%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL759-1 : 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 : n012.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:19:46 AM UTC 2026 % Result : Unsatisfiable 0.38s 0.53s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.01 % Problem : LCL759-1 : TPTP v9.3.1. Released v4.1.0. % 0.00/0.01 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.02/0.29 % Computer : n012.cluster.edu % 0.02/0.29 % Model : x86_64 x86_64 % 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.02/0.29 % Memory : 8046.5625MB % 0.02/0.29 % OS : Linux 6.8.0-71-generic % 0.02/0.29 % CPULimit : 300 % 0.02/0.29 % WCLimit : 300 % 0.02/0.29 % DateTime : Fri Sep 4 21:56:57 UTC 2026 % 0.02/0.29 % CPUTime : % 0.07/0.38 start to proof:theBenchmark % 0.22/0.50 %------------------------------------------- % 0.22/0.50 % File :CSE---1.7 % 0.22/0.50 % Problem :theBenchmark % 0.22/0.50 % Transform :cnf % 0.22/0.50 % Format :tptp:raw % 0.22/0.50 % Command :java -jar mcs_scs.jar %d %s % 0.22/0.50 % 0.22/0.50 % Result :Theorem 0.034312s % 0.22/0.50 % Output :CNFRefutation 0.034312s % 0.22/0.50 %------------------------------------------- % 0.22/0.50 %------------------------------------------------------------------------------ % 0.22/0.50 % File : LCL759-1 : TPTP v9.3.1. Released v4.1.0. % 0.22/0.50 % Domain : Logic Calculi % 0.22/0.50 % Problem : Strong normalization of typed lambda calculus 060_3 % 0.22/0.50 % Version : Especial. % 0.22/0.50 % English : % 0.22/0.50 % 0.22/0.50 % Refs : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java % 0.22/0.50 % : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe % 0.22/0.50 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 0.22/0.50 % Source : [Nip10] % 0.22/0.50 % Names : StrongNorm-060_3 [Nip10] % 0.22/0.50 % 0.22/0.50 % Status : Unsatisfiable % 0.22/0.50 % Rating : 0.25 v9.3.0, 0.09 v9.1.0, 0.10 v9.0.0, 0.15 v8.2.0, 0.14 v8.1.0, 0.16 v7.5.0, 0.21 v7.4.0, 0.18 v7.3.0, 0.08 v7.0.0, 0.27 v6.3.0, 0.18 v6.2.0, 0.30 v6.1.0, 0.29 v6.0.0, 0.40 v5.5.0, 0.50 v5.4.0, 0.55 v5.3.0, 0.56 v5.2.0, 0.50 v5.1.0, 0.59 v5.0.0, 0.57 v4.1.0 % 0.22/0.50 % Syntax : Number of clauses : 637 ( 156 unt; 86 nHn; 322 RR) % 0.22/0.50 % Number of literals : 1445 ( 492 equ; 750 neg) % 0.22/0.50 % Maximal clause size : 6 ( 2 avg) % 0.22/0.50 % Maximal term depth : 10 ( 2 avg) % 0.22/0.50 % Number of predicates : 48 ( 47 usr; 0 prp; 1-3 aty) % 0.22/0.50 % Number of functors : 44 ( 44 usr; 12 con; 0-6 aty) % 0.22/0.50 % Number of variables : 1651 ( 214 sgn) % 0.22/0.50 % SPC : CNF_UNS_RFO_SEQ_NHN % 0.22/0.50 % 0.22/0.50 % Comments : % 0.22/0.50 %------------------------------------------------------------------------------ % 0.22/0.50 cnf(cls_dvd__imp__mod__0_0,axiom, % 0.22/0.50 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.50 | c_Divides_Odiv__class_Omod(V_b,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 0.22/0.50 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_add__neg__neg_0,axiom, % 0.22/0.50 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.22/0.50 | 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) % 0.22/0.50 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.22/0.50 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_nat__0__less__mult__iff_0,axiom, % 0.22/0.50 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 0.22/0.50 | ~ 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) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_nat__0__less__mult__iff_1,axiom, % 0.22/0.50 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.22/0.50 | ~ 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) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_lift__subst__lt_0,axiom, % 0.22/0.50 ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_j)),V_i) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat))) % 0.22/0.50 | ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_combine__common__factor_0,axiom, % 0.22/0.50 ( ~ class_Ring__and__Field_Osemiring(T_a) % 0.22/0.50 | 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) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_left__add__mult__distrib_0,axiom, % 0.22/0.50 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) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_one__less__power_0,axiom, % 0.22/0.50 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.22/0.50 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 0.22/0.50 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.22/0.50 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_of__nat__Suc_0,axiom, % 0.22/0.50 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.22/0.50 | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(V_m),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_mult__less__cancel1_0,axiom, % 0.22/0.50 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.22/0.50 | ~ 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) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_mult__less__cancel2_0,axiom, % 0.22/0.50 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.22/0.50 | ~ 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) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_nat__mult__eq__cancel1_0,axiom, % 0.22/0.50 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) % 0.22/0.50 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.22/0.50 | V_m = V_n ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_of__nat__1_0,axiom, % 0.22/0.50 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.22/0.50 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_nat__mult__eq__1__iff_0,axiom, % 0.22/0.50 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) % 0.22/0.50 | V_m = c_HOL_Oone__class_Oone(tc_nat) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_nat__mult__eq__1__iff_1,axiom, % 0.22/0.50 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) % 0.22/0.50 | V_n = c_HOL_Oone__class_Oone(tc_nat) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_mod__add__right__eq_0,axiom, % 0.22/0.50 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.50 | 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) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_mod__add__left__eq_0,axiom, % 0.22/0.50 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.50 | 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) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_dvd_Oless__trans_1,axiom, % 0.22/0.50 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat) % 0.22/0.50 | c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat) % 0.22/0.50 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat) % 0.22/0.50 | c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat) % 0.22/0.50 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_mod__less__divisor_0,axiom, % 0.22/0.50 ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_n,tc_nat) % 0.22/0.50 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_power__one_0,axiom, % 0.22/0.50 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.22/0.50 | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_lift_Osimps_I1_J_1,axiom, % 0.22/0.50 ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(V_i)),V_k) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat))) % 0.22/0.50 | c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_add__cancel__21_0,axiom, % 0.22/0.50 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.22/0.50 | 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) % 0.22/0.50 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z) = V_u ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_power__add_0,axiom, % 0.22/0.50 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.22/0.50 | 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) ) ). % 0.22/0.50 % 0.22/0.50 cnf(cls_add__gr__0_0,axiom, % 0.22/0.50 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.22/0.50 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 0.22/0.51 | ~ 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.51 | 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)) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.51 | 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)) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.51 | 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.51 | 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom, % 0.22/0.51 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a) % 0.22/0.51 | 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)) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom, % 0.22/0.51 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.22/0.51 | 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)) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_comm__monoid__add_Omult__assoc_0,axiom, % 0.22/0.51 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.22/0.51 | 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)) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_nat__add__assoc_0,axiom, % 0.22/0.51 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)) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_nat__add__left__commute_0,axiom, % 0.22/0.51 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)) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_add__cancel__21_1,axiom, % 0.22/0.51 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.22/0.51 | 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)) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_class__semiring_Oadd__a_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.51 | 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_xt1_I10_J_0,axiom, % 0.22/0.51 ( ~ class_Orderings_Oorder(T_a) % 0.22/0.51 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_order__less__trans_0,axiom, % 0.22/0.51 ( ~ class_Orderings_Opreorder(T_a) % 0.22/0.51 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_power__Suc__less__one_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.22/0.51 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),c_HOL_Oone__class_Oone(T_a),T_a) % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_mod__add__eq_0,axiom, % 0.22/0.51 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.51 | 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.51 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_nat__mult__commute_0,axiom, % 0.22/0.51 c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) = c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_class__semiring_Omul__c_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.51 | c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_class__semiring_Osemiring__rules_I35_J_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.51 | 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_class__semiring_Opwr__Suc_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.51 | 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_power__Suc_0,axiom, % 0.22/0.51 ( ~ class_Power_Opower(T_a) % 0.22/0.51 | 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_power__Suc2_0,axiom, % 0.22/0.51 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.22/0.51 | 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_class__semiring_Opwr__pwr_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.51 | 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_dvd__mult__cancel1_1,axiom, % 0.22/0.51 ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 0.22/0.51 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_m,tc_nat) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_dvd__mult__cancel2_1,axiom, % 0.22/0.51 ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 0.22/0.51 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),V_m,tc_nat),V_m,tc_nat) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_class__ringb_Oadd__mul__solve_1,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.22/0.51 | ~ class_Int_Onumber__ring(T_a) % 0.22/0.51 | 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)) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_class__ringb_Onoteq__reduce_1,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.22/0.51 | ~ class_Int_Onumber__ring(T_a) % 0.22/0.51 | 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)) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_natgb_Onoteq__reduce_1,axiom, % 0.22/0.51 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)) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_natgb_Oadd__mul__solve_1,axiom, % 0.22/0.51 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)) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_Suc__eq__plus1_0,axiom, % 0.22/0.51 c_Suc(V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Oone__class_Oone(tc_nat)) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_Suc__eq__plus1__left_0,axiom, % 0.22/0.51 c_Suc(V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),V_n) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_mod__mod__trivial_0,axiom, % 0.22/0.51 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.51 | 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_of__nat__power_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.22/0.51 | c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),V_n,T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_div__self_0,axiom, % 0.22/0.51 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.51 | c_Divides_Odiv__class_Odiv(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a) % 0.22/0.51 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_dvd__triv__right_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.51 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_dvd__triv__left_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.51 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_dvdI_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Odvd(T_a) % 0.22/0.51 | c_Ring__and__Field_Odvd__class_Odvd(V_b,c_HOL_Otimes__class_Otimes(V_b,V_k,T_a),T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_class__semiring_Osemiring__rules_I11_J_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.51 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.51 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_mult__1__right_0,axiom, % 0.22/0.51 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.22/0.51 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_mult__1__left_0,axiom, % 0.22/0.51 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.22/0.51 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_mult__1_0,axiom, % 0.22/0.51 ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) % 0.22/0.51 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_nat__mult__1_0,axiom, % 0.22/0.51 c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) = V_n ). % 0.22/0.51 % 0.22/0.51 cnf(cls_nat__mult__1__right_0,axiom, % 0.22/0.51 c_HOL_Otimes__class_Otimes(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = V_n ). % 0.22/0.51 % 0.22/0.51 cnf(cls_class__semiring_Omul__1_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.51 | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_x,T_a) = V_x ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_listsp_ONil_0,axiom, % 0.22/0.51 c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_div__mult__self__is__m_0,axiom, % 0.22/0.51 ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_n,tc_nat) = V_m % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_div__mult__self1__is__m_0,axiom, % 0.22/0.51 ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),V_n,tc_nat) = V_m % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_dvd__mult__cancel__right_2,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.22/0.51 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_dvd__mult__cancel__left_2,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.22/0.51 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_nat__mult__dvd__cancel__disj_2,axiom, % 0.22/0.51 ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_zmod__simps_I4_J_0,axiom, % 0.22/0.51 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.51 | 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_div__add_0,axiom, % 0.22/0.51 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.51 | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y),V_z,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(V_x,V_z,T_a)),c_Divides_Odiv__class_Odiv(V_y,V_z,T_a)) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_div__mod__equality2_0,axiom, % 0.22/0.51 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.51 | 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_div__mod__equality_0,axiom, % 0.22/0.51 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.51 | 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_less__add__Suc1_0,axiom, % 0.22/0.51 c_HOL_Oord__class_Oless(V_i,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_m)),tc_nat) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_less__add__Suc2_0,axiom, % 0.22/0.51 c_HOL_Oord__class_Oless(V_i,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_i)),tc_nat) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_less__iff__Suc__add_1,axiom, % 0.22/0.51 c_HOL_Oord__class_Oless(V_m,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_x)),tc_nat) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_power__strict__decreasing_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.22/0.51 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_N,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_termination__basic__simps_I1_J_0,axiom, % 0.22/0.51 ( c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat) % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_termination__basic__simps_I2_J_0,axiom, % 0.22/0.51 ( c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat) % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(V_x,V_z,tc_nat) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_add__lessD1_0,axiom, % 0.22/0.51 ( c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_k,tc_nat) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_trans__less__add1_0,axiom, % 0.22/0.51 ( c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_m),tc_nat) % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_trans__less__add2_0,axiom, % 0.22/0.51 ( c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_j),tc_nat) % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_dvd__mod__imp__dvd_0,axiom, % 0.22/0.51 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.51 | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_dvd__mod__iff_1,axiom, % 0.22/0.51 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.51 | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_dvd__mod__iff_0,axiom, % 0.22/0.51 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.51 | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_dvd__mod_0,axiom, % 0.22/0.51 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.51 | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_Suc__times__mod__eq_0,axiom, % 0.22/0.51 ( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)),V_k,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),V_k,tc_nat) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_nat__1__eq__mult__iff_2,axiom, % 0.22/0.51 c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_substn_Osimps_I3_J_0,axiom, % 0.22/0.51 c_Lambda_Osubstn(c_Lambda_OdB_OAbs(V_t),V_s,V_k) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(V_t,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.51 | 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_dvd__eq__mod__eq__0_1,axiom, % 0.22/0.51 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.51 | c_Divides_Odiv__class_Omod(V_b,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.22/0.51 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_dvd__div__mult_0,axiom, % 0.22/0.51 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.51 | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_c,T_a) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),V_a,T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_not__square__less__zero_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.51 | ~ 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_Suc__mult__less__cancel1_1,axiom, % 0.22/0.51 ( 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) % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_Suc__mult__less__cancel1_0,axiom, % 0.22/0.51 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.22/0.51 | ~ 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_nat__dvd__1__iff__1_1,axiom, % 0.22/0.51 c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_natgb_Oadd__cancel_0,axiom, % 0.22/0.51 ( 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) % 0.22/0.51 | V_y = V_z ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_nat__add__right__cancel_0,axiom, % 0.22/0.51 ( 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) % 0.22/0.51 | V_m = V_n ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_nat__add__left__cancel_0,axiom, % 0.22/0.51 ( 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) % 0.22/0.51 | V_m = V_n ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_class__ringb_Oadd__cancel_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.22/0.51 | ~ class_Int_Onumber__ring(T_a) % 0.22/0.51 | 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) % 0.22/0.51 | V_y = V_z ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_add__imp__eq_0,axiom, % 0.22/0.51 ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a) % 0.22/0.51 | 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) % 0.22/0.51 | V_b = V_c ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_add__left__cancel_0,axiom, % 0.22/0.51 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 0.22/0.51 | 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) % 0.22/0.51 | V_b = V_c ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_add__right__cancel_0,axiom, % 0.22/0.51 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 0.22/0.51 | 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) % 0.22/0.51 | V_b = V_c ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_dvd__power__same_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.51 | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_subst__subst_0,axiom, % 0.22/0.51 ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_v),V_i)),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_v),V_j)),V_i) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i)),V_v),V_j) % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_mod__mult__left__eq_0,axiom, % 0.22/0.51 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.51 | 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_mod__mult__right__eq_0,axiom, % 0.22/0.51 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.51 | 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_div__dvd__div_0,axiom, % 0.22/0.51 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.51 | c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_div__dvd__div_1,axiom, % 0.22/0.51 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.51 | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_div__less_0,axiom, % 0.22/0.51 ( c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) % 0.22/0.51 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_sum__squares__gt__zero__iff_1,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.51 | 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) % 0.22/0.51 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_sum__squares__gt__zero__iff_2,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.51 | 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) % 0.22/0.51 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.51 | 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)) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_of__nat__less__0__iff_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.22/0.51 | ~ 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_dvd__add_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.51 | c_Ring__and__Field_Odvd__class_Odvd(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 0.22/0.51 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_mult__less__cancel__left__disj_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.51 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.22/0.51 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.22/0.51 | ~ 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_mult__less__cancel__left__disj_3,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.51 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.22/0.51 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.22/0.51 | ~ 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) ) ). % 0.22/0.51 % 0.22/0.51 cnf(cls_mult__less__cancel__right__disj_0,axiom, % 0.22/0.51 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.51 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.22/0.51 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.22/0.52 | ~ 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__less__cancel__right__disj_3,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.22/0.52 | ~ 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_nat__mult__eq__1__iff_2,axiom, % 0.22/0.52 c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd__div__mult__self_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_a,T_a) = V_b % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd__mult__div__cancel_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),T_a) = V_b % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_lift_Osimps_I1_J_0,axiom, % 0.22/0.52 ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(V_i)),V_k) = c_Lambda_OdB_OVar(V_i) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_lift__preserves__beta_0,axiom, % 0.22/0.52 ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,V_r),V_i),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)) % 0.22/0.52 | ~ c_Lambda_Obeta(V_r,V_s) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_power__Suc__less_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_lift__subst_0,axiom, % 0.22/0.52 ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_j)),V_i) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)),V_j) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_j,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_lift__lift_0,axiom, % 0.22/0.52 ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)),c_Suc(V_k)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_i) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mod__mult__distrib2_0,axiom, % 0.22/0.52 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) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mod__mult__distrib_0,axiom, % 0.22/0.52 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) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__less__cancel2_2,axiom, % 0.22/0.52 ( 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__less__cancel1_2,axiom, % 0.22/0.52 ( 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__less__mono2_0,axiom, % 0.22/0.52 ( 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__less__mono1_0,axiom, % 0.22/0.52 ( 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_nat__mult__less__cancel1_0,axiom, % 0.22/0.52 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.22/0.52 | ~ 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_nat__mult__less__cancel1_1,axiom, % 0.22/0.52 ( 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__less__cancel__left__neg_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.22/0.52 | ~ 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__less__cancel__left__neg_1,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__less__cancel__left__pos_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.22/0.52 | ~ 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__less__cancel__left__pos_1,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__strict__left__mono__neg_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__strict__left__mono_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__less__cancel__left__disj_4,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__less__cancel__left__disj_5,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__strict__right__mono__neg_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__strict__right__mono_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__less__cancel__right__disj_4,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__less__cancel__right__disj_5,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__strict__left__mono__comm_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_div__add1__eq_0,axiom, % 0.22/0.52 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)) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_nat__power__less__imp__less_0,axiom, % 0.22/0.52 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_i,V_m,tc_nat),c_Power_Opower__class_Opower(V_i,V_n,tc_nat),tc_nat) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_i,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_div__mult__mult1_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_div__mult__mult2_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_nat__mult__div__cancel__disj_1,axiom, % 0.22/0.52 ( 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) % 0.22/0.52 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_subst__lemma_0,axiom, % 0.22/0.52 ( ~ c_Type_Otyping(V_e_H,V_u,V_U) % 0.22/0.52 | ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T) % 0.22/0.52 | c_Type_Otyping(V_e_H,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),V_T) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_zero__less__two_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a)),T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mod__mult__self3_0,axiom, % 0.22/0.52 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) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mod__mult__self1_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mod__mult__self2_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.52 | 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_split__div__lemma_2,axiom, % 0.22/0.52 ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.22/0.52 | 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_nat__mult__dvd__cancel__disj_0,axiom, % 0.22/0.52 ( c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) % 0.22/0.52 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd__mult__cancel__left_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.22/0.52 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) % 0.22/0.52 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd__mult__cancel__right_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.22/0.52 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) % 0.22/0.52 | V_c = c_HOL_Ozero__class_Ozero(T_a) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_div__add__self1_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a),V_b,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)),c_HOL_Oone__class_Oone(T_a)) % 0.22/0.52 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_div__add__self2_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_b,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)),c_HOL_Oone__class_Oone(T_a)) % 0.22/0.52 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_sum__squares__gt__zero__iff_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.52 | ~ 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_nat__zero__less__power__iff_2,axiom, % 0.22/0.52 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_less__1__mult_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Otimes__class_Otimes(V_m,V_n,T_a),T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_n,T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_m,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_div__by__1_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | c_Divides_Odiv__class_Odiv(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_split__mod_1,axiom, % 0.22/0.52 ( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) % 0.22/0.52 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) % 0.22/0.52 | ~ 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))) % 0.22/0.52 | hBOOL(hAPP(V_P,V_j)) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_add__gr__0_2,axiom, % 0.22/0.52 ( 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_add__gr__0_1,axiom, % 0.22/0.52 ( 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom, % 0.22/0.52 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.22/0.52 | ~ 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom, % 0.22/0.52 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd_Oless__le__trans_1,axiom, % 0.22/0.52 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat) % 0.22/0.52 | c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd_Ole__less__trans_1,axiom, % 0.22/0.52 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat) % 0.22/0.52 | c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_power__eq__0__iff_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 0.22/0.52 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 0.22/0.52 | ~ class_Ring__and__Field_Omult__zero(T_a) % 0.22/0.52 | ~ class_Power_Opower(T_a) % 0.22/0.52 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.22/0.52 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_field__power__not__zero_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(T_a) % 0.22/0.52 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.22/0.52 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_class__semiring_Omul__0_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.52 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__zero__left_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 0.22/0.52 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__zero__right_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Omult__zero(T_a) % 0.22/0.52 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__eq__0__iff_1,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 0.22/0.52 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__eq__0__iff_2,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 0.22/0.52 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.52 | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.52 | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd__0__right_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.52 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_one__neq__zero_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 0.22/0.52 | c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_no__zero__divirors__neq0_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 0.22/0.52 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.22/0.52 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 0.22/0.52 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_no__zero__divisors_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 0.22/0.52 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.22/0.52 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 0.22/0.52 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__eq__0__iff_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) % 0.22/0.52 | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.22/0.52 | V_b = c_HOL_Ozero__class_Ozero(T_a) % 0.22/0.52 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_comm__monoid__add_Omult__commute_0,axiom, % 0.22/0.52 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.22/0.52 | 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_nat__add__commute_0,axiom, % 0.22/0.52 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) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_less__add__eq__less_0,axiom, % 0.22/0.52 ( 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat) % 0.22/0.52 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_class__semiring_Oadd__c_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.52 | 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd__power_1,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.52 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a),T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_of__nat__eq__iff_0,axiom, % 0.22/0.52 ( ~ class_Nat_Osemiring__char__0(T_a) % 0.22/0.52 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) % 0.22/0.52 | V_m = V_n ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mod__div__trivial_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_div__if_0,axiom, % 0.22/0.52 ( c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mod__mult__eq_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_power__commutes_0,axiom, % 0.22/0.52 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.22/0.52 | 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_class__semiring_Omul__pwr_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.52 | 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_div__mult__self2_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | 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)) % 0.22/0.52 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_div__mult__self1_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | 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)) % 0.22/0.52 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_class__semiring_Osemiring__rules_I4_J_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.52 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_m),V_m) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a)),V_m,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_class__semiring_Osemiring__rules_I33_J_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.52 | c_Power_Opower__class_Opower(V_x,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_x ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_power__one__right_0,axiom, % 0.22/0.52 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.22/0.52 | c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mod__add__cong_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 0.22/0.52 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 0.22/0.52 | 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom, % 0.22/0.52 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom, % 0.22/0.52 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.22/0.52 | ~ 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_even__less__0__iff_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.22/0.52 | ~ 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_even__less__0__iff_1,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_zero__less__mult__pos2_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.22/0.52 | ~ 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_zero__less__mult__pos_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.22/0.52 | ~ 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__pos__pos_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__neg__neg_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_nat__0__less__mult__iff_2,axiom, % 0.22/0.52 ( 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_zero__less__power_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_nat__zero__less__power__iff_1,axiom, % 0.22/0.52 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(V_x,V_n,tc_nat),tc_nat) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_x,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__Suc__right_0,axiom, % 0.22/0.52 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)) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__Suc_0,axiom, % 0.22/0.52 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)) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_split__div_1,axiom, % 0.22/0.52 ( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) % 0.22/0.52 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) % 0.22/0.52 | ~ 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))) % 0.22/0.52 | hBOOL(hAPP(V_P,V_i)) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_div__power_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),V_n,T_a) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_shift__eq_0,axiom, % 0.22/0.52 hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ). % 0.22/0.52 % 0.22/0.52 cnf(cls_substn_Osimps_I1_J_2,axiom, % 0.22/0.52 ( c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_i),V_s,V_k) = c_Lambda_OdB_OVar(V_i) % 0.22/0.52 | V_i = V_k % 0.22/0.52 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_not__one__less__zero_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_not__sum__squares__lt__zero_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.22/0.52 | ~ 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_of__nat__mult_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.22/0.52 | 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mod__mult__self4_0,axiom, % 0.22/0.52 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) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_class__ringb_Oadd__mul__solve_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.22/0.52 | ~ class_Int_Onumber__ring(T_a) % 0.22/0.52 | 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)) % 0.22/0.52 | V_y = V_z % 0.22/0.52 | V_w = V_x ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_class__ringb_Onoteq__reduce_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.22/0.52 | ~ class_Int_Onumber__ring(T_a) % 0.22/0.52 | 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)) % 0.22/0.52 | V_c = V_d % 0.22/0.52 | V_a = V_b ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_natgb_Onoteq__reduce_0,axiom, % 0.22/0.52 ( 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)) % 0.22/0.52 | V_c = V_d % 0.22/0.52 | V_a = V_b ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_natgb_Oadd__mul__solve_0,axiom, % 0.22/0.52 ( 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)) % 0.22/0.52 | V_y = V_z % 0.22/0.52 | V_w = V_x ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_div__mult__self2__is__id_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = V_a % 0.22/0.52 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_div__mult__self1__is__id_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = V_a % 0.22/0.52 | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__eq__self__implies__10_0,axiom, % 0.22/0.52 ( V_m != c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) % 0.22/0.52 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 0.22/0.52 | V_n = c_HOL_Oone__class_Oone(tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mod__mult__cong_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a) % 0.22/0.52 | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a) % 0.22/0.52 | 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.52 | 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.52 | 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.52 | 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_class__semiring_Osemiring__rules_I2_J_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.52 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_m,T_a)),V_m) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a)),V_m,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.52 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_m),c_HOL_Otimes__class_Otimes(V_a,V_m,T_a)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a)),V_m,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mod__by__1_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | c_Divides_Odiv__class_Omod(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd__reduce_0,axiom, % 0.22/0.52 ( c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k),tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd__reduce_1,axiom, % 0.22/0.52 ( c_Ring__and__Field_Odvd__class_Odvd(V_k,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k),tc_nat) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mod__if_0,axiom, % 0.22/0.52 ( c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = V_m % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_nat__less__le_1,axiom, % 0.22/0.52 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_less__not__refl_0,axiom, % 0.22/0.52 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_order__less__le_1,axiom, % 0.22/0.52 ( ~ class_Orderings_Oorder(T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_linorder__neq__iff_1,axiom, % 0.22/0.52 ( ~ class_Orderings_Olinorder(T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_order__less__irrefl_0,axiom, % 0.22/0.52 ( ~ class_Orderings_Opreorder(T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_add__pos__pos_0,axiom, % 0.22/0.52 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_power__gt1__lemma_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_linorder__neqE__ordered__idom_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.22/0.52 | V_x = V_y ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_not__less__iff__gr__or__eq_0,axiom, % 0.22/0.52 ( ~ class_Orderings_Olinorder(T_a) % 0.22/0.52 | V_x = V_y % 0.22/0.52 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd_Oeq__iff_2,axiom, % 0.22/0.52 ( V_x = V_y % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd_Oantisym_0,axiom, % 0.22/0.52 ( V_x = V_y % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd_Oless__le_0,axiom, % 0.22/0.52 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat) % 0.22/0.52 | V_x = V_y % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd__antisym_0,axiom, % 0.22/0.52 ( V_m = V_n % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_n,V_m,tc_nat) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_nat__neq__iff_0,axiom, % 0.22/0.52 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 0.22/0.52 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.22/0.52 | V_m = V_n ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_nat__less__cases_0,axiom, % 0.22/0.52 ( hBOOL(hAPP(hAPP(V_P,V_n),V_m)) % 0.22/0.52 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 0.22/0.52 | V_m = V_n % 0.22/0.52 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd_Oantisym__conv_0,axiom, % 0.22/0.52 ( V_x = V_y % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd_Ole__neq__trans_0,axiom, % 0.22/0.52 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_a,tc_nat) % 0.22/0.52 | V_a = V_b % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd_Oneq__le__trans_0,axiom, % 0.22/0.52 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_a,tc_nat) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,tc_nat) % 0.22/0.52 | V_a = V_b ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_linorder__neqE__nat_0,axiom, % 0.22/0.52 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat) % 0.22/0.52 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 0.22/0.52 | V_x = V_y ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_linorder__neqE_0,axiom, % 0.22/0.52 ( ~ class_Orderings_Olinorder(T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.22/0.52 | V_x = V_y ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_linorder__less__linear_0,axiom, % 0.22/0.52 ( ~ class_Orderings_Olinorder(T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.22/0.52 | V_x = V_y % 0.22/0.52 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_linorder__antisym__conv3_0,axiom, % 0.22/0.52 ( ~ class_Orderings_Olinorder(T_a) % 0.22/0.52 | V_x = V_y % 0.22/0.52 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_nat__dvd__not__less_0,axiom, % 0.22/0.52 ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_n,V_m,tc_nat) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_add__strict__mono_0,axiom, % 0.22/0.52 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_add__less__mono_0,axiom, % 0.22/0.52 ( 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd__trans_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.52 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd__refl_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.52 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_a,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd_Oeq__iff_0,axiom, % 0.22/0.52 c_Ring__and__Field_Odvd__class_Odvd(V_x,V_x,tc_nat) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd_Oless__trans_0,axiom, % 0.22/0.52 ( c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat) % 0.22/0.52 | c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat) % 0.22/0.52 | c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd_Oorder__trans_0,axiom, % 0.22/0.52 ( c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_power__gt1_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),T_a) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_of__nat__less__iff_1,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.22/0.52 | 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) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_of__nat__less__iff_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.22/0.52 | ~ 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd__mult__cancel__right_1,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.22/0.52 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd__mult__cancel__left_1,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.22/0.52 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_nat__mult__dvd__cancel__disj_1,axiom, % 0.22/0.52 c_Ring__and__Field_Odvd__class_Odvd(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) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_zero__less__one_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_div__mult1__eq_0,axiom, % 0.22/0.52 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)) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__less__cancel1_1,axiom, % 0.22/0.52 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.22/0.52 | ~ 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mult__less__cancel2_1,axiom, % 0.22/0.52 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.22/0.52 | ~ 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) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_nat__mult__dvd__cancel1_1,axiom, % 0.22/0.52 ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_nat__mult__dvd__cancel1_0,axiom, % 0.22/0.52 ( c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_dvd__mult__cancel_0,axiom, % 0.22/0.52 ( c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) % 0.22/0.52 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_less__add__one_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.22/0.52 | c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a)),T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_div__less__dividend_0,axiom, % 0.22/0.52 ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat),V_m,tc_nat) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 0.22/0.52 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_div__by__0_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | c_Divides_Odiv__class_Odiv(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_div__0_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_double__eq__0__iff_0,axiom, % 0.22/0.52 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.22/0.52 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.22/0.52 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_class__ringb_Oadd__r0__iff_0,axiom, % 0.22/0.52 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.22/0.52 | ~ class_Int_Onumber__ring(T_a) % 0.22/0.52 | V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_a) % 0.22/0.52 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mod__self_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | c_Divides_Odiv__class_Omod(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.52 % 0.22/0.52 cnf(cls_mod__by__0_0,axiom, % 0.22/0.52 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.52 | c_Divides_Odiv__class_Omod(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_mod__0_0,axiom, % 0.22/0.53 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.53 | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_double__eq__0__iff_1,axiom, % 0.22/0.53 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.22/0.53 | 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) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_zero__neq__one_0,axiom, % 0.22/0.53 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 0.22/0.53 | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_dvd__0__left_0,axiom, % 0.22/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.53 | V_a = c_HOL_Ozero__class_Ozero(T_a) % 0.22/0.53 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_class__semiring_Oadd__0_0,axiom, % 0.22/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.53 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_x) = V_x ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_comm__monoid__add_Omult__1_0,axiom, % 0.22/0.53 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.22/0.53 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_class__ringb_Oadd__r0__iff_1,axiom, % 0.22/0.53 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.22/0.53 | ~ class_Int_Onumber__ring(T_a) % 0.22/0.53 | V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Ozero__class_Ozero(T_a)) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_comm__monoid__add_Omult__1__right_0,axiom, % 0.22/0.53 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.22/0.53 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_add__0__left_0,axiom, % 0.22/0.53 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.22/0.53 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_monoid__add__class_Oadd__0__right_0,axiom, % 0.22/0.53 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.22/0.53 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom, % 0.22/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.53 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom, % 0.22/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.53 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_power__0__left_0,axiom, % 0.22/0.53 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 0.22/0.53 | ~ class_Power_Opower(T_a) % 0.22/0.53 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_split__mod_5,axiom, % 0.22/0.53 ( ~ hBOOL(hAPP(V_P,V_n)) % 0.22/0.53 | hBOOL(hAPP(V_P,c_Divides_Odiv__class_Omod(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_split__mod_0,axiom, % 0.22/0.53 ( ~ hBOOL(hAPP(V_P,c_Divides_Odiv__class_Omod(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) % 0.22/0.53 | hBOOL(hAPP(V_P,V_n)) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_mult__cancel2_1,axiom, % 0.22/0.53 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) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_mult__cancel1_1,axiom, % 0.22/0.53 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) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_lexn_Oinduct_0,axiom, % 0.22/0.53 ( hBOOL(hAPP(V_P,V_nat)) % 0.22/0.53 | hBOOL(hAPP(V_P,v_sko__List__Xlexn__Xinduct__1(V_P))) % 0.22/0.53 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_zero__induct_1,axiom, % 0.22/0.53 ( hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) % 0.22/0.53 | ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(V_P))) % 0.22/0.53 | ~ hBOOL(hAPP(V_P,V_k)) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_neq0__conv_1,axiom, % 0.22/0.53 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_split__div_H_6,axiom, % 0.22/0.53 ( hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) % 0.22/0.53 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_split__div_5,axiom, % 0.22/0.53 ( ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) % 0.22/0.53 | hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_split__div_0,axiom, % 0.22/0.53 ( ~ hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) % 0.22/0.53 | hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_gr0I_0,axiom, % 0.22/0.53 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.22/0.53 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_nat__induct_0,axiom, % 0.22/0.53 ( hBOOL(hAPP(V_P,V_n)) % 0.22/0.53 | hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(V_P))) % 0.22/0.53 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_mult__is__0_2,axiom, % 0.22/0.53 c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_mult__is__0_1,axiom, % 0.22/0.53 c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_mult__is__0_0,axiom, % 0.22/0.53 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.22/0.53 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 0.22/0.53 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_add__is__0_1,axiom, % 0.22/0.53 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.22/0.53 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_add__is__0_0,axiom, % 0.22/0.53 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.22/0.53 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_mult__cancel2_0,axiom, % 0.22/0.53 ( c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat) != c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat) % 0.22/0.53 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) % 0.22/0.53 | V_m = V_n ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_mult__cancel1_0,axiom, % 0.22/0.53 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) % 0.22/0.53 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) % 0.22/0.53 | V_m = V_n ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_nat__mult__eq__cancel__disj_0,axiom, % 0.22/0.53 ( c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) % 0.22/0.53 | V_m = V_n % 0.22/0.53 | V_k = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_natgb_Oadd__r0__iff_0,axiom, % 0.22/0.53 ( V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_a) % 0.22/0.53 | V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_add__eq__self__zero_0,axiom, % 0.22/0.53 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != V_m % 0.22/0.53 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_replicate_Oinduct_0,axiom, % 0.22/0.53 ( hBOOL(hAPP(V_P,V_nat)) % 0.22/0.53 | hBOOL(hAPP(V_P,v_sko__List__Xreplicate__Xinduct__1(V_P))) % 0.22/0.53 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_nat_Oinducts_0,axiom, % 0.22/0.53 ( hBOOL(hAPP(V_P,V_nat)) % 0.22/0.53 | hBOOL(hAPP(V_P,v_sko__Nat__Xnat__Xinducts__1(V_P))) % 0.22/0.53 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_add__is__0_2,axiom, % 0.22/0.53 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) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_nat_Oinduct_0,axiom, % 0.22/0.53 ( hBOOL(hAPP(V_P,V_nat)) % 0.22/0.53 | hBOOL(hAPP(V_P,v_sko__Nat__Xnat__Xinduct__1(V_P))) % 0.22/0.53 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_gr__implies__not0_0,axiom, % 0.22/0.53 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_not__less0_0,axiom, % 0.22/0.53 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_upt_Oinduct_0,axiom, % 0.22/0.53 ( hBOOL(hAPP(V_P,V_nat)) % 0.22/0.53 | hBOOL(hAPP(V_P,v_sko__List__Xupt__Xinduct__1(V_P))) % 0.22/0.53 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_natgb_Oadd__r0__iff_1,axiom, % 0.22/0.53 V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_plus__nat_Oadd__0_0,axiom, % 0.22/0.53 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n) = V_n ). % 0.22/0.53 % 0.22/0.53 cnf(cls_Nat_Oadd__0__right_0,axiom, % 0.22/0.53 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat)) = V_m ). % 0.22/0.53 % 0.22/0.53 cnf(cls_n__less__n__mult__m_0,axiom, % 0.22/0.53 ( c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),tc_nat) % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_n__less__m__mult__n_0,axiom, % 0.22/0.53 ( c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_one__less__mult_0,axiom, % 0.22/0.53 ( 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) % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_Suc__mult__cancel1_0,axiom, % 0.22/0.53 ( 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) % 0.22/0.53 | V_m = V_n ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_less__SucI_0,axiom, % 0.22/0.53 ( c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_Suc__lessD_0,axiom, % 0.22/0.53 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_mod__Suc__eq__Suc__mod_0,axiom, % 0.22/0.53 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) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_less__trans__Suc_0,axiom, % 0.22/0.53 ( c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat) % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_less__Suc__eq_2,axiom, % 0.22/0.53 c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_lessI_0,axiom, % 0.22/0.53 c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_not__less__less__Suc__eq_0,axiom, % 0.22/0.53 ( V_n = V_m % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 0.22/0.53 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_less__antisym_0,axiom, % 0.22/0.53 ( V_m = V_n % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 0.22/0.53 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_less__SucE_0,axiom, % 0.22/0.53 ( V_m = V_n % 0.22/0.53 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_add__Suc_0,axiom, % 0.22/0.53 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)) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_add__Suc__right_0,axiom, % 0.22/0.53 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)) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_mod__Suc_1,axiom, % 0.22/0.53 ( 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)) % 0.22/0.53 | c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) = V_n ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_add__Suc__shift_0,axiom, % 0.22/0.53 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)) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_Suc__lessI_0,axiom, % 0.22/0.53 ( c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) % 0.22/0.53 | c_Suc(V_m) = V_n % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_not__less__less__Suc__eq_1,axiom, % 0.22/0.53 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 0.22/0.53 | c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_not__less__eq_1,axiom, % 0.22/0.53 ( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_not__less__eq_0,axiom, % 0.22/0.53 ( c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 0.22/0.53 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_less__Suc__eq__0__disj_3,axiom, % 0.22/0.53 ( c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat) % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(V_x,V_n,tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_Suc__less__eq_0,axiom, % 0.22/0.53 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_Suc__mono_0,axiom, % 0.22/0.53 ( c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_lift_Osimps_I2_J_0,axiom, % 0.22/0.53 hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_s),V_k)),hAPP(hAPP(c_Lambda_Olift,V_t),V_k)) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_appR_0,axiom, % 0.22/0.53 ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_s),hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_t)) % 0.22/0.53 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_appL_0,axiom, % 0.22/0.53 ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_u),hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)) % 0.22/0.53 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_substn_Osimps_I2_J_0,axiom, % 0.22/0.53 c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(V_t,V_s,V_k)),c_Lambda_Osubstn(V_u,V_s,V_k)) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_subst__Abs_0,axiom, % 0.22/0.53 hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(V_t)),V_s),V_k) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_s),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_abs_0,axiom, % 0.22/0.53 ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t)) % 0.22/0.53 | ~ c_Lambda_Obeta(V_s,V_t) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_map__is__Nil__conv_0,axiom, % 0.22/0.53 ( c_List_Omap(V_f,V_xs,T_b,T_a) != c_List_Olist_ONil(T_a) % 0.22/0.53 | V_xs = c_List_Olist_ONil(T_b) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_Nil__is__map__conv_0,axiom, % 0.22/0.53 ( c_List_Olist_ONil(T_a) != c_List_Omap(V_f,V_xs,T_b,T_a) % 0.22/0.53 | V_xs = c_List_Olist_ONil(T_b) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_map__is__Nil__conv_1,axiom, % 0.22/0.53 c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_Nil__is__map__conv_1,axiom, % 0.22/0.53 c_List_Olist_ONil(T_a) = c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_foldl__Nil_0,axiom, % 0.22/0.53 c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a ). % 0.22/0.53 % 0.22/0.53 cnf(cls_foldl__assoc_0,axiom, % 0.22/0.53 ( ~ class_OrderedGroup_Osemigroup__add(T_a) % 0.22/0.53 | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y),V_zs,T_a,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_y,V_zs,T_a,T_a)) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_subst__preserves__beta_0,axiom, % 0.22/0.53 ( c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_t),V_i),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),V_i)) % 0.22/0.53 | ~ c_Lambda_Obeta(V_r,V_s) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_subst__lift_0,axiom, % 0.22/0.53 hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k) = V_t ). % 0.22/0.53 % 0.22/0.53 cnf(cls_lift__types_0,axiom, % 0.22/0.53 ( c_Type_Otypings(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts) % 0.22/0.53 | ~ c_Type_Otypings(V_e,V_ts,V_Ts) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_beta__cases_I1_J_0,axiom, % 0.22/0.53 ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_typing__elims_I1_J_0,axiom, % 0.22/0.53 ( hAPP(V_e,V_i) = V_T % 0.22/0.53 | ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_typing_OVar_0,axiom, % 0.22/0.53 c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_lift__IT_0,axiom, % 0.22/0.53 ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,V_t),V_i))) % 0.22/0.53 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_dB_Osize_I2_J_0,axiom, % 0.22/0.53 c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB1)),c_Lambda_OdB_OdB__size(V_dB2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_dB_Osize_I5_J_0,axiom, % 0.22/0.53 c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(V_dB2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_dB_Osize_I3_J_0,axiom, % 0.22/0.53 c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(V_dB)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_dB_Osize_I6_J_0,axiom, % 0.22/0.53 c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(V_dB),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_power__eq__0__iff_2,axiom, % 0.22/0.53 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 0.22/0.53 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 0.22/0.53 | ~ class_Ring__and__Field_Omult__zero(T_a) % 0.22/0.53 | ~ class_Power_Opower(T_a) % 0.22/0.53 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 0.22/0.53 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_power__0__left_1,axiom, % 0.22/0.53 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 0.22/0.53 | ~ class_Power_Opower(T_a) % 0.22/0.53 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 0.22/0.53 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_mult__left__idem_0,axiom, % 0.22/0.53 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 0.22/0.53 | 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) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_div__mult__div__if__dvd_0,axiom, % 0.22/0.53 ( ~ class_Divides_Osemiring__div(T_a) % 0.22/0.53 | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),c_Divides_Odiv__class_Odiv(V_w,V_z,T_a),T_a) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_x,V_w,T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) % 0.22/0.53 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_w,T_a) % 0.22/0.53 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_nat__mod__eq__iff_1,axiom, % 0.22/0.53 ( 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)) % 0.22/0.53 | c_Divides_Odiv__class_Omod(V_x,V_n,tc_nat) = c_Divides_Odiv__class_Omod(V_y,V_n,tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_of__nat__0__less__iff_1,axiom, % 0.22/0.53 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.22/0.53 | 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) % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_of__nat__0__less__iff_0,axiom, % 0.22/0.53 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.22/0.53 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.22/0.53 | ~ 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) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_one__dvd_0,axiom, % 0.22/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.22/0.53 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_power__inject__exp_0,axiom, % 0.22/0.53 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.22/0.53 | c_Power_Opower__class_Opower(V_a,V_m,T_a) != c_Power_Opower__class_Opower(V_a,V_n,T_a) % 0.22/0.53 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 0.22/0.53 | V_m = V_n ) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_power__eq__if_0,axiom, % 0.22/0.53 c_Power_Opower__class_Opower(V_p,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ). % 0.22/0.53 % 0.22/0.53 cnf(cls_power__0_0,axiom, % 0.22/0.53 ( ~ class_Power_Opower(T_a) % 0.38/0.53 | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_class__semiring_Opwr__0_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.38/0.53 | c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat__mult__div__cancel1_0,axiom, % 0.38/0.53 ( 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) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_div__mult__mult1__if_0,axiom, % 0.38/0.53 ( ~ class_Divides_Osemiring__div(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat__mult__div__cancel__disj_0,axiom, % 0.38/0.53 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) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_class__semiring_Osemiring__rules_I27_J_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_class__semiring_Osemiring__rules_I28_J_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mod__add__self2_0,axiom, % 0.38/0.53 ( ~ class_Divides_Osemiring__div(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mod__add__self1_0,axiom, % 0.38/0.53 ( ~ class_Divides_Osemiring__div(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_shift__gt_0,axiom, % 0.38/0.53 ( hAPP(c_Type_Oshift(V_e,V_i,V_T,T_a),V_j) = hAPP(V_e,V_j) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mult__pos__neg2_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.38/0.53 | 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) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mult__pos__neg_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.38/0.53 | 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) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mult__neg__pos_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) % 0.38/0.53 | 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) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dvd__mult__right_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.38/0.53 | c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) % 0.38/0.53 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dvd__mult__left_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.38/0.53 | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) % 0.38/0.53 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dvd__mult2_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.38/0.53 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 0.38/0.53 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dvd__mult_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.38/0.53 | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) % 0.38/0.53 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_pos__add__strict_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.38/0.53 | c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mod__mult2__eq_0,axiom, % 0.38/0.53 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)) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mod__mod__cancel_0,axiom, % 0.38/0.53 ( ~ class_Divides_Osemiring__div(T_a) % 0.38/0.53 | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(V_a,V_c,T_a) % 0.38/0.53 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_b,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_power__strict__increasing__iff_1,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.38/0.53 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_power__strict__increasing__iff_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.38/0.53 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_power__strict__increasing_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.38/0.53 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_a,V_N,T_a),T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_power__less__imp__less__exp_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.38/0.53 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_not__add__less1_0,axiom, % 0.38/0.53 ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_not__add__less2_0,axiom, % 0.38/0.53 ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_power__less__power__Suc_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.38/0.53 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_div__mult2__eq_0,axiom, % 0.38/0.53 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) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mult__dvd__mono_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.38/0.53 | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) % 0.38/0.53 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_d,T_a) % 0.38/0.53 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mod__lemma_0,axiom, % 0.38/0.53 ( 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) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_r,V_b,tc_nat) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_c,tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.38/0.53 | ~ class_Int_Onumber__ring(T_a) % 0.38/0.53 | 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)) % 0.38/0.53 | V_c = V_d % 0.38/0.53 | V_r = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_natgb_Oadd__scale__eq__noteq_0,axiom, % 0.38/0.53 ( 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)) % 0.38/0.53 | V_c = V_d % 0.38/0.53 | V_r = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_sum__squares__eq__zero__iff_1,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.38/0.53 | 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) % 0.38/0.53 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_sum__squares__eq__zero__iff_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.38/0.53 | 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) % 0.38/0.53 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dvd__power_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.38/0.53 | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_add__strict__right__mono_0,axiom, % 0.38/0.53 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.38/0.53 | 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) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_add__less__cancel__right_1,axiom, % 0.38/0.53 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.38/0.53 | 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) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_add__less__cancel__right_0,axiom, % 0.38/0.53 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.38/0.53 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.38/0.53 | ~ 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_add__strict__left__mono_0,axiom, % 0.38/0.53 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.38/0.53 | 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) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_add__less__cancel__left_1,axiom, % 0.38/0.53 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.38/0.53 | 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) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_add__less__cancel__left_0,axiom, % 0.38/0.53 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.38/0.53 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.38/0.53 | ~ 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_add__less__mono1_0,axiom, % 0.38/0.53 ( 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) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat__add__left__cancel__less_0,axiom, % 0.38/0.53 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.38/0.53 | ~ 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat__add__left__cancel__less_1,axiom, % 0.38/0.53 ( 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) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_subject__reduction_0,axiom, % 0.38/0.53 ( c_Type_Otyping(V_e,V_t_H,V_T) % 0.38/0.53 | ~ c_Lambda_Obeta(V_t,V_t_H) % 0.38/0.53 | ~ c_Type_Otyping(V_e,V_t,V_T) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dvd__mult__cancel1_0,axiom, % 0.38/0.53 ( V_n = c_HOL_Oone__class_Oone(tc_nat) % 0.38/0.53 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_m,tc_nat) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dvd__mult__cancel2_0,axiom, % 0.38/0.53 ( V_n = c_HOL_Oone__class_Oone(tc_nat) % 0.38/0.53 | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),V_m,tc_nat) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mult__idem_0,axiom, % 0.38/0.53 ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) % 0.38/0.53 | c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = V_x ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mod__mult__self2__is__0_0,axiom, % 0.38/0.53 ( ~ class_Divides_Osemiring__div(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mod__mult__self1__is__0_0,axiom, % 0.38/0.53 ( ~ class_Divides_Osemiring__div(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mod__eq__0__iff_1,axiom, % 0.38/0.53 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) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat__dvd__1__iff__1_0,axiom, % 0.38/0.53 ( V_m = c_HOL_Oone__class_Oone(tc_nat) % 0.38/0.53 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_semiring__div__class_Omod__div__equality_H_0,axiom, % 0.38/0.53 ( ~ class_Divides_Osemiring__div(T_a) % 0.38/0.53 | 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 ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_sum__squares__eq__zero__iff_2,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mult__less__cancel__right__disj_2,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.38/0.53 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.38/0.53 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.38/0.53 | ~ 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mult__less__cancel__right__disj_1,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.38/0.53 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.38/0.53 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.38/0.53 | ~ 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mult__less__cancel__left__disj_2,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.38/0.53 | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.38/0.53 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.38/0.53 | ~ 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mult__less__cancel__left__disj_1,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a) % 0.38/0.53 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.38/0.53 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) % 0.38/0.53 | ~ 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat__zero__less__power__iff_0,axiom, % 0.38/0.53 ( V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 0.38/0.53 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_x,tc_nat) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(V_x,V_n,tc_nat),tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_of__nat__add_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.38/0.53 | 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)) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_power__mult__distrib_0,axiom, % 0.38/0.53 ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_class__semiring_Opwr__mul_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_zmod__simps_I1_J_0,axiom, % 0.38/0.53 ( ~ class_Divides_Osemiring__div(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_zmod__simps_I2_J_0,axiom, % 0.38/0.53 ( ~ class_Divides_Osemiring__div(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_power__mult_0,axiom, % 0.38/0.53 ( ~ class_OrderedGroup_Omonoid__mult(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mod__div__equality2_0,axiom, % 0.38/0.53 ( ~ class_Divides_Osemiring__div(T_a) % 0.38/0.53 | 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 ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mod__div__equality_0,axiom, % 0.38/0.53 ( ~ class_Divides_Osemiring__div(T_a) % 0.38/0.53 | 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 ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mod__div__decomp_0,axiom, % 0.38/0.53 ( ~ class_Divides_Osemiring__div(T_a) % 0.38/0.53 | 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)) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mod__mult__mult2_0,axiom, % 0.38/0.53 ( ~ class_Divides_Osemiring__div(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mod__mult__mult1_0,axiom, % 0.38/0.53 ( ~ class_Divides_Osemiring__div(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_lift_Osimps_I3_J_0,axiom, % 0.38/0.53 hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(V_s)),V_k) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,V_s),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat__1__eq__mult__iff_0,axiom, % 0.38/0.53 ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) % 0.38/0.53 | V_m = c_HOL_Oone__class_Oone(tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat__1__eq__mult__iff_1,axiom, % 0.38/0.53 ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) % 0.38/0.53 | V_n = c_HOL_Oone__class_Oone(tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom, % 0.38/0.53 ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat__mult__assoc_0,axiom, % 0.38/0.53 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) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_class__semiring_Omul__a_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.38/0.53 | 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)) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_comm__semiring__class_Odistrib_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring(T_a) % 0.38/0.53 | 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)) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_add__mult__distrib_0,axiom, % 0.38/0.53 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)) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_add__mult__distrib2_0,axiom, % 0.38/0.53 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)) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_class__semiring_Omul__d_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.38/0.53 | 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)) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_lift__type_0,axiom, % 0.38/0.53 ( c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,V_t),V_i),V_T) % 0.38/0.53 | ~ c_Type_Otyping(V_e,V_t,V_T) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_xt1_I9_J_0,axiom, % 0.38/0.53 ( ~ class_Orderings_Oorder(T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_not__less__iff__gr__or__eq_1,axiom, % 0.38/0.53 ( ~ class_Orderings_Olinorder(T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dvd_Ole__less__trans_0,axiom, % 0.38/0.53 ( c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat) % 0.38/0.53 | c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat) % 0.38/0.53 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat) % 0.38/0.53 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dvd_Oless__le__trans_0,axiom, % 0.38/0.53 ( c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat) % 0.38/0.53 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat) % 0.38/0.53 | c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat) % 0.38/0.53 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_order__less__asym_0,axiom, % 0.38/0.53 ( ~ class_Orderings_Opreorder(T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_order__less__asym_H_0,axiom, % 0.38/0.53 ( ~ class_Orderings_Opreorder(T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_power__eq__0__iff_1,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 0.38/0.53 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 0.38/0.53 | ~ class_Ring__and__Field_Omult__zero(T_a) % 0.38/0.53 | ~ class_Power_Opower(T_a) % 0.38/0.53 | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_of__nat__0_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.38/0.53 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_power__0__Suc_0,axiom, % 0.38/0.53 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 0.38/0.53 | ~ class_Power_Opower(T_a) % 0.38/0.53 | 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) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat_Oexhaust_0,axiom, % 0.38/0.53 ( V_y = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(V_y)) % 0.38/0.53 | V_y = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_add__is__1_2,axiom, % 0.38/0.53 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.38/0.53 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 0.38/0.53 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_add__is__1_1,axiom, % 0.38/0.53 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.38/0.53 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.38/0.53 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_add__is__1_5,axiom, % 0.38/0.53 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)) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_zero__induct_0,axiom, % 0.38/0.53 ( hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) % 0.38/0.53 | hBOOL(hAPP(V_P,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(V_P)))) % 0.38/0.53 | ~ hBOOL(hAPP(V_P,V_k)) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat__power__eq__Suc__0__iff_0,axiom, % 0.38/0.53 ( c_Power_Opower__class_Opower(V_x,V_m,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.38/0.53 | V_x = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.38/0.53 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_one__is__add_4,axiom, % 0.38/0.53 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)) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_lexn_Oinduct_1,axiom, % 0.38/0.53 ( hBOOL(hAPP(V_P,V_nat)) % 0.38/0.53 | ~ hBOOL(hAPP(V_P,c_Suc(v_sko__List__Xlexn__Xinduct__1(V_P)))) % 0.38/0.53 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mod__1_0,axiom, % 0.38/0.53 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) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mult__eq__1__iff_2,axiom, % 0.38/0.53 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)) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dvd__1__iff__1_1,axiom, % 0.38/0.53 c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_one__is__add_2,axiom, % 0.38/0.53 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) % 0.38/0.53 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 0.38/0.53 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_one__is__add_1,axiom, % 0.38/0.53 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) % 0.38/0.53 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.38/0.53 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_less__Suc0_1,axiom, % 0.38/0.53 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_One__nat__def_0,axiom, % 0.38/0.53 c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_shift__commute_0,axiom, % 0.38/0.53 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) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat__induct_1,axiom, % 0.38/0.53 ( hBOOL(hAPP(V_P,V_n)) % 0.38/0.53 | ~ hBOOL(hAPP(V_P,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(V_P)))) % 0.38/0.53 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mult__eq__1__iff_1,axiom, % 0.38/0.53 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.38/0.53 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mult__eq__1__iff_0,axiom, % 0.38/0.53 ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.38/0.53 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_replicate_Oinduct_1,axiom, % 0.38/0.53 ( hBOOL(hAPP(V_P,V_nat)) % 0.38/0.53 | ~ hBOOL(hAPP(V_P,c_Suc(v_sko__List__Xreplicate__Xinduct__1(V_P)))) % 0.38/0.53 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_upt_Oinduct_1,axiom, % 0.38/0.53 ( hBOOL(hAPP(V_P,V_nat)) % 0.38/0.53 | ~ hBOOL(hAPP(V_P,c_Suc(v_sko__List__Xupt__Xinduct__1(V_P)))) % 0.38/0.53 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat_Onchotomy_0,axiom, % 0.38/0.53 ( V_v = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(V_v)) % 0.38/0.53 | V_v = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat__power__eq__Suc__0__iff_1,axiom, % 0.38/0.53 c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat_Oinduct_1,axiom, % 0.38/0.53 ( hBOOL(hAPP(V_P,V_nat)) % 0.38/0.53 | ~ hBOOL(hAPP(V_P,c_Suc(v_sko__Nat__Xnat__Xinduct__1(V_P)))) % 0.38/0.53 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_add__is__1_4,axiom, % 0.38/0.53 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)) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_less__Suc0_0,axiom, % 0.38/0.53 ( V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat_Oinducts_1,axiom, % 0.38/0.53 ( hBOOL(hAPP(V_P,V_nat)) % 0.38/0.53 | ~ hBOOL(hAPP(V_P,c_Suc(v_sko__Nat__Xnat__Xinducts__1(V_P)))) % 0.38/0.53 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_not0__implies__Suc_0,axiom, % 0.38/0.53 ( V_n = c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(V_n)) % 0.38/0.53 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dvd__1__left_0,axiom, % 0.38/0.53 c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_k,tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_one__is__add_5,axiom, % 0.38/0.53 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))) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_one__is__add_3,axiom, % 0.38/0.53 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) % 0.38/0.53 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.38/0.53 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_one__is__add_0,axiom, % 0.38/0.53 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) % 0.38/0.53 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 0.38/0.53 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_zero__less__Suc_0,axiom, % 0.38/0.53 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_gr0__conv__Suc_1,axiom, % 0.38/0.53 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_mod__Suc_0,axiom, % 0.38/0.53 ( c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) != V_n % 0.38/0.53 | c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_add__is__1_3,axiom, % 0.38/0.53 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.38/0.53 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.38/0.53 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_add__is__1_0,axiom, % 0.38/0.53 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.38/0.53 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 0.38/0.53 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat__power__eq__Suc__0__iff_2,axiom, % 0.38/0.53 c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_power__Suc__0_0,axiom, % 0.38/0.53 c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dvd__1__iff__1_0,axiom, % 0.38/0.53 ( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.38/0.53 | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_div__1_0,axiom, % 0.38/0.53 c_Divides_Odiv__class_Odiv(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = V_m ). % 0.38/0.53 % 0.38/0.53 cnf(cls_foldl__absorb0_0,axiom, % 0.38/0.53 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.38/0.53 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_zs,T_a,T_a)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_x,V_zs,T_a,T_a) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_substn__subst__0_0,axiom, % 0.38/0.53 c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),c_HOL_Ozero__class_Ozero(tc_nat)) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dB_Osize_I4_J_0,axiom, % 0.38/0.53 c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(V_nat),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dB_Osize_I1_J_0,axiom, % 0.38/0.53 c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(V_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_App__eq__foldl__conv_4,axiom, % 0.38/0.53 hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_App__eq__foldl__conv_0,axiom, % 0.38/0.53 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) % 0.38/0.53 | hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = V_t ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_apps__preserves__beta_0,axiom, % 0.38/0.53 ( c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)) % 0.38/0.53 | ~ c_Lambda_Obeta(V_r,V_s) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_substs__lemma_0,axiom, % 0.38/0.53 ( c_Type_Otypings(V_e,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts) % 0.38/0.53 | ~ c_Type_Otypings(c_Type_Oshift(V_e,V_i,V_T,tc_Type_Otype),V_ts,V_Ts) % 0.38/0.53 | ~ c_Type_Otyping(V_e,V_u,V_T) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_subst__lt_0,axiom, % 0.38/0.53 ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_j)),V_u),V_i) = c_Lambda_OdB_OVar(V_j) % 0.38/0.53 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_subst__Var_2,axiom, % 0.38/0.53 ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i)),V_s),V_k) = c_Lambda_OdB_OVar(V_i) % 0.38/0.53 | V_i = V_k % 0.38/0.53 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_subst__Var_1,axiom, % 0.38/0.53 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 0.38/0.53 | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_x)),V_s),V_x) = V_s ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_lifts__IT_0,axiom, % 0.38/0.53 ( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) % 0.38/0.53 | ~ c_List_Olistsp(c_InductTermi_OIT,V_ts,tc_Lambda_OdB) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_Abs__eq__apps__conv_1,axiom, % 0.38/0.53 ( c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.38/0.53 | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_Abs__eq__apps__conv_2,axiom, % 0.38/0.53 c_Lambda_OdB_OAbs(V_r) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_apps__eq__Abs__conv_1,axiom, % 0.38/0.53 ( c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r) % 0.38/0.53 | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_apps__eq__Abs__conv_2,axiom, % 0.38/0.53 c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(V_r) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_var__app__type__eq_0,axiom, % 0.38/0.53 ( V_T = V_U % 0.38/0.53 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_U) % 0.38/0.53 | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_Var__eq__apps__conv_2,axiom, % 0.38/0.53 c_Lambda_OdB_OVar(V_m) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_Var__eq__apps__conv_1,axiom, % 0.38/0.53 ( c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.38/0.53 | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_beta_0,axiom, % 0.38/0.53 c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),c_HOL_Ozero__class_Ozero(tc_nat))) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_IT_OVar_0,axiom, % 0.38/0.53 ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) % 0.38/0.53 | ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_lift__map_0,axiom, % 0.38/0.53 hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_t),V_i),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_subst__App_0,axiom, % 0.38/0.53 hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_s),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_k)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_s),V_k)) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dB_Osimps_I7_J_0,axiom, % 0.38/0.53 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dB_Osimps_I8_J_0,axiom, % 0.38/0.53 hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dB_Osimps_I1_J_0,axiom, % 0.38/0.53 ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H) % 0.38/0.53 | V_nat = V_nat_H ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dB_Osimps_I9_J_0,axiom, % 0.38/0.53 c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_Var__apps__eq__Var__apps__conv_0,axiom, % 0.38/0.53 ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.38/0.53 | V_m = V_n ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_Var__apps__eq__Var__apps__conv_1,axiom, % 0.38/0.53 ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.38/0.53 | V_rs = V_ss ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_subst__eq_0,axiom, % 0.38/0.53 hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u ). % 0.38/0.53 % 0.38/0.53 cnf(cls_n__not__Suc__n_0,axiom, % 0.38/0.53 V_n != c_Suc(V_n) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_Suc__n__not__n_0,axiom, % 0.38/0.53 c_Suc(V_n) != V_n ). % 0.38/0.53 % 0.38/0.53 cnf(cls_Suc__neq__Zero_0,axiom, % 0.38/0.53 c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat_Osimps_I3_J_0,axiom, % 0.38/0.53 c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_apps__eq__Abs__conv_0,axiom, % 0.38/0.53 ( c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r) % 0.38/0.53 | V_s = c_Lambda_OdB_OAbs(V_r) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_Abs__apps__eq__Abs__apps__conv_0,axiom, % 0.38/0.53 ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.38/0.53 | V_r = V_s ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_Abs__apps__eq__Abs__apps__conv_1,axiom, % 0.38/0.53 ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.38/0.53 | V_rs = V_ss ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dB_Osimps_I2_J_0,axiom, % 0.38/0.53 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) % 0.38/0.53 | V_dB1 = V_dB1_H ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dB_Osimps_I2_J_1,axiom, % 0.38/0.53 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) % 0.38/0.53 | V_dB2 = V_dB2_H ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_Var__eq__apps__conv_0,axiom, % 0.38/0.53 ( c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.38/0.53 | c_Lambda_OdB_OVar(V_m) = V_s ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dB_Osimps_I4_J_0,axiom, % 0.38/0.53 c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dB_Osimps_I3_J_0,axiom, % 0.38/0.53 ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H) % 0.38/0.53 | V_dB = V_dB_H ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_Var__apps__neq__Abs__apps_0,axiom, % 0.38/0.53 c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_Beta_0,axiom, % 0.38/0.53 ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r)),V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) % 0.38/0.53 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_s)) % 0.38/0.53 | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_s),c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dB_Osimps_I6_J_0,axiom, % 0.38/0.53 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat_Oinject_0,axiom, % 0.38/0.53 ( c_Suc(V_nat) != c_Suc(V_nat_H) % 0.38/0.53 | V_nat = V_nat_H ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_Suc__inject_0,axiom, % 0.38/0.53 ( c_Suc(V_x) != c_Suc(V_y) % 0.38/0.53 | V_x = V_y ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_subst__map_0,axiom, % 0.38/0.53 hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_Zero__neq__Suc_0,axiom, % 0.38/0.53 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_nat_Osimps_I2_J_0,axiom, % 0.38/0.53 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_COMBC__def_0,axiom, % 0.38/0.53 hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_Abs__eq__apps__conv_0,axiom, % 0.38/0.53 ( c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.38/0.53 | c_Lambda_OdB_OAbs(V_r) = V_s ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_apps__eq__tail__conv_0,axiom, % 0.38/0.53 ( c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ts,tc_Lambda_OdB,tc_Lambda_OdB) % 0.38/0.53 | V_r = V_s ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_Lambda_0,axiom, % 0.38/0.53 ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r))) % 0.38/0.53 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_r)) ) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_Abs__App__neq__Var__apps_0,axiom, % 0.38/0.53 hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_dB_Osimps_I5_J_0,axiom, % 0.38/0.53 hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_conjecture_0,negated_conjecture, % 0.38/0.53 hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_conjecture_1,negated_conjecture, % 0.38/0.53 hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(V_i))),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(V_i)),V_j)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_j,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_conjecture_2,negated_conjecture, % 0.38/0.53 hBOOL(hAPP(c_InductTermi_OIT,v_s)) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_conjecture_3,negated_conjecture, % 0.38/0.53 hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(V_i)),V_j))) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_conjecture_4,negated_conjecture, % 0.38/0.53 ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_fun__Orderings_Opreorder,axiom, % 0.38/0.53 ( class_Orderings_Opreorder(tc_fun(T_2,T_1)) % 0.38/0.53 | ~ class_Orderings_Opreorder(T_1) ) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_fun__Orderings_Oorder,axiom, % 0.38/0.53 ( class_Orderings_Oorder(tc_fun(T_2,T_1)) % 0.38/0.53 | ~ class_Orderings_Oorder(T_1) ) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom, % 0.38/0.53 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom, % 0.38/0.53 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom, % 0.38/0.53 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom, % 0.38/0.53 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom, % 0.38/0.53 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 0.38/0.53 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom, % 0.38/0.53 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom, % 0.38/0.53 class_Ring__and__Field_Ono__zero__divisors(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom, % 0.38/0.53 class_Ring__and__Field_Oordered__semidom(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom, % 0.38/0.53 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom, % 0.38/0.53 class_OrderedGroup_Oab__semigroup__mult(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom, % 0.38/0.53 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom, % 0.38/0.53 class_OrderedGroup_Oab__semigroup__add(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom, % 0.38/0.53 class_Ring__and__Field_Ocomm__semiring(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom, % 0.38/0.53 class_OrderedGroup_Ocomm__monoid__add(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom, % 0.38/0.53 class_Ring__and__Field_Ozero__neq__one(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__OrderedGroup_Osemigroup__add,axiom, % 0.38/0.53 class_OrderedGroup_Osemigroup__add(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom, % 0.38/0.53 class_Ring__and__Field_Osemiring__1(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom, % 0.38/0.53 class_Ring__and__Field_Osemiring__0(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom, % 0.38/0.53 class_Ring__and__Field_Omult__zero(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom, % 0.38/0.53 class_OrderedGroup_Omonoid__mult(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom, % 0.38/0.53 class_Ring__and__Field_Osemiring(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom, % 0.38/0.53 class_OrderedGroup_Omonoid__add(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__Divides_Osemiring__div,axiom, % 0.38/0.53 class_Divides_Osemiring__div(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom, % 0.38/0.53 class_Nat_Osemiring__char__0(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__Ring__and__Field_Odvd,axiom, % 0.38/0.53 class_Ring__and__Field_Odvd(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__Orderings_Opreorder,axiom, % 0.38/0.53 class_Orderings_Opreorder(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__Orderings_Olinorder,axiom, % 0.38/0.53 class_Orderings_Olinorder(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__Orderings_Oorder,axiom, % 0.38/0.53 class_Orderings_Oorder(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(clsarity_nat__Power_Opower,axiom, % 0.38/0.53 class_Power_Opower(tc_nat) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_ATP__Linkup_OCOMBC__def_0,axiom, % 0.38/0.53 hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_ATP__Linkup_OCOMBB__def_0,axiom, % 0.38/0.53 c_COMBB(V_P,V_Q,V_R,T_b,T_a,T_c) = hAPP(V_P,hAPP(V_Q,V_R)) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom, % 0.38/0.53 c_fequal(V_x,V_x,T_a) ). % 0.38/0.53 % 0.38/0.53 cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom, % 0.38/0.53 ( V_X = V_Y % 0.38/0.53 | ~ c_fequal(V_X,V_Y,T_a) ) ). % 0.38/0.53 % 0.38/0.53 %------------------------------------------------------------------------------ % 0.38/0.53 %------------------------------------------- % 0.38/0.53 % Proof found % 0.38/0.53 % SZS status Theorem for theBenchmark % 0.38/0.53 % SZS output start Proof % 0.38/0.53 %ClaNum:756(EqnAxiom:121) % 0.38/0.53 %VarNum:3643(SingletonVarNum:1377) % 0.38/0.53 %MaxLitNum:6 % 0.38/0.53 %MaxfuncDepth:6 % 0.38/0.53 %SharedTerms:95 % 0.38/0.53 %goalClause: 154 216 249 252 275 % 0.38/0.53 %singleGoalClaCount:5 % 0.38/0.53 [122]P1(a1) % 0.38/0.53 [123]P9(a1) % 0.38/0.53 [124]P25(a1) % 0.38/0.53 [125]P26(a1) % 0.38/0.53 [126]P44(a1) % 0.38/0.53 [127]P10(a1) % 0.38/0.53 [128]P27(a1) % 0.38/0.53 [129]P11(a1) % 0.38/0.53 [130]P15(a1) % 0.38/0.53 [131]P28(a1) % 0.38/0.53 [132]P31(a1) % 0.38/0.53 [133]P32(a1) % 0.38/0.53 [134]P34(a1) % 0.38/0.53 [135]P20(a1) % 0.38/0.53 [136]P16(a1) % 0.38/0.53 [137]P19(a1) % 0.38/0.53 [138]P41(a1) % 0.38/0.53 [139]P35(a1) % 0.38/0.53 [140]P46(a1) % 0.38/0.53 [141]P36(a1) % 0.38/0.53 [142]P37(a1) % 0.38/0.53 [143]P12(a1) % 0.38/0.53 [144]P29(a1) % 0.38/0.53 [145]P23(a1) % 0.38/0.53 [146]P21(a1) % 0.38/0.53 [147]P45(a1) % 0.38/0.53 [148]P30(a1) % 0.38/0.53 [149]P24(a1) % 0.38/0.53 [150]P17(a1) % 0.38/0.53 [151]P33(a1) % 0.38/0.53 [154]P47(f28(a15,a33)) % 0.38/0.53 [210]E(f14(f28(f28(f4(a1),f3(a1)),f5(a1)),f28(f28(f4(a1),f3(a1)),f5(a1)),a1),f28(f28(f4(a1),f3(a1)),f5(a1))) % 0.38/0.53 [249]P47(f28(a15,f25(a17,f28(f28(f28(a22,a34),a33),f3(a1)),a37,a19,a19))) % 0.38/0.53 [275]~P47(f28(a15,f25(a17,f28(f28(a17,f16(f28(f28(f28(a22,a34),f2(f28(f28(f4(a1),a35),f5(a1)))),f28(f28(f4(a1),a36),f5(a1))))),f28(f28(f28(a22,a33),f2(a35)),a36)),f26(f8(f8(a22,f2(a35),a19,a19,f31(a1,a19)),a36,a19,a1,a19),a37,a19,a19),a19,a19))) % 0.38/0.53 [157]P2(x1571,x1571,a1) % 0.38/0.53 [267]~P4(x2671,x2671,a1) % 0.38/0.53 [269]~P4(x2691,f3(a1),a1) % 0.38/0.53 [152]E(f18(f2(x1521)),f3(a1)) % 0.38/0.53 [153]E(f20(f2(x1531),a19),f3(a1)) % 0.38/0.53 [156]E(f28(f28(f4(a1),x1561),f3(a1)),x1561) % 0.38/0.53 [160]E(f14(x1601,f5(a1),a1),x1601) % 0.38/0.53 [161]E(f14(f5(a1),x1611,a1),x1611) % 0.38/0.53 [164]E(f14(x1641,f3(a1),a1),f3(a1)) % 0.38/0.53 [165]E(f29(x1651,f3(a1),a1),f5(a1)) % 0.38/0.53 [166]E(f14(f3(a1),x1661,a1),f3(a1)) % 0.38/0.53 [176]E(f29(x1761,f3(a1),a1),f28(f28(f4(a1),f3(a1)),f5(a1))) % 0.38/0.53 [181]P4(x1811,f28(f28(f4(a1),x1811),f5(a1)),a1) % 0.38/0.53 [183]P4(f3(a1),f28(f28(f4(a1),x1831),f5(a1)),a1) % 0.38/0.53 [185]P2(f28(f28(f4(a1),f3(a1)),f5(a1)),x1851,a1) % 0.38/0.53 [189]P4(f3(a1),f29(x1891,f3(a1),a1),a1) % 0.38/0.53 [261]~E(f28(f28(f4(a1),x2611),f5(a1)),x2611) % 0.38/0.53 [265]~E(f28(f28(f4(a1),x2651),f5(a1)),f3(a1)) % 0.38/0.53 [158]E(f28(f28(f4(a1),f3(a1)),x1581),x1581) % 0.38/0.53 [186]E(f7(x1861,f28(f28(f4(a1),f3(a1)),f5(a1)),a1),x1861) % 0.38/0.53 [187]E(f6(x1871,f28(f28(f4(a1),f3(a1)),f5(a1)),a1),f3(a1)) % 0.38/0.53 [190]E(f28(f28(f4(a1),f18(x1901)),f28(f28(f4(a1),f3(a1)),f5(a1))),f18(f16(x1901))) % 0.38/0.53 [194]E(f29(f28(f28(f4(a1),f3(a1)),f5(a1)),x1941,a1),f28(f28(f4(a1),f3(a1)),f5(a1))) % 0.38/0.53 [195]E(f28(f28(f4(a1),f20(x1951,a19)),f28(f28(f4(a1),f3(a1)),f5(a1))),f20(f16(x1951),a19)) % 0.38/0.53 [159]P6(x1591,x1591,x1592) % 0.38/0.53 [168]P3(x1681,f21(x1682),x1682) % 0.38/0.53 [171]P7(x1711,f2(x1712),f28(x1711,x1712)) % 0.38/0.53 [174]E(f14(x1741,x1742,a1),f14(x1742,x1741,a1)) % 0.38/0.53 [254]~E(f16(x2541),f2(x2542)) % 0.38/0.53 [255]~P5(f2(x2551),x2552) % 0.38/0.53 [177]E(f14(x1771,f3(a1),a1),f14(x1772,f3(a1),a1)) % 0.38/0.53 [178]E(f14(f3(a1),x1781,a1),f14(f3(a1),x1782,a1)) % 0.38/0.53 [179]E(f28(f28(f28(a22,x1791),x1792),f3(a1)),f24(x1791,x1792,f3(a1))) % 0.38/0.53 [184]E(f6(f14(x1841,x1842,a1),x1841,a1),f3(a1)) % 0.38/0.53 [200]P2(f14(f3(a1),x2001,a1),f14(f3(a1),x2002,a1),a1) % 0.38/0.53 [226]P4(x2261,f28(f28(f4(a1),f28(f28(f4(a1),x2262),x2261)),f5(a1)),a1) % 0.38/0.53 [228]P4(x2281,f28(f28(f4(a1),f28(f28(f4(a1),x2281),x2282)),f5(a1)),a1) % 0.38/0.53 [172]E(f28(f28(f4(a1),x1721),x1722),f28(f28(f4(a1),x1722),x1721)) % 0.38/0.53 [201]E(f7(f14(f3(a1),x2011,a1),f14(f3(a1),x2012,a1),a1),f3(a1)) % 0.38/0.53 [202]P5(f28(f28(a17,f16(x2021)),x2022),f28(f28(f28(a22,x2021),x2022),f3(a1))) % 0.38/0.53 [203]E(f14(x2031,f28(f28(f4(a1),x2032),f5(a1)),a1),f28(f28(f4(a1),x2031),f14(x2031,x2032,a1))) % 0.38/0.53 [204]E(f14(f28(f28(f4(a1),x2041),f5(a1)),x2042,a1),f28(f28(f4(a1),x2042),f14(x2041,x2042,a1))) % 0.38/0.53 [222]E(f28(f28(f4(a1),f28(f28(f4(a1),f18(x2221)),f18(x2222))),f28(f28(f4(a1),f3(a1)),f5(a1))),f18(f28(f28(a17,x2221),x2222))) % 0.38/0.53 [230]E(f28(f28(f4(a1),f28(f28(f4(a1),f20(x2301,a19)),f20(x2302,a19))),f28(f28(f4(a1),f3(a1)),f5(a1))),f20(f28(f28(a17,x2301),x2302),a19)) % 0.38/0.53 [231]E(f6(f28(f28(f4(a1),f6(x2311,x2312,a1)),f5(a1)),x2312,a1),f6(f28(f28(f4(a1),x2311),f5(a1)),x2312,a1)) % 0.38/0.53 [271]~P4(f28(f28(f4(a1),x2711),x2712),x2712,a1) % 0.38/0.53 [272]~P4(f28(f28(f4(a1),x2721),x2722),x2721,a1) % 0.38/0.53 [175]E(f28(f28(f28(a22,f2(x1751)),x1752),x1751),x1752) % 0.38/0.53 [207]E(f16(f28(f28(a23,x2071),f28(f28(f4(a1),x2072),f5(a1)))),f28(f28(a23,f16(x2071)),x2072)) % 0.38/0.53 [215]E(f28(f28(f4(a1),f28(f28(f4(a1),x2151),f5(a1))),x2152),f28(f28(f4(a1),x2151),f28(f28(f4(a1),x2152),f5(a1)))) % 0.38/0.53 [216]P47(f28(a15,f28(f28(f28(a22,a33),f2(x2161)),x2162))) % 0.38/0.53 [220]E(f28(f28(f4(a1),f28(f28(f4(a1),x2201),f5(a1))),x2202),f28(f28(f4(a1),f28(f28(f4(a1),x2201),x2202)),f5(a1))) % 0.38/0.53 [252]P47(f28(a15,f25(a17,f28(f28(f28(a22,f28(f28(f28(a22,a34),f2(f28(f28(f4(a1),x2521),f5(a1)))),f28(f28(f4(a1),x2522),f5(a1)))),f28(f28(f28(a22,a33),f2(x2521)),x2522)),f3(a1)),f26(f8(f8(a22,f2(x2521),a19,a19,f31(a1,a19)),x2522,a19,a1,a19),a37,a19,a19),a19,a19))) % 0.38/0.53 [197]E(f26(x1971,f21(x1972),x1972,x1973),f21(x1973)) % 0.38/0.53 [205]E(f7(f7(x2051,x2052,a1),x2053,a1),f7(x2051,f14(x2052,x2053,a1),a1)) % 0.38/0.53 [206]E(f14(f14(x2061,x2062,a1),x2063,a1),f14(x2061,f14(x2062,x2063,a1),a1)) % 0.38/0.53 [217]E(f6(f14(x2171,x2172,a1),f14(x2171,x2173,a1),a1),f14(x2171,f6(x2172,x2173,a1),a1)) % 0.38/0.53 [218]E(f6(f14(x2181,x2182,a1),f14(x2183,x2182,a1),a1),f14(f6(x2181,x2183,a1),x2182,a1)) % 0.38/0.53 [244]E(f28(f28(f4(a1),f14(x2441,f6(f7(x2442,x2441,a1),x2443,a1),a1)),f6(x2442,x2441,a1)),f6(x2442,f14(x2441,x2443,a1),a1)) % 0.38/0.53 [256]~E(f2(x2561),f28(f28(a17,x2562),x2563)) % 0.38/0.53 [257]~E(f16(x2571),f28(f28(a17,x2572),x2573)) % 0.38/0.53 [258]~E(f28(f28(a17,x2581),x2582),f2(x2583)) % 0.38/0.53 [259]~E(f28(f28(a17,x2591),x2592),f16(x2593)) % 0.38/0.53 [245]E(f6(f28(f28(f4(a1),f28(f28(f4(a1),f14(x2451,x2452,a1)),x2453)),f5(a1)),x2452,a1),f6(f28(f28(f4(a1),x2453),f5(a1)),x2452,a1)) % 0.38/0.53 [250]E(f25(a17,f28(f28(a23,x2501),x2502),f26(f8(a23,x2502,a19,a1,a19),x2503,a19,a19),a19,a19),f28(f28(a23,f25(a17,x2501,x2503,a19,a19)),x2502)) % 0.38/0.53 [199]E(f28(f28(f4(a1),x1991),f28(f28(f4(a1),x1992),x1993)),f28(f28(f4(a1),x1992),f28(f28(f4(a1),x1991),x1993))) % 0.38/0.53 [212]E(f16(f24(x2121,x2122,f28(f28(f4(a1),x2123),f5(a1)))),f24(f16(x2121),x2122,x2123)) % 0.38/0.53 [219]E(f28(f28(a17,f28(f28(a23,x2191),x2192)),f28(f28(a23,x2193),x2192)),f28(f28(a23,f28(f28(a17,x2191),x2193)),x2192)) % 0.38/0.53 [223]E(f28(f28(f4(a1),f14(x2231,x2232,a1)),f14(x2231,x2233,a1)),f14(x2231,f28(f28(f4(a1),x2232),x2233),a1)) % 0.38/0.53 [224]E(f28(f28(f4(a1),f14(x2241,x2242,a1)),f14(x2243,x2242,a1)),f14(f28(f28(f4(a1),x2241),x2243),x2242,a1)) % 0.38/0.53 [229]E(f6(f28(f28(f4(a1),f14(x2291,x2292,a1)),x2293),x2292,a1),f6(x2293,x2292,a1)) % 0.38/0.53 [234]E(f16(f28(f28(f28(a22,x2341),f28(f28(a23,x2342),f3(a1))),f28(f28(f4(a1),x2343),f5(a1)))),f28(f28(f28(a22,f16(x2341)),x2342),x2343)) % 0.38/0.53 [242]E(f28(f28(f4(a1),f14(x2421,f7(x2422,x2423,a1),a1)),f7(f14(x2421,f6(x2422,x2423,a1),a1),x2423,a1)),f7(f14(x2421,x2422,a1),x2423,a1)) % 0.38/0.53 [248]E(f28(f28(f4(a1),f28(f28(f4(a1),f7(x2481,x2482,a1)),f7(x2483,x2482,a1))),f7(f28(f28(f4(a1),f6(x2481,x2482,a1)),f6(x2483,x2482,a1)),x2482,a1)),f7(f28(f28(f4(a1),x2481),x2483),x2482,a1)) % 0.38/0.53 [211]E(f28(f28(f4(a1),f28(f28(f4(a1),x2111),x2112)),x2113),f28(f28(f4(a1),x2111),f28(f28(f4(a1),x2112),x2113))) % 0.38/0.53 [214]E(f28(f28(f28(a22,f28(f28(a23,x2141),x2142)),x2143),x2142),x2141) % 0.38/0.53 [225]E(f28(f30(x2251,x2252,x2253,x2254),x2252),x2253) % 0.38/0.53 [236]E(f25(x2361,x2362,f21(x2363),x2364,x2363),x2362) % 0.38/0.53 [274]~E(f25(a17,f16(x2741),x2742,a19,a19),f25(a17,f2(x2743),x2744,a19,a19)) % 0.38/0.53 [221]E(f28(f28(a17,f24(x2211,x2212,x2213)),f24(x2214,x2212,x2213)),f24(f28(f28(a17,x2211),x2214),x2212,x2213)) % 0.38/0.53 [273]~E(f28(f28(a17,f16(x2731)),x2732),f25(a17,f2(x2733),x2734,a19,a19)) % 0.38/0.53 [235]E(f28(f28(a17,f28(f28(f28(a22,x2351),x2352),x2353)),f28(f28(f28(a22,x2354),x2352),x2353)),f28(f28(f28(a22,f28(f28(a17,x2351),x2354)),x2352),x2353)) % 0.38/0.53 [251]E(f25(a17,f28(f28(f28(a22,x2511),x2512),x2513),f26(f8(f8(a22,x2512,a19,a19,f31(a1,a19)),x2513,a19,a1,a19),x2514,a19,a19),a19,a19),f28(f28(f28(a22,f25(a17,x2511,x2514,a19,a19)),x2512),x2513)) % 0.38/0.53 [241]E(f28(f28(f4(a1),f14(x2411,x2412,a1)),f28(f28(f4(a1),f14(x2413,x2412,a1)),x2414)),f28(f28(f4(a1),f14(f28(f28(f4(a1),x2411),x2413),x2412,a1)),x2414)) % 0.38/0.53 [243]E(f30(f30(x2431,f3(a1),x2432,x2433),f28(f28(f4(a1),x2434),f5(a1)),x2435,x2433),f30(f30(x2431,x2434,x2435,x2433),f3(a1),x2432,x2433)) % 0.38/0.53 [247]E(f28(f8(x2471,x2472,x2473,x2474,x2475),x2476),f28(f28(x2471,x2476),x2472)) % 0.38/0.53 [279]~P46(x2791)+~E(f5(x2791),f3(x2791)) % 0.38/0.53 [286]E(x2861,f3(a1))+P4(f3(a1),x2861,a1) % 0.38/0.53 [328]~P26(x3281)+P4(f3(x3281),f5(x3281),x3281) % 0.38/0.53 [342]E(x3421,f5(a1))+~P2(x3421,f5(a1),a1) % 0.38/0.53 [362]~P26(x3621)+~P4(f5(x3621),f3(x3621),x3621) % 0.38/0.53 [280]~P44(x2801)+E(f27(f3(a1),x2801),f3(x2801)) % 0.38/0.53 [281]~P44(x2811)+E(f27(f5(a1),x2811),f5(x2811)) % 0.38/0.53 [292]E(x2921,f3(a1))+E(f28(f28(f4(a1),f9(x2921)),f5(a1)),x2921) % 0.38/0.53 [293]E(x2931,f3(a1))+E(f28(f28(f4(a1),f10(x2931)),f5(a1)),x2931) % 0.38/0.53 [294]E(x2941,f3(a1))+E(f28(f28(f4(a1),f11(x2941)),f5(a1)),x2941) % 0.38/0.53 [333]~P22(x3331)+E(f28(f28(f4(x3331),f3(x3331)),f3(x3331)),f3(x3331)) % 0.38/0.53 [335]~P47(f28(a15,x3351))+P47(f28(a15,f16(x3351))) % 0.38/0.53 [439]~P26(x4391)+P4(f3(x4391),f28(f28(f4(x4391),f5(x4391)),f5(x4391)),x4391) % 0.38/0.53 [473]~P4(f3(a1),x4731,a1)+P2(f14(x4731,f5(a1),a1),x4731,a1) % 0.38/0.53 [474]~P4(f3(a1),x4741,a1)+P2(f14(f5(a1),x4741,a1),x4741,a1) % 0.38/0.53 [483]E(x4831,f3(a1))+~P4(x4831,f28(f28(f4(a1),f3(a1)),f5(a1)),a1) % 0.38/0.53 [513]~P2(x5131,f28(f28(f4(a1),f3(a1)),f5(a1)),a1)+E(x5131,f28(f28(f4(a1),f3(a1)),f5(a1))) % 0.38/0.53 [618]~P40(x6181)+E(f28(f28(f4(x6181),f14(f3(x6181),f3(x6181),x6181)),f14(f3(x6181),f3(x6181),x6181)),f3(x6181)) % 0.38/0.53 [728]~P40(x7281)+~P4(f3(x7281),f28(f28(f4(x7281),f14(f3(x7281),f3(x7281),x7281)),f14(f3(x7281),f3(x7281),x7281)),x7281) % 0.38/0.53 [752]~P3(a15,x7521,a19)+P3(a15,f26(f8(a23,f3(a1),a19,a1,a19),x7521,a19,a19),a19) % 0.38/0.53 [287]~P27(x2872)+P2(x2871,x2871,x2872) % 0.38/0.53 [344]~P4(x3442,x3442,x3441)+~P28(x3441) % 0.38/0.53 [345]~P4(x3452,x3452,x3451)+~P31(x3451) % 0.38/0.53 [346]~P4(x3462,x3462,x3461)+~P29(x3461) % 0.38/0.53 [276]E(x2761,x2762)+~E(f2(x2761),f2(x2762)) % 0.38/0.53 [277]E(x2771,x2772)+~E(f16(x2771),f16(x2772)) % 0.38/0.53 [282]~P28(x2822)+P28(f31(x2821,x2822)) % 0.38/0.53 [283]~P31(x2832)+P31(f31(x2831,x2832)) % 0.38/0.53 [284]~P5(x2841,x2842)+P5(f16(x2841),f16(x2842)) % 0.38/0.53 [288]~P18(x2882)+E(f14(x2881,x2881,x2882),x2881) % 0.38/0.53 [289]~P1(x2892)+E(f6(x2891,x2891,x2892),f3(x2892)) % 0.38/0.53 [298]~P27(x2982)+P2(x2981,f3(x2982),x2982) % 0.38/0.53 [299]~P27(x2991)+P2(f5(x2991),x2992,x2991) % 0.38/0.53 [340]E(x3401,f5(a1))+~E(f14(x3402,x3401,a1),f5(a1)) % 0.38/0.53 [341]E(x3411,f5(a1))+~E(f14(x3411,x3412,a1),f5(a1)) % 0.38/0.53 [382]~P4(x3821,x3822,a1)+E(f6(x3821,x3822,a1),x3821) % 0.38/0.53 [383]~P4(x3831,x3832,a1)+E(f7(x3831,x3832,a1),f3(a1)) % 0.38/0.53 [384]~P26(x3841)+~P4(f27(x3842,x3841),f3(x3841),x3841) % 0.38/0.53 [469]P4(f6(x4691,x4692,a1),x4692,a1)+~P4(f3(a1),x4692,a1) % 0.38/0.53 [472]~P4(f3(a1),x4721,a1)+P4(f3(a1),f29(x4721,x4722,a1),a1) % 0.38/0.53 [488]~P40(x4881)+~P4(f14(x4882,x4882,x4881),f3(x4881),x4881) % 0.38/0.53 [510]P4(f3(a1),x5101,a1)+~P4(f3(a1),f14(x5102,x5101,a1),a1) % 0.38/0.53 [511]P4(f3(a1),x5111,a1)+~P4(f3(a1),f14(x5111,x5112,a1),a1) % 0.38/0.53 [290]~P10(x2902)+E(f29(x2901,f5(a1),x2902),x2901) % 0.38/0.53 [291]~P27(x2912)+E(f29(x2911,f5(a1),x2912),x2911) % 0.38/0.53 [295]~P27(x2951)+E(f28(f28(f4(x2951),x2952),f3(x2951)),x2952) % 0.38/0.53 [296]~P15(x2961)+E(f28(f28(f4(x2961),x2962),f3(x2961)),x2962) % 0.38/0.53 [297]~P21(x2971)+E(f28(f28(f4(x2971),x2972),f3(x2971)),x2972) % 0.38/0.53 [300]~P1(x3002)+E(f6(x3001,f3(x3002),x3002),x3001) % 0.38/0.53 [301]~P10(x3012)+E(f14(x3011,f5(x3012),x3012),x3011) % 0.38/0.53 [302]~P27(x3022)+E(f14(x3021,f5(x3022),x3022),x3021) % 0.38/0.53 [303]~P1(x3032)+E(f7(x3031,f5(x3032),x3032),x3031) % 0.38/0.53 [304]~P10(x3041)+E(f14(f5(x3041),x3042,x3041),x3042) % 0.38/0.53 [306]~P27(x3061)+E(f14(f5(x3061),x3062,x3061),x3062) % 0.38/0.53 [307]~P20(x3071)+E(f14(f5(x3071),x3072,x3071),x3072) % 0.38/0.53 [308]~P27(x3082)+E(f29(x3081,f3(a1),x3082),f5(x3082)) % 0.38/0.53 [309]~P32(x3092)+E(f29(x3091,f3(a1),x3092),f5(x3092)) % 0.38/0.53 [311]~P1(x3112)+E(f6(x3111,f5(x3112),x3112),f3(x3112)) % 0.38/0.53 [312]~P27(x3122)+E(f14(x3121,f3(x3122),x3122),f3(x3122)) % 0.38/0.53 [313]~P37(x3132)+E(f14(x3131,f3(x3132),x3132),f3(x3132)) % 0.38/0.53 [314]~P42(x3142)+E(f14(x3141,f3(x3142),x3142),f3(x3142)) % 0.38/0.53 [315]~P1(x3152)+E(f7(x3151,f3(x3152),x3152),f3(x3152)) % 0.38/0.53 [316]~P1(x3161)+E(f6(f3(x3161),x3162,x3161),f3(x3161)) % 0.38/0.53 [318]~P27(x3181)+E(f14(f3(x3181),x3182,x3181),f3(x3181)) % 0.38/0.53 [319]~P37(x3191)+E(f14(f3(x3191),x3192,x3191),f3(x3191)) % 0.38/0.53 [320]~P42(x3201)+E(f14(f3(x3201),x3202,x3201),f3(x3201)) % 0.38/0.53 [321]~P10(x3211)+E(f29(f5(x3211),x3212,x3211),f5(x3211)) % 0.38/0.53 [322]~P1(x3221)+E(f7(f3(x3221),x3222,x3221),f3(x3221)) % 0.38/0.53 [420]~P26(x4202)+P4(x4201,f28(f28(f4(x4202),x4201),f5(x4202)),x4202) % 0.38/0.53 [435]P4(x4351,x4352,a1)+P4(x4352,f28(f28(f4(a1),x4351),f5(a1)),a1) % 0.38/0.53 [451]E(x4511,f28(f28(f4(a1),f3(a1)),f5(a1)))+~E(f14(x4512,x4511,a1),f28(f28(f4(a1),f3(a1)),f5(a1))) % 0.38/0.53 [452]E(x4521,f28(f28(f4(a1),f3(a1)),f5(a1)))+~E(f14(x4521,x4522,a1),f28(f28(f4(a1),f3(a1)),f5(a1))) % 0.38/0.53 [470]~P4(f3(a1),x4702,a1)+E(f7(f14(x4701,x4702,a1),x4702,a1),x4701) % 0.38/0.53 [471]~P4(f3(a1),x4711,a1)+E(f7(f14(x4711,x4712,a1),x4711,a1),x4712) % 0.38/0.53 [524]~P4(x5241,x5242,a1)+~P4(x5242,f28(f28(f4(a1),x5241),f5(a1)),a1) % 0.38/0.53 [611]P4(x6111,x6112,a1)+~P4(f28(f28(f4(a1),x6111),f5(a1)),f28(f28(f4(a1),x6112),f5(a1)),a1) % 0.38/0.53 [324]~P27(x3241)+E(f28(f28(f4(x3241),f3(x3241)),x3242),x3242) % 0.38/0.53 [325]~P15(x3251)+E(f28(f28(f4(x3251),f3(x3251)),x3252),x3252) % 0.38/0.53 [326]~P21(x3261)+E(f28(f28(f4(x3261),f3(x3261)),x3262),x3262) % 0.38/0.53 [330]E(x3301,f3(a1))+~E(f28(f28(f4(a1),x3302),x3301),x3302) % 0.38/0.53 [331]E(x3311,f3(a1))+~E(f28(f28(f4(a1),x3312),x3311),f3(a1)) % 0.38/0.53 [332]E(x3321,f3(a1))+~E(f28(f28(f4(a1),x3321),x3322),f3(a1)) % 0.38/0.53 [381]~P4(x3811,x3812,a1)+E(f28(f28(a23,f2(x3811)),x3812),f2(x3811)) % 0.38/0.53 [437]P4(x4371,x4372,a1)+E(f28(f28(a23,f2(x4371)),x4372),f2(f28(f28(f4(a1),x4371),f5(a1)))) % 0.38/0.53 [440]~P44(x4402)+E(f27(f28(f28(f4(a1),x4401),f5(a1)),x4402),f28(f28(f4(x4402),f5(x4402)),f27(x4401,x4402))) % 0.38/0.53 [441]~P47(f28(a15,x4411))+P47(f28(a15,f28(f28(a23,x4411),x4412))) % 0.38/0.53 [453]~P2(x4531,x4532,a1)+P2(x4531,f28(f28(f4(a1),x4532),x4531),a1) % 0.38/0.53 [475]~P27(x4751)+E(f28(f28(f4(x4751),x4752),x4752),f14(f28(f28(f4(x4751),f5(x4751)),f5(x4751)),x4752,x4751)) % 0.38/0.53 [494]P2(x4941,x4942,a1)+~P2(x4941,f28(f28(f4(a1),x4942),x4941),a1) % 0.38/0.53 [502]~P47(f28(x5021,x5022))+P47(f28(x5021,f6(x5022,f3(a1),a1))) % 0.38/0.53 [509]~P47(f28(x5091,f3(a1)))+P47(f28(x5091,f7(x5092,f3(a1),a1))) % 0.38/0.53 [594]P47(f28(x5941,x5942))+~P47(f28(x5941,f6(x5942,f3(a1),a1))) % 0.38/0.53 [597]P47(f28(x5971,f3(a1)))+~P47(f28(x5971,f7(x5972,f3(a1),a1))) % 0.38/0.53 [678]~E(f28(f28(f4(a1),f6(x6781,x6782,a1)),f5(a1)),x6782)+E(f6(f28(f28(f4(a1),x6781),f5(a1)),x6782,a1),f3(a1)) % 0.38/0.53 [692]~P4(f5(a1),x6921,a1)+E(f6(f28(f28(f4(a1),f14(x6921,x6922,a1)),f5(a1)),x6921,a1),f5(a1)) % 0.38/0.53 [695]E(f28(f28(f4(a1),f6(x6951,x6952,a1)),f5(a1)),x6952)+E(f6(f28(f28(f4(a1),x6951),f5(a1)),x6952,a1),f28(f28(f4(a1),f6(x6951,x6952,a1)),f5(a1))) % 0.38/0.53 [725]~P4(f3(a1),x7252,a1)+P4(x7251,f14(x7252,f28(f28(f4(a1),f7(x7251,x7252,a1)),f5(a1)),a1),a1) % 0.38/0.53 [751]~P3(a15,x7512,a19)+P47(f28(a15,f25(a17,f2(x7511),x7512,a19,a19))) % 0.38/0.53 [337]E(x3371,x3372)+~P6(x3371,x3372,x3373) % 0.38/0.53 [358]~P7(x3581,f2(x3582),x3583)+E(f28(x3581,x3582),x3583) % 0.38/0.53 [364]~P27(x3643)+E(f14(x3641,x3642,x3643),f14(x3642,x3641,x3643)) % 0.38/0.53 [397]~P27(x3973)+P2(x3971,f14(x3972,x3971,x3973),x3973) % 0.38/0.53 [398]~P27(x3983)+P2(x3981,f14(x3981,x3982,x3983),x3983) % 0.38/0.53 [399]~P34(x3993)+P2(x3991,f14(x3991,x3992,x3993),x3993) % 0.38/0.53 [557]~P2(x5572,x5573,a1)+P2(f14(x5571,x5572,a1),f14(x5571,x5573,a1),a1) % 0.38/0.53 [631]P4(x6311,x6312,a1)+~P4(f14(x6313,x6311,a1),f14(x6313,x6312,a1),a1) % 0.38/0.53 [632]P4(x6321,x6322,a1)+~P4(f14(x6321,x6323,a1),f14(x6322,x6323,a1),a1) % 0.38/0.53 [633]~P4(f14(x6332,x6331,a1),f14(x6333,x6331,a1),a1)+P4(f3(a1),x6331,a1) % 0.38/0.53 [634]~P4(f14(x6341,x6342,a1),f14(x6341,x6343,a1),a1)+P4(f3(a1),x6341,a1) % 0.38/0.53 [730]~E(f2(x7302),f25(a17,x7303,x7301,a19,a19))+E(x7301,f21(a19)) % 0.38/0.53 [731]~E(f16(x7312),f25(a17,x7313,x7311,a19,a19))+E(x7311,f21(a19)) % 0.38/0.53 [732]~E(f25(a17,x7322,x7321,a19,a19),f16(x7323))+E(x7321,f21(a19)) % 0.38/0.53 [734]E(x7341,f16(x7342))+~E(f25(a17,x7341,x7343,a19,a19),f16(x7342)) % 0.38/0.53 [735]E(f2(x7351),x7352)+~E(f2(x7351),f25(a17,x7352,x7353,a19,a19)) % 0.38/0.53 [736]E(f16(x7361),x7362)+~E(f16(x7361),f25(a17,x7362,x7363,a19,a19)) % 0.38/0.53 [743]E(x7431,x7432)+~E(f25(a17,x7431,x7433,a19,a19),f25(a17,x7432,x7433,a19,a19)) % 0.38/0.53 [750]~P5(x7501,x7503)+P5(f25(a17,x7501,x7502,a19,a19),f25(a17,x7503,x7502,a19,a19)) % 0.38/0.53 [408]~P1(x4083)+E(f6(f14(x4081,x4082,x4083),x4082,x4083),f3(x4083)) % 0.38/0.53 [409]~P1(x4093)+E(f6(f14(x4091,x4092,x4093),x4091,x4093),f3(x4093)) % 0.38/0.53 [410]~P1(x4103)+E(f7(f6(x4101,x4102,x4103),x4102,x4103),f3(x4103)) % 0.38/0.53 [425]~P5(x4251,x4253)+P5(f28(f28(a23,x4251),x4252),f28(f28(a23,x4253),x4252)) % 0.38/0.53 [426]~P5(x4261,x4263)+P5(f28(f28(a17,x4261),x4262),f28(f28(a17,x4263),x4262)) % 0.38/0.53 [427]~P5(x4272,x4273)+P5(f28(f28(a17,x4271),x4272),f28(f28(a17,x4271),x4273)) % 0.38/0.53 [438]~P44(x4382)+E(f29(f27(x4381,x4382),x4383,x4382),f27(f29(x4381,x4383,a1),x4382)) % 0.38/0.53 [449]~P18(x4493)+E(f14(x4491,f14(x4491,x4492,x4493),x4493),f14(x4491,x4492,x4493)) % 0.38/0.53 [450]~P1(x4503)+E(f6(f6(x4501,x4502,x4503),x4502,x4503),f6(x4501,x4502,x4503)) % 0.38/0.53 [461]~P44(x4612)+E(f14(f27(x4611,x4612),f27(x4613,x4612),x4612),f27(f14(x4611,x4613,a1),x4612)) % 0.38/0.53 [503]~P38(x5032)+P2(f14(x5031,f3(x5032),x5032),f14(x5033,f3(x5032),x5032),x5032) % 0.38/0.53 [504]~P38(x5041)+P2(f14(f3(x5041),x5042,x5041),f14(f3(x5041),x5043,x5041),x5041) % 0.38/0.53 [520]E(x5201,f3(a1))+E(f7(f14(x5201,x5202,a1),f14(x5201,x5203,a1),a1),f7(x5202,x5203,a1)) % 0.38/0.53 [544]~P10(x5443)+E(f14(f29(x5441,x5442,x5443),x5441,x5443),f14(x5441,f29(x5441,x5442,x5443),x5443)) % 0.38/0.53 [582]~P4(f3(a1),x5821,a1)+E(f7(f14(x5821,x5822,a1),f14(x5821,x5823,a1),a1),f7(x5822,x5823,a1)) % 0.38/0.53 [713]~P1(x7131)+E(f28(f28(f4(x7131),f14(x7132,f7(x7133,x7132,x7131),x7131)),f6(x7133,x7132,x7131)),x7133) % 0.38/0.53 [714]~P1(x7141)+E(f28(f28(f4(x7141),f14(f7(x7142,x7143,x7141),x7143,x7141)),f6(x7142,x7143,x7141)),x7142) % 0.38/0.53 [726]~P40(x7261)+~P4(f28(f28(f4(x7261),f14(x7262,x7262,x7261)),f14(x7263,x7263,x7261)),f3(x7261),x7261) % 0.38/0.53 [737]E(f28(f28(a17,x7371),x7372),x7373)+~E(f28(f28(a17,x7371),x7372),f25(a17,x7373,f21(a19),a19,a19)) % 0.38/0.53 [360]~P27(x3601)+E(f28(f28(f4(x3601),x3602),x3603),f28(f28(f4(x3601),x3603),x3602)) % 0.38/0.53 [361]~P15(x3611)+E(f28(f28(f4(x3611),x3612),x3613),f28(f28(f4(x3611),x3613),x3612)) % 0.38/0.53 [386]E(x3861,x3862)+~E(f28(f28(f4(a1),x3863),x3861),f28(f28(f4(a1),x3863),x3862)) % 0.38/0.53 [387]E(x3871,x3872)+~E(f28(f28(f4(a1),x3871),x3873),f28(f28(f4(a1),x3872),x3873)) % 0.38/0.53 [455]~P4(x4551,x4553,a1)+P4(x4551,f28(f28(f4(a1),x4552),x4553),a1) % 0.38/0.53 [457]~P4(x4571,x4572,a1)+P4(x4571,f28(f28(f4(a1),x4572),x4573),a1) % 0.38/0.53 [495]P4(x4951,x4952,a1)+~P4(f28(f28(f4(a1),x4951),x4953),x4952,a1) % 0.38/0.53 [505]~P1(x5051)+E(f7(f14(f3(x5051),x5052,x5051),f14(f3(x5051),x5053,x5051),x5051),f3(x5051)) % 0.38/0.53 [521]~P4(x5211,x5213,a1)+P4(f28(f28(f4(a1),x5211),x5212),f28(f28(f4(a1),x5213),x5212),a1) % 0.38/0.53 [522]~P4(x5222,x5223,a1)+P4(f28(f28(f4(a1),x5221),x5222),f28(f28(f4(a1),x5221),x5223),a1) % 0.38/0.53 [525]~P27(x5253)+E(f14(x5251,f29(x5251,x5252,x5253),x5253),f29(x5251,f28(f28(f4(a1),x5252),f5(a1)),x5253)) % 0.38/0.53 [526]~P27(x5263)+E(f14(f29(x5261,x5262,x5263),x5261,x5263),f29(x5261,f28(f28(f4(a1),x5262),f5(a1)),x5263)) % 0.38/0.53 [528]~P27(x5283)+E(f29(x5281,f28(f28(f4(a1),x5282),f5(a1)),x5283),f14(x5281,f29(x5281,x5282,x5283),x5283)) % 0.38/0.53 [529]~P32(x5293)+E(f29(x5291,f28(f28(f4(a1),x5292),f5(a1)),x5293),f14(x5291,f29(x5291,x5292,x5293),x5293)) % 0.38/0.53 [530]~P10(x5303)+E(f29(x5301,f28(f28(f4(a1),x5302),f5(a1)),x5303),f14(f29(x5301,x5302,x5303),x5301,x5303)) % 0.38/0.53 [547]~P27(x5471)+E(f28(f28(f4(x5471),x5472),f14(x5473,x5472,x5471)),f14(f28(f28(f4(x5471),x5473),f5(x5471)),x5472,x5471)) % 0.38/0.53 [593]P4(x5931,x5932,a1)+~P4(f28(f28(f4(a1),x5933),x5931),f28(f28(f4(a1),x5933),x5932),a1) % 0.38/0.53 [614]~P27(x6141)+E(f28(f28(f4(x6141),f14(x6142,x6143,x6141)),x6143),f14(f28(f28(f4(x6141),x6142),f5(x6141)),x6143,x6141)) % 0.38/0.53 [638]E(x6381,x6382)+~E(f14(f28(f28(f4(a1),x6383),f5(a1)),x6381,a1),f14(f28(f28(f4(a1),x6383),f5(a1)),x6382,a1)) % 0.38/0.53 [686]~P1(x6861)+E(f28(f28(f4(x6861),f6(x6862,x6863,x6861)),f14(f7(x6862,x6863,x6861),x6863,x6861)),x6862) % 0.38/0.53 [705]~P4(x7052,x7053,a1)+P4(f14(f28(f28(f4(a1),x7051),f5(a1)),x7052,a1),f14(f28(f28(f4(a1),x7051),f5(a1)),x7053,a1),a1) % 0.38/0.53 [742]~P21(x7421)+E(f28(f28(f4(x7421),x7422),f25(f4(x7421),f3(x7421),x7423,x7421,x7421)),f25(f4(x7421),x7422,x7423,x7421,x7421)) % 0.38/0.53 [433]~P4(x4331,x4333,a1)+E(f28(f28(f28(a22,f2(x4331)),x4332),x4333),f2(x4331)) % 0.38/0.53 [442]~P1(x4421)+E(f6(f28(f28(f4(x4421),x4422),x4423),x4423,x4421),f6(x4422,x4423,x4421)) % 0.38/0.53 [443]~P1(x4431)+E(f6(f28(f28(f4(x4431),x4432),x4433),x4432,x4431),f6(x4433,x4432,x4431)) % 0.38/0.53 [468]~P44(x4681)+E(f28(f28(f4(x4681),f27(x4682,x4681)),f27(x4683,x4681)),f27(f28(f28(f4(a1),x4682),x4683),x4681)) % 0.38/0.53 [700]~P4(x7002,f28(f28(f4(a1),x7003),f5(a1)),a1)+E(f28(f28(a23,f28(f28(a23,x7001),x7002)),f28(f28(f4(a1),x7003),f5(a1))),f28(f28(a23,f28(f28(a23,x7001),x7003)),x7002)) % 0.38/0.53 [580]~E(f26(x5803,x5801,x5802,x5804),f21(x5804))+E(x5801,f21(x5802)) % 0.38/0.53 [365]E(x3651,x3652)+~E(f28(f28(a17,x3653),x3651),f28(f28(a17,x3654),x3652)) % 0.38/0.53 [366]E(x3661,x3662)+~E(f28(f28(a17,x3661),x3663),f28(f28(a17,x3662),x3664)) % 0.38/0.53 [534]~P27(x5343)+E(f29(f29(x5341,x5342,x5343),x5344,x5343),f29(x5341,f14(x5342,x5344,a1),x5343)) % 0.38/0.53 [535]~P10(x5353)+E(f29(f29(x5351,x5352,x5353),x5354,x5353),f29(x5351,f14(x5352,x5354,a1),x5353)) % 0.38/0.53 [539]~P27(x5394)+E(f14(x5391,f14(x5392,x5393,x5394),x5394),f14(x5392,f14(x5391,x5393,x5394),x5394)) % 0.38/0.53 [542]~P27(x5423)+E(f14(f14(x5421,x5422,x5423),x5424,x5423),f14(x5421,f14(x5422,x5424,x5423),x5423)) % 0.38/0.53 [543]~P17(x5433)+E(f14(f14(x5431,x5432,x5433),x5434,x5433),f14(x5431,f14(x5432,x5434,x5433),x5433)) % 0.38/0.54 [545]~P27(x5453)+E(f14(f14(x5451,x5452,x5453),x5454,x5453),f14(f14(x5451,x5454,x5453),x5452,x5453)) % 0.38/0.54 [606]~P27(x6063)+E(f14(f29(x6061,x6062,x6063),f29(x6064,x6062,x6063),x6063),f29(f14(x6061,x6064,x6063),x6062,x6063)) % 0.38/0.54 [607]~P20(x6073)+E(f14(f29(x6071,x6072,x6073),f29(x6074,x6072,x6073),x6073),f29(f14(x6071,x6074,x6073),x6072,x6073)) % 0.38/0.54 [608]~P1(x6083)+E(f6(f14(x6081,x6082,x6083),f14(x6081,x6084,x6083),x6083),f14(x6081,f6(x6082,x6084,x6083),x6083)) % 0.38/0.54 [609]~P1(x6093)+E(f6(f14(x6091,x6092,x6093),f14(x6094,x6092,x6093),x6093),f14(f6(x6091,x6094,x6093),x6092,x6093)) % 0.38/0.54 [745]E(x7451,x7452)+~E(f25(a17,f2(x7453),x7451,a19,a19),f25(a17,f2(x7454),x7452,a19,a19)) % 0.38/0.54 [746]E(x7461,x7462)+~E(f25(a17,f16(x7463),x7461,a19,a19),f25(a17,f16(x7464),x7462,a19,a19)) % 0.38/0.54 [747]E(x7471,x7472)+~E(f25(a17,f2(x7471),x7473,a19,a19),f25(a17,f2(x7472),x7474,a19,a19)) % 0.38/0.54 [748]E(x7481,x7482)+~E(f25(a17,f16(x7481),x7483,a19,a19),f25(a17,f16(x7482),x7484,a19,a19)) % 0.38/0.54 [577]~P5(x5771,x5774)+P5(f28(f28(f28(a22,x5771),x5772),x5773),f28(f28(f28(a22,x5774),x5772),x5773)) % 0.38/0.54 [598]~P1(x5981)+E(f6(f28(f28(f4(x5981),x5982),f14(x5983,x5984,x5981)),x5984,x5981),f6(x5982,x5984,x5981)) % 0.38/0.54 [599]~P1(x5991)+E(f6(f28(f28(f4(x5991),x5992),f14(x5993,x5994,x5991)),x5993,x5991),f6(x5992,x5993,x5991)) % 0.38/0.54 [663]~P1(x6634)+E(f6(f14(x6631,f6(x6632,x6633,x6634),x6634),x6633,x6634),f6(f14(x6631,x6632,x6634),x6633,x6634)) % 0.38/0.54 [665]~P1(x6653)+E(f6(f14(f6(x6651,x6652,x6653),x6654,x6653),x6652,x6653),f6(f14(x6651,x6654,x6653),x6652,x6653)) % 0.38/0.54 [708]~P1(x7083)+E(f6(f14(f6(x7081,x7082,x7083),f6(x7084,x7082,x7083),x7083),x7082,x7083),f6(f14(x7081,x7084,x7083),x7082,x7083)) % 0.38/0.54 [515]~P14(x5151)+E(f28(f28(f4(x5151),x5152),f28(f28(f4(x5151),x5153),x5154)),f28(f28(f4(x5151),x5153),f28(f28(f4(x5151),x5152),x5154))) % 0.38/0.54 [516]~P27(x5161)+E(f28(f28(f4(x5161),x5162),f28(f28(f4(x5161),x5163),x5164)),f28(f28(f4(x5161),x5163),f28(f28(f4(x5161),x5162),x5164))) % 0.38/0.54 [517]~P15(x5171)+E(f28(f28(f4(x5171),x5172),f28(f28(f4(x5171),x5173),x5174)),f28(f28(f4(x5171),x5173),f28(f28(f4(x5171),x5172),x5174))) % 0.38/0.54 [591]~P27(x5913)+E(f14(f29(x5911,x5912,x5913),f29(x5911,x5914,x5913),x5913),f29(x5911,f28(f28(f4(a1),x5912),x5914),x5913)) % 0.38/0.54 [592]~P10(x5923)+E(f14(f29(x5921,x5922,x5923),f29(x5921,x5924,x5923),x5923),f29(x5921,f28(f28(f4(a1),x5922),x5924),x5923)) % 0.38/0.54 [653]~P1(x6531)+E(f6(f28(f28(f4(x6531),x6532),f6(x6533,x6534,x6531)),x6534,x6531),f6(f28(f28(f4(x6531),x6532),x6533),x6534,x6531)) % 0.38/0.54 [655]~P27(x6551)+E(f28(f28(f4(x6551),f14(x6552,x6553,x6551)),f14(x6552,x6554,x6551)),f14(x6552,f28(f28(f4(x6551),x6553),x6554),x6551)) % 0.38/0.54 [657]~P33(x6571)+E(f28(f28(f4(x6571),f14(x6572,x6573,x6571)),f14(x6574,x6573,x6571)),f14(f28(f28(f4(x6571),x6572),x6574),x6573,x6571)) % 0.38/0.54 [658]~P27(x6581)+E(f28(f28(f4(x6581),f14(x6582,x6583,x6581)),f14(x6584,x6583,x6581)),f14(f28(f28(f4(x6581),x6582),x6584),x6583,x6581)) % 0.38/0.54 [707]~P1(x7071)+E(f6(f28(f28(f4(x7071),f6(x7072,x7073,x7071)),x7074),x7073,x7071),f6(f28(f28(f4(x7071),x7072),x7074),x7073,x7071)) % 0.38/0.54 [717]~P1(x7171)+E(f6(f28(f28(f4(x7171),f6(x7172,x7173,x7171)),f6(x7174,x7173,x7171)),x7173,x7171),f6(f28(f28(f4(x7171),x7172),x7174),x7173,x7171)) % 0.38/0.54 [738]~P1(x7381)+E(f28(f28(f4(x7381),f28(f28(f4(x7381),f14(x7382,f7(x7383,x7382,x7381),x7381)),f6(x7383,x7382,x7381))),x7384),f28(f28(f4(x7381),x7383),x7384)) % 0.38/0.54 [739]~P1(x7391)+E(f28(f28(f4(x7391),f28(f28(f4(x7391),f14(f7(x7392,x7393,x7391),x7393,x7391)),f6(x7392,x7393,x7391))),x7394),f28(f28(f4(x7391),x7392),x7394)) % 0.38/0.54 [744]~P30(x7441)+E(f25(f4(x7441),f28(f28(f4(x7441),x7442),x7443),x7444,x7441,x7441),f28(f28(f4(x7441),x7442),f25(f4(x7441),x7443,x7444,x7441,x7441))) % 0.38/0.54 [588]~P27(x5881)+E(f28(f28(f4(x5881),f28(f28(f4(x5881),x5882),x5883)),x5884),f28(f28(f4(x5881),x5882),f28(f28(f4(x5881),x5883),x5884))) % 0.38/0.54 [589]~P11(x5891)+E(f28(f28(f4(x5891),f28(f28(f4(x5891),x5892),x5893)),x5894),f28(f28(f4(x5891),x5892),f28(f28(f4(x5891),x5893),x5894))) % 0.38/0.54 [590]~P15(x5901)+E(f28(f28(f4(x5901),f28(f28(f4(x5901),x5902),x5903)),x5904),f28(f28(f4(x5901),x5902),f28(f28(f4(x5901),x5903),x5904))) % 0.38/0.54 [649]~P27(x6491)+E(f28(f28(f4(x6491),f28(f28(f4(x6491),x6492),x6493)),x6494),f28(f28(f4(x6491),f28(f28(f4(x6491),x6492),x6494)),x6493)) % 0.38/0.54 [724]~P4(x7242,f28(f28(f4(a1),x7244),f5(a1)),a1)+E(f28(f28(f28(a22,f28(f28(a23,x7241),x7242)),f28(f28(a23,x7243),x7242)),f28(f28(f4(a1),x7244),f5(a1))),f28(f28(a23,f28(f28(f28(a22,x7241),x7243),x7244)),x7242)) % 0.38/0.54 [733]~P4(x7334,f28(f28(f4(a1),x7332),f5(a1)),a1)+E(f28(f28(f28(a22,f28(f28(a23,x7331),f28(f28(f4(a1),x7332),f5(a1)))),f28(f28(a23,x7333),x7332)),x7334),f28(f28(a23,f28(f28(f28(a22,x7331),x7333),x7334)),x7332)) % 0.38/0.54 [666]~P27(x6663)+E(f14(f14(x6661,x6662,x6663),f14(x6664,x6665,x6663),x6663),f14(f14(x6661,x6664,x6663),f14(x6662,x6665,x6663),x6663)) % 0.38/0.54 [680]E(f6(x6801,x6802,a1),f6(x6803,x6802,a1))+~E(f28(f28(f4(a1),x6801),f14(x6802,x6804,a1)),f28(f28(f4(a1),x6803),f14(x6802,x6805,a1))) % 0.38/0.54 [689]~P4(x6895,x6892,a1)+E(f28(f30(x6891,x6892,x6893,x6894),x6895),f28(x6891,x6895)) % 0.38/0.54 [701]~P7(x7011,x7014,x7015)+P7(f30(x7011,x7012,x7013,a32),f28(f28(a23,x7014),x7012),x7015) % 0.38/0.54 [753]~P8(x7531,x7534,x7535)+P8(f30(x7531,x7532,x7533,a32),f26(f8(a23,x7532,a19,a1,a19),x7534,a19,a19),x7535) % 0.38/0.54 [704]~P27(x7041)+E(f28(f28(f4(x7041),f28(f28(f4(x7041),x7042),x7043)),f28(f28(f4(x7041),x7044),x7045)),f28(f28(f4(x7041),f28(f28(f4(x7041),x7042),x7044)),f28(f28(f4(x7041),x7043),x7045))) % 0.38/0.54 [727]~P25(x7271)+E(f28(f28(f4(x7271),f14(x7272,x7273,x7271)),f28(f28(f4(x7271),f14(x7274,x7273,x7271)),x7275)),f28(f28(f4(x7271),f14(f28(f28(f4(x7271),x7272),x7274),x7273,x7271)),x7275)) % 0.38/0.54 [749]~P4(x7493,f28(f28(f4(a1),x7494),f5(a1)),a1)+E(f28(f28(f28(a22,f28(f28(f28(a22,x7491),f28(f28(a23,x7492),x7493)),f28(f28(f4(a1),x7494),f5(a1)))),f28(f28(f28(a22,x7495),x7492),x7494)),x7493),f28(f28(f28(a22,f28(f28(f28(a22,x7491),x7495),x7493)),x7492),x7494)) % 0.38/0.54 [354]E(x3541,x3542)+P4(x3542,x3541,a1)+P4(x3541,x3542,a1) % 0.38/0.54 [407]E(x4071,x4072)+~P2(x4072,x4071,a1)+~P2(x4071,x4072,a1) % 0.38/0.54 [310]~P1(x3102)+E(f7(x3101,x3101,x3102),f5(x3102))+E(x3101,f3(x3102)) % 0.38/0.54 [343]~E(f14(x3432,x3431,a1),x3432)+E(x3431,f5(a1))+E(x3432,f3(a1)) % 0.38/0.54 [347]E(x3471,f3(a1))+E(x3472,f3(a1))+~E(f14(x3472,x3471,a1),f3(a1)) % 0.38/0.54 [352]~P27(x3522)+~P2(f3(x3522),x3521,x3522)+E(x3521,f3(x3522)) % 0.38/0.54 [429]~P26(x4291)+P4(f3(x4291),f27(x4292,x4291),x4291)+~P4(f3(a1),x4292,a1) % 0.38/0.54 [434]~P26(x4342)+~P4(f3(x4342),f27(x4341,x4342),x4342)+P4(f3(a1),x4341,a1) % 0.38/0.54 [480]~P4(x4802,x4801,a1)+~P2(x4801,x4802,a1)+~P4(f3(a1),x4802,a1) % 0.38/0.54 [514]E(x5141,f3(a1))+P4(f3(a1),x5142,a1)+~P4(f3(a1),f29(x5142,x5141,a1),a1) % 0.38/0.54 [546]P4(f7(x5461,x5462,a1),x5461,a1)+~P4(f3(a1),x5461,a1)+~P4(f5(a1),x5462,a1) % 0.38/0.54 [551]~P4(f3(a1),x5512,a1)+~P4(f3(a1),x5511,a1)+P4(f3(a1),f14(x5511,x5512,a1),a1) % 0.38/0.54 [552]~P2(f14(x5522,x5521,a1),x5522,a1)+E(x5521,f5(a1))+~P4(f3(a1),x5522,a1) % 0.38/0.54 [553]~P2(f14(x5531,x5532,a1),x5532,a1)+E(x5531,f5(a1))+~P4(f3(a1),x5532,a1) % 0.38/0.54 [327]~P38(x3271)+~P13(x3271)+E(f28(f28(f4(x3271),x3272),f3(x3271)),x3272) % 0.38/0.54 [375]P47(f28(x3751,x3752))+P47(f28(x3751,f38(x3751)))+~P47(f28(x3751,f3(a1))) % 0.38/0.54 [376]P47(f28(x3761,x3762))+P47(f28(x3761,f12(x3761)))+~P47(f28(x3761,f3(a1))) % 0.38/0.54 [377]P47(f28(x3771,x3772))+P47(f28(x3771,f39(x3771)))+~P47(f28(x3771,f3(a1))) % 0.38/0.54 [378]P47(f28(x3781,x3782))+P47(f28(x3781,f40(x3781)))+~P47(f28(x3781,f3(a1))) % 0.38/0.54 [379]P47(f28(x3791,x3792))+P47(f28(x3791,f41(x3791)))+~P47(f28(x3791,f3(a1))) % 0.38/0.54 [380]P47(f28(x3801,x3802))+P47(f28(x3801,f42(x3801)))+~P47(f28(x3801,f3(a1))) % 0.38/0.54 [388]~P47(f28(x3881,x3882))+~P47(f28(x3881,f13(x3881)))+P47(f28(x3881,f3(a1))) % 0.38/0.54 [460]E(x4601,f3(a1))+E(x4602,f28(f28(f4(a1),f3(a1)),f5(a1)))+~E(f29(x4602,x4601,a1),f28(f28(f4(a1),f3(a1)),f5(a1))) % 0.38/0.54 [497]~P4(x4971,x4972,a1)+P4(f28(f28(f4(a1),x4971),f5(a1)),x4972,a1)+E(f28(f28(f4(a1),x4971),f5(a1)),x4972) % 0.38/0.54 [499]E(x4991,x4992)+P4(x4992,x4991,a1)+~P4(x4992,f28(f28(f4(a1),x4991),f5(a1)),a1) % 0.38/0.54 [501]E(x5011,x5012)+P4(x5011,x5012,a1)+~P4(x5011,f28(f28(f4(a1),x5012),f5(a1)),a1) % 0.38/0.54 [696]P4(x6961,f14(x6962,x6961,a1),a1)+~P4(f28(f28(f4(a1),f3(a1)),f5(a1)),x6962,a1)+~P4(f28(f28(f4(a1),f3(a1)),f5(a1)),x6961,a1) % 0.38/0.54 [697]P4(x6971,f14(x6971,x6972,a1),a1)+~P4(f28(f28(f4(a1),f3(a1)),f5(a1)),x6972,a1)+~P4(f28(f28(f4(a1),f3(a1)),f5(a1)),x6971,a1) % 0.38/0.54 [711]~P4(f28(f28(f4(a1),f3(a1)),f5(a1)),x7112,a1)+~P4(f28(f28(f4(a1),f3(a1)),f5(a1)),x7111,a1)+P4(f28(f28(f4(a1),f3(a1)),f5(a1)),f14(x7111,x7112,a1),a1) % 0.38/0.54 [349]~P22(x3492)+E(x3491,f3(x3492))+~E(f28(f28(f4(x3492),x3491),x3491),f3(x3492)) % 0.38/0.54 [395]E(x3951,f3(a1))+E(x3952,f3(a1))+~E(f28(f28(f4(a1),x3952),x3951),f28(f28(f4(a1),f3(a1)),f5(a1))) % 0.38/0.54 [396]E(x3961,f3(a1))+E(x3962,f3(a1))+~E(f28(f28(f4(a1),f3(a1)),f5(a1)),f28(f28(f4(a1),x3962),x3961)) % 0.38/0.54 [419]~P32(x4191)+~P45(x4191)+E(f29(f3(x4191),f28(f28(f4(a1),x4192),f5(a1)),x4191),f3(x4191)) % 0.38/0.54 [444]E(x4441,f3(a1))+E(x4441,f28(f28(f4(a1),f3(a1)),f5(a1)))+~E(f28(f28(f4(a1),x4442),x4441),f28(f28(f4(a1),f3(a1)),f5(a1))) % 0.38/0.54 [445]E(x4451,f3(a1))+E(x4451,f28(f28(f4(a1),f3(a1)),f5(a1)))+~E(f28(f28(f4(a1),x4451),x4452),f28(f28(f4(a1),f3(a1)),f5(a1))) % 0.38/0.54 [446]E(x4461,f3(a1))+E(x4461,f28(f28(f4(a1),f3(a1)),f5(a1)))+~E(f28(f28(f4(a1),f3(a1)),f5(a1)),f28(f28(f4(a1),x4462),x4461)) % 0.38/0.54 [447]E(x4471,f3(a1))+E(x4471,f28(f28(f4(a1),f3(a1)),f5(a1)))+~E(f28(f28(f4(a1),f3(a1)),f5(a1)),f28(f28(f4(a1),x4471),x4472)) % 0.38/0.54 [484]~P22(x4841)+~P4(f3(x4841),x4842,x4841)+P4(f3(x4841),f28(f28(f4(x4841),x4842),x4842),x4841) % 0.38/0.54 [485]~P22(x4851)+~P4(x4852,f3(x4851),x4851)+P4(f28(f28(f4(x4851),x4852),x4852),f3(x4851),x4851) % 0.38/0.54 [486]~P39(x4861)+~P4(x4862,f3(x4861),x4861)+P4(f28(f28(f4(x4861),x4862),x4862),f3(x4861),x4861) % 0.38/0.54 [489]E(x4891,f28(f28(f4(a1),f3(a1)),f5(a1)))+E(x4892,f28(f28(f4(a1),f3(a1)),f5(a1)))+~E(f28(f28(f4(a1),x4892),x4891),f28(f28(f4(a1),f3(a1)),f5(a1))) % 0.38/0.54 [490]E(x4901,f28(f28(f4(a1),f3(a1)),f5(a1)))+E(x4902,f28(f28(f4(a1),f3(a1)),f5(a1)))+~E(f28(f28(f4(a1),f3(a1)),f5(a1)),f28(f28(f4(a1),x4902),x4901)) % 0.38/0.54 [531]~P22(x5312)+P4(x5311,f3(x5312),x5312)+~P4(f28(f28(f4(x5312),x5311),x5311),f3(x5312),x5312) % 0.38/0.54 [532]~P39(x5322)+P4(x5321,f3(x5322),x5322)+~P4(f28(f28(f4(x5322),x5321),x5321),f3(x5322),x5322) % 0.38/0.54 [533]~P22(x5331)+P4(f3(x5331),x5332,x5331)+~P4(f3(x5331),f28(f28(f4(x5331),x5332),x5332),x5331) % 0.38/0.54 [556]P4(f3(a1),x5561,a1)+P4(f3(a1),x5562,a1)+~P4(f3(a1),f28(f28(f4(a1),x5561),x5562),a1) % 0.38/0.54 [563]~P47(f28(x5631,x5632))+P47(f28(x5631,f3(a1)))+P47(f28(x5631,f28(f28(f4(a1),f13(x5631)),f5(a1)))) % 0.38/0.54 [643]P47(f28(x6431,x6432))+~P47(f28(x6431,f3(a1)))+~P47(f28(x6431,f28(f28(f4(a1),f38(x6431)),f5(a1)))) % 0.38/0.54 [644]P47(f28(x6441,x6442))+~P47(f28(x6441,f3(a1)))+~P47(f28(x6441,f28(f28(f4(a1),f12(x6441)),f5(a1)))) % 0.38/0.54 [645]P47(f28(x6451,x6452))+~P47(f28(x6451,f3(a1)))+~P47(f28(x6451,f28(f28(f4(a1),f39(x6451)),f5(a1)))) % 0.38/0.54 [646]P47(f28(x6461,x6462))+~P47(f28(x6461,f3(a1)))+~P47(f28(x6461,f28(f28(f4(a1),f40(x6461)),f5(a1)))) % 0.38/0.54 [647]P47(f28(x6471,x6472))+~P47(f28(x6471,f3(a1)))+~P47(f28(x6471,f28(f28(f4(a1),f41(x6471)),f5(a1)))) % 0.38/0.54 [648]P47(f28(x6481,x6482))+~P47(f28(x6481,f3(a1)))+~P47(f28(x6481,f28(f28(f4(a1),f42(x6481)),f5(a1)))) % 0.38/0.54 [421]~P4(x4213,x4212,x4211)+~P28(x4211)+~P4(x4212,x4213,x4211) % 0.38/0.54 [423]~P4(x4233,x4232,x4231)+~P31(x4231)+~P4(x4232,x4233,x4231) % 0.38/0.54 [424]~P4(x4243,x4242,x4241)+~P29(x4241)+~P4(x4242,x4243,x4241) % 0.38/0.54 [448]~P2(x4481,x4483,a1)+P2(x4481,x4482,a1)+~P2(x4483,x4482,a1) % 0.38/0.54 [285]~P12(x2853)+E(x2851,x2852)+~E(f27(x2851,x2853),f27(x2852,x2853)) % 0.38/0.54 [351]~P43(x3512)+~E(f29(x3511,x3513,x3512),f3(x3512))+E(x3511,f3(x3512)) % 0.38/0.54 [389]~P1(x3893)+~P2(x3892,x3891,x3893)+E(f6(x3891,x3892,x3893),f3(x3893)) % 0.38/0.54 [390]~P1(x3903)+P2(x3901,x3902,x3903)+~E(f6(x3902,x3901,x3903),f3(x3903)) % 0.38/0.54 [412]E(x4121,x4122)+~E(f14(x4123,x4121,a1),f14(x4123,x4122,a1))+E(x4123,f3(a1)) % 0.38/0.54 [413]E(x4131,x4132)+~E(f14(x4131,x4133,a1),f14(x4132,x4133,a1))+E(x4133,f3(a1)) % 0.38/0.54 [432]~P26(x4322)+~P4(x4321,x4323,a1)+P4(f27(x4321,x4322),f27(x4323,x4322),x4322) % 0.38/0.54 [459]~P26(x4593)+~P4(f27(x4591,x4593),f27(x4592,x4593),x4593)+P4(x4591,x4592,a1) % 0.38/0.54 [481]E(x4811,x4812)+~E(f14(x4813,x4811,a1),f14(x4813,x4812,a1))+~P4(f3(a1),x4813,a1) % 0.38/0.54 [482]~P27(x4823)+P2(x4821,f29(x4821,x4822,x4823),x4823)+~P4(f3(a1),x4822,a1) % 0.38/0.54 [487]~P26(x4871)+~P4(f3(x4871),x4872,x4871)+P4(f3(x4871),f29(x4872,x4873,x4871),x4871) % 0.38/0.54 [602]~P4(x6021,x6023,a1)+P4(f14(x6021,x6022,a1),f14(x6023,x6022,a1),a1)+~P4(f3(a1),x6022,a1) % 0.38/0.54 [605]~P4(x6052,x6053,a1)+P4(f14(x6051,x6052,a1),f14(x6051,x6053,a1),a1)+~P4(f3(a1),x6051,a1) % 0.38/0.54 [635]P2(x6352,x6353,a1)+E(x6351,f3(a1))+~P2(f14(x6351,x6352,a1),f14(x6351,x6353,a1),a1) % 0.38/0.54 [675]P2(x6751,x6752,a1)+~P2(f14(x6753,x6751,a1),f14(x6753,x6752,a1),a1)+~P4(f3(a1),x6753,a1) % 0.38/0.54 [677]P4(x6771,x6772,a1)+~P4(f29(x6773,x6771,a1),f29(x6773,x6772,a1),a1)+~P4(f3(a1),x6773,a1) % 0.38/0.54 [372]E(x3721,x3722)+P4(x3722,x3721,a1)+E(f24(f2(x3721),x3723,x3722),f2(x3721)) % 0.38/0.54 [417]~P1(x4172)+E(x4171,f3(x4172))+E(f7(f14(x4173,x4171,x4172),x4171,x4172),x4173) % 0.38/0.54 [418]~P1(x4182)+E(x4181,f3(x4182))+E(f7(f14(x4181,x4183,x4182),x4181,x4182),x4183) % 0.38/0.54 [478]~P1(x4783)+~P2(x4781,x4782,x4783)+E(f14(x4781,f7(x4782,x4781,x4783),x4783),x4782) % 0.38/0.54 [479]~P1(x4793)+~P2(x4792,x4791,x4793)+E(f14(f7(x4791,x4792,x4793),x4792,x4793),x4791) % 0.38/0.54 [523]~P4(x5231,x5233,a1)+~P4(x5233,x5232,a1)+P4(f28(f28(f4(a1),x5231),f5(a1)),x5232,a1) % 0.38/0.54 [640]~P26(x6401)+~P4(f5(x6401),x6402,x6401)+P4(f5(x6401),f14(x6402,f29(x6402,x6403,x6401),x6401),x6401) % 0.38/0.54 [685]~P26(x6853)+~P4(f5(x6853),x6851,x6853)+P4(f29(x6851,x6852,x6853),f14(x6851,f29(x6851,x6852,x6853),x6853),x6853) % 0.38/0.54 [687]~P40(x6872)+E(x6871,f3(x6872))+~E(f28(f28(f4(x6872),f14(x6873,x6873,x6872)),f14(x6871,x6871,x6872)),f3(x6872)) % 0.38/0.54 [688]~P40(x6882)+E(x6881,f3(x6882))+~E(f28(f28(f4(x6882),f14(x6881,x6881,x6882)),f14(x6883,x6883,x6882)),f3(x6882)) % 0.38/0.54 [715]~P40(x7152)+E(x7151,f3(x7152))+P4(f3(x7152),f28(f28(f4(x7152),f14(x7153,x7153,x7152)),f14(x7151,x7151,x7152)),x7152) % 0.38/0.54 [716]~P40(x7162)+E(x7161,f3(x7162))+P4(f3(x7162),f28(f28(f4(x7162),f14(x7161,x7161,x7162)),f14(x7163,x7163,x7162)),x7162) % 0.38/0.54 [630]~P26(x6301)+~P4(f5(x6301),x6302,x6301)+P4(f5(x6301),f29(x6302,f28(f28(f4(a1),x6303),f5(a1)),x6301),x6301) % 0.38/0.54 [400]E(x4001,x4002)+P4(x4002,x4001,a1)+E(f28(f28(f28(a22,f2(x4001)),x4003),x4002),f2(x4001)) % 0.38/0.54 [612]~P1(x6122)+E(x6121,f3(x6122))+E(f7(f28(f28(f4(x6122),x6123),x6121),x6121,x6122),f28(f28(f4(x6122),f7(x6123,x6121,x6122)),f5(x6122))) % 0.38/0.54 [613]~P1(x6132)+E(x6131,f3(x6132))+E(f7(f28(f28(f4(x6132),x6131),x6133),x6131,x6132),f28(f28(f4(x6132),f7(x6133,x6131,x6132)),f5(x6132))) % 0.38/0.54 [755]~P47(f28(a15,x7552))+~P47(f28(a15,f25(a17,f28(f28(f28(a22,x7551),x7552),f3(a1)),x7553,a19,a19)))+P47(f28(a15,f25(a17,f28(f28(a17,f16(x7551)),x7552),x7553,a19,a19))) % 0.38/0.54 [393]~P7(x3931,x3934,x3933)+P7(x3931,x3932,x3933)+~P5(x3934,x3932) % 0.38/0.54 [476]~P27(x4764)+~P2(x4761,x4763,x4764)+P2(x4761,f14(x4762,x4763,x4764),x4764) % 0.38/0.54 [477]~P27(x4774)+~P2(x4771,x4772,x4774)+P2(x4771,f14(x4772,x4773,x4774),x4774) % 0.38/0.54 [518]~P27(x5183)+P2(x5181,x5182,x5183)+~P2(f14(x5184,x5181,x5183),x5182,x5183) % 0.38/0.54 [519]~P27(x5193)+P2(x5191,x5192,x5193)+~P2(f14(x5191,x5194,x5193),x5192,x5193) % 0.38/0.54 [566]~P38(x5663)+~P2(x5661,x5664,x5663)+P2(f14(x5661,x5662,x5663),f14(x5664,x5662,x5663),x5663) % 0.38/0.54 [567]~P38(x5673)+~P2(x5672,x5674,x5673)+P2(f14(x5671,x5672,x5673),f14(x5671,x5674,x5673),x5673) % 0.38/0.54 [568]~P27(x5683)+~P2(x5681,x5684,x5683)+P2(f29(x5681,x5682,x5683),f29(x5684,x5682,x5683),x5683) % 0.38/0.54 [512]~P1(x5123)+~P2(x5124,x5122,x5123)+E(f6(f6(x5121,x5122,x5123),x5124,x5123),f6(x5121,x5124,x5123)) % 0.38/0.54 [548]~P1(x5482)+E(x5481,f3(x5482))+E(f7(f14(x5483,x5481,x5482),f14(x5484,x5481,x5482),x5482),f7(x5483,x5484,x5482)) % 0.38/0.54 [549]~P1(x5492)+E(x5491,f3(x5492))+E(f7(f14(x5491,x5493,x5492),f14(x5491,x5494,x5492),x5492),f7(x5493,x5494,x5492)) % 0.38/0.54 [585]~P1(x5853)+~P2(x5854,x5851,x5853)+E(f7(f14(x5851,x5852,x5853),x5854,x5853),f14(f7(x5851,x5854,x5853),x5852,x5853)) % 0.38/0.54 [639]E(x6391,x6392)+E(x6393,f3(a1))+~E(f28(f28(f4(a1),x6394),f14(x6393,x6391,a1)),f28(f28(f4(a1),x6394),f14(x6393,x6392,a1))) % 0.38/0.54 [651]~P1(x6513)+~P2(x6514,x6511,x6513)+E(f7(f29(x6511,x6512,x6513),f29(x6514,x6512,x6513),x6513),f29(f7(x6511,x6514,x6513),x6512,x6513)) % 0.38/0.54 [710]~P38(x7101)+~P13(x7101)+E(f28(f28(f4(x7101),f14(x7102,x7103,x7101)),f14(x7102,x7104,x7101)),f28(f28(f4(x7101),f14(x7102,x7104,x7101)),f14(x7102,x7103,x7101))) % 0.38/0.54 [720]E(x7201,x7202)+E(x7203,x7204)+~E(f28(f28(f4(a1),f14(x7203,x7201,a1)),f14(x7204,x7202,a1)),f28(f28(f4(a1),f14(x7203,x7202,a1)),f14(x7204,x7201,a1))) % 0.38/0.54 [414]~P16(x4143)+E(x4141,x4142)+~E(f28(f28(f4(x4143),x4144),x4141),f28(f28(f4(x4143),x4144),x4142)) % 0.38/0.54 [415]~P19(x4153)+E(x4151,x4152)+~E(f28(f28(f4(x4153),x4154),x4151),f28(f28(f4(x4153),x4154),x4152)) % 0.38/0.54 [416]~P19(x4163)+E(x4161,x4162)+~E(f28(f28(f4(x4163),x4161),x4164),f28(f28(f4(x4163),x4162),x4164)) % 0.38/0.54 [496]~P4(x4964,x4963,a1)+P4(x4961,x4962,a1)+~E(f28(f28(f4(a1),x4961),x4963),f28(f28(f4(a1),x4964),x4962)) % 0.38/0.54 [559]~P23(x5591)+~P4(x5592,x5594,x5591)+P4(f28(f28(f4(x5591),x5592),x5593),f28(f28(f4(x5591),x5594),x5593),x5591) % 0.38/0.54 [560]~P24(x5601)+~P4(x5602,x5604,x5601)+P4(f28(f28(f4(x5601),x5602),x5603),f28(f28(f4(x5601),x5604),x5603),x5601) % 0.38/0.54 [561]~P23(x5611)+~P4(x5613,x5614,x5611)+P4(f28(f28(f4(x5611),x5612),x5613),f28(f28(f4(x5611),x5612),x5614),x5611) % 0.38/0.54 [562]~P24(x5621)+~P4(x5623,x5624,x5621)+P4(f28(f28(f4(x5621),x5622),x5623),f28(f28(f4(x5621),x5622),x5624),x5621) % 0.38/0.54 [581]~P4(x5812,x5814,a1)+~P4(x5811,x5813,a1)+P4(f28(f28(f4(a1),x5811),x5812),f28(f28(f4(a1),x5813),x5814),a1) % 0.38/0.54 [636]~P24(x6363)+P4(x6361,x6362,x6363)+~P4(f28(f28(f4(x6363),x6364),x6361),f28(f28(f4(x6363),x6364),x6362),x6363) % 0.38/0.54 [637]~P24(x6373)+P4(x6371,x6372,x6373)+~P4(f28(f28(f4(x6373),x6371),x6374),f28(f28(f4(x6373),x6372),x6374),x6373) % 0.38/0.54 [661]~P1(x6612)+E(x6611,f3(x6612))+E(f7(f28(f28(f4(x6612),x6613),f14(x6614,x6611,x6612)),x6611,x6612),f28(f28(f4(x6612),x6614),f7(x6613,x6611,x6612))) % 0.38/0.54 [662]~P1(x6622)+E(x6621,f3(x6622))+E(f7(f28(f28(f4(x6622),x6623),f14(x6621,x6624,x6622)),x6621,x6622),f28(f28(f4(x6622),x6624),f7(x6623,x6621,x6622))) % 0.38/0.54 [729]~P4(x7294,x7291,a1)+~P4(f3(a1),x7293,a1)+P4(f28(f28(f4(a1),f14(x7291,f6(x7292,x7293,a1),a1)),x7294),f14(x7291,x7293,a1),a1) % 0.38/0.54 [754]E(x7541,x7542)+~P7(x7543,f25(a17,f2(x7544),x7545,a19,a19),x7541)+~P7(x7543,f25(a17,f2(x7544),x7545,a19,a19),x7542) % 0.38/0.54 [578]~P14(x5781)+E(f28(f28(f4(x5781),x5782),x5783),x5784)+~E(f28(f28(f4(x5781),x5782),f28(f28(f4(x5781),x5785),x5783)),f28(f28(f4(x5781),x5785),x5784)) % 0.38/0.54 [721]~P7(x7211,x7213,x7216)+~P7(f30(x7211,x7214,x7216,a32),x7212,x7215)+P7(x7211,f28(f28(f28(a22,x7212),x7213),x7214),x7215) % 0.38/0.54 [756]~P7(x7561,x7562,x7566)+~P8(f30(x7561,x7563,x7566,a32),x7564,x7565)+P8(x7561,f26(f8(f8(a22,x7562,a19,a19,f31(a1,a19)),x7563,a19,a1,a19),x7564,a19,a19),x7565) % 0.38/0.54 [336]~P32(x3362)+~P45(x3362)+E(x3361,f3(a1))+E(f29(f3(x3362),x3361,x3362),f3(x3362)) % 0.38/0.54 [367]P4(x3671,x3672,x3673)+~P39(x3673)+E(x3671,x3672)+P4(x3672,x3671,x3673) % 0.38/0.54 [371]P4(x3711,x3712,x3713)+~P29(x3713)+E(x3711,x3712)+P4(x3712,x3711,x3713) % 0.38/0.54 [356]~P36(x3562)+~E(f14(x3563,x3561,x3562),f3(x3562))+E(x3561,f3(x3562))+E(x3563,f3(x3562)) % 0.38/0.54 [357]~P42(x3572)+~E(f14(x3573,x3571,x3572),f3(x3572))+E(x3571,f3(x3572))+E(x3573,f3(x3572)) % 0.38/0.54 [565]~P26(x5651)+~P4(f5(x5651),x5652,x5651)+P4(f5(x5651),f29(x5652,x5653,x5651),x5651)+~P4(f3(a1),x5653,a1) % 0.38/0.54 [571]~P40(x5711)+~P4(x5713,f3(x5711),x5711)+~P4(x5712,f3(x5711),x5711)+P4(f3(x5711),f14(x5712,x5713,x5711),x5711) % 0.38/0.54 [572]~P41(x5721)+~P4(f3(x5721),x5723,x5721)+~P4(f3(x5721),x5722,x5721)+P4(f3(x5721),f14(x5722,x5723,x5721),x5721) % 0.38/0.54 [573]~P26(x5731)+~P4(f5(x5731),x5733,x5731)+~P4(f5(x5731),x5732,x5731)+P4(f5(x5731),f14(x5732,x5733,x5731),x5731) % 0.38/0.54 [574]~P41(x5743)+~P4(x5742,f3(x5743),x5743)+~P4(f3(x5743),x5741,x5743)+P4(f14(x5741,x5742,x5743),f3(x5743),x5743) % 0.38/0.54 [576]~P41(x5763)+~P4(x5761,f3(x5763),x5763)+~P4(f3(x5763),x5762,x5763)+P4(f14(x5761,x5762,x5763),f3(x5763),x5763) % 0.38/0.54 [595]~P41(x5951)+~P4(f3(x5951),f14(x5953,x5952,x5951),x5951)+P4(f3(x5951),x5952,x5951)+~P4(f3(x5951),x5953,x5951) % 0.38/0.54 [596]~P41(x5961)+~P4(f3(x5961),f14(x5962,x5963,x5961),x5961)+P4(f3(x5961),x5962,x5961)+~P4(f3(x5961),x5963,x5961) % 0.38/0.54 [699]~P26(x6993)+~P4(x6991,f5(x6993),x6993)+~P4(f3(x6993),x6991,x6993)+P4(f14(x6991,f29(x6991,x6992,x6993),x6993),f29(x6991,x6992,x6993),x6993) % 0.38/0.54 [350]~P38(x3502)+~P13(x3502)+E(x3501,f3(x3502))+~E(f28(f28(f4(x3502),x3503),x3501),x3503) % 0.38/0.54 [569]~P9(x5691)+~P4(f3(x5691),x5693,x5691)+~P4(f3(x5691),x5692,x5691)+P4(f3(x5691),f28(f28(f4(x5691),x5692),x5693),x5691) % 0.38/0.54 [570]~P9(x5701)+~P4(x5703,f3(x5701),x5701)+~P4(x5702,f3(x5701),x5701)+P4(f28(f28(f4(x5701),x5702),x5703),f3(x5701),x5701) % 0.38/0.54 [679]~P26(x6793)+~P4(x6791,f5(x6793),x6793)+~P4(f3(x6793),x6791,x6793)+P4(f29(x6791,f28(f28(f4(a1),x6792),f5(a1)),x6793),f5(x6793),x6793) % 0.38/0.54 [463]~P27(x4633)+~P2(x4631,x4634,x4633)+P2(x4631,x4632,x4633)+~P2(x4634,x4632,x4633) % 0.38/0.54 [464]~P28(x4643)+~P4(x4641,x4644,x4643)+P4(x4641,x4642,x4643)+~P4(x4644,x4642,x4643) % 0.38/0.54 [465]~P31(x4653)+~P4(x4651,x4654,x4653)+P4(x4651,x4652,x4653)+~P4(x4654,x4652,x4653) % 0.38/0.54 [493]~P26(x4934)+E(x4931,x4932)+~P4(f5(x4934),x4933,x4934)+~E(f29(x4933,x4931,x4934),f29(x4933,x4932,x4934)) % 0.38/0.54 [555]~P1(x5554)+~P2(x5551,x5553,x5554)+~P2(x5551,x5552,x5554)+P2(x5551,f6(x5552,x5553,x5554),x5554) % 0.38/0.54 [584]~P1(x5843)+P2(x5841,x5842,x5843)+~P2(x5841,x5844,x5843)+~P2(x5841,f6(x5842,x5844,x5843),x5843) % 0.38/0.54 [617]~P26(x6173)+~P4(x6172,x6174,a1)+~P4(f5(x6173),x6171,x6173)+P4(f29(x6171,x6172,x6173),f29(x6171,x6174,x6173),x6173) % 0.38/0.54 [620]~P40(x6203)+~P4(x6204,x6201,x6203)+~P4(x6202,f3(x6203),x6203)+P4(f14(x6201,x6202,x6203),f14(x6204,x6202,x6203),x6203) % 0.38/0.54 [623]~P40(x6233)+~P4(x6234,x6232,x6233)+~P4(x6231,f3(x6233),x6233)+P4(f14(x6231,x6232,x6233),f14(x6231,x6234,x6233),x6233) % 0.38/0.54 [624]~P40(x6243)+~P4(x6241,x6244,x6243)+~P4(f3(x6243),x6242,x6243)+P4(f14(x6241,x6242,x6243),f14(x6244,x6242,x6243),x6243) % 0.38/0.54 [625]~P41(x6253)+~P4(x6251,x6254,x6253)+~P4(f3(x6253),x6252,x6253)+P4(f14(x6251,x6252,x6253),f14(x6254,x6252,x6253),x6253) % 0.38/0.54 [627]~P40(x6273)+~P4(x6272,x6274,x6273)+~P4(f3(x6273),x6271,x6273)+P4(f14(x6271,x6272,x6273),f14(x6271,x6274,x6273),x6273) % 0.38/0.54 [628]~P41(x6283)+~P4(x6282,x6284,x6283)+~P4(f3(x6283),x6281,x6283)+P4(f14(x6281,x6282,x6283),f14(x6281,x6284,x6283),x6283) % 0.38/0.54 [629]~P35(x6293)+~P4(x6292,x6294,x6293)+~P4(f3(x6293),x6291,x6293)+P4(f14(x6291,x6292,x6293),f14(x6291,x6294,x6293),x6293) % 0.38/0.54 [641]~P38(x6412)+P2(x6413,x6414,x6412)+~P2(f14(x6411,x6413,x6412),f14(x6411,x6414,x6412),x6412)+E(x6411,f3(x6412)) % 0.38/0.54 [642]~P38(x6422)+P2(x6423,x6424,x6422)+~P2(f14(x6423,x6421,x6422),f14(x6424,x6421,x6422),x6422)+E(x6421,f3(x6422)) % 0.38/0.54 [659]P4(x6592,x6591,x6593)+~P40(x6593)+P4(x6591,x6592,x6593)+~P4(f14(x6594,x6591,x6593),f14(x6594,x6592,x6593),x6593) % 0.38/0.54 [660]P4(x6602,x6601,x6603)+~P40(x6603)+P4(x6601,x6602,x6603)+~P4(f14(x6601,x6604,x6603),f14(x6602,x6604,x6603),x6603) % 0.38/0.54 [667]~P40(x6673)+P4(x6671,x6672,x6673)+~P4(f14(x6671,x6674,x6673),f14(x6672,x6674,x6673),x6673)+P4(x6674,f3(x6673),x6673) % 0.38/0.54 [668]~P40(x6683)+P4(x6681,x6682,x6683)+~P4(f14(x6684,x6681,x6683),f14(x6684,x6682,x6683),x6683)+P4(x6684,f3(x6683),x6683) % 0.38/0.54 [669]~P40(x6693)+P4(x6691,x6692,x6693)+~P4(f14(x6694,x6692,x6693),f14(x6694,x6691,x6693),x6693)+P4(f3(x6693),x6694,x6693) % 0.38/0.54 [670]~P40(x6703)+P4(x6701,x6702,x6703)+~P4(f14(x6702,x6704,x6703),f14(x6701,x6704,x6703),x6703)+P4(f3(x6703),x6704,x6703) % 0.38/0.54 [671]~P40(x6712)+~P4(f14(x6713,x6711,x6712),f14(x6714,x6711,x6712),x6712)+P4(x6711,f3(x6712),x6712)+P4(f3(x6712),x6711,x6712) % 0.38/0.54 [672]~P40(x6722)+~P4(f14(x6721,x6723,x6722),f14(x6721,x6724,x6722),x6722)+P4(x6721,f3(x6722),x6722)+P4(f3(x6722),x6721,x6722) % 0.38/0.54 [682]~P26(x6823)+~P4(f29(x6824,x6821,x6823),f29(x6824,x6822,x6823),x6823)+P4(x6821,x6822,a1)+~P4(f5(x6823),x6824,x6823) % 0.38/0.54 [683]~P40(x6833)+P4(x6831,x6832,x6833)+~P4(f14(x6834,x6832,x6833),f14(x6834,x6831,x6833),x6833)+~P4(x6834,f3(x6833),x6833) % 0.38/0.54 [684]~P40(x6843)+P4(x6841,x6842,x6843)+~P4(f14(x6844,x6841,x6843),f14(x6844,x6842,x6843),x6843)+~P4(f3(x6843),x6844,x6843) % 0.38/0.54 [428]~P38(x4283)+~P13(x4283)+E(x4281,x4282)+~E(f28(f28(f4(x4283),x4284),x4281),f28(f28(f4(x4283),x4284),x4282)) % 0.38/0.54 [550]~P27(x5502)+~P2(x5501,x5504,x5502)+~P2(x5501,x5503,x5502)+P2(x5501,f28(f28(f4(x5502),x5503),x5504),x5502) % 0.38/0.54 [558]~P26(x5582)+~P4(x5581,x5584,x5582)+~P4(f3(x5582),x5583,x5582)+P4(x5581,f28(f28(f4(x5582),x5583),x5584),x5582) % 0.38/0.54 [702]~P1(x7021)+~P2(x7023,x7024,x7021)+~P2(x7023,x7022,x7021)+E(f28(f28(f4(x7021),f7(x7022,x7023,x7021)),f7(x7024,x7023,x7021)),f7(f28(f28(f4(x7021),x7022),x7024),x7023,x7021)) % 0.38/0.54 [740]~P4(x7404,x7401,a1)+E(x7401,f3(a1))+P47(f28(x7402,x7403))+~P47(f28(x7402,f7(f28(f28(f4(a1),f14(x7401,x7403,a1)),x7404),x7401,a1))) % 0.38/0.54 [741]~P4(x7413,x7411,a1)+E(x7411,f3(a1))+P47(f28(x7412,x7413))+~P47(f28(x7412,f6(f28(f28(f4(a1),f14(x7411,x7414,a1)),x7413),x7411,a1))) % 0.38/0.54 [615]~P27(x6153)+~P2(x6152,x6155,x6153)+~P2(x6151,x6154,x6153)+P2(f14(x6151,x6152,x6153),f14(x6154,x6155,x6153),x6153) % 0.38/0.54 [703]~P1(x7033)+~P2(x7035,x7032,x7033)+~P2(x7034,x7031,x7033)+E(f7(f14(x7031,x7032,x7033),f14(x7034,x7035,x7033),x7033),f14(f7(x7031,x7034,x7033),f7(x7032,x7035,x7033),x7033)) % 0.38/0.54 [610]~P23(x6101)+~P4(x6103,x6105,x6101)+~P4(x6102,x6104,x6101)+P4(f28(f28(f4(x6101),x6102),x6103),f28(f28(f4(x6101),x6104),x6105),x6101) % 0.38/0.54 [698]~P1(x6983)+~E(f6(x6981,x6984,x6983),f6(x6985,x6984,x6983))+~E(f6(x6982,x6984,x6983),f6(x6986,x6984,x6983))+E(f6(f14(x6981,x6982,x6983),x6984,x6983),f6(f14(x6985,x6986,x6983),x6984,x6983)) % 0.38/0.54 [694]~P1(x6941)+~E(f6(x6942,x6944,x6941),f6(x6945,x6944,x6941))+~E(f6(x6943,x6944,x6941),f6(x6946,x6944,x6941))+E(f6(f28(f28(f4(x6941),x6942),x6943),x6944,x6941),f6(f28(f28(f4(x6941),x6945),x6946),x6944,x6941)) % 0.38/0.54 [373]~P32(x3732)+~P46(x3732)+~P36(x3732)+~P37(x3732)+~E(f29(x3731,f3(a1),x3732),f3(x3732)) % 0.38/0.54 [654]~P1(x6543)+~P2(x6542,x6544,x6543)+~P2(x6542,x6541,x6543)+~P2(x6541,x6544,x6543)+P2(f7(x6541,x6542,x6543),f7(x6544,x6542,x6543),x6543) % 0.38/0.54 [673]~P26(x6733)+~P4(x6734,x6732,a1)+~P4(x6731,f5(x6733),x6733)+~P4(f3(x6733),x6731,x6733)+P4(f29(x6731,x6732,x6733),f29(x6731,x6734,x6733),x6733) % 0.38/0.54 [693]~P1(x6933)+~P2(x6934,x6931,x6933)+P2(x6931,x6932,x6933)+~P2(x6934,x6932,x6933)+~P2(f7(x6931,x6934,x6933),f7(x6932,x6934,x6933),x6933) % 0.38/0.54 [650]~P38(x6504)+~P13(x6504)+E(x6501,x6502)+E(x6503,f3(x6504))+~E(f28(f28(f4(x6504),x6505),f14(x6503,x6501,x6504)),f28(f28(f4(x6504),x6505),f14(x6503,x6502,x6504))) % 0.38/0.54 [723]~P38(x7235)+~P13(x7235)+E(x7231,x7232)+E(x7233,x7234)+~E(f28(f28(f4(x7235),f14(x7233,x7231,x7235)),f14(x7234,x7232,x7235)),f28(f28(f4(x7235),f14(x7233,x7232,x7235)),f14(x7234,x7231,x7235))) % 0.38/0.54 [348]~P32(x3482)+~P46(x3482)+~P36(x3482)+~P37(x3482)+E(x3481,f3(a1))+E(f29(f3(x3482),x3481,x3482),f3(x3482)) % 0.38/0.54 [374]~P32(x3742)+~P46(x3742)+~P36(x3742)+~P37(x3742)+~E(f29(x3741,x3743,x3742),f3(x3742))+E(x3741,f3(x3742)) % 0.38/0.54 %EqnAxiom % 0.38/0.54 [1]E(x11,x11) % 0.38/0.54 [2]E(x22,x21)+~E(x21,x22) % 0.38/0.54 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.38/0.54 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 0.38/0.54 [5]~E(x51,x52)+E(f18(x51),f18(x52)) % 0.38/0.54 [6]~E(x61,x62)+E(f3(x61),f3(x62)) % 0.38/0.54 [7]~E(x71,x72)+E(f30(x71,x73,x74,x75),f30(x72,x73,x74,x75)) % 0.38/0.54 [8]~E(x81,x82)+E(f30(x83,x81,x84,x85),f30(x83,x82,x84,x85)) % 0.38/0.54 [9]~E(x91,x92)+E(f30(x93,x94,x91,x95),f30(x93,x94,x92,x95)) % 0.38/0.54 [10]~E(x101,x102)+E(f30(x103,x104,x105,x101),f30(x103,x104,x105,x102)) % 0.38/0.54 [11]~E(x111,x112)+E(f20(x111,x113),f20(x112,x113)) % 0.38/0.54 [12]~E(x121,x122)+E(f20(x123,x121),f20(x123,x122)) % 0.38/0.54 [13]~E(x131,x132)+E(f28(x131,x133),f28(x132,x133)) % 0.38/0.54 [14]~E(x141,x142)+E(f28(x143,x141),f28(x143,x142)) % 0.38/0.54 [15]~E(x151,x152)+E(f6(x151,x153,x154),f6(x152,x153,x154)) % 0.38/0.54 [16]~E(x161,x162)+E(f6(x163,x161,x164),f6(x163,x162,x164)) % 0.38/0.54 [17]~E(x171,x172)+E(f6(x173,x174,x171),f6(x173,x174,x172)) % 0.38/0.54 [18]~E(x181,x182)+E(f4(x181),f4(x182)) % 0.38/0.54 [19]~E(x191,x192)+E(f14(x191,x193,x194),f14(x192,x193,x194)) % 0.38/0.54 [20]~E(x201,x202)+E(f14(x203,x201,x204),f14(x203,x202,x204)) % 0.38/0.54 [21]~E(x211,x212)+E(f14(x213,x214,x211),f14(x213,x214,x212)) % 0.38/0.54 [22]~E(x221,x222)+E(f5(x221),f5(x222)) % 0.38/0.54 [23]~E(x231,x232)+E(f16(x231),f16(x232)) % 0.38/0.54 [24]~E(x241,x242)+E(f21(x241),f21(x242)) % 0.38/0.54 [25]~E(x251,x252)+E(f25(x251,x253,x254,x255,x256),f25(x252,x253,x254,x255,x256)) % 0.38/0.54 [26]~E(x261,x262)+E(f25(x263,x261,x264,x265,x266),f25(x263,x262,x264,x265,x266)) % 0.38/0.54 [27]~E(x271,x272)+E(f25(x273,x274,x271,x275,x276),f25(x273,x274,x272,x275,x276)) % 0.38/0.54 [28]~E(x281,x282)+E(f25(x283,x284,x285,x281,x286),f25(x283,x284,x285,x282,x286)) % 0.38/0.54 [29]~E(x291,x292)+E(f25(x293,x294,x295,x296,x291),f25(x293,x294,x295,x296,x292)) % 0.38/0.54 [30]~E(x301,x302)+E(f31(x301,x303),f31(x302,x303)) % 0.38/0.54 [31]~E(x311,x312)+E(f31(x313,x311),f31(x313,x312)) % 0.38/0.54 [32]~E(x321,x322)+E(f7(x321,x323,x324),f7(x322,x323,x324)) % 0.38/0.54 [33]~E(x331,x332)+E(f7(x333,x331,x334),f7(x333,x332,x334)) % 0.38/0.54 [34]~E(x341,x342)+E(f7(x343,x344,x341),f7(x343,x344,x342)) % 0.38/0.54 [35]~E(x351,x352)+E(f24(x351,x353,x354),f24(x352,x353,x354)) % 0.38/0.54 [36]~E(x361,x362)+E(f24(x363,x361,x364),f24(x363,x362,x364)) % 0.38/0.54 [37]~E(x371,x372)+E(f24(x373,x374,x371),f24(x373,x374,x372)) % 0.38/0.54 [38]~E(x381,x382)+E(f29(x381,x383,x384),f29(x382,x383,x384)) % 0.38/0.54 [39]~E(x391,x392)+E(f29(x393,x391,x394),f29(x393,x392,x394)) % 0.38/0.54 [40]~E(x401,x402)+E(f29(x403,x404,x401),f29(x403,x404,x402)) % 0.38/0.54 [41]~E(x411,x412)+E(f8(x411,x413,x414,x415,x416),f8(x412,x413,x414,x415,x416)) % 0.38/0.54 [42]~E(x421,x422)+E(f8(x423,x421,x424,x425,x426),f8(x423,x422,x424,x425,x426)) % 0.38/0.54 [43]~E(x431,x432)+E(f8(x433,x434,x431,x435,x436),f8(x433,x434,x432,x435,x436)) % 0.38/0.54 [44]~E(x441,x442)+E(f8(x443,x444,x445,x441,x446),f8(x443,x444,x445,x442,x446)) % 0.38/0.54 [45]~E(x451,x452)+E(f8(x453,x454,x455,x456,x451),f8(x453,x454,x455,x456,x452)) % 0.38/0.54 [46]~E(x461,x462)+E(f26(x461,x463,x464,x465),f26(x462,x463,x464,x465)) % 0.38/0.54 [47]~E(x471,x472)+E(f26(x473,x471,x474,x475),f26(x473,x472,x474,x475)) % 0.38/0.54 [48]~E(x481,x482)+E(f26(x483,x484,x481,x485),f26(x483,x484,x482,x485)) % 0.38/0.54 [49]~E(x491,x492)+E(f26(x493,x494,x495,x491),f26(x493,x494,x495,x492)) % 0.38/0.54 [50]~E(x501,x502)+E(f27(x501,x503),f27(x502,x503)) % 0.38/0.54 [51]~E(x511,x512)+E(f27(x513,x511),f27(x513,x512)) % 0.38/0.54 [52]~E(x521,x522)+E(f38(x521),f38(x522)) % 0.38/0.54 [53]~E(x531,x532)+E(f10(x531),f10(x532)) % 0.38/0.54 [54]~E(x541,x542)+E(f40(x541),f40(x542)) % 0.38/0.54 [55]~E(x551,x552)+E(f13(x551),f13(x552)) % 0.38/0.54 [56]~E(x561,x562)+E(f11(x561),f11(x562)) % 0.38/0.54 [57]~E(x571,x572)+E(f12(x571),f12(x572)) % 0.38/0.54 [58]~E(x581,x582)+E(f39(x581),f39(x582)) % 0.38/0.54 [59]~E(x591,x592)+E(f9(x591),f9(x592)) % 0.38/0.54 [60]~E(x601,x602)+E(f42(x601),f42(x602)) % 0.38/0.54 [61]~E(x611,x612)+E(f41(x611),f41(x612)) % 0.38/0.54 [62]~P1(x621)+P1(x622)+~E(x621,x622) % 0.38/0.54 [63]~P9(x631)+P9(x632)+~E(x631,x632) % 0.38/0.54 [64]~P25(x641)+P25(x642)+~E(x641,x642) % 0.38/0.54 [65]~P26(x651)+P26(x652)+~E(x651,x652) % 0.38/0.54 [66]~P44(x661)+P44(x662)+~E(x661,x662) % 0.38/0.54 [67]~P10(x671)+P10(x672)+~E(x671,x672) % 0.38/0.54 [68]~P27(x681)+P27(x682)+~E(x681,x682) % 0.38/0.54 [69]~P11(x691)+P11(x692)+~E(x691,x692) % 0.38/0.54 [70]~P15(x701)+P15(x702)+~E(x701,x702) % 0.38/0.54 [71]~P28(x711)+P28(x712)+~E(x711,x712) % 0.38/0.54 [72]~P31(x721)+P31(x722)+~E(x721,x722) % 0.38/0.54 [73]~P32(x731)+P32(x732)+~E(x731,x732) % 0.38/0.54 [74]~P34(x741)+P34(x742)+~E(x741,x742) % 0.38/0.54 [75]~P20(x751)+P20(x752)+~E(x751,x752) % 0.38/0.54 [76]~P16(x761)+P16(x762)+~E(x761,x762) % 0.38/0.54 [77]~P19(x771)+P19(x772)+~E(x771,x772) % 0.38/0.54 [78]~P41(x781)+P41(x782)+~E(x781,x782) % 0.38/0.54 [79]~P35(x791)+P35(x792)+~E(x791,x792) % 0.38/0.54 [80]~P46(x801)+P46(x802)+~E(x801,x802) % 0.38/0.54 [81]~P36(x811)+P36(x812)+~E(x811,x812) % 0.38/0.54 [82]~P37(x821)+P37(x822)+~E(x821,x822) % 0.38/0.54 [83]~P12(x831)+P12(x832)+~E(x831,x832) % 0.38/0.54 [84]~P29(x841)+P29(x842)+~E(x841,x842) % 0.38/0.54 [85]~P23(x851)+P23(x852)+~E(x851,x852) % 0.38/0.54 [86]~P21(x861)+P21(x862)+~E(x861,x862) % 0.38/0.54 [87]~P45(x871)+P45(x872)+~E(x871,x872) % 0.38/0.54 [88]~P30(x881)+P30(x882)+~E(x881,x882) % 0.38/0.54 [89]~P24(x891)+P24(x892)+~E(x891,x892) % 0.38/0.54 [90]~P17(x901)+P17(x902)+~E(x901,x902) % 0.38/0.54 [91]~P33(x911)+P33(x912)+~E(x911,x912) % 0.38/0.54 [92]~P47(x921)+P47(x922)+~E(x921,x922) % 0.38/0.54 [93]P2(x932,x933,x934)+~E(x931,x932)+~P2(x931,x933,x934) % 0.38/0.54 [94]P2(x943,x942,x944)+~E(x941,x942)+~P2(x943,x941,x944) % 0.38/0.54 [95]P2(x953,x954,x952)+~E(x951,x952)+~P2(x953,x954,x951) % 0.38/0.54 [96]P6(x962,x963,x964)+~E(x961,x962)+~P6(x961,x963,x964) % 0.38/0.54 [97]P6(x973,x972,x974)+~E(x971,x972)+~P6(x973,x971,x974) % 0.38/0.54 [98]P6(x983,x984,x982)+~E(x981,x982)+~P6(x983,x984,x981) % 0.38/0.54 [99]P4(x992,x993,x994)+~E(x991,x992)+~P4(x991,x993,x994) % 0.38/0.54 [100]P4(x1003,x1002,x1004)+~E(x1001,x1002)+~P4(x1003,x1001,x1004) % 0.38/0.54 [101]P4(x1013,x1014,x1012)+~E(x1011,x1012)+~P4(x1013,x1014,x1011) % 0.38/0.54 [102]P3(x1022,x1023,x1024)+~E(x1021,x1022)+~P3(x1021,x1023,x1024) % 0.38/0.54 [103]P3(x1033,x1032,x1034)+~E(x1031,x1032)+~P3(x1033,x1031,x1034) % 0.38/0.54 [104]P3(x1043,x1044,x1042)+~E(x1041,x1042)+~P3(x1043,x1044,x1041) % 0.38/0.54 [105]P7(x1052,x1053,x1054)+~E(x1051,x1052)+~P7(x1051,x1053,x1054) % 0.38/0.54 [106]P7(x1063,x1062,x1064)+~E(x1061,x1062)+~P7(x1063,x1061,x1064) % 0.38/0.54 [107]P7(x1073,x1074,x1072)+~E(x1071,x1072)+~P7(x1073,x1074,x1071) % 0.38/0.54 [108]~P40(x1081)+P40(x1082)+~E(x1081,x1082) % 0.38/0.54 [109]~P22(x1091)+P22(x1092)+~E(x1091,x1092) % 0.38/0.54 [110]~P38(x1101)+P38(x1102)+~E(x1101,x1102) % 0.38/0.54 [111]~P39(x1111)+P39(x1112)+~E(x1111,x1112) % 0.38/0.54 [112]P5(x1122,x1123)+~E(x1121,x1122)+~P5(x1121,x1123) % 0.38/0.54 [113]P5(x1133,x1132)+~E(x1131,x1132)+~P5(x1133,x1131) % 0.38/0.54 [114]P8(x1142,x1143,x1144)+~E(x1141,x1142)+~P8(x1141,x1143,x1144) % 0.38/0.54 [115]P8(x1153,x1152,x1154)+~E(x1151,x1152)+~P8(x1153,x1151,x1154) % 0.38/0.54 [116]P8(x1163,x1164,x1162)+~E(x1161,x1162)+~P8(x1163,x1164,x1161) % 0.38/0.54 [117]~P13(x1171)+P13(x1172)+~E(x1171,x1172) % 0.38/0.54 [118]~P18(x1181)+P18(x1182)+~E(x1181,x1182) % 0.38/0.54 [119]~P14(x1191)+P14(x1192)+~E(x1191,x1192) % 0.38/0.54 [120]~P42(x1201)+P42(x1202)+~E(x1201,x1202) % 0.38/0.54 [121]~P43(x1211)+P43(x1212)+~E(x1211,x1212) % 0.38/0.54 % 0.38/0.54 %------------------------------------------- % 0.38/0.54 cnf(797,plain, % 0.38/0.54 (~P4(f28(f28(f4(a1),x7971),x7972),x7972,a1)), % 0.38/0.54 inference(rename_variables,[],[271])). % 0.38/0.54 cnf(803,plain, % 0.38/0.54 (~P4(f28(f28(f4(a1),x8031),x8032),x8032,a1)), % 0.38/0.54 inference(rename_variables,[],[271])). % 0.38/0.54 cnf(817,plain, % 0.38/0.54 (~E(f28(f28(f4(a1),x8171),f5(a1)),x8171)), % 0.38/0.54 inference(rename_variables,[],[261])). % 0.38/0.54 cnf(823,plain, % 0.38/0.54 (~P4(x8231,x8231,a1)), % 0.38/0.54 inference(rename_variables,[],[267])). % 0.38/0.54 cnf(832,plain, % 0.38/0.54 (~E(f28(f28(f4(a1),x8321),f5(a1)),x8321)), % 0.38/0.54 inference(rename_variables,[],[261])). % 0.38/0.54 cnf(835,plain, % 0.38/0.54 (~E(f28(f28(f4(a1),x8351),f5(a1)),x8351)), % 0.38/0.54 inference(rename_variables,[],[261])). % 0.38/0.54 cnf(838,plain, % 0.38/0.54 (~E(f28(f28(f4(a1),x8381),f5(a1)),x8381)), % 0.38/0.54 inference(rename_variables,[],[261])). % 0.38/0.54 cnf(845,plain, % 0.38/0.54 ($false), % 0.38/0.54 inference(scs_inference,[],[216,252,275,197,181,226,228,261,817,832,835,838,160,172,267,823,271,797,803,337,358,435,451,455,457,469,495,522,580,611,633,634,680,730,731,732,2,13,524,755]), % 0.38/0.54 ['proof']). % 0.38/0.54 % SZS output end Proof % 0.38/0.54 % Total time :0.034312s %------------------------------------------------------------------------------