%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL792-1 : TPTP v9.3.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n029.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 11:19:51 AM UTC 2026 % Result : Unsatisfiable 1.21s 1.22s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL792-1 : TPTP v9.3.1. Released v4.1.0. % 0.00/0.03 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.09/0.35 % Computer : n029.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sun Sep 6 01:51:55 UTC 2026 % 0.09/0.36 % CPUTime : % 0.25/0.51 start to proof:theBenchmark % 0.89/1.12 %------------------------------------------- % 0.89/1.12 % File :CSE---1.7 % 0.89/1.12 % Problem :theBenchmark % 0.89/1.12 % Transform :cnf % 0.89/1.12 % Format :tptp:raw % 0.89/1.12 % Command :java -jar mcs_scs.jar %d %s % 0.89/1.12 % 0.89/1.12 % Result :Theorem 0.110198s % 0.89/1.12 % Output :CNFRefutation 0.110198s % 0.89/1.12 %------------------------------------------- % 0.89/1.13 %------------------------------------------------------------------------------ % 0.89/1.13 % File : LCL792-1 : TPTP v9.3.1. Released v4.1.0. % 0.89/1.13 % Domain : Logic Calculi % 0.89/1.13 % Problem : Strong normalization of typed lambda calculus 138_36 % 0.89/1.13 % Version : Especial. % 0.89/1.13 % English : % 0.89/1.13 % 0.89/1.13 % Refs : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java % 0.89/1.13 % : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe % 0.89/1.13 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 0.89/1.13 % Source : [Nip10] % 0.89/1.13 % Names : StrongNorm-138_36 [Nip10] % 0.89/1.13 % 0.89/1.13 % Status : Unsatisfiable % 0.89/1.13 % Rating : 0.17 v9.3.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 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 % 0.89/1.13 % Syntax : Number of clauses : 1229 ( 152 unt; 184 nHn; 735 RR) % 0.89/1.13 % Number of literals : 3514 ( 745 equ;2121 neg) % 0.89/1.13 % Maximal clause size : 6 ( 2 avg) % 0.98/1.13 % Maximal term depth : 5 ( 1 avg) % 0.98/1.13 % Number of predicates : 71 ( 70 usr; 0 prp; 1-3 aty) % 0.98/1.13 % Number of functors : 35 ( 35 usr; 4 con; 0-3 aty) % 0.98/1.13 % Number of variables : 3503 ( 223 sgn) % 0.98/1.13 % SPC : CNF_UNS_RFO_SEQ_NHN % 0.98/1.13 % 0.98/1.13 % Comments : % 0.98/1.13 %------------------------------------------------------------------------------ % 0.98/1.13 cnf(cls_add__Suc_0,axiom, % 0.98/1.13 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)) ). % 0.98/1.13 % 0.98/1.13 cnf(cls_abs__le__mult_0,axiom, % 0.98/1.13 ( ~ class_Ring__and__Field_Olordered__ring(T_a) % 0.98/1.13 | 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) ) ). % 0.98/1.13 % 0.98/1.13 cnf(cls_neg__le__iff__le_0,axiom, % 0.98/1.13 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.98/1.13 | c_lessequals(V_a,V_b,T_a) % 0.98/1.13 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 0.98/1.13 % 0.98/1.13 cnf(cls_le__imp__neg__le_0,axiom, % 0.98/1.13 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.98/1.13 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 0.98/1.13 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.98/1.13 % 0.98/1.13 cnf(cls_div__add_0,axiom, % 0.98/1.13 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.13 | 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) % 0.98/1.13 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,T_a) % 0.98/1.13 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,T_a) ) ). % 0.98/1.13 % 0.98/1.13 cnf(cls_eq__add__iff2_1,axiom, % 0.98/1.13 ( ~ class_Ring__and__Field_Oring(T_a) % 0.98/1.13 | 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) ) ). % 0.98/1.13 % 0.98/1.13 cnf(cls_nat__less__add__iff1_0,axiom, % 0.98/1.13 ( 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) % 0.98/1.13 | ~ 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) % 0.98/1.13 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 0.98/1.13 % 0.98/1.13 cnf(cls_nat__less__add__iff1_1,axiom, % 0.98/1.13 ( 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) % 0.98/1.13 | ~ 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) % 0.98/1.13 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 0.98/1.13 % 0.98/1.13 cnf(cls_nat__less__add__iff2_0,axiom, % 0.98/1.13 ( 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) % 0.98/1.13 | ~ 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) % 0.98/1.13 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.98/1.13 % 0.98/1.13 cnf(cls_nat__less__add__iff2_1,axiom, % 0.98/1.13 ( 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) % 0.98/1.13 | ~ 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) % 0.98/1.13 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.98/1.13 % 0.98/1.13 cnf(cls_eq__add__iff2_0,axiom, % 0.98/1.13 ( ~ class_Ring__and__Field_Oring(T_a) % 0.98/1.13 | 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) % 0.98/1.13 | 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) ) ). % 0.98/1.13 % 0.98/1.13 cnf(cls_eq__add__iff1_0,axiom, % 0.98/1.13 ( ~ class_Ring__and__Field_Oring(T_a) % 0.98/1.13 | 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) % 0.98/1.13 | 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 ) ). % 0.98/1.13 % 0.98/1.13 cnf(cls_div__mod__equality2_0,axiom, % 0.98/1.13 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.13 | 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) ) ). % 0.98/1.13 % 0.98/1.13 cnf(cls_div__mod__equality_0,axiom, % 0.98/1.13 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.13 | 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) ) ). % 0.98/1.13 % 0.98/1.13 cnf(cls_less__add__Suc1_0,axiom, % 0.98/1.13 c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_i,V_m,tc_nat)),tc_nat) ). % 0.98/1.13 % 0.98/1.13 cnf(cls_less__add__Suc2_0,axiom, % 0.98/1.13 c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_i,tc_nat)),tc_nat) ). % 0.98/1.13 % 0.98/1.13 cnf(cls_less__iff__Suc__add_1,axiom, % 0.98/1.14 c_HOL_Oord__class_Oless(V_m,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat)),tc_nat) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_le__diff__conv2_0,axiom, % 0.98/1.14 ( c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) % 0.98/1.14 | ~ c_lessequals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) % 0.98/1.14 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_le__diff__conv2_1,axiom, % 0.98/1.14 ( c_lessequals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) % 0.98/1.14 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) % 0.98/1.14 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_min__max_Ole__sup__iff_2,axiom, % 0.98/1.14 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.14 | c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) % 0.98/1.14 | ~ c_lessequals(V_y,V_z,T_a) % 0.98/1.14 | ~ c_lessequals(V_x,V_z,T_a) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_min__max_Osup__least_0,axiom, % 0.98/1.14 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.14 | c_lessequals(c_Orderings_Oord__class_Omax(V_y,V_z,T_a),V_x,T_a) % 0.98/1.14 | ~ c_lessequals(V_z,V_x,T_a) % 0.98/1.14 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_min__max_Ole__supI_0,axiom, % 0.98/1.14 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.14 | c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) % 0.98/1.14 | ~ c_lessequals(V_b,V_x,T_a) % 0.98/1.14 | ~ c_lessequals(V_a,V_x,T_a) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_le__maxI1_0,axiom, % 0.98/1.14 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.14 | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_le__maxI2_0,axiom, % 0.98/1.14 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.14 | c_lessequals(V_y,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_zero__less__abs__iff_1,axiom, % 0.98/1.14 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.14 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) % 0.98/1.14 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_bot__least_0,axiom, % 0.98/1.14 ( ~ class_Orderings_Obot(T_a) % 0.98/1.14 | c_lessequals(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_abs__minus__le__zero_0,axiom, % 0.98/1.14 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.14 | 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) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_min__max_Oinf__sup__distrib2_0,axiom, % 0.98/1.14 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.14 | 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) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_min__max_Oinf__sup__distrib1_0,axiom, % 0.98/1.14 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.14 | 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) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_power__strict__decreasing_0,axiom, % 0.98/1.14 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.14 | 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) % 0.98/1.14 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 0.98/1.14 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.14 | ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_add__increasing_0,axiom, % 0.98/1.14 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.98/1.14 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.98/1.14 | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 0.98/1.14 | ~ c_lessequals(V_b,V_c,T_a) % 0.98/1.14 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_add__increasing2_0,axiom, % 0.98/1.14 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.98/1.14 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.98/1.14 | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 0.98/1.14 | ~ c_lessequals(V_b,V_a,T_a) % 0.98/1.14 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_le__imp__power__dvd_0,axiom, % 0.98/1.14 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.14 | 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) % 0.98/1.14 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_Suc__leI_0,axiom, % 0.98/1.14 ( c_lessequals(c_Suc(V_m),V_n,tc_nat) % 0.98/1.14 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_Suc__le__eq_0,axiom, % 0.98/1.14 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.98/1.14 | ~ c_lessequals(c_Suc(V_m),V_n,tc_nat) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_less__eq__Suc__le_0,axiom, % 0.98/1.14 ( c_lessequals(c_Suc(V_n),V_m,tc_nat) % 0.98/1.14 | ~ c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_less__eq__Suc__le_1,axiom, % 0.98/1.14 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 0.98/1.14 | ~ c_lessequals(c_Suc(V_n),V_m,tc_nat) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_le__zero__iff__zero__pprt_1,axiom, % 0.98/1.14 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.98/1.14 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.98/1.14 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_le__zero__iff__zero__pprt_0,axiom, % 0.98/1.14 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.98/1.14 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 0.98/1.14 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_termination__basic__simps_I1_J_0,axiom, % 0.98/1.14 ( c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) % 0.98/1.14 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_termination__basic__simps_I2_J_0,axiom, % 0.98/1.14 ( c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) % 0.98/1.14 | ~ c_HOL_Oord__class_Oless(V_x,V_z,tc_nat) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_add__lessD1_0,axiom, % 0.98/1.14 ( c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) % 0.98/1.14 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_trans__less__add1_0,axiom, % 0.98/1.14 ( c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat) % 0.98/1.14 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_trans__less__add2_0,axiom, % 0.98/1.14 ( c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat) % 0.98/1.14 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_power__decreasing_0,axiom, % 0.98/1.14 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.14 | 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) % 0.98/1.14 | ~ c_lessequals(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 0.98/1.14 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.14 | ~ c_lessequals(V_n,V_N,tc_nat) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_divide__le__0__iff_4,axiom, % 0.98/1.14 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.14 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.14 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.14 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.14 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_divide__le__0__iff_5,axiom, % 0.98/1.14 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.14 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.14 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.14 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.14 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_le__add__iff2_1,axiom, % 0.98/1.14 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.98/1.14 | 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) % 0.98/1.14 | ~ 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) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_le__add__iff2_0,axiom, % 0.98/1.14 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.98/1.14 | 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) % 0.98/1.14 | ~ 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) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_le__add__iff1_1,axiom, % 0.98/1.14 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.98/1.14 | 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) % 0.98/1.14 | ~ 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) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_le__add__iff1_0,axiom, % 0.98/1.14 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.98/1.14 | 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) % 0.98/1.14 | ~ 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) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_dvd__mod__imp__dvd_0,axiom, % 0.98/1.14 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.14 | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) % 0.98/1.14 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) % 0.98/1.14 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_dvd__mod__iff_1,axiom, % 0.98/1.14 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.14 | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) % 0.98/1.14 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) % 0.98/1.14 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_dvd__mod__iff_0,axiom, % 0.98/1.14 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.14 | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) % 0.98/1.14 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) % 0.98/1.14 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_dvd__mod_0,axiom, % 0.98/1.14 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.14 | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) % 0.98/1.14 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) % 0.98/1.14 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_Suc__diff__le_0,axiom, % 0.98/1.14 ( 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)) % 0.98/1.14 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_zero__le__divide__1__iff_1,axiom, % 0.98/1.14 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.14 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.14 | 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) % 0.98/1.14 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_zero__le__divide__1__iff_0,axiom, % 0.98/1.14 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.14 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.14 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.14 | ~ 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) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_sum__squares__ge__zero_0,axiom, % 0.98/1.14 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.14 | 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) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_inverse__le__1__iff_1,axiom, % 0.98/1.14 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.14 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.14 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 0.98/1.14 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.14 % 0.98/1.14 cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom, % 0.98/1.14 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.15 | c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_comm__monoid__add_Omult__commute_0,axiom, % 0.98/1.15 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.98/1.15 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_nat__add__commute_0,axiom, % 0.98/1.15 c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_less__add__eq__less_0,axiom, % 0.98/1.15 ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) % 0.98/1.15 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat) % 0.98/1.15 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_class__semiring_Oadd__c_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.15 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_y,V_x,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_divide__le__0__iff_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.15 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.15 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.15 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.15 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_divide__le__0__iff_1,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.15 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.15 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.15 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.15 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_divide__le__0__iff_2,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.15 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.15 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.15 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.15 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_divide__le__0__iff_3,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.15 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.15 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.15 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.15 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_mult__eq__1__iff_0,axiom, % 0.98/1.15 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.98/1.15 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_mult__eq__1__iff_1,axiom, % 0.98/1.15 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.98/1.15 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_mult__sgn__abs_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.15 | 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 ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_diff__less__mono2_0,axiom, % 0.98/1.15 ( 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) % 0.98/1.15 | ~ c_HOL_Oord__class_Oless(V_m,V_l,tc_nat) % 0.98/1.15 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_power__minus_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oring__1(T_a) % 0.98/1.15 | 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) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_dvd__power_1,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.15 | 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) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_le__imp__inverse__le__neg_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.15 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 0.98/1.15 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.15 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_inverse__le__imp__le__neg_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.15 | c_lessequals(V_b,V_a,T_a) % 0.98/1.15 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.15 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_inverse__le__imp__le_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.15 | c_lessequals(V_b,V_a,T_a) % 0.98/1.15 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.15 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_le__imp__inverse__le_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.15 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 0.98/1.15 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.15 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_of__nat__eq__iff_0,axiom, % 0.98/1.15 ( ~ class_Nat_Osemiring__char__0(T_a) % 0.98/1.15 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) % 0.98/1.15 | V_m = V_n ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_mod__div__trivial_0,axiom, % 0.98/1.15 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.15 | 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) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_divide__le__eq_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.15 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.15 | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 0.98/1.15 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.15 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_divide__le__eq_6,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.15 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.15 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 0.98/1.15 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.15 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_le__divide__eq_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.15 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.15 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 0.98/1.15 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.15 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_le__divide__eq_6,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.15 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.15 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 0.98/1.15 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.15 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_mult__imp__div__pos__le_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.15 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) % 0.98/1.15 | ~ c_lessequals(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a) % 0.98/1.15 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_mult__imp__le__div__pos_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.15 | c_lessequals(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 0.98/1.15 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a) % 0.98/1.15 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_mult__less__imp__less__right_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.98/1.15 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.98/1.15 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.15 | ~ 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) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_mult__less__imp__less__left_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.98/1.15 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.98/1.15 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.15 | ~ 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) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_mult__right__less__imp__less_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 0.98/1.15 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.98/1.15 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.15 | ~ 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) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_mult__left__less__imp__less_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 0.98/1.15 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.98/1.15 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.15 | ~ 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) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_square__eq__iff_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.98/1.15 | c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) != c_HOL_Otimes__class_Otimes(V_b,V_b,T_a) % 0.98/1.15 | V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a) % 0.98/1.15 | V_a = V_b ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_add__Suc__right_0,axiom, % 0.98/1.15 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)) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_abs__idempotent_0,axiom, % 0.98/1.15 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.15 | 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) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_power__0__Suc_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 0.98/1.15 | ~ class_Power_Opower(T_a) % 0.98/1.15 | 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) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_one__le__power_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.15 | c_lessequals(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 0.98/1.15 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_abs__le__D1_0,axiom, % 0.98/1.15 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.15 | c_lessequals(V_a,V_b,T_a) % 0.98/1.15 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_mult__strict__mono_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.98/1.15 | 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) % 0.98/1.15 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.15 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.15 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 0.98/1.15 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_class__fieldgb_Oinverse__divide_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.15 | ~ class_Int_Onumber__ring(T_a) % 0.98/1.15 | 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) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_inverse__eq__divide_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.15 | 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) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_zmod__simps_I4_J_0,axiom, % 0.98/1.15 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.15 | 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) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_dvd__mult__cancel__left_2,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.98/1.15 | 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) % 0.98/1.15 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_dvd__mult__cancel__right_2,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.98/1.15 | 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) % 0.98/1.15 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_divide__left__mono_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.15 | 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) % 0.98/1.15 | ~ 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) % 0.98/1.15 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.15 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_divide__left__mono__neg_0,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.15 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.15 | 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) % 0.98/1.15 | ~ 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) % 0.98/1.15 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.15 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_min__max_Oinf__le1_0,axiom, % 0.98/1.15 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.15 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_x,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_min__max_Oinf__le2_0,axiom, % 0.98/1.15 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.15 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_y,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_min__max_Ole__infI_0,axiom, % 0.98/1.15 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.15 | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) % 0.98/1.15 | ~ c_lessequals(V_x,V_b,T_a) % 0.98/1.15 | ~ c_lessequals(V_x,V_a,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_min__max_Ole__inf__iff_2,axiom, % 0.98/1.15 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.15 | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) % 0.98/1.15 | ~ c_lessequals(V_x,V_z,T_a) % 0.98/1.15 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_min__max_Oinf__greatest_0,axiom, % 0.98/1.15 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.15 | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) % 0.98/1.15 | ~ c_lessequals(V_x,V_z,T_a) % 0.98/1.15 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_eq__add__iff1_1,axiom, % 0.98/1.15 ( ~ class_Ring__and__Field_Oring(T_a) % 0.98/1.15 | 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) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_le__minus__self__iff_0,axiom, % 0.98/1.15 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.98/1.15 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.15 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_le__minus__self__iff_1,axiom, % 0.98/1.15 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.98/1.15 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 0.98/1.15 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_minus__le__self__iff_0,axiom, % 0.98/1.15 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.98/1.15 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.15 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_minus__le__self__iff_1,axiom, % 0.98/1.15 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.98/1.15 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) % 0.98/1.15 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_less__eq__neg__nonpos_0,axiom, % 0.98/1.15 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 0.98/1.15 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.15 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_less__eq__neg__nonpos_1,axiom, % 0.98/1.15 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 0.98/1.15 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 0.98/1.15 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.15 % 0.98/1.15 cnf(cls_neg__less__eq__nonneg_0,axiom, % 0.98/1.15 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 0.98/1.16 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.16 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_neg__less__eq__nonneg_1,axiom, % 0.98/1.16 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 0.98/1.16 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) % 0.98/1.16 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_zero__le__power_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.16 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 0.98/1.16 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_diff__is__0__eq_1,axiom, % 0.98/1.16 ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) % 0.98/1.16 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_diff__is__0__eq_0,axiom, % 0.98/1.16 ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.98/1.16 | c_lessequals(V_m,V_n,tc_nat) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_min__diff__distrib__left_0,axiom, % 0.98/1.16 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_max__less__iff__conj_2,axiom, % 0.98/1.16 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.16 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(V_x,V_z,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_diff__Suc__diff__eq2_0,axiom, % 0.98/1.16 ( 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) % 0.98/1.16 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_replicate__eq__replicate_0,axiom, % 0.98/1.16 ( c_List_Oreplicate(V_m,V_x,T_a) != c_List_Oreplicate(V_n,V_y,T_a) % 0.98/1.16 | V_m = V_n ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_class__semiring_Omul__1_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.16 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_x,T_a) = V_x ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_mult__1_0,axiom, % 0.98/1.16 ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) % 0.98/1.16 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_mult__1__left_0,axiom, % 0.98/1.16 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.98/1.16 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_mult__1__right_0,axiom, % 0.98/1.16 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.98/1.16 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.16 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_class__semiring_Osemiring__rules_I11_J_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.16 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_add__strict__increasing_0,axiom, % 0.98/1.16 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.98/1.16 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.98/1.16 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 0.98/1.16 | ~ c_lessequals(V_b,V_c,T_a) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_lem0_0,axiom, % 0.98/1.16 ( c_HOL_Oord__class_Oless(V_m,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) % 0.98/1.16 | ~ c_lessequals(V_m,V_n,tc_nat) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_dvdI_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Odvd(T_a) % 0.98/1.16 | c_Ring__and__Field_Odvd__class_Odvd(V_b,c_HOL_Otimes__class_Otimes(V_b,V_k,T_a),T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_dvd__triv__left_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.16 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_dvd__triv__right_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.16 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_abs__diff__triangle__ineq_0,axiom, % 0.98/1.16 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_frac__less2_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.16 | 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) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(V_w,V_z,T_a) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 0.98/1.16 | ~ c_lessequals(V_x,V_y,T_a) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_div__self_0,axiom, % 0.98/1.16 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.16 | c_Divides_Odiv__class_Odiv(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 0.98/1.16 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_power__one__over_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.16 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_add__is__1_4,axiom, % 0.98/1.16 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)) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_mod__mod__trivial_0,axiom, % 0.98/1.16 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_of__nat__le__iff_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.16 | c_lessequals(V_m,V_n,tc_nat) % 0.98/1.16 | ~ 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_of__nat__le__iff_1,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.16 | 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) % 0.98/1.16 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_subst__preserves__beta_0,axiom, % 0.98/1.16 ( c_Lambda_Obeta(c_Lambda_Osubst(V_r,V_t,V_i),c_Lambda_Osubst(V_s,V_t,V_i)) % 0.98/1.16 | ~ c_Lambda_Obeta(V_r,V_s) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_nonzero__minus__divide__right_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.16 | 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) % 0.98/1.16 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_divide__less__0__1__iff_1,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.16 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.16 | 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) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_divide__less__0__1__iff_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.16 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.16 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.16 | ~ 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_neg__less__0__iff__less_0,axiom, % 0.98/1.16 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.98/1.16 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_neg__less__0__iff__less_1,axiom, % 0.98/1.16 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.98/1.16 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_min__less__iff__conj_2,axiom, % 0.98/1.16 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.16 | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_natgb_Oadd__mul__solve_1,axiom, % 0.98/1.16 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) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_natgb_Onoteq__reduce_1,axiom, % 0.98/1.16 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) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_class__ringb_Onoteq__reduce_1,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.98/1.16 | ~ class_Int_Onumber__ring(T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_class__ringb_Oadd__mul__solve_1,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.98/1.16 | ~ class_Int_Onumber__ring(T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_max__Suc__Suc_0,axiom, % 0.98/1.16 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)) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_less__Suc0_0,axiom, % 0.98/1.16 ( V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom, % 0.98/1.16 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.98/1.16 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.16 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom, % 0.98/1.16 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.98/1.16 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) % 0.98/1.16 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_abs__triangle__ineq3_0,axiom, % 0.98/1.16 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_min__max_Oinf__left__idem_0,axiom, % 0.98/1.16 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_subst__Var_2,axiom, % 0.98/1.16 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_i),V_s,V_k) = c_Lambda_OdB_OVar(V_i) % 0.98/1.16 | V_i = V_k % 0.98/1.16 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_abs__mult__less_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.16 | 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) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_b,T_a),V_d,T_a) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_c,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_nat__diff__add__eq2_0,axiom, % 0.98/1.16 ( 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) % 0.98/1.16 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_nat__diff__add__eq1_0,axiom, % 0.98/1.16 ( 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) % 0.98/1.16 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_diff__add__cancel_0,axiom, % 0.98/1.16 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.98/1.16 | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_inverse__nonnegative__iff__nonnegative_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.16 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.16 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.16 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_inverse__nonnegative__iff__nonnegative_1,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.16 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.16 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 0.98/1.16 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_inverse__inverse__eq_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 0.98/1.16 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.16 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_mult__le__cancel2_1,axiom, % 0.98/1.16 ( 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) % 0.98/1.16 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_mult__le__cancel1_1,axiom, % 0.98/1.16 ( 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) % 0.98/1.16 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_class__semiring_Opwr__pwr_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_power__Suc2_0,axiom, % 0.98/1.16 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_power__Suc_0,axiom, % 0.98/1.16 ( ~ class_Power_Opower(T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_class__semiring_Opwr__Suc_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_class__semiring_Osemiring__rules_I35_J_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_add__le__mono_0,axiom, % 0.98/1.16 ( 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) % 0.98/1.16 | ~ c_lessequals(V_k,V_l,tc_nat) % 0.98/1.16 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_add__mono_0,axiom, % 0.98/1.16 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 0.98/1.16 | 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) % 0.98/1.16 | ~ c_lessequals(V_c,V_d,T_a) % 0.98/1.16 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_less__Suc__eq__le_1,axiom, % 0.98/1.16 ( c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) % 0.98/1.16 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_less__Suc__eq__le_0,axiom, % 0.98/1.16 ( c_lessequals(V_m,V_n,tc_nat) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_le__less__Suc__eq_1,axiom, % 0.98/1.16 ( ~ c_lessequals(V_x,V_x,tc_nat) % 0.98/1.16 | c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_class__semiring_Omul__c_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.16 | c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_nat__mult__commute_0,axiom, % 0.98/1.16 c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) = c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_add__nonneg__eq__0__iff_2,axiom, % 0.98/1.16 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.98/1.16 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.16 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.16 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_diff__less__Suc_0,axiom, % 0.98/1.16 c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_Suc(V_m),tc_nat) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_mod__add__eq_0,axiom, % 0.98/1.16 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_add__nonneg__nonneg_0,axiom, % 0.98/1.16 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.98/1.16 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) % 0.98/1.16 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.16 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_zero__le__power__abs_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_inverse__less__imp__less_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.16 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.16 | ~ 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_less__imp__inverse__less_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.16 | 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) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_abs__of__neg_0,axiom, % 0.98/1.16 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.16 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_abs__if__lattice_0,axiom, % 0.98/1.16 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.16 | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 0.98/1.16 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_abs__if_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Oabs__if(T_a) % 0.98/1.16 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 0.98/1.16 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_mod__minus__cong_0,axiom, % 0.98/1.16 ( ~ class_Divides_Oring__div(T_a) % 0.98/1.16 | c_Divides_Odiv__class_Omod(V_a,V_b,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_b,T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_mod__mult__eq_0,axiom, % 0.98/1.16 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_dvd__diff_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 0.98/1.16 | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a) % 0.98/1.16 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,T_a) % 0.98/1.16 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_power__commutes_0,axiom, % 0.98/1.16 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_le__max__iff__disj_0,axiom, % 0.98/1.16 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.16 | c_lessequals(V_z,V_y,T_a) % 0.98/1.16 | c_lessequals(V_z,V_x,T_a) % 0.98/1.16 | ~ c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_class__semiring_Omul__pwr_0,axiom, % 0.98/1.16 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_liftn__lift_0,axiom, % 0.98/1.16 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) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_nat__eq__add__iff1_1,axiom, % 0.98/1.16 ( ~ c_lessequals(V_j,V_i,tc_nat) % 0.98/1.16 | 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) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_min__max_Ole__inf__iff_1,axiom, % 0.98/1.16 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.16 | c_lessequals(V_x,V_z,T_a) % 0.98/1.16 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_min__max_Ole__inf__iff_0,axiom, % 0.98/1.16 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.16 | c_lessequals(V_x,V_y,T_a) % 0.98/1.16 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_min__le__iff__disj_2,axiom, % 0.98/1.16 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.16 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 0.98/1.16 | ~ c_lessequals(V_y,V_z,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_min__le__iff__disj_1,axiom, % 0.98/1.16 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.16 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 0.98/1.16 | ~ c_lessequals(V_x,V_z,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_min__max_Ole__infI2_0,axiom, % 0.98/1.16 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.16 | c_lessequals(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 0.98/1.16 | ~ c_lessequals(V_b,V_x,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_min__max_Ole__infI1_0,axiom, % 0.98/1.16 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.16 | c_lessequals(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 0.98/1.16 | ~ c_lessequals(V_a,V_x,T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_min__max_Ole__infE_1,axiom, % 0.98/1.16 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.16 | c_lessequals(V_x,V_b,T_a) % 0.98/1.16 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_min__max_Ole__infE_0,axiom, % 0.98/1.16 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.16 | c_lessequals(V_x,V_a,T_a) % 0.98/1.16 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) ) ). % 0.98/1.16 % 0.98/1.16 cnf(cls_div__mult__self2_0,axiom, % 0.98/1.16 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.17 | 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) % 0.98/1.17 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_div__mult__self1_0,axiom, % 0.98/1.17 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.17 | 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) % 0.98/1.17 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_sgn__greater_1,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_sgn__greater_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_divide__less__eq_1,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_divide__less__eq_4,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_divide__less__eq_5,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_divide__less__eq_7,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_less__divide__eq_1,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_less__divide__eq_4,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_less__divide__eq_5,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_less__divide__eq_7,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_inverse__le__1__iff_2,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.17 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 0.98/1.17 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_x,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_class__semiring_Osemiring__rules_I4_J_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.17 | 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_add__nonneg__eq__0__iff_1,axiom, % 0.98/1.17 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.98/1.17 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.98/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 0.98/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 0.98/1.17 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_add__nonneg__eq__0__iff_0,axiom, % 0.98/1.17 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.98/1.17 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.98/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 0.98/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 0.98/1.17 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_Suc__inject_0,axiom, % 0.98/1.17 ( c_Suc(V_x) != c_Suc(V_y) % 0.98/1.17 | V_x = V_y ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_nat_Oinject_0,axiom, % 0.98/1.17 ( c_Suc(V_nat) != c_Suc(V_nat_H) % 0.98/1.17 | V_nat = V_nat_H ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_abs__ge__minus__self_0,axiom, % 0.98/1.17 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.17 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_diff__divide__distrib_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.17 | 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_abs__ge__self_0,axiom, % 0.98/1.17 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.17 | c_lessequals(V_a,c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_dB_Osimps_I6_J_0,axiom, % 0.98/1.17 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_less__add__iff2_1,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.98/1.17 | 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) % 0.98/1.17 | ~ 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_less__add__iff2_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.98/1.17 | 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) % 0.98/1.17 | ~ 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_less__add__iff1_1,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.98/1.17 | 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) % 0.98/1.17 | ~ 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_less__add__iff1_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.98/1.17 | 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) % 0.98/1.17 | ~ 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_nat__eq__add__iff1_0,axiom, % 0.98/1.17 ( 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) % 0.98/1.17 | ~ c_lessequals(V_j,V_i,tc_nat) % 0.98/1.17 | 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 ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_nat__eq__add__iff2_0,axiom, % 0.98/1.17 ( 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) % 0.98/1.17 | ~ c_lessequals(V_i,V_j,tc_nat) % 0.98/1.17 | 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_min__le__iff__disj_0,axiom, % 0.98/1.17 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.17 | c_lessequals(V_y,V_z,T_a) % 0.98/1.17 | c_lessequals(V_x,V_z,T_a) % 0.98/1.17 | ~ c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_nat__eq__add__iff2_1,axiom, % 0.98/1.17 ( ~ c_lessequals(V_i,V_j,tc_nat) % 0.98/1.17 | 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_eq__divide__eq_4,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.17 | 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_mod__add__cong_0,axiom, % 0.98/1.17 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.17 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 0.98/1.17 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 0.98/1.17 | 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_less__Suc0_1,axiom, % 0.98/1.17 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom, % 0.98/1.17 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.98/1.17 | 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) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom, % 0.98/1.17 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.17 | ~ 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_even__less__0__iff_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.17 | ~ 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_even__less__0__iff_1,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.17 | 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) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_one__is__add_1,axiom, % 0.98/1.17 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) % 0.98/1.17 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.98/1.17 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_one__is__add_2,axiom, % 0.98/1.17 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) % 0.98/1.17 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 0.98/1.17 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_zero__less__mult__pos2_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.17 | ~ 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_zero__less__mult__pos_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.17 | ~ 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_mult__pos__pos_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.98/1.17 | 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) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_mult__neg__neg_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.17 | 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) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_nat__0__less__mult__iff_2,axiom, % 0.98/1.17 ( 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) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_power__less__imp__less__base_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.98/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.17 | ~ 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_min__max_Ole__sup__iff_1,axiom, % 0.98/1.17 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.17 | c_lessequals(V_y,V_z,T_a) % 0.98/1.17 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_min__max_Ole__sup__iff_0,axiom, % 0.98/1.17 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.17 | c_lessequals(V_x,V_z,T_a) % 0.98/1.17 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_le__max__iff__disj_2,axiom, % 0.98/1.17 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.17 | c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 0.98/1.17 | ~ c_lessequals(V_z,V_y,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_le__max__iff__disj_1,axiom, % 0.98/1.17 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.17 | c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 0.98/1.17 | ~ c_lessequals(V_z,V_x,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_min__max_Ole__supI2_0,axiom, % 0.98/1.17 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.17 | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 0.98/1.17 | ~ c_lessequals(V_x,V_b,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_min__max_Ole__supI1_0,axiom, % 0.98/1.17 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.17 | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 0.98/1.17 | ~ c_lessequals(V_x,V_a,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_min__max_Ole__supE_1,axiom, % 0.98/1.17 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.17 | c_lessequals(V_b,V_x,T_a) % 0.98/1.17 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_min__max_Ole__supE_0,axiom, % 0.98/1.17 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.17 | c_lessequals(V_a,V_x,T_a) % 0.98/1.17 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_le__diff__conv_0,axiom, % 0.98/1.17 ( c_lessequals(V_j,c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),tc_nat) % 0.98/1.17 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_le__diff__conv_1,axiom, % 0.98/1.17 ( c_lessequals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) % 0.98/1.17 | ~ c_lessequals(V_j,c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),tc_nat) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_zero__less__power_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.17 | 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) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_less__max__iff__disj_0,axiom, % 0.98/1.17 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_mult__Suc__right_0,axiom, % 0.98/1.17 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) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_mult__Suc_0,axiom, % 0.98/1.17 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) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_eq__neg__iff__add__eq__0_1,axiom, % 0.98/1.17 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.98/1.17 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.98/1.17 | V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_minus__unique_0,axiom, % 0.98/1.17 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.98/1.17 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.98/1.17 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_abs__less__iff_1,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_div__power_0,axiom, % 0.98/1.17 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.17 | 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) % 0.98/1.17 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_not__one__less__zero_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_abs__less__iff_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_sgn__if_1,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Osgn__if(T_a) % 0.98/1.17 | c_HOL_Osgn__class_Osgn(V_x,T_a) = c_HOL_Oone__class_Oone(T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 0.98/1.17 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_dB_Osimps_I3_J_0,axiom, % 0.98/1.17 ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H) % 0.98/1.17 | V_dB = V_dB_H ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_not__sum__squares__lt__zero_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.17 | ~ 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_nat__le__add__iff1_0,axiom, % 0.98/1.17 ( 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) % 0.98/1.17 | ~ 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) % 0.98/1.17 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_nat__le__add__iff1_1,axiom, % 0.98/1.17 ( 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) % 0.98/1.17 | ~ 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) % 0.98/1.17 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_nat__le__add__iff2_0,axiom, % 0.98/1.17 ( 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) % 0.98/1.17 | ~ 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) % 0.98/1.17 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_nat__le__add__iff2_1,axiom, % 0.98/1.17 ( 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) % 0.98/1.17 | ~ 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) % 0.98/1.17 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_divide__le__eq_8,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.17 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.17 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 0.98/1.17 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_le__divide__eq_8,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.17 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.17 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 0.98/1.17 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_of__nat__mult_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.98/1.17 | 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_min__less__iff__disj_0,axiom, % 0.98/1.17 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_class__ringb_Oadd__mul__solve_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.98/1.17 | ~ class_Int_Onumber__ring(T_a) % 0.98/1.17 | 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) % 0.98/1.17 | V_y = V_z % 0.98/1.17 | V_w = V_x ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_class__ringb_Onoteq__reduce_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.98/1.17 | ~ class_Int_Onumber__ring(T_a) % 0.98/1.17 | 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) % 0.98/1.17 | V_c = V_d % 0.98/1.17 | V_a = V_b ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_natgb_Onoteq__reduce_0,axiom, % 0.98/1.17 ( 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) % 0.98/1.17 | V_c = V_d % 0.98/1.17 | V_a = V_b ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_natgb_Oadd__mul__solve_0,axiom, % 0.98/1.17 ( 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) % 0.98/1.17 | V_y = V_z % 0.98/1.17 | V_w = V_x ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_abs__div__pos_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.17 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.17 | 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) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_inverse__less__imp__less__neg_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.17 | ~ 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_less__imp__inverse__less__neg_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.17 | 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) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_le__zero__iff__pprt__id_0,axiom, % 0.98/1.17 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.98/1.17 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) = V_a % 0.98/1.17 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_le__zero__iff__pprt__id_1,axiom, % 0.98/1.17 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.98/1.17 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) != V_a % 0.98/1.17 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_power__Suc__less__one_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.17 | 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) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_order__less__trans_0,axiom, % 0.98/1.17 ( ~ class_Orderings_Opreorder(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_xt1_I10_J_0,axiom, % 0.98/1.17 ( ~ class_Orderings_Oorder(T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.98/1.17 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_sgn__if_2,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Osgn__if(T_a) % 0.98/1.17 | c_HOL_Osgn__class_Osgn(V_x,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a) % 0.98/1.17 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 0.98/1.17 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_min__max_Ole__iff__sup_0,axiom, % 0.98/1.17 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.17 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = V_y % 0.98/1.17 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_min__max_Ole__iff__sup_1,axiom, % 0.98/1.17 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.17 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) != V_y % 0.98/1.17 | c_lessequals(V_x,V_y,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_min__max_Osup__absorb1_0,axiom, % 0.98/1.17 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.17 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = V_x % 0.98/1.17 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_class__semiring_Oadd__a_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.17 | 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_add__cancel__21_1,axiom, % 0.98/1.17 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.98/1.17 | 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_nat__add__left__commute_0,axiom, % 0.98/1.17 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) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_nat__add__assoc_0,axiom, % 0.98/1.17 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) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_comm__monoid__add_Omult__assoc_0,axiom, % 0.98/1.17 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.98/1.17 | 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom, % 0.98/1.17 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.98/1.17 | 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom, % 0.98/1.17 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a) % 0.98/1.17 | 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.17 | 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.17 | 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.17 | 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom, % 0.98/1.17 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.17 | 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_add__gr__0_0,axiom, % 0.98/1.17 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.98/1.17 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 0.98/1.17 | ~ 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_power__add_0,axiom, % 0.98/1.17 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.98/1.17 | 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) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_one__le__mult__iff_1,axiom, % 0.98/1.17 ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) % 0.98/1.17 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ). % 0.98/1.17 % 0.98/1.17 cnf(cls_one__le__mult__iff_0,axiom, % 0.98/1.17 ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 0.98/1.18 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_add__cancel__21_0,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.98/1.18 | 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) % 0.98/1.18 | c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) = V_u ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_abs__triangle__ineq_0,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_trans__le__add2_0,axiom, % 0.98/1.18 ( c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat) % 0.98/1.18 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_trans__le__add1_0,axiom, % 0.98/1.18 ( c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat) % 0.98/1.18 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_add__leE_1,axiom, % 0.98/1.18 ( c_lessequals(V_k,V_n,tc_nat) % 0.98/1.18 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),V_n,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_add__leE_0,axiom, % 0.98/1.18 ( c_lessequals(V_m,V_n,tc_nat) % 0.98/1.18 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),V_n,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_termination__basic__simps_I4_J_0,axiom, % 0.98/1.18 ( c_lessequals(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) % 0.98/1.18 | ~ c_lessequals(V_x,V_z,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_termination__basic__simps_I3_J_0,axiom, % 0.98/1.18 ( c_lessequals(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) % 0.98/1.18 | ~ c_lessequals(V_x,V_y,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_mod__diff__left__eq_0,axiom, % 0.98/1.18 ( ~ class_Divides_Oring__div(T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_mod__diff__right__eq_0,axiom, % 0.98/1.18 ( ~ class_Divides_Oring__div(T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_inverse__positive__imp__positive_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.18 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_nonzero__abs__divide_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.18 | 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) % 0.98/1.18 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_power__one_0,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.98/1.18 | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_nonzero__abs__inverse_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.18 | 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) % 0.98/1.18 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_min__max_Ole__iff__inf_0,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = V_x % 0.98/1.18 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_min__max_Ole__iff__inf_1,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) != V_x % 0.98/1.18 | c_lessequals(V_x,V_y,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_min__max_Oinf__absorb2_0,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = V_y % 0.98/1.18 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_max__diff__distrib__left_0,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_not__leE_0,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.98/1.18 | c_lessequals(V_y,V_x,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_linorder__antisym__conv2_1,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | ~ c_lessequals(V_x,V_x,T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_linorder__antisym__conv1_1,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_x,V_x,T_a) % 0.98/1.18 | c_lessequals(V_x,V_x,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_linorder__not__less_1,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.98/1.18 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_linorder__not__less_0,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | c_lessequals(V_y,V_x,T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_linorder__not__le_1,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | ~ c_lessequals(V_x,V_y,T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_linorder__not__le_0,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.98/1.18 | c_lessequals(V_x,V_y,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_less__le__not__le_1,axiom, % 0.98/1.18 ( ~ class_Orderings_Opreorder(T_a) % 0.98/1.18 | ~ c_lessequals(V_y,V_x,T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_subst__Var_1,axiom, % 0.98/1.18 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 0.98/1.18 | c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_neg__0__le__iff__le_0,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.98/1.18 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_neg__0__le__iff__le_1,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.98/1.18 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 0.98/1.18 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_divide__self__if_1,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.18 | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 0.98/1.18 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_divide__self_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.18 | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 0.98/1.18 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_right__inverse__eq_1,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.18 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 0.98/1.18 | c_HOL_Oinverse__class_Odivide(V_x,V_x,T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_mod__add__left__eq_0,axiom, % 0.98/1.18 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_mod__add__right__eq_0,axiom, % 0.98/1.18 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_zero__le__divide__iff_3,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.18 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.18 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_zero__le__divide__iff_2,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.18 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.18 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_zero__le__divide__iff_1,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.18 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.18 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_zero__le__divide__iff_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.18 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.18 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_min__max_Oinf__assoc_0,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_min__max_Oinf__left__commute_0,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_one__is__add_5,axiom, % 0.98/1.18 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) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_add__strict__increasing2_0,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.98/1.18 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 0.98/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_power__increasing_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.18 | 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) % 0.98/1.18 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 0.98/1.18 | ~ c_lessequals(V_n,V_N,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_diff__le__mono2_0,axiom, % 0.98/1.18 ( 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) % 0.98/1.18 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_diff__le__mono_0,axiom, % 0.98/1.18 ( 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) % 0.98/1.18 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_le__diff__iff_1,axiom, % 0.98/1.18 ( 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) % 0.98/1.18 | ~ c_lessequals(V_m,V_n,tc_nat) % 0.98/1.18 | ~ c_lessequals(V_k,V_n,tc_nat) % 0.98/1.18 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_le__diff__iff_0,axiom, % 0.98/1.18 ( c_lessequals(V_m,V_n,tc_nat) % 0.98/1.18 | ~ 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) % 0.98/1.18 | ~ c_lessequals(V_k,V_n,tc_nat) % 0.98/1.18 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_diff__add__0_0,axiom, % 0.98/1.18 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) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_diff__diff__left_0,axiom, % 0.98/1.18 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) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_power__mono_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.18 | 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) % 0.98/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.18 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_eq__eqI_1,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.98/1.18 | c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) % 0.98/1.18 | V_xa = V_y ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_eq__eqI_0,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.98/1.18 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 0.98/1.18 | V_x_H = V_y_H ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_eq__diff__iff_0,axiom, % 0.98/1.18 ( c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat) != c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat) % 0.98/1.18 | ~ c_lessequals(V_k,V_n,tc_nat) % 0.98/1.18 | ~ c_lessequals(V_k,V_m,tc_nat) % 0.98/1.18 | V_m = V_n ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_min__max_Oinf__sup__absorb_0,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) = V_x ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_nat__mult__eq__cancel1_0,axiom, % 0.98/1.18 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.98/1.18 | V_m = V_n ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_one__is__add_3,axiom, % 0.98/1.18 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) % 0.98/1.18 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.98/1.18 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_one__is__add_0,axiom, % 0.98/1.18 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) % 0.98/1.18 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 0.98/1.18 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_mult__less__cancel2_0,axiom, % 0.98/1.18 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.98/1.18 | ~ 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_mult__less__cancel1_0,axiom, % 0.98/1.18 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.98/1.18 | ~ 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_of__nat__Suc_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_inverse__le__1__iff_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.18 | c_lessequals(c_HOL_Oone__class_Oone(T_a),V_x,T_a) % 0.98/1.18 | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.18 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_add__Suc__shift_0,axiom, % 0.98/1.18 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) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_mult__le__cancel2_0,axiom, % 0.98/1.18 ( c_lessequals(V_m,V_n,tc_nat) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.98/1.18 | ~ 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_mult__le__cancel1_0,axiom, % 0.98/1.18 ( c_lessequals(V_m,V_n,tc_nat) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.98/1.18 | ~ 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_nat__mult__le__cancel1_0,axiom, % 0.98/1.18 ( c_lessequals(V_m,V_n,tc_nat) % 0.98/1.18 | ~ 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) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_nat__mult__le__cancel1_1,axiom, % 0.98/1.18 ( 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) % 0.98/1.18 | ~ c_lessequals(V_m,V_n,tc_nat) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_mult__le__cancel__left__neg_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.18 | c_lessequals(V_b,V_a,T_a) % 0.98/1.18 | ~ 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) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_mult__le__cancel__left__neg_1,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.18 | 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) % 0.98/1.18 | ~ c_lessequals(V_b,V_a,T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_mult__le__cancel__left__pos_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.18 | c_lessequals(V_a,V_b,T_a) % 0.98/1.18 | ~ 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) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_mult__le__cancel__left__pos_1,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.18 | 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) % 0.98/1.18 | ~ c_lessequals(V_a,V_b,T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_mult__left__le__imp__le_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.98/1.18 | c_lessequals(V_a,V_b,T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.18 | ~ 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_mult__right__le__imp__le_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.98/1.18 | c_lessequals(V_a,V_b,T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.18 | ~ 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_one__less__mult_0,axiom, % 0.98/1.18 ( 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) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_le__divide__eq_7,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.18 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 0.98/1.18 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.18 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_abs__mult__self_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_nat__size_0,axiom, % 0.98/1.18 c_Nat_Osize__class_Osize(V_n,tc_nat) = V_n ). % 0.98/1.18 % 0.98/1.18 cnf(cls_nonzero__inverse__minus__eq_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 0.98/1.18 | 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) % 0.98/1.18 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_nonzero__power__inverse_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 0.98/1.18 | 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) % 0.98/1.18 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_diff__Suc__Suc_0,axiom, % 0.98/1.18 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) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_dB_Osimps_I4_J_0,axiom, % 0.98/1.18 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_neg__less__iff__less_1,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.98/1.18 | 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) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_neg__less__iff__less_0,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.98/1.18 | ~ 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_add__nonpos__neg_0,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.98/1.18 | 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) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.18 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_add__neg__nonpos_0,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.98/1.18 | 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) % 0.98/1.18 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_div__mult__self2__is__id_0,axiom, % 0.98/1.18 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.18 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = V_a % 0.98/1.18 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_div__mult__self1__is__id_0,axiom, % 0.98/1.18 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.18 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = V_a % 0.98/1.18 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_less__SucE_0,axiom, % 0.98/1.18 ( V_m = V_n % 0.98/1.18 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_less__antisym_0,axiom, % 0.98/1.18 ( V_m = V_n % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_not__less__less__Suc__eq_0,axiom, % 0.98/1.18 ( V_n = V_m % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_sum__squares__le__zero__iff_2,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_mod__mult__cong_0,axiom, % 0.98/1.18 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.18 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 0.98/1.18 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_diff__add__assoc_0,axiom, % 0.98/1.18 ( 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) % 0.98/1.18 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_diff__add__assoc2_0,axiom, % 0.98/1.18 ( 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) % 0.98/1.18 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_add__frac__eq_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.18 | 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) % 0.98/1.18 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 0.98/1.18 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_mult__eq__1__iff_2,axiom, % 0.98/1.18 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)) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_divide__eq__eq_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.18 | V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) % 0.98/1.18 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_eq__divide__eq_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.18 | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b % 0.98/1.18 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_zero__le__one_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.18 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_abs__power__minus_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_class__semiring_Osemiring__rules_I2_J_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_diff__diff__right_0,axiom, % 0.98/1.18 ( 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) % 0.98/1.18 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_inverse__less__1__iff_1,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 0.98/1.18 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_less__imp__diff__less_0,axiom, % 0.98/1.18 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_abs__le__zero__iff_0,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.18 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 0.98/1.18 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_nat_Osize_I4_J_0,axiom, % 0.98/1.18 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) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_mod__by__1_0,axiom, % 0.98/1.18 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.18 | c_Divides_Odiv__class_Omod(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_abs__mult__pos_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.18 | 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) % 0.98/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_divide__le__0__1__iff_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.18 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.18 | ~ 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_divide__le__0__1__iff_1,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.18 | 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) % 0.98/1.18 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_one__le__inverse__iff_1,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.18 | c_lessequals(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 0.98/1.18 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_dvd__abs__iff_1,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.18 | c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a) % 0.98/1.18 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_dvd__abs__iff_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.18 | c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) % 0.98/1.18 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_abs__dvd__iff_1,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.18 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a) % 0.98/1.18 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_abs__dvd__iff_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.18 | c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) % 0.98/1.18 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_one__is__add_4,axiom, % 0.98/1.18 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) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_less__le__not__le_2,axiom, % 0.98/1.18 ( ~ class_Orderings_Opreorder(T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.98/1.18 | c_lessequals(V_y,V_x,T_a) % 0.98/1.18 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_nat__less__le_1,axiom, % 0.98/1.18 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_less__not__refl_0,axiom, % 0.98/1.18 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_order__less__le_1,axiom, % 0.98/1.18 ( ~ class_Orderings_Oorder(T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_linorder__neq__iff_1,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_order__less__irrefl_0,axiom, % 0.98/1.18 ( ~ class_Orderings_Opreorder(T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_le__imp__diff__is__add_1,axiom, % 0.98/1.18 ( ~ c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_k,V_i,tc_nat),tc_nat) % 0.98/1.18 | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k,V_i,tc_nat),V_i,tc_nat) = V_k ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_min__max_Oinf__idem_0,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | c_Orderings_Oord__class_Omin(V_x,V_x,T_a) = V_x ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_eq__divide__imp_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.18 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 0.98/1.18 | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_divide__eq__imp_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.18 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 0.98/1.18 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_divide__eq__eq_3,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.18 | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a % 0.98/1.18 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_eq__divide__eq_3,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.18 | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) % 0.98/1.18 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_estimate__by__abs_0,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 0.98/1.18 | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) % 0.98/1.18 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_liftn_Osimps_I1_J_1,axiom, % 0.98/1.18 ( 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)) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_beta_0,axiom, % 0.98/1.18 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))) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_add__pos__pos_0,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.98/1.18 | 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) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_le__add1_0,axiom, % 0.98/1.18 c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_le__add2_0,axiom, % 0.98/1.18 c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_le__iff__add_1,axiom, % 0.98/1.18 c_lessequals(V_m,c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat),tc_nat) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_nat__minus__add__max_0,axiom, % 0.98/1.18 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) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_compl__eq__compl__iff_0,axiom, % 0.98/1.18 ( ~ class_Lattices_Oboolean__algebra(T_a) % 0.98/1.18 | c_HOL_Ouminus__class_Ouminus(V_x,T_a) != c_HOL_Ouminus__class_Ouminus(V_y,T_a) % 0.98/1.18 | V_x = V_y ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_neg__equal__iff__equal_0,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.98/1.18 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(V_b,T_a) % 0.98/1.18 | V_a = V_b ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_power__divide_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_not__one__le__zero_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.18 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_negative__imp__inverse__negative_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_inverse__negative__iff__negative_1,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_inverse__negative__iff__negative_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.18 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_power__gt1__lemma_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.18 | 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) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_linorder__neqE__ordered__idom_0,axiom, % 0.98/1.18 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.98/1.18 | V_x = V_y ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_not__less__iff__gr__or__eq_0,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | V_x = V_y % 0.98/1.18 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_le__antisym_0,axiom, % 0.98/1.18 ( V_m = V_n % 0.98/1.18 | ~ c_lessequals(V_n,V_m,tc_nat) % 0.98/1.18 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_nat__neq__iff_0,axiom, % 0.98/1.18 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.98/1.18 | V_m = V_n ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_linorder__neqE__nat_0,axiom, % 0.98/1.18 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 0.98/1.18 | V_x = V_y ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_order__eq__iff_2,axiom, % 0.98/1.18 ( ~ class_Orderings_Oorder(T_a) % 0.98/1.18 | V_x = V_y % 0.98/1.18 | ~ c_lessequals(V_y,V_x,T_a) % 0.98/1.18 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_linorder__neqE_0,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.98/1.18 | V_x = V_y ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_order__antisym_0,axiom, % 0.98/1.18 ( ~ class_Orderings_Oorder(T_a) % 0.98/1.18 | V_x = V_y % 0.98/1.18 | ~ c_lessequals(V_y,V_x,T_a) % 0.98/1.18 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_order__antisym__conv_0,axiom, % 0.98/1.18 ( ~ class_Orderings_Oorder(T_a) % 0.98/1.18 | V_x = V_y % 0.98/1.18 | ~ c_lessequals(V_x,V_y,T_a) % 0.98/1.18 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_linorder__less__linear_0,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.98/1.18 | V_x = V_y % 0.98/1.18 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_linorder__antisym__conv3_0,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | V_x = V_y % 0.98/1.18 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.98/1.18 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_mod__diff__cong_0,axiom, % 0.98/1.18 ( ~ class_Divides_Oring__div(T_a) % 0.98/1.18 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 0.98/1.18 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 0.98/1.18 | 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) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_le__iff__diff__le__0_1,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.98/1.18 | c_lessequals(V_a,V_b,T_a) % 0.98/1.18 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_le__iff__diff__le__0_0,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.98/1.18 | c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.18 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_min__max_Osup__idem_0,axiom, % 0.98/1.18 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.18 | c_Orderings_Oord__class_Omax(V_x,V_x,T_a) = V_x ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_abs__of__nonneg_0,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.18 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 0.98/1.18 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_dB_Osimps_I2_J_1,axiom, % 0.98/1.18 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) % 0.98/1.18 | V_dB2 = V_dB2_H ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_dB_Osimps_I2_J_0,axiom, % 0.98/1.18 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) % 0.98/1.18 | V_dB1 = V_dB1_H ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_add__strict__mono_0,axiom, % 0.98/1.18 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.98/1.18 | 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) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_add__less__mono_0,axiom, % 0.98/1.18 ( 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) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_termination__basic__simps_I5_J_0,axiom, % 0.98/1.18 ( c_lessequals(V_x,V_y,tc_nat) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_nat__less__le_0,axiom, % 0.98/1.18 ( c_lessequals(V_m,V_n,tc_nat) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_order__le__less_1,axiom, % 0.98/1.18 ( ~ class_Orderings_Oorder(T_a) % 0.98/1.18 | c_lessequals(V_x,V_y,T_a) % 0.98/1.18 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.98/1.18 % 0.98/1.18 cnf(cls_order__less__imp__le_0,axiom, % 0.98/1.18 ( ~ class_Orderings_Opreorder(T_a) % 0.98/1.18 | c_lessequals(V_x,V_y,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_minus__add__cancel_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.98/1.19 | 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 ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_add__cancel__end_1,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.98/1.19 | 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 ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_inverse__1_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 0.98/1.19 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_le__divide__eq_5,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 0.98/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_divide__le__eq_7,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_divide__le__eq_5,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_minus__divide__divide_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_diff__cancel2_0,axiom, % 0.98/1.19 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) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_diff__cancel_0,axiom, % 0.98/1.19 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) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_zero__less__Suc_0,axiom, % 0.98/1.19 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_gr0__conv__Suc_1,axiom, % 0.98/1.19 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_one__le__inverse__iff_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_min__max_Oless__supI1_0,axiom, % 0.98/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_x,V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_min__max_Oless__supI2_0,axiom, % 0.98/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_x,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_less__max__iff__disj_1,axiom, % 0.98/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_less__max__iff__disj_2,axiom, % 0.98/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_max__less__iff__conj_0,axiom, % 0.98/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_max__less__iff__conj_1,axiom, % 0.98/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_min__max_Oinf__commute_0,axiom, % 0.98/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.19 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = c_Orderings_Oord__class_Omin(V_y,V_x,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_one__less__power_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_left__add__mult__distrib_0,axiom, % 0.98/1.19 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) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_combine__common__factor_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Osemiring(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_diff__le__self_0,axiom, % 0.98/1.19 c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_left__minus_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_right__minus_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_ab__left__minus_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_eq__neg__iff__add__eq__0_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_nat__0__less__mult__iff_1,axiom, % 0.98/1.19 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.98/1.19 | ~ 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_nat__0__less__mult__iff_0,axiom, % 0.98/1.19 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 0.98/1.19 | ~ 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_add__neg__neg_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_power__strict__mono_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_sum__squares__le__zero__iff_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.19 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 0.98/1.19 | ~ 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_sum__squares__le__zero__iff_1,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.19 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 0.98/1.19 | ~ 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_diff__mult__distrib2_0,axiom, % 0.98/1.19 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) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_diff__mult__distrib_0,axiom, % 0.98/1.19 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) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_power__diff_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_lessequals(V_n,V_m,tc_nat) % 0.98/1.19 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_dvd__imp__mod__0_0,axiom, % 0.98/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.19 | c_Divides_Odiv__class_Omod(V_b,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 0.98/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_dvd__eq__mod__eq__0_1,axiom, % 0.98/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.19 | c_Divides_Odiv__class_Omod(V_b,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.98/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_min__max_Oless__infI1_0,axiom, % 0.98/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_x,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_min__max_Oless__infI2_0,axiom, % 0.98/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_b,V_x,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_min__less__iff__conj_0,axiom, % 0.98/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_min__less__iff__conj_1,axiom, % 0.98/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_min__less__iff__disj_1,axiom, % 0.98/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_x,V_z,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_min__less__iff__disj_2,axiom, % 0.98/1.19 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_Nat_Odiff__diff__eq_0,axiom, % 0.98/1.19 ( 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) % 0.98/1.19 | ~ c_lessequals(V_k,V_n,tc_nat) % 0.98/1.19 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_diff__commute_0,axiom, % 0.98/1.19 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) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_inverse__nonpositive__iff__nonpositive_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_inverse__nonpositive__iff__nonpositive_1,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_add__nonneg__pos_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_add__pos__nonneg_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_dvd__div__mult_0,axiom, % 0.98/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_abs__le__zero__iff_1,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_inverse__mult__distrib_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_nonzero__inverse__mult__distrib_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 0.98/1.19 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_diff__less__mono_0,axiom, % 0.98/1.19 ( 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) % 0.98/1.19 | ~ c_lessequals(V_c,V_a,tc_nat) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__le__0__iff_4,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__le__0__iff_5,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_split__mult__neg__le_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_split__mult__neg__le_1,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__nonneg__nonpos_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__nonpos__nonneg_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__nonneg__nonpos2_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_not__square__less__zero_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.19 | ~ 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_Suc__mult__less__cancel1_1,axiom, % 0.98/1.19 ( 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) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_Suc__mult__less__cancel1_0,axiom, % 0.98/1.19 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.98/1.19 | ~ 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_Suc__lessI_0,axiom, % 0.98/1.19 ( c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) % 0.98/1.19 | c_Suc(V_m) = V_n % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_not__less__eq__eq_1,axiom, % 0.98/1.19 ( ~ c_lessequals(V_m,V_n,tc_nat) % 0.98/1.19 | ~ c_lessequals(c_Suc(V_n),V_m,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_not__less__eq__eq_0,axiom, % 0.98/1.19 ( c_lessequals(c_Suc(V_n),V_m,tc_nat) % 0.98/1.19 | c_lessequals(V_m,V_n,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_natgb_Oadd__cancel_0,axiom, % 0.98/1.19 ( c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat) != c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat) % 0.98/1.19 | V_y = V_z ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_nat__add__right__cancel_0,axiom, % 0.98/1.19 ( c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat) != c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat) % 0.98/1.19 | V_m = V_n ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_nat__add__left__cancel_0,axiom, % 0.98/1.19 ( c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) % 0.98/1.19 | V_m = V_n ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_class__ringb_Oadd__cancel_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.98/1.19 | ~ class_Int_Onumber__ring(T_a) % 0.98/1.19 | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) % 0.98/1.19 | V_y = V_z ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_add__imp__eq_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a) % 0.98/1.19 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) % 0.98/1.19 | V_b = V_c ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_add__left__cancel_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 0.98/1.19 | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) % 0.98/1.19 | V_b = V_c ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_add__right__cancel_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 0.98/1.19 | c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) != c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) % 0.98/1.19 | V_b = V_c ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_abs__minus__cancel_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_inverse__eq__1__iff_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | c_HOL_Oinverse__class_Oinverse(V_x,T_a) != c_HOL_Oone__class_Oone(T_a) % 0.98/1.19 | V_x = c_HOL_Oone__class_Oone(T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_inverse__less__1__iff_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_x,T_a) % 0.98/1.19 | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_abs__leI_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 0.98/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_abs__le__iff_2,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 0.98/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_divide__1_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.19 | c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_min__add__distrib__left_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_le__add__diff_0,axiom, % 0.98/1.19 ( 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) % 0.98/1.19 | ~ c_lessequals(V_k,V_n,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__left__le__one__le_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Otimes__class_Otimes(V_y,V_x,T_a),V_x,T_a) % 0.98/1.19 | ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_divide__nonpos__neg_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_divide__nonneg__pos_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__right__le__one__le_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_x,T_a) % 0.98/1.19 | ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mod__diff__eq_0,axiom, % 0.98/1.19 ( ~ class_Divides_Oring__div(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_power__abs_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_abs__of__nat_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_dvd__power__same_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_abs__inverse_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_divide__strict__right__mono_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_divide__strict__right__mono__neg_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_abs__divide_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_abs__of__pos_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.19 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_inverse__positive__iff__positive_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_inverse__positive__iff__positive_1,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_positive__imp__inverse__positive_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mod__mult__left__eq_0,axiom, % 0.98/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.19 | 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),V_b,T_a),V_c,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mod__mult__right__eq_0,axiom, % 0.98/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.19 | 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(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_add__is__1_3,axiom, % 0.98/1.19 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.98/1.19 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.98/1.19 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_add__is__1_0,axiom, % 0.98/1.19 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.98/1.19 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 0.98/1.19 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_one__less__inverse__iff_2,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_inverse__eq__1__iff_1,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_dvd__trans_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 0.98/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 0.98/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_dvd__refl_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_zero__le__divide__iff_4,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_zero__le__divide__iff_5,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) % 0.98/1.19 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_frac__le_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_lessequals(V_w,V_z,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 0.98/1.19 | ~ c_lessequals(V_x,V_y,T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_power__gt1_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_beta__cases_I1_J_0,axiom, % 0.98/1.19 ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_diff__Suc__diff__eq1_0,axiom, % 0.98/1.19 ( 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) % 0.98/1.19 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_less__iff__diff__less__0_1,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.98/1.19 | ~ 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_less__iff__diff__less__0_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_abs__not__less__zero_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_of__nat__less__iff_1,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_of__nat__less__iff_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.98/1.19 | ~ 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_dvd__mult__cancel__right_1,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_dvd__mult__cancel__left_1,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_lessI_0,axiom, % 0.98/1.19 c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_less__Suc__eq_2,axiom, % 0.98/1.19 c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_less__trans__Suc_0,axiom, % 0.98/1.19 ( c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_add__le__cancel__right_1,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_add__le__cancel__right_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.98/1.19 | c_lessequals(V_a,V_b,T_a) % 0.98/1.19 | ~ 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_add__le__cancel__left_1,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_add__le__cancel__left_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.98/1.19 | c_lessequals(V_a,V_b,T_a) % 0.98/1.19 | ~ 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_add__right__mono_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_add__left__mono_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_add__le__mono1_0,axiom, % 0.98/1.19 ( 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) % 0.98/1.19 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_nat__add__left__cancel__le_0,axiom, % 0.98/1.19 ( c_lessequals(V_m,V_n,tc_nat) % 0.98/1.19 | ~ 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_nat__add__left__cancel__le_1,axiom, % 0.98/1.19 ( 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) % 0.98/1.19 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_abs__eq__mult_3,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_abs__eq__mult_2,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.19 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_abs__eq__mult_1,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_abs__eq__mult_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_abs__mult_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_zero__less__one_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__frac__frac_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_minus__mult__right_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oring(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_minus__mult__left_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oring(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_le__imp__diff__is__add_0,axiom, % 0.98/1.19 ( ~ c_lessequals(V_i,V_j,tc_nat) % 0.98/1.19 | V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_le__add__diff__inverse_0,axiom, % 0.98/1.19 ( c_HOL_Oplus__class_Oplus(V_n,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = V_m % 0.98/1.19 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_le__add__diff__inverse2_0,axiom, % 0.98/1.19 ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat) = V_m % 0.98/1.19 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__less__cancel1_1,axiom, % 0.98/1.19 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.98/1.19 | ~ 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__less__cancel2_1,axiom, % 0.98/1.19 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.98/1.19 | ~ 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_le__eq__neg_1,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.98/1.19 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_le__eq__neg_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_divide__strict__left__mono__neg_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ 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) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_divide__strict__left__mono_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ 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) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_less__add__one_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_add__diff__assoc_0,axiom, % 0.98/1.19 ( 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) % 0.98/1.19 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_add__diff__assoc2_0,axiom, % 0.98/1.19 ( 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) % 0.98/1.19 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_drop__drop_0,axiom, % 0.98/1.19 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) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_power__le__imp__le__base_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.19 | c_lessequals(V_a,V_b,T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.19 | ~ 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__left__idem_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_one__less__inverse__iff_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.19 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_div__mult__div__if__dvd_0,axiom, % 0.98/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_w,T_a) % 0.98/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_neg__le__0__iff__le_1,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_neg__le__0__iff__le_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_of__nat__0__less__iff_1,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_of__nat__0__less__iff_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.98/1.19 | ~ 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__less__le__imp__less_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.19 | ~ c_lessequals(V_c,V_d,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__le__less__imp__less_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 0.98/1.19 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_one__dvd_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.19 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_power__inject__exp_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.19 | c_Power_Opower__class_Opower(V_a,V_m,T_a) != c_Power_Opower__class_Opower(V_a,V_n,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 0.98/1.19 | V_m = V_n ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_power__0_0,axiom, % 0.98/1.19 ( ~ class_Power_Opower(T_a) % 0.98/1.19 | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_class__semiring_Opwr__0_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.19 | c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_div__mult__mult1__if_0,axiom, % 0.98/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_sgn__1__neg_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.19 | c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_sgn__neg_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.19 | c_HOL_Osgn__class_Osgn(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_class__semiring_Osemiring__rules_I27_J_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_class__semiring_Osemiring__rules_I28_J_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_minus__mult__commute_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oring(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_abs__less__iff_2,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mod__add__self2_0,axiom, % 0.98/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mod__add__self1_0,axiom, % 0.98/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_abs__triangle__ineq4_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_dvd__power__le_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_lessequals(V_n,V_m,tc_nat) % 0.98/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__le__0__iff_3,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.19 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__le__0__iff_2,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.19 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__le__0__iff_1,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__le__0__iff_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.19 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__pos__neg2_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__pos__neg_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_mult__neg__pos_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.98/1.19 | 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) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_abs__le__D2_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.19 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 0.98/1.19 | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_Suc__leD_0,axiom, % 0.98/1.19 ( c_lessequals(V_m,V_n,tc_nat) % 0.98/1.19 | ~ c_lessequals(c_Suc(V_m),V_n,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_le__SucI_0,axiom, % 0.98/1.19 ( c_lessequals(V_m,c_Suc(V_n),tc_nat) % 0.98/1.19 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_n__less__m__mult__n_0,axiom, % 0.98/1.19 ( c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_n__less__n__mult__m_0,axiom, % 0.98/1.19 ( c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),tc_nat) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_add__minus__cancel_0,axiom, % 0.98/1.19 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.98/1.19 | 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 ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_class__fieldgb_Odivide__inverse_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.19 | ~ class_Int_Onumber__ring(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_divide__inverse_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.19 | 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) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_Suc__n__not__le__n_0,axiom, % 0.98/1.19 ~ c_lessequals(c_Suc(V_n),V_n,tc_nat) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_dvd__mult__right_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 0.98/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_dvd__mult__left_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 0.98/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_dvd__mult2_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 0.98/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_dvd__mult_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 0.98/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_less__diff__iff_0,axiom, % 0.98/1.19 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.98/1.19 | ~ 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) % 0.98/1.19 | ~ c_lessequals(V_k,V_n,tc_nat) % 0.98/1.19 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_less__diff__iff_1,axiom, % 0.98/1.19 ( 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) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.98/1.19 | ~ c_lessequals(V_k,V_n,tc_nat) % 0.98/1.19 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_pos__add__strict_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_subst__lt_0,axiom, % 0.98/1.19 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_j),V_u,V_i) = c_Lambda_OdB_OVar(V_j) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_sgn__less_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_sgn__less_1,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.19 | c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.19 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_Suc__diff__diff_0,axiom, % 0.98/1.19 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) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_dvd__minus__iff_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 0.98/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) % 0.98/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_dvd__minus__iff_1,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 0.98/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) % 0.98/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_minus__dvd__iff_0,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 0.98/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) % 0.98/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_minus__dvd__iff_1,axiom, % 0.98/1.19 ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a) % 0.98/1.19 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) % 0.98/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_div__dvd__div_0,axiom, % 0.98/1.19 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.19 | c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 0.98/1.19 | ~ 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) % 0.98/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 0.98/1.19 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.98/1.19 % 0.98/1.19 cnf(cls_div__dvd__div_1,axiom, % 0.98/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 0.98/1.20 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 0.98/1.20 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_nonzero__minus__divide__divide_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_class__ring_Osub__add_0,axiom, % 0.98/1.20 ( ~ class_Int_Onumber__ring(T_a) % 0.98/1.20 | 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_diff__def_0,axiom, % 0.98/1.20 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.98/1.20 | 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_diff__minus_0,axiom, % 0.98/1.20 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.98/1.20 | 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_ab__diff__minus_0,axiom, % 0.98/1.20 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.98/1.20 | 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_Suc__mult__le__cancel1_1,axiom, % 0.98/1.20 ( 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) % 0.98/1.20 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_Suc__mult__le__cancel1_0,axiom, % 0.98/1.20 ( c_lessequals(V_m,V_n,tc_nat) % 0.98/1.20 | ~ 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_sum__squares__gt__zero__iff_1,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_sum__squares__gt__zero__iff_2,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.20 | 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_add__num__frac_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_add__frac__num_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_appR_0,axiom, % 0.98/1.20 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_u,V_s),c_Lambda_OdB_OApp(V_u,V_t)) % 0.98/1.20 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_appL_0,axiom, % 0.98/1.20 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_s,V_u),c_Lambda_OdB_OApp(V_t,V_u)) % 0.98/1.20 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_of__nat__less__0__iff_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.20 | ~ 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_divide__less__0__iff_3,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.20 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.20 | ~ 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_divide__less__0__iff_2,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.20 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.20 | ~ 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_divide__less__0__iff_1,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.20 | ~ 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_divide__less__0__iff_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.98/1.20 | ~ 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_less__half__sum_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_gt__half__sum_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_group__add__class_Odiff__0_0,axiom, % 0.98/1.20 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.98/1.20 | 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_min__max_Osup__commute_0,axiom, % 0.98/1.20 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.20 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = c_Orderings_Oord__class_Omax(V_y,V_x,T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_power__eq__imp__eq__base_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.20 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_Power_Opower__class_Opower(V_b,V_n,T_a) % 0.98/1.20 | V_a = V_b % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.98/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_add__cancel__end_0,axiom, % 0.98/1.20 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.98/1.20 | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != V_y % 0.98/1.20 | V_x = c_HOL_Ouminus__class_Ouminus(V_z,T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_abs__sgn_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.98/1.20 | 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_liftn_Osimps_I1_J_0,axiom, % 0.98/1.20 ( c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(V_i) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__divide__mult__cancel__left_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__divide__mult__cancel__right_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_division__ring__inverse__add_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 0.98/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_inverse__add_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 0.98/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_dvd__add_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.98/1.20 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) % 0.98/1.20 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 0.98/1.20 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_le__Suc__eq_2,axiom, % 0.98/1.20 c_lessequals(c_Suc(V_n),c_Suc(V_n),tc_nat) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_one__less__inverse__iff_1,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.20 | c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_drop__replicate_0,axiom, % 0.98/1.20 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) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_min__max_Odistrib__inf__le_0,axiom, % 0.98/1.20 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.20 | 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_liftn_Osimps_I2_J_0,axiom, % 0.98/1.20 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)) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_zero__le__pprt_0,axiom, % 0.98/1.20 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.98/1.20 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a),T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_divide__pos__pos_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_divide__neg__neg_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_zero__less__divide__iff_4,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_zero__less__divide__iff_5,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 0.98/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_nat_Osize_I2_J_0,axiom, % 0.98/1.20 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) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_min__max_Osup__inf__absorb_0,axiom, % 0.98/1.20 ( ~ class_Orderings_Olinorder(T_a) % 0.98/1.20 | c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) = V_x ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mod__minus__eq_0,axiom, % 0.98/1.20 ( ~ class_Divides_Oring__div(T_a) % 0.98/1.20 | 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_le__square_0,axiom, % 0.98/1.20 c_lessequals(V_m,c_HOL_Otimes__class_Otimes(V_m,V_m,tc_nat),tc_nat) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__less__cancel__left__disj_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.20 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.20 | ~ 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__less__cancel__left__disj_3,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.20 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.98/1.20 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.98/1.20 | ~ 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__less__cancel__right__disj_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.20 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.20 | ~ 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__less__cancel__right__disj_3,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.20 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.98/1.20 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.98/1.20 | ~ 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__frac__num_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 0.98/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 0.98/1.20 | 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) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_diff__diff__cancel_0,axiom, % 0.98/1.20 ( c_HOL_Ominus__class_Ominus(V_n,c_HOL_Ominus__class_Ominus(V_n,V_i,tc_nat),tc_nat) = V_i % 0.98/1.20 | ~ c_lessequals(V_i,V_n,tc_nat) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_dvd__div__mult__self_0,axiom, % 0.98/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.20 | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_a,T_a) = V_b % 0.98/1.20 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_dvd__mult__div__cancel_0,axiom, % 0.98/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 0.98/1.20 | c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),T_a) = V_b % 0.98/1.20 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_lift_Osimps_I1_J_0,axiom, % 0.98/1.20 ( c_Lambda_Olift(c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(V_i) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_power__Suc__less_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_min__Suc__Suc_0,axiom, % 0.98/1.20 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)) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_le__SucE_0,axiom, % 0.98/1.20 ( V_m = c_Suc(V_n) % 0.98/1.20 | c_lessequals(V_m,V_n,tc_nat) % 0.98/1.20 | ~ c_lessequals(V_m,c_Suc(V_n),tc_nat) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_not__less__less__Suc__eq_1,axiom, % 0.98/1.20 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 0.98/1.20 | c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_not__less__eq_1,axiom, % 0.98/1.20 ( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_not__less__eq_0,axiom, % 0.98/1.20 ( c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 0.98/1.20 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_abs__of__nonpos_0,axiom, % 0.98/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 0.98/1.20 | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 0.98/1.20 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__less__cancel2_2,axiom, % 0.98/1.20 ( 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__less__cancel1_2,axiom, % 0.98/1.20 ( 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__less__mono2_0,axiom, % 0.98/1.20 ( 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__less__mono1_0,axiom, % 0.98/1.20 ( 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_nat__mult__less__cancel1_0,axiom, % 0.98/1.20 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.98/1.20 | ~ 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_nat__mult__less__cancel1_1,axiom, % 0.98/1.20 ( 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__less__cancel__left__neg_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.20 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.98/1.20 | ~ 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__less__cancel__left__neg_1,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__less__cancel__left__pos_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.20 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.98/1.20 | ~ 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__less__cancel__left__pos_1,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__strict__left__mono__neg_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__strict__left__mono_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__less__cancel__left__disj_4,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__less__cancel__left__disj_5,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.98/1.20 | 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) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.98/1.20 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.98/1.20 % 0.98/1.20 cnf(cls_mult__strict__right__mono__neg_0,axiom, % 0.98/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__strict__right__mono_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__less__cancel__right__disj_4,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__less__cancel__right__disj_5,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__strict__left__mono__comm_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_less__divide__eq_9,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_less__divide__eq_8,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_less__divide__eq_3,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_less__divide__eq_2,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_divide__less__eq_9,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_divide__less__eq_8,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_divide__less__eq_3,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_divide__less__eq_2,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_max__add__distrib__left_0,axiom, % 1.21/1.20 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.21/1.20 | 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_sgn__sgn_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.20 | 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mod__mod__cancel_0,axiom, % 1.21/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_subst__Var__IT_0,axiom, % 1.21/1.20 ( c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) % 1.21/1.20 | ~ c_InductTermi_OIT(V_r) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_zero__less__divide__1__iff_1,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_zero__less__divide__1__iff_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.20 | ~ 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom, % 1.21/1.20 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.20 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom, % 1.21/1.20 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.20 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_abs__if__lattice_1,axiom, % 1.21/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.20 | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) % 1.21/1.20 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.21/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_abs__if_1,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oabs__if(T_a) % 1.21/1.20 | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a % 1.21/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_power__strict__increasing__iff_1,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_power__strict__increasing__iff_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 1.21/1.20 | ~ 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_power__strict__increasing_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_power__less__imp__less__exp_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.21/1.20 | ~ 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_not__add__less1_0,axiom, % 1.21/1.20 ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_i,tc_nat) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_not__add__less2_0,axiom, % 1.21/1.20 ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_i,tc_nat) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_nonzero__power__divide_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_inverse__negative__imp__negative_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_of__nat__diff_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oring__1(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_power__less__power__Suc_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_inverse__divide_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__dvd__mono_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_d,T_a) % 1.21/1.20 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__right__mono__neg_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__left__mono__neg_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__right__mono_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.20 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__left__mono_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.20 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__mono1_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Omult__mono1(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.20 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.20 | ~ class_Int_Onumber__ring(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | V_c = V_d % 1.21/1.20 | V_r = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_natgb_Oadd__scale__eq__noteq_0,axiom, % 1.21/1.20 ( 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) % 1.21/1.20 | V_c = V_d % 1.21/1.20 | V_r = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_sum__squares__eq__zero__iff_1,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_sum__squares__eq__zero__iff_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_abs__add__abs_0,axiom, % 1.21/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.20 | 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_less__diff__conv_0,axiom, % 1.21/1.20 ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_less__diff__conv_1,axiom, % 1.21/1.20 ( c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_divide__le__eq_1,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.20 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_divide__le__eq_4,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_le__divide__eq_1,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.20 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_le__divide__eq_4,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_Suc__n__not__n_0,axiom, % 1.21/1.20 c_Suc(V_n) != V_n ). % 1.21/1.20 % 1.21/1.20 cnf(cls_n__not__Suc__n_0,axiom, % 1.21/1.20 V_n != c_Suc(V_n) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_inverse__unique_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.21/1.20 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.21/1.20 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_zero__less__abs__iff_0,axiom, % 1.21/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.20 | ~ 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__imp__less__div__pos_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__imp__div__pos__less_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_divide__less__eq_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_divide__less__eq_6,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_less__divide__eq_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_less__divide__eq_6,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_divide__neg__pos_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_divide__pos__neg_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_divide__less__0__iff_4,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_divide__less__0__iff_5,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_dvd__power_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.20 | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_add__strict__right__mono_0,axiom, % 1.21/1.20 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_add__less__cancel__right_1,axiom, % 1.21/1.20 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_add__less__cancel__right_0,axiom, % 1.21/1.20 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.20 | ~ 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_add__strict__left__mono_0,axiom, % 1.21/1.20 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_add__less__cancel__left_1,axiom, % 1.21/1.20 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_add__less__cancel__left_0,axiom, % 1.21/1.20 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.20 | ~ 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_add__less__mono1_0,axiom, % 1.21/1.20 ( 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_nat__add__left__cancel__less_0,axiom, % 1.21/1.20 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.21/1.20 | ~ 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_nat__add__left__cancel__less_1,axiom, % 1.21/1.20 ( 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) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_one__le__mult__iff_2,axiom, % 1.21/1.20 ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) % 1.21/1.20 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) % 1.21/1.20 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_xt1_I6_J_0,axiom, % 1.21/1.20 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.20 | c_lessequals(V_z,V_x,T_a) % 1.21/1.20 | ~ c_lessequals(V_z,V_y,T_a) % 1.21/1.20 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_xt1_I7_J_0,axiom, % 1.21/1.20 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.21/1.20 | ~ c_lessequals(V_z,V_y,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_xt1_I8_J_0,axiom, % 1.21/1.20 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 1.21/1.20 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_add__nonpos__nonpos_0,axiom, % 1.21/1.20 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 1.21/1.20 | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_power__le__dvd_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.20 | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_b,T_a) % 1.21/1.20 | ~ c_lessequals(V_m,V_n,tc_nat) % 1.21/1.20 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_order__trans_0,axiom, % 1.21/1.20 ( ~ class_Orderings_Opreorder(T_a) % 1.21/1.20 | c_lessequals(V_x,V_z,T_a) % 1.21/1.20 | ~ c_lessequals(V_y,V_z,T_a) % 1.21/1.20 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_le__refl_0,axiom, % 1.21/1.20 c_lessequals(V_n,V_n,tc_nat) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_le__trans_0,axiom, % 1.21/1.20 ( c_lessequals(V_i,V_k,tc_nat) % 1.21/1.20 | ~ c_lessequals(V_j,V_k,tc_nat) % 1.21/1.20 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_eq__imp__le_0,axiom, % 1.21/1.20 c_lessequals(V_x,V_x,tc_nat) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_order__eq__iff_0,axiom, % 1.21/1.20 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.20 | c_lessequals(V_x,V_x,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_order__eq__refl_0,axiom, % 1.21/1.20 ( ~ class_Orderings_Opreorder(T_a) % 1.21/1.20 | c_lessequals(V_x,V_x,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_order__le__less__trans_0,axiom, % 1.21/1.20 ( ~ class_Orderings_Opreorder(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 1.21/1.20 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_order__less__le__trans_0,axiom, % 1.21/1.20 ( ~ class_Orderings_Opreorder(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 1.21/1.20 | ~ c_lessequals(V_y,V_z,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_le__add__right__mono_0,axiom, % 1.21/1.20 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.20 | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) % 1.21/1.20 | ~ c_lessequals(V_c,V_d,T_a) % 1.21/1.20 | ~ c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_subst__eq_0,axiom, % 1.21/1.20 c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u ). % 1.21/1.20 % 1.21/1.20 cnf(cls_dB_Osimps_I9_J_0,axiom, % 1.21/1.20 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OApp(V_dB1,V_dB2) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_inverse__less__1__iff_2,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_x,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_min__diff_0,axiom, % 1.21/1.20 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) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_add__is__1_5,axiom, % 1.21/1.20 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)) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_zero__less__divide__iff_3,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.20 | ~ 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_zero__less__divide__iff_2,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.20 | ~ 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_zero__less__divide__iff_1,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.20 | ~ 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_zero__less__divide__iff_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.20 | ~ 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_divide__nonneg__neg_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_divide__nonpos__pos_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.20 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 1.21/1.20 | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__idem_0,axiom, % 1.21/1.20 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 1.21/1.20 | c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = V_x ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mod__mult__self2__is__0_0,axiom, % 1.21/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.20 | 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mod__mult__self1__is__0_0,axiom, % 1.21/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.20 | 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_dB_Osimps_I1_J_0,axiom, % 1.21/1.20 ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H) % 1.21/1.20 | V_nat = V_nat_H ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__strict__mono_H_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_le__less__Suc__eq_0,axiom, % 1.21/1.20 ( V_n = V_m % 1.21/1.20 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 1.21/1.20 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_division__ring__inverse__diff_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_dB_Osimps_I8_J_0,axiom, % 1.21/1.20 c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_dB_Osimps_I7_J_0,axiom, % 1.21/1.20 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_semiring__div__class_Omod__div__equality_H_0,axiom, % 1.21/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.20 | 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 ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__le__mono1_0,axiom, % 1.21/1.20 ( 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) % 1.21/1.20 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__le__mono2_0,axiom, % 1.21/1.20 ( 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) % 1.21/1.20 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__le__cancel1_2,axiom, % 1.21/1.20 ( 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) % 1.21/1.20 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__le__cancel2_2,axiom, % 1.21/1.20 ( 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) % 1.21/1.20 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_app__Var__IT_0,axiom, % 1.21/1.20 ( c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) % 1.21/1.20 | ~ c_InductTermi_OIT(V_t) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_power__inject__base_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | V_a = V_b % 1.21/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_div__mult__mult1_0,axiom, % 1.21/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_div__mult__mult2_0,axiom, % 1.21/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__le__mono_0,axiom, % 1.21/1.20 ( 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) % 1.21/1.20 | ~ c_lessequals(V_k,V_l,tc_nat) % 1.21/1.20 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_le__cube_0,axiom, % 1.21/1.20 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) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__mono_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.20 | ~ c_lessequals(V_c,V_d,T_a) % 1.21/1.20 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mult__mono_H_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.20 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.20 | ~ c_lessequals(V_c,V_d,T_a) % 1.21/1.20 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_field__inverse_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_left__inverse_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_right__inverse_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_square__eq__iff_1,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.20 | 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_min__max_Osup__assoc_0,axiom, % 1.21/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.20 | 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_minus__mult__minus_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oring(T_a) % 1.21/1.20 | 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_min__max_Osup__left__commute_0,axiom, % 1.21/1.20 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.20 | 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_diff__minus__eq__add_0,axiom, % 1.21/1.20 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.20 | 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_zero__less__two_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.21/1.20 | 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mod__mult__self1_0,axiom, % 1.21/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.20 | 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_mod__mult__self2_0,axiom, % 1.21/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.20 | 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_diff__frac__eq_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.20 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.20 | 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_dvd__mult__cancel__left_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.20 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) % 1.21/1.20 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.20 | ~ 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_dvd__mult__cancel__right_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.20 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) % 1.21/1.20 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.20 | ~ 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) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_abs__one_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.20 | c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_of__nat__0__le__iff_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.21/1.20 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_zero__le__imp__of__nat_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.21/1.20 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_div__add__self1_0,axiom, % 1.21/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_div__add__self2_0,axiom, % 1.21/1.20 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_nonzero__inverse__eq__divide_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.21/1.20 | 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) % 1.21/1.20 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.20 % 1.21/1.20 cnf(cls_sum__squares__gt__zero__iff_0,axiom, % 1.21/1.20 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.21 | ~ 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_le__divide__eq_9,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.21/1.21 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.21 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) % 1.21/1.21 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_le__divide__eq_3,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) % 1.21/1.21 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_le__divide__eq_2,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.21 | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_divide__le__eq_9,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.21/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.21 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) % 1.21/1.21 | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_divide__le__eq_3,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) % 1.21/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_divide__le__eq_2,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.21 | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_abs_0,axiom, % 1.21/1.21 ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t)) % 1.21/1.21 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_min__max_Osup__left__idem_0,axiom, % 1.21/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_zero__le__mult__iff_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.21 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.21 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_zero__le__mult__iff_1,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.21 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.21 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_zero__le__mult__iff_2,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.21 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.21 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_zero__le__mult__iff_3,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.21 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.21 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_diff__add__inverse2_0,axiom, % 1.21/1.21 c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_n,tc_nat) = V_m ). % 1.21/1.21 % 1.21/1.21 cnf(cls_diff__add__inverse_0,axiom, % 1.21/1.21 c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_n,tc_nat) = V_m ). % 1.21/1.21 % 1.21/1.21 cnf(cls_add__diff__cancel_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.21 | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_one__le__inverse__iff_2,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) % 1.21/1.21 | ~ c_lessequals(V_x,c_HOL_Oone__class_Oone(T_a),T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_power__le__imp__le__exp_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.21/1.21 | c_lessequals(V_m,V_n,tc_nat) % 1.21/1.21 | ~ 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) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_power__increasing__iff_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.21/1.21 | c_lessequals(V_x,V_y,tc_nat) % 1.21/1.21 | ~ 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) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_power__increasing__iff_1,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.21/1.21 | 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) % 1.21/1.21 | ~ c_lessequals(V_x,V_y,tc_nat) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_minus__divide__right_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_minus__divide__left_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_add__divide__distrib_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_less__1__mult_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 1.21/1.21 | 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) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_n,T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_m,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_abs__minus__commute_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_minus__minus_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.21 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_double__compl_0,axiom, % 1.21/1.21 ( ~ class_Lattices_Oboolean__algebra(T_a) % 1.21/1.21 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = V_x ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_equation__minus__iff_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.21 | V_b = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_equation__minus__iff_1,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.21 | V_a = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_minus__equation__iff_1,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.21 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_div__by__1_0,axiom, % 1.21/1.21 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.21 | c_Divides_Odiv__class_Odiv(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_minus__diff__eq_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_add__le__less__mono_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.21/1.21 | 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) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 1.21/1.21 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_add__less__le__mono_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 1.21/1.21 | 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) % 1.21/1.21 | ~ c_lessequals(V_c,V_d,T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_dB_Osimps_I5_J_0,axiom, % 1.21/1.21 c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_less__Suc__eq__0__disj_3,axiom, % 1.21/1.21 ( c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_x,V_n,tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_Suc__less__eq_0,axiom, % 1.21/1.21 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_Suc__mono_0,axiom, % 1.21/1.21 ( c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_add__gr__0_2,axiom, % 1.21/1.21 ( 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) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_add__gr__0_1,axiom, % 1.21/1.21 ( 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) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 1.21/1.21 | ~ 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.21 | 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) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_le__minus__iff_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.21 | c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.21/1.21 | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_le__minus__iff_1,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.21 | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.21/1.21 | ~ c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_minus__le__iff_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.21 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) % 1.21/1.21 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_minus__le__iff_1,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.21 | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.21/1.21 | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_less__minus__iff_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_less__minus__iff_1,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_minus__less__iff_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_minus__less__iff_1,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_eq__divide__eq_2,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_inverse__nonzero__iff__nonzero_1,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_inverse__zero_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_nonzero__inverse__eq__imp__eq_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.21/1.21 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a) % 1.21/1.21 | V_a = V_b % 1.21/1.21 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_abs__eq__0_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.21 | c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_minus__zero_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.21 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_neg__equal__zero_1,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.21/1.21 | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_inverse__nonzero__iff__nonzero_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_inverse__zero__imp__zero_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.21/1.21 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_power__eq__0__iff_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.21/1.21 | ~ class_Power_Opower(T_a) % 1.21/1.21 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_field__power__not__zero_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(T_a) % 1.21/1.21 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_neg__0__equal__iff__equal_1,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.21 | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_sgn0_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Osgn__if(T_a) % 1.21/1.21 | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_sgn__0__0_1,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.21 | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_class__semiring_Omul__0_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.21 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mult__zero__left_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 1.21/1.21 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mult__zero__right_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 1.21/1.21 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mult__eq__0__iff_1,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.21/1.21 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mult__eq__0__iff_2,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.21/1.21 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.21 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.21 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_zero__less__diff_0,axiom, % 1.21/1.21 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.21/1.21 | ~ 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_zero__less__diff_1,axiom, % 1.21/1.21 ( 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) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_Suc__lessD_0,axiom, % 1.21/1.21 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_less__SucI_0,axiom, % 1.21/1.21 ( c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_inverse__eq__iff__eq_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a) % 1.21/1.21 | V_a = V_b ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_sum__squares__eq__zero__iff_2,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mult__less__cancel__right__disj_2,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mult__less__cancel__right__disj_1,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mult__less__cancel__left__disj_2,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.21 | ~ 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mult__less__cancel__left__disj_1,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.21 | ~ 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_subst__App_0,axiom, % 1.21/1.21 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)) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_Suc__mult__cancel1_0,axiom, % 1.21/1.21 ( 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) % 1.21/1.21 | V_m = V_n ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_Suc__pred_0,axiom, % 1.21/1.21 ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_of__nat__add_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_diff__less_0,axiom, % 1.21/1.21 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_min__max_Odistrib__sup__le_0,axiom, % 1.21/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_le__eqI_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.21 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.21/1.21 | c_lessequals(V_y_H,V_x_H,T_a) % 1.21/1.21 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_le__eqI_1,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.21 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.21/1.21 | c_lessequals(V_y,V_x,T_a) % 1.21/1.21 | ~ c_lessequals(V_y_H,V_x_H,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_less__eqI_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.21 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_less__eqI_1,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.21 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_power__mult__distrib_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_class__semiring_Opwr__mul_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_zmod__simps_I1_J_0,axiom, % 1.21/1.21 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_zmod__simps_I2_J_0,axiom, % 1.21/1.21 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_neg__0__less__iff__less_1,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_neg__0__less__iff__less_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_add__diff__inverse_0,axiom, % 1.21/1.21 ( c_HOL_Oplus__class_Oplus(V_n,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = V_m % 1.21/1.21 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_diff__Suc__less_0,axiom, % 1.21/1.21 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_n,c_Suc(V_i),tc_nat),V_n,tc_nat) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_inf__period_I4_J_1,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Odvd(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Ocomm__ring(T_a) % 1.21/1.21 | c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a) % 1.21/1.21 | ~ 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) % 1.21/1.21 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_inf__period_I4_J_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Odvd(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Ocomm__ring(T_a) % 1.21/1.21 | 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) % 1.21/1.21 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a) % 1.21/1.21 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_frac__eq__eq_1,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.21/1.21 | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) != c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) % 1.21/1.21 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_frac__eq__eq_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.21/1.21 | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) != c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) % 1.21/1.21 | V_z = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) = c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_add__is__1_1,axiom, % 1.21/1.21 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.21/1.21 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.21/1.21 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_add__is__1_2,axiom, % 1.21/1.21 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 1.21/1.21 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 1.21/1.21 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_min__max_Osup__inf__distrib2_0,axiom, % 1.21/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_min__max_Osup__inf__distrib1_0,axiom, % 1.21/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_power__mult_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mod__div__equality2_0,axiom, % 1.21/1.21 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.21 | 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 ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mod__div__equality_0,axiom, % 1.21/1.21 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.21 | 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 ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mod__div__decomp_0,axiom, % 1.21/1.21 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_xt1_I11_J_0,axiom, % 1.21/1.21 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.21/1.21 | V_a = V_b % 1.21/1.21 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_xt1_I12_J_0,axiom, % 1.21/1.21 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.21/1.21 | ~ c_lessequals(V_b,V_a,T_a) % 1.21/1.21 | V_a = V_b ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_nat__less__le_2,axiom, % 1.21/1.21 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.21/1.21 | V_m = V_n % 1.21/1.21 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_le__eq__less__or__eq_0,axiom, % 1.21/1.21 ( V_m = V_n % 1.21/1.21 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.21/1.21 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_le__neq__implies__less_0,axiom, % 1.21/1.21 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 1.21/1.21 | V_m = V_n % 1.21/1.21 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_order__le__less_0,axiom, % 1.21/1.21 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.21 | V_x = V_y % 1.21/1.21 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.21/1.21 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_order__less__le_2,axiom, % 1.21/1.21 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.21/1.21 | V_x = V_y % 1.21/1.21 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_order__le__neq__trans_0,axiom, % 1.21/1.21 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.21 | V_a = V_b % 1.21/1.21 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_order__neq__le__trans_0,axiom, % 1.21/1.21 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.21 | ~ c_lessequals(V_a,V_b,T_a) % 1.21/1.21 | V_a = V_b ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_linorder__antisym__conv1_0,axiom, % 1.21/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.21 | V_x = V_y % 1.21/1.21 | ~ c_lessequals(V_x,V_y,T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_linorder__antisym__conv2_0,axiom, % 1.21/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.21 | V_x = V_y % 1.21/1.21 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.21/1.21 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_divide__right__mono__neg_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | 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) % 1.21/1.21 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.21 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_divide__right__mono_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | 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) % 1.21/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 1.21/1.21 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_power__inverse_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_inverse__minus__eq_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_sgn__times_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mult__nonneg__nonneg_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 1.21/1.21 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.21/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_zero__le__mult__iff_5,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.21 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.21/1.21 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.21 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_zero__le__mult__iff_4,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.21 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.21/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_zero__le__square_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 1.21/1.21 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mult__nonpos__nonpos_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.21/1.21 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.21/1.21 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.21 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_split__mult__pos__le_1,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.21/1.21 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.21/1.21 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.21 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_split__mult__pos__le_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 1.21/1.21 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 1.21/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 1.21/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mod__mult__mult2_0,axiom, % 1.21/1.21 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mod__mult__mult1_0,axiom, % 1.21/1.21 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_less__minus__self__iff_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_less__minus__self__iff_1,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_right__inverse__eq_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.21/1.21 | c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.21/1.21 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_a = V_b ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_abs__ge__zero_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.21 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_class__ring_Oneg__mul_0,axiom, % 1.21/1.21 ( ~ class_Int_Onumber__ring(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_Suc__le__mono_0,axiom, % 1.21/1.21 ( c_lessequals(V_n,V_m,tc_nat) % 1.21/1.21 | ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_Suc__le__mono_1,axiom, % 1.21/1.21 ( c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) % 1.21/1.21 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_divide__eq__eq_4,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_sgn__1__pos_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.21 | c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Oone__class_Oone(T_a) % 1.21/1.21 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_sgn__pos_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.21 | c_HOL_Osgn__class_Osgn(V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_abs__triangle__ineq2_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_dvd__div__neg_0,axiom, % 1.21/1.21 ( ~ class_Divides_Oring__div(T_a) % 1.21/1.21 | 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) % 1.21/1.21 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_dvd__neg__div_0,axiom, % 1.21/1.21 ( ~ class_Divides_Oring__div(T_a) % 1.21/1.21 | 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) % 1.21/1.21 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_nat__mult__assoc_0,axiom, % 1.21/1.21 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) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_class__semiring_Omul__a_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_comm__semiring__class_Odistrib_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_add__mult__distrib_0,axiom, % 1.21/1.21 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) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_add__mult__distrib2_0,axiom, % 1.21/1.21 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) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_class__semiring_Omul__d_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_dvd__if__abs__eq_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.21 | c_HOL_Oabs__class_Oabs(V_l,T_a) != c_HOL_Oabs__class_Oabs(V_k,T_a) % 1.21/1.21 | c_Ring__and__Field_Odvd__class_Odvd(V_l,V_k,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_minus__add__distrib_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_minus__add_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_frac__less_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__field(T_a) % 1.21/1.21 | 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) % 1.21/1.21 | ~ c_lessequals(V_w,V_z,T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.21/1.21 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_xt1_I9_J_0,axiom, % 1.21/1.21 ( ~ class_Orderings_Oorder(T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_not__less__iff__gr__or__eq_1,axiom, % 1.21/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_nat__le__linear_0,axiom, % 1.21/1.21 ( c_lessequals(V_n,V_m,tc_nat) % 1.21/1.21 | c_lessequals(V_m,V_n,tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_linorder__linear_0,axiom, % 1.21/1.21 ( ~ class_Orderings_Olinorder(T_a) % 1.21/1.21 | c_lessequals(V_y,V_x,T_a) % 1.21/1.21 | c_lessequals(V_x,V_y,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_order__less__asym_0,axiom, % 1.21/1.21 ( ~ class_Orderings_Opreorder(T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_order__less__asym_H_0,axiom, % 1.21/1.21 ( ~ class_Orderings_Opreorder(T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 1.21/1.21 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_neg__equal__0__iff__equal_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.21 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_dvd__0__right_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.21 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_one__neq__zero_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.21/1.21 | c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_no__zero__divirors__neq0_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.21/1.21 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_no__zero__divisors_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.21/1.21 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mult__eq__0__iff_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 1.21/1.21 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_div__by__0_0,axiom, % 1.21/1.21 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.21 | c_Divides_Odiv__class_Odiv(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_div__0_0,axiom, % 1.21/1.21 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.21 | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_double__eq__0__iff_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.21 | c_HOL_Oplus__class_Oplus(V_a,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_class__ringb_Osubr0__iff_1,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.21 | ~ class_Int_Onumber__ring(T_a) % 1.21/1.21 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_diff__self_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.21 | c_HOL_Ominus__class_Ominus(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_diff__0__right_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.21 | c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_right__minus__eq_1,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.21 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_eq__iff__diff__eq__0_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.21/1.21 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_class__ringb_Oadd__r0__iff_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.21 | ~ class_Int_Onumber__ring(T_a) % 1.21/1.21 | V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) % 1.21/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mod__self_0,axiom, % 1.21/1.21 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.21 | c_Divides_Odiv__class_Omod(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mod__by__0_0,axiom, % 1.21/1.21 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.21 | c_Divides_Odiv__class_Omod(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_pprt__0_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.21 | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mod__0_0,axiom, % 1.21/1.21 ( ~ class_Divides_Osemiring__div(T_a) % 1.21/1.21 | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_double__eq__0__iff_1,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_abs__eq__0_1,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) % 1.21/1.21 | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_neg__0__equal__iff__equal_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.21 | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Ouminus__class_Ouminus(V_a,T_a) % 1.21/1.21 | c_HOL_Ozero__class_Ozero(T_a) = V_a ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_zero__neq__one_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.21/1.21 | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_nonzero__inverse__inverse__eq_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Odivision__ring(T_a) % 1.21/1.21 | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a % 1.21/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_dvd__0__left_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_class__ringb_Osubr0__iff_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.21 | ~ class_Int_Onumber__ring(T_a) % 1.21/1.21 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_x = V_y ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_right__minus__eq_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 1.21/1.21 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_a = V_b ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_eq__iff__diff__eq__0_1,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 1.21/1.21 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_a = V_b ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_divide__eq__eq_1,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_divide__zero_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_divide__zero__left_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.21/1.21 | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_divide__self__if_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ofield(T_a) % 1.21/1.21 | ~ class_Ring__and__Field_Odivision__by__zero(T_a) % 1.21/1.21 | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_sgn__0__0_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 1.21/1.21 | c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_class__semiring_Oadd__0_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.21 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = V_x ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_comm__monoid__add_Omult__1_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.21/1.21 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_class__ringb_Oadd__r0__iff_1,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Oidom(T_a) % 1.21/1.21 | ~ class_Int_Onumber__ring(T_a) % 1.21/1.21 | V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_comm__monoid__add_Omult__1__right_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 1.21/1.21 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_add__0__left_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 1.21/1.21 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_monoid__add__class_Oadd__0__right_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 1.21/1.21 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.21 | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 1.21/1.21 | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_neg__equal__zero_0,axiom, % 1.21/1.21 ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a) % 1.21/1.21 | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != V_a % 1.21/1.21 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_power__0__left_0,axiom, % 1.21/1.21 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 1.21/1.21 | ~ class_Power_Opower(T_a) % 1.21/1.21 | 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) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_nat_Osize_I3_J_0,axiom, % 1.21/1.21 c_Nat_Osize__class_Osize(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_le__0__eq_1,axiom, % 1.21/1.21 c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mult__cancel2_1,axiom, % 1.21/1.21 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) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mult__cancel1_1,axiom, % 1.21/1.21 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) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_neq0__conv_1,axiom, % 1.21/1.21 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_liftn__0_0,axiom, % 1.21/1.21 c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k) = V_t ). % 1.21/1.21 % 1.21/1.21 cnf(cls_gr0I_0,axiom, % 1.21/1.21 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 1.21/1.21 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_Suc__neq__Zero_0,axiom, % 1.21/1.21 c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_nat_Osimps_I3_J_0,axiom, % 1.21/1.21 c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_diffs0__imp__equal_0,axiom, % 1.21/1.21 ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.21/1.21 | c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.21/1.21 | V_m = V_n ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_le__0__eq_0,axiom, % 1.21/1.21 ( V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 1.21/1.21 | ~ c_lessequals(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mult__is__0_2,axiom, % 1.21/1.21 c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mult__is__0_1,axiom, % 1.21/1.21 c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mult__is__0_0,axiom, % 1.21/1.21 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.21/1.21 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 1.21/1.21 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_add__is__0_1,axiom, % 1.21/1.21 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.21/1.21 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_add__is__0_0,axiom, % 1.21/1.21 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 1.21/1.21 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_min__0R_0,axiom, % 1.21/1.21 c_Orderings_Oord__class_Omin(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_min__0L_0,axiom, % 1.21/1.21 c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mult__cancel2_0,axiom, % 1.21/1.21 ( c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat) != c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat) % 1.21/1.21 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) % 1.21/1.21 | V_m = V_n ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_mult__cancel1_0,axiom, % 1.21/1.21 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) % 1.21/1.21 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) % 1.21/1.21 | V_m = V_n ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_nat__mult__eq__cancel__disj_0,axiom, % 1.21/1.21 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) % 1.21/1.21 | V_m = V_n % 1.21/1.21 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_minus__nat_Odiff__0_0,axiom, % 1.21/1.21 c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ). % 1.21/1.21 % 1.21/1.21 cnf(cls_diff__self__eq__0_0,axiom, % 1.21/1.21 c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_natgb_Oadd__r0__iff_0,axiom, % 1.21/1.21 ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) % 1.21/1.21 | V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_add__eq__self__zero_0,axiom, % 1.21/1.21 ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != V_m % 1.21/1.21 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_Zero__neq__Suc_0,axiom, % 1.21/1.21 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_nat_Osimps_I2_J_0,axiom, % 1.21/1.21 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_nat__gcd_Osimps_0,axiom, % 1.21/1.21 c_Nitpick_Onat__gcd(V_x,c_HOL_Ozero__class_Ozero(tc_nat)) = V_x ). % 1.21/1.21 % 1.21/1.21 cnf(cls_nat_Osize_I1_J_0,axiom, % 1.21/1.21 c_nat_Onat__size(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_char__size_0,axiom, % 1.21/1.21 c_String_Ochar_Ochar__size(V_c) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_add__is__0_2,axiom, % 1.21/1.21 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) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_gr__implies__not0_0,axiom, % 1.21/1.21 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_not__less0_0,axiom, % 1.21/1.21 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_bot__nat__def_0,axiom, % 1.21/1.21 c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_drop__0_0,axiom, % 1.21/1.21 c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),V_xs,T_a) = V_xs ). % 1.21/1.21 % 1.21/1.21 cnf(cls_diff__0__eq__0_0,axiom, % 1.21/1.21 c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_le0_0,axiom, % 1.21/1.21 c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ). % 1.21/1.21 % 1.21/1.21 cnf(cls_size__char_0,axiom, % 1.21/1.22 c_Nat_Osize__class_Osize(V_c,tc_String_Ochar) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(cls_replicate__eq__replicate_2,axiom, % 1.21/1.22 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) ). % 1.21/1.22 % 1.21/1.22 cnf(cls_max__0R_0,axiom, % 1.21/1.22 c_Orderings_Oord__class_Omax(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_n ). % 1.21/1.22 % 1.21/1.22 cnf(cls_max__0L_0,axiom, % 1.21/1.22 c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ). % 1.21/1.22 % 1.21/1.22 cnf(cls_replicate__eq__replicate_1,axiom, % 1.21/1.22 ( c_List_Oreplicate(V_m,V_x,T_a) != c_List_Oreplicate(V_n,V_y,T_a) % 1.21/1.22 | V_x = V_y % 1.21/1.22 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.21/1.22 % 1.21/1.22 cnf(cls_natgb_Oadd__r0__iff_1,axiom, % 1.21/1.22 V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(cls_plus__nat_Oadd__0_0,axiom, % 1.21/1.22 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ). % 1.21/1.22 % 1.21/1.22 cnf(cls_Nat_Oadd__0__right_0,axiom, % 1.21/1.22 c_HOL_Oplus__class_Oplus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ). % 1.21/1.22 % 1.21/1.22 cnf(cls_lift_Osimps_I2_J_0,axiom, % 1.21/1.22 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)) ). % 1.21/1.22 % 1.21/1.22 cnf(cls_subst__lift_0,axiom, % 1.21/1.22 c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ). % 1.21/1.22 % 1.21/1.22 cnf(cls_lift__preserves__beta_0,axiom, % 1.21/1.22 ( c_Lambda_Obeta(c_Lambda_Olift(V_r,V_i),c_Lambda_Olift(V_s,V_i)) % 1.21/1.22 | ~ c_Lambda_Obeta(V_r,V_s) ) ). % 1.21/1.22 % 1.21/1.22 cnf(cls_Var__IT_0,axiom, % 1.21/1.22 c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)) ). % 1.21/1.22 % 1.21/1.22 cnf(cls_Var_I3_J_0,axiom, % 1.21/1.22 c_InductTermi_OIT(v_ua______) ). % 1.21/1.22 % 1.21/1.22 cnf(cls_Lambda_0,axiom, % 1.21/1.22 ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r)) % 1.21/1.22 | ~ c_InductTermi_OIT(V_r) ) ). % 1.21/1.22 % 1.21/1.22 cnf(cls_power__eq__0__iff_2,axiom, % 1.21/1.22 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.21/1.22 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.21/1.22 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.21/1.22 | ~ class_Power_Opower(T_a) % 1.21/1.22 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.22 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.21/1.22 % 1.21/1.22 cnf(cls_power__0__left_1,axiom, % 1.21/1.22 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 1.21/1.22 | ~ class_Power_Opower(T_a) % 1.21/1.22 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 1.21/1.22 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 1.21/1.22 % 1.21/1.22 cnf(cls_power__eq__0__iff_1,axiom, % 1.21/1.22 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 1.21/1.22 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 1.21/1.22 | ~ class_Ring__and__Field_Omult__zero(T_a) % 1.21/1.22 | ~ class_Power_Opower(T_a) % 1.21/1.22 | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.22 % 1.21/1.22 cnf(cls_of__nat__0_0,axiom, % 1.21/1.22 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 1.21/1.22 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 1.21/1.22 % 1.21/1.22 cnf(cls_lift__IT_0,axiom, % 1.21/1.22 ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i)) % 1.21/1.22 | ~ c_InductTermi_OIT(V_t) ) ). % 1.21/1.22 % 1.21/1.22 cnf(cls_uIT_0,axiom, % 1.21/1.22 c_InductTermi_OIT(v_u____) ). % 1.21/1.22 % 1.21/1.22 cnf(cls_conjecture_0,negated_conjecture, % 1.21/1.22 ~ c_InductTermi_OIT(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom, % 1.21/1.22 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom, % 1.21/1.22 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom, % 1.21/1.22 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,axiom, % 1.21/1.22 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom, % 1.21/1.22 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom, % 1.21/1.22 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom, % 1.21/1.22 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 1.21/1.22 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom, % 1.21/1.22 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Ring__and__Field_Opordered__semiring,axiom, % 1.21/1.22 class_Ring__and__Field_Opordered__semiring(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Ring__and__Field_Oordered__semiring,axiom, % 1.21/1.22 class_Ring__and__Field_Oordered__semiring(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom, % 1.21/1.22 class_Ring__and__Field_Ono__zero__divisors(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom, % 1.21/1.22 class_Ring__and__Field_Oordered__semidom(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom, % 1.21/1.22 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom, % 1.21/1.22 class_OrderedGroup_Oab__semigroup__mult(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom, % 1.21/1.22 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom, % 1.21/1.22 class_OrderedGroup_Oab__semigroup__add(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom, % 1.21/1.22 class_Ring__and__Field_Ocomm__semiring(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom, % 1.21/1.22 class_OrderedGroup_Ocomm__monoid__add(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom, % 1.21/1.22 class_Ring__and__Field_Ozero__neq__one(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom, % 1.21/1.22 class_Ring__and__Field_Osemiring__1(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom, % 1.21/1.22 class_Ring__and__Field_Osemiring__0(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Ring__and__Field_Omult__mono1,axiom, % 1.21/1.22 class_Ring__and__Field_Omult__mono1(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom, % 1.21/1.22 class_Ring__and__Field_Omult__zero(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Ring__and__Field_Omult__mono,axiom, % 1.21/1.22 class_Ring__and__Field_Omult__mono(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom, % 1.21/1.22 class_OrderedGroup_Omonoid__mult(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom, % 1.21/1.22 class_Ring__and__Field_Osemiring(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom, % 1.21/1.22 class_OrderedGroup_Omonoid__add(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Divides_Osemiring__div,axiom, % 1.21/1.22 class_Divides_Osemiring__div(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom, % 1.21/1.22 class_Nat_Osemiring__char__0(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Ring__and__Field_Odvd,axiom, % 1.21/1.22 class_Ring__and__Field_Odvd(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Orderings_Opreorder,axiom, % 1.21/1.22 class_Orderings_Opreorder(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Orderings_Olinorder,axiom, % 1.21/1.22 class_Orderings_Olinorder(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Orderings_Oorder,axiom, % 1.21/1.22 class_Orderings_Oorder(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Orderings_Obot,axiom, % 1.21/1.22 class_Orderings_Obot(tc_nat) ). % 1.21/1.22 % 1.21/1.22 cnf(clsarity_nat__Power_Opower,axiom, % 1.21/1.22 class_Power_Opower(tc_nat) ). % 1.21/1.22 % 1.21/1.22 %------------------------------------------------------------------------------ % 1.21/1.22 %------------------------------------------- % 1.21/1.22 % Proof found % 1.21/1.22 % SZS status Theorem for theBenchmark % 1.21/1.22 % SZS output start Proof % 1.21/1.22 %ClaNum:1374(EqnAxiom:146) % 1.21/1.22 %VarNum:9535(SingletonVarNum:3027) % 1.21/1.22 %MaxLitNum:6 % 1.21/1.22 %MaxfuncDepth:4 % 1.21/1.22 %SharedTerms:62 % 1.21/1.22 %goalClause: 289 % 1.21/1.22 %singleGoalClaCount:1 % 1.21/1.22 [147]P1(a1) % 1.21/1.22 [148]P8(a1) % 1.21/1.22 [149]P9(a1) % 1.21/1.22 [150]P33(a1) % 1.21/1.22 [151]P10(a1) % 1.21/1.22 [152]P11(a1) % 1.21/1.22 [153]P34(a1) % 1.21/1.22 [154]P12(a1) % 1.21/1.22 [155]P56(a1) % 1.21/1.22 [156]P57(a1) % 1.21/1.22 [157]P58(a1) % 1.21/1.22 [158]P35(a1) % 1.21/1.22 [159]P21(a1) % 1.21/1.22 [160]P22(a1) % 1.21/1.22 [161]P42(a1) % 1.21/1.22 [162]P27(a1) % 1.21/1.22 [163]P31(a1) % 1.21/1.22 [164]P68(a1) % 1.21/1.22 [165]P36(a1) % 1.21/1.22 [166]P37(a1) % 1.21/1.22 [167]P15(a1) % 1.21/1.22 [168]P32(a1) % 1.21/1.22 [169]P59(a1) % 1.21/1.22 [170]P60(a1) % 1.21/1.22 [171]P17(a1) % 1.21/1.22 [172]P20(a1) % 1.21/1.22 [173]P45(a1) % 1.21/1.22 [174]P2(a33) % 1.21/1.22 [175]P2(a34) % 1.21/1.22 [176]P46(a1) % 1.21/1.22 [177]P50(a1) % 1.21/1.22 [178]P61(a1) % 1.21/1.22 [179]P69(a1) % 1.21/1.22 [180]P51(a1) % 1.21/1.22 [181]P52(a1) % 1.21/1.22 [182]P18(a1) % 1.21/1.22 [183]P38(a1) % 1.21/1.22 [184]P23(a1) % 1.21/1.22 [185]E(f2(a1),f14(a1)) % 1.21/1.22 [186]E(f27(f2(a1)),f2(a1)) % 1.21/1.22 [289]~P2(f20(a34,f2(a1))) % 1.21/1.22 [224]E(f11(f30(f2(a1)),f30(f2(a1)),a1),f30(f2(a1))) % 1.21/1.22 [193]P4(x1931,x1931,a1) % 1.21/1.22 [291]~P3(x2911,x2911,a1) % 1.21/1.22 [187]P2(f15(x1871)) % 1.21/1.22 [188]E(f18(x1881,a1),x1881) % 1.21/1.22 [189]E(f18(x1891,a32),f2(a1)) % 1.21/1.22 [194]E(f3(x1941,x1941,a1),f2(a1)) % 1.21/1.22 [195]P4(f2(a1),x1951,a1) % 1.21/1.22 [210]P3(x2101,f30(x2101),a1) % 1.21/1.22 [215]P3(f2(a1),f30(x2151),a1) % 1.21/1.22 [237]P4(x2371,f11(x2371,x2371,a1),a1) % 1.21/1.22 [277]~E(f30(x2771),x2771) % 1.21/1.22 [281]~E(f30(x2811),f2(a1)) % 1.21/1.22 [293]~P3(x2931,f2(a1),a1) % 1.21/1.22 [294]~P4(f30(x2941),x2941,a1) % 1.21/1.22 [190]E(f25(x1901,f2(a1)),x1901) % 1.21/1.22 [197]E(f9(x1971,f2(a1),a1),x1971) % 1.21/1.22 [198]E(f3(x1981,f2(a1),a1),x1981) % 1.21/1.22 [199]E(f28(x1991,f2(a1),a1),x1991) % 1.21/1.22 [200]E(f9(f2(a1),x2001,a1),x2001) % 1.21/1.22 [201]E(f28(f2(a1),x2011,a1),x2011) % 1.21/1.22 [204]E(f11(x2041,f2(a1),a1),f2(a1)) % 1.21/1.22 [205]E(f29(x2051,f2(a1),a1),f2(a1)) % 1.21/1.22 [206]E(f11(f2(a1),x2061,a1),f2(a1)) % 1.21/1.22 [207]E(f3(f2(a1),x2071,a1),f2(a1)) % 1.21/1.22 [208]E(f29(f2(a1),x2081,a1),f2(a1)) % 1.21/1.22 [267]P4(x2671,f11(x2671,f11(x2671,x2671,a1),a1),a1) % 1.21/1.22 [223]E(f9(f27(x2231),f30(f2(a1)),a1),f27(f30(x2231))) % 1.21/1.22 [228]E(f9(f18(x2281,a1),f30(f2(a1)),a1),f18(f30(x2281),a1)) % 1.21/1.22 [225]E(f9(x2251,x2252,a1),f9(x2252,x2251,a1)) % 1.21/1.22 [226]E(f11(x2261,x2262,a1),f11(x2262,x2261,a1)) % 1.21/1.22 [234]P4(x2341,f9(x2342,x2341,a1),a1) % 1.21/1.22 [236]P4(x2361,f9(x2361,x2362,a1),a1) % 1.21/1.22 [238]P4(f3(x2381,x2382,a1),x2381,a1) % 1.21/1.22 [242]P3(f3(x2421,x2422,a1),f30(x2421),a1) % 1.21/1.22 [283]~E(f17(x2831),f15(x2832)) % 1.21/1.22 [288]~P5(f15(x2881),x2882) % 1.21/1.22 [296]~P3(f9(x2961,x2962,a1),x2962,a1) % 1.21/1.22 [297]~P3(f9(x2971,x2972,a1),x2971,a1) % 1.21/1.22 [202]E(f19(f2(a1),x2021,x2022),x2021) % 1.21/1.22 [203]E(f21(f2(a1),x2031,x2032),x2031) % 1.21/1.22 [212]E(f22(f15(x2121),x2122,x2121),x2122) % 1.21/1.22 [229]E(f11(x2291,f2(a1),a1),f11(x2292,f2(a1),a1)) % 1.21/1.22 [230]E(f11(f2(a1),x2301,a1),f11(f2(a1),x2302,a1)) % 1.21/1.22 [232]E(f9(f30(x2321),x2322,a1),f9(x2321,f30(x2322),a1)) % 1.21/1.22 [233]E(f3(f30(x2331),f30(x2332),a1),f3(x2331,x2332,a1)) % 1.21/1.22 [239]E(f3(f9(x2391,x2392,a1),x2392,a1),x2391) % 1.21/1.22 [240]E(f3(f9(x2401,x2402,a1),x2401,a1),x2402) % 1.21/1.22 [241]E(f3(x2411,f9(x2411,x2412,a1),a1),f2(a1)) % 1.21/1.22 [243]P5(f16(f17(x2431),x2432),f22(x2431,x2432,f2(a1))) % 1.21/1.22 [244]E(f30(f9(x2441,x2442,a1)),f9(x2441,f30(x2442),a1)) % 1.21/1.22 [245]E(f30(f9(x2451,x2452,a1)),f9(f30(x2451),x2452,a1)) % 1.21/1.22 [246]E(f28(f30(x2461),f30(x2462),a1),f30(f28(x2461,x2462,a1))) % 1.21/1.22 [247]E(f29(f30(x2471),f30(x2472),a1),f30(f29(x2471,x2472,a1))) % 1.21/1.22 [249]E(f9(f3(x2491,x2492,a1),x2492,a1),f28(x2491,x2492,a1)) % 1.21/1.22 [250]E(f9(x2501,f11(x2501,x2502,a1),a1),f11(x2501,f30(x2502),a1)) % 1.21/1.22 [251]E(f9(x2511,f11(x2512,x2511,a1),a1),f11(f30(x2512),x2511,a1)) % 1.21/1.22 [252]P3(x2521,f30(f9(x2522,x2521,a1)),a1) % 1.21/1.22 [254]P3(x2541,f30(f9(x2541,x2542,a1)),a1) % 1.21/1.22 [284]~E(f15(x2841),f16(x2842,x2843)) % 1.21/1.22 [285]~E(f17(x2851),f16(x2852,x2853)) % 1.21/1.22 [286]~E(f16(x2861,x2862),f15(x2863)) % 1.21/1.22 [287]~E(f16(x2871,x2872),f17(x2873)) % 1.21/1.22 [222]E(f22(f20(x2221,x2222),x2223,x2222),x2221) % 1.21/1.22 [227]E(f16(f20(x2271,x2272),f20(x2273,x2272)),f20(f16(x2271,x2273),x2272)) % 1.21/1.22 [231]E(f23(f2(a1),x2311,x2312),f23(f2(a1),x2313,x2312)) % 1.21/1.22 [248]E(f20(f19(x2481,x2482,x2483),x2483),f19(f30(x2481),x2482,x2483)) % 1.21/1.22 [257]E(f9(x2571,f9(x2572,x2573,a1),a1),f9(x2572,f9(x2571,x2573,a1),a1)) % 1.21/1.22 [258]E(f9(f9(x2581,x2582,a1),x2583,a1),f9(x2581,f9(x2582,x2583,a1),a1)) % 1.21/1.22 [259]E(f11(f11(x2591,x2592,a1),x2593,a1),f11(x2591,f11(x2592,x2593,a1),a1)) % 1.21/1.22 [260]E(f3(f3(x2601,x2602,a1),x2603,a1),f3(x2601,f9(x2602,x2603,a1),a1)) % 1.21/1.22 [261]E(f3(f3(x2611,x2612,a1),x2613,a1),f3(f3(x2611,x2613,a1),x2612,a1)) % 1.21/1.22 [262]E(f3(f9(x2621,x2622,a1),f9(x2623,x2622,a1),a1),f3(x2621,x2623,a1)) % 1.21/1.22 [263]E(f3(f9(x2631,x2632,a1),f9(x2631,x2633,a1),a1),f3(x2632,x2633,a1)) % 1.21/1.22 [266]E(f3(f3(f30(x2661),x2662,a1),f30(x2663),a1),f3(f3(x2661,x2662,a1),x2663,a1)) % 1.21/1.22 [268]E(f9(f11(x2681,x2682,a1),f11(x2681,x2683,a1),a1),f11(x2681,f9(x2682,x2683,a1),a1)) % 1.21/1.22 [269]E(f3(f11(x2691,x2692,a1),f11(x2691,x2693,a1),a1),f11(x2691,f3(x2692,x2693,a1),a1)) % 1.21/1.22 [270]E(f9(f11(x2701,x2702,a1),f11(x2703,x2702,a1),a1),f11(f9(x2701,x2703,a1),x2702,a1)) % 1.21/1.22 [271]E(f3(f11(x2711,x2712,a1),f11(x2713,x2712,a1),a1),f11(f3(x2711,x2713,a1),x2712,a1)) % 1.21/1.22 [272]E(f29(f3(x2721,x2722,a1),f3(x2723,x2722,a1),a1),f3(f29(x2721,x2723,a1),x2722,a1)) % 1.21/1.22 [255]E(f16(f19(x2551,x2552,x2553),f19(x2551,x2554,x2553)),f19(x2551,f16(x2552,x2554),x2553)) % 1.21/1.22 [256]E(f16(f22(x2561,x2562,x2563),f22(x2564,x2562,x2563)),f22(f16(x2561,x2564),x2562,x2563)) % 1.21/1.22 [264]E(f21(x2641,f23(x2642,x2643,x2644),x2644),f23(f3(x2642,x2641,a1),x2643,x2644)) % 1.21/1.22 [265]E(f21(x2651,f21(x2652,x2653,x2654),x2654),f21(f9(x2651,x2652,a1),x2653,x2654)) % 1.21/1.22 [275]E(f9(f11(x2751,x2752,a1),f9(f11(x2753,x2752,a1),x2754,a1),a1),f9(f11(f9(x2751,x2753,a1),x2752,a1),x2754,a1)) % 1.21/1.22 [302]~P2(x3021)+P2(f17(x3021)) % 1.21/1.22 [304]~P69(x3041)+~E(f10(x3041),f2(x3041)) % 1.21/1.22 [341]E(x3411,f2(a1))+P3(f2(a1),x3411,a1) % 1.21/1.22 [397]~P33(x3971)+P4(f2(x3971),f10(x3971),x3971) % 1.21/1.22 [398]~P33(x3981)+P3(f2(x3981),f10(x3981),x3981) % 1.21/1.22 [428]E(x4281,f2(a1))+~P4(x4281,f2(a1),a1) % 1.21/1.22 [478]~P33(x4781)+~P4(f10(x4781),f2(x4781),x4781) % 1.21/1.22 [479]~P33(x4791)+~P3(f10(x4791),f2(x4791),x4791) % 1.21/1.22 [305]~P68(x3051)+E(f24(f2(a1),x3051),f2(x3051)) % 1.21/1.22 [307]~P28(x3071)+E(f4(f2(x3071),x3071),f2(x3071)) % 1.21/1.22 [308]~P53(x3081)+E(f4(f10(x3081),x3081),f10(x3081)) % 1.21/1.22 [309]~P29(x3091)+E(f13(f2(x3091),x3091),f2(x3091)) % 1.21/1.22 [310]~P24(x3101)+E(f13(f2(x3101),x3101),f2(x3101)) % 1.21/1.22 [311]~P25(x3111)+E(f26(f2(x3111),x3111),f2(x3111)) % 1.21/1.22 [312]~P43(x3121)+E(f7(f2(x3121),x3121),f2(x3121)) % 1.21/1.22 [313]~P44(x3131)+E(f7(f10(x3131),x3131),f10(x3131)) % 1.21/1.22 [314]~P53(x3141)+E(f12(f2(x3141),x3141),f2(x3141)) % 1.21/1.22 [315]~P70(x3151)+E(f12(f2(x3151),x3151),f2(x3151)) % 1.21/1.22 [400]~P25(x4001)+E(f9(f2(x4001),f2(x4001),x4001),f2(x4001)) % 1.21/1.22 [457]~P28(x4571)+P4(f4(f2(x4571),x4571),f2(x4571),x4571) % 1.21/1.22 [460]E(x4601,f2(a1))+~P3(x4601,f30(f2(a1)),a1) % 1.21/1.22 [583]~P28(x5831)+~P3(f2(x5831),f4(f2(x5831),x5831),x5831) % 1.21/1.22 [693]~P33(x6931)+P3(f2(x6931),f9(f10(x6931),f10(x6931),x6931),x6931) % 1.21/1.22 [896]~P55(x8961)+E(f9(f11(f2(x8961),f2(x8961),x8961),f11(f2(x8961),f2(x8961),x8961),x8961),f2(x8961)) % 1.21/1.22 [1311]~P55(x13111)+P4(f9(f11(f2(x13111),f2(x13111),x13111),f11(f2(x13111),f2(x13111),x13111),x13111),f2(x13111),x13111) % 1.21/1.22 [1351]~P55(x13511)+~P3(f2(x13511),f9(f11(f2(x13511),f2(x13511),x13511),f11(f2(x13511),f2(x13511),x13511),x13511),x13511) % 1.21/1.22 [736]~P3(f2(a1),x7361,a1)+E(f30(f3(x7361,f30(f2(a1)),a1)),x7361) % 1.21/1.22 [347]~P36(x3472)+P4(x3471,x3471,x3472) % 1.21/1.22 [348]~P37(x3482)+P4(x3481,x3481,x3482) % 1.21/1.22 [349]~P34(x3492)+P6(x3491,x3491,x3492) % 1.21/1.22 [431]~P3(x4312,x4312,x4311)+~P8(x4311) % 1.21/1.22 [432]~P3(x4322,x4322,x4321)+~P36(x4321) % 1.21/1.22 [433]~P3(x4332,x4332,x4331)+~P37(x4331) % 1.21/1.22 [459]P4(x4592,x4591,a1)+P4(x4591,x4592,a1) % 1.21/1.22 [523]~P3(x5231,x5232,a1)+P4(x5231,x5232,a1) % 1.21/1.22 [299]E(x2991,x2992)+~E(f30(x2991),f30(x2992)) % 1.21/1.22 [300]E(x3001,x3002)+~E(f15(x3001),f15(x3002)) % 1.21/1.22 [301]E(x3011,x3012)+~E(f17(x3011),f17(x3012)) % 1.21/1.22 [317]~P2(x3171)+P2(f20(x3171,x3172)) % 1.21/1.22 [334]~P5(x3341,x3342)+P5(f17(x3341),f17(x3342)) % 1.21/1.22 [350]~P19(x3502)+E(f11(x3501,x3501,x3502),x3501) % 1.21/1.22 [351]~P8(x3512)+E(f28(x3511,x3511,x3512),x3511) % 1.21/1.22 [352]~P8(x3522)+E(f29(x3521,x3521,x3522),x3521) % 1.21/1.22 [355]~P24(x3552)+E(f3(x3551,x3551,x3552),f2(x3552)) % 1.21/1.22 [356]~P16(x3562)+E(f3(x3561,x3561,x3562),f2(x3562)) % 1.21/1.22 [357]~P1(x3572)+E(f5(x3571,x3571,x3572),f2(x3572)) % 1.21/1.22 [358]~P34(x3582)+P6(x3581,f2(x3582),x3582) % 1.21/1.22 [359]~P9(x3591)+P4(f14(x3591),x3592,x3591) % 1.21/1.22 [360]~P34(x3601)+P6(f10(x3601),x3602,x3601) % 1.21/1.22 [413]~P28(x4132)+P4(x4131,f4(x4131,x4132),x4132) % 1.21/1.22 [415]~E(f9(x4152,x4151,a1),x4152)+E(x4151,f2(a1)) % 1.21/1.22 [421]E(x4211,f2(a1))+~E(f9(x4212,x4211,a1),f2(a1)) % 1.21/1.22 [422]E(x4221,f2(a1))+~E(f9(x4221,x4222,a1),f2(a1)) % 1.21/1.22 [434]~P28(x4341)+P4(f2(x4341),f4(x4342,x4341),x4341) % 1.21/1.22 [435]~P25(x4351)+P4(f2(x4351),f26(x4352,x4351),x4351) % 1.21/1.22 [437]~P33(x4371)+P4(f2(x4371),f24(x4372,x4371),x4371) % 1.21/1.22 [480]P3(x4801,x4802,a1)+P3(x4802,f30(x4801),a1) % 1.21/1.22 [482]P4(x4821,x4822,a1)+P4(f30(x4822),x4821,a1) % 1.21/1.22 [483]~P28(x4832)+P4(f13(x4831,x4832),f4(x4831,x4832),x4832) % 1.21/1.22 [526]~P4(x5261,x5262,a1)+E(f3(x5261,x5262,a1),f2(a1)) % 1.21/1.22 [530]P4(x5301,x5302,a1)+~E(f3(x5301,x5302,a1),f2(a1)) % 1.21/1.22 [537]~P4(x5371,x5372,a1)+P4(x5371,f30(x5372),a1) % 1.21/1.22 [538]~P4(x5381,x5382,a1)+P3(x5381,f30(x5382),a1) % 1.21/1.22 [539]~P3(x5391,x5392,a1)+P3(x5391,f30(x5392),a1) % 1.21/1.22 [542]~P3(x5421,x5422,a1)+P4(f30(x5421),x5422,a1) % 1.21/1.22 [543]~P28(x5431)+~P3(f4(x5432,x5431),f2(x5431),x5431) % 1.21/1.22 [544]~P33(x5441)+~P3(f24(x5442,x5441),f2(x5441),x5441) % 1.21/1.22 [546]P4(x5461,x5462,a1)+~P3(x5461,f30(x5462),a1) % 1.21/1.22 [547]P4(x5471,x5472,a1)+~P4(f30(x5471),x5472,a1) % 1.21/1.22 [549]P3(x5491,x5492,a1)+~P4(f30(x5491),x5492,a1) % 1.21/1.22 [550]P3(x5501,x5502,a1)+~P3(f30(x5501),x5502,a1) % 1.21/1.22 [565]~P4(x5651,x5652,a1)+P4(f30(x5651),f30(x5652),a1) % 1.21/1.22 [567]~P3(x5671,x5672,a1)+P3(f30(x5671),f30(x5672),a1) % 1.21/1.22 [581]P4(x5811,x5812,a1)+~P4(f30(x5811),f30(x5812),a1) % 1.21/1.22 [582]P3(x5821,x5822,a1)+~P3(f30(x5821),f30(x5822),a1) % 1.21/1.22 [615]~P55(x6151)+P4(f2(x6151),f11(x6152,x6152,x6151),x6151) % 1.21/1.22 [622]~P3(x6221,x6222,a1)+~P3(x6222,f30(x6221),a1) % 1.21/1.22 [623]~P4(x6231,x6232,a1)+~P4(f30(x6232),x6231,a1) % 1.21/1.22 [786]~P3(x7862,x7861,a1)+P3(f2(a1),f3(x7861,x7862,a1),a1) % 1.21/1.22 [827]~P55(x8271)+~P3(f11(x8272,x8272,x8271),f2(x8271),x8271) % 1.21/1.22 [862]P3(x8621,x8622,a1)+~P3(f2(a1),f3(x8622,x8621,a1),a1) % 1.21/1.22 [863]P3(f2(a1),x8631,a1)+~P3(f2(a1),f11(x8632,x8631,a1),a1) % 1.21/1.22 [864]P3(f2(a1),x8641,a1)+~P3(f2(a1),f11(x8641,x8642,a1),a1) % 1.21/1.22 [330]~P24(x3302)+E(f13(f13(x3301,x3302),x3302),x3301) % 1.21/1.22 [331]~P13(x3312)+E(f13(f13(x3311,x3312),x3312),x3311) % 1.21/1.22 [335]~P2(x3351)+P2(f16(x3351,f15(x3352))) % 1.21/1.22 [343]~P28(x3432)+E(f4(f4(x3431,x3432),x3432),f4(x3431,x3432)) % 1.21/1.22 [344]~P28(x3442)+E(f4(f13(x3441,x3442),x3442),f4(x3441,x3442)) % 1.21/1.22 [345]~P53(x3452)+E(f4(f24(x3451,x3452),x3452),f24(x3451,x3452)) % 1.21/1.22 [346]~P53(x3462)+E(f12(f12(x3461,x3462),x3462),f12(x3461,x3462)) % 1.21/1.22 [361]~P11(x3612)+E(f9(x3611,f2(x3612),x3612),x3611) % 1.21/1.22 [362]~P34(x3622)+E(f9(x3621,f2(x3622),x3622),x3621) % 1.21/1.22 [363]~P23(x3632)+E(f9(x3631,f2(x3632),x3632),x3631) % 1.21/1.22 [364]~P34(x3642)+E(f11(x3641,f10(x3642),x3642),x3641) % 1.21/1.22 [365]~P22(x3652)+E(f11(x3651,f10(x3652),x3652),x3651) % 1.21/1.22 [366]~P1(x3662)+E(f6(x3661,f10(x3662),x3662),x3661) % 1.21/1.22 [367]~P24(x3672)+E(f3(x3671,f2(x3672),x3672),x3671) % 1.21/1.22 [368]~P1(x3682)+E(f5(x3681,f2(x3682),x3682),x3681) % 1.21/1.22 [369]~P47(x3692)+E(f8(x3691,f10(x3692),x3692),x3691) % 1.21/1.22 [370]~P11(x3701)+E(f9(f2(x3701),x3702,x3701),x3702) % 1.21/1.22 [372]~P34(x3721)+E(f9(f2(x3721),x3722,x3721),x3722) % 1.21/1.22 [373]~P23(x3731)+E(f9(f2(x3731),x3732,x3731),x3732) % 1.21/1.22 [375]~P34(x3751)+E(f11(f10(x3751),x3752,x3751),x3752) % 1.21/1.22 [376]~P21(x3761)+E(f11(f10(x3761),x3762,x3761),x3762) % 1.21/1.22 [377]~P22(x3771)+E(f11(f10(x3771),x3772,x3771),x3772) % 1.21/1.22 [378]~P34(x3782)+E(f31(x3781,f2(a1),x3782),f10(x3782)) % 1.21/1.22 [379]~P35(x3792)+E(f31(x3791,f2(a1),x3792),f10(x3792)) % 1.21/1.22 [383]~P34(x3832)+E(f11(x3831,f2(x3832),x3832),f2(x3832)) % 1.21/1.22 [384]~P52(x3842)+E(f11(x3841,f2(x3842),x3842),f2(x3842)) % 1.21/1.22 [385]~P64(x3852)+E(f11(x3851,f2(x3852),x3852),f2(x3852)) % 1.21/1.22 [386]~P1(x3862)+E(f6(x3861,f2(x3862),x3862),f2(x3862)) % 1.21/1.22 [387]~P1(x3872)+E(f5(x3871,f10(x3872),x3872),f2(x3872)) % 1.21/1.22 [389]~P34(x3891)+E(f11(f2(x3891),x3892,x3891),f2(x3891)) % 1.21/1.22 [390]~P52(x3901)+E(f11(f2(x3901),x3902,x3901),f2(x3901)) % 1.21/1.22 [391]~P64(x3911)+E(f11(f2(x3911),x3912,x3911),f2(x3911)) % 1.21/1.22 [392]~P1(x3921)+E(f6(f2(x3921),x3922,x3921),f2(x3921)) % 1.21/1.22 [393]~P1(x3931)+E(f5(f2(x3931),x3932,x3931),f2(x3931)) % 1.21/1.22 [394]~P22(x3941)+E(f31(f10(x3941),x3942,x3941),f10(x3941)) % 1.21/1.22 [395]~P47(x3951)+E(f8(f2(x3951),x3952,x3951),f2(x3951)) % 1.21/1.22 [405]~P47(x4051)+E(f8(f10(x4051),x4052,x4051),f7(x4052,x4051)) % 1.21/1.22 [406]~P24(x4061)+E(f3(f2(x4061),x4062,x4061),f13(x4062,x4061)) % 1.21/1.22 [423]~P24(x4232)+E(f9(x4231,f13(x4231,x4232),x4232),f2(x4232)) % 1.21/1.22 [425]~P24(x4252)+E(f9(f13(x4251,x4252),x4251,x4252),f2(x4252)) % 1.21/1.22 [426]~P16(x4262)+E(f9(f13(x4261,x4262),x4261,x4262),f2(x4262)) % 1.21/1.22 [448]~P53(x4482)+E(f11(x4481,f12(x4481,x4482),x4482),f4(x4481,x4482)) % 1.21/1.22 [453]E(x4531,f30(f2(a1)))+~E(f11(x4532,x4531,a1),f30(f2(a1))) % 1.21/1.22 [454]E(x4541,f30(f2(a1)))+~E(f11(x4541,x4542,a1),f30(f2(a1))) % 1.21/1.22 [468]~P3(x4681,x4682,a1)+E(f20(f15(x4681),x4682),f15(x4681)) % 1.21/1.22 [485]~P68(x4851)+E(f9(f10(x4851),f24(x4852,x4851),x4851),f24(f30(x4852),x4851)) % 1.21/1.22 [486]~P53(x4862)+E(f11(f12(x4861,x4862),f4(x4861,x4862),x4862),x4861) % 1.21/1.22 [545]~P28(x5452)+P4(f13(f4(x5451,x5452),x5452),f2(x5452),x5452) % 1.21/1.22 [585]~P53(x5852)+E(f11(f4(x5851,x5852),f4(x5851,x5852),x5852),f11(x5851,x5851,x5852)) % 1.21/1.22 [587]~P48(x5872)+E(f11(f13(x5871,x5872),f13(x5871,x5872),x5872),f11(x5871,x5871,x5872)) % 1.21/1.22 [639]~P33(x6392)+P3(x6391,f9(x6391,f10(x6392),x6392),x6392) % 1.21/1.22 [710]P3(x7102,x7101,a1)+E(f9(x7101,f3(x7102,x7101,a1),a1),x7102) % 1.21/1.22 [783]~P4(x7831,x7832,a1)+E(f9(x7831,f3(x7832,x7831,a1),a1),x7832) % 1.21/1.22 [784]~P4(x7842,x7841,a1)+E(f3(x7841,f3(x7841,x7842,a1),a1),x7842) % 1.21/1.22 [785]~P4(x7852,x7851,a1)+E(f9(f3(x7851,x7852,a1),x7852,a1),x7851) % 1.21/1.22 [793]~P4(x7932,x7931,a1)+E(f30(f3(x7931,x7932,a1)),f3(f30(x7931),x7932,a1)) % 1.21/1.22 [816]~P3(f2(a1),x8161,a1)+P3(f3(x8161,f30(x8162),a1),x8161,a1) % 1.21/1.22 [918]P4(f30(f2(a1)),x9181,a1)+~P4(f30(f2(a1)),f11(x9182,x9181,a1),a1) % 1.21/1.22 [919]P4(f30(f2(a1)),x9191,a1)+~P4(f30(f2(a1)),f11(x9191,x9192,a1),a1) % 1.21/1.22 [484]~P14(x4841)+E(f11(f13(f10(x4841),x4841),x4842,x4841),f13(x4842,x4841)) % 1.21/1.22 [788]~P34(x7882)+E(f9(x7881,x7881,x7882),f11(f9(f10(x7882),f10(x7882),x7882),x7881,x7882)) % 1.21/1.22 [416]~P5(x4161,x4163)+P5(f20(x4161,x4162),f20(x4163,x4162)) % 1.21/1.22 [417]~P5(x4171,x4173)+P5(f16(x4171,x4172),f16(x4173,x4172)) % 1.21/1.22 [418]~P5(x4182,x4183)+P5(f16(x4181,x4182),f16(x4181,x4183)) % 1.21/1.22 [491]~P11(x4913)+E(f9(x4911,x4912,x4913),f9(x4912,x4911,x4913)) % 1.21/1.22 [493]~P34(x4933)+E(f9(x4931,x4932,x4933),f9(x4932,x4931,x4933)) % 1.21/1.22 [495]~P34(x4953)+E(f11(x4951,x4952,x4953),f11(x4952,x4951,x4953)) % 1.21/1.22 [496]~P8(x4963)+E(f28(x4961,x4962,x4963),f28(x4962,x4961,x4963)) % 1.21/1.22 [497]~P8(x4973)+E(f29(x4971,x4972,x4973),f29(x4972,x4971,x4973)) % 1.21/1.22 [589]E(x5891,x5892)+~E(f9(x5893,x5891,a1),f9(x5893,x5892,a1)) % 1.21/1.22 [590]E(x5901,x5902)+~E(f9(x5901,x5903,a1),f9(x5902,x5903,a1)) % 1.21/1.22 [591]~P8(x5913)+P4(x5911,f28(x5912,x5911,x5913),x5913) % 1.21/1.22 [592]~P8(x5923)+P4(x5921,f28(x5921,x5922,x5923),x5923) % 1.21/1.22 [593]~P34(x5933)+P6(x5931,f11(x5932,x5931,x5933),x5933) % 1.21/1.22 [594]~P34(x5943)+P6(x5941,f11(x5941,x5942,x5943),x5943) % 1.21/1.22 [595]~P42(x5953)+P6(x5951,f11(x5951,x5952,x5953),x5953) % 1.21/1.22 [596]~P8(x5963)+P4(f29(x5961,x5962,x5963),x5962,x5963) % 1.21/1.22 [597]~P8(x5973)+P4(f29(x5971,x5972,x5973),x5971,x5973) % 1.21/1.22 [772]~P4(x7721,x7723,a1)+P4(x7721,f9(x7722,x7723,a1),a1) % 1.21/1.22 [774]~P4(x7741,x7742,a1)+P4(x7741,f9(x7742,x7743,a1),a1) % 1.21/1.22 [776]~P3(x7761,x7763,a1)+P3(x7761,f9(x7762,x7763,a1),a1) % 1.21/1.22 [778]~P3(x7781,x7782,a1)+P3(x7781,f9(x7782,x7783,a1),a1) % 1.21/1.22 [779]~P3(x7791,x7793,a1)+P3(f3(x7791,x7792,a1),x7793,a1) % 1.21/1.22 [851]P4(x8511,x8512,a1)+~P4(f9(x8513,x8511,a1),x8512,a1) % 1.21/1.22 [852]P4(x8521,x8522,a1)+~P4(f9(x8521,x8523,a1),x8522,a1) % 1.21/1.22 [853]P3(x8531,x8532,a1)+~P3(f9(x8531,x8533,a1),x8532,a1) % 1.21/1.22 [882]P4(f11(x8822,x8821,a1),f11(x8823,x8821,a1),a1)+P3(f2(a1),x8821,a1) % 1.21/1.22 [883]P4(f11(x8831,x8832,a1),f11(x8831,x8833,a1),a1)+P3(f2(a1),x8831,a1) % 1.21/1.22 [951]~P4(x9511,x9513,a1)+P4(f9(x9511,x9512,a1),f9(x9513,x9512,a1),a1) % 1.21/1.22 [952]~P4(x9522,x9523,a1)+P4(f9(x9521,x9522,a1),f9(x9521,x9523,a1),a1) % 1.21/1.22 [954]~P4(x9541,x9543,a1)+P4(f11(x9541,x9542,a1),f11(x9543,x9542,a1),a1) % 1.21/1.22 [956]~P4(x9562,x9563,a1)+P4(f11(x9561,x9562,a1),f11(x9561,x9563,a1),a1) % 1.21/1.22 [957]~P4(x9571,x9573,a1)+P4(f3(x9571,x9572,a1),f3(x9573,x9572,a1),a1) % 1.21/1.22 [958]~P4(x9583,x9582,a1)+P4(f3(x9581,x9582,a1),f3(x9581,x9583,a1),a1) % 1.21/1.22 [959]~P3(x9591,x9593,a1)+P3(f9(x9591,x9592,a1),f9(x9593,x9592,a1),a1) % 1.21/1.22 [960]~P3(x9602,x9603,a1)+P3(f9(x9601,x9602,a1),f9(x9601,x9603,a1),a1) % 1.21/1.22 [1078]~P4(f3(x10781,x10783,a1),x10782,a1)+P4(x10781,f9(x10782,x10783,a1),a1) % 1.21/1.22 [1079]~P3(f9(x10791,x10793,a1),x10792,a1)+P3(x10791,f3(x10792,x10793,a1),a1) % 1.21/1.22 [1080]~P4(x10801,f9(x10803,x10802,a1),a1)+P4(f3(x10801,x10802,a1),x10803,a1) % 1.21/1.22 [1081]~P3(x10811,f3(x10813,x10812,a1),a1)+P3(f9(x10811,x10812,a1),x10813,a1) % 1.21/1.22 [1167]P4(x11671,x11672,a1)+~P4(f9(x11673,x11671,a1),f9(x11673,x11672,a1),a1) % 1.21/1.22 [1168]P3(x11681,x11682,a1)+~P3(f9(x11683,x11681,a1),f9(x11683,x11682,a1),a1) % 1.21/1.22 [1169]P3(x11691,x11692,a1)+~P3(f11(x11693,x11691,a1),f11(x11693,x11692,a1),a1) % 1.21/1.22 [1170]P3(x11701,x11702,a1)+~P3(f11(x11701,x11703,a1),f11(x11702,x11703,a1),a1) % 1.21/1.22 [1173]~P3(f11(x11732,x11731,a1),f11(x11733,x11731,a1),a1)+P3(f2(a1),x11731,a1) % 1.21/1.22 [1174]~P3(f11(x11741,x11742,a1),f11(x11741,x11743,a1),a1)+P3(f2(a1),x11741,a1) % 1.21/1.22 [518]~P2(x5181)+P2(f22(x5181,f15(x5182),x5183)) % 1.21/1.22 [531]~P14(x5313)+E(f9(x5311,f13(x5312,x5313),x5313),f3(x5311,x5312,x5313)) % 1.21/1.22 [532]~P24(x5323)+E(f9(x5321,f13(x5322,x5323),x5323),f3(x5321,x5322,x5323)) % 1.21/1.22 [534]~P16(x5343)+E(f9(x5341,f13(x5342,x5343),x5343),f3(x5341,x5342,x5343)) % 1.21/1.22 [535]~P47(x5353)+E(f11(x5351,f7(x5352,x5353),x5353),f8(x5351,x5352,x5353)) % 1.21/1.22 [536]~P24(x5363)+E(f3(x5361,f13(x5362,x5363),x5363),f9(x5361,x5362,x5363)) % 1.21/1.22 [553]~P3(x5532,x5533,a1)+E(f19(x5531,f15(x5532),x5533),f15(x5532)) % 1.21/1.22 [554]~P3(x5541,x5543,a1)+E(f22(f15(x5541),x5542,x5543),f15(x5541)) % 1.21/1.22 [584]~P66(x5842)+E(f11(f13(x5841,x5842),x5843,x5842),f11(x5841,f13(x5843,x5842),x5842)) % 1.21/1.22 [586]~P66(x5862)+E(f11(f13(x5861,x5862),f13(x5863,x5862),x5862),f11(x5861,x5863,x5862)) % 1.21/1.22 [598]~P8(x5983)+E(f28(x5981,f29(x5981,x5982,x5983),x5983),x5981) % 1.21/1.22 [599]~P8(x5993)+E(f29(x5991,f28(x5991,x5992,x5993),x5993),x5991) % 1.21/1.22 [600]~P24(x6003)+E(f9(f3(x6001,x6002,x6003),x6002,x6003),x6001) % 1.21/1.22 [601]~P24(x6013)+E(f3(f9(x6011,x6012,x6013),x6012,x6013),x6011) % 1.21/1.22 [603]~P1(x6033)+E(f6(f5(x6031,x6032,x6033),x6032,x6033),f2(x6033)) % 1.21/1.22 [604]~P1(x6043)+E(f5(f11(x6041,x6042,x6043),x6042,x6043),f2(x6043)) % 1.21/1.22 [605]~P1(x6053)+E(f5(f11(x6051,x6052,x6053),x6051,x6053),f2(x6053)) % 1.21/1.22 [647]~P16(x6473)+E(f13(f3(x6471,x6472,x6473),x6473),f3(x6472,x6471,x6473)) % 1.21/1.22 [656]E(x6561,x6562)+~E(f11(f30(x6563),x6561,a1),f11(f30(x6563),x6562,a1)) % 1.21/1.22 [680]~P16(x6802)+E(f9(f13(x6801,x6802),f9(x6803,x6801,x6802),x6802),x6803) % 1.21/1.22 [681]~P24(x6812)+E(f9(f13(x6811,x6812),f9(x6811,x6813,x6812),x6812),x6813) % 1.21/1.22 [704]~P66(x7043)+E(f11(x7041,f13(x7042,x7043),x7043),f13(f11(x7041,x7042,x7043),x7043)) % 1.21/1.22 [705]~P53(x7052)+E(f31(f4(x7051,x7052),x7053,x7052),f4(f31(x7051,x7053,x7052),x7052)) % 1.21/1.22 [706]~P66(x7062)+E(f11(f13(x7061,x7062),x7063,x7062),f13(f11(x7061,x7063,x7062),x7062)) % 1.21/1.22 [707]~P47(x7072)+E(f8(f13(x7071,x7072),x7073,x7072),f13(f8(x7071,x7073,x7072),x7072)) % 1.21/1.22 [735]P3(x7352,x7353,a1)+E(f19(x7351,f15(x7352),x7353),f15(f9(x7352,x7351,a1))) % 1.21/1.22 [737]~P19(x7373)+E(f11(x7371,f11(x7371,x7372,x7373),x7373),f11(x7371,x7372,x7373)) % 1.21/1.22 [738]~P8(x7383)+E(f28(x7381,f28(x7381,x7382,x7383),x7383),f28(x7381,x7382,x7383)) % 1.21/1.22 [739]~P8(x7393)+E(f29(x7391,f29(x7391,x7392,x7393),x7393),f29(x7391,x7392,x7393)) % 1.21/1.22 [740]~P1(x7403)+E(f5(f9(x7401,x7402,x7403),x7402,x7403),f5(x7401,x7402,x7403)) % 1.21/1.22 [741]~P1(x7413)+E(f5(f9(x7411,x7412,x7413),x7411,x7413),f5(x7412,x7411,x7413)) % 1.21/1.22 [742]~P1(x7423)+E(f5(f5(x7421,x7422,x7423),x7422,x7423),f5(x7421,x7422,x7423)) % 1.21/1.22 [743]~P53(x7431)+P4(f2(x7431),f31(f4(x7432,x7431),x7433,x7431),x7431) % 1.21/1.22 [749]~P35(x7493)+E(f11(x7491,f31(x7491,x7492,x7493),x7493),f31(x7491,f30(x7492),x7493)) % 1.21/1.22 [750]~P22(x7503)+E(f11(f31(x7501,x7502,x7503),x7501,x7503),f31(x7501,f30(x7502),x7503)) % 1.21/1.22 [751]~P34(x7513)+E(f11(x7511,f31(x7511,x7512,x7513),x7513),f31(x7511,f30(x7512),x7513)) % 1.21/1.22 [752]~P34(x7523)+E(f11(f31(x7521,x7522,x7523),x7521,x7523),f31(x7521,f30(x7522),x7523)) % 1.21/1.22 [755]~P68(x7552)+E(f9(f24(x7551,x7552),f24(x7553,x7552),x7552),f24(f9(x7551,x7553,a1),x7552)) % 1.21/1.22 [756]~P68(x7562)+E(f11(f24(x7561,x7562),f24(x7563,x7562),x7562),f24(f11(x7561,x7563,a1),x7562)) % 1.21/1.22 [757]~P53(x7572)+E(f11(f4(x7571,x7572),f4(x7573,x7572),x7572),f4(f11(x7571,x7573,x7572),x7572)) % 1.21/1.22 [758]~P24(x7582)+E(f9(f13(x7581,x7582),f13(x7583,x7582),x7582),f13(f9(x7583,x7581,x7582),x7582)) % 1.21/1.22 [759]~P16(x7592)+E(f9(f13(x7591,x7592),f13(x7593,x7592),x7592),f13(f9(x7591,x7593,x7592),x7592)) % 1.21/1.22 [760]~P53(x7602)+E(f11(f12(x7601,x7602),f12(x7603,x7602),x7602),f12(f11(x7601,x7603,x7602),x7602)) % 1.21/1.22 [791]~P28(x7913)+E(f4(f3(x7911,x7912,x7913),x7913),f4(f3(x7912,x7911,x7913),x7913)) % 1.21/1.22 [849]~P48(x8492)+P6(f11(x8491,f2(x8492),x8492),f11(x8493,f2(x8492),x8492),x8492) % 1.21/1.22 [850]~P48(x8501)+P6(f11(f2(x8501),x8502,x8501),f11(f2(x8501),x8503,x8501),x8501) % 1.21/1.22 [913]~P22(x9133)+E(f11(f31(x9131,x9132,x9133),x9131,x9133),f11(x9131,f31(x9131,x9132,x9133),x9133)) % 1.21/1.22 [1024]~P3(x10242,x10243,a1)+P3(f11(f30(x10241),x10242,a1),f11(f30(x10241),x10243,a1),a1) % 1.21/1.22 [1055]~P4(x10552,x10553,a1)+E(f3(f9(x10551,x10552,a1),x10553,a1),f3(x10551,f3(x10553,x10552,a1),a1)) % 1.21/1.22 [1056]~P4(x10563,x10562,a1)+E(f3(f9(x10561,x10562,a1),x10563,a1),f9(x10561,f3(x10562,x10563,a1),a1)) % 1.21/1.22 [1058]~P4(x10583,x10581,a1)+E(f3(f9(x10581,x10582,a1),x10583,a1),f9(f3(x10581,x10583,a1),x10582,a1)) % 1.21/1.22 [1095]~P67(x10951)+E(f11(f31(f13(f10(x10951),x10951),x10952,x10951),f31(x10953,x10952,x10951),x10951),f31(f13(x10953,x10951),x10952,x10951)) % 1.21/1.22 [1134]~P4(x11343,x11342,a1)+P4(x11341,f3(f9(x11342,x11341,a1),x11343,a1),a1) % 1.21/1.22 [1188]~P1(x11883)+E(f9(f11(x11881,f6(x11882,x11881,x11883),x11883),f5(x11882,x11881,x11883),x11883),x11882) % 1.21/1.22 [1189]~P1(x11893)+E(f9(f11(f6(x11891,x11892,x11893),x11892,x11893),f5(x11891,x11892,x11893),x11893),x11891) % 1.21/1.22 [1191]P4(x11911,x11912,a1)+~P4(f11(f30(x11913),x11911,a1),f11(f30(x11913),x11912,a1),a1) % 1.21/1.22 [1195]~P28(x11953)+P4(f4(f9(x11951,x11952,x11953),x11953),f9(f4(x11951,x11953),f4(x11952,x11953),x11953),x11953) % 1.21/1.22 [1196]~P49(x11963)+P4(f4(f11(x11961,x11962,x11963),x11963),f11(f4(x11961,x11963),f4(x11962,x11963),x11963),x11963) % 1.21/1.22 [1197]~P28(x11973)+P4(f4(f3(x11971,x11972,x11973),x11973),f9(f4(x11971,x11973),f4(x11972,x11973),x11973),x11973) % 1.21/1.22 [1198]~P28(x11982)+P4(f3(f4(x11981,x11982),f4(x11983,x11982),x11982),f4(f3(x11981,x11983,x11982),x11982),x11982) % 1.21/1.22 [1287]~P55(x12871)+P4(f2(x12871),f9(f11(x12872,x12872,x12871),f11(x12873,x12873,x12871),x12871),x12871) % 1.21/1.22 [1342]~P55(x13421)+~P3(f9(f11(x13422,x13422,x13421),f11(x13423,x13423,x13421),x13421),f2(x13421),x13421) % 1.21/1.22 [734]~P24(x7342)+E(f9(x7341,f9(f13(x7341,x7342),x7343,x7342),x7342),x7343) % 1.21/1.22 [854]~P53(x8542)+E(f4(f31(f13(x8541,x8542),x8543,x8542),x8542),f4(f31(x8541,x8543,x8542),x8542)) % 1.21/1.22 [859]~P1(x8591)+E(f6(f11(f2(x8591),x8592,x8591),f11(f2(x8591),x8593,x8591),x8591),f2(x8591)) % 1.21/1.22 [931]~P28(x9312)+E(f4(f9(f4(x9311,x9312),f4(x9313,x9312),x9312),x9312),f9(f4(x9311,x9312),f4(x9313,x9312),x9312)) % 1.21/1.22 [947]~P34(x9473)+E(f9(x9471,f11(x9472,x9471,x9473),x9473),f11(f9(x9472,f10(x9473),x9473),x9471,x9473)) % 1.21/1.22 [948]~P34(x9483)+E(f9(f11(x9481,x9482,x9483),x9482,x9483),f11(f9(x9481,f10(x9483),x9483),x9482,x9483)) % 1.21/1.22 [1040]~P7(x10403)+E(f5(f13(f5(x10401,x10402,x10403),x10403),x10402,x10403),f5(f13(x10401,x10403),x10402,x10403)) % 1.21/1.22 [1187]~P1(x11873)+E(f9(f5(x11871,x11872,x11873),f11(f6(x11871,x11872,x11873),x11872,x11873),x11873),x11871) % 1.21/1.22 [1201]~P4(x12012,x12013,a1)+E(f3(f9(x12011,x12012,a1),f30(x12013),a1),f3(x12011,f30(f3(x12013,x12012,a1)),a1)) % 1.21/1.22 [1202]~P4(x12022,x12021,a1)+E(f3(f30(f3(x12021,x12022,a1)),x12023,a1),f3(f30(x12021),f9(x12022,x12023,a1),a1)) % 1.21/1.22 [1319]~P28(x13192)+P4(f4(f3(f4(x13191,x13192),f4(x13193,x13192),x13192),x13192),f4(f3(x13191,x13193,x13192),x13192),x13192) % 1.21/1.22 [325]E(x3251,x3252)+~E(f16(x3253,x3251),f16(x3254,x3252)) % 1.21/1.22 [326]E(x3261,x3262)+~E(f16(x3261,x3263),f16(x3262,x3264)) % 1.21/1.22 [792]~P5(x7921,x7924)+P5(f22(x7921,x7922,x7923),f22(x7924,x7922,x7923)) % 1.21/1.22 [894]~P34(x8943)+E(f31(f31(x8941,x8942,x8943),x8944,x8943),f31(x8941,f11(x8942,x8944,a1),x8943)) % 1.21/1.22 [895]~P22(x8953)+E(f31(f31(x8951,x8952,x8953),x8954,x8953),f31(x8951,f11(x8952,x8954,a1),x8953)) % 1.21/1.22 [898]~P11(x8984)+E(f9(x8981,f9(x8982,x8983,x8984),x8984),f9(x8982,f9(x8981,x8983,x8984),x8984)) % 1.21/1.22 [899]~P34(x8994)+E(f9(x8991,f9(x8992,x8993,x8994),x8994),f9(x8992,f9(x8991,x8993,x8994),x8994)) % 1.21/1.22 [900]~P16(x9004)+E(f9(x9001,f9(x9002,x9003,x9004),x9004),f9(x9002,f9(x9001,x9003,x9004),x9004)) % 1.21/1.22 [901]~P34(x9014)+E(f11(x9011,f11(x9012,x9013,x9014),x9014),f11(x9012,f11(x9011,x9013,x9014),x9014)) % 1.21/1.22 [902]~P8(x9024)+E(f28(x9021,f28(x9022,x9023,x9024),x9024),f28(x9022,f28(x9021,x9023,x9024),x9024)) % 1.21/1.22 [903]~P8(x9034)+E(f29(x9031,f29(x9032,x9033,x9034),x9034),f29(x9032,f29(x9031,x9033,x9034),x9034)) % 1.21/1.22 [908]~P11(x9083)+E(f9(f9(x9081,x9082,x9083),x9084,x9083),f9(x9081,f9(x9082,x9084,x9083),x9083)) % 1.21/1.22 [909]~P34(x9093)+E(f9(f9(x9091,x9092,x9093),x9094,x9093),f9(x9091,f9(x9092,x9094,x9093),x9093)) % 1.21/1.22 [910]~P15(x9103)+E(f9(f9(x9101,x9102,x9103),x9104,x9103),f9(x9101,f9(x9102,x9104,x9103),x9103)) % 1.21/1.22 [911]~P34(x9113)+E(f11(f11(x9111,x9112,x9113),x9114,x9113),f11(x9111,f11(x9112,x9114,x9113),x9113)) % 1.21/1.22 [912]~P18(x9123)+E(f11(f11(x9121,x9122,x9123),x9124,x9123),f11(x9121,f11(x9122,x9124,x9123),x9123)) % 1.21/1.22 [914]~P8(x9143)+E(f28(f28(x9141,x9142,x9143),x9144,x9143),f28(x9141,f28(x9142,x9144,x9143),x9143)) % 1.21/1.22 [915]~P8(x9153)+E(f29(f29(x9151,x9152,x9153),x9154,x9153),f29(x9151,f29(x9152,x9154,x9153),x9153)) % 1.21/1.22 [916]~P34(x9163)+E(f9(f9(x9161,x9162,x9163),x9164,x9163),f9(f9(x9161,x9164,x9163),x9162,x9163)) % 1.21/1.22 [917]~P34(x9173)+E(f11(f11(x9171,x9172,x9173),x9174,x9173),f11(f11(x9171,x9174,x9173),x9172,x9173)) % 1.21/1.22 [1102]~P22(x11023)+E(f11(f31(x11021,x11022,x11023),f31(x11021,x11024,x11023),x11023),f31(x11021,f9(x11022,x11024,a1),x11023)) % 1.21/1.22 [1103]~P34(x11033)+E(f11(f31(x11031,x11032,x11033),f31(x11031,x11034,x11033),x11033),f31(x11031,f9(x11032,x11034,a1),x11033)) % 1.21/1.22 [1106]~P34(x11063)+E(f9(f11(x11061,x11062,x11063),f11(x11061,x11064,x11063),x11063),f11(x11061,f9(x11062,x11064,x11063),x11063)) % 1.21/1.22 [1107]~P8(x11073)+E(f29(f28(x11071,x11072,x11073),f28(x11071,x11074,x11073),x11073),f28(x11071,f29(x11072,x11074,x11073),x11073)) % 1.21/1.22 [1108]~P8(x11083)+E(f28(f29(x11081,x11082,x11083),f29(x11081,x11084,x11083),x11083),f29(x11081,f28(x11082,x11084,x11083),x11083)) % 1.21/1.22 [1109]~P10(x11093)+E(f28(f9(x11091,x11092,x11093),f9(x11094,x11092,x11093),x11093),f9(f28(x11091,x11094,x11093),x11092,x11093)) % 1.21/1.22 [1110]~P10(x11103)+E(f29(f9(x11101,x11102,x11103),f9(x11104,x11102,x11103),x11103),f9(f29(x11101,x11104,x11103),x11102,x11103)) % 1.21/1.22 [1112]~P38(x11123)+E(f9(f11(x11121,x11122,x11123),f11(x11124,x11122,x11123),x11123),f11(f9(x11121,x11124,x11123),x11122,x11123)) % 1.21/1.22 [1113]~P30(x11133)+E(f28(f3(x11131,x11132,x11133),f3(x11134,x11132,x11133),x11133),f3(f28(x11131,x11134,x11133),x11132,x11133)) % 1.21/1.22 [1114]~P30(x11143)+E(f29(f3(x11141,x11142,x11143),f3(x11144,x11142,x11143),x11143),f3(f29(x11141,x11144,x11143),x11142,x11143)) % 1.21/1.22 [1115]~P8(x11153)+E(f29(f28(x11151,x11152,x11153),f28(x11154,x11152,x11153),x11153),f28(f29(x11151,x11154,x11153),x11152,x11153)) % 1.21/1.22 [1116]~P8(x11163)+E(f28(f29(x11161,x11162,x11163),f29(x11164,x11162,x11163),x11163),f29(f28(x11161,x11164,x11163),x11162,x11163)) % 1.21/1.22 [1117]~P34(x11173)+E(f11(f31(x11171,x11172,x11173),f31(x11174,x11172,x11173),x11173),f31(f11(x11171,x11174,x11173),x11172,x11173)) % 1.21/1.22 [1118]~P21(x11183)+E(f11(f31(x11181,x11182,x11183),f31(x11184,x11182,x11183),x11183),f31(f11(x11181,x11184,x11183),x11182,x11183)) % 1.21/1.22 [1119]~P47(x11193)+E(f9(f8(x11191,x11192,x11193),f8(x11194,x11192,x11193),x11193),f8(f9(x11191,x11194,x11193),x11192,x11193)) % 1.21/1.22 [1120]~P47(x11203)+E(f3(f8(x11201,x11202,x11203),f8(x11204,x11202,x11203),x11203),f8(f3(x11201,x11204,x11203),x11202,x11203)) % 1.21/1.22 [1121]~P1(x11213)+E(f5(f11(x11211,x11212,x11213),f11(x11211,x11214,x11213),x11213),f11(x11211,f5(x11212,x11214,x11213),x11213)) % 1.21/1.22 [1122]~P34(x11223)+E(f9(f11(x11221,x11222,x11223),f11(x11224,x11222,x11223),x11223),f11(f9(x11221,x11224,x11223),x11222,x11223)) % 1.21/1.22 [1123]~P1(x11233)+E(f5(f11(x11231,x11232,x11233),f11(x11234,x11232,x11233),x11233),f11(f5(x11231,x11234,x11233),x11232,x11233)) % 1.21/1.22 [1338]~P8(x13384)+P4(f28(x13381,f29(x13382,x13383,x13384),x13384),f29(f28(x13381,x13382,x13384),f28(x13381,x13383,x13384),x13384),x13384) % 1.21/1.22 [1339]~P8(x13393)+P4(f28(f29(x13391,x13392,x13393),f29(x13391,x13394,x13393),x13393),f29(x13391,f28(x13392,x13394,x13393),x13393),x13393) % 1.21/1.22 [1104]~P1(x11044)+E(f5(f9(x11041,f11(x11042,x11043,x11044),x11044),x11043,x11044),f5(x11041,x11043,x11044)) % 1.21/1.22 [1105]~P1(x11054)+E(f5(f9(x11051,f11(x11052,x11053,x11054),x11054),x11052,x11054),f5(x11051,x11052,x11054)) % 1.21/1.22 [1222]~P1(x12224)+E(f5(f11(x12221,f5(x12222,x12223,x12224),x12224),x12223,x12224),f5(f11(x12221,x12222,x12224),x12223,x12224)) % 1.21/1.22 [1223]~P7(x12234)+E(f5(f3(x12231,f5(x12232,x12233,x12234),x12234),x12233,x12234),f5(f3(x12231,x12232,x12234),x12233,x12234)) % 1.21/1.22 [1226]~P7(x12263)+E(f5(f3(f5(x12261,x12262,x12263),x12264,x12263),x12262,x12263),f5(f3(x12261,x12264,x12263),x12262,x12263)) % 1.21/1.22 [1227]~P1(x12274)+E(f5(f9(x12271,f5(x12272,x12273,x12274),x12274),x12273,x12274),f5(f9(x12271,x12272,x12274),x12273,x12274)) % 1.21/1.22 [1228]~P1(x12283)+E(f5(f9(f5(x12281,x12282,x12283),x12284,x12283),x12282,x12283),f5(f9(x12281,x12284,x12283),x12282,x12283)) % 1.21/1.22 [1229]~P1(x12293)+E(f5(f11(f5(x12291,x12292,x12293),x12294,x12293),x12292,x12293),f5(f11(x12291,x12294,x12293),x12292,x12293)) % 1.21/1.22 [1320]~P1(x13203)+E(f5(f9(f5(x13201,x13202,x13203),f5(x13204,x13202,x13203),x13203),x13202,x13203),f5(f9(x13201,x13204,x13203),x13202,x13203)) % 1.21/1.22 [1321]~P1(x13213)+E(f5(f11(f5(x13211,x13212,x13213),f5(x13214,x13212,x13213),x13213),x13212,x13213),f5(f11(x13211,x13214,x13213),x13212,x13213)) % 1.21/1.22 [1322]~P7(x13223)+E(f5(f3(f5(x13221,x13222,x13223),f5(x13224,x13222,x13223),x13223),x13222,x13223),f5(f3(x13221,x13224,x13223),x13222,x13223)) % 1.21/1.22 [1347]~P1(x13473)+E(f9(f9(f11(x13471,f6(x13472,x13471,x13473),x13473),f5(x13472,x13471,x13473),x13473),x13474,x13473),f9(x13472,x13474,x13473)) % 1.21/1.22 [1348]~P1(x13483)+E(f9(f9(f11(f6(x13481,x13482,x13483),x13482,x13483),f5(x13481,x13482,x13483),x13483),x13484,x13483),f9(x13481,x13484,x13483)) % 1.21/1.22 [1353]~P4(x13531,x13533,a1)+E(f9(f11(x13531,x13532,a1),f9(f11(f3(x13533,x13531,a1),x13532,a1),x13534,a1),a1),f9(f11(x13533,x13532,a1),x13534,a1)) % 1.21/1.22 [610]E(x6101,x6102)+~E(f23(x6101,x6103,x6104),f23(x6102,x6105,x6104)) % 1.21/1.22 [1230]~P34(x12303)+E(f9(f9(x12301,x12302,x12303),f9(x12304,x12305,x12303),x12303),f9(f9(x12301,x12304,x12303),f9(x12302,x12305,x12303),x12303)) % 1.21/1.22 [1231]~P34(x12313)+E(f11(f11(x12311,x12312,x12313),f11(x12314,x12315,x12313),x12313),f11(f11(x12311,x12314,x12313),f11(x12312,x12315,x12313),x12313)) % 1.21/1.22 [1335]~P59(x13353)+E(f9(f11(x13351,x13352,x13353),f9(f11(x13354,x13352,x13353),x13355,x13353),x13353),f9(f11(f9(x13351,x13354,x13353),x13352,x13353),x13355,x13353)) % 1.21/1.22 [1374]~P28(x13743)+P4(f4(f3(f9(x13741,x13742,x13743),f9(x13744,x13745,x13743),x13743),x13743),f9(f4(f3(x13741,x13744,x13743),x13743),f4(f3(x13742,x13745,x13743),x13743),x13743),x13743) % 1.21/1.22 [1350]~P66(x13503)+E(f9(f11(x13501,x13502,x13503),f9(f11(f3(x13504,x13501,x13503),x13502,x13503),x13505,x13503),x13503),f9(f11(x13504,x13502,x13503),x13505,x13503)) % 1.21/1.22 [1356]~P4(x13561,x13564,a1)+E(f3(f9(f11(x13561,x13562,a1),x13563,a1),f9(f11(x13564,x13562,a1),x13565,a1),a1),f3(x13563,f9(f11(f3(x13564,x13561,a1),x13562,a1),x13565,a1),a1)) % 1.21/1.22 [1357]~P4(x13574,x13571,a1)+E(f3(f9(f11(x13571,x13572,a1),x13573,a1),f9(f11(x13574,x13572,a1),x13575,a1),a1),f3(f9(f11(f3(x13571,x13574,a1),x13572,a1),x13573,a1),x13575,a1)) % 1.21/1.22 [319]~P43(x3191)+~P47(x3191)+E(f7(f10(x3191),x3191),f10(x3191)) % 1.21/1.22 [649]~P31(x6491)+~P4(f2(x6491),f2(x6491),x6491)+E(f9(f2(x6491),f2(x6491),x6491),f2(x6491)) % 1.21/1.22 [472]E(x4721,x4722)+P3(x4722,x4721,a1)+P3(x4721,x4722,a1) % 1.21/1.22 [529]E(x5291,x5292)+P3(x5291,x5292,a1)+~P4(x5291,x5292,a1) % 1.21/1.22 [602]E(x6021,x6022)+~P4(x6022,x6021,a1)+~P4(x6021,x6022,a1) % 1.21/1.22 [316]~P29(x3162)+~E(f13(x3161,x3162),x3161)+E(x3161,f2(x3162)) % 1.21/1.22 [320]~P28(x3202)+~E(f4(x3201,x3202),f2(x3202))+E(x3201,f2(x3202)) % 1.21/1.22 [321]~P24(x3212)+~E(f13(x3211,x3212),f2(x3212))+E(x3211,f2(x3212)) % 1.21/1.22 [322]~P44(x3222)+~E(f7(x3221,x3222),f2(x3222))+E(x3221,f2(x3222)) % 1.21/1.22 [323]~P53(x3232)+~E(f12(x3231,x3232),f2(x3232))+E(x3231,f2(x3232)) % 1.21/1.22 [324]~P24(x3241)+~E(f13(x3242,x3241),f2(x3241))+E(f2(x3241),x3242) % 1.21/1.22 [380]~P1(x3802)+E(f6(x3801,x3801,x3802),f10(x3802))+E(x3801,f2(x3802)) % 1.21/1.22 [382]~P47(x3822)+E(f8(x3821,x3821,x3822),f10(x3822))+E(x3821,f2(x3822)) % 1.21/1.22 [396]~P48(x3962)+~P14(x3962)+E(f3(x3961,x3961,x3962),f2(x3962)) % 1.21/1.22 [409]~P39(x4092)+P3(x4091,f2(x4092),x4092)+E(f4(x4091,x4092),x4091) % 1.21/1.22 [427]~P25(x4271)+P4(f2(x4271),x4272,x4271)+~E(f26(x4272,x4271),x4272) % 1.21/1.22 [440]E(x4401,f2(a1))+E(x4402,f2(a1))+~E(f11(x4402,x4401,a1),f2(a1)) % 1.21/1.22 [441]~P25(x4412)+P4(x4411,f2(x4412),x4412)+~E(f26(x4411,x4412),f2(x4412)) % 1.21/1.22 [442]~P53(x4421)+P3(f2(x4421),x4422,x4421)+~E(f12(x4422,x4421),f10(x4421)) % 1.21/1.22 [447]~P28(x4472)+P3(f2(x4472),f4(x4471,x4472),x4472)+E(x4471,f2(x4472)) % 1.21/1.22 [455]~P25(x4552)+~E(f9(x4551,x4551,x4552),f2(x4552))+E(x4551,f2(x4552)) % 1.21/1.22 [469]~P34(x4692)+~P6(f2(x4692),x4691,x4692)+E(x4691,f2(x4692)) % 1.21/1.22 [503]~P28(x5032)+~P4(f2(x5032),x5031,x5032)+E(f4(x5031,x5032),x5031) % 1.21/1.22 [504]~P28(x5042)+~P3(f2(x5042),x5041,x5042)+E(f4(x5041,x5042),x5041) % 1.21/1.22 [505]~P25(x5052)+~P4(f2(x5052),x5051,x5052)+E(f26(x5051,x5052),x5051) % 1.21/1.22 [512]~P25(x5122)+~P4(x5121,f2(x5122),x5122)+E(f26(x5121,x5122),f2(x5122)) % 1.21/1.22 [513]~P53(x5132)+~P3(f2(x5132),x5131,x5132)+E(f12(x5131,x5132),f10(x5132)) % 1.21/1.22 [519]~P28(x5192)+~P4(x5191,f2(x5192),x5192)+E(f4(x5191,x5192),f13(x5191,x5192)) % 1.21/1.22 [520]~P28(x5202)+~P3(x5201,f2(x5202),x5202)+E(f4(x5201,x5202),f13(x5201,x5202)) % 1.21/1.22 [521]~P39(x5212)+~P3(x5211,f2(x5212),x5212)+E(f4(x5211,x5212),f13(x5211,x5212)) % 1.21/1.22 [555]~P3(x5551,x5552,a1)+E(f30(x5551),x5552)+P3(f30(x5551),x5552,a1) % 1.21/1.22 [556]E(x5561,x5562)+P3(x5562,x5561,a1)+~P3(x5562,f30(x5561),a1) % 1.21/1.22 [558]E(x5581,x5582)+P3(x5581,x5582,a1)+~P3(x5581,f30(x5582),a1) % 1.21/1.22 [563]~P28(x5632)+~P4(f4(x5631,x5632),f2(x5632),x5632)+E(x5631,f2(x5632)) % 1.21/1.22 [578]P4(x5781,x5782,a1)+E(x5781,f30(x5782))+~P4(x5781,f30(x5782),a1) % 1.21/1.22 [621]E(x6211,x6212)+~E(f3(x6212,x6211,a1),f2(a1))+~E(f3(x6211,x6212,a1),f2(a1)) % 1.21/1.22 [625]E(x6251,x6252)+~P4(x6252,x6251,a1)+~P3(x6251,f30(x6252),a1) % 1.21/1.22 [648]~P33(x6481)+P3(f2(x6481),f24(x6482,x6481),x6481)+~P3(f2(a1),x6482,a1) % 1.21/1.22 [650]~P25(x6502)+~P4(x6501,f2(x6502),x6502)+P4(x6501,f13(x6501,x6502),x6502) % 1.21/1.22 [651]~P29(x6512)+~P4(x6511,f2(x6512),x6512)+P4(x6511,f13(x6511,x6512),x6512) % 1.21/1.22 [652]~P53(x6522)+~P3(x6521,f2(x6522),x6522)+P3(x6521,f13(x6521,x6522),x6522) % 1.21/1.22 [653]~P25(x6532)+~P4(f2(x6532),x6531,x6532)+P4(f13(x6531,x6532),x6531,x6532) % 1.21/1.22 [654]~P29(x6542)+~P4(f2(x6542),x6541,x6542)+P4(f13(x6541,x6542),x6541,x6542) % 1.21/1.22 [665]~P30(x6651)+~P4(x6652,f2(x6651),x6651)+P4(f2(x6651),f13(x6652,x6651),x6651) % 1.21/1.22 [666]~P30(x6661)+~P3(x6662,f2(x6661),x6661)+P3(f2(x6661),f13(x6662,x6661),x6661) % 1.21/1.22 [667]~P54(x6671)+~P3(f2(x6671),x6672,x6671)+P3(f2(x6671),f7(x6672,x6671),x6671) % 1.21/1.22 [668]~P53(x6681)+~P3(f2(x6681),x6682,x6681)+P3(f2(x6681),f12(x6682,x6681),x6681) % 1.21/1.22 [669]~P54(x6692)+~P3(x6691,f2(x6692),x6692)+P3(f7(x6691,x6692),f2(x6692),x6692) % 1.21/1.22 [670]~P53(x6702)+~P3(x6701,f2(x6702),x6702)+P3(f12(x6701,x6702),f2(x6702),x6702) % 1.21/1.22 [671]~P30(x6712)+~P4(f2(x6712),x6711,x6712)+P4(f13(x6711,x6712),f2(x6712),x6712) % 1.21/1.22 [672]~P30(x6722)+~P3(f2(x6722),x6721,x6722)+P3(f13(x6721,x6722),f2(x6722),x6722) % 1.21/1.22 [675]~P25(x6752)+~P4(x6751,f13(x6751,x6752),x6752)+P4(x6751,f2(x6752),x6752) % 1.21/1.22 [676]~P29(x6762)+~P4(x6761,f13(x6761,x6762),x6762)+P4(x6761,f2(x6762),x6762) % 1.21/1.22 [677]~P53(x6772)+~P3(x6771,f13(x6771,x6772),x6772)+P3(x6771,f2(x6772),x6772) % 1.21/1.22 [678]~P25(x6781)+~P4(f13(x6782,x6781),x6782,x6781)+P4(f2(x6781),x6782,x6781) % 1.21/1.22 [679]~P29(x6791)+~P4(f13(x6792,x6791),x6792,x6791)+P4(f2(x6791),x6792,x6791) % 1.21/1.22 [696]~P33(x6962)+~P3(f2(x6962),f24(x6961,x6962),x6962)+P3(f2(a1),x6961,a1) % 1.21/1.22 [698]~P30(x6982)+~P4(f2(x6982),f13(x6981,x6982),x6982)+P4(x6981,f2(x6982),x6982) % 1.21/1.22 [699]~P30(x6992)+~P3(f2(x6992),f13(x6991,x6992),x6992)+P3(x6991,f2(x6992),x6992) % 1.21/1.22 [700]~P53(x7002)+~P3(f12(x7001,x7002),f2(x7002),x7002)+P3(x7001,f2(x7002),x7002) % 1.21/1.22 [701]~P53(x7011)+~P3(f2(x7011),f12(x7012,x7011),x7011)+P3(f2(x7011),x7012,x7011) % 1.21/1.22 [702]~P30(x7021)+~P4(f13(x7022,x7021),f2(x7021),x7021)+P4(f2(x7021),x7022,x7021) % 1.21/1.22 [703]~P30(x7031)+~P3(f13(x7032,x7031),f2(x7031),x7031)+P3(f2(x7031),x7032,x7031) % 1.21/1.22 [819]~P25(x8191)+~P4(f2(x8191),x8192,x8191)+P4(f2(x8191),f9(x8192,x8192,x8191),x8191) % 1.21/1.22 [822]~P25(x8221)+~P3(f2(x8221),x8222,x8221)+P3(f2(x8221),f9(x8222,x8222,x8221),x8221) % 1.21/1.22 [824]~P25(x8242)+~P4(x8241,f2(x8242),x8242)+P4(f9(x8241,x8241,x8242),f2(x8242),x8242) % 1.21/1.22 [825]~P25(x8252)+~P3(x8251,f2(x8252),x8252)+P3(f9(x8251,x8251,x8252),f2(x8252),x8252) % 1.21/1.22 [826]~P53(x8262)+~P3(x8261,f2(x8262),x8262)+P3(f9(x8261,x8261,x8262),f2(x8262),x8262) % 1.21/1.22 [920]~P25(x9202)+~P4(f9(x9201,x9201,x9202),f2(x9202),x9202)+P4(x9201,f2(x9202),x9202) % 1.21/1.22 [921]~P25(x9212)+~P3(f9(x9211,x9211,x9212),f2(x9212),x9212)+P3(x9211,f2(x9212),x9212) % 1.21/1.22 [922]~P53(x9222)+~P3(f9(x9221,x9221,x9222),f2(x9222),x9222)+P3(x9221,f2(x9222),x9222) % 1.21/1.22 [923]~P25(x9231)+~P4(f2(x9231),f9(x9232,x9232,x9231),x9231)+P4(f2(x9231),x9232,x9231) % 1.21/1.22 [924]~P25(x9241)+~P3(f2(x9241),f9(x9242,x9242,x9241),x9241)+P3(f2(x9241),x9242,x9241) % 1.21/1.22 [925]P3(f3(x9251,x9252,a1),x9251,a1)+~P3(f2(a1),x9252,a1)+~P3(f2(a1),x9251,a1) % 1.21/1.22 [930]~P3(f2(a1),x9302,a1)+~P3(f2(a1),x9301,a1)+P3(f2(a1),f11(x9301,x9302,a1),a1) % 1.21/1.22 [987]P3(f2(a1),x9871,a1)+P3(f2(a1),x9872,a1)+~P3(f2(a1),f9(x9871,x9872,a1),a1) % 1.21/1.22 [336]~P44(x3362)+E(x3361,f2(x3362))+E(f7(f7(x3361,x3362),x3362),x3361) % 1.21/1.22 [340]~P43(x3402)+~P44(x3402)+E(f7(f7(x3401,x3402),x3402),x3401) % 1.21/1.22 [399]~P48(x3992)+~P14(x3992)+E(f9(x3991,f2(x3992),x3992),x3991) % 1.21/1.22 [404]~P43(x4042)+~P47(x4042)+E(f8(x4041,f2(x4042),x4042),f2(x4042)) % 1.21/1.22 [410]~P58(x4101)+~P35(x4101)+E(f31(f2(x4101),f30(x4102),x4101),f2(x4101)) % 1.21/1.22 [429]~P54(x4292)+E(x4291,f2(x4292))+E(f7(f4(x4291,x4292),x4292),f4(f7(x4291,x4292),x4292)) % 1.21/1.22 [430]~P44(x4302)+E(x4301,f2(x4302))+E(f7(f13(x4301,x4302),x4302),f13(f7(x4301,x4302),x4302)) % 1.21/1.22 [438]~P54(x4382)+~P43(x4382)+E(f7(f4(x4381,x4382),x4382),f4(f7(x4381,x4382),x4382)) % 1.21/1.22 [439]~P43(x4392)+~P44(x4392)+E(f7(f13(x4391,x4392),x4392),f13(f7(x4391,x4392),x4392)) % 1.21/1.22 [443]~P44(x4432)+E(x4431,f2(x4432))+E(f11(x4431,f7(x4431,x4432),x4432),f10(x4432)) % 1.21/1.22 [444]~P47(x4442)+E(x4441,f2(x4442))+E(f11(f7(x4441,x4442),x4441,x4442),f10(x4442)) % 1.21/1.22 [445]~P44(x4452)+E(x4451,f2(x4452))+E(f11(f7(x4451,x4452),x4451,x4452),f10(x4452)) % 1.21/1.22 [452]E(x4521,f2(a1))+E(x4522,f2(a1))+~E(f9(x4522,x4521,a1),f30(f2(a1))) % 1.21/1.22 [463]E(x4631,f2(a1))+E(x4631,f30(f2(a1)))+~E(f9(x4632,x4631,a1),f30(f2(a1))) % 1.21/1.22 [464]E(x4641,f2(a1))+E(x4641,f30(f2(a1)))+~E(f9(x4641,x4642,a1),f30(f2(a1))) % 1.21/1.22 [477]E(x4771,f30(f2(a1)))+E(x4772,f30(f2(a1)))+~E(f9(x4772,x4771,a1),f30(f2(a1))) % 1.21/1.22 [514]~P53(x5142)+P3(x5141,f2(x5142),x5142)+~E(f12(x5141,x5142),f13(f10(x5142),x5142)) % 1.21/1.22 [524]~P53(x5242)+~P3(x5241,f2(x5242),x5242)+E(f12(x5241,x5242),f13(f10(x5242),x5242)) % 1.21/1.22 [985]P3(x9851,f11(x9852,x9851,a1),a1)+~P3(f30(f2(a1)),x9852,a1)+~P3(f30(f2(a1)),x9851,a1) % 1.21/1.22 [986]P3(x9861,f11(x9861,x9862,a1),a1)+~P3(f30(f2(a1)),x9862,a1)+~P3(f30(f2(a1)),x9861,a1) % 1.21/1.22 [1037]~P4(f30(f2(a1)),x10372,a1)+~P4(f30(f2(a1)),x10371,a1)+P4(f30(f2(a1)),f11(x10371,x10372,a1),a1) % 1.21/1.22 [1038]~P3(f30(f2(a1)),x10382,a1)+~P3(f30(f2(a1)),x10381,a1)+P3(f30(f2(a1)),f11(x10381,x10382,a1),a1) % 1.21/1.22 [674]~P43(x6741)+~P47(x6741)+E(f8(f11(f2(x6741),x6742,x6741),x6742,x6741),f2(x6741)) % 1.21/1.22 [498]P4(x4982,x4981,x4983)+~P8(x4983)+P4(x4981,x4982,x4983) % 1.21/1.22 [501]P3(x5012,x5011,x5013)+~P8(x5013)+P4(x5011,x5012,x5013) % 1.21/1.22 [551]~P36(x5513)+~P3(x5511,x5512,x5513)+P4(x5511,x5512,x5513) % 1.21/1.22 [552]~P37(x5523)+~P3(x5521,x5522,x5523)+P4(x5521,x5522,x5523) % 1.21/1.22 [627]~P3(x6273,x6272,x6271)+~P8(x6271)+~P4(x6272,x6273,x6271) % 1.21/1.22 [629]~P3(x6293,x6292,x6291)+~P8(x6291)+~P3(x6292,x6293,x6291) % 1.21/1.22 [630]~P3(x6303,x6302,x6301)+~P36(x6301)+~P4(x6302,x6303,x6301) % 1.21/1.22 [632]~P3(x6323,x6322,x6321)+~P36(x6321)+~P3(x6322,x6323,x6321) % 1.21/1.22 [633]~P3(x6333,x6332,x6331)+~P37(x6331)+~P3(x6332,x6333,x6331) % 1.21/1.22 [733]~P4(x7331,x7333,a1)+P4(x7331,x7332,a1)+~P4(x7333,x7332,a1) % 1.21/1.22 [337]~P24(x3373)+E(x3371,x3372)+~E(f13(x3371,x3373),f13(x3372,x3373)) % 1.21/1.22 [338]~P13(x3383)+E(x3381,x3382)+~E(f13(x3381,x3383),f13(x3382,x3383)) % 1.21/1.22 [339]~P12(x3393)+E(x3391,x3392)+~E(f24(x3391,x3393),f24(x3392,x3393)) % 1.21/1.22 [449]~P24(x4493)+E(x4491,x4492)+~E(f3(x4491,x4492,x4493),f2(x4493)) % 1.21/1.22 [450]~P16(x4503)+E(x4501,x4502)+~E(f3(x4501,x4502,x4503),f2(x4503)) % 1.21/1.22 [456]~P65(x4562)+~E(f31(x4561,x4563,x4562),f2(x4562))+E(x4561,f2(x4562)) % 1.21/1.22 [458]~P53(x4583)+P6(x4581,x4582,x4583)+~E(f4(x4581,x4583),f4(x4582,x4583)) % 1.21/1.22 [487]~P24(x4873)+~E(f9(x4871,x4872,x4873),f2(x4873))+E(x4871,f13(x4872,x4873)) % 1.21/1.22 [488]~P24(x4882)+~E(f9(x4881,x4883,x4882),f2(x4882))+E(f13(x4881,x4882),x4883) % 1.21/1.22 [489]~P44(x4892)+~E(f11(x4891,x4893,x4892),f10(x4892))+E(f7(x4891,x4892),x4893) % 1.21/1.22 [559]~P8(x5593)+~P4(x5591,x5592,x5593)+E(f28(x5591,x5592,x5593),x5592) % 1.21/1.22 [560]~P8(x5603)+~P4(x5602,x5601,x5603)+E(f28(x5601,x5602,x5603),x5601) % 1.21/1.22 [561]~P8(x5613)+~P4(x5612,x5611,x5613)+E(f29(x5611,x5612,x5613),x5612) % 1.21/1.22 [562]~P8(x5623)+~P4(x5621,x5622,x5623)+E(f29(x5621,x5622,x5623),x5621) % 1.21/1.22 [568]~P8(x5683)+P4(x5681,x5682,x5683)+~E(f28(x5681,x5682,x5683),x5682) % 1.21/1.22 [569]~P8(x5693)+P4(x5691,x5692,x5693)+~E(f29(x5691,x5692,x5693),x5691) % 1.21/1.22 [579]~P1(x5793)+~P6(x5792,x5791,x5793)+E(f5(x5791,x5792,x5793),f2(x5793)) % 1.21/1.22 [580]~P1(x5803)+P6(x5801,x5802,x5803)+~E(f5(x5802,x5801,x5803),f2(x5803)) % 1.21/1.22 [607]E(x6071,x6072)+~E(f11(x6073,x6071,a1),f11(x6073,x6072,a1))+E(x6073,f2(a1)) % 1.21/1.22 [608]E(x6081,x6082)+~E(f11(x6081,x6083,a1),f11(x6082,x6083,a1))+E(x6083,f2(a1)) % 1.21/1.22 [611]~P53(x6113)+~P6(x6111,x6112,x6113)+P6(x6111,f4(x6112,x6113),x6113) % 1.21/1.22 [612]~P40(x6123)+~P6(x6121,x6122,x6123)+P6(x6121,f13(x6122,x6123),x6123) % 1.21/1.22 [613]~P53(x6132)+~P6(x6131,x6133,x6132)+P6(f4(x6131,x6132),x6133,x6132) % 1.21/1.22 [614]~P40(x6142)+~P6(x6141,x6143,x6142)+P6(f13(x6141,x6142),x6143,x6142) % 1.21/1.22 [658]~P53(x6583)+P6(x6581,x6582,x6583)+~P6(x6581,f4(x6582,x6583),x6583) % 1.21/1.22 [659]~P40(x6593)+P6(x6591,x6592,x6593)+~P6(x6591,f13(x6592,x6593),x6593) % 1.21/1.22 [660]~P28(x6603)+P4(x6601,x6602,x6603)+~P4(f4(x6601,x6603),x6602,x6603) % 1.21/1.22 [661]~P53(x6613)+P6(x6611,x6612,x6613)+~P6(f4(x6611,x6613),x6612,x6613) % 1.21/1.22 [662]~P40(x6623)+P6(x6621,x6622,x6623)+~P6(f13(x6621,x6623),x6622,x6623) % 1.21/1.22 [663]~P53(x6633)+P3(x6631,x6632,x6633)+~P3(f4(x6631,x6633),x6632,x6633) % 1.21/1.22 [691]~P33(x6912)+~P4(x6911,x6913,a1)+P4(f24(x6911,x6912),f24(x6913,x6912),x6912) % 1.21/1.22 [692]~P33(x6922)+~P3(x6921,x6923,a1)+P3(f24(x6921,x6922),f24(x6923,x6922),x6922) % 1.21/1.22 [694]~P30(x6942)+~P4(x6943,x6941,x6942)+P4(f13(x6941,x6942),f13(x6943,x6942),x6942) % 1.21/1.22 [695]~P30(x6952)+~P3(x6953,x6951,x6952)+P3(f13(x6951,x6952),f13(x6953,x6952),x6952) % 1.21/1.22 [722]~P30(x7223)+~P4(x7222,f13(x7221,x7223),x7223)+P4(x7221,f13(x7222,x7223),x7223) % 1.21/1.22 [724]~P30(x7243)+~P3(x7242,f13(x7241,x7243),x7243)+P3(x7241,f13(x7242,x7243),x7243) % 1.21/1.22 [726]~P30(x7262)+~P4(f13(x7263,x7262),x7261,x7262)+P4(f13(x7261,x7262),x7263,x7262) % 1.21/1.22 [727]~P28(x7272)+~P4(f4(x7271,x7272),x7273,x7272)+P4(f13(x7271,x7272),x7273,x7272) % 1.21/1.22 [729]~P30(x7292)+~P3(f13(x7293,x7292),x7291,x7292)+P3(f13(x7291,x7292),x7293,x7292) % 1.21/1.22 [730]~P53(x7302)+~P3(f4(x7301,x7302),x7303,x7302)+P3(f13(x7301,x7302),x7303,x7302) % 1.21/1.22 [744]~P3(x7441,x7443,a1)+~P3(x7443,x7442,a1)+P3(f30(x7441),x7442,a1) % 1.21/1.22 [745]~P33(x7453)+~P4(f24(x7451,x7453),f24(x7452,x7453),x7453)+P4(x7451,x7452,a1) % 1.21/1.22 [746]~P33(x7463)+~P3(f24(x7461,x7463),f24(x7462,x7463),x7463)+P3(x7461,x7462,a1) % 1.21/1.22 [753]~P30(x7533)+P4(x7531,x7532,x7533)+~P4(f13(x7532,x7533),f13(x7531,x7533),x7533) % 1.21/1.22 [754]~P30(x7543)+P3(x7541,x7542,x7543)+~P3(f13(x7542,x7543),f13(x7541,x7543),x7543) % 1.21/1.22 [814]E(x8141,x8142)+~E(f11(x8143,x8141,a1),f11(x8143,x8142,a1))+~P3(f2(a1),x8143,a1) % 1.21/1.22 [815]~P34(x8153)+P6(x8151,f31(x8151,x8152,x8153),x8153)+~P3(f2(a1),x8152,a1) % 1.21/1.22 [817]~P30(x8173)+~P4(x8171,x8172,x8173)+P4(f3(x8171,x8172,x8173),f2(x8173),x8173) % 1.21/1.22 [818]~P30(x8183)+~P3(x8181,x8182,x8183)+P3(f3(x8181,x8182,x8183),f2(x8183),x8183) % 1.21/1.22 [820]~P33(x8201)+~P4(f2(x8201),x8202,x8201)+P4(f2(x8201),f31(x8202,x8203,x8201),x8201) % 1.21/1.22 [821]~P33(x8211)+~P4(f10(x8211),x8212,x8211)+P4(f10(x8211),f31(x8212,x8213,x8211),x8211) % 1.21/1.22 [823]~P33(x8231)+~P3(f2(x8231),x8232,x8231)+P3(f2(x8231),f31(x8232,x8233,x8231),x8231) % 1.21/1.22 [858]~P25(x8583)+~P4(x8581,f13(x8582,x8583),x8583)+P4(f9(x8581,x8582,x8583),f2(x8583),x8583) % 1.21/1.22 [888]~P30(x8883)+P4(x8881,x8882,x8883)+~P4(f3(x8881,x8882,x8883),f2(x8883),x8883) % 1.21/1.22 [889]~P30(x8893)+P3(x8891,x8892,x8893)+~P3(f3(x8891,x8892,x8893),f2(x8893),x8893) % 1.21/1.22 [897]~P4(x8971,x8972,a1)+P3(x8971,f9(x8972,x8973,a1),a1)+~P3(f2(a1),x8973,a1) % 1.21/1.22 [962]~P25(x9623)+~P4(f9(x9621,x9622,x9623),f2(x9623),x9623)+P4(x9621,f13(x9622,x9623),x9623) % 1.21/1.22 [1093]~P4(x10932,x10931,a1)+~P3(x10931,x10933,a1)+P3(f3(x10931,x10932,a1),f3(x10933,x10932,a1),a1) % 1.21/1.22 [1094]~P3(x10943,x10942,a1)+~P3(x10943,x10941,a1)+P3(f3(x10941,x10942,a1),f3(x10941,x10943,a1),a1) % 1.21/1.22 [1098]~P3(x10981,x10983,a1)+P3(f11(x10981,x10982,a1),f11(x10983,x10982,a1),a1)+~P3(f2(a1),x10982,a1) % 1.21/1.22 [1101]~P3(x11012,x11013,a1)+P3(f11(x11011,x11012,a1),f11(x11011,x11013,a1),a1)+~P3(f2(a1),x11011,a1) % 1.21/1.22 [1182]~P4(x11823,x11822,a1)+~P4(f9(x11821,x11823,a1),x11822,a1)+P4(x11821,f3(x11822,x11823,a1),a1) % 1.21/1.22 [1183]~P4(x11832,x11833,a1)+~P4(x11831,f3(x11833,x11832,a1),a1)+P4(f9(x11831,x11832,a1),x11833,a1) % 1.21/1.22 [1247]P4(x12471,x12472,a1)+~P4(f11(x12473,x12471,a1),f11(x12473,x12472,a1),a1)+~P3(f2(a1),x12473,a1) % 1.21/1.22 [1248]P4(x12481,x12482,a1)+~P4(f11(x12481,x12483,a1),f11(x12482,x12483,a1),a1)+~P3(f2(a1),x12483,a1) % 1.21/1.22 [511]E(x5111,x5112)+P3(x5112,x5111,a1)+E(f22(f15(x5111),x5113,x5112),f15(x5111)) % 1.21/1.22 [609]~P47(x6092)+E(x6091,f2(x6092))+E(f8(f13(x6093,x6092),f13(x6091,x6092),x6092),f8(x6093,x6091,x6092)) % 1.21/1.22 [617]~P1(x6172)+E(x6171,f2(x6172))+E(f6(f11(x6173,x6171,x6172),x6171,x6172),x6173) % 1.21/1.22 [618]~P1(x6182)+E(x6181,f2(x6182))+E(f6(f11(x6181,x6183,x6182),x6181,x6182),x6183) % 1.21/1.22 [619]~P47(x6192)+E(x6191,f2(x6192))+E(f8(f11(x6193,x6191,x6192),x6191,x6192),x6193) % 1.21/1.22 [620]~P43(x6202)+~P47(x6202)+E(f8(f13(x6201,x6202),f13(x6203,x6202),x6202),f8(x6201,x6203,x6202)) % 1.21/1.22 [664]~P43(x6643)+~P47(x6643)+E(f7(f8(x6641,x6642,x6643),x6643),f8(x6642,x6641,x6643)) % 1.21/1.22 [719]~P47(x7192)+E(x7191,f2(x7192))+E(f8(x7193,f13(x7191,x7192),x7192),f13(f8(x7193,x7191,x7192),x7192)) % 1.21/1.22 [720]~P44(x7202)+E(x7201,f2(x7202))+E(f31(f7(x7201,x7202),x7203,x7202),f7(f31(x7201,x7203,x7202),x7202)) % 1.21/1.22 [731]~P43(x7313)+~P47(x7313)+E(f8(x7311,f13(x7312,x7313),x7313),f13(f8(x7311,x7312,x7313),x7313)) % 1.21/1.22 [732]~P43(x7322)+~P44(x7322)+E(f31(f7(x7321,x7322),x7323,x7322),f7(f31(x7321,x7323,x7322),x7322)) % 1.21/1.22 [770]~P54(x7702)+E(x7701,f2(x7702))+E(f8(f4(x7703,x7702),f4(x7701,x7702),x7702),f4(f8(x7703,x7701,x7702),x7702)) % 1.21/1.22 [780]~P54(x7802)+~P43(x7802)+E(f8(f4(x7801,x7802),f4(x7803,x7802),x7802),f4(f8(x7801,x7803,x7802),x7802)) % 1.21/1.22 [781]~P43(x7812)+~P47(x7812)+E(f11(f7(x7811,x7812),f7(x7813,x7812),x7812),f7(f11(x7811,x7813,x7812),x7812)) % 1.21/1.22 [812]~P1(x8123)+~P6(x8121,x8122,x8123)+E(f11(x8121,f6(x8122,x8121,x8123),x8123),x8122) % 1.21/1.22 [813]~P1(x8133)+~P6(x8132,x8131,x8133)+E(f11(f6(x8131,x8132,x8133),x8132,x8133),x8131) % 1.21/1.22 [832]~P33(x8321)+~P3(f10(x8321),x8322,x8321)+P3(f10(x8321),f31(x8322,f30(x8323),x8321),x8321) % 1.21/1.22 [839]~P7(x8393)+~P6(x8392,x8391,x8393)+E(f6(x8391,f13(x8392,x8393),x8393),f13(f6(x8391,x8392,x8393),x8393)) % 1.21/1.22 [840]~P7(x8402)+~P6(x8403,x8401,x8402)+E(f6(f13(x8401,x8402),x8403,x8402),f13(f6(x8401,x8403,x8402),x8402)) % 1.21/1.22 [861]~P53(x8612)+~P4(f2(x8612),x8613,x8612)+E(f11(f4(x8611,x8612),x8613,x8612),f4(f11(x8611,x8613,x8612),x8612)) % 1.21/1.22 [867]~P67(x8672)+~P4(x8673,x8671,a1)+E(f3(f24(x8671,x8672),f24(x8673,x8672),x8672),f24(f3(x8671,x8673,a1),x8672)) % 1.21/1.22 [933]~P1(x9332)+E(x9331,f2(x9332))+E(f6(f9(x9333,x9331,x9332),x9331,x9332),f9(f6(x9333,x9331,x9332),f10(x9332),x9332)) % 1.21/1.22 [934]~P1(x9342)+E(x9341,f2(x9342))+E(f6(f9(x9341,x9343,x9342),x9341,x9342),f9(f6(x9343,x9341,x9342),f10(x9342),x9342)) % 1.21/1.22 [1124]~P55(x11242)+E(x11241,f2(x11242))+~E(f9(f11(x11243,x11243,x11242),f11(x11241,x11241,x11242),x11242),f2(x11242)) % 1.21/1.22 [1125]~P55(x11252)+E(x11251,f2(x11252))+~E(f9(f11(x11251,x11251,x11252),f11(x11253,x11253,x11252),x11252),f2(x11252)) % 1.21/1.22 [1176]~P4(x11762,x11763,a1)+~P4(x11762,x11761,a1)+E(f3(f3(x11761,x11762,a1),f3(x11763,x11762,a1),a1),f3(x11761,x11763,a1)) % 1.21/1.22 [1181]~P33(x11811)+~P3(f10(x11811),x11812,x11811)+P3(f10(x11811),f11(x11812,f31(x11812,x11813,x11811),x11811),x11811) % 1.21/1.22 [1270]~P33(x12703)+~P3(f10(x12703),x12701,x12703)+P3(f31(x12701,x12702,x12703),f11(x12701,f31(x12701,x12702,x12703),x12703),x12703) % 1.21/1.22 [1288]~P55(x12882)+E(x12881,f2(x12882))+P3(f2(x12882),f9(f11(x12883,x12883,x12882),f11(x12881,x12881,x12882),x12882),x12882) % 1.21/1.22 [1289]~P55(x12892)+E(x12891,f2(x12892))+P3(f2(x12892),f9(f11(x12891,x12891,x12892),f11(x12893,x12893,x12892),x12892),x12892) % 1.21/1.22 [1343]~P55(x13432)+E(x13431,f2(x13432))+~P4(f9(f11(x13433,x13433,x13432),f11(x13431,x13431,x13432),x13432),f2(x13432),x13432) % 1.21/1.22 [1344]~P55(x13442)+E(x13441,f2(x13442))+~P4(f9(f11(x13441,x13441,x13442),f11(x13443,x13443,x13442),x13442),f2(x13442),x13442) % 1.21/1.22 [963]~P43(x9631)+~P47(x9631)+E(f31(f8(f10(x9631),x9632,x9631),x9633,x9631),f8(f10(x9631),f31(x9632,x9633,x9631),x9631)) % 1.21/1.22 [1317]~P54(x13173)+~P3(x13171,x13172,x13173)+P3(x13171,f8(f9(x13171,x13172,x13173),f9(f10(x13173),f10(x13173),x13173),x13173),x13173) % 1.21/1.22 [1318]~P54(x13183)+~P3(x13181,x13182,x13183)+P3(f8(f9(x13181,x13182,x13183),f9(f10(x13183),f10(x13183),x13183),x13183),x13182,x13183) % 1.21/1.22 [634]~P17(x6344)+E(x6341,x6342)+~E(f9(x6343,x6341,x6344),f9(x6343,x6342,x6344)) % 1.21/1.22 [635]~P20(x6354)+E(x6351,x6352)+~E(f9(x6353,x6351,x6354),f9(x6353,x6352,x6354)) % 1.21/1.22 [636]~P16(x6364)+E(x6361,x6362)+~E(f3(x6363,x6363,x6364),f3(x6361,x6362,x6364)) % 1.21/1.22 [637]~P20(x6374)+E(x6371,x6372)+~E(f9(x6371,x6373,x6374),f9(x6372,x6373,x6374)) % 1.21/1.22 [638]~P16(x6383)+E(x6381,x6382)+~E(f3(x6381,x6382,x6383),f3(x6384,x6384,x6383)) % 1.21/1.22 [795]~P8(x7954)+~P4(x7951,x7953,x7954)+P4(x7951,f28(x7952,x7953,x7954),x7954) % 1.21/1.22 [797]~P8(x7974)+~P4(x7971,x7972,x7974)+P4(x7971,f28(x7972,x7973,x7974),x7974) % 1.21/1.22 [798]~P34(x7984)+~P6(x7981,x7983,x7984)+P6(x7981,f11(x7982,x7983,x7984),x7984) % 1.21/1.22 [799]~P34(x7994)+~P6(x7991,x7992,x7994)+P6(x7991,f11(x7992,x7993,x7994),x7994) % 1.21/1.22 [801]~P8(x8014)+~P3(x8011,x8013,x8014)+P3(x8011,f28(x8012,x8013,x8014),x8014) % 1.21/1.22 [803]~P8(x8034)+~P3(x8031,x8032,x8034)+P3(x8031,f28(x8032,x8033,x8034),x8034) % 1.21/1.22 [805]~P8(x8053)+~P4(x8052,x8054,x8053)+P4(f29(x8051,x8052,x8053),x8054,x8053) % 1.21/1.22 [807]~P8(x8073)+~P4(x8071,x8074,x8073)+P4(f29(x8071,x8072,x8073),x8074,x8073) % 1.21/1.22 [809]~P8(x8093)+~P3(x8092,x8094,x8093)+P3(f29(x8091,x8092,x8093),x8094,x8093) % 1.21/1.22 [811]~P8(x8113)+~P3(x8111,x8114,x8113)+P3(f29(x8111,x8112,x8113),x8114,x8113) % 1.21/1.22 [860]~P3(x8604,x8603,a1)+P3(x8601,x8602,a1)+~E(f9(x8601,x8603,a1),f9(x8604,x8602,a1)) % 1.21/1.22 [869]~P8(x8693)+P4(x8691,x8692,x8693)+~P4(x8691,f29(x8694,x8692,x8693),x8693) % 1.21/1.22 [871]~P8(x8713)+P4(x8711,x8712,x8713)+~P4(x8711,f29(x8712,x8714,x8713),x8713) % 1.21/1.22 [872]~P8(x8723)+P3(x8721,x8722,x8723)+~P3(x8721,f29(x8724,x8722,x8723),x8723) % 1.21/1.22 [873]~P8(x8733)+P3(x8731,x8732,x8733)+~P3(x8731,f29(x8732,x8734,x8733),x8733) % 1.21/1.22 [875]~P8(x8753)+P4(x8751,x8752,x8753)+~P4(f28(x8754,x8751,x8753),x8752,x8753) % 1.21/1.22 [877]~P8(x8773)+P4(x8771,x8772,x8773)+~P4(f28(x8771,x8774,x8773),x8772,x8773) % 1.21/1.22 [878]~P34(x8783)+P6(x8781,x8782,x8783)+~P6(f11(x8784,x8781,x8783),x8782,x8783) % 1.21/1.22 [879]~P34(x8793)+P6(x8791,x8792,x8793)+~P6(f11(x8791,x8794,x8793),x8792,x8793) % 1.21/1.22 [880]~P8(x8803)+P3(x8801,x8802,x8803)+~P3(f28(x8804,x8801,x8803),x8802,x8803) % 1.21/1.22 [881]~P8(x8813)+P3(x8811,x8812,x8813)+~P3(f28(x8811,x8814,x8813),x8812,x8813) % 1.21/1.22 [972]~P34(x9723)+~P4(x9722,x9724,a1)+P6(f31(x9721,x9722,x9723),f31(x9721,x9724,x9723),x9723) % 1.21/1.22 [974]~P10(x9743)+~P4(x9741,x9744,x9743)+P4(f9(x9741,x9742,x9743),f9(x9744,x9742,x9743),x9743) % 1.21/1.22 [975]~P27(x9753)+~P4(x9751,x9754,x9753)+P4(f9(x9751,x9752,x9753),f9(x9754,x9752,x9753),x9753) % 1.21/1.22 [976]~P10(x9763)+~P4(x9762,x9764,x9763)+P4(f9(x9761,x9762,x9763),f9(x9761,x9764,x9763),x9763) % 1.21/1.22 [977]~P27(x9773)+~P4(x9772,x9774,x9773)+P4(f9(x9771,x9772,x9773),f9(x9771,x9774,x9773),x9773) % 1.21/1.22 [978]~P48(x9783)+~P6(x9781,x9784,x9783)+P6(f11(x9781,x9782,x9783),f11(x9784,x9782,x9783),x9783) % 1.21/1.22 [979]~P48(x9793)+~P6(x9792,x9794,x9793)+P6(f11(x9791,x9792,x9793),f11(x9791,x9794,x9793),x9793) % 1.21/1.22 [980]~P34(x9803)+~P6(x9801,x9804,x9803)+P6(f31(x9801,x9802,x9803),f31(x9804,x9802,x9803),x9803) % 1.21/1.22 [981]~P10(x9813)+~P3(x9811,x9814,x9813)+P3(f9(x9811,x9812,x9813),f9(x9814,x9812,x9813),x9813) % 1.21/1.22 [982]~P32(x9823)+~P3(x9821,x9824,x9823)+P3(f9(x9821,x9822,x9823),f9(x9824,x9822,x9823),x9823) % 1.21/1.22 [983]~P10(x9833)+~P3(x9832,x9834,x9833)+P3(f9(x9831,x9832,x9833),f9(x9831,x9834,x9833),x9833) % 1.21/1.22 [984]~P32(x9843)+~P3(x9842,x9844,x9843)+P3(f9(x9841,x9842,x9843),f9(x9841,x9844,x9843),x9843) % 1.21/1.22 [1090]~P4(x10902,x10904,a1)+~P4(x10901,x10903,a1)+P4(f9(x10901,x10902,a1),f9(x10903,x10904,a1),a1) % 1.21/1.22 [1091]~P4(x10912,x10914,a1)+~P4(x10911,x10913,a1)+P4(f11(x10911,x10912,a1),f11(x10913,x10914,a1),a1) % 1.21/1.22 [1092]~P3(x10922,x10924,a1)+~P3(x10921,x10923,a1)+P3(f9(x10921,x10922,a1),f9(x10923,x10924,a1),a1) % 1.21/1.22 [1177]~P10(x11773)+P4(x11771,x11772,x11773)+~P4(f9(x11774,x11771,x11773),f9(x11774,x11772,x11773),x11773) % 1.21/1.22 [1178]~P10(x11783)+P4(x11781,x11782,x11783)+~P4(f9(x11781,x11784,x11783),f9(x11782,x11784,x11783),x11783) % 1.21/1.22 [1179]~P10(x11793)+P3(x11791,x11792,x11793)+~P3(f9(x11794,x11791,x11793),f9(x11794,x11792,x11793),x11793) % 1.21/1.22 [1180]~P10(x11803)+P3(x11801,x11802,x11803)+~P3(f9(x11801,x11804,x11803),f9(x11802,x11804,x11803),x11803) % 1.21/1.22 [831]~P16(x8313)+E(x8311,f13(x8312,x8313))+~E(f9(x8311,f9(x8314,x8312,x8313),x8313),x8314) % 1.21/1.22 [865]~P1(x8653)+~P6(x8654,x8652,x8653)+E(f5(f5(x8651,x8652,x8653),x8654,x8653),f5(x8651,x8654,x8653)) % 1.21/1.22 [926]~P1(x9262)+E(x9261,f2(x9262))+E(f6(f11(x9263,x9261,x9262),f11(x9264,x9261,x9262),x9262),f6(x9263,x9264,x9262)) % 1.21/1.22 [927]~P1(x9272)+E(x9271,f2(x9272))+E(f6(f11(x9271,x9273,x9272),f11(x9271,x9274,x9272),x9272),f6(x9273,x9274,x9272)) % 1.21/1.22 [929]~P43(x9293)+~P47(x9293)+E(f8(f11(x9291,x9292,x9293),x9294,x9293),f11(f8(x9291,x9294,x9293),x9292,x9293)) % 1.21/1.22 [932]~P7(x9322)+~E(f5(x9321,x9323,x9322),f5(x9324,x9323,x9322))+E(f5(f13(x9321,x9322),x9323,x9322),f5(f13(x9324,x9322),x9323,x9322)) % 1.21/1.22 [1083]~P1(x10833)+~P6(x10834,x10831,x10833)+E(f6(f11(x10831,x10832,x10833),x10834,x10833),f11(f6(x10831,x10834,x10833),x10832,x10833)) % 1.21/1.22 [1126]~P47(x11262)+E(x11261,f2(x11262))+E(f8(f31(x11263,x11264,x11262),f31(x11261,x11264,x11262),x11262),f31(f8(x11263,x11261,x11262),x11264,x11262)) % 1.21/1.22 [1127]~P43(x11273)+~P47(x11273)+E(f8(f31(x11271,x11272,x11273),f31(x11274,x11272,x11273),x11273),f31(f8(x11271,x11274,x11273),x11272,x11273)) % 1.21/1.22 [1175]~P26(x11754)+~P4(f9(x11751,x11753,x11754),x11752,x11754)+P4(x11751,f9(x11752,f4(x11753,x11754),x11754),x11754) % 1.21/1.22 [1190]E(x11901,x11902)+E(x11903,f2(a1))+~E(f9(x11904,f11(x11903,x11901,a1),a1),f9(x11904,f11(x11903,x11902,a1),a1)) % 1.21/1.22 [1208]~P1(x12083)+~P6(x12084,x12081,x12083)+E(f6(f31(x12081,x12082,x12083),f31(x12084,x12082,x12083),x12083),f31(f6(x12081,x12084,x12083),x12082,x12083)) % 1.21/1.22 [1240]~P48(x12403)+~P14(x12403)+E(f9(f11(x12401,x12402,x12403),f11(x12401,x12404,x12403),x12403),f9(f11(x12401,x12404,x12403),f11(x12401,x12402,x12403),x12403)) % 1.21/1.22 [1332]E(x13321,x13322)+E(x13323,x13324)+~E(f9(f11(x13323,x13321,a1),f11(x13324,x13322,a1),a1),f9(f11(x13323,x13322,a1),f11(x13324,x13321,a1),a1)) % 1.21/1.22 [1237]~P1(x12372)+E(x12371,f2(x12372))+E(f6(f9(x12373,f11(x12374,x12371,x12372),x12372),x12371,x12372),f9(x12374,f6(x12373,x12371,x12372),x12372)) % 1.21/1.22 [1238]~P1(x12382)+E(x12381,f2(x12382))+E(f6(f9(x12383,f11(x12381,x12384,x12382),x12382),x12381,x12382),f9(x12384,f6(x12383,x12381,x12382),x12382)) % 1.21/1.22 [624]E(x6241,x6242)+~E(f23(x6243,x6241,x6244),f23(x6245,x6242,x6244))+E(x6243,f2(a1)) % 1.21/1.22 [1075]~P16(x10753)+E(f9(x10751,x10752,x10753),x10754)+~E(f9(x10751,f9(x10755,x10752,x10753),x10753),f9(x10755,x10754,x10753)) % 1.21/1.22 [1241]~P43(x12413)+~P47(x12413)+E(f8(f11(x12411,x12412,x12413),f11(x12414,x12415,x12413),x12413),f11(f8(x12411,x12414,x12413),f8(x12412,x12415,x12413),x12413)) % 1.21/1.22 [1340]~P4(x13403,x13402,a1)+~E(f9(f11(x13403,x13404,a1),x13401,a1),f9(f11(x13402,x13404,a1),x13405,a1))+E(x13401,f9(f11(f3(x13402,x13403,a1),x13404,a1),x13405,a1)) % 1.21/1.22 [1341]~P4(x13412,x13411,a1)+~E(f9(f11(x13411,x13413,a1),x13414,a1),f9(f11(x13412,x13413,a1),x13415,a1))+E(f9(f11(f3(x13411,x13412,a1),x13413,a1),x13414,a1),x13415) % 1.21/1.22 [1362]~P4(x13623,x13622,a1)+~P4(f9(f11(x13623,x13624,a1),x13621,a1),f9(f11(x13622,x13624,a1),x13625,a1),a1)+P4(x13621,f9(f11(f3(x13622,x13623,a1),x13624,a1),x13625,a1),a1) % 1.21/1.22 [1363]~P4(x13633,x13632,a1)+~P3(f9(f11(x13633,x13634,a1),x13631,a1),f9(f11(x13632,x13634,a1),x13635,a1),a1)+P3(x13631,f9(f11(f3(x13632,x13633,a1),x13634,a1),x13635,a1),a1) % 1.21/1.22 [1364]~P4(x13642,x13641,a1)+~P4(f9(f11(x13641,x13643,a1),x13644,a1),f9(f11(x13642,x13643,a1),x13645,a1),a1)+P4(f9(f11(f3(x13641,x13642,a1),x13643,a1),x13644,a1),x13645,a1) % 1.21/1.22 [1365]~P4(x13652,x13651,a1)+~P3(f9(f11(x13651,x13653,a1),x13654,a1),f9(f11(x13652,x13653,a1),x13655,a1),a1)+P3(f9(f11(f3(x13651,x13652,a1),x13653,a1),x13654,a1),x13655,a1) % 1.21/1.22 [1370]~P4(x13701,x13704,a1)+P4(f9(f11(x13701,x13702,a1),x13703,a1),f9(f11(x13704,x13702,a1),x13705,a1),a1)+~P4(x13703,f9(f11(f3(x13704,x13701,a1),x13702,a1),x13705,a1),a1) % 1.21/1.22 [1371]~P4(x13711,x13714,a1)+P3(f9(f11(x13711,x13712,a1),x13713,a1),f9(f11(x13714,x13712,a1),x13715,a1),a1)+~P3(x13713,f9(f11(f3(x13714,x13711,a1),x13712,a1),x13715,a1),a1) % 1.21/1.22 [1372]~P4(x13724,x13721,a1)+P4(f9(f11(x13721,x13722,a1),x13723,a1),f9(f11(x13724,x13722,a1),x13725,a1),a1)+~P4(f9(f11(f3(x13721,x13724,a1),x13722,a1),x13723,a1),x13725,a1) % 1.21/1.22 [1373]~P4(x13734,x13731,a1)+P3(f9(f11(x13731,x13732,a1),x13733,a1),f9(f11(x13734,x13732,a1),x13735,a1),a1)+~P3(f9(f11(f3(x13731,x13734,a1),x13732,a1),x13733,a1),x13735,a1) % 1.21/1.22 [1336]~P66(x13364)+~E(f9(f11(x13363,x13365,x13364),x13361,x13364),f9(f11(x13362,x13365,x13364),x13366,x13364))+E(x13361,f9(f11(f3(x13362,x13363,x13364),x13365,x13364),x13366,x13364)) % 1.21/1.22 [1337]~P66(x13373)+~E(f9(f11(x13371,x13374,x13373),x13375,x13373),f9(f11(x13372,x13374,x13373),x13376,x13373))+E(f9(f11(f3(x13371,x13372,x13373),x13374,x13373),x13375,x13373),x13376) % 1.21/1.22 [1358]~P62(x13584)+~P4(f9(f11(x13583,x13585,x13584),x13581,x13584),f9(f11(x13582,x13585,x13584),x13586,x13584),x13584)+P4(x13581,f9(f11(f3(x13582,x13583,x13584),x13585,x13584),x13586,x13584),x13584) % 1.21/1.22 [1359]~P62(x13594)+~P3(f9(f11(x13593,x13595,x13594),x13591,x13594),f9(f11(x13592,x13595,x13594),x13596,x13594),x13594)+P3(x13591,f9(f11(f3(x13592,x13593,x13594),x13595,x13594),x13596,x13594),x13594) % 1.21/1.22 [1360]~P62(x13603)+~P4(f9(f11(x13601,x13604,x13603),x13605,x13603),f9(f11(x13602,x13604,x13603),x13606,x13603),x13603)+P4(f9(f11(f3(x13601,x13602,x13603),x13604,x13603),x13605,x13603),x13606,x13603) % 1.21/1.22 [1361]~P62(x13613)+~P3(f9(f11(x13611,x13614,x13613),x13615,x13613),f9(f11(x13612,x13614,x13613),x13616,x13613),x13613)+P3(f9(f11(f3(x13611,x13612,x13613),x13614,x13613),x13615,x13613),x13616,x13613) % 1.21/1.22 [1366]~P62(x13663)+P4(f9(f11(x13661,x13662,x13663),x13664,x13663),f9(f11(x13665,x13662,x13663),x13666,x13663),x13663)+~P4(x13664,f9(f11(f3(x13665,x13661,x13663),x13662,x13663),x13666,x13663),x13663) % 1.21/1.22 [1367]~P62(x13673)+P3(f9(f11(x13671,x13672,x13673),x13674,x13673),f9(f11(x13675,x13672,x13673),x13676,x13673),x13673)+~P3(x13674,f9(f11(f3(x13675,x13671,x13673),x13672,x13673),x13676,x13673),x13673) % 1.21/1.22 [1368]~P62(x13683)+P4(f9(f11(x13681,x13682,x13683),x13684,x13683),f9(f11(x13685,x13682,x13683),x13686,x13683),x13683)+~P4(f9(f11(f3(x13681,x13685,x13683),x13682,x13683),x13684,x13683),x13686,x13683) % 1.21/1.22 [1369]~P62(x13693)+P3(f9(f11(x13691,x13692,x13693),x13694,x13693),f9(f11(x13695,x13692,x13693),x13696,x13693),x13693)+~P3(f9(f11(f3(x13691,x13695,x13693),x13692,x13693),x13694,x13693),x13696,x13693) % 1.21/1.22 [333]~P43(x3332)+~P47(x3332)+~E(f7(x3331,x3332),f10(x3332))+E(x3331,f10(x3332)) % 1.21/1.22 [420]~P8(x4202)+~P26(x4202)+P3(x4201,f2(x4202),x4202)+E(f4(x4201,x4202),x4201) % 1.21/1.22 [517]~P70(x5172)+~P3(f2(x5172),x5171,x5172)+E(f12(x5171,x5172),f10(x5172))+E(x5171,f2(x5172)) % 1.21/1.22 [525]~P8(x5252)+~P26(x5252)+~P3(x5251,f2(x5252),x5252)+E(f4(x5251,x5252),f13(x5251,x5252)) % 1.21/1.22 [683]~P54(x6831)+~P43(x6831)+~P4(f2(x6831),x6832,x6831)+P4(f2(x6831),f7(x6832,x6831),x6831) % 1.21/1.22 [685]~P54(x6852)+~P43(x6852)+~P4(x6851,f2(x6852),x6852)+P4(f7(x6851,x6852),f2(x6852),x6852) % 1.21/1.22 [686]~P54(x6862)+~P43(x6862)+~P4(x6861,f2(x6862),x6862)+P4(f7(x6861,x6862),f10(x6862),x6862) % 1.21/1.22 [688]~P54(x6882)+~P43(x6882)+~P4(x6881,f2(x6882),x6882)+P3(f7(x6881,x6882),f10(x6882),x6882) % 1.21/1.22 [689]~P54(x6892)+~P43(x6892)+~P4(f10(x6892),x6891,x6892)+P4(f7(x6891,x6892),f10(x6892),x6892) % 1.21/1.22 [690]~P54(x6902)+~P43(x6902)+~P3(f10(x6902),x6901,x6902)+P3(f7(x6901,x6902),f10(x6902),x6902) % 1.21/1.22 [708]~P54(x7082)+~P3(f7(x7081,x7082),f2(x7082),x7082)+P3(x7081,f2(x7082),x7082)+E(x7081,f2(x7082)) % 1.21/1.22 [709]~P54(x7092)+~P3(f2(x7092),f7(x7091,x7092),x7092)+P3(f2(x7092),x7091,x7092)+E(x7091,f2(x7092)) % 1.21/1.22 [711]~P54(x7112)+~P43(x7112)+~P4(f10(x7112),f7(x7111,x7112),x7112)+P4(x7111,f10(x7112),x7112) % 1.21/1.22 [712]~P54(x7122)+~P43(x7122)+~P3(f10(x7122),f7(x7121,x7122),x7122)+P3(x7121,f10(x7122),x7122) % 1.21/1.22 [713]~P54(x7132)+~P43(x7132)+~P4(f7(x7131,x7132),f2(x7132),x7132)+P4(x7131,f2(x7132),x7132) % 1.21/1.22 [714]~P54(x7142)+~P43(x7142)+~P3(f7(x7141,x7142),f2(x7142),x7142)+P3(x7141,f2(x7142),x7142) % 1.21/1.22 [715]~P54(x7151)+~P43(x7151)+~P4(f2(x7151),f7(x7152,x7151),x7151)+P4(f2(x7151),x7152,x7151) % 1.21/1.22 [716]~P54(x7161)+~P43(x7161)+~P4(f10(x7161),f7(x7162,x7161),x7161)+P3(f2(x7161),x7162,x7161) % 1.21/1.22 [717]~P54(x7171)+~P43(x7171)+~P3(f2(x7171),f7(x7172,x7171),x7171)+P3(f2(x7171),x7172,x7171) % 1.21/1.22 [718]~P54(x7181)+~P43(x7181)+~P3(f10(x7181),f7(x7182,x7181),x7181)+P3(f2(x7181),x7182,x7181) % 1.21/1.22 [408]~P58(x4082)+~P35(x4082)+E(x4081,f2(a1))+E(f31(f2(x4082),x4081,x4082),f2(x4082)) % 1.21/1.22 [467]~P70(x4672)+P3(f2(x4672),x4671,x4672)+E(x4671,f2(x4672))+E(f12(x4671,x4672),f13(f10(x4672),x4672)) % 1.21/1.22 [833]~P54(x8331)+~P43(x8331)+~P4(f2(x8331),x8332,x8331)+P4(f2(x8331),f8(f10(x8331),x8332,x8331),x8331) % 1.21/1.22 [834]~P54(x8341)+~P43(x8341)+~P3(f2(x8341),x8342,x8341)+P3(f2(x8341),f8(f10(x8341),x8342,x8341),x8341) % 1.21/1.22 [835]~P54(x8351)+~P43(x8351)+~P4(x8352,f2(x8351),x8351)+P4(f8(f10(x8351),x8352,x8351),f2(x8351),x8351) % 1.21/1.22 [836]~P54(x8361)+~P43(x8361)+~P3(x8362,f2(x8361),x8361)+P3(f8(f10(x8361),x8362,x8361),f2(x8361),x8361) % 1.21/1.22 [964]~P54(x9642)+~P43(x9642)+P4(x9641,f2(x9642),x9642)+~P4(f8(f10(x9642),x9641,x9642),f2(x9642),x9642) % 1.21/1.22 [965]~P54(x9652)+~P43(x9652)+P3(x9651,f2(x9652),x9652)+~P3(f8(f10(x9652),x9651,x9652),f2(x9652),x9652) % 1.21/1.22 [966]~P54(x9661)+~P43(x9661)+P4(f2(x9661),x9662,x9661)+~P4(f2(x9661),f8(f10(x9661),x9662,x9661),x9661) % 1.21/1.22 [967]~P54(x9671)+~P43(x9671)+P3(f2(x9671),x9672,x9671)+~P3(f2(x9671),f8(f10(x9671),x9672,x9671),x9671) % 1.21/1.22 [509]P3(x5091,x5092,x5093)+~P8(x5093)+E(x5091,x5092)+P3(x5092,x5091,x5093) % 1.21/1.22 [510]P3(x5101,x5102,x5103)+~P53(x5103)+E(x5101,x5102)+P3(x5102,x5101,x5103) % 1.21/1.22 [571]~P8(x5713)+~P4(x5711,x5712,x5713)+E(x5711,x5712)+P3(x5711,x5712,x5713) % 1.21/1.22 [577]~P37(x5773)+~P4(x5771,x5772,x5773)+E(x5771,x5772)+P3(x5771,x5772,x5773) % 1.21/1.22 [642]~P4(x6422,x6421,x6423)+~P4(x6421,x6422,x6423)+E(x6421,x6422)+~P37(x6423) % 1.21/1.22 [697]P3(x6972,x6971,x6973)+~P36(x6973)+~P4(x6972,x6971,x6973)+P4(x6971,x6972,x6973) % 1.21/1.22 [342]~P43(x3423)+~P44(x3423)+E(x3421,x3422)+~E(f7(x3421,x3423),f7(x3422,x3423)) % 1.21/1.22 [465]~P47(x4653)+E(x4651,x4652)+~E(f8(x4651,x4652,x4653),f10(x4653))+E(x4652,f2(x4653)) % 1.21/1.22 [466]~P48(x4662)+~P14(x4662)+~E(f9(x4663,x4661,x4662),x4663)+E(x4661,f2(x4662)) % 1.21/1.22 [470]~P48(x4703)+~P14(x4703)+E(x4701,x4702)+~E(f3(x4701,x4702,x4703),f2(x4703)) % 1.21/1.22 [474]~P51(x4742)+~E(f11(x4743,x4741,x4742),f2(x4742))+E(x4741,f2(x4742))+E(x4743,f2(x4742)) % 1.21/1.22 [475]~P64(x4752)+~E(f11(x4753,x4751,x4752),f2(x4752))+E(x4751,f2(x4752))+E(x4753,f2(x4752)) % 1.21/1.22 [682]~P48(x6823)+E(x6821,x6822)+~E(f11(x6821,x6821,x6823),f11(x6822,x6822,x6823))+E(x6821,f13(x6822,x6823)) % 1.21/1.22 [841]~P54(x8412)+~P4(x8413,x8411,x8412)+~P3(x8411,f2(x8412),x8412)+P4(f7(x8411,x8412),f7(x8413,x8412),x8412) % 1.21/1.22 [842]~P54(x8422)+~P3(x8423,x8421,x8422)+~P3(x8421,f2(x8422),x8422)+P3(f7(x8421,x8422),f7(x8423,x8422),x8422) % 1.21/1.22 [843]~P54(x8432)+~P4(x8433,x8431,x8432)+~P3(f2(x8432),x8433,x8432)+P4(f7(x8431,x8432),f7(x8433,x8432),x8432) % 1.21/1.22 [844]~P54(x8442)+~P3(x8443,x8441,x8442)+~P3(f2(x8442),x8443,x8442)+P3(f7(x8441,x8442),f7(x8443,x8442),x8442) % 1.21/1.22 [856]~P28(x8562)+~P4(x8561,x8563,x8562)+~P4(f13(x8561,x8562),x8563,x8562)+P4(f4(x8561,x8562),x8563,x8562) % 1.21/1.22 [857]~P53(x8572)+~P3(x8571,x8573,x8572)+~P3(f13(x8571,x8572),x8573,x8572)+P3(f4(x8571,x8572),x8573,x8572) % 1.21/1.22 [890]~P54(x8903)+P4(x8901,x8902,x8903)+~P3(x8901,f2(x8903),x8903)+~P4(f7(x8902,x8903),f7(x8901,x8903),x8903) % 1.21/1.22 [891]~P54(x8913)+P3(x8911,x8912,x8913)+~P3(x8911,f2(x8913),x8913)+~P3(f7(x8912,x8913),f7(x8911,x8913),x8913) % 1.21/1.22 [892]~P54(x8923)+P4(x8921,x8922,x8923)+~P3(f2(x8923),x8922,x8923)+~P4(f7(x8922,x8923),f7(x8921,x8923),x8923) % 1.21/1.22 [893]~P54(x8933)+P3(x8931,x8932,x8933)+~P3(f2(x8933),x8932,x8933)+~P3(f7(x8932,x8933),f7(x8931,x8933),x8933) % 1.21/1.22 [928]E(x9281,x9282)+~P4(x9283,x9282,a1)+~P4(x9283,x9281,a1)+~E(f3(x9281,x9283,a1),f3(x9282,x9283,a1)) % 1.21/1.22 [973]~P33(x9731)+~P3(f10(x9731),x9732,x9731)+P3(f10(x9731),f31(x9732,x9733,x9731),x9731)+~P3(f2(a1),x9733,a1) % 1.21/1.22 [989]~P62(x9891)+~P4(x9893,f2(x9891),x9891)+~P4(x9892,f2(x9891),x9891)+P4(f2(x9891),f11(x9892,x9893,x9891),x9891) % 1.21/1.22 [990]~P55(x9901)+~P4(x9903,f2(x9901),x9901)+~P4(x9902,f2(x9901),x9901)+P4(f2(x9901),f11(x9902,x9903,x9901),x9901) % 1.21/1.22 [991]~P54(x9911)+~P4(x9912,f2(x9911),x9911)+~P3(x9913,f2(x9911),x9911)+P4(f2(x9911),f8(x9912,x9913,x9911),x9911) % 1.21/1.22 [992]~P55(x9921)+~P3(x9923,f2(x9921),x9921)+~P3(x9922,f2(x9921),x9921)+P3(f2(x9921),f11(x9922,x9923,x9921),x9921) % 1.21/1.22 [993]~P54(x9931)+~P3(x9933,f2(x9931),x9931)+~P3(x9932,f2(x9931),x9931)+P3(f2(x9931),f8(x9932,x9933,x9931),x9931) % 1.21/1.22 [994]~P31(x9941)+~P4(f2(x9941),x9943,x9941)+~P4(f2(x9941),x9942,x9941)+P4(f2(x9941),f9(x9942,x9943,x9941),x9941) % 1.21/1.22 [995]~P62(x9951)+~P4(f2(x9951),x9953,x9951)+~P4(f2(x9951),x9952,x9951)+P4(f2(x9951),f11(x9952,x9953,x9951),x9951) % 1.21/1.22 [996]~P55(x9961)+~P4(f2(x9961),x9963,x9961)+~P4(f2(x9961),x9962,x9961)+P4(f2(x9961),f11(x9962,x9963,x9961),x9961) % 1.21/1.22 [997]~P60(x9971)+~P4(f2(x9971),x9973,x9971)+~P4(f2(x9971),x9972,x9971)+P4(f2(x9971),f11(x9972,x9973,x9971),x9971) % 1.21/1.22 [998]~P54(x9981)+~P4(f2(x9981),x9982,x9981)+~P3(f2(x9981),x9983,x9981)+P4(f2(x9981),f8(x9982,x9983,x9981),x9981) % 1.21/1.22 [999]~P31(x9991)+~P4(f2(x9991),x9993,x9991)+~P3(f2(x9991),x9992,x9991)+P3(f2(x9991),f9(x9992,x9993,x9991),x9991) % 1.21/1.22 [1000]~P31(x10001)+~P4(f2(x10001),x10002,x10001)+~P3(f2(x10001),x10003,x10001)+P3(f2(x10001),f9(x10002,x10003,x10001),x10001) % 1.21/1.22 [1001]~P31(x10011)+~P3(f2(x10011),x10013,x10011)+~P3(f2(x10011),x10012,x10011)+P3(f2(x10011),f9(x10012,x10013,x10011),x10011) % 1.21/1.22 [1002]~P56(x10021)+~P3(f2(x10021),x10023,x10021)+~P3(f2(x10021),x10022,x10021)+P3(f2(x10021),f11(x10022,x10023,x10021),x10021) % 1.21/1.22 [1003]~P54(x10031)+~P3(f2(x10031),x10033,x10031)+~P3(f2(x10031),x10032,x10031)+P3(f2(x10031),f8(x10032,x10033,x10031),x10031) % 1.21/1.22 [1004]~P33(x10041)+~P3(f10(x10041),x10043,x10041)+~P3(f10(x10041),x10042,x10041)+P3(f10(x10041),f11(x10042,x10043,x10041),x10041) % 1.21/1.22 [1005]~P31(x10053)+~P4(x10052,f2(x10053),x10053)+~P4(x10051,f2(x10053),x10053)+P4(f9(x10051,x10052,x10053),f2(x10053),x10053) % 1.21/1.22 [1006]~P31(x10063)+~P4(x10062,f2(x10063),x10063)+~P3(x10061,f2(x10063),x10063)+P3(f9(x10061,x10062,x10063),f2(x10063),x10063) % 1.21/1.22 [1007]~P31(x10073)+~P4(x10071,f2(x10073),x10073)+~P3(x10072,f2(x10073),x10073)+P3(f9(x10071,x10072,x10073),f2(x10073),x10073) % 1.21/1.22 [1008]~P31(x10083)+~P3(x10082,f2(x10083),x10083)+~P3(x10081,f2(x10083),x10083)+P3(f9(x10081,x10082,x10083),f2(x10083),x10083) % 1.21/1.22 [1009]~P55(x10093)+~P4(x10092,f2(x10093),x10093)+~P4(f2(x10093),x10091,x10093)+P4(f11(x10091,x10092,x10093),f2(x10093),x10093) % 1.21/1.22 [1010]~P55(x10103)+~P4(x10101,f2(x10103),x10103)+~P4(f2(x10103),x10102,x10103)+P4(f11(x10101,x10102,x10103),f2(x10103),x10103) % 1.21/1.22 [1012]~P60(x10123)+~P4(x10122,f2(x10123),x10123)+~P4(f2(x10123),x10121,x10123)+P4(f11(x10121,x10122,x10123),f2(x10123),x10123) % 1.21/1.22 [1015]~P60(x10153)+~P4(x10151,f2(x10153),x10153)+~P4(f2(x10153),x10152,x10153)+P4(f11(x10151,x10152,x10153),f2(x10153),x10153) % 1.21/1.22 [1016]~P54(x10163)+~P4(x10161,f2(x10163),x10163)+~P3(f2(x10163),x10162,x10163)+P4(f8(x10161,x10162,x10163),f2(x10163),x10163) % 1.21/1.22 [1017]~P54(x10173)+~P3(x10172,f2(x10173),x10173)+~P4(f2(x10173),x10171,x10173)+P4(f8(x10171,x10172,x10173),f2(x10173),x10173) % 1.21/1.22 [1018]~P56(x10183)+~P3(x10182,f2(x10183),x10183)+~P3(f2(x10183),x10181,x10183)+P3(f11(x10181,x10182,x10183),f2(x10183),x10183) % 1.21/1.22 [1020]~P56(x10203)+~P3(x10201,f2(x10203),x10203)+~P3(f2(x10203),x10202,x10203)+P3(f11(x10201,x10202,x10203),f2(x10203),x10203) % 1.21/1.22 [1021]~P54(x10213)+~P3(x10212,f2(x10213),x10213)+~P3(f2(x10213),x10211,x10213)+P3(f8(x10211,x10212,x10213),f2(x10213),x10213) % 1.21/1.22 [1022]~P54(x10223)+~P3(x10221,f2(x10223),x10223)+~P3(f2(x10223),x10222,x10223)+P3(f8(x10221,x10222,x10223),f2(x10223),x10223) % 1.21/1.22 [1042]~P55(x10422)+~P4(f11(x10423,x10421,x10422),f2(x10422),x10422)+P4(x10421,f2(x10422),x10422)+P4(x10423,f2(x10422),x10422) % 1.21/1.22 [1043]~P55(x10432)+~P4(f2(x10432),f11(x10433,x10431,x10432),x10432)+P4(x10431,f2(x10432),x10432)+P4(f2(x10432),x10433,x10432) % 1.21/1.22 [1044]~P55(x10442)+~P4(f2(x10442),f11(x10441,x10443,x10442),x10442)+P4(x10441,f2(x10442),x10442)+P4(f2(x10442),x10443,x10442) % 1.21/1.22 [1045]~P55(x10452)+~P4(f2(x10452),f11(x10453,x10451,x10452),x10452)+P4(x10451,f2(x10452),x10452)+P4(f2(x10452),x10451,x10452) % 1.21/1.22 [1046]~P55(x10462)+~P4(f2(x10462),f11(x10461,x10463,x10462),x10462)+P4(x10461,f2(x10462),x10462)+P4(f2(x10462),x10461,x10462) % 1.21/1.22 [1047]~P55(x10472)+~P4(f11(x10473,x10471,x10472),f2(x10472),x10472)+P4(x10471,f2(x10472),x10472)+P4(f2(x10472),x10471,x10472) % 1.21/1.22 [1048]~P55(x10482)+~P4(f11(x10481,x10483,x10482),f2(x10482),x10482)+P4(x10481,f2(x10482),x10482)+P4(f2(x10482),x10481,x10482) % 1.21/1.22 [1049]~P55(x10491)+~P4(f11(x10492,x10493,x10491),f2(x10491),x10491)+P4(f2(x10491),x10492,x10491)+P4(f2(x10491),x10493,x10491) % 1.21/1.22 [1088]~P56(x10881)+~P3(f2(x10881),f11(x10883,x10882,x10881),x10881)+P3(f2(x10881),x10882,x10881)+~P3(f2(x10881),x10883,x10881) % 1.21/1.22 [1089]~P56(x10891)+~P3(f2(x10891),f11(x10892,x10893,x10891),x10891)+P3(f2(x10891),x10892,x10891)+~P3(f2(x10891),x10893,x10891) % 1.21/1.22 [1292]~P4(x12923,x12921,a1)+P4(x12921,x12922,a1)+~P4(x12923,x12922,a1)+~P4(f3(x12921,x12923,a1),f3(x12922,x12923,a1),a1) % 1.21/1.22 [1293]~P4(x12933,x12931,a1)+P3(x12931,x12932,a1)+~P4(x12933,x12932,a1)+~P3(f3(x12931,x12933,a1),f3(x12932,x12933,a1),a1) % 1.21/1.22 [645]~P43(x6452)+~P47(x6452)+E(x6451,f2(x6452))+E(f11(f8(x6453,x6451,x6452),x6451,x6452),x6453) % 1.21/1.22 [787]~P44(x7872)+E(x7871,f2(x7872))+E(x7873,f2(x7872))+E(f11(f7(x7871,x7872),f7(x7873,x7872),x7872),f7(f11(x7873,x7871,x7872),x7872)) % 1.21/1.22 [866]~P54(x8662)+~P43(x8662)+~P3(f2(x8662),x8663,x8662)+E(f8(f4(x8661,x8662),x8663,x8662),f4(f8(x8661,x8663,x8662),x8662)) % 1.21/1.22 [1039]~P33(x10393)+~P3(x10391,f10(x10393),x10393)+~P3(f2(x10393),x10391,x10393)+P3(f31(x10391,f30(x10392),x10393),f10(x10393),x10393) % 1.21/1.22 [1084]~P63(x10842)+~P4(x10843,f2(x10842),x10842)+~P4(x10841,f2(x10842),x10842)+E(f11(f4(x10841,x10842),f4(x10843,x10842),x10842),f4(f11(x10841,x10843,x10842),x10842)) % 1.21/1.22 [1085]~P63(x10852)+~P4(x10853,f2(x10852),x10852)+~P4(f2(x10852),x10851,x10852)+E(f11(f4(x10851,x10852),f4(x10853,x10852),x10852),f4(f11(x10851,x10853,x10852),x10852)) % 1.21/1.22 [1086]~P63(x10862)+~P4(x10861,f2(x10862),x10862)+~P4(f2(x10862),x10863,x10862)+E(f11(f4(x10861,x10862),f4(x10863,x10862),x10862),f4(f11(x10861,x10863,x10862),x10862)) % 1.21/1.22 [1087]~P63(x10872)+~P4(f2(x10872),x10873,x10872)+~P4(f2(x10872),x10871,x10872)+E(f11(f4(x10871,x10872),f4(x10873,x10872),x10872),f4(f11(x10871,x10873,x10872),x10872)) % 1.21/1.22 [1252]~P44(x12522)+E(x12521,f2(x12522))+E(x12523,f2(x12522))+E(f11(f11(f7(x12523,x12522),f9(x12523,x12521,x12522),x12522),f7(x12521,x12522),x12522),f9(f7(x12523,x12522),f7(x12521,x12522),x12522)) % 1.21/1.22 [1253]~P44(x12532)+E(x12531,f2(x12532))+E(x12533,f2(x12532))+E(f11(f11(f7(x12533,x12532),f3(x12531,x12533,x12532),x12532),f7(x12531,x12532),x12532),f3(f7(x12533,x12532),f7(x12531,x12532),x12532)) % 1.21/1.22 [1254]~P47(x12542)+E(x12541,f2(x12542))+E(x12543,f2(x12542))+E(f11(f11(f9(x12543,x12541,x12542),f7(x12543,x12542),x12542),f7(x12541,x12542),x12542),f9(f7(x12543,x12542),f7(x12541,x12542),x12542)) % 1.21/1.22 [1310]~P33(x13103)+~P3(x13101,f10(x13103),x13103)+~P3(f2(x13103),x13101,x13103)+P3(f11(x13101,f31(x13101,x13102,x13103),x13103),f31(x13101,x13102,x13103),x13103) % 1.21/1.22 [761]~P36(x7613)+~P4(x7611,x7614,x7613)+P4(x7611,x7612,x7613)+~P4(x7614,x7612,x7613) % 1.21/1.22 [762]~P37(x7623)+~P4(x7621,x7624,x7623)+P4(x7621,x7622,x7623)+~P4(x7624,x7622,x7623) % 1.21/1.22 [763]~P34(x7633)+~P6(x7631,x7634,x7633)+P6(x7631,x7632,x7633)+~P6(x7634,x7632,x7633) % 1.21/1.22 [764]~P36(x7643)+~P3(x7641,x7644,x7643)+P3(x7641,x7642,x7643)+~P4(x7644,x7642,x7643) % 1.21/1.22 [765]~P36(x7653)+~P3(x7654,x7652,x7653)+P3(x7651,x7652,x7653)+~P4(x7651,x7654,x7653) % 1.21/1.22 [766]~P36(x7663)+~P3(x7661,x7664,x7663)+P3(x7661,x7662,x7663)+~P3(x7664,x7662,x7663) % 1.21/1.22 [767]~P37(x7673)+~P3(x7671,x7674,x7673)+P3(x7671,x7672,x7673)+~P4(x7674,x7672,x7673) % 1.21/1.22 [768]~P37(x7683)+~P3(x7684,x7682,x7683)+P3(x7681,x7682,x7683)+~P4(x7681,x7684,x7683) % 1.21/1.22 [769]~P37(x7693)+~P3(x7691,x7694,x7693)+P3(x7691,x7692,x7693)+~P3(x7694,x7692,x7693) % 1.21/1.22 [657]~P48(x6574)+~P14(x6574)+E(x6571,x6572)+~E(f9(x6573,x6571,x6574),f9(x6573,x6572,x6574)) % 1.21/1.22 [830]~P33(x8304)+E(x8301,x8302)+~P3(f10(x8304),x8303,x8304)+~E(f31(x8303,x8301,x8304),f31(x8303,x8302,x8304)) % 1.21/1.22 [937]~P8(x9374)+~P4(x9371,x9373,x9374)+~P4(x9371,x9372,x9374)+P4(x9371,f29(x9372,x9373,x9374),x9374) % 1.21/1.22 [938]~P34(x9384)+~P6(x9381,x9383,x9384)+~P6(x9381,x9382,x9384)+P6(x9381,f9(x9382,x9383,x9384),x9384) % 1.21/1.22 [939]~P40(x9394)+~P6(x9391,x9393,x9394)+~P6(x9391,x9392,x9394)+P6(x9391,f3(x9392,x9393,x9394),x9394) % 1.21/1.22 [941]~P1(x9414)+~P6(x9411,x9413,x9414)+~P6(x9411,x9412,x9414)+P6(x9411,f5(x9412,x9413,x9414),x9414) % 1.21/1.22 [942]~P8(x9424)+~P3(x9421,x9423,x9424)+~P3(x9421,x9422,x9424)+P3(x9421,f29(x9422,x9423,x9424),x9424) % 1.21/1.22 [945]~P8(x9453)+~P4(x9452,x9454,x9453)+~P4(x9451,x9454,x9453)+P4(f28(x9451,x9452,x9453),x9454,x9453) % 1.21/1.22 [946]~P8(x9463)+~P3(x9462,x9464,x9463)+~P3(x9461,x9464,x9463)+P3(f28(x9461,x9462,x9463),x9464,x9463) % 1.21/1.22 [961]~P33(x9614)+~P3(x9611,x9613,x9614)+~P3(f2(x9614),x9612,x9614)+P3(x9611,f9(x9612,x9613,x9614),x9614) % 1.21/1.22 [1025]~P8(x10253)+P4(x10251,x10252,x10253)+P4(x10251,x10254,x10253)+~P4(x10251,f28(x10252,x10254,x10253),x10253) % 1.21/1.22 [1026]~P8(x10263)+P3(x10261,x10262,x10263)+P3(x10261,x10264,x10263)+~P3(x10261,f28(x10262,x10264,x10263),x10263) % 1.21/1.22 [1027]~P8(x10273)+P4(x10271,x10272,x10273)+P4(x10274,x10272,x10273)+~P4(f29(x10271,x10274,x10273),x10272,x10273) % 1.21/1.22 [1028]~P8(x10283)+P3(x10281,x10282,x10283)+P3(x10284,x10282,x10283)+~P3(f29(x10281,x10284,x10283),x10282,x10283) % 1.21/1.22 [1077]~P1(x10773)+P6(x10771,x10772,x10773)+~P6(x10771,x10774,x10773)+~P6(x10771,f5(x10772,x10774,x10773),x10773) % 1.21/1.22 [1139]~P33(x11393)+~P4(x11392,x11394,a1)+~P4(f10(x11393),x11391,x11393)+P4(f31(x11391,x11392,x11393),f31(x11391,x11394,x11393),x11393) % 1.21/1.22 [1140]~P33(x11403)+~P4(x11402,x11404,a1)+~P3(f10(x11403),x11401,x11403)+P4(f31(x11401,x11402,x11403),f31(x11401,x11404,x11403),x11403) % 1.21/1.22 [1142]~P33(x11423)+~P3(x11422,x11424,a1)+~P3(f10(x11423),x11421,x11423)+P3(f31(x11421,x11422,x11423),f31(x11421,x11424,x11423),x11423) % 1.21/1.22 [1145]~P62(x11453)+~P4(x11454,x11451,x11453)+~P4(x11452,f2(x11453),x11453)+P4(f11(x11451,x11452,x11453),f11(x11454,x11452,x11453),x11453) % 1.21/1.22 [1146]~P62(x11463)+~P4(x11464,x11462,x11463)+~P4(x11461,f2(x11463),x11463)+P4(f11(x11461,x11462,x11463),f11(x11461,x11464,x11463),x11463) % 1.21/1.22 [1147]~P55(x11473)+~P4(x11474,x11472,x11473)+~P3(x11471,f2(x11473),x11473)+P4(f11(x11471,x11472,x11473),f11(x11471,x11474,x11473),x11473) % 1.21/1.22 [1149]~P55(x11493)+~P3(x11494,x11491,x11493)+~P3(x11492,f2(x11493),x11493)+P3(f11(x11491,x11492,x11493),f11(x11494,x11492,x11493),x11493) % 1.21/1.22 [1152]~P55(x11523)+~P3(x11524,x11522,x11523)+~P3(x11521,f2(x11523),x11523)+P3(f11(x11521,x11522,x11523),f11(x11521,x11524,x11523),x11523) % 1.21/1.22 [1153]~P54(x11533)+~P3(x11534,x11531,x11533)+~P3(x11532,f2(x11533),x11533)+P3(f8(x11531,x11532,x11533),f8(x11534,x11532,x11533),x11533) % 1.21/1.23 [1154]~P46(x11543)+~P4(x11541,x11544,x11543)+~P4(f2(x11543),x11542,x11543)+P4(f11(x11541,x11542,x11543),f11(x11544,x11542,x11543),x11543) % 1.21/1.23 [1155]~P55(x11553)+~P4(x11552,x11554,x11553)+~P3(f2(x11553),x11551,x11553)+P4(f11(x11551,x11552,x11553),f11(x11551,x11554,x11553),x11553) % 1.21/1.23 [1156]~P46(x11563)+~P4(x11562,x11564,x11563)+~P4(f2(x11563),x11561,x11563)+P4(f11(x11561,x11562,x11563),f11(x11561,x11564,x11563),x11563) % 1.21/1.23 [1157]~P50(x11573)+~P4(x11572,x11574,x11573)+~P4(f2(x11573),x11571,x11573)+P4(f11(x11571,x11572,x11573),f11(x11571,x11574,x11573),x11573) % 1.21/1.23 [1158]~P33(x11583)+~P4(x11581,x11584,x11583)+~P4(f2(x11583),x11581,x11583)+P4(f31(x11581,x11582,x11583),f31(x11584,x11582,x11583),x11583) % 1.21/1.23 [1159]~P55(x11593)+~P3(x11591,x11594,x11593)+~P3(f2(x11593),x11592,x11593)+P3(f11(x11591,x11592,x11593),f11(x11594,x11592,x11593),x11593) % 1.21/1.23 [1160]~P56(x11603)+~P3(x11601,x11604,x11603)+~P3(f2(x11603),x11602,x11603)+P3(f11(x11601,x11602,x11603),f11(x11604,x11602,x11603),x11603) % 1.21/1.23 [1162]~P55(x11623)+~P3(x11622,x11624,x11623)+~P3(f2(x11623),x11621,x11623)+P3(f11(x11621,x11622,x11623),f11(x11621,x11624,x11623),x11623) % 1.21/1.23 [1163]~P56(x11633)+~P3(x11632,x11634,x11633)+~P3(f2(x11633),x11631,x11633)+P3(f11(x11631,x11632,x11633),f11(x11631,x11634,x11633),x11633) % 1.21/1.23 [1164]~P45(x11643)+~P3(x11642,x11644,x11643)+~P3(f2(x11643),x11641,x11643)+P3(f11(x11641,x11642,x11643),f11(x11641,x11644,x11643),x11643) % 1.21/1.23 [1165]~P54(x11653)+~P3(x11651,x11654,x11653)+~P3(f2(x11653),x11652,x11653)+P3(f8(x11651,x11652,x11653),f8(x11654,x11652,x11653),x11653) % 1.21/1.23 [1184]~P48(x11842)+P6(x11843,x11844,x11842)+~P6(f11(x11841,x11843,x11842),f11(x11841,x11844,x11842),x11842)+E(x11841,f2(x11842)) % 1.21/1.23 [1185]~P48(x11852)+P6(x11853,x11854,x11852)+~P6(f11(x11853,x11851,x11852),f11(x11854,x11851,x11852),x11852)+E(x11851,f2(x11852)) % 1.21/1.23 [1203]~P54(x12034)+~P3(f2(x12034),x12033,x12034)+~P4(f11(x12031,x12033,x12034),x12032,x12034)+P4(x12031,f8(x12032,x12033,x12034),x12034) % 1.21/1.23 [1204]~P54(x12044)+~P3(f2(x12044),x12043,x12044)+~P3(f11(x12041,x12043,x12044),x12042,x12044)+P3(x12041,f8(x12042,x12043,x12044),x12044) % 1.21/1.23 [1205]~P54(x12053)+~P3(f2(x12053),x12052,x12053)+~P4(x12051,f11(x12054,x12052,x12053),x12053)+P4(f8(x12051,x12052,x12053),x12054,x12053) % 1.21/1.23 [1206]~P54(x12063)+~P3(f2(x12063),x12062,x12063)+~P3(x12061,f11(x12064,x12062,x12063),x12063)+P3(f8(x12061,x12062,x12063),x12064,x12063) % 1.21/1.23 [1219]P3(x12192,x12191,x12193)+~P55(x12193)+P3(x12191,x12192,x12193)+~P3(f11(x12194,x12191,x12193),f11(x12194,x12192,x12193),x12193) % 1.21/1.23 [1220]P3(x12202,x12201,x12203)+~P55(x12203)+P3(x12201,x12202,x12203)+~P3(f11(x12201,x12204,x12203),f11(x12202,x12204,x12203),x12203) % 1.21/1.23 [1232]~P55(x12323)+P3(x12321,x12322,x12323)+~P3(f11(x12321,x12324,x12323),f11(x12322,x12324,x12323),x12323)+P3(x12324,f2(x12323),x12323) % 1.21/1.23 [1233]~P55(x12333)+P3(x12331,x12332,x12333)+~P3(f11(x12334,x12331,x12333),f11(x12334,x12332,x12333),x12333)+P3(x12334,f2(x12333),x12333) % 1.21/1.23 [1234]~P55(x12343)+P3(x12341,x12342,x12343)+~P3(f11(x12344,x12342,x12343),f11(x12344,x12341,x12343),x12343)+P3(f2(x12343),x12344,x12343) % 1.21/1.23 [1235]~P55(x12353)+P3(x12351,x12352,x12353)+~P3(f11(x12352,x12354,x12353),f11(x12351,x12354,x12353),x12353)+P3(f2(x12353),x12354,x12353) % 1.21/1.23 [1242]~P55(x12422)+~P3(f11(x12423,x12421,x12422),f11(x12424,x12421,x12422),x12422)+P3(x12421,f2(x12422),x12422)+P3(f2(x12422),x12421,x12422) % 1.21/1.23 [1243]~P55(x12432)+~P3(f11(x12431,x12433,x12432),f11(x12431,x12434,x12432),x12432)+P3(x12431,f2(x12432),x12432)+P3(f2(x12432),x12431,x12432) % 1.21/1.23 [1256]~P33(x12563)+~P4(f31(x12564,x12561,x12563),f31(x12564,x12562,x12563),x12563)+P4(x12561,x12562,a1)+~P3(f10(x12563),x12564,x12563) % 1.21/1.23 [1258]~P33(x12583)+~P3(f31(x12584,x12581,x12583),f31(x12584,x12582,x12583),x12583)+P3(x12581,x12582,a1)+~P3(f10(x12583),x12584,x12583) % 1.21/1.23 [1259]~P55(x12593)+P4(x12591,x12592,x12593)+~P4(f11(x12594,x12592,x12593),f11(x12594,x12591,x12593),x12593)+~P3(x12594,f2(x12593),x12593) % 1.21/1.23 [1260]~P55(x12603)+P3(x12601,x12602,x12603)+~P3(f11(x12604,x12602,x12603),f11(x12604,x12601,x12603),x12603)+~P3(x12604,f2(x12603),x12603) % 1.21/1.23 [1261]~P55(x12613)+P4(x12611,x12612,x12613)+~P4(f11(x12614,x12611,x12613),f11(x12614,x12612,x12613),x12613)+~P3(f2(x12613),x12614,x12613) % 1.21/1.23 [1262]~P56(x12623)+P4(x12621,x12622,x12623)+~P4(f11(x12624,x12621,x12623),f11(x12624,x12622,x12623),x12623)+~P3(f2(x12623),x12624,x12623) % 1.21/1.23 [1263]~P56(x12633)+P4(x12631,x12632,x12633)+~P4(f11(x12631,x12634,x12633),f11(x12632,x12634,x12633),x12633)+~P3(f2(x12633),x12634,x12633) % 1.21/1.23 [1264]~P33(x12643)+P3(x12641,x12642,x12643)+~P4(f2(x12643),x12642,x12643)+~P3(f31(x12641,x12644,x12643),f31(x12642,x12644,x12643),x12643) % 1.21/1.23 [1265]~P55(x12653)+P3(x12651,x12652,x12653)+~P3(f11(x12654,x12651,x12653),f11(x12654,x12652,x12653),x12653)+~P3(f2(x12653),x12654,x12653) % 1.21/1.23 [1266]~P56(x12663)+P3(x12661,x12662,x12663)+~P3(f11(x12664,x12661,x12663),f11(x12664,x12662,x12663),x12663)+~P4(f2(x12663),x12664,x12663) % 1.21/1.23 [1267]~P56(x12673)+P3(x12671,x12672,x12673)+~P3(f11(x12671,x12674,x12673),f11(x12672,x12674,x12673),x12673)+~P4(f2(x12673),x12674,x12673) % 1.21/1.23 [1268]~P57(x12683)+P3(x12681,x12682,x12683)+~P3(f11(x12684,x12681,x12683),f11(x12684,x12682,x12683),x12683)+~P4(f2(x12683),x12684,x12683) % 1.21/1.23 [1269]~P57(x12693)+P3(x12691,x12692,x12693)+~P3(f11(x12691,x12694,x12693),f11(x12692,x12694,x12693),x12693)+~P4(f2(x12693),x12694,x12693) % 1.21/1.23 [949]~P43(x9492)+~P47(x9492)+E(x9491,f2(x9492))+E(f8(f11(x9493,x9491,x9492),f11(x9494,x9491,x9492),x9492),f8(x9493,x9494,x9492)) % 1.21/1.23 [950]~P43(x9502)+~P47(x9502)+E(x9501,f2(x9502))+E(f8(f11(x9501,x9503,x9502),f11(x9501,x9504,x9502),x9502),f8(x9503,x9504,x9502)) % 1.21/1.23 [1207]~P47(x12072)+~P4(x12074,x12073,a1)+E(x12071,f2(x12072))+E(f8(f31(x12071,x12073,x12072),f31(x12071,x12074,x12072),x12072),f31(x12071,f3(x12073,x12074,a1),x12072)) % 1.21/1.23 [1290]~P1(x12903)+~P6(x12902,x12904,x12903)+~P6(x12902,x12901,x12903)+E(f9(f6(x12901,x12902,x12903),f6(x12904,x12902,x12903),x12903),f6(f9(x12901,x12904,x12903),x12902,x12903)) % 1.21/1.23 [1291]~P33(x12913)+P4(x12911,x12912,x12913)+~P4(f2(x12913),x12912,x12913)+~P4(f31(x12911,f30(x12914),x12913),f31(x12912,f30(x12914),x12913),x12913) % 1.21/1.23 [1250]~P43(x12502)+~P47(x12502)+E(x12501,f2(x12502))+E(f8(f9(x12503,f11(x12504,x12501,x12502),x12502),x12501,x12502),f9(x12504,f8(x12503,x12501,x12502),x12502)) % 1.21/1.23 [1251]~P43(x12512)+~P47(x12512)+E(x12511,f2(x12512))+E(f8(f9(x12513,f11(x12514,x12511,x12512),x12512),x12511,x12512),f9(f8(x12513,x12511,x12512),x12514,x12512)) % 1.21/1.23 [884]~P30(x8843)+~P4(x8845,x8844,x8843)+P4(x8841,x8842,x8843)+~E(f3(x8844,x8845,x8843),f3(x8842,x8841,x8843)) % 1.21/1.23 [885]~P30(x8853)+~P4(x8855,x8854,x8853)+P4(x8851,x8852,x8853)+~E(f3(x8852,x8851,x8853),f3(x8854,x8855,x8853)) % 1.21/1.23 [886]~P30(x8863)+~P3(x8864,x8865,x8863)+P3(x8861,x8862,x8863)+~E(f3(x8864,x8865,x8863),f3(x8861,x8862,x8863)) % 1.21/1.23 [887]~P30(x8873)+~P3(x8874,x8875,x8873)+P3(x8871,x8872,x8873)+~E(f3(x8871,x8872,x8873),f3(x8874,x8875,x8873)) % 1.21/1.23 [1128]~P34(x11283)+~P6(x11281,x11284,x11283)+~P4(x11282,x11285,a1)+P6(f31(x11281,x11282,x11283),f31(x11284,x11285,x11283),x11283) % 1.21/1.23 [1129]~P27(x11293)+~P4(x11292,x11295,x11293)+~P4(x11291,x11294,x11293)+P4(f9(x11291,x11292,x11293),f9(x11294,x11295,x11293),x11293) % 1.21/1.23 [1130]~P34(x11303)+~P6(x11302,x11305,x11303)+~P6(x11301,x11304,x11303)+P6(f11(x11301,x11302,x11303),f11(x11304,x11305,x11303),x11303) % 1.21/1.23 [1131]~P32(x11313)+~P4(x11312,x11315,x11313)+~P3(x11311,x11314,x11313)+P3(f9(x11311,x11312,x11313),f9(x11314,x11315,x11313),x11313) % 1.21/1.23 [1132]~P32(x11323)+~P4(x11321,x11324,x11323)+~P3(x11322,x11325,x11323)+P3(f9(x11321,x11322,x11323),f9(x11324,x11325,x11323),x11323) % 1.21/1.23 [1133]~P32(x11333)+~P3(x11332,x11335,x11333)+~P3(x11331,x11334,x11333)+P3(f9(x11331,x11332,x11333),f9(x11334,x11335,x11333),x11333) % 1.21/1.23 [1193]~P34(x11933)+~P6(f31(x11931,x11935,x11933),x11934,x11933)+P6(f31(x11931,x11932,x11933),x11934,x11933)+~P4(x11932,x11935,a1) % 1.21/1.23 [1194]~P30(x11944)+~P4(x11945,x11943,x11944)+~P4(x11941,f9(x11942,x11945,x11944),x11944)+P4(x11941,f9(x11942,x11943,x11944),x11944) % 1.21/1.23 [1294]~P53(x12942)+~P3(f4(x12941,x12942),x12944,x12942)+~P3(f4(x12943,x12942),x12945,x12942)+P3(f11(f4(x12941,x12942),f4(x12943,x12942),x12942),f11(x12944,x12945,x12942),x12942) % 1.21/1.23 [1312]~P1(x13123)+~P6(x13125,x13122,x13123)+~P6(x13124,x13121,x13123)+E(f6(f11(x13121,x13122,x13123),f11(x13124,x13125,x13123),x13123),f11(f6(x13121,x13124,x13123),f6(x13122,x13125,x13123),x13123)) % 1.21/1.23 [1345]~P47(x13452)+E(x13451,f2(x13452))+E(x13453,f2(x13452))+E(f8(f9(f11(x13454,x13451,x13452),f11(x13455,x13453,x13452),x13452),f11(x13453,x13451,x13452),x13452),f9(f8(x13454,x13453,x13452),f8(x13455,x13451,x13452),x13452)) % 1.21/1.23 [1346]~P47(x13462)+E(x13461,f2(x13462))+E(x13463,f2(x13462))+E(f8(f3(f11(x13464,x13461,x13462),f11(x13465,x13463,x13462),x13462),f11(x13463,x13461,x13462),x13462),f3(f8(x13464,x13463,x13462),f8(x13465,x13461,x13462),x13462)) % 1.21/1.23 [1307]~P1(x13073)+~E(f5(x13071,x13074,x13073),f5(x13075,x13074,x13073))+~E(f5(x13072,x13074,x13073),f5(x13076,x13074,x13073))+E(f5(f9(x13071,x13072,x13073),x13074,x13073),f5(f9(x13075,x13076,x13073),x13074,x13073)) % 1.21/1.23 [1308]~P1(x13083)+~E(f5(x13081,x13084,x13083),f5(x13085,x13084,x13083))+~E(f5(x13082,x13084,x13083),f5(x13086,x13084,x13083))+E(f5(f11(x13081,x13082,x13083),x13084,x13083),f5(f11(x13085,x13086,x13083),x13084,x13083)) % 1.21/1.23 [1309]~P7(x13093)+~E(f5(x13091,x13094,x13093),f5(x13095,x13094,x13093))+~E(f5(x13092,x13094,x13093),f5(x13096,x13094,x13093))+E(f5(f3(x13091,x13092,x13093),x13094,x13093),f5(f3(x13095,x13096,x13093),x13094,x13093)) % 1.21/1.23 [828]~P54(x8282)+~P43(x8282)+P4(f10(x8282),x8281,x8282)+~P4(f7(x8281,x8282),f10(x8282),x8282)+P4(x8281,f2(x8282),x8282) % 1.21/1.23 [829]~P54(x8292)+~P43(x8292)+P3(f10(x8292),x8291,x8292)+~P3(f7(x8291,x8292),f10(x8292),x8292)+P4(x8291,f2(x8292),x8292) % 1.21/1.23 [837]~P54(x8371)+~P43(x8371)+~P3(f2(x8371),x8372,x8371)+~P4(x8372,f10(x8371),x8371)+P4(f10(x8371),f7(x8372,x8371),x8371) % 1.21/1.23 [838]~P54(x8381)+~P43(x8381)+~P3(f2(x8381),x8382,x8381)+~P3(x8382,f10(x8381),x8381)+P3(f10(x8381),f7(x8382,x8381),x8381) % 1.21/1.23 [515]~P35(x5152)+~P69(x5152)+~P51(x5152)+~P52(x5152)+~E(f31(x5151,f2(a1),x5152),f2(x5152)) % 1.21/1.23 [353]~P44(x3533)+E(x3531,x3532)+~E(f7(x3531,x3533),f7(x3532,x3533))+E(x3532,f2(x3533))+E(x3531,f2(x3533)) % 1.21/1.23 [845]~P31(x8452)+~P4(f2(x8452),x8451,x8452)+~P4(f2(x8452),x8453,x8452)+~E(f9(x8453,x8451,x8452),f2(x8452))+E(x8451,f2(x8452)) % 1.21/1.23 [846]~P31(x8462)+~P4(f2(x8462),x8463,x8462)+~P4(f2(x8462),x8461,x8462)+~E(f9(x8461,x8463,x8462),f2(x8462))+E(x8461,f2(x8462)) % 1.21/1.23 [1029]~P54(x10291)+~P43(x10291)+~P4(x10293,f2(x10291),x10291)+~P4(x10292,f2(x10291),x10291)+P4(f2(x10291),f8(x10292,x10293,x10291),x10291) % 1.21/1.23 [1031]~P54(x10311)+~P43(x10311)+~P4(f2(x10311),x10313,x10311)+~P4(f2(x10311),x10312,x10311)+P4(f2(x10311),f8(x10312,x10313,x10311),x10311) % 1.21/1.23 [1033]~P54(x10333)+~P43(x10333)+~P4(x10332,f2(x10333),x10333)+~P4(f2(x10333),x10331,x10333)+P4(f8(x10331,x10332,x10333),f2(x10333),x10333) % 1.21/1.23 [1034]~P54(x10343)+~P43(x10343)+~P4(x10341,f2(x10343),x10343)+~P4(f2(x10343),x10342,x10343)+P4(f8(x10341,x10342,x10343),f2(x10343),x10343) % 1.21/1.23 [1059]~P54(x10592)+~P43(x10592)+~P4(f8(x10593,x10591,x10592),f2(x10592),x10592)+P4(x10591,f2(x10592),x10592)+P4(x10593,f2(x10592),x10592) % 1.21/1.23 [1060]~P54(x10602)+~P43(x10602)+~P3(f8(x10603,x10601,x10602),f2(x10602),x10602)+P3(x10601,f2(x10602),x10602)+P3(x10603,f2(x10602),x10602) % 1.21/1.23 [1061]~P54(x10612)+~P43(x10612)+~P4(f2(x10612),f8(x10613,x10611,x10612),x10612)+P4(x10611,f2(x10612),x10612)+P4(f2(x10612),x10613,x10612) % 1.21/1.23 [1062]~P54(x10622)+~P43(x10622)+~P4(f2(x10622),f8(x10621,x10623,x10622),x10622)+P4(x10621,f2(x10622),x10622)+P4(f2(x10622),x10623,x10622) % 1.21/1.23 [1063]~P54(x10632)+~P43(x10632)+~P4(f2(x10632),f8(x10633,x10631,x10632),x10632)+P4(x10631,f2(x10632),x10632)+P4(f2(x10632),x10631,x10632) % 1.21/1.23 [1064]~P54(x10642)+~P43(x10642)+~P4(f2(x10642),f8(x10641,x10643,x10642),x10642)+P4(x10641,f2(x10642),x10642)+P4(f2(x10642),x10641,x10642) % 1.21/1.23 [1065]~P54(x10652)+~P43(x10652)+~P3(f2(x10652),f8(x10653,x10651,x10652),x10652)+P3(x10651,f2(x10652),x10652)+P3(f2(x10652),x10653,x10652) % 1.21/1.23 [1066]~P54(x10662)+~P43(x10662)+~P3(f2(x10662),f8(x10661,x10663,x10662),x10662)+P3(x10661,f2(x10662),x10662)+P3(f2(x10662),x10663,x10662) % 1.21/1.23 [1067]~P54(x10672)+~P43(x10672)+~P3(f2(x10672),f8(x10673,x10671,x10672),x10672)+P3(x10671,f2(x10672),x10672)+P3(f2(x10672),x10671,x10672) % 1.21/1.23 [1068]~P54(x10682)+~P43(x10682)+~P3(f2(x10682),f8(x10681,x10683,x10682),x10682)+P3(x10681,f2(x10682),x10682)+P3(f2(x10682),x10681,x10682) % 1.21/1.23 [1069]~P54(x10692)+~P43(x10692)+~P4(f8(x10693,x10691,x10692),f2(x10692),x10692)+P4(x10691,f2(x10692),x10692)+P4(f2(x10692),x10691,x10692) % 1.21/1.23 [1070]~P54(x10702)+~P43(x10702)+~P4(f8(x10701,x10703,x10702),f2(x10702),x10702)+P4(x10701,f2(x10702),x10702)+P4(f2(x10702),x10701,x10702) % 1.21/1.23 [1071]~P54(x10712)+~P43(x10712)+~P3(f8(x10713,x10711,x10712),f2(x10712),x10712)+P3(x10711,f2(x10712),x10712)+P3(f2(x10712),x10711,x10712) % 1.21/1.23 [1072]~P54(x10722)+~P43(x10722)+~P3(f8(x10721,x10723,x10722),f2(x10722),x10722)+P3(x10721,f2(x10722),x10722)+P3(f2(x10722),x10721,x10722) % 1.21/1.23 [1073]~P54(x10731)+~P43(x10731)+~P4(f8(x10732,x10733,x10731),f2(x10731),x10731)+P4(f2(x10731),x10732,x10731)+P4(f2(x10731),x10733,x10731) % 1.21/1.23 [1074]~P54(x10741)+~P43(x10741)+~P3(f8(x10742,x10743,x10741),f2(x10741),x10741)+P3(f2(x10741),x10742,x10741)+P3(f2(x10741),x10743,x10741) % 1.21/1.23 [1143]~P53(x11433)+~P4(x11431,f10(x11433),x11433)+~P4(f2(x11433),x11432,x11433)+~P4(f2(x11433),x11431,x11433)+P4(f11(x11431,x11432,x11433),x11432,x11433) % 1.21/1.23 [1144]~P53(x11443)+~P4(x11442,f10(x11443),x11443)+~P4(f2(x11443),x11442,x11443)+~P4(f2(x11443),x11441,x11443)+P4(f11(x11441,x11442,x11443),x11441,x11443) % 1.21/1.23 [968]~P10(x9684)+~P11(x9684)+~P4(x9681,x9683,x9684)+~P4(f2(x9684),x9682,x9684)+P4(x9681,f9(x9682,x9683,x9684),x9684) % 1.21/1.23 [969]~P10(x9694)+~P11(x9694)+~P4(x9691,x9692,x9694)+~P4(f2(x9694),x9693,x9694)+P4(x9691,f9(x9692,x9693,x9694),x9694) % 1.21/1.23 [970]~P10(x9704)+~P11(x9704)+~P4(x9701,x9703,x9704)+~P3(f2(x9704),x9702,x9704)+P3(x9701,f9(x9702,x9703,x9704),x9704) % 1.21/1.23 [971]~P10(x9714)+~P11(x9714)+~P3(x9711,x9713,x9714)+~P4(f2(x9714),x9712,x9714)+P3(x9711,f9(x9712,x9713,x9714),x9714) % 1.21/1.23 [1171]~P54(x11713)+~P43(x11713)+~P4(x11714,x11711,x11713)+~P4(x11712,f2(x11713),x11713)+P4(f8(x11711,x11712,x11713),f8(x11714,x11712,x11713),x11713) % 1.21/1.23 [1172]~P54(x11723)+~P43(x11723)+~P4(x11721,x11724,x11723)+~P4(f2(x11723),x11722,x11723)+P4(f8(x11721,x11722,x11723),f8(x11724,x11722,x11723),x11723) % 1.21/1.23 [1209]~P54(x12094)+~P43(x12094)+~P3(f2(x12094),x12093,x12094)+~P4(f8(x12091,x12093,x12094),x12092,x12094)+P4(x12091,f11(x12092,x12093,x12094),x12094) % 1.21/1.23 [1211]~P54(x12114)+~P43(x12114)+~P3(f2(x12114),x12113,x12114)+~P3(f8(x12111,x12113,x12114),x12112,x12114)+P3(x12111,f11(x12112,x12113,x12114),x12114) % 1.21/1.23 [1213]~P54(x12133)+~P43(x12133)+~P3(f2(x12133),x12132,x12133)+~P4(x12131,f8(x12134,x12132,x12133),x12133)+P4(f11(x12131,x12132,x12133),x12134,x12133) % 1.21/1.23 [1215]~P54(x12153)+~P43(x12153)+~P3(f2(x12153),x12152,x12153)+~P3(x12151,f8(x12154,x12152,x12153),x12153)+P3(f11(x12151,x12152,x12153),x12154,x12153) % 1.21/1.23 [1218]~P1(x12183)+~P6(x12182,x12184,x12183)+~P6(x12182,x12181,x12183)+~P6(x12181,x12184,x12183)+P6(f6(x12181,x12182,x12183),f6(x12184,x12182,x12183),x12183) % 1.21/1.23 [1236]~P33(x12363)+~P3(x12361,x12364,x12363)+~P4(f2(x12363),x12361,x12363)+P3(f31(x12361,x12362,x12363),f31(x12364,x12362,x12363),x12363)+~P3(f2(a1),x12362,a1) % 1.21/1.23 [1244]~P33(x12443)+~P4(x12444,x12442,a1)+~P4(x12441,f10(x12443),x12443)+~P4(f2(x12443),x12441,x12443)+P4(f31(x12441,x12442,x12443),f31(x12441,x12444,x12443),x12443) % 1.21/1.23 [1245]~P33(x12453)+~P3(x12454,x12452,a1)+~P3(x12451,f10(x12453),x12453)+~P3(f2(x12453),x12451,x12453)+P3(f31(x12451,x12452,x12453),f31(x12451,x12454,x12453),x12453) % 1.21/1.23 [1306]~P1(x13063)+~P6(x13064,x13061,x13063)+P6(x13061,x13062,x13063)+~P6(x13064,x13062,x13063)+~P6(f6(x13061,x13064,x13063),f6(x13062,x13064,x13063),x13063) % 1.21/1.23 [1313]~P54(x13133)+~P3(x13132,x13134,x13133)+~P3(x13131,f2(x13133),x13133)+~P3(f2(x13133),f11(x13132,x13134,x13133),x13133)+P3(f8(x13131,x13132,x13133),f8(x13131,x13134,x13133),x13133) % 1.21/1.23 [1314]~P54(x13143)+~P4(x13144,x13142,x13143)+~P4(f2(x13143),x13141,x13143)+~P3(f2(x13143),f11(x13142,x13144,x13143),x13143)+P4(f8(x13141,x13142,x13143),f8(x13141,x13144,x13143),x13143) % 1.21/1.23 [1315]~P54(x13153)+~P3(x13154,x13152,x13153)+~P3(f2(x13153),x13151,x13153)+~P3(f2(x13153),f11(x13152,x13154,x13153),x13153)+P3(f8(x13151,x13152,x13153),f8(x13151,x13154,x13153),x13153) % 1.21/1.23 [1041]~P33(x10414)+E(x10411,x10412)+~P4(f2(x10414),x10412,x10414)+~P4(f2(x10414),x10411,x10414)+~E(f31(x10411,f30(x10413),x10414),f31(x10412,f30(x10413),x10414)) % 1.21/1.23 [847]~P47(x8472)+~E(f8(x8474,x8473,x8472),f8(x8475,x8471,x8472))+E(f11(x8474,x8471,x8472),f11(x8475,x8473,x8472))+E(x8471,f2(x8472))+E(x8473,f2(x8472)) % 1.21/1.23 [848]~P47(x8482)+~E(f11(x8484,x8483,x8482),f11(x8485,x8481,x8482))+E(f8(x8484,x8481,x8482),f8(x8485,x8483,x8482))+E(x8481,f2(x8482))+E(x8483,f2(x8482)) % 1.21/1.23 [1217]~P48(x12174)+~P14(x12174)+E(x12171,x12172)+E(x12173,f2(x12174))+~E(f9(x12175,f11(x12173,x12171,x12174),x12174),f9(x12175,f11(x12173,x12172,x12174),x12174)) % 1.21/1.23 [1334]~P48(x13345)+~P14(x13345)+E(x13341,x13342)+E(x13343,x13344)+~E(f9(f11(x13343,x13341,x13345),f11(x13344,x13342,x13345),x13345),f9(f11(x13343,x13342,x13345),f11(x13344,x13341,x13345),x13345)) % 1.21/1.23 [1354]~P42(x13545)+~P41(x13545)+~P6(x13541,x13544,x13545)+~P6(x13541,f9(x13542,x13546,x13545),x13545)+P6(x13541,f9(f3(x13542,f11(x13543,x13544,x13545),x13545),x13546,x13545),x13545) % 1.21/1.23 [1355]~P42(x13554)+~P41(x13554)+~P6(x13551,x13555,x13554)+P6(x13551,f9(x13552,x13553,x13554),x13554)+~P6(x13551,f9(f3(x13552,f11(x13556,x13555,x13554),x13554),x13553,x13554),x13554) % 1.21/1.23 [446]~P35(x4462)+~P69(x4462)+~P51(x4462)+~P52(x4462)+E(x4461,f2(a1))+E(f31(f2(x4462),x4461,x4462),f2(x4462)) % 1.21/1.23 [516]~P35(x5162)+~P69(x5162)+~P51(x5162)+~P52(x5162)+~E(f31(x5161,x5163,x5162),f2(x5162))+E(x5161,f2(x5162)) % 1.21/1.23 [1050]~P54(x10502)+~P43(x10502)+P3(x10501,f2(x10502),x10502)+P3(f2(x10502),x10501,x10502)+~P4(x10503,f2(x10502),x10502)+P4(x10503,f8(x10504,x10501,x10502),x10502) % 1.21/1.23 [1051]~P54(x10512)+~P43(x10512)+P3(x10511,f2(x10512),x10512)+P3(f2(x10512),x10511,x10512)+~P3(x10513,f2(x10512),x10512)+P3(x10513,f8(x10514,x10511,x10512),x10512) % 1.21/1.23 [1052]~P54(x10522)+~P43(x10522)+P3(x10521,f2(x10522),x10522)+P3(f2(x10522),x10521,x10522)+~P4(f2(x10522),x10524,x10522)+P4(f8(x10523,x10521,x10522),x10524,x10522) % 1.21/1.23 [1053]~P54(x10532)+~P43(x10532)+P3(x10531,f2(x10532),x10532)+P3(f2(x10532),x10531,x10532)+~P3(f2(x10532),x10534,x10532)+P3(f8(x10533,x10531,x10532),x10534,x10532) % 1.21/1.23 [1135]~P54(x11352)+~P43(x11352)+P4(x11351,f2(x11352),x11352)+P3(f2(x11352),x11353,x11352)+~P4(x11351,f8(x11354,x11353,x11352),x11352)+P3(x11353,f2(x11352),x11352) % 1.21/1.23 [1136]~P54(x11362)+~P43(x11362)+P3(x11361,f2(x11362),x11362)+P3(f2(x11362),x11361,x11362)+~P3(x11363,f8(x11364,x11361,x11362),x11362)+P3(x11363,f2(x11362),x11362) % 1.21/1.23 [1137]~P54(x11372)+~P43(x11372)+P3(x11371,f2(x11372),x11372)+P3(f2(x11372),x11371,x11372)+~P4(f8(x11374,x11371,x11372),x11373,x11372)+P4(f2(x11372),x11373,x11372) % 1.21/1.23 [1138]~P54(x11382)+~P43(x11382)+P3(x11381,f2(x11382),x11382)+P3(f2(x11382),x11381,x11382)+~P3(f8(x11384,x11381,x11382),x11383,x11382)+P3(f2(x11382),x11383,x11382) % 1.21/1.23 [1166]~P33(x11664)+E(x11661,x11662)+~P4(f2(x11664),x11662,x11664)+~P4(f2(x11664),x11661,x11664)+~E(f31(x11661,x11663,x11664),f31(x11662,x11663,x11664))+~P3(f2(a1),x11663,a1) % 1.21/1.23 [1271]~P54(x12712)+~P43(x12712)+~P4(f11(x12713,x12711,x12712),x12714,x12712)+P3(x12711,f2(x12712),x12712)+~P4(x12713,f2(x12712),x12712)+P4(x12713,f8(x12714,x12711,x12712),x12712) % 1.21/1.23 [1272]~P54(x12722)+~P43(x12722)+~P3(f11(x12723,x12721,x12722),x12724,x12722)+P3(x12721,f2(x12722),x12722)+~P3(x12723,f2(x12722),x12722)+P3(x12723,f8(x12724,x12721,x12722),x12722) % 1.21/1.23 [1273]~P54(x12732)+~P43(x12732)+~P4(x12733,f11(x12734,x12731,x12732),x12732)+P3(x12731,f2(x12732),x12732)+~P4(f2(x12732),x12734,x12732)+P4(f8(x12733,x12731,x12732),x12734,x12732) % 1.21/1.23 [1274]~P54(x12742)+~P43(x12742)+~P3(x12743,f11(x12744,x12741,x12742),x12742)+P3(x12741,f2(x12742),x12742)+~P3(f2(x12742),x12744,x12742)+P3(f8(x12743,x12741,x12742),x12744,x12742) % 1.21/1.23 [1275]~P54(x12751)+~P43(x12751)+~P4(x12754,f8(x12753,x12752,x12751),x12751)+~P3(x12752,f2(x12751),x12751)+P3(f2(x12751),x12752,x12751)+P4(x12753,f11(x12754,x12752,x12751),x12751) % 1.21/1.23 [1276]~P54(x12761)+~P43(x12761)+~P4(x12764,f11(x12763,x12762,x12761),x12761)+~P4(x12763,f2(x12761),x12761)+P3(f2(x12761),x12762,x12761)+P4(x12763,f8(x12764,x12762,x12761),x12761) % 1.21/1.23 [1277]~P54(x12771)+~P43(x12771)+~P4(x12774,f11(x12773,x12772,x12771),x12771)+~P3(x12772,f2(x12771),x12771)+P3(f2(x12771),x12772,x12771)+P4(x12773,f8(x12774,x12772,x12771),x12771) % 1.21/1.23 [1278]~P54(x12781)+~P43(x12781)+~P3(x12784,f8(x12783,x12782,x12781),x12781)+~P3(x12782,f2(x12781),x12781)+P3(f2(x12781),x12782,x12781)+P3(x12783,f11(x12784,x12782,x12781),x12781) % 1.21/1.23 [1279]~P54(x12791)+~P43(x12791)+~P3(x12794,f11(x12793,x12792,x12791),x12791)+~P3(x12792,f2(x12791),x12791)+P3(f2(x12791),x12792,x12791)+P3(x12793,f8(x12794,x12792,x12791),x12791) % 1.21/1.23 [1280]~P54(x12801)+~P43(x12801)+~P3(x12804,f11(x12803,x12802,x12801),x12801)+~P3(x12803,f2(x12801),x12801)+P3(f2(x12801),x12802,x12801)+P3(x12803,f8(x12804,x12802,x12801),x12801) % 1.21/1.23 [1281]~P54(x12811)+~P43(x12811)+~P4(f8(x12814,x12812,x12811),x12813,x12811)+~P3(x12812,f2(x12811),x12811)+P3(f2(x12811),x12812,x12811)+P4(f11(x12813,x12812,x12811),x12814,x12811) % 1.21/1.23 [1282]~P54(x12821)+~P43(x12821)+~P4(f11(x12824,x12822,x12821),x12823,x12821)+~P3(x12822,f2(x12821),x12821)+P3(f2(x12821),x12822,x12821)+P4(f8(x12823,x12822,x12821),x12824,x12821) % 1.21/1.23 [1283]~P54(x12831)+~P43(x12831)+~P3(f8(x12834,x12832,x12831),x12833,x12831)+~P3(x12832,f2(x12831),x12831)+P3(f2(x12831),x12832,x12831)+P3(f11(x12833,x12832,x12831),x12834,x12831) % 1.21/1.23 [1284]~P54(x12841)+~P43(x12841)+~P3(f11(x12844,x12842,x12841),x12843,x12841)+~P3(x12842,f2(x12841),x12841)+P3(f2(x12841),x12842,x12841)+P3(f8(x12843,x12842,x12841),x12844,x12841) % 1.21/1.23 [1285]~P54(x12851)+~P43(x12851)+~P4(f11(x12854,x12852,x12851),x12853,x12851)+~P4(f2(x12851),x12854,x12851)+P3(f2(x12851),x12852,x12851)+P4(f8(x12853,x12852,x12851),x12854,x12851) % 1.21/1.23 [1286]~P54(x12861)+~P43(x12861)+~P3(f11(x12864,x12862,x12861),x12863,x12861)+~P3(f2(x12861),x12864,x12861)+P3(f2(x12861),x12862,x12861)+P3(f8(x12863,x12862,x12861),x12864,x12861) % 1.21/1.23 [1316]~P54(x13163)+~P43(x13163)+~P4(x13162,x13164,x13163)+~P4(x13161,f2(x13163),x13163)+~P3(f2(x13163),f11(x13162,x13164,x13163),x13163)+P4(f8(x13161,x13162,x13163),f8(x13161,x13164,x13163),x13163) % 1.21/1.23 [1323]~P54(x13234)+~P43(x13234)+~P4(x13231,f2(x13234),x13234)+~P4(x13232,f11(x13231,x13233,x13234),x13234)+~P4(f11(x13231,x13233,x13234),x13232,x13234)+P4(x13231,f8(x13232,x13233,x13234),x13234) % 1.21/1.23 [1324]~P54(x13244)+~P43(x13244)+~P3(x13243,f2(x13244),x13244)+~P4(x13242,f11(x13241,x13243,x13244),x13244)+~P4(f11(x13241,x13243,x13244),x13242,x13244)+P4(x13241,f8(x13242,x13243,x13244),x13244) % 1.21/1.23 [1325]~P54(x13254)+~P43(x13254)+~P3(x13253,f2(x13254),x13254)+~P3(x13252,f11(x13251,x13253,x13254),x13254)+~P3(f11(x13251,x13253,x13254),x13252,x13254)+P3(x13251,f8(x13252,x13253,x13254),x13254) % 1.21/1.23 [1326]~P54(x13264)+~P43(x13264)+~P3(x13261,f2(x13264),x13264)+~P3(x13262,f11(x13261,x13263,x13264),x13264)+~P3(f11(x13261,x13263,x13264),x13262,x13264)+P3(x13261,f8(x13262,x13263,x13264),x13264) % 1.21/1.23 [1327]~P54(x13273)+~P43(x13273)+~P3(x13272,f2(x13273),x13273)+~P4(x13271,f11(x13274,x13272,x13273),x13273)+~P4(f11(x13274,x13272,x13273),x13271,x13273)+P4(f8(x13271,x13272,x13273),x13274,x13273) % 1.21/1.23 [1328]~P54(x13283)+~P43(x13283)+~P3(x13282,f2(x13283),x13283)+~P3(x13281,f11(x13284,x13282,x13283),x13283)+~P3(f11(x13284,x13282,x13283),x13281,x13283)+P3(f8(x13281,x13282,x13283),x13284,x13283) % 1.21/1.23 [1329]~P54(x13293)+~P43(x13293)+~P4(f2(x13293),x13294,x13293)+~P4(x13291,f11(x13294,x13292,x13293),x13293)+~P4(f11(x13294,x13292,x13293),x13291,x13293)+P4(f8(x13291,x13292,x13293),x13294,x13293) % 1.21/1.23 [1330]~P54(x13303)+~P43(x13303)+~P3(f2(x13303),x13304,x13303)+~P3(x13301,f11(x13304,x13302,x13303),x13303)+~P3(f11(x13304,x13302,x13303),x13301,x13303)+P3(f8(x13301,x13302,x13303),x13304,x13303) % 1.21/1.23 [1295]~P61(x12953)+~P4(x12952,x12955,x12953)+~P4(x12951,x12954,x12953)+~P4(f2(x12953),x12954,x12953)+~P4(f2(x12953),x12952,x12953)+P4(f11(x12951,x12952,x12953),f11(x12954,x12955,x12953),x12953) % 1.21/1.23 [1296]~P61(x12963)+~P4(x12962,x12965,x12963)+~P4(x12961,x12964,x12963)+~P4(f2(x12963),x12962,x12963)+~P4(f2(x12963),x12961,x12963)+P4(f11(x12961,x12962,x12963),f11(x12964,x12965,x12963),x12963) % 1.21/1.23 [1297]~P54(x12973)+~P4(x12975,x12972,x12973)+~P4(x12971,x12974,x12973)+~P4(f2(x12973),x12971,x12973)+~P3(f2(x12973),x12975,x12973)+P4(f8(x12971,x12972,x12973),f8(x12974,x12975,x12973),x12973) % 1.21/1.23 [1298]~P56(x12983)+~P4(x12982,x12985,x12983)+~P3(x12981,x12984,x12983)+~P4(f2(x12983),x12981,x12983)+~P3(f2(x12983),x12982,x12983)+P3(f11(x12981,x12982,x12983),f11(x12984,x12985,x12983),x12983) % 1.21/1.23 [1299]~P56(x12993)+~P4(x12991,x12994,x12993)+~P3(x12992,x12995,x12993)+~P4(f2(x12993),x12992,x12993)+~P3(f2(x12993),x12991,x12993)+P3(f11(x12991,x12992,x12993),f11(x12994,x12995,x12993),x12993) % 1.21/1.23 [1300]~P56(x13003)+~P3(x13002,x13005,x13003)+~P3(x13001,x13004,x13003)+~P4(f2(x13003),x13002,x13003)+~P4(f2(x13003),x13001,x13003)+P3(f11(x13001,x13002,x13003),f11(x13004,x13005,x13003),x13003) % 1.21/1.23 [1301]~P56(x13013)+~P3(x13012,x13015,x13013)+~P3(x13011,x13014,x13013)+~P4(f2(x13013),x13012,x13013)+~P3(f2(x13013),x13014,x13013)+P3(f11(x13011,x13012,x13013),f11(x13014,x13015,x13013),x13013) % 1.21/1.23 [1302]~P54(x13023)+~P4(x13025,x13022,x13023)+~P3(x13021,x13024,x13023)+~P4(f2(x13023),x13021,x13023)+~P3(f2(x13023),x13025,x13023)+P3(f8(x13021,x13022,x13023),f8(x13024,x13025,x13023),x13023) % 1.21/1.23 [1303]~P54(x13033)+~P4(x13031,x13034,x13033)+~P3(x13035,x13032,x13033)+~P3(f2(x13033),x13035,x13033)+~P3(f2(x13033),x13031,x13033)+P3(f8(x13031,x13032,x13033),f8(x13034,x13035,x13033),x13033) % 1.21/1.23 %EqnAxiom % 1.21/1.23 [1]E(x11,x11) % 1.21/1.23 [2]E(x22,x21)+~E(x21,x22) % 1.21/1.23 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.21/1.23 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 1.21/1.23 [5]~E(x51,x52)+E(f14(x51),f14(x52)) % 1.21/1.23 [6]~E(x61,x62)+E(f9(x61,x63,x64),f9(x62,x63,x64)) % 1.21/1.23 [7]~E(x71,x72)+E(f9(x73,x71,x74),f9(x73,x72,x74)) % 1.21/1.23 [8]~E(x81,x82)+E(f9(x83,x84,x81),f9(x83,x84,x82)) % 1.21/1.23 [9]~E(x91,x92)+E(f27(x91),f27(x92)) % 1.21/1.23 [10]~E(x101,x102)+E(f4(x101,x103),f4(x102,x103)) % 1.21/1.23 [11]~E(x111,x112)+E(f4(x113,x111),f4(x113,x112)) % 1.21/1.23 [12]~E(x121,x122)+E(f15(x121),f15(x122)) % 1.21/1.23 [13]~E(x131,x132)+E(f18(x131,x133),f18(x132,x133)) % 1.21/1.23 [14]~E(x141,x142)+E(f18(x143,x141),f18(x143,x142)) % 1.21/1.23 [15]~E(x151,x152)+E(f11(x151,x153,x154),f11(x152,x153,x154)) % 1.21/1.23 [16]~E(x161,x162)+E(f11(x163,x161,x164),f11(x163,x162,x164)) % 1.21/1.23 [17]~E(x171,x172)+E(f11(x173,x174,x171),f11(x173,x174,x172)) % 1.21/1.23 [18]~E(x181,x182)+E(f3(x181,x183,x184),f3(x182,x183,x184)) % 1.21/1.23 [19]~E(x191,x192)+E(f3(x193,x191,x194),f3(x193,x192,x194)) % 1.21/1.23 [20]~E(x201,x202)+E(f3(x203,x204,x201),f3(x203,x204,x202)) % 1.21/1.23 [21]~E(x211,x212)+E(f8(x211,x213,x214),f8(x212,x213,x214)) % 1.21/1.23 [22]~E(x221,x222)+E(f8(x223,x221,x224),f8(x223,x222,x224)) % 1.21/1.23 [23]~E(x231,x232)+E(f8(x233,x234,x231),f8(x233,x234,x232)) % 1.21/1.23 [24]~E(x241,x242)+E(f25(x241,x243),f25(x242,x243)) % 1.21/1.23 [25]~E(x251,x252)+E(f25(x253,x251),f25(x253,x252)) % 1.21/1.23 [26]~E(x261,x262)+E(f5(x261,x263,x264),f5(x262,x263,x264)) % 1.21/1.23 [27]~E(x271,x272)+E(f5(x273,x271,x274),f5(x273,x272,x274)) % 1.21/1.23 [28]~E(x281,x282)+E(f5(x283,x284,x281),f5(x283,x284,x282)) % 1.21/1.23 [29]~E(x291,x292)+E(f10(x291),f10(x292)) % 1.21/1.23 [30]~E(x301,x302)+E(f30(x301),f30(x302)) % 1.21/1.23 [31]~E(x311,x312)+E(f28(x311,x313,x314),f28(x312,x313,x314)) % 1.21/1.23 [32]~E(x321,x322)+E(f28(x323,x321,x324),f28(x323,x322,x324)) % 1.21/1.23 [33]~E(x331,x332)+E(f28(x333,x334,x331),f28(x333,x334,x332)) % 1.21/1.23 [34]~E(x341,x342)+E(f22(x341,x343,x344),f22(x342,x343,x344)) % 1.21/1.23 [35]~E(x351,x352)+E(f22(x353,x351,x354),f22(x353,x352,x354)) % 1.21/1.23 [36]~E(x361,x362)+E(f22(x363,x364,x361),f22(x363,x364,x362)) % 1.21/1.23 [37]~E(x371,x372)+E(f6(x371,x373,x374),f6(x372,x373,x374)) % 1.21/1.23 [38]~E(x381,x382)+E(f6(x383,x381,x384),f6(x383,x382,x384)) % 1.21/1.23 [39]~E(x391,x392)+E(f6(x393,x394,x391),f6(x393,x394,x392)) % 1.21/1.23 [40]~E(x401,x402)+E(f13(x401,x403),f13(x402,x403)) % 1.21/1.23 [41]~E(x411,x412)+E(f13(x413,x411),f13(x413,x412)) % 1.21/1.23 [42]~E(x421,x422)+E(f31(x421,x423,x424),f31(x422,x423,x424)) % 1.21/1.23 [43]~E(x431,x432)+E(f31(x433,x431,x434),f31(x433,x432,x434)) % 1.21/1.23 [44]~E(x441,x442)+E(f31(x443,x444,x441),f31(x443,x444,x442)) % 1.21/1.23 [45]~E(x451,x452)+E(f12(x451,x453),f12(x452,x453)) % 1.21/1.23 [46]~E(x461,x462)+E(f12(x463,x461),f12(x463,x462)) % 1.21/1.23 [47]~E(x471,x472)+E(f17(x471),f17(x472)) % 1.21/1.23 [48]~E(x481,x482)+E(f29(x481,x483,x484),f29(x482,x483,x484)) % 1.21/1.23 [49]~E(x491,x492)+E(f29(x493,x491,x494),f29(x493,x492,x494)) % 1.21/1.23 [50]~E(x501,x502)+E(f29(x503,x504,x501),f29(x503,x504,x502)) % 1.21/1.23 [51]~E(x511,x512)+E(f7(x511,x513),f7(x512,x513)) % 1.21/1.23 [52]~E(x521,x522)+E(f7(x523,x521),f7(x523,x522)) % 1.21/1.23 [53]~E(x531,x532)+E(f19(x531,x533,x534),f19(x532,x533,x534)) % 1.21/1.23 [54]~E(x541,x542)+E(f19(x543,x541,x544),f19(x543,x542,x544)) % 1.21/1.23 [55]~E(x551,x552)+E(f19(x553,x554,x551),f19(x553,x554,x552)) % 1.21/1.23 [56]~E(x561,x562)+E(f16(x561,x563),f16(x562,x563)) % 1.21/1.23 [57]~E(x571,x572)+E(f16(x573,x571),f16(x573,x572)) % 1.21/1.23 [58]~E(x581,x582)+E(f20(x581,x583),f20(x582,x583)) % 1.21/1.23 [59]~E(x591,x592)+E(f20(x593,x591),f20(x593,x592)) % 1.21/1.23 [60]~E(x601,x602)+E(f23(x601,x603,x604),f23(x602,x603,x604)) % 1.21/1.23 [61]~E(x611,x612)+E(f23(x613,x611,x614),f23(x613,x612,x614)) % 1.21/1.23 [62]~E(x621,x622)+E(f23(x623,x624,x621),f23(x623,x624,x622)) % 1.21/1.23 [63]~E(x631,x632)+E(f24(x631,x633),f24(x632,x633)) % 1.21/1.23 [64]~E(x641,x642)+E(f24(x643,x641),f24(x643,x642)) % 1.21/1.23 [65]~E(x651,x652)+E(f26(x651,x653),f26(x652,x653)) % 1.21/1.23 [66]~E(x661,x662)+E(f26(x663,x661),f26(x663,x662)) % 1.21/1.23 [67]~E(x671,x672)+E(f21(x671,x673,x674),f21(x672,x673,x674)) % 1.21/1.23 [68]~E(x681,x682)+E(f21(x683,x681,x684),f21(x683,x682,x684)) % 1.21/1.23 [69]~E(x691,x692)+E(f21(x693,x694,x691),f21(x693,x694,x692)) % 1.21/1.23 [70]~P1(x701)+P1(x702)+~E(x701,x702) % 1.21/1.23 [71]~P8(x711)+P8(x712)+~E(x711,x712) % 1.21/1.23 [72]~P9(x721)+P9(x722)+~E(x721,x722) % 1.21/1.23 [73]~P33(x731)+P33(x732)+~E(x731,x732) % 1.21/1.23 [74]~P10(x741)+P10(x742)+~E(x741,x742) % 1.21/1.23 [75]~P11(x751)+P11(x752)+~E(x751,x752) % 1.21/1.23 [76]~P34(x761)+P34(x762)+~E(x761,x762) % 1.21/1.23 [77]~P12(x771)+P12(x772)+~E(x771,x772) % 1.21/1.23 [78]~P56(x781)+P56(x782)+~E(x781,x782) % 1.21/1.23 [79]~P57(x791)+P57(x792)+~E(x791,x792) % 1.21/1.23 [80]~P58(x801)+P58(x802)+~E(x801,x802) % 1.21/1.23 [81]~P35(x811)+P35(x812)+~E(x811,x812) % 1.21/1.23 [82]~P21(x821)+P21(x822)+~E(x821,x822) % 1.21/1.23 [83]~P22(x831)+P22(x832)+~E(x831,x832) % 1.21/1.23 [84]~P42(x841)+P42(x842)+~E(x841,x842) % 1.21/1.23 [85]~P27(x851)+P27(x852)+~E(x851,x852) % 1.21/1.23 [86]~P31(x861)+P31(x862)+~E(x861,x862) % 1.21/1.23 [87]~P68(x871)+P68(x872)+~E(x871,x872) % 1.21/1.23 [88]~P36(x881)+P36(x882)+~E(x881,x882) % 1.21/1.23 [89]~P37(x891)+P37(x892)+~E(x891,x892) % 1.21/1.23 [90]~P15(x901)+P15(x902)+~E(x901,x902) % 1.21/1.23 [91]~P32(x911)+P32(x912)+~E(x911,x912) % 1.21/1.23 [92]~P59(x921)+P59(x922)+~E(x921,x922) % 1.21/1.23 [93]~P60(x931)+P60(x932)+~E(x931,x932) % 1.21/1.23 [94]~P17(x941)+P17(x942)+~E(x941,x942) % 1.21/1.23 [95]~P20(x951)+P20(x952)+~E(x951,x952) % 1.21/1.23 [96]~P45(x961)+P45(x962)+~E(x961,x962) % 1.21/1.23 [97]~P2(x971)+P2(x972)+~E(x971,x972) % 1.21/1.23 [98]P4(x982,x983,x984)+~E(x981,x982)+~P4(x981,x983,x984) % 1.21/1.23 [99]P4(x993,x992,x994)+~E(x991,x992)+~P4(x993,x991,x994) % 1.21/1.23 [100]P4(x1003,x1004,x1002)+~E(x1001,x1002)+~P4(x1003,x1004,x1001) % 1.21/1.23 [101]~P46(x1011)+P46(x1012)+~E(x1011,x1012) % 1.21/1.23 [102]~P50(x1021)+P50(x1022)+~E(x1021,x1022) % 1.21/1.23 [103]~P61(x1031)+P61(x1032)+~E(x1031,x1032) % 1.21/1.23 [104]~P69(x1041)+P69(x1042)+~E(x1041,x1042) % 1.21/1.23 [105]~P51(x1051)+P51(x1052)+~E(x1051,x1052) % 1.21/1.23 [106]~P52(x1061)+P52(x1062)+~E(x1061,x1062) % 1.21/1.23 [107]~P18(x1071)+P18(x1072)+~E(x1071,x1072) % 1.21/1.23 [108]~P38(x1081)+P38(x1082)+~E(x1081,x1082) % 1.21/1.23 [109]~P23(x1091)+P23(x1092)+~E(x1091,x1092) % 1.21/1.23 [110]P3(x1102,x1103,x1104)+~E(x1101,x1102)+~P3(x1101,x1103,x1104) % 1.21/1.23 [111]P3(x1113,x1112,x1114)+~E(x1111,x1112)+~P3(x1113,x1111,x1114) % 1.21/1.23 [112]P3(x1123,x1124,x1122)+~E(x1121,x1122)+~P3(x1123,x1124,x1121) % 1.21/1.23 [113]~P43(x1131)+P43(x1132)+~E(x1131,x1132) % 1.21/1.23 [114]~P54(x1141)+P54(x1142)+~E(x1141,x1142) % 1.21/1.23 [115]~P44(x1151)+P44(x1152)+~E(x1151,x1152) % 1.21/1.23 [116]~P28(x1161)+P28(x1162)+~E(x1161,x1162) % 1.21/1.23 [117]P5(x1172,x1173)+~E(x1171,x1172)+~P5(x1171,x1173) % 1.21/1.23 [118]P5(x1183,x1182)+~E(x1181,x1182)+~P5(x1183,x1181) % 1.21/1.23 [119]P6(x1192,x1193,x1194)+~E(x1191,x1192)+~P6(x1191,x1193,x1194) % 1.21/1.23 [120]P6(x1203,x1202,x1204)+~E(x1201,x1202)+~P6(x1203,x1201,x1204) % 1.21/1.23 [121]P6(x1213,x1214,x1212)+~E(x1211,x1212)+~P6(x1213,x1214,x1211) % 1.21/1.23 [122]~P30(x1221)+P30(x1222)+~E(x1221,x1222) % 1.21/1.23 [123]~P55(x1231)+P55(x1232)+~E(x1231,x1232) % 1.21/1.23 [124]~P47(x1241)+P47(x1242)+~E(x1241,x1242) % 1.21/1.23 [125]~P24(x1251)+P24(x1252)+~E(x1251,x1252) % 1.21/1.23 [126]~P66(x1261)+P66(x1262)+~E(x1261,x1262) % 1.21/1.23 [127]~P7(x1271)+P7(x1272)+~E(x1271,x1272) % 1.21/1.23 [128]~P63(x1281)+P63(x1282)+~E(x1281,x1282) % 1.21/1.23 [129]~P53(x1291)+P53(x1292)+~E(x1291,x1292) % 1.21/1.23 [130]~P26(x1301)+P26(x1302)+~E(x1301,x1302) % 1.21/1.23 [131]~P25(x1311)+P25(x1312)+~E(x1311,x1312) % 1.21/1.23 [132]~P14(x1321)+P14(x1322)+~E(x1321,x1322) % 1.21/1.23 [133]~P67(x1331)+P67(x1332)+~E(x1331,x1332) % 1.21/1.23 [134]~P48(x1341)+P48(x1342)+~E(x1341,x1342) % 1.21/1.23 [135]~P62(x1351)+P62(x1352)+~E(x1351,x1352) % 1.21/1.23 [136]~P16(x1361)+P16(x1362)+~E(x1361,x1362) % 1.21/1.23 [137]~P13(x1371)+P13(x1372)+~E(x1371,x1372) % 1.21/1.23 [138]~P40(x1381)+P40(x1382)+~E(x1381,x1382) % 1.21/1.23 [139]~P19(x1391)+P19(x1392)+~E(x1391,x1392) % 1.21/1.23 [140]~P29(x1401)+P29(x1402)+~E(x1401,x1402) % 1.21/1.23 [141]~P41(x1411)+P41(x1412)+~E(x1411,x1412) % 1.21/1.23 [142]~P39(x1421)+P39(x1422)+~E(x1421,x1422) % 1.21/1.23 [143]~P64(x1431)+P64(x1432)+~E(x1431,x1432) % 1.21/1.23 [144]~P49(x1441)+P49(x1442)+~E(x1441,x1442) % 1.21/1.23 [145]~P70(x1451)+P70(x1452)+~E(x1451,x1452) % 1.21/1.23 [146]~P65(x1461)+P65(x1462)+~E(x1461,x1462) % 1.21/1.23 % 1.21/1.23 %------------------------------------------- % 1.21/1.23 cnf(1421,plain, % 1.21/1.23 ($false), % 1.21/1.23 inference(scs_inference,[],[289,175,317]), % 1.21/1.23 ['proof']). % 1.21/1.23 % SZS output end Proof % 1.21/1.23 % Total time :0.110198s %------------------------------------------------------------------------------