%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL846-1 : TPTP v9.3.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n011.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:19:59 AM UTC 2026 % Result : Unsatisfiable 1.09s 1.25s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL846-1 : TPTP v9.3.1. Released v4.1.0. % 0.00/0.03 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.08/0.35 % Computer : n011.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.08/0.35 % CPULimit : 300 % 0.08/0.35 % WCLimit : 300 % 0.08/0.35 % DateTime : Fri Sep 4 14:06:13 UTC 2026 % 0.12/0.36 % CPUTime : % 0.23/0.51 start to proof:theBenchmark % 0.94/1.15 %------------------------------------------- % 0.94/1.15 % File :CSE---1.7 % 0.94/1.15 % Problem :theBenchmark % 0.94/1.15 % Transform :cnf % 0.94/1.15 % Format :tptp:raw % 0.94/1.15 % Command :java -jar mcs_scs.jar %d %s % 0.94/1.15 % 0.94/1.15 % Result :Theorem 0.115360s % 0.94/1.15 % Output :CNFRefutation 0.115360s % 0.94/1.15 %------------------------------------------- % 0.94/1.16 %------------------------------------------------------------------------------ % 0.94/1.16 % File : LCL846-1 : TPTP v9.3.1. Released v4.1.0. % 0.94/1.16 % Domain : Logic Calculi % 0.94/1.16 % Problem : Strong normalization of typed lambda calculus 262_39 % 0.94/1.16 % Version : Especial. % 0.94/1.16 % English : % 0.94/1.16 % 0.94/1.16 % Refs : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java % 0.94/1.16 % : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe % 0.94/1.16 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 0.94/1.16 % Source : [Nip10] % 0.94/1.16 % Names : StrongNorm-262_39 [Nip10] % 0.94/1.16 % 0.94/1.16 % Status : Unsatisfiable % 0.94/1.16 % Rating : 0.17 v9.3.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.07 v6.4.0, 0.00 v6.2.0, 0.20 v6.1.0, 0.07 v6.0.0, 0.20 v5.3.0, 0.22 v5.2.0, 0.19 v5.1.0, 0.29 v4.1.0 % 0.94/1.16 % Syntax : Number of clauses : 1230 ( 153 unt; 184 nHn; 736 RR) % 0.94/1.16 % Number of literals : 3515 ( 745 equ;2121 neg) % 0.94/1.16 % Maximal clause size : 6 ( 2 avg) % 0.94/1.16 % Maximal term depth : 5 ( 1 avg) % 0.94/1.16 % Number of predicates : 71 ( 70 usr; 0 prp; 1-3 aty) % 0.94/1.16 % Number of functors : 35 ( 35 usr; 4 con; 0-3 aty) % 0.94/1.16 % Number of variables : 3503 ( 223 sgn) % 0.94/1.16 % SPC : CNF_UNS_RFO_SEQ_NHN % 0.94/1.16 % 0.94/1.16 % Comments : % 0.94/1.16 %------------------------------------------------------------------------------ % 0.94/1.16 cnf(cls_add__Suc_0,axiom, % 0.94/1.16 c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_abs__le__mult_0,axiom, % 0.94/1.16 ( ~ class_Ring__and__Field_Olordered__ring(T_a) % 0.94/1.16 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) ) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_neg__le__iff__le_0,axiom, % 0.94/1.16 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.94/1.16 | c_lessequals(V_a,V_b,T_a) % 0.94/1.16 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_le__imp__neg__le_0,axiom, % 0.94/1.16 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.94/1.16 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 0.94/1.16 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_div__add_0,axiom, % 0.94/1.16 ( ~ class_Divides_Osemiring__div(T_a) % 0.94/1.16 | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_x,V_z,T_a),c_Divides_Odiv__class_Odiv(V_y,V_z,T_a),T_a) % 0.94/1.16 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,T_a) % 0.94/1.16 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,T_a) ) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_eq__add__iff2_1,axiom, % 0.94/1.16 ( ~ class_Ring__and__Field_Oring(T_a) % 0.94/1.16 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a) ) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_nat__less__add__iff1_0,axiom, % 0.94/1.16 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat) % 0.94/1.16 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) % 0.94/1.16 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_nat__less__add__iff1_1,axiom, % 0.94/1.16 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) % 0.94/1.16 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat) % 0.94/1.16 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_nat__less__add__iff2_0,axiom, % 0.94/1.16 ( c_HOL_Oord__class_Oless(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) % 0.94/1.16 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) % 0.94/1.16 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_nat__less__add__iff2_1,axiom, % 0.94/1.16 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) % 0.94/1.16 | ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) % 0.94/1.16 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_eq__add__iff2_0,axiom, % 0.94/1.16 ( ~ class_Ring__and__Field_Oring(T_a) % 0.94/1.16 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a) % 0.94/1.16 | V_c = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a) ) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_eq__add__iff1_0,axiom, % 0.94/1.16 ( ~ class_Ring__and__Field_Oring(T_a) % 0.94/1.16 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a) % 0.94/1.16 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) = V_d ) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_div__mod__equality2_0,axiom, % 0.94/1.16 ( ~ class_Divides_Osemiring__div(T_a) % 0.94/1.16 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) ) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_div__mod__equality_0,axiom, % 0.94/1.16 ( ~ class_Divides_Osemiring__div(T_a) % 0.94/1.16 | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) ) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_less__add__Suc1_0,axiom, % 0.94/1.16 c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_i,V_m,tc_nat)),tc_nat) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_less__add__Suc2_0,axiom, % 0.94/1.16 c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_i,tc_nat)),tc_nat) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_less__iff__Suc__add_1,axiom, % 0.94/1.16 c_HOL_Oord__class_Oless(V_m,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat)),tc_nat) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_le__diff__conv2_0,axiom, % 0.94/1.16 ( c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) % 0.94/1.16 | ~ c_lessequals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) % 0.94/1.16 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_le__diff__conv2_1,axiom, % 0.94/1.16 ( c_lessequals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) % 0.94/1.16 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) % 0.94/1.16 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_min__max_Ole__sup__iff_2,axiom, % 0.94/1.16 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.16 | c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) % 0.94/1.16 | ~ c_lessequals(V_y,V_z,T_a) % 0.94/1.16 | ~ c_lessequals(V_x,V_z,T_a) ) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_min__max_Osup__least_0,axiom, % 0.94/1.16 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.16 | c_lessequals(c_Orderings_Oord__class_Omax(V_y,V_z,T_a),V_x,T_a) % 0.94/1.16 | ~ c_lessequals(V_z,V_x,T_a) % 0.94/1.16 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.94/1.16 % 0.94/1.16 cnf(cls_min__max_Ole__supI_0,axiom, % 0.94/1.16 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.17 | c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) % 0.94/1.17 | ~ c_lessequals(V_b,V_x,T_a) % 0.94/1.17 | ~ c_lessequals(V_a,V_x,T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_le__maxI1_0,axiom, % 0.94/1.17 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.17 | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_le__maxI2_0,axiom, % 0.94/1.17 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.17 | c_lessequals(V_y,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_zero__less__abs__iff_1,axiom, % 0.94/1.17 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.94/1.17 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) % 0.94/1.17 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_bot__least_0,axiom, % 0.94/1.17 ( ~ class_Orderings_Obot(T_a) % 0.94/1.17 | c_lessequals(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_abs__minus__le__zero_0,axiom, % 0.94/1.17 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.94/1.17 | c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_min__max_Oinf__sup__distrib2_0,axiom, % 0.94/1.17 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.17 | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_y,V_z,T_a),V_x,T_a) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_y,V_x,T_a),c_Orderings_Oord__class_Omin(V_z,V_x,T_a),T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_min__max_Oinf__sup__distrib1_0,axiom, % 0.94/1.17 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.17 | c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),c_Orderings_Oord__class_Omin(V_x,V_z,T_a),T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_power__strict__decreasing_0,axiom, % 0.94/1.17 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.94/1.17 | 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) % 0.94/1.17 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 0.94/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.94/1.17 | ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_add__increasing_0,axiom, % 0.94/1.17 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.94/1.17 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.94/1.17 | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 0.94/1.17 | ~ c_lessequals(V_b,V_c,T_a) % 0.94/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_add__increasing2_0,axiom, % 0.94/1.17 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.94/1.17 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.94/1.17 | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 0.94/1.17 | ~ c_lessequals(V_b,V_a,T_a) % 0.94/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_le__imp__power__dvd_0,axiom, % 0.94/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.94/1.17 | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 0.94/1.17 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_Suc__leI_0,axiom, % 0.94/1.17 ( c_lessequals(c_Suc(V_m),V_n,tc_nat) % 0.94/1.17 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_Suc__le__eq_0,axiom, % 0.94/1.17 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.94/1.17 | ~ c_lessequals(c_Suc(V_m),V_n,tc_nat) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_less__eq__Suc__le_0,axiom, % 0.94/1.17 ( c_lessequals(c_Suc(V_n),V_m,tc_nat) % 0.94/1.17 | ~ c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_less__eq__Suc__le_1,axiom, % 0.94/1.17 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 0.94/1.17 | ~ c_lessequals(c_Suc(V_n),V_m,tc_nat) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_le__zero__iff__zero__pprt_1,axiom, % 0.94/1.17 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.94/1.17 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.94/1.17 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_le__zero__iff__zero__pprt_0,axiom, % 0.94/1.17 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.94/1.17 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 0.94/1.17 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_termination__basic__simps_I1_J_0,axiom, % 0.94/1.17 ( c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) % 0.94/1.17 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_termination__basic__simps_I2_J_0,axiom, % 0.94/1.17 ( c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) % 0.94/1.17 | ~ c_HOL_Oord__class_Oless(V_x,V_z,tc_nat) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_add__lessD1_0,axiom, % 0.94/1.17 ( c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) % 0.94/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_trans__less__add1_0,axiom, % 0.94/1.17 ( c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat) % 0.94/1.17 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_trans__less__add2_0,axiom, % 0.94/1.17 ( c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat) % 0.94/1.17 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_power__decreasing_0,axiom, % 0.94/1.17 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.94/1.17 | c_lessequals(c_Power_Opower__class_Opower(V_a,V_N,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 0.94/1.17 | ~ c_lessequals(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 0.94/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.94/1.17 | ~ c_lessequals(V_n,V_N,tc_nat) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_divide__le__0__iff_4,axiom, % 0.94/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.17 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.17 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_divide__le__0__iff_5,axiom, % 0.94/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.17 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.94/1.17 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_le__add__iff2_1,axiom, % 0.94/1.17 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.94/1.17 | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) % 0.94/1.17 | ~ c_lessequals(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_le__add__iff2_0,axiom, % 0.94/1.17 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.94/1.17 | c_lessequals(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) % 0.94/1.17 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_le__add__iff1_1,axiom, % 0.94/1.17 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.94/1.17 | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) % 0.94/1.17 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_le__add__iff1_0,axiom, % 0.94/1.17 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.94/1.17 | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a) % 0.94/1.17 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_dvd__mod__imp__dvd_0,axiom, % 0.94/1.17 ( ~ class_Divides_Osemiring__div(T_a) % 0.94/1.17 | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) % 0.94/1.17 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) % 0.94/1.17 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_dvd__mod__iff_1,axiom, % 0.94/1.17 ( ~ class_Divides_Osemiring__div(T_a) % 0.94/1.17 | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) % 0.94/1.17 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) % 0.94/1.17 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_dvd__mod__iff_0,axiom, % 0.94/1.17 ( ~ class_Divides_Osemiring__div(T_a) % 0.94/1.17 | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) % 0.94/1.17 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) % 0.94/1.17 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_dvd__mod_0,axiom, % 0.94/1.17 ( ~ class_Divides_Osemiring__div(T_a) % 0.94/1.17 | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) % 0.94/1.17 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) % 0.94/1.17 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_Suc__diff__le_0,axiom, % 0.94/1.17 ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) % 0.94/1.17 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_zero__le__divide__1__iff_1,axiom, % 0.94/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.17 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) % 0.94/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_zero__le__divide__1__iff_0,axiom, % 0.94/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.17 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.94/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_sum__squares__ge__zero_0,axiom, % 0.94/1.17 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.94/1.17 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_inverse__le__1__iff_1,axiom, % 0.94/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.17 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 0.94/1.17 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom, % 0.94/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.94/1.17 | c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_comm__monoid__add_Omult__commute_0,axiom, % 0.94/1.17 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.94/1.17 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_nat__add__commute_0,axiom, % 0.94/1.17 c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_less__add__eq__less_0,axiom, % 0.94/1.17 ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) % 0.94/1.17 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat) % 0.94/1.17 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_class__semiring_Oadd__c_0,axiom, % 0.94/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.94/1.17 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_y,V_x,T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_divide__le__0__iff_0,axiom, % 0.94/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.17 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.17 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.94/1.17 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_divide__le__0__iff_1,axiom, % 0.94/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.17 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.94/1.17 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.94/1.17 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.94/1.17 % 0.94/1.17 cnf(cls_divide__le__0__iff_2,axiom, % 0.94/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.17 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.17 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.17 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.94/1.17 % 0.94/1.18 cnf(cls_divide__le__0__iff_3,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.18 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.94/1.18 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.18 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_mult__eq__1__iff_0,axiom, % 0.94/1.18 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.94/1.18 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_mult__eq__1__iff_1,axiom, % 0.94/1.18 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.94/1.18 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_mult__sgn__abs_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.94/1.18 | c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_x,T_a),c_HOL_Oabs__class_Oabs(V_x,T_a),T_a) = V_x ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_diff__less__mono2_0,axiom, % 0.94/1.18 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat) % 0.94/1.18 | ~ c_HOL_Oord__class_Oless(V_m,V_l,tc_nat) % 0.94/1.18 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_power__minus_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oring__1(T_a) % 0.94/1.18 | 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) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_dvd__power_1,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.94/1.18 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a),T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_le__imp__inverse__le__neg_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.18 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 0.94/1.18 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.18 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_inverse__le__imp__le__neg_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.18 | c_lessequals(V_b,V_a,T_a) % 0.94/1.18 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.18 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_inverse__le__imp__le_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.18 | c_lessequals(V_b,V_a,T_a) % 0.94/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.94/1.18 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_le__imp__inverse__le_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.18 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 0.94/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.94/1.18 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_of__nat__eq__iff_0,axiom, % 0.94/1.18 ( ~ class_Nat_Osemiring__char__0(T_a) % 0.94/1.18 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) % 0.94/1.18 | V_m = V_n ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_mod__div__trivial_0,axiom, % 0.94/1.18 ( ~ class_Divides_Osemiring__div(T_a) % 0.94/1.18 | c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_divide__le__eq_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.18 | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 0.94/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.94/1.18 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_divide__le__eq_6,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.18 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 0.94/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.94/1.18 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_le__divide__eq_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.18 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 0.94/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.94/1.18 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_le__divide__eq_6,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.18 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 0.94/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.94/1.18 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_mult__imp__div__pos__le_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.18 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) % 0.94/1.18 | ~ c_lessequals(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a) % 0.94/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_mult__imp__le__div__pos_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.18 | c_lessequals(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 0.94/1.18 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a) % 0.94/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_mult__less__imp__less__right_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.94/1.18 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.94/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.94/1.18 | ~ 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) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_mult__less__imp__less__left_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.94/1.18 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.94/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.94/1.18 | ~ 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) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_mult__right__less__imp__less_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 0.94/1.18 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.94/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.94/1.18 | ~ 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) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_mult__left__less__imp__less_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 0.94/1.18 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.94/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.94/1.18 | ~ 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) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_square__eq__iff_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.94/1.18 | c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) != c_HOL_Otimes__class_Otimes(V_b,V_b,T_a) % 0.94/1.18 | V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a) % 0.94/1.18 | V_a = V_b ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_add__Suc__right_0,axiom, % 0.94/1.18 c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_abs__idempotent_0,axiom, % 0.94/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.94/1.18 | c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_a,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_power__0__Suc_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 0.94/1.18 | ~ class_Power_Opower(T_a) % 0.94/1.18 | 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) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_one__le__power_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.94/1.18 | c_lessequals(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 0.94/1.18 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_abs__le__D1_0,axiom, % 0.94/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.94/1.18 | c_lessequals(V_a,V_b,T_a) % 0.94/1.18 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_mult__strict__mono_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.94/1.18 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 0.94/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.94/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.94/1.18 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 0.94/1.18 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_class__fieldgb_Oinverse__divide_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.94/1.18 | ~ class_Int_Onumber__ring(T_a) % 0.94/1.18 | c_HOL_Oinverse__class_Oinverse(V_x,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_x,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_inverse__eq__divide_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.94/1.18 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_zmod__simps_I4_J_0,axiom, % 0.94/1.18 ( ~ class_Divides_Osemiring__div(T_a) % 0.94/1.18 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_dvd__mult__cancel__left_2,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.94/1.18 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 0.94/1.18 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_dvd__mult__cancel__right_2,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.94/1.18 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 0.94/1.18 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_divide__left__mono__neg_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.18 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a) % 0.94/1.18 | ~ 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) % 0.94/1.18 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.18 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_divide__left__mono_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.18 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a) % 0.94/1.18 | ~ 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) % 0.94/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.94/1.18 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_min__max_Oinf__le1_0,axiom, % 0.94/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.18 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_x,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_min__max_Oinf__le2_0,axiom, % 0.94/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.18 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_y,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_min__max_Ole__infI_0,axiom, % 0.94/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.18 | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) % 0.94/1.18 | ~ c_lessequals(V_x,V_b,T_a) % 0.94/1.18 | ~ c_lessequals(V_x,V_a,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_min__max_Ole__inf__iff_2,axiom, % 0.94/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.18 | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) % 0.94/1.18 | ~ c_lessequals(V_x,V_z,T_a) % 0.94/1.18 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_min__max_Oinf__greatest_0,axiom, % 0.94/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.18 | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) % 0.94/1.18 | ~ c_lessequals(V_x,V_z,T_a) % 0.94/1.18 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_eq__add__iff1_1,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oring(T_a) % 0.94/1.18 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_le__minus__self__iff_0,axiom, % 0.94/1.18 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.94/1.18 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.18 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_le__minus__self__iff_1,axiom, % 0.94/1.18 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.94/1.18 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 0.94/1.18 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_minus__le__self__iff_0,axiom, % 0.94/1.18 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.94/1.18 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.94/1.18 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_minus__le__self__iff_1,axiom, % 0.94/1.18 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.94/1.18 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) % 0.94/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_less__eq__neg__nonpos_0,axiom, % 0.94/1.18 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 0.94/1.18 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.18 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_less__eq__neg__nonpos_1,axiom, % 0.94/1.18 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 0.94/1.18 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 0.94/1.18 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_neg__less__eq__nonneg_0,axiom, % 0.94/1.18 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 0.94/1.18 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.94/1.18 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_neg__less__eq__nonneg_1,axiom, % 0.94/1.18 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 0.94/1.18 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) % 0.94/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_zero__le__power_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.94/1.18 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 0.94/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_diff__is__0__eq_1,axiom, % 0.94/1.18 ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) % 0.94/1.18 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_diff__is__0__eq_0,axiom, % 0.94/1.18 ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.94/1.18 | c_lessequals(V_m,V_n,tc_nat) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_min__diff__distrib__left_0,axiom, % 0.94/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.94/1.18 | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(V_x,V_z,T_a),c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_max__less__iff__conj_2,axiom, % 0.94/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.18 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) % 0.94/1.18 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.94/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_z,T_a) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_diff__Suc__diff__eq2_0,axiom, % 0.94/1.18 ( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),V_m,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(V_j),c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),tc_nat) % 0.94/1.18 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_replicate__eq__replicate_0,axiom, % 0.94/1.18 ( c_List_Oreplicate(V_m,V_x,T_a) != c_List_Oreplicate(V_n,V_y,T_a) % 0.94/1.18 | V_m = V_n ) ). % 0.94/1.18 % 0.94/1.18 cnf(cls_class__semiring_Omul__1_0,axiom, % 0.94/1.18 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.94/1.19 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_x,T_a) = V_x ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_mult__1_0,axiom, % 0.94/1.19 ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) % 0.94/1.19 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_mult__1__left_0,axiom, % 0.94/1.19 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.94/1.19 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_mult__1__right_0,axiom, % 0.94/1.19 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.94/1.19 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.94/1.19 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_class__semiring_Osemiring__rules_I11_J_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.94/1.19 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_add__strict__increasing_0,axiom, % 0.94/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.94/1.19 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.94/1.19 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 0.94/1.19 | ~ c_lessequals(V_b,V_c,T_a) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_lem0_0,axiom, % 0.94/1.19 ( c_HOL_Oord__class_Oless(V_m,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) % 0.94/1.19 | ~ c_lessequals(V_m,V_n,tc_nat) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_dvdI_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Odvd(T_a) % 0.94/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_b,c_HOL_Otimes__class_Otimes(V_b,V_k,T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_dvd__triv__left_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.94/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_dvd__triv__right_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.94/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_abs__diff__triangle__ineq_0,axiom, % 0.94/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.94/1.19 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_c,T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_b,V_d,T_a),T_a),T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_frac__less2_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.19 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_z,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_w,T_a),T_a) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(V_w,V_z,T_a) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 0.94/1.19 | ~ c_lessequals(V_x,V_y,T_a) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_div__self_0,axiom, % 0.94/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 0.94/1.19 | c_Divides_Odiv__class_Odiv(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 0.94/1.19 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_power__one__over_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.94/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.19 | 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) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_add__is__1_4,axiom, % 0.94/1.19 c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_mod__mod__trivial_0,axiom, % 0.94/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 0.94/1.19 | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_of__nat__le__iff_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.94/1.19 | c_lessequals(V_m,V_n,tc_nat) % 0.94/1.19 | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_of__nat__le__iff_1,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.94/1.19 | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) % 0.94/1.19 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_subst__preserves__beta_0,axiom, % 0.94/1.19 ( c_Lambda_Obeta(c_Lambda_Osubst(V_r,V_t,V_i),c_Lambda_Osubst(V_s,V_t,V_i)) % 0.94/1.19 | ~ c_Lambda_Obeta(V_r,V_s) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_nonzero__minus__divide__right_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.94/1.19 | 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) % 0.94/1.19 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_divide__less__0__1__iff_1,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.19 | 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) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_divide__less__0__1__iff_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.19 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.19 | ~ 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) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_neg__less__0__iff__less_0,axiom, % 0.94/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.94/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_neg__less__0__iff__less_1,axiom, % 0.94/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.94/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_min__less__iff__conj_2,axiom, % 0.94/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.19 | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_natgb_Oadd__mul__solve_1,axiom, % 0.94/1.19 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_natgb_Onoteq__reduce_1,axiom, % 0.94/1.19 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat),tc_nat) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_class__ringb_Onoteq__reduce_1,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.94/1.19 | ~ class_Int_Onumber__ring(T_a) % 0.94/1.19 | 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) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_class__ringb_Oadd__mul__solve_1,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.94/1.19 | ~ class_Int_Onumber__ring(T_a) % 0.94/1.19 | 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) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_max__Suc__Suc_0,axiom, % 0.94/1.19 c_Orderings_Oord__class_Omax(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(V_m,V_n,tc_nat)) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_less__Suc0_0,axiom, % 0.94/1.19 ( V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom, % 0.94/1.19 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.94/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.94/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom, % 0.94/1.19 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.94/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) % 0.94/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_abs__triangle__ineq3_0,axiom, % 0.94/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.94/1.19 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_min__max_Oinf__left__idem_0,axiom, % 0.94/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.19 | c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) = c_Orderings_Oord__class_Omin(V_x,V_y,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_subst__Var_2,axiom, % 0.94/1.19 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_i),V_s,V_k) = c_Lambda_OdB_OVar(V_i) % 0.94/1.19 | V_i = V_k % 0.94/1.19 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_abs__mult__less_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.94/1.19 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(V_c,V_d,T_a),T_a) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_b,T_a),V_d,T_a) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_c,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_nat__diff__add__eq2_0,axiom, % 0.94/1.19 ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) % 0.94/1.19 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_nat__diff__add__eq1_0,axiom, % 0.94/1.19 ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat) % 0.94/1.19 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_diff__add__cancel_0,axiom, % 0.94/1.19 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.94/1.19 | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_inverse__nonnegative__iff__nonnegative_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.94/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_inverse__nonnegative__iff__nonnegative_1,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 0.94/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_inverse__inverse__eq_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 0.94/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.19 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_mult__le__cancel2_1,axiom, % 0.94/1.19 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) % 0.94/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_mult__le__cancel1_1,axiom, % 0.94/1.19 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 0.94/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_class__semiring_Opwr__pwr_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.94/1.19 | c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_x,V_p,T_a),V_q,T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Otimes__class_Otimes(V_p,V_q,tc_nat),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_power__Suc2_0,axiom, % 0.94/1.19 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.94/1.19 | 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) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_power__Suc_0,axiom, % 0.94/1.19 ( ~ class_Power_Opower(T_a) % 0.94/1.19 | 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) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_class__semiring_Opwr__Suc_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.94/1.19 | 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) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_class__semiring_Osemiring__rules_I35_J_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.94/1.19 | 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) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_add__le__mono_0,axiom, % 0.94/1.19 ( c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_l,tc_nat),tc_nat) % 0.94/1.19 | ~ c_lessequals(V_k,V_l,tc_nat) % 0.94/1.19 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_add__mono_0,axiom, % 0.94/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 0.94/1.19 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) % 0.94/1.19 | ~ c_lessequals(V_c,V_d,T_a) % 0.94/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_less__Suc__eq__le_1,axiom, % 0.94/1.19 ( c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) % 0.94/1.19 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_less__Suc__eq__le_0,axiom, % 0.94/1.19 ( c_lessequals(V_m,V_n,tc_nat) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_le__less__Suc__eq_1,axiom, % 0.94/1.19 ( ~ c_lessequals(V_x,V_x,tc_nat) % 0.94/1.19 | c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_class__semiring_Omul__c_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.94/1.19 | c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_nat__mult__commute_0,axiom, % 0.94/1.19 c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) = c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_add__nonneg__eq__0__iff_2,axiom, % 0.94/1.19 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.94/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.19 | 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) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.94/1.19 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_diff__less__Suc_0,axiom, % 0.94/1.19 c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_Suc(V_m),tc_nat) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_mod__add__eq_0,axiom, % 0.94/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 0.94/1.19 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_add__nonneg__nonneg_0,axiom, % 0.94/1.19 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.94/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) % 0.94/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.94/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_zero__le__power__abs_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.94/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_a,T_a),V_n,T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_inverse__less__imp__less_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.19 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_less__imp__inverse__less_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.19 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_abs__of__neg_0,axiom, % 0.94/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.94/1.19 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_abs__if__lattice_0,axiom, % 0.94/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.19 | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 0.94/1.19 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_abs__if_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Oabs__if(T_a) % 0.94/1.19 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_mod__minus__cong_0,axiom, % 0.94/1.19 ( ~ class_Divides_Oring__div(T_a) % 0.94/1.19 | c_Divides_Odiv__class_Omod(V_a,V_b,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_b,T_a) % 0.94/1.19 | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a_H,T_a),V_b,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_mod__mult__eq_0,axiom, % 0.94/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 0.94/1.19 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_dvd__diff_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 0.94/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a) % 0.94/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,T_a) % 0.94/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_power__commutes_0,axiom, % 0.94/1.19 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.94/1.19 | 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) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_le__max__iff__disj_0,axiom, % 0.94/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.19 | c_lessequals(V_z,V_y,T_a) % 0.94/1.19 | c_lessequals(V_z,V_x,T_a) % 0.94/1.19 | ~ c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_class__semiring_Omul__pwr_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.94/1.19 | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_nat),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_liftn__lift_0,axiom, % 0.94/1.19 c_Lambda_Oliftn(c_Suc(V_n),V_t,V_k) = c_Lambda_Olift(c_Lambda_Oliftn(V_n,V_t,V_k),V_k) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_nat__eq__add__iff1_1,axiom, % 0.94/1.19 ( ~ c_lessequals(V_j,V_i,tc_nat) % 0.94/1.19 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),tc_nat) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_min__max_Ole__inf__iff_1,axiom, % 0.94/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.19 | c_lessequals(V_x,V_z,T_a) % 0.94/1.19 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_min__max_Ole__inf__iff_0,axiom, % 0.94/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.19 | c_lessequals(V_x,V_y,T_a) % 0.94/1.19 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_min__le__iff__disj_2,axiom, % 0.94/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.19 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 0.94/1.19 | ~ c_lessequals(V_y,V_z,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_min__le__iff__disj_1,axiom, % 0.94/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.19 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 0.94/1.19 | ~ c_lessequals(V_x,V_z,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_min__max_Ole__infI2_0,axiom, % 0.94/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.19 | c_lessequals(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 0.94/1.19 | ~ c_lessequals(V_b,V_x,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_min__max_Ole__infI1_0,axiom, % 0.94/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.19 | c_lessequals(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 0.94/1.19 | ~ c_lessequals(V_a,V_x,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_min__max_Ole__infE_1,axiom, % 0.94/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.19 | c_lessequals(V_x,V_b,T_a) % 0.94/1.19 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_min__max_Ole__infE_0,axiom, % 0.94/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.94/1.19 | c_lessequals(V_x,V_a,T_a) % 0.94/1.19 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_div__mult__self2_0,axiom, % 0.94/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 0.94/1.19 | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(V_c,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a) % 0.94/1.19 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_div__mult__self1_0,axiom, % 0.94/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 0.94/1.19 | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(V_c,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a) % 0.94/1.19 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_sgn__greater_1,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.94/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_sgn__greater_0,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.94/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.94/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) ) ). % 0.94/1.19 % 0.94/1.19 cnf(cls_divide__less__eq_1,axiom, % 0.94/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.19 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 0.94/1.20 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.94/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 0.94/1.20 % 0.94/1.20 cnf(cls_divide__less__eq_4,axiom, % 0.94/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.20 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 0.94/1.20 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 0.94/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.94/1.20 % 0.94/1.20 cnf(cls_divide__less__eq_5,axiom, % 0.94/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.20 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 0.94/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.94/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 0.94/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.94/1.20 % 0.94/1.20 cnf(cls_divide__less__eq_7,axiom, % 0.94/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.20 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 0.94/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.94/1.20 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.20 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 0.94/1.20 % 0.94/1.20 cnf(cls_less__divide__eq_1,axiom, % 0.94/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.20 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 0.94/1.20 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.94/1.20 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 0.94/1.20 % 0.94/1.20 cnf(cls_less__divide__eq_4,axiom, % 0.94/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 0.94/1.20 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.20 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 0.94/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.94/1.20 % 0.94/1.20 cnf(cls_less__divide__eq_5,axiom, % 0.94/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 0.94/1.20 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.20 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 0.94/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.94/1.20 % 0.94/1.20 cnf(cls_less__divide__eq_7,axiom, % 0.94/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 0.94/1.20 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.20 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.94/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 0.94/1.20 % 0.94/1.20 cnf(cls_inverse__le__1__iff_2,axiom, % 0.94/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.94/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.94/1.20 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 0.94/1.20 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_x,T_a) ) ). % 0.94/1.20 % 0.94/1.20 cnf(cls_class__semiring_Osemiring__rules_I4_J_0,axiom, % 0.94/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.94/1.20 | 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) ) ). % 0.94/1.20 % 0.94/1.20 cnf(cls_add__nonneg__eq__0__iff_1,axiom, % 0.94/1.20 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.94/1.20 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.94/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 0.94/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 0.94/1.20 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.94/1.20 % 0.94/1.20 cnf(cls_add__nonneg__eq__0__iff_0,axiom, % 0.94/1.20 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.94/1.20 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.94/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 0.94/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 0.94/1.20 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.94/1.20 % 0.94/1.20 cnf(cls_Suc__inject_0,axiom, % 0.94/1.20 ( c_Suc(V_x) != c_Suc(V_y) % 0.94/1.20 | V_x = V_y ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_nat_Oinject_0,axiom, % 1.09/1.20 ( c_Suc(V_nat) != c_Suc(V_nat_H) % 1.09/1.20 | V_nat = V_nat_H ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_abs__ge__minus__self_0,axiom, % 1.09/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.20 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_diff__divide__distrib_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.20 | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_abs__ge__self_0,axiom, % 1.09/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.20 | c_lessequals(V_a,c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_dB_Osimps_I6_J_0,axiom, % 1.09/1.20 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_less__add__iff2_1,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_less__add__iff2_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_less__add__iff1_1,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_less__add__iff1_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_nat__eq__add__iff1_0,axiom, % 1.09/1.20 ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat) % 1.09/1.20 | ~ c_lessequals(V_j,V_i,tc_nat) % 1.09/1.20 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat) = V_n ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_nat__eq__add__iff2_0,axiom, % 1.09/1.20 ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat) % 1.09/1.20 | ~ c_lessequals(V_i,V_j,tc_nat) % 1.09/1.20 | V_m = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_min__le__iff__disj_0,axiom, % 1.09/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.20 | c_lessequals(V_y,V_z,T_a) % 1.09/1.20 | c_lessequals(V_x,V_z,T_a) % 1.09/1.20 | ~ c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_nat__eq__add__iff2_1,axiom, % 1.09/1.20 ( ~ c_lessequals(V_i,V_j,tc_nat) % 1.09/1.20 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_eq__divide__eq_4,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.20 | 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) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_mod__add__cong_0,axiom, % 1.09/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.20 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 1.09/1.20 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 1.09/1.20 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a_H,V_b_H,T_a),V_c,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_less__Suc0_1,axiom, % 1.09/1.20 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom, % 1.09/1.20 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.09/1.20 | 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) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom, % 1.09/1.20 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.20 | ~ 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) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_even__less__0__iff_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.20 | ~ 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) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_even__less__0__iff_1,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.20 | 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) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_one__is__add_1,axiom, % 1.09/1.20 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) % 1.09/1.20 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.09/1.20 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_one__is__add_2,axiom, % 1.09/1.20 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) % 1.09/1.20 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 1.09/1.20 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_zero__less__mult__pos2_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.20 | ~ 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) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_zero__less__mult__pos_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.20 | ~ 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) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_mult__pos__pos_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.09/1.20 | 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) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_mult__neg__neg_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.20 | 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) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_nat__0__less__mult__iff_2,axiom, % 1.09/1.20 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_power__less__imp__less__base_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.09/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_min__max_Ole__sup__iff_1,axiom, % 1.09/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.20 | c_lessequals(V_y,V_z,T_a) % 1.09/1.20 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_min__max_Ole__sup__iff_0,axiom, % 1.09/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.20 | c_lessequals(V_x,V_z,T_a) % 1.09/1.20 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_le__max__iff__disj_2,axiom, % 1.09/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.20 | c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 1.09/1.20 | ~ c_lessequals(V_z,V_y,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_le__max__iff__disj_1,axiom, % 1.09/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.20 | c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 1.09/1.20 | ~ c_lessequals(V_z,V_x,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_min__max_Ole__supI2_0,axiom, % 1.09/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.20 | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 1.09/1.20 | ~ c_lessequals(V_x,V_b,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_min__max_Ole__supI1_0,axiom, % 1.09/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.20 | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 1.09/1.20 | ~ c_lessequals(V_x,V_a,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_min__max_Ole__supE_1,axiom, % 1.09/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.20 | c_lessequals(V_b,V_x,T_a) % 1.09/1.20 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_min__max_Ole__supE_0,axiom, % 1.09/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.20 | c_lessequals(V_a,V_x,T_a) % 1.09/1.20 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_le__diff__conv_0,axiom, % 1.09/1.20 ( c_lessequals(V_j,c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),tc_nat) % 1.09/1.20 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_le__diff__conv_1,axiom, % 1.09/1.20 ( c_lessequals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) % 1.09/1.20 | ~ c_lessequals(V_j,c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),tc_nat) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_zero__less__power_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.20 | 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) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_less__max__iff__disj_0,axiom, % 1.09/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_mult__Suc__right_0,axiom, % 1.09/1.20 c_HOL_Otimes__class_Otimes(V_m,c_Suc(V_n),tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_mult__Suc_0,axiom, % 1.09/1.20 c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_eq__neg__iff__add__eq__0_1,axiom, % 1.09/1.20 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.20 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.20 | V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_minus__unique_0,axiom, % 1.09/1.20 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.20 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.20 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_abs__less__iff_1,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_div__power_0,axiom, % 1.09/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.20 | c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),V_n,T_a) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a) % 1.09/1.20 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_not__one__less__zero_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_abs__less__iff_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_sgn__if_1,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Osgn__if(T_a) % 1.09/1.20 | c_HOL_Osgn__class_Osgn(V_x,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.09/1.20 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_dB_Osimps_I3_J_0,axiom, % 1.09/1.20 ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H) % 1.09/1.20 | V_dB = V_dB_H ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_not__sum__squares__lt__zero_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.20 | ~ 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) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_nat__le__add__iff1_0,axiom, % 1.09/1.20 ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat) % 1.09/1.20 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) % 1.09/1.20 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_nat__le__add__iff1_1,axiom, % 1.09/1.20 ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) % 1.09/1.20 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat) % 1.09/1.20 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_nat__le__add__iff2_0,axiom, % 1.09/1.20 ( c_lessequals(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) % 1.09/1.20 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) % 1.09/1.20 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_nat__le__add__iff2_1,axiom, % 1.09/1.20 ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) % 1.09/1.20 | ~ c_lessequals(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) % 1.09/1.20 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_divide__le__eq_8,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.20 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.20 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.09/1.20 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_le__divide__eq_8,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.20 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.20 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.09/1.20 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_of__nat__mult_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.09/1.20 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_min__less__iff__disj_0,axiom, % 1.09/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_class__ringb_Oadd__mul__solve_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.09/1.20 | ~ class_Int_Onumber__ring(T_a) % 1.09/1.20 | 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) % 1.09/1.20 | V_y = V_z % 1.09/1.20 | V_w = V_x ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_class__ringb_Onoteq__reduce_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.09/1.20 | ~ class_Int_Onumber__ring(T_a) % 1.09/1.20 | 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) % 1.09/1.20 | V_c = V_d % 1.09/1.20 | V_a = V_b ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_natgb_Onoteq__reduce_0,axiom, % 1.09/1.20 ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_d,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_d,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) % 1.09/1.20 | V_c = V_d % 1.09/1.20 | V_a = V_b ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_natgb_Oadd__mul__solve_0,axiom, % 1.09/1.20 ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_y,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_z,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat) % 1.09/1.20 | V_y = V_z % 1.09/1.20 | V_w = V_x ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_abs__div__pos_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.20 | c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_x,T_a),V_y,T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_inverse__less__imp__less__neg_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_less__imp__inverse__less__neg_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_le__zero__iff__pprt__id_0,axiom, % 1.09/1.20 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.09/1.20 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) = V_a % 1.09/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_le__zero__iff__pprt__id_1,axiom, % 1.09/1.20 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.09/1.20 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) != V_a % 1.09/1.20 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_power__Suc__less__one_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.20 | 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) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_order__less__trans_0,axiom, % 1.09/1.20 ( ~ class_Orderings_Opreorder(T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_xt1_I10_J_0,axiom, % 1.09/1.20 ( ~ class_Orderings_Oorder(T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_sgn__if_2,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Osgn__if(T_a) % 1.09/1.20 | c_HOL_Osgn__class_Osgn(V_x,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a) % 1.09/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.09/1.20 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_min__max_Ole__iff__sup_0,axiom, % 1.09/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.20 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = V_y % 1.09/1.20 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_min__max_Ole__iff__sup_1,axiom, % 1.09/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.20 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) != V_y % 1.09/1.20 | c_lessequals(V_x,V_y,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_min__max_Osup__absorb1_0,axiom, % 1.09/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.20 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = V_x % 1.09/1.20 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_class__semiring_Oadd__a_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.20 | 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) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_add__cancel__21_1,axiom, % 1.09/1.20 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.09/1.20 | 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) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_nat__add__left__commute_0,axiom, % 1.09/1.20 c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat),tc_nat) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_nat__add__assoc_0,axiom, % 1.09/1.20 c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_comm__monoid__add_Omult__assoc_0,axiom, % 1.09/1.20 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.09/1.20 | 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) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom, % 1.09/1.20 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.09/1.20 | 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) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom, % 1.09/1.20 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a) % 1.09/1.20 | 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) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.20 | 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) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.20 | 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) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.20 | 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) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom, % 1.09/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.20 | 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) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_add__gr__0_0,axiom, % 1.09/1.20 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.09/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 1.09/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_power__add_0,axiom, % 1.09/1.20 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.09/1.20 | c_Power_Opower__class_Opower(V_a,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_one__le__mult__iff_1,axiom, % 1.09/1.20 ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) % 1.09/1.20 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_one__le__mult__iff_0,axiom, % 1.09/1.20 ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 1.09/1.20 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_add__cancel__21_0,axiom, % 1.09/1.20 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.09/1.20 | 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) % 1.09/1.20 | c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) = V_u ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_abs__triangle__ineq_0,axiom, % 1.09/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.20 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_trans__le__add2_0,axiom, % 1.09/1.20 ( c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat) % 1.09/1.20 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_trans__le__add1_0,axiom, % 1.09/1.20 ( c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat) % 1.09/1.20 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_add__leE_1,axiom, % 1.09/1.20 ( c_lessequals(V_k,V_n,tc_nat) % 1.09/1.20 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),V_n,tc_nat) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_add__leE_0,axiom, % 1.09/1.20 ( c_lessequals(V_m,V_n,tc_nat) % 1.09/1.20 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),V_n,tc_nat) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_termination__basic__simps_I4_J_0,axiom, % 1.09/1.20 ( c_lessequals(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) % 1.09/1.20 | ~ c_lessequals(V_x,V_z,tc_nat) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_termination__basic__simps_I3_J_0,axiom, % 1.09/1.20 ( c_lessequals(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) % 1.09/1.20 | ~ c_lessequals(V_x,V_y,tc_nat) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_mod__diff__left__eq_0,axiom, % 1.09/1.20 ( ~ class_Divides_Oring__div(T_a) % 1.09/1.20 | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ). % 1.09/1.20 % 1.09/1.20 cnf(cls_mod__diff__right__eq_0,axiom, % 1.09/1.21 ( ~ class_Divides_Oring__div(T_a) % 1.09/1.21 | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_inverse__positive__imp__positive_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_nonzero__abs__divide_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) % 1.09/1.21 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_power__one_0,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.09/1.21 | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_nonzero__abs__inverse_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) % 1.09/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_min__max_Ole__iff__inf_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = V_x % 1.09/1.21 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_min__max_Ole__iff__inf_1,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) != V_x % 1.09/1.21 | c_lessequals(V_x,V_y,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_min__max_Oinf__absorb2_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = V_y % 1.09/1.21 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_max__diff__distrib__left_0,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.21 | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(V_x,V_z,T_a),c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_not__leE_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.09/1.21 | c_lessequals(V_y,V_x,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_linorder__antisym__conv2_1,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | ~ c_lessequals(V_x,V_x,T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_linorder__antisym__conv1_1,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_x,V_x,T_a) % 1.09/1.21 | c_lessequals(V_x,V_x,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_linorder__not__less_1,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.09/1.21 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_linorder__not__less_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | c_lessequals(V_y,V_x,T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_linorder__not__le_1,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | ~ c_lessequals(V_x,V_y,T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_linorder__not__le_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.09/1.21 | c_lessequals(V_x,V_y,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_less__le__not__le_1,axiom, % 1.09/1.21 ( ~ class_Orderings_Opreorder(T_a) % 1.09/1.21 | ~ c_lessequals(V_y,V_x,T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_subst__Var_1,axiom, % 1.09/1.21 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 1.09/1.21 | c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_neg__0__le__iff__le_0,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.21 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_neg__0__le__iff__le_1,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.21 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.09/1.21 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_divide__self__if_1,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.09/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_divide__self_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.21 | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.09/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_right__inverse__eq_1,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.21 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.21 | c_HOL_Oinverse__class_Odivide(V_x,V_x,T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_mod__add__left__eq_0,axiom, % 1.09/1.21 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.21 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_mod__add__right__eq_0,axiom, % 1.09/1.21 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.21 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_zero__le__divide__iff_3,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.21 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_zero__le__divide__iff_2,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.21 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_zero__le__divide__iff_1,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.21 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_zero__le__divide__iff_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.21 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_min__max_Oinf__assoc_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_min__max_Oinf__left__commute_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omin(V_y,c_Orderings_Oord__class_Omin(V_x,V_z,T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_one__is__add_5,axiom, % 1.09/1.21 c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_add__strict__increasing2_0,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.09/1.21 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_power__increasing_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.21 | c_lessequals(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_a,V_N,T_a),T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 1.09/1.21 | ~ c_lessequals(V_n,V_N,tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_diff__le__mono2_0,axiom, % 1.09/1.21 ( c_lessequals(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat) % 1.09/1.21 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_diff__le__mono_0,axiom, % 1.09/1.21 ( c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_l,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_l,tc_nat),tc_nat) % 1.09/1.21 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_le__diff__iff_1,axiom, % 1.09/1.21 ( c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) % 1.09/1.21 | ~ c_lessequals(V_m,V_n,tc_nat) % 1.09/1.21 | ~ c_lessequals(V_k,V_n,tc_nat) % 1.09/1.21 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_le__diff__iff_0,axiom, % 1.09/1.21 ( c_lessequals(V_m,V_n,tc_nat) % 1.09/1.21 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) % 1.09/1.21 | ~ c_lessequals(V_k,V_n,tc_nat) % 1.09/1.21 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_diff__add__0_0,axiom, % 1.09/1.21 c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_diff__diff__left_0,axiom, % 1.09/1.21 c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(V_i,c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_power__mono_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.21 | c_lessequals(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.21 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_eq__eqI_1,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.09/1.21 | c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) % 1.09/1.21 | V_xa = V_y ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_eq__eqI_0,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.09/1.21 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.09/1.21 | V_x_H = V_y_H ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_eq__diff__iff_0,axiom, % 1.09/1.21 ( c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat) != c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat) % 1.09/1.21 | ~ c_lessequals(V_k,V_n,tc_nat) % 1.09/1.21 | ~ c_lessequals(V_k,V_m,tc_nat) % 1.09/1.21 | V_m = V_n ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_min__max_Oinf__sup__absorb_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) = V_x ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_nat__mult__eq__cancel1_0,axiom, % 1.09/1.21 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.09/1.21 | V_m = V_n ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_one__is__add_3,axiom, % 1.09/1.21 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) % 1.09/1.21 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.09/1.21 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_one__is__add_0,axiom, % 1.09/1.21 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) % 1.09/1.21 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 1.09/1.21 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_mult__less__cancel2_0,axiom, % 1.09/1.21 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_mult__less__cancel1_0,axiom, % 1.09/1.21 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_of__nat__Suc_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.09/1.21 | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(V_m),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_inverse__le__1__iff_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | c_lessequals(c_HOL_Oone__class_Oone(T_a),V_x,T_a) % 1.09/1.21 | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_add__Suc__shift_0,axiom, % 1.09/1.21 c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_mult__le__cancel2_0,axiom, % 1.09/1.21 ( c_lessequals(V_m,V_n,tc_nat) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.09/1.21 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_mult__le__cancel1_0,axiom, % 1.09/1.21 ( c_lessequals(V_m,V_n,tc_nat) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.09/1.21 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_nat__mult__le__cancel1_0,axiom, % 1.09/1.21 ( c_lessequals(V_m,V_n,tc_nat) % 1.09/1.21 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_nat__mult__le__cancel1_1,axiom, % 1.09/1.21 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 1.09/1.21 | ~ c_lessequals(V_m,V_n,tc_nat) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_mult__le__cancel__left__neg_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.21 | c_lessequals(V_b,V_a,T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_mult__le__cancel__left__neg_1,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.21 | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.09/1.21 | ~ c_lessequals(V_b,V_a,T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_mult__le__cancel__left__pos_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.21 | c_lessequals(V_a,V_b,T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_mult__le__cancel__left__pos_1,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.21 | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.09/1.21 | ~ c_lessequals(V_a,V_b,T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_mult__left__le__imp__le_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.09/1.21 | c_lessequals(V_a,V_b,T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_mult__right__le__imp__le_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.09/1.21 | c_lessequals(V_a,V_b,T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_one__less__mult_0,axiom, % 1.09/1.21 ( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_le__divide__eq_7,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.09/1.21 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_abs__mult__self_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.21 | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_nat__size_0,axiom, % 1.09/1.21 c_Nat_Osize__class_Osize(V_n,tc_nat) = V_n ). % 1.09/1.21 % 1.09/1.21 cnf(cls_nonzero__inverse__minus__eq_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.09/1.21 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.09/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_nonzero__power__inverse_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.09/1.21 | c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) % 1.09/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_diff__Suc__Suc_0,axiom, % 1.09/1.21 c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_dB_Osimps_I4_J_0,axiom, % 1.09/1.21 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_neg__less__iff__less_1,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.21 | 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) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_neg__less__iff__less_0,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.09/1.21 | ~ 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) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_add__nonpos__neg_0,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.09/1.21 | 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) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.21 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_add__neg__nonpos_0,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.09/1.21 | 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) % 1.09/1.21 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_div__mult__self2__is__id_0,axiom, % 1.09/1.21 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.21 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = V_a % 1.09/1.21 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_div__mult__self1__is__id_0,axiom, % 1.09/1.21 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.21 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = V_a % 1.09/1.21 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_less__SucE_0,axiom, % 1.09/1.21 ( V_m = V_n % 1.09/1.21 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_less__antisym_0,axiom, % 1.09/1.21 ( V_m = V_n % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_not__less__less__Suc__eq_0,axiom, % 1.09/1.21 ( V_n = V_m % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_sum__squares__le__zero__iff_2,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.21 | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_mod__mult__cong_0,axiom, % 1.09/1.21 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.21 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 1.09/1.21 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 1.09/1.21 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a_H,V_b_H,T_a),V_c,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_diff__add__assoc_0,axiom, % 1.09/1.21 ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) % 1.09/1.21 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_diff__add__assoc2_0,axiom, % 1.09/1.21 ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) % 1.09/1.21 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_add__frac__eq_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.21 | 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) % 1.09/1.21 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.21 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_mult__eq__1__iff_2,axiom, % 1.09/1.21 c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.21 | 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) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.21 | 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) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.21 | 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) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_divide__eq__eq_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) % 1.09/1.21 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_eq__divide__eq_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b % 1.09/1.21 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_zero__le__one_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.21 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_abs__power__minus_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.21 | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_n,T_a),T_a) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_class__semiring_Osemiring__rules_I2_J_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.21 | 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) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.21 | 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) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_diff__diff__right_0,axiom, % 1.09/1.21 ( c_HOL_Ominus__class_Ominus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) % 1.09/1.21 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_inverse__less__1__iff_1,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.09/1.21 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_less__imp__diff__less_0,axiom, % 1.09/1.21 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_abs__le__zero__iff_0,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_nat_Osize_I4_J_0,axiom, % 1.09/1.21 c_Nat_Osize__class_Osize(c_Suc(V_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(V_nat,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_mod__by__1_0,axiom, % 1.09/1.21 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.21 | c_Divides_Odiv__class_Omod(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_abs__mult__pos_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.21 | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_y,T_a),V_x,T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_y,V_x,T_a),T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_divide__le__0__1__iff_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_divide__le__0__1__iff_1,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.21 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_one__le__inverse__iff_1,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | c_lessequals(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_dvd__abs__iff_1,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.21 | c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a) % 1.09/1.21 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_dvd__abs__iff_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.21 | c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) % 1.09/1.21 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_abs__dvd__iff_1,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.21 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a) % 1.09/1.21 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_abs__dvd__iff_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.21 | c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) % 1.09/1.21 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_one__is__add_4,axiom, % 1.09/1.21 c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_less__le__not__le_2,axiom, % 1.09/1.21 ( ~ class_Orderings_Opreorder(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.09/1.21 | c_lessequals(V_y,V_x,T_a) % 1.09/1.21 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_nat__less__le_1,axiom, % 1.09/1.21 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_less__not__refl_0,axiom, % 1.09/1.21 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_order__less__le_1,axiom, % 1.09/1.21 ( ~ class_Orderings_Oorder(T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_linorder__neq__iff_1,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_order__less__irrefl_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Opreorder(T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_le__imp__diff__is__add_1,axiom, % 1.09/1.21 ( ~ c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_k,V_i,tc_nat),tc_nat) % 1.09/1.21 | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k,V_i,tc_nat),V_i,tc_nat) = V_k ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_min__max_Oinf__idem_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | c_Orderings_Oord__class_Omin(V_x,V_x,T_a) = V_x ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_eq__divide__imp_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.21 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.21 | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_divide__eq__imp_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.21 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.21 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_divide__eq__eq_3,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a % 1.09/1.21 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_eq__divide__eq_3,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) % 1.09/1.21 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_estimate__by__abs_0,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.09/1.21 | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_liftn_Osimps_I1_J_1,axiom, % 1.09/1.21 ( c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(V_i,V_n,tc_nat)) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_beta_0,axiom, % 1.09/1.21 c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(V_s),V_t),c_Lambda_Osubst(V_s,V_t,c_HOL_Ozero__class_Ozero(tc_nat))) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_add__pos__pos_0,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.09/1.21 | 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) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_le__add1_0,axiom, % 1.09/1.21 c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_le__add2_0,axiom, % 1.09/1.21 c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_le__iff__add_1,axiom, % 1.09/1.21 c_lessequals(V_m,c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat),tc_nat) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_nat__minus__add__max_0,axiom, % 1.09/1.21 c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),V_m,tc_nat) = c_Orderings_Oord__class_Omax(V_n,V_m,tc_nat) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_compl__eq__compl__iff_0,axiom, % 1.09/1.21 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.09/1.21 | c_HOL_Ouminus__class_Ouminus(V_x,T_a) != c_HOL_Ouminus__class_Ouminus(V_y,T_a) % 1.09/1.21 | V_x = V_y ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_neg__equal__iff__equal_0,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.21 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(V_b,T_a) % 1.09/1.21 | V_a = V_b ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_power__divide_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | 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) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_not__one__le__zero_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_negative__imp__inverse__negative_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_inverse__negative__iff__negative_1,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_inverse__negative__iff__negative_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_power__gt1__lemma_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.21 | 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) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_linorder__neqE__ordered__idom_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.09/1.21 | V_x = V_y ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_not__less__iff__gr__or__eq_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | V_x = V_y % 1.09/1.21 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_le__antisym_0,axiom, % 1.09/1.21 ( V_m = V_n % 1.09/1.21 | ~ c_lessequals(V_n,V_m,tc_nat) % 1.09/1.21 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_nat__neq__iff_0,axiom, % 1.09/1.21 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.21 | V_m = V_n ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_linorder__neqE__nat_0,axiom, % 1.09/1.21 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 1.09/1.21 | V_x = V_y ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_order__eq__iff_2,axiom, % 1.09/1.21 ( ~ class_Orderings_Oorder(T_a) % 1.09/1.21 | V_x = V_y % 1.09/1.21 | ~ c_lessequals(V_y,V_x,T_a) % 1.09/1.21 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_linorder__neqE_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.09/1.21 | V_x = V_y ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_order__antisym_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Oorder(T_a) % 1.09/1.21 | V_x = V_y % 1.09/1.21 | ~ c_lessequals(V_y,V_x,T_a) % 1.09/1.21 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_order__antisym__conv_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Oorder(T_a) % 1.09/1.21 | V_x = V_y % 1.09/1.21 | ~ c_lessequals(V_x,V_y,T_a) % 1.09/1.21 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_linorder__less__linear_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.09/1.21 | V_x = V_y % 1.09/1.21 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_linorder__antisym__conv3_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | V_x = V_y % 1.09/1.21 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_mod__diff__cong_0,axiom, % 1.09/1.21 ( ~ class_Divides_Oring__div(T_a) % 1.09/1.21 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 1.09/1.21 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 1.09/1.21 | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a_H,V_b_H,T_a),V_c,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_le__iff__diff__le__0_1,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.21 | c_lessequals(V_a,V_b,T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_le__iff__diff__le__0_0,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.21 | c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.21 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_min__max_Osup__idem_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | c_Orderings_Oord__class_Omax(V_x,V_x,T_a) = V_x ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_abs__of__nonneg_0,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.21 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.09/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_dB_Osimps_I2_J_1,axiom, % 1.09/1.21 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) % 1.09/1.21 | V_dB2 = V_dB2_H ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_dB_Osimps_I2_J_0,axiom, % 1.09/1.21 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) % 1.09/1.21 | V_dB1 = V_dB1_H ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_add__strict__mono_0,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.09/1.21 | 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) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_add__less__mono_0,axiom, % 1.09/1.21 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_l,tc_nat),tc_nat) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_termination__basic__simps_I5_J_0,axiom, % 1.09/1.21 ( c_lessequals(V_x,V_y,tc_nat) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_nat__less__le_0,axiom, % 1.09/1.21 ( c_lessequals(V_m,V_n,tc_nat) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_order__le__less_1,axiom, % 1.09/1.21 ( ~ class_Orderings_Oorder(T_a) % 1.09/1.21 | c_lessequals(V_x,V_y,T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_order__less__imp__le_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Opreorder(T_a) % 1.09/1.21 | c_lessequals(V_x,V_y,T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_minus__add__cancel_0,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.21 | 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 ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_add__cancel__end_1,axiom, % 1.09/1.21 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.09/1.21 | 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 ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_inverse__1_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.09/1.21 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_le__divide__eq_5,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.09/1.21 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.21 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_divide__le__eq_7,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.21 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_divide__le__eq_5,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_minus__divide__divide_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | 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) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_diff__cancel2_0,axiom, % 1.09/1.21 c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_diff__cancel_0,axiom, % 1.09/1.21 c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_zero__less__Suc_0,axiom, % 1.09/1.21 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_gr0__conv__Suc_1,axiom, % 1.09/1.21 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_one__le__inverse__iff_0,axiom, % 1.09/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.09/1.21 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_min__max_Oless__supI1_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_x,V_a,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_min__max_Oless__supI2_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_x,V_b,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_less__max__iff__disj_1,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_less__max__iff__disj_2,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_max__less__iff__conj_0,axiom, % 1.09/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.21 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.09/1.21 | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 1.09/1.21 % 1.09/1.21 cnf(cls_max__less__iff__conj_1,axiom, % 1.09/1.22 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_min__max_Oinf__commute_0,axiom, % 1.09/1.22 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.22 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = c_Orderings_Oord__class_Omin(V_y,V_x,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_one__less__power_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.22 | 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) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_left__add__mult__distrib_0,axiom, % 1.09/1.22 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_k,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_u,tc_nat),V_k,tc_nat) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_combine__common__factor_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Osemiring(T_a) % 1.09/1.22 | 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) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_diff__le__self_0,axiom, % 1.09/1.22 c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_left__minus_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.22 | 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) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_right__minus_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.22 | 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) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_ab__left__minus_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.09/1.22 | 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) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_eq__neg__iff__add__eq__0_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.22 | 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) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_nat__0__less__mult__iff_1,axiom, % 1.09/1.22 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_nat__0__less__mult__iff_0,axiom, % 1.09/1.22 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__neg__neg_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.09/1.22 | 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) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_power__strict__mono_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_sum__squares__le__zero__iff_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.22 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_sum__squares__le__zero__iff_1,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.22 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_diff__mult__distrib2_0,axiom, % 1.09/1.22 c_HOL_Otimes__class_Otimes(V_k,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_diff__mult__distrib_0,axiom, % 1.09/1.22 c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_power__diff_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.22 | c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.09/1.22 | ~ c_lessequals(V_n,V_m,tc_nat) % 1.09/1.22 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_dvd__imp__mod__0_0,axiom, % 1.09/1.22 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.22 | c_Divides_Odiv__class_Omod(V_b,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_dvd__eq__mod__eq__0_1,axiom, % 1.09/1.22 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.22 | c_Divides_Odiv__class_Omod(V_b,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.22 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_min__max_Oless__infI1_0,axiom, % 1.09/1.22 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_a,V_x,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_min__max_Oless__infI2_0,axiom, % 1.09/1.22 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_b,V_x,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_min__less__iff__conj_0,axiom, % 1.09/1.22 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_min__less__iff__conj_1,axiom, % 1.09/1.22 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_min__less__iff__disj_1,axiom, % 1.09/1.22 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_x,V_z,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_min__less__iff__disj_2,axiom, % 1.09/1.22 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_Nat_Odiff__diff__eq_0,axiom, % 1.09/1.22 ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) % 1.09/1.22 | ~ c_lessequals(V_k,V_n,tc_nat) % 1.09/1.22 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_diff__commute_0,axiom, % 1.09/1.22 c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_k,tc_nat),V_j,tc_nat) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_inverse__nonpositive__iff__nonpositive_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.22 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_inverse__nonpositive__iff__nonpositive_1,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__nonneg__pos_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.09/1.22 | 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) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__pos__nonneg_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.09/1.22 | 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) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_dvd__div__mult_0,axiom, % 1.09/1.22 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.22 | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_c,T_a) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),V_a,T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_abs__le__zero__iff_1,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_inverse__mult__distrib_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.22 | c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_nonzero__inverse__mult__distrib_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.09/1.22 | c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.09/1.22 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.22 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_diff__less__mono_0,axiom, % 1.09/1.22 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_c,tc_nat),c_HOL_Ominus__class_Ominus(V_b,V_c,tc_nat),tc_nat) % 1.09/1.22 | ~ c_lessequals(V_c,V_a,tc_nat) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_a,V_b,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__le__0__iff_4,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__le__0__iff_5,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.22 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_split__mult__neg__le_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_split__mult__neg__le_1,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.22 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__nonneg__nonpos_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__nonpos__nonneg_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.22 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__nonneg__nonpos2_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_not__square__less__zero_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.22 | ~ 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) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_Suc__mult__less__cancel1_1,axiom, % 1.09/1.22 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_Suc__mult__less__cancel1_0,axiom, % 1.09/1.22 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_Suc__lessI_0,axiom, % 1.09/1.22 ( c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) % 1.09/1.22 | c_Suc(V_m) = V_n % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_not__less__eq__eq_1,axiom, % 1.09/1.22 ( ~ c_lessequals(V_m,V_n,tc_nat) % 1.09/1.22 | ~ c_lessequals(c_Suc(V_n),V_m,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_not__less__eq__eq_0,axiom, % 1.09/1.22 ( c_lessequals(c_Suc(V_n),V_m,tc_nat) % 1.09/1.22 | c_lessequals(V_m,V_n,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_natgb_Oadd__cancel_0,axiom, % 1.09/1.22 ( c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat) != c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat) % 1.09/1.22 | V_y = V_z ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_nat__add__right__cancel_0,axiom, % 1.09/1.22 ( c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat) != c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat) % 1.09/1.22 | V_m = V_n ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_nat__add__left__cancel_0,axiom, % 1.09/1.22 ( c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) % 1.09/1.22 | V_m = V_n ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_class__ringb_Oadd__cancel_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.09/1.22 | ~ class_Int_Onumber__ring(T_a) % 1.09/1.22 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) % 1.09/1.22 | V_y = V_z ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__imp__eq_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a) % 1.09/1.22 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) % 1.09/1.22 | V_b = V_c ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__left__cancel_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 1.09/1.22 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) % 1.09/1.22 | V_b = V_c ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__right__cancel_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 1.09/1.22 | c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) != c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) % 1.09/1.22 | V_b = V_c ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_abs__minus__cancel_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.22 | c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_inverse__eq__1__iff_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.22 | c_HOL_Oinverse__class_Oinverse(V_x,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.09/1.22 | V_x = c_HOL_Oone__class_Oone(T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_inverse__less__1__iff_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_x,T_a) % 1.09/1.22 | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_abs__leI_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.09/1.22 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_abs__le__iff_2,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.09/1.22 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_divide__1_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.22 | c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_min__add__distrib__left_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.09/1.22 | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_le__add__diff_0,axiom, % 1.09/1.22 ( c_lessequals(V_m,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_k,tc_nat),tc_nat) % 1.09/1.22 | ~ c_lessequals(V_k,V_n,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__right__le__one__le_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_x,T_a) % 1.09/1.22 | ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__left__le__one__le_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Otimes__class_Otimes(V_y,V_x,T_a),V_x,T_a) % 1.09/1.22 | ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_divide__nonpos__neg_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_divide__nonneg__pos_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mod__diff__eq_0,axiom, % 1.09/1.22 ( ~ class_Divides_Oring__div(T_a) % 1.09/1.22 | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_power__abs_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.22 | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_a,T_a),V_n,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_abs__of__nat_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.22 | c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) = c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_dvd__power__same_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.22 | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_abs__inverse_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.22 | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_divide__strict__right__mono_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.22 | 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) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_divide__strict__right__mono__neg_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.22 | 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) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_abs__divide_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.22 | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_abs__of__pos_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.22 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_inverse__positive__iff__positive_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_inverse__positive__iff__positive_1,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_positive__imp__inverse__positive_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mod__mult__left__eq_0,axiom, % 1.09/1.22 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.22 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mod__mult__right__eq_0,axiom, % 1.09/1.22 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.22 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__is__1_3,axiom, % 1.09/1.22 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.09/1.22 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.09/1.22 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__is__1_0,axiom, % 1.09/1.22 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.09/1.22 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 1.09/1.22 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_inverse__eq__1__iff_1,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.22 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_one__less__inverse__iff_2,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_dvd__trans_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.22 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_dvd__refl_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.22 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_zero__le__divide__iff_4,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_zero__le__divide__iff_5,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) % 1.09/1.22 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_frac__le_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_z,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_w,T_a),T_a) % 1.09/1.22 | ~ c_lessequals(V_w,V_z,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 1.09/1.22 | ~ c_lessequals(V_x,V_y,T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_power__gt1_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.22 | 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) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_beta__cases_I1_J_0,axiom, % 1.09/1.22 ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_diff__Suc__diff__eq1_0,axiom, % 1.09/1.22 ( c_HOL_Ominus__class_Ominus(V_m,c_Suc(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),c_Suc(V_j),tc_nat) % 1.09/1.22 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_less__iff__diff__less__0_1,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_less__iff__diff__less__0_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_abs__not__less__zero_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_of__nat__less__iff_1,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_of__nat__less__iff_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_dvd__mult__cancel__right_1,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.09/1.22 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_dvd__mult__cancel__left_1,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.09/1.22 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_lessI_0,axiom, % 1.09/1.22 c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_less__Suc__eq_2,axiom, % 1.09/1.22 c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_less__trans__Suc_0,axiom, % 1.09/1.22 ( c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__le__cancel__right_1,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) % 1.09/1.22 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__le__cancel__right_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.09/1.22 | c_lessequals(V_a,V_b,T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__le__cancel__left_1,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) % 1.09/1.22 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__le__cancel__left_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.09/1.22 | c_lessequals(V_a,V_b,T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__right__mono_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) % 1.09/1.22 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__left__mono_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) % 1.09/1.22 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__le__mono1_0,axiom, % 1.09/1.22 ( c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat) % 1.09/1.22 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_nat__add__left__cancel__le_0,axiom, % 1.09/1.22 ( c_lessequals(V_m,V_n,tc_nat) % 1.09/1.22 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_nat__add__left__cancel__le_1,axiom, % 1.09/1.22 ( c_lessequals(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) % 1.09/1.22 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_abs__eq__mult_3,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.09/1.22 | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) % 1.09/1.22 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_abs__eq__mult_2,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.09/1.22 | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.22 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_abs__eq__mult_1,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.09/1.22 | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) % 1.09/1.22 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_abs__eq__mult_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 1.09/1.22 | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_abs__mult_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.22 | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_zero__less__one_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__frac__frac_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.22 | 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) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_minus__mult__right_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oring(T_a) % 1.09/1.22 | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_minus__mult__left_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oring(T_a) % 1.09/1.22 | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_le__imp__diff__is__add_0,axiom, % 1.09/1.22 ( ~ c_lessequals(V_i,V_j,tc_nat) % 1.09/1.22 | V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_le__add__diff__inverse_0,axiom, % 1.09/1.22 ( c_HOL_Oplus__class_Oplus(V_n,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = V_m % 1.09/1.22 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_le__add__diff__inverse2_0,axiom, % 1.09/1.22 ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat) = V_m % 1.09/1.22 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__less__cancel1_1,axiom, % 1.09/1.22 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__less__cancel2_1,axiom, % 1.09/1.22 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_le__eq__neg_1,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.09/1.22 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_le__eq__neg_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_divide__strict__left__mono__neg_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_divide__strict__left__mono_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_less__add__one_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.22 | 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) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__diff__assoc_0,axiom, % 1.09/1.22 ( c_HOL_Oplus__class_Oplus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat) % 1.09/1.22 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__diff__assoc2_0,axiom, % 1.09/1.22 ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_k,tc_nat) % 1.09/1.22 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_drop__drop_0,axiom, % 1.09/1.22 c_List_Odrop(V_n,c_List_Odrop(V_m,V_xs,T_a),T_a) = c_List_Odrop(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_xs,T_a) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_power__le__imp__le__base_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.22 | c_lessequals(V_a,V_b,T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.22 | ~ c_lessequals(c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),c_Power_Opower__class_Opower(V_b,c_Suc(V_n),T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__left__idem_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 1.09/1.22 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_one__less__inverse__iff_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_div__mult__div__if__dvd_0,axiom, % 1.09/1.22 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.22 | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),c_Divides_Odiv__class_Odiv(V_w,V_z,T_a),T_a) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_x,V_w,T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_w,T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_neg__le__0__iff__le_1,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_neg__le__0__iff__le_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_of__nat__0__less__iff_1,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_of__nat__0__less__iff_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__less__le__imp__less_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.22 | ~ c_lessequals(V_c,V_d,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__le__less__imp__less_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.09/1.22 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_one__dvd_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.22 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_power__inject__exp_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.22 | c_Power_Opower__class_Opower(V_a,V_m,T_a) != c_Power_Opower__class_Opower(V_a,V_n,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 1.09/1.22 | V_m = V_n ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_power__0_0,axiom, % 1.09/1.22 ( ~ class_Power_Opower(T_a) % 1.09/1.22 | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_class__semiring_Opwr__0_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.22 | c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_div__mult__mult1__if_0,axiom, % 1.09/1.22 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.22 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_sgn__1__neg_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.22 | c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_sgn__neg_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.22 | c_HOL_Osgn__class_Osgn(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_class__semiring_Osemiring__rules_I27_J_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.22 | 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) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_class__semiring_Osemiring__rules_I28_J_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.22 | 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) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_minus__mult__commute_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oring(T_a) % 1.09/1.22 | 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) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_abs__less__iff_2,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mod__add__self2_0,axiom, % 1.09/1.22 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.22 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mod__add__self1_0,axiom, % 1.09/1.22 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.22 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_b,V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_abs__triangle__ineq4_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_dvd__power__le_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.22 | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_m,T_a),T_a) % 1.09/1.22 | ~ c_lessequals(V_n,V_m,tc_nat) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__le__0__iff_3,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.22 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__le__0__iff_2,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.22 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__le__0__iff_1,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.22 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__le__0__iff_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.22 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__pos__neg2_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__pos__neg_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_mult__neg__pos_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_abs__le__D2_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.22 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.09/1.22 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_Suc__leD_0,axiom, % 1.09/1.22 ( c_lessequals(V_m,V_n,tc_nat) % 1.09/1.22 | ~ c_lessequals(c_Suc(V_m),V_n,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_le__SucI_0,axiom, % 1.09/1.22 ( c_lessequals(V_m,c_Suc(V_n),tc_nat) % 1.09/1.22 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_n__less__m__mult__n_0,axiom, % 1.09/1.22 ( c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_n__less__n__mult__m_0,axiom, % 1.09/1.22 ( c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),tc_nat) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__minus__cancel_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.22 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a),T_a) = V_b ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_class__fieldgb_Odivide__inverse_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.22 | ~ class_Int_Onumber__ring(T_a) % 1.09/1.22 | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_divide__inverse_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.22 | c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_Suc__n__not__le__n_0,axiom, % 1.09/1.22 ~ c_lessequals(c_Suc(V_n),V_n,tc_nat) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_dvd__mult__right_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.22 | c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_dvd__mult__left_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.22 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_dvd__mult2_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.22 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_dvd__mult_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.22 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_less__diff__iff_0,axiom, % 1.09/1.22 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) % 1.09/1.22 | ~ c_lessequals(V_k,V_n,tc_nat) % 1.09/1.22 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_less__diff__iff_1,axiom, % 1.09/1.22 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.22 | ~ c_lessequals(V_k,V_n,tc_nat) % 1.09/1.22 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_pos__add__strict_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_subst__lt_0,axiom, % 1.09/1.22 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_j),V_u,V_i) = c_Lambda_OdB_OVar(V_j) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_sgn__less_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_sgn__less_1,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.22 | c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.22 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_Suc__diff__diff_0,axiom, % 1.09/1.22 c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat),c_Suc(V_k),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_dvd__minus__iff_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.09/1.22 | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_dvd__minus__iff_1,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.09/1.22 | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_minus__dvd__iff_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.09/1.22 | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_minus__dvd__iff_1,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 1.09/1.22 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_div__dvd__div_0,axiom, % 1.09/1.22 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.22 | c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_div__dvd__div_1,axiom, % 1.09/1.22 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.22 | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 1.09/1.22 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_nonzero__minus__divide__divide_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.22 | 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) % 1.09/1.22 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_class__ring_Osub__add_0,axiom, % 1.09/1.22 ( ~ class_Int_Onumber__ring(T_a) % 1.09/1.22 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_diff__def_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.09/1.22 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_diff__minus_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.22 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_ab__diff__minus_0,axiom, % 1.09/1.22 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.09/1.22 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_Suc__mult__le__cancel1_1,axiom, % 1.09/1.22 ( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat) % 1.09/1.22 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_Suc__mult__le__cancel1_0,axiom, % 1.09/1.22 ( c_lessequals(V_m,V_n,tc_nat) % 1.09/1.22 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_sum__squares__gt__zero__iff_1,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.22 | 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) % 1.09/1.22 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_sum__squares__gt__zero__iff_2,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.22 | 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) % 1.09/1.22 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.22 | 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) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__num__frac_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.22 | 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) % 1.09/1.22 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_add__frac__num_0,axiom, % 1.09/1.22 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.22 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.22 | 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) % 1.09/1.22 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.22 % 1.09/1.22 cnf(cls_appR_0,axiom, % 1.09/1.23 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_u,V_s),c_Lambda_OdB_OApp(V_u,V_t)) % 1.09/1.23 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_appL_0,axiom, % 1.09/1.23 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_s,V_u),c_Lambda_OdB_OApp(V_t,V_u)) % 1.09/1.23 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_of__nat__less__0__iff_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__less__0__iff_3,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ 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) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__less__0__iff_2,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ 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) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__less__0__iff_1,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.23 | ~ 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) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__less__0__iff_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.23 | ~ 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) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_less__half__sum_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_gt__half__sum_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_group__add__class_Odiff__0_0,axiom, % 1.09/1.23 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.23 | c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_min__max_Osup__commute_0,axiom, % 1.09/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.23 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = c_Orderings_Oord__class_Omax(V_y,V_x,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_power__eq__imp__eq__base_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.23 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_Power_Opower__class_Opower(V_b,V_n,T_a) % 1.09/1.23 | V_a = V_b % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.09/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_add__cancel__end_0,axiom, % 1.09/1.23 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.09/1.23 | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != V_y % 1.09/1.23 | V_x = c_HOL_Ouminus__class_Ouminus(V_z,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_abs__sgn_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.23 | c_HOL_Oabs__class_Oabs(V_k,T_a) = c_HOL_Otimes__class_Otimes(V_k,c_HOL_Osgn__class_Osgn(V_k,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_liftn_Osimps_I1_J_0,axiom, % 1.09/1.23 ( c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(V_i) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__divide__mult__cancel__left_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) % 1.09/1.23 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__divide__mult__cancel__right_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) % 1.09/1.23 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_division__ring__inverse__add_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.09/1.23 | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) % 1.09/1.23 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.23 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_inverse__add_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.23 | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) % 1.09/1.23 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.23 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_dvd__add_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.23 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) % 1.09/1.23 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 1.09/1.23 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_le__Suc__eq_2,axiom, % 1.09/1.23 c_lessequals(c_Suc(V_n),c_Suc(V_n),tc_nat) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_one__less__inverse__iff_1,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_drop__replicate_0,axiom, % 1.09/1.23 c_List_Odrop(V_i,c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(V_k,V_i,tc_nat),V_x,T_a) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_min__max_Odistrib__inf__le_0,axiom, % 1.09/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.23 | c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),c_Orderings_Oord__class_Omin(V_x,V_z,T_a),T_a),c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_liftn_Osimps_I2_J_0,axiom, % 1.09/1.23 c_Lambda_Oliftn(V_n,c_Lambda_OdB_OApp(V_s,V_t),V_k) = c_Lambda_OdB_OApp(c_Lambda_Oliftn(V_n,V_s,V_k),c_Lambda_Oliftn(V_n,V_t,V_k)) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_zero__le__pprt_0,axiom, % 1.09/1.23 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.09/1.23 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__pos__pos_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__neg__neg_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_zero__less__divide__iff_4,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_zero__less__divide__iff_5,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_nat_Osize_I2_J_0,axiom, % 1.09/1.23 c_nat_Onat__size(c_Suc(V_nat)) = c_HOL_Oplus__class_Oplus(c_nat_Onat__size(V_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_min__max_Osup__inf__absorb_0,axiom, % 1.09/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.23 | c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) = V_x ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mod__minus__eq_0,axiom, % 1.09/1.23 ( ~ class_Divides_Oring__div(T_a) % 1.09/1.23 | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_le__square_0,axiom, % 1.09/1.23 c_lessequals(V_m,c_HOL_Otimes__class_Otimes(V_m,V_m,tc_nat),tc_nat) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__less__cancel__left__disj_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__less__cancel__left__disj_3,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__less__cancel__right__disj_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__less__cancel__right__disj_3,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__frac__num_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),V_y,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_diff__diff__cancel_0,axiom, % 1.09/1.23 ( c_HOL_Ominus__class_Ominus(V_n,c_HOL_Ominus__class_Ominus(V_n,V_i,tc_nat),tc_nat) = V_i % 1.09/1.23 | ~ c_lessequals(V_i,V_n,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_dvd__div__mult__self_0,axiom, % 1.09/1.23 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.23 | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_a,T_a) = V_b % 1.09/1.23 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_dvd__mult__div__cancel_0,axiom, % 1.09/1.23 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.23 | c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),T_a) = V_b % 1.09/1.23 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_lift_Osimps_I1_J_0,axiom, % 1.09/1.23 ( c_Lambda_Olift(c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(V_i) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_power__Suc__less_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_min__Suc__Suc_0,axiom, % 1.09/1.23 c_Orderings_Oord__class_Omin(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(V_m,V_n,tc_nat)) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_le__SucE_0,axiom, % 1.09/1.23 ( V_m = c_Suc(V_n) % 1.09/1.23 | c_lessequals(V_m,V_n,tc_nat) % 1.09/1.23 | ~ c_lessequals(V_m,c_Suc(V_n),tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_not__less__less__Suc__eq_1,axiom, % 1.09/1.23 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_not__less__eq_1,axiom, % 1.09/1.23 ( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_not__less__eq_0,axiom, % 1.09/1.23 ( c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_abs__of__nonpos_0,axiom, % 1.09/1.23 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.23 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.09/1.23 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__less__cancel2_2,axiom, % 1.09/1.23 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__less__cancel1_2,axiom, % 1.09/1.23 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__less__mono2_0,axiom, % 1.09/1.23 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_j,tc_nat),tc_nat) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__less__mono1_0,axiom, % 1.09/1.23 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_k,tc_nat),tc_nat) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_nat__mult__less__cancel1_0,axiom, % 1.09/1.23 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_nat__mult__less__cancel1_1,axiom, % 1.09/1.23 ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__less__cancel__left__neg_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__less__cancel__left__neg_1,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__less__cancel__left__pos_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__less__cancel__left__pos_1,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__strict__left__mono__neg_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__strict__left__mono_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__less__cancel__left__disj_4,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__less__cancel__left__disj_5,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__strict__right__mono__neg_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__strict__right__mono_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__less__cancel__right__disj_4,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__less__cancel__right__disj_5,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__strict__left__mono__comm_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_less__divide__eq_9,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_less__divide__eq_8,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_less__divide__eq_3,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_less__divide__eq_2,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__less__eq_9,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__less__eq_8,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__less__eq_3,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__less__eq_2,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_max__add__distrib__left_0,axiom, % 1.09/1.23 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.09/1.23 | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_sgn__sgn_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.23 | c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) = c_HOL_Osgn__class_Osgn(V_a,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mod__mod__cancel_0,axiom, % 1.09/1.23 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.23 | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(V_a,V_c,T_a) % 1.09/1.23 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_subst__Var__IT_0,axiom, % 1.09/1.23 ( c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) % 1.09/1.23 | ~ c_InductTermi_OIT(V_r) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_zero__less__divide__1__iff_1,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_zero__less__divide__1__iff_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.23 | ~ 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) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom, % 1.09/1.23 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.09/1.23 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom, % 1.09/1.23 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.09/1.23 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_abs__if__lattice_1,axiom, % 1.09/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.23 | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.09/1.23 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.09/1.23 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_abs__if_1,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oabs__if(T_a) % 1.09/1.23 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.09/1.23 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_power__strict__increasing__iff_1,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_power__strict__increasing__iff_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 1.09/1.23 | ~ 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_power__strict__increasing_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_power__less__imp__less__exp_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.23 | ~ 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_not__add__less1_0,axiom, % 1.09/1.23 ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_i,tc_nat) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_not__add__less2_0,axiom, % 1.09/1.23 ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_i,tc_nat) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_nonzero__power__divide_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_inverse__negative__imp__negative_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_of__nat__diff_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oring__1(T_a) % 1.09/1.23 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) % 1.09/1.23 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_power__less__power__Suc_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_inverse__divide_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_b,V_a,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__dvd__mono_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.23 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.09/1.23 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_d,T_a) % 1.09/1.23 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__right__mono__neg_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.09/1.23 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.09/1.23 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__left__mono__neg_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.09/1.23 | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.09/1.23 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__right__mono_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 1.09/1.23 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 1.09/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__left__mono_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 1.09/1.23 | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.09/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__mono1_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Omult__mono1(T_a) % 1.09/1.23 | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 1.09/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.09/1.23 | ~ class_Int_Onumber__ring(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | V_c = V_d % 1.09/1.23 | V_r = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_natgb_Oadd__scale__eq__noteq_0,axiom, % 1.09/1.23 ( c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_c,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_d,tc_nat),tc_nat) % 1.09/1.23 | V_c = V_d % 1.09/1.23 | V_r = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_sum__squares__eq__zero__iff_1,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_sum__squares__eq__zero__iff_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_abs__add__abs_0,axiom, % 1.09/1.23 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.23 | c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_less__diff__conv_0,axiom, % 1.09/1.23 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_less__diff__conv_1,axiom, % 1.09/1.23 ( c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__le__eq_1,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__le__eq_4,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_le__divide__eq_1,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_le__divide__eq_4,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_Suc__n__not__n_0,axiom, % 1.09/1.23 c_Suc(V_n) != V_n ). % 1.09/1.23 % 1.09/1.23 cnf(cls_n__not__Suc__n_0,axiom, % 1.09/1.23 V_n != c_Suc(V_n) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_inverse__unique_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.09/1.23 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.09/1.23 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_zero__less__abs__iff_0,axiom, % 1.09/1.23 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__imp__less__div__pos_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__imp__div__pos__less_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__less__eq_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__less__eq_6,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_less__divide__eq_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_less__divide__eq_6,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__neg__pos_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__pos__neg_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__less__0__iff_4,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__less__0__iff_5,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_dvd__power_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.23 | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_add__strict__right__mono_0,axiom, % 1.09/1.23 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_add__less__cancel__right_1,axiom, % 1.09/1.23 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_add__less__cancel__right_0,axiom, % 1.09/1.23 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.09/1.23 | ~ 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) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_add__strict__left__mono_0,axiom, % 1.09/1.23 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_add__less__cancel__left_1,axiom, % 1.09/1.23 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.09/1.23 | 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) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_add__less__cancel__left_0,axiom, % 1.09/1.23 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.09/1.23 | ~ 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) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_add__less__mono1_0,axiom, % 1.09/1.23 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_nat__add__left__cancel__less_0,axiom, % 1.09/1.23 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_nat__add__left__cancel__less_1,axiom, % 1.09/1.23 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_one__le__mult__iff_2,axiom, % 1.09/1.23 ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) % 1.09/1.23 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) % 1.09/1.23 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_xt1_I6_J_0,axiom, % 1.09/1.23 ( ~ class_Orderings_Oorder(T_a) % 1.09/1.23 | c_lessequals(V_z,V_x,T_a) % 1.09/1.23 | ~ c_lessequals(V_z,V_y,T_a) % 1.09/1.23 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_xt1_I7_J_0,axiom, % 1.09/1.23 ( ~ class_Orderings_Oorder(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.09/1.23 | ~ c_lessequals(V_z,V_y,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_xt1_I8_J_0,axiom, % 1.09/1.23 ( ~ class_Orderings_Oorder(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.09/1.23 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_add__nonpos__nonpos_0,axiom, % 1.09/1.23 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.09/1.23 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_power__le__dvd_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.23 | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_b,T_a) % 1.09/1.23 | ~ c_lessequals(V_m,V_n,tc_nat) % 1.09/1.23 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_order__trans_0,axiom, % 1.09/1.23 ( ~ class_Orderings_Opreorder(T_a) % 1.09/1.23 | c_lessequals(V_x,V_z,T_a) % 1.09/1.23 | ~ c_lessequals(V_y,V_z,T_a) % 1.09/1.23 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_le__refl_0,axiom, % 1.09/1.23 c_lessequals(V_n,V_n,tc_nat) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_le__trans_0,axiom, % 1.09/1.23 ( c_lessequals(V_i,V_k,tc_nat) % 1.09/1.23 | ~ c_lessequals(V_j,V_k,tc_nat) % 1.09/1.23 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_eq__imp__le_0,axiom, % 1.09/1.23 c_lessequals(V_x,V_x,tc_nat) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_order__eq__iff_0,axiom, % 1.09/1.23 ( ~ class_Orderings_Oorder(T_a) % 1.09/1.23 | c_lessequals(V_x,V_x,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_order__eq__refl_0,axiom, % 1.09/1.23 ( ~ class_Orderings_Opreorder(T_a) % 1.09/1.23 | c_lessequals(V_x,V_x,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_order__le__less__trans_0,axiom, % 1.09/1.23 ( ~ class_Orderings_Opreorder(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.09/1.23 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_order__less__le__trans_0,axiom, % 1.09/1.23 ( ~ class_Orderings_Opreorder(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.09/1.23 | ~ c_lessequals(V_y,V_z,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_le__add__right__mono_0,axiom, % 1.09/1.23 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.23 | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) % 1.09/1.23 | ~ c_lessequals(V_c,V_d,T_a) % 1.09/1.23 | ~ c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_subst__eq_0,axiom, % 1.09/1.23 c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u ). % 1.09/1.23 % 1.09/1.23 cnf(cls_dB_Osimps_I9_J_0,axiom, % 1.09/1.23 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OApp(V_dB1,V_dB2) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_inverse__less__1__iff_2,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_x,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_min__diff_0,axiom, % 1.09/1.23 c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(V_m,V_i,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_i,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(V_m,V_n,tc_nat),V_i,tc_nat) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_add__is__1_5,axiom, % 1.09/1.23 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_zero__less__divide__iff_3,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.23 | ~ 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) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_zero__less__divide__iff_2,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.23 | ~ 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) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_zero__less__divide__iff_1,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.23 | ~ 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) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_zero__less__divide__iff_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.23 | ~ 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) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__nonneg__neg_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__nonpos__pos_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.09/1.23 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__idem_0,axiom, % 1.09/1.23 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 1.09/1.23 | c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = V_x ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mod__mult__self2__is__0_0,axiom, % 1.09/1.23 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.23 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mod__mult__self1__is__0_0,axiom, % 1.09/1.23 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.23 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_dB_Osimps_I1_J_0,axiom, % 1.09/1.23 ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H) % 1.09/1.23 | V_nat = V_nat_H ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__strict__mono_H_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.09/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_le__less__Suc__eq_0,axiom, % 1.09/1.23 ( V_n = V_m % 1.09/1.23 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 1.09/1.23 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_division__ring__inverse__diff_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.09/1.23 | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) % 1.09/1.23 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.23 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_dB_Osimps_I8_J_0,axiom, % 1.09/1.23 c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_dB_Osimps_I7_J_0,axiom, % 1.09/1.23 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_semiring__div__class_Omod__div__equality_H_0,axiom, % 1.09/1.23 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.23 | c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),T_a) = V_a ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__le__mono1_0,axiom, % 1.09/1.23 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_k,tc_nat),tc_nat) % 1.09/1.23 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__le__mono2_0,axiom, % 1.09/1.23 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_j,tc_nat),tc_nat) % 1.09/1.23 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__le__cancel1_2,axiom, % 1.09/1.23 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 1.09/1.23 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__le__cancel2_2,axiom, % 1.09/1.23 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) % 1.09/1.23 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_app__Var__IT_0,axiom, % 1.09/1.23 ( c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) % 1.09/1.23 | ~ c_InductTermi_OIT(V_t) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_power__inject__base_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.23 | c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) != c_Power_Opower__class_Opower(V_b,c_Suc(V_n),T_a) % 1.09/1.23 | V_a = V_b % 1.09/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_div__mult__mult1_0,axiom, % 1.09/1.23 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.23 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_Divides_Odiv__class_Odiv(V_a,V_b,T_a) % 1.09/1.23 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_div__mult__mult2_0,axiom, % 1.09/1.23 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.23 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_Divides_Odiv__class_Odiv(V_a,V_b,T_a) % 1.09/1.23 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__le__mono_0,axiom, % 1.09/1.23 ( c_lessequals(c_HOL_Otimes__class_Otimes(V_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_l,tc_nat),tc_nat) % 1.09/1.23 | ~ c_lessequals(V_k,V_l,tc_nat) % 1.09/1.23 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_le__cube_0,axiom, % 1.09/1.23 c_lessequals(V_m,c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_m,V_m,tc_nat),tc_nat),tc_nat) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__mono_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 1.09/1.23 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.09/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.23 | ~ c_lessequals(V_c,V_d,T_a) % 1.09/1.23 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mult__mono_H_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 1.09/1.23 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 1.09/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.23 | ~ c_lessequals(V_c,V_d,T_a) % 1.09/1.23 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_field__inverse_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.23 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.09/1.23 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_left__inverse_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.09/1.23 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.09/1.23 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_right__inverse_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.09/1.23 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a) % 1.09/1.23 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_square__eq__iff_1,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.09/1.23 | 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) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_min__max_Osup__assoc_0,axiom, % 1.09/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.23 | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_minus__mult__minus_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oring(T_a) % 1.09/1.23 | 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) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_min__max_Osup__left__commute_0,axiom, % 1.09/1.23 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.23 | c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omax(V_y,c_Orderings_Oord__class_Omax(V_x,V_z,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_diff__minus__eq__add_0,axiom, % 1.09/1.23 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.23 | c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_zero__less__two_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.23 | 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) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mod__mult__self1_0,axiom, % 1.09/1.23 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.23 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_mod__mult__self2_0,axiom, % 1.09/1.23 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.23 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_diff__frac__eq_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.23 | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) % 1.09/1.23 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.23 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.23 | 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) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_dvd__mult__cancel__left_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.09/1.23 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) % 1.09/1.23 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.23 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_dvd__mult__cancel__right_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.09/1.23 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) % 1.09/1.23 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.23 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_abs__one_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.23 | c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_of__nat__0__le__iff_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.23 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_zero__le__imp__of__nat_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.23 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_div__add__self1_0,axiom, % 1.09/1.23 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.23 | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_b,V_a,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.09/1.23 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_div__add__self2_0,axiom, % 1.09/1.23 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.23 | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.09/1.23 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_nonzero__inverse__eq__divide_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.23 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 1.09/1.23 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_sum__squares__gt__zero__iff_0,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.23 | ~ 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) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_le__divide__eq_9,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.09/1.23 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.09/1.23 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_le__divide__eq_3,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.09/1.23 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_le__divide__eq_2,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.23 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__le__eq_9,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.09/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.23 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.09/1.23 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.09/1.23 % 1.09/1.23 cnf(cls_divide__le__eq_3,axiom, % 1.09/1.23 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.23 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.23 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.09/1.23 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.23 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_divide__le__eq_2,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.24 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_abs_0,axiom, % 1.09/1.24 ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t)) % 1.09/1.24 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_min__max_Osup__left__idem_0,axiom, % 1.09/1.24 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.24 | c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) = c_Orderings_Oord__class_Omax(V_x,V_y,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_zero__le__mult__iff_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.24 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_zero__le__mult__iff_1,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.24 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_zero__le__mult__iff_2,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.24 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_zero__le__mult__iff_3,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.24 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_diff__add__inverse2_0,axiom, % 1.09/1.24 c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_n,tc_nat) = V_m ). % 1.09/1.24 % 1.09/1.24 cnf(cls_diff__add__inverse_0,axiom, % 1.09/1.24 c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_n,tc_nat) = V_m ). % 1.09/1.24 % 1.09/1.24 cnf(cls_add__diff__cancel_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.24 | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_one__le__inverse__iff_2,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.24 | c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) % 1.09/1.24 | ~ c_lessequals(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_power__le__imp__le__exp_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.24 | c_lessequals(V_m,V_n,tc_nat) % 1.09/1.24 | ~ c_lessequals(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_power__increasing__iff_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.24 | c_lessequals(V_x,V_y,tc_nat) % 1.09/1.24 | ~ c_lessequals(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_power__increasing__iff_1,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.24 | c_lessequals(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a) % 1.09/1.24 | ~ c_lessequals(V_x,V_y,tc_nat) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_minus__divide__right_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.24 | 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) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_minus__divide__left_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.24 | 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) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_add__divide__distrib_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.24 | 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) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_less__1__mult_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.09/1.24 | 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) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_n,T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_m,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_abs__minus__commute_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.24 | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_minus__minus_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.24 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_double__compl_0,axiom, % 1.09/1.24 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.09/1.24 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = V_x ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_equation__minus__iff_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.24 | V_b = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_equation__minus__iff_1,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.24 | V_a = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_minus__equation__iff_1,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.24 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_div__by__1_0,axiom, % 1.09/1.24 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.24 | c_Divides_Odiv__class_Odiv(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_minus__diff__eq_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.09/1.24 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_add__le__less__mono_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.09/1.24 | 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) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.09/1.24 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_add__less__le__mono_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.09/1.24 | 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) % 1.09/1.24 | ~ c_lessequals(V_c,V_d,T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_dB_Osimps_I5_J_0,axiom, % 1.09/1.24 c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_less__Suc__eq__0__disj_3,axiom, % 1.09/1.24 ( c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_x,V_n,tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_Suc__less__eq_0,axiom, % 1.09/1.24 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_Suc__mono_0,axiom, % 1.09/1.24 ( c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_add__gr__0_2,axiom, % 1.09/1.24 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_add__gr__0_1,axiom, % 1.09/1.24 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_le__minus__iff_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.24 | c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.09/1.24 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_le__minus__iff_1,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.24 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.09/1.24 | ~ c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_minus__le__iff_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.24 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) % 1.09/1.24 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_minus__le__iff_1,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.24 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.09/1.24 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_less__minus__iff_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_less__minus__iff_1,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_minus__less__iff_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_minus__less__iff_1,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_eq__divide__eq_2,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.24 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_inverse__nonzero__iff__nonzero_1,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.09/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.24 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_inverse__zero_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.24 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_nonzero__inverse__eq__imp__eq_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.09/1.24 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a) % 1.09/1.24 | V_a = V_b % 1.09/1.24 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_abs__eq__0_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.24 | c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_minus__zero_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.24 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_neg__equal__zero_1,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.09/1.24 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_inverse__nonzero__iff__nonzero_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.09/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.24 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_inverse__zero__imp__zero_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.09/1.24 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_power__eq__0__iff_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.09/1.24 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.09/1.24 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.09/1.24 | ~ class_Power_Opower(T_a) % 1.09/1.24 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_field__power__not__zero_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(T_a) % 1.09/1.24 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_neg__0__equal__iff__equal_1,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.24 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_sgn0_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Osgn__if(T_a) % 1.09/1.24 | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_sgn__0__0_1,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.24 | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_class__semiring_Omul__0_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mult__zero__left_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mult__zero__right_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mult__eq__0__iff_1,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mult__eq__0__iff_2,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_zero__less__diff_0,axiom, % 1.09/1.24 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_zero__less__diff_1,axiom, % 1.09/1.24 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_Suc__lessD_0,axiom, % 1.09/1.24 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_less__SucI_0,axiom, % 1.09/1.24 ( c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_inverse__eq__iff__eq_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.09/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.24 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a) % 1.09/1.24 | V_a = V_b ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_sum__squares__eq__zero__iff_2,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.24 | 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) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mult__less__cancel__right__disj_2,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mult__less__cancel__right__disj_1,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mult__less__cancel__left__disj_2,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mult__less__cancel__left__disj_1,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_subst__App_0,axiom, % 1.09/1.24 c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_Suc__mult__cancel1_0,axiom, % 1.09/1.24 ( c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat) % 1.09/1.24 | V_m = V_n ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_Suc__pred_0,axiom, % 1.09/1.24 ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_of__nat__add_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.09/1.24 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),T_a) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_diff__less_0,axiom, % 1.09/1.24 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_min__max_Odistrib__sup__le_0,axiom, % 1.09/1.24 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.24 | c_lessequals(c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),c_Orderings_Oord__class_Omax(V_x,V_z,T_a),T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_le__eqI_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.24 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.09/1.24 | c_lessequals(V_y_H,V_x_H,T_a) % 1.09/1.24 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_le__eqI_1,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.24 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.09/1.24 | c_lessequals(V_y,V_x,T_a) % 1.09/1.24 | ~ c_lessequals(V_y_H,V_x_H,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_less__eqI_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.24 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_less__eqI_1,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.24 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_power__mult__distrib_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) % 1.09/1.24 | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_n,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_class__semiring_Opwr__mul_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.24 | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_q,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_q,T_a),c_Power_Opower__class_Opower(V_y,V_q,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_zmod__simps_I1_J_0,axiom, % 1.09/1.24 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.24 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_zmod__simps_I2_J_0,axiom, % 1.09/1.24 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.24 | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_neg__0__less__iff__less_1,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_neg__0__less__iff__less_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_add__diff__inverse_0,axiom, % 1.09/1.24 ( c_HOL_Oplus__class_Oplus(V_n,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = V_m % 1.09/1.24 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_diff__Suc__less_0,axiom, % 1.09/1.24 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_n,c_Suc(V_i),tc_nat),V_n,tc_nat) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_inf__period_I4_J_1,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Odvd(T_a) % 1.09/1.24 | ~ class_Ring__and__Field_Ocomm__ring(T_a) % 1.09/1.24 | c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a) % 1.09/1.24 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_x,c_HOL_Otimes__class_Otimes(V_k,V_D,T_a),T_a),V_t,T_a),T_a) % 1.09/1.24 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_inf__period_I4_J_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Odvd(T_a) % 1.09/1.24 | ~ class_Ring__and__Field_Ocomm__ring(T_a) % 1.09/1.24 | c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_x,c_HOL_Otimes__class_Otimes(V_k,V_D,T_a),T_a),V_t,T_a),T_a) % 1.09/1.24 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a) % 1.09/1.24 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_frac__eq__eq_1,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) != c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) % 1.09/1.24 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_frac__eq__eq_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.24 | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) != c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) % 1.09/1.24 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) = c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_add__is__1_1,axiom, % 1.09/1.24 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.09/1.24 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.09/1.24 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_add__is__1_2,axiom, % 1.09/1.24 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.09/1.24 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 1.09/1.24 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_min__max_Osup__inf__distrib2_0,axiom, % 1.09/1.24 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.24 | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_y,V_z,T_a),V_x,T_a) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_y,V_x,T_a),c_Orderings_Oord__class_Omax(V_z,V_x,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_min__max_Osup__inf__distrib1_0,axiom, % 1.09/1.24 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.24 | c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),c_Orderings_Oord__class_Omax(V_x,V_z,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_power__mult_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.09/1.24 | c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mod__div__equality2_0,axiom, % 1.09/1.24 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.24 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) = V_a ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mod__div__equality_0,axiom, % 1.09/1.24 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.24 | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) = V_a ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mod__div__decomp_0,axiom, % 1.09/1.24 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.24 | V_a = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_xt1_I11_J_0,axiom, % 1.09/1.24 ( ~ class_Orderings_Oorder(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.09/1.24 | V_a = V_b % 1.09/1.24 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_xt1_I12_J_0,axiom, % 1.09/1.24 ( ~ class_Orderings_Oorder(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.09/1.24 | ~ c_lessequals(V_b,V_a,T_a) % 1.09/1.24 | V_a = V_b ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_nat__less__le_2,axiom, % 1.09/1.24 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.24 | V_m = V_n % 1.09/1.24 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_le__eq__less__or__eq_0,axiom, % 1.09/1.24 ( V_m = V_n % 1.09/1.24 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.24 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_le__neq__implies__less_0,axiom, % 1.09/1.24 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.09/1.24 | V_m = V_n % 1.09/1.24 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_order__le__less_0,axiom, % 1.09/1.24 ( ~ class_Orderings_Oorder(T_a) % 1.09/1.24 | V_x = V_y % 1.09/1.24 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.09/1.24 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_order__less__le_2,axiom, % 1.09/1.24 ( ~ class_Orderings_Oorder(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.09/1.24 | V_x = V_y % 1.09/1.24 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_order__le__neq__trans_0,axiom, % 1.09/1.24 ( ~ class_Orderings_Oorder(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.09/1.24 | V_a = V_b % 1.09/1.24 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_order__neq__le__trans_0,axiom, % 1.09/1.24 ( ~ class_Orderings_Oorder(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.09/1.24 | ~ c_lessequals(V_a,V_b,T_a) % 1.09/1.24 | V_a = V_b ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_linorder__antisym__conv1_0,axiom, % 1.09/1.24 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.24 | V_x = V_y % 1.09/1.24 | ~ c_lessequals(V_x,V_y,T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_linorder__antisym__conv2_0,axiom, % 1.09/1.24 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.24 | V_x = V_y % 1.09/1.24 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.09/1.24 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_divide__right__mono__neg_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.24 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),T_a) % 1.09/1.24 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.24 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_divide__right__mono_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.24 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.09/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.09/1.24 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_power__inverse_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.09/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.24 | c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_inverse__minus__eq_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.09/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.24 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_sgn__times_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.24 | c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Osgn__class_Osgn(V_b,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mult__nonneg__nonneg_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.09/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.09/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_zero__le__mult__iff_5,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.09/1.24 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.24 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_zero__le__mult__iff_4,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.09/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_zero__le__square_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.09/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mult__nonpos__nonpos_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.09/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.09/1.24 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.24 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_split__mult__pos__le_1,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.09/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.09/1.24 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.24 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_split__mult__pos__le_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.09/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.09/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.09/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mod__mult__mult2_0,axiom, % 1.09/1.24 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.24 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mod__mult__mult1_0,axiom, % 1.09/1.24 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.24 | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_c,c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_less__minus__self__iff_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_less__minus__self__iff_1,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_right__inverse__eq_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.24 | c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.09/1.24 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_a = V_b ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_abs__ge__zero_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.24 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_class__ring_Oneg__mul_0,axiom, % 1.09/1.24 ( ~ class_Int_Onumber__ring(T_a) % 1.09/1.24 | 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) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_Suc__le__mono_0,axiom, % 1.09/1.24 ( c_lessequals(V_n,V_m,tc_nat) % 1.09/1.24 | ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_Suc__le__mono_1,axiom, % 1.09/1.24 ( c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) % 1.09/1.24 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_divide__eq__eq_4,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.24 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a),V_c,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_sgn__1__pos_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.24 | c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_sgn__pos_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.24 | c_HOL_Osgn__class_Osgn(V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_abs__triangle__ineq2_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.24 | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_dvd__div__neg_0,axiom, % 1.09/1.24 ( ~ class_Divides_Oring__div(T_a) % 1.09/1.24 | c_Divides_Odiv__class_Odiv(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),T_a) % 1.09/1.24 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_dvd__neg__div_0,axiom, % 1.09/1.24 ( ~ class_Divides_Oring__div(T_a) % 1.09/1.24 | c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),T_a) % 1.09/1.24 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,V_rx,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ry,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_nat__mult__assoc_0,axiom, % 1.09/1.24 c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_class__semiring_Omul__a_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_comm__semiring__class_Odistrib_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_add__mult__distrib_0,axiom, % 1.09/1.24 c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_add__mult__distrib2_0,axiom, % 1.09/1.24 c_HOL_Otimes__class_Otimes(V_k,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_class__semiring_Omul__d_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_dvd__if__abs__eq_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.24 | c_HOL_Oabs__class_Oabs(V_l,T_a) != c_HOL_Oabs__class_Oabs(V_k,T_a) % 1.09/1.24 | c_Ring__and__Field_Odvd__class_Odvd(V_l,V_k,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_minus__add__distrib_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.09/1.24 | 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) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_minus__add_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.24 | 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) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_frac__less_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.09/1.24 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_z,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_w,T_a),T_a) % 1.09/1.24 | ~ c_lessequals(V_w,V_z,T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.09/1.24 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_xt1_I9_J_0,axiom, % 1.09/1.24 ( ~ class_Orderings_Oorder(T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_not__less__iff__gr__or__eq_1,axiom, % 1.09/1.24 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_nat__le__linear_0,axiom, % 1.09/1.24 ( c_lessequals(V_n,V_m,tc_nat) % 1.09/1.24 | c_lessequals(V_m,V_n,tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_linorder__linear_0,axiom, % 1.09/1.24 ( ~ class_Orderings_Olinorder(T_a) % 1.09/1.24 | c_lessequals(V_y,V_x,T_a) % 1.09/1.24 | c_lessequals(V_x,V_y,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_order__less__asym_0,axiom, % 1.09/1.24 ( ~ class_Orderings_Opreorder(T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_order__less__asym_H_0,axiom, % 1.09/1.24 ( ~ class_Orderings_Opreorder(T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.09/1.24 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_neg__equal__0__iff__equal_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.24 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_dvd__0__right_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.24 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_one__neq__zero_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.09/1.24 | c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_no__zero__divirors__neq0_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_no__zero__divisors_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mult__eq__0__iff_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.09/1.24 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_div__by__0_0,axiom, % 1.09/1.24 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.24 | c_Divides_Odiv__class_Odiv(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_div__0_0,axiom, % 1.09/1.24 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.24 | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_double__eq__0__iff_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.09/1.24 | c_HOL_Oplus__class_Oplus(V_a,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_class__ringb_Osubr0__iff_1,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.09/1.24 | ~ class_Int_Onumber__ring(T_a) % 1.09/1.24 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_diff__self_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.24 | c_HOL_Ominus__class_Ominus(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_diff__0__right_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.24 | c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_right__minus__eq_1,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.24 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_eq__iff__diff__eq__0_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.09/1.24 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_class__ringb_Oadd__r0__iff_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.09/1.24 | ~ class_Int_Onumber__ring(T_a) % 1.09/1.24 | V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) % 1.09/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mod__self_0,axiom, % 1.09/1.24 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.24 | c_Divides_Odiv__class_Omod(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mod__by__0_0,axiom, % 1.09/1.24 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.24 | c_Divides_Odiv__class_Omod(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_pprt__0_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.09/1.24 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mod__0_0,axiom, % 1.09/1.24 ( ~ class_Divides_Osemiring__div(T_a) % 1.09/1.24 | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_double__eq__0__iff_1,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.09/1.24 | 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) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_abs__eq__0_1,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.09/1.24 | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_neg__0__equal__iff__equal_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.24 | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.09/1.24 | c_HOL_Ozero__class_Ozero(T_a) = V_a ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_zero__neq__one_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.09/1.24 | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_nonzero__inverse__inverse__eq_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.09/1.24 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a % 1.09/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_dvd__0__left_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_class__ringb_Osubr0__iff_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.09/1.24 | ~ class_Int_Onumber__ring(T_a) % 1.09/1.24 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_x = V_y ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_right__minus__eq_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.09/1.24 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_a = V_b ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_eq__iff__diff__eq__0_1,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.09/1.24 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_a = V_b ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_divide__eq__eq_1,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.24 | c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_divide__zero_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.24 | c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_divide__zero__left_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.24 | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_divide__self__if_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.09/1.24 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.09/1.24 | 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) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_sgn__0__0_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.09/1.24 | c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_class__semiring_Oadd__0_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.24 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = V_x ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_comm__monoid__add_Omult__1_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.09/1.24 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_class__ringb_Oadd__r0__iff_1,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.09/1.24 | ~ class_Int_Onumber__ring(T_a) % 1.09/1.24 | V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_comm__monoid__add_Omult__1__right_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.09/1.24 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_add__0__left_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 1.09/1.24 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_monoid__add__class_Oadd__0__right_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 1.09/1.24 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.24 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.09/1.24 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_neg__equal__zero_0,axiom, % 1.09/1.24 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.09/1.24 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != V_a % 1.09/1.24 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_power__0__left_0,axiom, % 1.09/1.24 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 1.09/1.24 | ~ class_Power_Opower(T_a) % 1.09/1.24 | 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) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_nat_Osize_I3_J_0,axiom, % 1.09/1.24 c_Nat_Osize__class_Osize(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_le__0__eq_1,axiom, % 1.09/1.24 c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mult__cancel2_1,axiom, % 1.09/1.24 c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mult__cancel1_1,axiom, % 1.09/1.24 c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_neq0__conv_1,axiom, % 1.09/1.24 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_liftn__0_0,axiom, % 1.09/1.24 c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k) = V_t ). % 1.09/1.24 % 1.09/1.24 cnf(cls_gr0I_0,axiom, % 1.09/1.24 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.09/1.24 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_Suc__neq__Zero_0,axiom, % 1.09/1.24 c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_nat_Osimps_I3_J_0,axiom, % 1.09/1.24 c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_diffs0__imp__equal_0,axiom, % 1.09/1.24 ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.09/1.24 | c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.09/1.24 | V_m = V_n ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_le__0__eq_0,axiom, % 1.09/1.24 ( V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 1.09/1.24 | ~ c_lessequals(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mult__is__0_2,axiom, % 1.09/1.24 c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mult__is__0_1,axiom, % 1.09/1.24 c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mult__is__0_0,axiom, % 1.09/1.24 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.09/1.24 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 1.09/1.24 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_add__is__0_1,axiom, % 1.09/1.24 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.09/1.24 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_add__is__0_0,axiom, % 1.09/1.24 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.09/1.24 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_min__0R_0,axiom, % 1.09/1.24 c_Orderings_Oord__class_Omin(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_min__0L_0,axiom, % 1.09/1.24 c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mult__cancel2_0,axiom, % 1.09/1.24 ( c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat) != c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat) % 1.09/1.24 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) % 1.09/1.24 | V_m = V_n ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_mult__cancel1_0,axiom, % 1.09/1.24 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) % 1.09/1.24 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) % 1.09/1.24 | V_m = V_n ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_nat__mult__eq__cancel__disj_0,axiom, % 1.09/1.24 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) % 1.09/1.24 | V_m = V_n % 1.09/1.24 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_minus__nat_Odiff__0_0,axiom, % 1.09/1.24 c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ). % 1.09/1.24 % 1.09/1.24 cnf(cls_diff__self__eq__0_0,axiom, % 1.09/1.24 c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_natgb_Oadd__r0__iff_0,axiom, % 1.09/1.24 ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) % 1.09/1.24 | V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_add__eq__self__zero_0,axiom, % 1.09/1.24 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != V_m % 1.09/1.24 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_Zero__neq__Suc_0,axiom, % 1.09/1.24 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_nat_Osimps_I2_J_0,axiom, % 1.09/1.24 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ). % 1.09/1.24 % 1.09/1.24 cnf(cls_nat__gcd_Osimps_0,axiom, % 1.09/1.25 c_Nitpick_Onat__gcd(V_x,c_HOL_Ozero__class_Ozero(tc_nat)) = V_x ). % 1.09/1.25 % 1.09/1.25 cnf(cls_nat_Osize_I1_J_0,axiom, % 1.09/1.25 c_nat_Onat__size(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_char__size_0,axiom, % 1.09/1.25 c_String_Ochar_Ochar__size(V_c) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_add__is__0_2,axiom, % 1.09/1.25 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_gr__implies__not0_0,axiom, % 1.09/1.25 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_not__less0_0,axiom, % 1.09/1.25 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_bot__nat__def_0,axiom, % 1.09/1.25 c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_drop__0_0,axiom, % 1.09/1.25 c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),V_xs,T_a) = V_xs ). % 1.09/1.25 % 1.09/1.25 cnf(cls_diff__0__eq__0_0,axiom, % 1.09/1.25 c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_le0_0,axiom, % 1.09/1.25 c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_size__char_0,axiom, % 1.09/1.25 c_Nat_Osize__class_Osize(V_c,tc_String_Ochar) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_replicate__eq__replicate_2,axiom, % 1.09/1.25 c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_max__0R_0,axiom, % 1.09/1.25 c_Orderings_Oord__class_Omax(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_n ). % 1.09/1.25 % 1.09/1.25 cnf(cls_max__0L_0,axiom, % 1.09/1.25 c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ). % 1.09/1.25 % 1.09/1.25 cnf(cls_replicate__eq__replicate_1,axiom, % 1.09/1.25 ( c_List_Oreplicate(V_m,V_x,T_a) != c_List_Oreplicate(V_n,V_y,T_a) % 1.09/1.25 | V_x = V_y % 1.09/1.25 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_natgb_Oadd__r0__iff_1,axiom, % 1.09/1.25 V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_plus__nat_Oadd__0_0,axiom, % 1.09/1.25 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ). % 1.09/1.25 % 1.09/1.25 cnf(cls_Nat_Oadd__0__right_0,axiom, % 1.09/1.25 c_HOL_Oplus__class_Oplus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ). % 1.09/1.25 % 1.09/1.25 cnf(cls_lift_Osimps_I2_J_0,axiom, % 1.09/1.25 c_Lambda_Olift(c_Lambda_OdB_OApp(V_s,V_t),V_k) = c_Lambda_OdB_OApp(c_Lambda_Olift(V_s,V_k),c_Lambda_Olift(V_t,V_k)) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_subst__lift_0,axiom, % 1.09/1.25 c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ). % 1.09/1.25 % 1.09/1.25 cnf(cls_lift__preserves__beta_0,axiom, % 1.09/1.25 ( c_Lambda_Obeta(c_Lambda_Olift(V_r,V_i),c_Lambda_Olift(V_s,V_i)) % 1.09/1.25 | ~ c_Lambda_Obeta(V_r,V_s) ) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_App_I2_J_0,axiom, % 1.09/1.25 c_InductTermi_OIT(v_s____) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_Var__IT_0,axiom, % 1.09/1.25 c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_Lambda_0,axiom, % 1.09/1.25 ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r)) % 1.09/1.25 | ~ c_InductTermi_OIT(V_r) ) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_power__eq__0__iff_2,axiom, % 1.09/1.25 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.09/1.25 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.09/1.25 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.09/1.25 | ~ class_Power_Opower(T_a) % 1.09/1.25 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.25 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_power__0__left_1,axiom, % 1.09/1.25 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 1.09/1.25 | ~ class_Power_Opower(T_a) % 1.09/1.25 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.09/1.25 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_power__eq__0__iff_1,axiom, % 1.09/1.25 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.09/1.25 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.09/1.25 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.09/1.25 | ~ class_Power_Opower(T_a) % 1.09/1.25 | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_of__nat__0_0,axiom, % 1.09/1.25 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.09/1.25 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_lift__IT_0,axiom, % 1.09/1.25 ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i)) % 1.09/1.25 | ~ c_InductTermi_OIT(V_t) ) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_App_I4_J_0,axiom, % 1.09/1.25 c_InductTermi_OIT(v_ta____) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_CHAINED_0,axiom, % 1.09/1.25 c_InductTermi_OIT(v_ta____) ). % 1.09/1.25 % 1.09/1.25 cnf(cls_conjecture_0,negated_conjecture, % 1.09/1.25 ~ c_InductTermi_OIT(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom, % 1.09/1.25 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom, % 1.09/1.25 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom, % 1.09/1.25 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,axiom, % 1.09/1.25 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom, % 1.09/1.25 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom, % 1.09/1.25 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom, % 1.09/1.25 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 1.09/1.25 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom, % 1.09/1.25 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Ring__and__Field_Opordered__semiring,axiom, % 1.09/1.25 class_Ring__and__Field_Opordered__semiring(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Ring__and__Field_Oordered__semiring,axiom, % 1.09/1.25 class_Ring__and__Field_Oordered__semiring(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom, % 1.09/1.25 class_Ring__and__Field_Ono__zero__divisors(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom, % 1.09/1.25 class_Ring__and__Field_Oordered__semidom(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom, % 1.09/1.25 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom, % 1.09/1.25 class_OrderedGroup_Oab__semigroup__mult(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom, % 1.09/1.25 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom, % 1.09/1.25 class_OrderedGroup_Oab__semigroup__add(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom, % 1.09/1.25 class_Ring__and__Field_Ocomm__semiring(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom, % 1.09/1.25 class_OrderedGroup_Ocomm__monoid__add(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom, % 1.09/1.25 class_Ring__and__Field_Ozero__neq__one(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom, % 1.09/1.25 class_Ring__and__Field_Osemiring__1(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom, % 1.09/1.25 class_Ring__and__Field_Osemiring__0(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Ring__and__Field_Omult__mono1,axiom, % 1.09/1.25 class_Ring__and__Field_Omult__mono1(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom, % 1.09/1.25 class_Ring__and__Field_Omult__zero(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Ring__and__Field_Omult__mono,axiom, % 1.09/1.25 class_Ring__and__Field_Omult__mono(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom, % 1.09/1.25 class_OrderedGroup_Omonoid__mult(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom, % 1.09/1.25 class_Ring__and__Field_Osemiring(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom, % 1.09/1.25 class_OrderedGroup_Omonoid__add(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Divides_Osemiring__div,axiom, % 1.09/1.25 class_Divides_Osemiring__div(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom, % 1.09/1.25 class_Nat_Osemiring__char__0(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Ring__and__Field_Odvd,axiom, % 1.09/1.25 class_Ring__and__Field_Odvd(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Orderings_Opreorder,axiom, % 1.09/1.25 class_Orderings_Opreorder(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Orderings_Olinorder,axiom, % 1.09/1.25 class_Orderings_Olinorder(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Orderings_Oorder,axiom, % 1.09/1.25 class_Orderings_Oorder(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Orderings_Obot,axiom, % 1.09/1.25 class_Orderings_Obot(tc_nat) ). % 1.09/1.25 % 1.09/1.25 cnf(clsarity_nat__Power_Opower,axiom, % 1.09/1.25 class_Power_Opower(tc_nat) ). % 1.09/1.25 % 1.09/1.25 %------------------------------------------------------------------------------ % 1.09/1.25 %------------------------------------------- % 1.09/1.25 % Proof found % 1.09/1.25 % SZS status Theorem for theBenchmark % 1.09/1.25 % SZS output start Proof % 1.09/1.25 %ClaNum:1375(EqnAxiom:146) % 1.09/1.25 %VarNum:9535(SingletonVarNum:3027) % 1.09/1.25 %MaxLitNum:6 % 1.09/1.25 %MaxfuncDepth:4 % 1.09/1.25 %SharedTerms:62 % 1.09/1.25 %goalClause: 290 % 1.09/1.25 %singleGoalClaCount:1 % 1.09/1.25 [147]P1(a1) % 1.09/1.25 [148]P8(a1) % 1.09/1.25 [149]P9(a1) % 1.09/1.25 [150]P33(a1) % 1.09/1.25 [151]P10(a1) % 1.09/1.25 [152]P11(a1) % 1.09/1.25 [153]P34(a1) % 1.09/1.25 [154]P12(a1) % 1.09/1.25 [155]P56(a1) % 1.09/1.25 [156]P57(a1) % 1.09/1.25 [157]P58(a1) % 1.09/1.25 [158]P35(a1) % 1.09/1.25 [159]P21(a1) % 1.09/1.25 [160]P22(a1) % 1.09/1.25 [161]P42(a1) % 1.09/1.25 [162]P27(a1) % 1.09/1.25 [163]P31(a1) % 1.09/1.25 [164]P68(a1) % 1.09/1.25 [165]P36(a1) % 1.09/1.25 [166]P37(a1) % 1.09/1.25 [167]P15(a1) % 1.09/1.25 [168]P32(a1) % 1.09/1.25 [169]P59(a1) % 1.09/1.25 [170]P60(a1) % 1.09/1.25 [171]P17(a1) % 1.09/1.25 [172]P20(a1) % 1.09/1.25 [173]P45(a1) % 1.09/1.25 [174]P2(a33) % 1.09/1.25 [176]P2(a34) % 1.09/1.25 [177]P46(a1) % 1.09/1.25 [178]P50(a1) % 1.09/1.25 [179]P61(a1) % 1.09/1.25 [180]P69(a1) % 1.09/1.25 [181]P51(a1) % 1.09/1.25 [182]P52(a1) % 1.09/1.25 [183]P18(a1) % 1.09/1.25 [184]P38(a1) % 1.09/1.25 [185]P23(a1) % 1.09/1.25 [186]E(f2(a1),f14(a1)) % 1.09/1.25 [187]E(f27(f2(a1)),f2(a1)) % 1.09/1.25 [290]~P2(f20(a34,f2(a1))) % 1.09/1.25 [225]E(f11(f30(f2(a1)),f30(f2(a1)),a1),f30(f2(a1))) % 1.09/1.25 [194]P4(x1941,x1941,a1) % 1.09/1.25 [292]~P3(x2921,x2921,a1) % 1.09/1.25 [188]P2(f15(x1881)) % 1.09/1.25 [189]E(f18(x1891,a1),x1891) % 1.09/1.25 [190]E(f18(x1901,a32),f2(a1)) % 1.09/1.25 [195]E(f3(x1951,x1951,a1),f2(a1)) % 1.09/1.25 [196]P4(f2(a1),x1961,a1) % 1.09/1.25 [211]P3(x2111,f30(x2111),a1) % 1.09/1.25 [216]P3(f2(a1),f30(x2161),a1) % 1.09/1.25 [238]P4(x2381,f11(x2381,x2381,a1),a1) % 1.09/1.25 [278]~E(f30(x2781),x2781) % 1.09/1.25 [282]~E(f30(x2821),f2(a1)) % 1.09/1.25 [294]~P3(x2941,f2(a1),a1) % 1.09/1.25 [295]~P4(f30(x2951),x2951,a1) % 1.09/1.25 [191]E(f25(x1911,f2(a1)),x1911) % 1.09/1.25 [198]E(f9(x1981,f2(a1),a1),x1981) % 1.09/1.25 [199]E(f3(x1991,f2(a1),a1),x1991) % 1.09/1.25 [200]E(f28(x2001,f2(a1),a1),x2001) % 1.09/1.25 [201]E(f9(f2(a1),x2011,a1),x2011) % 1.09/1.25 [202]E(f28(f2(a1),x2021,a1),x2021) % 1.09/1.25 [205]E(f11(x2051,f2(a1),a1),f2(a1)) % 1.09/1.25 [206]E(f29(x2061,f2(a1),a1),f2(a1)) % 1.09/1.25 [207]E(f11(f2(a1),x2071,a1),f2(a1)) % 1.09/1.25 [208]E(f3(f2(a1),x2081,a1),f2(a1)) % 1.09/1.25 [209]E(f29(f2(a1),x2091,a1),f2(a1)) % 1.09/1.25 [268]P4(x2681,f11(x2681,f11(x2681,x2681,a1),a1),a1) % 1.09/1.25 [224]E(f9(f27(x2241),f30(f2(a1)),a1),f27(f30(x2241))) % 1.09/1.25 [229]E(f9(f18(x2291,a1),f30(f2(a1)),a1),f18(f30(x2291),a1)) % 1.09/1.25 [226]E(f9(x2261,x2262,a1),f9(x2262,x2261,a1)) % 1.09/1.25 [227]E(f11(x2271,x2272,a1),f11(x2272,x2271,a1)) % 1.09/1.25 [235]P4(x2351,f9(x2352,x2351,a1),a1) % 1.09/1.25 [237]P4(x2371,f9(x2371,x2372,a1),a1) % 1.09/1.25 [239]P4(f3(x2391,x2392,a1),x2391,a1) % 1.09/1.25 [243]P3(f3(x2431,x2432,a1),f30(x2431),a1) % 1.09/1.25 [284]~E(f17(x2841),f15(x2842)) % 1.09/1.25 [289]~P5(f15(x2891),x2892) % 1.09/1.25 [297]~P3(f9(x2971,x2972,a1),x2972,a1) % 1.09/1.25 [298]~P3(f9(x2981,x2982,a1),x2981,a1) % 1.09/1.25 [203]E(f19(f2(a1),x2031,x2032),x2031) % 1.09/1.25 [204]E(f21(f2(a1),x2041,x2042),x2041) % 1.09/1.25 [213]E(f22(f15(x2131),x2132,x2131),x2132) % 1.09/1.25 [230]E(f11(x2301,f2(a1),a1),f11(x2302,f2(a1),a1)) % 1.09/1.25 [231]E(f11(f2(a1),x2311,a1),f11(f2(a1),x2312,a1)) % 1.09/1.25 [233]E(f9(f30(x2331),x2332,a1),f9(x2331,f30(x2332),a1)) % 1.09/1.25 [234]E(f3(f30(x2341),f30(x2342),a1),f3(x2341,x2342,a1)) % 1.09/1.25 [240]E(f3(f9(x2401,x2402,a1),x2402,a1),x2401) % 1.09/1.25 [241]E(f3(f9(x2411,x2412,a1),x2411,a1),x2412) % 1.09/1.25 [242]E(f3(x2421,f9(x2421,x2422,a1),a1),f2(a1)) % 1.09/1.25 [244]P5(f16(f17(x2441),x2442),f22(x2441,x2442,f2(a1))) % 1.09/1.25 [245]E(f30(f9(x2451,x2452,a1)),f9(x2451,f30(x2452),a1)) % 1.09/1.25 [246]E(f30(f9(x2461,x2462,a1)),f9(f30(x2461),x2462,a1)) % 1.09/1.25 [247]E(f28(f30(x2471),f30(x2472),a1),f30(f28(x2471,x2472,a1))) % 1.09/1.25 [248]E(f29(f30(x2481),f30(x2482),a1),f30(f29(x2481,x2482,a1))) % 1.09/1.25 [250]E(f9(f3(x2501,x2502,a1),x2502,a1),f28(x2501,x2502,a1)) % 1.09/1.25 [251]E(f9(x2511,f11(x2511,x2512,a1),a1),f11(x2511,f30(x2512),a1)) % 1.09/1.25 [252]E(f9(x2521,f11(x2522,x2521,a1),a1),f11(f30(x2522),x2521,a1)) % 1.09/1.25 [253]P3(x2531,f30(f9(x2532,x2531,a1)),a1) % 1.09/1.25 [255]P3(x2551,f30(f9(x2551,x2552,a1)),a1) % 1.09/1.25 [285]~E(f15(x2851),f16(x2852,x2853)) % 1.09/1.25 [286]~E(f17(x2861),f16(x2862,x2863)) % 1.09/1.25 [287]~E(f16(x2871,x2872),f15(x2873)) % 1.09/1.25 [288]~E(f16(x2881,x2882),f17(x2883)) % 1.09/1.25 [223]E(f22(f20(x2231,x2232),x2233,x2232),x2231) % 1.09/1.25 [228]E(f16(f20(x2281,x2282),f20(x2283,x2282)),f20(f16(x2281,x2283),x2282)) % 1.09/1.25 [232]E(f23(f2(a1),x2321,x2322),f23(f2(a1),x2323,x2322)) % 1.09/1.25 [249]E(f20(f19(x2491,x2492,x2493),x2493),f19(f30(x2491),x2492,x2493)) % 1.09/1.25 [258]E(f9(x2581,f9(x2582,x2583,a1),a1),f9(x2582,f9(x2581,x2583,a1),a1)) % 1.09/1.25 [259]E(f9(f9(x2591,x2592,a1),x2593,a1),f9(x2591,f9(x2592,x2593,a1),a1)) % 1.09/1.25 [260]E(f11(f11(x2601,x2602,a1),x2603,a1),f11(x2601,f11(x2602,x2603,a1),a1)) % 1.09/1.25 [261]E(f3(f3(x2611,x2612,a1),x2613,a1),f3(x2611,f9(x2612,x2613,a1),a1)) % 1.09/1.25 [262]E(f3(f3(x2621,x2622,a1),x2623,a1),f3(f3(x2621,x2623,a1),x2622,a1)) % 1.09/1.25 [263]E(f3(f9(x2631,x2632,a1),f9(x2633,x2632,a1),a1),f3(x2631,x2633,a1)) % 1.09/1.25 [264]E(f3(f9(x2641,x2642,a1),f9(x2641,x2643,a1),a1),f3(x2642,x2643,a1)) % 1.09/1.25 [267]E(f3(f3(f30(x2671),x2672,a1),f30(x2673),a1),f3(f3(x2671,x2672,a1),x2673,a1)) % 1.09/1.25 [269]E(f9(f11(x2691,x2692,a1),f11(x2691,x2693,a1),a1),f11(x2691,f9(x2692,x2693,a1),a1)) % 1.09/1.25 [270]E(f3(f11(x2701,x2702,a1),f11(x2701,x2703,a1),a1),f11(x2701,f3(x2702,x2703,a1),a1)) % 1.09/1.25 [271]E(f9(f11(x2711,x2712,a1),f11(x2713,x2712,a1),a1),f11(f9(x2711,x2713,a1),x2712,a1)) % 1.09/1.25 [272]E(f3(f11(x2721,x2722,a1),f11(x2723,x2722,a1),a1),f11(f3(x2721,x2723,a1),x2722,a1)) % 1.09/1.25 [273]E(f29(f3(x2731,x2732,a1),f3(x2733,x2732,a1),a1),f3(f29(x2731,x2733,a1),x2732,a1)) % 1.09/1.25 [256]E(f16(f19(x2561,x2562,x2563),f19(x2561,x2564,x2563)),f19(x2561,f16(x2562,x2564),x2563)) % 1.09/1.25 [257]E(f16(f22(x2571,x2572,x2573),f22(x2574,x2572,x2573)),f22(f16(x2571,x2574),x2572,x2573)) % 1.09/1.25 [265]E(f21(x2651,f23(x2652,x2653,x2654),x2654),f23(f3(x2652,x2651,a1),x2653,x2654)) % 1.09/1.25 [266]E(f21(x2661,f21(x2662,x2663,x2664),x2664),f21(f9(x2661,x2662,a1),x2663,x2664)) % 1.09/1.25 [276]E(f9(f11(x2761,x2762,a1),f9(f11(x2763,x2762,a1),x2764,a1),a1),f9(f11(f9(x2761,x2763,a1),x2762,a1),x2764,a1)) % 1.09/1.25 [303]~P2(x3031)+P2(f17(x3031)) % 1.09/1.25 [305]~P69(x3051)+~E(f10(x3051),f2(x3051)) % 1.09/1.25 [342]E(x3421,f2(a1))+P3(f2(a1),x3421,a1) % 1.09/1.25 [398]~P33(x3981)+P4(f2(x3981),f10(x3981),x3981) % 1.09/1.25 [399]~P33(x3991)+P3(f2(x3991),f10(x3991),x3991) % 1.09/1.25 [429]E(x4291,f2(a1))+~P4(x4291,f2(a1),a1) % 1.09/1.25 [479]~P33(x4791)+~P4(f10(x4791),f2(x4791),x4791) % 1.09/1.25 [480]~P33(x4801)+~P3(f10(x4801),f2(x4801),x4801) % 1.09/1.25 [306]~P68(x3061)+E(f24(f2(a1),x3061),f2(x3061)) % 1.09/1.25 [308]~P28(x3081)+E(f4(f2(x3081),x3081),f2(x3081)) % 1.09/1.25 [309]~P53(x3091)+E(f4(f10(x3091),x3091),f10(x3091)) % 1.09/1.25 [310]~P29(x3101)+E(f13(f2(x3101),x3101),f2(x3101)) % 1.09/1.25 [311]~P24(x3111)+E(f13(f2(x3111),x3111),f2(x3111)) % 1.09/1.25 [312]~P25(x3121)+E(f26(f2(x3121),x3121),f2(x3121)) % 1.09/1.25 [313]~P43(x3131)+E(f7(f2(x3131),x3131),f2(x3131)) % 1.09/1.25 [314]~P44(x3141)+E(f7(f10(x3141),x3141),f10(x3141)) % 1.09/1.25 [315]~P53(x3151)+E(f12(f2(x3151),x3151),f2(x3151)) % 1.09/1.25 [316]~P70(x3161)+E(f12(f2(x3161),x3161),f2(x3161)) % 1.09/1.25 [401]~P25(x4011)+E(f9(f2(x4011),f2(x4011),x4011),f2(x4011)) % 1.09/1.25 [458]~P28(x4581)+P4(f4(f2(x4581),x4581),f2(x4581),x4581) % 1.09/1.25 [461]E(x4611,f2(a1))+~P3(x4611,f30(f2(a1)),a1) % 1.09/1.25 [584]~P28(x5841)+~P3(f2(x5841),f4(f2(x5841),x5841),x5841) % 1.09/1.25 [694]~P33(x6941)+P3(f2(x6941),f9(f10(x6941),f10(x6941),x6941),x6941) % 1.09/1.25 [897]~P55(x8971)+E(f9(f11(f2(x8971),f2(x8971),x8971),f11(f2(x8971),f2(x8971),x8971),x8971),f2(x8971)) % 1.09/1.25 [1312]~P55(x13121)+P4(f9(f11(f2(x13121),f2(x13121),x13121),f11(f2(x13121),f2(x13121),x13121),x13121),f2(x13121),x13121) % 1.09/1.25 [1352]~P55(x13521)+~P3(f2(x13521),f9(f11(f2(x13521),f2(x13521),x13521),f11(f2(x13521),f2(x13521),x13521),x13521),x13521) % 1.09/1.25 [737]~P3(f2(a1),x7371,a1)+E(f30(f3(x7371,f30(f2(a1)),a1)),x7371) % 1.09/1.25 [348]~P36(x3482)+P4(x3481,x3481,x3482) % 1.09/1.25 [349]~P37(x3492)+P4(x3491,x3491,x3492) % 1.09/1.25 [350]~P34(x3502)+P6(x3501,x3501,x3502) % 1.09/1.25 [432]~P3(x4322,x4322,x4321)+~P8(x4321) % 1.09/1.25 [433]~P3(x4332,x4332,x4331)+~P36(x4331) % 1.09/1.25 [434]~P3(x4342,x4342,x4341)+~P37(x4341) % 1.09/1.25 [460]P4(x4602,x4601,a1)+P4(x4601,x4602,a1) % 1.09/1.25 [524]~P3(x5241,x5242,a1)+P4(x5241,x5242,a1) % 1.09/1.25 [300]E(x3001,x3002)+~E(f30(x3001),f30(x3002)) % 1.09/1.25 [301]E(x3011,x3012)+~E(f15(x3011),f15(x3012)) % 1.09/1.25 [302]E(x3021,x3022)+~E(f17(x3021),f17(x3022)) % 1.09/1.25 [318]~P2(x3181)+P2(f20(x3181,x3182)) % 1.09/1.25 [335]~P5(x3351,x3352)+P5(f17(x3351),f17(x3352)) % 1.09/1.25 [351]~P19(x3512)+E(f11(x3511,x3511,x3512),x3511) % 1.09/1.25 [352]~P8(x3522)+E(f28(x3521,x3521,x3522),x3521) % 1.09/1.25 [353]~P8(x3532)+E(f29(x3531,x3531,x3532),x3531) % 1.09/1.25 [356]~P24(x3562)+E(f3(x3561,x3561,x3562),f2(x3562)) % 1.09/1.25 [357]~P16(x3572)+E(f3(x3571,x3571,x3572),f2(x3572)) % 1.09/1.25 [358]~P1(x3582)+E(f5(x3581,x3581,x3582),f2(x3582)) % 1.09/1.25 [359]~P34(x3592)+P6(x3591,f2(x3592),x3592) % 1.09/1.25 [360]~P9(x3601)+P4(f14(x3601),x3602,x3601) % 1.09/1.25 [361]~P34(x3611)+P6(f10(x3611),x3612,x3611) % 1.09/1.25 [414]~P28(x4142)+P4(x4141,f4(x4141,x4142),x4142) % 1.09/1.25 [416]~E(f9(x4162,x4161,a1),x4162)+E(x4161,f2(a1)) % 1.09/1.25 [422]E(x4221,f2(a1))+~E(f9(x4222,x4221,a1),f2(a1)) % 1.09/1.25 [423]E(x4231,f2(a1))+~E(f9(x4231,x4232,a1),f2(a1)) % 1.09/1.25 [435]~P28(x4351)+P4(f2(x4351),f4(x4352,x4351),x4351) % 1.09/1.25 [436]~P25(x4361)+P4(f2(x4361),f26(x4362,x4361),x4361) % 1.09/1.25 [438]~P33(x4381)+P4(f2(x4381),f24(x4382,x4381),x4381) % 1.09/1.25 [481]P3(x4811,x4812,a1)+P3(x4812,f30(x4811),a1) % 1.09/1.25 [483]P4(x4831,x4832,a1)+P4(f30(x4832),x4831,a1) % 1.09/1.25 [484]~P28(x4842)+P4(f13(x4841,x4842),f4(x4841,x4842),x4842) % 1.09/1.25 [527]~P4(x5271,x5272,a1)+E(f3(x5271,x5272,a1),f2(a1)) % 1.09/1.25 [531]P4(x5311,x5312,a1)+~E(f3(x5311,x5312,a1),f2(a1)) % 1.09/1.25 [538]~P4(x5381,x5382,a1)+P4(x5381,f30(x5382),a1) % 1.09/1.25 [539]~P4(x5391,x5392,a1)+P3(x5391,f30(x5392),a1) % 1.09/1.25 [540]~P3(x5401,x5402,a1)+P3(x5401,f30(x5402),a1) % 1.09/1.25 [543]~P3(x5431,x5432,a1)+P4(f30(x5431),x5432,a1) % 1.09/1.25 [544]~P28(x5441)+~P3(f4(x5442,x5441),f2(x5441),x5441) % 1.09/1.25 [545]~P33(x5451)+~P3(f24(x5452,x5451),f2(x5451),x5451) % 1.09/1.25 [547]P4(x5471,x5472,a1)+~P3(x5471,f30(x5472),a1) % 1.09/1.25 [548]P4(x5481,x5482,a1)+~P4(f30(x5481),x5482,a1) % 1.09/1.25 [550]P3(x5501,x5502,a1)+~P4(f30(x5501),x5502,a1) % 1.09/1.25 [551]P3(x5511,x5512,a1)+~P3(f30(x5511),x5512,a1) % 1.09/1.25 [566]~P4(x5661,x5662,a1)+P4(f30(x5661),f30(x5662),a1) % 1.09/1.25 [568]~P3(x5681,x5682,a1)+P3(f30(x5681),f30(x5682),a1) % 1.09/1.25 [582]P4(x5821,x5822,a1)+~P4(f30(x5821),f30(x5822),a1) % 1.09/1.25 [583]P3(x5831,x5832,a1)+~P3(f30(x5831),f30(x5832),a1) % 1.09/1.25 [616]~P55(x6161)+P4(f2(x6161),f11(x6162,x6162,x6161),x6161) % 1.09/1.25 [623]~P3(x6231,x6232,a1)+~P3(x6232,f30(x6231),a1) % 1.09/1.25 [624]~P4(x6241,x6242,a1)+~P4(f30(x6242),x6241,a1) % 1.09/1.25 [787]~P3(x7872,x7871,a1)+P3(f2(a1),f3(x7871,x7872,a1),a1) % 1.09/1.25 [828]~P55(x8281)+~P3(f11(x8282,x8282,x8281),f2(x8281),x8281) % 1.09/1.25 [863]P3(x8631,x8632,a1)+~P3(f2(a1),f3(x8632,x8631,a1),a1) % 1.09/1.25 [864]P3(f2(a1),x8641,a1)+~P3(f2(a1),f11(x8642,x8641,a1),a1) % 1.09/1.25 [865]P3(f2(a1),x8651,a1)+~P3(f2(a1),f11(x8651,x8652,a1),a1) % 1.09/1.25 [331]~P24(x3312)+E(f13(f13(x3311,x3312),x3312),x3311) % 1.09/1.25 [332]~P13(x3322)+E(f13(f13(x3321,x3322),x3322),x3321) % 1.09/1.25 [336]~P2(x3361)+P2(f16(x3361,f15(x3362))) % 1.09/1.25 [344]~P28(x3442)+E(f4(f4(x3441,x3442),x3442),f4(x3441,x3442)) % 1.09/1.25 [345]~P28(x3452)+E(f4(f13(x3451,x3452),x3452),f4(x3451,x3452)) % 1.09/1.25 [346]~P53(x3462)+E(f4(f24(x3461,x3462),x3462),f24(x3461,x3462)) % 1.09/1.25 [347]~P53(x3472)+E(f12(f12(x3471,x3472),x3472),f12(x3471,x3472)) % 1.09/1.25 [362]~P11(x3622)+E(f9(x3621,f2(x3622),x3622),x3621) % 1.09/1.25 [363]~P34(x3632)+E(f9(x3631,f2(x3632),x3632),x3631) % 1.09/1.25 [364]~P23(x3642)+E(f9(x3641,f2(x3642),x3642),x3641) % 1.09/1.25 [365]~P34(x3652)+E(f11(x3651,f10(x3652),x3652),x3651) % 1.09/1.25 [366]~P22(x3662)+E(f11(x3661,f10(x3662),x3662),x3661) % 1.09/1.25 [367]~P1(x3672)+E(f6(x3671,f10(x3672),x3672),x3671) % 1.09/1.25 [368]~P24(x3682)+E(f3(x3681,f2(x3682),x3682),x3681) % 1.09/1.25 [369]~P1(x3692)+E(f5(x3691,f2(x3692),x3692),x3691) % 1.09/1.25 [370]~P47(x3702)+E(f8(x3701,f10(x3702),x3702),x3701) % 1.09/1.25 [371]~P11(x3711)+E(f9(f2(x3711),x3712,x3711),x3712) % 1.09/1.25 [373]~P34(x3731)+E(f9(f2(x3731),x3732,x3731),x3732) % 1.09/1.25 [374]~P23(x3741)+E(f9(f2(x3741),x3742,x3741),x3742) % 1.09/1.25 [376]~P34(x3761)+E(f11(f10(x3761),x3762,x3761),x3762) % 1.09/1.25 [377]~P21(x3771)+E(f11(f10(x3771),x3772,x3771),x3772) % 1.09/1.25 [378]~P22(x3781)+E(f11(f10(x3781),x3782,x3781),x3782) % 1.09/1.25 [379]~P34(x3792)+E(f31(x3791,f2(a1),x3792),f10(x3792)) % 1.09/1.25 [380]~P35(x3802)+E(f31(x3801,f2(a1),x3802),f10(x3802)) % 1.09/1.25 [384]~P34(x3842)+E(f11(x3841,f2(x3842),x3842),f2(x3842)) % 1.09/1.25 [385]~P52(x3852)+E(f11(x3851,f2(x3852),x3852),f2(x3852)) % 1.09/1.25 [386]~P64(x3862)+E(f11(x3861,f2(x3862),x3862),f2(x3862)) % 1.09/1.25 [387]~P1(x3872)+E(f6(x3871,f2(x3872),x3872),f2(x3872)) % 1.09/1.25 [388]~P1(x3882)+E(f5(x3881,f10(x3882),x3882),f2(x3882)) % 1.09/1.25 [390]~P34(x3901)+E(f11(f2(x3901),x3902,x3901),f2(x3901)) % 1.09/1.25 [391]~P52(x3911)+E(f11(f2(x3911),x3912,x3911),f2(x3911)) % 1.09/1.25 [392]~P64(x3921)+E(f11(f2(x3921),x3922,x3921),f2(x3921)) % 1.09/1.25 [393]~P1(x3931)+E(f6(f2(x3931),x3932,x3931),f2(x3931)) % 1.09/1.25 [394]~P1(x3941)+E(f5(f2(x3941),x3942,x3941),f2(x3941)) % 1.09/1.25 [395]~P22(x3951)+E(f31(f10(x3951),x3952,x3951),f10(x3951)) % 1.09/1.25 [396]~P47(x3961)+E(f8(f2(x3961),x3962,x3961),f2(x3961)) % 1.09/1.25 [406]~P47(x4061)+E(f8(f10(x4061),x4062,x4061),f7(x4062,x4061)) % 1.09/1.25 [407]~P24(x4071)+E(f3(f2(x4071),x4072,x4071),f13(x4072,x4071)) % 1.09/1.25 [424]~P24(x4242)+E(f9(x4241,f13(x4241,x4242),x4242),f2(x4242)) % 1.09/1.25 [426]~P24(x4262)+E(f9(f13(x4261,x4262),x4261,x4262),f2(x4262)) % 1.09/1.25 [427]~P16(x4272)+E(f9(f13(x4271,x4272),x4271,x4272),f2(x4272)) % 1.09/1.25 [449]~P53(x4492)+E(f11(x4491,f12(x4491,x4492),x4492),f4(x4491,x4492)) % 1.09/1.25 [454]E(x4541,f30(f2(a1)))+~E(f11(x4542,x4541,a1),f30(f2(a1))) % 1.09/1.25 [455]E(x4551,f30(f2(a1)))+~E(f11(x4551,x4552,a1),f30(f2(a1))) % 1.09/1.25 [469]~P3(x4691,x4692,a1)+E(f20(f15(x4691),x4692),f15(x4691)) % 1.09/1.25 [486]~P68(x4861)+E(f9(f10(x4861),f24(x4862,x4861),x4861),f24(f30(x4862),x4861)) % 1.09/1.25 [487]~P53(x4872)+E(f11(f12(x4871,x4872),f4(x4871,x4872),x4872),x4871) % 1.09/1.25 [546]~P28(x5462)+P4(f13(f4(x5461,x5462),x5462),f2(x5462),x5462) % 1.09/1.25 [586]~P53(x5862)+E(f11(f4(x5861,x5862),f4(x5861,x5862),x5862),f11(x5861,x5861,x5862)) % 1.09/1.25 [588]~P48(x5882)+E(f11(f13(x5881,x5882),f13(x5881,x5882),x5882),f11(x5881,x5881,x5882)) % 1.09/1.25 [640]~P33(x6402)+P3(x6401,f9(x6401,f10(x6402),x6402),x6402) % 1.09/1.25 [711]P3(x7112,x7111,a1)+E(f9(x7111,f3(x7112,x7111,a1),a1),x7112) % 1.09/1.25 [784]~P4(x7841,x7842,a1)+E(f9(x7841,f3(x7842,x7841,a1),a1),x7842) % 1.09/1.25 [785]~P4(x7852,x7851,a1)+E(f3(x7851,f3(x7851,x7852,a1),a1),x7852) % 1.09/1.25 [786]~P4(x7862,x7861,a1)+E(f9(f3(x7861,x7862,a1),x7862,a1),x7861) % 1.09/1.25 [794]~P4(x7942,x7941,a1)+E(f30(f3(x7941,x7942,a1)),f3(f30(x7941),x7942,a1)) % 1.09/1.25 [817]~P3(f2(a1),x8171,a1)+P3(f3(x8171,f30(x8172),a1),x8171,a1) % 1.09/1.25 [919]P4(f30(f2(a1)),x9191,a1)+~P4(f30(f2(a1)),f11(x9192,x9191,a1),a1) % 1.09/1.25 [920]P4(f30(f2(a1)),x9201,a1)+~P4(f30(f2(a1)),f11(x9201,x9202,a1),a1) % 1.09/1.25 [485]~P14(x4851)+E(f11(f13(f10(x4851),x4851),x4852,x4851),f13(x4852,x4851)) % 1.09/1.25 [789]~P34(x7892)+E(f9(x7891,x7891,x7892),f11(f9(f10(x7892),f10(x7892),x7892),x7891,x7892)) % 1.09/1.25 [417]~P5(x4171,x4173)+P5(f20(x4171,x4172),f20(x4173,x4172)) % 1.09/1.25 [418]~P5(x4181,x4183)+P5(f16(x4181,x4182),f16(x4183,x4182)) % 1.09/1.25 [419]~P5(x4192,x4193)+P5(f16(x4191,x4192),f16(x4191,x4193)) % 1.09/1.25 [492]~P11(x4923)+E(f9(x4921,x4922,x4923),f9(x4922,x4921,x4923)) % 1.09/1.25 [494]~P34(x4943)+E(f9(x4941,x4942,x4943),f9(x4942,x4941,x4943)) % 1.09/1.25 [496]~P34(x4963)+E(f11(x4961,x4962,x4963),f11(x4962,x4961,x4963)) % 1.09/1.25 [497]~P8(x4973)+E(f28(x4971,x4972,x4973),f28(x4972,x4971,x4973)) % 1.09/1.25 [498]~P8(x4983)+E(f29(x4981,x4982,x4983),f29(x4982,x4981,x4983)) % 1.09/1.25 [590]E(x5901,x5902)+~E(f9(x5903,x5901,a1),f9(x5903,x5902,a1)) % 1.09/1.25 [591]E(x5911,x5912)+~E(f9(x5911,x5913,a1),f9(x5912,x5913,a1)) % 1.09/1.25 [592]~P8(x5923)+P4(x5921,f28(x5922,x5921,x5923),x5923) % 1.09/1.25 [593]~P8(x5933)+P4(x5931,f28(x5931,x5932,x5933),x5933) % 1.09/1.25 [594]~P34(x5943)+P6(x5941,f11(x5942,x5941,x5943),x5943) % 1.09/1.25 [595]~P34(x5953)+P6(x5951,f11(x5951,x5952,x5953),x5953) % 1.09/1.25 [596]~P42(x5963)+P6(x5961,f11(x5961,x5962,x5963),x5963) % 1.09/1.25 [597]~P8(x5973)+P4(f29(x5971,x5972,x5973),x5972,x5973) % 1.09/1.25 [598]~P8(x5983)+P4(f29(x5981,x5982,x5983),x5981,x5983) % 1.09/1.25 [773]~P4(x7731,x7733,a1)+P4(x7731,f9(x7732,x7733,a1),a1) % 1.09/1.25 [775]~P4(x7751,x7752,a1)+P4(x7751,f9(x7752,x7753,a1),a1) % 1.09/1.25 [777]~P3(x7771,x7773,a1)+P3(x7771,f9(x7772,x7773,a1),a1) % 1.09/1.25 [779]~P3(x7791,x7792,a1)+P3(x7791,f9(x7792,x7793,a1),a1) % 1.09/1.25 [780]~P3(x7801,x7803,a1)+P3(f3(x7801,x7802,a1),x7803,a1) % 1.09/1.25 [852]P4(x8521,x8522,a1)+~P4(f9(x8523,x8521,a1),x8522,a1) % 1.09/1.25 [853]P4(x8531,x8532,a1)+~P4(f9(x8531,x8533,a1),x8532,a1) % 1.09/1.25 [854]P3(x8541,x8542,a1)+~P3(f9(x8541,x8543,a1),x8542,a1) % 1.09/1.25 [883]P4(f11(x8832,x8831,a1),f11(x8833,x8831,a1),a1)+P3(f2(a1),x8831,a1) % 1.09/1.25 [884]P4(f11(x8841,x8842,a1),f11(x8841,x8843,a1),a1)+P3(f2(a1),x8841,a1) % 1.09/1.25 [952]~P4(x9521,x9523,a1)+P4(f9(x9521,x9522,a1),f9(x9523,x9522,a1),a1) % 1.09/1.25 [953]~P4(x9532,x9533,a1)+P4(f9(x9531,x9532,a1),f9(x9531,x9533,a1),a1) % 1.09/1.25 [955]~P4(x9551,x9553,a1)+P4(f11(x9551,x9552,a1),f11(x9553,x9552,a1),a1) % 1.09/1.25 [957]~P4(x9572,x9573,a1)+P4(f11(x9571,x9572,a1),f11(x9571,x9573,a1),a1) % 1.09/1.25 [958]~P4(x9581,x9583,a1)+P4(f3(x9581,x9582,a1),f3(x9583,x9582,a1),a1) % 1.09/1.25 [959]~P4(x9593,x9592,a1)+P4(f3(x9591,x9592,a1),f3(x9591,x9593,a1),a1) % 1.09/1.25 [960]~P3(x9601,x9603,a1)+P3(f9(x9601,x9602,a1),f9(x9603,x9602,a1),a1) % 1.09/1.25 [961]~P3(x9612,x9613,a1)+P3(f9(x9611,x9612,a1),f9(x9611,x9613,a1),a1) % 1.09/1.25 [1079]~P4(f3(x10791,x10793,a1),x10792,a1)+P4(x10791,f9(x10792,x10793,a1),a1) % 1.09/1.25 [1080]~P3(f9(x10801,x10803,a1),x10802,a1)+P3(x10801,f3(x10802,x10803,a1),a1) % 1.09/1.25 [1081]~P4(x10811,f9(x10813,x10812,a1),a1)+P4(f3(x10811,x10812,a1),x10813,a1) % 1.09/1.25 [1082]~P3(x10821,f3(x10823,x10822,a1),a1)+P3(f9(x10821,x10822,a1),x10823,a1) % 1.09/1.25 [1168]P4(x11681,x11682,a1)+~P4(f9(x11683,x11681,a1),f9(x11683,x11682,a1),a1) % 1.09/1.25 [1169]P3(x11691,x11692,a1)+~P3(f9(x11693,x11691,a1),f9(x11693,x11692,a1),a1) % 1.09/1.25 [1170]P3(x11701,x11702,a1)+~P3(f11(x11703,x11701,a1),f11(x11703,x11702,a1),a1) % 1.09/1.25 [1171]P3(x11711,x11712,a1)+~P3(f11(x11711,x11713,a1),f11(x11712,x11713,a1),a1) % 1.09/1.25 [1174]~P3(f11(x11742,x11741,a1),f11(x11743,x11741,a1),a1)+P3(f2(a1),x11741,a1) % 1.09/1.25 [1175]~P3(f11(x11751,x11752,a1),f11(x11751,x11753,a1),a1)+P3(f2(a1),x11751,a1) % 1.09/1.25 [519]~P2(x5191)+P2(f22(x5191,f15(x5192),x5193)) % 1.09/1.25 [532]~P14(x5323)+E(f9(x5321,f13(x5322,x5323),x5323),f3(x5321,x5322,x5323)) % 1.09/1.25 [533]~P24(x5333)+E(f9(x5331,f13(x5332,x5333),x5333),f3(x5331,x5332,x5333)) % 1.09/1.25 [535]~P16(x5353)+E(f9(x5351,f13(x5352,x5353),x5353),f3(x5351,x5352,x5353)) % 1.09/1.25 [536]~P47(x5363)+E(f11(x5361,f7(x5362,x5363),x5363),f8(x5361,x5362,x5363)) % 1.09/1.25 [537]~P24(x5373)+E(f3(x5371,f13(x5372,x5373),x5373),f9(x5371,x5372,x5373)) % 1.09/1.25 [554]~P3(x5542,x5543,a1)+E(f19(x5541,f15(x5542),x5543),f15(x5542)) % 1.09/1.25 [555]~P3(x5551,x5553,a1)+E(f22(f15(x5551),x5552,x5553),f15(x5551)) % 1.09/1.25 [585]~P66(x5852)+E(f11(f13(x5851,x5852),x5853,x5852),f11(x5851,f13(x5853,x5852),x5852)) % 1.09/1.25 [587]~P66(x5872)+E(f11(f13(x5871,x5872),f13(x5873,x5872),x5872),f11(x5871,x5873,x5872)) % 1.09/1.25 [599]~P8(x5993)+E(f28(x5991,f29(x5991,x5992,x5993),x5993),x5991) % 1.09/1.25 [600]~P8(x6003)+E(f29(x6001,f28(x6001,x6002,x6003),x6003),x6001) % 1.09/1.25 [601]~P24(x6013)+E(f9(f3(x6011,x6012,x6013),x6012,x6013),x6011) % 1.09/1.25 [602]~P24(x6023)+E(f3(f9(x6021,x6022,x6023),x6022,x6023),x6021) % 1.09/1.25 [604]~P1(x6043)+E(f6(f5(x6041,x6042,x6043),x6042,x6043),f2(x6043)) % 1.09/1.25 [605]~P1(x6053)+E(f5(f11(x6051,x6052,x6053),x6052,x6053),f2(x6053)) % 1.09/1.25 [606]~P1(x6063)+E(f5(f11(x6061,x6062,x6063),x6061,x6063),f2(x6063)) % 1.09/1.25 [648]~P16(x6483)+E(f13(f3(x6481,x6482,x6483),x6483),f3(x6482,x6481,x6483)) % 1.09/1.25 [657]E(x6571,x6572)+~E(f11(f30(x6573),x6571,a1),f11(f30(x6573),x6572,a1)) % 1.09/1.25 [681]~P16(x6812)+E(f9(f13(x6811,x6812),f9(x6813,x6811,x6812),x6812),x6813) % 1.09/1.25 [682]~P24(x6822)+E(f9(f13(x6821,x6822),f9(x6821,x6823,x6822),x6822),x6823) % 1.09/1.25 [705]~P66(x7053)+E(f11(x7051,f13(x7052,x7053),x7053),f13(f11(x7051,x7052,x7053),x7053)) % 1.09/1.25 [706]~P53(x7062)+E(f31(f4(x7061,x7062),x7063,x7062),f4(f31(x7061,x7063,x7062),x7062)) % 1.09/1.25 [707]~P66(x7072)+E(f11(f13(x7071,x7072),x7073,x7072),f13(f11(x7071,x7073,x7072),x7072)) % 1.09/1.25 [708]~P47(x7082)+E(f8(f13(x7081,x7082),x7083,x7082),f13(f8(x7081,x7083,x7082),x7082)) % 1.09/1.25 [736]P3(x7362,x7363,a1)+E(f19(x7361,f15(x7362),x7363),f15(f9(x7362,x7361,a1))) % 1.09/1.25 [738]~P19(x7383)+E(f11(x7381,f11(x7381,x7382,x7383),x7383),f11(x7381,x7382,x7383)) % 1.09/1.25 [739]~P8(x7393)+E(f28(x7391,f28(x7391,x7392,x7393),x7393),f28(x7391,x7392,x7393)) % 1.09/1.25 [740]~P8(x7403)+E(f29(x7401,f29(x7401,x7402,x7403),x7403),f29(x7401,x7402,x7403)) % 1.09/1.25 [741]~P1(x7413)+E(f5(f9(x7411,x7412,x7413),x7412,x7413),f5(x7411,x7412,x7413)) % 1.09/1.25 [742]~P1(x7423)+E(f5(f9(x7421,x7422,x7423),x7421,x7423),f5(x7422,x7421,x7423)) % 1.09/1.25 [743]~P1(x7433)+E(f5(f5(x7431,x7432,x7433),x7432,x7433),f5(x7431,x7432,x7433)) % 1.09/1.25 [744]~P53(x7441)+P4(f2(x7441),f31(f4(x7442,x7441),x7443,x7441),x7441) % 1.09/1.25 [750]~P35(x7503)+E(f11(x7501,f31(x7501,x7502,x7503),x7503),f31(x7501,f30(x7502),x7503)) % 1.09/1.25 [751]~P22(x7513)+E(f11(f31(x7511,x7512,x7513),x7511,x7513),f31(x7511,f30(x7512),x7513)) % 1.09/1.25 [752]~P34(x7523)+E(f11(x7521,f31(x7521,x7522,x7523),x7523),f31(x7521,f30(x7522),x7523)) % 1.09/1.25 [753]~P34(x7533)+E(f11(f31(x7531,x7532,x7533),x7531,x7533),f31(x7531,f30(x7532),x7533)) % 1.09/1.25 [756]~P68(x7562)+E(f9(f24(x7561,x7562),f24(x7563,x7562),x7562),f24(f9(x7561,x7563,a1),x7562)) % 1.09/1.25 [757]~P68(x7572)+E(f11(f24(x7571,x7572),f24(x7573,x7572),x7572),f24(f11(x7571,x7573,a1),x7572)) % 1.09/1.25 [758]~P53(x7582)+E(f11(f4(x7581,x7582),f4(x7583,x7582),x7582),f4(f11(x7581,x7583,x7582),x7582)) % 1.09/1.25 [759]~P24(x7592)+E(f9(f13(x7591,x7592),f13(x7593,x7592),x7592),f13(f9(x7593,x7591,x7592),x7592)) % 1.09/1.25 [760]~P16(x7602)+E(f9(f13(x7601,x7602),f13(x7603,x7602),x7602),f13(f9(x7601,x7603,x7602),x7602)) % 1.09/1.25 [761]~P53(x7612)+E(f11(f12(x7611,x7612),f12(x7613,x7612),x7612),f12(f11(x7611,x7613,x7612),x7612)) % 1.09/1.25 [792]~P28(x7923)+E(f4(f3(x7921,x7922,x7923),x7923),f4(f3(x7922,x7921,x7923),x7923)) % 1.09/1.25 [850]~P48(x8502)+P6(f11(x8501,f2(x8502),x8502),f11(x8503,f2(x8502),x8502),x8502) % 1.09/1.25 [851]~P48(x8511)+P6(f11(f2(x8511),x8512,x8511),f11(f2(x8511),x8513,x8511),x8511) % 1.09/1.25 [914]~P22(x9143)+E(f11(f31(x9141,x9142,x9143),x9141,x9143),f11(x9141,f31(x9141,x9142,x9143),x9143)) % 1.09/1.25 [1025]~P3(x10252,x10253,a1)+P3(f11(f30(x10251),x10252,a1),f11(f30(x10251),x10253,a1),a1) % 1.09/1.25 [1056]~P4(x10562,x10563,a1)+E(f3(f9(x10561,x10562,a1),x10563,a1),f3(x10561,f3(x10563,x10562,a1),a1)) % 1.09/1.25 [1057]~P4(x10573,x10572,a1)+E(f3(f9(x10571,x10572,a1),x10573,a1),f9(x10571,f3(x10572,x10573,a1),a1)) % 1.09/1.25 [1059]~P4(x10593,x10591,a1)+E(f3(f9(x10591,x10592,a1),x10593,a1),f9(f3(x10591,x10593,a1),x10592,a1)) % 1.09/1.25 [1096]~P67(x10961)+E(f11(f31(f13(f10(x10961),x10961),x10962,x10961),f31(x10963,x10962,x10961),x10961),f31(f13(x10963,x10961),x10962,x10961)) % 1.09/1.25 [1135]~P4(x11353,x11352,a1)+P4(x11351,f3(f9(x11352,x11351,a1),x11353,a1),a1) % 1.09/1.25 [1189]~P1(x11893)+E(f9(f11(x11891,f6(x11892,x11891,x11893),x11893),f5(x11892,x11891,x11893),x11893),x11892) % 1.09/1.25 [1190]~P1(x11903)+E(f9(f11(f6(x11901,x11902,x11903),x11902,x11903),f5(x11901,x11902,x11903),x11903),x11901) % 1.09/1.25 [1192]P4(x11921,x11922,a1)+~P4(f11(f30(x11923),x11921,a1),f11(f30(x11923),x11922,a1),a1) % 1.09/1.25 [1196]~P28(x11963)+P4(f4(f9(x11961,x11962,x11963),x11963),f9(f4(x11961,x11963),f4(x11962,x11963),x11963),x11963) % 1.09/1.25 [1197]~P49(x11973)+P4(f4(f11(x11971,x11972,x11973),x11973),f11(f4(x11971,x11973),f4(x11972,x11973),x11973),x11973) % 1.09/1.25 [1198]~P28(x11983)+P4(f4(f3(x11981,x11982,x11983),x11983),f9(f4(x11981,x11983),f4(x11982,x11983),x11983),x11983) % 1.09/1.25 [1199]~P28(x11992)+P4(f3(f4(x11991,x11992),f4(x11993,x11992),x11992),f4(f3(x11991,x11993,x11992),x11992),x11992) % 1.09/1.25 [1288]~P55(x12881)+P4(f2(x12881),f9(f11(x12882,x12882,x12881),f11(x12883,x12883,x12881),x12881),x12881) % 1.09/1.25 [1343]~P55(x13431)+~P3(f9(f11(x13432,x13432,x13431),f11(x13433,x13433,x13431),x13431),f2(x13431),x13431) % 1.09/1.25 [735]~P24(x7352)+E(f9(x7351,f9(f13(x7351,x7352),x7353,x7352),x7352),x7353) % 1.09/1.25 [855]~P53(x8552)+E(f4(f31(f13(x8551,x8552),x8553,x8552),x8552),f4(f31(x8551,x8553,x8552),x8552)) % 1.09/1.25 [860]~P1(x8601)+E(f6(f11(f2(x8601),x8602,x8601),f11(f2(x8601),x8603,x8601),x8601),f2(x8601)) % 1.09/1.25 [932]~P28(x9322)+E(f4(f9(f4(x9321,x9322),f4(x9323,x9322),x9322),x9322),f9(f4(x9321,x9322),f4(x9323,x9322),x9322)) % 1.09/1.25 [948]~P34(x9483)+E(f9(x9481,f11(x9482,x9481,x9483),x9483),f11(f9(x9482,f10(x9483),x9483),x9481,x9483)) % 1.09/1.25 [949]~P34(x9493)+E(f9(f11(x9491,x9492,x9493),x9492,x9493),f11(f9(x9491,f10(x9493),x9493),x9492,x9493)) % 1.09/1.25 [1041]~P7(x10413)+E(f5(f13(f5(x10411,x10412,x10413),x10413),x10412,x10413),f5(f13(x10411,x10413),x10412,x10413)) % 1.09/1.25 [1188]~P1(x11883)+E(f9(f5(x11881,x11882,x11883),f11(f6(x11881,x11882,x11883),x11882,x11883),x11883),x11881) % 1.09/1.25 [1202]~P4(x12022,x12023,a1)+E(f3(f9(x12021,x12022,a1),f30(x12023),a1),f3(x12021,f30(f3(x12023,x12022,a1)),a1)) % 1.09/1.25 [1203]~P4(x12032,x12031,a1)+E(f3(f30(f3(x12031,x12032,a1)),x12033,a1),f3(f30(x12031),f9(x12032,x12033,a1),a1)) % 1.09/1.25 [1320]~P28(x13202)+P4(f4(f3(f4(x13201,x13202),f4(x13203,x13202),x13202),x13202),f4(f3(x13201,x13203,x13202),x13202),x13202) % 1.09/1.25 [326]E(x3261,x3262)+~E(f16(x3263,x3261),f16(x3264,x3262)) % 1.09/1.25 [327]E(x3271,x3272)+~E(f16(x3271,x3273),f16(x3272,x3274)) % 1.09/1.25 [793]~P5(x7931,x7934)+P5(f22(x7931,x7932,x7933),f22(x7934,x7932,x7933)) % 1.09/1.25 [895]~P34(x8953)+E(f31(f31(x8951,x8952,x8953),x8954,x8953),f31(x8951,f11(x8952,x8954,a1),x8953)) % 1.09/1.25 [896]~P22(x8963)+E(f31(f31(x8961,x8962,x8963),x8964,x8963),f31(x8961,f11(x8962,x8964,a1),x8963)) % 1.09/1.25 [899]~P11(x8994)+E(f9(x8991,f9(x8992,x8993,x8994),x8994),f9(x8992,f9(x8991,x8993,x8994),x8994)) % 1.09/1.25 [900]~P34(x9004)+E(f9(x9001,f9(x9002,x9003,x9004),x9004),f9(x9002,f9(x9001,x9003,x9004),x9004)) % 1.09/1.25 [901]~P16(x9014)+E(f9(x9011,f9(x9012,x9013,x9014),x9014),f9(x9012,f9(x9011,x9013,x9014),x9014)) % 1.09/1.25 [902]~P34(x9024)+E(f11(x9021,f11(x9022,x9023,x9024),x9024),f11(x9022,f11(x9021,x9023,x9024),x9024)) % 1.09/1.25 [903]~P8(x9034)+E(f28(x9031,f28(x9032,x9033,x9034),x9034),f28(x9032,f28(x9031,x9033,x9034),x9034)) % 1.09/1.25 [904]~P8(x9044)+E(f29(x9041,f29(x9042,x9043,x9044),x9044),f29(x9042,f29(x9041,x9043,x9044),x9044)) % 1.09/1.25 [909]~P11(x9093)+E(f9(f9(x9091,x9092,x9093),x9094,x9093),f9(x9091,f9(x9092,x9094,x9093),x9093)) % 1.09/1.25 [910]~P34(x9103)+E(f9(f9(x9101,x9102,x9103),x9104,x9103),f9(x9101,f9(x9102,x9104,x9103),x9103)) % 1.09/1.25 [911]~P15(x9113)+E(f9(f9(x9111,x9112,x9113),x9114,x9113),f9(x9111,f9(x9112,x9114,x9113),x9113)) % 1.09/1.25 [912]~P34(x9123)+E(f11(f11(x9121,x9122,x9123),x9124,x9123),f11(x9121,f11(x9122,x9124,x9123),x9123)) % 1.09/1.25 [913]~P18(x9133)+E(f11(f11(x9131,x9132,x9133),x9134,x9133),f11(x9131,f11(x9132,x9134,x9133),x9133)) % 1.09/1.25 [915]~P8(x9153)+E(f28(f28(x9151,x9152,x9153),x9154,x9153),f28(x9151,f28(x9152,x9154,x9153),x9153)) % 1.09/1.25 [916]~P8(x9163)+E(f29(f29(x9161,x9162,x9163),x9164,x9163),f29(x9161,f29(x9162,x9164,x9163),x9163)) % 1.09/1.25 [917]~P34(x9173)+E(f9(f9(x9171,x9172,x9173),x9174,x9173),f9(f9(x9171,x9174,x9173),x9172,x9173)) % 1.09/1.25 [918]~P34(x9183)+E(f11(f11(x9181,x9182,x9183),x9184,x9183),f11(f11(x9181,x9184,x9183),x9182,x9183)) % 1.09/1.25 [1103]~P22(x11033)+E(f11(f31(x11031,x11032,x11033),f31(x11031,x11034,x11033),x11033),f31(x11031,f9(x11032,x11034,a1),x11033)) % 1.09/1.25 [1104]~P34(x11043)+E(f11(f31(x11041,x11042,x11043),f31(x11041,x11044,x11043),x11043),f31(x11041,f9(x11042,x11044,a1),x11043)) % 1.09/1.25 [1107]~P34(x11073)+E(f9(f11(x11071,x11072,x11073),f11(x11071,x11074,x11073),x11073),f11(x11071,f9(x11072,x11074,x11073),x11073)) % 1.09/1.25 [1108]~P8(x11083)+E(f29(f28(x11081,x11082,x11083),f28(x11081,x11084,x11083),x11083),f28(x11081,f29(x11082,x11084,x11083),x11083)) % 1.09/1.25 [1109]~P8(x11093)+E(f28(f29(x11091,x11092,x11093),f29(x11091,x11094,x11093),x11093),f29(x11091,f28(x11092,x11094,x11093),x11093)) % 1.09/1.25 [1110]~P10(x11103)+E(f28(f9(x11101,x11102,x11103),f9(x11104,x11102,x11103),x11103),f9(f28(x11101,x11104,x11103),x11102,x11103)) % 1.09/1.25 [1111]~P10(x11113)+E(f29(f9(x11111,x11112,x11113),f9(x11114,x11112,x11113),x11113),f9(f29(x11111,x11114,x11113),x11112,x11113)) % 1.09/1.25 [1113]~P38(x11133)+E(f9(f11(x11131,x11132,x11133),f11(x11134,x11132,x11133),x11133),f11(f9(x11131,x11134,x11133),x11132,x11133)) % 1.09/1.25 [1114]~P30(x11143)+E(f28(f3(x11141,x11142,x11143),f3(x11144,x11142,x11143),x11143),f3(f28(x11141,x11144,x11143),x11142,x11143)) % 1.09/1.25 [1115]~P30(x11153)+E(f29(f3(x11151,x11152,x11153),f3(x11154,x11152,x11153),x11153),f3(f29(x11151,x11154,x11153),x11152,x11153)) % 1.09/1.25 [1116]~P8(x11163)+E(f29(f28(x11161,x11162,x11163),f28(x11164,x11162,x11163),x11163),f28(f29(x11161,x11164,x11163),x11162,x11163)) % 1.09/1.25 [1117]~P8(x11173)+E(f28(f29(x11171,x11172,x11173),f29(x11174,x11172,x11173),x11173),f29(f28(x11171,x11174,x11173),x11172,x11173)) % 1.09/1.25 [1118]~P34(x11183)+E(f11(f31(x11181,x11182,x11183),f31(x11184,x11182,x11183),x11183),f31(f11(x11181,x11184,x11183),x11182,x11183)) % 1.09/1.25 [1119]~P21(x11193)+E(f11(f31(x11191,x11192,x11193),f31(x11194,x11192,x11193),x11193),f31(f11(x11191,x11194,x11193),x11192,x11193)) % 1.09/1.25 [1120]~P47(x11203)+E(f9(f8(x11201,x11202,x11203),f8(x11204,x11202,x11203),x11203),f8(f9(x11201,x11204,x11203),x11202,x11203)) % 1.09/1.25 [1121]~P47(x11213)+E(f3(f8(x11211,x11212,x11213),f8(x11214,x11212,x11213),x11213),f8(f3(x11211,x11214,x11213),x11212,x11213)) % 1.09/1.25 [1122]~P1(x11223)+E(f5(f11(x11221,x11222,x11223),f11(x11221,x11224,x11223),x11223),f11(x11221,f5(x11222,x11224,x11223),x11223)) % 1.09/1.25 [1123]~P34(x11233)+E(f9(f11(x11231,x11232,x11233),f11(x11234,x11232,x11233),x11233),f11(f9(x11231,x11234,x11233),x11232,x11233)) % 1.09/1.25 [1124]~P1(x11243)+E(f5(f11(x11241,x11242,x11243),f11(x11244,x11242,x11243),x11243),f11(f5(x11241,x11244,x11243),x11242,x11243)) % 1.09/1.25 [1339]~P8(x13394)+P4(f28(x13391,f29(x13392,x13393,x13394),x13394),f29(f28(x13391,x13392,x13394),f28(x13391,x13393,x13394),x13394),x13394) % 1.09/1.25 [1340]~P8(x13403)+P4(f28(f29(x13401,x13402,x13403),f29(x13401,x13404,x13403),x13403),f29(x13401,f28(x13402,x13404,x13403),x13403),x13403) % 1.09/1.25 [1105]~P1(x11054)+E(f5(f9(x11051,f11(x11052,x11053,x11054),x11054),x11053,x11054),f5(x11051,x11053,x11054)) % 1.09/1.25 [1106]~P1(x11064)+E(f5(f9(x11061,f11(x11062,x11063,x11064),x11064),x11062,x11064),f5(x11061,x11062,x11064)) % 1.09/1.25 [1223]~P1(x12234)+E(f5(f11(x12231,f5(x12232,x12233,x12234),x12234),x12233,x12234),f5(f11(x12231,x12232,x12234),x12233,x12234)) % 1.09/1.25 [1224]~P7(x12244)+E(f5(f3(x12241,f5(x12242,x12243,x12244),x12244),x12243,x12244),f5(f3(x12241,x12242,x12244),x12243,x12244)) % 1.09/1.25 [1227]~P7(x12273)+E(f5(f3(f5(x12271,x12272,x12273),x12274,x12273),x12272,x12273),f5(f3(x12271,x12274,x12273),x12272,x12273)) % 1.09/1.25 [1228]~P1(x12284)+E(f5(f9(x12281,f5(x12282,x12283,x12284),x12284),x12283,x12284),f5(f9(x12281,x12282,x12284),x12283,x12284)) % 1.09/1.25 [1229]~P1(x12293)+E(f5(f9(f5(x12291,x12292,x12293),x12294,x12293),x12292,x12293),f5(f9(x12291,x12294,x12293),x12292,x12293)) % 1.09/1.25 [1230]~P1(x12303)+E(f5(f11(f5(x12301,x12302,x12303),x12304,x12303),x12302,x12303),f5(f11(x12301,x12304,x12303),x12302,x12303)) % 1.09/1.25 [1321]~P1(x13213)+E(f5(f9(f5(x13211,x13212,x13213),f5(x13214,x13212,x13213),x13213),x13212,x13213),f5(f9(x13211,x13214,x13213),x13212,x13213)) % 1.09/1.25 [1322]~P1(x13223)+E(f5(f11(f5(x13221,x13222,x13223),f5(x13224,x13222,x13223),x13223),x13222,x13223),f5(f11(x13221,x13224,x13223),x13222,x13223)) % 1.09/1.25 [1323]~P7(x13233)+E(f5(f3(f5(x13231,x13232,x13233),f5(x13234,x13232,x13233),x13233),x13232,x13233),f5(f3(x13231,x13234,x13233),x13232,x13233)) % 1.09/1.25 [1348]~P1(x13483)+E(f9(f9(f11(x13481,f6(x13482,x13481,x13483),x13483),f5(x13482,x13481,x13483),x13483),x13484,x13483),f9(x13482,x13484,x13483)) % 1.09/1.25 [1349]~P1(x13493)+E(f9(f9(f11(f6(x13491,x13492,x13493),x13492,x13493),f5(x13491,x13492,x13493),x13493),x13494,x13493),f9(x13491,x13494,x13493)) % 1.09/1.25 [1354]~P4(x13541,x13543,a1)+E(f9(f11(x13541,x13542,a1),f9(f11(f3(x13543,x13541,a1),x13542,a1),x13544,a1),a1),f9(f11(x13543,x13542,a1),x13544,a1)) % 1.09/1.25 [611]E(x6111,x6112)+~E(f23(x6111,x6113,x6114),f23(x6112,x6115,x6114)) % 1.09/1.25 [1231]~P34(x12313)+E(f9(f9(x12311,x12312,x12313),f9(x12314,x12315,x12313),x12313),f9(f9(x12311,x12314,x12313),f9(x12312,x12315,x12313),x12313)) % 1.09/1.25 [1232]~P34(x12323)+E(f11(f11(x12321,x12322,x12323),f11(x12324,x12325,x12323),x12323),f11(f11(x12321,x12324,x12323),f11(x12322,x12325,x12323),x12323)) % 1.09/1.25 [1336]~P59(x13363)+E(f9(f11(x13361,x13362,x13363),f9(f11(x13364,x13362,x13363),x13365,x13363),x13363),f9(f11(f9(x13361,x13364,x13363),x13362,x13363),x13365,x13363)) % 1.09/1.25 [1375]~P28(x13753)+P4(f4(f3(f9(x13751,x13752,x13753),f9(x13754,x13755,x13753),x13753),x13753),f9(f4(f3(x13751,x13754,x13753),x13753),f4(f3(x13752,x13755,x13753),x13753),x13753),x13753) % 1.09/1.25 [1351]~P66(x13513)+E(f9(f11(x13511,x13512,x13513),f9(f11(f3(x13514,x13511,x13513),x13512,x13513),x13515,x13513),x13513),f9(f11(x13514,x13512,x13513),x13515,x13513)) % 1.09/1.25 [1357]~P4(x13571,x13574,a1)+E(f3(f9(f11(x13571,x13572,a1),x13573,a1),f9(f11(x13574,x13572,a1),x13575,a1),a1),f3(x13573,f9(f11(f3(x13574,x13571,a1),x13572,a1),x13575,a1),a1)) % 1.09/1.25 [1358]~P4(x13584,x13581,a1)+E(f3(f9(f11(x13581,x13582,a1),x13583,a1),f9(f11(x13584,x13582,a1),x13585,a1),a1),f3(f9(f11(f3(x13581,x13584,a1),x13582,a1),x13583,a1),x13585,a1)) % 1.09/1.25 [320]~P43(x3201)+~P47(x3201)+E(f7(f10(x3201),x3201),f10(x3201)) % 1.09/1.25 [650]~P31(x6501)+~P4(f2(x6501),f2(x6501),x6501)+E(f9(f2(x6501),f2(x6501),x6501),f2(x6501)) % 1.09/1.25 [473]E(x4731,x4732)+P3(x4732,x4731,a1)+P3(x4731,x4732,a1) % 1.09/1.25 [530]E(x5301,x5302)+P3(x5301,x5302,a1)+~P4(x5301,x5302,a1) % 1.09/1.25 [603]E(x6031,x6032)+~P4(x6032,x6031,a1)+~P4(x6031,x6032,a1) % 1.09/1.25 [317]~P29(x3172)+~E(f13(x3171,x3172),x3171)+E(x3171,f2(x3172)) % 1.09/1.25 [321]~P28(x3212)+~E(f4(x3211,x3212),f2(x3212))+E(x3211,f2(x3212)) % 1.09/1.25 [322]~P24(x3222)+~E(f13(x3221,x3222),f2(x3222))+E(x3221,f2(x3222)) % 1.09/1.25 [323]~P44(x3232)+~E(f7(x3231,x3232),f2(x3232))+E(x3231,f2(x3232)) % 1.09/1.25 [324]~P53(x3242)+~E(f12(x3241,x3242),f2(x3242))+E(x3241,f2(x3242)) % 1.09/1.25 [325]~P24(x3251)+~E(f13(x3252,x3251),f2(x3251))+E(f2(x3251),x3252) % 1.09/1.25 [381]~P1(x3812)+E(f6(x3811,x3811,x3812),f10(x3812))+E(x3811,f2(x3812)) % 1.09/1.25 [383]~P47(x3832)+E(f8(x3831,x3831,x3832),f10(x3832))+E(x3831,f2(x3832)) % 1.09/1.25 [397]~P48(x3972)+~P14(x3972)+E(f3(x3971,x3971,x3972),f2(x3972)) % 1.09/1.25 [410]~P39(x4102)+P3(x4101,f2(x4102),x4102)+E(f4(x4101,x4102),x4101) % 1.09/1.25 [428]~P25(x4281)+P4(f2(x4281),x4282,x4281)+~E(f26(x4282,x4281),x4282) % 1.09/1.25 [441]E(x4411,f2(a1))+E(x4412,f2(a1))+~E(f11(x4412,x4411,a1),f2(a1)) % 1.09/1.25 [442]~P25(x4422)+P4(x4421,f2(x4422),x4422)+~E(f26(x4421,x4422),f2(x4422)) % 1.09/1.25 [443]~P53(x4431)+P3(f2(x4431),x4432,x4431)+~E(f12(x4432,x4431),f10(x4431)) % 1.09/1.25 [448]~P28(x4482)+P3(f2(x4482),f4(x4481,x4482),x4482)+E(x4481,f2(x4482)) % 1.09/1.25 [456]~P25(x4562)+~E(f9(x4561,x4561,x4562),f2(x4562))+E(x4561,f2(x4562)) % 1.09/1.25 [470]~P34(x4702)+~P6(f2(x4702),x4701,x4702)+E(x4701,f2(x4702)) % 1.09/1.25 [504]~P28(x5042)+~P4(f2(x5042),x5041,x5042)+E(f4(x5041,x5042),x5041) % 1.09/1.25 [505]~P28(x5052)+~P3(f2(x5052),x5051,x5052)+E(f4(x5051,x5052),x5051) % 1.09/1.25 [506]~P25(x5062)+~P4(f2(x5062),x5061,x5062)+E(f26(x5061,x5062),x5061) % 1.09/1.25 [513]~P25(x5132)+~P4(x5131,f2(x5132),x5132)+E(f26(x5131,x5132),f2(x5132)) % 1.09/1.25 [514]~P53(x5142)+~P3(f2(x5142),x5141,x5142)+E(f12(x5141,x5142),f10(x5142)) % 1.09/1.25 [520]~P28(x5202)+~P4(x5201,f2(x5202),x5202)+E(f4(x5201,x5202),f13(x5201,x5202)) % 1.09/1.25 [521]~P28(x5212)+~P3(x5211,f2(x5212),x5212)+E(f4(x5211,x5212),f13(x5211,x5212)) % 1.09/1.25 [522]~P39(x5222)+~P3(x5221,f2(x5222),x5222)+E(f4(x5221,x5222),f13(x5221,x5222)) % 1.09/1.25 [556]~P3(x5561,x5562,a1)+E(f30(x5561),x5562)+P3(f30(x5561),x5562,a1) % 1.09/1.25 [557]E(x5571,x5572)+P3(x5572,x5571,a1)+~P3(x5572,f30(x5571),a1) % 1.09/1.25 [559]E(x5591,x5592)+P3(x5591,x5592,a1)+~P3(x5591,f30(x5592),a1) % 1.09/1.25 [564]~P28(x5642)+~P4(f4(x5641,x5642),f2(x5642),x5642)+E(x5641,f2(x5642)) % 1.09/1.25 [579]P4(x5791,x5792,a1)+E(x5791,f30(x5792))+~P4(x5791,f30(x5792),a1) % 1.09/1.25 [622]E(x6221,x6222)+~E(f3(x6222,x6221,a1),f2(a1))+~E(f3(x6221,x6222,a1),f2(a1)) % 1.09/1.25 [626]E(x6261,x6262)+~P4(x6262,x6261,a1)+~P3(x6261,f30(x6262),a1) % 1.09/1.25 [649]~P33(x6491)+P3(f2(x6491),f24(x6492,x6491),x6491)+~P3(f2(a1),x6492,a1) % 1.09/1.25 [651]~P25(x6512)+~P4(x6511,f2(x6512),x6512)+P4(x6511,f13(x6511,x6512),x6512) % 1.09/1.25 [652]~P29(x6522)+~P4(x6521,f2(x6522),x6522)+P4(x6521,f13(x6521,x6522),x6522) % 1.09/1.25 [653]~P53(x6532)+~P3(x6531,f2(x6532),x6532)+P3(x6531,f13(x6531,x6532),x6532) % 1.09/1.25 [654]~P25(x6542)+~P4(f2(x6542),x6541,x6542)+P4(f13(x6541,x6542),x6541,x6542) % 1.09/1.25 [655]~P29(x6552)+~P4(f2(x6552),x6551,x6552)+P4(f13(x6551,x6552),x6551,x6552) % 1.09/1.25 [666]~P30(x6661)+~P4(x6662,f2(x6661),x6661)+P4(f2(x6661),f13(x6662,x6661),x6661) % 1.09/1.25 [667]~P30(x6671)+~P3(x6672,f2(x6671),x6671)+P3(f2(x6671),f13(x6672,x6671),x6671) % 1.09/1.25 [668]~P54(x6681)+~P3(f2(x6681),x6682,x6681)+P3(f2(x6681),f7(x6682,x6681),x6681) % 1.09/1.25 [669]~P53(x6691)+~P3(f2(x6691),x6692,x6691)+P3(f2(x6691),f12(x6692,x6691),x6691) % 1.09/1.25 [670]~P54(x6702)+~P3(x6701,f2(x6702),x6702)+P3(f7(x6701,x6702),f2(x6702),x6702) % 1.09/1.25 [671]~P53(x6712)+~P3(x6711,f2(x6712),x6712)+P3(f12(x6711,x6712),f2(x6712),x6712) % 1.09/1.25 [672]~P30(x6722)+~P4(f2(x6722),x6721,x6722)+P4(f13(x6721,x6722),f2(x6722),x6722) % 1.09/1.25 [673]~P30(x6732)+~P3(f2(x6732),x6731,x6732)+P3(f13(x6731,x6732),f2(x6732),x6732) % 1.09/1.25 [676]~P25(x6762)+~P4(x6761,f13(x6761,x6762),x6762)+P4(x6761,f2(x6762),x6762) % 1.09/1.25 [677]~P29(x6772)+~P4(x6771,f13(x6771,x6772),x6772)+P4(x6771,f2(x6772),x6772) % 1.09/1.25 [678]~P53(x6782)+~P3(x6781,f13(x6781,x6782),x6782)+P3(x6781,f2(x6782),x6782) % 1.09/1.25 [679]~P25(x6791)+~P4(f13(x6792,x6791),x6792,x6791)+P4(f2(x6791),x6792,x6791) % 1.09/1.25 [680]~P29(x6801)+~P4(f13(x6802,x6801),x6802,x6801)+P4(f2(x6801),x6802,x6801) % 1.09/1.25 [697]~P33(x6972)+~P3(f2(x6972),f24(x6971,x6972),x6972)+P3(f2(a1),x6971,a1) % 1.09/1.25 [699]~P30(x6992)+~P4(f2(x6992),f13(x6991,x6992),x6992)+P4(x6991,f2(x6992),x6992) % 1.09/1.25 [700]~P30(x7002)+~P3(f2(x7002),f13(x7001,x7002),x7002)+P3(x7001,f2(x7002),x7002) % 1.09/1.25 [701]~P53(x7012)+~P3(f12(x7011,x7012),f2(x7012),x7012)+P3(x7011,f2(x7012),x7012) % 1.09/1.25 [702]~P53(x7021)+~P3(f2(x7021),f12(x7022,x7021),x7021)+P3(f2(x7021),x7022,x7021) % 1.09/1.25 [703]~P30(x7031)+~P4(f13(x7032,x7031),f2(x7031),x7031)+P4(f2(x7031),x7032,x7031) % 1.09/1.25 [704]~P30(x7041)+~P3(f13(x7042,x7041),f2(x7041),x7041)+P3(f2(x7041),x7042,x7041) % 1.09/1.25 [820]~P25(x8201)+~P4(f2(x8201),x8202,x8201)+P4(f2(x8201),f9(x8202,x8202,x8201),x8201) % 1.09/1.25 [823]~P25(x8231)+~P3(f2(x8231),x8232,x8231)+P3(f2(x8231),f9(x8232,x8232,x8231),x8231) % 1.09/1.25 [825]~P25(x8252)+~P4(x8251,f2(x8252),x8252)+P4(f9(x8251,x8251,x8252),f2(x8252),x8252) % 1.09/1.25 [826]~P25(x8262)+~P3(x8261,f2(x8262),x8262)+P3(f9(x8261,x8261,x8262),f2(x8262),x8262) % 1.09/1.25 [827]~P53(x8272)+~P3(x8271,f2(x8272),x8272)+P3(f9(x8271,x8271,x8272),f2(x8272),x8272) % 1.09/1.25 [921]~P25(x9212)+~P4(f9(x9211,x9211,x9212),f2(x9212),x9212)+P4(x9211,f2(x9212),x9212) % 1.09/1.25 [922]~P25(x9222)+~P3(f9(x9221,x9221,x9222),f2(x9222),x9222)+P3(x9221,f2(x9222),x9222) % 1.09/1.25 [923]~P53(x9232)+~P3(f9(x9231,x9231,x9232),f2(x9232),x9232)+P3(x9231,f2(x9232),x9232) % 1.09/1.25 [924]~P25(x9241)+~P4(f2(x9241),f9(x9242,x9242,x9241),x9241)+P4(f2(x9241),x9242,x9241) % 1.09/1.25 [925]~P25(x9251)+~P3(f2(x9251),f9(x9252,x9252,x9251),x9251)+P3(f2(x9251),x9252,x9251) % 1.09/1.25 [926]P3(f3(x9261,x9262,a1),x9261,a1)+~P3(f2(a1),x9262,a1)+~P3(f2(a1),x9261,a1) % 1.09/1.25 [931]~P3(f2(a1),x9312,a1)+~P3(f2(a1),x9311,a1)+P3(f2(a1),f11(x9311,x9312,a1),a1) % 1.09/1.25 [988]P3(f2(a1),x9881,a1)+P3(f2(a1),x9882,a1)+~P3(f2(a1),f9(x9881,x9882,a1),a1) % 1.09/1.25 [337]~P44(x3372)+E(x3371,f2(x3372))+E(f7(f7(x3371,x3372),x3372),x3371) % 1.09/1.25 [341]~P43(x3412)+~P44(x3412)+E(f7(f7(x3411,x3412),x3412),x3411) % 1.09/1.25 [400]~P48(x4002)+~P14(x4002)+E(f9(x4001,f2(x4002),x4002),x4001) % 1.09/1.25 [405]~P43(x4052)+~P47(x4052)+E(f8(x4051,f2(x4052),x4052),f2(x4052)) % 1.09/1.25 [411]~P58(x4111)+~P35(x4111)+E(f31(f2(x4111),f30(x4112),x4111),f2(x4111)) % 1.09/1.25 [430]~P54(x4302)+E(x4301,f2(x4302))+E(f7(f4(x4301,x4302),x4302),f4(f7(x4301,x4302),x4302)) % 1.09/1.25 [431]~P44(x4312)+E(x4311,f2(x4312))+E(f7(f13(x4311,x4312),x4312),f13(f7(x4311,x4312),x4312)) % 1.09/1.25 [439]~P54(x4392)+~P43(x4392)+E(f7(f4(x4391,x4392),x4392),f4(f7(x4391,x4392),x4392)) % 1.09/1.25 [440]~P43(x4402)+~P44(x4402)+E(f7(f13(x4401,x4402),x4402),f13(f7(x4401,x4402),x4402)) % 1.09/1.25 [444]~P44(x4442)+E(x4441,f2(x4442))+E(f11(x4441,f7(x4441,x4442),x4442),f10(x4442)) % 1.09/1.25 [445]~P47(x4452)+E(x4451,f2(x4452))+E(f11(f7(x4451,x4452),x4451,x4452),f10(x4452)) % 1.09/1.25 [446]~P44(x4462)+E(x4461,f2(x4462))+E(f11(f7(x4461,x4462),x4461,x4462),f10(x4462)) % 1.09/1.25 [453]E(x4531,f2(a1))+E(x4532,f2(a1))+~E(f9(x4532,x4531,a1),f30(f2(a1))) % 1.09/1.25 [464]E(x4641,f2(a1))+E(x4641,f30(f2(a1)))+~E(f9(x4642,x4641,a1),f30(f2(a1))) % 1.09/1.25 [465]E(x4651,f2(a1))+E(x4651,f30(f2(a1)))+~E(f9(x4651,x4652,a1),f30(f2(a1))) % 1.09/1.25 [478]E(x4781,f30(f2(a1)))+E(x4782,f30(f2(a1)))+~E(f9(x4782,x4781,a1),f30(f2(a1))) % 1.09/1.25 [515]~P53(x5152)+P3(x5151,f2(x5152),x5152)+~E(f12(x5151,x5152),f13(f10(x5152),x5152)) % 1.09/1.25 [525]~P53(x5252)+~P3(x5251,f2(x5252),x5252)+E(f12(x5251,x5252),f13(f10(x5252),x5252)) % 1.09/1.25 [986]P3(x9861,f11(x9862,x9861,a1),a1)+~P3(f30(f2(a1)),x9862,a1)+~P3(f30(f2(a1)),x9861,a1) % 1.09/1.25 [987]P3(x9871,f11(x9871,x9872,a1),a1)+~P3(f30(f2(a1)),x9872,a1)+~P3(f30(f2(a1)),x9871,a1) % 1.09/1.25 [1038]~P4(f30(f2(a1)),x10382,a1)+~P4(f30(f2(a1)),x10381,a1)+P4(f30(f2(a1)),f11(x10381,x10382,a1),a1) % 1.09/1.25 [1039]~P3(f30(f2(a1)),x10392,a1)+~P3(f30(f2(a1)),x10391,a1)+P3(f30(f2(a1)),f11(x10391,x10392,a1),a1) % 1.09/1.25 [675]~P43(x6751)+~P47(x6751)+E(f8(f11(f2(x6751),x6752,x6751),x6752,x6751),f2(x6751)) % 1.09/1.25 [499]P4(x4992,x4991,x4993)+~P8(x4993)+P4(x4991,x4992,x4993) % 1.09/1.25 [502]P3(x5022,x5021,x5023)+~P8(x5023)+P4(x5021,x5022,x5023) % 1.09/1.25 [552]~P36(x5523)+~P3(x5521,x5522,x5523)+P4(x5521,x5522,x5523) % 1.09/1.25 [553]~P37(x5533)+~P3(x5531,x5532,x5533)+P4(x5531,x5532,x5533) % 1.09/1.25 [628]~P3(x6283,x6282,x6281)+~P8(x6281)+~P4(x6282,x6283,x6281) % 1.09/1.25 [630]~P3(x6303,x6302,x6301)+~P8(x6301)+~P3(x6302,x6303,x6301) % 1.09/1.25 [631]~P3(x6313,x6312,x6311)+~P36(x6311)+~P4(x6312,x6313,x6311) % 1.09/1.25 [633]~P3(x6333,x6332,x6331)+~P36(x6331)+~P3(x6332,x6333,x6331) % 1.09/1.25 [634]~P3(x6343,x6342,x6341)+~P37(x6341)+~P3(x6342,x6343,x6341) % 1.09/1.25 [734]~P4(x7341,x7343,a1)+P4(x7341,x7342,a1)+~P4(x7343,x7342,a1) % 1.09/1.25 [338]~P24(x3383)+E(x3381,x3382)+~E(f13(x3381,x3383),f13(x3382,x3383)) % 1.09/1.25 [339]~P13(x3393)+E(x3391,x3392)+~E(f13(x3391,x3393),f13(x3392,x3393)) % 1.09/1.25 [340]~P12(x3403)+E(x3401,x3402)+~E(f24(x3401,x3403),f24(x3402,x3403)) % 1.09/1.25 [450]~P24(x4503)+E(x4501,x4502)+~E(f3(x4501,x4502,x4503),f2(x4503)) % 1.09/1.25 [451]~P16(x4513)+E(x4511,x4512)+~E(f3(x4511,x4512,x4513),f2(x4513)) % 1.09/1.25 [457]~P65(x4572)+~E(f31(x4571,x4573,x4572),f2(x4572))+E(x4571,f2(x4572)) % 1.09/1.25 [459]~P53(x4593)+P6(x4591,x4592,x4593)+~E(f4(x4591,x4593),f4(x4592,x4593)) % 1.09/1.25 [488]~P24(x4883)+~E(f9(x4881,x4882,x4883),f2(x4883))+E(x4881,f13(x4882,x4883)) % 1.09/1.25 [489]~P24(x4892)+~E(f9(x4891,x4893,x4892),f2(x4892))+E(f13(x4891,x4892),x4893) % 1.09/1.25 [490]~P44(x4902)+~E(f11(x4901,x4903,x4902),f10(x4902))+E(f7(x4901,x4902),x4903) % 1.09/1.25 [560]~P8(x5603)+~P4(x5601,x5602,x5603)+E(f28(x5601,x5602,x5603),x5602) % 1.09/1.25 [561]~P8(x5613)+~P4(x5612,x5611,x5613)+E(f28(x5611,x5612,x5613),x5611) % 1.09/1.25 [562]~P8(x5623)+~P4(x5622,x5621,x5623)+E(f29(x5621,x5622,x5623),x5622) % 1.09/1.25 [563]~P8(x5633)+~P4(x5631,x5632,x5633)+E(f29(x5631,x5632,x5633),x5631) % 1.09/1.25 [569]~P8(x5693)+P4(x5691,x5692,x5693)+~E(f28(x5691,x5692,x5693),x5692) % 1.09/1.25 [570]~P8(x5703)+P4(x5701,x5702,x5703)+~E(f29(x5701,x5702,x5703),x5701) % 1.09/1.25 [580]~P1(x5803)+~P6(x5802,x5801,x5803)+E(f5(x5801,x5802,x5803),f2(x5803)) % 1.09/1.25 [581]~P1(x5813)+P6(x5811,x5812,x5813)+~E(f5(x5812,x5811,x5813),f2(x5813)) % 1.09/1.25 [608]E(x6081,x6082)+~E(f11(x6083,x6081,a1),f11(x6083,x6082,a1))+E(x6083,f2(a1)) % 1.09/1.25 [609]E(x6091,x6092)+~E(f11(x6091,x6093,a1),f11(x6092,x6093,a1))+E(x6093,f2(a1)) % 1.09/1.25 [612]~P53(x6123)+~P6(x6121,x6122,x6123)+P6(x6121,f4(x6122,x6123),x6123) % 1.09/1.25 [613]~P40(x6133)+~P6(x6131,x6132,x6133)+P6(x6131,f13(x6132,x6133),x6133) % 1.09/1.25 [614]~P53(x6142)+~P6(x6141,x6143,x6142)+P6(f4(x6141,x6142),x6143,x6142) % 1.09/1.25 [615]~P40(x6152)+~P6(x6151,x6153,x6152)+P6(f13(x6151,x6152),x6153,x6152) % 1.09/1.25 [659]~P53(x6593)+P6(x6591,x6592,x6593)+~P6(x6591,f4(x6592,x6593),x6593) % 1.09/1.25 [660]~P40(x6603)+P6(x6601,x6602,x6603)+~P6(x6601,f13(x6602,x6603),x6603) % 1.09/1.25 [661]~P28(x6613)+P4(x6611,x6612,x6613)+~P4(f4(x6611,x6613),x6612,x6613) % 1.09/1.25 [662]~P53(x6623)+P6(x6621,x6622,x6623)+~P6(f4(x6621,x6623),x6622,x6623) % 1.09/1.25 [663]~P40(x6633)+P6(x6631,x6632,x6633)+~P6(f13(x6631,x6633),x6632,x6633) % 1.09/1.25 [664]~P53(x6643)+P3(x6641,x6642,x6643)+~P3(f4(x6641,x6643),x6642,x6643) % 1.09/1.25 [692]~P33(x6922)+~P4(x6921,x6923,a1)+P4(f24(x6921,x6922),f24(x6923,x6922),x6922) % 1.09/1.25 [693]~P33(x6932)+~P3(x6931,x6933,a1)+P3(f24(x6931,x6932),f24(x6933,x6932),x6932) % 1.09/1.25 [695]~P30(x6952)+~P4(x6953,x6951,x6952)+P4(f13(x6951,x6952),f13(x6953,x6952),x6952) % 1.09/1.25 [696]~P30(x6962)+~P3(x6963,x6961,x6962)+P3(f13(x6961,x6962),f13(x6963,x6962),x6962) % 1.09/1.25 [723]~P30(x7233)+~P4(x7232,f13(x7231,x7233),x7233)+P4(x7231,f13(x7232,x7233),x7233) % 1.09/1.25 [725]~P30(x7253)+~P3(x7252,f13(x7251,x7253),x7253)+P3(x7251,f13(x7252,x7253),x7253) % 1.09/1.25 [727]~P30(x7272)+~P4(f13(x7273,x7272),x7271,x7272)+P4(f13(x7271,x7272),x7273,x7272) % 1.09/1.25 [728]~P28(x7282)+~P4(f4(x7281,x7282),x7283,x7282)+P4(f13(x7281,x7282),x7283,x7282) % 1.09/1.25 [730]~P30(x7302)+~P3(f13(x7303,x7302),x7301,x7302)+P3(f13(x7301,x7302),x7303,x7302) % 1.09/1.25 [731]~P53(x7312)+~P3(f4(x7311,x7312),x7313,x7312)+P3(f13(x7311,x7312),x7313,x7312) % 1.09/1.25 [745]~P3(x7451,x7453,a1)+~P3(x7453,x7452,a1)+P3(f30(x7451),x7452,a1) % 1.09/1.25 [746]~P33(x7463)+~P4(f24(x7461,x7463),f24(x7462,x7463),x7463)+P4(x7461,x7462,a1) % 1.09/1.25 [747]~P33(x7473)+~P3(f24(x7471,x7473),f24(x7472,x7473),x7473)+P3(x7471,x7472,a1) % 1.09/1.25 [754]~P30(x7543)+P4(x7541,x7542,x7543)+~P4(f13(x7542,x7543),f13(x7541,x7543),x7543) % 1.09/1.25 [755]~P30(x7553)+P3(x7551,x7552,x7553)+~P3(f13(x7552,x7553),f13(x7551,x7553),x7553) % 1.09/1.25 [815]E(x8151,x8152)+~E(f11(x8153,x8151,a1),f11(x8153,x8152,a1))+~P3(f2(a1),x8153,a1) % 1.09/1.25 [816]~P34(x8163)+P6(x8161,f31(x8161,x8162,x8163),x8163)+~P3(f2(a1),x8162,a1) % 1.09/1.25 [818]~P30(x8183)+~P4(x8181,x8182,x8183)+P4(f3(x8181,x8182,x8183),f2(x8183),x8183) % 1.09/1.25 [819]~P30(x8193)+~P3(x8191,x8192,x8193)+P3(f3(x8191,x8192,x8193),f2(x8193),x8193) % 1.09/1.25 [821]~P33(x8211)+~P4(f2(x8211),x8212,x8211)+P4(f2(x8211),f31(x8212,x8213,x8211),x8211) % 1.09/1.25 [822]~P33(x8221)+~P4(f10(x8221),x8222,x8221)+P4(f10(x8221),f31(x8222,x8223,x8221),x8221) % 1.09/1.25 [824]~P33(x8241)+~P3(f2(x8241),x8242,x8241)+P3(f2(x8241),f31(x8242,x8243,x8241),x8241) % 1.09/1.25 [859]~P25(x8593)+~P4(x8591,f13(x8592,x8593),x8593)+P4(f9(x8591,x8592,x8593),f2(x8593),x8593) % 1.09/1.25 [889]~P30(x8893)+P4(x8891,x8892,x8893)+~P4(f3(x8891,x8892,x8893),f2(x8893),x8893) % 1.09/1.25 [890]~P30(x8903)+P3(x8901,x8902,x8903)+~P3(f3(x8901,x8902,x8903),f2(x8903),x8903) % 1.09/1.25 [898]~P4(x8981,x8982,a1)+P3(x8981,f9(x8982,x8983,a1),a1)+~P3(f2(a1),x8983,a1) % 1.09/1.25 [963]~P25(x9633)+~P4(f9(x9631,x9632,x9633),f2(x9633),x9633)+P4(x9631,f13(x9632,x9633),x9633) % 1.09/1.25 [1094]~P4(x10942,x10941,a1)+~P3(x10941,x10943,a1)+P3(f3(x10941,x10942,a1),f3(x10943,x10942,a1),a1) % 1.09/1.25 [1095]~P3(x10953,x10952,a1)+~P3(x10953,x10951,a1)+P3(f3(x10951,x10952,a1),f3(x10951,x10953,a1),a1) % 1.09/1.25 [1099]~P3(x10991,x10993,a1)+P3(f11(x10991,x10992,a1),f11(x10993,x10992,a1),a1)+~P3(f2(a1),x10992,a1) % 1.09/1.25 [1102]~P3(x11022,x11023,a1)+P3(f11(x11021,x11022,a1),f11(x11021,x11023,a1),a1)+~P3(f2(a1),x11021,a1) % 1.09/1.25 [1183]~P4(x11833,x11832,a1)+~P4(f9(x11831,x11833,a1),x11832,a1)+P4(x11831,f3(x11832,x11833,a1),a1) % 1.09/1.25 [1184]~P4(x11842,x11843,a1)+~P4(x11841,f3(x11843,x11842,a1),a1)+P4(f9(x11841,x11842,a1),x11843,a1) % 1.09/1.25 [1248]P4(x12481,x12482,a1)+~P4(f11(x12483,x12481,a1),f11(x12483,x12482,a1),a1)+~P3(f2(a1),x12483,a1) % 1.09/1.25 [1249]P4(x12491,x12492,a1)+~P4(f11(x12491,x12493,a1),f11(x12492,x12493,a1),a1)+~P3(f2(a1),x12493,a1) % 1.09/1.25 [512]E(x5121,x5122)+P3(x5122,x5121,a1)+E(f22(f15(x5121),x5123,x5122),f15(x5121)) % 1.09/1.25 [610]~P47(x6102)+E(x6101,f2(x6102))+E(f8(f13(x6103,x6102),f13(x6101,x6102),x6102),f8(x6103,x6101,x6102)) % 1.09/1.25 [618]~P1(x6182)+E(x6181,f2(x6182))+E(f6(f11(x6183,x6181,x6182),x6181,x6182),x6183) % 1.09/1.25 [619]~P1(x6192)+E(x6191,f2(x6192))+E(f6(f11(x6191,x6193,x6192),x6191,x6192),x6193) % 1.09/1.25 [620]~P47(x6202)+E(x6201,f2(x6202))+E(f8(f11(x6203,x6201,x6202),x6201,x6202),x6203) % 1.09/1.25 [621]~P43(x6212)+~P47(x6212)+E(f8(f13(x6211,x6212),f13(x6213,x6212),x6212),f8(x6211,x6213,x6212)) % 1.09/1.25 [665]~P43(x6653)+~P47(x6653)+E(f7(f8(x6651,x6652,x6653),x6653),f8(x6652,x6651,x6653)) % 1.09/1.25 [720]~P47(x7202)+E(x7201,f2(x7202))+E(f8(x7203,f13(x7201,x7202),x7202),f13(f8(x7203,x7201,x7202),x7202)) % 1.09/1.25 [721]~P44(x7212)+E(x7211,f2(x7212))+E(f31(f7(x7211,x7212),x7213,x7212),f7(f31(x7211,x7213,x7212),x7212)) % 1.09/1.25 [732]~P43(x7323)+~P47(x7323)+E(f8(x7321,f13(x7322,x7323),x7323),f13(f8(x7321,x7322,x7323),x7323)) % 1.09/1.25 [733]~P43(x7332)+~P44(x7332)+E(f31(f7(x7331,x7332),x7333,x7332),f7(f31(x7331,x7333,x7332),x7332)) % 1.09/1.25 [771]~P54(x7712)+E(x7711,f2(x7712))+E(f8(f4(x7713,x7712),f4(x7711,x7712),x7712),f4(f8(x7713,x7711,x7712),x7712)) % 1.09/1.25 [781]~P54(x7812)+~P43(x7812)+E(f8(f4(x7811,x7812),f4(x7813,x7812),x7812),f4(f8(x7811,x7813,x7812),x7812)) % 1.09/1.25 [782]~P43(x7822)+~P47(x7822)+E(f11(f7(x7821,x7822),f7(x7823,x7822),x7822),f7(f11(x7821,x7823,x7822),x7822)) % 1.09/1.25 [813]~P1(x8133)+~P6(x8131,x8132,x8133)+E(f11(x8131,f6(x8132,x8131,x8133),x8133),x8132) % 1.09/1.25 [814]~P1(x8143)+~P6(x8142,x8141,x8143)+E(f11(f6(x8141,x8142,x8143),x8142,x8143),x8141) % 1.09/1.25 [833]~P33(x8331)+~P3(f10(x8331),x8332,x8331)+P3(f10(x8331),f31(x8332,f30(x8333),x8331),x8331) % 1.09/1.25 [840]~P7(x8403)+~P6(x8402,x8401,x8403)+E(f6(x8401,f13(x8402,x8403),x8403),f13(f6(x8401,x8402,x8403),x8403)) % 1.09/1.25 [841]~P7(x8412)+~P6(x8413,x8411,x8412)+E(f6(f13(x8411,x8412),x8413,x8412),f13(f6(x8411,x8413,x8412),x8412)) % 1.09/1.25 [862]~P53(x8622)+~P4(f2(x8622),x8623,x8622)+E(f11(f4(x8621,x8622),x8623,x8622),f4(f11(x8621,x8623,x8622),x8622)) % 1.09/1.25 [868]~P67(x8682)+~P4(x8683,x8681,a1)+E(f3(f24(x8681,x8682),f24(x8683,x8682),x8682),f24(f3(x8681,x8683,a1),x8682)) % 1.09/1.25 [934]~P1(x9342)+E(x9341,f2(x9342))+E(f6(f9(x9343,x9341,x9342),x9341,x9342),f9(f6(x9343,x9341,x9342),f10(x9342),x9342)) % 1.09/1.25 [935]~P1(x9352)+E(x9351,f2(x9352))+E(f6(f9(x9351,x9353,x9352),x9351,x9352),f9(f6(x9353,x9351,x9352),f10(x9352),x9352)) % 1.09/1.25 [1125]~P55(x11252)+E(x11251,f2(x11252))+~E(f9(f11(x11253,x11253,x11252),f11(x11251,x11251,x11252),x11252),f2(x11252)) % 1.09/1.25 [1126]~P55(x11262)+E(x11261,f2(x11262))+~E(f9(f11(x11261,x11261,x11262),f11(x11263,x11263,x11262),x11262),f2(x11262)) % 1.09/1.25 [1177]~P4(x11772,x11773,a1)+~P4(x11772,x11771,a1)+E(f3(f3(x11771,x11772,a1),f3(x11773,x11772,a1),a1),f3(x11771,x11773,a1)) % 1.09/1.25 [1182]~P33(x11821)+~P3(f10(x11821),x11822,x11821)+P3(f10(x11821),f11(x11822,f31(x11822,x11823,x11821),x11821),x11821) % 1.09/1.25 [1271]~P33(x12713)+~P3(f10(x12713),x12711,x12713)+P3(f31(x12711,x12712,x12713),f11(x12711,f31(x12711,x12712,x12713),x12713),x12713) % 1.09/1.25 [1289]~P55(x12892)+E(x12891,f2(x12892))+P3(f2(x12892),f9(f11(x12893,x12893,x12892),f11(x12891,x12891,x12892),x12892),x12892) % 1.09/1.25 [1290]~P55(x12902)+E(x12901,f2(x12902))+P3(f2(x12902),f9(f11(x12901,x12901,x12902),f11(x12903,x12903,x12902),x12902),x12902) % 1.09/1.25 [1344]~P55(x13442)+E(x13441,f2(x13442))+~P4(f9(f11(x13443,x13443,x13442),f11(x13441,x13441,x13442),x13442),f2(x13442),x13442) % 1.09/1.25 [1345]~P55(x13452)+E(x13451,f2(x13452))+~P4(f9(f11(x13451,x13451,x13452),f11(x13453,x13453,x13452),x13452),f2(x13452),x13452) % 1.09/1.25 [964]~P43(x9641)+~P47(x9641)+E(f31(f8(f10(x9641),x9642,x9641),x9643,x9641),f8(f10(x9641),f31(x9642,x9643,x9641),x9641)) % 1.09/1.25 [1318]~P54(x13183)+~P3(x13181,x13182,x13183)+P3(x13181,f8(f9(x13181,x13182,x13183),f9(f10(x13183),f10(x13183),x13183),x13183),x13183) % 1.09/1.25 [1319]~P54(x13193)+~P3(x13191,x13192,x13193)+P3(f8(f9(x13191,x13192,x13193),f9(f10(x13193),f10(x13193),x13193),x13193),x13192,x13193) % 1.09/1.25 [635]~P17(x6354)+E(x6351,x6352)+~E(f9(x6353,x6351,x6354),f9(x6353,x6352,x6354)) % 1.09/1.25 [636]~P20(x6364)+E(x6361,x6362)+~E(f9(x6363,x6361,x6364),f9(x6363,x6362,x6364)) % 1.09/1.25 [637]~P16(x6374)+E(x6371,x6372)+~E(f3(x6373,x6373,x6374),f3(x6371,x6372,x6374)) % 1.09/1.25 [638]~P20(x6384)+E(x6381,x6382)+~E(f9(x6381,x6383,x6384),f9(x6382,x6383,x6384)) % 1.09/1.25 [639]~P16(x6393)+E(x6391,x6392)+~E(f3(x6391,x6392,x6393),f3(x6394,x6394,x6393)) % 1.09/1.25 [796]~P8(x7964)+~P4(x7961,x7963,x7964)+P4(x7961,f28(x7962,x7963,x7964),x7964) % 1.09/1.25 [798]~P8(x7984)+~P4(x7981,x7982,x7984)+P4(x7981,f28(x7982,x7983,x7984),x7984) % 1.09/1.25 [799]~P34(x7994)+~P6(x7991,x7993,x7994)+P6(x7991,f11(x7992,x7993,x7994),x7994) % 1.09/1.25 [800]~P34(x8004)+~P6(x8001,x8002,x8004)+P6(x8001,f11(x8002,x8003,x8004),x8004) % 1.09/1.25 [802]~P8(x8024)+~P3(x8021,x8023,x8024)+P3(x8021,f28(x8022,x8023,x8024),x8024) % 1.09/1.25 [804]~P8(x8044)+~P3(x8041,x8042,x8044)+P3(x8041,f28(x8042,x8043,x8044),x8044) % 1.09/1.25 [806]~P8(x8063)+~P4(x8062,x8064,x8063)+P4(f29(x8061,x8062,x8063),x8064,x8063) % 1.09/1.25 [808]~P8(x8083)+~P4(x8081,x8084,x8083)+P4(f29(x8081,x8082,x8083),x8084,x8083) % 1.09/1.25 [810]~P8(x8103)+~P3(x8102,x8104,x8103)+P3(f29(x8101,x8102,x8103),x8104,x8103) % 1.09/1.25 [812]~P8(x8123)+~P3(x8121,x8124,x8123)+P3(f29(x8121,x8122,x8123),x8124,x8123) % 1.09/1.25 [861]~P3(x8614,x8613,a1)+P3(x8611,x8612,a1)+~E(f9(x8611,x8613,a1),f9(x8614,x8612,a1)) % 1.09/1.25 [870]~P8(x8703)+P4(x8701,x8702,x8703)+~P4(x8701,f29(x8704,x8702,x8703),x8703) % 1.09/1.25 [872]~P8(x8723)+P4(x8721,x8722,x8723)+~P4(x8721,f29(x8722,x8724,x8723),x8723) % 1.09/1.25 [873]~P8(x8733)+P3(x8731,x8732,x8733)+~P3(x8731,f29(x8734,x8732,x8733),x8733) % 1.09/1.25 [874]~P8(x8743)+P3(x8741,x8742,x8743)+~P3(x8741,f29(x8742,x8744,x8743),x8743) % 1.09/1.25 [876]~P8(x8763)+P4(x8761,x8762,x8763)+~P4(f28(x8764,x8761,x8763),x8762,x8763) % 1.09/1.25 [878]~P8(x8783)+P4(x8781,x8782,x8783)+~P4(f28(x8781,x8784,x8783),x8782,x8783) % 1.09/1.25 [879]~P34(x8793)+P6(x8791,x8792,x8793)+~P6(f11(x8794,x8791,x8793),x8792,x8793) % 1.09/1.25 [880]~P34(x8803)+P6(x8801,x8802,x8803)+~P6(f11(x8801,x8804,x8803),x8802,x8803) % 1.09/1.25 [881]~P8(x8813)+P3(x8811,x8812,x8813)+~P3(f28(x8814,x8811,x8813),x8812,x8813) % 1.09/1.25 [882]~P8(x8823)+P3(x8821,x8822,x8823)+~P3(f28(x8821,x8824,x8823),x8822,x8823) % 1.09/1.25 [973]~P34(x9733)+~P4(x9732,x9734,a1)+P6(f31(x9731,x9732,x9733),f31(x9731,x9734,x9733),x9733) % 1.09/1.25 [975]~P10(x9753)+~P4(x9751,x9754,x9753)+P4(f9(x9751,x9752,x9753),f9(x9754,x9752,x9753),x9753) % 1.09/1.25 [976]~P27(x9763)+~P4(x9761,x9764,x9763)+P4(f9(x9761,x9762,x9763),f9(x9764,x9762,x9763),x9763) % 1.09/1.25 [977]~P10(x9773)+~P4(x9772,x9774,x9773)+P4(f9(x9771,x9772,x9773),f9(x9771,x9774,x9773),x9773) % 1.09/1.25 [978]~P27(x9783)+~P4(x9782,x9784,x9783)+P4(f9(x9781,x9782,x9783),f9(x9781,x9784,x9783),x9783) % 1.09/1.25 [979]~P48(x9793)+~P6(x9791,x9794,x9793)+P6(f11(x9791,x9792,x9793),f11(x9794,x9792,x9793),x9793) % 1.09/1.25 [980]~P48(x9803)+~P6(x9802,x9804,x9803)+P6(f11(x9801,x9802,x9803),f11(x9801,x9804,x9803),x9803) % 1.09/1.25 [981]~P34(x9813)+~P6(x9811,x9814,x9813)+P6(f31(x9811,x9812,x9813),f31(x9814,x9812,x9813),x9813) % 1.09/1.25 [982]~P10(x9823)+~P3(x9821,x9824,x9823)+P3(f9(x9821,x9822,x9823),f9(x9824,x9822,x9823),x9823) % 1.09/1.25 [983]~P32(x9833)+~P3(x9831,x9834,x9833)+P3(f9(x9831,x9832,x9833),f9(x9834,x9832,x9833),x9833) % 1.09/1.25 [984]~P10(x9843)+~P3(x9842,x9844,x9843)+P3(f9(x9841,x9842,x9843),f9(x9841,x9844,x9843),x9843) % 1.09/1.25 [985]~P32(x9853)+~P3(x9852,x9854,x9853)+P3(f9(x9851,x9852,x9853),f9(x9851,x9854,x9853),x9853) % 1.09/1.25 [1091]~P4(x10912,x10914,a1)+~P4(x10911,x10913,a1)+P4(f9(x10911,x10912,a1),f9(x10913,x10914,a1),a1) % 1.09/1.25 [1092]~P4(x10922,x10924,a1)+~P4(x10921,x10923,a1)+P4(f11(x10921,x10922,a1),f11(x10923,x10924,a1),a1) % 1.09/1.25 [1093]~P3(x10932,x10934,a1)+~P3(x10931,x10933,a1)+P3(f9(x10931,x10932,a1),f9(x10933,x10934,a1),a1) % 1.09/1.25 [1178]~P10(x11783)+P4(x11781,x11782,x11783)+~P4(f9(x11784,x11781,x11783),f9(x11784,x11782,x11783),x11783) % 1.09/1.25 [1179]~P10(x11793)+P4(x11791,x11792,x11793)+~P4(f9(x11791,x11794,x11793),f9(x11792,x11794,x11793),x11793) % 1.09/1.25 [1180]~P10(x11803)+P3(x11801,x11802,x11803)+~P3(f9(x11804,x11801,x11803),f9(x11804,x11802,x11803),x11803) % 1.09/1.25 [1181]~P10(x11813)+P3(x11811,x11812,x11813)+~P3(f9(x11811,x11814,x11813),f9(x11812,x11814,x11813),x11813) % 1.09/1.25 [832]~P16(x8323)+E(x8321,f13(x8322,x8323))+~E(f9(x8321,f9(x8324,x8322,x8323),x8323),x8324) % 1.09/1.25 [866]~P1(x8663)+~P6(x8664,x8662,x8663)+E(f5(f5(x8661,x8662,x8663),x8664,x8663),f5(x8661,x8664,x8663)) % 1.09/1.25 [927]~P1(x9272)+E(x9271,f2(x9272))+E(f6(f11(x9273,x9271,x9272),f11(x9274,x9271,x9272),x9272),f6(x9273,x9274,x9272)) % 1.09/1.25 [928]~P1(x9282)+E(x9281,f2(x9282))+E(f6(f11(x9281,x9283,x9282),f11(x9281,x9284,x9282),x9282),f6(x9283,x9284,x9282)) % 1.09/1.25 [930]~P43(x9303)+~P47(x9303)+E(f8(f11(x9301,x9302,x9303),x9304,x9303),f11(f8(x9301,x9304,x9303),x9302,x9303)) % 1.09/1.25 [933]~P7(x9332)+~E(f5(x9331,x9333,x9332),f5(x9334,x9333,x9332))+E(f5(f13(x9331,x9332),x9333,x9332),f5(f13(x9334,x9332),x9333,x9332)) % 1.09/1.25 [1084]~P1(x10843)+~P6(x10844,x10841,x10843)+E(f6(f11(x10841,x10842,x10843),x10844,x10843),f11(f6(x10841,x10844,x10843),x10842,x10843)) % 1.09/1.25 [1127]~P47(x11272)+E(x11271,f2(x11272))+E(f8(f31(x11273,x11274,x11272),f31(x11271,x11274,x11272),x11272),f31(f8(x11273,x11271,x11272),x11274,x11272)) % 1.09/1.25 [1128]~P43(x11283)+~P47(x11283)+E(f8(f31(x11281,x11282,x11283),f31(x11284,x11282,x11283),x11283),f31(f8(x11281,x11284,x11283),x11282,x11283)) % 1.09/1.25 [1176]~P26(x11764)+~P4(f9(x11761,x11763,x11764),x11762,x11764)+P4(x11761,f9(x11762,f4(x11763,x11764),x11764),x11764) % 1.09/1.25 [1191]E(x11911,x11912)+E(x11913,f2(a1))+~E(f9(x11914,f11(x11913,x11911,a1),a1),f9(x11914,f11(x11913,x11912,a1),a1)) % 1.09/1.25 [1209]~P1(x12093)+~P6(x12094,x12091,x12093)+E(f6(f31(x12091,x12092,x12093),f31(x12094,x12092,x12093),x12093),f31(f6(x12091,x12094,x12093),x12092,x12093)) % 1.09/1.25 [1241]~P48(x12413)+~P14(x12413)+E(f9(f11(x12411,x12412,x12413),f11(x12411,x12414,x12413),x12413),f9(f11(x12411,x12414,x12413),f11(x12411,x12412,x12413),x12413)) % 1.09/1.25 [1333]E(x13331,x13332)+E(x13333,x13334)+~E(f9(f11(x13333,x13331,a1),f11(x13334,x13332,a1),a1),f9(f11(x13333,x13332,a1),f11(x13334,x13331,a1),a1)) % 1.09/1.25 [1238]~P1(x12382)+E(x12381,f2(x12382))+E(f6(f9(x12383,f11(x12384,x12381,x12382),x12382),x12381,x12382),f9(x12384,f6(x12383,x12381,x12382),x12382)) % 1.09/1.25 [1239]~P1(x12392)+E(x12391,f2(x12392))+E(f6(f9(x12393,f11(x12391,x12394,x12392),x12392),x12391,x12392),f9(x12394,f6(x12393,x12391,x12392),x12392)) % 1.09/1.25 [625]E(x6251,x6252)+~E(f23(x6253,x6251,x6254),f23(x6255,x6252,x6254))+E(x6253,f2(a1)) % 1.09/1.25 [1076]~P16(x10763)+E(f9(x10761,x10762,x10763),x10764)+~E(f9(x10761,f9(x10765,x10762,x10763),x10763),f9(x10765,x10764,x10763)) % 1.09/1.25 [1242]~P43(x12423)+~P47(x12423)+E(f8(f11(x12421,x12422,x12423),f11(x12424,x12425,x12423),x12423),f11(f8(x12421,x12424,x12423),f8(x12422,x12425,x12423),x12423)) % 1.09/1.25 [1341]~P4(x13413,x13412,a1)+~E(f9(f11(x13413,x13414,a1),x13411,a1),f9(f11(x13412,x13414,a1),x13415,a1))+E(x13411,f9(f11(f3(x13412,x13413,a1),x13414,a1),x13415,a1)) % 1.09/1.25 [1342]~P4(x13422,x13421,a1)+~E(f9(f11(x13421,x13423,a1),x13424,a1),f9(f11(x13422,x13423,a1),x13425,a1))+E(f9(f11(f3(x13421,x13422,a1),x13423,a1),x13424,a1),x13425) % 1.09/1.25 [1363]~P4(x13633,x13632,a1)+~P4(f9(f11(x13633,x13634,a1),x13631,a1),f9(f11(x13632,x13634,a1),x13635,a1),a1)+P4(x13631,f9(f11(f3(x13632,x13633,a1),x13634,a1),x13635,a1),a1) % 1.09/1.25 [1364]~P4(x13643,x13642,a1)+~P3(f9(f11(x13643,x13644,a1),x13641,a1),f9(f11(x13642,x13644,a1),x13645,a1),a1)+P3(x13641,f9(f11(f3(x13642,x13643,a1),x13644,a1),x13645,a1),a1) % 1.09/1.25 [1365]~P4(x13652,x13651,a1)+~P4(f9(f11(x13651,x13653,a1),x13654,a1),f9(f11(x13652,x13653,a1),x13655,a1),a1)+P4(f9(f11(f3(x13651,x13652,a1),x13653,a1),x13654,a1),x13655,a1) % 1.09/1.25 [1366]~P4(x13662,x13661,a1)+~P3(f9(f11(x13661,x13663,a1),x13664,a1),f9(f11(x13662,x13663,a1),x13665,a1),a1)+P3(f9(f11(f3(x13661,x13662,a1),x13663,a1),x13664,a1),x13665,a1) % 1.09/1.25 [1371]~P4(x13711,x13714,a1)+P4(f9(f11(x13711,x13712,a1),x13713,a1),f9(f11(x13714,x13712,a1),x13715,a1),a1)+~P4(x13713,f9(f11(f3(x13714,x13711,a1),x13712,a1),x13715,a1),a1) % 1.09/1.25 [1372]~P4(x13721,x13724,a1)+P3(f9(f11(x13721,x13722,a1),x13723,a1),f9(f11(x13724,x13722,a1),x13725,a1),a1)+~P3(x13723,f9(f11(f3(x13724,x13721,a1),x13722,a1),x13725,a1),a1) % 1.09/1.25 [1373]~P4(x13734,x13731,a1)+P4(f9(f11(x13731,x13732,a1),x13733,a1),f9(f11(x13734,x13732,a1),x13735,a1),a1)+~P4(f9(f11(f3(x13731,x13734,a1),x13732,a1),x13733,a1),x13735,a1) % 1.09/1.25 [1374]~P4(x13744,x13741,a1)+P3(f9(f11(x13741,x13742,a1),x13743,a1),f9(f11(x13744,x13742,a1),x13745,a1),a1)+~P3(f9(f11(f3(x13741,x13744,a1),x13742,a1),x13743,a1),x13745,a1) % 1.09/1.25 [1337]~P66(x13374)+~E(f9(f11(x13373,x13375,x13374),x13371,x13374),f9(f11(x13372,x13375,x13374),x13376,x13374))+E(x13371,f9(f11(f3(x13372,x13373,x13374),x13375,x13374),x13376,x13374)) % 1.09/1.25 [1338]~P66(x13383)+~E(f9(f11(x13381,x13384,x13383),x13385,x13383),f9(f11(x13382,x13384,x13383),x13386,x13383))+E(f9(f11(f3(x13381,x13382,x13383),x13384,x13383),x13385,x13383),x13386) % 1.09/1.25 [1359]~P62(x13594)+~P4(f9(f11(x13593,x13595,x13594),x13591,x13594),f9(f11(x13592,x13595,x13594),x13596,x13594),x13594)+P4(x13591,f9(f11(f3(x13592,x13593,x13594),x13595,x13594),x13596,x13594),x13594) % 1.09/1.25 [1360]~P62(x13604)+~P3(f9(f11(x13603,x13605,x13604),x13601,x13604),f9(f11(x13602,x13605,x13604),x13606,x13604),x13604)+P3(x13601,f9(f11(f3(x13602,x13603,x13604),x13605,x13604),x13606,x13604),x13604) % 1.09/1.25 [1361]~P62(x13613)+~P4(f9(f11(x13611,x13614,x13613),x13615,x13613),f9(f11(x13612,x13614,x13613),x13616,x13613),x13613)+P4(f9(f11(f3(x13611,x13612,x13613),x13614,x13613),x13615,x13613),x13616,x13613) % 1.09/1.25 [1362]~P62(x13623)+~P3(f9(f11(x13621,x13624,x13623),x13625,x13623),f9(f11(x13622,x13624,x13623),x13626,x13623),x13623)+P3(f9(f11(f3(x13621,x13622,x13623),x13624,x13623),x13625,x13623),x13626,x13623) % 1.09/1.25 [1367]~P62(x13673)+P4(f9(f11(x13671,x13672,x13673),x13674,x13673),f9(f11(x13675,x13672,x13673),x13676,x13673),x13673)+~P4(x13674,f9(f11(f3(x13675,x13671,x13673),x13672,x13673),x13676,x13673),x13673) % 1.09/1.25 [1368]~P62(x13683)+P3(f9(f11(x13681,x13682,x13683),x13684,x13683),f9(f11(x13685,x13682,x13683),x13686,x13683),x13683)+~P3(x13684,f9(f11(f3(x13685,x13681,x13683),x13682,x13683),x13686,x13683),x13683) % 1.09/1.25 [1369]~P62(x13693)+P4(f9(f11(x13691,x13692,x13693),x13694,x13693),f9(f11(x13695,x13692,x13693),x13696,x13693),x13693)+~P4(f9(f11(f3(x13691,x13695,x13693),x13692,x13693),x13694,x13693),x13696,x13693) % 1.09/1.25 [1370]~P62(x13703)+P3(f9(f11(x13701,x13702,x13703),x13704,x13703),f9(f11(x13705,x13702,x13703),x13706,x13703),x13703)+~P3(f9(f11(f3(x13701,x13705,x13703),x13702,x13703),x13704,x13703),x13706,x13703) % 1.09/1.25 [334]~P43(x3342)+~P47(x3342)+~E(f7(x3341,x3342),f10(x3342))+E(x3341,f10(x3342)) % 1.09/1.25 [421]~P8(x4212)+~P26(x4212)+P3(x4211,f2(x4212),x4212)+E(f4(x4211,x4212),x4211) % 1.09/1.25 [518]~P70(x5182)+~P3(f2(x5182),x5181,x5182)+E(f12(x5181,x5182),f10(x5182))+E(x5181,f2(x5182)) % 1.09/1.25 [526]~P8(x5262)+~P26(x5262)+~P3(x5261,f2(x5262),x5262)+E(f4(x5261,x5262),f13(x5261,x5262)) % 1.09/1.25 [684]~P54(x6841)+~P43(x6841)+~P4(f2(x6841),x6842,x6841)+P4(f2(x6841),f7(x6842,x6841),x6841) % 1.09/1.25 [686]~P54(x6862)+~P43(x6862)+~P4(x6861,f2(x6862),x6862)+P4(f7(x6861,x6862),f2(x6862),x6862) % 1.09/1.25 [687]~P54(x6872)+~P43(x6872)+~P4(x6871,f2(x6872),x6872)+P4(f7(x6871,x6872),f10(x6872),x6872) % 1.09/1.25 [689]~P54(x6892)+~P43(x6892)+~P4(x6891,f2(x6892),x6892)+P3(f7(x6891,x6892),f10(x6892),x6892) % 1.09/1.25 [690]~P54(x6902)+~P43(x6902)+~P4(f10(x6902),x6901,x6902)+P4(f7(x6901,x6902),f10(x6902),x6902) % 1.09/1.25 [691]~P54(x6912)+~P43(x6912)+~P3(f10(x6912),x6911,x6912)+P3(f7(x6911,x6912),f10(x6912),x6912) % 1.09/1.25 [709]~P54(x7092)+~P3(f7(x7091,x7092),f2(x7092),x7092)+P3(x7091,f2(x7092),x7092)+E(x7091,f2(x7092)) % 1.09/1.25 [710]~P54(x7102)+~P3(f2(x7102),f7(x7101,x7102),x7102)+P3(f2(x7102),x7101,x7102)+E(x7101,f2(x7102)) % 1.09/1.25 [712]~P54(x7122)+~P43(x7122)+~P4(f10(x7122),f7(x7121,x7122),x7122)+P4(x7121,f10(x7122),x7122) % 1.09/1.25 [713]~P54(x7132)+~P43(x7132)+~P3(f10(x7132),f7(x7131,x7132),x7132)+P3(x7131,f10(x7132),x7132) % 1.09/1.25 [714]~P54(x7142)+~P43(x7142)+~P4(f7(x7141,x7142),f2(x7142),x7142)+P4(x7141,f2(x7142),x7142) % 1.09/1.25 [715]~P54(x7152)+~P43(x7152)+~P3(f7(x7151,x7152),f2(x7152),x7152)+P3(x7151,f2(x7152),x7152) % 1.09/1.25 [716]~P54(x7161)+~P43(x7161)+~P4(f2(x7161),f7(x7162,x7161),x7161)+P4(f2(x7161),x7162,x7161) % 1.09/1.25 [717]~P54(x7171)+~P43(x7171)+~P4(f10(x7171),f7(x7172,x7171),x7171)+P3(f2(x7171),x7172,x7171) % 1.09/1.25 [718]~P54(x7181)+~P43(x7181)+~P3(f2(x7181),f7(x7182,x7181),x7181)+P3(f2(x7181),x7182,x7181) % 1.09/1.25 [719]~P54(x7191)+~P43(x7191)+~P3(f10(x7191),f7(x7192,x7191),x7191)+P3(f2(x7191),x7192,x7191) % 1.09/1.25 [409]~P58(x4092)+~P35(x4092)+E(x4091,f2(a1))+E(f31(f2(x4092),x4091,x4092),f2(x4092)) % 1.09/1.25 [468]~P70(x4682)+P3(f2(x4682),x4681,x4682)+E(x4681,f2(x4682))+E(f12(x4681,x4682),f13(f10(x4682),x4682)) % 1.09/1.25 [834]~P54(x8341)+~P43(x8341)+~P4(f2(x8341),x8342,x8341)+P4(f2(x8341),f8(f10(x8341),x8342,x8341),x8341) % 1.09/1.25 [835]~P54(x8351)+~P43(x8351)+~P3(f2(x8351),x8352,x8351)+P3(f2(x8351),f8(f10(x8351),x8352,x8351),x8351) % 1.09/1.25 [836]~P54(x8361)+~P43(x8361)+~P4(x8362,f2(x8361),x8361)+P4(f8(f10(x8361),x8362,x8361),f2(x8361),x8361) % 1.09/1.25 [837]~P54(x8371)+~P43(x8371)+~P3(x8372,f2(x8371),x8371)+P3(f8(f10(x8371),x8372,x8371),f2(x8371),x8371) % 1.09/1.25 [965]~P54(x9652)+~P43(x9652)+P4(x9651,f2(x9652),x9652)+~P4(f8(f10(x9652),x9651,x9652),f2(x9652),x9652) % 1.09/1.25 [966]~P54(x9662)+~P43(x9662)+P3(x9661,f2(x9662),x9662)+~P3(f8(f10(x9662),x9661,x9662),f2(x9662),x9662) % 1.09/1.25 [967]~P54(x9671)+~P43(x9671)+P4(f2(x9671),x9672,x9671)+~P4(f2(x9671),f8(f10(x9671),x9672,x9671),x9671) % 1.09/1.25 [968]~P54(x9681)+~P43(x9681)+P3(f2(x9681),x9682,x9681)+~P3(f2(x9681),f8(f10(x9681),x9682,x9681),x9681) % 1.09/1.25 [510]P3(x5101,x5102,x5103)+~P8(x5103)+E(x5101,x5102)+P3(x5102,x5101,x5103) % 1.09/1.25 [511]P3(x5111,x5112,x5113)+~P53(x5113)+E(x5111,x5112)+P3(x5112,x5111,x5113) % 1.09/1.25 [572]~P8(x5723)+~P4(x5721,x5722,x5723)+E(x5721,x5722)+P3(x5721,x5722,x5723) % 1.09/1.25 [578]~P37(x5783)+~P4(x5781,x5782,x5783)+E(x5781,x5782)+P3(x5781,x5782,x5783) % 1.09/1.25 [643]~P4(x6432,x6431,x6433)+~P4(x6431,x6432,x6433)+E(x6431,x6432)+~P37(x6433) % 1.09/1.25 [698]P3(x6982,x6981,x6983)+~P36(x6983)+~P4(x6982,x6981,x6983)+P4(x6981,x6982,x6983) % 1.09/1.25 [343]~P43(x3433)+~P44(x3433)+E(x3431,x3432)+~E(f7(x3431,x3433),f7(x3432,x3433)) % 1.09/1.25 [466]~P47(x4663)+E(x4661,x4662)+~E(f8(x4661,x4662,x4663),f10(x4663))+E(x4662,f2(x4663)) % 1.09/1.25 [467]~P48(x4672)+~P14(x4672)+~E(f9(x4673,x4671,x4672),x4673)+E(x4671,f2(x4672)) % 1.09/1.25 [471]~P48(x4713)+~P14(x4713)+E(x4711,x4712)+~E(f3(x4711,x4712,x4713),f2(x4713)) % 1.09/1.25 [475]~P51(x4752)+~E(f11(x4753,x4751,x4752),f2(x4752))+E(x4751,f2(x4752))+E(x4753,f2(x4752)) % 1.09/1.25 [476]~P64(x4762)+~E(f11(x4763,x4761,x4762),f2(x4762))+E(x4761,f2(x4762))+E(x4763,f2(x4762)) % 1.09/1.25 [683]~P48(x6833)+E(x6831,x6832)+~E(f11(x6831,x6831,x6833),f11(x6832,x6832,x6833))+E(x6831,f13(x6832,x6833)) % 1.09/1.25 [842]~P54(x8422)+~P4(x8423,x8421,x8422)+~P3(x8421,f2(x8422),x8422)+P4(f7(x8421,x8422),f7(x8423,x8422),x8422) % 1.09/1.25 [843]~P54(x8432)+~P3(x8433,x8431,x8432)+~P3(x8431,f2(x8432),x8432)+P3(f7(x8431,x8432),f7(x8433,x8432),x8432) % 1.09/1.25 [844]~P54(x8442)+~P4(x8443,x8441,x8442)+~P3(f2(x8442),x8443,x8442)+P4(f7(x8441,x8442),f7(x8443,x8442),x8442) % 1.09/1.25 [845]~P54(x8452)+~P3(x8453,x8451,x8452)+~P3(f2(x8452),x8453,x8452)+P3(f7(x8451,x8452),f7(x8453,x8452),x8452) % 1.09/1.25 [857]~P28(x8572)+~P4(x8571,x8573,x8572)+~P4(f13(x8571,x8572),x8573,x8572)+P4(f4(x8571,x8572),x8573,x8572) % 1.09/1.25 [858]~P53(x8582)+~P3(x8581,x8583,x8582)+~P3(f13(x8581,x8582),x8583,x8582)+P3(f4(x8581,x8582),x8583,x8582) % 1.09/1.25 [891]~P54(x8913)+P4(x8911,x8912,x8913)+~P3(x8911,f2(x8913),x8913)+~P4(f7(x8912,x8913),f7(x8911,x8913),x8913) % 1.09/1.25 [892]~P54(x8923)+P3(x8921,x8922,x8923)+~P3(x8921,f2(x8923),x8923)+~P3(f7(x8922,x8923),f7(x8921,x8923),x8923) % 1.09/1.25 [893]~P54(x8933)+P4(x8931,x8932,x8933)+~P3(f2(x8933),x8932,x8933)+~P4(f7(x8932,x8933),f7(x8931,x8933),x8933) % 1.09/1.25 [894]~P54(x8943)+P3(x8941,x8942,x8943)+~P3(f2(x8943),x8942,x8943)+~P3(f7(x8942,x8943),f7(x8941,x8943),x8943) % 1.09/1.25 [929]E(x9291,x9292)+~P4(x9293,x9292,a1)+~P4(x9293,x9291,a1)+~E(f3(x9291,x9293,a1),f3(x9292,x9293,a1)) % 1.09/1.25 [974]~P33(x9741)+~P3(f10(x9741),x9742,x9741)+P3(f10(x9741),f31(x9742,x9743,x9741),x9741)+~P3(f2(a1),x9743,a1) % 1.09/1.25 [990]~P62(x9901)+~P4(x9903,f2(x9901),x9901)+~P4(x9902,f2(x9901),x9901)+P4(f2(x9901),f11(x9902,x9903,x9901),x9901) % 1.09/1.25 [991]~P55(x9911)+~P4(x9913,f2(x9911),x9911)+~P4(x9912,f2(x9911),x9911)+P4(f2(x9911),f11(x9912,x9913,x9911),x9911) % 1.09/1.25 [992]~P54(x9921)+~P4(x9922,f2(x9921),x9921)+~P3(x9923,f2(x9921),x9921)+P4(f2(x9921),f8(x9922,x9923,x9921),x9921) % 1.09/1.25 [993]~P55(x9931)+~P3(x9933,f2(x9931),x9931)+~P3(x9932,f2(x9931),x9931)+P3(f2(x9931),f11(x9932,x9933,x9931),x9931) % 1.09/1.25 [994]~P54(x9941)+~P3(x9943,f2(x9941),x9941)+~P3(x9942,f2(x9941),x9941)+P3(f2(x9941),f8(x9942,x9943,x9941),x9941) % 1.09/1.25 [995]~P31(x9951)+~P4(f2(x9951),x9953,x9951)+~P4(f2(x9951),x9952,x9951)+P4(f2(x9951),f9(x9952,x9953,x9951),x9951) % 1.09/1.25 [996]~P62(x9961)+~P4(f2(x9961),x9963,x9961)+~P4(f2(x9961),x9962,x9961)+P4(f2(x9961),f11(x9962,x9963,x9961),x9961) % 1.09/1.25 [997]~P55(x9971)+~P4(f2(x9971),x9973,x9971)+~P4(f2(x9971),x9972,x9971)+P4(f2(x9971),f11(x9972,x9973,x9971),x9971) % 1.09/1.25 [998]~P60(x9981)+~P4(f2(x9981),x9983,x9981)+~P4(f2(x9981),x9982,x9981)+P4(f2(x9981),f11(x9982,x9983,x9981),x9981) % 1.09/1.25 [999]~P54(x9991)+~P4(f2(x9991),x9992,x9991)+~P3(f2(x9991),x9993,x9991)+P4(f2(x9991),f8(x9992,x9993,x9991),x9991) % 1.09/1.25 [1000]~P31(x10001)+~P4(f2(x10001),x10003,x10001)+~P3(f2(x10001),x10002,x10001)+P3(f2(x10001),f9(x10002,x10003,x10001),x10001) % 1.09/1.25 [1001]~P31(x10011)+~P4(f2(x10011),x10012,x10011)+~P3(f2(x10011),x10013,x10011)+P3(f2(x10011),f9(x10012,x10013,x10011),x10011) % 1.09/1.25 [1002]~P31(x10021)+~P3(f2(x10021),x10023,x10021)+~P3(f2(x10021),x10022,x10021)+P3(f2(x10021),f9(x10022,x10023,x10021),x10021) % 1.09/1.25 [1003]~P56(x10031)+~P3(f2(x10031),x10033,x10031)+~P3(f2(x10031),x10032,x10031)+P3(f2(x10031),f11(x10032,x10033,x10031),x10031) % 1.09/1.25 [1004]~P54(x10041)+~P3(f2(x10041),x10043,x10041)+~P3(f2(x10041),x10042,x10041)+P3(f2(x10041),f8(x10042,x10043,x10041),x10041) % 1.09/1.25 [1005]~P33(x10051)+~P3(f10(x10051),x10053,x10051)+~P3(f10(x10051),x10052,x10051)+P3(f10(x10051),f11(x10052,x10053,x10051),x10051) % 1.09/1.25 [1006]~P31(x10063)+~P4(x10062,f2(x10063),x10063)+~P4(x10061,f2(x10063),x10063)+P4(f9(x10061,x10062,x10063),f2(x10063),x10063) % 1.09/1.25 [1007]~P31(x10073)+~P4(x10072,f2(x10073),x10073)+~P3(x10071,f2(x10073),x10073)+P3(f9(x10071,x10072,x10073),f2(x10073),x10073) % 1.09/1.25 [1008]~P31(x10083)+~P4(x10081,f2(x10083),x10083)+~P3(x10082,f2(x10083),x10083)+P3(f9(x10081,x10082,x10083),f2(x10083),x10083) % 1.09/1.25 [1009]~P31(x10093)+~P3(x10092,f2(x10093),x10093)+~P3(x10091,f2(x10093),x10093)+P3(f9(x10091,x10092,x10093),f2(x10093),x10093) % 1.09/1.25 [1010]~P55(x10103)+~P4(x10102,f2(x10103),x10103)+~P4(f2(x10103),x10101,x10103)+P4(f11(x10101,x10102,x10103),f2(x10103),x10103) % 1.09/1.25 [1011]~P55(x10113)+~P4(x10111,f2(x10113),x10113)+~P4(f2(x10113),x10112,x10113)+P4(f11(x10111,x10112,x10113),f2(x10113),x10113) % 1.09/1.25 [1013]~P60(x10133)+~P4(x10132,f2(x10133),x10133)+~P4(f2(x10133),x10131,x10133)+P4(f11(x10131,x10132,x10133),f2(x10133),x10133) % 1.09/1.25 [1016]~P60(x10163)+~P4(x10161,f2(x10163),x10163)+~P4(f2(x10163),x10162,x10163)+P4(f11(x10161,x10162,x10163),f2(x10163),x10163) % 1.09/1.25 [1017]~P54(x10173)+~P4(x10171,f2(x10173),x10173)+~P3(f2(x10173),x10172,x10173)+P4(f8(x10171,x10172,x10173),f2(x10173),x10173) % 1.09/1.25 [1018]~P54(x10183)+~P3(x10182,f2(x10183),x10183)+~P4(f2(x10183),x10181,x10183)+P4(f8(x10181,x10182,x10183),f2(x10183),x10183) % 1.09/1.25 [1019]~P56(x10193)+~P3(x10192,f2(x10193),x10193)+~P3(f2(x10193),x10191,x10193)+P3(f11(x10191,x10192,x10193),f2(x10193),x10193) % 1.09/1.25 [1021]~P56(x10213)+~P3(x10211,f2(x10213),x10213)+~P3(f2(x10213),x10212,x10213)+P3(f11(x10211,x10212,x10213),f2(x10213),x10213) % 1.09/1.25 [1022]~P54(x10223)+~P3(x10222,f2(x10223),x10223)+~P3(f2(x10223),x10221,x10223)+P3(f8(x10221,x10222,x10223),f2(x10223),x10223) % 1.09/1.25 [1023]~P54(x10233)+~P3(x10231,f2(x10233),x10233)+~P3(f2(x10233),x10232,x10233)+P3(f8(x10231,x10232,x10233),f2(x10233),x10233) % 1.09/1.25 [1043]~P55(x10432)+~P4(f11(x10433,x10431,x10432),f2(x10432),x10432)+P4(x10431,f2(x10432),x10432)+P4(x10433,f2(x10432),x10432) % 1.09/1.25 [1044]~P55(x10442)+~P4(f2(x10442),f11(x10443,x10441,x10442),x10442)+P4(x10441,f2(x10442),x10442)+P4(f2(x10442),x10443,x10442) % 1.09/1.25 [1045]~P55(x10452)+~P4(f2(x10452),f11(x10451,x10453,x10452),x10452)+P4(x10451,f2(x10452),x10452)+P4(f2(x10452),x10453,x10452) % 1.09/1.25 [1046]~P55(x10462)+~P4(f2(x10462),f11(x10463,x10461,x10462),x10462)+P4(x10461,f2(x10462),x10462)+P4(f2(x10462),x10461,x10462) % 1.09/1.25 [1047]~P55(x10472)+~P4(f2(x10472),f11(x10471,x10473,x10472),x10472)+P4(x10471,f2(x10472),x10472)+P4(f2(x10472),x10471,x10472) % 1.09/1.25 [1048]~P55(x10482)+~P4(f11(x10483,x10481,x10482),f2(x10482),x10482)+P4(x10481,f2(x10482),x10482)+P4(f2(x10482),x10481,x10482) % 1.09/1.25 [1049]~P55(x10492)+~P4(f11(x10491,x10493,x10492),f2(x10492),x10492)+P4(x10491,f2(x10492),x10492)+P4(f2(x10492),x10491,x10492) % 1.09/1.25 [1050]~P55(x10501)+~P4(f11(x10502,x10503,x10501),f2(x10501),x10501)+P4(f2(x10501),x10502,x10501)+P4(f2(x10501),x10503,x10501) % 1.09/1.25 [1089]~P56(x10891)+~P3(f2(x10891),f11(x10893,x10892,x10891),x10891)+P3(f2(x10891),x10892,x10891)+~P3(f2(x10891),x10893,x10891) % 1.09/1.25 [1090]~P56(x10901)+~P3(f2(x10901),f11(x10902,x10903,x10901),x10901)+P3(f2(x10901),x10902,x10901)+~P3(f2(x10901),x10903,x10901) % 1.09/1.25 [1293]~P4(x12933,x12931,a1)+P4(x12931,x12932,a1)+~P4(x12933,x12932,a1)+~P4(f3(x12931,x12933,a1),f3(x12932,x12933,a1),a1) % 1.09/1.25 [1294]~P4(x12943,x12941,a1)+P3(x12941,x12942,a1)+~P4(x12943,x12942,a1)+~P3(f3(x12941,x12943,a1),f3(x12942,x12943,a1),a1) % 1.09/1.25 [646]~P43(x6462)+~P47(x6462)+E(x6461,f2(x6462))+E(f11(f8(x6463,x6461,x6462),x6461,x6462),x6463) % 1.09/1.25 [788]~P44(x7882)+E(x7881,f2(x7882))+E(x7883,f2(x7882))+E(f11(f7(x7881,x7882),f7(x7883,x7882),x7882),f7(f11(x7883,x7881,x7882),x7882)) % 1.09/1.25 [867]~P54(x8672)+~P43(x8672)+~P3(f2(x8672),x8673,x8672)+E(f8(f4(x8671,x8672),x8673,x8672),f4(f8(x8671,x8673,x8672),x8672)) % 1.09/1.25 [1040]~P33(x10403)+~P3(x10401,f10(x10403),x10403)+~P3(f2(x10403),x10401,x10403)+P3(f31(x10401,f30(x10402),x10403),f10(x10403),x10403) % 1.09/1.25 [1085]~P63(x10852)+~P4(x10853,f2(x10852),x10852)+~P4(x10851,f2(x10852),x10852)+E(f11(f4(x10851,x10852),f4(x10853,x10852),x10852),f4(f11(x10851,x10853,x10852),x10852)) % 1.09/1.25 [1086]~P63(x10862)+~P4(x10863,f2(x10862),x10862)+~P4(f2(x10862),x10861,x10862)+E(f11(f4(x10861,x10862),f4(x10863,x10862),x10862),f4(f11(x10861,x10863,x10862),x10862)) % 1.09/1.25 [1087]~P63(x10872)+~P4(x10871,f2(x10872),x10872)+~P4(f2(x10872),x10873,x10872)+E(f11(f4(x10871,x10872),f4(x10873,x10872),x10872),f4(f11(x10871,x10873,x10872),x10872)) % 1.09/1.25 [1088]~P63(x10882)+~P4(f2(x10882),x10883,x10882)+~P4(f2(x10882),x10881,x10882)+E(f11(f4(x10881,x10882),f4(x10883,x10882),x10882),f4(f11(x10881,x10883,x10882),x10882)) % 1.09/1.25 [1253]~P44(x12532)+E(x12531,f2(x12532))+E(x12533,f2(x12532))+E(f11(f11(f7(x12533,x12532),f9(x12533,x12531,x12532),x12532),f7(x12531,x12532),x12532),f9(f7(x12533,x12532),f7(x12531,x12532),x12532)) % 1.09/1.25 [1254]~P44(x12542)+E(x12541,f2(x12542))+E(x12543,f2(x12542))+E(f11(f11(f7(x12543,x12542),f3(x12541,x12543,x12542),x12542),f7(x12541,x12542),x12542),f3(f7(x12543,x12542),f7(x12541,x12542),x12542)) % 1.09/1.25 [1255]~P47(x12552)+E(x12551,f2(x12552))+E(x12553,f2(x12552))+E(f11(f11(f9(x12553,x12551,x12552),f7(x12553,x12552),x12552),f7(x12551,x12552),x12552),f9(f7(x12553,x12552),f7(x12551,x12552),x12552)) % 1.09/1.25 [1311]~P33(x13113)+~P3(x13111,f10(x13113),x13113)+~P3(f2(x13113),x13111,x13113)+P3(f11(x13111,f31(x13111,x13112,x13113),x13113),f31(x13111,x13112,x13113),x13113) % 1.09/1.25 [762]~P36(x7623)+~P4(x7621,x7624,x7623)+P4(x7621,x7622,x7623)+~P4(x7624,x7622,x7623) % 1.09/1.25 [763]~P37(x7633)+~P4(x7631,x7634,x7633)+P4(x7631,x7632,x7633)+~P4(x7634,x7632,x7633) % 1.09/1.25 [764]~P34(x7643)+~P6(x7641,x7644,x7643)+P6(x7641,x7642,x7643)+~P6(x7644,x7642,x7643) % 1.09/1.26 [765]~P36(x7653)+~P3(x7651,x7654,x7653)+P3(x7651,x7652,x7653)+~P4(x7654,x7652,x7653) % 1.09/1.26 [766]~P36(x7663)+~P3(x7664,x7662,x7663)+P3(x7661,x7662,x7663)+~P4(x7661,x7664,x7663) % 1.09/1.26 [767]~P36(x7673)+~P3(x7671,x7674,x7673)+P3(x7671,x7672,x7673)+~P3(x7674,x7672,x7673) % 1.09/1.26 [768]~P37(x7683)+~P3(x7681,x7684,x7683)+P3(x7681,x7682,x7683)+~P4(x7684,x7682,x7683) % 1.09/1.26 [769]~P37(x7693)+~P3(x7694,x7692,x7693)+P3(x7691,x7692,x7693)+~P4(x7691,x7694,x7693) % 1.09/1.26 [770]~P37(x7703)+~P3(x7701,x7704,x7703)+P3(x7701,x7702,x7703)+~P3(x7704,x7702,x7703) % 1.09/1.26 [658]~P48(x6584)+~P14(x6584)+E(x6581,x6582)+~E(f9(x6583,x6581,x6584),f9(x6583,x6582,x6584)) % 1.09/1.26 [831]~P33(x8314)+E(x8311,x8312)+~P3(f10(x8314),x8313,x8314)+~E(f31(x8313,x8311,x8314),f31(x8313,x8312,x8314)) % 1.09/1.26 [938]~P8(x9384)+~P4(x9381,x9383,x9384)+~P4(x9381,x9382,x9384)+P4(x9381,f29(x9382,x9383,x9384),x9384) % 1.09/1.26 [939]~P34(x9394)+~P6(x9391,x9393,x9394)+~P6(x9391,x9392,x9394)+P6(x9391,f9(x9392,x9393,x9394),x9394) % 1.09/1.26 [940]~P40(x9404)+~P6(x9401,x9403,x9404)+~P6(x9401,x9402,x9404)+P6(x9401,f3(x9402,x9403,x9404),x9404) % 1.09/1.26 [942]~P1(x9424)+~P6(x9421,x9423,x9424)+~P6(x9421,x9422,x9424)+P6(x9421,f5(x9422,x9423,x9424),x9424) % 1.09/1.26 [943]~P8(x9434)+~P3(x9431,x9433,x9434)+~P3(x9431,x9432,x9434)+P3(x9431,f29(x9432,x9433,x9434),x9434) % 1.09/1.26 [946]~P8(x9463)+~P4(x9462,x9464,x9463)+~P4(x9461,x9464,x9463)+P4(f28(x9461,x9462,x9463),x9464,x9463) % 1.09/1.26 [947]~P8(x9473)+~P3(x9472,x9474,x9473)+~P3(x9471,x9474,x9473)+P3(f28(x9471,x9472,x9473),x9474,x9473) % 1.09/1.26 [962]~P33(x9624)+~P3(x9621,x9623,x9624)+~P3(f2(x9624),x9622,x9624)+P3(x9621,f9(x9622,x9623,x9624),x9624) % 1.09/1.26 [1026]~P8(x10263)+P4(x10261,x10262,x10263)+P4(x10261,x10264,x10263)+~P4(x10261,f28(x10262,x10264,x10263),x10263) % 1.09/1.26 [1027]~P8(x10273)+P3(x10271,x10272,x10273)+P3(x10271,x10274,x10273)+~P3(x10271,f28(x10272,x10274,x10273),x10273) % 1.09/1.26 [1028]~P8(x10283)+P4(x10281,x10282,x10283)+P4(x10284,x10282,x10283)+~P4(f29(x10281,x10284,x10283),x10282,x10283) % 1.09/1.26 [1029]~P8(x10293)+P3(x10291,x10292,x10293)+P3(x10294,x10292,x10293)+~P3(f29(x10291,x10294,x10293),x10292,x10293) % 1.09/1.26 [1078]~P1(x10783)+P6(x10781,x10782,x10783)+~P6(x10781,x10784,x10783)+~P6(x10781,f5(x10782,x10784,x10783),x10783) % 1.09/1.26 [1140]~P33(x11403)+~P4(x11402,x11404,a1)+~P4(f10(x11403),x11401,x11403)+P4(f31(x11401,x11402,x11403),f31(x11401,x11404,x11403),x11403) % 1.09/1.26 [1141]~P33(x11413)+~P4(x11412,x11414,a1)+~P3(f10(x11413),x11411,x11413)+P4(f31(x11411,x11412,x11413),f31(x11411,x11414,x11413),x11413) % 1.09/1.26 [1143]~P33(x11433)+~P3(x11432,x11434,a1)+~P3(f10(x11433),x11431,x11433)+P3(f31(x11431,x11432,x11433),f31(x11431,x11434,x11433),x11433) % 1.09/1.26 [1146]~P62(x11463)+~P4(x11464,x11461,x11463)+~P4(x11462,f2(x11463),x11463)+P4(f11(x11461,x11462,x11463),f11(x11464,x11462,x11463),x11463) % 1.09/1.26 [1147]~P62(x11473)+~P4(x11474,x11472,x11473)+~P4(x11471,f2(x11473),x11473)+P4(f11(x11471,x11472,x11473),f11(x11471,x11474,x11473),x11473) % 1.09/1.26 [1148]~P55(x11483)+~P4(x11484,x11482,x11483)+~P3(x11481,f2(x11483),x11483)+P4(f11(x11481,x11482,x11483),f11(x11481,x11484,x11483),x11483) % 1.09/1.26 [1150]~P55(x11503)+~P3(x11504,x11501,x11503)+~P3(x11502,f2(x11503),x11503)+P3(f11(x11501,x11502,x11503),f11(x11504,x11502,x11503),x11503) % 1.09/1.26 [1153]~P55(x11533)+~P3(x11534,x11532,x11533)+~P3(x11531,f2(x11533),x11533)+P3(f11(x11531,x11532,x11533),f11(x11531,x11534,x11533),x11533) % 1.09/1.26 [1154]~P54(x11543)+~P3(x11544,x11541,x11543)+~P3(x11542,f2(x11543),x11543)+P3(f8(x11541,x11542,x11543),f8(x11544,x11542,x11543),x11543) % 1.09/1.26 [1155]~P46(x11553)+~P4(x11551,x11554,x11553)+~P4(f2(x11553),x11552,x11553)+P4(f11(x11551,x11552,x11553),f11(x11554,x11552,x11553),x11553) % 1.09/1.26 [1156]~P55(x11563)+~P4(x11562,x11564,x11563)+~P3(f2(x11563),x11561,x11563)+P4(f11(x11561,x11562,x11563),f11(x11561,x11564,x11563),x11563) % 1.09/1.26 [1157]~P46(x11573)+~P4(x11572,x11574,x11573)+~P4(f2(x11573),x11571,x11573)+P4(f11(x11571,x11572,x11573),f11(x11571,x11574,x11573),x11573) % 1.09/1.26 [1158]~P50(x11583)+~P4(x11582,x11584,x11583)+~P4(f2(x11583),x11581,x11583)+P4(f11(x11581,x11582,x11583),f11(x11581,x11584,x11583),x11583) % 1.09/1.26 [1159]~P33(x11593)+~P4(x11591,x11594,x11593)+~P4(f2(x11593),x11591,x11593)+P4(f31(x11591,x11592,x11593),f31(x11594,x11592,x11593),x11593) % 1.09/1.26 [1160]~P55(x11603)+~P3(x11601,x11604,x11603)+~P3(f2(x11603),x11602,x11603)+P3(f11(x11601,x11602,x11603),f11(x11604,x11602,x11603),x11603) % 1.09/1.26 [1161]~P56(x11613)+~P3(x11611,x11614,x11613)+~P3(f2(x11613),x11612,x11613)+P3(f11(x11611,x11612,x11613),f11(x11614,x11612,x11613),x11613) % 1.09/1.26 [1163]~P55(x11633)+~P3(x11632,x11634,x11633)+~P3(f2(x11633),x11631,x11633)+P3(f11(x11631,x11632,x11633),f11(x11631,x11634,x11633),x11633) % 1.09/1.26 [1164]~P56(x11643)+~P3(x11642,x11644,x11643)+~P3(f2(x11643),x11641,x11643)+P3(f11(x11641,x11642,x11643),f11(x11641,x11644,x11643),x11643) % 1.09/1.26 [1165]~P45(x11653)+~P3(x11652,x11654,x11653)+~P3(f2(x11653),x11651,x11653)+P3(f11(x11651,x11652,x11653),f11(x11651,x11654,x11653),x11653) % 1.09/1.26 [1166]~P54(x11663)+~P3(x11661,x11664,x11663)+~P3(f2(x11663),x11662,x11663)+P3(f8(x11661,x11662,x11663),f8(x11664,x11662,x11663),x11663) % 1.09/1.26 [1185]~P48(x11852)+P6(x11853,x11854,x11852)+~P6(f11(x11851,x11853,x11852),f11(x11851,x11854,x11852),x11852)+E(x11851,f2(x11852)) % 1.09/1.26 [1186]~P48(x11862)+P6(x11863,x11864,x11862)+~P6(f11(x11863,x11861,x11862),f11(x11864,x11861,x11862),x11862)+E(x11861,f2(x11862)) % 1.09/1.26 [1204]~P54(x12044)+~P3(f2(x12044),x12043,x12044)+~P4(f11(x12041,x12043,x12044),x12042,x12044)+P4(x12041,f8(x12042,x12043,x12044),x12044) % 1.09/1.26 [1205]~P54(x12054)+~P3(f2(x12054),x12053,x12054)+~P3(f11(x12051,x12053,x12054),x12052,x12054)+P3(x12051,f8(x12052,x12053,x12054),x12054) % 1.09/1.26 [1206]~P54(x12063)+~P3(f2(x12063),x12062,x12063)+~P4(x12061,f11(x12064,x12062,x12063),x12063)+P4(f8(x12061,x12062,x12063),x12064,x12063) % 1.09/1.26 [1207]~P54(x12073)+~P3(f2(x12073),x12072,x12073)+~P3(x12071,f11(x12074,x12072,x12073),x12073)+P3(f8(x12071,x12072,x12073),x12074,x12073) % 1.09/1.26 [1220]P3(x12202,x12201,x12203)+~P55(x12203)+P3(x12201,x12202,x12203)+~P3(f11(x12204,x12201,x12203),f11(x12204,x12202,x12203),x12203) % 1.09/1.26 [1221]P3(x12212,x12211,x12213)+~P55(x12213)+P3(x12211,x12212,x12213)+~P3(f11(x12211,x12214,x12213),f11(x12212,x12214,x12213),x12213) % 1.09/1.26 [1233]~P55(x12333)+P3(x12331,x12332,x12333)+~P3(f11(x12331,x12334,x12333),f11(x12332,x12334,x12333),x12333)+P3(x12334,f2(x12333),x12333) % 1.09/1.26 [1234]~P55(x12343)+P3(x12341,x12342,x12343)+~P3(f11(x12344,x12341,x12343),f11(x12344,x12342,x12343),x12343)+P3(x12344,f2(x12343),x12343) % 1.09/1.26 [1235]~P55(x12353)+P3(x12351,x12352,x12353)+~P3(f11(x12354,x12352,x12353),f11(x12354,x12351,x12353),x12353)+P3(f2(x12353),x12354,x12353) % 1.09/1.26 [1236]~P55(x12363)+P3(x12361,x12362,x12363)+~P3(f11(x12362,x12364,x12363),f11(x12361,x12364,x12363),x12363)+P3(f2(x12363),x12364,x12363) % 1.09/1.26 [1243]~P55(x12432)+~P3(f11(x12433,x12431,x12432),f11(x12434,x12431,x12432),x12432)+P3(x12431,f2(x12432),x12432)+P3(f2(x12432),x12431,x12432) % 1.09/1.26 [1244]~P55(x12442)+~P3(f11(x12441,x12443,x12442),f11(x12441,x12444,x12442),x12442)+P3(x12441,f2(x12442),x12442)+P3(f2(x12442),x12441,x12442) % 1.09/1.26 [1257]~P33(x12573)+~P4(f31(x12574,x12571,x12573),f31(x12574,x12572,x12573),x12573)+P4(x12571,x12572,a1)+~P3(f10(x12573),x12574,x12573) % 1.09/1.26 [1259]~P33(x12593)+~P3(f31(x12594,x12591,x12593),f31(x12594,x12592,x12593),x12593)+P3(x12591,x12592,a1)+~P3(f10(x12593),x12594,x12593) % 1.09/1.26 [1260]~P55(x12603)+P4(x12601,x12602,x12603)+~P4(f11(x12604,x12602,x12603),f11(x12604,x12601,x12603),x12603)+~P3(x12604,f2(x12603),x12603) % 1.09/1.26 [1261]~P55(x12613)+P3(x12611,x12612,x12613)+~P3(f11(x12614,x12612,x12613),f11(x12614,x12611,x12613),x12613)+~P3(x12614,f2(x12613),x12613) % 1.09/1.26 [1262]~P55(x12623)+P4(x12621,x12622,x12623)+~P4(f11(x12624,x12621,x12623),f11(x12624,x12622,x12623),x12623)+~P3(f2(x12623),x12624,x12623) % 1.09/1.26 [1263]~P56(x12633)+P4(x12631,x12632,x12633)+~P4(f11(x12634,x12631,x12633),f11(x12634,x12632,x12633),x12633)+~P3(f2(x12633),x12634,x12633) % 1.09/1.26 [1264]~P56(x12643)+P4(x12641,x12642,x12643)+~P4(f11(x12641,x12644,x12643),f11(x12642,x12644,x12643),x12643)+~P3(f2(x12643),x12644,x12643) % 1.09/1.26 [1265]~P33(x12653)+P3(x12651,x12652,x12653)+~P4(f2(x12653),x12652,x12653)+~P3(f31(x12651,x12654,x12653),f31(x12652,x12654,x12653),x12653) % 1.09/1.26 [1266]~P55(x12663)+P3(x12661,x12662,x12663)+~P3(f11(x12664,x12661,x12663),f11(x12664,x12662,x12663),x12663)+~P3(f2(x12663),x12664,x12663) % 1.09/1.26 [1267]~P56(x12673)+P3(x12671,x12672,x12673)+~P3(f11(x12674,x12671,x12673),f11(x12674,x12672,x12673),x12673)+~P4(f2(x12673),x12674,x12673) % 1.09/1.26 [1268]~P56(x12683)+P3(x12681,x12682,x12683)+~P3(f11(x12681,x12684,x12683),f11(x12682,x12684,x12683),x12683)+~P4(f2(x12683),x12684,x12683) % 1.09/1.26 [1269]~P57(x12693)+P3(x12691,x12692,x12693)+~P3(f11(x12694,x12691,x12693),f11(x12694,x12692,x12693),x12693)+~P4(f2(x12693),x12694,x12693) % 1.09/1.26 [1270]~P57(x12703)+P3(x12701,x12702,x12703)+~P3(f11(x12701,x12704,x12703),f11(x12702,x12704,x12703),x12703)+~P4(f2(x12703),x12704,x12703) % 1.09/1.26 [950]~P43(x9502)+~P47(x9502)+E(x9501,f2(x9502))+E(f8(f11(x9503,x9501,x9502),f11(x9504,x9501,x9502),x9502),f8(x9503,x9504,x9502)) % 1.09/1.26 [951]~P43(x9512)+~P47(x9512)+E(x9511,f2(x9512))+E(f8(f11(x9511,x9513,x9512),f11(x9511,x9514,x9512),x9512),f8(x9513,x9514,x9512)) % 1.09/1.26 [1208]~P47(x12082)+~P4(x12084,x12083,a1)+E(x12081,f2(x12082))+E(f8(f31(x12081,x12083,x12082),f31(x12081,x12084,x12082),x12082),f31(x12081,f3(x12083,x12084,a1),x12082)) % 1.09/1.26 [1291]~P1(x12913)+~P6(x12912,x12914,x12913)+~P6(x12912,x12911,x12913)+E(f9(f6(x12911,x12912,x12913),f6(x12914,x12912,x12913),x12913),f6(f9(x12911,x12914,x12913),x12912,x12913)) % 1.09/1.26 [1292]~P33(x12923)+P4(x12921,x12922,x12923)+~P4(f2(x12923),x12922,x12923)+~P4(f31(x12921,f30(x12924),x12923),f31(x12922,f30(x12924),x12923),x12923) % 1.09/1.26 [1251]~P43(x12512)+~P47(x12512)+E(x12511,f2(x12512))+E(f8(f9(x12513,f11(x12514,x12511,x12512),x12512),x12511,x12512),f9(x12514,f8(x12513,x12511,x12512),x12512)) % 1.09/1.26 [1252]~P43(x12522)+~P47(x12522)+E(x12521,f2(x12522))+E(f8(f9(x12523,f11(x12524,x12521,x12522),x12522),x12521,x12522),f9(f8(x12523,x12521,x12522),x12524,x12522)) % 1.09/1.26 [885]~P30(x8853)+~P4(x8855,x8854,x8853)+P4(x8851,x8852,x8853)+~E(f3(x8854,x8855,x8853),f3(x8852,x8851,x8853)) % 1.09/1.26 [886]~P30(x8863)+~P4(x8865,x8864,x8863)+P4(x8861,x8862,x8863)+~E(f3(x8862,x8861,x8863),f3(x8864,x8865,x8863)) % 1.09/1.26 [887]~P30(x8873)+~P3(x8874,x8875,x8873)+P3(x8871,x8872,x8873)+~E(f3(x8874,x8875,x8873),f3(x8871,x8872,x8873)) % 1.09/1.26 [888]~P30(x8883)+~P3(x8884,x8885,x8883)+P3(x8881,x8882,x8883)+~E(f3(x8881,x8882,x8883),f3(x8884,x8885,x8883)) % 1.09/1.26 [1129]~P34(x11293)+~P6(x11291,x11294,x11293)+~P4(x11292,x11295,a1)+P6(f31(x11291,x11292,x11293),f31(x11294,x11295,x11293),x11293) % 1.09/1.26 [1130]~P27(x11303)+~P4(x11302,x11305,x11303)+~P4(x11301,x11304,x11303)+P4(f9(x11301,x11302,x11303),f9(x11304,x11305,x11303),x11303) % 1.09/1.26 [1131]~P34(x11313)+~P6(x11312,x11315,x11313)+~P6(x11311,x11314,x11313)+P6(f11(x11311,x11312,x11313),f11(x11314,x11315,x11313),x11313) % 1.09/1.26 [1132]~P32(x11323)+~P4(x11322,x11325,x11323)+~P3(x11321,x11324,x11323)+P3(f9(x11321,x11322,x11323),f9(x11324,x11325,x11323),x11323) % 1.09/1.26 [1133]~P32(x11333)+~P4(x11331,x11334,x11333)+~P3(x11332,x11335,x11333)+P3(f9(x11331,x11332,x11333),f9(x11334,x11335,x11333),x11333) % 1.09/1.26 [1134]~P32(x11343)+~P3(x11342,x11345,x11343)+~P3(x11341,x11344,x11343)+P3(f9(x11341,x11342,x11343),f9(x11344,x11345,x11343),x11343) % 1.09/1.26 [1194]~P34(x11943)+~P6(f31(x11941,x11945,x11943),x11944,x11943)+P6(f31(x11941,x11942,x11943),x11944,x11943)+~P4(x11942,x11945,a1) % 1.09/1.26 [1195]~P30(x11954)+~P4(x11955,x11953,x11954)+~P4(x11951,f9(x11952,x11955,x11954),x11954)+P4(x11951,f9(x11952,x11953,x11954),x11954) % 1.09/1.26 [1295]~P53(x12952)+~P3(f4(x12951,x12952),x12954,x12952)+~P3(f4(x12953,x12952),x12955,x12952)+P3(f11(f4(x12951,x12952),f4(x12953,x12952),x12952),f11(x12954,x12955,x12952),x12952) % 1.09/1.26 [1313]~P1(x13133)+~P6(x13135,x13132,x13133)+~P6(x13134,x13131,x13133)+E(f6(f11(x13131,x13132,x13133),f11(x13134,x13135,x13133),x13133),f11(f6(x13131,x13134,x13133),f6(x13132,x13135,x13133),x13133)) % 1.09/1.26 [1346]~P47(x13462)+E(x13461,f2(x13462))+E(x13463,f2(x13462))+E(f8(f9(f11(x13464,x13461,x13462),f11(x13465,x13463,x13462),x13462),f11(x13463,x13461,x13462),x13462),f9(f8(x13464,x13463,x13462),f8(x13465,x13461,x13462),x13462)) % 1.09/1.26 [1347]~P47(x13472)+E(x13471,f2(x13472))+E(x13473,f2(x13472))+E(f8(f3(f11(x13474,x13471,x13472),f11(x13475,x13473,x13472),x13472),f11(x13473,x13471,x13472),x13472),f3(f8(x13474,x13473,x13472),f8(x13475,x13471,x13472),x13472)) % 1.09/1.26 [1308]~P1(x13083)+~E(f5(x13081,x13084,x13083),f5(x13085,x13084,x13083))+~E(f5(x13082,x13084,x13083),f5(x13086,x13084,x13083))+E(f5(f9(x13081,x13082,x13083),x13084,x13083),f5(f9(x13085,x13086,x13083),x13084,x13083)) % 1.09/1.26 [1309]~P1(x13093)+~E(f5(x13091,x13094,x13093),f5(x13095,x13094,x13093))+~E(f5(x13092,x13094,x13093),f5(x13096,x13094,x13093))+E(f5(f11(x13091,x13092,x13093),x13094,x13093),f5(f11(x13095,x13096,x13093),x13094,x13093)) % 1.09/1.26 [1310]~P7(x13103)+~E(f5(x13101,x13104,x13103),f5(x13105,x13104,x13103))+~E(f5(x13102,x13104,x13103),f5(x13106,x13104,x13103))+E(f5(f3(x13101,x13102,x13103),x13104,x13103),f5(f3(x13105,x13106,x13103),x13104,x13103)) % 1.09/1.26 [829]~P54(x8292)+~P43(x8292)+P4(f10(x8292),x8291,x8292)+~P4(f7(x8291,x8292),f10(x8292),x8292)+P4(x8291,f2(x8292),x8292) % 1.09/1.26 [830]~P54(x8302)+~P43(x8302)+P3(f10(x8302),x8301,x8302)+~P3(f7(x8301,x8302),f10(x8302),x8302)+P4(x8301,f2(x8302),x8302) % 1.09/1.26 [838]~P54(x8381)+~P43(x8381)+~P3(f2(x8381),x8382,x8381)+~P4(x8382,f10(x8381),x8381)+P4(f10(x8381),f7(x8382,x8381),x8381) % 1.09/1.26 [839]~P54(x8391)+~P43(x8391)+~P3(f2(x8391),x8392,x8391)+~P3(x8392,f10(x8391),x8391)+P3(f10(x8391),f7(x8392,x8391),x8391) % 1.09/1.26 [516]~P35(x5162)+~P69(x5162)+~P51(x5162)+~P52(x5162)+~E(f31(x5161,f2(a1),x5162),f2(x5162)) % 1.09/1.26 [354]~P44(x3543)+E(x3541,x3542)+~E(f7(x3541,x3543),f7(x3542,x3543))+E(x3542,f2(x3543))+E(x3541,f2(x3543)) % 1.09/1.26 [846]~P31(x8462)+~P4(f2(x8462),x8461,x8462)+~P4(f2(x8462),x8463,x8462)+~E(f9(x8463,x8461,x8462),f2(x8462))+E(x8461,f2(x8462)) % 1.09/1.26 [847]~P31(x8472)+~P4(f2(x8472),x8473,x8472)+~P4(f2(x8472),x8471,x8472)+~E(f9(x8471,x8473,x8472),f2(x8472))+E(x8471,f2(x8472)) % 1.09/1.26 [1030]~P54(x10301)+~P43(x10301)+~P4(x10303,f2(x10301),x10301)+~P4(x10302,f2(x10301),x10301)+P4(f2(x10301),f8(x10302,x10303,x10301),x10301) % 1.09/1.26 [1032]~P54(x10321)+~P43(x10321)+~P4(f2(x10321),x10323,x10321)+~P4(f2(x10321),x10322,x10321)+P4(f2(x10321),f8(x10322,x10323,x10321),x10321) % 1.09/1.26 [1034]~P54(x10343)+~P43(x10343)+~P4(x10342,f2(x10343),x10343)+~P4(f2(x10343),x10341,x10343)+P4(f8(x10341,x10342,x10343),f2(x10343),x10343) % 1.09/1.26 [1035]~P54(x10353)+~P43(x10353)+~P4(x10351,f2(x10353),x10353)+~P4(f2(x10353),x10352,x10353)+P4(f8(x10351,x10352,x10353),f2(x10353),x10353) % 1.09/1.26 [1060]~P54(x10602)+~P43(x10602)+~P4(f8(x10603,x10601,x10602),f2(x10602),x10602)+P4(x10601,f2(x10602),x10602)+P4(x10603,f2(x10602),x10602) % 1.09/1.26 [1061]~P54(x10612)+~P43(x10612)+~P3(f8(x10613,x10611,x10612),f2(x10612),x10612)+P3(x10611,f2(x10612),x10612)+P3(x10613,f2(x10612),x10612) % 1.09/1.26 [1062]~P54(x10622)+~P43(x10622)+~P4(f2(x10622),f8(x10623,x10621,x10622),x10622)+P4(x10621,f2(x10622),x10622)+P4(f2(x10622),x10623,x10622) % 1.09/1.26 [1063]~P54(x10632)+~P43(x10632)+~P4(f2(x10632),f8(x10631,x10633,x10632),x10632)+P4(x10631,f2(x10632),x10632)+P4(f2(x10632),x10633,x10632) % 1.09/1.26 [1064]~P54(x10642)+~P43(x10642)+~P4(f2(x10642),f8(x10643,x10641,x10642),x10642)+P4(x10641,f2(x10642),x10642)+P4(f2(x10642),x10641,x10642) % 1.09/1.26 [1065]~P54(x10652)+~P43(x10652)+~P4(f2(x10652),f8(x10651,x10653,x10652),x10652)+P4(x10651,f2(x10652),x10652)+P4(f2(x10652),x10651,x10652) % 1.09/1.26 [1066]~P54(x10662)+~P43(x10662)+~P3(f2(x10662),f8(x10663,x10661,x10662),x10662)+P3(x10661,f2(x10662),x10662)+P3(f2(x10662),x10663,x10662) % 1.09/1.26 [1067]~P54(x10672)+~P43(x10672)+~P3(f2(x10672),f8(x10671,x10673,x10672),x10672)+P3(x10671,f2(x10672),x10672)+P3(f2(x10672),x10673,x10672) % 1.09/1.26 [1068]~P54(x10682)+~P43(x10682)+~P3(f2(x10682),f8(x10683,x10681,x10682),x10682)+P3(x10681,f2(x10682),x10682)+P3(f2(x10682),x10681,x10682) % 1.09/1.26 [1069]~P54(x10692)+~P43(x10692)+~P3(f2(x10692),f8(x10691,x10693,x10692),x10692)+P3(x10691,f2(x10692),x10692)+P3(f2(x10692),x10691,x10692) % 1.09/1.26 [1070]~P54(x10702)+~P43(x10702)+~P4(f8(x10703,x10701,x10702),f2(x10702),x10702)+P4(x10701,f2(x10702),x10702)+P4(f2(x10702),x10701,x10702) % 1.09/1.26 [1071]~P54(x10712)+~P43(x10712)+~P4(f8(x10711,x10713,x10712),f2(x10712),x10712)+P4(x10711,f2(x10712),x10712)+P4(f2(x10712),x10711,x10712) % 1.09/1.26 [1072]~P54(x10722)+~P43(x10722)+~P3(f8(x10723,x10721,x10722),f2(x10722),x10722)+P3(x10721,f2(x10722),x10722)+P3(f2(x10722),x10721,x10722) % 1.09/1.26 [1073]~P54(x10732)+~P43(x10732)+~P3(f8(x10731,x10733,x10732),f2(x10732),x10732)+P3(x10731,f2(x10732),x10732)+P3(f2(x10732),x10731,x10732) % 1.09/1.26 [1074]~P54(x10741)+~P43(x10741)+~P4(f8(x10742,x10743,x10741),f2(x10741),x10741)+P4(f2(x10741),x10742,x10741)+P4(f2(x10741),x10743,x10741) % 1.09/1.26 [1075]~P54(x10751)+~P43(x10751)+~P3(f8(x10752,x10753,x10751),f2(x10751),x10751)+P3(f2(x10751),x10752,x10751)+P3(f2(x10751),x10753,x10751) % 1.09/1.26 [1144]~P53(x11443)+~P4(x11441,f10(x11443),x11443)+~P4(f2(x11443),x11442,x11443)+~P4(f2(x11443),x11441,x11443)+P4(f11(x11441,x11442,x11443),x11442,x11443) % 1.09/1.26 [1145]~P53(x11453)+~P4(x11452,f10(x11453),x11453)+~P4(f2(x11453),x11452,x11453)+~P4(f2(x11453),x11451,x11453)+P4(f11(x11451,x11452,x11453),x11451,x11453) % 1.09/1.26 [969]~P10(x9694)+~P11(x9694)+~P4(x9691,x9693,x9694)+~P4(f2(x9694),x9692,x9694)+P4(x9691,f9(x9692,x9693,x9694),x9694) % 1.09/1.26 [970]~P10(x9704)+~P11(x9704)+~P4(x9701,x9702,x9704)+~P4(f2(x9704),x9703,x9704)+P4(x9701,f9(x9702,x9703,x9704),x9704) % 1.09/1.26 [971]~P10(x9714)+~P11(x9714)+~P4(x9711,x9713,x9714)+~P3(f2(x9714),x9712,x9714)+P3(x9711,f9(x9712,x9713,x9714),x9714) % 1.09/1.26 [972]~P10(x9724)+~P11(x9724)+~P3(x9721,x9723,x9724)+~P4(f2(x9724),x9722,x9724)+P3(x9721,f9(x9722,x9723,x9724),x9724) % 1.09/1.26 [1172]~P54(x11723)+~P43(x11723)+~P4(x11724,x11721,x11723)+~P4(x11722,f2(x11723),x11723)+P4(f8(x11721,x11722,x11723),f8(x11724,x11722,x11723),x11723) % 1.09/1.26 [1173]~P54(x11733)+~P43(x11733)+~P4(x11731,x11734,x11733)+~P4(f2(x11733),x11732,x11733)+P4(f8(x11731,x11732,x11733),f8(x11734,x11732,x11733),x11733) % 1.09/1.26 [1210]~P54(x12104)+~P43(x12104)+~P3(f2(x12104),x12103,x12104)+~P4(f8(x12101,x12103,x12104),x12102,x12104)+P4(x12101,f11(x12102,x12103,x12104),x12104) % 1.09/1.26 [1212]~P54(x12124)+~P43(x12124)+~P3(f2(x12124),x12123,x12124)+~P3(f8(x12121,x12123,x12124),x12122,x12124)+P3(x12121,f11(x12122,x12123,x12124),x12124) % 1.09/1.26 [1214]~P54(x12143)+~P43(x12143)+~P3(f2(x12143),x12142,x12143)+~P4(x12141,f8(x12144,x12142,x12143),x12143)+P4(f11(x12141,x12142,x12143),x12144,x12143) % 1.09/1.26 [1216]~P54(x12163)+~P43(x12163)+~P3(f2(x12163),x12162,x12163)+~P3(x12161,f8(x12164,x12162,x12163),x12163)+P3(f11(x12161,x12162,x12163),x12164,x12163) % 1.09/1.26 [1219]~P1(x12193)+~P6(x12192,x12194,x12193)+~P6(x12192,x12191,x12193)+~P6(x12191,x12194,x12193)+P6(f6(x12191,x12192,x12193),f6(x12194,x12192,x12193),x12193) % 1.09/1.26 [1237]~P33(x12373)+~P3(x12371,x12374,x12373)+~P4(f2(x12373),x12371,x12373)+P3(f31(x12371,x12372,x12373),f31(x12374,x12372,x12373),x12373)+~P3(f2(a1),x12372,a1) % 1.09/1.26 [1245]~P33(x12453)+~P4(x12454,x12452,a1)+~P4(x12451,f10(x12453),x12453)+~P4(f2(x12453),x12451,x12453)+P4(f31(x12451,x12452,x12453),f31(x12451,x12454,x12453),x12453) % 1.09/1.26 [1246]~P33(x12463)+~P3(x12464,x12462,a1)+~P3(x12461,f10(x12463),x12463)+~P3(f2(x12463),x12461,x12463)+P3(f31(x12461,x12462,x12463),f31(x12461,x12464,x12463),x12463) % 1.09/1.26 [1307]~P1(x13073)+~P6(x13074,x13071,x13073)+P6(x13071,x13072,x13073)+~P6(x13074,x13072,x13073)+~P6(f6(x13071,x13074,x13073),f6(x13072,x13074,x13073),x13073) % 1.09/1.26 [1314]~P54(x13143)+~P3(x13142,x13144,x13143)+~P3(x13141,f2(x13143),x13143)+~P3(f2(x13143),f11(x13142,x13144,x13143),x13143)+P3(f8(x13141,x13142,x13143),f8(x13141,x13144,x13143),x13143) % 1.09/1.26 [1315]~P54(x13153)+~P4(x13154,x13152,x13153)+~P4(f2(x13153),x13151,x13153)+~P3(f2(x13153),f11(x13152,x13154,x13153),x13153)+P4(f8(x13151,x13152,x13153),f8(x13151,x13154,x13153),x13153) % 1.09/1.26 [1316]~P54(x13163)+~P3(x13164,x13162,x13163)+~P3(f2(x13163),x13161,x13163)+~P3(f2(x13163),f11(x13162,x13164,x13163),x13163)+P3(f8(x13161,x13162,x13163),f8(x13161,x13164,x13163),x13163) % 1.09/1.26 [1042]~P33(x10424)+E(x10421,x10422)+~P4(f2(x10424),x10422,x10424)+~P4(f2(x10424),x10421,x10424)+~E(f31(x10421,f30(x10423),x10424),f31(x10422,f30(x10423),x10424)) % 1.09/1.26 [848]~P47(x8482)+~E(f8(x8484,x8483,x8482),f8(x8485,x8481,x8482))+E(f11(x8484,x8481,x8482),f11(x8485,x8483,x8482))+E(x8481,f2(x8482))+E(x8483,f2(x8482)) % 1.09/1.26 [849]~P47(x8492)+~E(f11(x8494,x8493,x8492),f11(x8495,x8491,x8492))+E(f8(x8494,x8491,x8492),f8(x8495,x8493,x8492))+E(x8491,f2(x8492))+E(x8493,f2(x8492)) % 1.09/1.26 [1218]~P48(x12184)+~P14(x12184)+E(x12181,x12182)+E(x12183,f2(x12184))+~E(f9(x12185,f11(x12183,x12181,x12184),x12184),f9(x12185,f11(x12183,x12182,x12184),x12184)) % 1.09/1.26 [1335]~P48(x13355)+~P14(x13355)+E(x13351,x13352)+E(x13353,x13354)+~E(f9(f11(x13353,x13351,x13355),f11(x13354,x13352,x13355),x13355),f9(f11(x13353,x13352,x13355),f11(x13354,x13351,x13355),x13355)) % 1.09/1.26 [1355]~P42(x13555)+~P41(x13555)+~P6(x13551,x13554,x13555)+~P6(x13551,f9(x13552,x13556,x13555),x13555)+P6(x13551,f9(f3(x13552,f11(x13553,x13554,x13555),x13555),x13556,x13555),x13555) % 1.09/1.26 [1356]~P42(x13564)+~P41(x13564)+~P6(x13561,x13565,x13564)+P6(x13561,f9(x13562,x13563,x13564),x13564)+~P6(x13561,f9(f3(x13562,f11(x13566,x13565,x13564),x13564),x13563,x13564),x13564) % 1.09/1.26 [447]~P35(x4472)+~P69(x4472)+~P51(x4472)+~P52(x4472)+E(x4471,f2(a1))+E(f31(f2(x4472),x4471,x4472),f2(x4472)) % 1.09/1.26 [517]~P35(x5172)+~P69(x5172)+~P51(x5172)+~P52(x5172)+~E(f31(x5171,x5173,x5172),f2(x5172))+E(x5171,f2(x5172)) % 1.09/1.26 [1051]~P54(x10512)+~P43(x10512)+P3(x10511,f2(x10512),x10512)+P3(f2(x10512),x10511,x10512)+~P4(x10513,f2(x10512),x10512)+P4(x10513,f8(x10514,x10511,x10512),x10512) % 1.09/1.26 [1052]~P54(x10522)+~P43(x10522)+P3(x10521,f2(x10522),x10522)+P3(f2(x10522),x10521,x10522)+~P3(x10523,f2(x10522),x10522)+P3(x10523,f8(x10524,x10521,x10522),x10522) % 1.09/1.26 [1053]~P54(x10532)+~P43(x10532)+P3(x10531,f2(x10532),x10532)+P3(f2(x10532),x10531,x10532)+~P4(f2(x10532),x10534,x10532)+P4(f8(x10533,x10531,x10532),x10534,x10532) % 1.09/1.26 [1054]~P54(x10542)+~P43(x10542)+P3(x10541,f2(x10542),x10542)+P3(f2(x10542),x10541,x10542)+~P3(f2(x10542),x10544,x10542)+P3(f8(x10543,x10541,x10542),x10544,x10542) % 1.09/1.26 [1136]~P54(x11362)+~P43(x11362)+P4(x11361,f2(x11362),x11362)+P3(f2(x11362),x11363,x11362)+~P4(x11361,f8(x11364,x11363,x11362),x11362)+P3(x11363,f2(x11362),x11362) % 1.09/1.26 [1137]~P54(x11372)+~P43(x11372)+P3(x11371,f2(x11372),x11372)+P3(f2(x11372),x11371,x11372)+~P3(x11373,f8(x11374,x11371,x11372),x11372)+P3(x11373,f2(x11372),x11372) % 1.09/1.26 [1138]~P54(x11382)+~P43(x11382)+P3(x11381,f2(x11382),x11382)+P3(f2(x11382),x11381,x11382)+~P4(f8(x11384,x11381,x11382),x11383,x11382)+P4(f2(x11382),x11383,x11382) % 1.09/1.26 [1139]~P54(x11392)+~P43(x11392)+P3(x11391,f2(x11392),x11392)+P3(f2(x11392),x11391,x11392)+~P3(f8(x11394,x11391,x11392),x11393,x11392)+P3(f2(x11392),x11393,x11392) % 1.09/1.26 [1167]~P33(x11674)+E(x11671,x11672)+~P4(f2(x11674),x11672,x11674)+~P4(f2(x11674),x11671,x11674)+~E(f31(x11671,x11673,x11674),f31(x11672,x11673,x11674))+~P3(f2(a1),x11673,a1) % 1.09/1.26 [1272]~P54(x12722)+~P43(x12722)+~P4(f11(x12723,x12721,x12722),x12724,x12722)+P3(x12721,f2(x12722),x12722)+~P4(x12723,f2(x12722),x12722)+P4(x12723,f8(x12724,x12721,x12722),x12722) % 1.09/1.26 [1273]~P54(x12732)+~P43(x12732)+~P3(f11(x12733,x12731,x12732),x12734,x12732)+P3(x12731,f2(x12732),x12732)+~P3(x12733,f2(x12732),x12732)+P3(x12733,f8(x12734,x12731,x12732),x12732) % 1.09/1.26 [1274]~P54(x12742)+~P43(x12742)+~P4(x12743,f11(x12744,x12741,x12742),x12742)+P3(x12741,f2(x12742),x12742)+~P4(f2(x12742),x12744,x12742)+P4(f8(x12743,x12741,x12742),x12744,x12742) % 1.09/1.26 [1275]~P54(x12752)+~P43(x12752)+~P3(x12753,f11(x12754,x12751,x12752),x12752)+P3(x12751,f2(x12752),x12752)+~P3(f2(x12752),x12754,x12752)+P3(f8(x12753,x12751,x12752),x12754,x12752) % 1.09/1.26 [1276]~P54(x12761)+~P43(x12761)+~P4(x12764,f8(x12763,x12762,x12761),x12761)+~P3(x12762,f2(x12761),x12761)+P3(f2(x12761),x12762,x12761)+P4(x12763,f11(x12764,x12762,x12761),x12761) % 1.09/1.26 [1277]~P54(x12771)+~P43(x12771)+~P4(x12774,f11(x12773,x12772,x12771),x12771)+~P4(x12773,f2(x12771),x12771)+P3(f2(x12771),x12772,x12771)+P4(x12773,f8(x12774,x12772,x12771),x12771) % 1.09/1.26 [1278]~P54(x12781)+~P43(x12781)+~P4(x12784,f11(x12783,x12782,x12781),x12781)+~P3(x12782,f2(x12781),x12781)+P3(f2(x12781),x12782,x12781)+P4(x12783,f8(x12784,x12782,x12781),x12781) % 1.09/1.26 [1279]~P54(x12791)+~P43(x12791)+~P3(x12794,f8(x12793,x12792,x12791),x12791)+~P3(x12792,f2(x12791),x12791)+P3(f2(x12791),x12792,x12791)+P3(x12793,f11(x12794,x12792,x12791),x12791) % 1.09/1.26 [1280]~P54(x12801)+~P43(x12801)+~P3(x12804,f11(x12803,x12802,x12801),x12801)+~P3(x12802,f2(x12801),x12801)+P3(f2(x12801),x12802,x12801)+P3(x12803,f8(x12804,x12802,x12801),x12801) % 1.09/1.26 [1281]~P54(x12811)+~P43(x12811)+~P3(x12814,f11(x12813,x12812,x12811),x12811)+~P3(x12813,f2(x12811),x12811)+P3(f2(x12811),x12812,x12811)+P3(x12813,f8(x12814,x12812,x12811),x12811) % 1.09/1.26 [1282]~P54(x12821)+~P43(x12821)+~P4(f8(x12824,x12822,x12821),x12823,x12821)+~P3(x12822,f2(x12821),x12821)+P3(f2(x12821),x12822,x12821)+P4(f11(x12823,x12822,x12821),x12824,x12821) % 1.09/1.26 [1283]~P54(x12831)+~P43(x12831)+~P4(f11(x12834,x12832,x12831),x12833,x12831)+~P3(x12832,f2(x12831),x12831)+P3(f2(x12831),x12832,x12831)+P4(f8(x12833,x12832,x12831),x12834,x12831) % 1.09/1.26 [1284]~P54(x12841)+~P43(x12841)+~P3(f8(x12844,x12842,x12841),x12843,x12841)+~P3(x12842,f2(x12841),x12841)+P3(f2(x12841),x12842,x12841)+P3(f11(x12843,x12842,x12841),x12844,x12841) % 1.09/1.26 [1285]~P54(x12851)+~P43(x12851)+~P3(f11(x12854,x12852,x12851),x12853,x12851)+~P3(x12852,f2(x12851),x12851)+P3(f2(x12851),x12852,x12851)+P3(f8(x12853,x12852,x12851),x12854,x12851) % 1.09/1.26 [1286]~P54(x12861)+~P43(x12861)+~P4(f11(x12864,x12862,x12861),x12863,x12861)+~P4(f2(x12861),x12864,x12861)+P3(f2(x12861),x12862,x12861)+P4(f8(x12863,x12862,x12861),x12864,x12861) % 1.09/1.26 [1287]~P54(x12871)+~P43(x12871)+~P3(f11(x12874,x12872,x12871),x12873,x12871)+~P3(f2(x12871),x12874,x12871)+P3(f2(x12871),x12872,x12871)+P3(f8(x12873,x12872,x12871),x12874,x12871) % 1.09/1.26 [1317]~P54(x13173)+~P43(x13173)+~P4(x13172,x13174,x13173)+~P4(x13171,f2(x13173),x13173)+~P3(f2(x13173),f11(x13172,x13174,x13173),x13173)+P4(f8(x13171,x13172,x13173),f8(x13171,x13174,x13173),x13173) % 1.09/1.26 [1324]~P54(x13244)+~P43(x13244)+~P4(x13241,f2(x13244),x13244)+~P4(x13242,f11(x13241,x13243,x13244),x13244)+~P4(f11(x13241,x13243,x13244),x13242,x13244)+P4(x13241,f8(x13242,x13243,x13244),x13244) % 1.09/1.26 [1325]~P54(x13254)+~P43(x13254)+~P3(x13253,f2(x13254),x13254)+~P4(x13252,f11(x13251,x13253,x13254),x13254)+~P4(f11(x13251,x13253,x13254),x13252,x13254)+P4(x13251,f8(x13252,x13253,x13254),x13254) % 1.09/1.26 [1326]~P54(x13264)+~P43(x13264)+~P3(x13263,f2(x13264),x13264)+~P3(x13262,f11(x13261,x13263,x13264),x13264)+~P3(f11(x13261,x13263,x13264),x13262,x13264)+P3(x13261,f8(x13262,x13263,x13264),x13264) % 1.09/1.26 [1327]~P54(x13274)+~P43(x13274)+~P3(x13271,f2(x13274),x13274)+~P3(x13272,f11(x13271,x13273,x13274),x13274)+~P3(f11(x13271,x13273,x13274),x13272,x13274)+P3(x13271,f8(x13272,x13273,x13274),x13274) % 1.09/1.26 [1328]~P54(x13283)+~P43(x13283)+~P3(x13282,f2(x13283),x13283)+~P4(x13281,f11(x13284,x13282,x13283),x13283)+~P4(f11(x13284,x13282,x13283),x13281,x13283)+P4(f8(x13281,x13282,x13283),x13284,x13283) % 1.09/1.26 [1329]~P54(x13293)+~P43(x13293)+~P3(x13292,f2(x13293),x13293)+~P3(x13291,f11(x13294,x13292,x13293),x13293)+~P3(f11(x13294,x13292,x13293),x13291,x13293)+P3(f8(x13291,x13292,x13293),x13294,x13293) % 1.09/1.26 [1330]~P54(x13303)+~P43(x13303)+~P4(f2(x13303),x13304,x13303)+~P4(x13301,f11(x13304,x13302,x13303),x13303)+~P4(f11(x13304,x13302,x13303),x13301,x13303)+P4(f8(x13301,x13302,x13303),x13304,x13303) % 1.09/1.26 [1331]~P54(x13313)+~P43(x13313)+~P3(f2(x13313),x13314,x13313)+~P3(x13311,f11(x13314,x13312,x13313),x13313)+~P3(f11(x13314,x13312,x13313),x13311,x13313)+P3(f8(x13311,x13312,x13313),x13314,x13313) % 1.09/1.26 [1296]~P61(x12963)+~P4(x12962,x12965,x12963)+~P4(x12961,x12964,x12963)+~P4(f2(x12963),x12964,x12963)+~P4(f2(x12963),x12962,x12963)+P4(f11(x12961,x12962,x12963),f11(x12964,x12965,x12963),x12963) % 1.09/1.26 [1297]~P61(x12973)+~P4(x12972,x12975,x12973)+~P4(x12971,x12974,x12973)+~P4(f2(x12973),x12972,x12973)+~P4(f2(x12973),x12971,x12973)+P4(f11(x12971,x12972,x12973),f11(x12974,x12975,x12973),x12973) % 1.09/1.26 [1298]~P54(x12983)+~P4(x12985,x12982,x12983)+~P4(x12981,x12984,x12983)+~P4(f2(x12983),x12981,x12983)+~P3(f2(x12983),x12985,x12983)+P4(f8(x12981,x12982,x12983),f8(x12984,x12985,x12983),x12983) % 1.09/1.26 [1299]~P56(x12993)+~P4(x12992,x12995,x12993)+~P3(x12991,x12994,x12993)+~P4(f2(x12993),x12991,x12993)+~P3(f2(x12993),x12992,x12993)+P3(f11(x12991,x12992,x12993),f11(x12994,x12995,x12993),x12993) % 1.09/1.26 [1300]~P56(x13003)+~P4(x13001,x13004,x13003)+~P3(x13002,x13005,x13003)+~P4(f2(x13003),x13002,x13003)+~P3(f2(x13003),x13001,x13003)+P3(f11(x13001,x13002,x13003),f11(x13004,x13005,x13003),x13003) % 1.09/1.26 [1301]~P56(x13013)+~P3(x13012,x13015,x13013)+~P3(x13011,x13014,x13013)+~P4(f2(x13013),x13012,x13013)+~P4(f2(x13013),x13011,x13013)+P3(f11(x13011,x13012,x13013),f11(x13014,x13015,x13013),x13013) % 1.09/1.26 [1302]~P56(x13023)+~P3(x13022,x13025,x13023)+~P3(x13021,x13024,x13023)+~P4(f2(x13023),x13022,x13023)+~P3(f2(x13023),x13024,x13023)+P3(f11(x13021,x13022,x13023),f11(x13024,x13025,x13023),x13023) % 1.09/1.26 [1303]~P54(x13033)+~P4(x13035,x13032,x13033)+~P3(x13031,x13034,x13033)+~P4(f2(x13033),x13031,x13033)+~P3(f2(x13033),x13035,x13033)+P3(f8(x13031,x13032,x13033),f8(x13034,x13035,x13033),x13033) % 1.09/1.26 [1304]~P54(x13043)+~P4(x13041,x13044,x13043)+~P3(x13045,x13042,x13043)+~P3(f2(x13043),x13045,x13043)+~P3(f2(x13043),x13041,x13043)+P3(f8(x13041,x13042,x13043),f8(x13044,x13045,x13043),x13043) % 1.09/1.26 %EqnAxiom % 1.09/1.26 [1]E(x11,x11) % 1.09/1.26 [2]E(x22,x21)+~E(x21,x22) % 1.09/1.26 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.09/1.26 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 1.09/1.26 [5]~E(x51,x52)+E(f14(x51),f14(x52)) % 1.09/1.26 [6]~E(x61,x62)+E(f9(x61,x63,x64),f9(x62,x63,x64)) % 1.09/1.26 [7]~E(x71,x72)+E(f9(x73,x71,x74),f9(x73,x72,x74)) % 1.09/1.26 [8]~E(x81,x82)+E(f9(x83,x84,x81),f9(x83,x84,x82)) % 1.09/1.26 [9]~E(x91,x92)+E(f27(x91),f27(x92)) % 1.09/1.26 [10]~E(x101,x102)+E(f4(x101,x103),f4(x102,x103)) % 1.09/1.26 [11]~E(x111,x112)+E(f4(x113,x111),f4(x113,x112)) % 1.09/1.26 [12]~E(x121,x122)+E(f15(x121),f15(x122)) % 1.09/1.26 [13]~E(x131,x132)+E(f18(x131,x133),f18(x132,x133)) % 1.09/1.26 [14]~E(x141,x142)+E(f18(x143,x141),f18(x143,x142)) % 1.09/1.26 [15]~E(x151,x152)+E(f11(x151,x153,x154),f11(x152,x153,x154)) % 1.09/1.26 [16]~E(x161,x162)+E(f11(x163,x161,x164),f11(x163,x162,x164)) % 1.09/1.26 [17]~E(x171,x172)+E(f11(x173,x174,x171),f11(x173,x174,x172)) % 1.09/1.26 [18]~E(x181,x182)+E(f3(x181,x183,x184),f3(x182,x183,x184)) % 1.09/1.26 [19]~E(x191,x192)+E(f3(x193,x191,x194),f3(x193,x192,x194)) % 1.09/1.26 [20]~E(x201,x202)+E(f3(x203,x204,x201),f3(x203,x204,x202)) % 1.09/1.26 [21]~E(x211,x212)+E(f8(x211,x213,x214),f8(x212,x213,x214)) % 1.09/1.26 [22]~E(x221,x222)+E(f8(x223,x221,x224),f8(x223,x222,x224)) % 1.09/1.26 [23]~E(x231,x232)+E(f8(x233,x234,x231),f8(x233,x234,x232)) % 1.09/1.26 [24]~E(x241,x242)+E(f25(x241,x243),f25(x242,x243)) % 1.09/1.26 [25]~E(x251,x252)+E(f25(x253,x251),f25(x253,x252)) % 1.09/1.26 [26]~E(x261,x262)+E(f5(x261,x263,x264),f5(x262,x263,x264)) % 1.09/1.26 [27]~E(x271,x272)+E(f5(x273,x271,x274),f5(x273,x272,x274)) % 1.09/1.26 [28]~E(x281,x282)+E(f5(x283,x284,x281),f5(x283,x284,x282)) % 1.09/1.26 [29]~E(x291,x292)+E(f10(x291),f10(x292)) % 1.09/1.26 [30]~E(x301,x302)+E(f30(x301),f30(x302)) % 1.09/1.26 [31]~E(x311,x312)+E(f28(x311,x313,x314),f28(x312,x313,x314)) % 1.09/1.26 [32]~E(x321,x322)+E(f28(x323,x321,x324),f28(x323,x322,x324)) % 1.09/1.26 [33]~E(x331,x332)+E(f28(x333,x334,x331),f28(x333,x334,x332)) % 1.09/1.26 [34]~E(x341,x342)+E(f22(x341,x343,x344),f22(x342,x343,x344)) % 1.09/1.26 [35]~E(x351,x352)+E(f22(x353,x351,x354),f22(x353,x352,x354)) % 1.09/1.26 [36]~E(x361,x362)+E(f22(x363,x364,x361),f22(x363,x364,x362)) % 1.09/1.26 [37]~E(x371,x372)+E(f6(x371,x373,x374),f6(x372,x373,x374)) % 1.09/1.26 [38]~E(x381,x382)+E(f6(x383,x381,x384),f6(x383,x382,x384)) % 1.09/1.26 [39]~E(x391,x392)+E(f6(x393,x394,x391),f6(x393,x394,x392)) % 1.09/1.26 [40]~E(x401,x402)+E(f13(x401,x403),f13(x402,x403)) % 1.09/1.26 [41]~E(x411,x412)+E(f13(x413,x411),f13(x413,x412)) % 1.09/1.26 [42]~E(x421,x422)+E(f31(x421,x423,x424),f31(x422,x423,x424)) % 1.09/1.26 [43]~E(x431,x432)+E(f31(x433,x431,x434),f31(x433,x432,x434)) % 1.09/1.26 [44]~E(x441,x442)+E(f31(x443,x444,x441),f31(x443,x444,x442)) % 1.09/1.26 [45]~E(x451,x452)+E(f12(x451,x453),f12(x452,x453)) % 1.09/1.26 [46]~E(x461,x462)+E(f12(x463,x461),f12(x463,x462)) % 1.09/1.26 [47]~E(x471,x472)+E(f17(x471),f17(x472)) % 1.09/1.26 [48]~E(x481,x482)+E(f29(x481,x483,x484),f29(x482,x483,x484)) % 1.09/1.26 [49]~E(x491,x492)+E(f29(x493,x491,x494),f29(x493,x492,x494)) % 1.09/1.26 [50]~E(x501,x502)+E(f29(x503,x504,x501),f29(x503,x504,x502)) % 1.09/1.26 [51]~E(x511,x512)+E(f7(x511,x513),f7(x512,x513)) % 1.09/1.26 [52]~E(x521,x522)+E(f7(x523,x521),f7(x523,x522)) % 1.09/1.26 [53]~E(x531,x532)+E(f19(x531,x533,x534),f19(x532,x533,x534)) % 1.09/1.26 [54]~E(x541,x542)+E(f19(x543,x541,x544),f19(x543,x542,x544)) % 1.09/1.26 [55]~E(x551,x552)+E(f19(x553,x554,x551),f19(x553,x554,x552)) % 1.09/1.26 [56]~E(x561,x562)+E(f16(x561,x563),f16(x562,x563)) % 1.09/1.26 [57]~E(x571,x572)+E(f16(x573,x571),f16(x573,x572)) % 1.09/1.26 [58]~E(x581,x582)+E(f20(x581,x583),f20(x582,x583)) % 1.09/1.26 [59]~E(x591,x592)+E(f20(x593,x591),f20(x593,x592)) % 1.09/1.26 [60]~E(x601,x602)+E(f23(x601,x603,x604),f23(x602,x603,x604)) % 1.09/1.26 [61]~E(x611,x612)+E(f23(x613,x611,x614),f23(x613,x612,x614)) % 1.09/1.26 [62]~E(x621,x622)+E(f23(x623,x624,x621),f23(x623,x624,x622)) % 1.09/1.26 [63]~E(x631,x632)+E(f24(x631,x633),f24(x632,x633)) % 1.09/1.26 [64]~E(x641,x642)+E(f24(x643,x641),f24(x643,x642)) % 1.09/1.26 [65]~E(x651,x652)+E(f26(x651,x653),f26(x652,x653)) % 1.09/1.26 [66]~E(x661,x662)+E(f26(x663,x661),f26(x663,x662)) % 1.09/1.26 [67]~E(x671,x672)+E(f21(x671,x673,x674),f21(x672,x673,x674)) % 1.09/1.26 [68]~E(x681,x682)+E(f21(x683,x681,x684),f21(x683,x682,x684)) % 1.09/1.26 [69]~E(x691,x692)+E(f21(x693,x694,x691),f21(x693,x694,x692)) % 1.09/1.26 [70]~P1(x701)+P1(x702)+~E(x701,x702) % 1.09/1.26 [71]~P8(x711)+P8(x712)+~E(x711,x712) % 1.09/1.26 [72]~P9(x721)+P9(x722)+~E(x721,x722) % 1.09/1.26 [73]~P33(x731)+P33(x732)+~E(x731,x732) % 1.09/1.26 [74]~P10(x741)+P10(x742)+~E(x741,x742) % 1.09/1.26 [75]~P11(x751)+P11(x752)+~E(x751,x752) % 1.09/1.26 [76]~P34(x761)+P34(x762)+~E(x761,x762) % 1.09/1.26 [77]~P12(x771)+P12(x772)+~E(x771,x772) % 1.09/1.26 [78]~P56(x781)+P56(x782)+~E(x781,x782) % 1.09/1.26 [79]~P57(x791)+P57(x792)+~E(x791,x792) % 1.09/1.26 [80]~P58(x801)+P58(x802)+~E(x801,x802) % 1.09/1.26 [81]~P35(x811)+P35(x812)+~E(x811,x812) % 1.09/1.26 [82]~P21(x821)+P21(x822)+~E(x821,x822) % 1.09/1.26 [83]~P22(x831)+P22(x832)+~E(x831,x832) % 1.09/1.26 [84]~P42(x841)+P42(x842)+~E(x841,x842) % 1.09/1.26 [85]~P27(x851)+P27(x852)+~E(x851,x852) % 1.09/1.26 [86]~P31(x861)+P31(x862)+~E(x861,x862) % 1.09/1.26 [87]~P68(x871)+P68(x872)+~E(x871,x872) % 1.09/1.26 [88]~P36(x881)+P36(x882)+~E(x881,x882) % 1.09/1.26 [89]~P37(x891)+P37(x892)+~E(x891,x892) % 1.09/1.26 [90]~P15(x901)+P15(x902)+~E(x901,x902) % 1.09/1.26 [91]~P32(x911)+P32(x912)+~E(x911,x912) % 1.09/1.26 [92]~P59(x921)+P59(x922)+~E(x921,x922) % 1.09/1.26 [93]~P60(x931)+P60(x932)+~E(x931,x932) % 1.09/1.26 [94]~P17(x941)+P17(x942)+~E(x941,x942) % 1.09/1.26 [95]~P20(x951)+P20(x952)+~E(x951,x952) % 1.09/1.26 [96]~P45(x961)+P45(x962)+~E(x961,x962) % 1.09/1.26 [97]~P2(x971)+P2(x972)+~E(x971,x972) % 1.09/1.26 [98]P4(x982,x983,x984)+~E(x981,x982)+~P4(x981,x983,x984) % 1.09/1.26 [99]P4(x993,x992,x994)+~E(x991,x992)+~P4(x993,x991,x994) % 1.09/1.26 [100]P4(x1003,x1004,x1002)+~E(x1001,x1002)+~P4(x1003,x1004,x1001) % 1.09/1.26 [101]P3(x1012,x1013,x1014)+~E(x1011,x1012)+~P3(x1011,x1013,x1014) % 1.09/1.26 [102]P3(x1023,x1022,x1024)+~E(x1021,x1022)+~P3(x1023,x1021,x1024) % 1.09/1.26 [103]P3(x1033,x1034,x1032)+~E(x1031,x1032)+~P3(x1033,x1034,x1031) % 1.09/1.26 [104]~P46(x1041)+P46(x1042)+~E(x1041,x1042) % 1.09/1.26 [105]~P50(x1051)+P50(x1052)+~E(x1051,x1052) % 1.09/1.26 [106]~P61(x1061)+P61(x1062)+~E(x1061,x1062) % 1.09/1.26 [107]~P69(x1071)+P69(x1072)+~E(x1071,x1072) % 1.09/1.26 [108]~P51(x1081)+P51(x1082)+~E(x1081,x1082) % 1.09/1.26 [109]~P52(x1091)+P52(x1092)+~E(x1091,x1092) % 1.09/1.26 [110]~P18(x1101)+P18(x1102)+~E(x1101,x1102) % 1.09/1.26 [111]~P38(x1111)+P38(x1112)+~E(x1111,x1112) % 1.09/1.26 [112]~P23(x1121)+P23(x1122)+~E(x1121,x1122) % 1.09/1.26 [113]~P7(x1131)+P7(x1132)+~E(x1131,x1132) % 1.09/1.26 [114]~P54(x1141)+P54(x1142)+~E(x1141,x1142) % 1.09/1.26 [115]P6(x1152,x1153,x1154)+~E(x1151,x1152)+~P6(x1151,x1153,x1154) % 1.09/1.26 [116]P6(x1163,x1162,x1164)+~E(x1161,x1162)+~P6(x1163,x1161,x1164) % 1.09/1.26 [117]P6(x1173,x1174,x1172)+~E(x1171,x1172)+~P6(x1173,x1174,x1171) % 1.09/1.26 [118]~P43(x1181)+P43(x1182)+~E(x1181,x1182) % 1.09/1.26 [119]~P24(x1191)+P24(x1192)+~E(x1191,x1192) % 1.09/1.26 [120]~P19(x1201)+P19(x1202)+~E(x1201,x1202) % 1.09/1.26 [121]~P62(x1211)+P62(x1212)+~E(x1211,x1212) % 1.09/1.26 [122]~P47(x1221)+P47(x1222)+~E(x1221,x1222) % 1.09/1.26 [123]~P53(x1231)+P53(x1232)+~E(x1231,x1232) % 1.09/1.26 [124]~P30(x1241)+P30(x1242)+~E(x1241,x1242) % 1.09/1.26 [125]~P66(x1251)+P66(x1252)+~E(x1251,x1252) % 1.09/1.26 [126]~P16(x1261)+P16(x1262)+~E(x1261,x1262) % 1.09/1.26 [127]~P55(x1271)+P55(x1272)+~E(x1271,x1272) % 1.09/1.26 [128]~P25(x1281)+P25(x1282)+~E(x1281,x1282) % 1.09/1.26 [129]~P26(x1291)+P26(x1292)+~E(x1291,x1292) % 1.09/1.26 [130]~P28(x1301)+P28(x1302)+~E(x1301,x1302) % 1.09/1.26 [131]~P14(x1311)+P14(x1312)+~E(x1311,x1312) % 1.09/1.26 [132]P5(x1322,x1323)+~E(x1321,x1322)+~P5(x1321,x1323) % 1.09/1.26 [133]P5(x1333,x1332)+~E(x1331,x1332)+~P5(x1333,x1331) % 1.09/1.26 [134]~P40(x1341)+P40(x1342)+~E(x1341,x1342) % 1.09/1.26 [135]~P48(x1351)+P48(x1352)+~E(x1351,x1352) % 1.09/1.26 [136]~P44(x1361)+P44(x1362)+~E(x1361,x1362) % 1.09/1.26 [137]~P29(x1371)+P29(x1372)+~E(x1371,x1372) % 1.09/1.26 [138]~P63(x1381)+P63(x1382)+~E(x1381,x1382) % 1.09/1.26 [139]~P67(x1391)+P67(x1392)+~E(x1391,x1392) % 1.09/1.26 [140]~P13(x1401)+P13(x1402)+~E(x1401,x1402) % 1.09/1.26 [141]~P39(x1411)+P39(x1412)+~E(x1411,x1412) % 1.09/1.26 [142]~P65(x1421)+P65(x1422)+~E(x1421,x1422) % 1.09/1.26 [143]~P64(x1431)+P64(x1432)+~E(x1431,x1432) % 1.09/1.26 [144]~P41(x1441)+P41(x1442)+~E(x1441,x1442) % 1.09/1.26 [145]~P70(x1451)+P70(x1452)+~E(x1451,x1452) % 1.09/1.26 [146]~P49(x1461)+P49(x1462)+~E(x1461,x1462) % 1.09/1.26 % 1.09/1.26 %------------------------------------------- % 1.09/1.26 cnf(1422,plain, % 1.09/1.26 ($false), % 1.09/1.26 inference(scs_inference,[],[290,176,318]), % 1.09/1.26 ['proof']). % 1.09/1.26 % SZS output end Proof % 1.09/1.26 % Total time :0.115360s %------------------------------------------------------------------------------