%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL851-1 : 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 : n001.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 11:20:00 AM UTC 2026 % Result : Unsatisfiable 0.70s 0.97s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL851-1 : TPTP v9.3.1. Released v4.1.0. % 0.00/0.02 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.06/0.34 % Computer : n001.cluster.edu % 0.06/0.34 % Model : x86_64 x86_64 % 0.06/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.06/0.34 % Memory : 8046.5625MB % 0.06/0.34 % OS : Linux 6.8.0-71-generic % 0.06/0.34 % CPULimit : 300 % 0.06/0.34 % WCLimit : 300 % 0.06/0.34 % DateTime : Sat Sep 5 17:10:32 UTC 2026 % 0.06/0.35 % CPUTime : % 0.13/0.44 start to proof:theBenchmark % 0.70/0.91 %------------------------------------------- % 0.70/0.91 % File :CSE---1.7 % 0.70/0.91 % Problem :theBenchmark % 0.70/0.91 % Transform :cnf % 0.70/0.91 % Format :tptp:raw % 0.70/0.91 % Command :java -jar mcs_scs.jar %d %s % 0.70/0.91 % 0.70/0.91 % Result :Theorem 0.099854s % 0.70/0.91 % Output :CNFRefutation 0.099854s % 0.70/0.91 %------------------------------------------- % 0.70/0.91 %------------------------------------------------------------------------------ % 0.70/0.91 % File : LCL851-1 : TPTP v9.3.1. Released v4.1.0. % 0.70/0.91 % Domain : Logic Calculi % 0.70/0.91 % Problem : Strong normalization of typed lambda calculus 270_7 % 0.70/0.91 % Version : Especial. % 0.70/0.91 % English : % 0.70/0.91 % 0.70/0.91 % Refs : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java % 0.70/0.91 % : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe % 0.70/0.91 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 0.70/0.91 % Source : [Nip10] % 0.70/0.91 % Names : StrongNorm-270_7 [Nip10] % 0.70/0.91 % 0.70/0.91 % Status : Unsatisfiable % 0.70/0.91 % Rating : 0.17 v9.3.0, 0.09 v9.1.0, 0.10 v8.1.0, 0.05 v7.5.0, 0.11 v7.4.0, 0.12 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.00 v6.2.0, 0.20 v6.1.0, 0.14 v6.0.0, 0.20 v5.5.0, 0.40 v5.3.0, 0.39 v5.2.0, 0.31 v5.1.0, 0.41 v5.0.0, 0.36 v4.1.0 % 0.70/0.91 % Syntax : Number of clauses : 946 ( 186 unt; 114 nHn; 497 RR) % 0.70/0.91 % Number of literals : 2292 ( 587 equ;1264 neg) % 0.70/0.91 % Maximal clause size : 6 ( 2 avg) % 0.70/0.91 % Maximal term depth : 7 ( 2 avg) % 0.70/0.91 % Number of predicates : 59 ( 58 usr; 0 prp; 1-6 aty) % 0.70/0.91 % Number of functors : 59 ( 59 usr; 9 con; 0-5 aty) % 0.70/0.91 % Number of variables : 2927 ( 446 sgn) % 0.70/0.91 % SPC : CNF_UNS_RFO_SEQ_NHN % 0.70/0.91 % 0.70/0.91 % Comments : % 0.70/0.91 %------------------------------------------------------------------------------ % 0.70/0.91 cnf(cls_less__add__Suc1_0,axiom, % 0.70/0.91 c_HOL_Oord__class_Oless(V_i,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_m)),tc_nat) ). % 0.70/0.91 % 0.70/0.91 cnf(cls_less__add__Suc2_0,axiom, % 0.70/0.91 c_HOL_Oord__class_Oless(V_i,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_i)),tc_nat) ). % 0.70/0.91 % 0.70/0.91 cnf(cls_less__iff__Suc__add_1,axiom, % 0.70/0.91 c_HOL_Oord__class_Oless(V_m,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_x)),tc_nat) ). % 0.70/0.91 % 0.70/0.91 cnf(cls_le__diff__conv2_0,axiom, % 0.70/0.91 ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat) % 0.70/0.91 | ~ c_lessequals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) % 0.70/0.91 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.70/0.91 % 0.70/0.91 cnf(cls_le__diff__conv2_1,axiom, % 0.70/0.91 ( c_lessequals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) % 0.70/0.91 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat) % 0.70/0.91 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.70/0.91 % 0.70/0.92 cnf(cls_div__mod__equality_0,axiom, % 0.70/0.92 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.92 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),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))),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_div__mod__equality2_0,axiom, % 0.70/0.92 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.92 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),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))),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_infinite__descent0_2,axiom, % 0.70/0.92 ( hBOOL(hAPP(V_P,V_n)) % 0.70/0.92 | hBOOL(hAPP(V_P,V_x)) % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(V_x,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(V_P),tc_nat) % 0.70/0.92 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_eq__add__iff1_0,axiom, % 0.70/0.92 ( ~ class_Ring__and__Field_Oring(T_a) % 0.70/0.92 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_e,T_a)),V_c) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_b,V_e,T_a)),V_d) % 0.70/0.92 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a)),V_c) = V_d ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_eq__add__iff2_0,axiom, % 0.70/0.92 ( ~ class_Ring__and__Field_Oring(T_a) % 0.70/0.92 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_e,T_a)),V_c) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_b,V_e,T_a)),V_d) % 0.70/0.92 | V_c = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a)),V_d) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_nat__less__add__iff2_1,axiom, % 0.70/0.92 ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),V_n),tc_nat) % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(V_m,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat)),V_n),tc_nat) % 0.70/0.92 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_nat__less__add__iff2_0,axiom, % 0.70/0.92 ( c_HOL_Oord__class_Oless(V_m,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat)),V_n),tc_nat) % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),V_n),tc_nat) % 0.70/0.92 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_nat__less__add__iff1_1,axiom, % 0.70/0.92 ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),V_n),tc_nat) % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat)),V_m),V_n,tc_nat) % 0.70/0.92 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_nat__less__add__iff1_0,axiom, % 0.70/0.92 ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat)),V_m),V_n,tc_nat) % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),V_n),tc_nat) % 0.70/0.92 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_eq__add__iff2_1,axiom, % 0.70/0.92 ( ~ class_Ring__and__Field_Oring(T_a) % 0.70/0.92 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_e,T_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a)),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_b,V_e,T_a)),V_d) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_split__div__lemma_0,axiom, % 0.70/0.92 ( V_q = c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat) % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Otimes__class_Otimes(V_n,c_Suc(V_q),tc_nat),tc_nat) % 0.70/0.92 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_n,V_q,tc_nat),V_m,tc_nat) % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_add__Suc_0,axiom, % 0.70/0.92 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_add__Suc__right_0,axiom, % 0.70/0.92 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_power__0__Suc_0,axiom, % 0.70/0.92 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 0.70/0.92 | ~ class_Power_Opower(T_a) % 0.70/0.92 | 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) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_mult__strict__mono_0,axiom, % 0.70/0.92 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.70/0.92 | 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) % 0.70/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_zmod__simps_I4_J_0,axiom, % 0.70/0.92 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.92 | 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) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_nat_Oinduct_1,axiom, % 0.70/0.92 ( hBOOL(hAPP(V_P,V_nat)) % 0.70/0.92 | ~ hBOOL(hAPP(V_P,c_Suc(v_sko__Nat__Xnat__Xinduct__1(V_P)))) % 0.70/0.92 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_min__max_Oinf__le1_0,axiom, % 0.70/0.92 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.92 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_x,T_a) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_min__max_Oinf__le2_0,axiom, % 0.70/0.92 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.92 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_y,T_a) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_min__max_Ole__infI_0,axiom, % 0.70/0.92 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.92 | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) % 0.70/0.92 | ~ c_lessequals(V_x,V_b,T_a) % 0.70/0.92 | ~ c_lessequals(V_x,V_a,T_a) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_min__max_Ole__inf__iff_2,axiom, % 0.70/0.92 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.92 | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) % 0.70/0.92 | ~ c_lessequals(V_x,V_z,T_a) % 0.70/0.92 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_min__max_Oinf__greatest_0,axiom, % 0.70/0.92 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.92 | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) % 0.70/0.92 | ~ c_lessequals(V_x,V_z,T_a) % 0.70/0.92 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_eq__add__iff1_1,axiom, % 0.70/0.92 ( ~ class_Ring__and__Field_Oring(T_a) % 0.70/0.92 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_e,T_a)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_b,V_e,T_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a)),V_c)) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_zero__le__power_0,axiom, % 0.70/0.92 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.70/0.92 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 0.70/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_diff__is__0__eq_1,axiom, % 0.70/0.92 ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.92 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_diff__is__0__eq_0,axiom, % 0.70/0.92 ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.92 | c_lessequals(V_m,V_n,tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_min__diff__distrib__left_0,axiom, % 0.70/0.92 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.70/0.92 | 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) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_max__less__iff__conj_2,axiom, % 0.70/0.92 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.92 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(V_x,V_z,T_a) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_div__mult__self1__is__m_0,axiom, % 0.70/0.92 ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),V_n,tc_nat) = V_m % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_div__mult__self__is__m_0,axiom, % 0.70/0.92 ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_n,tc_nat) = V_m % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_diff__Suc__diff__eq2_0,axiom, % 0.70/0.92 ( 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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),tc_nat) % 0.70/0.92 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_replicate__eq__replicate_0,axiom, % 0.70/0.92 ( c_List_Oreplicate(V_m,V_x,T_a) != c_List_Oreplicate(V_n,V_y,T_a) % 0.70/0.92 | V_m = V_n ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_add__strict__increasing_0,axiom, % 0.70/0.92 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.70/0.92 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.70/0.92 | c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a) % 0.70/0.92 | ~ c_lessequals(V_b,V_c,T_a) % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_lem0_0,axiom, % 0.70/0.92 ( c_HOL_Oord__class_Oless(V_m,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k),tc_nat) % 0.70/0.92 | ~ c_lessequals(V_m,V_n,tc_nat) % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_add__is__1_4,axiom, % 0.70/0.92 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_mod__mod__trivial_0,axiom, % 0.70/0.92 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.92 | 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) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_of__nat__le__iff_0,axiom, % 0.70/0.92 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.70/0.92 | c_lessequals(V_m,V_n,tc_nat) % 0.70/0.92 | ~ 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) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_of__nat__le__iff_1,axiom, % 0.70/0.92 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.70/0.92 | 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) % 0.70/0.92 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_subst__preserves__beta_0,axiom, % 0.70/0.92 ( c_Lambda_Obeta(c_Lambda_Osubst(V_r,V_t,V_i),c_Lambda_Osubst(V_s,V_t,V_i)) % 0.70/0.92 | ~ c_Lambda_Obeta(V_r,V_s) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_min__less__iff__conj_2,axiom, % 0.70/0.92 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.92 | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_natgb_Oadd__mul__solve_1,axiom, % 0.70/0.92 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat)) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_natgb_Onoteq__reduce_1,axiom, % 0.70/0.92 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat)) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_class__ringb_Onoteq__reduce_1,axiom, % 0.70/0.92 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.70/0.92 | ~ class_Int_Onumber__ring(T_a) % 0.70/0.92 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_c,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_d,T_a)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_d,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_c,T_a)) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_class__ringb_Oadd__mul__solve_1,axiom, % 0.70/0.92 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.70/0.92 | ~ class_Int_Onumber__ring(T_a) % 0.70/0.92 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a)) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_max__Suc__Suc_0,axiom, % 0.70/0.92 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)) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_less__Suc0_0,axiom, % 0.70/0.92 ( V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom, % 0.70/0.92 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.70/0.92 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.70/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom, % 0.70/0.92 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.70/0.92 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a) % 0.70/0.92 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_div__le__dividend_0,axiom, % 0.70/0.92 c_lessequals(c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat),V_m,tc_nat) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_min__max_Oinf__left__idem_0,axiom, % 0.70/0.92 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.92 | 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) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_subst__Var_2,axiom, % 0.70/0.92 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_i),V_s,V_k) = c_Lambda_OdB_OVar(V_i) % 0.70/0.92 | V_i = V_k % 0.70/0.92 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_nat__diff__add__eq2_0,axiom, % 0.70/0.92 ( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat)),V_n),tc_nat) % 0.70/0.92 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_nat__diff__add__eq1_0,axiom, % 0.70/0.92 ( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),V_n),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat)),V_m),V_n,tc_nat) % 0.70/0.92 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_diff__add__cancel_0,axiom, % 0.70/0.92 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.70/0.92 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ominus__class_Ominus(V_a,V_b,T_a)),V_b) = V_a ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_nat__diff__split__asm_1,axiom, % 0.70/0.92 ( ~ hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_b),V_x),V_b,tc_nat))) % 0.70/0.92 | hBOOL(hAPP(V_P,V_x)) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_nat__diff__split_1,axiom, % 0.70/0.92 ( ~ hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_b),V_d),V_b,tc_nat))) % 0.70/0.92 | hBOOL(hAPP(V_P,V_d)) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_mod__Suc_1,axiom, % 0.70/0.92 ( c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) % 0.70/0.92 | c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) = V_n ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_mult__le__cancel2_1,axiom, % 0.70/0.92 ( 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) % 0.70/0.92 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_mult__le__cancel1_1,axiom, % 0.70/0.92 ( 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) % 0.70/0.92 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_class__semiring_Opwr__pwr_0,axiom, % 0.70/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.92 | 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) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_nat_Oinducts_1,axiom, % 0.70/0.92 ( hBOOL(hAPP(V_P,V_nat)) % 0.70/0.92 | ~ hBOOL(hAPP(V_P,c_Suc(v_sko__Nat__Xnat__Xinducts__1(V_P)))) % 0.70/0.92 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_power__Suc2_0,axiom, % 0.70/0.92 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.70/0.92 | 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) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_power__Suc_0,axiom, % 0.70/0.92 ( ~ class_Power_Opower(T_a) % 0.70/0.92 | 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) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_class__semiring_Opwr__Suc_0,axiom, % 0.70/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.92 | 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) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_class__semiring_Osemiring__rules_I35_J_0,axiom, % 0.70/0.92 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.92 | 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) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_add__le__mono_0,axiom, % 0.70/0.92 ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_l),tc_nat) % 0.70/0.92 | ~ c_lessequals(V_k,V_l,tc_nat) % 0.70/0.92 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_add__mono_0,axiom, % 0.70/0.92 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 0.70/0.92 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a) % 0.70/0.92 | ~ c_lessequals(V_c,V_d,T_a) % 0.70/0.92 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_comm__monoid__add_Opower__Suc2_0,axiom, % 0.70/0.92 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.70/0.92 | c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),V_a,c_Suc(V_n),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),V_a,V_n,T_a)),V_a) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_comm__monoid__add_Opower__Suc_0,axiom, % 0.70/0.92 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.70/0.92 | c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),V_a,c_Suc(V_n),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),V_a,V_n,T_a)) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_less__Suc__eq__le_1,axiom, % 0.70/0.92 ( c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) % 0.70/0.92 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.70/0.92 % 0.70/0.92 cnf(cls_less__Suc__eq__le_0,axiom, % 0.70/0.92 ( c_lessequals(V_m,V_n,tc_nat) % 0.70/0.92 | ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ). % 0.70/0.92 % 0.70/0.93 cnf(cls_le__less__Suc__eq_1,axiom, % 0.70/0.93 ( ~ c_lessequals(V_x,V_x,tc_nat) % 0.70/0.93 | c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_class__semiring_Omul__c_0,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.93 | c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_nat__mult__commute_0,axiom, % 0.70/0.93 c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) = c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_add__nonneg__eq__0__iff_2,axiom, % 0.70/0.93 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.70/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.93 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.93 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_diff__less__Suc_0,axiom, % 0.70/0.93 c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_Suc(V_m),tc_nat) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_comm__monoid__add_Opower__add_0,axiom, % 0.70/0.93 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.70/0.93 | c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),V_a,V_m,T_a)),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),V_a,V_n,T_a)) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_comm__monoid__add_Opower__mult__distrib_0,axiom, % 0.70/0.93 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.70/0.93 | c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_n,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),V_a,V_n,T_a)),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),V_b,V_n,T_a)) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_mod__add__eq_0,axiom, % 0.70/0.93 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.93 | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(V_a,V_c,T_a)),c_Divides_Odiv__class_Omod(V_b,V_c,T_a)),V_c,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_add__nonneg__nonneg_0,axiom, % 0.70/0.93 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.70/0.93 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a) % 0.70/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_order__less__trans_0,axiom, % 0.70/0.93 ( ~ class_Orderings_Opreorder(T_a) % 0.70/0.93 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_xt1_I10_J_0,axiom, % 0.70/0.93 ( ~ class_Orderings_Oorder(T_a) % 0.70/0.93 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_typing__elims_I2_J_1,axiom, % 0.70/0.93 ( c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)) % 0.70/0.93 | ~ c_Type_Otyping(V_e,c_Lambda_OdB_OApp(V_t,V_u),V_T) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_min__max_Ole__iff__sup_0,axiom, % 0.70/0.93 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.93 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = V_y % 0.70/0.93 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_min__max_Ole__iff__sup_1,axiom, % 0.70/0.93 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.93 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) != V_y % 0.70/0.93 | c_lessequals(V_x,V_y,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_min__max_Osup__absorb1_0,axiom, % 0.70/0.93 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.93 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = V_x % 0.70/0.93 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_class__semiring_Oadd__a_0,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.93 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)),V_z) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_add__cancel__21_1,axiom, % 0.70/0.93 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.70/0.93 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_nat__add__left__commute_0,axiom, % 0.70/0.93 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_nat__add__assoc_0,axiom, % 0.70/0.93 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),V_k) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_comm__monoid__add_Omult__assoc_0,axiom, % 0.70/0.93 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.70/0.93 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom, % 0.70/0.93 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.70/0.93 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom, % 0.70/0.93 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a) % 0.70/0.93 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.93 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.93 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.93 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_d)) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.93 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_add__gr__0_0,axiom, % 0.70/0.93 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.70/0.93 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_power__add_0,axiom, % 0.70/0.93 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.70/0.93 | c_Power_Opower__class_Opower(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),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) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_min__max_Ole__sup__iff_2,axiom, % 0.70/0.93 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.93 | c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) % 0.70/0.93 | ~ c_lessequals(V_y,V_z,T_a) % 0.70/0.93 | ~ c_lessequals(V_x,V_z,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_min__max_Osup__least_0,axiom, % 0.70/0.93 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.93 | c_lessequals(c_Orderings_Oord__class_Omax(V_y,V_z,T_a),V_x,T_a) % 0.70/0.93 | ~ c_lessequals(V_z,V_x,T_a) % 0.70/0.93 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_min__max_Ole__supI_0,axiom, % 0.70/0.93 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.93 | c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) % 0.70/0.93 | ~ c_lessequals(V_b,V_x,T_a) % 0.70/0.93 | ~ c_lessequals(V_a,V_x,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_le__maxI1_0,axiom, % 0.70/0.93 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.93 | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_le__maxI2_0,axiom, % 0.70/0.93 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.93 | c_lessequals(V_y,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_bot__least_0,axiom, % 0.70/0.93 ( ~ class_Orderings_Obot(T_a) % 0.70/0.93 | c_lessequals(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_nat__rec__Suc_0,axiom, % 0.70/0.93 c_Nat_Onat_Onat__rec(V_f1,V_f2,c_Suc(V_nat),T_a) = hAPP(hAPP(V_f2,V_nat),c_Nat_Onat_Onat__rec(V_f1,V_f2,V_nat,T_a)) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_gb__semiring_Opwr__pwr_0,axiom, % 0.70/0.93 ( hAPP(hAPP(V_pwr,hAPP(hAPP(V_pwr,V_x),V_p)),V_q) = hAPP(hAPP(V_pwr,V_x),c_HOL_Otimes__class_Otimes(V_p,V_q,tc_nat)) % 0.70/0.93 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_min__max_Oinf__sup__distrib2_0,axiom, % 0.70/0.93 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.93 | 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) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_min__max_Oinf__sup__distrib1_0,axiom, % 0.70/0.93 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.93 | 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) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_Divides_Omod__div__equality_H_0,axiom, % 0.70/0.93 c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = c_HOL_Ominus__class_Ominus(V_m,c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat),V_n,tc_nat),tc_nat) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_add__increasing_0,axiom, % 0.70/0.93 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.70/0.93 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.70/0.93 | c_lessequals(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a) % 0.70/0.93 | ~ c_lessequals(V_b,V_c,T_a) % 0.70/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_add__increasing2_0,axiom, % 0.70/0.93 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.70/0.93 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.70/0.93 | c_lessequals(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a) % 0.70/0.93 | ~ c_lessequals(V_b,V_a,T_a) % 0.70/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_upt_Oinduct_1,axiom, % 0.70/0.93 ( hBOOL(hAPP(V_P,V_nat)) % 0.70/0.93 | ~ hBOOL(hAPP(V_P,c_Suc(v_sko__List__Xupt__Xinduct__1(V_P)))) % 0.70/0.93 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_type_Osimps_I1_J_0,axiom, % 0.70/0.93 ( c_Type_Otype_OAtom(V_nat) != c_Type_Otype_OAtom(V_nat_H) % 0.70/0.93 | V_nat = V_nat_H ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_replicate_Oinduct_1,axiom, % 0.70/0.93 ( hBOOL(hAPP(V_P,V_nat)) % 0.70/0.93 | ~ hBOOL(hAPP(V_P,c_Suc(v_sko__List__Xreplicate__Xinduct__1(V_P)))) % 0.70/0.93 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_Suc__leI_0,axiom, % 0.70/0.93 ( c_lessequals(c_Suc(V_m),V_n,tc_nat) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_Suc__le__eq_0,axiom, % 0.70/0.93 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.93 | ~ c_lessequals(c_Suc(V_m),V_n,tc_nat) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_less__eq__Suc__le_0,axiom, % 0.70/0.93 ( c_lessequals(c_Suc(V_n),V_m,tc_nat) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_less__eq__Suc__le_1,axiom, % 0.70/0.93 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 0.70/0.93 | ~ c_lessequals(c_Suc(V_n),V_m,tc_nat) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_termination__basic__simps_I1_J_0,axiom, % 0.70/0.93 ( c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_termination__basic__simps_I2_J_0,axiom, % 0.70/0.93 ( c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(V_x,V_z,tc_nat) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_add__lessD1_0,axiom, % 0.70/0.93 ( c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_k,tc_nat) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_trans__less__add1_0,axiom, % 0.70/0.93 ( c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_m),tc_nat) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_trans__less__add2_0,axiom, % 0.70/0.93 ( c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_j),tc_nat) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_le__add__iff2_1,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.70/0.93 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_e,T_a)),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_b,V_e,T_a)),V_d),T_a) % 0.70/0.93 | ~ c_lessequals(V_c,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a)),V_d),T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_le__add__iff2_0,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.70/0.93 | c_lessequals(V_c,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a)),V_d),T_a) % 0.70/0.93 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_e,T_a)),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_b,V_e,T_a)),V_d),T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_le__add__iff1_1,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.70/0.93 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_e,T_a)),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_b,V_e,T_a)),V_d),T_a) % 0.70/0.93 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a)),V_c),V_d,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_le__add__iff1_0,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.70/0.93 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a)),V_c),V_d,T_a) % 0.70/0.93 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_e,T_a)),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_b,V_e,T_a)),V_d),T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_Suc__diff__le_0,axiom, % 0.70/0.93 ( 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)) % 0.70/0.93 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_sum__squares__ge__zero_0,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.93 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a)),T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.93 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_comm__monoid__add_Omult__commute_0,axiom, % 0.70/0.93 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.70/0.93 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_nat__add__commute_0,axiom, % 0.70/0.93 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_less__add__eq__less_0,axiom, % 0.70/0.93 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_l) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat) % 0.70/0.93 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_class__semiring_Oadd__c_0,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.93 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_x) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_mult__eq__1__iff_0,axiom, % 0.70/0.93 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.70/0.93 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_mult__eq__1__iff_1,axiom, % 0.70/0.93 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.70/0.93 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_mod__le__divisor_0,axiom, % 0.70/0.93 ( c_lessequals(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_n,tc_nat) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_power_Opower_Opower__Suc_0,axiom, % 0.70/0.93 c_Power_Opower_Opower(V_one,V_times,V_a,c_Suc(V_n),T_a) = hAPP(hAPP(V_times,V_a),c_Power_Opower_Opower(V_one,V_times,V_a,V_n,T_a)) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_diff__less__mono2_0,axiom, % 0.70/0.93 ( 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) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(V_m,V_l,tc_nat) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_nat__induct_1,axiom, % 0.70/0.93 ( hBOOL(hAPP(V_P,V_n)) % 0.70/0.93 | ~ hBOOL(hAPP(V_P,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(V_P)))) % 0.70/0.93 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_of__nat__eq__iff_0,axiom, % 0.70/0.93 ( ~ class_Nat_Osemiring__char__0(T_a) % 0.70/0.93 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) % 0.70/0.93 | V_m = V_n ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_div__le__mono2_0,axiom, % 0.70/0.93 ( c_lessequals(c_Divides_Odiv__class_Odiv(V_k,V_n,tc_nat),c_Divides_Odiv__class_Odiv(V_k,V_m,tc_nat),tc_nat) % 0.70/0.93 | ~ c_lessequals(V_m,V_n,tc_nat) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_mod__div__trivial_0,axiom, % 0.70/0.93 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.93 | 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) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_div__if_0,axiom, % 0.70/0.93 ( c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_mult__less__imp__less__right_0,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.70/0.93 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.70/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.93 | ~ 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) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_mult__less__imp__less__left_0,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.70/0.93 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.70/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.93 | ~ 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) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_mult__right__less__imp__less_0,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 0.70/0.93 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.70/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.93 | ~ 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) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_mult__left__less__imp__less_0,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Oordered__semiring(T_a) % 0.70/0.93 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.70/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.93 | ~ 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) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_mod__mult__eq_0,axiom, % 0.70/0.93 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.93 | 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) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_power__commutes_0,axiom, % 0.70/0.93 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.70/0.93 | 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) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_split__div_H_7,axiom, % 0.70/0.93 ( hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat))) % 0.70/0.93 | ~ hBOOL(hAPP(V_P,V_x)) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Otimes__class_Otimes(V_n,c_Suc(V_x),tc_nat),tc_nat) % 0.70/0.93 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_n,V_x,tc_nat),V_m,tc_nat) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_le__max__iff__disj_0,axiom, % 0.70/0.93 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.93 | c_lessequals(V_z,V_y,T_a) % 0.70/0.93 | c_lessequals(V_z,V_x,T_a) % 0.70/0.93 | ~ c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_class__semiring_Omul__pwr_0,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.93 | 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,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_p),V_q),T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_ex__least__nat__le_0,axiom, % 0.70/0.93 ( c_lessequals(c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1(V_P,V_n),V_n,tc_nat) % 0.70/0.93 | ~ hBOOL(hAPP(V_P,V_n)) % 0.70/0.93 | hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_gb__semiring_Omul__pwr_0,axiom, % 0.70/0.93 ( hAPP(hAPP(V_mul,hAPP(hAPP(V_pwr,V_x),V_p)),hAPP(hAPP(V_pwr,V_x),V_q)) = hAPP(hAPP(V_pwr,V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_p),V_q)) % 0.70/0.93 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_liftn__lift_0,axiom, % 0.70/0.93 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) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_nat__eq__add__iff1_1,axiom, % 0.70/0.93 ( ~ c_lessequals(V_j,V_i,tc_nat) % 0.70/0.93 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),V_m) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat)),V_m)) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_Var__IT_0,axiom, % 0.70/0.93 c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_min__max_Ole__inf__iff_1,axiom, % 0.70/0.93 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.93 | c_lessequals(V_x,V_z,T_a) % 0.70/0.93 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_min__max_Ole__inf__iff_0,axiom, % 0.70/0.93 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.93 | c_lessequals(V_x,V_y,T_a) % 0.70/0.93 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_min__le__iff__disj_2,axiom, % 0.70/0.93 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.93 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 0.70/0.93 | ~ c_lessequals(V_y,V_z,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_min__le__iff__disj_1,axiom, % 0.70/0.93 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.93 | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 0.70/0.93 | ~ c_lessequals(V_x,V_z,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_min__max_Ole__infI2_0,axiom, % 0.70/0.93 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.93 | c_lessequals(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 0.70/0.93 | ~ c_lessequals(V_b,V_x,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_min__max_Ole__infI1_0,axiom, % 0.70/0.93 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.93 | c_lessequals(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 0.70/0.93 | ~ c_lessequals(V_a,V_x,T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_min__max_Ole__infE_1,axiom, % 0.70/0.93 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.93 | c_lessequals(V_x,V_b,T_a) % 0.70/0.93 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_min__max_Ole__infE_0,axiom, % 0.70/0.93 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.93 | c_lessequals(V_x,V_a,T_a) % 0.70/0.93 | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_div__mult__self2_0,axiom, % 0.70/0.93 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.93 | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a)),V_b,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)) % 0.70/0.93 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_div__mult__self1_0,axiom, % 0.70/0.93 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.93 | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a)),V_b,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)) % 0.70/0.93 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_div__if_1,axiom, % 0.70/0.93 ( c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat) = c_Suc(c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat)) % 0.70/0.93 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_add__nonneg__eq__0__iff_1,axiom, % 0.70/0.93 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.70/0.93 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) != c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 0.70/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 0.70/0.93 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_add__nonneg__eq__0__iff_0,axiom, % 0.70/0.93 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.70/0.93 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) != c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 0.70/0.93 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 0.70/0.93 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_Suc__inject_0,axiom, % 0.70/0.93 ( c_Suc(V_x) != c_Suc(V_y) % 0.70/0.93 | V_x = V_y ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_nat_Oinject_0,axiom, % 0.70/0.93 ( c_Suc(V_nat) != c_Suc(V_nat_H) % 0.70/0.93 | V_nat = V_nat_H ) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_dB_Osimps_I6_J_0,axiom, % 0.70/0.93 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ). % 0.70/0.93 % 0.70/0.93 cnf(cls_less__add__iff2_1,axiom, % 0.70/0.93 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.70/0.93 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_e,T_a)),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_b,V_e,T_a)),V_d),T_a) % 0.70/0.93 | ~ c_HOL_Oord__class_Oless(V_c,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a)),V_d),T_a) ) ). % 0.70/0.93 % 0.70/0.94 cnf(cls_less__add__iff2_0,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(V_c,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a)),V_d),T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_e,T_a)),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_b,V_e,T_a)),V_d),T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_less__add__iff1_1,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_e,T_a)),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_b,V_e,T_a)),V_d),T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a)),V_c),V_d,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_less__add__iff1_0,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a)),V_c),V_d,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_e,T_a)),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_b,V_e,T_a)),V_d),T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_le__mod__geq_0,axiom, % 0.70/0.94 ( c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat) % 0.70/0.94 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_nat__eq__add__iff1_0,axiom, % 0.70/0.94 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),V_m) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),V_n) % 0.70/0.94 | ~ c_lessequals(V_j,V_i,tc_nat) % 0.70/0.94 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat)),V_m) = V_n ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_nat__eq__add__iff2_0,axiom, % 0.70/0.94 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),V_m) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),V_n) % 0.70/0.94 | ~ c_lessequals(V_i,V_j,tc_nat) % 0.70/0.94 | V_m = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat)),V_n) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__le__iff__disj_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_lessequals(V_y,V_z,T_a) % 0.70/0.94 | c_lessequals(V_x,V_z,T_a) % 0.70/0.94 | ~ c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_nat__eq__add__iff2_1,axiom, % 0.70/0.94 ( ~ c_lessequals(V_i,V_j,tc_nat) % 0.70/0.94 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat)),V_n)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),V_n) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mod__add__cong_0,axiom, % 0.70/0.94 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.94 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 0.70/0.94 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 0.70/0.94 | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_less__Suc0_1,axiom, % 0.70/0.94 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom, % 0.70/0.94 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom, % 0.70/0.94 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_even__less__0__iff_0,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_even__less__0__iff_1,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_one__is__add_1,axiom, % 0.70/0.94 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) % 0.70/0.94 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.70/0.94 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_one__is__add_2,axiom, % 0.70/0.94 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) % 0.70/0.94 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.94 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_zero__less__mult__pos2_0,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.70/0.94 | ~ 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) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_zero__less__mult__pos_0,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.70/0.94 | ~ 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) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mult__pos__pos_0,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.70/0.94 | 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) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mult__neg__neg_0,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.94 | 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) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_nat__0__less__mult__iff_2,axiom, % 0.70/0.94 ( 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) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_power__less__imp__less__base_0,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.70/0.94 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.94 | ~ 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) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__max_Ole__sup__iff_1,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_lessequals(V_y,V_z,T_a) % 0.70/0.94 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_one__le__mult__iff_1,axiom, % 0.70/0.94 ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) % 0.70/0.94 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_one__le__mult__iff_0,axiom, % 0.70/0.94 ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 0.70/0.94 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_add__cancel__21_0,axiom, % 0.70/0.94 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.70/0.94 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_u) % 0.70/0.94 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z) = V_u ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_trans__le__add2_0,axiom, % 0.70/0.94 ( c_lessequals(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_j),tc_nat) % 0.70/0.94 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_trans__le__add1_0,axiom, % 0.70/0.94 ( c_lessequals(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_m),tc_nat) % 0.70/0.94 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_add__leE_1,axiom, % 0.70/0.94 ( c_lessequals(V_k,V_n,tc_nat) % 0.70/0.94 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k),V_n,tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_add__leE_0,axiom, % 0.70/0.94 ( c_lessequals(V_m,V_n,tc_nat) % 0.70/0.94 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k),V_n,tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_termination__basic__simps_I4_J_0,axiom, % 0.70/0.94 ( c_lessequals(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat) % 0.70/0.94 | ~ c_lessequals(V_x,V_z,tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_termination__basic__simps_I3_J_0,axiom, % 0.70/0.94 ( c_lessequals(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat) % 0.70/0.94 | ~ c_lessequals(V_x,V_y,tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mod__diff__left__eq_0,axiom, % 0.70/0.94 ( ~ class_Divides_Oring__div(T_a) % 0.70/0.94 | 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) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mod__diff__right__eq_0,axiom, % 0.70/0.94 ( ~ class_Divides_Oring__div(T_a) % 0.70/0.94 | 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) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__max_Ole__iff__inf_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = V_x % 0.70/0.94 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__max_Ole__iff__inf_1,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) != V_x % 0.70/0.94 | c_lessequals(V_x,V_y,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__max_Oinf__absorb2_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = V_y % 0.70/0.94 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_max__diff__distrib__left_0,axiom, % 0.70/0.94 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.70/0.94 | 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) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mod__less__divisor_0,axiom, % 0.70/0.94 ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_n,tc_nat) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_not__leE_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.70/0.94 | c_lessequals(V_y,V_x,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_linorder__antisym__conv2_1,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | ~ c_lessequals(V_x,V_x,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_linorder__antisym__conv1_1,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(V_x,V_x,T_a) % 0.70/0.94 | c_lessequals(V_x,V_x,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_linorder__not__less_1,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.70/0.94 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_linorder__not__less_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_lessequals(V_y,V_x,T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_linorder__not__le_1,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | ~ c_lessequals(V_x,V_y,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_linorder__not__le_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.70/0.94 | c_lessequals(V_x,V_y,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_less__le__not__le_1,axiom, % 0.70/0.94 ( ~ class_Orderings_Opreorder(T_a) % 0.70/0.94 | ~ c_lessequals(V_y,V_x,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_infinite__descent0_0,axiom, % 0.70/0.94 ( hBOOL(hAPP(V_P,V_n)) % 0.70/0.94 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(V_P),tc_nat) % 0.70/0.94 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_subst__Var_1,axiom, % 0.70/0.94 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 0.70/0.94 | c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_of__nat__aux_Osimps_I2_J_0,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.70/0.94 | c_Nat_Osemiring__1__class_Oof__nat__aux(V_inc,c_Suc(V_n),V_i,T_a) = c_Nat_Osemiring__1__class_Oof__nat__aux(V_inc,V_n,hAPP(V_inc,V_i),T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mod__add__left__eq_0,axiom, % 0.70/0.94 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.94 | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(V_a,V_c,T_a)),V_b),V_c,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mod__add__right__eq_0,axiom, % 0.70/0.94 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.94 | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a)),V_c,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_type__induct_2,axiom, % 0.70/0.94 ( hBOOL(hAPP(V_P,V_T)) % 0.70/0.94 | ~ hBOOL(hAPP(V_P,c_Type_Osko__Type__Xtype__induct__1__1(V_P))) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__max_Oinf__assoc_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | 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) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__max_Oinf__left__commute_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | 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) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_one__is__add_5,axiom, % 0.70/0.94 c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_add__strict__increasing2_0,axiom, % 0.70/0.94 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.70/0.94 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 0.70/0.94 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_diff__le__mono2_0,axiom, % 0.70/0.94 ( 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) % 0.70/0.94 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_diff__le__mono_0,axiom, % 0.70/0.94 ( 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) % 0.70/0.94 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_le__diff__iff_1,axiom, % 0.70/0.94 ( 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) % 0.70/0.94 | ~ c_lessequals(V_m,V_n,tc_nat) % 0.70/0.94 | ~ c_lessequals(V_k,V_n,tc_nat) % 0.70/0.94 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_le__diff__iff_0,axiom, % 0.70/0.94 ( c_lessequals(V_m,V_n,tc_nat) % 0.70/0.94 | ~ 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) % 0.70/0.94 | ~ c_lessequals(V_k,V_n,tc_nat) % 0.70/0.94 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_diff__add__0_0,axiom, % 0.70/0.94 c_HOL_Ominus__class_Ominus(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_diff__diff__left_0,axiom, % 0.70/0.94 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,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k),tc_nat) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_power__mono_0,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.70/0.94 | 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) % 0.70/0.94 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.70/0.94 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_eq__eqI_1,axiom, % 0.70/0.94 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.70/0.94 | c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) % 0.70/0.94 | V_xa = V_y ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_eq__eqI_0,axiom, % 0.70/0.94 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.70/0.94 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 0.70/0.94 | V_x_H = V_y_H ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_eq__diff__iff_0,axiom, % 0.70/0.94 ( c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat) != c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat) % 0.70/0.94 | ~ c_lessequals(V_k,V_n,tc_nat) % 0.70/0.94 | ~ c_lessequals(V_k,V_m,tc_nat) % 0.70/0.94 | V_m = V_n ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__max_Oinf__sup__absorb_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) = V_x ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_nat__mult__eq__cancel1_0,axiom, % 0.70/0.94 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.70/0.94 | V_m = V_n ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_one__is__add_3,axiom, % 0.70/0.94 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) % 0.70/0.94 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.70/0.94 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_one__is__add_0,axiom, % 0.70/0.94 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) % 0.70/0.94 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.94 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mult__less__cancel2_0,axiom, % 0.70/0.94 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.70/0.94 | ~ 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) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mult__less__cancel1_0,axiom, % 0.70/0.94 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.70/0.94 | ~ 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) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_add__Suc__shift_0,axiom, % 0.70/0.94 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mult__le__cancel2_0,axiom, % 0.70/0.94 ( c_lessequals(V_m,V_n,tc_nat) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.70/0.94 | ~ 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) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mult__le__cancel1_0,axiom, % 0.70/0.94 ( c_lessequals(V_m,V_n,tc_nat) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.70/0.94 | ~ 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) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_nat__mult__le__cancel1_0,axiom, % 0.70/0.94 ( c_lessequals(V_m,V_n,tc_nat) % 0.70/0.94 | ~ 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) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_nat__mult__le__cancel1_1,axiom, % 0.70/0.94 ( 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) % 0.70/0.94 | ~ c_lessequals(V_m,V_n,tc_nat) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mult__le__cancel__left__neg_0,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.94 | c_lessequals(V_b,V_a,T_a) % 0.70/0.94 | ~ 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) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mult__le__cancel__left__neg_1,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.94 | 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) % 0.70/0.94 | ~ c_lessequals(V_b,V_a,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mult__le__cancel__left__pos_0,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.94 | c_lessequals(V_a,V_b,T_a) % 0.70/0.94 | ~ 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) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mult__le__cancel__left__pos_1,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.94 | 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) % 0.70/0.94 | ~ c_lessequals(V_a,V_b,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mult__left__le__imp__le_0,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.70/0.94 | c_lessequals(V_a,V_b,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.94 | ~ 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) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mult__right__le__imp__le_0,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.70/0.94 | c_lessequals(V_a,V_b,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.94 | ~ 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) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_one__less__mult_0,axiom, % 0.70/0.94 ( 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) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_diff__cancel2_0,axiom, % 0.70/0.94 c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_diff__cancel_0,axiom, % 0.70/0.94 c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_zero__less__Suc_0,axiom, % 0.70/0.94 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_gr0__conv__Suc_1,axiom, % 0.70/0.94 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__max_Oless__supI1_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_x,V_a,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__max_Oless__supI2_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_x,V_b,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_less__max__iff__disj_1,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_less__max__iff__disj_2,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_max__less__iff__conj_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_max__less__iff__conj_1,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__max_Oinf__commute_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = c_Orderings_Oord__class_Omin(V_y,V_x,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_left__add__mult__distrib_0,axiom, % 0.70/0.94 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),V_k)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_u,tc_nat)),V_k) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_combine__common__factor_0,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Osemiring(T_a) % 0.70/0.94 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_e,T_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_b,V_e,T_a)),V_c)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_e,T_a)),V_c) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_diff__le__self_0,axiom, % 0.70/0.94 c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_nat__0__less__mult__iff_1,axiom, % 0.70/0.94 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.70/0.94 | ~ 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) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_nat__0__less__mult__iff_0,axiom, % 0.70/0.94 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 0.70/0.94 | ~ 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) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_add__neg__neg_0,axiom, % 0.70/0.94 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_power__strict__mono_0,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.70/0.94 | 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) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.70/0.94 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_sum__squares__le__zero__iff_0,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.94 | V_x = c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.94 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a)),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_sum__squares__le__zero__iff_1,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.94 | V_y = c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.94 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a)),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_nat_Osplit__asm_1,axiom, % 0.70/0.94 ( ~ hBOOL(hAPP(V_P,c_Nat_Onat_Onat__case(V_f1,V_f2,c_Suc(V_xa),t_a))) % 0.70/0.94 | hBOOL(hAPP(V_P,hAPP(V_f2,V_xa))) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_nat_Osplit_1,axiom, % 0.70/0.94 ( ~ hBOOL(hAPP(V_P,c_Nat_Onat_Onat__case(V_f1,V_f2,c_Suc(V_nat),t_a))) % 0.70/0.94 | hBOOL(hAPP(V_P,hAPP(V_f2,V_nat))) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_diff__mult__distrib2_0,axiom, % 0.70/0.94 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) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_diff__mult__distrib_0,axiom, % 0.70/0.94 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) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__max_Oless__infI1_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_a,V_x,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__max_Oless__infI2_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_b,V_x,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__less__iff__conj_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__less__iff__conj_1,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__less__iff__disj_1,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_x,V_z,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__less__iff__disj_2,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_Nat_Odiff__diff__eq_0,axiom, % 0.70/0.94 ( 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) % 0.70/0.94 | ~ c_lessequals(V_k,V_n,tc_nat) % 0.70/0.94 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_diff__commute_0,axiom, % 0.70/0.94 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) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_add__nonneg__pos_0,axiom, % 0.70/0.94 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.94 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_add__pos__nonneg_0,axiom, % 0.70/0.94 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.70/0.94 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a) % 0.70/0.94 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_comm__monoid__add_Opower__mult_0,axiom, % 0.70/0.94 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.70/0.94 | c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),V_a,V_m,T_a),V_n,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_diff__less__mono_0,axiom, % 0.70/0.94 ( 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) % 0.70/0.94 | ~ c_lessequals(V_c,V_a,tc_nat) % 0.70/0.94 | ~ c_HOL_Oord__class_Oless(V_a,V_b,tc_nat) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mult__le__0__iff_4,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.94 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.94 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.94 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_mult__le__0__iff_5,axiom, % 0.70/0.94 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.94 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.94 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.94 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__max_Ole__sup__iff_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_lessequals(V_x,V_z,T_a) % 0.70/0.94 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_le__max__iff__disj_2,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 0.70/0.94 | ~ c_lessequals(V_z,V_y,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_le__max__iff__disj_1,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 0.70/0.94 | ~ c_lessequals(V_z,V_x,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__max_Ole__supI2_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 0.70/0.94 | ~ c_lessequals(V_x,V_b,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__max_Ole__supI1_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 0.70/0.94 | ~ c_lessequals(V_x,V_a,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__max_Ole__supE_1,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_lessequals(V_b,V_x,T_a) % 0.70/0.94 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_min__max_Ole__supE_0,axiom, % 0.70/0.94 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.94 | c_lessequals(V_a,V_x,T_a) % 0.70/0.94 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) ) ). % 0.70/0.94 % 0.70/0.94 cnf(cls_le__diff__conv_0,axiom, % 0.70/0.94 ( c_lessequals(V_j,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),tc_nat) % 0.70/0.94 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) ) ). % 0.70/0.94 % 0.70/0.95 cnf(cls_le__diff__conv_1,axiom, % 0.70/0.95 ( c_lessequals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) % 0.70/0.95 | ~ c_lessequals(V_j,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_zero__less__power_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.70/0.95 | 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) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_less__max__iff__disj_0,axiom, % 0.70/0.95 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mult__Suc__right_0,axiom, % 0.70/0.95 c_HOL_Otimes__class_Otimes(V_m,c_Suc(V_n),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mult__Suc_0,axiom, % 0.70/0.95 c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_split__div_1,axiom, % 0.70/0.95 ( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) % 0.70/0.95 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.95 | ~ hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat)),V_j),V_k,tc_nat))) % 0.70/0.95 | hBOOL(hAPP(V_P,V_i)) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_nat__case__Suc_0,axiom, % 0.70/0.95 c_Nat_Onat_Onat__case(V_f1,V_f2,c_Suc(V_nat),T_a) = hAPP(V_f2,V_nat) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_App_I2_J_0,axiom, % 0.70/0.95 c_InductTermi_OIT(v_s____) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_dB_Osimps_I3_J_0,axiom, % 0.70/0.95 ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H) % 0.70/0.95 | V_dB = V_dB_H ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_not__sum__squares__lt__zero_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a)),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_nat__le__add__iff1_0,axiom, % 0.70/0.95 ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat)),V_m),V_n,tc_nat) % 0.70/0.95 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),V_n),tc_nat) % 0.70/0.95 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_nat__le__add__iff1_1,axiom, % 0.70/0.95 ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),V_n),tc_nat) % 0.70/0.95 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat)),V_m),V_n,tc_nat) % 0.70/0.95 | ~ c_lessequals(V_j,V_i,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_nat__le__add__iff2_0,axiom, % 0.70/0.95 ( c_lessequals(V_m,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat)),V_n),tc_nat) % 0.70/0.95 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),V_n),tc_nat) % 0.70/0.95 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_nat__le__add__iff2_1,axiom, % 0.70/0.95 ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),V_n),tc_nat) % 0.70/0.95 | ~ c_lessequals(V_m,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat)),V_n),tc_nat) % 0.70/0.95 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_of__nat__mult_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.70/0.95 | 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) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mod__mult__self4_0,axiom, % 0.70/0.95 c_Divides_Odiv__class_Omod(c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)),V_m)),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_min__less__iff__disj_0,axiom, % 0.70/0.95 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_class__ringb_Oadd__mul__solve_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.70/0.95 | ~ class_Int_Onumber__ring(T_a) % 0.70/0.95 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_w,V_y,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_w,V_z,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a)) % 0.70/0.95 | V_y = V_z % 0.70/0.95 | V_w = V_x ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_class__ringb_Onoteq__reduce_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.70/0.95 | ~ class_Int_Onumber__ring(T_a) % 0.70/0.95 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_c,T_a)),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_d,T_a)),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a)) % 0.70/0.95 | V_c = V_d % 0.70/0.95 | V_a = V_b ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_natgb_Onoteq__reduce_0,axiom, % 0.70/0.95 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_a,V_c,tc_nat)),c_HOL_Otimes__class_Otimes(V_b,V_d,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_a,V_d,tc_nat)),c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat)) % 0.70/0.95 | V_c = V_d % 0.70/0.95 | V_a = V_b ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_natgb_Oadd__mul__solve_0,axiom, % 0.70/0.95 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_w,V_y,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_w,V_z,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat)) % 0.70/0.95 | V_y = V_z % 0.70/0.95 | V_w = V_x ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_diff__Suc__Suc_0,axiom, % 0.70/0.95 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) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_dB_Osimps_I4_J_0,axiom, % 0.70/0.95 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_add__nonpos__neg_0,axiom, % 0.70/0.95 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.95 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_add__neg__nonpos_0,axiom, % 0.70/0.95 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.95 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_div__mult__self2__is__id_0,axiom, % 0.70/0.95 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.95 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = V_a % 0.70/0.95 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_div__mult__self1__is__id_0,axiom, % 0.70/0.95 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.95 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = V_a % 0.70/0.95 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_less__SucE_0,axiom, % 0.70/0.95 ( V_m = V_n % 0.70/0.95 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_less__antisym_0,axiom, % 0.70/0.95 ( V_m = V_n % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_not__less__less__Suc__eq_0,axiom, % 0.70/0.95 ( V_n = V_m % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_sum__squares__le__zero__iff_2,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.95 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),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)),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mod__mult__cong_0,axiom, % 0.70/0.95 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.95 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 0.70/0.95 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 0.70/0.95 | 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) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_diff__add__assoc_0,axiom, % 0.70/0.95 ( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_k,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)) % 0.70/0.95 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_diff__add__assoc2_0,axiom, % 0.70/0.95 ( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_k,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),V_i) % 0.70/0.95 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mult__eq__1__iff_2,axiom, % 0.70/0.95 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)) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.95 | 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) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.95 | 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) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.95 | 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) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mult__div__cancel_0,axiom, % 0.70/0.95 c_HOL_Otimes__class_Otimes(V_n,c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),tc_nat) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_div__mod__equality_H_0,axiom, % 0.70/0.95 c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat),V_n,tc_nat) = c_HOL_Ominus__class_Ominus(V_m,c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),tc_nat) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_diff__diff__right_0,axiom, % 0.70/0.95 ( 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(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat) % 0.70/0.95 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mod__1_0,axiom, % 0.70/0.95 c_Divides_Odiv__class_Omod(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_comm__monoid__add_Opower__one_0,axiom, % 0.70/0.95 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.70/0.95 | c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_less__imp__diff__less_0,axiom, % 0.70/0.95 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_type_Orecs_I1_J_0,axiom, % 0.70/0.95 c_Type_Otype_Otype__rec(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),T_a) = hAPP(V_f1,V_nat) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_lexn_Oinduct_1,axiom, % 0.70/0.95 ( hBOOL(hAPP(V_P,V_nat)) % 0.70/0.95 | ~ hBOOL(hAPP(V_P,c_Suc(v_sko__List__Xlexn__Xinduct__1(V_P)))) % 0.70/0.95 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mod__if_0,axiom, % 0.70/0.95 ( c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = V_m % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_one__is__add_4,axiom, % 0.70/0.95 c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_less__le__not__le_2,axiom, % 0.70/0.95 ( ~ class_Orderings_Opreorder(T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.70/0.95 | c_lessequals(V_y,V_x,T_a) % 0.70/0.95 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_nat__less__le_1,axiom, % 0.70/0.95 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_less__not__refl_0,axiom, % 0.70/0.95 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_order__less__le_1,axiom, % 0.70/0.95 ( ~ class_Orderings_Oorder(T_a) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_linorder__neq__iff_1,axiom, % 0.70/0.95 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_order__less__irrefl_0,axiom, % 0.70/0.95 ( ~ class_Orderings_Opreorder(T_a) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_le__imp__diff__is__add_1,axiom, % 0.70/0.95 ( ~ c_lessequals(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_i),tc_nat) % 0.70/0.95 | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_i),V_i,tc_nat) = V_k ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_min__max_Oinf__idem_0,axiom, % 0.70/0.95 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.95 | c_Orderings_Oord__class_Omin(V_x,V_x,T_a) = V_x ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_liftn_Osimps_I1_J_1,axiom, % 0.70/0.95 ( c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_n)) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_beta_0,axiom, % 0.70/0.95 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))) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_add__pos__pos_0,axiom, % 0.70/0.95 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_le__add1_0,axiom, % 0.70/0.95 c_lessequals(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),tc_nat) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_le__add2_0,axiom, % 0.70/0.95 c_lessequals(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_le__iff__add_1,axiom, % 0.70/0.95 c_lessequals(V_m,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_x),tc_nat) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_nat__minus__add__max_0,axiom, % 0.70/0.95 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat)),V_m) = c_Orderings_Oord__class_Omax(V_n,V_m,tc_nat) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_linorder__neqE__ordered__idom_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.70/0.95 | V_x = V_y ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_not__less__iff__gr__or__eq_0,axiom, % 0.70/0.95 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.95 | V_x = V_y % 0.70/0.95 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_le__antisym_0,axiom, % 0.70/0.95 ( V_m = V_n % 0.70/0.95 | ~ c_lessequals(V_n,V_m,tc_nat) % 0.70/0.95 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_nat__neq__iff_0,axiom, % 0.70/0.95 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.95 | V_m = V_n ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_nat__less__cases_0,axiom, % 0.70/0.95 ( hBOOL(hAPP(hAPP(V_P,V_n),V_m)) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 0.70/0.95 | V_m = V_n % 0.70/0.95 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_linorder__neqE__nat_0,axiom, % 0.70/0.95 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 0.70/0.95 | V_x = V_y ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_order__eq__iff_2,axiom, % 0.70/0.95 ( ~ class_Orderings_Oorder(T_a) % 0.70/0.95 | V_x = V_y % 0.70/0.95 | ~ c_lessequals(V_y,V_x,T_a) % 0.70/0.95 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_linorder__neqE_0,axiom, % 0.70/0.95 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.70/0.95 | V_x = V_y ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_order__antisym_0,axiom, % 0.70/0.95 ( ~ class_Orderings_Oorder(T_a) % 0.70/0.95 | V_x = V_y % 0.70/0.95 | ~ c_lessequals(V_y,V_x,T_a) % 0.70/0.95 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_order__antisym__conv_0,axiom, % 0.70/0.95 ( ~ class_Orderings_Oorder(T_a) % 0.70/0.95 | V_x = V_y % 0.70/0.95 | ~ c_lessequals(V_x,V_y,T_a) % 0.70/0.95 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_linorder__less__linear_0,axiom, % 0.70/0.95 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.70/0.95 | V_x = V_y % 0.70/0.95 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_linorder__antisym__conv3_0,axiom, % 0.70/0.95 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.95 | V_x = V_y % 0.70/0.95 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mod__diff__cong_0,axiom, % 0.70/0.95 ( ~ class_Divides_Oring__div(T_a) % 0.70/0.95 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 0.70/0.95 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 0.70/0.95 | 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) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_le__iff__diff__le__0_1,axiom, % 0.70/0.95 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.70/0.95 | c_lessequals(V_a,V_b,T_a) % 0.70/0.95 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_le__iff__diff__le__0_0,axiom, % 0.70/0.95 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.70/0.95 | c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.95 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_min__max_Osup__idem_0,axiom, % 0.70/0.95 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.95 | c_Orderings_Oord__class_Omax(V_x,V_x,T_a) = V_x ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_dB_Osimps_I2_J_1,axiom, % 0.70/0.95 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) % 0.70/0.95 | V_dB2 = V_dB2_H ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_dB_Osimps_I2_J_0,axiom, % 0.70/0.95 ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) % 0.70/0.95 | V_dB1 = V_dB1_H ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_add__strict__mono_0,axiom, % 0.70/0.95 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_add__less__mono_0,axiom, % 0.70/0.95 ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_l),tc_nat) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_termination__basic__simps_I5_J_0,axiom, % 0.70/0.95 ( c_lessequals(V_x,V_y,tc_nat) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_nat__less__le_0,axiom, % 0.70/0.95 ( c_lessequals(V_m,V_n,tc_nat) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_order__le__less_1,axiom, % 0.70/0.95 ( ~ class_Orderings_Oorder(T_a) % 0.70/0.95 | c_lessequals(V_x,V_y,T_a) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_order__less__imp__le_0,axiom, % 0.70/0.95 ( ~ class_Orderings_Opreorder(T_a) % 0.70/0.95 | c_lessequals(V_x,V_y,T_a) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_beta__cases_I1_J_0,axiom, % 0.70/0.95 ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_diff__Suc__diff__eq1_0,axiom, % 0.70/0.95 ( 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(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k),c_Suc(V_j),tc_nat) % 0.70/0.95 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_less__iff__diff__less__0_1,axiom, % 0.70/0.95 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.70/0.95 | ~ 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) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_less__iff__diff__less__0_0,axiom, % 0.70/0.95 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.70/0.95 | 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) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_of__nat__less__iff_1,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.70/0.95 | 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) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_split__mult__neg__le_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 0.70/0.95 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.95 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.95 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_split__mult__neg__le_1,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 0.70/0.95 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.95 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.95 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mult__nonneg__nonpos_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 0.70/0.95 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.95 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.95 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mult__nonpos__nonneg_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 0.70/0.95 | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.95 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.95 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mult__nonneg__nonpos2_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 0.70/0.95 | c_lessequals(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.95 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.95 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_not__square__less__zero_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.95 | ~ 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) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_Suc__mult__less__cancel1_1,axiom, % 0.70/0.95 ( 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) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_Suc__mult__less__cancel1_0,axiom, % 0.70/0.95 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.95 | ~ 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) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_Suc__lessI_0,axiom, % 0.70/0.95 ( c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) % 0.70/0.95 | c_Suc(V_m) = V_n % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_not__less__eq__eq_1,axiom, % 0.70/0.95 ( ~ c_lessequals(V_m,V_n,tc_nat) % 0.70/0.95 | ~ c_lessequals(c_Suc(V_n),V_m,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_not__less__eq__eq_0,axiom, % 0.70/0.95 ( c_lessequals(c_Suc(V_n),V_m,tc_nat) % 0.70/0.95 | c_lessequals(V_m,V_n,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_natgb_Oadd__cancel_0,axiom, % 0.70/0.95 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_y) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z) % 0.70/0.95 | V_y = V_z ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_nat__add__right__cancel_0,axiom, % 0.70/0.95 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k) % 0.70/0.95 | V_m = V_n ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_nat__add__left__cancel_0,axiom, % 0.70/0.95 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n) % 0.70/0.95 | V_m = V_n ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_class__ringb_Oadd__cancel_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.70/0.95 | ~ class_Int_Onumber__ring(T_a) % 0.70/0.95 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z) % 0.70/0.95 | V_y = V_z ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_add__imp__eq_0,axiom, % 0.70/0.95 ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a) % 0.70/0.95 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c) % 0.70/0.95 | V_b = V_c ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_add__left__cancel_0,axiom, % 0.70/0.95 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 0.70/0.95 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c) % 0.70/0.95 | V_b = V_c ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_add__right__cancel_0,axiom, % 0.70/0.95 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 0.70/0.95 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a) % 0.70/0.95 | V_b = V_c ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mod__less__eq__dividend_0,axiom, % 0.70/0.95 c_lessequals(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_m,tc_nat) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_min__add__distrib__left_0,axiom, % 0.70/0.95 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.70/0.95 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Orderings_Oord__class_Omin(V_x,V_y,T_a)),V_z) = c_Orderings_Oord__class_Omin(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z),T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_le__add__diff_0,axiom, % 0.70/0.95 ( c_lessequals(V_m,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_k,tc_nat),tc_nat) % 0.70/0.95 | ~ c_lessequals(V_k,V_n,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mod__diff__eq_0,axiom, % 0.70/0.95 ( ~ class_Divides_Oring__div(T_a) % 0.70/0.95 | 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) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Opwr__mul_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_pwr,hAPP(hAPP(V_mul,V_x),V_y)),V_q) = hAPP(hAPP(V_mul,hAPP(hAPP(V_pwr,V_x),V_q)),hAPP(hAPP(V_pwr,V_y),V_q)) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Omul__d_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_add,V_y),V_z)) = hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_x),V_y)),hAPP(hAPP(V_mul,V_x),V_z)) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Omul__c_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_mul,V_x),V_y) = hAPP(hAPP(V_mul,V_y),V_x) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Omul__a_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_mul,V_y),V_z)) = hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_x),V_y)),V_z) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Omul__1_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_mul,V_r1),V_x) = V_x % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Omul__0_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_mul,V_r0),V_x) = V_r0 % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Oadd__c_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_add,V_x),V_y) = hAPP(hAPP(V_add,V_y),V_x) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Oadd__a_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_add,V_x),hAPP(hAPP(V_add,V_y),V_z)) = hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_x),V_y)),V_z) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Oadd__0_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_add,V_r0),V_x) = V_x % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I25_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_add,V_a),hAPP(hAPP(V_add,V_c),V_d)) = hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_c)),V_d) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I24_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_add,V_a),V_c) = hAPP(hAPP(V_add,V_c),V_a) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I23_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_b)),V_c) = hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_c)),V_b) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I22_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_add,V_a),hAPP(hAPP(V_add,V_c),V_d)) = hAPP(hAPP(V_add,V_c),hAPP(hAPP(V_add,V_a),V_d)) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I21_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_b)),V_c) = hAPP(hAPP(V_add,V_a),hAPP(hAPP(V_add,V_b),V_c)) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I20_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_b)),hAPP(hAPP(V_add,V_c),V_d)) = hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_c)),hAPP(hAPP(V_add,V_b),V_d)) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I19_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_rx),V_ry)) = hAPP(hAPP(V_mul,V_rx),hAPP(hAPP(V_mul,V_lx),V_ry)) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I18_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_rx),V_ry)) = hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_rx)),V_ry) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I17_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),V_rx) = hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_ly),V_rx)) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I16_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),V_rx) = hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_rx)),V_ly) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I15_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),hAPP(hAPP(V_mul,V_rx),V_ry)) = hAPP(hAPP(V_mul,V_rx),hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),V_ry)) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I14_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),hAPP(hAPP(V_mul,V_rx),V_ry)) = hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_ly),hAPP(hAPP(V_mul,V_rx),V_ry))) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I13_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),hAPP(hAPP(V_mul,V_rx),V_ry)) = hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_rx)),hAPP(hAPP(V_mul,V_ly),V_ry)) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I12_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_mul,V_a),V_r1) = V_a % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I11_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_mul,V_r1),V_a) = V_a % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I10_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_mul,V_a),V_r0) = V_r0 % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I9_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_mul,V_r0),V_a) = V_r0 % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I8_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_b)),V_c) = hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_a),V_c)),hAPP(hAPP(V_mul,V_b),V_c)) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I7_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_mul,V_a),V_b) = hAPP(hAPP(V_mul,V_b),V_a) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I6_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_add,V_a),V_r0) = V_a % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I5_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_add,V_r0),V_a) = V_a % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I4_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_add,V_m),V_m) = hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_r1),V_r1)),V_m) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I3_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_add,V_m),hAPP(hAPP(V_mul,V_a),V_m)) = hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_r1)),V_m) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I2_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_a),V_m)),V_m) = hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_r1)),V_m) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_gb__semiring_Osemiring__rules_I1_J_0,axiom, % 0.70/0.95 ( hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_a),V_m)),hAPP(hAPP(V_mul,V_b),V_m)) = hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_b)),V_m) % 0.70/0.95 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mod__Suc_0,axiom, % 0.70/0.95 ( c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) != V_n % 0.70/0.95 | c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_type_Osplit__asm_0,axiom, % 0.70/0.95 ( ~ hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_xc),t_a))) % 0.70/0.95 | hBOOL(hAPP(V_P,hAPP(V_f1,V_xc))) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_type_Osplit_0,axiom, % 0.70/0.95 ( ~ hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),t_a))) % 0.70/0.95 | hBOOL(hAPP(V_P,hAPP(V_f1,V_nat))) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mod__mult__left__eq_0,axiom, % 0.70/0.95 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.95 | 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) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mod__mult__right__eq_0,axiom, % 0.70/0.95 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.95 | 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) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_add__is__1_3,axiom, % 0.70/0.95 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.70/0.95 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.70/0.95 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_add__is__1_0,axiom, % 0.70/0.95 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.70/0.95 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.95 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_Suc__diff__diff_0,axiom, % 0.70/0.95 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) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_div__le__mono_0,axiom, % 0.70/0.95 ( c_lessequals(c_Divides_Odiv__class_Odiv(V_m,V_k,tc_nat),c_Divides_Odiv__class_Odiv(V_n,V_k,tc_nat),tc_nat) % 0.70/0.95 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_div__less_0,axiom, % 0.70/0.95 ( c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_Suc__mult__le__cancel1_1,axiom, % 0.70/0.95 ( 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) % 0.70/0.95 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_Suc__mult__le__cancel1_0,axiom, % 0.70/0.95 ( c_lessequals(V_m,V_n,tc_nat) % 0.70/0.95 | ~ 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) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_sum__squares__gt__zero__iff_1,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a)),T_a) % 0.70/0.95 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_sum__squares__gt__zero__iff_2,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a)),T_a) % 0.70/0.95 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_Lambda_0,axiom, % 0.70/0.95 ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r)) % 0.70/0.95 | ~ c_InductTermi_OIT(V_r) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.95 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d)) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_appR_0,axiom, % 0.70/0.95 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_u,V_s),c_Lambda_OdB_OApp(V_u,V_t)) % 0.70/0.95 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_appL_0,axiom, % 0.70/0.95 ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_s,V_u),c_Lambda_OdB_OApp(V_t,V_u)) % 0.70/0.95 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_of__nat__less__0__iff_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.70/0.95 | ~ 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) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_min__max_Osup__commute_0,axiom, % 0.70/0.95 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.95 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = c_Orderings_Oord__class_Omax(V_y,V_x,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_power__eq__imp__eq__base_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.70/0.95 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_Power_Opower__class_Opower(V_b,V_n,T_a) % 0.70/0.95 | V_a = V_b % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.70/0.95 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.95 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_liftn_Osimps_I1_J_0,axiom, % 0.70/0.95 ( c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(V_i) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_le__Suc__eq_2,axiom, % 0.70/0.95 c_lessequals(c_Suc(V_n),c_Suc(V_n),tc_nat) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_drop__replicate_0,axiom, % 0.70/0.95 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) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_min__max_Odistrib__inf__le_0,axiom, % 0.70/0.95 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.95 | 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) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_liftn_Osimps_I2_J_0,axiom, % 0.70/0.95 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)) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_nat_Osize_I2_J_0,axiom, % 0.70/0.95 c_nat_Onat__size(c_Suc(V_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_nat_Onat__size(V_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_min__max_Osup__inf__absorb_0,axiom, % 0.70/0.95 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.95 | c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) = V_x ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_le__square_0,axiom, % 0.70/0.95 c_lessequals(V_m,c_HOL_Otimes__class_Otimes(V_m,V_m,tc_nat),tc_nat) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mult__less__cancel__left__disj_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.95 | ~ 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) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mult__less__cancel__left__disj_3,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.70/0.95 | ~ 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) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mult__less__cancel__right__disj_0,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.95 | ~ 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) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_mult__less__cancel__right__disj_3,axiom, % 0.70/0.95 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.70/0.95 | ~ 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) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_diff__diff__cancel_0,axiom, % 0.70/0.95 ( c_HOL_Ominus__class_Ominus(V_n,c_HOL_Ominus__class_Ominus(V_n,V_i,tc_nat),tc_nat) = V_i % 0.70/0.95 | ~ c_lessequals(V_i,V_n,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_lift_Osimps_I1_J_0,axiom, % 0.70/0.95 ( c_Lambda_Olift(c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(V_i) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_min__Suc__Suc_0,axiom, % 0.70/0.95 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)) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_le__SucE_0,axiom, % 0.70/0.95 ( V_m = c_Suc(V_n) % 0.70/0.95 | c_lessequals(V_m,V_n,tc_nat) % 0.70/0.95 | ~ c_lessequals(V_m,c_Suc(V_n),tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_not__less__less__Suc__eq_1,axiom, % 0.70/0.95 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 0.70/0.95 | c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_not__less__eq_1,axiom, % 0.70/0.95 ( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.95 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) ). % 0.70/0.95 % 0.70/0.95 cnf(cls_not__less__eq_0,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mod__mult__distrib2_0,axiom, % 0.70/0.96 c_HOL_Otimes__class_Otimes(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mod__mult__distrib_0,axiom, % 0.70/0.96 c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_k,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__less__cancel2_2,axiom, % 0.70/0.96 ( 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__less__cancel1_2,axiom, % 0.70/0.96 ( 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_of__nat__less__iff_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.96 | ~ 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_lessI_0,axiom, % 0.70/0.96 c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_less__Suc__eq_2,axiom, % 0.70/0.96 c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_less__trans__Suc_0,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__le__cancel__right_1,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.70/0.96 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) % 0.70/0.96 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__le__cancel__right_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.70/0.96 | c_lessequals(V_a,V_b,T_a) % 0.70/0.96 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__le__cancel__left_1,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.70/0.96 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a) % 0.70/0.96 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__le__cancel__left_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.70/0.96 | c_lessequals(V_a,V_b,T_a) % 0.70/0.96 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__right__mono_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 0.70/0.96 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) % 0.70/0.96 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__left__mono_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 0.70/0.96 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a) % 0.70/0.96 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__le__mono1_0,axiom, % 0.70/0.96 ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k),tc_nat) % 0.70/0.96 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_nat__add__left__cancel__le_0,axiom, % 0.70/0.96 ( c_lessequals(V_m,V_n,tc_nat) % 0.70/0.96 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_nat__add__left__cancel__le_1,axiom, % 0.70/0.96 ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat) % 0.70/0.96 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_le__imp__diff__is__add_0,axiom, % 0.70/0.96 ( ~ c_lessequals(V_i,V_j,tc_nat) % 0.70/0.96 | V_j = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat)),V_i) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_le__add__diff__inverse_0,axiom, % 0.70/0.96 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) = V_m % 0.70/0.96 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_le__add__diff__inverse2_0,axiom, % 0.70/0.96 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)),V_n) = V_m % 0.70/0.96 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_div__mult1__eq_0,axiom, % 0.70/0.96 c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,tc_nat),V_c,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat),tc_nat)),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat),tc_nat),V_c,tc_nat)) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_gb__semiring_Osemiring__rules_I27_J_0,axiom, % 0.70/0.96 ( hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_pwr,V_x),V_q)) = hAPP(hAPP(V_pwr,V_x),c_Suc(V_q)) % 0.70/0.96 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_gb__semiring_Osemiring__rules_I28_J_0,axiom, % 0.70/0.96 ( hAPP(hAPP(V_mul,hAPP(hAPP(V_pwr,V_x),V_q)),V_x) = hAPP(hAPP(V_pwr,V_x),c_Suc(V_q)) % 0.70/0.96 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_gb__semiring_Osemiring__rules_I35_J_0,axiom, % 0.70/0.96 ( hAPP(hAPP(V_pwr,V_x),c_Suc(V_q)) = hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_pwr,V_x),V_q)) % 0.70/0.96 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_gb__semiring_Opwr__Suc_0,axiom, % 0.70/0.96 ( hAPP(hAPP(V_pwr,V_x),c_Suc(V_n)) = hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_pwr,V_x),V_n)) % 0.70/0.96 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__less__cancel1_1,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.96 | ~ 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__less__cancel2_1,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.96 | ~ 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__diff__assoc_0,axiom, % 0.70/0.96 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_k,tc_nat) % 0.70/0.96 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__diff__assoc2_0,axiom, % 0.70/0.96 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),V_i) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_k,tc_nat) % 0.70/0.96 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_drop__drop_0,axiom, % 0.70/0.96 c_List_Odrop(V_n,c_List_Odrop(V_m,V_xs,T_a),T_a) = c_List_Odrop(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_xs,T_a) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_power__le__imp__le__base_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.70/0.96 | c_lessequals(V_a,V_b,T_a) % 0.70/0.96 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.96 | ~ 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__left__idem_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 0.70/0.96 | 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_nat__mod__eq__iff_1,axiom, % 0.70/0.96 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Otimes__class_Otimes(V_n,V_xa,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),c_HOL_Otimes__class_Otimes(V_n,V_xb,tc_nat)) % 0.70/0.96 | c_Divides_Odiv__class_Omod(V_x,V_n,tc_nat) = c_Divides_Odiv__class_Omod(V_y,V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_of__nat__0__less__iff_1,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_of__nat__0__less__iff_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.70/0.96 | ~ 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__less__le__imp__less_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.96 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.70/0.96 | ~ c_lessequals(V_c,V_d,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__le__less__imp__less_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 0.70/0.96 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_nat__mult__div__cancel1_0,axiom, % 0.70/0.96 ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_div__mult__mult1__if_0,axiom, % 0.70/0.96 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.96 | 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_nat__mult__div__cancel__disj_0,axiom, % 0.70/0.96 c_Divides_Odiv__class_Odiv(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),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_class__semiring_Osemiring__rules_I27_J_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.96 | 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_class__semiring_Osemiring__rules_I28_J_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.96 | 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mod__add__self2_0,axiom, % 0.70/0.96 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.96 | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mod__add__self1_0,axiom, % 0.70/0.96 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.96 | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__le__0__iff_3,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.96 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__le__0__iff_2,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__le__0__iff_1,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.96 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.70/0.96 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__le__0__iff_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.70/0.96 | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__pos__neg2_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__pos__neg_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__neg__pos_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_comm__monoid__add_Opower__commutes_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.70/0.96 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),V_a,V_n,T_a)),V_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),V_a,V_n,T_a)) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_Suc__leD_0,axiom, % 0.70/0.96 ( c_lessequals(V_m,V_n,tc_nat) % 0.70/0.96 | ~ c_lessequals(c_Suc(V_m),V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_le__SucI_0,axiom, % 0.70/0.96 ( c_lessequals(V_m,c_Suc(V_n),tc_nat) % 0.70/0.96 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_n__less__m__mult__n_0,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_n__less__n__mult__m_0,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_Suc__n__not__le__n_0,axiom, % 0.70/0.96 ~ c_lessequals(c_Suc(V_n),V_n,tc_nat) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_less__diff__iff_0,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.96 | ~ 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) % 0.70/0.96 | ~ c_lessequals(V_k,V_n,tc_nat) % 0.70/0.96 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_less__diff__iff_1,axiom, % 0.70/0.96 ( 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.96 | ~ c_lessequals(V_k,V_n,tc_nat) % 0.70/0.96 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_pos__add__strict_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mod__mult2__eq_0,axiom, % 0.70/0.96 c_Divides_Odiv__class_Omod(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat),tc_nat)),c_Divides_Odiv__class_Omod(V_a,V_b,tc_nat)) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_subst__lt_0,axiom, % 0.70/0.96 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_j),V_u,V_i) = c_Lambda_OdB_OVar(V_j) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_subst__Var__IT_0,axiom, % 0.70/0.96 ( c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)) % 0.70/0.96 | ~ c_InductTermi_OIT(V_r) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.70/0.96 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.70/0.96 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_not__add__less1_0,axiom, % 0.70/0.96 ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_not__add__less2_0,axiom, % 0.70/0.96 ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_of__nat__diff_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oring__1(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_div__mult2__eq_0,axiom, % 0.70/0.96 c_Divides_Odiv__class_Odiv(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mod__lemma_0,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Omod(V_q,V_c,tc_nat),tc_nat)),V_r),c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_r,V_b,tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_c,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__right__mono__neg_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__left__mono__neg_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__right__mono_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.96 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__left__mono_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Omult__mono(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.96 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__mono1_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Omult__mono1(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.96 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mod__if_1,axiom, % 0.70/0.96 ( c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.70/0.96 | ~ class_Int_Onumber__ring(T_a) % 0.70/0.96 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Otimes__class_Otimes(V_r,V_c,T_a)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Otimes__class_Otimes(V_r,V_d,T_a)) % 0.70/0.96 | V_c = V_d % 0.70/0.96 | V_r = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_natgb_Oadd__scale__eq__noteq_0,axiom, % 0.70/0.96 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Otimes__class_Otimes(V_r,V_c,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Otimes__class_Otimes(V_r,V_d,tc_nat)) % 0.70/0.96 | V_c = V_d % 0.70/0.96 | V_r = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_sum__squares__eq__zero__iff_1,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a)) != c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.96 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_sum__squares__eq__zero__iff_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a)) != c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.96 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_le__div__geq_0,axiom, % 0.70/0.96 ( c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat) = c_Suc(c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat)) % 0.70/0.96 | ~ c_lessequals(V_n,V_m,tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_less__diff__conv_0,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_less__diff__conv_1,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_Suc__n__not__n_0,axiom, % 0.70/0.96 c_Suc(V_n) != V_n ). % 0.70/0.96 % 0.70/0.96 cnf(cls_n__not__Suc__n_0,axiom, % 0.70/0.96 V_n != c_Suc(V_n) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mod__Suc__eq__Suc__mod_0,axiom, % 0.70/0.96 c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)),V_n,tc_nat) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__strict__right__mono_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__less__cancel__right_1,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__less__cancel__right_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__strict__left__mono_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__less__cancel__left_1,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__less__cancel__left_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__less__mono1_0,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k),tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_nat__add__left__cancel__less_0,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_nat__add__left__cancel__less_1,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_zero__induct_0,axiom, % 0.70/0.96 ( hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) % 0.70/0.96 | hBOOL(hAPP(V_P,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(V_P)))) % 0.70/0.96 | ~ hBOOL(hAPP(V_P,V_k)) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_one__le__mult__iff_2,axiom, % 0.70/0.96 ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) % 0.70/0.96 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) % 0.70/0.96 | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_xt1_I6_J_0,axiom, % 0.70/0.96 ( ~ class_Orderings_Oorder(T_a) % 0.70/0.96 | c_lessequals(V_z,V_x,T_a) % 0.70/0.96 | ~ c_lessequals(V_z,V_y,T_a) % 0.70/0.96 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_xt1_I7_J_0,axiom, % 0.70/0.96 ( ~ class_Orderings_Oorder(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.70/0.96 | ~ c_lessequals(V_z,V_y,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_xt1_I8_J_0,axiom, % 0.70/0.96 ( ~ class_Orderings_Oorder(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.70/0.96 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__nonpos__nonpos_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.70/0.96 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_order__trans_0,axiom, % 0.70/0.96 ( ~ class_Orderings_Opreorder(T_a) % 0.70/0.96 | c_lessequals(V_x,V_z,T_a) % 0.70/0.96 | ~ c_lessequals(V_y,V_z,T_a) % 0.70/0.96 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_le__refl_0,axiom, % 0.70/0.96 c_lessequals(V_n,V_n,tc_nat) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_le__trans_0,axiom, % 0.70/0.96 ( c_lessequals(V_i,V_k,tc_nat) % 0.70/0.96 | ~ c_lessequals(V_j,V_k,tc_nat) % 0.70/0.96 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__less__mono2_0,axiom, % 0.70/0.96 ( 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__less__mono1_0,axiom, % 0.70/0.96 ( 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_nat__mult__less__cancel1_0,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.96 | ~ 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_nat__mult__less__cancel1_1,axiom, % 0.70/0.96 ( 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__less__cancel__left__neg_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.70/0.96 | ~ 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__less__cancel__left__neg_1,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__less__cancel__left__pos_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.70/0.96 | ~ 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__less__cancel__left__pos_1,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__strict__left__mono__neg_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__strict__left__mono_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__less__cancel__left__disj_4,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__less__cancel__left__disj_5,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__strict__right__mono__neg_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__strict__right__mono_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__less__cancel__right__disj_4,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__less__cancel__right__disj_5,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__strict__left__mono__comm_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_div__add1__eq_0,axiom, % 0.70/0.96 c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_a),V_b),V_c,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(V_a,V_c,tc_nat)),c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(V_a,V_c,tc_nat)),c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat)),V_c,tc_nat)) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_max__add__distrib__left_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.70/0.96 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Orderings_Oord__class_Omax(V_x,V_y,T_a)),V_z) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_app__Var__IT_0,axiom, % 0.70/0.96 ( c_InductTermi_OIT(c_Lambda_OdB_OApp(V_t,c_Lambda_OdB_OVar(V_i))) % 0.70/0.96 | ~ c_InductTermi_OIT(V_t) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_power__inject__base_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | V_a = V_b % 0.70/0.96 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.96 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_div__mult__mult1_0,axiom, % 0.70/0.96 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_div__mult__mult2_0,axiom, % 0.70/0.96 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_nat__mult__div__cancel__disj_1,axiom, % 0.70/0.96 ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat) % 0.70/0.96 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__le__mono_0,axiom, % 0.70/0.96 ( 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) % 0.70/0.96 | ~ c_lessequals(V_k,V_l,tc_nat) % 0.70/0.96 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_le__cube_0,axiom, % 0.70/0.96 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) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__mono_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.96 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.96 | ~ c_lessequals(V_c,V_d,T_a) % 0.70/0.96 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__mono_H_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Opordered__semiring(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.96 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.70/0.96 | ~ c_lessequals(V_c,V_d,T_a) % 0.70/0.96 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_min__max_Osup__assoc_0,axiom, % 0.70/0.96 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.96 | 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_min__max_Osup__left__commute_0,axiom, % 0.70/0.96 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.96 | 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mod__mult__self3_0,axiom, % 0.70/0.96 c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)),V_m),V_n,tc_nat) = c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mod__mult__self1_0,axiom, % 0.70/0.96 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.96 | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a)),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mod__mult__self2_0,axiom, % 0.70/0.96 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.96 | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a)),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.96 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_m,T_a)),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_m,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_split__div__lemma_2,axiom, % 0.70/0.96 ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_m,c_HOL_Otimes__class_Otimes(V_n,c_Suc(c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)),tc_nat),tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_of__nat__0__le__iff_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.70/0.96 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_zero__le__imp__of__nat_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.70/0.96 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_sum__squares__gt__zero__iff_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_abs_0,axiom, % 0.70/0.96 ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t)) % 0.70/0.96 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_min__max_Osup__left__idem_0,axiom, % 0.70/0.96 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.96 | 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_div__1_0,axiom, % 0.70/0.96 c_Divides_Odiv__class_Odiv(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = V_m ). % 0.70/0.96 % 0.70/0.96 cnf(cls_zero__le__mult__iff_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.70/0.96 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_zero__le__mult__iff_1,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.70/0.96 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_zero__le__mult__iff_2,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.96 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_zero__le__mult__iff_3,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.96 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_diff__add__inverse2_0,axiom, % 0.70/0.96 c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),V_n,tc_nat) = V_m ). % 0.70/0.96 % 0.70/0.96 cnf(cls_diff__add__inverse_0,axiom, % 0.70/0.96 c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_n,tc_nat) = V_m ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__diff__cancel_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.70/0.96 | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_b,T_a) = V_a ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_type_Osimps_I5_J_0,axiom, % 0.70/0.96 c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),T_a) = hAPP(V_f1,V_nat) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_nat__gcd_Osimps_1,axiom, % 0.70/0.96 ( c_Nitpick_Onat__gcd(V_x,V_y) = c_Nitpick_Onat__gcd(V_y,c_Divides_Odiv__class_Omod(V_x,V_y,tc_nat)) % 0.70/0.96 | V_y = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_split__mod_1,axiom, % 0.70/0.96 ( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) % 0.70/0.96 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.96 | ~ hBOOL(hAPP(V_P,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat)),V_j),V_k,tc_nat))) % 0.70/0.96 | hBOOL(hAPP(V_P,V_j)) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__le__less__mono_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 0.70/0.96 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__less__le__mono_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a) % 0.70/0.96 | ~ c_lessequals(V_c,V_d,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_dB_Osimps_I5_J_0,axiom, % 0.70/0.96 c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_less__Suc__eq__0__disj_3,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_x,V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_Suc__less__eq_0,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_Suc__mono_0,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__gr__0_2,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__gr__0_1,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_typing__elims_I3_J_0,axiom, % 0.70/0.96 ( V_T = c_Type_Otype_OFun(c_Type_Osko__Type__Xtyping__elims__3__1(V_T,V_e,V_t),c_Type_Osko__Type__Xtyping__elims__3__2(V_T,V_e,V_t)) % 0.70/0.96 | ~ c_Type_Otyping(V_e,c_Lambda_OdB_OAbs(V_t),V_T) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_power__eq__0__iff_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 0.70/0.96 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 0.70/0.96 | ~ class_Ring__and__Field_Omult__zero(T_a) % 0.70/0.96 | ~ class_Power_Opower(T_a) % 0.70/0.96 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.96 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_field__power__not__zero_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(T_a) % 0.70/0.96 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.96 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_class__semiring_Omul__0_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.96 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__zero__left_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 0.70/0.96 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__zero__right_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 0.70/0.96 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__eq__0__iff_1,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 0.70/0.96 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__eq__0__iff_2,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 0.70/0.96 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.96 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.96 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_no__zero__divirors__neq0_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 0.70/0.96 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.96 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.96 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_no__zero__divisors_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 0.70/0.96 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.96 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.96 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__eq__0__iff_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 0.70/0.96 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.96 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.96 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_div__by__0_0,axiom, % 0.70/0.96 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.96 | c_Divides_Odiv__class_Odiv(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_div__0_0,axiom, % 0.70/0.96 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.96 | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_double__eq__0__iff_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.70/0.96 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.96 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_class__ringb_Osubr0__iff_1,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.70/0.96 | ~ class_Int_Onumber__ring(T_a) % 0.70/0.96 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_diff__self_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.70/0.96 | c_HOL_Ominus__class_Ominus(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_diff__0__right_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.70/0.96 | c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_right__minus__eq_1,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.70/0.96 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_eq__iff__diff__eq__0_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.70/0.96 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_class__ringb_Oadd__r0__iff_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.70/0.96 | ~ class_Int_Onumber__ring(T_a) % 0.70/0.96 | V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_a) % 0.70/0.96 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mod__self_0,axiom, % 0.70/0.96 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.96 | c_Divides_Odiv__class_Omod(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mod__by__0_0,axiom, % 0.70/0.96 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.96 | c_Divides_Odiv__class_Omod(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mod__0_0,axiom, % 0.70/0.96 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.96 | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_double__eq__0__iff_1,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.70/0.96 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_class__ringb_Osubr0__iff_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.70/0.96 | ~ class_Int_Onumber__ring(T_a) % 0.70/0.96 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.96 | V_x = V_y ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_right__minus__eq_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.70/0.96 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.96 | V_a = V_b ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_eq__iff__diff__eq__0_1,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.70/0.96 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.96 | V_a = V_b ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_class__semiring_Oadd__0_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.96 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_x) = V_x ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_comm__monoid__add_Omult__1_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.70/0.96 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_class__ringb_Oadd__r0__iff_1,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.70/0.96 | ~ class_Int_Onumber__ring(T_a) % 0.70/0.96 | V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Ozero__class_Ozero(T_a)) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_comm__monoid__add_Omult__1__right_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.70/0.96 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__0__left_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.70/0.96 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_monoid__add__class_Oadd__0__right_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.70/0.96 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.96 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.96 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_comm__monoid__add_Opower__0_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.70/0.96 | c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_split__mod_5,axiom, % 0.70/0.96 ( ~ hBOOL(hAPP(V_P,V_n)) % 0.70/0.96 | hBOOL(hAPP(V_P,c_Divides_Odiv__class_Omod(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_eq__imp__le_0,axiom, % 0.70/0.96 c_lessequals(V_x,V_x,tc_nat) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_order__eq__iff_0,axiom, % 0.70/0.96 ( ~ class_Orderings_Oorder(T_a) % 0.70/0.96 | c_lessequals(V_x,V_x,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_order__eq__refl_0,axiom, % 0.70/0.96 ( ~ class_Orderings_Opreorder(T_a) % 0.70/0.96 | c_lessequals(V_x,V_x,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_order__le__less__trans_0,axiom, % 0.70/0.96 ( ~ class_Orderings_Opreorder(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.70/0.96 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_order__less__le__trans_0,axiom, % 0.70/0.96 ( ~ class_Orderings_Opreorder(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.70/0.96 | ~ c_lessequals(V_y,V_z,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_le__add__right__mono_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.70/0.96 | c_lessequals(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a) % 0.70/0.96 | ~ c_lessequals(V_c,V_d,T_a) % 0.70/0.96 | ~ c_lessequals(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_subst__eq_0,axiom, % 0.70/0.96 c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u ). % 0.70/0.96 % 0.70/0.96 cnf(cls_dB_Osimps_I9_J_0,axiom, % 0.70/0.96 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OApp(V_dB1,V_dB2) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_min__diff_0,axiom, % 0.70/0.96 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) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_nat__diff__split_0,axiom, % 0.70/0.96 ( hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_a,V_b,tc_nat) % 0.70/0.96 | ~ hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(V_a,V_b,tc_nat))) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__is__1_5,axiom, % 0.70/0.96 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__idem_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 0.70/0.96 | c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = V_x ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mod__mult__self2__is__0_0,axiom, % 0.70/0.96 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.96 | 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mod__mult__self1__is__0_0,axiom, % 0.70/0.96 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.96 | 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mod__eq__0__iff_1,axiom, % 0.70/0.96 c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_d,V_x,tc_nat),V_d,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_dB_Osimps_I1_J_0,axiom, % 0.70/0.96 ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H) % 0.70/0.96 | V_nat = V_nat_H ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_ex__least__nat__le_1,axiom, % 0.70/0.96 ( ~ hBOOL(hAPP(V_P,V_i)) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_i,c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1(V_P,V_n),tc_nat) % 0.70/0.96 | ~ hBOOL(hAPP(V_P,V_n)) % 0.70/0.96 | hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__strict__mono_H_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.70/0.96 | 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) % 0.70/0.96 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.96 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_le__less__Suc__eq_0,axiom, % 0.70/0.96 ( V_n = V_m % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 0.70/0.96 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_dB_Osimps_I8_J_0,axiom, % 0.70/0.96 c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_dB_Osimps_I7_J_0,axiom, % 0.70/0.96 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_semiring__div__class_Omod__div__equality_H_0,axiom, % 0.70/0.96 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.96 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),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)) = V_a ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__le__mono1_0,axiom, % 0.70/0.96 ( 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) % 0.70/0.96 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__le__mono2_0,axiom, % 0.70/0.96 ( 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) % 0.70/0.96 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__le__cancel1_2,axiom, % 0.70/0.96 ( 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) % 0.70/0.96 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__le__cancel2_2,axiom, % 0.70/0.96 ( 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) % 0.70/0.96 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_zero__less__diff_0,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.96 | ~ 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_zero__less__diff_1,axiom, % 0.70/0.96 ( 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) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_Suc__lessD_0,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_less__SucI_0,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_sum__squares__eq__zero__iff_2,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),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)) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__less__cancel__right__disj_2,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.70/0.96 | ~ 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__less__cancel__right__disj_1,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.96 | ~ 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__less__cancel__left__disj_2,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.70/0.96 | ~ 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_mult__less__cancel__left__disj_1,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.70/0.96 | ~ 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_subst__App_0,axiom, % 0.70/0.96 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)) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_Suc__mult__cancel1_0,axiom, % 0.70/0.96 ( 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) % 0.70/0.96 | V_m = V_n ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_Suc__pred_0,axiom, % 0.70/0.96 ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_of__nat__add_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.70/0.96 | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_diff__less_0,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_min__max_Odistrib__sup__le_0,axiom, % 0.70/0.96 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.96 | 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_le__eqI_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.70/0.96 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 0.70/0.96 | c_lessequals(V_y_H,V_x_H,T_a) % 0.70/0.96 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_le__eqI_1,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.70/0.96 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 0.70/0.96 | c_lessequals(V_y,V_x,T_a) % 0.70/0.96 | ~ c_lessequals(V_y_H,V_x_H,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_less__eqI_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.70/0.96 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_less__eqI_1,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.70/0.96 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 0.70/0.96 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_power__mult__distrib_0,axiom, % 0.70/0.96 ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) % 0.70/0.96 | 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_class__semiring_Opwr__mul_0,axiom, % 0.70/0.96 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.96 | 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_zmod__simps_I1_J_0,axiom, % 0.70/0.96 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.96 | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(V_a,V_c,T_a)),V_b),V_c,T_a) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_zmod__simps_I2_J_0,axiom, % 0.70/0.96 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.96 | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a)),V_c,T_a) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__diff__inverse_0,axiom, % 0.70/0.96 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) = V_m % 0.70/0.96 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_diff__Suc__less_0,axiom, % 0.70/0.96 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_n,c_Suc(V_i),tc_nat),V_n,tc_nat) % 0.70/0.96 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__is__1_1,axiom, % 0.70/0.96 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.70/0.96 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.70/0.96 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_add__is__1_2,axiom, % 0.70/0.96 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.70/0.96 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.96 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_min__max_Osup__inf__distrib2_0,axiom, % 0.70/0.96 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.96 | 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) ) ). % 0.70/0.96 % 0.70/0.96 cnf(cls_min__max_Osup__inf__distrib1_0,axiom, % 0.70/0.96 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.96 | 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) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_power__mult_0,axiom, % 0.70/0.97 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.70/0.97 | 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) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_mod__div__equality2_0,axiom, % 0.70/0.97 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.97 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),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)) = V_a ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_mod__div__equality_0,axiom, % 0.70/0.97 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.97 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),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)) = V_a ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_mod__div__decomp_0,axiom, % 0.70/0.97 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.97 | V_a = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),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)) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_xt1_I11_J_0,axiom, % 0.70/0.97 ( ~ class_Orderings_Oorder(T_a) % 0.70/0.97 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.70/0.97 | V_a = V_b % 0.70/0.97 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_xt1_I12_J_0,axiom, % 0.70/0.97 ( ~ class_Orderings_Oorder(T_a) % 0.70/0.97 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.70/0.97 | ~ c_lessequals(V_b,V_a,T_a) % 0.70/0.97 | V_a = V_b ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_nat__less__le_2,axiom, % 0.70/0.97 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.97 | V_m = V_n % 0.70/0.97 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_le__eq__less__or__eq_0,axiom, % 0.70/0.97 ( V_m = V_n % 0.70/0.97 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.97 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_le__neq__implies__less_0,axiom, % 0.70/0.97 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.70/0.97 | V_m = V_n % 0.70/0.97 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_order__le__less_0,axiom, % 0.70/0.97 ( ~ class_Orderings_Oorder(T_a) % 0.70/0.97 | V_x = V_y % 0.70/0.97 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.70/0.97 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_order__less__le_2,axiom, % 0.70/0.97 ( ~ class_Orderings_Oorder(T_a) % 0.70/0.97 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.70/0.97 | V_x = V_y % 0.70/0.97 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_order__le__neq__trans_0,axiom, % 0.70/0.97 ( ~ class_Orderings_Oorder(T_a) % 0.70/0.97 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.70/0.97 | V_a = V_b % 0.70/0.97 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_order__neq__le__trans_0,axiom, % 0.70/0.97 ( ~ class_Orderings_Oorder(T_a) % 0.70/0.97 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.70/0.97 | ~ c_lessequals(V_a,V_b,T_a) % 0.70/0.97 | V_a = V_b ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_linorder__antisym__conv1_0,axiom, % 0.70/0.97 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.97 | V_x = V_y % 0.70/0.97 | ~ c_lessequals(V_x,V_y,T_a) % 0.70/0.97 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_linorder__antisym__conv2_0,axiom, % 0.70/0.97 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.97 | V_x = V_y % 0.70/0.97 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.70/0.97 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_mult__nonneg__nonneg_0,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) % 0.70/0.97 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 0.70/0.97 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.97 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_zero__le__mult__iff_5,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.97 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 0.70/0.97 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.97 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_zero__le__mult__iff_4,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.97 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 0.70/0.97 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.97 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_zero__le__square_0,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.70/0.97 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_mult__nonpos__nonpos_0,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.70/0.97 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 0.70/0.97 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.97 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_split__mult__pos__le_1,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.70/0.97 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 0.70/0.97 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.70/0.97 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_split__mult__pos__le_0,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Opordered__ring(T_a) % 0.70/0.97 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) % 0.70/0.97 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.70/0.97 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_split__div__lemma_1,axiom, % 0.70/0.97 ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.70/0.97 | c_lessequals(c_HOL_Otimes__class_Otimes(V_n,c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat),tc_nat),V_m,tc_nat) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_mod__mult__mult2_0,axiom, % 0.70/0.97 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.97 | 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) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_mod__mult__mult1_0,axiom, % 0.70/0.97 ( ~ class_Divides_Osemiring__div(T_a) % 0.70/0.97 | 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) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_Suc__le__mono_0,axiom, % 0.70/0.97 ( c_lessequals(V_n,V_m,tc_nat) % 0.70/0.97 | ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_Suc__le__mono_1,axiom, % 0.70/0.97 ( c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) % 0.70/0.97 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom, % 0.70/0.97 ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a) % 0.70/0.97 | 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) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.97 | 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) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.97 | 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) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.97 | 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) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.97 | 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) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_nat__mult__assoc_0,axiom, % 0.70/0.97 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) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_class__semiring_Omul__a_0,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.97 | 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) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.97 | c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_c,T_a)),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a)) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_comm__semiring__class_Odistrib_0,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Ocomm__semiring(T_a) % 0.70/0.97 | c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_c,T_a)),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a)) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_add__mult__distrib_0,axiom, % 0.70/0.97 c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),V_k,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat)),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat)) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_add__mult__distrib2_0,axiom, % 0.70/0.97 c_HOL_Otimes__class_Otimes(V_k,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_class__semiring_Omul__d_0,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.70/0.97 | c_HOL_Otimes__class_Otimes(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a)) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_xt1_I9_J_0,axiom, % 0.70/0.97 ( ~ class_Orderings_Oorder(T_a) % 0.70/0.97 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.70/0.97 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_not__less__iff__gr__or__eq_1,axiom, % 0.70/0.97 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.97 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.70/0.97 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_nat__le__linear_0,axiom, % 0.70/0.97 ( c_lessequals(V_n,V_m,tc_nat) % 0.70/0.97 | c_lessequals(V_m,V_n,tc_nat) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_linorder__linear_0,axiom, % 0.70/0.97 ( ~ class_Orderings_Olinorder(T_a) % 0.70/0.97 | c_lessequals(V_y,V_x,T_a) % 0.70/0.97 | c_lessequals(V_x,V_y,T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_order__less__asym_0,axiom, % 0.70/0.97 ( ~ class_Orderings_Opreorder(T_a) % 0.70/0.97 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.70/0.97 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_order__less__asym_H_0,axiom, % 0.70/0.97 ( ~ class_Orderings_Opreorder(T_a) % 0.70/0.97 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.70/0.97 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_split__mod_0,axiom, % 0.70/0.97 ( ~ hBOOL(hAPP(V_P,c_Divides_Odiv__class_Omod(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) % 0.70/0.97 | hBOOL(hAPP(V_P,V_n)) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_power_Opower_Opower__0_0,axiom, % 0.70/0.97 c_Power_Opower_Opower(V_one,V_times,V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = V_one ). % 0.70/0.97 % 0.70/0.97 cnf(cls_le__0__eq_1,axiom, % 0.70/0.97 c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_mult__cancel2_1,axiom, % 0.70/0.97 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) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_mult__cancel1_1,axiom, % 0.70/0.97 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) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_of__nat__aux_Osimps_I1_J_0,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.70/0.97 | c_Nat_Osemiring__1__class_Oof__nat__aux(V_inc,c_HOL_Ozero__class_Ozero(tc_nat),V_i,T_a) = V_i ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_lexn_Oinduct_0,axiom, % 0.70/0.97 ( hBOOL(hAPP(V_P,V_nat)) % 0.70/0.97 | hBOOL(hAPP(V_P,v_sko__List__Xlexn__Xinduct__1(V_P))) % 0.70/0.97 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_zero__induct_1,axiom, % 0.70/0.97 ( hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) % 0.70/0.97 | ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(V_P))) % 0.70/0.97 | ~ hBOOL(hAPP(V_P,V_k)) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_neq0__conv_1,axiom, % 0.70/0.97 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_liftn__0_0,axiom, % 0.70/0.97 c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k) = V_t ). % 0.70/0.97 % 0.70/0.97 cnf(cls_split__div_H_6,axiom, % 0.70/0.97 ( hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) % 0.70/0.97 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_split__div_5,axiom, % 0.70/0.97 ( ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) % 0.70/0.97 | hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_split__div_0,axiom, % 0.70/0.97 ( ~ hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) % 0.70/0.97 | hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_gr0I_0,axiom, % 0.70/0.97 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.70/0.97 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_nat__rec__0_0,axiom, % 0.70/0.97 c_Nat_Onat_Onat__rec(V_f1,V_f2,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = V_f1 ). % 0.70/0.97 % 0.70/0.97 cnf(cls_ex__least__nat__le_2,axiom, % 0.70/0.97 ( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1(V_P,V_n))) % 0.70/0.97 | ~ hBOOL(hAPP(V_P,V_n)) % 0.70/0.97 | hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_Suc__neq__Zero_0,axiom, % 0.70/0.97 c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_nat_Osimps_I3_J_0,axiom, % 0.70/0.97 c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_diffs0__imp__equal_0,axiom, % 0.70/0.97 ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.97 | c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.97 | V_m = V_n ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_le__0__eq_0,axiom, % 0.70/0.97 ( V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.97 | ~ c_lessequals(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_nat__induct_0,axiom, % 0.70/0.97 ( hBOOL(hAPP(V_P,V_n)) % 0.70/0.97 | hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(V_P))) % 0.70/0.97 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_mult__is__0_2,axiom, % 0.70/0.97 c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_mult__is__0_1,axiom, % 0.70/0.97 c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_mult__is__0_0,axiom, % 0.70/0.97 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.97 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.97 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_add__is__0_1,axiom, % 0.70/0.97 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.97 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_add__is__0_0,axiom, % 0.70/0.97 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.97 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_Nitpick_Onat__case__def_0,axiom, % 0.70/0.97 c_Nat_Onat_Onat__case(V_x,V_f,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = V_x ). % 0.70/0.97 % 0.70/0.97 cnf(cls_nat__case__0_0,axiom, % 0.70/0.97 c_Nat_Onat_Onat__case(V_f1,V_f2,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = V_f1 ). % 0.70/0.97 % 0.70/0.97 cnf(cls_min__0R_0,axiom, % 0.70/0.97 c_Orderings_Oord__class_Omin(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_min__0L_0,axiom, % 0.70/0.97 c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_mult__cancel2_0,axiom, % 0.70/0.97 ( c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat) != c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat) % 0.70/0.97 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.97 | V_m = V_n ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_mult__cancel1_0,axiom, % 0.70/0.97 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) % 0.70/0.97 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) % 0.70/0.97 | V_m = V_n ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_nat__mult__eq__cancel__disj_0,axiom, % 0.70/0.97 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) % 0.70/0.97 | V_m = V_n % 0.70/0.97 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_minus__nat_Odiff__0_0,axiom, % 0.70/0.97 c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ). % 0.70/0.97 % 0.70/0.97 cnf(cls_diff__self__eq__0_0,axiom, % 0.70/0.97 c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_natgb_Oadd__r0__iff_0,axiom, % 0.70/0.97 ( V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_a) % 0.70/0.97 | V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_add__eq__self__zero_0,axiom, % 0.70/0.97 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != V_m % 0.70/0.97 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_replicate_Oinduct_0,axiom, % 0.70/0.97 ( hBOOL(hAPP(V_P,V_nat)) % 0.70/0.97 | hBOOL(hAPP(V_P,v_sko__List__Xreplicate__Xinduct__1(V_P))) % 0.70/0.97 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_Zero__neq__Suc_0,axiom, % 0.70/0.97 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_nat_Osimps_I2_J_0,axiom, % 0.70/0.97 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_nat_Osplit_0,axiom, % 0.70/0.97 ( ~ hBOOL(hAPP(V_P,c_Nat_Onat_Onat__case(V_f1,V_f2,c_HOL_Ozero__class_Ozero(tc_nat),t_a))) % 0.70/0.97 | hBOOL(hAPP(V_P,V_f1)) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_nat_Oinducts_0,axiom, % 0.70/0.97 ( hBOOL(hAPP(V_P,V_nat)) % 0.70/0.97 | hBOOL(hAPP(V_P,v_sko__Nat__Xnat__Xinducts__1(V_P))) % 0.70/0.97 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_nat__gcd_Osimps_0,axiom, % 0.70/0.97 c_Nitpick_Onat__gcd(V_x,c_HOL_Ozero__class_Ozero(tc_nat)) = V_x ). % 0.70/0.97 % 0.70/0.97 cnf(cls_nat_Osize_I1_J_0,axiom, % 0.70/0.97 c_nat_Onat__size(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_char__size_0,axiom, % 0.70/0.97 c_String_Ochar_Ochar__size(V_c) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_add__is__0_2,axiom, % 0.70/0.97 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_nat_Oinduct_0,axiom, % 0.70/0.97 ( hBOOL(hAPP(V_P,V_nat)) % 0.70/0.97 | hBOOL(hAPP(V_P,v_sko__Nat__Xnat__Xinduct__1(V_P))) % 0.70/0.97 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_gr__implies__not0_0,axiom, % 0.70/0.97 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_not__less0_0,axiom, % 0.70/0.97 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_bot__nat__def_0,axiom, % 0.70/0.97 c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_upt_Oinduct_0,axiom, % 0.70/0.97 ( hBOOL(hAPP(V_P,V_nat)) % 0.70/0.97 | hBOOL(hAPP(V_P,v_sko__List__Xupt__Xinduct__1(V_P))) % 0.70/0.97 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_drop__0_0,axiom, % 0.70/0.97 c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),V_xs,T_a) = V_xs ). % 0.70/0.97 % 0.70/0.97 cnf(cls_diff__0__eq__0_0,axiom, % 0.70/0.97 c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_infinite__descent0_1,axiom, % 0.70/0.97 ( hBOOL(hAPP(V_P,V_n)) % 0.70/0.97 | ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(V_P))) % 0.70/0.97 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_le0_0,axiom, % 0.70/0.97 c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_size__char_0,axiom, % 0.70/0.97 c_Nat_Osize__class_Osize(V_c,tc_String_Ochar) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_replicate__eq__replicate_2,axiom, % 0.70/0.97 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) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_max__0R_0,axiom, % 0.70/0.97 c_Orderings_Oord__class_Omax(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_n ). % 0.70/0.97 % 0.70/0.97 cnf(cls_max__0L_0,axiom, % 0.70/0.97 c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ). % 0.70/0.97 % 0.70/0.97 cnf(cls_replicate__eq__replicate_1,axiom, % 0.70/0.97 ( c_List_Oreplicate(V_m,V_x,T_a) != c_List_Oreplicate(V_n,V_y,T_a) % 0.70/0.97 | V_x = V_y % 0.70/0.97 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_natgb_Oadd__r0__iff_1,axiom, % 0.70/0.97 V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_plus__nat_Oadd__0_0,axiom, % 0.70/0.97 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n) = V_n ). % 0.70/0.97 % 0.70/0.97 cnf(cls_Nat_Oadd__0__right_0,axiom, % 0.70/0.97 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat)) = V_m ). % 0.70/0.97 % 0.70/0.97 cnf(cls_gb__semiring_Opwr__0_0,axiom, % 0.70/0.97 ( hAPP(hAPP(V_pwr,V_x),c_HOL_Ozero__class_Ozero(tc_nat)) = V_r1 % 0.70/0.97 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_subject__reduction_0,axiom, % 0.70/0.97 ( c_Type_Otyping(V_e,V_t_H,V_T) % 0.70/0.97 | ~ c_Lambda_Obeta(V_t,V_t_H) % 0.70/0.97 | ~ c_Type_Otyping(V_e,V_t,V_T) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_typing__elims_I1_J_0,axiom, % 0.70/0.97 ( hAPP(V_e,V_i) = V_T % 0.70/0.97 | ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_typing_OVar_0,axiom, % 0.70/0.97 c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_typing__elims_I2_J_0,axiom, % 0.70/0.97 ( c_Type_Otyping(V_e,V_t,c_Type_Otype_OFun(c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u),V_T)) % 0.70/0.97 | ~ c_Type_Otyping(V_e,c_Lambda_OdB_OApp(V_t,V_u),V_T) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_abs__typeE_0,axiom, % 0.70/0.97 ( c_Type_Otyping(c_Type_Oshift(V_e,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(V_e,V_t),tc_Type_Otype),V_t,c_Type_Osko__Type__Xabs__typeE__1__2(V_e,V_t)) % 0.70/0.97 | ~ c_Type_Otyping(V_e,c_Lambda_OdB_OAbs(V_t),V_T) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_typing__elims_I3_J_1,axiom, % 0.70/0.97 ( c_Type_Otyping(c_Type_Oshift(V_e,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(V_T,V_e,V_t),tc_Type_Otype),V_t,c_Type_Osko__Type__Xtyping__elims__3__2(V_T,V_e,V_t)) % 0.70/0.97 | ~ c_Type_Otyping(V_e,c_Lambda_OdB_OAbs(V_t),V_T) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_type_Osimps_I4_J_0,axiom, % 0.70/0.97 c_Type_Otype_OFun(V_type1_H,V_type2_H) != c_Type_Otype_OAtom(V_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_type__induct_1,axiom, % 0.70/0.97 ( c_Type_Osko__Type__Xtype__induct__1__1(V_P) != c_Type_Otype_OFun(V_T1,V_T2) % 0.70/0.97 | hBOOL(hAPP(V_P,V_T)) % 0.70/0.97 | hBOOL(hAPP(V_P,V_T2)) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_type__induct_0,axiom, % 0.70/0.97 ( c_Type_Osko__Type__Xtype__induct__1__1(V_P) != c_Type_Otype_OFun(V_T1a,V_x) % 0.70/0.97 | hBOOL(hAPP(V_P,V_T)) % 0.70/0.97 | hBOOL(hAPP(V_P,V_T1a)) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_type_Orecs_I2_J_0,axiom, % 0.70/0.97 c_Type_Otype_Otype__rec(V_f1,V_f2,c_Type_Otype_OFun(V_type1,V_type2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f2,V_type1),V_type2),c_Type_Otype_Otype__rec(V_f1,V_f2,V_type1,T_a)),c_Type_Otype_Otype__rec(V_f1,V_f2,V_type2,T_a)) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_type_Osimps_I6_J_0,axiom, % 0.70/0.97 c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OFun(V_type1,V_type2),T_a) = hAPP(hAPP(V_f2,V_type1),V_type2) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_type_Osplit__asm_1,axiom, % 0.70/0.97 ( ~ hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OFun(V_xa,V_xb),t_a))) % 0.70/0.97 | hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_xa),V_xb))) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_type_Osplit_1,axiom, % 0.70/0.97 ( ~ hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OFun(V_type1,V_type2),t_a))) % 0.70/0.97 | hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_type1),V_type2))) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_type_Osimps_I3_J_0,axiom, % 0.70/0.97 c_Type_Otype_OAtom(V_nat) != c_Type_Otype_OFun(V_type1_H,V_type2_H) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_lift__IT_0,axiom, % 0.70/0.97 ( c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i)) % 0.70/0.97 | ~ c_InductTermi_OIT(V_t) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_lift_Osimps_I2_J_0,axiom, % 0.70/0.97 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)) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_subst__lift_0,axiom, % 0.70/0.97 c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ). % 0.70/0.97 % 0.70/0.97 cnf(cls_lift__preserves__beta_0,axiom, % 0.70/0.97 ( c_Lambda_Obeta(c_Lambda_Olift(V_r,V_i),c_Lambda_Olift(V_s,V_i)) % 0.70/0.97 | ~ c_Lambda_Obeta(V_r,V_s) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_shift__gt_0,axiom, % 0.70/0.97 ( hAPP(c_Type_Oshift(V_e,V_i,V_T,T_a),V_j) = hAPP(V_e,V_j) % 0.70/0.97 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_subst__type__IT_0,axiom, % 0.70/0.97 ( c_InductTermi_OIT(c_Lambda_Osubst(V_t,V_u,V_i)) % 0.70/0.97 | ~ c_Type_Otyping(V_e,V_u,V_U) % 0.70/0.97 | ~ c_InductTermi_OIT(V_u) % 0.70/0.97 | ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),V_t,V_T) % 0.70/0.97 | ~ c_InductTermi_OIT(V_t) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_power__eq__0__iff_2,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 0.70/0.97 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 0.70/0.97 | ~ class_Ring__and__Field_Omult__zero(T_a) % 0.70/0.97 | ~ class_Power_Opower(T_a) % 0.70/0.97 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.97 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_power__0__left_1,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 0.70/0.97 | ~ class_Power_Opower(T_a) % 0.70/0.97 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 0.70/0.97 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_power__eq__0__iff_1,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 0.70/0.97 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 0.70/0.97 | ~ class_Ring__and__Field_Omult__zero(T_a) % 0.70/0.97 | ~ class_Power_Opower(T_a) % 0.70/0.97 | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_of__nat__0_0,axiom, % 0.70/0.97 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.70/0.97 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_App_I4_J_0,axiom, % 0.70/0.97 c_InductTermi_OIT(v_ta____) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_shift__commute_0,axiom, % 0.70/0.97 c_Type_Oshift(c_Type_Oshift(V_e,V_i,V_U,T_a),c_HOL_Ozero__class_Ozero(tc_nat),V_T,T_a) = c_Type_Oshift(c_Type_Oshift(V_e,c_HOL_Ozero__class_Ozero(tc_nat),V_T,T_a),c_Suc(V_i),V_U,T_a) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_typing_OApp_0,axiom, % 0.70/0.97 ( c_Type_Otyping(V_env,c_Lambda_OdB_OApp(V_s,V_t),V_U) % 0.70/0.97 | ~ c_Type_Otyping(V_env,V_t,V_T) % 0.70/0.97 | ~ c_Type_Otyping(V_env,V_s,c_Type_Otype_OFun(V_T,V_U)) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_subst__lemma_0,axiom, % 0.70/0.97 ( ~ c_Type_Otyping(V_e_H,V_u,V_U) % 0.70/0.97 | ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T) % 0.70/0.97 | c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_Abs_0,axiom, % 0.70/0.97 ( c_Type_Otyping(V_env,c_Lambda_OdB_OAbs(V_t),c_Type_Otype_OFun(V_T,V_U)) % 0.70/0.97 | ~ c_Type_Otyping(c_Type_Oshift(V_env,c_HOL_Ozero__class_Ozero(tc_nat),V_T,tc_Type_Otype),V_t,V_U) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_App_I1_J_0,axiom, % 0.70/0.97 c_Type_Otyping(v_ea____,v_s____,c_Type_Otype_OFun(v_Ta____,v_U____)) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_calculation_0,axiom, % 0.70/0.97 c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Otype_OFun(v_Ta____,v_U____),tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Otype_OFun(v_Ta____,v_U____)) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_lift__type_0,axiom, % 0.70/0.97 ( c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),c_Lambda_Olift(V_t,V_i),V_T) % 0.70/0.97 | ~ c_Type_Otyping(V_e,V_t,V_T) ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_type_Osimps_I2_J_0,axiom, % 0.70/0.97 ( c_Type_Otype_OFun(V_type1,V_type2) != c_Type_Otype_OFun(V_type1_H,V_type2_H) % 0.70/0.97 | V_type1 = V_type1_H ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_type_Osimps_I2_J_1,axiom, % 0.70/0.97 ( c_Type_Otype_OFun(V_type1,V_type2) != c_Type_Otype_OFun(V_type1_H,V_type2_H) % 0.70/0.97 | V_type2 = V_type2_H ) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_shift__eq_0,axiom, % 0.70/0.97 hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ). % 0.70/0.97 % 0.70/0.97 cnf(cls_App_I3_J_0,axiom, % 0.70/0.97 c_Type_Otyping(v_ea____,v_ta____,v_Ta____) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_conjecture_0,negated_conjecture, % 0.70/0.97 ~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Otype_OFun(v_Ta____,v_U____),tc_Type_Otype),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_Ta____) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_fun__Orderings_Opreorder,axiom, % 0.70/0.97 ( class_Orderings_Opreorder(tc_fun(T_2,T_1)) % 0.70/0.97 | ~ class_Orderings_Opreorder(T_1) ) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_fun__Orderings_Oorder,axiom, % 0.70/0.97 ( class_Orderings_Oorder(tc_fun(T_2,T_1)) % 0.70/0.97 | ~ class_Orderings_Oorder(T_1) ) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_fun__Orderings_Obot,axiom, % 0.70/0.97 ( class_Orderings_Obot(tc_fun(T_2,T_1)) % 0.70/0.97 | ~ class_Orderings_Obot(T_1) ) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom, % 0.70/0.97 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom, % 0.70/0.97 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom, % 0.70/0.97 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,axiom, % 0.70/0.97 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom, % 0.70/0.97 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom, % 0.70/0.97 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom, % 0.70/0.97 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 0.70/0.97 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom, % 0.70/0.97 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Ring__and__Field_Opordered__semiring,axiom, % 0.70/0.97 class_Ring__and__Field_Opordered__semiring(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Ring__and__Field_Oordered__semiring,axiom, % 0.70/0.97 class_Ring__and__Field_Oordered__semiring(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom, % 0.70/0.97 class_Ring__and__Field_Ono__zero__divisors(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom, % 0.70/0.97 class_Ring__and__Field_Oordered__semidom(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom, % 0.70/0.97 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom, % 0.70/0.97 class_OrderedGroup_Oab__semigroup__mult(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom, % 0.70/0.97 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom, % 0.70/0.97 class_OrderedGroup_Oab__semigroup__add(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom, % 0.70/0.97 class_Ring__and__Field_Ocomm__semiring(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom, % 0.70/0.97 class_OrderedGroup_Ocomm__monoid__add(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom, % 0.70/0.97 class_Ring__and__Field_Ozero__neq__one(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom, % 0.70/0.97 class_Ring__and__Field_Osemiring__1(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom, % 0.70/0.97 class_Ring__and__Field_Osemiring__0(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Ring__and__Field_Omult__mono1,axiom, % 0.70/0.97 class_Ring__and__Field_Omult__mono1(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom, % 0.70/0.97 class_Ring__and__Field_Omult__zero(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Ring__and__Field_Omult__mono,axiom, % 0.70/0.97 class_Ring__and__Field_Omult__mono(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom, % 0.70/0.97 class_OrderedGroup_Omonoid__mult(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom, % 0.70/0.97 class_Ring__and__Field_Osemiring(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom, % 0.70/0.97 class_OrderedGroup_Omonoid__add(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Divides_Osemiring__div,axiom, % 0.70/0.97 class_Divides_Osemiring__div(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom, % 0.70/0.97 class_Nat_Osemiring__char__0(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Orderings_Opreorder,axiom, % 0.70/0.97 class_Orderings_Opreorder(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Orderings_Olinorder,axiom, % 0.70/0.97 class_Orderings_Olinorder(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Orderings_Oorder,axiom, % 0.70/0.97 class_Orderings_Oorder(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Orderings_Obot,axiom, % 0.70/0.97 class_Orderings_Obot(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(clsarity_nat__Power_Opower,axiom, % 0.70/0.97 class_Power_Opower(tc_nat) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom, % 0.70/0.97 c_fequal(V_x,V_x,T_a) ). % 0.70/0.97 % 0.70/0.97 cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom, % 0.70/0.97 ( V_X = V_Y % 0.70/0.97 | ~ c_fequal(V_X,V_Y,T_a) ) ). % 0.70/0.97 % 0.70/0.97 %------------------------------------------------------------------------------ % 0.70/0.97 %------------------------------------------- % 0.70/0.97 % Proof found % 0.70/0.97 % SZS status Theorem for theBenchmark % 0.70/0.97 % SZS output start Proof % 0.70/0.97 %ClaNum:1131(EqnAxiom:186) % 0.70/0.97 %VarNum:6358(SingletonVarNum:2417) % 0.70/0.97 %MaxLitNum:6 % 0.70/0.97 %MaxfuncDepth:6 % 0.70/0.97 %SharedTerms:74 % 0.70/0.97 %goalClause: 371 % 0.70/0.97 %singleGoalClaCount:1 % 0.70/0.97 [187]P1(a1) % 0.70/0.97 [188]P10(a1) % 0.70/0.97 [189]P11(a1) % 0.70/0.97 [190]P35(a1) % 0.70/0.97 [191]P12(a1) % 0.70/0.97 [192]P36(a1) % 0.70/0.97 [193]P13(a1) % 0.70/0.97 [194]P14(a1) % 0.70/0.97 [195]P37(a1) % 0.70/0.97 [196]P23(a1) % 0.70/0.97 [197]P28(a1) % 0.70/0.97 [198]P30(a1) % 0.70/0.97 [199]P33(a1) % 0.70/0.97 [200]P34(a1) % 0.70/0.97 [201]P15(a1) % 0.70/0.97 [202]P32(a1) % 0.70/0.97 [203]P16(a1) % 0.70/0.97 [204]P47(a1) % 0.70/0.97 [205]P2(a49) % 0.70/0.97 [206]P2(a53) % 0.70/0.97 [207]P56(a1) % 0.70/0.97 [208]P48(a1) % 0.70/0.97 [209]P31(a1) % 0.70/0.97 [210]P49(a1) % 0.70/0.97 [211]P19(a1) % 0.70/0.97 [212]P22(a1) % 0.70/0.97 [213]P39(a1) % 0.70/0.97 [214]P41(a1) % 0.70/0.97 [215]P42(a1) % 0.70/0.97 [216]P50(a1) % 0.70/0.97 [217]P57(a1) % 0.70/0.97 [218]P43(a1) % 0.70/0.97 [219]P44(a1) % 0.70/0.97 [220]P24(a1) % 0.70/0.97 [221]P25(a1) % 0.70/0.97 [222]P20(a1) % 0.70/0.97 [223]P38(a1) % 0.70/0.97 [229]P5(a50,a53,a51) % 0.70/0.97 [224]E(f2(a1),f12(a1)) % 0.70/0.97 [259]P5(a50,a49,f33(a51,a52)) % 0.70/0.97 [225]E(f27(f2(a1)),f2(a1)) % 0.70/0.97 [335]P5(f35(a50,f2(a1),f33(a51,a52),a47),f13(f2(a1)),f33(a51,a52)) % 0.70/0.97 [371]~P5(f35(a50,f2(a1),f33(a51,a52),a47),f18(a53,f2(a1)),a51) % 0.70/0.97 [266]E(f11(f30(f2(a1)),f30(f2(a1)),a1),f30(f2(a1))) % 0.70/0.97 [233]P7(x2331,x2331,a1) % 0.70/0.97 [364]~P3(x3641,x3641,a1) % 0.70/0.97 [226]P2(f13(x2261)) % 0.70/0.97 [227]E(f16(x2271,a44),f2(a1)) % 0.70/0.97 [236]E(f4(x2361,x2361,a1),f2(a1)) % 0.70/0.97 [237]P7(f2(a1),x2371,a1) % 0.70/0.97 [250]P3(x2501,f30(x2501),a1) % 0.70/0.97 [254]P3(f2(a1),f30(x2541),a1) % 0.70/0.97 [284]P7(x2841,f11(x2841,x2841,a1),a1) % 0.70/0.97 [349]~E(f30(x3491),x3491) % 0.70/0.97 [353]~E(f30(x3531),f2(a1)) % 0.70/0.97 [366]~P3(x3661,f2(a1),a1) % 0.70/0.97 [367]~P7(f30(x3671),x3671,a1) % 0.70/0.97 [228]E(f26(x2281,f2(a1)),x2281) % 0.70/0.97 [231]E(f45(f45(f3(a1),x2311),f2(a1)),x2311) % 0.70/0.97 [238]E(f4(x2381,f2(a1),a1),x2381) % 0.70/0.97 [239]E(f28(x2391,f2(a1),a1),x2391) % 0.70/0.97 [240]E(f28(f2(a1),x2401,a1),x2401) % 0.70/0.97 [244]E(f11(x2441,f2(a1),a1),f2(a1)) % 0.70/0.97 [245]E(f29(x2451,f2(a1),a1),f2(a1)) % 0.70/0.97 [246]E(f4(f2(a1),x2461,a1),f2(a1)) % 0.70/0.97 [247]E(f11(f2(a1),x2471,a1),f2(a1)) % 0.70/0.97 [248]E(f29(f2(a1),x2481,a1),f2(a1)) % 0.70/0.97 [324]P7(x3241,f11(x3241,f11(x3241,x3241,a1),a1),a1) % 0.70/0.97 [234]E(f45(f45(f3(a1),f2(a1)),x2341),x2341) % 0.70/0.97 [256]E(f5(x2561,f30(f2(a1)),a1),x2561) % 0.70/0.97 [257]E(f10(x2571,f30(f2(a1)),a1),f2(a1)) % 0.70/0.97 [262]E(f45(f45(f3(a1),f27(x2621)),f30(f2(a1))),f27(f30(x2621))) % 0.70/0.97 [235]P8(x2351,x2351,x2352) % 0.70/0.97 [267]P5(x2671,f13(x2672),f45(x2671,x2672)) % 0.70/0.97 [269]E(f11(x2691,x2692,a1),f11(x2692,x2691,a1)) % 0.70/0.97 [285]P7(f4(x2851,x2852,a1),x2851,a1) % 0.70/0.97 [286]P7(f5(x2861,x2862,a1),x2861,a1) % 0.70/0.97 [287]P7(f10(x2871,x2872,a1),x2871,a1) % 0.70/0.97 [289]P3(f4(x2891,x2892,a1),f30(x2891),a1) % 0.70/0.97 [355]~E(f15(x3551),f13(x3552)) % 0.70/0.97 [362]~P6(f13(x3621),x3622) % 0.70/0.97 [242]E(f17(f2(a1),x2421,x2422),x2421) % 0.70/0.97 [243]E(f19(f2(a1),x2431,x2432),x2431) % 0.70/0.97 [252]E(f20(f13(x2521),x2522,x2521),x2522) % 0.70/0.97 [272]E(f11(x2721,f2(a1),a1),f11(x2722,f2(a1),a1)) % 0.70/0.97 [273]E(f11(f2(a1),x2731,a1),f11(f2(a1),x2732,a1)) % 0.70/0.97 [275]E(f4(f30(x2751),f30(x2752),a1),f4(x2751,x2752,a1)) % 0.70/0.97 [288]E(f10(f11(x2881,x2882,a1),x2881,a1),f2(a1)) % 0.70/0.97 [290]P6(f14(f15(x2901),x2902),f20(x2901,x2902,f2(a1))) % 0.70/0.97 [291]E(f29(f30(x2911),f30(x2912),a1),f30(f29(x2911,x2912,a1))) % 0.70/0.97 [292]E(f28(f30(x2921),f30(x2922),a1),f30(f28(x2921,x2922,a1))) % 0.70/0.97 [294]E(f45(f45(f3(a1),x2941),f11(x2941,x2942,a1)),f11(x2941,f30(x2942),a1)) % 0.70/0.97 [295]E(f45(f45(f3(a1),x2951),f11(x2952,x2951,a1)),f11(f30(x2952),x2951,a1)) % 0.70/0.97 [315]E(f11(x3151,f5(x3152,x3151,a1),a1),f4(x3152,f10(x3152,x3151,a1),a1)) % 0.70/0.97 [317]E(f11(f5(x3171,x3172,a1),x3172,a1),f4(x3171,f10(x3171,x3172,a1),a1)) % 0.70/0.97 [268]E(f45(f45(f3(a1),x2681),x2682),f45(f45(f3(a1),x2682),x2681)) % 0.70/0.97 [271]E(f45(f45(f3(a1),f30(x2711)),x2712),f45(f45(f3(a1),x2711),f30(x2712))) % 0.70/0.97 [276]P7(x2761,f45(f45(f3(a1),x2762),x2761),a1) % 0.70/0.97 [278]P7(x2781,f45(f45(f3(a1),x2781),x2782),a1) % 0.70/0.97 [306]E(f5(f11(f2(a1),x3061,a1),f11(f2(a1),x3062,a1),a1),f2(a1)) % 0.70/0.97 [311]E(f45(f45(f3(a1),f4(x3111,x3112,a1)),x3112),f28(x3111,x3112,a1)) % 0.70/0.97 [321]E(f10(f30(f10(x3211,x3212,a1)),x3212,a1),f10(f30(x3211),x3212,a1)) % 0.70/0.97 [325]E(f4(x3251,f11(f5(x3251,x3252,a1),x3252,a1),a1),f10(x3251,x3252,a1)) % 0.70/0.97 [369]~P3(f45(f45(f3(a1),x3691),x3692),x3692,a1) % 0.70/0.97 [370]~P3(f45(f45(f3(a1),x3701),x3702),x3701,a1) % 0.70/0.97 [279]E(f4(f45(f45(f3(a1),x2791),x2792),x2792,a1),x2791) % 0.70/0.97 [280]E(f4(f45(f45(f3(a1),x2801),x2802),x2801,a1),x2802) % 0.70/0.97 [281]E(f4(x2811,f45(f45(f3(a1),x2811),x2812),a1),f2(a1)) % 0.70/0.97 [282]E(f30(f45(f45(f3(a1),x2821),x2822)),f45(f45(f3(a1),x2821),f30(x2822))) % 0.70/0.97 [283]E(f30(f45(f45(f3(a1),x2831),x2832)),f45(f45(f3(a1),f30(x2831)),x2832)) % 0.70/0.97 [296]P3(x2961,f30(f45(f45(f3(a1),x2962),x2961)),a1) % 0.70/0.97 [298]P3(x2981,f30(f45(f45(f3(a1),x2981),x2982)),a1) % 0.70/0.97 [356]~E(f13(x3561),f14(x3562,x3563)) % 0.70/0.97 [357]~E(f34(x3571),f33(x3572,x3573)) % 0.70/0.97 [358]~E(f15(x3581),f14(x3582,x3583)) % 0.70/0.97 [359]~E(f14(x3591,x3592),f13(x3593)) % 0.70/0.97 [360]~E(f14(x3601,x3602),f15(x3603)) % 0.70/0.97 [361]~E(f33(x3611,x3612),f34(x3613)) % 0.70/0.97 [265]E(f20(f18(x2651,x2652),x2653,x2652),x2651) % 0.70/0.97 [270]E(f14(f18(x2701,x2702),f18(x2703,x2702)),f18(f14(x2701,x2703),x2702)) % 0.70/0.97 [274]E(f21(f2(a1),x2741,x2742),f21(f2(a1),x2743,x2742)) % 0.70/0.97 [293]E(f18(f17(x2931,x2932,x2933),x2933),f17(f30(x2931),x2932,x2933)) % 0.70/0.97 [299]E(f22(x2991,x2992,f2(a1),x2993),x2991) % 0.70/0.97 [301]E(f23(x3011,x3012,f2(a1),x3013),x3011) % 0.70/0.97 [316]E(f5(f5(x3161,x3162,a1),x3163,a1),f5(x3161,f11(x3162,x3163,a1),a1)) % 0.70/0.97 [318]E(f11(f11(x3181,x3182,a1),x3183,a1),f11(x3181,f11(x3182,x3183,a1),a1)) % 0.70/0.97 [319]E(f4(f4(x3191,x3192,a1),x3193,a1),f4(f4(x3191,x3193,a1),x3192,a1)) % 0.70/0.97 [322]E(f4(f4(f30(x3221),x3222,a1),f30(x3223),a1),f4(f4(x3221,x3222,a1),x3223,a1)) % 0.70/0.97 [326]E(f4(f11(x3261,x3262,a1),f11(x3261,x3263,a1),a1),f11(x3261,f4(x3262,x3263,a1),a1)) % 0.70/0.97 [327]E(f10(f11(x3271,x3272,a1),f11(x3271,x3273,a1),a1),f11(x3271,f10(x3272,x3273,a1),a1)) % 0.70/0.97 [328]E(f4(f11(x3281,x3282,a1),f11(x3283,x3282,a1),a1),f11(f4(x3281,x3283,a1),x3282,a1)) % 0.70/0.97 [329]E(f10(f11(x3291,x3292,a1),f11(x3293,x3292,a1),a1),f11(f10(x3291,x3293,a1),x3292,a1)) % 0.70/0.97 [330]E(f29(f4(x3301,x3302,a1),f4(x3303,x3302,a1),a1),f4(f29(x3301,x3303,a1),x3302,a1)) % 0.70/0.97 [344]E(f45(f45(f3(a1),f11(x3441,f10(f5(x3442,x3441,a1),x3443,a1),a1)),f10(x3442,x3441,a1)),f10(x3442,f11(x3441,x3443,a1),a1)) % 0.70/0.97 [305]E(f45(f45(f3(a1),x3051),f45(f45(f3(a1),x3052),x3053)),f45(f45(f3(a1),x3052),f45(f45(f3(a1),x3051),x3053))) % 0.70/0.97 [307]E(f4(f45(f45(f3(a1),x3071),x3072),f45(f45(f3(a1),x3073),x3072),a1),f4(x3071,x3073,a1)) % 0.70/0.97 [308]E(f4(f45(f45(f3(a1),x3081),x3082),f45(f45(f3(a1),x3081),x3083),a1),f4(x3082,x3083,a1)) % 0.70/0.97 [309]E(f4(x3091,f45(f45(f3(a1),x3092),x3093),a1),f4(f4(x3091,x3092,a1),x3093,a1)) % 0.70/0.97 [331]E(f45(f45(f3(a1),f11(x3311,x3312,a1)),f11(x3311,x3313,a1)),f11(x3311,f45(f45(f3(a1),x3312),x3313),a1)) % 0.70/0.97 [332]E(f45(f45(f3(a1),f11(x3321,x3322,a1)),f11(x3323,x3322,a1)),f11(f45(f45(f3(a1),x3321),x3323),x3322,a1)) % 0.70/0.97 [334]E(f10(f45(f45(f3(a1),f11(x3341,x3342,a1)),x3343),x3342,a1),f10(x3343,x3342,a1)) % 0.70/0.97 [343]E(f45(f45(f3(a1),f11(x3431,f5(x3432,x3433,a1),a1)),f5(f11(x3431,f10(x3432,x3433,a1),a1),x3433,a1)),f5(f11(x3431,x3432,a1),x3433,a1)) % 0.70/0.97 [346]E(f45(f45(f3(a1),f45(f45(f3(a1),f5(x3461,x3462,a1)),f5(x3463,x3462,a1))),f5(f45(f45(f3(a1),f10(x3461,x3462,a1)),f10(x3463,x3462,a1)),x3462,a1)),f5(f45(f45(f3(a1),x3461),x3463),x3462,a1)) % 0.70/0.97 [323]E(f45(f45(f3(a1),f45(f45(f3(a1),x3231),x3232)),x3233),f45(f45(f3(a1),x3231),f45(f45(f3(a1),x3232),x3233))) % 0.70/0.97 [339]E(f10(f30(f45(f45(f3(a1),f11(x3391,x3392,a1)),x3393)),x3392,a1),f10(f30(x3393),x3392,a1)) % 0.70/0.97 [302]E(f23(x3021,x3022,f30(x3023),x3024),f45(x3022,x3023)) % 0.70/0.97 [303]E(f42(x3031,x3032,f34(x3033),x3034),f45(x3031,x3033)) % 0.70/0.97 [304]E(f43(x3041,x3042,f34(x3043),x3044),f45(x3041,x3043)) % 0.70/0.97 [312]E(f14(f17(x3121,x3122,x3123),f17(x3121,x3124,x3123)),f17(x3121,f14(x3122,x3124),x3123)) % 0.70/0.97 [313]E(f14(f20(x3131,x3132,x3133),f20(x3134,x3132,x3133)),f20(f14(x3131,x3134),x3132,x3133)) % 0.70/0.97 [320]E(f19(x3201,f21(x3202,x3203,x3204),x3204),f21(f4(x3202,x3201,a1),x3203,x3204)) % 0.70/0.97 [333]E(f45(f35(x3331,x3332,x3333,x3334),x3332),x3333) % 0.70/0.97 [338]E(f45(f45(x3381,x3382),f22(x3383,x3381,x3382,x3384)),f22(x3383,x3381,f30(x3382),x3384)) % 0.70/0.97 [340]E(f31(x3401,x3402,x3403,f2(a1),x3404),x3401) % 0.70/0.97 [310]E(f19(x3101,f19(x3102,x3103,x3104),x3104),f19(f45(f45(f3(a1),x3101),x3102),x3103,x3104)) % 0.70/0.97 [341]E(f45(f45(f3(a1),f11(x3411,x3412,a1)),f45(f45(f3(a1),f11(x3413,x3412,a1)),x3414)),f45(f45(f3(a1),f11(f45(f45(f3(a1),x3411),x3413),x3412,a1)),x3414)) % 0.70/0.97 [314]E(f43(x3141,x3142,f33(x3143,x3144),x3145),f45(f45(x3142,x3143),x3144)) % 0.70/0.97 [342]E(f35(f35(x3421,f2(a1),x3422,x3423),f30(x3424),x3425,x3423),f35(f35(x3421,x3424,x3425,x3423),f2(a1),x3422,x3423)) % 0.70/0.97 [345]E(f45(f45(f45(f45(x3451,x3452),x3453),f42(x3454,x3451,x3452,x3455)),f42(x3454,x3451,x3453,x3455)),f42(x3454,x3451,f33(x3452,x3453),x3455)) % 0.70/0.97 [347]E(f45(f45(x3471,x3472),f31(x3473,x3471,x3472,x3474,x3475)),f31(x3473,x3471,x3472,f30(x3474),x3475)) % 0.70/0.97 [377]~P2(x3771)+P2(f15(x3771)) % 0.70/0.97 [390]E(x3901,f2(a1))+P3(f2(a1),x3901,a1) % 0.70/0.97 [437]E(x4371,f2(a1))+~P7(x4371,f2(a1),a1) % 0.70/0.97 [378]~P56(x3781)+E(f24(f2(a1),x3781),f2(x3781)) % 0.70/0.97 [426]~P27(x4261)+E(f45(f45(f3(x4261),f2(x4261)),f2(x4261)),f2(x4261)) % 0.70/0.97 [460]E(x4601,f2(a1))+~P3(x4601,f30(f2(a1)),a1) % 0.70/0.97 [899]~P46(x8991)+E(f45(f45(f3(x8991),f11(f2(x8991),f2(x8991),x8991)),f11(f2(x8991),f2(x8991),x8991)),f2(x8991)) % 0.70/0.97 [1028]~P46(x10281)+P7(f45(f45(f3(x10281),f11(f2(x10281),f2(x10281),x10281)),f11(f2(x10281),f2(x10281),x10281)),f2(x10281),x10281) % 0.70/0.97 [1046]~P46(x10461)+~P3(f2(x10461),f45(f45(f3(x10461),f11(f2(x10461),f2(x10461),x10461)),f11(f2(x10461),f2(x10461),x10461)),x10461) % 0.70/0.97 [620]~P3(f2(a1),x6201,a1)+E(f30(f4(x6201,f30(f2(a1)),a1)),x6201) % 0.70/0.97 [391]~P33(x3912)+P7(x3911,x3911,x3912) % 0.70/0.97 [392]~P34(x3922)+P7(x3921,x3921,x3922) % 0.70/0.97 [438]~P3(x4382,x4382,x4381)+~P12(x4381) % 0.70/0.97 [439]~P3(x4392,x4392,x4391)+~P33(x4391) % 0.70/0.97 [440]~P3(x4402,x4402,x4401)+~P34(x4401) % 0.70/0.97 [459]P7(x4592,x4591,a1)+P7(x4591,x4592,a1) % 0.70/0.97 [502]~P3(x5021,x5022,a1)+P7(x5021,x5022,a1) % 0.70/0.97 [373]E(x3731,x3732)+~E(f30(x3731),f30(x3732)) % 0.70/0.97 [374]E(x3741,x3742)+~E(f13(x3741),f13(x3742)) % 0.70/0.97 [375]E(x3751,x3752)+~E(f34(x3751),f34(x3752)) % 0.70/0.97 [376]E(x3761,x3762)+~E(f15(x3761),f15(x3762)) % 0.70/0.97 [379]~P33(x3792)+P33(f48(x3791,x3792)) % 0.70/0.97 [380]~P34(x3802)+P34(f48(x3801,x3802)) % 0.70/0.97 [381]~P32(x3812)+P32(f48(x3811,x3812)) % 0.70/0.97 [382]~P2(x3821)+P2(f18(x3821,x3822)) % 0.70/0.97 [387]~P6(x3871,x3872)+P6(f15(x3871),f15(x3872)) % 0.70/0.97 [393]~P21(x3932)+E(f11(x3931,x3931,x3932),x3931) % 0.70/0.97 [394]~P12(x3942)+E(f29(x3941,x3941,x3942),x3941) % 0.70/0.97 [395]~P12(x3952)+E(f28(x3951,x3951,x3952),x3951) % 0.70/0.97 [397]~P26(x3972)+E(f4(x3971,x3971,x3972),f2(x3972)) % 0.70/0.97 [398]~P18(x3982)+E(f4(x3981,x3981,x3982),f2(x3982)) % 0.70/0.97 [399]~P1(x3992)+E(f10(x3991,x3991,x3992),f2(x3992)) % 0.70/0.97 [403]~P32(x4031)+P7(f12(x4031),x4032,x4031) % 0.70/0.97 [442]~P36(x4421)+P7(f2(x4421),f24(x4422,x4421),x4421) % 0.70/0.97 [472]P3(x4721,x4722,a1)+P3(x4722,f30(x4721),a1) % 0.70/0.97 [474]P7(x4741,x4742,a1)+P7(f30(x4742),x4741,a1) % 0.70/0.97 [503]~P3(x5031,x5032,a1)+E(f10(x5031,x5032,a1),x5031) % 0.70/0.97 [504]~P7(x5041,x5042,a1)+E(f4(x5041,x5042,a1),f2(a1)) % 0.70/0.97 [505]~P3(x5051,x5052,a1)+E(f5(x5051,x5052,a1),f2(a1)) % 0.70/0.97 [509]P7(x5091,x5092,a1)+~E(f4(x5091,x5092,a1),f2(a1)) % 0.70/0.97 [510]~P3(x5101,x5102,a1)+P3(x5101,f30(x5102),a1) % 0.70/0.97 [511]~P7(x5111,x5112,a1)+P3(x5111,f30(x5112),a1) % 0.70/0.97 [513]~P7(x5131,x5132,a1)+P7(x5131,f30(x5132),a1) % 0.70/0.97 [515]~P3(x5151,x5152,a1)+P7(f30(x5151),x5152,a1) % 0.70/0.97 [516]~P36(x5161)+~P3(f24(x5162,x5161),f2(x5161),x5161) % 0.70/0.97 [517]P7(x5171,x5172,a1)+~P3(x5171,f30(x5172),a1) % 0.70/0.97 [518]P3(x5181,x5182,a1)+~P3(f30(x5181),x5182,a1) % 0.70/0.97 [520]P3(x5201,x5202,a1)+~P7(f30(x5201),x5202,a1) % 0.70/0.97 [521]P7(x5211,x5212,a1)+~P7(f30(x5211),x5212,a1) % 0.70/0.97 [538]~P3(x5381,x5382,a1)+P3(f30(x5381),f30(x5382),a1) % 0.70/0.97 [539]~P7(x5391,x5392,a1)+P7(f30(x5391),f30(x5392),a1) % 0.70/0.97 [555]P3(x5551,x5552,a1)+~P3(f30(x5551),f30(x5552),a1) % 0.70/0.97 [556]P7(x5561,x5562,a1)+~P7(f30(x5561),f30(x5562),a1) % 0.70/0.97 [578]~P46(x5781)+P7(f2(x5781),f11(x5782,x5782,x5781),x5781) % 0.70/0.97 [582]~P3(x5821,x5822,a1)+~P3(x5822,f30(x5821),a1) % 0.70/0.97 [583]~P7(x5831,x5832,a1)+~P7(f30(x5832),x5831,a1) % 0.70/0.97 [659]~P3(x6592,x6591,a1)+P3(f2(a1),f4(x6591,x6592,a1),a1) % 0.70/0.97 [660]P3(f10(x6601,x6602,a1),x6602,a1)+~P3(f2(a1),x6602,a1) % 0.70/0.97 [661]P7(f10(x6611,x6612,a1),x6612,a1)+~P3(f2(a1),x6612,a1) % 0.70/0.97 [696]~P46(x6961)+~P3(f11(x6962,x6962,x6961),f2(x6961),x6961) % 0.70/0.97 [709]P3(x7091,x7092,a1)+~P3(f2(a1),f4(x7092,x7091,a1),a1) % 0.70/0.97 [712]P3(f2(a1),x7121,a1)+~P3(f2(a1),f11(x7122,x7121,a1),a1) % 0.70/0.97 [713]P3(f2(a1),x7131,a1)+~P3(f2(a1),f11(x7131,x7132,a1),a1) % 0.70/0.97 [388]~P2(x3881)+P2(f14(x3881,f13(x3882))) % 0.70/0.97 [400]~P14(x4001)+E(f45(f45(f3(x4001),x4002),f2(x4001)),x4002) % 0.70/0.97 [401]~P37(x4011)+E(f45(f45(f3(x4011),x4012),f2(x4011)),x4012) % 0.70/0.97 [402]~P24(x4021)+E(f45(f45(f3(x4021),x4022),f2(x4021)),x4022) % 0.70/0.97 [404]~P26(x4042)+E(f4(x4041,f2(x4042),x4042),x4041) % 0.70/0.97 [405]~P1(x4052)+E(f10(x4051,f2(x4052),x4052),x4051) % 0.70/0.97 [406]~P1(x4062)+E(f5(x4061,f2(x4062),x4062),f2(x4062)) % 0.70/0.97 [407]~P37(x4072)+E(f11(x4071,f2(x4072),x4072),f2(x4072)) % 0.70/0.97 [408]~P44(x4082)+E(f11(x4081,f2(x4082),x4082),f2(x4082)) % 0.70/0.97 [409]~P52(x4092)+E(f11(x4091,f2(x4092),x4092),f2(x4092)) % 0.70/0.97 [410]~P1(x4101)+E(f5(f2(x4101),x4102,x4101),f2(x4101)) % 0.70/0.97 [412]~P37(x4121)+E(f11(f2(x4121),x4122,x4121),f2(x4121)) % 0.70/0.97 [413]~P44(x4131)+E(f11(f2(x4131),x4132,x4131),f2(x4131)) % 0.70/0.97 [414]~P52(x4141)+E(f11(f2(x4141),x4142,x4141),f2(x4141)) % 0.70/0.97 [415]~P1(x4151)+E(f10(f2(x4151),x4152,x4151),f2(x4151)) % 0.70/0.97 [449]P58(f45(x4491,x4492))+~P58(f45(x4491,f36(x4491))) % 0.70/0.97 [455]E(x4551,f30(f2(a1)))+~E(f11(x4552,x4551,a1),f30(f2(a1))) % 0.70/0.97 [456]E(x4561,f30(f2(a1)))+~E(f11(x4561,x4562,a1),f30(f2(a1))) % 0.70/0.97 [461]~P3(x4611,x4612,a1)+E(f18(f13(x4611),x4612),f13(x4611)) % 0.70/0.97 [500]E(x5001,f2(a1))+E(f26(x5001,f10(x5002,x5001,a1)),f26(x5002,x5001)) % 0.70/0.97 [614]P3(x6142,x6141,a1)+E(f45(f45(f3(a1),x6141),f4(x6142,x6141,a1)),x6142) % 0.70/0.97 [644]~E(f30(f10(x6441,x6442,a1)),x6442)+E(f10(f30(x6441),x6442,a1),f2(a1)) % 0.70/0.97 [653]~P7(x6531,x6532,a1)+E(f45(f45(f3(a1),x6531),f4(x6532,x6531,a1)),x6532) % 0.70/0.97 [658]~P7(x6582,x6581,a1)+E(f4(x6581,f4(x6581,x6582,a1),a1),x6582) % 0.70/0.97 [662]~P3(f2(a1),x6622,a1)+E(f5(f11(x6621,x6622,a1),x6622,a1),x6621) % 0.70/0.97 [663]~P3(f2(a1),x6631,a1)+E(f5(f11(x6631,x6632,a1),x6631,a1),x6632) % 0.70/0.97 [665]~P7(x6652,x6651,a1)+E(f30(f4(x6651,x6652,a1)),f4(f30(x6651),x6652,a1)) % 0.70/0.97 [684]~P3(f2(a1),x6841,a1)+P3(f4(x6841,f30(x6842),a1),x6841,a1) % 0.70/0.97 [688]P3(x6881,x6882,a1)+E(f10(f4(x6881,x6882,a1),x6882,a1),f10(x6881,x6882,a1)) % 0.70/0.97 [698]E(f30(f10(x6981,x6982,a1)),x6982)+E(f30(f10(x6981,x6982,a1)),f10(f30(x6981),x6982,a1)) % 0.70/0.97 [705]~P7(x7052,x7051,a1)+E(f10(f4(x7051,x7052,a1),x7052,a1),f10(x7051,x7052,a1)) % 0.70/0.97 [763]P7(f30(f2(a1)),x7631,a1)+~P7(f30(f2(a1)),f11(x7632,x7631,a1),a1) % 0.70/0.97 [764]P7(f30(f2(a1)),x7641,a1)+~P7(f30(f2(a1)),f11(x7641,x7642,a1),a1) % 0.70/0.97 [898]~P3(f2(a1),x8981,a1)+P7(f11(x8981,f5(x8982,x8981,a1),a1),x8982,a1) % 0.70/0.97 [1041]~P14(x10411)+E(f31(f2(x10411),f3(x10411),f2(x10411),x10412,x10411),f2(x10411)) % 0.70/0.97 [416]~P14(x4161)+E(f45(f45(f3(x4161),f2(x4161)),x4162),x4162) % 0.70/0.97 [418]~P37(x4181)+E(f45(f45(f3(x4181),f2(x4181)),x4182),x4182) % 0.70/0.97 [419]~P24(x4191)+E(f45(f45(f3(x4191),f2(x4191)),x4192),x4192) % 0.70/0.97 [423]E(x4231,f2(a1))+~E(f45(f45(f3(a1),x4232),x4231),x4232) % 0.70/0.97 [424]E(x4241,f2(a1))+~E(f45(f45(f3(a1),x4242),x4241),f2(a1)) % 0.70/0.97 [425]E(x4251,f2(a1))+~E(f45(f45(f3(a1),x4251),x4252),f2(a1)) % 0.70/0.97 [707]~P58(f45(x7071,x7072))+P58(f45(x7071,f10(x7072,f2(a1),a1))) % 0.70/0.97 [711]~P58(f45(x7111,f2(a1)))+P58(f45(x7111,f5(x7112,f2(a1),a1))) % 0.70/0.97 [771]~P7(x7712,x7711,a1)+E(f45(f45(f3(a1),f4(x7711,x7712,a1)),x7712),x7711) % 0.70/0.97 [868]P58(f45(x8681,x8682))+~P58(f45(x8681,f10(x8682,f2(a1),a1))) % 0.70/0.97 [874]P58(f45(x8741,f2(a1)))+~P58(f45(x8741,f5(x8742,f2(a1),a1))) % 0.70/0.97 [1008]~P3(f2(a1),x10082,a1)+P3(x10081,f11(x10082,f30(f5(x10081,x10082,a1)),a1),a1) % 0.70/0.97 [429]E(x4291,x4292)+~P8(x4291,x4292,x4293) % 0.70/0.97 [430]~P6(x4301,x4303)+P6(f14(x4301,x4302),f14(x4303,x4302)) % 0.70/0.97 [431]~P6(x4312,x4313)+P6(f14(x4311,x4312),f14(x4311,x4313)) % 0.70/0.97 [432]~P6(x4321,x4323)+P6(f18(x4321,x4322),f18(x4323,x4322)) % 0.70/0.97 [468]~P5(x4681,f13(x4682),x4683)+E(f45(x4681,x4682),x4683) % 0.70/0.97 [477]~P37(x4773)+E(f11(x4771,x4772,x4773),f11(x4772,x4771,x4773)) % 0.70/0.97 [478]~P12(x4783)+E(f29(x4781,x4782,x4783),f29(x4782,x4781,x4783)) % 0.70/0.97 [479]~P12(x4793)+E(f28(x4791,x4792,x4793),f28(x4792,x4791,x4793)) % 0.70/0.97 [561]~P12(x5613)+P7(x5611,f28(x5612,x5611,x5613),x5613) % 0.70/0.97 [562]~P12(x5623)+P7(x5621,f28(x5621,x5622,x5623),x5623) % 0.70/0.97 [563]~P12(x5633)+P7(f29(x5631,x5632,x5633),x5632,x5633) % 0.70/0.97 [564]~P12(x5643)+P7(f29(x5641,x5642,x5643),x5641,x5643) % 0.70/0.97 [656]~P3(x6561,x6563,a1)+P3(f4(x6561,x6562,a1),x6563,a1) % 0.70/0.97 [732]P7(f11(x7322,x7321,a1),f11(x7323,x7321,a1),a1)+P3(f2(a1),x7321,a1) % 0.70/0.97 [733]P7(f11(x7331,x7332,a1),f11(x7331,x7333,a1),a1)+P3(f2(a1),x7331,a1) % 0.70/0.97 [781]~P7(x7811,x7813,a1)+P7(f4(x7811,x7812,a1),f4(x7813,x7812,a1),a1) % 0.70/0.97 [782]~P7(x7823,x7822,a1)+P7(f4(x7821,x7822,a1),f4(x7821,x7823,a1),a1) % 0.70/0.97 [783]~P7(x7831,x7833,a1)+P7(f5(x7831,x7832,a1),f5(x7833,x7832,a1),a1) % 0.70/0.97 [785]~P7(x7851,x7853,a1)+P7(f11(x7851,x7852,a1),f11(x7853,x7852,a1),a1) % 0.70/0.97 [787]~P7(x7872,x7873,a1)+P7(f11(x7871,x7872,a1),f11(x7871,x7873,a1),a1) % 0.70/0.97 [920]P3(x9201,x9202,a1)+~P3(f11(x9203,x9201,a1),f11(x9203,x9202,a1),a1) % 0.70/0.97 [921]P3(x9211,x9212,a1)+~P3(f11(x9211,x9213,a1),f11(x9212,x9213,a1),a1) % 0.70/0.97 [922]~P3(f11(x9222,x9221,a1),f11(x9223,x9221,a1),a1)+P3(f2(a1),x9221,a1) % 0.70/0.97 [923]~P3(f11(x9231,x9232,a1),f11(x9231,x9233,a1),a1)+P3(f2(a1),x9231,a1) % 0.70/0.97 [493]~P2(x4931)+P2(f20(x4931,f13(x4932),x4933)) % 0.70/0.97 [527]~P3(x5272,x5273,a1)+E(f17(x5271,f13(x5272),x5273),f13(x5272)) % 0.70/0.97 [528]~P3(x5281,x5283,a1)+E(f20(f13(x5281),x5282,x5283),f13(x5281)) % 0.70/0.97 [565]~P12(x5653)+E(f29(x5651,f28(x5651,x5652,x5653),x5653),x5651) % 0.70/0.97 [566]~P12(x5663)+E(f28(x5661,f29(x5661,x5662,x5663),x5663),x5661) % 0.70/0.97 [568]~P1(x5683)+E(f5(f10(x5681,x5682,x5683),x5682,x5683),f2(x5683)) % 0.70/0.97 [569]~P1(x5693)+E(f10(f11(x5691,x5692,x5693),x5692,x5693),f2(x5693)) % 0.70/0.97 [570]~P1(x5703)+E(f10(f11(x5701,x5702,x5703),x5701,x5703),f2(x5703)) % 0.70/0.97 [602]E(x6021,x6022)+~E(f11(f30(x6023),x6021,a1),f11(f30(x6023),x6022,a1)) % 0.70/0.97 [621]~P21(x6213)+E(f11(x6211,f11(x6211,x6212,x6213),x6213),f11(x6211,x6212,x6213)) % 0.70/0.97 [622]~P12(x6223)+E(f29(x6221,f29(x6221,x6222,x6223),x6223),f29(x6221,x6222,x6223)) % 0.70/0.97 [623]~P12(x6233)+E(f28(x6231,f28(x6231,x6232,x6233),x6233),f28(x6231,x6232,x6233)) % 0.70/0.97 [624]~P1(x6243)+E(f10(f10(x6241,x6242,x6243),x6242,x6243),f10(x6241,x6242,x6243)) % 0.70/0.97 [637]~P11(x6373)+E(f11(x6371,f32(x6371,x6372,x6373),x6373),f32(x6371,f30(x6372),x6373)) % 0.70/0.97 [640]~P23(x6403)+E(f11(f32(x6401,x6402,x6403),x6401,x6403),f32(x6401,f30(x6402),x6403)) % 0.70/0.97 [641]~P37(x6413)+E(f11(x6411,f32(x6411,x6412,x6413),x6413),f32(x6411,f30(x6412),x6413)) % 0.70/0.97 [642]~P37(x6423)+E(f11(f32(x6421,x6422,x6423),x6421,x6423),f32(x6421,f30(x6422),x6423)) % 0.70/0.97 [643]~P56(x6432)+E(f11(f24(x6431,x6432),f24(x6433,x6432),x6432),f24(f11(x6431,x6433,a1),x6432)) % 0.70/0.97 [685]~P56(x6853)+E(f25(x6851,f2(a1),x6852,x6853),x6852) % 0.70/0.97 [731]E(x7311,f2(a1))+E(f5(f11(x7311,x7312,a1),f11(x7311,x7313,a1),a1),f5(x7312,x7313,a1)) % 0.70/0.97 [742]~P5(x7422,f15(x7423),x7421)+E(f33(f39(x7421,x7422,x7423),f41(x7421,x7422,x7423)),x7421) % 0.70/0.97 [759]~P23(x7593)+E(f11(f32(x7591,x7592,x7593),x7591,x7593),f11(x7591,f32(x7591,x7592,x7593),x7593)) % 0.70/0.97 [829]~P3(x8292,x8293,a1)+P3(f11(f30(x8291),x8292,a1),f11(f30(x8291),x8293,a1),a1) % 0.70/0.97 [857]~P3(f2(a1),x8571,a1)+E(f5(f11(x8571,x8572,a1),f11(x8571,x8573,a1),a1),f5(x8572,x8573,a1)) % 0.70/0.97 [939]P7(x9391,x9392,a1)+~P7(f11(f30(x9393),x9391,a1),f11(f30(x9393),x9392,a1),a1) % 0.70/0.97 [1010]~P5(x10101,f15(x10102),x10103)+P5(f35(x10101,f2(a1),f37(x10101,x10102),a47),x10102,f38(x10101,x10102)) % 0.70/0.97 [1020]~P1(x10201)+E(f45(f45(f3(x10201),f11(x10202,f5(x10203,x10202,x10201),x10201)),f10(x10203,x10202,x10201)),x10203) % 0.70/0.97 [1021]~P1(x10211)+E(f45(f45(f3(x10211),f11(f5(x10212,x10213,x10211),x10213,x10211)),f10(x10212,x10213,x10211)),x10212) % 0.70/0.97 [1022]~P46(x10221)+P7(f2(x10221),f45(f45(f3(x10221),f11(x10222,x10222,x10221)),f11(x10223,x10223,x10221)),x10221) % 0.70/0.97 [1030]~P5(x10301,f15(x10303),x10302)+P5(f35(x10301,f2(a1),f39(x10302,x10301,x10303),a47),x10303,f41(x10302,x10301,x10303)) % 0.70/0.97 [1042]~P46(x10421)+~P3(f45(f45(f3(x10421),f11(x10422,x10422,x10421)),f11(x10423,x10423,x10421)),f2(x10421),x10421) % 0.70/0.97 [469]~P14(x4691)+E(f45(f45(f3(x4691),x4692),x4693),f45(f45(f3(x4691),x4693),x4692)) % 0.70/0.97 [471]~P37(x4711)+E(f45(f45(f3(x4711),x4712),x4713),f45(f45(f3(x4711),x4713),x4712)) % 0.70/0.97 [523]E(x5231,x5232)+~E(f45(f45(f3(a1),x5233),x5231),f45(f45(f3(a1),x5233),x5232)) % 0.70/0.97 [524]E(x5241,x5242)+~E(f45(f45(f3(a1),x5241),x5243),f45(f45(f3(a1),x5242),x5243)) % 0.70/0.97 [626]~P3(x6261,x6263,a1)+P3(x6261,f45(f45(f3(a1),x6262),x6263),a1) % 0.70/0.97 [628]~P3(x6281,x6282,a1)+P3(x6281,f45(f45(f3(a1),x6282),x6283),a1) % 0.70/0.97 [630]~P7(x6301,x6303,a1)+P7(x6301,f45(f45(f3(a1),x6302),x6303),a1) % 0.70/0.97 [632]~P7(x6321,x6322,a1)+P7(x6321,f45(f45(f3(a1),x6322),x6323),a1) % 0.70/0.97 [697]~P26(x6971)+E(f45(f45(f3(x6971),f4(x6972,x6973,x6971)),x6973),x6972) % 0.70/0.97 [699]P3(x6991,x6992,a1)+~P3(f45(f45(f3(a1),x6991),x6993),x6992,a1) % 0.70/0.97 [700]P7(x7001,x7002,a1)+~P7(f45(f45(f3(a1),x7003),x7001),x7002,a1) % 0.70/0.97 [701]P7(x7011,x7012,a1)+~P7(f45(f45(f3(a1),x7011),x7013),x7012,a1) % 0.70/0.97 [708]~P1(x7081)+E(f5(f11(f2(x7081),x7082,x7081),f11(f2(x7081),x7083,x7081),x7081),f2(x7081)) % 0.70/0.97 [734]~P3(x7341,x7343,a1)+P3(f45(f45(f3(a1),x7341),x7342),f45(f45(f3(a1),x7343),x7342),a1) % 0.70/0.97 [735]~P3(x7352,x7353,a1)+P3(f45(f45(f3(a1),x7351),x7352),f45(f45(f3(a1),x7351),x7353),a1) % 0.70/0.97 [736]~P7(x7361,x7363,a1)+P7(f45(f45(f3(a1),x7361),x7362),f45(f45(f3(a1),x7363),x7362),a1) % 0.70/0.97 [737]~P7(x7372,x7373,a1)+P7(f45(f45(f3(a1),x7371),x7372),f45(f45(f3(a1),x7371),x7373),a1) % 0.70/0.97 [840]P3(x8401,f4(x8402,x8403,a1),a1)+~P3(f45(f45(f3(a1),x8401),x8403),x8402,a1) % 0.70/0.97 [841]P7(f4(x8411,x8412,a1),x8413,a1)+~P7(x8411,f45(f45(f3(a1),x8413),x8412),a1) % 0.70/0.97 [844]~P7(f4(x8441,x8443,a1),x8442,a1)+P7(x8441,f45(f45(f3(a1),x8442),x8443),a1) % 0.70/0.97 [845]~P3(x8451,f4(x8453,x8452,a1),a1)+P3(f45(f45(f3(a1),x8451),x8452),x8453,a1) % 0.70/0.97 [865]P3(x8651,x8652,a1)+~P3(f45(f45(f3(a1),x8653),x8651),f45(f45(f3(a1),x8653),x8652),a1) % 0.70/0.97 [866]P7(x8661,x8662,a1)+~P7(f45(f45(f3(a1),x8663),x8661),f45(f45(f3(a1),x8663),x8662),a1) % 0.70/0.97 [936]~P7(x9362,x9363,a1)+E(f4(f45(f45(f3(a1),x9361),x9362),f30(x9363),a1),f4(x9361,f30(f4(x9363,x9362,a1)),a1)) % 0.70/0.97 [988]~P1(x9881)+E(f45(f45(f3(x9881),f10(x9882,x9883,x9881)),f11(f5(x9882,x9883,x9881),x9883,x9881)),x9882) % 0.70/0.97 [1051]P58(f45(x10511,x10512))+~P58(f45(x10511,f23(x10512,x10513,f2(a1),a46))) % 0.70/0.97 [559]~P26(x5591)+E(f4(f45(f45(f3(x5591),x5592),x5593),x5593,x5591),x5592) % 0.70/0.97 [615]P3(x6152,x6153,a1)+E(f17(x6151,f13(x6152),x6153),f13(f45(f45(f3(a1),x6152),x6151))) % 0.70/0.97 [617]~P1(x6171)+E(f10(f45(f45(f3(x6171),x6172),x6173),x6173,x6171),f10(x6172,x6173,x6171)) % 0.70/0.97 [618]~P1(x6181)+E(f10(f45(f45(f3(x6181),x6182),x6183),x6182,x6181),f10(x6183,x6182,x6181)) % 0.70/0.97 [657]~P56(x6571)+E(f45(f45(f3(x6571),f24(x6572,x6571)),f24(x6573,x6571)),f24(f45(f45(f3(a1),x6572),x6573),x6571)) % 0.70/0.97 [839]~P7(x8393,x8392,a1)+E(f4(f45(f45(f3(a1),x8391),x8392),x8393,a1),f45(f45(f3(a1),x8391),f4(x8392,x8393,a1))) % 0.70/0.97 [842]~P7(x8422,x8423,a1)+E(f4(f45(f45(f3(a1),x8421),x8422),x8423,a1),f4(x8421,f4(x8423,x8422,a1),a1)) % 0.70/0.97 [867]~P7(x8673,x8672,a1)+P7(x8671,f4(f45(f45(f3(a1),x8672),x8671),x8673,a1),a1) % 0.70/0.97 [932]~P7(x9323,x9321,a1)+E(f4(f45(f45(f3(a1),x9321),x9322),x9323,a1),f45(f45(f3(a1),f4(x9321,x9323,a1)),x9322)) % 0.70/0.97 [937]~P7(x9372,x9371,a1)+E(f4(f30(x9371),f45(f45(f3(a1),x9372),x9373),a1),f4(f30(f4(x9371,x9372,a1)),x9373,a1)) % 0.70/0.97 [1087]~P14(x10871)+E(f45(f45(f3(x10871),f31(f2(x10871),f3(x10871),x10872,x10873,x10871)),x10872),f31(f2(x10871),f3(x10871),x10872,f30(x10873),x10871)) % 0.70/0.97 [1032]P58(f45(x10321,x10322))+~P58(f45(x10321,f4(f45(f45(f3(a1),x10323),x10322),x10323,a1))) % 0.70/0.97 [383]E(x3831,x3832)+~E(f14(x3833,x3831),f14(x3834,x3832)) % 0.70/0.97 [384]E(x3841,x3842)+~E(f33(x3843,x3841),f33(x3844,x3842)) % 0.70/0.97 [385]E(x3851,x3852)+~E(f14(x3851,x3853),f14(x3852,x3854)) % 0.70/0.97 [386]E(x3861,x3862)+~E(f33(x3861,x3863),f33(x3862,x3864)) % 0.70/0.97 [664]~P6(x6641,x6644)+P6(f20(x6641,x6642,x6643),f20(x6644,x6642,x6643)) % 0.70/0.97 [1009]~P5(x10091,f14(x10094,x10092),x10093)+P5(x10091,x10092,f40(x10093,x10091,x10094,x10092)) % 0.70/0.97 [750]~P37(x7503)+E(f32(f32(x7501,x7502,x7503),x7504,x7503),f32(x7501,f11(x7502,x7504,a1),x7503)) % 0.70/0.97 [751]~P23(x7513)+E(f32(f32(x7511,x7512,x7513),x7514,x7513),f32(x7511,f11(x7512,x7514,a1),x7513)) % 0.70/0.97 [752]~P37(x7524)+E(f11(x7521,f11(x7522,x7523,x7524),x7524),f11(x7522,f11(x7521,x7523,x7524),x7524)) % 0.70/0.97 [753]~P12(x7534)+E(f29(x7531,f29(x7532,x7533,x7534),x7534),f29(x7532,f29(x7531,x7533,x7534),x7534)) % 0.70/0.97 [754]~P12(x7544)+E(f28(x7541,f28(x7542,x7543,x7544),x7544),f28(x7542,f28(x7541,x7543,x7544),x7544)) % 0.70/0.97 [757]~P37(x7573)+E(f11(f11(x7571,x7572,x7573),x7574,x7573),f11(x7571,f11(x7572,x7574,x7573),x7573)) % 0.70/0.97 [758]~P20(x7583)+E(f11(f11(x7581,x7582,x7583),x7584,x7583),f11(x7581,f11(x7582,x7584,x7583),x7583)) % 0.70/0.97 [760]~P12(x7603)+E(f29(f29(x7601,x7602,x7603),x7604,x7603),f29(x7601,f29(x7602,x7604,x7603),x7603)) % 0.70/0.97 [761]~P12(x7613)+E(f28(f28(x7611,x7612,x7613),x7614,x7613),f28(x7611,f28(x7612,x7614,x7613),x7613)) % 0.70/0.97 [762]~P37(x7623)+E(f11(f11(x7621,x7622,x7623),x7624,x7623),f11(f11(x7621,x7624,x7623),x7622,x7623)) % 0.70/0.97 [884]~P12(x8843)+E(f28(f29(x8841,x8842,x8843),f29(x8841,x8844,x8843),x8843),f29(x8841,f28(x8842,x8844,x8843),x8843)) % 0.70/0.97 [885]~P12(x8853)+E(f29(f28(x8851,x8852,x8853),f28(x8851,x8854,x8853),x8853),f28(x8851,f29(x8852,x8854,x8853),x8853)) % 0.70/0.97 [886]~P29(x8863)+E(f29(f4(x8861,x8862,x8863),f4(x8864,x8862,x8863),x8863),f4(f29(x8861,x8864,x8863),x8862,x8863)) % 0.70/0.97 [887]~P29(x8873)+E(f28(f4(x8871,x8872,x8873),f4(x8874,x8872,x8873),x8873),f4(f28(x8871,x8874,x8873),x8872,x8873)) % 0.70/0.97 [888]~P37(x8883)+E(f11(f32(x8881,x8882,x8883),f32(x8884,x8882,x8883),x8883),f32(f11(x8881,x8884,x8883),x8882,x8883)) % 0.70/0.97 [889]~P25(x8893)+E(f11(f32(x8891,x8892,x8893),f32(x8894,x8892,x8893),x8893),f32(f11(x8891,x8894,x8893),x8892,x8893)) % 0.70/0.97 [890]~P12(x8903)+E(f28(f29(x8901,x8902,x8903),f29(x8904,x8902,x8903),x8903),f29(f28(x8901,x8904,x8903),x8902,x8903)) % 0.70/0.97 [891]~P12(x8913)+E(f29(f28(x8911,x8912,x8913),f28(x8914,x8912,x8913),x8913),f28(f29(x8911,x8914,x8913),x8912,x8913)) % 0.70/0.97 [892]~P1(x8923)+E(f10(f11(x8921,x8922,x8923),f11(x8921,x8924,x8923),x8923),f11(x8921,f10(x8922,x8924,x8923),x8923)) % 0.70/0.97 [893]~P1(x8933)+E(f10(f11(x8931,x8932,x8933),f11(x8934,x8932,x8933),x8933),f11(f10(x8931,x8934,x8933),x8932,x8933)) % 0.70/0.97 [947]~P56(x9474)+E(f25(x9471,x9472,f45(x9471,x9473),x9474),f25(x9471,f30(x9472),x9473,x9474)) % 0.70/0.97 [1025]~P12(x10254)+P7(f28(x10251,f29(x10252,x10253,x10254),x10254),f29(f28(x10251,x10252,x10254),f28(x10251,x10253,x10254),x10254),x10254) % 0.70/0.97 [1026]~P12(x10263)+P7(f28(f29(x10261,x10262,x10263),f29(x10261,x10264,x10263),x10263),f29(x10261,f28(x10262,x10264,x10263),x10263),x10263) % 0.70/0.97 [1027]P5(x10271,f15(x10272),f33(x10273,x10274))+~P5(f35(x10271,f2(a1),x10273,a47),x10272,x10274) % 0.70/0.97 [1039]~P5(x10391,f14(x10392,x10394),x10393)+P5(x10391,x10392,f33(f40(x10393,x10391,x10392,x10394),x10393)) % 0.70/0.97 [875]~P1(x8751)+E(f10(f45(f45(f3(x8751),x8752),f11(x8753,x8754,x8751)),x8754,x8751),f10(x8752,x8754,x8751)) % 0.70/0.97 [876]~P1(x8761)+E(f10(f45(f45(f3(x8761),x8762),f11(x8763,x8764,x8761)),x8763,x8761),f10(x8762,x8763,x8761)) % 0.70/0.97 [959]~P9(x9594)+E(f10(f4(x9591,f10(x9592,x9593,x9594),x9594),x9593,x9594),f10(f4(x9591,x9592,x9594),x9593,x9594)) % 0.70/0.97 [960]~P1(x9604)+E(f10(f11(x9601,f10(x9602,x9603,x9604),x9604),x9603,x9604),f10(f11(x9601,x9602,x9604),x9603,x9604)) % 0.70/0.97 [961]~P9(x9613)+E(f10(f4(f10(x9611,x9612,x9613),x9614,x9613),x9612,x9613),f10(f4(x9611,x9614,x9613),x9612,x9613)) % 0.70/0.97 [963]~P1(x9633)+E(f10(f11(f10(x9631,x9632,x9633),x9634,x9633),x9632,x9633),f10(f11(x9631,x9634,x9633),x9632,x9633)) % 0.70/0.97 [1014]~P9(x10143)+E(f10(f4(f10(x10141,x10142,x10143),f10(x10144,x10142,x10143),x10143),x10142,x10143),f10(f4(x10141,x10144,x10143),x10142,x10143)) % 0.70/0.97 [1015]~P1(x10153)+E(f10(f11(f10(x10151,x10152,x10153),f10(x10154,x10152,x10153),x10153),x10152,x10153),f10(f11(x10151,x10154,x10153),x10152,x10153)) % 0.70/0.97 [1054]P58(f45(x10541,f45(x10542,x10543)))+~P58(f45(x10541,f23(x10544,x10542,f30(x10543),a46))) % 0.70/0.97 [1056]P58(f45(x10561,f45(x10562,x10563)))+~P58(f45(x10561,f43(x10562,x10564,f34(x10563),a46))) % 0.70/0.97 [1086]~P14(x10861)+E(f31(f2(x10861),f3(x10861),f31(f2(x10861),f3(x10861),x10862,x10863,x10861),x10864,x10861),f31(f2(x10861),f3(x10861),x10862,f11(x10863,x10864,a1),x10861)) % 0.70/0.97 [716]~P14(x7161)+E(f45(f45(f3(x7161),x7162),f45(f45(f3(x7161),x7163),x7164)),f45(f45(f3(x7161),x7163),f45(f45(f3(x7161),x7162),x7164))) % 0.70/0.97 [717]~P37(x7171)+E(f45(f45(f3(x7171),x7172),f45(f45(f3(x7171),x7173),x7174)),f45(f45(f3(x7171),x7173),f45(f45(f3(x7171),x7172),x7174))) % 0.70/0.97 [718]~P18(x7181)+E(f45(f45(f3(x7181),x7182),f45(f45(f3(x7181),x7183),x7184)),f45(f45(f3(x7181),x7183),f45(f45(f3(x7181),x7182),x7184))) % 0.70/0.97 [863]~P37(x8633)+E(f11(f32(x8631,x8632,x8633),f32(x8631,x8634,x8633),x8633),f32(x8631,f45(f45(f3(a1),x8632),x8634),x8633)) % 0.70/0.97 [864]~P23(x8643)+E(f11(f32(x8641,x8642,x8643),f32(x8641,x8644,x8643),x8643),f32(x8641,f45(f45(f3(a1),x8642),x8644),x8643)) % 0.70/0.97 [945]~P13(x9451)+E(f29(f45(f45(f3(x9451),x9452),x9453),f45(f45(f3(x9451),x9454),x9453),x9451),f45(f45(f3(x9451),f29(x9452,x9454,x9451)),x9453)) % 0.70/0.97 [946]~P13(x9461)+E(f28(f45(f45(f3(x9461),x9462),x9463),f45(f45(f3(x9461),x9464),x9463),x9461),f45(f45(f3(x9461),f28(x9462,x9464,x9461)),x9463)) % 0.70/0.97 [949]~P1(x9491)+E(f10(f45(f45(f3(x9491),x9492),f10(x9493,x9494,x9491)),x9494,x9491),f10(f45(f45(f3(x9491),x9492),x9493),x9494,x9491)) % 0.70/0.97 [950]~P37(x9501)+E(f45(f45(f3(x9501),f11(x9502,x9503,x9501)),f11(x9502,x9504,x9501)),f11(x9502,f45(f45(f3(x9501),x9503),x9504),x9501)) % 0.70/0.97 [952]~P38(x9521)+E(f45(f45(f3(x9521),f11(x9522,x9523,x9521)),f11(x9524,x9523,x9521)),f11(f45(f45(f3(x9521),x9522),x9524),x9523,x9521)) % 0.70/0.97 [953]~P37(x9531)+E(f45(f45(f3(x9531),f11(x9532,x9533,x9531)),f11(x9534,x9533,x9531)),f11(f45(f45(f3(x9531),x9532),x9534),x9533,x9531)) % 0.70/0.97 [1013]~P1(x10131)+E(f10(f45(f45(f3(x10131),f10(x10132,x10133,x10131)),x10134),x10133,x10131),f10(f45(f45(f3(x10131),x10132),x10134),x10133,x10131)) % 0.70/0.97 [1029]~P1(x10291)+E(f10(f45(f45(f3(x10291),f10(x10292,x10293,x10291)),f10(x10294,x10293,x10291)),x10293,x10291),f10(f45(f45(f3(x10291),x10292),x10294),x10293,x10291)) % 0.70/0.97 [1073]~P1(x10731)+E(f45(f45(f3(x10731),f45(f45(f3(x10731),f11(x10732,f5(x10733,x10732,x10731),x10731)),f10(x10733,x10732,x10731))),x10734),f45(f45(f3(x10731),x10733),x10734)) % 0.70/0.97 [1074]~P1(x10741)+E(f45(f45(f3(x10741),f45(f45(f3(x10741),f11(f5(x10742,x10743,x10741),x10743,x10741)),f10(x10742,x10743,x10741))),x10744),f45(f45(f3(x10741),x10742),x10744)) % 0.70/0.97 [1089]~P14(x10891)+E(f45(f45(f3(x10891),f31(f2(x10891),f3(x10891),x10892,x10893,x10891)),f31(f2(x10891),f3(x10891),x10892,x10894,x10891)),f31(f2(x10891),f3(x10891),x10892,f45(f45(f3(a1),x10893),x10894),x10891)) % 0.70/0.97 [1090]~P14(x10901)+E(f45(f45(f3(x10901),f31(f2(x10901),f3(x10901),x10902,x10903,x10901)),f31(f2(x10901),f3(x10901),x10904,x10903,x10901)),f31(f2(x10901),f3(x10901),f45(f45(f3(x10901),x10902),x10904),x10903,x10901)) % 0.70/0.97 [860]~P14(x8601)+E(f45(f45(f3(x8601),f45(f45(f3(x8601),x8602),x8603)),x8604),f45(f45(f3(x8601),x8602),f45(f45(f3(x8601),x8603),x8604))) % 0.70/0.97 [861]~P37(x8611)+E(f45(f45(f3(x8611),f45(f45(f3(x8611),x8612),x8613)),x8614),f45(f45(f3(x8611),x8612),f45(f45(f3(x8611),x8613),x8614))) % 0.70/0.97 [862]~P15(x8621)+E(f45(f45(f3(x8621),f45(f45(f3(x8621),x8622),x8623)),x8624),f45(f45(f3(x8621),x8622),f45(f45(f3(x8621),x8623),x8624))) % 0.70/0.97 [943]~P37(x9431)+E(f45(f45(f3(x9431),f45(f45(f3(x9431),x9432),x9433)),x9434),f45(f45(f3(x9431),f45(f45(f3(x9431),x9432),x9434)),x9433)) % 0.70/0.97 [1060]~P7(x10601,x10603,a1)+E(f45(f45(f3(a1),f11(x10601,x10602,a1)),f45(f45(f3(a1),f11(f4(x10603,x10601,a1),x10602,a1)),x10604)),f45(f45(f3(a1),f11(x10603,x10602,a1)),x10604)) % 0.70/0.97 [574]E(x5741,x5742)+~E(f21(x5741,x5743,x5744),f21(x5742,x5745,x5744)) % 0.70/0.97 [1004]~P5(x10041,x10044,x10045)+P5(f35(x10041,x10042,x10043,a47),f18(x10044,x10042),x10045) % 0.70/0.97 [964]~P37(x9643)+E(f11(f11(x9641,x9642,x9643),f11(x9644,x9645,x9643),x9643),f11(f11(x9641,x9644,x9643),f11(x9642,x9645,x9643),x9643)) % 0.70/0.97 [976]E(f10(x9761,x9762,a1),f10(x9763,x9762,a1))+~E(f45(f45(f3(a1),x9761),f11(x9762,x9764,a1)),f45(f45(f3(a1),x9763),f11(x9762,x9765,a1))) % 0.70/0.97 [991]~P3(x9915,x9912,a1)+E(f45(f35(x9911,x9912,x9913,x9914),x9915),f45(x9911,x9915)) % 0.70/0.97 [1062]P58(f45(x10621,f45(f45(x10622,x10623),x10624)))+~P58(f45(x10621,f43(x10625,x10622,f33(x10623,x10624),a46))) % 0.70/0.97 [1011]~P37(x10111)+E(f45(f45(f3(x10111),f45(f45(f3(x10111),x10112),x10113)),f45(f45(f3(x10111),x10114),x10115)),f45(f45(f3(x10111),f45(f45(f3(x10111),x10112),x10114)),f45(f45(f3(x10111),x10113),x10115))) % 0.70/0.97 [1058]~P55(x10581)+E(f45(f45(f3(x10581),f11(x10582,x10583,x10581)),f45(f45(f3(x10581),f11(f4(x10584,x10582,x10581),x10583,x10581)),x10585)),f45(f45(f3(x10581),f11(x10584,x10583,x10581)),x10585)) % 0.70/0.97 [1063]~P7(x10631,x10634,a1)+E(f4(f45(f45(f3(a1),f11(x10631,x10632,a1)),x10633),f45(f45(f3(a1),f11(x10634,x10632,a1)),x10635),a1),f4(x10633,f45(f45(f3(a1),f11(f4(x10634,x10631,a1),x10632,a1)),x10635),a1)) % 0.70/0.97 [1064]~P7(x10644,x10641,a1)+E(f4(f45(f45(f3(a1),f11(x10641,x10642,a1)),x10643),f45(f45(f3(a1),f11(x10644,x10642,a1)),x10645),a1),f4(f45(f45(f3(a1),f11(f4(x10641,x10644,a1),x10642,a1)),x10643),x10645,a1)) % 0.70/0.97 [1045]~P48(x10451)+E(f45(f45(f3(x10451),f11(x10452,x10453,x10451)),f45(f45(f3(x10451),f11(x10454,x10453,x10451)),x10455)),f45(f45(f3(x10451),f11(f45(f45(f3(x10451),x10452),x10454),x10453,x10451)),x10455)) % 0.70/0.97 [1092]~P4(x10924,x10921,x10925,x10926,x10922,x10927)+E(f45(f45(x10921,x10922),x10923),x10923) % 0.70/0.97 [1093]~P4(x10934,x10931,x10935,x10933,x10936,x10937)+E(f45(f45(x10931,x10932),x10933),x10933) % 0.70/0.97 [1095]~P4(x10951,x10954,x10955,x10952,x10956,x10957)+E(f45(f45(x10951,x10952),x10953),x10953) % 0.70/0.97 [1096]~P4(x10964,x10961,x10965,x10966,x10963,x10967)+E(f45(f45(x10961,x10962),x10963),x10962) % 0.70/0.97 [1098]~P4(x10984,x10981,x10985,x10982,x10986,x10987)+E(f45(f45(x10981,x10982),x10983),x10982) % 0.70/0.97 [1099]~P4(x10991,x10994,x10995,x10993,x10996,x10997)+E(f45(f45(x10991,x10992),x10993),x10992) % 0.70/0.97 [1100]~P4(x11004,x11005,x11001,x11006,x11003,x11007)+E(f45(f45(x11001,x11002),f2(a1)),x11003) % 0.70/0.97 [1108]~P4(x11081,x11083,x11085,x11086,x11084,x11087)+E(f45(f45(x11081,x11082),x11082),f45(f45(x11083,f45(f45(x11081,x11084),x11084)),x11082)) % 0.70/0.97 [1102]~P4(x11024,x11021,x11025,x11026,x11027,x11028)+E(f45(f45(x11021,x11022),x11023),f45(f45(x11021,x11023),x11022)) % 0.70/0.97 [1104]~P4(x11041,x11044,x11045,x11046,x11047,x11048)+E(f45(f45(x11041,x11042),x11043),f45(f45(x11041,x11043),x11042)) % 0.70/0.97 [1107]~P4(x11075,x11071,x11073,x11076,x11077,x11078)+E(f45(f45(x11071,x11072),f45(f45(x11073,x11072),x11074)),f45(f45(x11073,x11072),f30(x11074))) % 0.70/0.97 [1111]~P4(x11115,x11111,x11112,x11116,x11117,x11118)+E(f45(f45(x11111,f45(f45(x11112,x11113),x11114)),x11113),f45(f45(x11112,x11113),f30(x11114))) % 0.70/0.97 [1112]~P4(x11121,x11123,x11126,x11127,x11125,x11128)+E(f45(f45(x11121,x11122),f45(f45(x11123,x11124),x11122)),f45(f45(x11123,f45(f45(x11121,x11124),x11125)),x11122)) % 0.70/0.97 [1120]~P4(x11201,x11202,x11206,x11207,x11205,x11208)+E(f45(f45(x11201,f45(f45(x11202,x11203),x11204)),x11204),f45(f45(x11202,f45(f45(x11201,x11203),x11205)),x11204)) % 0.70/0.97 [1109]~P4(x11095,x11091,x11096,x11097,x11098,x11099)+E(f45(f45(x11091,x11092),f45(f45(x11091,x11093),x11094)),f45(f45(x11091,x11093),f45(f45(x11091,x11092),x11094))) % 0.70/0.97 [1110]~P4(x11101,x11105,x11106,x11107,x11108,x11109)+E(f45(f45(x11101,x11102),f45(f45(x11101,x11103),x11104)),f45(f45(x11101,x11103),f45(f45(x11101,x11102),x11104))) % 0.70/0.97 [1123]~P4(x11231,x11232,x11236,x11237,x11238,x11239)+E(f45(f45(x11231,f45(f45(x11232,x11233),x11234)),f45(f45(x11232,x11233),x11235)),f45(f45(x11232,x11233),f45(f45(x11231,x11234),x11235))) % 0.70/0.97 [1117]~P4(x11175,x11171,x11176,x11177,x11178,x11179)+E(f45(f45(x11171,f45(f45(x11171,x11172),x11173)),x11174),f45(f45(x11171,x11172),f45(f45(x11171,x11173),x11174))) % 0.70/0.97 [1118]~P4(x11181,x11185,x11186,x11187,x11188,x11189)+E(f45(f45(x11181,f45(f45(x11181,x11182),x11183)),x11184),f45(f45(x11181,x11182),f45(f45(x11181,x11183),x11184))) % 0.70/0.97 [1119]~P4(x11195,x11196,x11191,x11197,x11198,x11199)+E(f45(f45(x11191,f45(f45(x11191,x11192),x11193)),x11194),f45(f45(x11191,x11192),f11(x11193,x11194,a1))) % 0.70/0.97 [1121]~P4(x11215,x11211,x11216,x11217,x11218,x11219)+E(f45(f45(x11211,f45(f45(x11211,x11212),x11213)),x11214),f45(f45(x11211,f45(f45(x11211,x11212),x11214)),x11213)) % 0.70/0.97 [1122]~P4(x11221,x11225,x11226,x11227,x11228,x11229)+E(f45(f45(x11221,f45(f45(x11221,x11222),x11223)),x11224),f45(f45(x11221,f45(f45(x11221,x11222),x11224)),x11223)) % 0.70/0.97 [1124]~P4(x11246,x11241,x11242,x11247,x11248,x11249)+E(f45(f45(x11241,f45(f45(x11242,x11243),x11244)),f45(f45(x11242,x11243),x11245)),f45(f45(x11242,x11243),f45(f45(f3(a1),x11244),x11245))) % 0.70/0.97 [1125]~P4(x11256,x11251,x11252,x11257,x11258,x11259)+E(f45(f45(x11251,f45(f45(x11252,x11253),x11254)),f45(f45(x11252,x11255),x11254)),f45(f45(x11252,f45(f45(x11251,x11253),x11255)),x11254)) % 0.70/0.97 [1127]~P4(x11271,x11272,x11276,x11277,x11278,x11279)+E(f45(f45(x11271,f45(f45(x11272,x11273),x11274)),f45(f45(x11272,x11275),x11274)),f45(f45(x11272,f45(f45(x11271,x11273),x11275)),x11274)) % 0.70/0.97 [1129]~P4(x11296,x11291,x11297,x11298,x11299,x112910)+E(f45(f45(x11291,f45(f45(x11291,x11292),x11293)),f45(f45(x11291,x11294),x11295)),f45(f45(x11291,f45(f45(x11291,x11292),x11294)),f45(f45(x11291,x11293),x11295))) % 0.70/0.97 [1130]~P4(x11301,x11306,x11307,x11308,x11309,x113010)+E(f45(f45(x11301,f45(f45(x11301,x11302),x11303)),f45(f45(x11301,x11304),x11305)),f45(f45(x11301,f45(f45(x11301,x11302),x11304)),f45(f45(x11301,x11303),x11305))) % 0.70/0.97 [601]~P30(x6011)+~P7(f2(x6011),f2(x6011),x6011)+E(f45(f45(f3(x6011),f2(x6011)),f2(x6011)),f2(x6011)) % 0.70/0.97 [464]E(x4641,x4642)+P3(x4642,x4641,a1)+P3(x4641,x4642,a1) % 0.70/0.97 [508]E(x5081,x5082)+P3(x5081,x5082,a1)+~P7(x5081,x5082,a1) % 0.70/0.97 [567]E(x5671,x5672)+~P7(x5672,x5671,a1)+~P7(x5671,x5672,a1) % 0.70/0.97 [420]~P40(x4202)+~P17(x4202)+E(f4(x4201,x4201,x4202),f2(x4202)) % 0.70/0.97 [443]E(x4431,f2(a1))+E(x4432,f2(a1))+~E(f11(x4432,x4431,a1),f2(a1)) % 0.70/0.97 [529]~P3(x5291,x5292,a1)+E(f30(x5291),x5292)+P3(f30(x5291),x5292,a1) % 0.70/0.97 [530]E(x5301,x5302)+P3(x5302,x5301,a1)+~P3(x5302,f30(x5301),a1) % 0.70/0.97 [532]E(x5321,x5322)+P3(x5321,x5322,a1)+~P3(x5321,f30(x5322),a1) % 0.70/0.97 [553]P7(x5531,x5532,a1)+E(x5531,f30(x5532))+~P7(x5531,f30(x5532),a1) % 0.70/0.97 [581]E(x5811,x5812)+~E(f4(x5812,x5811,a1),f2(a1))+~E(f4(x5811,x5812,a1),f2(a1)) % 0.70/0.97 [585]E(x5851,x5852)+~P7(x5852,x5851,a1)+~P3(x5851,f30(x5852),a1) % 0.70/0.97 [600]~P36(x6001)+P3(f2(x6001),f24(x6002,x6001),x6001)+~P3(f2(a1),x6002,a1) % 0.70/0.97 [612]~P36(x6122)+~P3(f2(x6122),f24(x6121,x6122),x6122)+P3(f2(a1),x6121,a1) % 0.70/0.97 [765]P3(f4(x7651,x7652,a1),x7651,a1)+~P3(f2(a1),x7652,a1)+~P3(f2(a1),x7651,a1) % 0.70/0.97 [769]~P3(f2(a1),x7692,a1)+~P3(f2(a1),x7691,a1)+P3(f2(a1),f11(x7691,x7692,a1),a1) % 0.70/0.97 [421]~P40(x4211)+~P17(x4211)+E(f45(f45(f3(x4211),x4212),f2(x4211)),x4212) % 0.70/0.97 [428]~P10(x4281)+~P11(x4281)+E(f32(f2(x4281),f30(x4282),x4281),f2(x4281)) % 0.70/0.97 [494]P58(f45(x4941,x4942))+P58(f45(x4941,f54(x4941)))+~P58(f45(x4941,f2(a1))) % 0.70/0.97 [495]P58(f45(x4951,x4952))+P58(f45(x4951,f58(x4951)))+~P58(f45(x4951,f2(a1))) % 0.70/0.97 [496]P58(f45(x4961,x4962))+P58(f45(x4961,f55(x4961)))+~P58(f45(x4961,f2(a1))) % 0.70/0.97 [497]P58(f45(x4971,x4972))+P58(f45(x4971,f56(x4971)))+~P58(f45(x4971,f2(a1))) % 0.70/0.97 [498]P58(f45(x4981,x4982))+P58(f45(x4981,f6(x4981)))+~P58(f45(x4981,f2(a1))) % 0.70/0.97 [499]P58(f45(x4991,x4992))+P58(f45(x4991,f57(x4991)))+~P58(f45(x4991,f2(a1))) % 0.70/0.97 [542]P3(f2(a1),f7(x5421),a1)+P58(f45(x5421,x5422))+~P58(f45(x5421,f2(a1))) % 0.70/0.97 [552]~P58(f45(x5521,x5522))+~P58(f45(x5521,f9(x5521)))+P58(f45(x5521,f2(a1))) % 0.70/0.97 [554]P58(f45(x5541,x5542))+~P58(f45(x5541,f7(x5541)))+~P58(f45(x5541,f2(a1))) % 0.70/0.97 [557]P7(f8(x5571,x5572),x5572,a1)+~P58(f45(x5571,x5572))+P58(f45(x5571,f2(a1))) % 0.70/0.97 [560]~P58(f45(x5601,x5602))+P58(f45(x5601,f8(x5601,x5602)))+P58(f45(x5601,f2(a1))) % 0.70/0.97 [809]P3(x8091,f11(x8092,x8091,a1),a1)+~P3(f30(f2(a1)),x8092,a1)+~P3(f30(f2(a1)),x8091,a1) % 0.70/0.97 [810]P3(x8101,f11(x8101,x8102,a1),a1)+~P3(f30(f2(a1)),x8102,a1)+~P3(f30(f2(a1)),x8101,a1) % 0.70/0.97 [836]~P3(f30(f2(a1)),x8362,a1)+~P3(f30(f2(a1)),x8361,a1)+P3(f30(f2(a1)),f11(x8361,x8362,a1),a1) % 0.70/0.97 [837]~P7(f30(f2(a1)),x8372,a1)+~P7(f30(f2(a1)),x8371,a1)+P7(f30(f2(a1)),f11(x8371,x8372,a1),a1) % 0.70/0.97 [436]E(x4361,f2(a1))+E(x4362,f2(a1))+~E(f45(f45(f3(a1),x4362),x4361),f30(f2(a1))) % 0.70/0.97 [446]E(x4461,f2(a1))+E(x4461,f30(f2(a1)))+~E(f45(f45(f3(a1),x4462),x4461),f30(f2(a1))) % 0.70/0.97 [447]E(x4471,f2(a1))+E(x4471,f30(f2(a1)))+~E(f45(f45(f3(a1),x4471),x4472),f30(f2(a1))) % 0.70/0.97 [451]E(x4511,f30(f2(a1)))+E(x4512,f30(f2(a1)))+~E(f45(f45(f3(a1),x4512),x4511),f30(f2(a1))) % 0.70/0.97 [452]~P27(x4522)+E(x4521,f2(x4522))+~E(f45(f45(f3(x4522),x4521),x4521),f2(x4522)) % 0.70/0.97 [551]~P58(f45(x5511,x5512))+P58(f45(x5511,f2(a1)))+P58(f45(x5511,f30(f9(x5511)))) % 0.70/0.97 [604]P58(f45(x6041,x6042))+~P58(f45(x6041,f2(a1)))+~P58(f45(x6041,f30(f54(x6041)))) % 0.70/0.97 [605]P58(f45(x6051,x6052))+~P58(f45(x6051,f2(a1)))+~P58(f45(x6051,f30(f58(x6051)))) % 0.70/0.97 [606]P58(f45(x6061,x6062))+~P58(f45(x6061,f2(a1)))+~P58(f45(x6061,f30(f55(x6061)))) % 0.70/0.97 [607]P58(f45(x6071,x6072))+~P58(f45(x6071,f2(a1)))+~P58(f45(x6071,f30(f56(x6071)))) % 0.70/0.97 [608]P58(f45(x6081,x6082))+~P58(f45(x6081,f2(a1)))+~P58(f45(x6081,f30(f6(x6081)))) % 0.70/0.97 [609]P58(f45(x6091,x6092))+~P58(f45(x6091,f2(a1)))+~P58(f45(x6091,f30(f57(x6091)))) % 0.70/0.97 [689]~P27(x6891)+~P3(f2(x6891),x6892,x6891)+P3(f2(x6891),f45(f45(f3(x6891),x6892),x6892),x6891) % 0.70/0.97 [690]~P27(x6901)+~P7(f2(x6901),x6902,x6901)+P7(f2(x6901),f45(f45(f3(x6901),x6902),x6902),x6901) % 0.70/0.97 [691]~P27(x6911)+~P3(x6912,f2(x6911),x6911)+P3(f45(f45(f3(x6911),x6912),x6912),f2(x6911),x6911) % 0.70/0.97 [692]~P45(x6921)+~P3(x6922,f2(x6921),x6921)+P3(f45(f45(f3(x6921),x6922),x6922),f2(x6921),x6921) % 0.70/0.97 [693]~P27(x6931)+~P7(x6932,f2(x6931),x6931)+P7(f45(f45(f3(x6931),x6932),x6932),f2(x6931),x6931) % 0.70/0.97 [743]~P27(x7432)+P3(x7431,f2(x7432),x7432)+~P3(f45(f45(f3(x7432),x7431),x7431),f2(x7432),x7432) % 0.70/0.97 [744]~P45(x7442)+P3(x7441,f2(x7442),x7442)+~P3(f45(f45(f3(x7442),x7441),x7441),f2(x7442),x7442) % 0.70/0.97 [745]~P27(x7452)+P7(x7451,f2(x7452),x7452)+~P7(f45(f45(f3(x7452),x7451),x7451),f2(x7452),x7452) % 0.70/0.97 [746]~P27(x7461)+P3(f2(x7461),x7462,x7461)+~P3(f2(x7461),f45(f45(f3(x7461),x7462),x7462),x7461) % 0.70/0.97 [747]~P27(x7471)+P7(f2(x7471),x7472,x7471)+~P7(f2(x7471),f45(f45(f3(x7471),x7472),x7472),x7471) % 0.70/0.97 [780]P3(f2(a1),x7801,a1)+P3(f2(a1),x7802,a1)+~P3(f2(a1),f45(f45(f3(a1),x7801),x7802),a1) % 0.70/0.97 [940]P3(x9401,x9402,a1)+~P3(f2(a1),x9402,a1)+E(f30(f5(f4(x9401,x9402,a1),x9402,a1)),f5(x9401,x9402,a1)) % 0.70/0.97 [956]~P7(x9562,x9561,a1)+~P3(f2(a1),x9562,a1)+E(f30(f5(f4(x9561,x9562,a1),x9562,a1)),f5(x9561,x9562,a1)) % 0.70/0.97 [482]P7(x4822,x4821,x4823)+~P12(x4823)+P3(x4821,x4822,x4823) % 0.70/0.97 [484]P7(x4842,x4841,x4843)+~P12(x4843)+P7(x4841,x4842,x4843) % 0.70/0.97 [525]~P33(x5253)+~P3(x5251,x5252,x5253)+P7(x5251,x5252,x5253) % 0.70/0.97 [526]~P34(x5263)+~P3(x5261,x5262,x5263)+P7(x5261,x5262,x5263) % 0.70/0.97 [586]~P3(x5863,x5862,x5861)+~P12(x5861)+~P3(x5862,x5863,x5861) % 0.70/0.97 [588]~P7(x5883,x5882,x5881)+~P12(x5881)+~P3(x5882,x5883,x5881) % 0.70/0.97 [591]~P3(x5913,x5912,x5911)+~P33(x5911)+~P3(x5912,x5913,x5911) % 0.70/0.97 [592]~P7(x5923,x5922,x5921)+~P33(x5921)+~P3(x5922,x5923,x5921) % 0.70/0.97 [593]~P3(x5933,x5932,x5931)+~P34(x5931)+~P3(x5932,x5933,x5931) % 0.70/0.97 [619]~P7(x6191,x6193,a1)+P7(x6191,x6192,a1)+~P7(x6193,x6192,a1) % 0.70/0.97 [389]~P16(x3893)+E(x3891,x3892)+~E(f24(x3891,x3893),f24(x3892,x3893)) % 0.70/0.97 [453]~P26(x4533)+E(x4531,x4532)+~E(f4(x4531,x4532,x4533),f2(x4533)) % 0.70/0.97 [454]~P18(x4543)+E(x4541,x4542)+~E(f4(x4541,x4542,x4543),f2(x4543)) % 0.70/0.97 [458]~P53(x4582)+~E(f32(x4581,x4583,x4582),f2(x4582))+E(x4581,f2(x4582)) % 0.70/0.97 [533]~P12(x5333)+~P7(x5332,x5331,x5333)+E(f29(x5331,x5332,x5333),x5332) % 0.70/0.97 [534]~P12(x5343)+~P7(x5341,x5342,x5343)+E(f29(x5341,x5342,x5343),x5341) % 0.70/0.97 [535]~P12(x5353)+~P7(x5351,x5352,x5353)+E(f28(x5351,x5352,x5353),x5352) % 0.70/0.97 [536]~P12(x5363)+~P7(x5362,x5361,x5363)+E(f28(x5361,x5362,x5363),x5361) % 0.70/0.98 [540]~P12(x5403)+P7(x5401,x5402,x5403)+~E(f29(x5401,x5402,x5403),x5401) % 0.70/0.98 [541]~P12(x5413)+P7(x5411,x5412,x5413)+~E(f28(x5411,x5412,x5413),x5412) % 0.70/0.98 [572]E(x5721,x5722)+~E(f11(x5723,x5721,a1),f11(x5723,x5722,a1))+E(x5723,f2(a1)) % 0.70/0.98 [573]E(x5731,x5732)+~E(f11(x5731,x5733,a1),f11(x5732,x5733,a1))+E(x5733,f2(a1)) % 0.70/0.98 [610]~P36(x6102)+~P3(x6101,x6103,a1)+P3(f24(x6101,x6102),f24(x6103,x6102),x6102) % 0.70/0.98 [611]~P36(x6112)+~P7(x6111,x6113,a1)+P7(f24(x6111,x6112),f24(x6113,x6112),x6112) % 0.70/0.98 [633]~P3(x6331,x6333,a1)+~P3(x6333,x6332,a1)+P3(f30(x6331),x6332,a1) % 0.70/0.98 [635]~P36(x6353)+~P3(f24(x6351,x6353),f24(x6352,x6353),x6353)+P3(x6351,x6352,a1) % 0.70/0.98 [636]~P36(x6363)+~P7(f24(x6361,x6363),f24(x6362,x6363),x6363)+P7(x6361,x6362,a1) % 0.70/0.98 [683]E(x6831,x6832)+~E(f11(x6833,x6831,a1),f11(x6833,x6832,a1))+~P3(f2(a1),x6833,a1) % 0.70/0.98 [686]~P29(x6863)+~P3(x6861,x6862,x6863)+P3(f4(x6861,x6862,x6863),f2(x6863),x6863) % 0.70/0.98 [687]~P29(x6873)+~P7(x6871,x6872,x6873)+P7(f4(x6871,x6872,x6873),f2(x6873),x6873) % 0.70/0.98 [694]~P36(x6941)+~P3(f2(x6941),x6942,x6941)+P3(f2(x6941),f32(x6942,x6943,x6941),x6941) % 0.70/0.98 [695]~P36(x6951)+~P7(f2(x6951),x6952,x6951)+P7(f2(x6951),f32(x6952,x6953,x6951),x6951) % 0.70/0.98 [748]~P29(x7483)+P3(x7481,x7482,x7483)+~P3(f4(x7481,x7482,x7483),f2(x7483),x7483) % 0.70/0.98 [749]~P29(x7493)+P7(x7491,x7492,x7493)+~P7(f4(x7491,x7492,x7493),f2(x7493),x7493) % 0.70/0.98 [871]~P3(x8711,x8713,a1)+~P7(x8712,x8711,a1)+P3(f4(x8711,x8712,a1),f4(x8713,x8712,a1),a1) % 0.70/0.98 [872]~P3(x8723,x8722,a1)+~P3(x8723,x8721,a1)+P3(f4(x8721,x8722,a1),f4(x8721,x8723,a1),a1) % 0.70/0.98 [878]~P3(x8781,x8783,a1)+P3(f11(x8781,x8782,a1),f11(x8783,x8782,a1),a1)+~P3(f2(a1),x8782,a1) % 0.70/0.98 [881]~P3(x8812,x8813,a1)+P3(f11(x8811,x8812,a1),f11(x8811,x8813,a1),a1)+~P3(f2(a1),x8811,a1) % 0.70/0.98 [882]~P7(x8823,x8822,a1)+P7(f5(x8821,x8822,a1),f5(x8821,x8823,a1),a1)+~P3(f2(a1),x8823,a1) % 0.70/0.98 [974]P7(x9741,x9742,a1)+~P7(f11(x9743,x9741,a1),f11(x9743,x9742,a1),a1)+~P3(f2(a1),x9743,a1) % 0.70/0.98 [975]P7(x9751,x9752,a1)+~P7(f11(x9751,x9753,a1),f11(x9752,x9753,a1),a1)+~P3(f2(a1),x9753,a1) % 0.70/0.98 [490]E(x4901,x4902)+P3(x4902,x4901,a1)+E(f20(f13(x4901),x4903,x4902),f13(x4901)) % 0.70/0.98 [579]~P1(x5792)+E(x5791,f2(x5792))+E(f5(f11(x5793,x5791,x5792),x5791,x5792),x5793) % 0.70/0.98 [580]~P1(x5802)+E(x5801,f2(x5802))+E(f5(f11(x5801,x5803,x5802),x5801,x5802),x5803) % 0.70/0.98 [714]~P54(x7142)+~P7(x7143,x7141,a1)+E(f4(f24(x7141,x7142),f24(x7143,x7142),x7142),f24(f4(x7141,x7143,a1),x7142)) % 0.70/0.98 [933]~P7(x9332,x9333,a1)+~P7(x9332,x9331,a1)+E(f4(f4(x9331,x9332,a1),f4(x9333,x9332,a1),a1),f4(x9331,x9333,a1)) % 0.70/0.98 [934]~P3(x9342,x9343,a1)+~P58(f45(x9341,f4(x9342,x9343,a1)))+P58(f45(x9341,f2(a1))) % 0.70/0.98 [989]~P46(x9892)+E(x9891,f2(x9892))+~E(f45(f45(f3(x9892),f11(x9893,x9893,x9892)),f11(x9891,x9891,x9892)),f2(x9892)) % 0.70/0.98 [990]~P46(x9902)+E(x9901,f2(x9902))+~E(f45(f45(f3(x9902),f11(x9901,x9901,x9902)),f11(x9903,x9903,x9902)),f2(x9902)) % 0.70/0.98 [1023]~P46(x10232)+E(x10231,f2(x10232))+P3(f2(x10232),f45(f45(f3(x10232),f11(x10233,x10233,x10232)),f11(x10231,x10231,x10232)),x10232) % 0.70/0.98 [1024]~P46(x10242)+E(x10241,f2(x10242))+P3(f2(x10242),f45(f45(f3(x10242),f11(x10241,x10241,x10242)),f11(x10243,x10243,x10242)),x10242) % 0.70/0.98 [1043]~P46(x10432)+E(x10431,f2(x10432))+~P7(f45(f45(f3(x10432),f11(x10433,x10433,x10432)),f11(x10431,x10431,x10432)),f2(x10432),x10432) % 0.70/0.98 [1044]~P46(x10442)+E(x10441,f2(x10442))+~P7(f45(f45(f3(x10442),f11(x10441,x10441,x10442)),f11(x10443,x10443,x10442)),f2(x10442),x10442) % 0.70/0.98 [715]~P7(x7151,x7152,a1)+~P3(f2(a1),x7153,a1)+P3(x7151,f45(f45(f3(a1),x7152),x7153),a1) % 0.70/0.98 [924]~P7(x9243,x9242,a1)+P7(x9241,f4(x9242,x9243,a1),a1)+~P7(f45(f45(f3(a1),x9241),x9243),x9242,a1) % 0.70/0.98 [929]~P7(x9292,x9293,a1)+~P7(x9291,f4(x9293,x9292,a1),a1)+P7(f45(f45(f3(a1),x9291),x9292),x9293,a1) % 0.70/0.98 [558]~P5(x5581,x5584,x5583)+P5(x5581,x5582,x5583)+~P6(x5584,x5582) % 0.70/0.98 [433]~E(f36(x4331),f33(x4334,x4333))+P58(f45(x4331,x4332))+P58(f45(x4331,x4333)) % 0.70/0.98 [434]~E(f36(x4341),f33(x4343,x4344))+P58(f45(x4341,x4342))+P58(f45(x4341,x4343)) % 0.70/0.98 [594]~P18(x5944)+E(x5941,x5942)+~E(f4(x5943,x5943,x5944),f4(x5941,x5942,x5944)) % 0.70/0.98 [595]~P18(x5953)+E(x5951,x5952)+~E(f4(x5951,x5952,x5953),f4(x5954,x5954,x5953)) % 0.70/0.98 [667]~P12(x6674)+~P3(x6671,x6673,x6674)+P3(x6671,f28(x6672,x6673,x6674),x6674) % 0.70/0.98 [669]~P12(x6694)+~P3(x6691,x6692,x6694)+P3(x6691,f28(x6692,x6693,x6694),x6694) % 0.70/0.98 [671]~P12(x6714)+~P7(x6711,x6713,x6714)+P7(x6711,f28(x6712,x6713,x6714),x6714) % 0.70/0.98 [673]~P12(x6734)+~P7(x6731,x6732,x6734)+P7(x6731,f28(x6732,x6733,x6734),x6734) % 0.70/0.98 [675]~P12(x6753)+~P3(x6752,x6754,x6753)+P3(f29(x6751,x6752,x6753),x6754,x6753) % 0.70/0.98 [677]~P12(x6773)+~P3(x6771,x6774,x6773)+P3(f29(x6771,x6772,x6773),x6774,x6773) % 0.70/0.98 [679]~P12(x6793)+~P7(x6792,x6794,x6793)+P7(f29(x6791,x6792,x6793),x6794,x6793) % 0.70/0.98 [681]~P12(x6813)+~P7(x6811,x6814,x6813)+P7(f29(x6811,x6812,x6813),x6814,x6813) % 0.70/0.98 [719]~P12(x7193)+P3(x7191,x7192,x7193)+~P3(x7191,f29(x7194,x7192,x7193),x7193) % 0.70/0.98 [720]~P12(x7203)+P3(x7201,x7202,x7203)+~P3(x7201,f29(x7202,x7204,x7203),x7203) % 0.70/0.98 [722]~P12(x7223)+P7(x7221,x7222,x7223)+~P7(x7221,f29(x7224,x7222,x7223),x7223) % 0.70/0.98 [724]~P12(x7243)+P7(x7241,x7242,x7243)+~P7(x7241,f29(x7242,x7244,x7243),x7243) % 0.70/0.98 [725]~P12(x7253)+P3(x7251,x7252,x7253)+~P3(f28(x7254,x7251,x7253),x7252,x7253) % 0.70/0.98 [726]~P12(x7263)+P3(x7261,x7262,x7263)+~P3(f28(x7261,x7264,x7263),x7262,x7263) % 0.70/0.98 [728]~P12(x7283)+P7(x7281,x7282,x7283)+~P7(f28(x7284,x7281,x7283),x7282,x7283) % 0.70/0.98 [730]~P12(x7303)+P7(x7301,x7302,x7303)+~P7(f28(x7301,x7304,x7303),x7302,x7303) % 0.70/0.98 [873]~P7(x8732,x8734,a1)+~P7(x8731,x8733,a1)+P7(f11(x8731,x8732,a1),f11(x8733,x8734,a1),a1) % 0.70/0.98 [766]~P1(x7662)+E(x7661,f2(x7662))+E(f5(f11(x7663,x7661,x7662),f11(x7664,x7661,x7662),x7662),f5(x7663,x7664,x7662)) % 0.70/0.98 [767]~P1(x7672)+E(x7671,f2(x7672))+E(f5(f11(x7671,x7673,x7672),f11(x7671,x7674,x7672),x7672),f5(x7673,x7674,x7672)) % 0.70/0.98 [930]E(x9301,x9302)+E(x9303,f2(a1))+~E(f45(f45(f3(a1),x9304),f11(x9303,x9301,a1)),f45(f45(f3(a1),x9304),f11(x9303,x9302,a1))) % 0.70/0.98 [1017]~P40(x10171)+~P17(x10171)+E(f45(f45(f3(x10171),f11(x10172,x10173,x10171)),f11(x10172,x10174,x10171)),f45(f45(f3(x10171),f11(x10172,x10174,x10171)),f11(x10172,x10173,x10171))) % 0.70/0.98 [1036]E(x10361,x10362)+E(x10363,x10364)+~E(f45(f45(f3(a1),f11(x10363,x10361,a1)),f11(x10364,x10362,a1)),f45(f45(f3(a1),f11(x10363,x10362,a1)),f11(x10364,x10361,a1))) % 0.70/0.98 [575]~P19(x5753)+E(x5751,x5752)+~E(f45(f45(f3(x5753),x5754),x5751),f45(f45(f3(x5753),x5754),x5752)) % 0.70/0.98 [576]~P22(x5763)+E(x5761,x5762)+~E(f45(f45(f3(x5763),x5764),x5761),f45(f45(f3(x5763),x5764),x5762)) % 0.70/0.98 [577]~P22(x5773)+E(x5771,x5772)+~E(f45(f45(f3(x5773),x5771),x5774),f45(f45(f3(x5773),x5772),x5774)) % 0.70/0.98 [702]~P3(x7024,x7023,a1)+P3(x7021,x7022,a1)+~E(f45(f45(f3(a1),x7021),x7023),f45(f45(f3(a1),x7024),x7022)) % 0.70/0.98 [789]~P13(x7891)+~P3(x7892,x7894,x7891)+P3(f45(f45(f3(x7891),x7892),x7893),f45(f45(f3(x7891),x7894),x7893),x7891) % 0.70/0.98 [790]~P31(x7901)+~P3(x7902,x7904,x7901)+P3(f45(f45(f3(x7901),x7902),x7903),f45(f45(f3(x7901),x7904),x7903),x7901) % 0.70/0.98 [791]~P13(x7911)+~P3(x7913,x7914,x7911)+P3(f45(f45(f3(x7911),x7912),x7913),f45(f45(f3(x7911),x7912),x7914),x7911) % 0.70/0.98 [792]~P31(x7921)+~P3(x7923,x7924,x7921)+P3(f45(f45(f3(x7921),x7922),x7923),f45(f45(f3(x7921),x7922),x7924),x7921) % 0.70/0.98 [793]~P13(x7931)+~P7(x7932,x7934,x7931)+P7(f45(f45(f3(x7931),x7932),x7933),f45(f45(f3(x7931),x7934),x7933),x7931) % 0.70/0.98 [794]~P28(x7941)+~P7(x7942,x7944,x7941)+P7(f45(f45(f3(x7941),x7942),x7943),f45(f45(f3(x7941),x7944),x7943),x7941) % 0.70/0.98 [795]~P13(x7951)+~P7(x7953,x7954,x7951)+P7(f45(f45(f3(x7951),x7952),x7953),f45(f45(f3(x7951),x7952),x7954),x7951) % 0.70/0.98 [796]~P28(x7961)+~P7(x7963,x7964,x7961)+P7(f45(f45(f3(x7961),x7962),x7963),f45(f45(f3(x7961),x7962),x7964),x7961) % 0.70/0.98 [855]~P3(x8552,x8554,a1)+~P3(x8551,x8553,a1)+P3(f45(f45(f3(a1),x8551),x8552),f45(f45(f3(a1),x8553),x8554),a1) % 0.70/0.98 [856]~P7(x8562,x8564,a1)+~P7(x8561,x8563,a1)+P7(f45(f45(f3(a1),x8561),x8562),f45(f45(f3(a1),x8563),x8564),a1) % 0.70/0.98 [925]~P13(x9253)+P3(x9251,x9252,x9253)+~P3(f45(f45(f3(x9253),x9254),x9251),f45(f45(f3(x9253),x9254),x9252),x9253) % 0.70/0.98 [926]~P13(x9263)+P3(x9261,x9262,x9263)+~P3(f45(f45(f3(x9263),x9261),x9264),f45(f45(f3(x9263),x9262),x9264),x9263) % 0.70/0.98 [927]~P13(x9273)+P7(x9271,x9272,x9273)+~P7(f45(f45(f3(x9273),x9274),x9271),f45(f45(f3(x9273),x9274),x9272),x9273) % 0.70/0.98 [928]~P13(x9283)+P7(x9281,x9282,x9283)+~P7(f45(f45(f3(x9283),x9281),x9284),f45(f45(f3(x9283),x9282),x9284),x9283) % 0.70/0.98 [957]~P1(x9572)+E(x9571,f2(x9572))+E(f5(f45(f45(f3(x9572),x9573),f11(x9574,x9571,x9572)),x9571,x9572),f45(f45(f3(x9572),x9574),f5(x9573,x9571,x9572))) % 0.70/0.98 [958]~P1(x9582)+E(x9581,f2(x9582))+E(f5(f45(f45(f3(x9582),x9583),f11(x9581,x9584,x9582)),x9581,x9582),f45(f45(f3(x9582),x9584),f5(x9583,x9581,x9582))) % 0.70/0.98 [1052]~P3(x10524,x10521,a1)+~P3(f2(a1),x10523,a1)+P3(f45(f45(f3(a1),f11(x10521,f10(x10522,x10523,a1),a1)),x10524),f11(x10521,x10523,a1),a1) % 0.70/0.98 [584]E(x5841,x5842)+~E(f21(x5843,x5841,x5844),f21(x5845,x5842,x5844))+E(x5843,f2(a1)) % 0.70/0.98 [706]~P5(x7061,x7063,x7065)+~P5(x7061,x7062,f33(x7065,x7064))+P5(x7061,f14(x7062,x7063),x7064) % 0.70/0.98 [843]~P18(x8431)+E(f45(f45(f3(x8431),x8432),x8433),x8434)+~E(f45(f45(f3(x8431),x8432),f45(f45(f3(x8431),x8435),x8433)),f45(f45(f3(x8431),x8435),x8434)) % 0.70/0.98 [1049]~P7(x10493,x10492,a1)+~E(f45(f45(f3(a1),f11(x10493,x10494,a1)),x10491),f45(f45(f3(a1),f11(x10492,x10494,a1)),x10495))+E(x10491,f45(f45(f3(a1),f11(f4(x10492,x10493,a1),x10494,a1)),x10495)) % 0.70/0.98 [1050]~P7(x10502,x10501,a1)+~E(f45(f45(f3(a1),f11(x10501,x10503,a1)),x10504),f45(f45(f3(a1),f11(x10502,x10503,a1)),x10505))+E(f45(f45(f3(a1),f11(f4(x10501,x10502,a1),x10503,a1)),x10504),x10505) % 0.70/0.98 [1065]~P7(x10653,x10652,a1)+~P3(f45(f45(f3(a1),f11(x10653,x10654,a1)),x10651),f45(f45(f3(a1),f11(x10652,x10654,a1)),x10655),a1)+P3(x10651,f45(f45(f3(a1),f11(f4(x10652,x10653,a1),x10654,a1)),x10655),a1) % 0.70/0.98 [1066]~P7(x10663,x10662,a1)+~P7(f45(f45(f3(a1),f11(x10663,x10664,a1)),x10661),f45(f45(f3(a1),f11(x10662,x10664,a1)),x10665),a1)+P7(x10661,f45(f45(f3(a1),f11(f4(x10662,x10663,a1),x10664,a1)),x10665),a1) % 0.70/0.98 [1067]~P7(x10672,x10671,a1)+~P3(f45(f45(f3(a1),f11(x10671,x10673,a1)),x10674),f45(f45(f3(a1),f11(x10672,x10673,a1)),x10675),a1)+P3(f45(f45(f3(a1),f11(f4(x10671,x10672,a1),x10673,a1)),x10674),x10675,a1) % 0.70/0.98 [1068]~P7(x10682,x10681,a1)+~P7(f45(f45(f3(a1),f11(x10681,x10683,a1)),x10684),f45(f45(f3(a1),f11(x10682,x10683,a1)),x10685),a1)+P7(f45(f45(f3(a1),f11(f4(x10681,x10682,a1),x10683,a1)),x10684),x10685,a1) % 0.70/0.98 [1075]~P7(x10751,x10754,a1)+P3(f45(f45(f3(a1),f11(x10751,x10752,a1)),x10753),f45(f45(f3(a1),f11(x10754,x10752,a1)),x10755),a1)+~P3(x10753,f45(f45(f3(a1),f11(f4(x10754,x10751,a1),x10752,a1)),x10755),a1) % 0.70/0.98 [1076]~P7(x10761,x10764,a1)+P7(f45(f45(f3(a1),f11(x10761,x10762,a1)),x10763),f45(f45(f3(a1),f11(x10764,x10762,a1)),x10765),a1)+~P7(x10763,f45(f45(f3(a1),f11(f4(x10764,x10761,a1),x10762,a1)),x10765),a1) % 0.70/0.98 [1077]~P7(x10774,x10771,a1)+P3(f45(f45(f3(a1),f11(x10771,x10772,a1)),x10773),f45(f45(f3(a1),f11(x10774,x10772,a1)),x10775),a1)+~P3(f45(f45(f3(a1),f11(f4(x10771,x10774,a1),x10772,a1)),x10773),x10775,a1) % 0.70/0.98 [1078]~P7(x10784,x10781,a1)+P7(f45(f45(f3(a1),f11(x10781,x10782,a1)),x10783),f45(f45(f3(a1),f11(x10784,x10782,a1)),x10785),a1)+~P7(f45(f45(f3(a1),f11(f4(x10781,x10784,a1),x10782,a1)),x10783),x10785,a1) % 0.70/0.98 [1034]~P5(x10341,x10343,x10346)+P5(x10341,f20(x10342,x10343,x10344),x10345)+~P5(f35(x10341,x10344,x10346,a47),x10342,x10345) % 0.70/0.98 [1047]~P55(x10472)+~E(f45(f45(f3(x10472),f11(x10474,x10475,x10472)),x10471),f45(f45(f3(x10472),f11(x10473,x10475,x10472)),x10476))+E(x10471,f45(f45(f3(x10472),f11(f4(x10473,x10474,x10472),x10475,x10472)),x10476)) % 0.70/0.98 [1048]~P55(x10481)+~E(f45(f45(f3(x10481),f11(x10482,x10484,x10481)),x10485),f45(f45(f3(x10481),f11(x10483,x10484,x10481)),x10486))+E(f45(f45(f3(x10481),f11(f4(x10482,x10483,x10481),x10484,x10481)),x10485),x10486) % 0.70/0.98 [1069]~P51(x10692)+~P3(f45(f45(f3(x10692),f11(x10694,x10695,x10692)),x10691),f45(f45(f3(x10692),f11(x10693,x10695,x10692)),x10696),x10692)+P3(x10691,f45(f45(f3(x10692),f11(f4(x10693,x10694,x10692),x10695,x10692)),x10696),x10692) % 0.70/0.98 [1070]~P51(x10702)+~P7(f45(f45(f3(x10702),f11(x10704,x10705,x10702)),x10701),f45(f45(f3(x10702),f11(x10703,x10705,x10702)),x10706),x10702)+P7(x10701,f45(f45(f3(x10702),f11(f4(x10703,x10704,x10702),x10705,x10702)),x10706),x10702) % 0.70/0.98 [1071]~P51(x10711)+~P3(f45(f45(f3(x10711),f11(x10712,x10714,x10711)),x10715),f45(f45(f3(x10711),f11(x10713,x10714,x10711)),x10716),x10711)+P3(f45(f45(f3(x10711),f11(f4(x10712,x10713,x10711),x10714,x10711)),x10715),x10716,x10711) % 0.70/0.98 [1072]~P51(x10721)+~P7(f45(f45(f3(x10721),f11(x10722,x10724,x10721)),x10725),f45(f45(f3(x10721),f11(x10723,x10724,x10721)),x10726),x10721)+P7(f45(f45(f3(x10721),f11(f4(x10722,x10723,x10721),x10724,x10721)),x10725),x10726,x10721) % 0.70/0.98 [1079]~P51(x10791)+P3(f45(f45(f3(x10791),f11(x10792,x10793,x10791)),x10794),f45(f45(f3(x10791),f11(x10795,x10793,x10791)),x10796),x10791)+~P3(x10794,f45(f45(f3(x10791),f11(f4(x10795,x10792,x10791),x10793,x10791)),x10796),x10791) % 0.70/0.98 [1080]~P51(x10801)+P7(f45(f45(f3(x10801),f11(x10802,x10803,x10801)),x10804),f45(f45(f3(x10801),f11(x10805,x10803,x10801)),x10806),x10801)+~P7(x10804,f45(f45(f3(x10801),f11(f4(x10805,x10802,x10801),x10803,x10801)),x10806),x10801) % 0.70/0.98 [1081]~P51(x10811)+P3(f45(f45(f3(x10811),f11(x10812,x10813,x10811)),x10814),f45(f45(f3(x10811),f11(x10815,x10813,x10811)),x10816),x10811)+~P3(f45(f45(f3(x10811),f11(f4(x10812,x10815,x10811),x10813,x10811)),x10814),x10816,x10811) % 0.70/0.98 [1082]~P51(x10821)+P7(f45(f45(f3(x10821),f11(x10822,x10823,x10821)),x10824),f45(f45(f3(x10821),f11(x10825,x10823,x10821)),x10826),x10821)+~P7(f45(f45(f3(x10821),f11(f4(x10822,x10825,x10821),x10823,x10821)),x10824),x10826,x10821) % 0.70/0.98 [427]~P10(x4272)+~P11(x4272)+E(x4271,f2(a1))+E(f32(f2(x4272),x4271,x4272),f2(x4272)) % 0.70/0.98 [488]P3(x4881,x4882,x4883)+~P12(x4883)+E(x4881,x4882)+P3(x4882,x4881,x4883) % 0.70/0.98 [489]P3(x4891,x4892,x4893)+~P45(x4893)+E(x4891,x4892)+P3(x4892,x4891,x4893) % 0.70/0.98 [544]~P12(x5443)+~P7(x5441,x5442,x5443)+E(x5441,x5442)+P3(x5441,x5442,x5443) % 0.70/0.98 [550]~P34(x5503)+~P7(x5501,x5502,x5503)+E(x5501,x5502)+P3(x5501,x5502,x5503) % 0.70/0.98 [599]~P7(x5992,x5991,x5993)+~P7(x5991,x5992,x5993)+E(x5991,x5992)+~P34(x5993) % 0.70/0.98 [613]P7(x6132,x6131,x6133)+~P33(x6133)+~P7(x6131,x6132,x6133)+P3(x6131,x6132,x6133) % 0.70/0.98 [462]~P40(x4623)+~P17(x4623)+E(x4621,x4622)+~E(f4(x4621,x4622,x4623),f2(x4623)) % 0.70/0.98 [466]~P43(x4662)+~E(f11(x4663,x4661,x4662),f2(x4662))+E(x4661,f2(x4662))+E(x4663,f2(x4662)) % 0.70/0.98 [467]~P52(x4672)+~E(f11(x4673,x4671,x4672),f2(x4672))+E(x4671,f2(x4672))+E(x4673,f2(x4672)) % 0.70/0.98 [768]E(x7681,x7682)+~P7(x7683,x7682,a1)+~P7(x7683,x7681,a1)+~E(f4(x7681,x7683,a1),f4(x7682,x7683,a1)) % 0.70/0.98 [811]~P46(x8111)+~P3(x8113,f2(x8111),x8111)+~P3(x8112,f2(x8111),x8111)+P3(f2(x8111),f11(x8112,x8113,x8111),x8111) % 0.70/0.98 [813]~P51(x8131)+~P7(x8133,f2(x8131),x8131)+~P7(x8132,f2(x8131),x8131)+P7(f2(x8131),f11(x8132,x8133,x8131),x8131) % 0.70/0.98 [814]~P46(x8141)+~P7(x8143,f2(x8141),x8141)+~P7(x8142,f2(x8141),x8141)+P7(f2(x8141),f11(x8142,x8143,x8141),x8141) % 0.70/0.98 [815]~P35(x8151)+~P3(f2(x8151),x8153,x8151)+~P3(f2(x8151),x8152,x8151)+P3(f2(x8151),f11(x8152,x8153,x8151),x8151) % 0.70/0.98 [816]~P51(x8161)+~P7(f2(x8161),x8163,x8161)+~P7(f2(x8161),x8162,x8161)+P7(f2(x8161),f11(x8162,x8163,x8161),x8161) % 0.70/0.98 [817]~P46(x8171)+~P7(f2(x8171),x8173,x8171)+~P7(f2(x8171),x8172,x8171)+P7(f2(x8171),f11(x8172,x8173,x8171),x8171) % 0.70/0.98 [818]~P49(x8181)+~P7(f2(x8181),x8183,x8181)+~P7(f2(x8181),x8182,x8181)+P7(f2(x8181),f11(x8182,x8183,x8181),x8181) % 0.70/0.98 [819]~P35(x8193)+~P3(x8192,f2(x8193),x8193)+~P3(f2(x8193),x8191,x8193)+P3(f11(x8191,x8192,x8193),f2(x8193),x8193) % 0.70/0.98 [821]~P35(x8213)+~P3(x8211,f2(x8213),x8213)+~P3(f2(x8213),x8212,x8213)+P3(f11(x8211,x8212,x8213),f2(x8213),x8213) % 0.70/0.98 [822]~P46(x8223)+~P7(x8222,f2(x8223),x8223)+~P7(f2(x8223),x8221,x8223)+P7(f11(x8221,x8222,x8223),f2(x8223),x8223) % 0.70/0.98 [823]~P46(x8233)+~P7(x8231,f2(x8233),x8233)+~P7(f2(x8233),x8232,x8233)+P7(f11(x8231,x8232,x8233),f2(x8233),x8233) % 0.70/0.98 [825]~P49(x8253)+~P7(x8252,f2(x8253),x8253)+~P7(f2(x8253),x8251,x8253)+P7(f11(x8251,x8252,x8253),f2(x8253),x8253) % 0.70/0.98 [828]~P49(x8283)+~P7(x8281,f2(x8283),x8283)+~P7(f2(x8283),x8282,x8283)+P7(f11(x8281,x8282,x8283),f2(x8283),x8283) % 0.70/0.98 [847]~P46(x8472)+~P7(f11(x8473,x8471,x8472),f2(x8472),x8472)+P7(x8471,f2(x8472),x8472)+P7(x8473,f2(x8472),x8472) % 0.70/0.98 [848]~P46(x8482)+~P7(f2(x8482),f11(x8483,x8481,x8482),x8482)+P7(x8481,f2(x8482),x8482)+P7(f2(x8482),x8483,x8482) % 0.70/0.98 [849]~P46(x8492)+~P7(f2(x8492),f11(x8491,x8493,x8492),x8492)+P7(x8491,f2(x8492),x8492)+P7(f2(x8492),x8493,x8492) % 0.70/0.98 [850]~P46(x8502)+~P7(f2(x8502),f11(x8503,x8501,x8502),x8502)+P7(x8501,f2(x8502),x8502)+P7(f2(x8502),x8501,x8502) % 0.70/0.98 [851]~P46(x8512)+~P7(f2(x8512),f11(x8511,x8513,x8512),x8512)+P7(x8511,f2(x8512),x8512)+P7(f2(x8512),x8511,x8512) % 0.70/0.98 [852]~P46(x8522)+~P7(f11(x8523,x8521,x8522),f2(x8522),x8522)+P7(x8521,f2(x8522),x8522)+P7(f2(x8522),x8521,x8522) % 0.70/0.98 [853]~P46(x8532)+~P7(f11(x8531,x8533,x8532),f2(x8532),x8532)+P7(x8531,f2(x8532),x8532)+P7(f2(x8532),x8531,x8532) % 0.70/0.98 [854]~P46(x8541)+~P7(f11(x8542,x8543,x8541),f2(x8541),x8541)+P7(f2(x8541),x8542,x8541)+P7(f2(x8541),x8543,x8541) % 0.70/0.98 [869]~P35(x8691)+~P3(f2(x8691),f11(x8693,x8692,x8691),x8691)+P3(f2(x8691),x8692,x8691)+~P3(f2(x8691),x8693,x8691) % 0.70/0.98 [870]~P35(x8701)+~P3(f2(x8701),f11(x8702,x8703,x8701),x8701)+P3(f2(x8701),x8702,x8701)+~P3(f2(x8701),x8703,x8701) % 0.70/0.98 [993]~P7(x9933,x9931,a1)+P3(x9931,x9932,a1)+~P7(x9933,x9932,a1)+~P3(f4(x9931,x9933,a1),f4(x9932,x9933,a1),a1) % 0.70/0.98 [994]~P7(x9943,x9941,a1)+P7(x9941,x9942,a1)+~P7(x9943,x9942,a1)+~P7(f4(x9941,x9943,a1),f4(x9942,x9943,a1),a1) % 0.70/0.98 [616]~P3(x6162,f7(x6161),a1)+P58(f45(x6161,x6162))+P58(f45(x6161,x6163))+~P58(f45(x6161,f2(a1))) % 0.70/0.98 [682]~P3(x6823,f8(x6821,x6822),a1)+~P58(f45(x6821,x6822))+~P58(f45(x6821,x6823))+P58(f45(x6821,f2(a1))) % 0.70/0.98 [1003]E(x10031,f5(x10032,x10033,a1))+~P7(f11(x10033,x10031,a1),x10032,a1)+~P3(f2(a1),x10033,a1)+~P3(x10032,f11(x10033,f30(x10031),a1),a1) % 0.70/0.98 [457]~P40(x4572)+~P17(x4572)+E(x4571,f2(x4572))+~E(f45(f45(f3(x4572),x4573),x4571),x4573) % 0.70/0.98 [801]~P30(x8011)+~P3(f2(x8011),x8013,x8011)+~P3(f2(x8011),x8012,x8011)+P3(f2(x8011),f45(f45(f3(x8011),x8012),x8013),x8011) % 0.70/0.98 [802]~P30(x8021)+~P3(f2(x8021),x8023,x8021)+~P7(f2(x8021),x8022,x8021)+P3(f2(x8021),f45(f45(f3(x8021),x8022),x8023),x8021) % 0.70/0.98 [803]~P30(x8031)+~P3(f2(x8031),x8032,x8031)+~P7(f2(x8031),x8033,x8031)+P3(f2(x8031),f45(f45(f3(x8031),x8032),x8033),x8031) % 0.70/0.98 [804]~P30(x8041)+~P7(f2(x8041),x8043,x8041)+~P7(f2(x8041),x8042,x8041)+P7(f2(x8041),f45(f45(f3(x8041),x8042),x8043),x8041) % 0.70/0.98 [805]~P30(x8051)+~P3(x8053,f2(x8051),x8051)+~P3(x8052,f2(x8051),x8051)+P3(f45(f45(f3(x8051),x8052),x8053),f2(x8051),x8051) % 0.70/0.98 [806]~P30(x8061)+~P3(x8063,f2(x8061),x8061)+~P7(x8062,f2(x8061),x8061)+P3(f45(f45(f3(x8061),x8062),x8063),f2(x8061),x8061) % 0.70/0.98 [807]~P30(x8071)+~P3(x8072,f2(x8071),x8071)+~P7(x8073,f2(x8071),x8071)+P3(f45(f45(f3(x8071),x8072),x8073),f2(x8071),x8071) % 0.70/0.98 [808]~P30(x8081)+~P7(x8083,f2(x8081),x8081)+~P7(x8082,f2(x8081),x8081)+P7(f45(f45(f3(x8081),x8082),x8083),f2(x8081),x8081) % 0.70/0.98 [645]~P33(x6453)+~P3(x6451,x6454,x6453)+P3(x6451,x6452,x6453)+~P3(x6454,x6452,x6453) % 0.70/0.98 [646]~P33(x6463)+~P7(x6461,x6464,x6463)+P3(x6461,x6462,x6463)+~P3(x6464,x6462,x6463) % 0.70/0.98 [647]~P33(x6473)+~P7(x6474,x6472,x6473)+P3(x6471,x6472,x6473)+~P3(x6471,x6474,x6473) % 0.70/0.98 [648]~P34(x6483)+~P3(x6481,x6484,x6483)+P3(x6481,x6482,x6483)+~P3(x6484,x6482,x6483) % 0.70/0.98 [649]~P34(x6493)+~P7(x6491,x6494,x6493)+P3(x6491,x6492,x6493)+~P3(x6494,x6492,x6493) % 0.70/0.98 [650]~P34(x6503)+~P7(x6504,x6502,x6503)+P3(x6501,x6502,x6503)+~P3(x6501,x6504,x6503) % 0.70/0.98 [651]~P33(x6513)+~P7(x6511,x6514,x6513)+P7(x6511,x6512,x6513)+~P7(x6514,x6512,x6513) % 0.70/0.98 [652]~P34(x6523)+~P7(x6521,x6524,x6523)+P7(x6521,x6522,x6523)+~P7(x6524,x6522,x6523) % 0.70/0.98 [772]~P12(x7724)+~P3(x7721,x7723,x7724)+~P3(x7721,x7722,x7724)+P3(x7721,f29(x7722,x7723,x7724),x7724) % 0.70/0.98 [775]~P12(x7754)+~P7(x7751,x7753,x7754)+~P7(x7751,x7752,x7754)+P7(x7751,f29(x7752,x7753,x7754),x7754) % 0.70/0.98 [776]~P12(x7763)+~P3(x7762,x7764,x7763)+~P3(x7761,x7764,x7763)+P3(f28(x7761,x7762,x7763),x7764,x7763) % 0.70/0.98 [779]~P12(x7793)+~P7(x7792,x7794,x7793)+~P7(x7791,x7794,x7793)+P7(f28(x7791,x7792,x7793),x7794,x7793) % 0.70/0.98 [832]~P12(x8323)+P3(x8321,x8322,x8323)+P3(x8321,x8324,x8323)+~P3(x8321,f28(x8322,x8324,x8323),x8323) % 0.70/0.98 [833]~P12(x8333)+P7(x8331,x8332,x8333)+P7(x8331,x8334,x8333)+~P7(x8331,f28(x8332,x8334,x8333),x8333) % 0.70/0.98 [834]~P12(x8343)+P3(x8341,x8342,x8343)+P3(x8344,x8342,x8343)+~P3(f29(x8341,x8344,x8343),x8342,x8343) % 0.70/0.98 [835]~P12(x8353)+P7(x8351,x8352,x8353)+P7(x8354,x8352,x8353)+~P7(f29(x8351,x8354,x8353),x8352,x8353) % 0.70/0.98 [901]~P46(x9013)+~P3(x9014,x9011,x9013)+~P3(x9012,f2(x9013),x9013)+P3(f11(x9011,x9012,x9013),f11(x9014,x9012,x9013),x9013) % 0.70/0.98 [904]~P46(x9043)+~P3(x9044,x9042,x9043)+~P3(x9041,f2(x9043),x9043)+P3(f11(x9041,x9042,x9043),f11(x9041,x9044,x9043),x9043) % 0.70/0.98 [905]~P51(x9053)+~P7(x9054,x9051,x9053)+~P7(x9052,f2(x9053),x9053)+P7(f11(x9051,x9052,x9053),f11(x9054,x9052,x9053),x9053) % 0.70/0.98 [906]~P51(x9063)+~P7(x9064,x9062,x9063)+~P7(x9061,f2(x9063),x9063)+P7(f11(x9061,x9062,x9063),f11(x9061,x9064,x9063),x9063) % 0.70/0.98 [907]~P46(x9073)+~P7(x9074,x9072,x9073)+~P3(x9071,f2(x9073),x9073)+P7(f11(x9071,x9072,x9073),f11(x9071,x9074,x9073),x9073) % 0.70/0.98 [908]~P35(x9083)+~P3(x9081,x9084,x9083)+~P3(f2(x9083),x9082,x9083)+P3(f11(x9081,x9082,x9083),f11(x9084,x9082,x9083),x9083) % 0.70/0.98 [909]~P46(x9093)+~P3(x9091,x9094,x9093)+~P3(f2(x9093),x9092,x9093)+P3(f11(x9091,x9092,x9093),f11(x9094,x9092,x9093),x9093) % 0.70/0.98 [910]~P35(x9103)+~P3(x9102,x9104,x9103)+~P3(f2(x9103),x9101,x9103)+P3(f11(x9101,x9102,x9103),f11(x9101,x9104,x9103),x9103) % 0.70/0.98 [912]~P46(x9123)+~P3(x9122,x9124,x9123)+~P3(f2(x9123),x9121,x9123)+P3(f11(x9121,x9122,x9123),f11(x9121,x9124,x9123),x9123) % 0.70/0.98 [913]~P42(x9133)+~P3(x9132,x9134,x9133)+~P3(f2(x9133),x9131,x9133)+P3(f11(x9131,x9132,x9133),f11(x9131,x9134,x9133),x9133) % 0.70/0.98 [914]~P39(x9143)+~P7(x9141,x9144,x9143)+~P7(f2(x9143),x9142,x9143)+P7(f11(x9141,x9142,x9143),f11(x9144,x9142,x9143),x9143) % 0.70/0.98 [915]~P46(x9153)+~P7(x9152,x9154,x9153)+~P3(f2(x9153),x9151,x9153)+P7(f11(x9151,x9152,x9153),f11(x9151,x9154,x9153),x9153) % 0.70/0.98 [916]~P39(x9163)+~P7(x9162,x9164,x9163)+~P7(f2(x9163),x9161,x9163)+P7(f11(x9161,x9162,x9163),f11(x9161,x9164,x9163),x9163) % 0.70/0.98 [917]~P41(x9173)+~P7(x9172,x9174,x9173)+~P7(f2(x9173),x9171,x9173)+P7(f11(x9171,x9172,x9173),f11(x9171,x9174,x9173),x9173) % 0.70/0.98 [918]~P36(x9183)+~P7(x9181,x9184,x9183)+~P7(f2(x9183),x9181,x9183)+P7(f32(x9181,x9182,x9183),f32(x9184,x9182,x9183),x9183) % 0.70/0.98 [954]P3(x9542,x9541,x9543)+~P46(x9543)+P3(x9541,x9542,x9543)+~P3(f11(x9544,x9541,x9543),f11(x9544,x9542,x9543),x9543) % 0.70/0.98 [955]P3(x9552,x9551,x9553)+~P46(x9553)+P3(x9551,x9552,x9553)+~P3(f11(x9551,x9554,x9553),f11(x9552,x9554,x9553),x9553) % 0.70/0.98 [965]~P46(x9653)+P3(x9651,x9652,x9653)+~P3(f11(x9651,x9654,x9653),f11(x9652,x9654,x9653),x9653)+P3(x9654,f2(x9653),x9653) % 0.70/0.98 [966]~P46(x9663)+P3(x9661,x9662,x9663)+~P3(f11(x9664,x9661,x9663),f11(x9664,x9662,x9663),x9663)+P3(x9664,f2(x9663),x9663) % 0.70/0.98 [967]~P46(x9673)+P3(x9671,x9672,x9673)+~P3(f11(x9674,x9672,x9673),f11(x9674,x9671,x9673),x9673)+P3(f2(x9673),x9674,x9673) % 0.70/0.98 [968]~P46(x9683)+P3(x9681,x9682,x9683)+~P3(f11(x9682,x9684,x9683),f11(x9681,x9684,x9683),x9683)+P3(f2(x9683),x9684,x9683) % 0.70/0.98 [970]~P46(x9702)+~P3(f11(x9703,x9701,x9702),f11(x9704,x9701,x9702),x9702)+P3(x9701,f2(x9702),x9702)+P3(f2(x9702),x9701,x9702) % 0.70/0.98 [971]~P46(x9712)+~P3(f11(x9711,x9713,x9712),f11(x9711,x9714,x9712),x9712)+P3(x9711,f2(x9712),x9712)+P3(f2(x9712),x9711,x9712) % 0.70/0.98 [977]~P46(x9773)+P3(x9771,x9772,x9773)+~P3(f11(x9774,x9772,x9773),f11(x9774,x9771,x9773),x9773)+~P3(x9774,f2(x9773),x9773) % 0.70/0.98 [978]~P46(x9783)+P7(x9781,x9782,x9783)+~P7(f11(x9784,x9782,x9783),f11(x9784,x9781,x9783),x9783)+~P3(x9784,f2(x9783),x9783) % 0.70/0.98 [979]~P35(x9793)+P3(x9791,x9792,x9793)+~P3(f11(x9794,x9791,x9793),f11(x9794,x9792,x9793),x9793)+~P7(f2(x9793),x9794,x9793) % 0.70/0.98 [980]~P35(x9803)+P3(x9801,x9802,x9803)+~P3(f11(x9801,x9804,x9803),f11(x9802,x9804,x9803),x9803)+~P7(f2(x9803),x9804,x9803) % 0.70/0.98 [981]~P36(x9813)+P3(x9811,x9812,x9813)+~P7(f2(x9813),x9812,x9813)+~P3(f32(x9811,x9814,x9813),f32(x9812,x9814,x9813),x9813) % 0.70/0.98 [982]~P46(x9823)+P3(x9821,x9822,x9823)+~P3(f11(x9824,x9821,x9823),f11(x9824,x9822,x9823),x9823)+~P3(f2(x9823),x9824,x9823) % 0.70/0.98 [983]~P47(x9833)+P3(x9831,x9832,x9833)+~P3(f11(x9834,x9831,x9833),f11(x9834,x9832,x9833),x9833)+~P7(f2(x9833),x9834,x9833) % 0.70/0.98 [984]~P47(x9843)+P3(x9841,x9842,x9843)+~P3(f11(x9841,x9844,x9843),f11(x9842,x9844,x9843),x9843)+~P7(f2(x9843),x9844,x9843) % 0.70/0.98 [985]~P35(x9853)+P7(x9851,x9852,x9853)+~P7(f11(x9854,x9851,x9853),f11(x9854,x9852,x9853),x9853)+~P3(f2(x9853),x9854,x9853) % 0.70/0.98 [986]~P35(x9863)+P7(x9861,x9862,x9863)+~P7(f11(x9861,x9864,x9863),f11(x9862,x9864,x9863),x9863)+~P3(f2(x9863),x9864,x9863) % 0.70/0.98 [987]~P46(x9873)+P7(x9871,x9872,x9873)+~P7(f11(x9874,x9871,x9873),f11(x9874,x9872,x9873),x9873)+~P3(f2(x9873),x9874,x9873) % 0.70/0.98 [992]~P36(x9923)+P7(x9921,x9922,x9923)+~P7(f2(x9923),x9922,x9923)+~P7(f32(x9921,f30(x9924),x9923),f32(x9922,f30(x9924),x9923),x9923) % 0.70/0.98 [1018]~P7(f11(x10183,x10184,a1),x10182,a1)+~P58(f45(x10181,x10184))+~P3(x10182,f11(x10183,f30(x10184),a1),a1)+P58(f45(x10181,f5(x10182,x10183,a1))) % 0.70/0.98 [596]~P40(x5963)+~P17(x5963)+E(x5961,x5962)+~E(f45(f45(f3(x5963),x5964),x5961),f45(f45(f3(x5963),x5964),x5962)) % 0.70/0.98 [788]~P36(x7882)+~P3(x7881,x7884,x7882)+~P3(f2(x7882),x7883,x7882)+P3(x7881,f45(f45(f3(x7882),x7883),x7884),x7882) % 0.70/0.98 [1083]~P3(x10834,x10831,a1)+E(x10831,f2(a1))+P58(f45(x10832,x10833))+~P58(f45(x10832,f5(f45(f45(f3(a1),f11(x10831,x10833,a1)),x10834),x10831,a1))) % 0.70/0.98 [1084]~P3(x10843,x10841,a1)+E(x10841,f2(a1))+P58(f45(x10842,x10843))+~P58(f45(x10842,f10(f45(f45(f3(a1),f11(x10841,x10844,a1)),x10843),x10841,a1))) % 0.70/0.98 [738]~P29(x7383)+~P3(x7384,x7385,x7383)+P3(x7381,x7382,x7383)+~E(f4(x7384,x7385,x7383),f4(x7381,x7382,x7383)) % 0.70/0.98 [739]~P29(x7393)+~P3(x7394,x7395,x7393)+P3(x7391,x7392,x7393)+~E(f4(x7391,x7392,x7393),f4(x7394,x7395,x7393)) % 0.70/0.98 [740]~P29(x7403)+~P7(x7405,x7404,x7403)+P7(x7401,x7402,x7403)+~E(f4(x7404,x7405,x7403),f4(x7402,x7401,x7403)) % 0.70/0.98 [741]~P29(x7413)+~P7(x7415,x7414,x7413)+P7(x7411,x7412,x7413)+~E(f4(x7412,x7411,x7413),f4(x7414,x7415,x7413)) % 0.70/0.98 [894]~P31(x8941)+~P3(x8943,x8945,x8941)+~P3(x8942,x8944,x8941)+P3(f45(f45(f3(x8941),x8942),x8943),f45(f45(f3(x8941),x8944),x8945),x8941) % 0.70/0.98 [895]~P31(x8951)+~P3(x8953,x8955,x8951)+~P7(x8952,x8954,x8951)+P3(f45(f45(f3(x8951),x8952),x8953),f45(f45(f3(x8951),x8954),x8955),x8951) % 0.70/0.98 [896]~P31(x8961)+~P3(x8962,x8964,x8961)+~P7(x8963,x8965,x8961)+P3(f45(f45(f3(x8961),x8962),x8963),f45(f45(f3(x8961),x8964),x8965),x8961) % 0.70/0.98 [897]~P28(x8971)+~P7(x8973,x8975,x8971)+~P7(x8972,x8974,x8971)+P7(f45(f45(f3(x8971),x8972),x8973),f45(f45(f3(x8971),x8974),x8975),x8971) % 0.70/0.98 [935]~P29(x9352)+~P7(x9355,x9354,x9352)+~P7(x9351,f45(f45(f3(x9352),x9353),x9355),x9352)+P7(x9351,f45(f45(f3(x9352),x9353),x9354),x9352) % 0.70/0.98 [1006]~P9(x10063)+~E(f10(x10061,x10064,x10063),f10(x10065,x10064,x10063))+~E(f10(x10062,x10064,x10063),f10(x10066,x10064,x10063))+E(f10(f4(x10061,x10062,x10063),x10064,x10063),f10(f4(x10065,x10066,x10063),x10064,x10063)) % 0.70/0.98 [1007]~P1(x10073)+~E(f10(x10071,x10074,x10073),f10(x10075,x10074,x10073))+~E(f10(x10072,x10074,x10073),f10(x10076,x10074,x10073))+E(f10(f11(x10071,x10072,x10073),x10074,x10073),f10(f11(x10075,x10076,x10073),x10074,x10073)) % 0.70/0.98 [1005]~P1(x10051)+~E(f10(x10052,x10054,x10051),f10(x10055,x10054,x10051))+~E(f10(x10053,x10054,x10051),f10(x10056,x10054,x10051))+E(f10(f45(f45(f3(x10051),x10052),x10053),x10054,x10051),f10(f45(f45(f3(x10051),x10055),x10056),x10054,x10051)) % 0.70/0.98 [491]~P11(x4912)+~P57(x4912)+~P43(x4912)+~P44(x4912)+~E(f32(x4911,f2(a1),x4912),f2(x4912)) % 0.70/0.98 [703]~P30(x7032)+~P7(f2(x7032),x7031,x7032)+~P7(f2(x7032),x7033,x7032)+E(x7031,f2(x7032))+~E(f45(f45(f3(x7032),x7033),x7031),f2(x7032)) % 0.70/0.98 [704]~P30(x7042)+~P7(f2(x7042),x7043,x7042)+~P7(f2(x7042),x7041,x7042)+E(x7041,f2(x7042))+~E(f45(f45(f3(x7042),x7041),x7043),f2(x7042)) % 0.70/0.98 [969]~P36(x9693)+~P3(x9691,x9694,x9693)+~P7(f2(x9693),x9691,x9693)+P3(f32(x9691,x9692,x9693),f32(x9694,x9692,x9693),x9693)+~P3(f2(a1),x9692,a1) % 0.70/0.98 [846]~P36(x8464)+E(x8461,x8462)+~P7(f2(x8464),x8462,x8464)+~P7(f2(x8464),x8461,x8464)+~E(f32(x8461,f30(x8463),x8464),f32(x8462,f30(x8463),x8464)) % 0.70/0.98 [797]~P13(x7972)+~P14(x7972)+~P3(x7971,x7974,x7972)+~P7(f2(x7972),x7973,x7972)+P3(x7971,f45(f45(f3(x7972),x7973),x7974),x7972) % 0.70/0.98 [798]~P13(x7982)+~P14(x7982)+~P7(x7981,x7984,x7982)+~P3(f2(x7982),x7983,x7982)+P3(x7981,f45(f45(f3(x7982),x7983),x7984),x7982) % 0.70/0.98 [799]~P13(x7992)+~P14(x7992)+~P7(x7991,x7994,x7992)+~P7(f2(x7992),x7993,x7992)+P7(x7991,f45(f45(f3(x7992),x7993),x7994),x7992) % 0.70/0.98 [800]~P13(x8002)+~P14(x8002)+~P7(x8001,x8003,x8002)+~P7(f2(x8002),x8004,x8002)+P7(x8001,f45(f45(f3(x8002),x8003),x8004),x8002) % 0.70/0.98 [944]~P40(x9444)+~P17(x9444)+E(x9441,x9442)+E(x9443,f2(x9444))+~E(f45(f45(f3(x9444),x9445),f11(x9443,x9441,x9444)),f45(f45(f3(x9444),x9445),f11(x9443,x9442,x9444))) % 0.70/0.98 [1038]~P40(x10385)+~P17(x10385)+E(x10381,x10382)+E(x10383,x10384)+~E(f45(f45(f3(x10385),f11(x10383,x10381,x10385)),f11(x10384,x10382,x10385)),f45(f45(f3(x10385),f11(x10383,x10382,x10385)),f11(x10384,x10381,x10385))) % 0.70/0.98 [1033]~P2(x10332)+~P2(x10331)+~P5(x10334,x10332,x10335)+~P5(f35(x10334,x10333,x10335,a47),x10331,x10336)+P2(f20(x10331,x10332,x10333)) % 0.70/0.98 [448]~P11(x4482)+~P57(x4482)+~P43(x4482)+~P44(x4482)+E(x4481,f2(a1))+E(f32(f2(x4482),x4481,x4482),f2(x4482)) % 0.70/0.98 [492]~P11(x4922)+~P57(x4922)+~P43(x4922)+~P44(x4922)+~E(f32(x4921,x4923,x4922),f2(x4922))+E(x4921,f2(x4922)) % 0.70/0.98 [919]~P36(x9194)+E(x9191,x9192)+~P7(f2(x9194),x9192,x9194)+~P7(f2(x9194),x9191,x9194)+~E(f32(x9191,x9193,x9194),f32(x9192,x9193,x9194))+~P3(f2(a1),x9193,a1) % 0.70/0.98 [995]~P35(x9953)+~P3(x9952,x9955,x9953)+~P3(x9951,x9954,x9953)+~P3(f2(x9953),x9954,x9953)+~P7(f2(x9953),x9952,x9953)+P3(f11(x9951,x9952,x9953),f11(x9954,x9955,x9953),x9953) % 0.70/0.98 [996]~P35(x9963)+~P3(x9962,x9965,x9963)+~P3(x9961,x9964,x9963)+~P7(f2(x9963),x9962,x9963)+~P7(f2(x9963),x9961,x9963)+P3(f11(x9961,x9962,x9963),f11(x9964,x9965,x9963),x9963) % 0.70/0.98 [997]~P35(x9973)+~P3(x9972,x9975,x9973)+~P7(x9971,x9974,x9973)+~P3(f2(x9973),x9971,x9973)+~P7(f2(x9973),x9972,x9973)+P3(f11(x9971,x9972,x9973),f11(x9974,x9975,x9973),x9973) % 0.70/0.98 [998]~P35(x9983)+~P3(x9981,x9984,x9983)+~P7(x9982,x9985,x9983)+~P3(f2(x9983),x9982,x9983)+~P7(f2(x9983),x9981,x9983)+P3(f11(x9981,x9982,x9983),f11(x9984,x9985,x9983),x9983) % 0.70/0.98 [999]~P50(x9993)+~P7(x9992,x9995,x9993)+~P7(x9991,x9994,x9993)+~P7(f2(x9993),x9994,x9993)+~P7(f2(x9993),x9992,x9993)+P7(f11(x9991,x9992,x9993),f11(x9994,x9995,x9993),x9993) % 0.70/0.98 [1000]~P50(x10003)+~P7(x10002,x10005,x10003)+~P7(x10001,x10004,x10003)+~P7(f2(x10003),x10002,x10003)+~P7(f2(x10003),x10001,x10003)+P7(f11(x10001,x10002,x10003),f11(x10004,x10005,x10003),x10003) % 0.70/0.98 %EqnAxiom % 0.70/0.98 [1]E(x11,x11) % 0.70/0.98 [2]E(x22,x21)+~E(x21,x22) % 0.70/0.98 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.70/0.98 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 0.70/0.98 [5]~E(x51,x52)+E(f12(x51),f12(x52)) % 0.70/0.98 [6]~E(x61,x62)+E(f45(x61,x63),f45(x62,x63)) % 0.70/0.98 [7]~E(x71,x72)+E(f45(x73,x71),f45(x73,x72)) % 0.70/0.98 [8]~E(x81,x82)+E(f27(x81),f27(x82)) % 0.70/0.98 [9]~E(x91,x92)+E(f11(x91,x93,x94),f11(x92,x93,x94)) % 0.70/0.98 [10]~E(x101,x102)+E(f11(x103,x101,x104),f11(x103,x102,x104)) % 0.70/0.98 [11]~E(x111,x112)+E(f11(x113,x114,x111),f11(x113,x114,x112)) % 0.70/0.98 [12]~E(x121,x122)+E(f13(x121),f13(x122)) % 0.70/0.98 [13]~E(x131,x132)+E(f16(x131,x133),f16(x132,x133)) % 0.70/0.98 [14]~E(x141,x142)+E(f16(x143,x141),f16(x143,x142)) % 0.70/0.98 [15]~E(x151,x152)+E(f4(x151,x153,x154),f4(x152,x153,x154)) % 0.70/0.98 [16]~E(x161,x162)+E(f4(x163,x161,x164),f4(x163,x162,x164)) % 0.70/0.98 [17]~E(x171,x172)+E(f4(x173,x174,x171),f4(x173,x174,x172)) % 0.70/0.98 [18]~E(x181,x182)+E(f3(x181),f3(x182)) % 0.70/0.98 [19]~E(x191,x192)+E(f26(x191,x193),f26(x192,x193)) % 0.70/0.98 [20]~E(x201,x202)+E(f26(x203,x201),f26(x203,x202)) % 0.70/0.98 [21]~E(x211,x212)+E(f28(x211,x213,x214),f28(x212,x213,x214)) % 0.70/0.98 [22]~E(x221,x222)+E(f28(x223,x221,x224),f28(x223,x222,x224)) % 0.70/0.98 [23]~E(x231,x232)+E(f28(x233,x234,x231),f28(x233,x234,x232)) % 0.70/0.98 [24]~E(x241,x242)+E(f5(x241,x243,x244),f5(x242,x243,x244)) % 0.70/0.98 [25]~E(x251,x252)+E(f5(x253,x251,x254),f5(x253,x252,x254)) % 0.70/0.98 [26]~E(x261,x262)+E(f5(x263,x264,x261),f5(x263,x264,x262)) % 0.70/0.98 [27]~E(x271,x272)+E(f30(x271),f30(x272)) % 0.70/0.98 [28]~E(x281,x282)+E(f32(x281,x283,x284),f32(x282,x283,x284)) % 0.70/0.98 [29]~E(x291,x292)+E(f32(x293,x291,x294),f32(x293,x292,x294)) % 0.70/0.98 [30]~E(x301,x302)+E(f32(x303,x304,x301),f32(x303,x304,x302)) % 0.70/0.98 [31]~E(x311,x312)+E(f29(x311,x313,x314),f29(x312,x313,x314)) % 0.70/0.98 [32]~E(x321,x322)+E(f29(x323,x321,x324),f29(x323,x322,x324)) % 0.70/0.98 [33]~E(x331,x332)+E(f29(x333,x334,x331),f29(x333,x334,x332)) % 0.70/0.98 [34]~E(x341,x342)+E(f24(x341,x343),f24(x342,x343)) % 0.70/0.98 [35]~E(x351,x352)+E(f24(x353,x351),f24(x353,x352)) % 0.70/0.98 [36]~E(x361,x362)+E(f10(x361,x363,x364),f10(x362,x363,x364)) % 0.70/0.98 [37]~E(x371,x372)+E(f10(x373,x371,x374),f10(x373,x372,x374)) % 0.70/0.98 [38]~E(x381,x382)+E(f10(x383,x384,x381),f10(x383,x384,x382)) % 0.70/0.98 [39]~E(x391,x392)+E(f20(x391,x393,x394),f20(x392,x393,x394)) % 0.70/0.98 [40]~E(x401,x402)+E(f20(x403,x401,x404),f20(x403,x402,x404)) % 0.70/0.98 [41]~E(x411,x412)+E(f20(x413,x414,x411),f20(x413,x414,x412)) % 0.70/0.98 [42]~E(x421,x422)+E(f35(x421,x423,x424,x425),f35(x422,x423,x424,x425)) % 0.70/0.98 [43]~E(x431,x432)+E(f35(x433,x431,x434,x435),f35(x433,x432,x434,x435)) % 0.70/0.98 [44]~E(x441,x442)+E(f35(x443,x444,x441,x445),f35(x443,x444,x442,x445)) % 0.70/0.98 [45]~E(x451,x452)+E(f35(x453,x454,x455,x451),f35(x453,x454,x455,x452)) % 0.70/0.98 [46]~E(x461,x462)+E(f56(x461),f56(x462)) % 0.70/0.98 [47]~E(x471,x472)+E(f31(x471,x473,x474,x475,x476),f31(x472,x473,x474,x475,x476)) % 0.70/0.98 [48]~E(x481,x482)+E(f31(x483,x481,x484,x485,x486),f31(x483,x482,x484,x485,x486)) % 0.70/0.98 [49]~E(x491,x492)+E(f31(x493,x494,x491,x495,x496),f31(x493,x494,x492,x495,x496)) % 0.70/0.98 [50]~E(x501,x502)+E(f31(x503,x504,x505,x501,x506),f31(x503,x504,x505,x502,x506)) % 0.70/0.98 [51]~E(x511,x512)+E(f31(x513,x514,x515,x516,x511),f31(x513,x514,x515,x516,x512)) % 0.70/0.98 [52]~E(x521,x522)+E(f14(x521,x523),f14(x522,x523)) % 0.70/0.98 [53]~E(x531,x532)+E(f14(x533,x531),f14(x533,x532)) % 0.70/0.98 [54]~E(x541,x542)+E(f37(x541,x543),f37(x542,x543)) % 0.70/0.98 [55]~E(x551,x552)+E(f37(x553,x551),f37(x553,x552)) % 0.70/0.98 [56]~E(x561,x562)+E(f43(x561,x563,x564,x565),f43(x562,x563,x564,x565)) % 0.70/0.98 [57]~E(x571,x572)+E(f43(x573,x571,x574,x575),f43(x573,x572,x574,x575)) % 0.70/0.98 [58]~E(x581,x582)+E(f43(x583,x584,x581,x585),f43(x583,x584,x582,x585)) % 0.70/0.98 [59]~E(x591,x592)+E(f43(x593,x594,x595,x591),f43(x593,x594,x595,x592)) % 0.70/0.98 [60]~E(x601,x602)+E(f33(x601,x603),f33(x602,x603)) % 0.70/0.98 [61]~E(x611,x612)+E(f33(x613,x611),f33(x613,x612)) % 0.70/0.98 [62]~E(x621,x622)+E(f15(x621),f15(x622)) % 0.70/0.98 [63]~E(x631,x632)+E(f18(x631,x633),f18(x632,x633)) % 0.70/0.98 [64]~E(x641,x642)+E(f18(x643,x641),f18(x643,x642)) % 0.70/0.98 [65]~E(x651,x652)+E(f58(x651),f58(x652)) % 0.70/0.98 [66]~E(x661,x662)+E(f54(x661),f54(x662)) % 0.70/0.98 [67]~E(x671,x672)+E(f55(x671),f55(x672)) % 0.70/0.98 [68]~E(x681,x682)+E(f23(x681,x683,x684,x685),f23(x682,x683,x684,x685)) % 0.70/0.98 [69]~E(x691,x692)+E(f23(x693,x691,x694,x695),f23(x693,x692,x694,x695)) % 0.70/0.98 [70]~E(x701,x702)+E(f23(x703,x704,x701,x705),f23(x703,x704,x702,x705)) % 0.70/0.98 [71]~E(x711,x712)+E(f23(x713,x714,x715,x711),f23(x713,x714,x715,x712)) % 0.70/0.98 [72]~E(x721,x722)+E(f40(x721,x723,x724,x725),f40(x722,x723,x724,x725)) % 0.70/0.98 [73]~E(x731,x732)+E(f40(x733,x731,x734,x735),f40(x733,x732,x734,x735)) % 0.70/0.98 [74]~E(x741,x742)+E(f40(x743,x744,x741,x745),f40(x743,x744,x742,x745)) % 0.70/0.98 [75]~E(x751,x752)+E(f40(x753,x754,x755,x751),f40(x753,x754,x755,x752)) % 0.70/0.98 [76]~E(x761,x762)+E(f34(x761),f34(x762)) % 0.70/0.98 [77]~E(x771,x772)+E(f48(x771,x773),f48(x772,x773)) % 0.70/0.98 [78]~E(x781,x782)+E(f48(x783,x781),f48(x783,x782)) % 0.70/0.98 [79]~E(x791,x792)+E(f22(x791,x793,x794,x795),f22(x792,x793,x794,x795)) % 0.70/0.98 [80]~E(x801,x802)+E(f22(x803,x801,x804,x805),f22(x803,x802,x804,x805)) % 0.70/0.98 [81]~E(x811,x812)+E(f22(x813,x814,x811,x815),f22(x813,x814,x812,x815)) % 0.70/0.98 [82]~E(x821,x822)+E(f22(x823,x824,x825,x821),f22(x823,x824,x825,x822)) % 0.70/0.98 [83]~E(x831,x832)+E(f57(x831),f57(x832)) % 0.70/0.98 [84]~E(x841,x842)+E(f39(x841,x843,x844),f39(x842,x843,x844)) % 0.70/0.98 [85]~E(x851,x852)+E(f39(x853,x851,x854),f39(x853,x852,x854)) % 0.70/0.98 [86]~E(x861,x862)+E(f39(x863,x864,x861),f39(x863,x864,x862)) % 0.70/0.98 [87]~E(x871,x872)+E(f21(x871,x873,x874),f21(x872,x873,x874)) % 0.70/0.98 [88]~E(x881,x882)+E(f21(x883,x881,x884),f21(x883,x882,x884)) % 0.70/0.98 [89]~E(x891,x892)+E(f21(x893,x894,x891),f21(x893,x894,x892)) % 0.70/0.98 [90]~E(x901,x902)+E(f17(x901,x903,x904),f17(x902,x903,x904)) % 0.70/0.98 [91]~E(x911,x912)+E(f17(x913,x911,x914),f17(x913,x912,x914)) % 0.70/0.98 [92]~E(x921,x922)+E(f17(x923,x924,x921),f17(x923,x924,x922)) % 0.70/0.98 [93]~E(x931,x932)+E(f36(x931),f36(x932)) % 0.70/0.98 [94]~E(x941,x942)+E(f19(x941,x943,x944),f19(x942,x943,x944)) % 0.70/0.98 [95]~E(x951,x952)+E(f19(x953,x951,x954),f19(x953,x952,x954)) % 0.70/0.98 [96]~E(x961,x962)+E(f19(x963,x964,x961),f19(x963,x964,x962)) % 0.70/0.98 [97]~E(x971,x972)+E(f25(x971,x973,x974,x975),f25(x972,x973,x974,x975)) % 0.70/0.98 [98]~E(x981,x982)+E(f25(x983,x981,x984,x985),f25(x983,x982,x984,x985)) % 0.70/0.98 [99]~E(x991,x992)+E(f25(x993,x994,x991,x995),f25(x993,x994,x992,x995)) % 0.70/0.98 [100]~E(x1001,x1002)+E(f25(x1003,x1004,x1005,x1001),f25(x1003,x1004,x1005,x1002)) % 0.70/0.98 [101]~E(x1011,x1012)+E(f41(x1011,x1013,x1014),f41(x1012,x1013,x1014)) % 0.70/0.98 [102]~E(x1021,x1022)+E(f41(x1023,x1021,x1024),f41(x1023,x1022,x1024)) % 0.70/0.98 [103]~E(x1031,x1032)+E(f41(x1033,x1034,x1031),f41(x1033,x1034,x1032)) % 0.70/0.98 [104]~E(x1041,x1042)+E(f7(x1041),f7(x1042)) % 0.70/0.98 [105]~E(x1051,x1052)+E(f6(x1051),f6(x1052)) % 0.70/0.98 [106]~E(x1061,x1062)+E(f42(x1061,x1063,x1064,x1065),f42(x1062,x1063,x1064,x1065)) % 0.70/0.98 [107]~E(x1071,x1072)+E(f42(x1073,x1071,x1074,x1075),f42(x1073,x1072,x1074,x1075)) % 0.70/0.98 [108]~E(x1081,x1082)+E(f42(x1083,x1084,x1081,x1085),f42(x1083,x1084,x1082,x1085)) % 0.70/0.98 [109]~E(x1091,x1092)+E(f42(x1093,x1094,x1095,x1091),f42(x1093,x1094,x1095,x1092)) % 0.70/0.98 [110]~E(x1101,x1102)+E(f9(x1101),f9(x1102)) % 0.70/0.98 [111]~E(x1111,x1112)+E(f8(x1111,x1113),f8(x1112,x1113)) % 0.70/0.98 [112]~E(x1121,x1122)+E(f8(x1123,x1121),f8(x1123,x1122)) % 0.70/0.98 [113]~E(x1131,x1132)+E(f38(x1131,x1133),f38(x1132,x1133)) % 0.70/0.98 [114]~E(x1141,x1142)+E(f38(x1143,x1141),f38(x1143,x1142)) % 0.70/0.98 [115]~P1(x1151)+P1(x1152)+~E(x1151,x1152) % 0.70/0.98 [116]~P10(x1161)+P10(x1162)+~E(x1161,x1162) % 0.70/0.98 [117]~P11(x1171)+P11(x1172)+~E(x1171,x1172) % 0.70/0.98 [118]~P35(x1181)+P35(x1182)+~E(x1181,x1182) % 0.70/0.98 [119]~P12(x1191)+P12(x1192)+~E(x1191,x1192) % 0.70/0.98 [120]~P36(x1201)+P36(x1202)+~E(x1201,x1202) % 0.70/0.98 [121]~P13(x1211)+P13(x1212)+~E(x1211,x1212) % 0.70/0.98 [122]~P14(x1221)+P14(x1222)+~E(x1221,x1222) % 0.70/0.98 [123]~P37(x1231)+P37(x1232)+~E(x1231,x1232) % 0.70/0.98 [124]~P23(x1241)+P23(x1242)+~E(x1241,x1242) % 0.70/0.98 [125]~P28(x1251)+P28(x1252)+~E(x1251,x1252) % 0.70/0.98 [126]~P30(x1261)+P30(x1262)+~E(x1261,x1262) % 0.70/0.98 [127]~P33(x1271)+P33(x1272)+~E(x1271,x1272) % 0.70/0.98 [128]~P34(x1281)+P34(x1282)+~E(x1281,x1282) % 0.70/0.98 [129]~P15(x1291)+P15(x1292)+~E(x1291,x1292) % 0.70/0.98 [130]~P32(x1301)+P32(x1302)+~E(x1301,x1302) % 0.70/0.98 [131]~P16(x1311)+P16(x1312)+~E(x1311,x1312) % 0.70/0.98 [132]~P47(x1321)+P47(x1322)+~E(x1321,x1322) % 0.70/0.98 [133]~P2(x1331)+P2(x1332)+~E(x1331,x1332) % 0.70/0.98 [134]P3(x1342,x1343,x1344)+~E(x1341,x1342)+~P3(x1341,x1343,x1344) % 0.70/0.98 [135]P3(x1353,x1352,x1354)+~E(x1351,x1352)+~P3(x1353,x1351,x1354) % 0.70/0.98 [136]P3(x1363,x1364,x1362)+~E(x1361,x1362)+~P3(x1363,x1364,x1361) % 0.70/0.98 [137]~P56(x1371)+P56(x1372)+~E(x1371,x1372) % 0.70/0.98 [138]~P48(x1381)+P48(x1382)+~E(x1381,x1382) % 0.70/0.98 [139]~P31(x1391)+P31(x1392)+~E(x1391,x1392) % 0.70/0.98 [140]~P49(x1401)+P49(x1402)+~E(x1401,x1402) % 0.70/0.98 [141]~P19(x1411)+P19(x1412)+~E(x1411,x1412) % 0.70/0.98 [142]~P22(x1421)+P22(x1422)+~E(x1421,x1422) % 0.70/0.98 [143]~P39(x1431)+P39(x1432)+~E(x1431,x1432) % 0.70/0.98 [144]~P41(x1441)+P41(x1442)+~E(x1441,x1442) % 0.70/0.98 [145]~P42(x1451)+P42(x1452)+~E(x1451,x1452) % 0.70/0.98 [146]~P50(x1461)+P50(x1462)+~E(x1461,x1462) % 0.70/0.98 [147]~P57(x1471)+P57(x1472)+~E(x1471,x1472) % 0.70/0.98 [148]~P43(x1481)+P43(x1482)+~E(x1481,x1482) % 0.70/0.98 [149]~P44(x1491)+P44(x1492)+~E(x1491,x1492) % 0.70/0.98 [150]~P24(x1501)+P24(x1502)+~E(x1501,x1502) % 0.70/0.98 [151]~P25(x1511)+P25(x1512)+~E(x1511,x1512) % 0.70/0.98 [152]~P20(x1521)+P20(x1522)+~E(x1521,x1522) % 0.70/0.98 [153]~P38(x1531)+P38(x1532)+~E(x1531,x1532) % 0.70/0.98 [154]~P46(x1541)+P46(x1542)+~E(x1541,x1542) % 0.70/0.98 [155]P5(x1552,x1553,x1554)+~E(x1551,x1552)+~P5(x1551,x1553,x1554) % 0.70/0.98 [156]P5(x1563,x1562,x1564)+~E(x1561,x1562)+~P5(x1563,x1561,x1564) % 0.70/0.98 [157]P5(x1573,x1574,x1572)+~E(x1571,x1572)+~P5(x1573,x1574,x1571) % 0.70/0.98 [158]P7(x1582,x1583,x1584)+~E(x1581,x1582)+~P7(x1581,x1583,x1584) % 0.70/0.98 [159]P7(x1593,x1592,x1594)+~E(x1591,x1592)+~P7(x1593,x1591,x1594) % 0.70/0.98 [160]P7(x1603,x1604,x1602)+~E(x1601,x1602)+~P7(x1603,x1604,x1601) % 0.70/0.98 [161]~P45(x1611)+P45(x1612)+~E(x1611,x1612) % 0.70/0.98 [162]P8(x1622,x1623,x1624)+~E(x1621,x1622)+~P8(x1621,x1623,x1624) % 0.70/0.98 [163]P8(x1633,x1632,x1634)+~E(x1631,x1632)+~P8(x1633,x1631,x1634) % 0.70/0.98 [164]P8(x1643,x1644,x1642)+~E(x1641,x1642)+~P8(x1643,x1644,x1641) % 0.70/0.98 [165]~P51(x1651)+P51(x1652)+~E(x1651,x1652) % 0.70/0.98 [166]~P27(x1661)+P27(x1662)+~E(x1661,x1662) % 0.70/0.98 [167]~P29(x1671)+P29(x1672)+~E(x1671,x1672) % 0.70/0.98 [168]P6(x1682,x1683)+~E(x1681,x1682)+~P6(x1681,x1683) % 0.70/0.98 [169]P6(x1693,x1692)+~E(x1691,x1692)+~P6(x1693,x1691) % 0.70/0.98 [170]~P26(x1701)+P26(x1702)+~E(x1701,x1702) % 0.70/0.98 [171]P4(x1712,x1713,x1714,x1715,x1716,x1717)+~E(x1711,x1712)+~P4(x1711,x1713,x1714,x1715,x1716,x1717) % 0.70/0.98 [172]P4(x1723,x1722,x1724,x1725,x1726,x1727)+~E(x1721,x1722)+~P4(x1723,x1721,x1724,x1725,x1726,x1727) % 0.70/0.98 [173]P4(x1733,x1734,x1732,x1735,x1736,x1737)+~E(x1731,x1732)+~P4(x1733,x1734,x1731,x1735,x1736,x1737) % 0.70/0.98 [174]P4(x1743,x1744,x1745,x1742,x1746,x1747)+~E(x1741,x1742)+~P4(x1743,x1744,x1745,x1741,x1746,x1747) % 0.70/0.98 [175]P4(x1753,x1754,x1755,x1756,x1752,x1757)+~E(x1751,x1752)+~P4(x1753,x1754,x1755,x1756,x1751,x1757) % 0.70/0.98 [176]P4(x1763,x1764,x1765,x1766,x1767,x1762)+~E(x1761,x1762)+~P4(x1763,x1764,x1765,x1766,x1767,x1761) % 0.70/0.98 [177]~P58(x1771)+P58(x1772)+~E(x1771,x1772) % 0.70/0.98 [178]~P40(x1781)+P40(x1782)+~E(x1781,x1782) % 0.70/0.98 [179]~P55(x1791)+P55(x1792)+~E(x1791,x1792) % 0.70/0.98 [180]~P52(x1801)+P52(x1802)+~E(x1801,x1802) % 0.70/0.98 [181]~P9(x1811)+P9(x1812)+~E(x1811,x1812) % 0.70/0.98 [182]~P17(x1821)+P17(x1822)+~E(x1821,x1822) % 0.70/0.98 [183]~P21(x1831)+P21(x1832)+~E(x1831,x1832) % 0.70/0.98 [184]~P18(x1841)+P18(x1842)+~E(x1841,x1842) % 0.70/0.98 [185]~P53(x1851)+P53(x1852)+~E(x1851,x1852) % 0.70/0.98 [186]~P54(x1861)+P54(x1862)+~E(x1861,x1862) % 0.70/0.98 % 0.70/0.98 %------------------------------------------- % 0.70/0.98 cnf(1172,plain, % 0.70/0.98 ($false), % 0.70/0.98 inference(scs_inference,[],[229,371,1004]), % 0.70/0.98 ['proof']). % 0.70/0.98 % SZS output end Proof % 0.70/0.98 % Total time :0.099854s %------------------------------------------------------------------------------