x11713)+~P3(f3(x11713),x11711,x11713)+P3(f14(x11711,x11712,x11713),f14(x11711,x11714,x11713),x11713) % 1.75/1.87 [1172]~P65(x11723)+~P3(x11722,x11724,x11723)+~P3(f3(x11723),x11721,x11723)+P3(f14(x11721,x11722,x11723),f14(x11721,x11724,x11723),x11723) % 1.75/1.87 [1173]~P71(x11733)+~P3(x11731,x11734,x11733)+~P3(f3(x11733),x11731,x11733)+P3(f28(x11731,x11732,x11733),f28(x11734,x11732,x11733),x11733) % 1.75/1.87 [1174]~P59(x11743)+~P2(x11741,x11744,x11743)+~P2(f3(x11743),x11742,x11743)+P2(f14(x11741,x11742,x11743),f14(x11744,x11742,x11743),x11743) % 1.75/1.87 [1175]~P69(x11753)+~P2(x11751,x11754,x11753)+~P2(f3(x11753),x11752,x11753)+P2(f14(x11751,x11752,x11753),f14(x11754,x11752,x11753),x11753) % 1.75/1.87 [1176]~P59(x11763)+~P2(x11762,x11764,x11763)+~P2(f3(x11763),x11761,x11763)+P2(f14(x11761,x11762,x11763),f14(x11761,x11764,x11763),x11763) % 1.75/1.87 [1178]~P69(x11783)+~P2(x11782,x11784,x11783)+~P2(f3(x11783),x11781,x11783)+P2(f14(x11781,x11782,x11783),f14(x11781,x11784,x11783),x11783) % 1.75/1.87 [1179]~P66(x11793)+~P2(x11792,x11794,x11793)+~P2(f3(x11793),x11791,x11793)+P2(f14(x11791,x11792,x11793),f14(x11791,x11794,x11793),x11793) % 1.75/1.87 [1180]~P60(x11803)+~P2(x11801,x11804,x11803)+~P2(f3(x11803),x11802,x11803)+P2(f9(x11801,x11802,x11803),f9(x11804,x11802,x11803),x11803) % 1.75/1.87 [1190]~P61(x11902)+P4(x11903,x11904,x11902)+~P4(f14(x11901,x11903,x11902),f14(x11901,x11904,x11902),x11902)+E(x11901,f3(x11902)) % 1.75/1.87 [1191]~P61(x11912)+P4(x11913,x11914,x11912)+~P4(f14(x11913,x11911,x11912),f14(x11914,x11911,x11912),x11912)+E(x11911,f3(x11912)) % 1.75/1.87 [1202]~P60(x12024)+~P2(f3(x12024),x12023,x12024)+~P3(f14(x12021,x12023,x12024),x12022,x12024)+P3(x12021,f9(x12022,x12023,x12024),x12024) % 1.75/1.87 [1203]~P60(x12034)+~P2(f3(x12034),x12033,x12034)+~P2(f14(x12031,x12033,x12034),x12032,x12034)+P2(x12031,f9(x12032,x12033,x12034),x12034) % 1.75/1.87 [1204]~P60(x12043)+~P2(f3(x12043),x12042,x12043)+~P3(x12041,f14(x12044,x12042,x12043),x12043)+P3(f9(x12041,x12042,x12043),x12044,x12043) % 1.75/1.87 [1205]~P60(x12053)+~P2(f3(x12053),x12052,x12053)+~P2(x12051,f14(x12054,x12052,x12053),x12053)+P2(f9(x12051,x12052,x12053),x12054,x12053) % 1.75/1.87 [1217]P2(x12172,x12171,x12173)+~P69(x12173)+P2(x12171,x12172,x12173)+~P2(f14(x12174,x12171,x12173),f14(x12174,x12172,x12173),x12173) % 1.75/1.87 [1218]P2(x12182,x12181,x12183)+~P69(x12183)+P2(x12181,x12182,x12183)+~P2(f14(x12181,x12184,x12183),f14(x12182,x12184,x12183),x12183) % 1.75/1.87 [1231]~P69(x12313)+P2(x12311,x12312,x12313)+~P2(f14(x12311,x12314,x12313),f14(x12312,x12314,x12313),x12313)+P2(x12314,f3(x12313),x12313) % 1.75/1.87 [1232]~P69(x12323)+P2(x12321,x12322,x12323)+~P2(f14(x12324,x12321,x12323),f14(x12324,x12322,x12323),x12323)+P2(x12324,f3(x12323),x12323) % 1.75/1.87 [1233]~P69(x12333)+P2(x12331,x12332,x12333)+~P2(f14(x12334,x12332,x12333),f14(x12334,x12331,x12333),x12333)+P2(f3(x12333),x12334,x12333) % 1.75/1.87 [1234]~P69(x12343)+P2(x12341,x12342,x12343)+~P2(f14(x12342,x12344,x12343),f14(x12341,x12344,x12343),x12343)+P2(f3(x12343),x12344,x12343) % 1.75/1.87 [1240]~P69(x12402)+~P2(f14(x12403,x12401,x12402),f14(x12404,x12401,x12402),x12402)+P2(x12401,f3(x12402),x12402)+P2(f3(x12402),x12401,x12402) % 1.75/1.87 [1241]~P69(x12412)+~P2(f14(x12411,x12413,x12412),f14(x12411,x12414,x12412),x12412)+P2(x12411,f3(x12412),x12412)+P2(f3(x12412),x12411,x12412) % 1.75/1.87 [1250]~P69(x12503)+P3(x12501,x12502,x12503)+~P3(f14(x12504,x12502,x12503),f14(x12504,x12501,x12503),x12503)+~P2(x12504,f3(x12503),x12503) % 1.75/1.87 [1251]~P69(x12513)+P2(x12511,x12512,x12513)+~P2(f14(x12514,x12512,x12513),f14(x12514,x12511,x12513),x12513)+~P2(x12514,f3(x12513),x12513) % 1.75/1.87 [1252]~P59(x12523)+P3(x12521,x12522,x12523)+~P3(f14(x12524,x12521,x12523),f14(x12524,x12522,x12523),x12523)+~P2(f3(x12523),x12524,x12523) % 1.75/1.87 [1253]~P59(x12533)+P3(x12531,x12532,x12533)+~P3(f14(x12531,x12534,x12533),f14(x12532,x12534,x12533),x12533)+~P2(f3(x12533),x12534,x12533) % 1.75/1.87 [1254]~P69(x12543)+P3(x12541,x12542,x12543)+~P3(f14(x12544,x12541,x12543),f14(x12544,x12542,x12543),x12543)+~P2(f3(x12543),x12544,x12543) % 1.75/1.87 [1255]~P59(x12553)+P2(x12551,x12552,x12553)+~P2(f14(x12554,x12551,x12553),f14(x12554,x12552,x12553),x12553)+~P3(f3(x12553),x12554,x12553) % 1.75/1.87 [1256]~P59(x12563)+P2(x12561,x12562,x12563)+~P2(f14(x12561,x12564,x12563),f14(x12562,x12564,x12563),x12563)+~P3(f3(x12563),x12564,x12563) % 1.75/1.87 [1257]~P69(x12573)+P2(x12571,x12572,x12573)+~P2(f14(x12574,x12571,x12573),f14(x12574,x12572,x12573),x12573)+~P2(f3(x12573),x12574,x12573) % 1.75/1.87 [1258]~P71(x12583)+P2(x12581,x12582,x12583)+~P3(f3(x12583),x12582,x12583)+~P2(f28(x12581,x12584,x12583),f28(x12582,x12584,x12583),x12583) % 1.75/1.87 [1259]~P72(x12593)+P2(x12591,x12592,x12593)+~P2(f14(x12594,x12591,x12593),f14(x12594,x12592,x12593),x12593)+~P3(f3(x12593),x12594,x12593) % 1.75/1.87 [1260]~P72(x12603)+P2(x12601,x12602,x12603)+~P2(f14(x12601,x12604,x12603),f14(x12602,x12604,x12603),x12603)+~P3(f3(x12603),x12604,x12603) % 1.75/1.87 [989]~P58(x9892)+~P62(x9892)+E(x9891,f3(x9892))+E(f9(f14(x9893,x9891,x9892),f14(x9894,x9891,x9892),x9892),f9(x9893,x9894,x9892)) % 1.75/1.87 [990]~P58(x9902)+~P62(x9902)+E(x9901,f3(x9902))+E(f9(f14(x9901,x9903,x9902),f14(x9901,x9904,x9902),x9902),f9(x9903,x9904,x9902)) % 1.75/1.87 [1183]~P52(x11832)+E(x11831,f3(x11832))+~P3(x11833,f3(a2),a2)+~P3(f24(x11831,x11832),f14(x11833,f24(x11834,x11832),a2),a2) % 1.75/1.87 [1281]~P1(x12813)+~P4(x12812,x12814,x12813)+~P4(x12812,x12811,x12813)+E(f12(f8(x12811,x12812,x12813),f8(x12814,x12812,x12813),x12813),f8(f12(x12811,x12814,x12813),x12812,x12813)) % 1.75/1.87 [1322]~P70(x13223)+~P2(x13221,f12(x13222,x13224,x13223),x13223)+~P2(f10(x13222,x13224,x13223),x13221,x13223)+P2(f6(f10(x13221,x13222,x13223),x13223),x13224,x13223) % 1.75/1.87 [1330]~P2(f14(x13304,x13301,a2),f14(x13302,x13303,a2),a2)+~P2(f3(a2),x13304,a2)+~P2(f3(a2),x13302,a2)+P2(f14(x13301,f5(x13302,a2),a2),f14(x13303,f5(x13304,a2),a2),a2) % 1.75/1.87 [1331]~P2(f14(x13313,x13312,a2),f14(x13311,x13314,a2),a2)+~P2(f3(a2),x13313,a2)+~P2(f3(a2),x13311,a2)+P2(f14(f5(x13311,a2),x13312,a2),f14(f5(x13313,a2),x13314,a2),a2) % 1.75/1.87 [1245]~P58(x12452)+~P62(x12452)+E(x12451,f3(x12452))+E(f9(f12(x12453,f14(x12454,x12451,x12452),x12452),x12451,x12452),f12(x12454,f9(x12453,x12451,x12452),x12452)) % 1.75/1.87 [1246]~P58(x12462)+~P62(x12462)+E(x12461,f3(x12462))+E(f9(f12(x12463,f14(x12464,x12461,x12462),x12462),x12461,x12462),f12(f9(x12463,x12461,x12462),x12464,x12462)) % 1.75/1.87 [1353]~P46(x13532)+E(x13531,f3(x13532))+E(x13533,f3(x13532))+E(f13(f14(f14(f5(x13533,x13532),f9(f10(x13533,x13531,x13532),x13534,x13532),x13532),f5(x13531,x13532),x13532),x13532),f9(f10(f5(x13533,x13532),f5(x13531,x13532),x13532),x13534,x13532)) % 1.75/1.87 [915]~P22(x9153)+~P3(x9155,x9154,x9153)+P3(x9151,x9152,x9153)+~E(f10(x9154,x9155,x9153),f10(x9152,x9151,x9153)) % 1.75/1.87 [916]~P22(x9163)+~P3(x9165,x9164,x9163)+P3(x9161,x9162,x9163)+~E(f10(x9162,x9161,x9163),f10(x9164,x9165,x9163)) % 1.75/1.87 [917]~P22(x9173)+~P2(x9174,x9175,x9173)+P2(x9171,x9172,x9173)+~E(f10(x9174,x9175,x9173),f10(x9171,x9172,x9173)) % 1.75/1.87 [918]~P22(x9183)+~P2(x9184,x9185,x9183)+P2(x9181,x9182,x9183)+~E(f10(x9181,x9182,x9183),f10(x9184,x9185,x9183)) % 1.75/1.87 [1149]~P54(x11493)+~P4(x11492,x11495,x11493)+~P4(x11491,x11494,x11493)+P4(f14(x11491,x11492,x11493),f14(x11494,x11495,x11493),x11493) % 1.75/1.87 [1150]~P36(x11503)+~P3(x11502,x11505,x11503)+~P3(x11501,x11504,x11503)+P3(f12(x11501,x11502,x11503),f12(x11504,x11505,x11503),x11503) % 1.75/1.87 [1151]~P38(x11513)+~P3(x11512,x11515,x11513)+~P2(x11511,x11514,x11513)+P2(f12(x11511,x11512,x11513),f12(x11514,x11515,x11513),x11513) % 1.75/1.87 [1152]~P38(x11523)+~P3(x11521,x11524,x11523)+~P2(x11522,x11525,x11523)+P2(f12(x11521,x11522,x11523),f12(x11524,x11525,x11523),x11523) % 1.75/1.87 [1153]~P38(x11533)+~P2(x11532,x11535,x11533)+~P2(x11531,x11534,x11533)+P2(f12(x11531,x11532,x11533),f12(x11534,x11535,x11533),x11533) % 1.75/1.87 [1197]~P22(x11974)+~P3(x11975,x11973,x11974)+~P3(x11971,f12(x11972,x11975,x11974),x11974)+P3(x11971,f12(x11972,x11973,x11974),x11974) % 1.75/1.87 [1284]~P70(x12842)+~P2(f6(x12841,x12842),x12844,x12842)+~P2(f6(x12843,x12842),x12845,x12842)+P2(f14(f6(x12841,x12842),f6(x12843,x12842),x12842),f14(x12844,x12845,x12842),x12842) % 1.75/1.87 [1296]~P48(x12963)+~P2(f24(x12962,x12963),x12965,a2)+~P2(f24(x12961,x12963),x12964,a2)+P2(f24(f14(x12961,x12962,x12963),x12963),f14(x12964,x12965,a2),a2) % 1.75/1.87 [1303]~P1(x13033)+~P4(x13035,x13032,x13033)+~P4(x13034,x13031,x13033)+E(f8(f14(x13031,x13032,x13033),f14(x13034,x13035,x13033),x13033),f14(f8(x13031,x13034,x13033),f8(x13032,x13035,x13033),x13033)) % 1.75/1.87 [1335]~P62(x13352)+E(x13351,f3(x13352))+E(x13353,f3(x13352))+E(f9(f12(f14(x13354,x13351,x13352),f14(x13355,x13353,x13352),x13352),f14(x13353,x13351,x13352),x13352),f12(f9(x13354,x13353,x13352),f9(x13355,x13351,x13352),x13352)) % 1.75/1.87 [1336]~P62(x13362)+E(x13361,f3(x13362))+E(x13363,f3(x13362))+E(f9(f10(f14(x13364,x13361,x13362),f14(x13365,x13363,x13362),x13362),f14(x13363,x13361,x13362),x13362),f10(f9(x13364,x13363,x13362),f9(x13365,x13361,x13362),x13362)) % 1.75/1.87 [1298]~P1(x12983)+~E(f7(x12981,x12984,x12983),f7(x12985,x12984,x12983))+~E(f7(x12982,x12984,x12983),f7(x12986,x12984,x12983))+E(f7(f14(x12981,x12982,x12983),x12984,x12983),f7(f14(x12985,x12986,x12983),x12984,x12983)) % 1.75/1.87 [1299]~P1(x12993)+~E(f7(x12991,x12994,x12993),f7(x12995,x12994,x12993))+~E(f7(x12992,x12994,x12993),f7(x12996,x12994,x12993))+E(f7(f12(x12991,x12992,x12993),x12994,x12993),f7(f12(x12995,x12996,x12993),x12994,x12993)) % 1.75/1.87 [1300]~P5(x13003)+~E(f7(x13001,x13004,x13003),f7(x13005,x13004,x13003))+~E(f7(x13002,x13004,x13003),f7(x13006,x13004,x13003))+E(f7(f10(x13001,x13002,x13003),x13004,x13003),f7(f10(x13005,x13006,x13003),x13004,x13003)) % 1.75/1.87 [863]~P58(x8632)+~P60(x8632)+P3(f4(x8632),x8631,x8632)+~P3(f5(x8631,x8632),f4(x8632),x8632)+P3(x8631,f3(x8632),x8632) % 1.75/1.87 [864]~P58(x8642)+~P60(x8642)+P2(f4(x8642),x8641,x8642)+~P2(f5(x8641,x8642),f4(x8642),x8642)+P3(x8641,f3(x8642),x8642) % 1.75/1.87 [877]~P58(x8771)+~P60(x8771)+~P2(f3(x8771),x8772,x8771)+~P3(x8772,f4(x8771),x8771)+P3(f4(x8771),f5(x8772,x8771),x8771) % 1.75/1.87 [878]~P58(x8781)+~P60(x8781)+~P2(f3(x8781),x8782,x8781)+~P2(x8782,f4(x8781),x8781)+P2(f4(x8781),f5(x8782,x8781),x8781) % 1.75/1.87 [380]~P57(x3803)+E(x3801,x3802)+~E(f5(x3801,x3803),f5(x3802,x3803))+E(x3802,f3(x3803))+E(x3801,f3(x3803)) % 1.75/1.87 [885]~P37(x8852)+~P3(f3(x8852),x8851,x8852)+~P3(f3(x8852),x8853,x8852)+~E(f12(x8853,x8851,x8852),f3(x8852))+E(x8851,f3(x8852)) % 1.75/1.87 [886]~P37(x8862)+~P3(f3(x8862),x8863,x8862)+~P3(f3(x8862),x8861,x8862)+~E(f12(x8861,x8863,x8862),f3(x8862))+E(x8861,f3(x8862)) % 1.75/1.87 [1053]~P58(x10531)+~P60(x10531)+~P3(x10533,f3(x10531),x10531)+~P3(x10532,f3(x10531),x10531)+P3(f3(x10531),f9(x10532,x10533,x10531),x10531) % 1.75/1.87 [1055]~P58(x10551)+~P60(x10551)+~P3(f3(x10551),x10553,x10551)+~P3(f3(x10551),x10552,x10551)+P3(f3(x10551),f9(x10552,x10553,x10551),x10551) % 1.75/1.87 [1057]~P58(x10573)+~P60(x10573)+~P3(x10572,f3(x10573),x10573)+~P3(f3(x10573),x10571,x10573)+P3(f9(x10571,x10572,x10573),f3(x10573),x10573) % 1.75/1.87 [1058]~P58(x10583)+~P60(x10583)+~P3(x10581,f3(x10583),x10583)+~P3(f3(x10583),x10582,x10583)+P3(f9(x10581,x10582,x10583),f3(x10583),x10583) % 1.75/1.87 [1076]~P58(x10762)+~P60(x10762)+~P3(f9(x10763,x10761,x10762),f3(x10762),x10762)+P3(x10761,f3(x10762),x10762)+P3(x10763,f3(x10762),x10762) % 1.75/1.87 [1077]~P58(x10772)+~P60(x10772)+~P2(f9(x10773,x10771,x10772),f3(x10772),x10772)+P2(x10771,f3(x10772),x10772)+P2(x10773,f3(x10772),x10772) % 1.75/1.87 [1078]~P58(x10782)+~P60(x10782)+~P3(f3(x10782),f9(x10783,x10781,x10782),x10782)+P3(x10781,f3(x10782),x10782)+P3(f3(x10782),x10783,x10782) % 1.75/1.87 [1079]~P58(x10792)+~P60(x10792)+~P3(f3(x10792),f9(x10791,x10793,x10792),x10792)+P3(x10791,f3(x10792),x10792)+P3(f3(x10792),x10793,x10792) % 1.75/1.87 [1080]~P58(x10802)+~P60(x10802)+~P3(f3(x10802),f9(x10803,x10801,x10802),x10802)+P3(x10801,f3(x10802),x10802)+P3(f3(x10802),x10801,x10802) % 1.75/1.87 [1081]~P58(x10812)+~P60(x10812)+~P3(f3(x10812),f9(x10811,x10813,x10812),x10812)+P3(x10811,f3(x10812),x10812)+P3(f3(x10812),x10811,x10812) % 1.75/1.87 [1082]~P58(x10822)+~P60(x10822)+~P2(f3(x10822),f9(x10823,x10821,x10822),x10822)+P2(x10821,f3(x10822),x10822)+P2(f3(x10822),x10823,x10822) % 1.75/1.87 [1083]~P58(x10832)+~P60(x10832)+~P2(f3(x10832),f9(x10831,x10833,x10832),x10832)+P2(x10831,f3(x10832),x10832)+P2(f3(x10832),x10833,x10832) % 1.75/1.87 [1084]~P58(x10842)+~P60(x10842)+~P2(f3(x10842),f9(x10843,x10841,x10842),x10842)+P2(x10841,f3(x10842),x10842)+P2(f3(x10842),x10841,x10842) % 1.75/1.87 [1085]~P58(x10852)+~P60(x10852)+~P2(f3(x10852),f9(x10851,x10853,x10852),x10852)+P2(x10851,f3(x10852),x10852)+P2(f3(x10852),x10851,x10852) % 1.75/1.87 [1086]~P58(x10862)+~P60(x10862)+~P3(f9(x10863,x10861,x10862),f3(x10862),x10862)+P3(x10861,f3(x10862),x10862)+P3(f3(x10862),x10861,x10862) % 1.75/1.87 [1087]~P58(x10872)+~P60(x10872)+~P3(f9(x10871,x10873,x10872),f3(x10872),x10872)+P3(x10871,f3(x10872),x10872)+P3(f3(x10872),x10871,x10872) % 1.75/1.87 [1088]~P58(x10882)+~P60(x10882)+~P2(f9(x10883,x10881,x10882),f3(x10882),x10882)+P2(x10881,f3(x10882),x10882)+P2(f3(x10882),x10881,x10882) % 1.75/1.87 [1089]~P58(x10892)+~P60(x10892)+~P2(f9(x10891,x10893,x10892),f3(x10892),x10892)+P2(x10891,f3(x10892),x10892)+P2(f3(x10892),x10891,x10892) % 1.75/1.87 [1090]~P58(x10901)+~P60(x10901)+~P3(f9(x10902,x10903,x10901),f3(x10901),x10901)+P3(f3(x10901),x10902,x10901)+P3(f3(x10901),x10903,x10901) % 1.75/1.87 [1091]~P58(x10911)+~P60(x10911)+~P2(f9(x10912,x10913,x10911),f3(x10911),x10911)+P2(f3(x10911),x10912,x10911)+P2(f3(x10911),x10913,x10911) % 1.75/1.87 [1158]~P70(x11583)+~P3(x11581,f4(x11583),x11583)+~P3(f3(x11583),x11582,x11583)+~P3(f3(x11583),x11581,x11583)+P3(f14(x11581,x11582,x11583),x11582,x11583) % 1.75/1.87 [1159]~P70(x11593)+~P3(x11592,f4(x11593),x11593)+~P3(f3(x11593),x11592,x11593)+~P3(f3(x11593),x11591,x11593)+P3(f14(x11591,x11592,x11593),x11591,x11593) % 1.75/1.87 [1000]~P35(x10004)+~P21(x10004)+~P3(x10001,x10003,x10004)+~P3(f3(x10004),x10002,x10004)+P3(x10001,f12(x10002,x10003,x10004),x10004) % 1.75/1.87 [1001]~P35(x10014)+~P21(x10014)+~P3(x10011,x10012,x10014)+~P3(f3(x10014),x10013,x10014)+P3(x10011,f12(x10012,x10013,x10014),x10014) % 1.75/1.87 [1002]~P35(x10024)+~P21(x10024)+~P3(x10021,x10023,x10024)+~P2(f3(x10024),x10022,x10024)+P2(x10021,f12(x10022,x10023,x10024),x10024) % 1.75/1.87 [1003]~P35(x10034)+~P21(x10034)+~P2(x10031,x10033,x10034)+~P3(f3(x10034),x10032,x10034)+P2(x10031,f12(x10032,x10033,x10034),x10034) % 1.75/1.87 [1181]~P58(x11813)+~P60(x11813)+~P3(x11814,x11811,x11813)+~P3(x11812,f3(x11813),x11813)+P3(f9(x11811,x11812,x11813),f9(x11814,x11812,x11813),x11813) % 1.75/1.87 [1182]~P58(x11823)+~P60(x11823)+~P3(x11821,x11824,x11823)+~P3(f3(x11823),x11822,x11823)+P3(f9(x11821,x11822,x11823),f9(x11824,x11822,x11823),x11823) % 1.75/1.87 [1207]~P58(x12074)+~P60(x12074)+~P2(f3(x12074),x12073,x12074)+~P3(f9(x12071,x12073,x12074),x12072,x12074)+P3(x12071,f14(x12072,x12073,x12074),x12074) % 1.75/1.87 [1209]~P58(x12094)+~P60(x12094)+~P2(f3(x12094),x12093,x12094)+~P2(f9(x12091,x12093,x12094),x12092,x12094)+P2(x12091,f14(x12092,x12093,x12094),x12094) % 1.75/1.87 [1211]~P58(x12113)+~P60(x12113)+~P2(f3(x12113),x12112,x12113)+~P3(x12111,f9(x12114,x12112,x12113),x12113)+P3(f14(x12111,x12112,x12113),x12114,x12113) % 1.75/1.87 [1213]~P58(x12133)+~P60(x12133)+~P2(f3(x12133),x12132,x12133)+~P2(x12131,f9(x12134,x12132,x12133),x12133)+P2(f14(x12131,x12132,x12133),x12134,x12133) % 1.75/1.87 [1216]~P1(x12163)+~P4(x12162,x12164,x12163)+~P4(x12162,x12161,x12163)+~P4(x12161,x12164,x12163)+P4(f8(x12161,x12162,x12163),f8(x12164,x12162,x12163),x12163) % 1.75/1.87 [1297]~P1(x12973)+~P4(x12974,x12971,x12973)+P4(x12971,x12972,x12973)+~P4(x12974,x12972,x12973)+~P4(f8(x12971,x12974,x12973),f8(x12972,x12974,x12973),x12973) % 1.75/1.87 [1304]~P60(x13043)+~P2(x13042,x13044,x13043)+~P2(x13041,f3(x13043),x13043)+~P2(f3(x13043),f14(x13042,x13044,x13043),x13043)+P2(f9(x13041,x13042,x13043),f9(x13041,x13044,x13043),x13043) % 1.75/1.87 [1305]~P60(x13053)+~P3(x13054,x13052,x13053)+~P3(f3(x13053),x13051,x13053)+~P2(f3(x13053),f14(x13052,x13054,x13053),x13053)+P3(f9(x13051,x13052,x13053),f9(x13051,x13054,x13053),x13053) % 1.75/1.87 [1306]~P60(x13063)+~P2(x13064,x13062,x13063)+~P2(f3(x13063),x13061,x13063)+~P2(f3(x13063),f14(x13062,x13064,x13063),x13063)+P2(f9(x13061,x13062,x13063),f9(x13061,x13064,x13063),x13063) % 1.75/1.87 [887]~P62(x8872)+~E(f9(x8874,x8873,x8872),f9(x8875,x8871,x8872))+E(f14(x8874,x8871,x8872),f14(x8875,x8873,x8872))+E(x8871,f3(x8872))+E(x8873,f3(x8872)) % 1.75/1.87 [888]~P62(x8882)+~E(f14(x8884,x8883,x8882),f14(x8885,x8881,x8882))+E(f9(x8884,x8881,x8882),f9(x8885,x8883,x8882))+E(x8881,f3(x8882))+E(x8883,f3(x8882)) % 1.75/1.87 [1215]~P61(x12154)+~P10(x12154)+E(x12151,x12152)+E(x12153,f3(x12154))+~E(f12(x12155,f14(x12153,x12151,x12154),x12154),f12(x12155,f14(x12153,x12152,x12154),x12154)) % 1.75/1.87 [1324]~P61(x13245)+~P10(x13245)+E(x13241,x13242)+E(x13243,x13244)+~E(f12(f14(x13243,x13241,x13245),f14(x13244,x13242,x13245),x13245),f12(f14(x13243,x13242,x13245),f14(x13244,x13241,x13245),x13245)) % 1.75/1.87 [1343]~P6(x13435)+~P7(x13435)+~P4(x13431,x13434,x13435)+~P4(x13431,f12(x13432,x13436,x13435),x13435)+P4(x13431,f12(f10(x13432,f14(x13433,x13434,x13435),x13435),x13436,x13435),x13435) % 1.75/1.87 [1344]~P6(x13444)+~P7(x13444)+~P4(x13441,x13445,x13444)+P4(x13441,f12(x13442,x13443,x13444),x13444)+~P4(x13441,f12(f10(x13442,f14(x13446,x13445,x13444),x13444),x13443,x13444),x13444) % 1.75/1.87 [553]~P67(x5532)+~P84(x5532)+~P68(x5532)+~P42(x5532)+~E(f28(x5531,x5533,x5532),f3(x5532))+E(x5531,f3(x5532)) % 1.75/1.87 [1071]~P58(x10712)+~P60(x10712)+P2(x10711,f3(x10712),x10712)+P2(f3(x10712),x10711,x10712)+~P3(x10713,f3(x10712),x10712)+P3(x10713,f9(x10714,x10711,x10712),x10712) % 1.75/1.87 [1072]~P58(x10722)+~P60(x10722)+P2(x10721,f3(x10722),x10722)+P2(f3(x10722),x10721,x10722)+~P2(x10723,f3(x10722),x10722)+P2(x10723,f9(x10724,x10721,x10722),x10722) % 1.75/1.87 [1073]~P58(x10732)+~P60(x10732)+P2(x10731,f3(x10732),x10732)+P2(f3(x10732),x10731,x10732)+~P3(f3(x10732),x10734,x10732)+P3(f9(x10733,x10731,x10732),x10734,x10732) % 1.75/1.87 [1074]~P58(x10742)+~P60(x10742)+P2(x10741,f3(x10742),x10742)+P2(f3(x10742),x10741,x10742)+~P2(f3(x10742),x10744,x10742)+P2(f9(x10743,x10741,x10742),x10744,x10742) % 1.75/1.87 [1154]~P58(x11542)+~P60(x11542)+P3(x11541,f3(x11542),x11542)+P2(f3(x11542),x11543,x11542)+~P3(x11541,f9(x11544,x11543,x11542),x11542)+P2(x11543,f3(x11542),x11542) % 1.75/1.87 [1155]~P58(x11552)+~P60(x11552)+P2(x11551,f3(x11552),x11552)+P2(f3(x11552),x11551,x11552)+~P2(x11553,f9(x11554,x11551,x11552),x11552)+P2(x11553,f3(x11552),x11552) % 1.75/1.87 [1156]~P58(x11562)+~P60(x11562)+P2(x11561,f3(x11562),x11562)+P2(f3(x11562),x11561,x11562)+~P3(f9(x11564,x11561,x11562),x11563,x11562)+P3(f3(x11562),x11563,x11562) % 1.75/1.87 [1157]~P58(x11572)+~P60(x11572)+P2(x11571,f3(x11572),x11572)+P2(f3(x11572),x11571,x11572)+~P2(f9(x11574,x11571,x11572),x11573,x11572)+P2(f3(x11572),x11573,x11572) % 1.75/1.87 [1262]~P58(x12622)+~P60(x12622)+~P3(f14(x12623,x12621,x12622),x12624,x12622)+P2(x12621,f3(x12622),x12622)+~P3(x12623,f3(x12622),x12622)+P3(x12623,f9(x12624,x12621,x12622),x12622) % 1.75/1.87 [1263]~P58(x12632)+~P60(x12632)+~P2(f14(x12633,x12631,x12632),x12634,x12632)+P2(x12631,f3(x12632),x12632)+~P2(x12633,f3(x12632),x12632)+P2(x12633,f9(x12634,x12631,x12632),x12632) % 1.75/1.87 [1264]~P58(x12642)+~P60(x12642)+~P3(x12643,f14(x12644,x12641,x12642),x12642)+P2(x12641,f3(x12642),x12642)+~P3(f3(x12642),x12644,x12642)+P3(f9(x12643,x12641,x12642),x12644,x12642) % 1.75/1.87 [1265]~P58(x12652)+~P60(x12652)+~P2(x12653,f14(x12654,x12651,x12652),x12652)+P2(x12651,f3(x12652),x12652)+~P2(f3(x12652),x12654,x12652)+P2(f9(x12653,x12651,x12652),x12654,x12652) % 1.75/1.87 [1266]~P58(x12661)+~P60(x12661)+~P3(x12664,f9(x12663,x12662,x12661),x12661)+~P2(x12662,f3(x12661),x12661)+P2(f3(x12661),x12662,x12661)+P3(x12663,f14(x12664,x12662,x12661),x12661) % 1.75/1.87 [1267]~P58(x12671)+~P60(x12671)+~P3(x12674,f14(x12673,x12672,x12671),x12671)+~P3(x12673,f3(x12671),x12671)+P2(f3(x12671),x12672,x12671)+P3(x12673,f9(x12674,x12672,x12671),x12671) % 1.75/1.87 [1268]~P58(x12681)+~P60(x12681)+~P3(x12684,f14(x12683,x12682,x12681),x12681)+~P2(x12682,f3(x12681),x12681)+P2(f3(x12681),x12682,x12681)+P3(x12683,f9(x12684,x12682,x12681),x12681) % 1.75/1.87 [1269]~P58(x12691)+~P60(x12691)+~P2(x12694,f9(x12693,x12692,x12691),x12691)+~P2(x12692,f3(x12691),x12691)+P2(f3(x12691),x12692,x12691)+P2(x12693,f14(x12694,x12692,x12691),x12691) % 1.75/1.87 [1270]~P58(x12701)+~P60(x12701)+~P2(x12704,f14(x12703,x12702,x12701),x12701)+~P2(x12702,f3(x12701),x12701)+P2(f3(x12701),x12702,x12701)+P2(x12703,f9(x12704,x12702,x12701),x12701) % 1.75/1.87 [1271]~P58(x12711)+~P60(x12711)+~P2(x12714,f14(x12713,x12712,x12711),x12711)+~P2(x12713,f3(x12711),x12711)+P2(f3(x12711),x12712,x12711)+P2(x12713,f9(x12714,x12712,x12711),x12711) % 1.75/1.87 [1272]~P58(x12721)+~P60(x12721)+~P3(f9(x12724,x12722,x12721),x12723,x12721)+~P2(x12722,f3(x12721),x12721)+P2(f3(x12721),x12722,x12721)+P3(f14(x12723,x12722,x12721),x12724,x12721) % 1.75/1.87 [1273]~P58(x12731)+~P60(x12731)+~P3(f14(x12734,x12732,x12731),x12733,x12731)+~P2(x12732,f3(x12731),x12731)+P2(f3(x12731),x12732,x12731)+P3(f9(x12733,x12732,x12731),x12734,x12731) % 1.75/1.87 [1274]~P58(x12741)+~P60(x12741)+~P2(f9(x12744,x12742,x12741),x12743,x12741)+~P2(x12742,f3(x12741),x12741)+P2(f3(x12741),x12742,x12741)+P2(f14(x12743,x12742,x12741),x12744,x12741) % 1.75/1.87 [1275]~P58(x12751)+~P60(x12751)+~P2(f14(x12754,x12752,x12751),x12753,x12751)+~P2(x12752,f3(x12751),x12751)+P2(f3(x12751),x12752,x12751)+P2(f9(x12753,x12752,x12751),x12754,x12751) % 1.75/1.87 [1276]~P58(x12761)+~P60(x12761)+~P3(f14(x12764,x12762,x12761),x12763,x12761)+~P3(f3(x12761),x12764,x12761)+P2(f3(x12761),x12762,x12761)+P3(f9(x12763,x12762,x12761),x12764,x12761) % 1.75/1.87 [1277]~P58(x12771)+~P60(x12771)+~P2(f14(x12774,x12772,x12771),x12773,x12771)+~P2(f3(x12771),x12774,x12771)+P2(f3(x12771),x12772,x12771)+P2(f9(x12773,x12772,x12771),x12774,x12771) % 1.75/1.87 [1307]~P58(x13073)+~P60(x13073)+~P3(x13072,x13074,x13073)+~P3(x13071,f3(x13073),x13073)+~P2(f3(x13073),f14(x13072,x13074,x13073),x13073)+P3(f9(x13071,x13072,x13073),f9(x13071,x13074,x13073),x13073) % 1.75/1.87 [1314]~P58(x13144)+~P60(x13144)+~P3(x13141,f3(x13144),x13144)+~P3(x13142,f14(x13141,x13143,x13144),x13144)+~P3(f14(x13141,x13143,x13144),x13142,x13144)+P3(x13141,f9(x13142,x13143,x13144),x13144) % 1.75/1.87 [1315]~P58(x13154)+~P60(x13154)+~P2(x13153,f3(x13154),x13154)+~P3(x13152,f14(x13151,x13153,x13154),x13154)+~P3(f14(x13151,x13153,x13154),x13152,x13154)+P3(x13151,f9(x13152,x13153,x13154),x13154) % 1.75/1.87 [1316]~P58(x13164)+~P60(x13164)+~P2(x13163,f3(x13164),x13164)+~P2(x13162,f14(x13161,x13163,x13164),x13164)+~P2(f14(x13161,x13163,x13164),x13162,x13164)+P2(x13161,f9(x13162,x13163,x13164),x13164) % 1.75/1.87 [1317]~P58(x13174)+~P60(x13174)+~P2(x13171,f3(x13174),x13174)+~P2(x13172,f14(x13171,x13173,x13174),x13174)+~P2(f14(x13171,x13173,x13174),x13172,x13174)+P2(x13171,f9(x13172,x13173,x13174),x13174) % 1.75/1.87 [1318]~P58(x13183)+~P60(x13183)+~P2(x13182,f3(x13183),x13183)+~P3(x13181,f14(x13184,x13182,x13183),x13183)+~P3(f14(x13184,x13182,x13183),x13181,x13183)+P3(f9(x13181,x13182,x13183),x13184,x13183) % 1.75/1.87 [1319]~P58(x13193)+~P60(x13193)+~P2(x13192,f3(x13193),x13193)+~P2(x13191,f14(x13194,x13192,x13193),x13193)+~P2(f14(x13194,x13192,x13193),x13191,x13193)+P2(f9(x13191,x13192,x13193),x13194,x13193) % 1.75/1.87 [1320]~P58(x13203)+~P60(x13203)+~P3(f3(x13203),x13204,x13203)+~P3(x13201,f14(x13204,x13202,x13203),x13203)+~P3(f14(x13204,x13202,x13203),x13201,x13203)+P3(f9(x13201,x13202,x13203),x13204,x13203) % 1.75/1.87 [1321]~P58(x13213)+~P60(x13213)+~P2(f3(x13213),x13214,x13213)+~P2(x13211,f14(x13214,x13212,x13213),x13213)+~P2(f14(x13214,x13212,x13213),x13211,x13213)+P2(f9(x13211,x13212,x13213),x13214,x13213) % 1.75/1.87 [1285]~P76(x12853)+~P3(x12852,x12855,x12853)+~P3(x12851,x12854,x12853)+~P3(f3(x12853),x12854,x12853)+~P3(f3(x12853),x12852,x12853)+P3(f14(x12851,x12852,x12853),f14(x12854,x12855,x12853),x12853) % 1.75/1.87 [1286]~P76(x12863)+~P3(x12862,x12865,x12863)+~P3(x12861,x12864,x12863)+~P3(f3(x12863),x12862,x12863)+~P3(f3(x12863),x12861,x12863)+P3(f14(x12861,x12862,x12863),f14(x12864,x12865,x12863),x12863) % 1.75/1.87 [1287]~P60(x12873)+~P3(x12875,x12872,x12873)+~P3(x12871,x12874,x12873)+~P3(f3(x12873),x12871,x12873)+~P2(f3(x12873),x12875,x12873)+P3(f9(x12871,x12872,x12873),f9(x12874,x12875,x12873),x12873) % 1.75/1.87 [1288]~P59(x12883)+~P3(x12882,x12885,x12883)+~P2(x12881,x12884,x12883)+~P3(f3(x12883),x12881,x12883)+~P2(f3(x12883),x12882,x12883)+P2(f14(x12881,x12882,x12883),f14(x12884,x12885,x12883),x12883) % 1.75/1.87 [1289]~P59(x12893)+~P3(x12891,x12894,x12893)+~P2(x12892,x12895,x12893)+~P3(f3(x12893),x12892,x12893)+~P2(f3(x12893),x12891,x12893)+P2(f14(x12891,x12892,x12893),f14(x12894,x12895,x12893),x12893) % 1.75/1.87 [1290]~P59(x12903)+~P2(x12902,x12905,x12903)+~P2(x12901,x12904,x12903)+~P3(f3(x12903),x12902,x12903)+~P3(f3(x12903),x12901,x12903)+P2(f14(x12901,x12902,x12903),f14(x12904,x12905,x12903),x12903) % 1.75/1.87 [1291]~P59(x12913)+~P2(x12912,x12915,x12913)+~P2(x12911,x12914,x12913)+~P3(f3(x12913),x12912,x12913)+~P2(f3(x12913),x12914,x12913)+P2(f14(x12911,x12912,x12913),f14(x12914,x12915,x12913),x12913) % 1.75/1.87 [1292]~P60(x12923)+~P3(x12925,x12922,x12923)+~P2(x12921,x12924,x12923)+~P3(f3(x12923),x12921,x12923)+~P2(f3(x12923),x12925,x12923)+P2(f9(x12921,x12922,x12923),f9(x12924,x12925,x12923),x12923) % 1.75/1.87 [1293]~P60(x12933)+~P3(x12931,x12934,x12933)+~P2(x12935,x12932,x12933)+~P2(f3(x12933),x12935,x12933)+~P2(f3(x12933),x12931,x12933)+P2(f9(x12931,x12932,x12933),f9(x12934,x12935,x12933),x12933) % 1.75/1.87 [1357]~P64(x13573)+~P3(x13577,x13572,x13573)+~P3(x13576,x13571,x13573)+~P3(x13572,x13575,x13573)+~P3(x13571,x13574,x13573)+P3(f14(x13571,x13572,x13573),f12(f12(f12(f14(f25(x13574,x13573),f25(x13575,x13573),x13573),f14(f25(x13576,x13573),f26(x13575,x13573),x13573),x13573),f14(f26(x13574,x13573),f25(x13577,x13573),x13573),x13573),f14(f26(x13576,x13573),f26(x13577,x13573),x13573),x13573),x13573) % 1.75/1.87 [1358]~P64(x13582)+~P3(x13587,x13583,x13582)+~P3(x13586,x13584,x13582)+~P3(x13585,x13587,x13582)+~P3(x13581,x13586,x13582)+P3(f12(f12(f12(f14(f26(x13581,x13582),f25(x13583,x13582),x13582),f14(f26(x13584,x13582),f26(x13583,x13582),x13582),x13582),f14(f25(x13581,x13582),f25(x13585,x13582),x13582),x13582),f14(f25(x13584,x13582),f26(x13585,x13582),x13582),x13582),f14(x13586,x13587,x13582),x13582) % 1.75/1.87 %EqnAxiom % 1.75/1.87 [1]E(x11,x11) % 1.75/1.87 [2]E(x22,x21)+~E(x21,x22) % 1.75/1.87 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.75/1.87 [4]~E(x41,x42)+E(f3(x41),f3(x42)) % 1.75/1.87 [5]~E(x51,x52)+E(f31(x51),f31(x52)) % 1.75/1.87 [6]~E(x61,x62)+E(f32(x61),f32(x62)) % 1.75/1.87 [7]~E(x71,x72)+E(f14(x71,x73,x74),f14(x72,x73,x74)) % 1.75/1.87 [8]~E(x81,x82)+E(f14(x83,x81,x84),f14(x83,x82,x84)) % 1.75/1.87 [9]~E(x91,x92)+E(f14(x93,x94,x91),f14(x93,x94,x92)) % 1.75/1.87 [10]~E(x101,x102)+E(f4(x101),f4(x102)) % 1.75/1.87 [11]~E(x111,x112)+E(f12(x111,x113,x114),f12(x112,x113,x114)) % 1.75/1.87 [12]~E(x121,x122)+E(f12(x123,x121,x124),f12(x123,x122,x124)) % 1.75/1.87 [13]~E(x131,x132)+E(f12(x133,x134,x131),f12(x133,x134,x132)) % 1.75/1.87 [14]~E(x141,x142)+E(f8(x141,x143,x144),f8(x142,x143,x144)) % 1.75/1.87 [15]~E(x151,x152)+E(f8(x153,x151,x154),f8(x153,x152,x154)) % 1.75/1.87 [16]~E(x161,x162)+E(f8(x163,x164,x161),f8(x163,x164,x162)) % 1.75/1.87 [17]~E(x171,x172)+E(f16(x171),f16(x172)) % 1.75/1.87 [18]~E(x181,x182)+E(f26(x181,x183),f26(x182,x183)) % 1.75/1.87 [19]~E(x191,x192)+E(f26(x193,x191),f26(x193,x192)) % 1.75/1.87 [20]~E(x201,x202)+E(f29(x201,x203,x204),f29(x202,x203,x204)) % 1.75/1.87 [21]~E(x211,x212)+E(f29(x213,x211,x214),f29(x213,x212,x214)) % 1.75/1.87 [22]~E(x221,x222)+E(f29(x223,x224,x221),f29(x223,x224,x222)) % 1.75/1.87 [23]~E(x231,x232)+E(f9(x231,x233,x234),f9(x232,x233,x234)) % 1.75/1.87 [24]~E(x241,x242)+E(f9(x243,x241,x244),f9(x243,x242,x244)) % 1.75/1.87 [25]~E(x251,x252)+E(f9(x253,x254,x251),f9(x253,x254,x252)) % 1.75/1.87 [26]~E(x261,x262)+E(f19(x261,x263,x264),f19(x262,x263,x264)) % 1.75/1.87 [27]~E(x271,x272)+E(f19(x273,x271,x274),f19(x273,x272,x274)) % 1.75/1.87 [28]~E(x281,x282)+E(f19(x283,x284,x281),f19(x283,x284,x282)) % 1.75/1.87 [29]~E(x291,x292)+E(f25(x291,x293),f25(x292,x293)) % 1.75/1.87 [30]~E(x301,x302)+E(f25(x303,x301),f25(x303,x302)) % 1.75/1.87 [31]~E(x311,x312)+E(f21(x311),f21(x312)) % 1.75/1.87 [32]~E(x321,x322)+E(f13(x321,x323),f13(x322,x323)) % 1.75/1.87 [33]~E(x331,x332)+E(f13(x333,x331),f13(x333,x332)) % 1.75/1.87 [34]~E(x341,x342)+E(f28(x341,x343,x344),f28(x342,x343,x344)) % 1.75/1.87 [35]~E(x351,x352)+E(f28(x353,x351,x354),f28(x353,x352,x354)) % 1.75/1.87 [36]~E(x361,x362)+E(f28(x363,x364,x361),f28(x363,x364,x362)) % 1.75/1.87 [37]~E(x371,x372)+E(f18(x371,x373,x374),f18(x372,x373,x374)) % 1.75/1.87 [38]~E(x381,x382)+E(f18(x383,x381,x384),f18(x383,x382,x384)) % 1.75/1.87 [39]~E(x391,x392)+E(f18(x393,x394,x391),f18(x393,x394,x392)) % 1.75/1.87 [40]~E(x401,x402)+E(f5(x401,x403),f5(x402,x403)) % 1.75/1.87 [41]~E(x411,x412)+E(f5(x413,x411),f5(x413,x412)) % 1.75/1.87 [42]~E(x421,x422)+E(f7(x421,x423,x424),f7(x422,x423,x424)) % 1.75/1.87 [43]~E(x431,x432)+E(f7(x433,x431,x434),f7(x433,x432,x434)) % 1.75/1.87 [44]~E(x441,x442)+E(f7(x443,x444,x441),f7(x443,x444,x442)) % 1.75/1.87 [45]~E(x451,x452)+E(f23(x451,x453),f23(x452,x453)) % 1.75/1.87 [46]~E(x461,x462)+E(f23(x463,x461),f23(x463,x462)) % 1.75/1.87 [47]~E(x471,x472)+E(f6(x471,x473),f6(x472,x473)) % 1.75/1.87 [48]~E(x481,x482)+E(f6(x483,x481),f6(x483,x482)) % 1.75/1.87 [49]~E(x491,x492)+E(f10(x491,x493,x494),f10(x492,x493,x494)) % 1.75/1.87 [50]~E(x501,x502)+E(f10(x503,x501,x504),f10(x503,x502,x504)) % 1.75/1.87 [51]~E(x511,x512)+E(f10(x513,x514,x511),f10(x513,x514,x512)) % 1.75/1.87 [52]~E(x521,x522)+E(f22(x521),f22(x522)) % 1.75/1.87 [53]~E(x531,x532)+E(f27(x531,x533,x534),f27(x532,x533,x534)) % 1.75/1.87 [54]~E(x541,x542)+E(f27(x543,x541,x544),f27(x543,x542,x544)) % 1.75/1.87 [55]~E(x551,x552)+E(f27(x553,x554,x551),f27(x553,x554,x552)) % 1.75/1.87 [56]~E(x561,x562)+E(f11(x561,x563),f11(x562,x563)) % 1.75/1.87 [57]~E(x571,x572)+E(f11(x573,x571),f11(x573,x572)) % 1.75/1.87 [58]~E(x581,x582)+E(f30(x581,x583),f30(x582,x583)) % 1.75/1.87 [59]~E(x591,x592)+E(f30(x593,x591),f30(x593,x592)) % 1.75/1.87 [60]~E(x601,x602)+E(f24(x601,x603),f24(x602,x603)) % 1.75/1.87 [61]~E(x611,x612)+E(f24(x613,x611),f24(x613,x612)) % 1.75/1.87 [62]~E(x621,x622)+E(f17(x621,x623),f17(x622,x623)) % 1.75/1.87 [63]~E(x631,x632)+E(f17(x633,x631),f17(x633,x632)) % 1.75/1.87 [64]~E(x641,x642)+E(f20(x641,x643),f20(x642,x643)) % 1.75/1.87 [65]~E(x651,x652)+E(f20(x653,x651),f20(x653,x652)) % 1.75/1.87 [66]~P1(x661)+P1(x662)+~E(x661,x662) % 1.75/1.87 [67]~P6(x671)+P6(x672)+~E(x671,x672) % 1.75/1.87 [68]~P62(x681)+P62(x682)+~E(x681,x682) % 1.75/1.87 [69]~P7(x691)+P7(x692)+~E(x691,x692) % 1.75/1.87 [70]~P8(x701)+P8(x702)+~E(x701,x702) % 1.75/1.87 [71]P2(x712,x713,x714)+~E(x711,x712)+~P2(x711,x713,x714) % 1.75/1.87 [72]P2(x723,x722,x724)+~E(x721,x722)+~P2(x723,x721,x724) % 1.75/1.87 [73]P2(x733,x734,x732)+~E(x731,x732)+~P2(x733,x734,x731) % 1.75/1.87 [74]~P54(x741)+P54(x742)+~E(x741,x742) % 1.75/1.87 [75]~P77(x751)+P77(x752)+~E(x751,x752) % 1.75/1.87 [76]~P22(x761)+P22(x762)+~E(x761,x762) % 1.75/1.87 [77]~P31(x771)+P31(x772)+~E(x771,x772) % 1.75/1.87 [78]~P57(x781)+P57(x782)+~E(x781,x782) % 1.75/1.87 [79]~P58(x791)+P58(x792)+~E(x791,x792) % 1.75/1.87 [80]~P59(x801)+P59(x802)+~E(x801,x802) % 1.75/1.87 [81]P3(x812,x813,x814)+~E(x811,x812)+~P3(x811,x813,x814) % 1.75/1.87 [82]P3(x823,x822,x824)+~E(x821,x822)+~P3(x823,x821,x824) % 1.75/1.87 [83]P3(x833,x834,x832)+~E(x831,x832)+~P3(x833,x834,x831) % 1.75/1.87 [84]~P44(x841)+P44(x842)+~E(x841,x842) % 1.75/1.87 [85]~P60(x851)+P60(x852)+~E(x851,x852) % 1.75/1.87 [86]~P32(x861)+P32(x862)+~E(x861,x862) % 1.75/1.87 [87]~P9(x871)+P9(x872)+~E(x871,x872) % 1.75/1.87 [88]~P69(x881)+P69(x882)+~E(x881,x882) % 1.75/1.87 [89]~P45(x891)+P45(x892)+~E(x891,x892) % 1.75/1.87 [90]~P16(x901)+P16(x902)+~E(x901,x902) % 1.75/1.87 [91]~P61(x911)+P61(x912)+~E(x911,x912) % 1.75/1.87 [92]~P10(x921)+P10(x922)+~E(x921,x922) % 1.75/1.87 [93]~P23(x931)+P23(x932)+~E(x931,x932) % 1.75/1.87 [94]~P33(x941)+P33(x942)+~E(x941,x942) % 1.75/1.87 [95]P4(x952,x953,x954)+~E(x951,x952)+~P4(x951,x953,x954) % 1.75/1.87 [96]P4(x963,x962,x964)+~E(x961,x962)+~P4(x963,x961,x964) % 1.75/1.87 [97]P4(x973,x974,x972)+~E(x971,x972)+~P4(x973,x974,x971) % 1.75/1.87 [98]~P73(x981)+P73(x982)+~E(x981,x982) % 1.75/1.87 [99]~P63(x991)+P63(x992)+~E(x991,x992) % 1.75/1.87 [100]~P28(x1001)+P28(x1002)+~E(x1001,x1002) % 1.75/1.87 [101]~P65(x1011)+P65(x1012)+~E(x1011,x1012) % 1.75/1.87 [102]~P34(x1021)+P34(x1022)+~E(x1021,x1022) % 1.75/1.87 [103]~P70(x1031)+P70(x1032)+~E(x1031,x1032) % 1.75/1.87 [104]~P71(x1041)+P71(x1042)+~E(x1041,x1042) % 1.75/1.87 [105]~P14(x1051)+P14(x1052)+~E(x1051,x1052) % 1.75/1.87 [106]~P46(x1061)+P46(x1062)+~E(x1061,x1062) % 1.75/1.87 [107]~P52(x1071)+P52(x1072)+~E(x1071,x1072) % 1.75/1.87 [108]~P47(x1081)+P47(x1082)+~E(x1081,x1082) % 1.75/1.87 [109]~P11(x1091)+P11(x1092)+~E(x1091,x1092) % 1.75/1.87 [110]~P37(x1101)+P37(x1102)+~E(x1101,x1102) % 1.75/1.87 [111]~P24(x1111)+P24(x1112)+~E(x1111,x1112) % 1.75/1.87 [112]~P13(x1121)+P13(x1122)+~E(x1121,x1122) % 1.75/1.87 [113]~P48(x1131)+P48(x1132)+~E(x1131,x1132) % 1.75/1.87 [114]~P74(x1141)+P74(x1142)+~E(x1141,x1142) % 1.75/1.87 [115]~P75(x1151)+P75(x1152)+~E(x1151,x1152) % 1.75/1.87 [116]~P5(x1161)+P5(x1162)+~E(x1161,x1162) % 1.75/1.87 [117]~P56(x1171)+P56(x1172)+~E(x1171,x1172) % 1.75/1.87 [118]~P39(x1181)+P39(x1182)+~E(x1181,x1182) % 1.75/1.87 [119]~P36(x1191)+P36(x1192)+~E(x1191,x1192) % 1.75/1.87 [120]~P35(x1201)+P35(x1202)+~E(x1201,x1202) % 1.75/1.87 [121]~P38(x1211)+P38(x1212)+~E(x1211,x1212) % 1.75/1.87 [122]~P82(x1221)+P82(x1222)+~E(x1221,x1222) % 1.75/1.87 [123]~P15(x1231)+P15(x1232)+~E(x1231,x1232) % 1.75/1.87 [124]~P50(x1241)+P50(x1242)+~E(x1241,x1242) % 1.75/1.87 [125]~P55(x1251)+P55(x1252)+~E(x1251,x1252) % 1.75/1.87 [126]~P83(x1261)+P83(x1262)+~E(x1261,x1262) % 1.75/1.87 [127]~P30(x1271)+P30(x1272)+~E(x1271,x1272) % 1.75/1.87 [128]~P76(x1281)+P76(x1282)+~E(x1281,x1282) % 1.75/1.87 [129]~P27(x1291)+P27(x1292)+~E(x1291,x1292) % 1.75/1.87 [130]~P25(x1301)+P25(x1302)+~E(x1301,x1302) % 1.75/1.87 [131]~P21(x1311)+P21(x1312)+~E(x1311,x1312) % 1.75/1.87 [132]~P40(x1321)+P40(x1322)+~E(x1321,x1322) % 1.75/1.87 [133]~P81(x1331)+P81(x1332)+~E(x1331,x1332) % 1.75/1.87 [134]~P29(x1341)+P29(x1342)+~E(x1341,x1342) % 1.75/1.87 [135]~P67(x1351)+P67(x1352)+~E(x1351,x1352) % 1.75/1.87 [136]~P42(x1361)+P42(x1362)+~E(x1361,x1362) % 1.75/1.87 [137]~P78(x1371)+P78(x1372)+~E(x1371,x1372) % 1.75/1.87 [138]~P84(x1381)+P84(x1382)+~E(x1381,x1382) % 1.75/1.87 [139]~P72(x1391)+P72(x1392)+~E(x1391,x1392) % 1.75/1.87 [140]~P17(x1401)+P17(x1402)+~E(x1401,x1402) % 1.75/1.87 [141]~P19(x1411)+P19(x1412)+~E(x1411,x1412) % 1.75/1.87 [142]~P80(x1421)+P80(x1422)+~E(x1421,x1422) % 1.75/1.87 [143]~P20(x1431)+P20(x1432)+~E(x1431,x1432) % 1.75/1.87 [144]~P49(x1441)+P49(x1442)+~E(x1441,x1442) % 1.75/1.87 [145]~P66(x1451)+P66(x1452)+~E(x1451,x1452) % 1.75/1.87 [146]~P51(x1461)+P51(x1462)+~E(x1461,x1462) % 1.75/1.87 [147]~P26(x1471)+P26(x1472)+~E(x1471,x1472) % 1.75/1.87 [148]~P53(x1481)+P53(x1482)+~E(x1481,x1482) % 1.75/1.87 [149]~P68(x1491)+P68(x1492)+~E(x1491,x1492) % 1.75/1.87 [150]~P41(x1501)+P41(x1502)+~E(x1501,x1502) % 1.75/1.87 [151]~P18(x1511)+P18(x1512)+~E(x1511,x1512) % 1.75/1.87 [152]~P64(x1521)+P64(x1522)+~E(x1521,x1522) % 1.75/1.87 [153]~P79(x1531)+P79(x1532)+~E(x1531,x1532) % 1.75/1.87 [154]~P12(x1541)+P12(x1542)+~E(x1541,x1542) % 1.75/1.87 [155]~P43(x1551)+P43(x1552)+~E(x1551,x1552) % 1.75/1.87 % 1.75/1.87 %------------------------------------------- % 1.75/1.88 cnf(1401,plain, % 1.75/1.88 (~P2(x14011,x14011,a2)), % 1.75/1.88 inference(rename_variables,[],[314])). % 1.75/1.88 cnf(1404,plain, % 1.75/1.88 (~P2(x14041,x14041,a2)), % 1.75/1.88 inference(rename_variables,[],[314])). % 1.75/1.88 cnf(1407,plain, % 1.75/1.88 (~P2(x14071,x14071,a2)), % 1.75/1.88 inference(rename_variables,[],[314])). % 1.75/1.88 cnf(1410,plain, % 1.75/1.88 (~P2(x14101,x14101,a2)), % 1.75/1.88 inference(rename_variables,[],[314])). % 1.75/1.88 cnf(1412,plain, % 1.75/1.88 (~E(f17(x14121,x14122),f32(a34))), % 1.75/1.88 inference(scs_inference,[],[271,314,1401,1404,1407,313,181,293,283,2,317,448,472,490,617,618,621,622,3])). % 1.75/1.88 cnf(1414,plain, % 1.75/1.88 (~P2(x14141,x14141,a2)), % 1.75/1.88 inference(rename_variables,[],[314])). % 1.75/1.88 cnf(1416,plain, % 1.75/1.88 (~P2(x14161,x14161,a2)), % 1.75/1.88 inference(rename_variables,[],[314])). % 1.75/1.88 cnf(1418,plain, % 1.75/1.88 (P3(x14181,x14181,a2)), % 1.75/1.88 inference(rename_variables,[],[291])). % 1.75/1.88 cnf(1420,plain, % 1.75/1.88 (P3(x14201,x14201,a2)), % 1.75/1.88 inference(rename_variables,[],[291])). % 1.75/1.88 cnf(1463,plain, % 1.75/1.88 (P3(x14631,x14631,a2)), % 1.75/1.88 inference(rename_variables,[],[291])). % 1.75/1.88 cnf(1470,plain, % 1.75/1.88 (~P2(x14701,x14701,a2)), % 1.75/1.88 inference(rename_variables,[],[314])). % 1.75/1.88 cnf(1477,plain, % 1.75/1.88 (~P2(x14771,x14771,a2)), % 1.75/1.88 inference(rename_variables,[],[314])). % 1.75/1.88 cnf(1480,plain, % 1.75/1.88 (~P2(x14801,x14801,a2)), % 1.75/1.88 inference(rename_variables,[],[314])). % 1.75/1.88 cnf(1485,plain, % 1.75/1.88 (~P2(x14851,x14851,a2)), % 1.75/1.88 inference(rename_variables,[],[314])). % 1.75/1.88 cnf(1490,plain, % 1.75/1.88 (~P2(x14901,x14901,a2)), % 1.75/1.88 inference(rename_variables,[],[314])). % 1.75/1.88 cnf(1497,plain, % 1.75/1.88 (~P2(x14971,x14971,a2)), % 1.75/1.88 inference(rename_variables,[],[314])). % 1.75/1.88 cnf(1505,plain, % 1.75/1.88 (P2(f3(a2),f32(a34),a2)), % 1.75/1.88 inference(scs_inference,[],[271,291,1418,1420,1463,314,1401,1404,1407,1410,1414,1416,1470,1477,1480,1485,1490,1497,313,302,303,162,164,165,166,179,180,181,187,191,195,196,197,243,262,290,311,292,293,295,315,310,283,2,317,448,472,490,617,618,621,622,3,71,72,81,82,341,346,347,348,349,350,351,352,411,489,498,499,509,522,523,537,557,585,648,671,705,718,719,720,738,739,740,741,742,743,772,774,776,777,779,780,798,799])). % 1.75/1.88 cnf(1852,plain, % 1.75/1.88 ($false), % 1.75/1.88 inference(scs_inference,[],[1412,1505,503]), % 1.75/1.88 ['proof']). % 1.75/1.88 % SZS output end Proof % 1.75/1.88 % Total time :0.810000s %------------------------------------------------------------------------------