%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL836-1 : 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 : n016.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 11:19:58 AM UTC 2026 % Result : Unsatisfiable 0.54s 0.79s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL836-1 : TPTP v9.3.1. Released v4.1.0. % 0.00/0.02 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.07/0.34 % Computer : n016.cluster.edu % 0.07/0.34 % Model : x86_64 x86_64 % 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.34 % Memory : 8046.5625MB % 0.07/0.34 % OS : Linux 6.8.0-71-generic % 0.07/0.34 % CPULimit : 300 % 0.07/0.34 % WCLimit : 300 % 0.07/0.34 % DateTime : Sat Sep 5 17:22:15 UTC 2026 % 0.07/0.34 % CPUTime : % 0.23/0.51 start to proof:theBenchmark % 0.54/0.73 %------------------------------------------- % 0.54/0.73 % File :CSE---1.7 % 0.54/0.73 % Problem :theBenchmark % 0.54/0.73 % Transform :cnf % 0.54/0.73 % Format :tptp:raw % 0.54/0.73 % Command :java -jar mcs_scs.jar %d %s % 0.54/0.73 % 0.54/0.73 % Result :Theorem 0.056376s % 0.54/0.73 % Output :CNFRefutation 0.056376s % 0.54/0.73 %------------------------------------------- % 0.54/0.73 %------------------------------------------------------------------------------ % 0.54/0.73 % File : LCL836-1 : TPTP v9.3.1. Released v4.1.0. % 0.54/0.73 % Domain : Logic Calculi % 0.54/0.73 % Problem : Strong normalization of typed lambda calculus 232_24 % 0.54/0.73 % Version : Especial. % 0.54/0.73 % English : % 0.54/0.73 % 0.54/0.73 % Refs : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java % 0.54/0.73 % : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe % 0.54/0.73 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 0.54/0.73 % Source : [Nip10] % 0.54/0.73 % Names : StrongNorm-232_24 [Nip10] % 0.54/0.73 % 0.54/0.73 % Status : Unsatisfiable % 0.54/0.73 % Rating : 0.17 v9.3.0, 0.05 v8.2.0, 0.10 v8.1.0, 0.16 v7.5.0, 0.11 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.20 v6.3.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.14 v6.0.0, 0.20 v5.5.0, 0.45 v5.3.0, 0.44 v5.1.0, 0.47 v5.0.0, 0.36 v4.1.0 % 0.54/0.73 % Syntax : Number of clauses : 625 ( 171 unt; 53 nHn; 322 RR) % 0.54/0.73 % Number of literals : 1377 ( 406 equ; 725 neg) % 0.54/0.73 % Maximal clause size : 6 ( 2 avg) % 0.54/0.73 % Maximal term depth : 9 ( 2 avg) % 0.54/0.73 % Number of predicates : 43 ( 42 usr; 0 prp; 1-6 aty) % 0.54/0.73 % Number of functors : 61 ( 61 usr; 20 con; 0-5 aty) % 0.54/0.73 % Number of variables : 2024 ( 401 sgn) % 0.54/0.73 % SPC : CNF_UNS_RFO_SEQ_NHN % 0.54/0.73 % 0.54/0.73 % Comments : % 0.54/0.73 %------------------------------------------------------------------------------ % 0.54/0.73 cnf(cls_min__max_Osup__absorb1_0,axiom, % 0.54/0.73 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.73 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = V_x % 0.54/0.73 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.54/0.73 % 0.54/0.73 cnf(cls_min__max_Ole__iff__sup_1,axiom, % 0.54/0.73 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.73 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) != V_y % 0.54/0.73 | c_lessequals(V_x,V_y,T_a) ) ). % 0.54/0.73 % 0.54/0.73 cnf(cls_min__max_Ole__iff__sup_0,axiom, % 0.54/0.73 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.73 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = V_y % 0.54/0.73 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.54/0.73 % 0.54/0.73 cnf(cls_xt1_I10_J_0,axiom, % 0.54/0.73 ( ~ class_Orderings_Oorder(T_a) % 0.54/0.73 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.54/0.73 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.54/0.73 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.54/0.73 % 0.54/0.73 cnf(cls_order__less__trans_0,axiom, % 0.54/0.73 ( ~ class_Orderings_Opreorder(T_a) % 0.54/0.73 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.54/0.73 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.54/0.73 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.54/0.73 % 0.54/0.73 cnf(cls_add__nonneg__nonneg_0,axiom, % 0.54/0.73 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.54/0.73 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a) % 0.54/0.73 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.54/0.73 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.54/0.73 % 0.54/0.73 cnf(cls_add__nonneg__eq__0__iff_2,axiom, % 0.54/0.73 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.54/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.54/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.54/0.74 | 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) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_add__mono_0,axiom, % 0.54/0.74 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 0.54/0.74 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a) % 0.54/0.74 | ~ c_lessequals(V_c,V_d,T_a) % 0.54/0.74 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_add__le__mono_0,axiom, % 0.54/0.74 ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_l),tc_nat) % 0.54/0.74 | ~ c_lessequals(V_k,V_l,tc_nat) % 0.54/0.74 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_append__step1I_0,axiom, % 0.54/0.74 ( ~ c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a) % 0.54/0.74 | c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,V_x,T_a),c_List_Oappend(V_xs,V_x,T_a),T_a) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_append__step1I_1,axiom, % 0.54/0.74 ( c_ListOrder_Ostep1(V_r,c_List_Oappend(V_x,V_vs,T_a),c_List_Oappend(V_x,V_us,T_a),T_a) % 0.54/0.74 | ~ c_ListOrder_Ostep1(V_r,V_vs,V_us,T_a) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_nat__diff__split_1,axiom, % 0.54/0.74 ( ~ hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_b),V_d),V_b,tc_nat))) % 0.54/0.74 | hBOOL(hAPP(V_P,V_d)) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_nat__diff__split__asm_1,axiom, % 0.54/0.74 ( ~ hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_b),V_x),V_b,tc_nat))) % 0.54/0.74 | hBOOL(hAPP(V_P,V_x)) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_diff__add__cancel_0,axiom, % 0.54/0.74 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.54/0.74 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ominus__class_Ominus(V_a,V_b,T_a)),V_b) = V_a ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_rtrancl__beta__Abs_0,axiom, % 0.54/0.74 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(V_s)),c_Lambda_OdB_OAbs(V_s_H))) % 0.54/0.74 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_subst__Var_2,axiom, % 0.54/0.74 ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i)),V_s),V_k) = c_Lambda_OdB_OVar(V_i) % 0.54/0.74 | V_i = V_k % 0.54/0.74 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_append__in__listsp__conv_0,axiom, % 0.54/0.74 ( c_List_Olistsp(V_A,V_xs,T_a) % 0.54/0.74 | ~ c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_append__in__listsp__conv_1,axiom, % 0.54/0.74 ( c_List_Olistsp(V_A,V_ys,T_a) % 0.54/0.74 | ~ c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom, % 0.54/0.74 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.54/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a) % 0.54/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom, % 0.54/0.74 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.54/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.54/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_dB_Osimps_I12_J_0,axiom, % 0.54/0.74 c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(V_f3,V_dB) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_of__nat__le__iff_1,axiom, % 0.54/0.74 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.54/0.74 | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) % 0.54/0.74 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_of__nat__le__iff_0,axiom, % 0.54/0.74 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.54/0.74 | c_lessequals(V_m,V_n,tc_nat) % 0.54/0.74 | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_Cons__step1__Cons_2,axiom, % 0.54/0.74 ( V_x = V_y % 0.54/0.74 | V_xs = V_ys % 0.54/0.74 | ~ c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_Cons__step1__Cons_4,axiom, % 0.54/0.74 ( ~ hBOOL(hAPP(hAPP(V_r,V_y),V_xa)) % 0.54/0.74 | c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_x,T_a),c_List_Olist_OCons(V_xa,V_x,T_a),T_a) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_lem0_0,axiom, % 0.54/0.74 ( c_HOL_Oord__class_Oless(V_m,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k),tc_nat) % 0.54/0.74 | ~ c_lessequals(V_m,V_n,tc_nat) % 0.54/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_add__strict__increasing_0,axiom, % 0.54/0.74 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.54/0.74 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.54/0.74 | c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a) % 0.54/0.74 | ~ c_lessequals(V_b,V_c,T_a) % 0.54/0.74 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_listsp_ONil_0,axiom, % 0.54/0.74 c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_replicate__eq__replicate_0,axiom, % 0.54/0.74 ( c_List_Oreplicate(V_m,V_x,T_a) != c_List_Oreplicate(V_n,V_y,T_a) % 0.54/0.74 | V_m = V_n ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_append__same__eq_0,axiom, % 0.54/0.74 ( c_List_Oappend(V_ys,V_xs,T_a) != c_List_Oappend(V_zs,V_xs,T_a) % 0.54/0.74 | V_ys = V_zs ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_same__append__eq_0,axiom, % 0.54/0.74 ( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Oappend(V_xs,V_zs,T_a) % 0.54/0.74 | V_ys = V_zs ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_max__less__iff__conj_2,axiom, % 0.54/0.74 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.74 | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) % 0.54/0.74 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.54/0.74 | ~ c_HOL_Oord__class_Oless(V_x,V_z,T_a) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_diff__is__0__eq_0,axiom, % 0.54/0.74 ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.54/0.74 | c_lessequals(V_m,V_n,tc_nat) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_diff__is__0__eq_1,axiom, % 0.54/0.74 ( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) % 0.54/0.74 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_zero__le__power_0,axiom, % 0.54/0.74 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.54/0.74 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) % 0.54/0.74 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_rtranclp_Ortrancl__refl_0,axiom, % 0.54/0.74 hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_Nitpick_Ortranclp__def_1,axiom, % 0.54/0.74 hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_accp__downwards_0,axiom, % 0.54/0.74 ( c_Wellfounded_Oaccp(V_r,V_b,T_a) % 0.54/0.74 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a)) % 0.54/0.74 | ~ c_Wellfounded_Oaccp(V_r,V_a,T_a) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_accp__downwards__aux_0,axiom, % 0.54/0.74 ( c_Wellfounded_Oaccp(V_r,V_b,T_a) % 0.54/0.74 | ~ c_Wellfounded_Oaccp(V_r,V_a,T_a) % 0.54/0.74 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a)) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_rtranclp__trans_0,axiom, % 0.54/0.74 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_z)) % 0.54/0.74 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_z)) % 0.54/0.74 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y)) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_IT__implies__termi_0,axiom, % 0.54/0.74 ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) % 0.54/0.74 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_termi__implies__IT_0,axiom, % 0.54/0.74 ( hBOOL(hAPP(c_InductTermi_OIT,V_r)) % 0.54/0.74 | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_r,tc_Lambda_OdB) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_infinite__descent0_2,axiom, % 0.54/0.74 ( hBOOL(hAPP(V_P,V_n)) % 0.54/0.74 | hBOOL(hAPP(V_P,V_x)) % 0.54/0.74 | ~ c_HOL_Oord__class_Oless(V_x,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(V_P),tc_nat) % 0.54/0.74 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_le__diff__conv2_0,axiom, % 0.54/0.74 ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat) % 0.54/0.74 | ~ c_lessequals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) % 0.54/0.74 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_le__diff__conv2_1,axiom, % 0.54/0.74 ( c_lessequals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) % 0.54/0.74 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat) % 0.54/0.74 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_min__max_Ole__sup__iff_2,axiom, % 0.54/0.74 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.74 | c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) % 0.54/0.74 | ~ c_lessequals(V_y,V_z,T_a) % 0.54/0.74 | ~ c_lessequals(V_x,V_z,T_a) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_min__max_Osup__least_0,axiom, % 0.54/0.74 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.74 | c_lessequals(c_Orderings_Oord__class_Omax(V_y,V_z,T_a),V_x,T_a) % 0.54/0.74 | ~ c_lessequals(V_z,V_x,T_a) % 0.54/0.74 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.54/0.74 % 0.54/0.74 cnf(cls_min__max_Ole__supI_0,axiom, % 0.54/0.74 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.74 | c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) % 0.54/0.74 | ~ c_lessequals(V_b,V_x,T_a) % 0.54/0.74 | ~ c_lessequals(V_a,V_x,T_a) ) ). % 0.54/0.74 % 0.54/0.75 cnf(cls_le__maxI1_0,axiom, % 0.54/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.75 | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_le__maxI2_0,axiom, % 0.54/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.75 | c_lessequals(V_y,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_append__Nil2_0,axiom, % 0.54/0.75 c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs ). % 0.54/0.75 % 0.54/0.75 cnf(cls_eq__Nil__appendI_0,axiom, % 0.54/0.75 V_x = c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_self__append__conv_1,axiom, % 0.54/0.75 V_xs = c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_append__Nil_0,axiom, % 0.54/0.75 c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys ). % 0.54/0.75 % 0.54/0.75 cnf(cls_self__append__conv2_1,axiom, % 0.54/0.75 V_ys = c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_subst__preserves__beta2_0,axiom, % 0.54/0.75 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_r),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_i))) % 0.54/0.75 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_bot__least_0,axiom, % 0.54/0.75 ( ~ class_Orderings_Obot(T_a) % 0.54/0.75 | c_lessequals(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_add__increasing_0,axiom, % 0.54/0.75 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.54/0.75 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.54/0.75 | c_lessequals(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a) % 0.54/0.75 | ~ c_lessequals(V_b,V_c,T_a) % 0.54/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_add__increasing2_0,axiom, % 0.54/0.75 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.54/0.75 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.54/0.75 | c_lessequals(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a) % 0.54/0.75 | ~ c_lessequals(V_b,V_a,T_a) % 0.54/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_map__replicate_0,axiom, % 0.54/0.75 c_List_Omap(V_f,c_List_Oreplicate(V_n,V_x,T_b),T_b,T_a) = c_List_Oreplicate(V_n,hAPP(V_f,V_x),T_a) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_termination__basic__simps_I1_J_0,axiom, % 0.54/0.75 ( c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat) % 0.54/0.75 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_termination__basic__simps_I2_J_0,axiom, % 0.54/0.75 ( c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat) % 0.54/0.75 | ~ c_HOL_Oord__class_Oless(V_x,V_z,tc_nat) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_add__lessD1_0,axiom, % 0.54/0.75 ( c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) % 0.54/0.75 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_k,tc_nat) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_trans__less__add1_0,axiom, % 0.54/0.75 ( c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_m),tc_nat) % 0.54/0.75 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_trans__less__add2_0,axiom, % 0.54/0.75 ( c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_j),tc_nat) % 0.54/0.75 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom, % 0.54/0.75 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.54/0.75 | 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) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_comm__monoid__add_Omult__commute_0,axiom, % 0.54/0.75 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.54/0.75 | 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) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_nat__add__commute_0,axiom, % 0.54/0.75 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) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_less__add__eq__less_0,axiom, % 0.54/0.75 ( 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) % 0.54/0.75 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat) % 0.54/0.75 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_class__semiring_Oadd__c_0,axiom, % 0.54/0.75 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.54/0.75 | 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) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_diff__less__mono2_0,axiom, % 0.54/0.75 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat) % 0.54/0.75 | ~ c_HOL_Oord__class_Oless(V_m,V_l,tc_nat) % 0.54/0.75 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_foldr__append_0,axiom, % 0.54/0.75 c_List_Ofoldr(V_f,c_List_Oappend(V_xs,V_ys,T_b),V_a,T_b,T_a) = c_List_Ofoldr(V_f,V_xs,c_List_Ofoldr(V_f,V_ys,V_a,T_b,T_a),T_b,T_a) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_Snoc__step1__SnocD_3,axiom, % 0.54/0.75 ( hBOOL(hAPP(hAPP(V_r,V_y),V_x)) % 0.54/0.75 | V_y = V_x % 0.54/0.75 | ~ c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_of__nat__eq__iff_0,axiom, % 0.54/0.75 ( ~ class_Nat_Osemiring__char__0(T_a) % 0.54/0.75 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) % 0.54/0.75 | V_m = V_n ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_typing__elims_I1_J_0,axiom, % 0.54/0.75 ( hAPP(V_e,V_i) = V_T % 0.54/0.75 | ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_le__max__iff__disj_0,axiom, % 0.54/0.75 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.75 | c_lessequals(V_z,V_y,T_a) % 0.54/0.75 | c_lessequals(V_z,V_x,T_a) % 0.54/0.75 | ~ c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_Nil__is__map__conv_0,axiom, % 0.54/0.75 ( c_List_Olist_ONil(T_a) != c_List_Omap(V_f,V_xs,T_b,T_a) % 0.54/0.75 | V_xs = c_List_Olist_ONil(T_b) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_drop__Nil_0,axiom, % 0.54/0.75 c_List_Odrop(V_n,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_gb__semiring_Omul__pwr_0,axiom, % 0.54/0.75 ( hAPP(hAPP(V_mul,hAPP(hAPP(V_pwr,V_x),V_p)),hAPP(hAPP(V_pwr,V_x),V_q)) = hAPP(hAPP(V_pwr,V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_p),V_q)) % 0.54/0.75 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_subst__preserves__beta_H_0,axiom, % 0.54/0.75 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_t),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),V_i))) % 0.54/0.75 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_subst__preserves__beta2_H_0,axiom, % 0.54/0.75 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_r),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_i))) % 0.54/0.75 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_add__nonneg__eq__0__iff_1,axiom, % 0.54/0.75 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.54/0.75 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) != c_HOL_Ozero__class_Ozero(T_a) % 0.54/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 0.54/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 0.54/0.75 | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_add__nonneg__eq__0__iff_0,axiom, % 0.54/0.75 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.54/0.75 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) != c_HOL_Ozero__class_Ozero(T_a) % 0.54/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) % 0.54/0.75 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) % 0.54/0.75 | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_foldr__conv__foldl_0,axiom, % 0.54/0.75 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a) % 0.54/0.75 | c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,V_a,T_a,T_a) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_a,V_xs,T_a,T_a) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_dB_Osimps_I6_J_0,axiom, % 0.54/0.75 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_r__into__rtranclp_0,axiom, % 0.54/0.75 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y)) % 0.54/0.75 | ~ hBOOL(hAPP(hAPP(V_r,V_x),V_y)) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_not__Nil__step1_0,axiom, % 0.54/0.75 ~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_not__step1__Nil_0,axiom, % 0.54/0.75 ~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom, % 0.54/0.75 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.54/0.75 | 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) % 0.54/0.75 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom, % 0.54/0.75 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.54/0.75 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.54/0.75 | ~ 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) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_class__semiring_Oadd__a_0,axiom, % 0.54/0.75 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.54/0.75 | 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) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_add__cancel__21_1,axiom, % 0.54/0.75 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.54/0.75 | 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)) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_nat__add__left__commute_0,axiom, % 0.54/0.75 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)) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_nat__add__assoc_0,axiom, % 0.54/0.75 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)) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_comm__monoid__add_Omult__assoc_0,axiom, % 0.54/0.75 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.54/0.75 | 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)) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom, % 0.54/0.75 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.54/0.75 | 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)) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom, % 0.54/0.75 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a) % 0.54/0.75 | 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)) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom, % 0.54/0.75 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.54/0.75 | 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) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom, % 0.54/0.75 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.54/0.75 | 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) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom, % 0.54/0.75 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.54/0.75 | 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)) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom, % 0.54/0.75 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.54/0.75 | 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)) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_add__gr__0_0,axiom, % 0.54/0.75 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.54/0.75 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 0.54/0.75 | ~ 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) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_conversep_Ointros_0,axiom, % 0.54/0.75 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_b),V_a)) % 0.54/0.75 | ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b)) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_conversep_Ocases_0,axiom, % 0.54/0.75 ( hBOOL(hAPP(hAPP(V_r,V_a2),V_a1)) % 0.54/0.75 | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a1),V_a2)) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_conversep__iff_1,axiom, % 0.54/0.75 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a),V_b)) % 0.54/0.75 | ~ hBOOL(hAPP(hAPP(V_r,V_b),V_a)) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_conversepD_0,axiom, % 0.54/0.75 ( hBOOL(hAPP(hAPP(V_r,V_b),V_a)) % 0.54/0.75 | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a),V_b)) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_drop__Cons_H_0,axiom, % 0.54/0.75 c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_add__cancel__21_0,axiom, % 0.54/0.75 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.54/0.75 | 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) % 0.54/0.75 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z) = V_u ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_trans__le__add2_0,axiom, % 0.54/0.75 ( c_lessequals(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_j),tc_nat) % 0.54/0.75 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.54/0.75 % 0.54/0.75 cnf(cls_trans__le__add1_0,axiom, % 0.54/0.75 ( c_lessequals(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_m),tc_nat) % 0.54/0.75 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.54/0.75 % 0.54/0.76 cnf(cls_add__leE_1,axiom, % 0.54/0.76 ( c_lessequals(V_k,V_n,tc_nat) % 0.54/0.76 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k),V_n,tc_nat) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_add__leE_0,axiom, % 0.54/0.76 ( c_lessequals(V_m,V_n,tc_nat) % 0.54/0.76 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k),V_n,tc_nat) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_termination__basic__simps_I4_J_0,axiom, % 0.54/0.76 ( c_lessequals(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat) % 0.54/0.76 | ~ c_lessequals(V_x,V_z,tc_nat) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_termination__basic__simps_I3_J_0,axiom, % 0.54/0.76 ( c_lessequals(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat) % 0.54/0.76 | ~ c_lessequals(V_x,V_y,tc_nat) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_dB_Osimps_I10_J_0,axiom, % 0.54/0.76 c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_max__diff__distrib__left_0,axiom, % 0.54/0.76 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.54/0.76 | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(V_x,V_z,T_a),c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_COMBC__def_0,axiom, % 0.54/0.76 hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_not__leE_0,axiom, % 0.54/0.76 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.76 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.54/0.76 | c_lessequals(V_y,V_x,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_linorder__antisym__conv2_1,axiom, % 0.54/0.76 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.76 | ~ c_lessequals(V_x,V_x,T_a) % 0.54/0.76 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_linorder__antisym__conv1_1,axiom, % 0.54/0.76 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.76 | c_HOL_Oord__class_Oless(V_x,V_x,T_a) % 0.54/0.76 | c_lessequals(V_x,V_x,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_linorder__not__less_1,axiom, % 0.54/0.76 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.76 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.54/0.76 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_linorder__not__less_0,axiom, % 0.54/0.76 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.76 | c_lessequals(V_y,V_x,T_a) % 0.54/0.76 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_linorder__not__le_1,axiom, % 0.54/0.76 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.76 | ~ c_lessequals(V_x,V_y,T_a) % 0.54/0.76 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_linorder__not__le_0,axiom, % 0.54/0.76 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.76 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.54/0.76 | c_lessequals(V_x,V_y,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_less__le__not__le_1,axiom, % 0.54/0.76 ( ~ class_Orderings_Opreorder(T_a) % 0.54/0.76 | ~ c_lessequals(V_y,V_x,T_a) % 0.54/0.76 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_infinite__descent0_0,axiom, % 0.54/0.76 ( hBOOL(hAPP(V_P,V_n)) % 0.54/0.76 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(V_P),tc_nat) % 0.54/0.76 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_subst__Var_1,axiom, % 0.54/0.76 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 0.54/0.76 | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_x)),V_s),V_x) = V_s ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_foldr_Osimps_I1_J_0,axiom, % 0.54/0.76 c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a) = V_a ). % 0.54/0.76 % 0.54/0.76 cnf(cls_map__is__Nil__conv_1,axiom, % 0.54/0.76 c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_add__strict__increasing2_0,axiom, % 0.54/0.76 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.54/0.76 | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.54/0.76 | c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a) % 0.54/0.76 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 0.54/0.76 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_diff__le__mono2_0,axiom, % 0.54/0.76 ( c_lessequals(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat) % 0.54/0.76 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_diff__le__mono_0,axiom, % 0.54/0.76 ( c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_l,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_l,tc_nat),tc_nat) % 0.54/0.76 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_le__diff__iff_1,axiom, % 0.54/0.76 ( c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) % 0.54/0.76 | ~ c_lessequals(V_m,V_n,tc_nat) % 0.54/0.76 | ~ c_lessequals(V_k,V_n,tc_nat) % 0.54/0.76 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_le__diff__iff_0,axiom, % 0.54/0.76 ( c_lessequals(V_m,V_n,tc_nat) % 0.54/0.76 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) % 0.54/0.76 | ~ c_lessequals(V_k,V_n,tc_nat) % 0.54/0.76 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_diff__add__0_0,axiom, % 0.54/0.76 c_HOL_Ominus__class_Ominus(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_diff__diff__left_0,axiom, % 0.54/0.76 c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k),tc_nat) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_power__mono_0,axiom, % 0.54/0.76 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.54/0.76 | c_lessequals(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) % 0.54/0.76 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.54/0.76 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_eq__eqI_1,axiom, % 0.54/0.76 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.54/0.76 | c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) % 0.54/0.76 | V_xa = V_y ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_eq__eqI_0,axiom, % 0.54/0.76 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.54/0.76 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 0.54/0.76 | V_x_H = V_y_H ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_eq__diff__iff_0,axiom, % 0.54/0.76 ( c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat) != c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat) % 0.54/0.76 | ~ c_lessequals(V_k,V_n,tc_nat) % 0.54/0.76 | ~ c_lessequals(V_k,V_m,tc_nat) % 0.54/0.76 | V_m = V_n ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_rtranclp__converseD_0,axiom, % 0.54/0.76 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_x)) % 0.54/0.76 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y)) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_rtranclp__converseI_0,axiom, % 0.54/0.76 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y)) % 0.54/0.76 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_x)) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_Snoc__step1__SnocD_1,axiom, % 0.54/0.76 ( hBOOL(hAPP(hAPP(V_r,V_y),V_x)) % 0.54/0.76 | c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a) % 0.54/0.76 | ~ c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_diff__cancel2_0,axiom, % 0.54/0.76 c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_diff__cancel_0,axiom, % 0.54/0.76 c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_min__max_Oless__supI1_0,axiom, % 0.54/0.76 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.76 | c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 0.54/0.76 | ~ c_HOL_Oord__class_Oless(V_x,V_a,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_min__max_Oless__supI2_0,axiom, % 0.54/0.76 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.76 | c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 0.54/0.76 | ~ c_HOL_Oord__class_Oless(V_x,V_b,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_less__max__iff__disj_1,axiom, % 0.54/0.76 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.76 | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 0.54/0.76 | ~ c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_less__max__iff__disj_2,axiom, % 0.54/0.76 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.76 | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 0.54/0.76 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_max__less__iff__conj_0,axiom, % 0.54/0.76 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.76 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.54/0.76 | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_max__less__iff__conj_1,axiom, % 0.54/0.76 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.76 | c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.54/0.76 | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_listsum_Osimps_I1_J_0,axiom, % 0.54/0.76 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.54/0.76 | c_List_Olistsum(c_List_Olist_ONil(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_diff__le__self_0,axiom, % 0.54/0.76 c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_typing_OVar_0,axiom, % 0.54/0.76 c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_add__neg__neg_0,axiom, % 0.54/0.76 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.54/0.76 | 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) % 0.54/0.76 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.54/0.76 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_power__strict__mono_0,axiom, % 0.54/0.76 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.54/0.76 | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) % 0.54/0.76 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.54/0.76 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.54/0.76 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_append__eq__Cons__conv_5,axiom, % 0.54/0.76 c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_append__Cons_0,axiom, % 0.54/0.76 c_List_Oappend(c_List_Olist_OCons(V_x,V_xs,T_a),V_ys,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xs,V_ys,T_a),T_a) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_rtrancl__beta__AppR_0,axiom, % 0.54/0.76 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t_H))) % 0.54/0.76 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_rtrancl__beta__AppL_0,axiom, % 0.54/0.76 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s_H),V_t))) % 0.54/0.76 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_Nat_Odiff__diff__eq_0,axiom, % 0.54/0.76 ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) % 0.54/0.76 | ~ c_lessequals(V_k,V_n,tc_nat) % 0.54/0.76 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_diff__commute_0,axiom, % 0.54/0.76 c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_k,tc_nat),V_j,tc_nat) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_map__eq__Cons__conv_3,axiom, % 0.54/0.76 c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xa,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xa,T_b,T_a),T_a) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_Cons__eq__map__conv_3,axiom, % 0.54/0.76 c_List_Olist_OCons(hAPP(V_f,V_xa),c_List_Omap(V_f,V_xb,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Olist_OCons(V_xa,V_xb,T_b),T_b,T_a) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_map_Osimps_I2_J_0,axiom, % 0.54/0.76 c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_add__nonneg__pos_0,axiom, % 0.54/0.76 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.54/0.76 | 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) % 0.54/0.76 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.54/0.76 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_add__pos__nonneg_0,axiom, % 0.54/0.76 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.54/0.76 | 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) % 0.54/0.76 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.54/0.76 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_diff__less__mono_0,axiom, % 0.54/0.76 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_c,tc_nat),c_HOL_Ominus__class_Ominus(V_b,V_c,tc_nat),tc_nat) % 0.54/0.76 | ~ c_lessequals(V_c,V_a,tc_nat) % 0.54/0.76 | ~ c_HOL_Oord__class_Oless(V_a,V_b,tc_nat) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_natgb_Oadd__cancel_0,axiom, % 0.54/0.76 ( 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) % 0.54/0.76 | V_y = V_z ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_nat__add__right__cancel_0,axiom, % 0.54/0.76 ( 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) % 0.54/0.76 | V_m = V_n ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_nat__add__left__cancel_0,axiom, % 0.54/0.76 ( 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) % 0.54/0.76 | V_m = V_n ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_class__ringb_Oadd__cancel_0,axiom, % 0.54/0.76 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.54/0.76 | ~ class_Int_Onumber__ring(T_a) % 0.54/0.76 | 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) % 0.54/0.76 | V_y = V_z ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_add__imp__eq_0,axiom, % 0.54/0.76 ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a) % 0.54/0.76 | 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) % 0.54/0.76 | V_b = V_c ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_add__left__cancel_0,axiom, % 0.54/0.76 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 0.54/0.76 | 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) % 0.54/0.76 | V_b = V_c ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_add__right__cancel_0,axiom, % 0.54/0.76 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 0.54/0.76 | 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) % 0.54/0.76 | V_b = V_c ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_Cons__eq__append__conv_5,axiom, % 0.54/0.76 c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_Cons__eq__appendI_0,axiom, % 0.54/0.76 c_List_Olist_OCons(V_x,c_List_Oappend(V_xs1,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xs1,T_a),V_zs,T_a) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_le__add__diff_0,axiom, % 0.54/0.76 ( c_lessequals(V_m,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_k,tc_nat),tc_nat) % 0.54/0.76 | ~ c_lessequals(V_k,V_n,tc_nat) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_neq__Nil__conv_1,axiom, % 0.54/0.76 c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_list_Osimps_I3_J_0,axiom, % 0.54/0.76 c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_gb__semiring_Opwr__mul_0,axiom, % 0.54/0.76 ( hAPP(hAPP(V_pwr,hAPP(hAPP(V_mul,V_x),V_y)),V_q) = hAPP(hAPP(V_mul,hAPP(hAPP(V_pwr,V_x),V_q)),hAPP(hAPP(V_pwr,V_y),V_q)) % 0.54/0.76 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_gb__semiring_Omul__d_0,axiom, % 0.54/0.76 ( hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_add,V_y),V_z)) = hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_x),V_y)),hAPP(hAPP(V_mul,V_x),V_z)) % 0.54/0.76 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_gb__semiring_Omul__c_0,axiom, % 0.54/0.76 ( hAPP(hAPP(V_mul,V_x),V_y) = hAPP(hAPP(V_mul,V_y),V_x) % 0.54/0.76 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_gb__semiring_Omul__a_0,axiom, % 0.54/0.76 ( hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_mul,V_y),V_z)) = hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_x),V_y)),V_z) % 0.54/0.76 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_gb__semiring_Omul__1_0,axiom, % 0.54/0.76 ( hAPP(hAPP(V_mul,V_r1),V_x) = V_x % 0.54/0.76 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_gb__semiring_Omul__0_0,axiom, % 0.54/0.76 ( hAPP(hAPP(V_mul,V_r0),V_x) = V_r0 % 0.54/0.76 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_gb__semiring_Oadd__c_0,axiom, % 0.54/0.76 ( hAPP(hAPP(V_add,V_x),V_y) = hAPP(hAPP(V_add,V_y),V_x) % 0.54/0.76 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_gb__semiring_Oadd__a_0,axiom, % 0.54/0.76 ( hAPP(hAPP(V_add,V_x),hAPP(hAPP(V_add,V_y),V_z)) = hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_x),V_y)),V_z) % 0.54/0.76 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_gb__semiring_Oadd__0_0,axiom, % 0.54/0.76 ( hAPP(hAPP(V_add,V_r0),V_x) = V_x % 0.54/0.76 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_gb__semiring_Osemiring__rules_I25_J_0,axiom, % 0.54/0.76 ( hAPP(hAPP(V_add,V_a),hAPP(hAPP(V_add,V_c),V_d)) = hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_c)),V_d) % 0.54/0.76 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_even__less__0__iff_0,axiom, % 0.54/0.76 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.54/0.76 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.54/0.76 | ~ 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) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_even__less__0__iff_1,axiom, % 0.54/0.76 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.54/0.76 | 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) % 0.54/0.76 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.54/0.76 % 0.54/0.76 cnf(cls_power__less__imp__less__base_0,axiom, % 0.54/0.76 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.54/0.76 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.54/0.77 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_min__max_Ole__sup__iff_1,axiom, % 0.54/0.77 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.77 | c_lessequals(V_y,V_z,T_a) % 0.54/0.77 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_min__max_Ole__sup__iff_0,axiom, % 0.54/0.77 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.77 | c_lessequals(V_x,V_z,T_a) % 0.54/0.77 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_le__max__iff__disj_2,axiom, % 0.54/0.77 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.77 | c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 0.54/0.77 | ~ c_lessequals(V_z,V_y,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_le__max__iff__disj_1,axiom, % 0.54/0.77 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.77 | c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) % 0.54/0.77 | ~ c_lessequals(V_z,V_x,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_min__max_Ole__supI2_0,axiom, % 0.54/0.77 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.77 | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 0.54/0.77 | ~ c_lessequals(V_x,V_b,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_min__max_Ole__supI1_0,axiom, % 0.54/0.77 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.77 | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a) % 0.54/0.77 | ~ c_lessequals(V_x,V_a,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_min__max_Ole__supE_1,axiom, % 0.54/0.77 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.77 | c_lessequals(V_b,V_x,T_a) % 0.54/0.77 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_min__max_Ole__supE_0,axiom, % 0.54/0.77 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.77 | c_lessequals(V_a,V_x,T_a) % 0.54/0.77 | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_le__diff__conv_0,axiom, % 0.54/0.77 ( c_lessequals(V_j,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),tc_nat) % 0.54/0.77 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_le__diff__conv_1,axiom, % 0.54/0.77 ( c_lessequals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) % 0.54/0.77 | ~ c_lessequals(V_j,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_zero__less__power_0,axiom, % 0.54/0.77 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.54/0.77 | 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) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_less__max__iff__disj_0,axiom, % 0.54/0.77 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.77 | c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.54/0.77 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_shift__eq_0,axiom, % 0.54/0.77 hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ). % 0.54/0.77 % 0.54/0.77 cnf(cls_substn_Osimps_I1_J_2,axiom, % 0.54/0.77 ( c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_i),V_s,V_k) = c_Lambda_OdB_OVar(V_i) % 0.54/0.77 | V_i = V_k % 0.54/0.77 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_Nil__is__append__conv_0,axiom, % 0.54/0.77 ( c_List_Olist_ONil(T_a) != c_List_Oappend(V_xs,V_ys,T_a) % 0.54/0.77 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_Nil__is__append__conv_1,axiom, % 0.54/0.77 ( c_List_Olist_ONil(T_a) != c_List_Oappend(V_xs,V_ys,T_a) % 0.54/0.77 | V_ys = c_List_Olist_ONil(T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_dB_Osimps_I3_J_0,axiom, % 0.54/0.77 ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H) % 0.54/0.77 | V_dB = V_dB_H ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_append__is__Nil__conv_0,axiom, % 0.54/0.77 ( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Olist_ONil(T_a) % 0.54/0.77 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_append__is__Nil__conv_1,axiom, % 0.54/0.77 ( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Olist_ONil(T_a) % 0.54/0.77 | V_ys = c_List_Olist_ONil(T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_conversep__eq_0,axiom, % 0.54/0.77 c_Predicate_Oconversep(c_fequal(T_a),T_a,T_a) = c_fequal(T_a) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_add__nonpos__neg_0,axiom, % 0.54/0.77 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.54/0.77 | 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) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.54/0.77 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_add__neg__nonpos_0,axiom, % 0.54/0.77 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.54/0.77 | 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) % 0.54/0.77 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_dB_Orecs_I1_J_0,axiom, % 0.54/0.77 c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_diff__add__assoc_0,axiom, % 0.54/0.77 ( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_k,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)) % 0.54/0.77 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_diff__add__assoc2_0,axiom, % 0.54/0.77 ( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_k,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),V_i) % 0.54/0.77 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_diff__diff__right_0,axiom, % 0.54/0.77 ( c_HOL_Ominus__class_Ominus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat) % 0.54/0.77 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_less__imp__diff__less_0,axiom, % 0.54/0.77 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_empty__replicate_1,axiom, % 0.54/0.77 c_List_Olist_ONil(T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_less__le__not__le_2,axiom, % 0.54/0.77 ( ~ class_Orderings_Opreorder(T_a) % 0.54/0.77 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.54/0.77 | c_lessequals(V_y,V_x,T_a) % 0.54/0.77 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_nat__less__le_1,axiom, % 0.54/0.77 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_less__not__refl_0,axiom, % 0.54/0.77 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_order__less__le_1,axiom, % 0.54/0.77 ( ~ class_Orderings_Oorder(T_a) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_linorder__neq__iff_1,axiom, % 0.54/0.77 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_order__less__irrefl_0,axiom, % 0.54/0.77 ( ~ class_Orderings_Opreorder(T_a) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_le__imp__diff__is__add_1,axiom, % 0.54/0.77 ( ~ c_lessequals(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_i),tc_nat) % 0.54/0.77 | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_i),V_i,tc_nat) = V_k ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_liftn_Osimps_I1_J_1,axiom, % 0.54/0.77 ( c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_n)) % 0.54/0.77 | c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_lift__preserves__beta_H_0,axiom, % 0.54/0.77 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,V_r),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i))) % 0.54/0.77 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_add__pos__pos_0,axiom, % 0.54/0.77 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.54/0.77 | 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) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_le__add1_0,axiom, % 0.54/0.77 c_lessequals(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),tc_nat) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_le__add2_0,axiom, % 0.54/0.77 c_lessequals(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_le__iff__add_1,axiom, % 0.54/0.77 c_lessequals(V_m,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_x),tc_nat) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_Cons__step1__Cons_3,axiom, % 0.54/0.77 ( c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a) % 0.54/0.77 | V_xs = V_ys % 0.54/0.77 | ~ c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_nat__minus__add__max_0,axiom, % 0.54/0.77 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat)),V_m) = c_Orderings_Oord__class_Omax(V_n,V_m,tc_nat) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_semigroup__add_Oadd__assoc_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_plus,hAPP(hAPP(V_plus,V_a),V_b)),V_c) = hAPP(hAPP(V_plus,V_a),hAPP(hAPP(V_plus,V_b),V_c)) % 0.54/0.77 | ~ c_OrderedGroup_Osemigroup__add(V_plus,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_listsum_Osimps_I2_J_0,axiom, % 0.54/0.77 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.54/0.77 | c_List_Olistsum(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Olistsum(V_xs,T_a)) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_map__append_0,axiom, % 0.54/0.77 c_List_Omap(V_f,c_List_Oappend(V_xs,V_ys,T_b),T_b,T_a) = c_List_Oappend(c_List_Omap(V_f,V_xs,T_b,T_a),c_List_Omap(V_f,V_ys,T_b,T_a),T_a) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_linorder__neqE__ordered__idom_0,axiom, % 0.54/0.77 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.54/0.77 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.54/0.77 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.54/0.77 | V_x = V_y ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_not__less__iff__gr__or__eq_0,axiom, % 0.54/0.77 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.77 | V_x = V_y % 0.54/0.77 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.54/0.77 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_le__antisym_0,axiom, % 0.54/0.77 ( V_m = V_n % 0.54/0.77 | ~ c_lessequals(V_n,V_m,tc_nat) % 0.54/0.77 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_nat__neq__iff_0,axiom, % 0.54/0.77 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 0.54/0.77 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.54/0.77 | V_m = V_n ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_nat__less__cases_0,axiom, % 0.54/0.77 ( hBOOL(hAPP(hAPP(V_P,V_n),V_m)) % 0.54/0.77 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 0.54/0.77 | V_m = V_n % 0.54/0.77 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_linorder__neqE__nat_0,axiom, % 0.54/0.77 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat) % 0.54/0.77 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 0.54/0.77 | V_x = V_y ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_order__eq__iff_2,axiom, % 0.54/0.77 ( ~ class_Orderings_Oorder(T_a) % 0.54/0.77 | V_x = V_y % 0.54/0.77 | ~ c_lessequals(V_y,V_x,T_a) % 0.54/0.77 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_linorder__neqE_0,axiom, % 0.54/0.77 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.77 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.54/0.77 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.54/0.77 | V_x = V_y ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_order__antisym_0,axiom, % 0.54/0.77 ( ~ class_Orderings_Oorder(T_a) % 0.54/0.77 | V_x = V_y % 0.54/0.77 | ~ c_lessequals(V_y,V_x,T_a) % 0.54/0.77 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_order__antisym__conv_0,axiom, % 0.54/0.77 ( ~ class_Orderings_Oorder(T_a) % 0.54/0.77 | V_x = V_y % 0.54/0.77 | ~ c_lessequals(V_x,V_y,T_a) % 0.54/0.77 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_append__replicate__commute_0,axiom, % 0.54/0.77 c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oappend(c_List_Oreplicate(V_k,V_x,T_a),c_List_Oreplicate(V_n,V_x,T_a),T_a) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_linorder__less__linear_0,axiom, % 0.54/0.77 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.77 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.54/0.77 | V_x = V_y % 0.54/0.77 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_linorder__antisym__conv3_0,axiom, % 0.54/0.77 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.77 | V_x = V_y % 0.54/0.77 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.54/0.77 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_le__iff__diff__le__0_1,axiom, % 0.54/0.77 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.54/0.77 | c_lessequals(V_a,V_b,T_a) % 0.54/0.77 | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_le__iff__diff__le__0_0,axiom, % 0.54/0.77 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.54/0.77 | c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.54/0.77 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_min__max_Osup__idem_0,axiom, % 0.54/0.77 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.77 | c_Orderings_Oord__class_Omax(V_x,V_x,T_a) = V_x ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_add__strict__mono_0,axiom, % 0.54/0.77 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.54/0.77 | 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) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_add__less__mono_0,axiom, % 0.54/0.77 ( 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) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_termination__basic__simps_I5_J_0,axiom, % 0.54/0.77 ( c_lessequals(V_x,V_y,tc_nat) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_nat__less__le_0,axiom, % 0.54/0.77 ( c_lessequals(V_m,V_n,tc_nat) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_order__le__less_1,axiom, % 0.54/0.77 ( ~ class_Orderings_Oorder(T_a) % 0.54/0.77 | c_lessequals(V_x,V_y,T_a) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_order__less__imp__le_0,axiom, % 0.54/0.77 ( ~ class_Orderings_Opreorder(T_a) % 0.54/0.77 | c_lessequals(V_x,V_y,T_a) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_list_Osimps_I2_J_0,axiom, % 0.54/0.77 c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_beta__cases_I1_J_0,axiom, % 0.54/0.77 ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_less__iff__diff__less__0_1,axiom, % 0.54/0.77 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.54/0.77 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_less__iff__diff__less__0_0,axiom, % 0.54/0.77 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.54/0.77 | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_of__nat__less__iff_1,axiom, % 0.54/0.77 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.54/0.77 | 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) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_of__nat__less__iff_0,axiom, % 0.54/0.77 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.54/0.77 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.54/0.77 | ~ 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) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_add__le__cancel__right_1,axiom, % 0.54/0.77 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.54/0.77 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) % 0.54/0.77 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_add__le__cancel__right_0,axiom, % 0.54/0.77 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.54/0.77 | c_lessequals(V_a,V_b,T_a) % 0.54/0.77 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_add__le__cancel__left_1,axiom, % 0.54/0.77 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.54/0.77 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a) % 0.54/0.77 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_add__le__cancel__left_0,axiom, % 0.54/0.77 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.54/0.77 | c_lessequals(V_a,V_b,T_a) % 0.54/0.77 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_add__right__mono_0,axiom, % 0.54/0.77 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 0.54/0.77 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) % 0.54/0.77 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_add__left__mono_0,axiom, % 0.54/0.77 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) % 0.54/0.77 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a) % 0.54/0.77 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_add__le__mono1_0,axiom, % 0.54/0.77 ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k),tc_nat) % 0.54/0.77 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_nat__add__left__cancel__le_0,axiom, % 0.54/0.77 ( c_lessequals(V_m,V_n,tc_nat) % 0.54/0.77 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_nat__add__left__cancel__le_1,axiom, % 0.54/0.77 ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat) % 0.54/0.77 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_le__imp__diff__is__add_0,axiom, % 0.54/0.77 ( ~ c_lessequals(V_i,V_j,tc_nat) % 0.54/0.77 | V_j = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat)),V_i) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_le__add__diff__inverse_0,axiom, % 0.54/0.77 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) = V_m % 0.54/0.77 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_le__add__diff__inverse2_0,axiom, % 0.54/0.77 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)),V_n) = V_m % 0.54/0.77 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_listsum__foldr_0,axiom, % 0.54/0.77 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.54/0.77 | c_List_Olistsum(V_xs,T_a) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_add__diff__assoc_0,axiom, % 0.54/0.77 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_k,tc_nat) % 0.54/0.77 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_add__diff__assoc2_0,axiom, % 0.54/0.77 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),V_i) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_k,tc_nat) % 0.54/0.77 | ~ c_lessequals(V_k,V_j,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_drop__drop_0,axiom, % 0.54/0.77 c_List_Odrop(V_n,c_List_Odrop(V_m,V_xs,T_a),T_a) = c_List_Odrop(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_xs,T_a) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_replicate__add_0,axiom, % 0.54/0.77 c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_x,T_a) = c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_m,V_x,T_a),T_a) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_of__nat__0__less__iff_1,axiom, % 0.54/0.77 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.54/0.77 | 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) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_of__nat__0__less__iff_0,axiom, % 0.54/0.77 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.54/0.77 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.54/0.77 | ~ 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) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_Snoc__step1__SnocD_2,axiom, % 0.54/0.77 ( V_ys = V_xs % 0.54/0.77 | V_y = V_x % 0.54/0.77 | ~ c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_lift__map_0,axiom, % 0.54/0.77 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) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_replicate__empty_0,axiom, % 0.54/0.77 ( c_List_Oreplicate(V_n,V_x,T_a) != c_List_Olist_ONil(T_a) % 0.54/0.77 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_append__in__listsp__conv_2,axiom, % 0.54/0.77 ( c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a) % 0.54/0.77 | ~ c_List_Olistsp(V_A,V_ys,T_a) % 0.54/0.77 | ~ c_List_Olistsp(V_A,V_xs,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I24_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_add,V_a),V_c) = hAPP(hAPP(V_add,V_c),V_a) % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I23_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_b)),V_c) = hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_c)),V_b) % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I22_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_add,V_a),hAPP(hAPP(V_add,V_c),V_d)) = hAPP(hAPP(V_add,V_c),hAPP(hAPP(V_add,V_a),V_d)) % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I21_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_b)),V_c) = hAPP(hAPP(V_add,V_a),hAPP(hAPP(V_add,V_b),V_c)) % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I20_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_b)),hAPP(hAPP(V_add,V_c),V_d)) = hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_c)),hAPP(hAPP(V_add,V_b),V_d)) % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I19_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_rx),V_ry)) = hAPP(hAPP(V_mul,V_rx),hAPP(hAPP(V_mul,V_lx),V_ry)) % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I18_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_rx),V_ry)) = hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_rx)),V_ry) % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I17_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),V_rx) = hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_ly),V_rx)) % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I16_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),V_rx) = hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_rx)),V_ly) % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I15_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),hAPP(hAPP(V_mul,V_rx),V_ry)) = hAPP(hAPP(V_mul,V_rx),hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),V_ry)) % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I14_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),hAPP(hAPP(V_mul,V_rx),V_ry)) = hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_ly),hAPP(hAPP(V_mul,V_rx),V_ry))) % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I13_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),hAPP(hAPP(V_mul,V_rx),V_ry)) = hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_rx)),hAPP(hAPP(V_mul,V_ly),V_ry)) % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I12_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_mul,V_a),V_r1) = V_a % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I11_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_mul,V_r1),V_a) = V_a % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I10_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_mul,V_a),V_r0) = V_r0 % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I9_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_mul,V_r0),V_a) = V_r0 % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I8_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_b)),V_c) = hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_a),V_c)),hAPP(hAPP(V_mul,V_b),V_c)) % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I7_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_mul,V_a),V_b) = hAPP(hAPP(V_mul,V_b),V_a) % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I6_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_add,V_a),V_r0) = V_a % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I5_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_add,V_r0),V_a) = V_a % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I4_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_add,V_m),V_m) = hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_r1),V_r1)),V_m) % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I3_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_add,V_m),hAPP(hAPP(V_mul,V_a),V_m)) = hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_r1)),V_m) % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I2_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_a),V_m)),V_m) = hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_r1)),V_m) % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_gb__semiring_Osemiring__rules_I1_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_a),V_m)),hAPP(hAPP(V_mul,V_b),V_m)) = hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_b)),V_m) % 0.54/0.77 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_Cons__step1__Cons_0,axiom, % 0.54/0.77 ( V_x = V_y % 0.54/0.77 | hBOOL(hAPP(hAPP(V_r,V_y),V_x)) % 0.54/0.77 | ~ c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom, % 0.54/0.77 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.54/0.77 | 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)) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_rtrancl__beta__App_0,axiom, % 0.54/0.77 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s_H),V_t_H))) % 0.54/0.77 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)) % 0.54/0.77 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_of__nat__less__0__iff_0,axiom, % 0.54/0.77 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.54/0.77 | ~ 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) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_min__max_Osup__commute_0,axiom, % 0.54/0.77 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.77 | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = c_Orderings_Oord__class_Omax(V_y,V_x,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_power__eq__imp__eq__base_0,axiom, % 0.54/0.77 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.54/0.77 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_Power_Opower__class_Opower(V_b,V_n,T_a) % 0.54/0.77 | V_a = V_b % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.54/0.77 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.54/0.77 | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_liftn_Osimps_I1_J_0,axiom, % 0.54/0.77 ( c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(V_i) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_drop__replicate_0,axiom, % 0.54/0.77 c_List_Odrop(V_i,c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(V_k,V_i,tc_nat),V_x,T_a) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_subject__reduction_H_0,axiom, % 0.54/0.77 ( c_Type_Otyping(V_e,V_t_H,V_T) % 0.54/0.77 | ~ c_Type_Otyping(V_e,V_t,V_T) % 0.54/0.77 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_replicate__empty_1,axiom, % 0.54/0.77 c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Olist_ONil(T_a) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_diff__diff__cancel_0,axiom, % 0.54/0.77 ( c_HOL_Ominus__class_Ominus(V_n,c_HOL_Ominus__class_Ominus(V_n,V_i,tc_nat),tc_nat) = V_i % 0.54/0.77 | ~ c_lessequals(V_i,V_n,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_lift_Osimps_I1_J_0,axiom, % 0.54/0.77 ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(V_i)),V_k) = c_Lambda_OdB_OVar(V_i) % 0.54/0.77 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_lift__preserves__beta_0,axiom, % 0.54/0.77 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,V_r),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i))) % 0.54/0.77 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ). % 0.54/0.77 % 0.54/0.77 cnf(cls_not__Cons__self2_0,axiom, % 0.54/0.78 c_List_Olist_OCons(V_x,V_t,T_a) != V_t ). % 0.54/0.78 % 0.54/0.78 cnf(cls_not__Cons__self_0,axiom, % 0.54/0.78 V_xs != c_List_Olist_OCons(V_x,V_xs,T_a) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_substn_Osimps_I1_J_1,axiom, % 0.54/0.78 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 0.54/0.78 | c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_x),V_s,V_x) = c_Lambda_Oliftn(V_x,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_Cons__eq__append__conv_4,axiom, % 0.54/0.78 c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_max__add__distrib__left_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.54/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Orderings_Oord__class_Omax(V_x,V_y,T_a)),V_z) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z),T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_subst__lemma_0,axiom, % 0.54/0.78 ( ~ c_Type_Otyping(V_e_H,V_u,V_U) % 0.54/0.78 | ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T) % 0.54/0.78 | c_Type_Otyping(V_e_H,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),V_T) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_Nil__is__map__conv_1,axiom, % 0.54/0.78 c_List_Olist_ONil(T_a) = c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_Snoc__step1__SnocD_0,axiom, % 0.54/0.78 ( V_ys = V_xs % 0.54/0.78 | c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a) % 0.54/0.78 | ~ c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_min__max_Osup__assoc_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.78 | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_min__max_Osup__left__commute_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.78 | c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omax(V_y,c_Orderings_Oord__class_Omax(V_x,V_z,T_a),T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_Nil__is__append__conv_2,axiom, % 0.54/0.78 c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_of__nat__0__le__iff_0,axiom, % 0.54/0.78 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.54/0.78 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_zero__le__imp__of__nat_0,axiom, % 0.54/0.78 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.54/0.78 | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_rtranclp__idemp_0,axiom, % 0.54/0.78 c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a) = c_Transitive__Closure_Ortranclp(V_r,T_a) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_abs_0,axiom, % 0.54/0.78 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_s)),c_Lambda_OdB_OAbs(V_t))) % 0.54/0.78 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_min__max_Osup__left__idem_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.78 | c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) = c_Orderings_Oord__class_Omax(V_x,V_y,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_replicate__append__same_0,axiom, % 0.54/0.78 c_List_Oappend(c_List_Oreplicate(V_i,V_x,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oreplicate(V_i,V_x,T_a),T_a) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_diff__add__inverse2_0,axiom, % 0.54/0.78 c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),V_n,tc_nat) = V_m ). % 0.54/0.78 % 0.54/0.78 cnf(cls_diff__add__inverse_0,axiom, % 0.54/0.78 c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_n,tc_nat) = V_m ). % 0.54/0.78 % 0.54/0.78 cnf(cls_add__diff__cancel_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.54/0.78 | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_b,T_a) = V_a ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_monoid__add_Oadd__0__right_0,axiom, % 0.54/0.78 ( hAPP(hAPP(V_plus,V_a),V_zero) = V_a % 0.54/0.78 | ~ c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_monoid__add_Oadd__0__left_0,axiom, % 0.54/0.78 ( hAPP(hAPP(V_plus,V_zero),V_a) = V_a % 0.54/0.78 | ~ c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_add__le__less__mono_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.54/0.78 | 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) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 0.54/0.78 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_add__less__le__mono_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.54/0.78 | 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) % 0.54/0.78 | ~ c_lessequals(V_c,V_d,T_a) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_add__gr__0_2,axiom, % 0.54/0.78 ( 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) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_add__gr__0_1,axiom, % 0.54/0.78 ( 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) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.54/0.78 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.54/0.78 | ~ 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) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.54/0.78 | 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) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_power__eq__0__iff_0,axiom, % 0.54/0.78 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 0.54/0.78 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 0.54/0.78 | ~ class_Ring__and__Field_Omult__zero(T_a) % 0.54/0.78 | ~ class_Power_Opower(T_a) % 0.54/0.78 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.54/0.78 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_field__power__not__zero_0,axiom, % 0.54/0.78 ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(T_a) % 0.54/0.78 | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.54/0.78 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_double__eq__0__iff_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.54/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.54/0.78 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_class__ringb_Osubr0__iff_1,axiom, % 0.54/0.78 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.54/0.78 | ~ class_Int_Onumber__ring(T_a) % 0.54/0.78 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_diff__self_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.54/0.78 | c_HOL_Ominus__class_Ominus(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_diff__0__right_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.54/0.78 | c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_right__minus__eq_1,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.54/0.78 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_eq__iff__diff__eq__0_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.54/0.78 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_class__ringb_Oadd__r0__iff_0,axiom, % 0.54/0.78 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.54/0.78 | ~ class_Int_Onumber__ring(T_a) % 0.54/0.78 | V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_a) % 0.54/0.78 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_double__eq__0__iff_1,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.54/0.78 | 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) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_class__ringb_Osubr0__iff_0,axiom, % 0.54/0.78 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.54/0.78 | ~ class_Int_Onumber__ring(T_a) % 0.54/0.78 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.54/0.78 | V_x = V_y ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_right__minus__eq_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.54/0.78 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.54/0.78 | V_a = V_b ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_eq__iff__diff__eq__0_1,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.54/0.78 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.54/0.78 | V_a = V_b ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_class__semiring_Oadd__0_0,axiom, % 0.54/0.78 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.54/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_x) = V_x ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_comm__monoid__add_Omult__1_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.54/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_class__ringb_Oadd__r0__iff_1,axiom, % 0.54/0.78 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.54/0.78 | ~ class_Int_Onumber__ring(T_a) % 0.54/0.78 | V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Ozero__class_Ozero(T_a)) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_comm__monoid__add_Omult__1__right_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.54/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_add__0__left_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.54/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_monoid__add__class_Oadd__0__right_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.54/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom, % 0.54/0.78 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.54/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom, % 0.54/0.78 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.54/0.78 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_le__0__eq_1,axiom, % 0.54/0.78 c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_neq0__conv_1,axiom, % 0.54/0.78 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_liftn__0_0,axiom, % 0.54/0.78 c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k) = V_t ). % 0.54/0.78 % 0.54/0.78 cnf(cls_gr0I_0,axiom, % 0.54/0.78 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.54/0.78 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_diffs0__imp__equal_0,axiom, % 0.54/0.78 ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.54/0.78 | c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.54/0.78 | V_m = V_n ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_le__0__eq_0,axiom, % 0.54/0.78 ( V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 0.54/0.78 | ~ c_lessequals(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_add__is__0_1,axiom, % 0.54/0.78 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.54/0.78 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_add__is__0_0,axiom, % 0.54/0.78 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.54/0.78 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_Nitpick_Onat__case__def_0,axiom, % 0.54/0.78 c_Nat_Onat_Onat__case(V_x,V_f,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = V_x ). % 0.54/0.78 % 0.54/0.78 cnf(cls_nat__case__0_0,axiom, % 0.54/0.78 c_Nat_Onat_Onat__case(V_f1,V_f2,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = V_f1 ). % 0.54/0.78 % 0.54/0.78 cnf(cls_minus__nat_Odiff__0_0,axiom, % 0.54/0.78 c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ). % 0.54/0.78 % 0.54/0.78 cnf(cls_diff__self__eq__0_0,axiom, % 0.54/0.78 c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_natgb_Oadd__r0__iff_0,axiom, % 0.54/0.78 ( V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_a) % 0.54/0.78 | V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_add__eq__self__zero_0,axiom, % 0.54/0.78 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != V_m % 0.54/0.78 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_dB_Orecs_I3_J_0,axiom, % 0.54/0.78 c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(hAPP(V_f3,V_dB),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB,T_a)) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_semigroup__add__class_Oaxioms_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Osemigroup__add(T_a) % 0.54/0.78 | c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(T_a),T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_shift__gt_0,axiom, % 0.54/0.78 ( hAPP(c_Type_Oshift(V_e,V_i,V_T,T_a),V_j) = hAPP(V_e,V_j) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_empty__replicate_0,axiom, % 0.54/0.78 ( c_List_Olist_ONil(T_a) != c_List_Oreplicate(V_n,V_x,T_a) % 0.54/0.78 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_less__diff__iff_0,axiom, % 0.54/0.78 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) % 0.54/0.78 | ~ c_lessequals(V_k,V_n,tc_nat) % 0.54/0.78 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_less__diff__iff_1,axiom, % 0.54/0.78 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.54/0.78 | ~ c_lessequals(V_k,V_n,tc_nat) % 0.54/0.78 | ~ c_lessequals(V_k,V_m,tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_pos__add__strict_0,axiom, % 0.54/0.78 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.54/0.78 | c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_subst__lt_0,axiom, % 0.54/0.78 ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_j)),V_u),V_i) = c_Lambda_OdB_OVar(V_j) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_foldr_Osimps_I2_J_0,axiom, % 0.54/0.78 c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a) = hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a)) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_dB_Osplit_2,axiom, % 0.54/0.78 ( ~ hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),t_a))) % 0.54/0.78 | hBOOL(hAPP(V_P,hAPP(V_f3,V_dB))) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_dB_Osplit__asm_2,axiom, % 0.54/0.78 ( ~ hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_xa),t_a))) % 0.54/0.78 | hBOOL(hAPP(V_P,hAPP(V_f3,V_xa))) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_conversep__conversep_0,axiom, % 0.54/0.78 c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a) = V_r ). % 0.54/0.78 % 0.54/0.78 cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.54/0.78 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.54/0.78 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.54/0.78 | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.54/0.78 | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_not__add__less1_0,axiom, % 0.54/0.78 ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_not__add__less2_0,axiom, % 0.54/0.78 ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_of__nat__diff_0,axiom, % 0.54/0.78 ( ~ class_Ring__and__Field_Oring__1(T_a) % 0.54/0.78 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) % 0.54/0.78 | ~ c_lessequals(V_n,V_m,tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_append__self__conv_0,axiom, % 0.54/0.78 ( c_List_Oappend(V_xs,V_ys,T_a) != V_xs % 0.54/0.78 | V_ys = c_List_Olist_ONil(T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_self__append__conv_0,axiom, % 0.54/0.78 ( V_xs != c_List_Oappend(V_xs,V_ys,T_a) % 0.54/0.78 | V_ys = c_List_Olist_ONil(T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_append__self__conv2_0,axiom, % 0.54/0.78 ( c_List_Oappend(V_xs,V_ys,T_a) != V_ys % 0.54/0.78 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_self__append__conv2_0,axiom, % 0.54/0.78 ( V_ys != c_List_Oappend(V_xs,V_ys,T_a) % 0.54/0.78 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_append__eq__Cons__conv_4,axiom, % 0.54/0.78 c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_less__diff__conv_0,axiom, % 0.54/0.78 ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_less__diff__conv_1,axiom, % 0.54/0.78 ( c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_add__strict__right__mono_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.54/0.78 | 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) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_add__less__cancel__right_1,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.54/0.78 | 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) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_add__less__cancel__right_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.54/0.78 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.54/0.78 | ~ 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) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_add__strict__left__mono_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.54/0.78 | 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) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_add__less__cancel__left_1,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.54/0.78 | 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) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_add__less__cancel__left_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.54/0.78 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.54/0.78 | ~ 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) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_add__less__mono1_0,axiom, % 0.54/0.78 ( 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) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_nat__add__left__cancel__less_0,axiom, % 0.54/0.78 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.54/0.78 | ~ 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) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_nat__add__left__cancel__less_1,axiom, % 0.54/0.78 ( 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) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_xt1_I6_J_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Oorder(T_a) % 0.54/0.78 | c_lessequals(V_z,V_x,T_a) % 0.54/0.78 | ~ c_lessequals(V_z,V_y,T_a) % 0.54/0.78 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_xt1_I7_J_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Oorder(T_a) % 0.54/0.78 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.54/0.78 | ~ c_lessequals(V_z,V_y,T_a) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_xt1_I8_J_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Oorder(T_a) % 0.54/0.78 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.54/0.78 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_add__nonpos__nonpos_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.54/0.78 | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.54/0.78 | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.54/0.78 | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_order__trans_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Opreorder(T_a) % 0.54/0.78 | c_lessequals(V_x,V_z,T_a) % 0.54/0.78 | ~ c_lessequals(V_y,V_z,T_a) % 0.54/0.78 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_le__refl_0,axiom, % 0.54/0.78 c_lessequals(V_n,V_n,tc_nat) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_le__trans_0,axiom, % 0.54/0.78 ( c_lessequals(V_i,V_k,tc_nat) % 0.54/0.78 | ~ c_lessequals(V_j,V_k,tc_nat) % 0.54/0.78 | ~ c_lessequals(V_i,V_j,tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_eq__imp__le_0,axiom, % 0.54/0.78 c_lessequals(V_x,V_x,tc_nat) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_order__eq__iff_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Oorder(T_a) % 0.54/0.78 | c_lessequals(V_x,V_x,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_order__eq__refl_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Opreorder(T_a) % 0.54/0.78 | c_lessequals(V_x,V_x,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_order__le__less__trans_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Opreorder(T_a) % 0.54/0.78 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.54/0.78 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_order__less__le__trans_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Opreorder(T_a) % 0.54/0.78 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.54/0.78 | ~ c_lessequals(V_y,V_z,T_a) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_le__add__right__mono_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.54/0.78 | c_lessequals(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a) % 0.54/0.78 | ~ c_lessequals(V_c,V_d,T_a) % 0.54/0.78 | ~ c_lessequals(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_list_Oinject_0,axiom, % 0.54/0.78 ( c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a) % 0.54/0.78 | V_a = V_a_H ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_list_Oinject_1,axiom, % 0.54/0.78 ( c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a) % 0.54/0.78 | V_list = V_list_H ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_subject__reduction_0,axiom, % 0.54/0.78 ( c_Type_Otyping(V_e,V_t_H,V_T) % 0.54/0.78 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) % 0.54/0.78 | ~ c_Type_Otyping(V_e,V_t,V_T) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_Cons__step1__Cons_1,axiom, % 0.54/0.78 ( c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a) % 0.54/0.78 | hBOOL(hAPP(hAPP(V_r,V_y),V_x)) % 0.54/0.78 | ~ c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_Cons__step1__Cons_5,axiom, % 0.54/0.78 ( c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_x,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) % 0.54/0.78 | ~ c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_nat__diff__split_0,axiom, % 0.54/0.78 ( hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_a,V_b,tc_nat) % 0.54/0.78 | ~ hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(V_a,V_b,tc_nat))) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_dB_Osplit_0,axiom, % 0.54/0.78 ( ~ hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),t_a))) % 0.54/0.78 | hBOOL(hAPP(V_P,hAPP(V_f1,V_nat))) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_dB_Osplit__asm_0,axiom, % 0.54/0.78 ( ~ hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_xd),t_a))) % 0.54/0.78 | hBOOL(hAPP(V_P,hAPP(V_f1,V_xd))) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_dB_Osimps_I1_J_0,axiom, % 0.54/0.78 ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H) % 0.54/0.78 | V_nat = V_nat_H ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_dB_Osimps_I7_J_0,axiom, % 0.54/0.78 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_replicate__app__Cons__same_0,axiom, % 0.54/0.78 c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),V_xs,T_a),T_a) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_zero__less__diff_0,axiom, % 0.54/0.78 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_zero__less__diff_1,axiom, % 0.54/0.78 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_drop__map_0,axiom, % 0.54/0.78 c_List_Odrop(V_n,c_List_Omap(V_f,V_xs,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Odrop(V_n,V_xs,T_b),T_b,T_a) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_of__nat__add_0,axiom, % 0.54/0.78 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.54/0.78 | 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)) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_diff__less_0,axiom, % 0.54/0.78 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_le__eqI_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.54/0.78 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 0.54/0.78 | c_lessequals(V_y_H,V_x_H,T_a) % 0.54/0.78 | ~ c_lessequals(V_y,V_x,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_le__eqI_1,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.54/0.78 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 0.54/0.78 | c_lessequals(V_y,V_x,T_a) % 0.54/0.78 | ~ c_lessequals(V_y_H,V_x_H,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_less__eqI_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.54/0.78 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 0.54/0.78 | c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_less__eqI_1,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.54/0.78 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 0.54/0.78 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_map__is__Nil__conv_0,axiom, % 0.54/0.78 ( c_List_Omap(V_f,V_xs,T_b,T_a) != c_List_Olist_ONil(T_a) % 0.54/0.78 | V_xs = c_List_Olist_ONil(T_b) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_listsum__append_0,axiom, % 0.54/0.78 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.54/0.78 | c_List_Olistsum(c_List_Oappend(V_xs,V_ys,T_a),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_List_Olistsum(V_xs,T_a)),c_List_Olistsum(V_ys,T_a)) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_add__diff__inverse_0,axiom, % 0.54/0.78 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) = V_m % 0.54/0.78 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_append1__eq__conv_0,axiom, % 0.54/0.78 ( c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) != c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a) % 0.54/0.78 | V_xs = V_ys ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_append1__eq__conv_1,axiom, % 0.54/0.78 ( c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) != c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a) % 0.54/0.78 | V_x = V_y ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_uT_0,axiom, % 0.54/0.78 c_Type_Otyping(v_e____,v_u____,v_T____) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_xt1_I11_J_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Oorder(T_a) % 0.54/0.78 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.54/0.78 | V_a = V_b % 0.54/0.78 | ~ c_lessequals(V_b,V_a,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_xt1_I12_J_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Oorder(T_a) % 0.54/0.78 | c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.54/0.78 | ~ c_lessequals(V_b,V_a,T_a) % 0.54/0.78 | V_a = V_b ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_nat__less__le_2,axiom, % 0.54/0.78 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.54/0.78 | V_m = V_n % 0.54/0.78 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_le__eq__less__or__eq_0,axiom, % 0.54/0.78 ( V_m = V_n % 0.54/0.78 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.54/0.78 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_le__neq__implies__less_0,axiom, % 0.54/0.78 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.54/0.78 | V_m = V_n % 0.54/0.78 | ~ c_lessequals(V_m,V_n,tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_order__le__less_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Oorder(T_a) % 0.54/0.78 | V_x = V_y % 0.54/0.78 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.54/0.78 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_order__less__le_2,axiom, % 0.54/0.78 ( ~ class_Orderings_Oorder(T_a) % 0.54/0.78 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.54/0.78 | V_x = V_y % 0.54/0.78 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_order__le__neq__trans_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Oorder(T_a) % 0.54/0.78 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.54/0.78 | V_a = V_b % 0.54/0.78 | ~ c_lessequals(V_a,V_b,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_order__neq__le__trans_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Oorder(T_a) % 0.54/0.78 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.54/0.78 | ~ c_lessequals(V_a,V_b,T_a) % 0.54/0.78 | V_a = V_b ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_linorder__antisym__conv1_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.78 | V_x = V_y % 0.54/0.78 | ~ c_lessequals(V_x,V_y,T_a) % 0.54/0.78 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_linorder__antisym__conv2_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.78 | V_x = V_y % 0.54/0.78 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.54/0.78 | ~ c_lessequals(V_x,V_y,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_append__is__Nil__conv_2,axiom, % 0.54/0.78 c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_lifts__IT_0,axiom, % 0.54/0.78 ( 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) % 0.54/0.78 | ~ c_List_Olistsp(c_InductTermi_OIT,V_ts,tc_Lambda_OdB) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_append__assoc_0,axiom, % 0.54/0.78 c_List_Oappend(c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a) = c_List_Oappend(V_xs,c_List_Oappend(V_ys,V_zs,T_a),T_a) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_append__eq__appendI_0,axiom, % 0.54/0.78 c_List_Oappend(V_xs,c_List_Oappend(V_xs1,V_us,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_xs1,T_a),V_us,T_a) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_append__eq__append__conv2_4,axiom, % 0.54/0.78 c_List_Oappend(c_List_Oappend(V_zs,V_x,T_a),V_ys,T_a) = c_List_Oappend(V_zs,c_List_Oappend(V_x,V_ys,T_a),T_a) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_append__eq__append__conv2_5,axiom, % 0.54/0.78 c_List_Oappend(V_xs,c_List_Oappend(V_x,V_ts,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_x,T_a),V_ts,T_a) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_lift__type_0,axiom, % 0.54/0.78 ( 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) % 0.54/0.78 | ~ c_Type_Otyping(V_e,V_t,V_T) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_xt1_I9_J_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Oorder(T_a) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_converse__rtranclp__into__rtranclp_0,axiom, % 0.54/0.78 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c)) % 0.54/0.78 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_c)) % 0.54/0.78 | ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b)) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_rtranclp_Ortrancl__into__rtrancl_0,axiom, % 0.54/0.78 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c)) % 0.54/0.78 | ~ hBOOL(hAPP(hAPP(V_r,V_b),V_c)) % 0.54/0.78 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_b)) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_not__less__iff__gr__or__eq_1,axiom, % 0.54/0.78 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_nat__le__linear_0,axiom, % 0.54/0.78 ( c_lessequals(V_n,V_m,tc_nat) % 0.54/0.78 | c_lessequals(V_m,V_n,tc_nat) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_accp_Ocases_0,axiom, % 0.54/0.78 ( c_Wellfounded_Oaccp(V_r,V_y,T_a) % 0.54/0.78 | ~ hBOOL(hAPP(hAPP(V_r,V_y),V_a)) % 0.54/0.78 | ~ c_Wellfounded_Oaccp(V_r,V_a,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_linorder__linear_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Olinorder(T_a) % 0.54/0.78 | c_lessequals(V_y,V_x,T_a) % 0.54/0.78 | c_lessequals(V_x,V_y,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_order__less__asym_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Opreorder(T_a) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_accp__downward_0,axiom, % 0.54/0.78 ( c_Wellfounded_Oaccp(V_r,V_a,T_a) % 0.54/0.78 | ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b)) % 0.54/0.78 | ~ c_Wellfounded_Oaccp(V_r,V_b,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_order__less__asym_H_0,axiom, % 0.54/0.78 ( ~ class_Orderings_Opreorder(T_a) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.54/0.78 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_nat_Osplit_0,axiom, % 0.54/0.78 ( ~ hBOOL(hAPP(V_P,c_Nat_Onat_Onat__case(V_f1,V_f2,c_HOL_Ozero__class_Ozero(tc_nat),t_a))) % 0.54/0.78 | hBOOL(hAPP(V_P,V_f1)) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_nat_Oinducts_0,axiom, % 0.54/0.78 ( hBOOL(hAPP(V_P,V_nat)) % 0.54/0.78 | hBOOL(hAPP(V_P,v_sko__Nat__Xnat__Xinducts__1(V_P))) % 0.54/0.78 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_nat__gcd_Osimps_0,axiom, % 0.54/0.78 c_Nitpick_Onat__gcd(V_x,c_HOL_Ozero__class_Ozero(tc_nat)) = V_x ). % 0.54/0.78 % 0.54/0.78 cnf(cls_nat_Osize_I1_J_0,axiom, % 0.54/0.78 c_nat_Onat__size(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_char__size_0,axiom, % 0.54/0.78 c_String_Ochar_Ochar__size(V_c) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_add__is__0_2,axiom, % 0.54/0.78 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) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_nat_Oinduct_0,axiom, % 0.54/0.78 ( hBOOL(hAPP(V_P,V_nat)) % 0.54/0.78 | hBOOL(hAPP(V_P,v_sko__Nat__Xnat__Xinduct__1(V_P))) % 0.54/0.78 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_gr__implies__not0_0,axiom, % 0.54/0.78 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_not__less0_0,axiom, % 0.54/0.78 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_bot__nat__def_0,axiom, % 0.54/0.78 c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_upt_Oinduct_0,axiom, % 0.54/0.78 ( hBOOL(hAPP(V_P,V_nat)) % 0.54/0.78 | hBOOL(hAPP(V_P,v_sko__List__Xupt__Xinduct__1(V_P))) % 0.54/0.78 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_drop__0_0,axiom, % 0.54/0.78 c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),V_xs,T_a) = V_xs ). % 0.54/0.78 % 0.54/0.78 cnf(cls_diff__0__eq__0_0,axiom, % 0.54/0.78 c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_infinite__descent0_1,axiom, % 0.54/0.78 ( hBOOL(hAPP(V_P,V_n)) % 0.54/0.78 | ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(V_P))) % 0.54/0.78 | ~ hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_le0_0,axiom, % 0.54/0.78 c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ). % 0.54/0.78 % 0.54/0.78 cnf(cls_size__char_0,axiom, % 0.54/0.79 c_Nat_Osize__class_Osize(V_c,tc_String_Ochar) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_replicate__eq__replicate_2,axiom, % 0.54/0.79 c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_max__0R_0,axiom, % 0.54/0.79 c_Orderings_Oord__class_Omax(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_n ). % 0.54/0.79 % 0.54/0.79 cnf(cls_max__0L_0,axiom, % 0.54/0.79 c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ). % 0.54/0.79 % 0.54/0.79 cnf(cls_replicate__eq__replicate_1,axiom, % 0.54/0.79 ( c_List_Oreplicate(V_m,V_x,T_a) != c_List_Oreplicate(V_n,V_y,T_a) % 0.54/0.79 | V_x = V_y % 0.54/0.79 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_natgb_Oadd__r0__iff_1,axiom, % 0.54/0.79 V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_plus__nat_Oadd__0_0,axiom, % 0.54/0.79 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n) = V_n ). % 0.54/0.79 % 0.54/0.79 cnf(cls_Nat_Oadd__0__right_0,axiom, % 0.54/0.79 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat)) = V_m ). % 0.54/0.79 % 0.54/0.79 cnf(cls_gb__semiring_Opwr__0_0,axiom, % 0.54/0.79 ( hAPP(hAPP(V_pwr,V_x),c_HOL_Ozero__class_Ozero(tc_nat)) = V_r1 % 0.54/0.79 | ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_foldl__foldr1_0,axiom, % 0.54/0.79 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.54/0.79 | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_xs,T_a,T_a) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_listsum_0,axiom, % 0.54/0.79 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.54/0.79 | c_List_Olistsum(V_xs,T_a) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_xs,T_a,T_a) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_foldl__foldr1__lemma_0,axiom, % 0.54/0.79 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.54/0.79 | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_a,V_xs,T_a,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a)) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_dB_Osimps_I8_J_0,axiom, % 0.54/0.79 hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_dB_Osimps_I9_J_0,axiom, % 0.54/0.79 c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_dB_Osplit__asm_1,axiom, % 0.54/0.79 ( ~ hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_xb),V_xc),t_a))) % 0.54/0.79 | hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_xb),V_xc))) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_dB_Osplit_1,axiom, % 0.54/0.79 ( ~ hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),t_a))) % 0.54/0.79 | hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_dB1),V_dB2))) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_dB_Osimps_I4_J_0,axiom, % 0.54/0.79 c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_lift_Osimps_I2_J_0,axiom, % 0.54/0.79 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)) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_dB_Osimps_I11_J_0,axiom, % 0.54/0.79 c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(V_f2,V_dB1),V_dB2) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_dB_Orecs_I2_J_0,axiom, % 0.54/0.79 c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f2,V_dB1),V_dB2),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB1,T_a)),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB2,T_a)) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_appR_0,axiom, % 0.54/0.79 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_s)),hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_t))) % 0.54/0.79 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_appL_0,axiom, % 0.54/0.79 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_u)),hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u))) % 0.54/0.79 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_liftn_Osimps_I2_J_0,axiom, % 0.54/0.79 c_Lambda_Oliftn(V_n,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(V_n,V_s,V_k)),c_Lambda_Oliftn(V_n,V_t,V_k)) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_substn_Osimps_I2_J_0,axiom, % 0.54/0.79 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)) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_dB_Osimps_I5_J_0,axiom, % 0.54/0.79 hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_substn__subst__n_0,axiom, % 0.54/0.79 c_Lambda_Osubstn(V_t,V_s,V_n) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),c_Lambda_Oliftn(V_n,V_s,c_HOL_Ozero__class_Ozero(tc_nat))),V_n) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_double__induction__lemma_0,axiom, % 0.54/0.79 ( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),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),tc_Lambda_OdB) % 0.54/0.79 | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_s,tc_Lambda_OdB) % 0.54/0.79 | c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),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),tc_Lambda_OdB) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_apps__preserves__beta2_0,axiom, % 0.54/0.79 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),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))) % 0.54/0.79 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_var__app__type__eq_0,axiom, % 0.54/0.79 ( V_T = V_U % 0.54/0.79 | ~ 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) % 0.54/0.79 | ~ 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) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_apps__preserves__betas_0,axiom, % 0.54/0.79 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) % 0.54/0.79 | ~ c_ListOrder_Ostep1(c_Lambda_Obeta,V_rs,V_ss,tc_Lambda_OdB) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_Abs__eq__apps__conv_1,axiom, % 0.54/0.79 ( c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.54/0.79 | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_Var__apps__neq__Abs__apps_0,axiom, % 0.54/0.79 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) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_Var__eq__apps__conv_2,axiom, % 0.54/0.79 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) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_Abs__eq__apps__conv_2,axiom, % 0.54/0.79 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) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_App__eq__foldl__conv_2,axiom, % 0.54/0.79 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB) % 0.54/0.79 | V_r = c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(V_r,V_s,V_t,V_ts),tc_Lambda_OdB,tc_Lambda_OdB) % 0.54/0.79 | V_ts = c_List_Olist_ONil(tc_Lambda_OdB) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_ex__head__tail_0,axiom, % 0.54/0.79 V_t = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(V_t),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(V_t),tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_apps__eq__Abs__conv_1,axiom, % 0.54/0.79 ( c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r) % 0.54/0.79 | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_apps__eq__Abs__conv_2,axiom, % 0.54/0.79 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) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_Var__eq__apps__conv_1,axiom, % 0.54/0.79 ( c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.54/0.79 | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_Abs__App__neq__Var__apps_0,axiom, % 0.54/0.79 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) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_semigroup__add_Ofoldl__assoc_0,axiom, % 0.54/0.79 ( c_List_Ofoldl(V_plus,hAPP(hAPP(V_plus,V_x),V_y),V_zs,T_a,T_a) = hAPP(hAPP(V_plus,V_x),c_List_Ofoldl(V_plus,V_y,V_zs,T_a,T_a)) % 0.54/0.79 | ~ c_OrderedGroup_Osemigroup__add(V_plus,T_a) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_foldl__Nil_0,axiom, % 0.54/0.79 c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a ). % 0.54/0.79 % 0.54/0.79 cnf(cls_foldl__assoc_0,axiom, % 0.54/0.79 ( ~ class_OrderedGroup_Osemigroup__add(T_a) % 0.54/0.79 | 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)) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_monoid__add_Ofoldl__absorb0_0,axiom, % 0.54/0.79 ( hAPP(hAPP(V_plus,V_x),c_List_Ofoldl(V_plus,V_zero,V_zs,T_a,T_a)) = c_List_Ofoldl(V_plus,V_x,V_zs,T_a,T_a) % 0.54/0.79 | ~ c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_foldl__Cons_0,axiom, % 0.54/0.79 c_List_Ofoldl(V_f,V_a,c_List_Olist_OCons(V_x,V_xs,T_b),T_a,T_b) = c_List_Ofoldl(V_f,hAPP(hAPP(V_f,V_a),V_x),V_xs,T_a,T_b) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_foldl__append_0,axiom, % 0.54/0.79 c_List_Ofoldl(V_f,V_a,c_List_Oappend(V_xs,V_ys,T_b),T_a,T_b) = c_List_Ofoldl(V_f,c_List_Ofoldl(V_f,V_a,V_xs,T_a,T_b),V_ys,T_a,T_b) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_subst__map_0,axiom, % 0.54/0.79 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) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_subst__eq_0,axiom, % 0.54/0.79 hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u ). % 0.54/0.79 % 0.54/0.79 cnf(cls_subst__preserves__beta_0,axiom, % 0.54/0.79 ( hBOOL(hAPP(hAPP(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))) % 0.54/0.79 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_subst__lift_0,axiom, % 0.54/0.79 hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k) = V_t ). % 0.54/0.79 % 0.54/0.79 cnf(cls_lift__IT_0,axiom, % 0.54/0.79 ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,V_t),V_i))) % 0.54/0.79 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_Var__IT_0,axiom, % 0.54/0.79 hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_Beta_I6_J_0,axiom, % 0.54/0.79 hBOOL(hAPP(c_InductTermi_OIT,v_ua______)) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_Lambda_0,axiom, % 0.54/0.79 ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r))) % 0.54/0.79 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_r)) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_SI2_0,axiom, % 0.54/0.79 ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),V_u),V_i))) % 0.54/0.79 | ~ c_Type_Otyping(V_e,V_u,v_T____) % 0.54/0.79 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u)) % 0.54/0.79 | ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),v_a____,V_T_H) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_beta_0,axiom, % 0.54/0.79 hBOOL(hAPP(hAPP(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)))) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_IT_OVar_0,axiom, % 0.54/0.79 ( 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))) % 0.54/0.79 | ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_T_0,axiom, % 0.54/0.79 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_power__eq__0__iff_2,axiom, % 0.54/0.79 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 0.54/0.79 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 0.54/0.79 | ~ class_Ring__and__Field_Omult__zero(T_a) % 0.54/0.79 | ~ class_Power_Opower(T_a) % 0.54/0.79 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 0.54/0.79 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_power__0__left_1,axiom, % 0.54/0.79 ( ~ class_Ring__and__Field_Osemiring__0(T_a) % 0.54/0.79 | ~ class_Power_Opower(T_a) % 0.54/0.79 | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) % 0.54/0.79 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_power__eq__0__iff_1,axiom, % 0.54/0.79 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 0.54/0.79 | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) % 0.54/0.79 | ~ class_Ring__and__Field_Omult__zero(T_a) % 0.54/0.79 | ~ class_Power_Opower(T_a) % 0.54/0.79 | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_of__nat__0_0,axiom, % 0.54/0.79 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.54/0.79 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_foldl__absorb0_0,axiom, % 0.54/0.79 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.54/0.79 | 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) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_substn__subst__0_0,axiom, % 0.54/0.79 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)) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_App__eq__foldl__conv_4,axiom, % 0.54/0.79 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) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_Var__apps__eq__Var__apps__conv_0,axiom, % 0.54/0.79 ( 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) % 0.54/0.79 | V_m = V_n ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_Var__apps__eq__Var__apps__conv_1,axiom, % 0.54/0.79 ( 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) % 0.54/0.79 | V_rs = V_ss ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_App__eq__foldl__conv_0,axiom, % 0.54/0.79 ( 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) % 0.54/0.79 | hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = V_t ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_apps__eq__Abs__conv_0,axiom, % 0.54/0.79 ( c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r) % 0.54/0.79 | V_s = c_Lambda_OdB_OAbs(V_r) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_Abs__apps__eq__Abs__apps__conv_0,axiom, % 0.54/0.79 ( 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) % 0.54/0.79 | V_r = V_s ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_Abs__apps__eq__Abs__apps__conv_1,axiom, % 0.54/0.79 ( 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) % 0.54/0.79 | V_rs = V_ss ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_apps__preserves__beta_0,axiom, % 0.54/0.79 ( hBOOL(hAPP(hAPP(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))) % 0.54/0.79 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_Var__eq__apps__conv_0,axiom, % 0.54/0.79 ( c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.54/0.79 | c_Lambda_OdB_OVar(V_m) = V_s ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_Abs__eq__apps__conv_0,axiom, % 0.54/0.79 ( c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.54/0.79 | c_Lambda_OdB_OAbs(V_r) = V_s ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_app__Var__IT_0,axiom, % 0.54/0.79 ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),c_Lambda_OdB_OVar(V_i)))) % 0.54/0.79 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_subst__Var__IT_0,axiom, % 0.54/0.79 ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),c_Lambda_OdB_OVar(V_i)),V_j))) % 0.54/0.79 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_r)) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_SI1_0,axiom, % 0.54/0.79 ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i))) % 0.54/0.79 | ~ c_Type_Otyping(V_e,V_u,v_T____) % 0.54/0.79 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u)) % 0.54/0.79 | ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),V_T_H) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_IT_OBeta_0,axiom, % 0.54/0.79 ( 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))) % 0.54/0.79 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_s)) % 0.54/0.79 | ~ 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))) ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_Beta_I3_J_0,axiom, % 0.54/0.79 hBOOL(hAPP(c_InductTermi_OIT,v_a____)) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_subst__App_0,axiom, % 0.54/0.79 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)) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_Beta_I1_J_0,axiom, % 0.54/0.79 hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_dB_Osimps_I2_J_0,axiom, % 0.54/0.79 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) % 0.54/0.79 | V_dB1 = V_dB1_H ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_dB_Osimps_I2_J_1,axiom, % 0.54/0.79 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) % 0.54/0.79 | V_dB2 = V_dB2_H ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_apps__eq__tail__conv_0,axiom, % 0.54/0.79 ( 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) % 0.54/0.79 | V_r = V_s ) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_uIT_0,axiom, % 0.54/0.79 hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_CHAINED_0,axiom, % 0.54/0.79 c_Type_Otyping(v_e____,v_u____,v_T____) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_CHAINED_0_01,axiom, % 0.54/0.79 hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_CHAINED_0_02,axiom, % 0.54/0.79 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_conjecture_0,negated_conjecture, % 0.54/0.79 ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_fun__Orderings_Opreorder,axiom, % 0.54/0.79 ( class_Orderings_Opreorder(tc_fun(T_2,T_1)) % 0.54/0.79 | ~ class_Orderings_Opreorder(T_1) ) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_fun__Orderings_Oorder,axiom, % 0.54/0.79 ( class_Orderings_Oorder(tc_fun(T_2,T_1)) % 0.54/0.79 | ~ class_Orderings_Oorder(T_1) ) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_fun__Orderings_Obot,axiom, % 0.54/0.79 ( class_Orderings_Obot(tc_fun(T_2,T_1)) % 0.54/0.79 | ~ class_Orderings_Obot(T_1) ) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom, % 0.54/0.79 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom, % 0.54/0.79 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom, % 0.54/0.79 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom, % 0.54/0.79 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 0.54/0.79 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom, % 0.54/0.79 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom, % 0.54/0.79 class_Ring__and__Field_Ono__zero__divisors(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom, % 0.54/0.79 class_Ring__and__Field_Oordered__semidom(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom, % 0.54/0.79 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom, % 0.54/0.79 class_OrderedGroup_Oab__semigroup__add(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom, % 0.54/0.79 class_OrderedGroup_Ocomm__monoid__add(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom, % 0.54/0.79 class_Ring__and__Field_Ozero__neq__one(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__OrderedGroup_Osemigroup__add,axiom, % 0.54/0.79 class_OrderedGroup_Osemigroup__add(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom, % 0.54/0.79 class_Ring__and__Field_Osemiring__1(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom, % 0.54/0.79 class_Ring__and__Field_Osemiring__0(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom, % 0.54/0.79 class_Ring__and__Field_Omult__zero(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom, % 0.54/0.79 class_OrderedGroup_Omonoid__add(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom, % 0.54/0.79 class_Nat_Osemiring__char__0(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__Orderings_Opreorder,axiom, % 0.54/0.79 class_Orderings_Opreorder(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__Orderings_Olinorder,axiom, % 0.54/0.79 class_Orderings_Olinorder(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__Orderings_Oorder,axiom, % 0.54/0.79 class_Orderings_Oorder(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__Orderings_Obot,axiom, % 0.54/0.79 class_Orderings_Obot(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_nat__Power_Opower,axiom, % 0.54/0.79 class_Power_Opower(tc_nat) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_bool__Orderings_Opreorder,axiom, % 0.54/0.79 class_Orderings_Opreorder(tc_bool) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_bool__Orderings_Oorder,axiom, % 0.54/0.79 class_Orderings_Oorder(tc_bool) ). % 0.54/0.79 % 0.54/0.79 cnf(clsarity_bool__Orderings_Obot,axiom, % 0.54/0.79 class_Orderings_Obot(tc_bool) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom, % 0.54/0.79 hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)) ). % 0.54/0.79 % 0.54/0.79 cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom, % 0.54/0.79 ( V_X = V_Y % 0.54/0.79 | ~ hBOOL(hAPP(hAPP(c_fequal(T_a),V_X),V_Y)) ) ). % 0.54/0.79 % 0.54/0.79 %------------------------------------------------------------------------------ % 0.54/0.79 %------------------------------------------- % 0.54/0.79 % Proof found % 0.54/0.79 % SZS status Theorem for theBenchmark % 0.54/0.79 % SZS output start Proof % 0.54/0.79 %ClaNum:785(EqnAxiom:162) % 0.54/0.79 %VarNum:3768(SingletonVarNum:1626) % 0.54/0.79 %MaxLitNum:6 % 0.54/0.79 %MaxfuncDepth:7 % 0.54/0.79 %SharedTerms:88 % 0.54/0.79 %goalClause: 331 % 0.54/0.79 %singleGoalClaCount:1 % 0.54/0.79 [163]P1(a1) % 0.54/0.79 [164]P28(a1) % 0.54/0.79 [165]P28(a2) % 0.54/0.79 [166]P29(a1) % 0.54/0.79 [167]P29(a2) % 0.54/0.79 [168]P2(a1) % 0.54/0.79 [169]P3(a1) % 0.54/0.79 [170]P30(a1) % 0.54/0.79 [171]P24(a1) % 0.54/0.79 [172]P4(a1) % 0.54/0.79 [173]P26(a1) % 0.54/0.79 [174]P26(a2) % 0.54/0.79 [175]P31(a1) % 0.54/0.79 [176]P5(a1) % 0.54/0.79 [177]P16(a1) % 0.54/0.79 [178]P20(a1) % 0.54/0.79 [179]P18(a1) % 0.54/0.79 [180]P19(a1) % 0.54/0.79 [181]P25(a1) % 0.54/0.79 [182]P37(a1) % 0.54/0.79 [183]P33(a1) % 0.54/0.79 [184]P34(a1) % 0.54/0.79 [185]P32(a1) % 0.54/0.79 [186]P27(a1) % 0.54/0.79 [187]P38(a1) % 0.54/0.79 [188]P39(a1) % 0.54/0.79 [199]P6(a52,a48,a50) % 0.54/0.79 [189]E(f3(a1),f8(a1)) % 0.54/0.79 [194]P42(f43(a10,a48)) % 0.54/0.79 [195]P42(f43(a10,a59)) % 0.54/0.79 [196]P42(f43(a10,a49)) % 0.54/0.79 [190]E(f35(f3(a1)),f3(a1)) % 0.54/0.79 [299]P6(f41(a52,a54,a50,a46),f27(a12,f43(f43(f43(a21,a55),a49),f3(a1)),a53,a44,a44),a51) % 0.54/0.79 [298]P6(f41(a52,a54,a50,a46),f27(a12,f43(f43(a12,f14(a55)),a49),a53,a44,a44),a51) % 0.54/0.79 [304]P42(f43(a10,f27(a12,f43(f43(f43(a21,a55),a49),f3(a1)),a53,a44,a44))) % 0.54/0.79 [331]~P42(f43(a10,f43(f43(f43(a21,f27(a12,f43(f43(f43(a21,a55),a49),f3(a1)),a53,a44,a44)),a48),a54))) % 0.54/0.79 [203]P13(x2031,x2031,a1) % 0.54/0.79 [315]~P8(x3151,x3151,a1) % 0.54/0.79 [191]E(f9(x1911,a42),f3(a1)) % 0.54/0.79 [206]E(f5(x2061,x2061,a1),f3(a1)) % 0.54/0.79 [207]P13(f3(a1),x2071,a1) % 0.54/0.79 [319]~P8(x3191,f3(a1),a1) % 0.54/0.79 [192]E(f34(x1921,f3(a1)),x1921) % 0.54/0.79 [197]P42(f43(a10,f11(x1971))) % 0.54/0.79 [201]E(f43(f43(f4(a1),x2011),f3(a1)),x2011) % 0.54/0.79 [208]E(f37(x2081,f3(a1),a1),x2081) % 0.54/0.79 [209]E(f5(x2091,f3(a1),a1),x2091) % 0.54/0.79 [210]E(f37(f3(a1),x2101,a1),x2101) % 0.54/0.79 [214]E(f5(f3(a1),x2141,a1),f3(a1)) % 0.54/0.79 [225]E(f38(f40(x2251),x2251,x2251),f40(x2251)) % 0.54/0.79 [285]E(f27(a12,f22(x2851),f23(x2851),a44,a44),x2851) % 0.54/0.79 [204]E(f43(f43(f4(a1),f3(a1)),x2041),x2041) % 0.54/0.79 [216]P7(x2161,f25(x2162),x2162) % 0.54/0.79 [228]P6(x2281,f11(x2282),f43(x2281,x2282)) % 0.54/0.79 [239]P13(f5(x2391,x2392,a1),x2391,a1) % 0.54/0.79 [309]~E(f11(x3091),f14(x3092)) % 0.54/0.79 [205]E(f36(f36(x2051,x2052),x2052),f36(x2051,x2052)) % 0.54/0.79 [212]E(f15(f3(a1),x2121,x2122),x2121) % 0.54/0.79 [213]E(f16(f3(a1),x2131,x2132),x2131) % 0.54/0.79 [220]E(f20(x2201,f25(x2202),x2202),x2201) % 0.54/0.79 [221]E(f20(f25(x2211),x2212,x2211),x2212) % 0.54/0.79 [223]E(f29(f3(a1),x2231,x2232),f25(x2232)) % 0.54/0.79 [224]E(f15(x2241,f25(x2242),x2242),f25(x2242)) % 0.54/0.79 [269]E(f43(f43(f43(a21,x2691),f16(f3(a1),x2692,f3(a1))),f3(a1)),f43(f43(f43(a21,x2691),x2692),f3(a1))) % 0.54/0.79 [229]E(f43(f43(f4(a1),x2291),x2292),f43(f43(f4(a1),x2292),x2291)) % 0.54/0.79 [230]P42(f43(f43(f40(x2301),x2302),x2302)) % 0.54/0.79 [233]P13(x2331,f43(f43(f4(a1),x2332),x2331),a1) % 0.54/0.79 [235]P13(x2351,f43(f43(f4(a1),x2351),x2352),a1) % 0.54/0.79 [255]E(f43(f43(f4(a1),f5(x2551,x2552,a1)),x2552),f37(x2551,x2552,a1)) % 0.54/0.79 [277]P42(f43(f43(a13,f43(f43(a12,f14(x2771)),x2772)),f43(f43(f43(a21,x2771),x2772),f3(a1)))) % 0.54/0.79 [324]~P42(f43(f43(a13,f11(x3241)),x3242)) % 0.54/0.79 [325]~P8(f43(f43(f4(a1),x3251),x3252),x3252,a1) % 0.54/0.79 [326]~P8(f43(f43(f4(a1),x3261),x3262),x3261,a1) % 0.54/0.79 [231]E(f43(f43(f43(a21,f11(x2311)),x2312),x2311),x2312) % 0.54/0.79 [236]E(f5(f43(f43(f4(a1),x2361),x2362),x2362,a1),x2361) % 0.54/0.79 [237]E(f5(f43(f43(f4(a1),x2371),x2372),x2371,a1),x2372) % 0.54/0.79 [238]E(f5(x2381,f43(f43(f4(a1),x2381),x2382),a1),f3(a1)) % 0.54/0.79 [317]~E(f26(x3171,x3172,x3173),x3172) % 0.54/0.79 [322]~E(f26(x3221,x3222,x3223),f25(x3223)) % 0.54/0.79 [327]~P10(x3271,x3272,f25(x3273),x3273) % 0.54/0.79 [328]~P10(x3281,f25(x3282),x3283,x3282) % 0.54/0.79 [232]E(f29(f3(a1),x2321,x2322),f29(f3(a1),x2323,x2322)) % 0.54/0.79 [240]E(f38(f38(x2401,x2402,x2403),x2403,x2402),x2401) % 0.54/0.79 [247]E(f32(x2471,x2472,f3(a1),x2473),x2471) % 0.54/0.79 [249]E(f30(x2491,f25(x2492),x2492,x2493),f25(x2493)) % 0.54/0.79 [256]E(f5(f5(x2561,x2562,a1),x2563,a1),f5(f5(x2561,x2563,a1),x2562,a1)) % 0.54/0.79 [310]~E(f14(x3101),f43(f43(a12,x3102),x3103)) % 0.54/0.79 [311]~E(f11(x3111),f43(f43(a12,x3112),x3113)) % 0.54/0.79 [312]~E(f43(f43(a12,x3121),x3122),f14(x3123)) % 0.54/0.79 [313]~E(f43(f43(a12,x3131),x3132),f11(x3133)) % 0.54/0.79 [242]P42(f43(f43(f36(x2421,x2422),x2423),x2423)) % 0.54/0.79 [272]E(f20(f29(x2721,x2722,x2723),f26(x2722,f25(x2723),x2723),x2723),f26(x2722,f29(x2721,x2722,x2723),x2723)) % 0.54/0.79 [306]E(f27(a12,f43(f43(a17,x3061),x3062),f30(f6(a17,x3062,a44,a1,a44),x3063,a44,a44),a44,a44),f43(f43(a17,f27(a12,x3061,x3063,a44,a44)),x3062)) % 0.54/0.79 [250]E(f43(f43(f4(a1),x2501),f43(f43(f4(a1),x2502),x2503)),f43(f43(f4(a1),x2502),f43(f43(f4(a1),x2501),x2503))) % 0.54/0.79 [251]E(f5(f43(f43(f4(a1),x2511),x2512),f43(f43(f4(a1),x2513),x2512),a1),f5(x2511,x2513,a1)) % 0.54/0.79 [252]E(f5(f43(f43(f4(a1),x2521),x2522),f43(f43(f4(a1),x2521),x2523),a1),f5(x2522,x2523,a1)) % 0.54/0.79 [253]E(f5(x2531,f43(f43(f4(a1),x2532),x2533),a1),f5(f5(x2531,x2532,a1),x2533,a1)) % 0.54/0.79 [270]E(f43(f43(a12,f43(f43(a17,x2701),x2702)),f43(f43(a17,x2703),x2702)),f43(f43(a17,f43(f43(a12,x2701),x2703)),x2702)) % 0.54/0.79 [266]E(f43(f43(f4(a1),f43(f43(f4(a1),x2661),x2662)),x2663),f43(f43(f4(a1),x2661),f43(f43(f4(a1),x2662),x2663))) % 0.54/0.79 [267]E(f43(f43(f43(a21,f43(f43(a17,x2671),x2672)),x2673),x2672),x2671) % 0.54/0.79 [257]E(f15(x2571,f29(x2572,x2573,x2574),x2574),f29(f5(x2572,x2571,a1),x2573,x2574)) % 0.54/0.79 [263]E(f20(f20(x2631,x2632,x2633),x2634,x2633),f20(x2631,f20(x2632,x2634,x2633),x2633)) % 0.54/0.79 [265]E(f26(x2651,f20(x2652,x2653,x2654),x2654),f20(f26(x2651,x2652,x2654),x2653,x2654)) % 0.54/0.79 [274]E(f43(f41(x2741,x2742,x2743,x2744),x2742),x2743) % 0.54/0.79 [275]E(f20(f29(x2751,x2752,x2753),f29(x2754,x2752,x2753),x2753),f20(f29(x2754,x2752,x2753),f29(x2751,x2752,x2753),x2753)) % 0.54/0.79 [283]E(f27(x2831,x2832,f25(x2833),x2834,x2833),x2832) % 0.54/0.79 [284]E(f28(x2841,f25(x2842),x2843,x2842,x2844),x2843) % 0.54/0.79 [330]~E(f27(a12,f11(x3301),x3302,a44,a44),f27(a12,f14(x3303),x3304,a44,a44)) % 0.54/0.79 [273]E(f43(f43(a12,f16(x2731,x2732,x2733)),f16(x2731,x2734,x2733)),f16(x2731,f43(f43(a12,x2732),x2734),x2733)) % 0.54/0.79 [276]E(f26(x2761,f20(f29(x2762,x2761,x2763),x2764,x2763),x2763),f20(f29(x2762,x2761,x2763),f26(x2761,x2764,x2763),x2763)) % 0.54/0.79 [329]~E(f43(f43(a12,f14(x3291)),x3292),f27(a12,f11(x3293),x3294,a44,a44)) % 0.54/0.79 [254]E(f15(x2541,f15(x2542,x2543,x2544),x2544),f15(f43(f43(f4(a1),x2541),x2542),x2543,x2544)) % 0.54/0.79 [268]E(f20(f29(x2681,x2682,x2683),f29(x2684,x2682,x2683),x2683),f29(f43(f43(f4(a1),x2681),x2684),x2682,x2683)) % 0.54/0.79 [279]E(f43(f43(a12,f43(f43(f43(a21,x2791),x2792),x2793)),f43(f43(f43(a21,x2794),x2792),x2793)),f43(f43(f43(a21,f43(f43(a12,x2791),x2794)),x2792),x2793)) % 0.54/0.79 [307]E(f27(a12,f43(f43(f43(a21,x3071),x3072),x3073),f30(f6(f6(a21,x3072,a44,a44,f47(a1,a44)),x3073,a44,a1,a44),x3074,a44,a44),a44,a44),f43(f43(f43(a21,f27(a12,x3071,x3074,a44,a44)),x3072),x3073)) % 0.54/0.79 [271]E(f30(x2711,f29(x2712,x2713,x2714),x2714,x2715),f29(x2712,f43(x2711,x2713),x2715)) % 0.54/0.79 [278]E(f15(x2781,f30(x2782,x2783,x2784,x2785),x2785),f30(x2782,f15(x2781,x2783,x2784),x2784,x2785)) % 0.54/0.79 [281]E(f30(x2811,f26(x2812,x2813,x2814),x2814,x2815),f26(f43(x2811,x2812),f30(x2811,x2813,x2814,x2815),x2815)) % 0.54/0.79 [282]E(f26(f43(x2821,x2822),f30(x2821,x2823,x2824,x2825),x2825),f30(x2821,f26(x2822,x2823,x2824),x2824,x2825)) % 0.54/0.79 [289]E(f18(x2891,x2892,x2893,f14(x2894),x2895),f43(x2893,x2894)) % 0.54/0.79 [290]E(f18(x2901,x2902,x2903,f11(x2904),x2905),f43(x2901,x2904)) % 0.54/0.79 [291]E(f19(x2911,x2912,x2913,f11(x2914),x2915),f43(x2911,x2914)) % 0.54/0.79 [294]E(f20(f30(x2941,x2942,x2943,x2944),f30(x2941,x2945,x2943,x2944),x2944),f30(x2941,f20(x2942,x2945,x2943),x2943,x2944)) % 0.54/0.79 [300]E(f43(f43(x3001,x3002),f19(x3003,x3004,x3001,x3002,x3005)),f19(x3003,x3004,x3001,f14(x3002),x3005)) % 0.54/0.79 [295]E(f43(f6(x2951,x2952,x2953,x2954,x2955),x2956),f43(f43(x2951,x2956),x2952)) % 0.54/0.79 [301]E(f28(x3011,f26(x3012,x3013,x3014),x3015,x3014,x3016),f43(f43(x3011,x3012),f28(x3011,x3013,x3015,x3014,x3016))) % 0.54/0.79 [302]E(f27(x3021,f27(x3021,x3022,x3023,x3024,x3025),x3026,x3024,x3025),f27(x3021,x3022,f20(x3023,x3026,x3025),x3024,x3025)) % 0.54/0.79 [303]E(f28(x3031,x3032,f28(x3031,x3033,x3034,x3035,x3036),x3035,x3036),f28(x3031,f20(x3032,x3033,x3035),x3034,x3035,x3036)) % 0.54/0.79 [293]E(f18(x2931,x2932,x2933,f43(f43(a12,x2934),x2935),x2936),f43(f43(x2932,x2934),x2935)) % 0.54/0.79 [297]E(f27(x2971,x2972,f26(x2973,x2974,x2975),x2976,x2975),f27(x2971,f43(f43(x2971,x2972),x2973),x2974,x2976,x2975)) % 0.54/0.79 [305]E(f43(f43(f43(f43(x3051,x3052),x3053),f19(x3054,x3051,x3055,x3052,x3056)),f19(x3054,x3051,x3055,x3053,x3056)),f19(x3054,x3051,x3055,f43(f43(a12,x3052),x3053),x3056)) % 0.54/0.79 [334]~P27(x3341)+P11(f4(x3341),x3341) % 0.54/0.79 [341]E(x3411,f3(a1))+P8(f3(a1),x3411,a1) % 0.54/0.79 [366]E(x3661,f3(a1))+~P13(x3661,f3(a1),a1) % 0.54/0.79 [478]P14(f38(a13,a44,a44),x4781,a44)+~P42(f43(a10,x4781)) % 0.54/0.79 [530]~P14(f38(a13,a44,a44),x5301,a44)+P42(f43(a10,x5301)) % 0.54/0.79 [335]~P38(x3351)+E(f33(f3(a1),x3351),f3(x3351)) % 0.54/0.79 [336]~P20(x3361)+E(f31(f25(x3361),x3361),f3(x3361)) % 0.54/0.79 [363]~P22(x3631)+E(f43(f43(f4(x3631),f3(x3631)),f3(x3631)),f3(x3631)) % 0.54/0.79 [364]~P42(f43(a10,x3641))+P42(f43(a10,f14(x3641))) % 0.54/0.79 [736]~P7(a10,x7361,a44)+P7(a10,f30(f6(a17,f3(a1),a44,a1,a44),x7361,a44,a44),a44) % 0.54/0.79 [342]~P28(x3422)+P13(x3421,x3421,x3422) % 0.54/0.79 [343]~P29(x3432)+P13(x3431,x3431,x3432) % 0.54/0.79 [371]~P8(x3712,x3712,x3711)+~P1(x3711) % 0.54/0.79 [372]~P8(x3722,x3722,x3721)+~P28(x3721) % 0.54/0.79 [373]~P8(x3732,x3732,x3731)+~P29(x3731) % 0.54/0.79 [388]P13(x3882,x3881,a1)+P13(x3881,x3882,a1) % 0.54/0.79 [417]~P8(x4171,x4172,a1)+P13(x4171,x4172,a1) % 0.54/0.79 [332]E(x3321,x3322)+~E(f14(x3321),f14(x3322)) % 0.54/0.79 [333]E(x3331,x3332)+~E(f11(x3331),f11(x3332)) % 0.54/0.79 [337]~P28(x3372)+P28(f47(x3371,x3372)) % 0.54/0.79 [338]~P29(x3382)+P29(f47(x3381,x3382)) % 0.54/0.79 [339]~P26(x3392)+P26(f47(x3391,x3392)) % 0.54/0.79 [344]~P1(x3442)+E(f37(x3441,x3441,x3442),x3441) % 0.54/0.79 [346]~P21(x3462)+E(f5(x3461,x3461,x3462),f3(x3462)) % 0.54/0.79 [347]~P17(x3472)+E(f5(x3471,x3471,x3472),f3(x3472)) % 0.54/0.79 [351]~P26(x3511)+P13(f8(x3511),x3512,x3511) % 0.54/0.79 [375]~P30(x3751)+P13(f3(x3751),f33(x3752,x3751),x3751) % 0.54/0.79 [419]~P13(x4191,x4192,a1)+E(f5(x4191,x4192,a1),f3(a1)) % 0.54/0.79 [423]P13(x4231,x4232,a1)+~E(f5(x4231,x4232,a1),f3(a1)) % 0.54/0.79 [424]~P30(x4241)+~P8(f33(x4242,x4241),f3(x4241),x4241) % 0.54/0.79 [517]~P8(x5172,x5171,a1)+P8(f3(a1),f5(x5171,x5172,a1),a1) % 0.54/0.79 [547]P8(x5471,x5472,a1)+~P8(f3(a1),f5(x5472,x5471,a1),a1) % 0.54/0.79 [348]~P4(x3481)+E(f43(f43(f4(x3481),x3482),f3(x3481)),x3482) % 0.54/0.79 [349]~P31(x3491)+E(f43(f43(f4(x3491),x3492),f3(x3491)),x3492) % 0.54/0.79 [350]~P20(x3501)+E(f43(f43(f4(x3501),x3502),f3(x3501)),x3502) % 0.54/0.79 [352]~P21(x3522)+E(f5(x3521,f3(x3522),x3522),x3521) % 0.54/0.79 [484]P8(x4842,x4841,a1)+E(f43(f43(f4(a1),x4841),f5(x4842,x4841,a1)),x4842) % 0.54/0.79 [501]~P42(f43(f43(a13,x5011),x5012))+P42(f43(f43(a13,f14(x5011)),f14(x5012))) % 0.54/0.79 [510]~P13(x5101,x5102,a1)+E(f43(f43(f4(a1),x5101),f5(x5102,x5101,a1)),x5102) % 0.54/0.79 [516]~P13(x5162,x5161,a1)+E(f5(x5161,f5(x5161,x5162,a1),a1),x5162) % 0.54/0.79 [702]~P20(x7021)+E(f28(f4(x7021),x7022,f3(x7021),x7021,x7021),f31(x7022,x7021)) % 0.54/0.79 [703]~P20(x7031)+E(f27(f4(x7031),f3(x7031),x7032,x7031,x7031),f31(x7032,x7031)) % 0.54/0.79 [723]~P20(x7231)+E(f28(f4(x7231),x7232,f3(x7231),x7231,x7231),f27(f4(x7231),f3(x7231),x7232,x7231,x7231)) % 0.54/0.79 [353]~P4(x3531)+E(f43(f43(f4(x3531),f3(x3531)),x3532),x3532) % 0.54/0.79 [355]~P31(x3551)+E(f43(f43(f4(x3551),f3(x3551)),x3552),x3552) % 0.54/0.79 [356]~P20(x3561)+E(f43(f43(f4(x3561),f3(x3561)),x3562),x3562) % 0.54/0.79 [360]E(x3601,f3(a1))+~E(f43(f43(f4(a1),x3602),x3601),x3602) % 0.54/0.79 [361]E(x3611,f3(a1))+~E(f43(f43(f4(a1),x3612),x3611),f3(a1)) % 0.54/0.79 [362]E(x3621,f3(a1))+~E(f43(f43(f4(a1),x3621),x3622),f3(a1)) % 0.54/0.79 [418]~P8(x4181,x4182,a1)+E(f43(f43(a17,f11(x4181)),x4182),f11(x4181)) % 0.54/0.79 [488]~P42(f43(a10,x4881))+P42(f43(a10,f43(f43(a17,x4881),x4882))) % 0.54/0.79 [513]~P42(f43(a10,x5131))+P42(f43(a10,f43(f43(a12,x5131),f11(x5132)))) % 0.54/0.79 [584]~P13(x5842,x5841,a1)+E(f43(f43(f4(a1),f5(x5841,x5842,a1)),x5842),x5841) % 0.54/0.79 [648]P42(f43(f43(f36(a13,a44),f14(x6481)),f14(x6482)))+~P42(f43(f43(f36(a13,a44),x6481),x6482)) % 0.54/0.79 [735]~P7(a10,x7352,a44)+P42(f43(a10,f27(a12,f11(x7351),x7352,a44,a44))) % 0.54/0.79 [369]~E(f20(x3693,x3691,x3692),x3693)+E(x3691,f25(x3692)) % 0.54/0.79 [370]~E(f20(x3701,x3703,x3702),x3703)+E(x3701,f25(x3702)) % 0.54/0.79 [377]~E(f29(x3771,x3772,x3773),f25(x3773))+E(x3771,f3(a1)) % 0.54/0.79 [381]~E(f20(x3813,x3811,x3812),f25(x3812))+E(x3811,f25(x3812)) % 0.54/0.79 [382]~E(f20(x3821,x3823,x3822),f25(x3822))+E(x3821,f25(x3822)) % 0.54/0.79 [392]~P6(x3921,f11(x3922),x3923)+E(f43(x3921,x3922),x3923) % 0.54/0.79 [396]~P1(x3963)+E(f37(x3961,x3962,x3963),f37(x3962,x3961,x3963)) % 0.54/0.79 [446]~P1(x4463)+P13(x4461,f37(x4462,x4461,x4463),x4463) % 0.54/0.79 [447]~P1(x4473)+P13(x4471,f37(x4471,x4472,x4473),x4473) % 0.54/0.79 [514]~P8(x5141,x5143,a1)+P8(f5(x5141,x5142,a1),x5143,a1) % 0.54/0.79 [590]~P13(x5901,x5903,a1)+P13(f5(x5901,x5902,a1),f5(x5903,x5902,a1),a1) % 0.54/0.79 [591]~P13(x5913,x5912,a1)+P13(f5(x5911,x5912,a1),f5(x5911,x5913,a1),a1) % 0.54/0.79 [715]~E(f14(x7152),f27(a12,x7153,x7151,a44,a44))+E(x7151,f25(a44)) % 0.54/0.79 [716]~E(f11(x7162),f27(a12,x7163,x7161,a44,a44))+E(x7161,f25(a44)) % 0.54/0.79 [717]~E(f27(a12,x7172,x7171,a44,a44),f14(x7173))+E(x7171,f25(a44)) % 0.54/0.79 [718]E(x7181,f14(x7182))+~E(f27(a12,x7181,x7183,a44,a44),f14(x7182)) % 0.54/0.79 [719]E(f14(x7191),x7192)+~E(f14(x7191),f27(a12,x7192,x7193,a44,a44)) % 0.54/0.79 [720]E(f11(x7201),x7202)+~E(f11(x7201),f27(a12,x7202,x7203,a44,a44)) % 0.54/0.79 [729]E(x7291,x7292)+~E(f27(a12,x7291,x7293,a44,a44),f27(a12,x7292,x7293,a44,a44)) % 0.54/0.79 [430]~P8(x4302,x4303,a1)+E(f16(x4301,f11(x4302),x4303),f11(x4302)) % 0.54/0.79 [485]~P20(x4851)+E(f43(f43(f4(x4851),x4852),f31(x4853,x4851)),f31(f26(x4852,x4853,x4851),x4851)) % 0.54/0.79 [490]~P1(x4903)+E(f37(x4901,f37(x4901,x4902,x4903),x4903),f37(x4901,x4902,x4903)) % 0.54/0.79 [526]~P20(x5261)+E(f43(f43(f4(x5261),f31(x5262,x5261)),f31(x5263,x5261)),f31(f20(x5262,x5263,x5261),x5261)) % 0.54/0.79 [721]E(f43(f43(a12,x7211),x7212),x7213)+~E(f43(f43(a12,x7211),x7212),f27(a12,x7213,f25(a44),a44,a44)) % 0.54/0.79 [722]~P16(x7221)+E(f28(f4(x7221),x7222,x7223,x7221,x7221),f27(f4(x7221),x7223,x7222,x7221,x7221)) % 0.54/0.79 [782]~P42(f43(f43(a13,x7821),x7823))+P42(f43(f43(a13,f27(a12,x7821,x7822,a44,a44)),f27(a12,x7823,x7822,a44,a44))) % 0.54/0.79 [784]~P10(a13,x7842,x7843,a44)+P42(f43(f43(a13,f27(a12,x7841,x7842,a44,a44)),f27(a12,x7841,x7843,a44,a44))) % 0.54/0.79 [393]~P4(x3931)+E(f43(f43(f4(x3931),x3932),x3933),f43(f43(f4(x3931),x3933),x3932)) % 0.54/0.79 [395]~P31(x3951)+E(f43(f43(f4(x3951),x3952),x3953),f43(f43(f4(x3951),x3953),x3952)) % 0.54/0.79 [426]E(x4261,x4262)+~E(f43(f43(f4(a1),x4263),x4261),f43(f43(f4(a1),x4263),x4262)) % 0.54/0.79 [427]E(x4271,x4272)+~E(f43(f43(f4(a1),x4271),x4273),f43(f43(f4(a1),x4272),x4273)) % 0.54/0.79 [449]E(x4491,x4492)+~P42(f43(f43(f40(x4493),x4491),x4492)) % 0.54/0.79 [492]~P13(x4921,x4923,a1)+P13(x4921,f43(f43(f4(a1),x4922),x4923),a1) % 0.54/0.79 [494]~P13(x4941,x4942,a1)+P13(x4941,f43(f43(f4(a1),x4942),x4943),a1) % 0.54/0.79 [496]~P8(x4961,x4963,a1)+P8(x4961,f43(f43(f4(a1),x4962),x4963),a1) % 0.54/0.79 [498]~P8(x4981,x4982,a1)+P8(x4981,f43(f43(f4(a1),x4982),x4983),a1) % 0.54/0.79 [540]~P21(x5401)+E(f43(f43(f4(x5401),f5(x5402,x5403,x5401)),x5403),x5402) % 0.54/0.79 [541]P13(x5411,x5412,a1)+~P13(f43(f43(f4(a1),x5413),x5411),x5412,a1) % 0.54/0.79 [542]P13(x5421,x5422,a1)+~P13(f43(f43(f4(a1),x5421),x5423),x5422,a1) % 0.54/0.79 [543]P8(x5431,x5432,a1)+~P8(f43(f43(f4(a1),x5431),x5433),x5432,a1) % 0.54/0.79 [562]~P13(x5621,x5623,a1)+P13(f43(f43(f4(a1),x5621),x5622),f43(f43(f4(a1),x5623),x5622),a1) % 0.54/0.79 [563]~P13(x5632,x5633,a1)+P13(f43(f43(f4(a1),x5631),x5632),f43(f43(f4(a1),x5631),x5633),a1) % 0.54/0.79 [564]~P8(x5641,x5643,a1)+P8(f43(f43(f4(a1),x5641),x5642),f43(f43(f4(a1),x5643),x5642),a1) % 0.54/0.79 [565]~P8(x5652,x5653,a1)+P8(f43(f43(f4(a1),x5651),x5652),f43(f43(f4(a1),x5651),x5653),a1) % 0.54/0.79 [618]P8(x6181,f5(x6182,x6183,a1),a1)+~P8(f43(f43(f4(a1),x6181),x6183),x6182,a1) % 0.54/0.79 [619]P13(f5(x6191,x6192,a1),x6193,a1)+~P13(x6191,f43(f43(f4(a1),x6193),x6192),a1) % 0.54/0.79 [622]~P13(f5(x6221,x6223,a1),x6222,a1)+P13(x6221,f43(f43(f4(a1),x6222),x6223),a1) % 0.54/0.79 [623]~P8(x6231,f5(x6233,x6232,a1),a1)+P8(f43(f43(f4(a1),x6231),x6232),x6233,a1) % 0.54/0.79 [635]P13(x6351,x6352,a1)+~P13(f43(f43(f4(a1),x6353),x6351),f43(f43(f4(a1),x6353),x6352),a1) % 0.54/0.79 [636]P8(x6361,x6362,a1)+~P8(f43(f43(f4(a1),x6363),x6361),f43(f43(f4(a1),x6363),x6362),a1) % 0.54/0.79 [675]~P42(f43(f43(a13,x6751),x6753))+P42(f43(f43(a13,f43(f43(a12,x6751),x6752)),f43(f43(a12,x6753),x6752))) % 0.54/0.79 [676]~P42(f43(f43(a13,x6762),x6763))+P42(f43(f43(a13,f43(f43(a12,x6761),x6762)),f43(f43(a12,x6761),x6763))) % 0.54/0.79 [677]~P42(f43(f43(a13,x6771),x6773))+P42(f43(f43(a13,f43(f43(a17,x6771),x6772)),f43(f43(a17,x6773),x6772))) % 0.54/0.79 [687]~P42(f43(f43(f36(a13,a44),x6871),x6873))+P42(f43(f43(f36(a13,a44),f43(f43(a12,x6871),x6872)),f43(f43(a12,x6873),x6872))) % 0.54/0.79 [688]~P42(f43(f43(f36(a13,a44),x6882),x6883))+P42(f43(f43(f36(a13,a44),f43(f43(a12,x6881),x6882)),f43(f43(a12,x6881),x6883))) % 0.54/0.79 [689]~P42(f43(f43(f36(a13,a44),x6891),x6893))+P42(f43(f43(f36(a13,a44),f43(f43(a17,x6891),x6892)),f43(f43(a17,x6893),x6892))) % 0.54/0.79 [711]P42(f43(x7111,x7112))+~P42(f43(x7111,f32(x7112,x7113,f3(a1),a45))) % 0.54/0.79 [725]~P20(x7251)+E(f43(f43(f4(x7251),x7252),f28(f4(x7251),x7253,f3(x7251),x7251,x7251)),f27(f4(x7251),x7252,x7253,x7251,x7251)) % 0.54/0.79 [726]~P20(x7261)+E(f43(f43(f4(x7261),x7262),f27(f4(x7261),f3(x7261),x7263,x7261,x7261)),f27(f4(x7261),x7262,x7263,x7261,x7261)) % 0.54/0.79 [783]P42(f43(f43(f36(a13,a44),f27(a12,x7831,x7832,a44,a44)),f27(a12,x7833,x7832,a44,a44)))+~P42(f43(f43(f36(a13,a44),x7831),x7833)) % 0.54/0.79 [445]~P21(x4451)+E(f5(f43(f43(f4(x4451),x4452),x4453),x4453,x4451),x4452) % 0.54/0.79 [481]~P8(x4811,x4813,a1)+E(f43(f43(f43(a21,f11(x4811)),x4812),x4813),f11(x4811)) % 0.54/0.79 [486]P8(x4862,x4863,a1)+E(f16(x4861,f11(x4862),x4863),f11(f43(f43(f4(a1),x4862),x4861))) % 0.54/0.79 [515]~P38(x5151)+E(f43(f43(f4(x5151),f33(x5152,x5151)),f33(x5153,x5151)),f33(f43(f43(f4(a1),x5152),x5153),x5151)) % 0.54/0.79 [617]~P13(x6173,x6172,a1)+E(f5(f43(f43(f4(a1),x6171),x6172),x6173,a1),f43(f43(f4(a1),x6171),f5(x6172,x6173,a1))) % 0.54/0.79 [620]~P13(x6202,x6203,a1)+E(f5(f43(f43(f4(a1),x6201),x6202),x6203,a1),f5(x6201,f5(x6203,x6202,a1),a1)) % 0.54/0.79 [637]~P13(x6373,x6372,a1)+P13(x6371,f5(f43(f43(f4(a1),x6372),x6371),x6373,a1),a1) % 0.54/0.79 [650]~P42(f43(a10,x6501))+P42(f43(a10,f43(f43(f43(a21,x6501),f11(x6502)),x6503))) % 0.54/0.79 [659]~P13(x6593,x6591,a1)+E(f5(f43(f43(f4(a1),x6591),x6592),x6593,a1),f43(f43(f4(a1),f5(x6591,x6593,a1)),x6592)) % 0.54/0.79 [696]P42(f43(x6961,x6962))+~P42(f43(x6961,f5(f43(f43(f4(a1),x6963),x6962),x6963,a1))) % 0.54/0.79 [452]E(x4521,x4522)+~E(f20(x4523,x4521,x4524),f20(x4523,x4522,x4524)) % 0.54/0.79 [453]E(x4531,x4532)+~E(f20(x4531,x4533,x4534),f20(x4532,x4533,x4534)) % 0.54/0.79 [548]P7(x5481,x5482,x5483)+~P7(x5481,f20(x5484,x5482,x5483),x5483) % 0.54/0.79 [549]P7(x5491,x5492,x5493)+~P7(x5491,f20(x5492,x5494,x5493),x5493) % 0.54/0.79 [627]~E(f30(x6273,x6271,x6272,x6274),f25(x6274))+E(x6271,f25(x6272)) % 0.54/0.79 [402]E(x4021,x4022)+~E(f43(f43(a12,x4023),x4021),f43(f43(a12,x4024),x4022)) % 0.54/0.79 [403]E(x4031,x4032)+~E(f43(f43(a12,x4031),x4033),f43(f43(a12,x4032),x4034)) % 0.54/0.79 [411]~P12(x4112,x4111,x4114)+E(f43(f43(x4111,x4112),x4113),x4113) % 0.54/0.79 [412]~P12(x4123,x4121,x4124)+E(f43(f43(x4121,x4122),x4123),x4122) % 0.54/0.79 [577]~P1(x5774)+E(f37(x5771,f37(x5772,x5773,x5774),x5774),f37(x5772,f37(x5771,x5773,x5774),x5774)) % 0.54/0.79 [578]~P1(x5783)+E(f37(f37(x5781,x5782,x5783),x5784,x5783),f37(x5781,f37(x5782,x5784,x5783),x5783)) % 0.54/0.79 [642]~P23(x6423)+E(f37(f5(x6421,x6422,x6423),f5(x6424,x6422,x6423),x6423),f5(f37(x6421,x6424,x6423),x6422,x6423)) % 0.54/0.79 [731]E(x7311,x7312)+~E(f27(a12,f14(x7313),x7311,a44,a44),f27(a12,f14(x7314),x7312,a44,a44)) % 0.54/0.79 [732]E(x7321,x7322)+~E(f27(a12,f11(x7323),x7321,a44,a44),f27(a12,f11(x7324),x7322,a44,a44)) % 0.54/0.79 [733]E(x7331,x7332)+~E(f27(a12,f14(x7331),x7333,a44,a44),f27(a12,f14(x7332),x7334,a44,a44)) % 0.54/0.79 [734]E(x7341,x7342)+~E(f27(a12,f11(x7341),x7343,a44,a44),f27(a12,f11(x7342),x7344,a44,a44)) % 0.54/0.79 [551]~P42(f43(f43(x5511,x5513),x5514))+P42(f43(f43(f36(x5511,x5512),x5513),x5514)) % 0.54/0.79 [553]~P4(x5531)+E(f43(f43(f4(x5531),x5532),f43(f43(f4(x5531),x5533),x5534)),f43(f43(f4(x5531),x5533),f43(f43(f4(x5531),x5532),x5534))) % 0.54/0.79 [554]~P31(x5541)+E(f43(f43(f4(x5541),x5542),f43(f43(f4(x5541),x5543),x5544)),f43(f43(f4(x5541),x5543),f43(f43(f4(x5541),x5542),x5544))) % 0.54/0.79 [555]~P17(x5551)+E(f43(f43(f4(x5551),x5552),f43(f43(f4(x5551),x5553),x5554)),f43(f43(f4(x5551),x5553),f43(f43(f4(x5551),x5552),x5554))) % 0.54/0.79 [666]~P24(x6661)+E(f37(f43(f43(f4(x6661),x6662),x6663),f43(f43(f4(x6661),x6664),x6663),x6661),f43(f43(f4(x6661),f37(x6662,x6664,x6661)),x6663)) % 0.54/0.79 [701]~P42(f43(f43(a13,x7011),x7014))+P42(f43(f43(a13,f43(f43(f43(a21,x7011),x7012),x7013)),f43(f43(f43(a21,x7014),x7012),x7013))) % 0.54/0.79 [704]~P42(f43(f43(a13,x7042),x7044))+P42(f43(f43(f36(a13,a44),f43(f43(f43(a21,x7041),x7042),x7043)),f43(f43(f43(a21,x7041),x7044),x7043))) % 0.54/0.79 [706]~P42(f43(f43(f36(x7061,x7062),x7064),x7063))+P42(f43(f43(f36(f38(x7061,x7062,x7062),x7062),x7063),x7064)) % 0.54/0.79 [707]~P42(f43(f43(f36(a13,a44),x7071),x7074))+P42(f43(f43(f36(a13,a44),f43(f43(f43(a21,x7071),x7072),x7073)),f43(f43(f43(a21,x7074),x7072),x7073))) % 0.54/0.79 [708]~P42(f43(f43(f36(a13,a44),x7082),x7084))+P42(f43(f43(f36(a13,a44),f43(f43(f43(a21,x7081),x7082),x7083)),f43(f43(f43(a21,x7081),x7084),x7083))) % 0.54/0.79 [714]P42(f43(f43(f36(x7141,x7142),x7143),x7144))+~P42(f43(f43(f36(f38(x7141,x7142,x7142),x7142),x7144),x7143)) % 0.54/0.79 [730]~P27(x7301)+E(f27(f4(x7301),f43(f43(f4(x7301),x7302),x7303),x7304,x7301,x7301),f43(f43(f4(x7301),x7302),f27(f4(x7301),x7303,x7304,x7301,x7301))) % 0.54/0.79 [632]~P4(x6321)+E(f43(f43(f4(x6321),f43(f43(f4(x6321),x6322),x6323)),x6324),f43(f43(f4(x6321),x6322),f43(f43(f4(x6321),x6323),x6324))) % 0.54/0.79 [633]~P31(x6331)+E(f43(f43(f4(x6331),f43(f43(f4(x6331),x6332),x6333)),x6334),f43(f43(f4(x6331),x6332),f43(f43(f4(x6331),x6333),x6334))) % 0.54/0.79 [634]~P16(x6341)+E(f43(f43(f4(x6341),f43(f43(f4(x6341),x6342),x6343)),x6344),f43(f43(f4(x6341),x6342),f43(f43(f4(x6341),x6343),x6344))) % 0.54/0.79 [665]~P31(x6651)+E(f43(f43(f4(x6651),f43(f43(f4(x6651),x6652),x6653)),x6654),f43(f43(f4(x6651),f43(f43(f4(x6651),x6652),x6654)),x6653)) % 0.54/0.79 [451]E(x4511,x4512)+~E(f26(x4513,x4511,x4514),f26(x4515,x4512,x4514)) % 0.54/0.79 [454]E(x4541,x4542)+~E(f26(x4541,x4543,x4544),f26(x4542,x4545,x4544)) % 0.54/0.79 [455]E(x4551,x4552)+~E(f29(x4551,x4553,x4554),f29(x4552,x4555,x4554)) % 0.54/0.79 [690]~P10(x6901,x6902,x6905,x6904)+P10(x6901,f20(x6902,x6903,x6904),f20(x6905,x6903,x6904),x6904) % 0.54/0.79 [691]~P10(x6911,x6913,x6915,x6914)+P10(x6911,f20(x6912,x6913,x6914),f20(x6912,x6915,x6914),x6914) % 0.54/0.79 [692]~P10(x6921,x6923,x6925,x6924)+P10(x6921,f26(x6922,x6923,x6924),f26(x6922,x6925,x6924),x6924) % 0.54/0.79 [671]P10(x6711,f26(x6712,x6713,x6714),f26(x6715,x6713,x6714),x6714)+~P42(f43(f43(x6711,x6712),x6715)) % 0.54/0.79 [672]~P8(x6725,x6722,a1)+E(f43(f41(x6721,x6722,x6723,x6724),x6725),f43(x6721,x6725)) % 0.54/0.79 [682]~P6(x6821,x6824,x6825)+P6(f41(x6821,x6822,x6823,a46),f43(f43(a17,x6824),x6822),x6825) % 0.54/0.79 [727]~P12(x7273,x7271,x7275)+E(f43(f43(x7271,x7272),f27(x7271,x7273,x7274,x7275,x7275)),f27(x7271,x7272,x7274,x7275,x7275)) % 0.54/0.79 [668]E(x6681,x6682)+~E(f20(x6683,f26(x6681,f25(x6684),x6684),x6684),f20(x6685,f26(x6682,f25(x6684),x6684),x6684)) % 0.54/0.79 [669]E(x6691,x6692)+~E(f20(x6691,f26(x6693,f25(x6694),x6694),x6694),f20(x6692,f26(x6695,f25(x6694),x6694),x6694)) % 0.54/0.79 [681]~P42(f43(f43(x6811,x6815),x6814))+P42(f43(f43(f38(x6811,x6812,x6813),x6814),x6815)) % 0.54/0.79 [694]P42(f43(f43(x6941,x6942),x6943))+~P42(f43(f43(f38(x6941,x6944,x6945),x6943),x6942)) % 0.54/0.79 [728]~P11(x7281,x7285)+E(f27(x7281,f43(f43(x7281,x7282),x7283),x7284,x7285,x7285),f43(f43(x7281,x7282),f27(x7281,x7283,x7284,x7285,x7285))) % 0.54/0.79 [739]P42(f43(x7391,f43(x7392,x7393)))+~P42(f43(x7391,f18(x7394,x7395,x7392,f14(x7393),a45))) % 0.54/0.79 [741]P42(f43(x7411,f43(x7412,x7413)))+~P42(f43(x7411,f18(x7412,x7414,x7415,f11(x7413),a45))) % 0.54/0.79 [581]~P11(x5811,x5815)+E(f43(f43(x5811,f43(f43(x5811,x5812),x5813)),x5814),f43(f43(x5811,x5812),f43(f43(x5811,x5813),x5814))) % 0.54/0.79 [683]~P31(x6831)+E(f43(f43(f4(x6831),f43(f43(f4(x6831),x6832),x6833)),f43(f43(f4(x6831),x6834),x6835)),f43(f43(f4(x6831),f43(f43(f4(x6831),x6832),x6834)),f43(f43(f4(x6831),x6833),x6835))) % 0.54/0.79 [744]P42(f43(x7441,f43(f43(x7442,x7443),x7444)))+~P42(f43(x7441,f18(x7445,x7442,x7446,f43(f43(a12,x7443),x7444),a45))) % 0.54/0.79 [746]~P9(x7464,x7461,x7465,x7466,x7462,x7467)+E(f43(f43(x7461,x7462),x7463),x7463) % 0.54/0.79 [747]~P9(x7474,x7471,x7475,x7473,x7476,x7477)+E(f43(f43(x7471,x7472),x7473),x7473) % 0.54/0.79 [749]~P9(x7491,x7494,x7495,x7492,x7496,x7497)+E(f43(f43(x7491,x7492),x7493),x7493) % 0.54/0.79 [750]~P9(x7504,x7501,x7505,x7506,x7503,x7507)+E(f43(f43(x7501,x7502),x7503),x7502) % 0.54/0.79 [752]~P9(x7524,x7521,x7525,x7522,x7526,x7527)+E(f43(f43(x7521,x7522),x7523),x7522) % 0.54/0.79 [753]~P9(x7531,x7534,x7535,x7533,x7536,x7537)+E(f43(f43(x7531,x7532),x7533),x7532) % 0.54/0.79 [754]~P9(x7544,x7545,x7541,x7546,x7543,x7547)+E(f43(f43(x7541,x7542),f3(a1)),x7543) % 0.54/0.79 [759]~P9(x7591,x7593,x7595,x7596,x7594,x7597)+E(f43(f43(x7591,x7592),x7592),f43(f43(x7593,f43(f43(x7591,x7594),x7594)),x7592)) % 0.54/0.79 [756]~P9(x7564,x7561,x7565,x7566,x7567,x7568)+E(f43(f43(x7561,x7562),x7563),f43(f43(x7561,x7563),x7562)) % 0.54/0.79 [758]~P9(x7581,x7584,x7585,x7586,x7587,x7588)+E(f43(f43(x7581,x7582),x7583),f43(f43(x7581,x7583),x7582)) % 0.54/0.79 [762]~P9(x7621,x7623,x7626,x7627,x7625,x7628)+E(f43(f43(x7621,x7622),f43(f43(x7623,x7624),x7622)),f43(f43(x7623,f43(f43(x7621,x7624),x7625)),x7622)) % 0.54/0.79 [769]~P9(x7691,x7692,x7696,x7697,x7695,x7698)+E(f43(f43(x7691,f43(f43(x7692,x7693),x7694)),x7694),f43(f43(x7692,f43(f43(x7691,x7693),x7695)),x7694)) % 0.54/0.79 [760]~P9(x7605,x7601,x7606,x7607,x7608,x7609)+E(f43(f43(x7601,x7602),f43(f43(x7601,x7603),x7604)),f43(f43(x7601,x7603),f43(f43(x7601,x7602),x7604))) % 0.54/0.79 [761]~P9(x7611,x7615,x7616,x7617,x7618,x7619)+E(f43(f43(x7611,x7612),f43(f43(x7611,x7613),x7614)),f43(f43(x7611,x7613),f43(f43(x7611,x7612),x7614))) % 0.54/0.79 [772]~P9(x7721,x7722,x7726,x7727,x7728,x7729)+E(f43(f43(x7721,f43(f43(x7722,x7723),x7724)),f43(f43(x7722,x7723),x7725)),f43(f43(x7722,x7723),f43(f43(x7721,x7724),x7725))) % 0.54/0.79 [767]~P9(x7675,x7671,x7676,x7677,x7678,x7679)+E(f43(f43(x7671,f43(f43(x7671,x7672),x7673)),x7674),f43(f43(x7671,x7672),f43(f43(x7671,x7673),x7674))) % 0.54/0.79 [768]~P9(x7681,x7685,x7686,x7687,x7688,x7689)+E(f43(f43(x7681,f43(f43(x7681,x7682),x7683)),x7684),f43(f43(x7681,x7682),f43(f43(x7681,x7683),x7684))) % 0.54/0.79 [770]~P9(x7705,x7701,x7706,x7707,x7708,x7709)+E(f43(f43(x7701,f43(f43(x7701,x7702),x7703)),x7704),f43(f43(x7701,f43(f43(x7701,x7702),x7704)),x7703)) % 0.54/0.79 [771]~P9(x7711,x7715,x7716,x7717,x7718,x7719)+E(f43(f43(x7711,f43(f43(x7711,x7712),x7713)),x7714),f43(f43(x7711,f43(f43(x7711,x7712),x7714)),x7713)) % 0.54/0.79 [773]~P9(x7736,x7731,x7732,x7737,x7738,x7739)+E(f43(f43(x7731,f43(f43(x7732,x7733),x7734)),f43(f43(x7732,x7733),x7735)),f43(f43(x7732,x7733),f43(f43(f4(a1),x7734),x7735))) % 0.54/0.79 [774]~P9(x7746,x7741,x7742,x7747,x7748,x7749)+E(f43(f43(x7741,f43(f43(x7742,x7743),x7744)),f43(f43(x7742,x7745),x7744)),f43(f43(x7742,f43(f43(x7741,x7743),x7745)),x7744)) % 0.54/0.79 [776]~P9(x7761,x7762,x7766,x7767,x7768,x7769)+E(f43(f43(x7761,f43(f43(x7762,x7763),x7764)),f43(f43(x7762,x7765),x7764)),f43(f43(x7762,f43(f43(x7761,x7763),x7765)),x7764)) % 0.54/0.79 [778]~P9(x7786,x7781,x7787,x7788,x7789,x77810)+E(f43(f43(x7781,f43(f43(x7781,x7782),x7783)),f43(f43(x7781,x7784),x7785)),f43(f43(x7781,f43(f43(x7781,x7782),x7784)),f43(f43(x7781,x7783),x7785))) % 0.54/0.79 [779]~P9(x7791,x7796,x7797,x7798,x7799,x77910)+E(f43(f43(x7791,f43(f43(x7791,x7792),x7793)),f43(f43(x7791,x7794),x7795)),f43(f43(x7791,f43(f43(x7791,x7792),x7794)),f43(f43(x7791,x7793),x7795))) % 0.54/0.79 [476]~P2(x4761)+~P13(f3(x4761),f3(x4761),x4761)+E(f43(f43(f4(x4761),f3(x4761)),f3(x4761)),f3(x4761)) % 0.54/0.79 [391]E(x3911,x3912)+P8(x3912,x3911,a1)+P8(x3911,x3912,a1) % 0.54/0.79 [422]E(x4221,x4222)+P8(x4221,x4222,a1)+~P13(x4221,x4222,a1) % 0.54/0.79 [450]E(x4501,x4502)+~P13(x4502,x4501,a1)+~P13(x4501,x4502,a1) % 0.54/0.79 [357]~P35(x3572)+~P15(x3572)+E(f5(x3571,x3571,x3572),f3(x3572)) % 0.54/0.79 [459]E(x4591,x4592)+~E(f5(x4592,x4591,a1),f3(a1))+~E(f5(x4591,x4592,a1),f3(a1)) % 0.54/0.79 [475]~P30(x4751)+P8(f3(x4751),f33(x4752,x4751),x4751)+~P8(f3(a1),x4752,a1) % 0.54/0.79 [482]~P30(x4822)+~P8(f3(x4822),f33(x4821,x4822),x4822)+P8(f3(a1),x4821,a1) % 0.54/0.79 [580]P8(f5(x5801,x5802,a1),x5801,a1)+~P8(f3(a1),x5802,a1)+~P8(f3(a1),x5801,a1) % 0.54/0.79 [358]~P35(x3581)+~P15(x3581)+E(f43(f43(f4(x3581),x3582),f3(x3581)),x3582) % 0.54/0.79 [413]P42(f43(x4131,x4132))+P42(f43(x4131,f56(x4131)))+~P42(f43(x4131,f3(a1))) % 0.54/0.79 [414]P42(f43(x4141,x4142))+P42(f43(x4141,f57(x4141)))+~P42(f43(x4141,f3(a1))) % 0.54/0.79 [415]P42(f43(x4151,x4152))+P42(f43(x4151,f58(x4151)))+~P42(f43(x4151,f3(a1))) % 0.54/0.79 [434]P8(f3(a1),f7(x4341),a1)+P42(f43(x4341,x4342))+~P42(f43(x4341,f3(a1))) % 0.54/0.79 [443]P42(f43(x4431,x4432))+~P42(f43(x4431,f7(x4431)))+~P42(f43(x4431,f3(a1))) % 0.54/0.79 [383]~P22(x3832)+E(x3831,f3(x3832))+~E(f43(f43(f4(x3832),x3831),x3831),f3(x3832)) % 0.54/0.79 [531]~P22(x5311)+~P13(f3(x5311),x5312,x5311)+P13(f3(x5311),f43(f43(f4(x5311),x5312),x5312),x5311) % 0.54/0.79 [532]~P22(x5321)+~P8(f3(x5321),x5322,x5321)+P8(f3(x5321),f43(f43(f4(x5321),x5322),x5322),x5321) % 0.54/0.79 [533]~P22(x5331)+~P13(x5332,f3(x5331),x5331)+P13(f43(f43(f4(x5331),x5332),x5332),f3(x5331),x5331) % 0.54/0.79 [534]~P22(x5341)+~P8(x5342,f3(x5341),x5341)+P8(f43(f43(f4(x5341),x5342),x5342),f3(x5341),x5341) % 0.54/0.79 [535]~P36(x5351)+~P8(x5352,f3(x5351),x5351)+P8(f43(f43(f4(x5351),x5352),x5352),f3(x5351),x5351) % 0.54/0.79 [570]~P22(x5702)+P13(x5701,f3(x5702),x5702)+~P13(f43(f43(f4(x5702),x5701),x5701),f3(x5702),x5702) % 0.54/0.79 [571]~P22(x5712)+P8(x5711,f3(x5712),x5712)+~P8(f43(f43(f4(x5712),x5711),x5711),f3(x5712),x5712) % 0.54/0.79 [572]~P36(x5722)+P8(x5721,f3(x5722),x5722)+~P8(f43(f43(f4(x5722),x5721),x5721),f3(x5722),x5722) % 0.54/0.79 [573]~P22(x5731)+P13(f3(x5731),x5732,x5731)+~P13(f3(x5731),f43(f43(f4(x5731),x5732),x5732),x5731) % 0.54/0.79 [574]~P22(x5741)+P8(f3(x5741),x5742,x5741)+~P8(f3(x5741),f43(f43(f4(x5741),x5742),x5742),x5741) % 0.54/0.79 [589]P8(f3(a1),x5891,a1)+P8(f3(a1),x5892,a1)+~P8(f3(a1),f43(f43(f4(a1),x5891),x5892),a1) % 0.54/0.79 [397]P13(x3972,x3971,x3973)+~P1(x3973)+P13(x3971,x3972,x3973) % 0.54/0.79 [400]P8(x4002,x4001,x4003)+~P1(x4003)+P13(x4001,x4002,x4003) % 0.54/0.79 [428]~P28(x4283)+~P8(x4281,x4282,x4283)+P13(x4281,x4282,x4283) % 0.54/0.79 [429]~P29(x4293)+~P8(x4291,x4292,x4293)+P13(x4291,x4292,x4293) % 0.54/0.79 [462]~P8(x4623,x4622,x4621)+~P1(x4621)+~P13(x4622,x4623,x4621) % 0.54/0.79 [464]~P8(x4643,x4642,x4641)+~P1(x4641)+~P8(x4642,x4643,x4641) % 0.54/0.79 [465]~P8(x4653,x4652,x4651)+~P28(x4651)+~P8(x4652,x4653,x4651) % 0.54/0.79 [466]~P8(x4663,x4662,x4661)+~P29(x4661)+~P13(x4662,x4663,x4661) % 0.54/0.79 [468]~P8(x4683,x4682,x4681)+~P29(x4681)+~P8(x4682,x4683,x4681) % 0.54/0.79 [489]~P13(x4891,x4893,a1)+P13(x4891,x4892,a1)+~P13(x4893,x4892,a1) % 0.54/0.79 [340]~P5(x3403)+E(x3401,x3402)+~E(f33(x3401,x3403),f33(x3402,x3403)) % 0.54/0.79 [384]~P21(x3843)+E(x3841,x3842)+~E(f5(x3841,x3842,x3843),f3(x3843)) % 0.54/0.79 [385]~P17(x3853)+E(x3851,x3852)+~E(f5(x3851,x3852,x3853),f3(x3853)) % 0.54/0.79 [387]~P40(x3872)+~E(f39(x3871,x3873,x3872),f3(x3872))+E(x3871,f3(x3872)) % 0.54/0.79 [431]~P1(x4313)+~P13(x4311,x4312,x4313)+E(f37(x4311,x4312,x4313),x4312) % 0.54/0.79 [432]~P1(x4323)+~P13(x4322,x4321,x4323)+E(f37(x4321,x4322,x4323),x4321) % 0.54/0.79 [433]~P1(x4333)+P13(x4331,x4332,x4333)+~E(f37(x4331,x4332,x4333),x4332) % 0.54/0.79 [479]~P30(x4792)+~P13(x4791,x4793,a1)+P13(f33(x4791,x4792),f33(x4793,x4792),x4792) % 0.54/0.79 [480]~P30(x4802)+~P8(x4801,x4803,a1)+P8(f33(x4801,x4802),f33(x4803,x4802),x4802) % 0.54/0.79 [499]~P30(x4993)+~P13(f33(x4991,x4993),f33(x4992,x4993),x4993)+P13(x4991,x4992,a1) % 0.54/0.79 [500]~P30(x5003)+~P8(f33(x5001,x5003),f33(x5002,x5003),x5003)+P8(x5001,x5002,a1) % 0.54/0.79 [528]~P23(x5283)+~P13(x5281,x5282,x5283)+P13(f5(x5281,x5282,x5283),f3(x5283),x5283) % 0.54/0.79 [529]~P23(x5293)+~P8(x5291,x5292,x5293)+P8(f5(x5291,x5292,x5293),f3(x5293),x5293) % 0.54/0.79 [538]~P30(x5381)+~P13(f3(x5381),x5382,x5381)+P13(f3(x5381),f39(x5382,x5383,x5381),x5381) % 0.54/0.79 [539]~P30(x5391)+~P8(f3(x5391),x5392,x5391)+P8(f3(x5391),f39(x5392,x5393,x5391),x5391) % 0.54/0.79 [575]~P23(x5753)+P13(x5751,x5752,x5753)+~P13(f5(x5751,x5752,x5753),f3(x5753),x5753) % 0.54/0.79 [576]~P23(x5763)+P8(x5761,x5762,x5763)+~P8(f5(x5761,x5762,x5763),f3(x5763),x5763) % 0.54/0.79 [638]~P13(x6382,x6381,a1)+~P8(x6381,x6383,a1)+P8(f5(x6381,x6382,a1),f5(x6383,x6382,a1),a1) % 0.54/0.79 [639]~P8(x6393,x6392,a1)+~P8(x6393,x6391,a1)+P8(f5(x6391,x6392,a1),f5(x6391,x6393,a1),a1) % 0.54/0.79 [550]~P41(x5502)+~P13(x5503,x5501,a1)+E(f5(f33(x5501,x5502),f33(x5503,x5502),x5502),f33(f5(x5501,x5503,a1),x5502)) % 0.54/0.79 [660]~P13(x6602,x6603,a1)+~P13(x6602,x6601,a1)+E(f5(f5(x6601,x6602,a1),f5(x6603,x6602,a1),a1),f5(x6601,x6603,a1)) % 0.54/0.79 [661]~P8(x6612,x6613,a1)+~P42(f43(x6611,f5(x6612,x6613,a1)))+P42(f43(x6611,f3(a1))) % 0.54/0.79 [552]~P13(x5521,x5522,a1)+~P8(f3(a1),x5523,a1)+P8(x5521,f43(f43(f4(a1),x5522),x5523),a1) % 0.54/0.79 [652]~P13(x6523,x6522,a1)+P13(x6521,f5(x6522,x6523,a1),a1)+~P13(f43(f43(f4(a1),x6521),x6523),x6522,a1) % 0.54/0.79 [657]~P13(x6572,x6573,a1)+~P13(x6571,f5(x6573,x6572,a1),a1)+P13(f43(f43(f4(a1),x6571),x6572),x6573,a1) % 0.54/0.79 [448]E(x4481,x4482)+P8(x4482,x4481,a1)+E(f43(f43(f43(a21,f11(x4481)),x4483),x4482),f11(x4481)) % 0.54/0.79 [737]~P14(f38(a13,a44,a44),x7372,a44)+~P14(f38(a13,a44,a44),f27(a12,f43(f43(f43(a21,x7371),x7372),f3(a1)),x7373,a44,a44),a44)+P14(f38(a13,a44,a44),f27(a12,f43(f43(a12,f14(x7371)),x7372),x7373,a44,a44),a44) % 0.54/0.79 [781]~P42(f43(a10,x7812))+~P42(f43(a10,f27(a12,f43(f43(f43(a21,x7811),x7812),f3(a1)),x7813,a44,a44)))+P42(f43(a10,f27(a12,f43(f43(a12,f14(x7811)),x7812),x7813,a44,a44))) % 0.54/0.79 [469]~P17(x4694)+E(x4691,x4692)+~E(f5(x4693,x4693,x4694),f5(x4691,x4692,x4694)) % 0.54/0.79 [470]~P17(x4703)+E(x4701,x4702)+~E(f5(x4701,x4702,x4703),f5(x4704,x4704,x4703)) % 0.54/0.79 [519]~P1(x5194)+~P13(x5191,x5193,x5194)+P13(x5191,f37(x5192,x5193,x5194),x5194) % 0.54/0.79 [521]~P1(x5214)+~P13(x5211,x5212,x5214)+P13(x5211,f37(x5212,x5213,x5214),x5214) % 0.54/0.79 [523]~P1(x5234)+~P8(x5231,x5233,x5234)+P8(x5231,f37(x5232,x5233,x5234),x5234) % 0.54/0.79 [525]~P1(x5254)+~P8(x5251,x5252,x5254)+P8(x5251,f37(x5252,x5253,x5254),x5254) % 0.54/0.79 [557]~P1(x5573)+P13(x5571,x5572,x5573)+~P13(f37(x5574,x5571,x5573),x5572,x5573) % 0.54/0.79 [559]~P1(x5593)+P13(x5591,x5592,x5593)+~P13(f37(x5591,x5594,x5593),x5592,x5593) % 0.54/0.79 [560]~P1(x5603)+P8(x5601,x5602,x5603)+~P8(f37(x5604,x5601,x5603),x5602,x5603) % 0.54/0.79 [561]~P1(x5613)+P8(x5611,x5612,x5613)+~P8(f37(x5611,x5614,x5613),x5612,x5613) % 0.54/0.79 [579]~P7(x5791,x5793,x5794)+~P7(x5791,x5792,x5794)+P7(x5791,f20(x5792,x5793,x5794),x5794) % 0.54/0.79 [527]P6(x5271,x5272,x5273)+~P6(x5271,x5274,x5273)+~P42(f43(f43(a13,x5274),x5272)) % 0.54/0.79 [537]P14(x5371,x5372,x5373)+~P14(x5371,x5374,x5373)+~P42(f43(f43(x5371,x5372),x5374)) % 0.54/0.79 [724]E(x7241,f25(a44))+E(f27(a12,x7242,f24(x7243,x7244,x7242,x7241),a44,a44),x7243)+~E(f43(f43(a12,x7243),x7244),f27(a12,x7242,x7241,a44,a44)) % 0.54/0.79 [456]~P18(x4563)+E(x4561,x4562)+~E(f43(f43(f4(x4563),x4564),x4561),f43(f43(f4(x4563),x4564),x4562)) % 0.54/0.79 [457]~P19(x4573)+E(x4571,x4572)+~E(f43(f43(f4(x4573),x4574),x4571),f43(f43(f4(x4573),x4574),x4572)) % 0.54/0.79 [458]~P19(x4583)+E(x4581,x4582)+~E(f43(f43(f4(x4583),x4581),x4584),f43(f43(f4(x4583),x4582),x4584)) % 0.54/0.79 [544]~P8(x5444,x5443,a1)+P8(x5441,x5442,a1)+~E(f43(f43(f4(a1),x5441),x5443),f43(f43(f4(a1),x5444),x5442)) % 0.54/0.79 [593]~P3(x5931)+~P13(x5932,x5934,x5931)+P13(f43(f43(f4(x5931),x5932),x5933),f43(f43(f4(x5931),x5934),x5933),x5931) % 0.54/0.79 [594]~P24(x5941)+~P13(x5942,x5944,x5941)+P13(f43(f43(f4(x5941),x5942),x5943),f43(f43(f4(x5941),x5944),x5943),x5941) % 0.54/0.79 [595]~P3(x5951)+~P13(x5953,x5954,x5951)+P13(f43(f43(f4(x5951),x5952),x5953),f43(f43(f4(x5951),x5952),x5954),x5951) % 0.54/0.79 [596]~P24(x5961)+~P13(x5963,x5964,x5961)+P13(f43(f43(f4(x5961),x5962),x5963),f43(f43(f4(x5961),x5962),x5964),x5961) % 0.54/0.79 [597]~P24(x5971)+~P8(x5972,x5974,x5971)+P8(f43(f43(f4(x5971),x5972),x5973),f43(f43(f4(x5971),x5974),x5973),x5971) % 0.54/0.79 [598]~P25(x5981)+~P8(x5982,x5984,x5981)+P8(f43(f43(f4(x5981),x5982),x5983),f43(f43(f4(x5981),x5984),x5983),x5981) % 0.54/0.79 [599]~P24(x5991)+~P8(x5993,x5994,x5991)+P8(f43(f43(f4(x5991),x5992),x5993),f43(f43(f4(x5991),x5992),x5994),x5991) % 0.54/0.79 [600]~P25(x6001)+~P8(x6003,x6004,x6001)+P8(f43(f43(f4(x6001),x6002),x6003),f43(f43(f4(x6001),x6002),x6004),x6001) % 0.54/0.79 [624]P6(x6241,x6242,x6243)+~P6(x6241,x6244,x6243)+~P42(f43(f43(f36(a13,a44),x6244),x6242)) % 0.54/0.79 [628]~P13(x6282,x6284,a1)+~P13(x6281,x6283,a1)+P13(f43(f43(f4(a1),x6281),x6282),f43(f43(f4(a1),x6283),x6284),a1) % 0.54/0.79 [629]~P8(x6292,x6294,a1)+~P8(x6291,x6293,a1)+P8(f43(f43(f4(a1),x6291),x6292),f43(f43(f4(a1),x6293),x6294),a1) % 0.54/0.79 [641]P14(x6411,x6412,x6413)+~P14(x6411,x6414,x6413)+~P42(f43(f43(f36(x6411,x6413),x6412),x6414)) % 0.54/0.79 [653]~P24(x6533)+P13(x6531,x6532,x6533)+~P13(f43(f43(f4(x6533),x6534),x6531),f43(f43(f4(x6533),x6534),x6532),x6533) % 0.54/0.79 [654]~P24(x6543)+P13(x6541,x6542,x6543)+~P13(f43(f43(f4(x6543),x6541),x6544),f43(f43(f4(x6543),x6542),x6544),x6543) % 0.54/0.79 [655]~P24(x6553)+P8(x6551,x6552,x6553)+~P8(f43(f43(f4(x6553),x6554),x6551),f43(f43(f4(x6553),x6554),x6552),x6553) % 0.54/0.79 [656]~P24(x6563)+P8(x6561,x6562,x6563)+~P8(f43(f43(f4(x6563),x6561),x6564),f43(f43(f4(x6563),x6562),x6564),x6563) % 0.54/0.79 [699]~P42(f43(f43(f36(a13,a44),x6991),x6993))+~P42(f43(f43(f36(a13,a44),x6992),x6994))+P42(f43(f43(f36(a13,a44),f43(f43(a12,x6991),x6992)),f43(f43(a12,x6993),x6994))) % 0.54/0.79 [460]E(x4601,x4602)+~E(f29(x4603,x4601,x4604),f29(x4605,x4602,x4604))+E(x4603,f3(a1)) % 0.54/0.79 [742]E(x7421,x7422)+~P6(x7423,f27(a12,f11(x7424),x7425,a44,a44),x7421)+~P6(x7423,f27(a12,f11(x7424),x7425,a44,a44),x7422) % 0.54/0.79 [673]~P42(f43(f43(x6731,x6735),x6734))+~P42(f43(f43(f36(x6731,x6732),x6733),x6735))+P42(f43(f43(f36(x6731,x6732),x6733),x6734)) % 0.54/0.79 [674]~P42(f43(f43(x6741,x6743),x6745))+~P42(f43(f43(f36(x6741,x6742),x6745),x6744))+P42(f43(f43(f36(x6741,x6742),x6743),x6744)) % 0.54/0.79 [685]~P42(f43(f43(f36(x6851,x6852),x6853),x6855))+P42(f43(f43(f36(x6851,x6852),x6853),x6854))+~P42(f43(f43(f36(x6851,x6852),x6855),x6854)) % 0.54/0.79 [621]~P17(x6211)+E(f43(f43(f4(x6211),x6212),x6213),x6214)+~E(f43(f43(f4(x6211),x6212),f43(f43(f4(x6211),x6215),x6213)),f43(f43(f4(x6211),x6215),x6214)) % 0.54/0.79 [684]E(x6841,x6842)+E(x6843,x6844)+~P10(x6845,f26(x6844,x6842,x6846),f26(x6843,x6841,x6846),x6846) % 0.54/0.79 [697]E(x6971,x6972)+P10(x6973,x6971,x6972,x6974)+~P10(x6973,f26(x6975,x6971,x6974),f26(x6976,x6972,x6974),x6974) % 0.54/0.79 [686]E(x6861,x6862)+~P10(x6863,f26(x6862,x6864,x6865),f26(x6861,x6866,x6865),x6865)+P42(f43(f43(x6863,x6862),x6861)) % 0.54/0.79 [698]P10(x6981,x6982,x6983,x6984)+~P10(x6981,f26(x6985,x6982,x6984),f26(x6986,x6983,x6984),x6984)+P42(f43(f43(x6981,x6985),x6986)) % 0.54/0.79 [700]~P6(x7001,x7003,x7006)+~P6(f41(x7001,x7004,x7006,a46),x7002,x7005)+P6(x7001,f43(f43(f43(a21,x7002),x7003),x7004),x7005) % 0.54/0.79 [709]E(x7091,x7092)+E(x7093,x7094)+~P10(x7095,f20(x7093,f26(x7091,f25(x7096),x7096),x7096),f20(x7094,f26(x7092,f25(x7096),x7096),x7096),x7096) % 0.54/0.79 [710]E(x7101,x7102)+~P10(x7103,f20(x7104,f26(x7101,f25(x7105),x7105),x7105),f20(x7106,f26(x7102,f25(x7105),x7105),x7105),x7105)+P42(f43(f43(x7103,x7101),x7102)) % 0.54/0.79 [712]E(x7121,x7122)+P10(x7123,x7121,x7122,x7124)+~P10(x7123,f20(x7121,f26(x7125,f25(x7124),x7124),x7124),f20(x7122,f26(x7126,f25(x7124),x7124),x7124),x7124) % 0.54/0.79 [713]P10(x7131,x7132,x7133,x7134)+~P10(x7131,f20(x7132,f26(x7135,f25(x7134),x7134),x7134),f20(x7133,f26(x7136,f25(x7134),x7134),x7134),x7134)+P42(f43(f43(x7131,x7135),x7136)) % 0.54/0.79 [365]~P32(x3652)+~P39(x3652)+E(x3651,f3(a1))+E(f39(f3(x3652),x3651,x3652),f3(x3652)) % 0.54/0.79 [407]P8(x4071,x4072,x4073)+~P1(x4073)+E(x4071,x4072)+P8(x4072,x4071,x4073) % 0.54/0.79 [408]P8(x4081,x4082,x4083)+~P36(x4083)+E(x4081,x4082)+P8(x4082,x4081,x4083) % 0.54/0.79 [436]~P1(x4363)+~P13(x4361,x4362,x4363)+E(x4361,x4362)+P8(x4361,x4362,x4363) % 0.54/0.79 [442]~P28(x4423)+~P13(x4421,x4422,x4423)+E(x4421,x4422)+P8(x4421,x4422,x4423) % 0.54/0.79 [474]~P13(x4742,x4741,x4743)+~P13(x4741,x4742,x4743)+E(x4741,x4742)+~P28(x4743) % 0.54/0.79 [483]P8(x4832,x4831,x4833)+~P29(x4833)+~P13(x4832,x4831,x4833)+P13(x4831,x4832,x4833) % 0.54/0.79 [389]~P35(x3893)+~P15(x3893)+E(x3891,x3892)+~E(f5(x3891,x3892,x3893),f3(x3893)) % 0.54/0.79 [582]E(x5821,x5822)+~P13(x5823,x5822,a1)+~P13(x5823,x5821,a1)+~E(f5(x5821,x5823,a1),f5(x5822,x5823,a1)) % 0.54/0.79 [678]~P13(x6783,x6781,a1)+P13(x6781,x6782,a1)+~P13(x6783,x6782,a1)+~P13(f5(x6781,x6783,a1),f5(x6782,x6783,a1),a1) % 0.54/0.79 [679]~P13(x6793,x6791,a1)+P8(x6791,x6792,a1)+~P13(x6793,x6792,a1)+~P8(f5(x6791,x6793,a1),f5(x6792,x6793,a1),a1) % 0.54/0.79 [487]~P8(x4872,f7(x4871),a1)+P42(f43(x4871,x4872))+P42(f43(x4871,x4873))+~P42(f43(x4871,f3(a1))) % 0.54/0.79 [386]~P35(x3862)+~P15(x3862)+E(x3861,f3(x3862))+~E(f43(f43(f4(x3862),x3863),x3861),x3863) % 0.54/0.79 [605]~P2(x6051)+~P13(f3(x6051),x6053,x6051)+~P13(f3(x6051),x6052,x6051)+P13(f3(x6051),f43(f43(f4(x6051),x6052),x6053),x6051) % 0.54/0.79 [606]~P2(x6061)+~P13(f3(x6061),x6063,x6061)+~P8(f3(x6061),x6062,x6061)+P8(f3(x6061),f43(f43(f4(x6061),x6062),x6063),x6061) % 0.54/0.79 [607]~P2(x6071)+~P13(f3(x6071),x6072,x6071)+~P8(f3(x6071),x6073,x6071)+P8(f3(x6071),f43(f43(f4(x6071),x6072),x6073),x6071) % 0.54/0.79 [608]~P2(x6081)+~P8(f3(x6081),x6083,x6081)+~P8(f3(x6081),x6082,x6081)+P8(f3(x6081),f43(f43(f4(x6081),x6082),x6083),x6081) % 0.54/0.79 [609]~P2(x6091)+~P13(x6093,f3(x6091),x6091)+~P13(x6092,f3(x6091),x6091)+P13(f43(f43(f4(x6091),x6092),x6093),f3(x6091),x6091) % 0.54/0.79 [610]~P2(x6101)+~P13(x6103,f3(x6101),x6101)+~P8(x6102,f3(x6101),x6101)+P8(f43(f43(f4(x6101),x6102),x6103),f3(x6101),x6101) % 0.54/0.79 [611]~P2(x6111)+~P13(x6112,f3(x6111),x6111)+~P8(x6113,f3(x6111),x6111)+P8(f43(f43(f4(x6111),x6112),x6113),f3(x6111),x6111) % 0.54/0.79 [612]~P2(x6121)+~P8(x6123,f3(x6121),x6121)+~P8(x6122,f3(x6121),x6121)+P8(f43(f43(f4(x6121),x6122),x6123),f3(x6121),x6121) % 0.54/0.79 [502]~P28(x5023)+~P13(x5021,x5024,x5023)+P13(x5021,x5022,x5023)+~P13(x5024,x5022,x5023) % 0.54/0.79 [503]~P29(x5033)+~P13(x5031,x5034,x5033)+P13(x5031,x5032,x5033)+~P13(x5034,x5032,x5033) % 0.54/0.79 [504]~P28(x5043)+~P8(x5041,x5044,x5043)+P8(x5041,x5042,x5043)+~P13(x5044,x5042,x5043) % 0.54/0.79 [505]~P28(x5053)+~P8(x5054,x5052,x5053)+P8(x5051,x5052,x5053)+~P13(x5051,x5054,x5053) % 0.54/0.79 [506]~P28(x5063)+~P8(x5061,x5064,x5063)+P8(x5061,x5062,x5063)+~P8(x5064,x5062,x5063) % 0.54/0.79 [507]~P29(x5073)+~P8(x5071,x5074,x5073)+P8(x5071,x5072,x5073)+~P13(x5074,x5072,x5073) % 0.54/0.79 [508]~P29(x5083)+~P8(x5084,x5082,x5083)+P8(x5081,x5082,x5083)+~P13(x5081,x5084,x5083) % 0.54/0.79 [509]~P29(x5093)+~P8(x5091,x5094,x5093)+P8(x5091,x5092,x5093)+~P8(x5094,x5092,x5093) % 0.54/0.79 [587]~P1(x5873)+~P13(x5872,x5874,x5873)+~P13(x5871,x5874,x5873)+P13(f37(x5871,x5872,x5873),x5874,x5873) % 0.54/0.79 [588]~P1(x5883)+~P8(x5882,x5884,x5883)+~P8(x5881,x5884,x5883)+P8(f37(x5881,x5882,x5883),x5884,x5883) % 0.54/0.79 [614]~P1(x6143)+P13(x6141,x6142,x6143)+P13(x6141,x6144,x6143)+~P13(x6141,f37(x6142,x6144,x6143),x6143) % 0.54/0.79 [615]~P1(x6153)+P8(x6151,x6152,x6153)+P8(x6151,x6154,x6153)+~P8(x6151,f37(x6152,x6154,x6153),x6153) % 0.54/0.79 [649]~P30(x6493)+~P13(x6491,x6494,x6493)+~P13(f3(x6493),x6491,x6493)+P13(f39(x6491,x6492,x6493),f39(x6494,x6492,x6493),x6493) % 0.54/0.79 [670]~P30(x6703)+P8(x6701,x6702,x6703)+~P13(f3(x6703),x6702,x6703)+~P8(f39(x6701,x6704,x6703),f39(x6702,x6704,x6703),x6703) % 0.54/0.79 [471]~P35(x4713)+~P15(x4713)+E(x4711,x4712)+~E(f43(f43(f4(x4713),x4714),x4711),f43(f43(f4(x4713),x4714),x4712)) % 0.54/0.79 [592]~P30(x5922)+~P8(x5921,x5924,x5922)+~P8(f3(x5922),x5923,x5922)+P8(x5921,f43(f43(f4(x5922),x5923),x5924),x5922) % 0.54/0.79 [705]~P6(x7053,x7051,a50)+~P6(f41(x7053,x7052,a50,a46),a49,x7054)+~P42(f43(a10,x7051))+P42(f43(a10,f43(f43(f43(a21,a49),x7051),x7052))) % 0.54/0.79 [785]~P6(x7853,x7851,a50)+~P6(f41(x7853,x7852,a50,a46),f27(a12,f43(f43(f43(a21,a55),a49),f3(a1)),a53,a44,a44),x7854)+~P42(f43(a10,x7851))+P42(f43(a10,f43(f43(f43(a21,f27(a12,f43(f43(f43(a21,a55),a49),f3(a1)),a53,a44,a44)),x7851),x7852))) % 0.54/0.79 [566]~P23(x5663)+~P13(x5665,x5664,x5663)+P13(x5661,x5662,x5663)+~E(f5(x5664,x5665,x5663),f5(x5662,x5661,x5663)) % 0.54/0.79 [567]~P23(x5673)+~P13(x5675,x5674,x5673)+P13(x5671,x5672,x5673)+~E(f5(x5672,x5671,x5673),f5(x5674,x5675,x5673)) % 0.54/0.79 [568]~P23(x5683)+~P8(x5684,x5685,x5683)+P8(x5681,x5682,x5683)+~E(f5(x5684,x5685,x5683),f5(x5681,x5682,x5683)) % 0.54/0.79 [569]~P23(x5693)+~P8(x5694,x5695,x5693)+P8(x5691,x5692,x5693)+~E(f5(x5691,x5692,x5693),f5(x5694,x5695,x5693)) % 0.54/0.79 [643]~P3(x6431)+~P13(x6433,x6435,x6431)+~P13(x6432,x6434,x6431)+P13(f43(f43(f4(x6431),x6432),x6433),f43(f43(f4(x6431),x6434),x6435),x6431) % 0.54/0.79 [644]~P25(x6441)+~P13(x6443,x6445,x6441)+~P8(x6442,x6444,x6441)+P8(f43(f43(f4(x6441),x6442),x6443),f43(f43(f4(x6441),x6444),x6445),x6441) % 0.54/0.79 [645]~P25(x6451)+~P13(x6452,x6454,x6451)+~P8(x6453,x6455,x6451)+P8(f43(f43(f4(x6451),x6452),x6453),f43(f43(f4(x6451),x6454),x6455),x6451) % 0.54/0.79 [646]~P25(x6461)+~P8(x6463,x6465,x6461)+~P8(x6462,x6464,x6461)+P8(f43(f43(f4(x6461),x6462),x6463),f43(f43(f4(x6461),x6464),x6465),x6461) % 0.54/0.79 [662]~P23(x6622)+~P13(x6625,x6624,x6622)+~P13(x6621,f43(f43(f4(x6622),x6623),x6625),x6622)+P13(x6621,f43(f43(f4(x6622),x6623),x6624),x6622) % 0.54/0.79 [409]~P37(x4092)+~P33(x4092)+~P34(x4092)+~P32(x4092)+~E(f39(x4091,f3(a1),x4092),f3(x4092)) % 0.54/0.79 [545]~P2(x5452)+~P13(f3(x5452),x5451,x5452)+~P13(f3(x5452),x5453,x5452)+E(x5451,f3(x5452))+~E(f43(f43(f4(x5452),x5453),x5451),f3(x5452)) % 0.54/0.79 [546]~P2(x5462)+~P13(f3(x5462),x5463,x5462)+~P13(f3(x5462),x5461,x5462)+E(x5461,f3(x5462))+~E(f43(f43(f4(x5462),x5461),x5463),f3(x5462)) % 0.54/0.79 [667]~P30(x6673)+~P8(x6671,x6674,x6673)+~P13(f3(x6673),x6671,x6673)+P8(f39(x6671,x6672,x6673),f39(x6674,x6672,x6673),x6673)+~P8(f3(a1),x6672,a1) % 0.54/0.79 [601]~P24(x6012)+~P4(x6012)+~P13(x6011,x6014,x6012)+~P13(f3(x6012),x6013,x6012)+P13(x6011,f43(f43(f4(x6012),x6013),x6014),x6012) % 0.54/0.79 [602]~P24(x6022)+~P4(x6022)+~P13(x6021,x6023,x6022)+~P13(f3(x6022),x6024,x6022)+P13(x6021,f43(f43(f4(x6022),x6023),x6024),x6022) % 0.54/0.79 [603]~P24(x6032)+~P4(x6032)+~P13(x6031,x6034,x6032)+~P8(f3(x6032),x6033,x6032)+P8(x6031,f43(f43(f4(x6032),x6033),x6034),x6032) % 0.54/0.79 [604]~P24(x6042)+~P4(x6042)+~P8(x6041,x6044,x6042)+~P13(f3(x6042),x6043,x6042)+P8(x6041,f43(f43(f4(x6042),x6043),x6044),x6042) % 0.54/0.79 [378]~P37(x3782)+~P33(x3782)+~P34(x3782)+~P32(x3782)+E(x3781,f3(a1))+E(f39(f3(x3782),x3781,x3782),f3(x3782)) % 0.54/0.79 [410]~P37(x4102)+~P33(x4102)+~P34(x4102)+~P32(x4102)+~E(f39(x4101,x4103,x4102),f3(x4102))+E(x4101,f3(x4102)) % 0.54/0.79 [651]~P30(x6514)+E(x6511,x6512)+~P13(f3(x6514),x6512,x6514)+~P13(f3(x6514),x6511,x6514)+~E(f39(x6511,x6513,x6514),f39(x6512,x6513,x6514))+~P8(f3(a1),x6513,a1) % 0.54/0.79 %EqnAxiom % 0.54/0.79 [1]E(x11,x11) % 0.54/0.79 [2]E(x22,x21)+~E(x21,x22) % 0.54/0.79 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.54/0.79 [4]~E(x41,x42)+E(f3(x41),f3(x42)) % 0.54/0.79 [5]~E(x51,x52)+E(f8(x51),f8(x52)) % 0.54/0.79 [6]~E(x61,x62)+E(f27(x61,x63,x64,x65,x66),f27(x62,x63,x64,x65,x66)) % 0.54/0.79 [7]~E(x71,x72)+E(f27(x73,x71,x74,x75,x76),f27(x73,x72,x74,x75,x76)) % 0.54/0.79 [8]~E(x81,x82)+E(f27(x83,x84,x81,x85,x86),f27(x83,x84,x82,x85,x86)) % 0.54/0.79 [9]~E(x91,x92)+E(f27(x93,x94,x95,x91,x96),f27(x93,x94,x95,x92,x96)) % 0.54/0.79 [10]~E(x101,x102)+E(f27(x103,x104,x105,x106,x101),f27(x103,x104,x105,x106,x102)) % 0.54/0.79 [11]~E(x111,x112)+E(f35(x111),f35(x112)) % 0.54/0.79 [12]~E(x121,x122)+E(f43(x121,x123),f43(x122,x123)) % 0.54/0.79 [13]~E(x131,x132)+E(f43(x133,x131),f43(x133,x132)) % 0.54/0.79 [14]~E(x141,x142)+E(f9(x141,x143),f9(x142,x143)) % 0.54/0.79 [15]~E(x151,x152)+E(f9(x153,x151),f9(x153,x152)) % 0.54/0.79 [16]~E(x161,x162)+E(f18(x161,x163,x164,x165,x166),f18(x162,x163,x164,x165,x166)) % 0.54/0.79 [17]~E(x171,x172)+E(f18(x173,x171,x174,x175,x176),f18(x173,x172,x174,x175,x176)) % 0.54/0.79 [18]~E(x181,x182)+E(f18(x183,x184,x181,x185,x186),f18(x183,x184,x182,x185,x186)) % 0.54/0.79 [19]~E(x191,x192)+E(f18(x193,x194,x195,x191,x196),f18(x193,x194,x195,x192,x196)) % 0.54/0.79 [20]~E(x201,x202)+E(f18(x203,x204,x205,x206,x201),f18(x203,x204,x205,x206,x202)) % 0.54/0.79 [21]~E(x211,x212)+E(f4(x211),f4(x212)) % 0.54/0.79 [22]~E(x221,x222)+E(f34(x221,x223),f34(x222,x223)) % 0.54/0.79 [23]~E(x231,x232)+E(f34(x233,x231),f34(x233,x232)) % 0.54/0.79 [24]~E(x241,x242)+E(f11(x241),f11(x242)) % 0.54/0.79 [25]~E(x251,x252)+E(f29(x251,x253,x254),f29(x252,x253,x254)) % 0.54/0.79 [26]~E(x261,x262)+E(f29(x263,x261,x264),f29(x263,x262,x264)) % 0.54/0.79 [27]~E(x271,x272)+E(f29(x273,x274,x271),f29(x273,x274,x272)) % 0.54/0.79 [28]~E(x281,x282)+E(f37(x281,x283,x284),f37(x282,x283,x284)) % 0.54/0.79 [29]~E(x291,x292)+E(f37(x293,x291,x294),f37(x293,x292,x294)) % 0.54/0.79 [30]~E(x301,x302)+E(f37(x303,x304,x301),f37(x303,x304,x302)) % 0.54/0.79 [31]~E(x311,x312)+E(f25(x311),f25(x312)) % 0.54/0.79 [32]~E(x321,x322)+E(f33(x321,x323),f33(x322,x323)) % 0.54/0.79 [33]~E(x331,x332)+E(f33(x333,x331),f33(x333,x332)) % 0.54/0.79 [34]~E(x341,x342)+E(f5(x341,x343,x344),f5(x342,x343,x344)) % 0.54/0.79 [35]~E(x351,x352)+E(f5(x353,x351,x354),f5(x353,x352,x354)) % 0.54/0.79 [36]~E(x361,x362)+E(f5(x363,x364,x361),f5(x363,x364,x362)) % 0.54/0.79 [37]~E(x371,x372)+E(f36(x371,x373),f36(x372,x373)) % 0.54/0.79 [38]~E(x381,x382)+E(f36(x383,x381),f36(x383,x382)) % 0.54/0.79 [39]~E(x391,x392)+E(f28(x391,x393,x394,x395,x396),f28(x392,x393,x394,x395,x396)) % 0.54/0.79 [40]~E(x401,x402)+E(f28(x403,x401,x404,x405,x406),f28(x403,x402,x404,x405,x406)) % 0.54/0.79 [41]~E(x411,x412)+E(f28(x413,x414,x411,x415,x416),f28(x413,x414,x412,x415,x416)) % 0.54/0.79 [42]~E(x421,x422)+E(f28(x423,x424,x425,x421,x426),f28(x423,x424,x425,x422,x426)) % 0.54/0.79 [43]~E(x431,x432)+E(f28(x433,x434,x435,x436,x431),f28(x433,x434,x435,x436,x432)) % 0.54/0.79 [44]~E(x441,x442)+E(f41(x441,x443,x444,x445),f41(x442,x443,x444,x445)) % 0.54/0.79 [45]~E(x451,x452)+E(f41(x453,x451,x454,x455),f41(x453,x452,x454,x455)) % 0.54/0.79 [46]~E(x461,x462)+E(f41(x463,x464,x461,x465),f41(x463,x464,x462,x465)) % 0.54/0.79 [47]~E(x471,x472)+E(f41(x473,x474,x475,x471),f41(x473,x474,x475,x472)) % 0.54/0.79 [48]~E(x481,x482)+E(f30(x481,x483,x484,x485),f30(x482,x483,x484,x485)) % 0.54/0.79 [49]~E(x491,x492)+E(f30(x493,x491,x494,x495),f30(x493,x492,x494,x495)) % 0.54/0.79 [50]~E(x501,x502)+E(f30(x503,x504,x501,x505),f30(x503,x504,x502,x505)) % 0.54/0.79 [51]~E(x511,x512)+E(f30(x513,x514,x515,x511),f30(x513,x514,x515,x512)) % 0.54/0.79 [52]~E(x521,x522)+E(f6(x521,x523,x524,x525,x526),f6(x522,x523,x524,x525,x526)) % 0.54/0.79 [53]~E(x531,x532)+E(f6(x533,x531,x534,x535,x536),f6(x533,x532,x534,x535,x536)) % 0.54/0.79 [54]~E(x541,x542)+E(f6(x543,x544,x541,x545,x546),f6(x543,x544,x542,x545,x546)) % 0.54/0.79 [55]~E(x551,x552)+E(f6(x553,x554,x555,x551,x556),f6(x553,x554,x555,x552,x556)) % 0.54/0.79 [56]~E(x561,x562)+E(f6(x563,x564,x565,x566,x561),f6(x563,x564,x565,x566,x562)) % 0.54/0.79 [57]~E(x571,x572)+E(f14(x571),f14(x572)) % 0.54/0.79 [58]~E(x581,x582)+E(f26(x581,x583,x584),f26(x582,x583,x584)) % 0.54/0.79 [59]~E(x591,x592)+E(f26(x593,x591,x594),f26(x593,x592,x594)) % 0.54/0.79 [60]~E(x601,x602)+E(f26(x603,x604,x601),f26(x603,x604,x602)) % 0.54/0.79 [61]~E(x611,x612)+E(f20(x611,x613,x614),f20(x612,x613,x614)) % 0.54/0.79 [62]~E(x621,x622)+E(f20(x623,x621,x624),f20(x623,x622,x624)) % 0.54/0.79 [63]~E(x631,x632)+E(f20(x633,x634,x631),f20(x633,x634,x632)) % 0.54/0.79 [64]~E(x641,x642)+E(f39(x641,x643,x644),f39(x642,x643,x644)) % 0.54/0.79 [65]~E(x651,x652)+E(f39(x653,x651,x654),f39(x653,x652,x654)) % 0.54/0.79 [66]~E(x661,x662)+E(f39(x663,x664,x661),f39(x663,x664,x662)) % 0.54/0.79 [67]~E(x671,x672)+E(f38(x671,x673,x674),f38(x672,x673,x674)) % 0.54/0.79 [68]~E(x681,x682)+E(f38(x683,x681,x684),f38(x683,x682,x684)) % 0.54/0.79 [69]~E(x691,x692)+E(f38(x693,x694,x691),f38(x693,x694,x692)) % 0.54/0.79 [70]~E(x701,x702)+E(f40(x701),f40(x702)) % 0.54/0.79 [71]~E(x711,x712)+E(f31(x711,x713),f31(x712,x713)) % 0.54/0.79 [72]~E(x721,x722)+E(f31(x723,x721),f31(x723,x722)) % 0.54/0.79 [73]~E(x731,x732)+E(f32(x731,x733,x734,x735),f32(x732,x733,x734,x735)) % 0.54/0.79 [74]~E(x741,x742)+E(f32(x743,x741,x744,x745),f32(x743,x742,x744,x745)) % 0.54/0.79 [75]~E(x751,x752)+E(f32(x753,x754,x751,x755),f32(x753,x754,x752,x755)) % 0.54/0.79 [76]~E(x761,x762)+E(f32(x763,x764,x765,x761),f32(x763,x764,x765,x762)) % 0.54/0.79 [77]~E(x771,x772)+E(f15(x771,x773,x774),f15(x772,x773,x774)) % 0.54/0.79 [78]~E(x781,x782)+E(f15(x783,x781,x784),f15(x783,x782,x784)) % 0.54/0.79 [79]~E(x791,x792)+E(f15(x793,x794,x791),f15(x793,x794,x792)) % 0.54/0.79 [80]~E(x801,x802)+E(f22(x801),f22(x802)) % 0.54/0.79 [81]~E(x811,x812)+E(f16(x811,x813,x814),f16(x812,x813,x814)) % 0.54/0.79 [82]~E(x821,x822)+E(f16(x823,x821,x824),f16(x823,x822,x824)) % 0.54/0.79 [83]~E(x831,x832)+E(f16(x833,x834,x831),f16(x833,x834,x832)) % 0.54/0.79 [84]~E(x841,x842)+E(f19(x841,x843,x844,x845,x846),f19(x842,x843,x844,x845,x846)) % 0.54/0.79 [85]~E(x851,x852)+E(f19(x853,x851,x854,x855,x856),f19(x853,x852,x854,x855,x856)) % 0.54/0.79 [86]~E(x861,x862)+E(f19(x863,x864,x861,x865,x866),f19(x863,x864,x862,x865,x866)) % 0.54/0.79 [87]~E(x871,x872)+E(f19(x873,x874,x875,x871,x876),f19(x873,x874,x875,x872,x876)) % 0.54/0.79 [88]~E(x881,x882)+E(f19(x883,x884,x885,x886,x881),f19(x883,x884,x885,x886,x882)) % 0.54/0.79 [89]~E(x891,x892)+E(f57(x891),f57(x892)) % 0.54/0.79 [90]~E(x901,x902)+E(f24(x901,x903,x904,x905),f24(x902,x903,x904,x905)) % 0.54/0.79 [91]~E(x911,x912)+E(f24(x913,x911,x914,x915),f24(x913,x912,x914,x915)) % 0.54/0.79 [92]~E(x921,x922)+E(f24(x923,x924,x921,x925),f24(x923,x924,x922,x925)) % 0.54/0.79 [93]~E(x931,x932)+E(f24(x933,x934,x935,x931),f24(x933,x934,x935,x932)) % 0.54/0.79 [94]~E(x941,x942)+E(f47(x941,x943),f47(x942,x943)) % 0.54/0.79 [95]~E(x951,x952)+E(f47(x953,x951),f47(x953,x952)) % 0.54/0.79 [96]~E(x961,x962)+E(f7(x961),f7(x962)) % 0.54/0.79 [97]~E(x971,x972)+E(f58(x971),f58(x972)) % 0.54/0.79 [98]~E(x981,x982)+E(f23(x981),f23(x982)) % 0.54/0.79 [99]~E(x991,x992)+E(f56(x991),f56(x992)) % 0.54/0.80 [100]~P1(x1001)+P1(x1002)+~E(x1001,x1002) % 0.54/0.80 [101]~P28(x1011)+P28(x1012)+~E(x1011,x1012) % 0.54/0.80 [102]P9(x1022,x1023,x1024,x1025,x1026,x1027)+~E(x1021,x1022)+~P9(x1021,x1023,x1024,x1025,x1026,x1027) % 0.54/0.80 [103]P9(x1033,x1032,x1034,x1035,x1036,x1037)+~E(x1031,x1032)+~P9(x1033,x1031,x1034,x1035,x1036,x1037) % 0.54/0.80 [104]P9(x1043,x1044,x1042,x1045,x1046,x1047)+~E(x1041,x1042)+~P9(x1043,x1044,x1041,x1045,x1046,x1047) % 0.54/0.80 [105]P9(x1053,x1054,x1055,x1052,x1056,x1057)+~E(x1051,x1052)+~P9(x1053,x1054,x1055,x1051,x1056,x1057) % 0.54/0.80 [106]P9(x1063,x1064,x1065,x1066,x1062,x1067)+~E(x1061,x1062)+~P9(x1063,x1064,x1065,x1066,x1061,x1067) % 0.54/0.80 [107]P9(x1073,x1074,x1075,x1076,x1077,x1072)+~E(x1071,x1072)+~P9(x1073,x1074,x1075,x1076,x1077,x1071) % 0.54/0.80 [108]~P29(x1081)+P29(x1082)+~E(x1081,x1082) % 0.54/0.80 [109]~P20(x1091)+P20(x1092)+~E(x1091,x1092) % 0.54/0.80 [110]~P2(x1101)+P2(x1102)+~E(x1101,x1102) % 0.54/0.80 [111]~P3(x1111)+P3(x1112)+~E(x1111,x1112) % 0.54/0.80 [112]~P30(x1121)+P30(x1122)+~E(x1121,x1122) % 0.54/0.80 [113]~P24(x1131)+P24(x1132)+~E(x1131,x1132) % 0.54/0.80 [114]~P4(x1141)+P4(x1142)+~E(x1141,x1142) % 0.54/0.80 [115]~P26(x1151)+P26(x1152)+~E(x1151,x1152) % 0.54/0.80 [116]P13(x1162,x1163,x1164)+~E(x1161,x1162)+~P13(x1161,x1163,x1164) % 0.54/0.80 [117]P13(x1173,x1172,x1174)+~E(x1171,x1172)+~P13(x1173,x1171,x1174) % 0.54/0.80 [118]P13(x1183,x1184,x1182)+~E(x1181,x1182)+~P13(x1183,x1184,x1181) % 0.54/0.80 [119]~P31(x1191)+P31(x1192)+~E(x1191,x1192) % 0.54/0.80 [120]~P5(x1201)+P5(x1202)+~E(x1201,x1202) % 0.54/0.80 [121]~P16(x1211)+P16(x1212)+~E(x1211,x1212) % 0.54/0.80 [122]P10(x1222,x1223,x1224,x1225)+~E(x1221,x1222)+~P10(x1221,x1223,x1224,x1225) % 0.54/0.80 [123]P10(x1233,x1232,x1234,x1235)+~E(x1231,x1232)+~P10(x1233,x1231,x1234,x1235) % 0.54/0.80 [124]P10(x1243,x1244,x1242,x1245)+~E(x1241,x1242)+~P10(x1243,x1244,x1241,x1245) % 0.54/0.80 [125]P10(x1253,x1254,x1255,x1252)+~E(x1251,x1252)+~P10(x1253,x1254,x1255,x1251) % 0.54/0.80 [126]~P18(x1261)+P18(x1262)+~E(x1261,x1262) % 0.54/0.80 [127]~P19(x1271)+P19(x1272)+~E(x1271,x1272) % 0.54/0.80 [128]~P25(x1281)+P25(x1282)+~E(x1281,x1282) % 0.54/0.80 [129]~P37(x1291)+P37(x1292)+~E(x1291,x1292) % 0.54/0.80 [130]~P33(x1301)+P33(x1302)+~E(x1301,x1302) % 0.54/0.80 [131]~P34(x1311)+P34(x1312)+~E(x1311,x1312) % 0.54/0.80 [132]~P32(x1321)+P32(x1322)+~E(x1321,x1322) % 0.54/0.80 [133]~P27(x1331)+P27(x1332)+~E(x1331,x1332) % 0.54/0.80 [134]~P38(x1341)+P38(x1342)+~E(x1341,x1342) % 0.54/0.80 [135]~P39(x1351)+P39(x1352)+~E(x1351,x1352) % 0.54/0.80 [136]~P42(x1361)+P42(x1362)+~E(x1361,x1362) % 0.54/0.80 [137]P8(x1372,x1373,x1374)+~E(x1371,x1372)+~P8(x1371,x1373,x1374) % 0.54/0.80 [138]P8(x1383,x1382,x1384)+~E(x1381,x1382)+~P8(x1383,x1381,x1384) % 0.54/0.80 [139]P8(x1393,x1394,x1392)+~E(x1391,x1392)+~P8(x1393,x1394,x1391) % 0.54/0.80 [140]~P17(x1401)+P17(x1402)+~E(x1401,x1402) % 0.54/0.80 [141]~P22(x1411)+P22(x1412)+~E(x1411,x1412) % 0.54/0.80 [142]~P40(x1421)+P40(x1422)+~E(x1421,x1422) % 0.54/0.80 [143]P6(x1432,x1433,x1434)+~E(x1431,x1432)+~P6(x1431,x1433,x1434) % 0.54/0.80 [144]P6(x1443,x1442,x1444)+~E(x1441,x1442)+~P6(x1443,x1441,x1444) % 0.54/0.80 [145]P6(x1453,x1454,x1452)+~E(x1451,x1452)+~P6(x1453,x1454,x1451) % 0.54/0.80 [146]~P36(x1461)+P36(x1462)+~E(x1461,x1462) % 0.54/0.80 [147]P14(x1472,x1473,x1474)+~E(x1471,x1472)+~P14(x1471,x1473,x1474) % 0.54/0.80 [148]P14(x1483,x1482,x1484)+~E(x1481,x1482)+~P14(x1483,x1481,x1484) % 0.54/0.80 [149]P14(x1493,x1494,x1492)+~E(x1491,x1492)+~P14(x1493,x1494,x1491) % 0.54/0.80 [150]P7(x1502,x1503,x1504)+~E(x1501,x1502)+~P7(x1501,x1503,x1504) % 0.54/0.80 [151]P7(x1513,x1512,x1514)+~E(x1511,x1512)+~P7(x1513,x1511,x1514) % 0.54/0.80 [152]P7(x1523,x1524,x1522)+~E(x1521,x1522)+~P7(x1523,x1524,x1521) % 0.54/0.80 [153]~P23(x1531)+P23(x1532)+~E(x1531,x1532) % 0.54/0.80 [154]~P35(x1541)+P35(x1542)+~E(x1541,x1542) % 0.54/0.80 [155]~P15(x1551)+P15(x1552)+~E(x1551,x1552) % 0.54/0.80 [156]~P21(x1561)+P21(x1562)+~E(x1561,x1562) % 0.54/0.80 [157]P11(x1572,x1573)+~E(x1571,x1572)+~P11(x1571,x1573) % 0.54/0.80 [158]P11(x1583,x1582)+~E(x1581,x1582)+~P11(x1583,x1581) % 0.54/0.80 [159]P12(x1592,x1593,x1594)+~E(x1591,x1592)+~P12(x1591,x1593,x1594) % 0.54/0.80 [160]P12(x1603,x1602,x1604)+~E(x1601,x1602)+~P12(x1603,x1601,x1604) % 0.54/0.80 [161]P12(x1613,x1614,x1612)+~E(x1611,x1612)+~P12(x1613,x1614,x1611) % 0.54/0.80 [162]~P41(x1621)+P41(x1622)+~E(x1621,x1622) % 0.54/0.80 % 0.54/0.80 %------------------------------------------- % 0.54/0.80 cnf(819,plain, % 0.54/0.80 ($false), % 0.54/0.80 inference(scs_inference,[],[199,299,194,331,785]), % 0.54/0.80 ['proof']). % 0.54/0.80 % SZS output end Proof % 0.54/0.80 % Total time :0.056376s %------------------------------------------------------------------------------