%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : ALG354-1 : 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 : n012.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Jun 24 03:41:25 EDT 2024 % Result : Unsatisfiable 1.17s 1.31s % Output : CNFRefutation 1.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.10 % Problem : ALG354-1 : TPTP v8.2.0. Released v4.1.0. % 0.09/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.10/0.31 % Computer : n012.cluster.edu % 0.10/0.31 % Model : x86_64 x86_64 % 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.31 % Memory : 8042.1875MB % 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.31 % CPULimit : 300 % 0.10/0.31 % WCLimit : 300 % 0.10/0.31 % DateTime : Wed Jun 19 16:43:39 EDT 2024 % 0.10/0.31 % CPUTime : % 0.16/0.56 start to proof:theBenchmark % 1.17/1.26 %------------------------------------------- % 1.17/1.26 % File :CSE---1.7 % 1.17/1.26 % Problem :theBenchmark % 1.17/1.26 % Transform :cnf % 1.17/1.26 % Format :tptp:raw % 1.17/1.26 % Command :java -jar mcs_scs.jar %d %s % 1.17/1.26 % 1.17/1.26 % Result :Theorem 0.560000s % 1.17/1.26 % Output :CNFRefutation 0.560000s % 1.17/1.26 %------------------------------------------- % 1.17/1.27 %------------------------------------------------------------------------------ % 1.17/1.27 % File : ALG354-1 : TPTP v8.2.0. Released v4.1.0. % 1.17/1.27 % Domain : General Algebra % 1.17/1.27 % Problem : Fundamental theorem of algebra 0212_59 % 1.17/1.27 % Version : Especial. % 1.17/1.27 % English : % 1.17/1.27 % 1.17/1.27 % Refs : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe % 1.17/1.27 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 1.17/1.27 % Source : [Nip10] % 1.17/1.27 % Names : Fundamental_Theorem_Algebra-0212_59 [Nip10] % 1.17/1.27 % 1.17/1.27 % Status : Unsatisfiable % 1.17/1.27 % Rating : 0.10 v8.1.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.07 v6.3.0, 0.00 v6.0.0, 0.10 v5.5.0, 0.35 v5.3.0, 0.28 v5.2.0, 0.25 v5.1.0, 0.29 v5.0.0, 0.14 v4.1.0 % 1.17/1.27 % Syntax : Number of clauses : 478 ( 127 unt; 76 nHn; 302 RR) % 1.17/1.27 % Number of literals : 1224 ( 280 equ; 685 neg) % 1.17/1.27 % Maximal clause size : 6 ( 2 avg) % 1.17/1.27 % Maximal term depth : 6 ( 1 avg) % 1.17/1.27 % Number of predicates : 51 ( 50 usr; 1 prp; 0-3 aty) % 1.17/1.27 % Number of functors : 16 ( 16 usr; 6 con; 0-3 aty) % 1.17/1.27 % Number of variables : 1070 ( 51 sgn) % 1.17/1.27 % SPC : CNF_UNS_RFO_SEQ_NHN % 1.17/1.27 % 1.17/1.27 % Comments : % 1.17/1.27 %------------------------------------------------------------------------------ % 1.17/1.27 cnf(cls_less__Suc0_1,axiom, % 1.17/1.27 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_less__Suc0_0,axiom, % 1.17/1.27 ( V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 1.17/1.27 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_nat__lt__two__imp__zero__or__one_0,axiom, % 1.17/1.27 ( V_x = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.17/1.27 | V_x = c_HOL_Ozero__class_Ozero(tc_nat) % 1.17/1.27 | ~ c_HOL_Oord__class_Oless(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_gr0__conv__Suc_1,axiom, % 1.17/1.27 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_zero__less__Suc_0,axiom, % 1.17/1.27 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_class__semiring_Opwr__0_0,axiom, % 1.17/1.27 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.27 | c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_power__0_0,axiom, % 1.17/1.27 ( ~ class_Power_Opower(T_a) % 1.17/1.27 | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_power__0__left_1,axiom, % 1.17/1.27 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 1.17/1.27 | ~ class_Power_Opower(T_a) % 1.17/1.27 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.27 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_power__eq__0__iff_2,axiom, % 1.17/1.27 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.17/1.27 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.17/1.27 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.17/1.27 | ~ class_Power_Opower(T_a) % 1.17/1.27 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.27 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_power__eq__0__iff_1,axiom, % 1.17/1.27 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.17/1.27 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.17/1.27 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.17/1.27 | ~ class_Power_Opower(T_a) % 1.17/1.27 | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_neq0__conv_1,axiom, % 1.17/1.27 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_gr0I_0,axiom, % 1.17/1.27 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.17/1.27 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_nat_Osimps_I3_J_0,axiom, % 1.17/1.27 c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_Suc__neq__Zero_0,axiom, % 1.17/1.27 c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_not__less0_0,axiom, % 1.17/1.27 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_gr__implies__not0_0,axiom, % 1.17/1.27 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_nat_Osimps_I2_J_0,axiom, % 1.17/1.27 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_Zero__neq__Suc_0,axiom, % 1.17/1.27 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_zero__less__power__eq_3,axiom, % 1.17/1.27 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.17/1.27 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a),T_a) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_zero__less__power__eq_2,axiom, % 1.17/1.27 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.17/1.27 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 1.17/1.27 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a),T_a) % 1.17/1.27 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_power__0__left_0,axiom, % 1.17/1.27 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 1.17/1.27 | ~ class_Power_Opower(T_a) % 1.17/1.27 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_minus__mult__left_0,axiom, % 1.17/1.27 ( ~ class_Ring__and__Field_Oring(T_a) % 1.17/1.27 | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_minus__mult__right_0,axiom, % 1.17/1.27 ( ~ class_Ring__and__Field_Oring(T_a) % 1.17/1.27 | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_mult_Ominus__left_0,axiom, % 1.17/1.27 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.17/1.27 | 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) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_mult__left_Ominus_0,axiom, % 1.17/1.27 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.17/1.27 | 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) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_mult_Ominus__right_0,axiom, % 1.17/1.27 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.17/1.27 | 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) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_mult__right_Ominus_0,axiom, % 1.17/1.27 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.17/1.27 | 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) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_square__eq__iff_1,axiom, % 1.17/1.27 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.17/1.27 | 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) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_minus__mult__minus_0,axiom, % 1.17/1.27 ( ~ class_Ring__and__Field_Oring(T_a) % 1.17/1.27 | 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) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom, % 1.17/1.27 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.27 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom, % 1.17/1.27 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.27 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_mult__left_Ozero_0,axiom, % 1.17/1.27 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.17/1.27 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_mult_Ozero__left_0,axiom, % 1.17/1.27 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.17/1.27 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_mult_Ozero__right_0,axiom, % 1.17/1.27 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.17/1.27 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_mult__right_Ozero_0,axiom, % 1.17/1.27 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.17/1.27 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_class__semiring_Omul__0_0,axiom, % 1.17/1.27 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.27 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_mult__zero__left_0,axiom, % 1.17/1.27 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 1.17/1.27 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_mult__zero__right_0,axiom, % 1.17/1.27 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 1.17/1.27 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_mult__eq__0__iff_1,axiom, % 1.17/1.27 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.17/1.27 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.27 % 1.17/1.27 cnf(cls_mult__eq__0__iff_2,axiom, % 1.17/1.27 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.17/1.27 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_minus__mult__commute_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oring(T_a) % 1.17/1.28 | 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) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_divide__less__eq_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_divide__less__eq_6,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_less__divide__eq_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_less__divide__eq_6,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_mult__imp__div__pos__less_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_mult__imp__less__div__pos_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_divide__less__eq_8,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_divide__less__eq_9,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_less__divide__eq_8,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_less__divide__eq_9,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_divide__less__eq_1,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_divide__less__eq_4,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_divide__less__eq_5,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_divide__less__eq_7,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_less__divide__eq_1,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_less__divide__eq_4,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_less__divide__eq_5,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_less__divide__eq_7,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_divide__strict__left__mono_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | 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) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_divide__strict__left__mono__neg_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | 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) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_less__minus__iff_0,axiom, % 1.17/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_less__minus__iff_1,axiom, % 1.17/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_minus__less__iff_0,axiom, % 1.17/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_minus__less__iff_1,axiom, % 1.17/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_neg__less__iff__less_0,axiom, % 1.17/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_neg__less__iff__less_1,axiom, % 1.17/1.28 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_less__Suc__eq__0__disj_3,axiom, % 1.17/1.28 ( c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_x,V_n,tc_nat) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_Suc__less__eq_0,axiom, % 1.17/1.28 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_Suc__mono_0,axiom, % 1.17/1.28 ( c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_one__less__power_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_mult__frac__frac_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | 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) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_mult__eq__0__iff_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.17/1.28 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.28 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.28 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_no__zero__divisors_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.17/1.28 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.28 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.28 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_no__zero__divirors__neq0_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.17/1.28 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.28 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.28 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_square__eq__iff_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.17/1.28 | c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) != c_HOL_Otimes__class_Otimes(V_b,V_b,T_a) % 1.17/1.28 | V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a) % 1.17/1.28 | V_a = V_b ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_mult__frac__num_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | 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) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_add__frac__eq_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.28 | 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) % 1.17/1.28 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.28 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_add__num__frac_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | 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) % 1.17/1.28 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_add__frac__num_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | 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) % 1.17/1.28 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_zero__less__divide__1__iff_1,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | 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) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_zero__less__divide__1__iff_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.28 | ~ 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) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_divide__less__0__1__iff_1,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | 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) % 1.17/1.28 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_divide__less__0__1__iff_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.28 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.28 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.28 | ~ 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) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_minus__add__distrib_0,axiom, % 1.17/1.28 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.17/1.28 | 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) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_minus__add_0,axiom, % 1.17/1.28 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.28 | 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) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_minus__add__cancel_0,axiom, % 1.17/1.28 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.28 | 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 ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_add__cancel__end_1,axiom, % 1.17/1.28 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.17/1.28 | 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 ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_add__minus__cancel_0,axiom, % 1.17/1.28 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.28 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a),T_a) = V_b ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_double__eq__0__iff_0,axiom, % 1.17/1.28 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.17/1.28 | c_HOL_Oplus__class_Oplus(V_a,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.28 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_class__ringb_Oadd__r0__iff_0,axiom, % 1.17/1.28 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.17/1.28 | ~ class_Int_Onumber__ring(T_a) % 1.17/1.28 | V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) % 1.17/1.28 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_double__eq__0__iff_1,axiom, % 1.17/1.28 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.17/1.28 | 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) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_add__cancel__end_0,axiom, % 1.17/1.28 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.17/1.28 | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != V_y % 1.17/1.28 | V_x = c_HOL_Ouminus__class_Ouminus(V_z,T_a) ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_monoid__add__class_Oadd__0__right_0,axiom, % 1.17/1.28 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 1.17/1.28 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_add__0__left_0,axiom, % 1.17/1.28 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 1.17/1.28 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.17/1.28 % 1.17/1.28 cnf(cls_comm__monoid__add_Omult__1__right_0,axiom, % 1.17/1.28 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.17/1.29 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_class__ringb_Oadd__r0__iff_1,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.17/1.29 | ~ class_Int_Onumber__ring(T_a) % 1.17/1.29 | V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_class__semiring_Oadd__0_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.29 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = V_x ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_comm__monoid__add_Omult__1_0,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.17/1.29 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.29 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.29 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_add__divide__distrib_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.29 | 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_divide_Oadd_0,axiom, % 1.17/1.29 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.17/1.29 | 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_zero__neq__one_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.17/1.29 | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_divide__1_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.29 | c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_one__neq__zero_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.17/1.29 | c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_field__power__not__zero_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(T_a) % 1.17/1.29 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.29 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_power__eq__0__iff_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.17/1.29 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.17/1.29 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.17/1.29 | ~ class_Power_Opower(T_a) % 1.17/1.29 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.29 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_power__divide_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.29 | 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_real__mult__1_0,axiom, % 1.17/1.29 c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) = V_z ). % 1.17/1.29 % 1.17/1.29 cnf(cls_real__mult__is__one_1,axiom, % 1.17/1.29 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) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_norm__minus__cancel_0,axiom, % 1.17/1.29 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.17/1.29 | 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_power__strict__decreasing_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_N,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_power__Suc__less__one_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__less__cancel__right__disj_2,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__less__cancel__right__disj_1,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__less__cancel__left__disj_2,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__less__cancel__left__disj_1,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_not__square__less__zero_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | ~ 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__less__cancel__right__disj_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__less__cancel__left__disj_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__pos__neg2_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__pos__neg_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__neg__pos_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_zero__less__mult__pos2_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_zero__less__mult__pos_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__pos__pos_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__neg__neg_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__strict__left__mono__comm_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__less__cancel__right__disj_5,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__less__cancel__right__disj_4,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__strict__right__mono_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__strict__right__mono__neg_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__less__cancel__left__disj_5,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__less__cancel__left__disj_4,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__strict__left__mono_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__strict__left__mono__neg_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__less__cancel__left__pos_1,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__less__cancel__left__pos_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__less__cancel__left__neg_1,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__less__cancel__left__neg_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_add__pos__pos_0,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.17/1.29 | 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) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.17/1.29 | 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) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.17/1.29 | ~ 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_pos__add__strict_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_even__less__0__iff_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_even__less__0__iff_1,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_add__neg__neg_0,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_sum__squares__eq__zero__iff_2,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_sum__squares__eq__zero__iff_1,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | 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) % 1.17/1.29 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_sum__squares__eq__zero__iff_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | 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) % 1.17/1.29 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.17/1.29 | ~ class_Int_Onumber__ring(T_a) % 1.17/1.29 | 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) % 1.17/1.29 | V_c = V_d % 1.17/1.29 | V_r = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_zero__less__one_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_not__one__less__zero_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_class__ring_Oneg__mul_0,axiom, % 1.17/1.29 ( ~ class_Int_Onumber__ring(T_a) % 1.17/1.29 | 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_zero__less__power_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.29 | 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) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_power__less__zero__eq_1,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | ~ 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_class__semiring_Osemiring__rules_I28_J_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.29 | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_q,T_a),V_x,T_a) = c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_class__semiring_Osemiring__rules_I27_J_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.29 | c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_class__semiring_Opwr__Suc_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.29 | c_Power_Opower__class_Opower(V_x,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_power__Suc2_0,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.17/1.29 | c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_a,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_power__Suc_0,axiom, % 1.17/1.29 ( ~ class_Power_Opower(T_a) % 1.17/1.29 | c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_class__semiring_Osemiring__rules_I35_J_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.29 | c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a) = c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_power__one__over_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.29 | 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_norm__mult_0,axiom, % 1.17/1.29 ( ~ class_RealVector_Oreal__normed__div__algebra(T_a) % 1.17/1.29 | 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_sum__squares__gt__zero__iff_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | ~ 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_not__sum__squares__lt__zero_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_sum__squares__gt__zero__iff_2,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | 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) % 1.17/1.29 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_sum__squares__gt__zero__iff_1,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.29 | 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) % 1.17/1.29 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_minus__minus_0,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.29 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_double__compl_0,axiom, % 1.17/1.29 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.17/1.29 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = V_x ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_equation__minus__iff_0,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.29 | V_b = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_equation__minus__iff_1,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.29 | V_a = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_minus__equation__iff_1,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.29 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__divide__mult__cancel__left_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.29 | 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) % 1.17/1.29 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_mult__divide__mult__cancel__right_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.29 | 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) % 1.17/1.29 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_divide__less__0__iff_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.17/1.29 | ~ 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_divide__less__0__iff_1,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.17/1.29 | ~ 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_divide__less__0__iff_2,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | ~ 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_divide__less__0__iff_3,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | ~ 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_Suc__lessI_0,axiom, % 1.17/1.29 ( c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) % 1.17/1.29 | c_Suc(V_m) = V_n % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_divide_Ozero_0,axiom, % 1.17/1.29 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.17/1.29 | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_divide__zero_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.29 | c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_divide__eq__eq_1,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.29 | c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_divide__zero__left_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.29 | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_left__minus_0,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.29 | 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_right__minus_0,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.29 | 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_ab__left__minus_0,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.17/1.29 | 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_eq__neg__iff__add__eq__0_0,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.29 | 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_divide_Ominus_0,axiom, % 1.17/1.29 ( ~ class_RealVector_Oreal__normed__field(T_a) % 1.17/1.29 | 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_minus__divide__divide_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.29 | 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_divide__self__if_1,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.29 | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.17/1.29 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_divide__self_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.29 | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.17/1.29 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_right__inverse__eq_1,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.29 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.29 | c_HOL_Oinverse__class_Odivide(V_x,V_x,T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_neg__0__equal__iff__equal_0,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.29 | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.17/1.29 | c_HOL_Ozero__class_Ozero(T_a) = V_a ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_real__mult__commute_0,axiom, % 1.17/1.29 c_HOL_Otimes__class_Otimes(V_z,V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,V_z,tc_RealDef_Oreal) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_neg__less__0__iff__less_0,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_neg__less__0__iff__less_1,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_nonzero__minus__divide__right_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.29 | 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) % 1.17/1.29 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_power__0__Suc_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 1.17/1.29 | ~ class_Power_Opower(T_a) % 1.17/1.29 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Suc(V_n),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_neg__equal__0__iff__equal_0,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.29 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.29 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_divide__eq__eq_3,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.29 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a % 1.17/1.29 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_eq__divide__eq_3,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.29 | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) % 1.17/1.29 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_divide__eq__imp_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.29 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.29 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_eq__divide__imp_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.29 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.29 | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_neg__equal__iff__equal_0,axiom, % 1.17/1.29 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.29 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(V_b,T_a) % 1.17/1.29 | V_a = V_b ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_compl__eq__compl__iff_0,axiom, % 1.17/1.29 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.17/1.29 | c_HOL_Ouminus__class_Ouminus(V_x,T_a) != c_HOL_Ouminus__class_Ouminus(V_y,T_a) % 1.17/1.29 | V_x = V_y ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_linorder__neqE__nat_0,axiom, % 1.17/1.29 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 1.17/1.29 | V_x = V_y ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_nat__neq__iff_0,axiom, % 1.17/1.29 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.17/1.29 | V_m = V_n ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_less__trans__Suc_0,axiom, % 1.17/1.29 ( c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) % 1.17/1.29 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_less__Suc__eq_2,axiom, % 1.17/1.29 c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_lessI_0,axiom, % 1.17/1.29 c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_n__not__Suc__n_0,axiom, % 1.17/1.29 V_n != c_Suc(V_n) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_Suc__n__not__n_0,axiom, % 1.17/1.29 c_Suc(V_n) != V_n ). % 1.17/1.29 % 1.17/1.29 cnf(cls_zero__less__divide__iff_0,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.17/1.29 | ~ 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) ) ). % 1.17/1.29 % 1.17/1.29 cnf(cls_zero__less__divide__iff_1,axiom, % 1.17/1.29 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.29 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.29 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.17/1.30 | ~ 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_zero__less__divide__iff_2,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.30 | ~ 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_zero__less__divide__iff_3,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.30 | ~ 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_less__SucI_0,axiom, % 1.17/1.30 ( c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_Suc__lessD_0,axiom, % 1.17/1.30 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_right__inverse__eq_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.30 | c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.17/1.30 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.30 | V_a = V_b ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_real__mult__assoc_0,axiom, % 1.17/1.30 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) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_real__add__mult__distrib_0,axiom, % 1.17/1.30 c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_z1,V_z2,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_z1,V_w,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_z2,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_minus__divide__right_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_minus__divide__left_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_neg__equal__zero_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.17/1.30 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != V_a % 1.17/1.30 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_divide__less__eq_2,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_divide__less__eq_3,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_less__divide__eq_2,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_less__divide__eq_3,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_not__less__less__Suc__eq_1,axiom, % 1.17/1.30 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_not__less__eq_1,axiom, % 1.17/1.30 ( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_not__less__eq_0,axiom, % 1.17/1.30 ( c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_divide__neg__neg_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_divide__pos__pos_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_zero__less__divide__iff_4,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_zero__less__divide__iff_5,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_nonzero__minus__divide__divide_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_divide__strict__right__mono_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_divide__strict__right__mono__neg_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_divide__self__if_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_nat_Oinject_0,axiom, % 1.17/1.30 ( c_Suc(V_nat) != c_Suc(V_nat_H) % 1.17/1.30 | V_nat = V_nat_H ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_Suc__inject_0,axiom, % 1.17/1.30 ( c_Suc(V_x) != c_Suc(V_y) % 1.17/1.30 | V_x = V_y ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_eq__divide__eq_4,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_minus__unique_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.30 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.30 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_eq__neg__iff__add__eq__0_1,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.30 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.30 | V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_not__less__less__Suc__eq_0,axiom, % 1.17/1.30 ( V_n = V_m % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_less__antisym_0,axiom, % 1.17/1.30 ( V_m = V_n % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_less__SucE_0,axiom, % 1.17/1.30 ( V_m = V_n % 1.17/1.30 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_divide__eq__eq_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.30 | V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) % 1.17/1.30 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_eq__divide__eq_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b % 1.17/1.30 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_less__not__refl_0,axiom, % 1.17/1.30 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_nat__less__le_1,axiom, % 1.17/1.30 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_neg__0__equal__iff__equal_1,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.30 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_minus__zero_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.17/1.30 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_neg__equal__zero_1,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.17/1.30 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_nonzero__power__divide_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_divide__neg__pos_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_divide__pos__neg_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_divide__less__0__iff_4,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_divide__less__0__iff_5,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_eq__divide__eq_2,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.30 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_neg__0__less__iff__less_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_neg__0__less__iff__less_1,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_frac__eq__eq_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.30 | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) != c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) % 1.17/1.30 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.30 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.30 | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) = c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_frac__eq__eq_1,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.30 | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) != c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) % 1.17/1.30 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.30 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.17/1.30 | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_less__minus__self__iff_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_less__minus__self__iff_1,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_divide__eq__eq_4,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.17/1.30 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_less__half__sum_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_gt__half__sum_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_zero__less__two_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_power__strict__increasing__iff_1,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_power__strict__increasing__iff_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_power__strict__increasing_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_a,V_N,T_a),T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_power__less__imp__less__exp_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_power__gt1_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_power__minus_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oring__1(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_norm__mult__less_0,axiom, % 1.17/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_y,T_a),V_s,tc_RealDef_Oreal) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),V_r,tc_RealDef_Oreal) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_norm__add__less_0,axiom, % 1.17/1.30 ( ~ class_RealVector_Oreal__normed__vector(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a),c_HOL_Oplus__class_Oplus(V_r,V_s,tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_y,T_a),V_s,tc_RealDef_Oreal) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),V_r,tc_RealDef_Oreal) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_power__Suc__less_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_xt1_I9_J_0,axiom, % 1.17/1.30 ( ~ class_Orderings_Oorder(T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_not__less__iff__gr__or__eq_1,axiom, % 1.17/1.30 ( ~ class_Orderings_Olinorder(T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_order__less__asym_0,axiom, % 1.17/1.30 ( ~ class_Orderings_Opreorder(T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_order__less__asym_H_0,axiom, % 1.17/1.30 ( ~ class_Orderings_Opreorder(T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_add__strict__right__mono_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_add__less__cancel__right_1,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_add__less__cancel__right_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.17/1.30 | ~ 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_add__strict__left__mono_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_add__less__cancel__left_1,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_add__less__cancel__left_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.17/1.30 | ~ 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_power__inject__exp_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.30 | c_Power_Opower__class_Opower(V_a,V_m,T_a) != c_Power_Opower__class_Opower(V_a,V_n,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 1.17/1.30 | V_m = V_n ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_add__strict__mono_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_order__less__irrefl_0,axiom, % 1.17/1.30 ( ~ class_Orderings_Opreorder(T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_real__less__def_1,axiom, % 1.17/1.30 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_order__less__le_1,axiom, % 1.17/1.30 ( ~ class_Orderings_Oorder(T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_linorder__neq__iff_1,axiom, % 1.17/1.30 ( ~ class_Orderings_Olinorder(T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I2_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__ringb_Oadd__mul__solve_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.17/1.30 | ~ class_Int_Onumber__ring(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | V_y = V_z % 1.17/1.30 | V_w = V_x ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__ringb_Onoteq__reduce_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.17/1.30 | ~ class_Int_Onumber__ring(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | V_c = V_d % 1.17/1.30 | V_a = V_b ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I4_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_power__commutes_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_comm__monoid__add_Omult__commute_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.17/1.30 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Oadd__c_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_y,V_x,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_add__cancel__21_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) = V_u ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_power__one_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.17/1.30 | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_norm__one_0,axiom, % 1.17/1.30 ( ~ class_RealVector_Oreal__normed__algebra__1(T_a) % 1.17/1.30 | c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_add__right__cancel_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 1.17/1.30 | c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) != c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) % 1.17/1.30 | V_b = V_c ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_add__left__cancel_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 1.17/1.30 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) % 1.17/1.30 | V_b = V_c ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_add__imp__eq_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a) % 1.17/1.30 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) % 1.17/1.30 | V_b = V_c ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__ringb_Oadd__cancel_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.17/1.30 | ~ class_Int_Onumber__ring(T_a) % 1.17/1.30 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) % 1.17/1.30 | V_y = V_z ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_mult__less__cancel__right__disj_3,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_mult__less__cancel__left__disj_3,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_comm__semiring__class_Odistrib_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Omul__d_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_mult_Oadd__left_0,axiom, % 1.17/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_mult__left_Oadd_0,axiom, % 1.17/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_mult_Oadd__right_0,axiom, % 1.17/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_mult__right_Oadd_0,axiom, % 1.17/1.30 ( ~ class_RealVector_Oreal__normed__algebra(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Omul__a_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_power__mult__distrib_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Opwr__mul_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_mult__idem_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 1.17/1.30 | c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = V_x ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_power__less__power__Suc_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_mult__left__idem_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 1.17/1.30 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_less__add__one_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_linorder__neqE__ordered__idom_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.17/1.30 | V_x = V_y ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_not__less__iff__gr__or__eq_0,axiom, % 1.17/1.30 ( ~ class_Orderings_Olinorder(T_a) % 1.17/1.30 | V_x = V_y % 1.17/1.30 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_linorder__antisym__conv3_0,axiom, % 1.17/1.30 ( ~ class_Orderings_Olinorder(T_a) % 1.17/1.30 | V_x = V_y % 1.17/1.30 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_linorder__less__linear_0,axiom, % 1.17/1.30 ( ~ class_Orderings_Olinorder(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.17/1.30 | V_x = V_y % 1.17/1.30 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_linorder__neqE_0,axiom, % 1.17/1.30 ( ~ class_Orderings_Olinorder(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.17/1.30 | V_x = V_y ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_power__gt1__lemma_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_ry,T_a),T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_mult__1__right_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.17/1.30 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_mult__1__left_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.17/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_mult__1_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) % 1.17/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Omul__1_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_x,T_a) = V_x ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I11_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__ringb_Oadd__mul__solve_1,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.17/1.30 | ~ class_Int_Onumber__ring(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__ringb_Onoteq__reduce_1,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.17/1.30 | ~ class_Int_Onumber__ring(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Omul__c_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_xt1_I10_J_0,axiom, % 1.17/1.30 ( ~ class_Orderings_Oorder(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_order__less__trans_0,axiom, % 1.17/1.30 ( ~ class_Orderings_Opreorder(T_a) % 1.17/1.30 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_comm__monoid__add_Omult__assoc_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Oadd__a_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_add__cancel__21_1,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom, % 1.17/1.30 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_combine__common__factor_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Osemiring(T_a) % 1.17/1.30 | 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) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_that_0,axiom, % 1.17/1.30 ( v_thesis____ % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(V_z,v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_less__1__mult_0,axiom, % 1.17/1.30 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.17/1.30 | 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) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_n,T_a) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_m,T_a) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_CHAINED_0,axiom, % 1.17/1.30 c_HOL_Oord__class_Oless(v_m____,v_na____,tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_CHAINED_0_01,axiom, % 1.17/1.30 v_m____ != c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_CHAINED_0_02,axiom, % 1.17/1.30 ( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(v_sko__CHAINED__1(v_b,v_m____),v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) % 1.17/1.30 | v_m____ = c_HOL_Ozero__class_Ozero(tc_nat) % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(v_m____,v_na____,tc_nat) ) ). % 1.17/1.30 % 1.17/1.30 cnf(cls_conjecture_0,negated_conjecture, % 1.17/1.30 ~ v_thesis____ ). % 1.17/1.30 % 1.17/1.30 cnf(cls_conjecture_1,negated_conjecture, % 1.17/1.30 ( v_thesis____ % 1.17/1.30 | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_Power_Opower__class_Opower(V_x,v_m____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom, % 1.17/1.30 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom, % 1.17/1.30 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom, % 1.17/1.30 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom, % 1.17/1.30 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom, % 1.17/1.30 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 1.17/1.30 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom, % 1.17/1.30 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom, % 1.17/1.30 class_Ring__and__Field_Ono__zero__divisors(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom, % 1.17/1.30 class_Ring__and__Field_Oordered__semidom(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom, % 1.17/1.30 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom, % 1.17/1.30 class_OrderedGroup_Oab__semigroup__mult(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom, % 1.17/1.30 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom, % 1.17/1.30 class_OrderedGroup_Oab__semigroup__add(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom, % 1.17/1.30 class_Ring__and__Field_Ocomm__semiring(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom, % 1.17/1.30 class_OrderedGroup_Ocomm__monoid__add(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom, % 1.17/1.30 class_Ring__and__Field_Ozero__neq__one(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom, % 1.17/1.30 class_Ring__and__Field_Osemiring__0(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom, % 1.17/1.30 class_Ring__and__Field_Omult__zero(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom, % 1.17/1.30 class_OrderedGroup_Omonoid__mult(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom, % 1.17/1.30 class_Ring__and__Field_Osemiring(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom, % 1.17/1.30 class_OrderedGroup_Omonoid__add(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__Orderings_Opreorder,axiom, % 1.17/1.30 class_Orderings_Opreorder(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__Orderings_Olinorder,axiom, % 1.17/1.30 class_Orderings_Olinorder(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__Orderings_Oorder,axiom, % 1.17/1.30 class_Orderings_Oorder(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_nat__Power_Opower,axiom, % 1.17/1.30 class_Power_Opower(tc_nat) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom, % 1.17/1.30 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom, % 1.17/1.30 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict,axiom, % 1.17/1.30 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors,axiom, % 1.17/1.30 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict,axiom, % 1.17/1.30 class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add,axiom, % 1.17/1.30 class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors,axiom, % 1.17/1.30 class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 1.17/1.30 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict,axiom, % 1.17/1.30 class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom, % 1.17/1.30 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,axiom, % 1.17/1.30 class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,axiom, % 1.17/1.30 class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add,axiom, % 1.17/1.30 class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add,axiom, % 1.17/1.30 class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom, % 1.17/1.30 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors,axiom, % 1.17/1.30 class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero,axiom, % 1.17/1.30 class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom,axiom, % 1.17/1.30 class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom, % 1.17/1.30 class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom, % 1.17/1.30 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult,axiom, % 1.17/1.30 class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom, % 1.17/1.30 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult,axiom, % 1.17/1.30 class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add,axiom, % 1.17/1.30 class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field,axiom, % 1.17/1.30 class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring,axiom, % 1.17/1.30 class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom, % 1.17/1.30 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add,axiom, % 1.17/1.30 class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one,axiom, % 1.17/1.30 class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) ). % 1.17/1.30 % 1.17/1.30 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,axiom, % 1.17/1.30 class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0,axiom, % 1.17/1.31 class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,axiom, % 1.17/1.31 class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero,axiom, % 1.17/1.31 class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult,axiom, % 1.17/1.31 class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring,axiom, % 1.17/1.31 class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add,axiom, % 1.17/1.31 class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom, % 1.17/1.31 class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1,axiom, % 1.17/1.31 class_Ring__and__Field_Oring__1(tc_RealDef_Oreal) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ofield,axiom, % 1.17/1.31 class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring,axiom, % 1.17/1.31 class_Ring__and__Field_Oring(tc_RealDef_Oreal) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oidom,axiom, % 1.17/1.31 class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom, % 1.17/1.31 class_Orderings_Opreorder(tc_RealDef_Oreal) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom, % 1.17/1.31 class_Orderings_Olinorder(tc_RealDef_Oreal) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_RealDef__Oreal__Orderings_Oorder,axiom, % 1.17/1.31 class_Orderings_Oorder(tc_RealDef_Oreal) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom, % 1.17/1.31 class_Int_Onumber__ring(tc_RealDef_Oreal) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_RealDef__Oreal__Power_Opower,axiom, % 1.17/1.31 class_Power_Opower(tc_RealDef_Oreal) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors,axiom, % 1.17/1.31 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,axiom, % 1.17/1.31 class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 1.17/1.31 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom, % 1.17/1.31 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add,axiom, % 1.17/1.31 class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom, % 1.17/1.31 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,axiom, % 1.17/1.31 class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom, % 1.17/1.31 class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom, % 1.17/1.31 class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom, % 1.17/1.31 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,axiom, % 1.17/1.31 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom, % 1.17/1.31 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,axiom, % 1.17/1.31 class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add,axiom, % 1.17/1.31 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring,axiom, % 1.17/1.31 class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom, % 1.17/1.31 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,axiom, % 1.17/1.31 class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom, % 1.17/1.31 class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0,axiom, % 1.17/1.31 class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,axiom, % 1.17/1.31 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,axiom, % 1.17/1.31 class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom, % 1.17/1.31 class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring,axiom, % 1.17/1.31 class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add,axiom, % 1.17/1.31 class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom, % 1.17/1.31 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1,axiom, % 1.17/1.31 class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom, % 1.17/1.31 class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring,axiom, % 1.17/1.31 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom, % 1.17/1.31 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom, % 1.17/1.31 class_Int_Onumber__ring(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 cnf(clsarity_Complex__Ocomplex__Power_Opower,axiom, % 1.17/1.31 class_Power_Opower(tc_Complex_Ocomplex) ). % 1.17/1.31 % 1.17/1.31 %------------------------------------------------------------------------------ % 1.17/1.31 %------------------------------------------- % 1.17/1.31 % Proof found % 1.17/1.31 % SZS status Theorem for theBenchmark % 1.17/1.31 % SZS output start Proof % 1.17/1.31 %ClaNum:554(EqnAxiom:76) % 1.17/1.31 %VarNum:2921(SingletonVarNum:876) % 1.17/1.31 %MaxLitNum:6 % 1.17/1.31 %MaxfuncDepth:5 % 1.17/1.31 %SharedTerms:129 % 1.17/1.31 %goalClause: 190 554 % 1.17/1.31 %singleGoalClaCount:1 % 1.17/1.31 [77]P1(a1) % 1.17/1.31 [78]P1(a2) % 1.17/1.31 [79]P1(a3) % 1.17/1.31 [80]P2(a1) % 1.17/1.31 [81]P2(a2) % 1.17/1.31 [82]P2(a3) % 1.17/1.31 [83]P32(a1) % 1.17/1.31 [84]P32(a2) % 1.17/1.31 [85]P32(a3) % 1.17/1.31 [86]P49(a1) % 1.17/1.31 [87]P49(a2) % 1.17/1.31 [88]P49(a3) % 1.17/1.31 [89]P33(a1) % 1.17/1.31 [90]P33(a2) % 1.17/1.31 [91]P33(a3) % 1.17/1.31 [92]P34(a1) % 1.17/1.31 [93]P34(a2) % 1.17/1.31 [94]P34(a3) % 1.17/1.31 [95]P38(a2) % 1.17/1.31 [96]P41(a2) % 1.17/1.31 [97]P41(a3) % 1.17/1.31 [98]P26(a2) % 1.17/1.31 [99]P26(a3) % 1.17/1.31 [100]P35(a2) % 1.17/1.31 [101]P35(a3) % 1.17/1.31 [102]P45(a2) % 1.17/1.31 [103]P45(a3) % 1.17/1.31 [104]P39(a2) % 1.17/1.31 [105]P36(a2) % 1.17/1.31 [106]P36(a3) % 1.17/1.31 [107]P3(a2) % 1.17/1.31 [108]P42(a1) % 1.17/1.31 [109]P42(a2) % 1.17/1.31 [110]P37(a2) % 1.17/1.31 [111]P37(a3) % 1.17/1.31 [112]P4(a2) % 1.17/1.31 [113]P4(a3) % 1.17/1.31 [114]P8(a2) % 1.17/1.31 [115]P8(a3) % 1.17/1.31 [116]P16(a2) % 1.17/1.31 [117]P5(a2) % 1.17/1.31 [118]P5(a3) % 1.17/1.31 [119]P17(a1) % 1.17/1.31 [120]P17(a2) % 1.17/1.31 [121]P17(a3) % 1.17/1.31 [122]P9(a1) % 1.17/1.31 [123]P9(a2) % 1.17/1.31 [124]P9(a3) % 1.17/1.31 [125]P27(a2) % 1.17/1.31 [126]P27(a3) % 1.17/1.31 [127]P46(a2) % 1.17/1.31 [128]P46(a3) % 1.17/1.31 [129]P30(a2) % 1.17/1.31 [130]P30(a3) % 1.17/1.31 [131]P43(a2) % 1.17/1.31 [132]P44(a1) % 1.17/1.31 [133]P44(a2) % 1.17/1.31 [134]P40(a1) % 1.17/1.31 [135]P40(a2) % 1.17/1.31 [136]P20(a1) % 1.17/1.31 [137]P20(a2) % 1.17/1.31 [138]P18(a1) % 1.17/1.31 [139]P18(a2) % 1.17/1.31 [140]P18(a3) % 1.17/1.31 [141]P28(a2) % 1.17/1.31 [142]P28(a3) % 1.17/1.31 [143]P19(a2) % 1.17/1.31 [144]P47(a2) % 1.17/1.31 [145]P47(a3) % 1.17/1.31 [146]P23(a1) % 1.17/1.31 [147]P23(a2) % 1.17/1.31 [148]P24(a1) % 1.17/1.31 [149]P24(a2) % 1.17/1.31 [150]P25(a1) % 1.17/1.31 [151]P25(a2) % 1.17/1.31 [152]P21(a1) % 1.17/1.31 [153]P21(a2) % 1.17/1.31 [154]P22(a1) % 1.17/1.31 [155]P22(a2) % 1.17/1.31 [156]P29(a2) % 1.17/1.31 [157]P29(a3) % 1.17/1.31 [158]P10(a1) % 1.17/1.31 [159]P10(a2) % 1.17/1.31 [160]P10(a3) % 1.17/1.31 [161]P11(a1) % 1.17/1.31 [162]P11(a2) % 1.17/1.31 [163]P11(a3) % 1.17/1.31 [164]P31(a1) % 1.17/1.31 [165]P31(a2) % 1.17/1.31 [166]P31(a3) % 1.17/1.31 [167]P12(a1) % 1.17/1.31 [168]P12(a2) % 1.17/1.31 [169]P12(a3) % 1.17/1.31 [170]P15(a1) % 1.17/1.31 [171]P15(a2) % 1.17/1.31 [172]P15(a3) % 1.17/1.31 [173]P13(a1) % 1.17/1.31 [174]P13(a2) % 1.17/1.31 [175]P13(a3) % 1.17/1.31 [176]P48(a1) % 1.17/1.31 [177]P48(a2) % 1.17/1.31 [178]P48(a3) % 1.17/1.31 [179]P6(a13,a15,a1) % 1.17/1.31 [190]~P50(a5000) % 1.17/1.31 [191]~E(f9(a1),a13) % 1.17/1.31 [199]~P6(x1991,x1991,a1) % 1.17/1.31 [200]~P6(x2001,x2001,a2) % 1.17/1.31 [182]P6(x1821,f8(x1821),a1) % 1.17/1.31 [185]P6(f9(a1),f8(x1851),a1) % 1.17/1.31 [193]~E(f8(x1931),x1931) % 1.17/1.31 [195]~E(f8(x1951),f9(a1)) % 1.17/1.31 [197]~E(f9(a1),f8(x1971)) % 1.17/1.31 [202]~P6(x2021,f9(a1),a1) % 1.17/1.31 [180]E(f6(f4(a2),x1801,a2),x1801) % 1.17/1.31 [187]E(f6(x1871,x1872,a2),f6(x1872,x1871,a2)) % 1.17/1.31 [188]E(f6(f6(x1881,x1882,a2),x1883,a2),f6(x1881,f6(x1882,x1883,a2),a2)) % 1.17/1.31 [189]E(f7(f6(x1891,x1892,a2),f6(x1893,x1892,a2),a2),f6(f7(x1891,x1893,a2),x1892,a2)) % 1.17/1.31 [207]~P49(x2071)+~E(f9(x2071),f4(x2071)) % 1.17/1.31 [222]E(x2221,f9(a1))+P6(f9(a1),x2221,a1) % 1.17/1.31 [257]~P42(x2571)+P6(f9(x2571),f4(x2571),x2571) % 1.17/1.31 [286]~P42(x2861)+~P6(f4(x2861),f9(x2861),x2861) % 1.17/1.31 [208]~P29(x2081)+E(f11(f4(x2081),x2081),f4(a2)) % 1.17/1.31 [210]~P8(x2101)+E(f10(f9(x2101),x2101),f9(x2101)) % 1.17/1.31 [211]~P19(x2111)+E(f10(f9(x2111),x2111),f9(x2111)) % 1.17/1.31 [259]~P16(x2591)+E(f7(f9(x2591),f9(x2591),x2591),f9(x2591)) % 1.17/1.31 [278]E(x2781,f9(a1))+~P6(x2781,f8(f9(a1)),a1) % 1.17/1.31 [345]~P42(x3451)+P6(f9(x3451),f7(f4(x3451),f4(x3451),x3451),x3451) % 1.17/1.31 [391]~P43(x3911)+E(f7(f6(f9(x3911),f9(x3911),x3911),f6(f9(x3911),f9(x3911),x3911),x3911),f9(x3911)) % 1.17/1.31 [551]~P43(x5511)+~P6(f9(x5511),f7(f6(f9(x5511),f9(x5511),x5511),f6(f9(x5511),f9(x5511),x5511),x5511),x5511) % 1.17/1.31 [554]P50(a5000)+~P6(f11(f7(f4(a3),f6(a14,f12(x5541,a13,a3),a3),a3),a3),f4(a2),a2) % 1.17/1.31 [272]~P6(x2722,x2722,x2721)+~P23(x2721) % 1.17/1.31 [273]~P6(x2732,x2732,x2731)+~P24(x2731) % 1.17/1.31 [274]~P6(x2742,x2742,x2741)+~P25(x2741) % 1.17/1.31 [205]E(x2051,x2052)+~E(f8(x2051),f8(x2052)) % 1.17/1.31 [224]~P14(x2242)+E(f6(x2241,x2241,x2242),x2241) % 1.17/1.31 [287]P6(x2871,x2872,a1)+P6(x2872,f8(x2871),a1) % 1.17/1.31 [304]~P6(x3041,x3042,a1)+P6(x3041,f8(x3042),a1) % 1.17/1.31 [306]P6(x3061,x3062,a1)+~P6(f8(x3061),x3062,a1) % 1.17/1.31 [312]~P6(x3121,x3122,a1)+P6(f8(x3121),f8(x3122),a1) % 1.17/1.31 [313]P6(x3131,x3132,a1)+~P6(f8(x3131),f8(x3132),a1) % 1.17/1.31 [321]~P6(x3211,x3212,a1)+~P6(x3212,f8(x3211),a1) % 1.17/1.31 [383]~P43(x3831)+~P6(f6(x3832,x3832,x3831),f9(x3831),x3831) % 1.17/1.31 [218]~P8(x2182)+E(f10(f10(x2181,x2182),x2182),x2181) % 1.17/1.31 [219]~P7(x2192)+E(f10(f10(x2191,x2192),x2192),x2191) % 1.17/1.31 [223]~P30(x2232)+E(f11(f10(x2231,x2232),x2232),f11(x2231,x2232)) % 1.17/1.31 [225]~P1(x2252)+E(f6(x2251,f4(x2252),x2252),x2251) % 1.17/1.31 [226]~P18(x2262)+E(f6(x2261,f4(x2262),x2262),x2261) % 1.17/1.31 [227]~P37(x2272)+E(f5(x2271,f4(x2272),x2272),x2271) % 1.17/1.31 [228]~P1(x2282)+E(f7(x2281,f9(x2282),x2282),x2281) % 1.17/1.31 [229]~P17(x2292)+E(f7(x2291,f9(x2292),x2292),x2291) % 1.17/1.31 [230]~P9(x2302)+E(f7(x2301,f9(x2302),x2302),x2301) % 1.17/1.31 [232]~P1(x2321)+E(f6(f4(x2321),x2322,x2321),x2322) % 1.17/1.31 [233]~P18(x2331)+E(f6(f4(x2331),x2332,x2331),x2332) % 1.17/1.31 [234]~P15(x2341)+E(f6(f4(x2341),x2342,x2341),x2342) % 1.17/1.31 [236]~P1(x2361)+E(f7(f9(x2361),x2362,x2361),x2362) % 1.17/1.31 [237]~P17(x2371)+E(f7(f9(x2371),x2372,x2371),x2372) % 1.17/1.31 [238]~P9(x2381)+E(f7(f9(x2381),x2382,x2381),x2382) % 1.17/1.31 [239]~P1(x2392)+E(f12(x2391,f9(a1),x2392),f4(x2392)) % 1.17/1.31 [240]~P2(x2402)+E(f12(x2401,f9(a1),x2402),f4(x2402)) % 1.17/1.31 [243]~P1(x2432)+E(f6(x2431,f9(x2432),x2432),f9(x2432)) % 1.17/1.31 [244]~P34(x2442)+E(f6(x2441,f9(x2442),x2442),f9(x2442)) % 1.17/1.31 [246]~P26(x2462)+E(f6(x2461,f9(x2462),x2462),f9(x2462)) % 1.17/1.31 [247]~P45(x2472)+E(f6(x2471,f9(x2472),x2472),f9(x2472)) % 1.17/1.31 [248]~P18(x2481)+E(f12(f4(x2481),x2482,x2481),f4(x2481)) % 1.17/1.31 [250]~P1(x2501)+E(f6(f9(x2501),x2502,x2501),f9(x2501)) % 1.17/1.31 [251]~P34(x2511)+E(f6(f9(x2511),x2512,x2511),f9(x2511)) % 1.17/1.31 [253]~P26(x2531)+E(f6(f9(x2531),x2532,x2531),f9(x2531)) % 1.17/1.31 [254]~P45(x2541)+E(f6(f9(x2541),x2542,x2541),f9(x2541)) % 1.17/1.31 [255]~P37(x2551)+E(f5(f9(x2551),x2552,x2551),f9(x2551)) % 1.17/1.31 [256]~P27(x2561)+E(f5(f9(x2561),x2562,x2561),f9(x2561)) % 1.17/1.31 [268]~P8(x2682)+E(f7(x2681,f10(x2681,x2682),x2682),f9(x2682)) % 1.17/1.31 [269]~P4(x2692)+E(f7(f10(x2691,x2692),x2691,x2692),f9(x2692)) % 1.17/1.31 [271]~P8(x2712)+E(f7(f10(x2711,x2712),x2711,x2712),f9(x2712)) % 1.17/1.31 [316]~P35(x3162)+E(f6(f10(x3161,x3162),f10(x3161,x3162),x3162),f6(x3161,x3161,x3162)) % 1.17/1.31 [329]~P42(x3292)+P6(x3291,f7(x3291,f4(x3292),x3292),x3292) % 1.17/1.31 [330]~P38(x3301)+P6(f9(x3301),f12(x3302,f9(a1),x3301),x3301) % 1.17/1.31 [289]~P5(x2891)+E(f6(f10(f4(x2891),x2891),x2892,x2891),f10(x2892,x2891)) % 1.17/1.31 [378]~P1(x3782)+E(f7(x3781,x3781,x3782),f6(f7(f4(x3782),f4(x3782),x3782),x3781,x3782)) % 1.17/1.31 [293]~P1(x2933)+E(f6(x2931,x2932,x2933),f6(x2932,x2931,x2933)) % 1.17/1.31 [295]~P1(x2953)+E(f7(x2951,x2952,x2953),f7(x2952,x2951,x2953)) % 1.17/1.31 [296]~P9(x2963)+E(f7(x2961,x2962,x2963),f7(x2962,x2961,x2963)) % 1.17/1.31 [314]~P41(x3142)+E(f6(f10(x3141,x3142),x3143,x3142),f6(x3141,f10(x3143,x3142),x3142)) % 1.17/1.31 [315]~P41(x3152)+E(f6(f10(x3151,x3152),f10(x3153,x3152),x3152),f6(x3151,x3153,x3152)) % 1.17/1.31 [342]~P4(x3422)+E(f7(f10(x3421,x3422),f7(x3423,x3421,x3422),x3422),x3423) % 1.17/1.31 [343]~P8(x3432)+E(f7(f10(x3431,x3432),f7(x3431,x3433,x3432),x3432),x3433) % 1.17/1.31 [349]~P41(x3493)+E(f6(x3491,f10(x3492,x3493),x3493),f10(f6(x3491,x3492,x3493),x3493)) % 1.17/1.31 [350]~P41(x3502)+E(f6(f10(x3501,x3502),x3503,x3502),f10(f6(x3501,x3503,x3502),x3502)) % 1.17/1.31 [351]~P37(x3512)+E(f5(f10(x3511,x3512),x3513,x3512),f10(f5(x3511,x3513,x3512),x3512)) % 1.17/1.31 [353]~P26(x3533)+E(f6(x3531,f10(x3532,x3533),x3533),f10(f6(x3531,x3532,x3533),x3533)) % 1.17/1.31 [355]~P26(x3552)+E(f6(f10(x3551,x3552),x3553,x3552),f10(f6(x3551,x3553,x3552),x3552)) % 1.17/1.31 [356]~P27(x3562)+E(f5(f10(x3561,x3562),x3563,x3562),f10(f5(x3561,x3563,x3562),x3562)) % 1.17/1.31 [364]~P14(x3643)+E(f6(x3641,f6(x3641,x3642,x3643),x3643),f6(x3641,x3642,x3643)) % 1.17/1.31 [368]~P2(x3683)+E(f6(x3681,f12(x3681,x3682,x3683),x3683),f12(x3681,f8(x3682),x3683)) % 1.17/1.31 [369]~P18(x3693)+E(f6(f12(x3691,x3692,x3693),x3691,x3693),f12(x3691,f8(x3692),x3693)) % 1.17/1.31 [370]~P1(x3703)+E(f6(x3701,f12(x3701,x3702,x3703),x3703),f12(x3701,f8(x3702),x3703)) % 1.17/1.31 [371]~P1(x3713)+E(f6(f12(x3711,x3712,x3713),x3711,x3713),f12(x3711,f8(x3712),x3713)) % 1.17/1.31 [373]~P28(x3732)+E(f6(f11(x3731,x3732),f11(x3733,x3732),a2),f11(f6(x3731,x3733,x3732),x3732)) % 1.17/1.31 [374]~P8(x3742)+E(f7(f10(x3741,x3742),f10(x3743,x3742),x3742),f10(f7(x3743,x3741,x3742),x3742)) % 1.17/1.31 [375]~P4(x3752)+E(f7(f10(x3751,x3752),f10(x3753,x3752),x3752),f10(f7(x3751,x3753,x3752),x3752)) % 1.17/1.31 [400]~P18(x4003)+E(f6(f12(x4001,x4002,x4003),x4001,x4003),f6(x4001,f12(x4001,x4002,x4003),x4003)) % 1.17/1.31 [457]~P47(x4571)+E(f6(f12(f10(f4(x4571),x4571),x4572,x4571),f12(x4573,x4572,x4571),x4571),f12(f10(x4573,x4571),x4572,x4571)) % 1.17/1.31 [549]~P43(x5491)+~P6(f7(f6(x5492,x5492,x5491),f6(x5493,x5493,x5491),x5491),f9(x5491),x5491) % 1.17/1.31 [363]~P8(x3632)+E(f7(x3631,f7(f10(x3631,x3632),x3633,x3632),x3632),x3633) % 1.17/1.31 [413]~P1(x4133)+E(f7(x4131,f6(x4132,x4131,x4133),x4133),f6(f7(x4132,f4(x4133),x4133),x4131,x4133)) % 1.17/1.31 [414]~P1(x4143)+E(f7(f6(x4141,x4142,x4143),x4142,x4143),f6(f7(x4141,f4(x4143),x4143),x4142,x4143)) % 1.17/1.31 [392]~P1(x3924)+E(f6(x3921,f6(x3922,x3923,x3924),x3924),f6(x3922,f6(x3921,x3923,x3924),x3924)) % 1.17/1.31 [393]~P1(x3934)+E(f7(x3931,f7(x3932,x3933,x3934),x3934),f7(x3932,f7(x3931,x3933,x3934),x3934)) % 1.17/1.31 [394]~P4(x3944)+E(f7(x3941,f7(x3942,x3943,x3944),x3944),f7(x3942,f7(x3941,x3943,x3944),x3944)) % 1.17/1.31 [395]~P9(x3954)+E(f7(x3951,f7(x3952,x3953,x3954),x3954),f7(x3952,f7(x3951,x3953,x3954),x3954)) % 1.17/1.31 [401]~P1(x4013)+E(f6(f6(x4011,x4012,x4013),x4014,x4013),f6(x4011,f6(x4012,x4014,x4013),x4013)) % 1.17/1.31 [402]~P12(x4023)+E(f6(f6(x4021,x4022,x4023),x4024,x4023),f6(x4021,f6(x4022,x4024,x4023),x4023)) % 1.17/1.31 [403]~P1(x4033)+E(f7(f7(x4031,x4032,x4033),x4034,x4033),f7(x4031,f7(x4032,x4034,x4033),x4033)) % 1.17/1.31 [404]~P9(x4043)+E(f7(f7(x4041,x4042,x4043),x4044,x4043),f7(x4041,f7(x4042,x4044,x4043),x4043)) % 1.17/1.31 [405]~P13(x4053)+E(f7(f7(x4051,x4052,x4053),x4054,x4053),f7(x4051,f7(x4052,x4054,x4053),x4053)) % 1.17/1.31 [406]~P1(x4063)+E(f6(f6(x4061,x4062,x4063),x4064,x4063),f6(f6(x4061,x4064,x4063),x4062,x4063)) % 1.17/1.31 [407]~P1(x4073)+E(f7(f7(x4071,x4072,x4073),x4074,x4073),f7(f7(x4071,x4074,x4073),x4072,x4073)) % 1.17/1.31 [458]~P1(x4583)+E(f7(f6(x4581,x4582,x4583),f6(x4581,x4584,x4583),x4583),f6(x4581,f7(x4582,x4584,x4583),x4583)) % 1.17/1.31 [460]~P26(x4603)+E(f7(f6(x4601,x4602,x4603),f6(x4601,x4604,x4603),x4603),f6(x4601,f7(x4602,x4604,x4603),x4603)) % 1.17/1.31 [461]~P1(x4613)+E(f6(f12(x4611,x4612,x4613),f12(x4614,x4612,x4613),x4613),f12(f6(x4611,x4614,x4613),x4612,x4613)) % 1.17/1.31 [462]~P15(x4623)+E(f6(f12(x4621,x4622,x4623),f12(x4624,x4622,x4623),x4623),f12(f6(x4621,x4624,x4623),x4622,x4623)) % 1.17/1.31 [465]~P26(x4653)+E(f7(f6(x4651,x4652,x4653),f6(x4654,x4652,x4653),x4653),f6(f7(x4651,x4654,x4653),x4652,x4653)) % 1.17/1.31 [466]~P31(x4663)+E(f7(f6(x4661,x4662,x4663),f6(x4664,x4662,x4663),x4663),f6(f7(x4661,x4664,x4663),x4662,x4663)) % 1.17/1.31 [467]~P37(x4673)+E(f7(f5(x4671,x4672,x4673),f5(x4674,x4672,x4673),x4673),f5(f7(x4671,x4674,x4673),x4672,x4673)) % 1.17/1.31 [468]~P27(x4683)+E(f7(f5(x4681,x4682,x4683),f5(x4684,x4682,x4683),x4683),f5(f7(x4681,x4684,x4683),x4682,x4683)) % 1.17/1.31 [469]~P1(x4693)+E(f7(f6(x4691,x4692,x4693),f6(x4694,x4692,x4693),x4693),f6(f7(x4691,x4694,x4693),x4692,x4693)) % 1.17/1.31 [504]~P1(x5043)+E(f6(f6(x5041,x5042,x5043),f6(x5044,x5045,x5043),x5043),f6(f6(x5041,x5044,x5043),f6(x5042,x5045,x5043),x5043)) % 1.17/1.31 [505]~P1(x5053)+E(f7(f7(x5051,x5052,x5053),f7(x5054,x5055,x5053),x5053),f7(f7(x5051,x5054,x5053),f7(x5052,x5055,x5053),x5053)) % 1.17/1.31 [548]~P48(x5483)+E(f7(f6(x5481,x5482,x5483),f7(f6(x5484,x5482,x5483),x5485,x5483),x5483),f7(f6(f7(x5481,x5484,x5483),x5482,x5483),x5485,x5483)) % 1.17/1.31 [552]~P6(a13,a15,a1)+E(f9(a1),a13)+P6(f11(f7(f4(a3),f6(a14,f12(f16(a14,a13),a13,a3),a3),a3),a3),f4(a2),a2) % 1.17/1.31 [305]E(x3051,f9(a1))+E(x3051,f8(f9(a1)))+~P6(x3051,f8(f8(f9(a1))),a1) % 1.17/1.31 [282]E(x2821,x2822)+P6(x2822,x2821,a1)+P6(x2821,x2822,a1) % 1.17/1.31 [212]~P19(x2122)+~E(f10(x2121,x2122),x2121)+E(x2121,f9(x2122)) % 1.17/1.31 [213]~P8(x2132)+~E(f10(x2131,x2132),f9(x2132))+E(x2131,f9(x2132)) % 1.17/1.31 [214]~P8(x2141)+~E(f10(x2142,x2141),f9(x2141))+E(f9(x2141),x2142) % 1.17/1.31 [242]~P37(x2422)+E(f5(x2421,x2421,x2422),f4(x2422))+E(x2421,f9(x2422)) % 1.17/1.31 [277]~P16(x2772)+~E(f7(x2771,x2771,x2772),f9(x2772))+E(x2771,f9(x2772)) % 1.17/1.31 [307]~P6(x3071,x3072,a1)+E(f8(x3071),x3072)+P6(f8(x3071),x3072,a1) % 1.17/1.31 [308]E(x3081,x3082)+P6(x3082,x3081,a1)+~P6(x3082,f8(x3081),a1) % 1.17/1.31 [310]E(x3101,x3102)+P6(x3101,x3102,a1)+~P6(x3101,f8(x3102),a1) % 1.17/1.31 [335]~P38(x3352)+~P6(x3351,f9(x3352),x3352)+P6(x3351,f10(x3351,x3352),x3352) % 1.17/1.31 [337]~P3(x3371)+~P6(x3372,f9(x3371),x3371)+P6(f9(x3371),f10(x3372,x3371),x3371) % 1.17/1.31 [338]~P3(x3382)+~P6(f9(x3382),x3381,x3382)+P6(f10(x3381,x3382),f9(x3382),x3382) % 1.17/1.31 [341]~P38(x3412)+~P6(x3411,f10(x3411,x3412),x3412)+P6(x3411,f9(x3412),x3412) % 1.17/1.31 [347]~P3(x3472)+~P6(f9(x3472),f10(x3471,x3472),x3472)+P6(x3471,f9(x3472),x3472) % 1.17/1.31 [348]~P3(x3481)+~P6(f10(x3482,x3481),f9(x3481),x3481)+P6(f9(x3481),x3482,x3481) % 1.17/1.31 [380]~P16(x3801)+~P6(f9(x3801),x3802,x3801)+P6(f9(x3801),f7(x3802,x3802,x3801),x3801) % 1.17/1.31 [381]~P38(x3812)+~P6(x3811,f9(x3812),x3812)+P6(f7(x3811,x3811,x3812),f9(x3812),x3812) % 1.17/1.31 [382]~P16(x3822)+~P6(x3821,f9(x3822),x3822)+P6(f7(x3821,x3821,x3822),f9(x3822),x3822) % 1.17/1.31 [409]~P38(x4092)+~P6(f7(x4091,x4091,x4092),f9(x4092),x4092)+P6(x4091,f9(x4092),x4092) % 1.17/1.31 [410]~P16(x4102)+~P6(f7(x4101,x4101,x4102),f9(x4102),x4102)+P6(x4101,f9(x4102),x4102) % 1.17/1.31 [411]~P16(x4111)+~P6(f9(x4111),f7(x4112,x4112,x4111),x4111)+P6(f9(x4111),x4112,x4111) % 1.17/1.31 [258]~P35(x2582)+~P5(x2582)+E(f7(x2581,f9(x2582),x2582),x2581) % 1.17/1.31 [263]~P36(x2632)+~P37(x2632)+E(f5(x2631,f9(x2632),x2632),f9(x2632)) % 1.17/1.31 [266]~P2(x2661)+~P32(x2661)+E(f12(f9(x2661),f8(x2662),x2661),f9(x2661)) % 1.17/1.31 [340]~P36(x3401)+~P37(x3401)+E(f5(f6(f9(x3401),x3402,x3401),x3402,x3401),f9(x3401)) % 1.17/1.31 [322]~P6(x3223,x3222,x3221)+~P23(x3221)+~P6(x3222,x3223,x3221) % 1.17/1.31 [323]~P6(x3233,x3232,x3231)+~P24(x3231)+~P6(x3232,x3233,x3231) % 1.17/1.31 [325]~P6(x3253,x3252,x3251)+~P25(x3251)+~P6(x3252,x3253,x3251) % 1.17/1.31 [220]~P8(x2203)+E(x2201,x2202)+~E(f10(x2201,x2203),f10(x2202,x2203)) % 1.17/1.31 [221]~P7(x2213)+E(x2211,x2212)+~E(f10(x2211,x2213),f10(x2212,x2213)) % 1.17/1.31 [276]~P46(x2762)+~E(f12(x2761,x2763,x2762),f9(x2762))+E(x2761,f9(x2762)) % 1.17/1.31 [290]~P8(x2903)+~E(f7(x2901,x2902,x2903),f9(x2903))+E(x2901,f10(x2902,x2903)) % 1.17/1.31 [291]~P8(x2912)+~E(f7(x2911,x2913,x2912),f9(x2912))+E(f10(x2911,x2912),x2913) % 1.17/1.31 [346]~P3(x3462)+~P6(x3463,x3461,x3462)+P6(f10(x3461,x3462),f10(x3463,x3462),x3462) % 1.17/1.31 [359]~P3(x3593)+~P6(x3592,f10(x3591,x3593),x3593)+P6(x3591,f10(x3592,x3593),x3593) % 1.17/1.31 [361]~P3(x3612)+~P6(f10(x3613,x3612),x3611,x3612)+P6(f10(x3611,x3612),x3613,x3612) % 1.17/1.31 [365]~P6(x3651,x3653,a1)+~P6(x3653,x3652,a1)+P6(f8(x3651),x3652,a1) % 1.17/1.31 [372]~P3(x3723)+P6(x3721,x3722,x3723)+~P6(f10(x3722,x3723),f10(x3721,x3723),x3723) % 1.17/1.31 [379]~P42(x3791)+~P6(f9(x3791),x3792,x3791)+P6(f9(x3791),f12(x3792,x3793,x3791),x3791) % 1.17/1.31 [408]~P38(x4082)+~P6(f12(x4081,x4083,x4082),f9(x4082),x4082)+P6(x4081,f9(x4082),x4082) % 1.17/1.31 [317]~P37(x3172)+E(x3171,f9(x3172))+E(f5(f10(x3173,x3172),f10(x3171,x3172),x3172),f5(x3173,x3171,x3172)) % 1.17/1.31 [319]~P37(x3192)+E(x3191,f9(x3192))+E(f5(f6(x3193,x3191,x3192),x3191,x3192),x3193) % 1.17/1.31 [320]~P36(x3202)+~P37(x3202)+E(f5(f10(x3201,x3202),f10(x3203,x3202),x3202),f5(x3201,x3203,x3202)) % 1.17/1.31 [357]~P37(x3572)+E(x3571,f9(x3572))+E(f5(x3573,f10(x3571,x3572),x3572),f10(f5(x3573,x3571,x3572),x3572)) % 1.17/1.31 [362]~P36(x3623)+~P37(x3623)+E(f5(x3621,f10(x3622,x3623),x3623),f10(f5(x3621,x3622,x3623),x3623)) % 1.17/1.31 [386]~P42(x3861)+~P6(f4(x3861),x3862,x3861)+P6(f4(x3861),f12(x3862,f8(x3863),x3861),x3861) % 1.17/1.31 [470]~P43(x4702)+E(x4701,f9(x4702))+~E(f7(f6(x4703,x4703,x4702),f6(x4701,x4701,x4702),x4702),f9(x4702)) % 1.17/1.31 [471]~P43(x4712)+E(x4711,f9(x4712))+~E(f7(f6(x4711,x4711,x4712),f6(x4713,x4713,x4712),x4712),f9(x4712)) % 1.17/1.31 [494]~P42(x4941)+~P6(f4(x4941),x4942,x4941)+P6(f4(x4941),f6(x4942,f12(x4942,x4943,x4941),x4941),x4941) % 1.17/1.31 [522]~P42(x5223)+~P6(f4(x5223),x5221,x5223)+P6(f12(x5221,x5222,x5223),f6(x5221,f12(x5221,x5222,x5223),x5223),x5223) % 1.17/1.31 [531]~P43(x5312)+E(x5311,f9(x5312))+P6(f9(x5312),f7(f6(x5313,x5313,x5312),f6(x5311,x5311,x5312),x5312),x5312) % 1.17/1.31 [532]~P43(x5322)+E(x5321,f9(x5322))+P6(f9(x5322),f7(f6(x5321,x5321,x5322),f6(x5323,x5323,x5322),x5322),x5322) % 1.17/1.31 [418]~P36(x4181)+~P37(x4181)+E(f12(f5(f4(x4181),x4182,x4181),x4183,x4181),f5(f4(x4181),f12(x4182,x4183,x4181),x4181)) % 1.17/1.31 [540]~P39(x5403)+~P6(x5401,x5402,x5403)+P6(x5401,f5(f7(x5401,x5402,x5403),f7(f4(x5403),f4(x5403),x5403),x5403),x5403) % 1.17/1.31 [541]~P39(x5413)+~P6(x5411,x5412,x5413)+P6(f5(f7(x5411,x5412,x5413),f7(f4(x5413),f4(x5413),x5413),x5413),x5412,x5413) % 1.17/1.31 [326]~P10(x3264)+E(x3261,x3262)+~E(f7(x3263,x3261,x3264),f7(x3263,x3262,x3264)) % 1.17/1.31 [327]~P11(x3274)+E(x3271,x3272)+~E(f7(x3273,x3271,x3274),f7(x3273,x3272,x3274)) % 1.17/1.31 [328]~P10(x3284)+E(x3281,x3282)+~E(f7(x3281,x3283,x3284),f7(x3282,x3283,x3284)) % 1.17/1.31 [423]~P21(x4233)+~P6(x4231,x4234,x4233)+P6(f7(x4231,x4232,x4233),f7(x4234,x4232,x4233),x4233) % 1.17/1.31 [424]~P22(x4243)+~P6(x4241,x4244,x4243)+P6(f7(x4241,x4242,x4243),f7(x4244,x4242,x4243),x4243) % 1.17/1.31 [425]~P21(x4253)+~P6(x4252,x4254,x4253)+P6(f7(x4251,x4252,x4253),f7(x4251,x4254,x4253),x4253) % 1.17/1.31 [426]~P22(x4263)+~P6(x4262,x4264,x4263)+P6(f7(x4261,x4262,x4263),f7(x4261,x4264,x4263),x4263) % 1.17/1.31 [492]~P22(x4923)+P6(x4921,x4922,x4923)+~P6(f7(x4924,x4921,x4923),f7(x4924,x4922,x4923),x4923) % 1.17/1.31 [493]~P22(x4933)+P6(x4931,x4932,x4933)+~P6(f7(x4931,x4934,x4933),f7(x4932,x4934,x4933),x4933) % 1.17/1.31 [385]~P4(x3853)+E(x3851,f10(x3852,x3853))+~E(f7(x3851,f7(x3854,x3852,x3853),x3853),x3854) % 1.17/1.31 [412]~P36(x4123)+~P37(x4123)+E(f5(f6(x4121,x4122,x4123),x4124,x4123),f6(f5(x4121,x4124,x4123),x4122,x4123)) % 1.17/1.31 [472]~P37(x4722)+E(x4721,f9(x4722))+E(f5(f12(x4723,x4724,x4722),f12(x4721,x4724,x4722),x4722),f12(f5(x4723,x4721,x4722),x4724,x4722)) % 1.17/1.31 [473]~P36(x4733)+~P37(x4733)+E(f5(f12(x4731,x4732,x4733),f12(x4734,x4732,x4733),x4733),f12(f5(x4731,x4734,x4733),x4732,x4733)) % 1.17/1.31 [512]~P35(x5123)+~P5(x5123)+E(f7(f6(x5121,x5122,x5123),f6(x5121,x5124,x5123),x5123),f7(f6(x5121,x5124,x5123),f6(x5121,x5122,x5123),x5123)) % 1.17/1.31 [454]~P4(x4543)+E(f7(x4541,x4542,x4543),x4544)+~E(f7(x4541,f7(x4545,x4542,x4543),x4543),f7(x4545,x4544,x4543)) % 1.17/1.31 [510]~P36(x5103)+~P37(x5103)+E(f5(f6(x5101,x5102,x5103),f6(x5104,x5105,x5103),x5103),f6(f5(x5101,x5104,x5103),f5(x5102,x5105,x5103),x5103)) % 1.17/1.31 [265]~P2(x2652)+~P32(x2652)+E(x2651,f9(a1))+E(f12(f9(x2652),x2651,x2652),f9(x2652)) % 1.17/1.31 [387]~P39(x3871)+~P36(x3871)+~P6(f9(x3871),x3872,x3871)+P6(f9(x3871),f5(f4(x3871),x3872,x3871),x3871) % 1.17/1.31 [388]~P39(x3881)+~P36(x3881)+~P6(x3882,f9(x3881),x3881)+P6(f5(f4(x3881),x3882,x3881),f9(x3881),x3881) % 1.17/1.31 [419]~P39(x4192)+~P36(x4192)+P6(x4191,f9(x4192),x4192)+~P6(f5(f4(x4192),x4191,x4192),f9(x4192),x4192) % 1.17/1.31 [420]~P39(x4201)+~P36(x4201)+P6(f9(x4201),x4202,x4201)+~P6(f9(x4201),f5(f4(x4201),x4202,x4201),x4201) % 1.17/1.31 [422]~P38(x4222)+P6(f9(x4222),f9(x4222),x4222)+~P6(f9(x4222),f12(f9(x4222),x4221,x4222),x4222)+E(x4221,f9(a1)) % 1.17/1.31 [297]P6(x2971,x2972,x2973)+~P38(x2973)+E(x2971,x2972)+P6(x2972,x2971,x2973) % 1.17/1.31 [301]P6(x3011,x3012,x3013)+~P24(x3013)+E(x3011,x3012)+P6(x3012,x3011,x3013) % 1.17/1.31 [279]~P37(x2793)+E(x2791,x2792)+~E(f5(x2791,x2792,x2793),f4(x2793))+E(x2792,f9(x2793)) % 1.17/1.31 [280]~P35(x2802)+~P5(x2802)+~E(f7(x2803,x2801,x2802),x2803)+E(x2801,f9(x2802)) % 1.17/1.31 [284]~P33(x2842)+~E(f6(x2843,x2841,x2842),f9(x2842))+E(x2841,f9(x2842))+E(x2843,f9(x2842)) % 1.17/1.31 [285]~P45(x2852)+~E(f6(x2853,x2851,x2852),f9(x2852))+E(x2851,f9(x2852))+E(x2853,f9(x2852)) % 1.17/1.31 [344]~P35(x3443)+E(x3441,x3442)+~E(f6(x3441,x3441,x3443),f6(x3442,x3442,x3443))+E(x3441,f10(x3442,x3443)) % 1.17/1.31 [421]~P42(x4211)+~P6(f4(x4211),x4212,x4211)+P6(f4(x4211),f12(x4212,x4213,x4211),x4211)+~P6(f9(a1),x4213,a1) % 1.17/1.31 [427]~P43(x4271)+~P6(x4273,f9(x4271),x4271)+~P6(x4272,f9(x4271),x4271)+P6(f9(x4271),f6(x4272,x4273,x4271),x4271) % 1.17/1.31 [428]~P39(x4281)+~P6(x4283,f9(x4281),x4281)+~P6(x4282,f9(x4281),x4281)+P6(f9(x4281),f5(x4282,x4283,x4281),x4281) % 1.17/1.31 [429]~P44(x4291)+~P6(f9(x4291),x4293,x4291)+~P6(f9(x4291),x4292,x4291)+P6(f9(x4291),f6(x4292,x4293,x4291),x4291) % 1.17/1.31 [430]~P39(x4301)+~P6(f9(x4301),x4303,x4301)+~P6(f9(x4301),x4302,x4301)+P6(f9(x4301),f5(x4302,x4303,x4301),x4301) % 1.17/1.31 [431]~P20(x4311)+~P6(f9(x4311),x4313,x4311)+~P6(f9(x4311),x4312,x4311)+P6(f9(x4311),f7(x4312,x4313,x4311),x4311) % 1.17/1.31 [432]~P42(x4321)+~P6(f4(x4321),x4323,x4321)+~P6(f4(x4321),x4322,x4321)+P6(f4(x4321),f6(x4322,x4323,x4321),x4321) % 1.17/1.31 [433]~P20(x4333)+~P6(x4332,f9(x4333),x4333)+~P6(x4331,f9(x4333),x4333)+P6(f7(x4331,x4332,x4333),f9(x4333),x4333) % 1.17/1.31 [434]~P44(x4343)+~P6(x4342,f9(x4343),x4343)+~P6(f9(x4343),x4341,x4343)+P6(f6(x4341,x4342,x4343),f9(x4343),x4343) % 1.17/1.31 [436]~P44(x4363)+~P6(x4361,f9(x4363),x4363)+~P6(f9(x4363),x4362,x4363)+P6(f6(x4361,x4362,x4363),f9(x4363),x4363) % 1.17/1.31 [437]~P39(x4373)+~P6(x4372,f9(x4373),x4373)+~P6(f9(x4373),x4371,x4373)+P6(f5(x4371,x4372,x4373),f9(x4373),x4373) % 1.17/1.31 [438]~P39(x4383)+~P6(x4381,f9(x4383),x4383)+~P6(f9(x4383),x4382,x4383)+P6(f5(x4381,x4382,x4383),f9(x4383),x4383) % 1.17/1.31 [455]~P44(x4551)+~P6(f9(x4551),f6(x4553,x4552,x4551),x4551)+P6(f9(x4551),x4552,x4551)+~P6(f9(x4551),x4553,x4551) % 1.17/1.31 [456]~P44(x4561)+~P6(f9(x4561),f6(x4562,x4563,x4561),x4561)+P6(f9(x4561),x4562,x4561)+~P6(f9(x4561),x4563,x4561) % 1.17/1.31 [333]~P36(x3332)+~P37(x3332)+E(x3331,f9(x3332))+E(f6(f5(x3333,x3331,x3332),x3331,x3332),x3333) % 1.17/1.31 [443]~P42(x4433)+~P6(x4431,f4(x4433),x4433)+~P6(f9(x4433),x4431,x4433)+P6(f12(x4431,f8(x4432),x4433),f4(x4433),x4433) % 1.17/1.31 [537]~P42(x5373)+~P6(x5371,f4(x5373),x5373)+~P6(f9(x5373),x5371,x5373)+P6(f6(x5371,f12(x5371,x5372,x5373),x5373),f12(x5371,x5372,x5373),x5373) % 1.17/1.31 [376]~P23(x3763)+~P6(x3761,x3764,x3763)+P6(x3761,x3762,x3763)+~P6(x3764,x3762,x3763) % 1.17/1.31 [377]~P25(x3773)+~P6(x3771,x3774,x3773)+P6(x3771,x3772,x3773)+~P6(x3774,x3772,x3773) % 1.17/1.31 [336]~P35(x3364)+~P5(x3364)+E(x3361,x3362)+~E(f7(x3363,x3361,x3364),f7(x3363,x3362,x3364)) % 1.17/1.31 [384]~P42(x3844)+E(x3841,x3842)+~P6(f4(x3844),x3843,x3844)+~E(f12(x3843,x3841,x3844),f12(x3843,x3842,x3844)) % 1.17/1.31 [417]~P42(x4174)+~P6(x4171,x4173,x4174)+~P6(f9(x4174),x4172,x4174)+P6(x4171,f7(x4172,x4173,x4174),x4174) % 1.17/1.31 [478]~P42(x4783)+~P6(x4782,x4784,a1)+~P6(f4(x4783),x4781,x4783)+P6(f12(x4781,x4782,x4783),f12(x4781,x4784,x4783),x4783) % 1.17/1.31 [480]~P43(x4803)+~P6(x4804,x4801,x4803)+~P6(x4802,f9(x4803),x4803)+P6(f6(x4801,x4802,x4803),f6(x4804,x4802,x4803),x4803) % 1.17/1.31 [483]~P43(x4833)+~P6(x4834,x4832,x4833)+~P6(x4831,f9(x4833),x4833)+P6(f6(x4831,x4832,x4833),f6(x4831,x4834,x4833),x4833) % 1.17/1.31 [484]~P39(x4843)+~P6(x4844,x4841,x4843)+~P6(x4842,f9(x4843),x4843)+P6(f5(x4841,x4842,x4843),f5(x4844,x4842,x4843),x4843) % 1.17/1.31 [485]~P43(x4853)+~P6(x4851,x4854,x4853)+~P6(f9(x4853),x4852,x4853)+P6(f6(x4851,x4852,x4853),f6(x4854,x4852,x4853),x4853) % 1.17/1.31 [486]~P44(x4863)+~P6(x4861,x4864,x4863)+~P6(f9(x4863),x4862,x4863)+P6(f6(x4861,x4862,x4863),f6(x4864,x4862,x4863),x4863) % 1.17/1.31 [488]~P43(x4883)+~P6(x4882,x4884,x4883)+~P6(f9(x4883),x4881,x4883)+P6(f6(x4881,x4882,x4883),f6(x4881,x4884,x4883),x4883) % 1.17/1.31 [489]~P44(x4893)+~P6(x4892,x4894,x4893)+~P6(f9(x4893),x4891,x4893)+P6(f6(x4891,x4892,x4893),f6(x4891,x4894,x4893),x4893) % 1.17/1.31 [490]~P40(x4903)+~P6(x4902,x4904,x4903)+~P6(f9(x4903),x4901,x4903)+P6(f6(x4901,x4902,x4903),f6(x4901,x4904,x4903),x4903) % 1.17/1.31 [491]~P39(x4913)+~P6(x4911,x4914,x4913)+~P6(f9(x4913),x4912,x4913)+P6(f5(x4911,x4912,x4913),f5(x4914,x4912,x4913),x4913) % 1.17/1.31 [495]~P39(x4954)+~P6(f9(x4954),x4953,x4954)+~P6(f6(x4951,x4953,x4954),x4952,x4954)+P6(x4951,f5(x4952,x4953,x4954),x4954) % 1.17/1.31 [496]~P39(x4963)+~P6(f9(x4963),x4962,x4963)+~P6(x4961,f6(x4964,x4962,x4963),x4963)+P6(f5(x4961,x4962,x4963),x4964,x4963) % 1.17/1.31 [502]P6(x5022,x5021,x5023)+~P43(x5023)+P6(x5021,x5022,x5023)+~P6(f6(x5024,x5021,x5023),f6(x5024,x5022,x5023),x5023) % 1.17/1.31 [503]P6(x5032,x5031,x5033)+~P43(x5033)+P6(x5031,x5032,x5033)+~P6(f6(x5031,x5034,x5033),f6(x5032,x5034,x5033),x5033) % 1.17/1.31 [506]~P43(x5063)+P6(x5061,x5062,x5063)+~P6(f6(x5061,x5064,x5063),f6(x5062,x5064,x5063),x5063)+P6(x5064,f9(x5063),x5063) % 1.17/1.31 [507]~P43(x5073)+P6(x5071,x5072,x5073)+~P6(f6(x5074,x5071,x5073),f6(x5074,x5072,x5073),x5073)+P6(x5074,f9(x5073),x5073) % 1.17/1.31 [508]~P43(x5083)+P6(x5081,x5082,x5083)+~P6(f6(x5084,x5082,x5083),f6(x5084,x5081,x5083),x5083)+P6(f9(x5083),x5084,x5083) % 1.17/1.31 [509]~P43(x5093)+P6(x5091,x5092,x5093)+~P6(f6(x5092,x5094,x5093),f6(x5091,x5094,x5093),x5093)+P6(f9(x5093),x5094,x5093) % 1.17/1.31 [513]~P43(x5132)+~P6(f6(x5133,x5131,x5132),f6(x5134,x5131,x5132),x5132)+P6(x5131,f9(x5132),x5132)+P6(f9(x5132),x5131,x5132) % 1.17/1.31 [514]~P43(x5142)+~P6(f6(x5141,x5143,x5142),f6(x5141,x5144,x5142),x5142)+P6(x5141,f9(x5142),x5142)+P6(f9(x5142),x5141,x5142) % 1.17/1.31 [519]~P42(x5193)+~P6(f12(x5194,x5191,x5193),f12(x5194,x5192,x5193),x5193)+P6(x5191,x5192,a1)+~P6(f4(x5193),x5194,x5193) % 1.17/1.31 [520]~P43(x5203)+P6(x5201,x5202,x5203)+~P6(f6(x5204,x5202,x5203),f6(x5204,x5201,x5203),x5203)+~P6(x5204,f9(x5203),x5203) % 1.17/1.31 [521]~P43(x5213)+P6(x5211,x5212,x5213)+~P6(f6(x5214,x5211,x5213),f6(x5214,x5212,x5213),x5213)+~P6(f9(x5213),x5214,x5213) % 1.17/1.31 [415]~P36(x4152)+~P37(x4152)+E(x4151,f9(x4152))+E(f5(f6(x4153,x4151,x4152),f6(x4154,x4151,x4152),x4152),f5(x4153,x4154,x4152)) % 1.17/1.31 [416]~P36(x4162)+~P37(x4162)+E(x4161,f9(x4162))+E(f5(f6(x4161,x4163,x4162),f6(x4161,x4164,x4162),x4162),f5(x4163,x4164,x4162)) % 1.17/1.31 [516]~P36(x5162)+~P37(x5162)+E(x5161,f9(x5162))+E(f5(f7(x5163,f6(x5164,x5161,x5162),x5162),x5161,x5162),f7(x5164,f5(x5163,x5161,x5162),x5162)) % 1.17/1.31 [517]~P36(x5172)+~P37(x5172)+E(x5171,f9(x5172))+E(f5(f7(x5173,f6(x5174,x5171,x5172),x5172),x5171,x5172),f7(f5(x5173,x5171,x5172),x5174,x5172)) % 1.17/1.31 [474]~P21(x4743)+~P6(x4742,x4745,x4743)+~P6(x4741,x4744,x4743)+P6(f7(x4741,x4742,x4743),f7(x4744,x4745,x4743),x4743) % 1.17/1.31 [535]~P26(x5353)+~P6(f11(x5352,x5353),x5355,a2)+~P6(f11(x5351,x5353),x5354,a2)+P6(f11(f6(x5351,x5352,x5353),x5353),f6(x5354,x5355,a2),a2) % 1.17/1.31 [536]~P30(x5363)+~P6(f11(x5362,x5363),x5365,a2)+~P6(f11(x5361,x5363),x5364,a2)+P6(f11(f7(x5361,x5362,x5363),x5363),f7(x5364,x5365,a2),a2) % 1.17/1.31 [550]~P37(x5502)+E(x5501,f9(x5502))+E(x5503,f9(x5502))+E(f5(f7(f6(x5504,x5501,x5502),f6(x5505,x5503,x5502),x5502),f6(x5503,x5501,x5502),x5502),f7(f5(x5504,x5503,x5502),f5(x5505,x5501,x5502),x5502)) % 1.17/1.31 [302]~P2(x3022)+~P49(x3022)+~P33(x3022)+~P34(x3022)+~E(f12(x3021,f9(a1),x3022),f9(x3022)) % 1.17/1.31 [446]~P39(x4462)+~P36(x4462)+~P6(f5(x4463,x4461,x4462),f9(x4462),x4462)+P6(x4461,f9(x4462),x4462)+P6(x4463,f9(x4462),x4462) % 1.17/1.31 [447]~P39(x4472)+~P36(x4472)+~P6(f9(x4472),f5(x4473,x4471,x4472),x4472)+P6(x4471,f9(x4472),x4472)+P6(f9(x4472),x4473,x4472) % 1.17/1.31 [448]~P39(x4482)+~P36(x4482)+~P6(f9(x4482),f5(x4481,x4483,x4482),x4482)+P6(x4481,f9(x4482),x4482)+P6(f9(x4482),x4483,x4482) % 1.17/1.31 [449]~P39(x4492)+~P36(x4492)+~P6(f9(x4492),f5(x4493,x4491,x4492),x4492)+P6(x4491,f9(x4492),x4492)+P6(f9(x4492),x4491,x4492) % 1.17/1.31 [450]~P39(x4502)+~P36(x4502)+~P6(f9(x4502),f5(x4501,x4503,x4502),x4502)+P6(x4501,f9(x4502),x4502)+P6(f9(x4502),x4501,x4502) % 1.17/1.31 [451]~P39(x4512)+~P36(x4512)+~P6(f5(x4513,x4511,x4512),f9(x4512),x4512)+P6(x4511,f9(x4512),x4512)+P6(f9(x4512),x4511,x4512) % 1.17/1.31 [452]~P39(x4522)+~P36(x4522)+~P6(f5(x4521,x4523,x4522),f9(x4522),x4522)+P6(x4521,f9(x4522),x4522)+P6(f9(x4522),x4521,x4522) % 1.17/1.31 [453]~P39(x4531)+~P36(x4531)+~P6(f5(x4532,x4533,x4531),f9(x4531),x4531)+P6(f9(x4531),x4532,x4531)+P6(f9(x4531),x4533,x4531) % 1.17/1.31 [497]~P39(x4974)+~P36(x4974)+~P6(f9(x4974),x4973,x4974)+~P6(f5(x4971,x4973,x4974),x4972,x4974)+P6(x4971,f6(x4972,x4973,x4974),x4974) % 1.17/1.31 [499]~P39(x4993)+~P36(x4993)+~P6(f9(x4993),x4992,x4993)+~P6(x4991,f5(x4994,x4992,x4993),x4993)+P6(f6(x4991,x4992,x4993),x4994,x4993) % 1.17/1.31 [515]~P42(x5153)+~P6(x5154,x5152,a1)+~P6(x5151,f4(x5153),x5153)+~P6(f9(x5153),x5151,x5153)+P6(f12(x5151,x5152,x5153),f12(x5151,x5154,x5153),x5153) % 1.17/1.31 [538]~P39(x5383)+~P6(x5382,x5384,x5383)+~P6(x5381,f9(x5383),x5383)+~P6(f9(x5383),f6(x5382,x5384,x5383),x5383)+P6(f5(x5381,x5382,x5383),f5(x5381,x5384,x5383),x5383) % 1.17/1.31 [539]~P39(x5393)+~P6(x5394,x5392,x5393)+~P6(f9(x5393),x5391,x5393)+~P6(f9(x5393),f6(x5392,x5394,x5393),x5393)+P6(f5(x5391,x5392,x5393),f5(x5391,x5394,x5393),x5393) % 1.17/1.31 [389]~P37(x3892)+~E(f5(x3894,x3893,x3892),f5(x3895,x3891,x3892))+E(f6(x3894,x3891,x3892),f6(x3895,x3893,x3892))+E(x3891,f9(x3892))+E(x3893,f9(x3892)) % 1.17/1.31 [390]~P37(x3902)+~E(f6(x3904,x3903,x3902),f6(x3905,x3901,x3902))+E(f5(x3904,x3901,x3902),f5(x3905,x3903,x3902))+E(x3901,f9(x3902))+E(x3903,f9(x3902)) % 1.17/1.31 [501]~P35(x5014)+~P5(x5014)+E(x5011,x5012)+E(x5013,f9(x5014))+~E(f7(x5015,f6(x5013,x5011,x5014),x5014),f7(x5015,f6(x5013,x5012,x5014),x5014)) % 1.17/1.31 [547]~P35(x5475)+~P5(x5475)+E(x5471,x5472)+E(x5473,x5474)+~E(f7(f6(x5473,x5471,x5475),f6(x5474,x5472,x5475),x5475),f7(f6(x5473,x5472,x5475),f6(x5474,x5471,x5475),x5475)) % 1.17/1.31 [275]~P2(x2752)+~P49(x2752)+~P33(x2752)+~P34(x2752)+E(x2751,f9(a1))+E(f12(f9(x2752),x2751,x2752),f9(x2752)) % 1.17/1.31 [303]~P2(x3032)+~P49(x3032)+~P33(x3032)+~P34(x3032)+~E(f12(x3031,x3033,x3032),f9(x3032))+E(x3031,f9(x3032)) % 1.17/1.31 [444]~P39(x4442)+~P36(x4442)+P6(x4441,f9(x4442),x4442)+P6(f9(x4442),x4441,x4442)+~P6(x4443,f9(x4442),x4442)+P6(x4443,f5(x4444,x4441,x4442),x4442) % 1.17/1.31 [445]~P39(x4452)+~P36(x4452)+P6(x4451,f9(x4452),x4452)+P6(f9(x4452),x4451,x4452)+~P6(f9(x4452),x4454,x4452)+P6(f5(x4453,x4451,x4452),x4454,x4452) % 1.17/1.31 [475]~P39(x4752)+~P36(x4752)+P6(x4751,f9(x4752),x4752)+P6(f9(x4752),x4751,x4752)+~P6(x4753,f5(x4754,x4751,x4752),x4752)+P6(x4753,f9(x4752),x4752) % 1.17/1.31 [476]~P39(x4762)+~P36(x4762)+P6(x4761,f9(x4762),x4762)+P6(f9(x4762),x4761,x4762)+~P6(f5(x4764,x4761,x4762),x4763,x4762)+P6(f9(x4762),x4763,x4762) % 1.17/1.31 [523]~P39(x5232)+~P36(x5232)+~P6(f6(x5233,x5231,x5232),x5234,x5232)+P6(x5231,f9(x5232),x5232)+~P6(x5233,f9(x5232),x5232)+P6(x5233,f5(x5234,x5231,x5232),x5232) % 1.17/1.31 [524]~P39(x5242)+~P36(x5242)+~P6(x5243,f6(x5244,x5241,x5242),x5242)+P6(x5241,f9(x5242),x5242)+~P6(f9(x5242),x5244,x5242)+P6(f5(x5243,x5241,x5242),x5244,x5242) % 1.17/1.31 [525]~P39(x5251)+~P36(x5251)+~P6(x5254,f5(x5253,x5252,x5251),x5251)+~P6(x5252,f9(x5251),x5251)+P6(f9(x5251),x5252,x5251)+P6(x5253,f6(x5254,x5252,x5251),x5251) % 1.17/1.31 [526]~P39(x5261)+~P36(x5261)+~P6(x5264,f6(x5263,x5262,x5261),x5261)+~P6(x5262,f9(x5261),x5261)+P6(f9(x5261),x5262,x5261)+P6(x5263,f5(x5264,x5262,x5261),x5261) % 1.17/1.31 [527]~P39(x5271)+~P36(x5271)+~P6(x5274,f6(x5273,x5272,x5271),x5271)+~P6(x5273,f9(x5271),x5271)+P6(f9(x5271),x5272,x5271)+P6(x5273,f5(x5274,x5272,x5271),x5271) % 1.17/1.31 [528]~P39(x5281)+~P36(x5281)+~P6(f5(x5284,x5282,x5281),x5283,x5281)+~P6(x5282,f9(x5281),x5281)+P6(f9(x5281),x5282,x5281)+P6(f6(x5283,x5282,x5281),x5284,x5281) % 1.17/1.31 [529]~P39(x5291)+~P36(x5291)+~P6(f6(x5294,x5292,x5291),x5293,x5291)+~P6(x5292,f9(x5291),x5291)+P6(f9(x5291),x5292,x5291)+P6(f5(x5293,x5292,x5291),x5294,x5291) % 1.17/1.31 [530]~P39(x5301)+~P36(x5301)+~P6(f6(x5304,x5302,x5301),x5303,x5301)+~P6(f9(x5301),x5304,x5301)+P6(f9(x5301),x5302,x5301)+P6(f5(x5303,x5302,x5301),x5304,x5301) % 1.17/1.31 [542]~P39(x5424)+~P36(x5424)+~P6(x5423,f9(x5424),x5424)+~P6(x5422,f6(x5421,x5423,x5424),x5424)+~P6(f6(x5421,x5423,x5424),x5422,x5424)+P6(x5421,f5(x5422,x5423,x5424),x5424) % 1.17/1.31 [543]~P39(x5434)+~P36(x5434)+~P6(x5431,f9(x5434),x5434)+~P6(x5432,f6(x5431,x5433,x5434),x5434)+~P6(f6(x5431,x5433,x5434),x5432,x5434)+P6(x5431,f5(x5432,x5433,x5434),x5434) % 1.17/1.31 [544]~P39(x5443)+~P36(x5443)+~P6(x5442,f9(x5443),x5443)+~P6(x5441,f6(x5444,x5442,x5443),x5443)+~P6(f6(x5444,x5442,x5443),x5441,x5443)+P6(f5(x5441,x5442,x5443),x5444,x5443) % 1.17/1.31 [545]~P39(x5453)+~P36(x5453)+~P6(f9(x5453),x5454,x5453)+~P6(x5451,f6(x5454,x5452,x5453),x5453)+~P6(f6(x5454,x5452,x5453),x5451,x5453)+P6(f5(x5451,x5452,x5453),x5454,x5453) % 1.17/1.31 %EqnAxiom % 1.17/1.31 [1]E(x11,x11) % 1.17/1.31 [2]E(x22,x21)+~E(x21,x22) % 1.17/1.31 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.17/1.31 [4]~E(x41,x42)+E(f4(x41),f4(x42)) % 1.17/1.31 [5]~E(x51,x52)+E(f6(x51,x53,x54),f6(x52,x53,x54)) % 1.17/1.31 [6]~E(x61,x62)+E(f6(x63,x61,x64),f6(x63,x62,x64)) % 1.17/1.31 [7]~E(x71,x72)+E(f6(x73,x74,x71),f6(x73,x74,x72)) % 1.17/1.31 [8]~E(x81,x82)+E(f8(x81),f8(x82)) % 1.17/1.31 [9]~E(x91,x92)+E(f9(x91),f9(x92)) % 1.17/1.31 [10]~E(x101,x102)+E(f11(x101,x103),f11(x102,x103)) % 1.17/1.31 [11]~E(x111,x112)+E(f11(x113,x111),f11(x113,x112)) % 1.17/1.31 [12]~E(x121,x122)+E(f7(x121,x123,x124),f7(x122,x123,x124)) % 1.17/1.31 [13]~E(x131,x132)+E(f7(x133,x131,x134),f7(x133,x132,x134)) % 1.17/1.31 [14]~E(x141,x142)+E(f7(x143,x144,x141),f7(x143,x144,x142)) % 1.17/1.31 [15]~E(x151,x152)+E(f12(x151,x153,x154),f12(x152,x153,x154)) % 1.17/1.31 [16]~E(x161,x162)+E(f12(x163,x161,x164),f12(x163,x162,x164)) % 1.17/1.31 [17]~E(x171,x172)+E(f12(x173,x174,x171),f12(x173,x174,x172)) % 1.17/1.31 [18]~E(x181,x182)+E(f5(x181,x183,x184),f5(x182,x183,x184)) % 1.17/1.31 [19]~E(x191,x192)+E(f5(x193,x191,x194),f5(x193,x192,x194)) % 1.17/1.31 [20]~E(x201,x202)+E(f5(x203,x204,x201),f5(x203,x204,x202)) % 1.17/1.31 [21]~E(x211,x212)+E(f10(x211,x213),f10(x212,x213)) % 1.17/1.31 [22]~E(x221,x222)+E(f10(x223,x221),f10(x223,x222)) % 1.17/1.31 [23]~E(x231,x232)+E(f16(x231,x233),f16(x232,x233)) % 1.17/1.31 [24]~E(x241,x242)+E(f16(x243,x241),f16(x243,x242)) % 1.17/1.31 [25]~P1(x251)+P1(x252)+~E(x251,x252) % 1.17/1.31 [26]P6(x262,x263,x264)+~E(x261,x262)+~P6(x261,x263,x264) % 1.17/1.31 [27]P6(x273,x272,x274)+~E(x271,x272)+~P6(x273,x271,x274) % 1.17/1.31 [28]P6(x283,x284,x282)+~E(x281,x282)+~P6(x283,x284,x281) % 1.17/1.31 [29]~P50(x291)+P50(x292)+~E(x291,x292) % 1.17/1.31 [30]~P2(x301)+P2(x302)+~E(x301,x302) % 1.17/1.31 [31]~P36(x311)+P36(x312)+~E(x311,x312) % 1.17/1.31 [32]~P39(x321)+P39(x322)+~E(x321,x322) % 1.17/1.31 [33]~P32(x331)+P32(x332)+~E(x331,x332) % 1.17/1.31 [34]~P43(x341)+P43(x342)+~E(x341,x342) % 1.17/1.31 [35]~P27(x351)+P27(x352)+~E(x351,x352) % 1.17/1.31 [36]~P49(x361)+P49(x362)+~E(x361,x362) % 1.17/1.31 [37]~P42(x371)+P42(x372)+~E(x371,x372) % 1.17/1.31 [38]~P38(x381)+P38(x382)+~E(x381,x382) % 1.17/1.31 [39]~P33(x391)+P33(x392)+~E(x391,x392) % 1.17/1.31 [40]~P23(x401)+P23(x402)+~E(x401,x402) % 1.17/1.31 [41]~P37(x411)+P37(x412)+~E(x411,x412) % 1.17/1.31 [42]~P34(x421)+P34(x422)+~E(x421,x422) % 1.17/1.31 [43]~P24(x431)+P24(x432)+~E(x431,x432) % 1.17/1.31 [44]~P35(x441)+P35(x442)+~E(x441,x442) % 1.17/1.31 [45]~P44(x451)+P44(x452)+~E(x451,x452) % 1.17/1.31 [46]~P41(x461)+P41(x462)+~E(x461,x462) % 1.17/1.31 [47]~P5(x471)+P5(x472)+~E(x471,x472) % 1.17/1.31 [48]~P26(x481)+P26(x482)+~E(x481,x482) % 1.17/1.31 [49]~P3(x491)+P3(x492)+~E(x491,x492) % 1.17/1.31 [50]~P8(x501)+P8(x502)+~E(x501,x502) % 1.17/1.31 [51]~P10(x511)+P10(x512)+~E(x511,x512) % 1.17/1.31 [52]~P45(x521)+P45(x522)+~E(x521,x522) % 1.17/1.31 [53]~P9(x531)+P9(x532)+~E(x531,x532) % 1.17/1.31 [54]~P48(x541)+P48(x542)+~E(x541,x542) % 1.17/1.31 [55]~P16(x551)+P16(x552)+~E(x551,x552) % 1.17/1.31 [56]~P40(x561)+P40(x562)+~E(x561,x562) % 1.17/1.31 [57]~P22(x571)+P22(x572)+~E(x571,x572) % 1.17/1.31 [58]~P31(x581)+P31(x582)+~E(x581,x582) % 1.17/1.31 [59]~P14(x591)+P14(x592)+~E(x591,x592) % 1.17/1.31 [60]~P12(x601)+P12(x602)+~E(x601,x602) % 1.17/1.31 [61]~P15(x611)+P15(x612)+~E(x611,x612) % 1.17/1.31 [62]~P4(x621)+P4(x622)+~E(x621,x622) % 1.17/1.31 [63]~P13(x631)+P13(x632)+~E(x631,x632) % 1.17/1.31 [64]~P25(x641)+P25(x642)+~E(x641,x642) % 1.17/1.31 [65]~P18(x651)+P18(x652)+~E(x651,x652) % 1.17/1.31 [66]~P7(x661)+P7(x662)+~E(x661,x662) % 1.17/1.31 [67]~P20(x671)+P20(x672)+~E(x671,x672) % 1.17/1.31 [68]~P46(x681)+P46(x682)+~E(x681,x682) % 1.17/1.31 [69]~P17(x691)+P17(x692)+~E(x691,x692) % 1.17/1.31 [70]~P29(x701)+P29(x702)+~E(x701,x702) % 1.17/1.31 [71]~P11(x711)+P11(x712)+~E(x711,x712) % 1.17/1.31 [72]~P30(x721)+P30(x722)+~E(x721,x722) % 1.17/1.31 [73]~P47(x731)+P47(x732)+~E(x731,x732) % 1.17/1.31 [74]~P21(x741)+P21(x742)+~E(x741,x742) % 1.17/1.31 [75]~P19(x751)+P19(x752)+~E(x751,x752) % 1.17/1.31 [76]~P28(x761)+P28(x762)+~E(x761,x762) % 1.17/1.31 % 1.17/1.31 %------------------------------------------- % 1.17/1.31 cnf(747,plain, % 1.17/1.31 (P6(f11(f7(f4(a3),f6(a14,f12(f16(a14,a13),a13,a3),a3),a3),a3),f4(a2),a2)), % 1.17/1.31 inference(scs_inference,[],[191,179,552])). % 1.17/1.31 cnf(748,plain, % 1.17/1.31 (~P6(f11(f7(f4(a3),f6(a14,f12(x7481,a13,a3),a3),a3),a3),f4(a2),a2)), % 1.17/1.31 inference(scs_inference,[],[190,554])). % 1.17/1.31 cnf(1004,plain, % 1.17/1.31 ($false), % 1.17/1.31 inference(scs_inference,[],[748,747]), % 1.17/1.31 ['proof']). % 1.17/1.31 % SZS output end Proof % 1.17/1.31 % Total time :0.560000s %------------------------------------------------------------------------------