%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL826-1 : 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 : n008.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 11:19:56 AM UTC 2026 % Result : Unsatisfiable 0.59s 0.71s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL826-1 : TPTP v9.3.1. Released v4.1.0. % 0.00/0.03 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.09/0.35 % Computer : n008.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sat Sep 5 09:27:38 UTC 2026 % 0.13/0.36 % CPUTime : % 0.22/0.52 start to proof:theBenchmark % 0.47/0.66 %------------------------------------------- % 0.47/0.66 % File :CSE---1.7 % 0.47/0.66 % Problem :theBenchmark % 0.47/0.66 % Transform :cnf % 0.47/0.66 % Format :tptp:raw % 0.47/0.66 % Command :java -jar mcs_scs.jar %d %s % 0.47/0.66 % 0.47/0.66 % Result :Theorem 0.048763s % 0.47/0.66 % Output :CNFRefutation 0.048763s % 0.47/0.66 %------------------------------------------- % 0.47/0.66 %------------------------------------------------------------------------------ % 0.47/0.66 % File : LCL826-1 : TPTP v9.3.1. Released v4.1.0. % 0.47/0.66 % Domain : Logic Calculi % 0.47/0.66 % Problem : Strong normalization of typed lambda calculus 205_27 % 0.47/0.66 % Version : Especial. % 0.47/0.66 % English : % 0.47/0.66 % 0.47/0.66 % Refs : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java % 0.47/0.66 % : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe % 0.47/0.66 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 0.47/0.66 % Source : [Nip10] % 0.47/0.66 % Names : StrongNorm-205_27 [Nip10] % 0.47/0.66 % 0.47/0.66 % Status : Unsatisfiable % 0.47/0.66 % Rating : 0.17 v9.3.0, 0.14 v9.1.0, 0.10 v8.1.0, 0.11 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.07 v6.0.0, 0.10 v5.5.0, 0.35 v5.3.0, 0.39 v5.2.0, 0.44 v5.1.0, 0.53 v5.0.0, 0.43 v4.1.0 % 0.47/0.67 % Syntax : Number of clauses : 413 ( 152 unt; 32 nHn; 219 RR) % 0.47/0.67 % Number of literals : 794 ( 294 equ; 374 neg) % 0.47/0.67 % Maximal clause size : 6 ( 1 avg) % 0.47/0.67 % Maximal term depth : 27 ( 2 avg) % 0.47/0.67 % Number of predicates : 31 ( 30 usr; 0 prp; 1-4 aty) % 0.47/0.67 % Number of functors : 76 ( 76 usr; 31 con; 0-5 aty) % 0.47/0.67 % Number of variables : 1069 ( 155 sgn) % 0.47/0.67 % SPC : CNF_UNS_RFO_SEQ_NHN % 0.47/0.67 % 0.47/0.67 % Comments : % 0.47/0.67 %------------------------------------------------------------------------------ % 0.47/0.67 cnf(cls_apps__preserves__betas_0,axiom, % 0.47/0.67 ( 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))) % 0.47/0.67 | ~ c_ListOrder_Ostep1(c_Lambda_Obeta,V_rs,V_ss,tc_Lambda_OdB) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_add__eq__if_1,axiom, % 0.47/0.67 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),V_n)) % 0.47/0.67 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_Suc__pred_H_0,axiom, % 0.47/0.67 ( V_n = c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) % 0.47/0.67 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_Suc__diff__1_0,axiom, % 0.47/0.67 ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = V_n % 0.47/0.67 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_diff__less_0,axiom, % 0.47/0.67 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat) % 0.47/0.67 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 0.47/0.67 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_zero__less__diff_1,axiom, % 0.47/0.67 ( 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) % 0.47/0.67 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_zero__less__diff_0,axiom, % 0.47/0.67 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.47/0.67 | ~ 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) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_nat__diff__split_0,axiom, % 0.47/0.67 ( hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) % 0.47/0.67 | ~ c_HOL_Oord__class_Oless(V_a,V_b,tc_nat) % 0.47/0.67 | ~ hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(V_a,V_b,tc_nat))) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_less__iff__diff__less__0_0,axiom, % 0.47/0.67 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.47/0.67 | 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) % 0.47/0.67 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_less__iff__diff__less__0_1,axiom, % 0.47/0.67 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.47/0.67 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.47/0.67 | ~ 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) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_add__diff__inverse_0,axiom, % 0.47/0.67 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) = V_m % 0.47/0.67 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_less__eqI_1,axiom, % 0.47/0.67 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.47/0.67 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 0.47/0.67 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.47/0.67 | ~ c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_less__eqI_0,axiom, % 0.47/0.67 ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a) % 0.47/0.67 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 0.47/0.67 | c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) % 0.47/0.67 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_less__diff__conv_1,axiom, % 0.47/0.67 ( c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) % 0.47/0.67 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_less__diff__conv_0,axiom, % 0.47/0.67 ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat) % 0.47/0.67 | ~ c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_of__nat__aux_Osimps_I1_J_0,axiom, % 0.47/0.67 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.47/0.67 | c_Nat_Osemiring__1__class_Oof__nat__aux(V_inc,c_HOL_Ozero__class_Ozero(tc_nat),V_i,T_a) = V_i ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_diffs0__imp__equal_0,axiom, % 0.47/0.67 ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.47/0.67 | c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.47/0.67 | V_m = V_n ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_less__imp__diff__less_0,axiom, % 0.47/0.67 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) % 0.47/0.67 | ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_diff__Suc__Suc_0,axiom, % 0.47/0.67 c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_minus__nat_Odiff__0_0,axiom, % 0.47/0.67 c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ). % 0.47/0.67 % 0.47/0.67 cnf(cls_diff__self__eq__0_0,axiom, % 0.47/0.67 c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_class__ringb_Osubr0__iff_1,axiom, % 0.47/0.67 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.47/0.67 | ~ class_Int_Onumber__ring(T_a) % 0.47/0.67 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_diff__self_0,axiom, % 0.47/0.67 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.47/0.67 | c_HOL_Ominus__class_Ominus(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_diff__0__right_0,axiom, % 0.47/0.67 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.47/0.67 | c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_right__minus__eq_1,axiom, % 0.47/0.67 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.47/0.67 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_eq__iff__diff__eq__0_0,axiom, % 0.47/0.67 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.47/0.67 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_diff__less__mono2_0,axiom, % 0.47/0.67 ( 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) % 0.47/0.67 | ~ c_HOL_Oord__class_Oless(V_m,V_l,tc_nat) % 0.47/0.67 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_diff__Suc__1_0,axiom, % 0.47/0.67 c_HOL_Ominus__class_Ominus(c_Suc(V_n),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = V_n ). % 0.47/0.67 % 0.47/0.67 cnf(cls_diff__add__cancel_0,axiom, % 0.47/0.67 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.47/0.67 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ominus__class_Ominus(V_a,V_b,T_a)),V_b) = V_a ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_nat__diff__split__asm_1,axiom, % 0.47/0.67 ( ~ 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))) % 0.47/0.67 | hBOOL(hAPP(V_P,V_x)) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_nat__diff__split_1,axiom, % 0.47/0.67 ( ~ 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))) % 0.47/0.67 | hBOOL(hAPP(V_P,V_d)) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_diff__less__Suc_0,axiom, % 0.47/0.67 c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_Suc(V_m),tc_nat) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_of__nat__aux_Osimps_I2_J_0,axiom, % 0.47/0.67 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.47/0.67 | c_Nat_Osemiring__1__class_Oof__nat__aux(V_inc,c_Suc(V_n),V_i,T_a) = c_Nat_Osemiring__1__class_Oof__nat__aux(V_inc,V_n,hAPP(V_inc,V_i),T_a) ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_diff__add__0_0,axiom, % 0.47/0.67 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) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_diff__diff__left_0,axiom, % 0.47/0.67 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) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_eq__eqI_1,axiom, % 0.47/0.67 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.47/0.67 | c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) % 0.47/0.67 | V_xa = V_y ) ). % 0.47/0.67 % 0.47/0.67 cnf(cls_eq__eqI_0,axiom, % 0.47/0.67 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.47/0.68 | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a) % 0.47/0.68 | V_x_H = V_y_H ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_diff__0__eq__0_0,axiom, % 0.47/0.68 c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_diff__cancel2_0,axiom, % 0.47/0.68 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) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_diff__cancel_0,axiom, % 0.47/0.68 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) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_class__ringb_Osubr0__iff_0,axiom, % 0.47/0.68 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.47/0.68 | ~ class_Int_Onumber__ring(T_a) % 0.47/0.68 | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.47/0.68 | V_x = V_y ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_right__minus__eq_0,axiom, % 0.47/0.68 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.47/0.68 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.47/0.68 | V_a = V_b ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_eq__iff__diff__eq__0_1,axiom, % 0.47/0.68 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.47/0.68 | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.47/0.68 | V_a = V_b ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_diff__commute_0,axiom, % 0.47/0.68 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) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_Suc__diff__diff_0,axiom, % 0.47/0.68 c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat),c_Suc(V_k),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_diff__Suc__eq__diff__pred_0,axiom, % 0.47/0.68 c_HOL_Ominus__class_Ominus(V_m,c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_n,tc_nat) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_head__Var__reduction_0,axiom, % 0.47/0.68 ( c_ListOrder_Ostep1(c_Lambda_Obeta,V_rs,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(V_n,V_rs,V_v),tc_Lambda_OdB) % 0.47/0.68 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_v)) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_diff__add__inverse2_0,axiom, % 0.47/0.68 c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),V_n,tc_nat) = V_m ). % 0.47/0.68 % 0.47/0.68 cnf(cls_diff__add__inverse_0,axiom, % 0.47/0.68 c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_n,tc_nat) = V_m ). % 0.47/0.68 % 0.47/0.68 cnf(cls_add__diff__cancel_0,axiom, % 0.47/0.68 ( ~ class_OrderedGroup_Ogroup__add(T_a) % 0.47/0.68 | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_b,T_a) = V_a ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_diff__Suc__less_0,axiom, % 0.47/0.68 ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_n,c_Suc(V_i),tc_nat),V_n,tc_nat) % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_Suc__pred_0,axiom, % 0.47/0.68 ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_shift__lt_0,axiom, % 0.47/0.68 ( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(T_a),V_e),V_i),V_T),V_j) = hAPP(V_e,c_HOL_Ominus__class_Ominus(V_j,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_type_Osize_I2_J_0,axiom, % 0.47/0.68 c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(V_type1)),c_Type_Otype_Otype__size(V_type2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_type_Osize_I4_J_0,axiom, % 0.47/0.68 c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_type1,tc_Type_Otype)),c_Nat_Osize__class_Osize(V_type2,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_head__Var__reduction_1,axiom, % 0.47/0.68 ( V_v = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(V_n,V_rs,V_v),tc_Lambda_OdB,tc_Lambda_OdB) % 0.47/0.68 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_v)) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_subst__gt_0,axiom, % 0.47/0.68 ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_j)),V_u),V_i) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(V_j,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_subst__Var_0,axiom, % 0.47/0.68 ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i)),V_s),V_k) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(V_i,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_list__app__typeE_1,axiom, % 0.47/0.68 ( c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeE__1__1(V_T,V_e,V_t,V_ts)) % 0.47/0.68 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_list__app__typeD_1,axiom, % 0.47/0.68 ( c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts)) % 0.47/0.68 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_substn_Osimps_I1_J_0,axiom, % 0.47/0.68 ( c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_i),V_s,V_k) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(V_i,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_semiring__1__class_Oof__nat__code_0,axiom, % 0.47/0.68 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.47/0.68 | c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) = c_Nat_Osemiring__1__class_Oof__nat__aux(hAPP(hAPP(c_COMBC(T_a,T_a,T_a),c_HOL_Oplus__class_Oplus(T_a)),c_HOL_Oone__class_Oone(T_a)),V_n,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_list__app__typeD_0,axiom, % 0.47/0.68 ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_t),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))) % 0.47/0.68 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_list__app__typeE_0,axiom, % 0.47/0.68 ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_t),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))) % 0.47/0.68 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_Var_I2_J_0,axiom, % 0.47/0.68 hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_ea______),v_ia______),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_Ha______)) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_funpow_Osimps_I2_J_0,axiom, % 0.47/0.68 c_Nat_Ocompow(c_Suc(V_n),V_f,T_a,T_a) = c_Fun_Ocomp(V_f,c_Nat_Ocompow(V_n,V_f,T_a,T_a),T_a,T_a,T_a) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_r__into__rtranclp_0,axiom, % 0.47/0.68 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y)) % 0.47/0.68 | ~ hBOOL(hAPP(hAPP(V_r,V_x),V_y)) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_one__is__add_1,axiom, % 0.47/0.68 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) % 0.47/0.68 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.47/0.68 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_one__is__add_2,axiom, % 0.47/0.68 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) % 0.47/0.68 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 0.47/0.68 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_foldl__absorb0_0,axiom, % 0.47/0.68 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.47/0.68 | 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) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_one__neq__zero_0,axiom, % 0.47/0.68 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 0.47/0.68 | c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_less__SucE_0,axiom, % 0.47/0.68 ( V_m = V_n % 0.47/0.68 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_less__antisym_0,axiom, % 0.47/0.68 ( V_m = V_n % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 0.47/0.68 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_not__less__less__Suc__eq_0,axiom, % 0.47/0.68 ( V_n = V_m % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 0.47/0.68 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_one__is__add_4,axiom, % 0.47/0.68 c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_liftn_Osimps_I1_J_1,axiom, % 0.47/0.68 ( 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)) % 0.47/0.68 | c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_liftn_Osimps_I3_J_0,axiom, % 0.47/0.68 c_Lambda_Oliftn(V_n,c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(V_n,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_add__strict__mono_0,axiom, % 0.47/0.68 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.47/0.68 | 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) % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a) % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_add__less__mono_0,axiom, % 0.47/0.68 ( 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) % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat) % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_nat_Osimps_I3_J_0,axiom, % 0.47/0.68 c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_Suc__neq__Zero_0,axiom, % 0.47/0.68 c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_lessI_0,axiom, % 0.47/0.68 c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_less__Suc__eq_2,axiom, % 0.47/0.68 c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_less__trans__Suc_0,axiom, % 0.47/0.68 ( c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat) % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_foldl__foldr1_0,axiom, % 0.47/0.68 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.47/0.68 | 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) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_less__add__one_0,axiom, % 0.47/0.68 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.47/0.68 | c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a)),T_a) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_apps__preserves__beta2_0,axiom, % 0.47/0.68 ( 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))) % 0.47/0.68 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_liftn__0_0,axiom, % 0.47/0.68 c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k) = V_t ). % 0.47/0.68 % 0.47/0.68 cnf(cls_not__add__less1_0,axiom, % 0.47/0.68 ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_not__add__less2_0,axiom, % 0.47/0.68 ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_Suc__n__not__n_0,axiom, % 0.47/0.68 c_Suc(V_n) != V_n ). % 0.47/0.68 % 0.47/0.68 cnf(cls_n__not__Suc__n_0,axiom, % 0.47/0.68 V_n != c_Suc(V_n) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_add__strict__right__mono_0,axiom, % 0.47/0.68 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.47/0.68 | 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) % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_add__less__cancel__right_1,axiom, % 0.47/0.68 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.47/0.68 | 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) % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_add__less__cancel__right_0,axiom, % 0.47/0.68 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.47/0.68 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.47/0.68 | ~ 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) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_add__strict__left__mono_0,axiom, % 0.47/0.68 ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) % 0.47/0.68 | 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) % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_add__less__cancel__left_1,axiom, % 0.47/0.68 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.47/0.68 | 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) % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_add__less__cancel__left_0,axiom, % 0.47/0.68 ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) % 0.47/0.68 | c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.47/0.68 | ~ 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) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_add__less__mono1_0,axiom, % 0.47/0.68 ( 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) % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_nat__add__left__cancel__less_0,axiom, % 0.47/0.68 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.47/0.68 | ~ 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) ) ). % 0.47/0.68 % 0.47/0.68 cnf(cls_nat__add__left__cancel__less_1,axiom, % 0.47/0.68 ( 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) % 0.47/0.68 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.47/0.68 % 0.47/0.69 cnf(cls_add__is__1_5,axiom, % 0.47/0.69 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_Suc__lessD_0,axiom, % 0.47/0.69 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_less__SucI_0,axiom, % 0.47/0.69 ( c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_of__nat__add_0,axiom, % 0.47/0.69 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.47/0.69 | 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)) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_add__is__1_1,axiom, % 0.47/0.69 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.47/0.69 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.47/0.69 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_add__is__1_2,axiom, % 0.47/0.69 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.47/0.69 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 0.47/0.69 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_dB_Osize_I2_J_0,axiom, % 0.47/0.69 c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB1)),c_Lambda_OdB_OdB__size(V_dB2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_lift_Osimps_I3_J_0,axiom, % 0.47/0.69 hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(V_s)),V_k) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,V_s),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_dB_Osize_I3_J_0,axiom, % 0.47/0.69 c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(V_dB)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_converse__rtranclp__into__rtranclp_0,axiom, % 0.47/0.69 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c)) % 0.47/0.69 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_c)) % 0.47/0.69 | ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b)) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_rtranclp_Ortrancl__into__rtrancl_0,axiom, % 0.47/0.69 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c)) % 0.47/0.69 | ~ hBOOL(hAPP(hAPP(V_r,V_b),V_c)) % 0.47/0.69 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_b)) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_False_0,axiom, % 0.47/0.69 v_n____ != v_i____ ). % 0.47/0.69 % 0.47/0.69 cnf(cls_var__app__typesE_0,axiom, % 0.47/0.69 ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_Lambda_OdB_OVar(V_i)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T,V_e,V_i,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))) % 0.47/0.69 | ~ hBOOL(hAPP(hAPP(hAPP(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)) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_substn_Osimps_I1_J_1,axiom, % 0.47/0.69 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 0.47/0.69 | 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)) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_IT_OVar_0,axiom, % 0.47/0.69 ( 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))) % 0.47/0.69 | ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_lift__subst_0,axiom, % 0.47/0.69 ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_j)),V_i) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)),V_j) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(V_j,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_lift__subst__lt_0,axiom, % 0.47/0.69 ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_j)),V_i) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat))) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_lift_Osimps_I1_J_1,axiom, % 0.47/0.69 ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(V_i)),V_k) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat))) % 0.47/0.69 | c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_typing__elims_I3_J_0,axiom, % 0.47/0.69 ( V_T = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(V_T,V_e,V_t)),c_Type_Osko__Type__Xtyping__elims__3__2(V_T,V_e,V_t)) % 0.47/0.69 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_Lambda_OdB_OAbs(V_t)),V_T)) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_var__app__types_0,axiom, % 0.47/0.69 ( V_U = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(V_T,V_U,V_e,V_us),V_T,tc_Type_Otype,tc_Type_Otype) % 0.47/0.69 | ~ hBOOL(hAPP(hAPP(hAPP(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)) % 0.47/0.69 | ~ c_Type_Otypings(V_e,V_ts,V_Ts) % 0.47/0.69 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_us,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom, % 0.47/0.69 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.47/0.69 | 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) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom, % 0.47/0.69 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.47/0.69 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) % 0.47/0.69 | ~ 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) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_of__nat__less__0__iff_0,axiom, % 0.47/0.69 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.47/0.69 | ~ 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) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_add__neg__neg_0,axiom, % 0.47/0.69 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.47/0.69 | 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) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom, % 0.47/0.69 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.47/0.69 | 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) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom, % 0.47/0.69 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.47/0.69 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.47/0.69 | ~ 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) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_even__less__0__iff_0,axiom, % 0.47/0.69 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.47/0.69 | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) % 0.47/0.69 | ~ 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) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_even__less__0__iff_1,axiom, % 0.47/0.69 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.47/0.69 | 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) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_not__one__less__zero_0,axiom, % 0.47/0.69 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_add__pos__pos_0,axiom, % 0.47/0.69 ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) % 0.47/0.69 | 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) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_zero__less__one_0,axiom, % 0.47/0.69 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.47/0.69 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_pos__add__strict_0,axiom, % 0.47/0.69 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.47/0.69 | c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_of__nat__0_0,axiom, % 0.47/0.69 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.47/0.69 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_of__nat__less__iff_1,axiom, % 0.47/0.69 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.47/0.69 | 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) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_of__nat__less__iff_0,axiom, % 0.47/0.69 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.47/0.69 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.47/0.69 | ~ 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) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_add__gr__0_1,axiom, % 0.47/0.69 ( 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) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_add__gr__0_2,axiom, % 0.47/0.69 ( 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) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_gr0__conv__Suc_1,axiom, % 0.47/0.69 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_zero__less__Suc_0,axiom, % 0.47/0.69 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_add__gr__0_0,axiom, % 0.47/0.69 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.47/0.69 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) % 0.47/0.69 | ~ 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) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_less__Suc0_0,axiom, % 0.47/0.69 ( V_n = c_HOL_Ozero__class_Ozero(tc_nat) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_less__Suc0_1,axiom, % 0.47/0.69 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_rtrancl__beta__App_0,axiom, % 0.47/0.69 ( 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))) % 0.47/0.69 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)) % 0.47/0.69 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_rtrancl__beta__AppL_0,axiom, % 0.47/0.69 ( 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))) % 0.47/0.69 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_rtrancl__beta__AppR_0,axiom, % 0.47/0.69 ( 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))) % 0.47/0.69 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_apps__preserves__beta_0,axiom, % 0.47/0.69 ( 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))) % 0.47/0.69 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_Abs__eq__apps__conv_0,axiom, % 0.47/0.69 ( c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.47/0.69 | c_Lambda_OdB_OAbs(V_r) = V_s ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_Abs__apps__eq__Abs__apps__conv_1,axiom, % 0.47/0.69 ( 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) % 0.47/0.69 | V_rs = V_ss ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_Abs__apps__eq__Abs__apps__conv_0,axiom, % 0.47/0.69 ( 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) % 0.47/0.69 | V_r = V_s ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_apps__eq__Abs__conv_0,axiom, % 0.47/0.69 ( c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r) % 0.47/0.69 | V_s = c_Lambda_OdB_OAbs(V_r) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_substn__subst__0_0,axiom, % 0.47/0.69 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)) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_beta__cases_I2_J_0,axiom, % 0.47/0.69 ( V_s = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s)) % 0.47/0.69 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_r)),V_s)) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_One__nat__def_0,axiom, % 0.47/0.69 c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_foldr__conv__foldl_0,axiom, % 0.47/0.69 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a) % 0.47/0.69 | 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) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_nat_Oinject_0,axiom, % 0.47/0.69 ( c_Suc(V_nat) != c_Suc(V_nat_H) % 0.47/0.69 | V_nat = V_nat_H ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_Suc__inject_0,axiom, % 0.47/0.69 ( c_Suc(V_x) != c_Suc(V_y) % 0.47/0.69 | V_x = V_y ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_double__eq__0__iff_0,axiom, % 0.47/0.69 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.47/0.69 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a) != c_HOL_Ozero__class_Ozero(T_a) % 0.47/0.69 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_add__is__0_1,axiom, % 0.47/0.69 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.47/0.69 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_add__is__0_0,axiom, % 0.47/0.69 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.47/0.69 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_liftn__lift_0,axiom, % 0.47/0.69 c_Lambda_Oliftn(c_Suc(V_n),V_t,V_k) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(V_n,V_t,V_k)),V_k) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_natgb_Oadd__r0__iff_0,axiom, % 0.47/0.69 ( V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_a) % 0.47/0.69 | V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_add__eq__self__zero_0,axiom, % 0.47/0.69 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != V_m % 0.47/0.69 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_class__ringb_Oadd__r0__iff_0,axiom, % 0.47/0.69 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.47/0.69 | ~ class_Int_Onumber__ring(T_a) % 0.47/0.69 | V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_a) % 0.47/0.69 | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_of__nat__eq__iff_0,axiom, % 0.47/0.69 ( ~ class_Nat_Osemiring__char__0(T_a) % 0.47/0.69 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) % 0.47/0.69 | V_m = V_n ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_foldl__assoc_0,axiom, % 0.47/0.69 ( ~ class_OrderedGroup_Osemigroup__add(T_a) % 0.47/0.69 | 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)) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_class__semiring_Oadd__c_0,axiom, % 0.47/0.69 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.47/0.69 | 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) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_less__add__eq__less_0,axiom, % 0.47/0.69 ( 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) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat) % 0.47/0.69 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_nat__add__commute_0,axiom, % 0.47/0.69 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) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_comm__monoid__add_Omult__commute_0,axiom, % 0.47/0.69 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.47/0.69 | 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) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom, % 0.47/0.69 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.47/0.69 | 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) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_substn_Osimps_I3_J_0,axiom, % 0.47/0.69 c_Lambda_Osubstn(c_Lambda_OdB_OAbs(V_t),V_s,V_k) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(V_t,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_trans__less__add2_0,axiom, % 0.47/0.69 ( c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_j),tc_nat) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_trans__less__add1_0,axiom, % 0.47/0.69 ( c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_m),tc_nat) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_add__lessD1_0,axiom, % 0.47/0.69 ( c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_k,tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_termination__basic__simps_I2_J_0,axiom, % 0.47/0.69 ( c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(V_x,V_z,tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_termination__basic__simps_I1_J_0,axiom, % 0.47/0.69 ( c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat) % 0.47/0.69 | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_less__iff__Suc__add_1,axiom, % 0.47/0.69 c_HOL_Oord__class_Oless(V_m,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_x)),tc_nat) ). % 0.47/0.69 % 0.47/0.69 cnf(cls_less__add__Suc2_0,axiom, % 0.47/0.69 c_HOL_Oord__class_Oless(V_i,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_i)),tc_nat) ). % 0.47/0.69 % 0.47/0.70 cnf(cls_less__add__Suc1_0,axiom, % 0.47/0.70 c_HOL_Oord__class_Oless(V_i,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_m)),tc_nat) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_Zero__neq__Suc_0,axiom, % 0.47/0.70 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_nat_Osimps_I2_J_0,axiom, % 0.47/0.70 c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_add__Suc_0,axiom, % 0.47/0.70 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_add__Suc__right_0,axiom, % 0.47/0.70 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_rtranclp__trans_0,axiom, % 0.47/0.70 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_z)) % 0.47/0.70 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_z)) % 0.47/0.70 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y)) ) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_Nitpick_Ortranclp__def_1,axiom, % 0.47/0.70 hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_rtranclp_Ortrancl__refl_0,axiom, % 0.47/0.70 hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_funpow__add_0,axiom, % 0.47/0.70 c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),V_f,T_a,T_a) = c_Fun_Ocomp(c_Nat_Ocompow(V_m,V_f,T_a,T_a),c_Nat_Ocompow(V_n,V_f,T_a,T_a),T_a,T_a,T_a) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_add__is__1_4,axiom, % 0.47/0.70 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_Suc__eq__plus1__left_0,axiom, % 0.47/0.70 c_Suc(V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),V_n) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_Suc__eq__plus1_0,axiom, % 0.47/0.70 c_Suc(V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Oone__class_Oone(tc_nat)) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_substn__subst__n_0,axiom, % 0.47/0.70 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) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_double__eq__0__iff_1,axiom, % 0.47/0.70 ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a) % 0.47/0.70 | 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) ) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_add__is__0_2,axiom, % 0.47/0.70 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) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_class__semiring_Oadd__a_0,axiom, % 0.47/0.70 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.47/0.70 | 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) ) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_add__cancel__21_1,axiom, % 0.47/0.70 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.47/0.70 | 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)) ) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_nat__add__left__commute_0,axiom, % 0.47/0.70 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)) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_nat__add__assoc_0,axiom, % 0.47/0.70 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)) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_comm__monoid__add_Omult__assoc_0,axiom, % 0.47/0.70 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.47/0.70 | 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)) ) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom, % 0.47/0.70 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.47/0.70 | 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)) ) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom, % 0.47/0.70 ( ~ class_OrderedGroup_Oab__semigroup__add(T_a) % 0.47/0.70 | 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)) ) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom, % 0.47/0.70 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.47/0.70 | 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) ) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom, % 0.47/0.70 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.47/0.70 | 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) ) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom, % 0.47/0.70 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.47/0.70 | 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)) ) ). % 0.47/0.70 % 0.47/0.70 cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom, % 0.59/0.70 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.59/0.70 | 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)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_add__cancel__21_0,axiom, % 0.59/0.70 ( ~ class_OrderedGroup_Oab__group__add(T_a) % 0.59/0.70 | 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) % 0.59/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z) = V_u ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_COMBK__def_0,axiom, % 0.59/0.70 hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P ). % 0.59/0.70 % 0.59/0.70 cnf(cls_one__is__add_5,axiom, % 0.59/0.70 c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_of__nat__1_0,axiom, % 0.59/0.70 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.59/0.70 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_zero__neq__one_0,axiom, % 0.59/0.70 ( ~ class_Ring__and__Field_Ozero__neq__one(T_a) % 0.59/0.70 | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_funpow__swap1_0,axiom, % 0.59/0.70 hAPP(V_f,hAPP(c_Nat_Ocompow(V_n,V_f,T_a,T_a),V_x)) = hAPP(c_Nat_Ocompow(V_n,V_f,T_a,T_a),hAPP(V_f,V_x)) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_one__is__add_3,axiom, % 0.59/0.70 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) % 0.59/0.70 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.59/0.70 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_one__is__add_0,axiom, % 0.59/0.70 ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) % 0.59/0.70 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 0.59/0.70 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_of__nat__Suc_0,axiom, % 0.59/0.70 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.59/0.70 | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(V_m),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_add__Suc__shift_0,axiom, % 0.59/0.70 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_dB_Osize_I5_J_0,axiom, % 0.59/0.70 c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(V_dB2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_foldl__foldr1__lemma_0,axiom, % 0.59/0.70 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.59/0.70 | 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)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_Suc__lessI_0,axiom, % 0.59/0.70 ( c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) % 0.59/0.70 | c_Suc(V_m) = V_n % 0.59/0.70 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_natgb_Oadd__cancel_0,axiom, % 0.59/0.70 ( 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) % 0.59/0.70 | V_y = V_z ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_nat__add__right__cancel_0,axiom, % 0.59/0.70 ( 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) % 0.59/0.70 | V_m = V_n ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_nat__add__left__cancel_0,axiom, % 0.59/0.70 ( 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) % 0.59/0.70 | V_m = V_n ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_class__ringb_Oadd__cancel_0,axiom, % 0.59/0.70 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.59/0.70 | ~ class_Int_Onumber__ring(T_a) % 0.59/0.70 | 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) % 0.59/0.70 | V_y = V_z ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_add__imp__eq_0,axiom, % 0.59/0.70 ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a) % 0.59/0.70 | 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) % 0.59/0.70 | V_b = V_c ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_add__left__cancel_0,axiom, % 0.59/0.70 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 0.59/0.70 | 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) % 0.59/0.70 | V_b = V_c ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_add__right__cancel_0,axiom, % 0.59/0.70 ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) % 0.59/0.70 | 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) % 0.59/0.70 | V_b = V_c ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_subst__subst_0,axiom, % 0.59/0.70 ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_v),V_i)),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_v),V_j)),V_i) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i)),V_v),V_j) % 0.59/0.70 | ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_apps__eq__tail__conv_0,axiom, % 0.59/0.70 ( 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) % 0.59/0.70 | V_r = V_s ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_add__is__1_3,axiom, % 0.59/0.70 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.59/0.70 | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.59/0.70 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_add__is__1_0,axiom, % 0.59/0.70 ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) % 0.59/0.70 | V_m = c_HOL_Ozero__class_Ozero(tc_nat) % 0.59/0.70 | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom, % 0.59/0.70 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.59/0.70 | 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)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_dB_Osize_I6_J_0,axiom, % 0.59/0.70 c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(V_dB),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_liftn_Osimps_I2_J_0,axiom, % 0.59/0.70 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)) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_not__less__less__Suc__eq_1,axiom, % 0.59/0.70 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 0.59/0.70 | c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_not__less__eq_1,axiom, % 0.59/0.70 ( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.59/0.70 | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_not__less__eq_0,axiom, % 0.59/0.70 ( c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) % 0.59/0.70 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_lift__lift_0,axiom, % 0.59/0.70 ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)),c_Suc(V_k)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_i) % 0.59/0.70 | ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_zero__less__two_0,axiom, % 0.59/0.70 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.59/0.70 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a)),T_a) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_rtranclp__idemp_0,axiom, % 0.59/0.70 c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a) = c_Transitive__Closure_Ortranclp(V_r,T_a) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_class__semiring_Oadd__0_0,axiom, % 0.59/0.70 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.59/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_x) = V_x ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_comm__monoid__add_Omult__1_0,axiom, % 0.59/0.70 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.59/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_natgb_Oadd__r0__iff_1,axiom, % 0.59/0.70 V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_plus__nat_Oadd__0_0,axiom, % 0.59/0.70 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n) = V_n ). % 0.59/0.70 % 0.59/0.70 cnf(cls_Nat_Oadd__0__right_0,axiom, % 0.59/0.70 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat)) = V_m ). % 0.59/0.70 % 0.59/0.70 cnf(cls_class__ringb_Oadd__r0__iff_1,axiom, % 0.59/0.70 ( ~ class_Ring__and__Field_Oidom(T_a) % 0.59/0.70 | ~ class_Int_Onumber__ring(T_a) % 0.59/0.70 | V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Ozero__class_Ozero(T_a)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_comm__monoid__add_Omult__1__right_0,axiom, % 0.59/0.70 ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a) % 0.59/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_add__0__left_0,axiom, % 0.59/0.70 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.59/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_monoid__add__class_Oadd__0__right_0,axiom, % 0.59/0.70 ( ~ class_OrderedGroup_Omonoid__add(T_a) % 0.59/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom, % 0.59/0.70 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.59/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom, % 0.59/0.70 ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) % 0.59/0.70 | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_substn_Osimps_I2_J_0,axiom, % 0.59/0.70 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)) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_less__Suc__eq__0__disj_3,axiom, % 0.59/0.70 ( c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat) % 0.59/0.70 | ~ c_HOL_Oord__class_Oless(V_x,V_n,tc_nat) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_Suc__less__eq_0,axiom, % 0.59/0.70 ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.59/0.70 | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_Suc__mono_0,axiom, % 0.59/0.70 ( c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) % 0.59/0.70 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_rtrancl__beta__Abs_0,axiom, % 0.59/0.70 ( 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))) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_beta__cases_I2_J_1,axiom, % 0.59/0.70 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),c_Lambda_Osko__Lambda__Xbeta__cases__2__1(V_r,V_s))) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_r)),V_s)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_dB_Osize_I1_J_0,axiom, % 0.59/0.70 c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(V_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_dB_Osize_I4_J_0,axiom, % 0.59/0.70 c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(V_nat),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_liftn_Osimps_I1_J_0,axiom, % 0.59/0.70 ( c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(V_i) % 0.59/0.70 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_substn_Osimps_I1_J_2,axiom, % 0.59/0.70 ( c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_i),V_s,V_k) = c_Lambda_OdB_OVar(V_i) % 0.59/0.70 | V_i = V_k % 0.59/0.70 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_K__record__comp_0,axiom, % 0.59/0.70 hAPP(c_Fun_Ocomp(c_COMBK(V_c,T_b,T_c),V_f,T_c,T_b,t_a),v_x) = V_c ). % 0.59/0.70 % 0.59/0.70 cnf(cls_subst__preserves__beta2_0,axiom, % 0.59/0.70 ( 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))) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_subst__preserves__beta_H_0,axiom, % 0.59/0.70 ( 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))) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_subst__preserves__beta2_H_0,axiom, % 0.59/0.70 ( 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))) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_Var__eq__apps__conv_0,axiom, % 0.59/0.70 ( c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.59/0.70 | c_Lambda_OdB_OVar(V_m) = V_s ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_Var__apps__eq__Var__apps__conv_1,axiom, % 0.59/0.70 ( 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) % 0.59/0.70 | V_rs = V_ss ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_Var__apps__eq__Var__apps__conv_0,axiom, % 0.59/0.70 ( 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) % 0.59/0.70 | V_m = V_n ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_funpow_Osimps_I1_J_0,axiom, % 0.59/0.70 c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),V_f,T_a,T_a) = c_Fun_Oid(T_a) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_typing__elims_I2_J_1,axiom, % 0.59/0.70 ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_u),c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u))) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_T)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_subst__Abs_0,axiom, % 0.59/0.70 hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(V_t)),V_s),V_k) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_s),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_subject__reduction_H_0,axiom, % 0.59/0.70 ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_t_H),V_T)) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_t),V_T)) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_nT_0,axiom, % 0.59/0.70 hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_shift__commute_0,axiom, % 0.59/0.70 hAPP(hAPP(hAPP(c_Type_Oshift(T_a),hAPP(hAPP(hAPP(c_Type_Oshift(T_a),V_e),V_i),V_U)),c_HOL_Ozero__class_Ozero(tc_nat)),V_T) = hAPP(hAPP(hAPP(c_Type_Oshift(T_a),hAPP(hAPP(hAPP(c_Type_Oshift(T_a),V_e),c_HOL_Ozero__class_Ozero(tc_nat)),V_T)),c_Suc(V_i)),V_U) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_var__app__types_1,axiom, % 0.59/0.70 ( c_Type_Otypings(V_e,V_us,c_Type_Osko__Type__Xvar__app__types__1__1(V_T,V_U,V_e,V_us)) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(hAPP(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)) % 0.59/0.70 | ~ c_Type_Otypings(V_e,V_ts,V_Ts) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_us,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_var__app__typesE_1,axiom, % 0.59/0.70 ( c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T,V_e,V_i,V_ts)) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(hAPP(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)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_typing__elims_I3_J_1,axiom, % 0.59/0.70 ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_e),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xtyping__elims__3__1(V_T,V_e,V_t))),V_t),c_Type_Osko__Type__Xtyping__elims__3__2(V_T,V_e,V_t))) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_Lambda_OdB_OAbs(V_t)),V_T)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_abs__typeE_0,axiom, % 0.59/0.70 ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_e),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xabs__typeE__1__1(V_e,V_t))),V_t),c_Type_Osko__Type__Xabs__typeE__1__2(V_e,V_t))) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_Lambda_OdB_OAbs(V_t)),V_T)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_lift__preserves__beta_H_0,axiom, % 0.59/0.70 ( 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))) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_list__app__typeI_0,axiom, % 0.59/0.70 ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)) % 0.59/0.70 | ~ c_Type_Otypings(V_e,V_ts,V_Ts) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_t),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,V_T,tc_Type_Otype,tc_Type_Otype))) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_Abs__App__neq__Var__apps_0,axiom, % 0.59/0.70 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) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_Var__apps__neq__Abs__apps_0,axiom, % 0.59/0.70 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) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_var__app__type__eq_0,axiom, % 0.59/0.70 ( V_T = V_U % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(hAPP(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)) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(hAPP(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)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_typing__elims_I2_J_0,axiom, % 0.59/0.70 ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_t),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)),V_T))) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_T)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_of__nat__0__less__iff_1,axiom, % 0.59/0.70 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.59/0.70 | 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) % 0.59/0.70 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_of__nat__0__less__iff_0,axiom, % 0.59/0.70 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.59/0.70 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.59/0.70 | ~ 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) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_Beta_0,axiom, % 0.59/0.70 ( 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))) % 0.59/0.70 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_s)) % 0.59/0.70 | ~ 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))) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_Cons_I3_J_0,axiom, % 0.59/0.70 c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_lift__map_0,axiom, % 0.59/0.70 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(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_lifts__IT_0,axiom, % 0.59/0.70 ( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) % 0.59/0.70 | ~ c_List_Olistsp(c_InductTermi_OIT,V_ts,tc_Lambda_OdB) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_subst__map_0,axiom, % 0.59/0.70 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(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),V_u)),V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_dB_Osimps_I5_J_0,axiom, % 0.59/0.70 hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_id__apply_0,axiom, % 0.59/0.70 hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 0.59/0.70 % 0.59/0.70 cnf(cls_abs_0,axiom, % 0.59/0.70 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_s)),c_Lambda_OdB_OAbs(V_t))) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_app__Var__IT_0,axiom, % 0.59/0.70 ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),c_Lambda_OdB_OVar(V_i)))) % 0.59/0.70 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_lift__preserves__beta_0,axiom, % 0.59/0.70 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,V_r),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i))) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_lift_Osimps_I1_J_0,axiom, % 0.59/0.70 ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(V_i)),V_k) = c_Lambda_OdB_OVar(V_i) % 0.59/0.70 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_lift__types_0,axiom, % 0.59/0.70 ( c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_e),V_i),V_U),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts) % 0.59/0.70 | ~ c_Type_Otypings(V_e,V_ts,V_Ts) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_appL_0,axiom, % 0.59/0.70 ( 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))) % 0.59/0.70 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)) ) ). % 0.59/0.70 % 0.59/0.70 cnf(cls_appR_0,axiom, % 0.59/0.71 ( 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))) % 0.59/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_o__eq__id__dest_0,axiom, % 0.59/0.71 ( c_Fun_Ocomp(V_a,V_b,T_c,T_b,T_a) != c_Fun_Ocomp(c_Fun_Oid(T_b),V_c,T_b,T_b,T_a) % 0.59/0.71 | hAPP(V_a,hAPP(V_b,V_v)) = hAPP(V_c,V_v) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_map__map_0,axiom, % 0.59/0.71 c_List_Omap(V_f,c_List_Omap(V_g,V_xs,T_c,T_b),T_b,T_a) = c_List_Omap(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_xs,T_c,T_a) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_subst__Var_1,axiom, % 0.59/0.71 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 0.59/0.71 | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_x)),V_s),V_x) = V_s ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_COMBC__def_0,axiom, % 0.59/0.71 hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_P),V_Q),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_not__less0_0,axiom, % 0.59/0.71 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_gr__implies__not0_0,axiom, % 0.59/0.71 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_xt1_I10_J_0,axiom, % 0.59/0.71 ( ~ class_Orderings_Oorder(T_a) % 0.59/0.71 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.59/0.71 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.59/0.71 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_order__less__trans_0,axiom, % 0.59/0.71 ( ~ class_Orderings_Opreorder(T_a) % 0.59/0.71 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.59/0.71 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.59/0.71 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_id__o_0,axiom, % 0.59/0.71 c_Fun_Ocomp(c_Fun_Oid(T_b),V_g,T_b,T_b,T_a) = V_g ). % 0.59/0.71 % 0.59/0.71 cnf(cls_o__id_0,axiom, % 0.59/0.71 c_Fun_Ocomp(V_f,c_Fun_Oid(T_a),T_a,T_b,T_a) = V_f ). % 0.59/0.71 % 0.59/0.71 cnf(cls_subst__Var_2,axiom, % 0.59/0.71 ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i)),V_s),V_k) = c_Lambda_OdB_OVar(V_i) % 0.59/0.71 | V_i = V_k % 0.59/0.71 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_lift_Osimps_I2_J_0,axiom, % 0.59/0.71 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)) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_o__apply_0,axiom, % 0.59/0.71 hAPP(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_x) = hAPP(V_f,hAPP(V_g,V_x)) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_o__eq__dest__lhs_0,axiom, % 0.59/0.71 hAPP(V_a,hAPP(V_b,V_v)) = hAPP(c_Fun_Ocomp(V_a,V_b,T_c,T_b,T_a),V_v) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_dB_Osimps_I6_J_0,axiom, % 0.59/0.71 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_dB_Osimps_I3_J_0,axiom, % 0.59/0.71 ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H) % 0.59/0.71 | V_dB = V_dB_H ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_dB_Osimps_I4_J_0,axiom, % 0.59/0.71 c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_nat__less__le_1,axiom, % 0.59/0.71 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_less__not__refl_0,axiom, % 0.59/0.71 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_order__less__le_1,axiom, % 0.59/0.71 ( ~ class_Orderings_Oorder(T_a) % 0.59/0.71 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_linorder__neq__iff_1,axiom, % 0.59/0.71 ( ~ class_Orderings_Olinorder(T_a) % 0.59/0.71 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_order__less__irrefl_0,axiom, % 0.59/0.71 ( ~ class_Orderings_Opreorder(T_a) % 0.59/0.71 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_beta_0,axiom, % 0.59/0.71 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)))) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_linorder__neqE__ordered__idom_0,axiom, % 0.59/0.71 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.59/0.71 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.59/0.71 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.59/0.71 | V_x = V_y ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_not__less__iff__gr__or__eq_0,axiom, % 0.59/0.71 ( ~ class_Orderings_Olinorder(T_a) % 0.59/0.71 | V_x = V_y % 0.59/0.71 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.59/0.71 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_nat__neq__iff_0,axiom, % 0.59/0.71 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 0.59/0.71 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.59/0.71 | V_m = V_n ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_nat__less__cases_0,axiom, % 0.59/0.71 ( hBOOL(hAPP(hAPP(V_P,V_n),V_m)) % 0.59/0.71 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 0.59/0.71 | V_m = V_n % 0.59/0.71 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_linorder__neqE__nat_0,axiom, % 0.59/0.71 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat) % 0.59/0.71 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 0.59/0.71 | V_x = V_y ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_linorder__neqE_0,axiom, % 0.59/0.71 ( ~ class_Orderings_Olinorder(T_a) % 0.59/0.71 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.59/0.71 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.59/0.71 | V_x = V_y ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_linorder__less__linear_0,axiom, % 0.59/0.71 ( ~ class_Orderings_Olinorder(T_a) % 0.59/0.71 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.59/0.71 | V_x = V_y % 0.59/0.71 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_linorder__antisym__conv3_0,axiom, % 0.59/0.71 ( ~ class_Orderings_Olinorder(T_a) % 0.59/0.71 | V_x = V_y % 0.59/0.71 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.59/0.71 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_dB_Osimps_I2_J_1,axiom, % 0.59/0.71 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) % 0.59/0.71 | V_dB2 = V_dB2_H ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_dB_Osimps_I2_J_0,axiom, % 0.59/0.71 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) % 0.59/0.71 | V_dB1 = V_dB1_H ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_App_0,axiom, % 0.59/0.71 ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_env),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_U)) % 0.59/0.71 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_env),V_t),V_T)) % 0.59/0.71 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_env),V_s),hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U))) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_beta__cases_I1_J_0,axiom, % 0.59/0.71 ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_fcomp__apply_0,axiom, % 0.59/0.71 hAPP(c_Fun_Ofcomp(V_f,V_g,T_b,T_c,T_a),V_x) = hAPP(V_g,hAPP(V_f,V_x)) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_gr0I_0,axiom, % 0.59/0.71 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.59/0.71 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_o__assoc_0,axiom, % 0.59/0.71 c_Fun_Ocomp(V_f,c_Fun_Ocomp(V_g,V_h,T_d,T_c,T_a),T_c,T_b,T_a) = c_Fun_Ocomp(c_Fun_Ocomp(V_f,V_g,T_c,T_b,T_d),V_h,T_d,T_b,T_a) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_neq0__conv_1,axiom, % 0.59/0.71 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_subst__lt_0,axiom, % 0.59/0.71 ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_j)),V_u),V_i) = c_Lambda_OdB_OVar(V_j) % 0.59/0.71 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_fcomp__id_0,axiom, % 0.59/0.71 c_Fun_Ofcomp(V_f,c_Fun_Oid(T_b),T_a,T_b,T_b) = V_f ). % 0.59/0.71 % 0.59/0.71 cnf(cls_id__fcomp_0,axiom, % 0.59/0.71 c_Fun_Ofcomp(c_Fun_Oid(T_a),V_g,T_a,T_a,T_b) = V_g ). % 0.59/0.71 % 0.59/0.71 cnf(cls_type_Osimps_I2_J_1,axiom, % 0.59/0.71 ( hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H) % 0.59/0.71 | V_type2 = V_type2_H ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_type_Osimps_I2_J_0,axiom, % 0.59/0.71 ( hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H) % 0.59/0.71 | V_type1 = V_type1_H ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_dB_Osimps_I9_J_0,axiom, % 0.59/0.71 c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_dB_Osimps_I1_J_0,axiom, % 0.59/0.71 ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H) % 0.59/0.71 | V_nat = V_nat_H ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_dB_Osimps_I8_J_0,axiom, % 0.59/0.71 hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_dB_Osimps_I7_J_0,axiom, % 0.59/0.71 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_o__eq__dest_0,axiom, % 0.59/0.71 ( c_Fun_Ocomp(V_a,V_b,T_c,T_b,T_a) != c_Fun_Ocomp(V_c,V_d,T_d,T_b,T_a) % 0.59/0.71 | hAPP(V_a,hAPP(V_b,V_v)) = hAPP(V_c,hAPP(V_d,V_v)) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_comp__cong_0,axiom, % 0.59/0.71 ( hAPP(V_f,hAPP(V_g,V_x)) != hAPP(V_f_H,hAPP(V_g_H,V_x_H)) % 0.59/0.71 | hAPP(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_x) = hAPP(c_Fun_Ocomp(V_f_H,V_g_H,T_d,T_a,T_e),V_x_H) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_fcomp__assoc_0,axiom, % 0.59/0.71 c_Fun_Ofcomp(c_Fun_Ofcomp(V_f,V_g,T_a,T_d,T_c),V_h,T_a,T_c,T_b) = c_Fun_Ofcomp(V_f,c_Fun_Ofcomp(V_g,V_h,T_d,T_c,T_b),T_a,T_d,T_b) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_xt1_I9_J_0,axiom, % 0.59/0.71 ( ~ class_Orderings_Oorder(T_a) % 0.59/0.71 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.59/0.71 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_not__less__iff__gr__or__eq_1,axiom, % 0.59/0.71 ( ~ class_Orderings_Olinorder(T_a) % 0.59/0.71 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.59/0.71 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_order__less__asym_0,axiom, % 0.59/0.71 ( ~ class_Orderings_Opreorder(T_a) % 0.59/0.71 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.59/0.71 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_order__less__asym_H_0,axiom, % 0.59/0.71 ( ~ class_Orderings_Opreorder(T_a) % 0.59/0.71 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.59/0.71 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_lift__type_0,axiom, % 0.59/0.71 ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_e),V_i),V_U)),hAPP(hAPP(c_Lambda_Olift,V_t),V_i)),V_T)) % 0.59/0.71 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_t),V_T)) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_Cons_I1_J_0,axiom, % 0.59/0.71 ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),V_u),V_ia))) % 0.59/0.71 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____)) % 0.59/0.71 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u)) % 0.59/0.71 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_a____),V_T_H)) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_uT_0,axiom, % 0.59/0.71 hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),v_T____)) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_subst__App_0,axiom, % 0.59/0.71 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)) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_subject__reduction_0,axiom, % 0.59/0.71 ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_t_H),V_T)) % 0.59/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) % 0.59/0.71 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_t),V_T)) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_subst__eq_0,axiom, % 0.59/0.71 hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u ). % 0.59/0.71 % 0.59/0.71 cnf(cls_subst__Var__IT_0,axiom, % 0.59/0.71 ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),c_Lambda_OdB_OVar(V_i)),V_j))) % 0.59/0.71 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_r)) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_o__def_0,axiom, % 0.59/0.71 hAPP(c_Fun_Ocomp(V_f,V_g,T_c,T_b,t_a),v_x) = hAPP(V_f,hAPP(V_g,v_x)) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_shift__gt_0,axiom, % 0.59/0.71 ( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(T_a),V_e),V_i),V_T),V_j) = hAPP(V_e,V_j) % 0.59/0.71 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_id__def_0,axiom, % 0.59/0.71 hAPP(c_Fun_Oid(t_a),v_x) = v_x ). % 0.59/0.71 % 0.59/0.71 cnf(cls_lift__IT_0,axiom, % 0.59/0.71 ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,V_t),V_i))) % 0.59/0.71 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_MI2_0,axiom, % 0.59/0.71 ( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2) % 0.59/0.71 | hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i))) % 0.59/0.71 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_u),V_T2)) % 0.59/0.71 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u)) % 0.59/0.71 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_e),V_i),V_T2)),V_t),V_Ta)) % 0.59/0.71 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_MI1_0,axiom, % 0.59/0.71 ( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2) % 0.59/0.71 | hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i))) % 0.59/0.71 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_u),V_T1)) % 0.59/0.71 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u)) % 0.59/0.71 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_e),V_i),V_T1)),V_t),V_Ta)) % 0.59/0.71 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_shift__eq_0,axiom, % 0.59/0.71 hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(T_a),V_e),V_x),V_T),V_x) = V_T ). % 0.59/0.71 % 0.59/0.71 cnf(cls_Abs_0,axiom, % 0.59/0.71 ( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_env),c_Lambda_OdB_OAbs(V_t)),hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U))) % 0.59/0.71 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_env),c_HOL_Ozero__class_Ozero(tc_nat)),V_T)),V_t),V_U)) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_Var__IT_0,axiom, % 0.59/0.71 hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_typing__elims_I1_J_0,axiom, % 0.59/0.71 ( hAPP(V_e,V_i) = V_T % 0.59/0.71 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_Lambda_OdB_OVar(V_i)),V_T)) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_Cons_I1_J_1,axiom, % 0.59/0.71 hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_sko__local__XCons__1__1(v_T____,v_a____,v_e____,v_i____))) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_Var_I4_J_0,axiom, % 0.59/0.71 hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_ea______),v_ua______),v_T____)) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_Cons_Ohyps_I1_J_1,axiom, % 0.59/0.71 hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_sko__local__XCons__Xhyps__1__1(v_T____,v_a____,v_e____,v_i____))) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_subst__preserves__beta_0,axiom, % 0.59/0.71 ( 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))) % 0.59/0.71 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_Var_I3_J_0,axiom, % 0.59/0.71 hBOOL(hAPP(c_InductTermi_OIT,v_ua______)) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_substs__lemma_0,axiom, % 0.59/0.71 ( c_Type_Otypings(V_e,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),V_u)),V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts) % 0.59/0.71 | ~ c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_e),V_i),V_T),V_ts,V_Ts) % 0.59/0.71 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_u),V_T)) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_typing_OVar_0,axiom, % 0.59/0.71 hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_env),c_Lambda_OdB_OVar(V_x)),hAPP(V_env,V_x))) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_Lambda_0,axiom, % 0.59/0.71 ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r))) % 0.59/0.71 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_r)) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_fcomp__def_0,axiom, % 0.59/0.71 hAPP(c_Fun_Ofcomp(V_f,V_g,t_a,T_c,T_b),v_x) = hAPP(V_g,hAPP(V_f,v_x)) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_uIT_0,axiom, % 0.59/0.71 hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_subst__lift_0,axiom, % 0.59/0.71 hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k) = V_t ). % 0.59/0.71 % 0.59/0.71 cnf(cls_subst__lemma_0,axiom, % 0.59/0.71 ( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e_H),V_u),V_U)) % 0.59/0.71 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_e_H),V_i),V_U)),V_t),V_T)) % 0.59/0.71 | hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e_H),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i)),V_T)) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_CHAINED_0,axiom, % 0.59/0.71 c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_CHAINED_0_01,axiom, % 0.59/0.71 c_List_Olistsp(hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_and),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_fun(tc_nat,tc_Type_Otype)),c_All(tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_Type_Otype,tc_bool),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_bool,tc_Type_Otype),c_All(tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_bool),tc_Type_Otype),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_nat))))),hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),c_COMBS(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Type_Otype),c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Type_Otype),c_COMBS(tc_nat,tc_bool,tc_bool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_Type_Otype),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_implies)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_bool))),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype)),tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_nat),c_Type_Otyping)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),c_Type_Oshift(tc_Type_Otype))),v_T____))))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies),c_InductTermi_OIT))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Lambda_OdB,tc_Type_Otype,tc_bool)),c_Type_Otyping)),v_T____)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_Lambda_OdB),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_Lambda_OdB,tc_bool,tc_nat),c_InductTermi_OIT))),c_Lambda_Osubst)))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),c_Ex(tc_Type_Otype)),hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)))),v_as____,tc_Lambda_OdB) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_CHAINED_1,axiom, % 0.59/0.71 hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_sko__CHAINED__1(v_T____,v_a____,v_e____,v_i____))) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_CHAINED_0_02,axiom, % 0.59/0.71 ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),V_u),V_ia))) % 0.59/0.71 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____)) % 0.59/0.71 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u)) % 0.59/0.71 | ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_a____),V_T_H)) ) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_conjecture_0,negated_conjecture, % 0.59/0.71 hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_a____),v_xa)) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_conjecture_1,negated_conjecture, % 0.59/0.71 hBOOL(hAPP(c_InductTermi_OIT,v_xb)) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_conjecture_2,negated_conjecture, % 0.59/0.71 hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_conjecture_3,negated_conjecture, % 0.59/0.71 ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_xb),v_xc))) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_fun__Orderings_Opreorder,axiom, % 0.59/0.71 ( class_Orderings_Opreorder(tc_fun(T_2,T_1)) % 0.59/0.71 | ~ class_Orderings_Opreorder(T_1) ) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_fun__Orderings_Oorder,axiom, % 0.59/0.71 ( class_Orderings_Oorder(tc_fun(T_2,T_1)) % 0.59/0.71 | ~ class_Orderings_Oorder(T_1) ) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom, % 0.59/0.71 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom, % 0.59/0.71 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom, % 0.59/0.71 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom, % 0.59/0.71 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom, % 0.59/0.71 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom, % 0.59/0.71 class_Ring__and__Field_Oordered__semidom(tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom, % 0.59/0.71 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom, % 0.59/0.71 class_OrderedGroup_Oab__semigroup__add(tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom, % 0.59/0.71 class_OrderedGroup_Ocomm__monoid__add(tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom, % 0.59/0.71 class_Ring__and__Field_Ozero__neq__one(tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_nat__OrderedGroup_Osemigroup__add,axiom, % 0.59/0.71 class_OrderedGroup_Osemigroup__add(tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom, % 0.59/0.71 class_Ring__and__Field_Osemiring__1(tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom, % 0.59/0.71 class_OrderedGroup_Omonoid__add(tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom, % 0.59/0.71 class_Nat_Osemiring__char__0(tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_nat__Orderings_Opreorder,axiom, % 0.59/0.71 class_Orderings_Opreorder(tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_nat__Orderings_Olinorder,axiom, % 0.59/0.71 class_Orderings_Olinorder(tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_nat__Orderings_Oorder,axiom, % 0.59/0.71 class_Orderings_Oorder(tc_nat) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_bool__Orderings_Opreorder,axiom, % 0.59/0.71 class_Orderings_Opreorder(tc_bool) ). % 0.59/0.71 % 0.59/0.71 cnf(clsarity_bool__Orderings_Oorder,axiom, % 0.59/0.71 class_Orderings_Oorder(tc_bool) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom, % 0.59/0.71 c_fequal(V_x,V_x,T_a) ). % 0.59/0.71 % 0.59/0.71 cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom, % 0.59/0.71 ( V_X = V_Y % 0.59/0.71 | ~ c_fequal(V_X,V_Y,T_a) ) ). % 0.59/0.71 % 0.59/0.71 %------------------------------------------------------------------------------ % 0.59/0.71 %------------------------------------------- % 0.59/0.71 % Proof found % 0.59/0.71 % SZS status Theorem for theBenchmark % 0.59/0.71 % SZS output start Proof % 0.59/0.71 %ClaNum:573(EqnAxiom:162) % 0.59/0.71 %VarNum:2144(SingletonVarNum:941) % 0.59/0.71 %MaxLitNum:6 % 0.59/0.71 %MaxfuncDepth:8 % 0.59/0.71 %SharedTerms:311 % 0.59/0.71 %goalClause: 188 211 264 310 % 0.59/0.71 %singleGoalClaCount:4 % 0.59/0.71 [163]P1(a1) % 0.59/0.71 [164]P2(a1) % 0.59/0.71 [165]P29(a1) % 0.59/0.71 [166]P17(a1) % 0.59/0.71 [167]P20(a1) % 0.59/0.71 [168]P18(a1) % 0.59/0.71 [169]P21(a1) % 0.59/0.71 [170]P3(a1) % 0.59/0.71 [171]P4(a1) % 0.59/0.71 [172]P22(a1) % 0.59/0.71 [173]P23(a1) % 0.59/0.71 [174]P12(a1) % 0.59/0.71 [175]P13(a1) % 0.59/0.71 [176]P14(a1) % 0.59/0.71 [177]P24(a1) % 0.59/0.71 [178]P24(a2) % 0.59/0.71 [179]P26(a1) % 0.59/0.71 [180]P26(a2) % 0.59/0.71 [181]P25(a1) % 0.59/0.71 [289]~E(a68,a64) % 0.59/0.71 [186]P30(f23(a17,a56)) % 0.59/0.71 [187]P30(f23(a17,a71)) % 0.59/0.71 [188]P30(f23(a17,a72)) % 0.59/0.71 [275]P30(f23(f23(f23(a37,f23(f23(f23(f38(a53),a61),a64),a58)),a62),f65(a58,a62,a61,a64))) % 0.59/0.71 [276]P30(f23(f23(f23(a37,f23(f23(f23(f38(a53),a61),a64),a58)),a62),f70(a58,a62,a61,a64))) % 0.59/0.71 [277]P30(f23(f23(f23(a37,f23(f23(f23(f38(a53),a61),a64),a58)),a62),f66(a58,a62,a61,a64))) % 0.59/0.71 [210]P30(f23(f23(f23(a37,a57),a71),a58)) % 0.59/0.71 [211]P30(f23(f23(f23(a37,a55),a72),a58)) % 0.59/0.71 [212]P30(f23(f23(f23(a37,a61),a56),a58)) % 0.59/0.71 [285]P30(f23(f23(f23(a37,f23(f23(f23(f38(a53),a57),a67),a58)),f31(a20,f3(a68),a69,a52,a52)),a59)) % 0.59/0.71 [286]P30(f23(f23(f23(a37,f23(f23(f23(f38(a53),a61),a64),a58)),f31(a20,f3(a68),a69,a52,a52)),a60)) % 0.59/0.71 [310]~P30(f23(a17,f23(f23(f23(a27,a62),a72),a74))) % 0.59/0.71 [264]P30(f23(f23(f23(a37,f23(f23(f23(f38(a53),a55),a74),a58)),a62),a73)) % 0.59/0.71 [281]P7(a17,f30(f23(f23(f7(a52,a1,a52),f23(f23(f7(a52,a52,f54(a1,a52)),a27),a56)),a64),a63,a52,a52),a52) % 0.59/0.71 [288]P7(f23(f23(f11(a52,a2,a2),f23(f23(f8(a2,f54(a2,a2),a52),a50),f23(f23(f8(f54(f54(a1,a53),a2),a2,a52),f9(f54(a1,a53))),f23(f23(f8(f54(f54(a1,a53),f54(a53,a2)),f54(f54(a1,a53),a2),a52),f23(f8(f54(a53,a2),a2,f54(a1,a53)),f9(a53))),f23(f23(f8(f54(f54(a1,a53),f54(a53,f54(a52,a2))),f54(f54(a1,a53),f54(a53,a2)),a52),f23(f8(f54(a53,f54(a52,a2)),f54(a53,a2),f54(a1,a53)),f23(f8(f54(a52,a2),a2,a53),f9(a52)))),f23(f23(f8(f54(f54(a1,a53),f54(a53,f54(a52,f54(a1,a2)))),f54(f54(a1,a53),f54(a53,f54(a52,a2))),a52),f23(f8(f54(a53,f54(a52,f54(a1,a2))),f54(a53,f54(a52,a2)),f54(a1,a53)),f23(f8(f54(a52,f54(a1,a2)),f54(a52,a2),a53),f23(f8(f54(a1,a2),a2,a52),f9(a1))))),f23(f23(f11(a52,f54(f54(a1,a53),f54(a52,f54(a1,a2))),f54(f54(a1,a53),f54(a53,f54(a52,f54(a1,a2))))),f23(f23(f8(f54(f54(a1,a53),f54(f54(a52,f54(a1,a2)),f54(a53,f54(a52,f54(a1,a2))))),f54(f54(f54(a1,a53),f54(a52,f54(a1,a2))),f54(f54(a1,a53),f54(a53,f54(a52,f54(a1,a2))))),a52),f11(f54(a1,a53),f54(a52,f54(a1,a2)),f54(a53,f54(a52,f54(a1,a2))))),f23(f23(f8(f54(f54(a1,a53),f54(a53,f54(f54(a52,f54(a1,a2)),f54(a52,f54(a1,a2))))),f54(f54(a1,a53),f54(f54(a52,f54(a1,a2)),f54(a53,f54(a52,f54(a1,a2))))),a52),f23(f8(f54(a53,f54(f54(a52,f54(a1,a2)),f54(a52,f54(a1,a2)))),f54(f54(a52,f54(a1,a2)),f54(a53,f54(a52,f54(a1,a2)))),f54(a1,a53)),f7(a53,f54(a52,f54(a1,a2)),f54(a52,f54(a1,a2))))),f23(f23(f8(f54(f54(a1,a53),f54(a53,f54(f54(a1,a2),f54(a1,a2)))),f54(f54(a1,a53),f54(a53,f54(f54(a52,f54(a1,a2)),f54(a52,f54(a1,a2))))),a52),f23(f8(f54(a53,f54(f54(a1,a2),f54(a1,a2))),f54(a53,f54(f54(a52,f54(a1,a2)),f54(a52,f54(a1,a2)))),f54(a1,a53)),f23(f8(f54(f54(a1,a2),f54(a1,a2)),f54(f54(a52,f54(a1,a2)),f54(a52,f54(a1,a2))),a53),f8(f54(a1,a2),f54(a1,a2),a52)))),f23(f23(f8(f54(f54(a1,a53),f54(a53,f54(a1,f54(a2,a2)))),f54(f54(a1,a53),f54(a53,f54(f54(a1,a2),f54(a1,a2)))),a52),f23(f8(f54(a53,f54(a1,f54(a2,a2))),f54(a53,f54(f54(a1,a2),f54(a1,a2))),f54(a1,a53)),f23(f8(f54(a1,f54(a2,a2)),f54(f54(a1,a2),f54(a1,a2)),a53),f11(a1,a2,a2)))),f23(f23(f8(f54(f54(a1,a53),f54(a53,f54(a1,a2))),f54(f54(a1,a53),f54(a53,f54(a1,f54(a2,a2)))),a52),f23(f8(f54(a53,f54(a1,a2)),f54(a53,f54(a1,f54(a2,a2))),f54(a1,a53)),f23(f8(f54(a1,a2),f54(a1,f54(a2,a2)),a53),f23(f8(a2,f54(a2,a2),a1),a51)))),f23(f23(f8(f54(f54(a1,a53),f54(a1,f54(a53,a2))),f54(f54(a1,a53),f54(a53,f54(a1,a2))),a52),f23(f8(f54(a1,f54(a53,a2)),f54(a53,f54(a1,a2)),f54(a1,a53)),f7(a1,a53,a2))),f23(f7(f54(a1,a53),a52,f54(a1,f54(a53,a2))),f23(f23(f8(f54(a1,f54(a52,f54(a53,a2))),f54(a52,f54(a1,f54(a53,a2))),f54(a1,a53)),f7(a1,a52,f54(a53,a2))),f23(f23(f8(f54(a1,f54(a1,a53)),f54(a1,f54(a52,f54(a53,a2))),f54(a1,a53)),f23(f8(f54(a1,a53),f54(a52,f54(a53,a2)),a1),a37)),f23(f23(f7(f54(a1,a53),a53,f54(a1,f54(a1,a53))),f23(f23(f8(f54(a1,f54(a53,f54(a1,a53))),f54(a53,f54(a1,f54(a1,a53))),f54(a1,a53)),f7(a1,a53,f54(a1,a53))),f38(a53))),a58))))))))))),f23(f23(f8(f54(f54(a1,a53),f54(a52,f54(a1,a2))),f54(f54(a1,a53),f54(a52,f54(a1,a2))),a52),f23(f8(f54(a52,f54(a1,a2)),f54(a52,f54(a1,a2)),f54(a1,a53)),f23(f11(a52,f54(a1,a2),f54(a1,a2)),f23(f23(f8(f54(a2,a2),f54(f54(a1,a2),f54(a1,a2)),a52),f8(a2,a2,a1)),f23(f23(f8(a2,f54(a2,a2),a52),a51),a17))))),f23(f23(f8(f54(a52,f54(a1,a2)),f54(f54(a1,a53),f54(a52,f54(a1,a2))),a52),f23(f7(f54(a1,a53),f54(a52,f54(a1,a2)),f54(a52,f54(a1,a2))),f23(f23(f8(f54(a52,f54(f54(a1,a2),f54(a1,a2))),f54(f54(a52,f54(a1,a2)),f54(a52,f54(a1,a2))),f54(a1,a53)),f11(a52,f54(a1,a2),f54(a1,a2))),f23(f23(f8(f54(a52,f54(a2,a2)),f54(a52,f54(f54(a1,a2),f54(a1,a2))),f54(a1,a53)),f23(f8(f54(a2,a2),f54(f54(a1,a2),f54(a1,a2)),a52),f8(a2,a2,a1))),f23(f23(f8(f54(a52,a2),f54(a52,f54(a2,a2)),f54(a1,a53)),f23(f8(a2,f54(a2,a2),a52),a51)),f23(f23(f7(f54(a1,a53),a53,f54(a52,a2)),f23(f23(f8(f54(a52,f54(a53,a2)),f54(a53,f54(a52,a2)),f54(a1,a53)),f7(a52,a53,a2)),a37)),a58)))))),f23(f23(f8(f54(a52,f54(a1,a52)),f54(a52,f54(a1,a2)),a52),f23(f8(f54(a1,a52),f54(a1,a2),a52),f23(f8(a52,a2,a1),a17))),a27)))))))))),f23(f23(f8(f54(a53,a2),a2,a52),f12(a53)),f23(a37,f23(f23(f23(f38(a53),a61),a64),a58)))),a63,a52) % 0.59/0.71 [303]~P6(x3031,x3031,a1) % 0.59/0.71 [195]E(f15(x1951,x1951,a1),f4(a1)) % 0.59/0.71 [305]~P6(x3051,f4(a1),a1) % 0.59/0.71 [182]E(f21(f3(x1821)),f4(a1)) % 0.59/0.71 [185]E(f24(f3(x1851),a52),f4(a1)) % 0.59/0.71 [189]P30(f23(a17,f3(x1891))) % 0.59/0.71 [191]E(f23(f23(f14(a1),x1911),f4(a1)),x1911) % 0.59/0.71 [196]E(f15(x1961,f4(a1),a1),x1961) % 0.59/0.71 [200]E(f15(f4(a1),x2001,a1),f4(a1)) % 0.59/0.71 [209]P6(x2091,f23(f23(f14(a1),x2091),f16(a1)),a1) % 0.59/0.71 [214]P6(f4(a1),f23(f23(f14(a1),x2141),f16(a1)),a1) % 0.59/0.71 [297]~E(f23(f23(f14(a1),x2971),f16(a1)),x2971) % 0.59/0.71 [301]~E(f23(f23(f14(a1),x3011),f16(a1)),f4(a1)) % 0.59/0.71 [192]E(f23(f23(f14(a1),f4(a1)),x1921),x1921) % 0.59/0.71 [217]E(f23(f23(f14(a1),f21(x2171)),f23(f23(f14(a1),f4(a1)),f16(a1))),f21(f18(x2171))) % 0.59/0.71 [222]E(f23(f23(f14(a1),f24(x2221,a52)),f23(f23(f14(a1),f4(a1)),f16(a1))),f24(f18(x2221),a52)) % 0.59/0.71 [194]P5(x1941,x1941,x1942) % 0.59/0.71 [291]~E(f18(x2911),f3(x2912)) % 0.59/0.71 [184]E(f23(f5(x1841),x1842),x1842) % 0.59/0.71 [193]E(f36(f36(x1931,x1932),x1932),f36(x1931,x1932)) % 0.59/0.71 [199]E(f25(f4(a1),x1991,x1992),x1991) % 0.59/0.71 [224]P30(f23(f23(f23(a37,x2241),f3(x2242)),f23(x2241,x2242))) % 0.59/0.71 [225]P6(f15(x2251,x2252,a1),f23(f23(f14(a1),x2251),f16(a1)),a1) % 0.59/0.71 [226]E(f29(f4(a1),x2261,x2262,x2262),f5(x2262)) % 0.59/0.71 [243]E(f23(f23(f23(a27,x2431),f25(f4(a1),x2432,f4(a1))),f4(a1)),f23(f23(f23(a27,x2431),x2432),f4(a1))) % 0.59/0.71 [249]P6(x2491,f23(f23(f14(a1),f23(f23(f14(a1),x2492),x2491)),f16(a1)),a1) % 0.59/0.71 [251]P6(x2511,f23(f23(f14(a1),f23(f23(f14(a1),x2511),x2512)),f16(a1)),a1) % 0.59/0.71 [201]E(f23(f23(f14(a1),x2011),x2012),f23(f23(f14(a1),x2012),x2011)) % 0.59/0.71 [232]E(f15(x2321,f23(f23(f14(a1),x2322),f16(a1)),a1),f15(f15(x2321,f16(a1),a1),x2322,a1)) % 0.59/0.71 [247]E(f23(f23(f14(a1),f23(f23(f14(a1),f39(x2471)),f39(x2472))),f23(f23(f14(a1),f4(a1)),f16(a1))),f39(f23(f23(a40,x2471),x2472))) % 0.59/0.71 [248]E(f23(f23(f14(a1),f23(f23(f14(a1),f21(x2481)),f21(x2482))),f23(f23(f14(a1),f4(a1)),f16(a1))),f21(f23(f23(a20,x2481),x2482))) % 0.59/0.71 [254]E(f23(f23(f14(a1),f23(f23(f14(a1),f24(x2541,a52)),f24(x2542,a52))),f23(f23(f14(a1),f4(a1)),f16(a1))),f24(f23(f23(a20,x2541),x2542),a52)) % 0.59/0.71 [255]E(f23(f23(f14(a1),f23(f23(f14(a1),f24(x2551,a53)),f24(x2552,a53))),f23(f23(f14(a1),f4(a1)),f16(a1))),f24(f23(f23(a40,x2551),x2552),a53)) % 0.59/0.71 [257]P30(f23(f23(a19,f23(f23(a20,f18(x2571)),x2572)),f23(f23(f23(a27,x2571),x2572),f4(a1)))) % 0.59/0.71 [307]~P30(f23(f23(a19,f3(x3071)),x3072)) % 0.59/0.71 [308]~P6(f23(f23(f14(a1),x3081),x3082),x3082,a1) % 0.59/0.71 [309]~P6(f23(f23(f14(a1),x3091),x3092),x3091,a1) % 0.59/0.71 [203]E(f23(f23(f23(a27,f3(x2031)),x2032),x2031),x2032) % 0.59/0.71 [205]E(f15(f23(f23(f14(a1),x2051),x2052),x2052,a1),x2051) % 0.59/0.71 [206]E(f15(f23(f23(f14(a1),x2061),x2062),x2061,a1),x2062) % 0.59/0.71 [207]E(f15(x2071,f23(f23(f14(a1),x2071),x2072),a1),f4(a1)) % 0.59/0.71 [234]E(f18(f23(f23(a26,x2341),f23(f23(f14(a1),x2342),f16(a1)))),f23(f23(a26,f18(x2341)),x2342)) % 0.59/0.71 [241]E(f23(f23(f14(a1),f23(f23(f14(a1),x2411),f16(a1))),x2412),f23(f23(f14(a1),x2411),f23(f23(f14(a1),x2412),f16(a1)))) % 0.59/0.71 [245]E(f23(f23(f14(a1),f23(f23(f14(a1),x2451),f16(a1))),x2452),f23(f23(f14(a1),f23(f23(f14(a1),x2451),x2452)),f16(a1))) % 0.59/0.71 [233]E(f15(f15(x2331,x2332,a1),x2333,a1),f15(f15(x2331,x2333,a1),x2332,a1)) % 0.59/0.71 [259]E(f10(x2591,f5(x2592),x2592,x2593,x2592),x2591) % 0.59/0.71 [260]E(f13(x2601,f5(x2602),x2603,x2602,x2602),x2601) % 0.59/0.71 [261]E(f10(f5(x2611),x2612,x2611,x2611,x2613),x2612) % 0.59/0.71 [262]E(f13(f5(x2621),x2622,x2621,x2621,x2623),x2622) % 0.59/0.71 [292]~E(f3(x2921),f23(f23(a20,x2922),x2923)) % 0.59/0.71 [293]~E(f18(x2931),f23(f23(a20,x2932),x2933)) % 0.59/0.71 [294]~E(f23(f23(a20,x2941),x2942),f3(x2943)) % 0.59/0.71 [295]~E(f23(f23(a20,x2951),x2952),f18(x2953)) % 0.59/0.72 [219]P30(f23(f23(f36(x2191,x2192),x2193),x2193)) % 0.59/0.72 [242]E(f25(f23(f23(f14(a1),x2421),f16(a1)),x2422,x2423),f23(f23(a26,f25(x2421,x2422,x2423)),x2423)) % 0.59/0.72 [253]E(f15(f15(f23(f23(f14(a1),x2531),f16(a1)),x2532,a1),f23(f23(f14(a1),x2533),f16(a1)),a1),f15(f15(x2531,x2532,a1),x2533,a1)) % 0.59/0.72 [266]E(f29(f23(f23(f14(a1),x2661),f16(a1)),x2662,x2663,x2663),f10(x2662,f29(x2661,x2662,x2663,x2663),x2663,x2663,x2663)) % 0.59/0.72 [227]E(f23(f23(f14(a1),x2271),f23(f23(f14(a1),x2272),x2273)),f23(f23(f14(a1),x2272),f23(f23(f14(a1),x2271),x2273))) % 0.59/0.72 [228]E(f15(f23(f23(f14(a1),x2281),x2282),f23(f23(f14(a1),x2283),x2282),a1),f15(x2281,x2283,a1)) % 0.59/0.72 [229]E(f15(f23(f23(f14(a1),x2291),x2292),f23(f23(f14(a1),x2291),x2293),a1),f15(x2292,x2293,a1)) % 0.59/0.72 [231]E(f15(x2311,f23(f23(f14(a1),x2312),x2313),a1),f15(f15(x2311,x2312,a1),x2313,a1)) % 0.59/0.72 [238]E(f18(f25(x2381,x2382,f23(f23(f14(a1),x2383),f16(a1)))),f25(x2381,f18(x2382),x2383)) % 0.59/0.72 [244]E(f23(f23(a20,f23(f23(a26,x2441),x2442)),f23(f23(a26,x2443),x2442)),f23(f23(a26,f23(f23(a20,x2441),x2443)),x2442)) % 0.59/0.72 [256]E(f18(f23(f23(f23(a27,x2561),f23(f23(a26,x2562),f4(a1))),f23(f23(f14(a1),x2563),f16(a1)))),f23(f23(f23(a27,f18(x2561)),x2562),x2563)) % 0.59/0.72 [265]E(f18(f23(f23(f23(a27,x2651),f25(f23(f23(f14(a1),x2652),f16(a1)),x2653,f4(a1))),f23(f23(f14(a1),x2652),f16(a1)))),f23(f23(f23(a27,f18(x2651)),f25(x2652,x2653,f4(a1))),x2652)) % 0.59/0.72 [237]E(f23(f23(f14(a1),f23(f23(f14(a1),x2371),x2372)),x2373),f23(f23(f14(a1),x2371),f23(f23(f14(a1),x2372),x2373))) % 0.59/0.72 [240]E(f23(f23(f23(a27,f23(f23(a26,x2401),x2402)),x2403),x2402),x2401) % 0.59/0.72 [284]E(f31(a20,f23(f23(a26,x2841),x2842),f30(f23(f23(f7(a52,a1,a52),a26),x2842),x2843,a52,a52),a52,a52),f23(f23(a26,f31(a20,x2841,x2843,a52,a52)),x2842)) % 0.59/0.72 [204]E(f23(f6(x2041,x2042,x2043),x2044),x2041) % 0.59/0.72 [312]~E(f31(a20,f18(x3121),x3122,a52,a52),f31(a20,f3(x3123),x3124,a52,a52)) % 0.59/0.72 [246]E(f23(f23(a20,f25(x2461,x2462,x2463)),f25(x2461,x2464,x2463)),f25(x2461,f23(f23(a20,x2462),x2464),x2463)) % 0.59/0.72 [263]E(f23(f29(x2631,x2632,x2633,x2633),f23(x2632,x2634)),f23(x2632,f23(f29(x2631,x2632,x2633,x2633),x2634))) % 0.59/0.72 [278]E(f23(f10(f6(x2781,x2782,x2783),x2784,x2783,x2782,a22),a55),x2781) % 0.59/0.72 [311]~E(f23(f23(a20,f18(x3111)),x3112),f31(a20,f3(x3113),x3114,a52,a52)) % 0.59/0.72 [274]E(f10(f29(x2741,x2742,x2743,x2743),f29(x2744,x2742,x2743,x2743),x2743,x2743,x2743),f29(f23(f23(f14(a1),x2741),x2744),x2742,x2743,x2743)) % 0.59/0.72 [223]E(f23(f23(f23(f23(f38(x2231),x2232),x2233),x2234),x2233),x2234) % 0.59/0.72 [258]E(f23(f23(a20,f23(f23(f23(a27,x2581),x2582),x2583)),f23(f23(f23(a27,x2584),x2582),x2583)),f23(f23(f23(a27,f23(f23(a20,x2581),x2584)),x2582),x2583)) % 0.59/0.72 [287]E(f31(a20,f23(f23(f23(a27,x2871),x2872),x2873),f30(f23(f23(f7(a52,a1,a52),f23(f23(f7(a52,a52,f54(a1,a52)),a27),x2872)),x2873),x2874,a52,a52),a52,a52),f23(f23(f23(a27,f31(a20,x2871,x2874,a52,a52)),x2872),x2873)) % 0.59/0.72 [267]E(f23(f23(f23(f38(x2671),f23(f23(f23(f38(x2671),x2672),f4(a1)),x2673)),f23(f23(f14(a1),x2674),f16(a1))),x2675),f23(f23(f23(f38(x2671),f23(f23(f23(f38(x2671),x2672),x2674),x2675)),f4(a1)),x2673)) % 0.59/0.72 [271]E(f23(f10(x2711,x2712,x2713,x2714,x2715),x2716),f23(x2711,f23(x2712,x2716))) % 0.59/0.72 [272]E(f23(f13(x2721,x2722,x2723,x2724,x2725),x2726),f23(x2722,f23(x2721,x2726))) % 0.59/0.72 [279]E(f30(x2791,f30(x2792,x2793,x2794,x2795),x2795,x2796),f30(f10(x2791,x2792,x2795,x2796,x2794),x2793,x2794,x2796)) % 0.59/0.72 [252]E(f23(f23(f23(f7(x2521,x2522,x2523),x2524),x2525),x2526),f23(f23(x2524,x2526),x2525)) % 0.59/0.72 [282]E(f10(x2821,f10(x2822,x2823,x2824,x2825,x2826),x2825,x2827,x2826),f10(f10(x2821,x2822,x2825,x2827,x2824),x2823,x2824,x2827,x2826)) % 0.59/0.72 [283]E(f13(f13(x2831,x2832,x2833,x2834,x2835),x2836,x2833,x2835,x2837),f13(x2831,f13(x2832,x2836,x2834,x2835,x2837),x2833,x2834,x2837)) % 0.59/0.72 [316]~P29(x3161)+~E(f16(x3161),f4(x3161)) % 0.59/0.72 [322]E(x3221,f4(a1))+P6(f4(a1),x3221,a1) % 0.59/0.72 [336]~P20(x3361)+P6(f4(x3361),f16(x3361),x3361) % 0.59/0.72 [357]~P20(x3571)+~P6(f16(x3571),f4(x3571),x3571) % 0.59/0.72 [317]~P1(x3171)+E(f34(f16(a1),x3171),f16(x3171)) % 0.59/0.72 [318]~P1(x3181)+E(f34(f4(a1),x3181),f4(x3181)) % 0.59/0.72 [341]~P16(x3411)+E(f23(f23(f14(x3411),f4(x3411)),f4(x3411)),f4(x3411)) % 0.59/0.72 [342]~P30(f23(a17,x3421))+P30(f23(a17,f18(x3421))) % 0.59/0.72 [402]~P20(x4021)+P6(f4(x4021),f23(f23(f14(x4021),f16(x4021)),f16(x4021)),x4021) % 0.59/0.72 [425]E(x4251,f4(a1))+~P6(x4251,f23(f23(f14(a1),f4(a1)),f16(a1)),a1) % 0.59/0.72 [471]~P6(f4(a1),x4711,a1)+E(f23(f23(f14(a1),f15(x4711,f16(a1),a1)),f16(a1)),x4711) % 0.59/0.72 [510]~P6(f4(a1),x5101,a1)+E(f23(f23(f14(a1),f15(x5101,f23(f23(f14(a1),f4(a1)),f16(a1)),a1)),f16(a1)),x5101) % 0.59/0.72 [525]~P7(a17,x5251,a52)+P7(a17,f30(f23(f23(f7(a52,a1,a52),a26),f4(a1)),x5251,a52,a52),a52) % 0.59/0.72 [344]~P6(x3442,x3442,x3441)+~P24(x3441) % 0.59/0.72 [345]~P6(x3452,x3452,x3451)+~P26(x3451) % 0.59/0.72 [346]~P6(x3462,x3462,x3461)+~P25(x3461) % 0.59/0.72 [313]E(x3131,x3132)+~E(f3(x3131),f3(x3132)) % 0.59/0.72 [314]E(x3141,x3142)+~E(f18(x3141),f18(x3142)) % 0.59/0.72 [319]~P24(x3192)+P24(f54(x3191,x3192)) % 0.59/0.72 [320]~P26(x3202)+P26(f54(x3201,x3202)) % 0.59/0.72 [324]~P15(x3242)+E(f15(x3241,x3241,x3242),f4(x3242)) % 0.59/0.72 [325]~P11(x3252)+E(f15(x3251,x3251,x3252),f4(x3252)) % 0.59/0.72 [368]~P20(x3681)+~P6(f34(x3682,x3681),f4(x3681),x3681) % 0.59/0.72 [424]~P6(x4242,x4241,a1)+P6(f4(a1),f15(x4241,x4242,a1),a1) % 0.59/0.72 [442]P6(x4421,x4422,a1)+~P6(f4(a1),f15(x4422,x4421,a1),a1) % 0.59/0.72 [326]~P2(x3261)+E(f23(f23(f14(x3261),x3262),f4(x3261)),x3262) % 0.59/0.72 [327]~P23(x3271)+E(f23(f23(f14(x3271),x3272),f4(x3271)),x3272) % 0.59/0.72 [328]~P12(x3281)+E(f23(f23(f14(x3281),x3282),f4(x3281)),x3282) % 0.59/0.72 [329]~P15(x3292)+E(f15(x3291,f4(x3292),x3292),x3291) % 0.59/0.72 [383]~P20(x3832)+P6(x3831,f23(f23(f14(x3832),x3831),f16(x3832)),x3832) % 0.59/0.72 [398]P6(x3981,x3982,a1)+P6(x3982,f23(f23(f14(a1),x3981),f16(a1)),a1) % 0.59/0.72 [401]P6(x4012,x4011,a1)+E(f23(f23(f14(a1),x4011),f15(x4012,x4011,a1)),x4012) % 0.59/0.72 [415]~P30(f23(f23(a19,x4151),x4152))+P30(f23(f23(a19,f18(x4151)),f18(x4152))) % 0.59/0.72 [452]~P6(x4521,x4522,a1)+~P6(x4522,f23(f23(f14(a1),x4521),f16(a1)),a1) % 0.59/0.72 [488]P6(x4881,x4882,a1)+~P6(f23(f23(f14(a1),x4881),f16(a1)),f23(f23(f14(a1),x4882),f16(a1)),a1) % 0.59/0.72 [511]~P1(x5111)+E(f35(f23(f23(f7(x5111,x5111,x5111),f14(x5111)),f16(x5111)),x5112,f4(x5111),x5111),f34(x5112,x5111)) % 0.59/0.72 [534]~P2(x5341)+E(f33(f14(x5341),x5342,f4(x5341),x5341,x5341),f31(f14(x5341),f4(x5341),x5342,x5341,x5341)) % 0.59/0.72 [330]~P2(x3301)+E(f23(f23(f14(x3301),f4(x3301)),x3302),x3302) % 0.59/0.72 [332]~P23(x3321)+E(f23(f23(f14(x3321),f4(x3321)),x3322),x3322) % 0.59/0.72 [333]~P12(x3331)+E(f23(f23(f14(x3331),f4(x3331)),x3332),x3332) % 0.59/0.72 [338]E(x3381,f4(a1))+~E(f23(f23(f14(a1),x3382),x3381),x3382) % 0.59/0.72 [339]E(x3391,f4(a1))+~E(f23(f23(f14(a1),x3392),x3391),f4(a1)) % 0.59/0.72 [340]E(x3401,f4(a1))+~E(f23(f23(f14(a1),x3401),x3402),f4(a1)) % 0.59/0.72 [367]~P6(x3671,x3672,a1)+E(f23(f23(a26,f3(x3671)),x3672),f3(x3671)) % 0.59/0.72 [393]E(f18(f28(x3931,x3932)),x3932)+~P30(f23(f23(a19,f18(x3931)),x3932)) % 0.59/0.72 [400]P6(x4001,x4002,a1)+E(f23(f23(a26,f3(x4001)),x4002),f3(f23(f23(f14(a1),x4001),f16(a1)))) % 0.59/0.72 [403]~P1(x4032)+E(f34(f23(f23(f14(a1),x4031),f16(a1)),x4032),f23(f23(f14(x4032),f16(x4032)),f34(x4031,x4032))) % 0.59/0.72 [405]~P30(f23(a17,x4051))+P30(f23(a17,f23(f23(a26,x4051),x4052))) % 0.59/0.72 [421]~P30(f23(a17,x4211))+P30(f23(a17,f23(f23(a20,x4211),f3(x4212)))) % 0.59/0.72 [437]P30(f23(f23(a19,x4371),f28(x4371,x4372)))+~P30(f23(f23(a19,f18(x4371)),x4372)) % 0.59/0.72 [486]~P6(f4(a1),x4861,a1)+P6(f15(x4861,f23(f23(f14(a1),x4862),f16(a1)),a1),x4861,a1) % 0.59/0.72 [491]P30(f23(f23(f36(a19,a52),f18(x4911)),f18(x4912)))+~P30(f23(f23(f36(a19,a52),x4911),x4912)) % 0.59/0.72 [518]E(x5181,f4(a1))+E(f23(f23(f14(a1),f23(f23(f14(a1),f15(x5181,f16(a1),a1)),x5182)),f16(a1)),f23(f23(f14(a1),x5181),x5182)) % 0.59/0.72 [554]~P7(a17,x5542,a52)+P30(f23(a17,f31(a20,f3(x5541),x5542,a52,a52))) % 0.59/0.72 [343]E(x3431,x3432)+~P5(x3431,x3432,x3433) % 0.59/0.72 [422]~P6(x4221,x4223,a1)+P6(f15(x4221,x4222,a1),x4223,a1) % 0.59/0.72 [529]E(x5291,f18(x5292))+~E(f31(a20,x5291,x5293,a52,a52),f18(x5292)) % 0.59/0.72 [530]E(f3(x5301),x5302)+~E(f3(x5301),f31(a20,x5302,x5303,a52,a52)) % 0.59/0.72 [531]E(f18(x5311),x5312)+~E(f18(x5311),f31(a20,x5312,x5313,a52,a52)) % 0.59/0.72 [543]E(x5431,x5432)+~E(f31(a20,x5431,x5433,a52,a52),f31(a20,x5432,x5433,a52,a52)) % 0.59/0.72 [372]~P6(x3722,x3723,a1)+E(f25(x3721,f3(x3722),x3723),f3(x3722)) % 0.59/0.72 [426]~P1(x4263)+E(f35(x4261,f4(a1),x4262,x4263),x4262) % 0.59/0.72 [533]~P3(x5331)+E(f33(f14(x5331),x5332,x5333,x5331,x5331),f31(f14(x5331),x5333,x5332,x5331,x5331)) % 0.59/0.72 [559]~P30(f23(f23(a19,x5591),x5593))+P30(f23(f23(a19,f31(a20,x5591,x5592,a52,a52)),f31(a20,x5593,x5592,a52,a52))) % 0.59/0.72 [561]~P8(a19,x5612,x5613,a52)+P30(f23(f23(a19,f31(a20,x5611,x5612,a52,a52)),f31(a20,x5611,x5613,a52,a52))) % 0.59/0.72 [355]~P23(x3551)+E(f23(f23(f14(x3551),x3552),x3553),f23(f23(f14(x3551),x3553),x3552)) % 0.59/0.72 [356]~P12(x3561)+E(f23(f23(f14(x3561),x3562),x3563),f23(f23(f14(x3561),x3563),x3562)) % 0.59/0.72 [370]E(x3701,x3702)+~E(f23(f23(f14(a1),x3703),x3701),f23(f23(f14(a1),x3703),x3702)) % 0.59/0.72 [371]E(x3711,x3712)+~E(f23(f23(f14(a1),x3711),x3713),f23(f23(f14(a1),x3712),x3713)) % 0.59/0.72 [411]~P6(x4111,x4113,a1)+P6(x4111,f23(f23(f14(a1),x4112),x4113),a1) % 0.59/0.72 [413]~P6(x4131,x4132,a1)+P6(x4131,f23(f23(f14(a1),x4132),x4133),a1) % 0.59/0.72 [433]~P15(x4331)+E(f23(f23(f14(x4331),f15(x4332,x4333,x4331)),x4333),x4332) % 0.59/0.72 [434]P6(x4341,x4342,a1)+~P6(f23(f23(f14(a1),x4341),x4343),x4342,a1) % 0.59/0.72 [449]~P6(x4491,x4493,a1)+P6(f23(f23(f14(a1),x4491),x4492),f23(f23(f14(a1),x4493),x4492),a1) % 0.59/0.72 [450]~P6(x4502,x4503,a1)+P6(f23(f23(f14(a1),x4501),x4502),f23(f23(f14(a1),x4501),x4503),a1) % 0.59/0.72 [459]E(f23(x4591,x4592),x4593)+~P30(f23(f23(f23(a37,x4591),f3(x4592)),x4593)) % 0.59/0.72 [474]P6(x4741,f15(x4742,x4743,a1),a1)+~P6(f23(f23(f14(a1),x4741),x4743),x4742,a1) % 0.59/0.72 [476]~P6(x4761,f15(x4763,x4762,a1),a1)+P6(f23(f23(f14(a1),x4761),x4762),x4763,a1) % 0.59/0.72 [484]P6(x4841,x4842,a1)+~P6(f23(f23(f14(a1),x4843),x4841),f23(f23(f14(a1),x4843),x4842),a1) % 0.59/0.72 [502]~P30(f23(f23(a19,x5021),x5023))+P30(f23(f23(a19,f23(f23(a20,x5021),x5022)),f23(f23(a20,x5023),x5022))) % 0.59/0.72 [503]~P30(f23(f23(a19,x5032),x5033))+P30(f23(f23(a19,f23(f23(a20,x5031),x5032)),f23(f23(a20,x5031),x5033))) % 0.59/0.72 [504]~P30(f23(f23(a19,x5041),x5043))+P30(f23(f23(a19,f23(f23(a26,x5041),x5042)),f23(f23(a26,x5043),x5042))) % 0.59/0.72 [505]E(f23(f23(a40,f41(x5051,x5052,x5053)),f47(x5051,x5052,x5053)),x5051)+~P30(f23(f23(f23(a37,x5052),f18(x5053)),x5051)) % 0.59/0.72 [512]~P30(f23(f23(f36(a19,a52),x5121),x5123))+P30(f23(f23(f36(a19,a52),f23(f23(a20,x5121),x5122)),f23(f23(a20,x5123),x5122))) % 0.59/0.72 [513]~P30(f23(f23(f36(a19,a52),x5132),x5133))+P30(f23(f23(f36(a19,a52),f23(f23(a20,x5131),x5132)),f23(f23(a20,x5131),x5133))) % 0.59/0.72 [514]~P30(f23(f23(f36(a19,a52),x5141),x5143))+P30(f23(f23(f36(a19,a52),f23(f23(a26,x5141),x5142)),f23(f23(a26,x5143),x5142))) % 0.59/0.72 [535]P30(f23(f23(f23(a37,f23(f23(f23(f38(a53),x5351),f4(a1)),f43(x5351,x5352))),x5352),f44(x5351,x5352)))+~P30(f23(f23(f23(a37,x5351),f18(x5352)),x5353)) % 0.59/0.72 [541]~P2(x5411)+E(f23(f23(f14(x5411),x5412),f33(f14(x5411),x5413,f4(x5411),x5411,x5411)),f31(f14(x5411),x5412,x5413,x5411,x5411)) % 0.59/0.72 [542]~P2(x5421)+E(f23(f23(f14(x5421),x5422),f31(f14(x5421),f4(x5421),x5423,x5421,x5421)),f31(f14(x5421),x5422,x5423,x5421,x5421)) % 0.59/0.72 [553]P30(f23(f23(f23(a37,f23(f23(f23(f38(a53),x5531),f4(a1)),f41(x5532,x5531,x5533))),x5533),f47(x5532,x5531,x5533)))+~P30(f23(f23(f23(a37,x5531),f18(x5533)),x5532)) % 0.59/0.72 [560]P30(f23(f23(f36(a19,a52),f31(a20,x5601,x5602,a52,a52)),f31(a20,x5603,x5602,a52,a52)))+~P30(f23(f23(f36(a19,a52),x5601),x5603)) % 0.59/0.72 [376]~P15(x3761)+E(f15(f23(f23(f14(x3761),x3762),x3763),x3763,x3761),x3762) % 0.59/0.72 [396]~P6(x3961,x3963,a1)+E(f23(f23(f23(a27,f3(x3961)),x3962),x3963),f3(x3961)) % 0.59/0.72 [404]P6(x4042,x4043,a1)+E(f25(x4041,f3(x4042),x4043),f3(f23(f23(f14(a1),x4042),x4041))) % 0.59/0.72 [423]~P1(x4231)+E(f23(f23(f14(x4231),f34(x4232,x4231)),f34(x4233,x4231)),f34(f23(f23(f14(a1),x4232),x4233),x4231)) % 0.59/0.72 [444]~P6(x4443,x4441,a1)+E(f23(f23(f23(a27,f3(x4441)),x4442),x4443),f3(f15(x4441,f16(a1),a1))) % 0.59/0.72 [492]~P30(f23(a17,x4921))+P30(f23(a17,f23(f23(f23(a27,x4921),f3(x4922)),x4923))) % 0.59/0.72 [506]~P6(x5062,f23(f23(f14(a1),x5063),f16(a1)),a1)+E(f23(f23(a26,f23(f23(a26,x5061),x5062)),f23(f23(f14(a1),x5063),f16(a1))),f23(f23(a26,f23(f23(a26,x5061),x5063)),x5062)) % 0.59/0.72 [562]P8(a19,x5621,f32(x5622,x5621,x5623),a52)+~P30(f23(f23(a19,f31(a20,f3(x5622),x5621,a52,a52)),x5623)) % 0.59/0.72 [566]E(f31(a20,f3(x5661),f32(x5661,x5662,x5663),a52,a52),x5663)+~P30(f23(f23(a19,f31(a20,f3(x5661),x5662,a52,a52)),x5663)) % 0.59/0.72 [516]P30(f23(x5161,x5162))+~P30(f23(x5161,f15(f23(f23(f14(a1),x5163),x5162),x5163,a1))) % 0.59/0.72 [358]E(x3581,x3582)+~E(f23(f23(a20,x3583),x3581),f23(f23(a20,x3584),x3582)) % 0.59/0.72 [359]E(x3591,x3592)+~E(f23(f23(a40,x3593),x3591),f23(f23(a40,x3594),x3592)) % 0.59/0.72 [360]E(x3601,x3602)+~E(f23(f23(a20,x3601),x3603),f23(f23(a20,x3602),x3604)) % 0.59/0.72 [361]E(x3611,x3612)+~E(f23(f23(a40,x3611),x3613),f23(f23(a40,x3612),x3614)) % 0.59/0.72 [545]E(x5451,x5452)+~E(f31(a20,f3(x5453),x5451,a52,a52),f31(a20,f3(x5454),x5452,a52,a52)) % 0.59/0.72 [546]E(x5461,x5462)+~E(f31(a20,f18(x5463),x5461,a52,a52),f31(a20,f18(x5464),x5462,a52,a52)) % 0.59/0.72 [547]E(x5471,x5472)+~E(f31(a20,f3(x5471),x5473,a52,a52),f31(a20,f3(x5472),x5474,a52,a52)) % 0.59/0.72 [548]E(x5481,x5482)+~E(f31(a20,f18(x5481),x5483,a52,a52),f31(a20,f18(x5482),x5484,a52,a52)) % 0.59/0.72 [445]~P30(f23(f23(x4451,x4453),x4454))+P30(f23(f23(f36(x4451,x4452),x4453),x4454)) % 0.59/0.72 [501]~P1(x5014)+E(f35(x5011,f23(f23(f14(a1),x5012),f16(a1)),x5013,x5014),f35(x5011,x5012,f23(x5011,x5013),x5014)) % 0.59/0.72 [563]P9(x5631,x5632,f45(x5633,x5631,x5634,x5632))+~P30(f23(f23(f23(a37,x5631),f31(a20,x5634,x5632,a52,a52)),x5633)) % 0.59/0.72 [564]P9(x5641,x5642,f46(x5643,x5641,x5644,x5642))+~P30(f23(f23(f23(a37,x5641),f31(a20,x5644,x5642,a52,a52)),x5643)) % 0.59/0.72 [568]~P30(f23(f23(f23(a37,x5681),f31(a20,x5682,x5684,a52,a52)),x5683))+P30(f23(f23(f23(a37,x5681),x5682),f33(a40,f45(x5683,x5681,x5682,x5684),x5683,a53,a53))) % 0.59/0.72 [569]~P30(f23(f23(f23(a37,x5691),f31(a20,x5692,x5694,a52,a52)),x5693))+P30(f23(f23(f23(a37,x5691),x5692),f33(a40,f46(x5693,x5691,x5692,x5694),x5693,a53,a53))) % 0.59/0.72 [446]~P11(x4461)+E(f23(f23(f14(x4461),x4462),f23(f23(f14(x4461),x4463),x4464)),f23(f23(f14(x4461),x4463),f23(f23(f14(x4461),x4462),x4464))) % 0.59/0.72 [447]~P23(x4471)+E(f23(f23(f14(x4471),x4472),f23(f23(f14(x4471),x4473),x4474)),f23(f23(f14(x4471),x4473),f23(f23(f14(x4471),x4472),x4474))) % 0.59/0.72 [448]~P12(x4481)+E(f23(f23(f14(x4481),x4482),f23(f23(f14(x4481),x4483),x4484)),f23(f23(f14(x4481),x4483),f23(f23(f14(x4481),x4482),x4484))) % 0.59/0.72 [519]~P30(f23(f23(a19,x5191),x5194))+P30(f23(f23(a19,f23(f23(f23(a27,x5191),x5192),x5193)),f23(f23(f23(a27,x5194),x5192),x5193))) % 0.59/0.72 [522]~P30(f23(f23(a19,x5222),x5224))+P30(f23(f23(f36(a19,a52),f23(f23(f23(a27,x5221),x5222),x5223)),f23(f23(f23(a27,x5221),x5224),x5223))) % 0.59/0.72 [523]~P30(f23(f23(f36(a19,a52),x5231),x5234))+P30(f23(f23(f36(a19,a52),f23(f23(f23(a27,x5231),x5232),x5233)),f23(f23(f23(a27,x5234),x5232),x5233))) % 0.59/0.72 [524]~P30(f23(f23(f36(a19,a52),x5242),x5244))+P30(f23(f23(f36(a19,a52),f23(f23(f23(a27,x5241),x5242),x5243)),f23(f23(f23(a27,x5241),x5244),x5243))) % 0.59/0.72 [527]P30(f23(f23(f23(a37,x5271),x5272),f42(x5273,x5271,x5274,x5272)))+~P30(f23(f23(f23(a37,x5271),f23(f23(a20,x5274),x5272)),x5273)) % 0.59/0.72 [544]~P22(x5441)+E(f31(f14(x5441),f23(f23(f14(x5441),x5442),x5443),x5444,x5441,x5441),f23(f23(f14(x5441),x5442),f31(f14(x5441),x5443,x5444,x5441,x5441))) % 0.59/0.72 [556]~P30(f23(f23(f23(a37,x5561),f23(f23(a20,x5562),x5564)),x5563))+P30(f23(f23(f23(a37,x5561),x5562),f23(f23(a40,f42(x5563,x5561,x5562,x5564)),x5563))) % 0.59/0.72 [565]P9(x5651,x5652,f48(x5653,x5651,x5654,x5652))+~P30(f23(f23(f23(a37,x5651),f31(a20,f3(x5654),x5652,a52,a52)),x5653)) % 0.59/0.72 [570]P30(f23(f23(f23(a37,x5701),f3(x5702)),f33(a40,f48(x5703,x5701,x5702,x5704),x5703,a53,a53)))+~P30(f23(f23(f23(a37,x5701),f31(a20,f3(x5702),x5704,a52,a52)),x5703)) % 0.59/0.72 [481]~P3(x4811)+E(f23(f23(f14(x4811),f23(f23(f14(x4811),x4812),x4813)),x4814),f23(f23(f14(x4811),x4812),f23(f23(f14(x4811),x4813),x4814))) % 0.59/0.72 [482]~P23(x4821)+E(f23(f23(f14(x4821),f23(f23(f14(x4821),x4822),x4823)),x4824),f23(f23(f14(x4821),x4822),f23(f23(f14(x4821),x4823),x4824))) % 0.59/0.72 [483]~P12(x4831)+E(f23(f23(f14(x4831),f23(f23(f14(x4831),x4832),x4833)),x4834),f23(f23(f14(x4831),x4832),f23(f23(f14(x4831),x4833),x4834))) % 0.59/0.72 [496]~P23(x4961)+E(f23(f23(f14(x4961),f23(f23(f14(x4961),x4962),x4963)),x4964),f23(f23(f14(x4961),f23(f23(f14(x4961),x4962),x4964)),x4963)) % 0.59/0.72 [520]~P6(x5202,f23(f23(f14(a1),x5204),f16(a1)),a1)+E(f23(f23(f23(a27,f23(f23(a26,x5201),x5202)),f23(f23(a26,x5203),x5202)),f23(f23(f14(a1),x5204),f16(a1))),f23(f23(a26,f23(f23(f23(a27,x5201),x5203),x5204)),x5202)) % 0.59/0.72 [528]~P6(x5284,f23(f23(f14(a1),x5282),f16(a1)),a1)+E(f23(f23(f23(a27,f23(f23(a26,x5281),f23(f23(f14(a1),x5282),f16(a1)))),f23(f23(a26,x5283),x5282)),x5284),f23(f23(a26,f23(f23(f23(a27,x5281),x5283),x5284)),x5282)) % 0.59/0.72 [536]P30(f23(f23(f23(a37,x5361),f18(x5362)),f23(f23(a40,x5363),x5364)))+~P30(f23(f23(f23(a37,f23(f23(f23(f38(a53),x5361),f4(a1)),x5363)),x5362),x5364)) % 0.59/0.72 [508]~P23(x5081)+E(f23(f23(f14(x5081),f23(f23(f14(x5081),x5082),x5083)),f23(f23(f14(x5081),x5084),x5085)),f23(f23(f14(x5081),f23(f23(f14(x5081),x5082),x5084)),f23(f23(f14(x5081),x5083),x5085))) % 0.59/0.72 [526]~P9(x5261,x5264,x5265)+P9(f23(f23(f23(f38(a53),x5261),x5262),x5263),f30(f23(f23(f7(a52,a1,a52),a26),x5262),x5264,a52,a52),x5265) % 0.59/0.72 [532]~P30(f23(f23(f23(a37,x5321),x5324),x5325))+P30(f23(f23(f23(a37,f23(f23(f23(f38(a53),x5321),x5322),x5323)),f23(f23(a26,x5324),x5322)),x5325)) % 0.59/0.72 [463]~P6(x4635,x4633,a1)+E(f23(f23(f23(f23(f38(x4631),x4632),x4633),x4634),x4635),f23(x4632,x4635)) % 0.59/0.72 [490]~P6(x4903,x4905,a1)+E(f23(f23(f23(f23(f38(x4901),x4902),x4903),x4904),x4905),f23(x4902,f15(x4905,f16(a1),a1))) % 0.59/0.72 [552]~P6(x5523,f23(f23(f14(a1),x5524),f16(a1)),a1)+E(f23(f23(f23(a27,f23(f23(f23(a27,x5521),f23(f23(a26,x5522),x5523)),f23(f23(f14(a1),x5524),f16(a1)))),f23(f23(f23(a27,x5525),x5522),x5524)),x5523),f23(f23(f23(a27,f23(f23(f23(a27,x5521),x5525),x5523)),x5522),x5524)) % 0.59/0.72 [549]~E(f10(x5491,x5492,x5495,x5496,x5497),f10(f5(x5496),x5494,x5496,x5496,x5497))+E(f23(x5491,f23(x5492,x5493)),f23(x5494,x5493)) % 0.59/0.72 [550]~E(f10(x5501,x5502,x5506,x5507,x5508),f10(x5504,x5505,x5509,x5507,x5508))+E(f23(x5501,f23(x5502,x5503)),f23(x5504,f23(x5505,x5503))) % 0.59/0.72 [555]~E(f23(x5551,f23(x5552,x5556)),f23(x5557,f23(x5558,x55511)))+E(f23(f10(x5551,x5552,x5553,x5554,x5555),x5556),f23(f10(x5557,x5558,x5559,x5554,x55510),x55511)) % 0.59/0.72 [353]E(x3531,x3532)+P6(x3532,x3531,a1)+P6(x3531,x3532,a1) % 0.59/0.72 [334]~P27(x3342)+~P10(x3342)+E(f15(x3341,x3341,x3342),f4(x3342)) % 0.59/0.72 [384]E(x3841,x3842)+~E(f15(x3842,x3841,a1),f4(a1))+~E(f15(x3841,x3842,a1),f4(a1)) % 0.59/0.72 [392]~P20(x3921)+P6(f4(x3921),f34(x3922,x3921),x3921)+~P6(f4(a1),x3922,a1) % 0.59/0.72 [397]~P20(x3972)+~P6(f4(x3972),f34(x3971,x3972),x3972)+P6(f4(a1),x3971,a1) % 0.59/0.72 [462]P6(f15(x4621,x4622,a1),x4621,a1)+~P6(f4(a1),x4622,a1)+~P6(f4(a1),x4621,a1) % 0.59/0.72 [335]~P27(x3351)+~P10(x3351)+E(f23(f23(f14(x3351),x3352),f4(x3351)),x3352) % 0.59/0.72 [436]~P6(x4361,x4362,a1)+P6(f23(f23(f14(a1),x4361),f16(a1)),x4362,a1)+E(f23(f23(f14(a1),x4361),f16(a1)),x4362) % 0.59/0.72 [439]E(x4391,x4392)+P6(x4392,x4391,a1)+~P6(x4392,f23(f23(f14(a1),x4391),f16(a1)),a1) % 0.59/0.72 [441]E(x4411,x4412)+P6(x4411,x4412,a1)+~P6(x4411,f23(f23(f14(a1),x4412),f16(a1)),a1) % 0.59/0.72 [347]~P16(x3472)+E(x3471,f4(x3472))+~E(f23(f23(f14(x3472),x3471),x3471),f4(x3472)) % 0.59/0.72 [377]E(x3771,f4(a1))+E(x3772,f4(a1))+~E(f23(f23(f14(a1),x3772),x3771),f23(f23(f14(a1),f4(a1)),f16(a1))) % 0.59/0.72 [378]E(x3781,f4(a1))+E(x3782,f4(a1))+~E(f23(f23(f14(a1),f4(a1)),f16(a1)),f23(f23(f14(a1),x3782),x3781)) % 0.59/0.72 [406]E(x4061,f4(a1))+E(x4061,f23(f23(f14(a1),f4(a1)),f16(a1)))+~E(f23(f23(f14(a1),x4062),x4061),f23(f23(f14(a1),f4(a1)),f16(a1))) % 0.59/0.72 [407]E(x4071,f4(a1))+E(x4071,f23(f23(f14(a1),f4(a1)),f16(a1)))+~E(f23(f23(f14(a1),x4071),x4072),f23(f23(f14(a1),f4(a1)),f16(a1))) % 0.59/0.72 [408]E(x4081,f4(a1))+E(x4081,f23(f23(f14(a1),f4(a1)),f16(a1)))+~E(f23(f23(f14(a1),f4(a1)),f16(a1)),f23(f23(f14(a1),x4082),x4081)) % 0.59/0.72 [409]E(x4091,f4(a1))+E(x4091,f23(f23(f14(a1),f4(a1)),f16(a1)))+~E(f23(f23(f14(a1),f4(a1)),f16(a1)),f23(f23(f14(a1),x4091),x4092)) % 0.59/0.72 [428]~P16(x4281)+~P6(f4(x4281),x4282,x4281)+P6(f4(x4281),f23(f23(f14(x4281),x4282),x4282),x4281) % 0.59/0.72 [429]~P16(x4291)+~P6(x4292,f4(x4291),x4291)+P6(f23(f23(f14(x4291),x4292),x4292),f4(x4291),x4291) % 0.59/0.72 [430]~P28(x4301)+~P6(x4302,f4(x4301),x4301)+P6(f23(f23(f14(x4301),x4302),x4302),f4(x4301),x4301) % 0.59/0.72 [431]E(x4311,f23(f23(f14(a1),f4(a1)),f16(a1)))+E(x4312,f23(f23(f14(a1),f4(a1)),f16(a1)))+~E(f23(f23(f14(a1),x4312),x4311),f23(f23(f14(a1),f4(a1)),f16(a1))) % 0.59/0.72 [432]E(x4321,f23(f23(f14(a1),f4(a1)),f16(a1)))+E(x4322,f23(f23(f14(a1),f4(a1)),f16(a1)))+~E(f23(f23(f14(a1),f4(a1)),f16(a1)),f23(f23(f14(a1),x4322),x4321)) % 0.59/0.72 [455]~P16(x4552)+P6(x4551,f4(x4552),x4552)+~P6(f23(f23(f14(x4552),x4551),x4551),f4(x4552),x4552) % 0.59/0.72 [456]~P28(x4562)+P6(x4561,f4(x4562),x4562)+~P6(f23(f23(f14(x4562),x4561),x4561),f4(x4562),x4562) % 0.59/0.72 [457]~P16(x4571)+P6(f4(x4571),x4572,x4571)+~P6(f4(x4571),f23(f23(f14(x4571),x4572),x4572),x4571) % 0.59/0.72 [464]P6(f4(a1),x4641,a1)+P6(f4(a1),x4642,a1)+~P6(f4(a1),f23(f23(f14(a1),x4641),x4642),a1) % 0.59/0.72 [385]~P6(x3853,x3852,x3851)+~P24(x3851)+~P6(x3852,x3853,x3851) % 0.59/0.72 [387]~P6(x3873,x3872,x3871)+~P26(x3871)+~P6(x3872,x3873,x3871) % 0.59/0.72 [388]~P6(x3883,x3882,x3881)+~P25(x3881)+~P6(x3882,x3883,x3881) % 0.59/0.72 [321]~P4(x3213)+E(x3211,x3212)+~E(f34(x3211,x3213),f34(x3212,x3213)) % 0.59/0.72 [348]~P15(x3483)+E(x3481,x3482)+~E(f15(x3481,x3482,x3483),f4(x3483)) % 0.59/0.72 [349]~P11(x3493)+E(x3491,x3492)+~E(f15(x3491,x3492,x3493),f4(x3493)) % 0.59/0.72 [395]~P20(x3952)+~P6(x3951,x3953,a1)+P6(f34(x3951,x3952),f34(x3953,x3952),x3952) % 0.59/0.72 [414]~P20(x4143)+~P6(f34(x4141,x4143),f34(x4142,x4143),x4143)+P6(x4141,x4142,a1) % 0.59/0.72 [427]~P19(x4273)+~P6(x4271,x4272,x4273)+P6(f15(x4271,x4272,x4273),f4(x4273),x4273) % 0.59/0.72 [458]~P19(x4583)+P6(x4581,x4582,x4583)+~P6(f15(x4581,x4582,x4583),f4(x4583),x4583) % 0.59/0.72 [485]~P6(x4853,x4852,a1)+~P6(x4853,x4851,a1)+P6(f15(x4851,x4852,a1),f15(x4851,x4853,a1),a1) % 0.59/0.72 [451]~P6(x4511,x4513,a1)+~P6(x4513,x4512,a1)+P6(f23(f23(f14(a1),x4511),f16(a1)),x4512,a1) % 0.59/0.72 [495]~P6(x4952,x4953,a1)+~P30(f23(x4951,f15(x4952,x4953,a1)))+P30(f23(x4951,f4(a1))) % 0.59/0.72 [379]E(x3791,x3792)+P6(x3792,x3791,a1)+E(f23(f23(f23(a27,f3(x3791)),x3793),x3792),f3(x3791)) % 0.59/0.72 [558]~P30(f23(a17,x5582))+~P30(f23(a17,f31(a20,f23(f23(f23(a27,x5581),x5582),f4(a1)),x5583,a52,a52)))+P30(f23(a17,f31(a20,f23(f23(a20,f18(x5581)),x5582),x5583,a52,a52))) % 0.59/0.72 [389]~P11(x3894)+E(x3891,x3892)+~E(f15(x3893,x3893,x3894),f15(x3891,x3892,x3894)) % 0.59/0.72 [390]~P11(x3903)+E(x3901,x3902)+~E(f15(x3901,x3902,x3903),f15(x3904,x3904,x3903)) % 0.59/0.72 [380]~P13(x3803)+E(x3801,x3802)+~E(f23(f23(f14(x3803),x3804),x3801),f23(f23(f14(x3803),x3804),x3802)) % 0.59/0.72 [381]~P14(x3813)+E(x3811,x3812)+~E(f23(f23(f14(x3813),x3814),x3811),f23(f23(f14(x3813),x3814),x3812)) % 0.59/0.72 [382]~P14(x3823)+E(x3821,x3822)+~E(f23(f23(f14(x3823),x3821),x3824),f23(f23(f14(x3823),x3822),x3824)) % 0.59/0.72 [435]~P6(x4354,x4353,a1)+P6(x4351,x4352,a1)+~E(f23(f23(f14(a1),x4351),x4353),f23(f23(f14(a1),x4354),x4352)) % 0.59/0.72 [466]~P17(x4661)+~P6(x4662,x4664,x4661)+P6(f23(f23(f14(x4661),x4662),x4663),f23(f23(f14(x4661),x4664),x4663),x4661) % 0.59/0.72 [467]~P18(x4671)+~P6(x4672,x4674,x4671)+P6(f23(f23(f14(x4671),x4672),x4673),f23(f23(f14(x4671),x4674),x4673),x4671) % 0.59/0.72 [468]~P17(x4681)+~P6(x4683,x4684,x4681)+P6(f23(f23(f14(x4681),x4682),x4683),f23(f23(f14(x4681),x4682),x4684),x4681) % 0.59/0.72 [469]~P18(x4691)+~P6(x4693,x4694,x4691)+P6(f23(f23(f14(x4691),x4692),x4693),f23(f23(f14(x4691),x4692),x4694),x4691) % 0.59/0.72 [478]~P6(x4782,x4784,a1)+~P6(x4781,x4783,a1)+P6(f23(f23(f14(a1),x4781),x4782),f23(f23(f14(a1),x4783),x4784),a1) % 0.59/0.72 [493]~P18(x4933)+P6(x4931,x4932,x4933)+~P6(f23(f23(f14(x4933),x4934),x4931),f23(f23(f14(x4933),x4934),x4932),x4933) % 0.59/0.72 [494]~P18(x4943)+P6(x4941,x4942,x4943)+~P6(f23(f23(f14(x4943),x4941),x4944),f23(f23(f14(x4943),x4942),x4944),x4943) % 0.59/0.72 [498]~P30(f23(f23(a19,x4984),x4982))+~P30(f23(f23(f23(a37,x4981),x4984),x4983))+P30(f23(f23(f23(a37,x4981),x4982),x4983)) % 0.59/0.72 [507]~P30(f23(f23(f36(a19,a52),x5074),x5072))+~P30(f23(f23(f23(a37,x5071),x5074),x5073))+P30(f23(f23(f23(a37,x5071),x5072),x5073)) % 0.59/0.72 [517]~P30(f23(f23(f36(a19,a52),x5171),x5173))+~P30(f23(f23(f36(a19,a52),x5172),x5174))+P30(f23(f23(f36(a19,a52),f23(f23(a20,x5171),x5172)),f23(f23(a20,x5173),x5174))) % 0.59/0.72 [499]~P30(f23(f23(x4991,x4995),x4994))+~P30(f23(f23(f36(x4991,x4992),x4993),x4995))+P30(f23(f23(f36(x4991,x4992),x4993),x4994)) % 0.59/0.72 [500]~P30(f23(f23(x5001,x5003),x5005))+~P30(f23(f23(f36(x5001,x5002),x5005),x5004))+P30(f23(f23(f36(x5001,x5002),x5003),x5004)) % 0.59/0.72 [509]~P30(f23(f23(f36(x5091,x5092),x5093),x5095))+P30(f23(f23(f36(x5091,x5092),x5093),x5094))+~P30(f23(f23(f36(x5091,x5092),x5095),x5094)) % 0.59/0.72 [567]~P9(x5671,x5673,x5675)+~P30(f23(f23(f23(a37,x5671),x5672),f33(a40,x5675,x5674,a53,a53)))+P30(f23(f23(f23(a37,x5671),f31(a20,x5672,x5673,a52,a52)),x5674)) % 0.59/0.72 [475]~P11(x4751)+E(f23(f23(f14(x4751),x4752),x4753),x4754)+~E(f23(f23(f14(x4751),x4752),f23(f23(f14(x4751),x4755),x4753)),f23(f23(f14(x4751),x4755),x4754)) % 0.59/0.72 [521]~P30(f23(f23(f23(a37,x5211),x5213),x5215))+~P30(f23(f23(f23(a37,x5211),x5212),f23(f23(a40,x5215),x5214)))+P30(f23(f23(f23(a37,x5211),f23(f23(a20,x5212),x5213)),x5214)) % 0.59/0.72 [571]E(x5711,x5712)+~P30(f23(f23(f23(a37,x5713),f31(a20,f3(x5714),x5715,a52,a52)),x5711))+~P30(f23(f23(f23(a37,x5713),f31(a20,f3(x5714),x5715,a52,a52)),x5712)) % 0.59/0.72 [551]~P30(f23(f23(f23(a37,x5511),x5513),x5516))+P30(f23(f23(f23(a37,x5511),f23(f23(f23(a27,x5512),x5513),x5514)),x5515))+~P30(f23(f23(f23(a37,f23(f23(f23(f38(a53),x5511),x5514),x5516)),x5512),x5515)) % 0.59/0.72 [557]~P9(f23(f23(f23(f38(a53),x5571),x5573),x5576),x5574,x5575)+P9(x5571,f30(f23(f23(f7(a52,a1,a52),f23(f23(f7(a52,a52,f54(a1,a52)),a27),x5572)),x5573),x5574,a52,a52),x5575)+~P30(f23(f23(f23(a37,x5571),x5572),x5576)) % 0.59/0.72 [362]P6(x3621,x3622,x3623)+~P28(x3623)+E(x3621,x3622)+P6(x3622,x3621,x3623) % 0.59/0.72 [366]P6(x3661,x3662,x3663)+~P25(x3663)+E(x3661,x3662)+P6(x3662,x3661,x3663) % 0.59/0.72 [351]~P27(x3513)+~P10(x3513)+E(x3511,x3512)+~E(f15(x3511,x3512,x3513),f4(x3513)) % 0.59/0.72 [350]~P27(x3502)+~P10(x3502)+E(x3501,f4(x3502))+~E(f23(f23(f14(x3502),x3503),x3501),x3503) % 0.59/0.72 [472]~P21(x4721)+~P6(f4(x4721),x4723,x4721)+~P6(f4(x4721),x4722,x4721)+P6(f4(x4721),f23(f23(f14(x4721),x4722),x4723),x4721) % 0.59/0.72 [473]~P21(x4731)+~P6(x4733,f4(x4731),x4731)+~P6(x4732,f4(x4731),x4731)+P6(f23(f23(f14(x4731),x4732),x4733),f4(x4731),x4731) % 0.59/0.72 [417]~P24(x4173)+~P6(x4171,x4174,x4173)+P6(x4171,x4172,x4173)+~P6(x4174,x4172,x4173) % 0.59/0.72 [418]~P26(x4183)+~P6(x4181,x4184,x4183)+P6(x4181,x4182,x4183)+~P6(x4184,x4182,x4183) % 0.59/0.72 [391]~P27(x3913)+~P10(x3913)+E(x3911,x3912)+~E(f23(f23(f14(x3913),x3914),x3911),f23(f23(f14(x3913),x3914),x3912)) % 0.59/0.72 [465]~P20(x4652)+~P6(x4651,x4654,x4652)+~P6(f4(x4652),x4653,x4652)+P6(x4651,f23(f23(f14(x4652),x4653),x4654),x4652) % 0.59/0.72 [538]~P30(f23(a17,x5381))+~P30(f23(f23(f23(a37,x5383),x5381),a58))+P30(f23(a17,f23(f23(f23(a27,a62),x5381),x5382)))+~P30(f23(f23(f23(a37,f23(f23(f23(f38(a53),x5383),x5382),a58)),a62),x5384)) % 0.59/0.72 [453]~P19(x4533)+~P6(x4534,x4535,x4533)+P6(x4531,x4532,x4533)+~E(f15(x4534,x4535,x4533),f15(x4531,x4532,x4533)) % 0.59/0.72 [454]~P19(x4543)+~P6(x4544,x4545,x4543)+P6(x4541,x4542,x4543)+~E(f15(x4541,x4542,x4543),f15(x4544,x4545,x4543)) % 0.59/0.72 [487]~P17(x4871)+~P6(x4873,x4875,x4871)+~P6(x4872,x4874,x4871)+P6(f23(f23(f14(x4871),x4872),x4873),f23(f23(f14(x4871),x4874),x4875),x4871) % 0.59/0.72 [572]~P9(x5721,x5725,x5726)+P9(x5721,x5722,f49(x5723,x5724,x5721,x5722))+~P30(f23(f23(f23(a37,x5721),f31(a20,f3(x5727),x5725,a52,a52)),x5724))+~P30(f23(f23(f23(a37,x5721),f31(a20,f31(a20,f3(x5727),x5725,a52,a52),x5722,a52,a52)),x5723)) % 0.59/0.72 [573]~P9(x5733,x5735,x5736)+E(f33(a40,f49(x5731,x5732,x5733,x5734),x5731,a53,a53),x5732)+~P30(f23(f23(f23(a37,x5733),f31(a20,f3(x5737),x5735,a52,a52)),x5732))+~P30(f23(f23(f23(a37,x5733),f31(a20,f31(a20,f3(x5737),x5735,a52,a52),x5734,a52,a52)),x5731)) % 0.59/0.72 [539]~P30(f23(a17,x5392))+~P30(f23(a17,x5391))+~E(f23(f23(a40,x5394),x5395),a58)+~P30(f23(f23(f23(a37,x5396),x5392),x5395))+P30(f23(a17,f23(f23(f23(a27,x5391),x5392),x5393)))+~P30(f23(f23(f23(a37,f23(f23(f23(f38(a53),x5396),x5393),x5395)),x5391),x5397)) % 0.59/0.72 [540]~P30(f23(a17,x5402))+~P30(f23(a17,x5401))+~E(f23(f23(a40,x5404),x5405),a58)+~P30(f23(f23(f23(a37,x5406),x5402),x5404))+P30(f23(a17,f23(f23(f23(a27,x5401),x5402),x5403)))+~P30(f23(f23(f23(a37,f23(f23(f23(f38(a53),x5406),x5403),x5404)),x5401),x5407)) % 0.59/0.72 %EqnAxiom % 0.59/0.72 [1]E(x11,x11) % 0.59/0.72 [2]E(x22,x21)+~E(x21,x22) % 0.59/0.72 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.59/0.72 [4]~E(x41,x42)+E(f3(x41),f3(x42)) % 0.59/0.72 [5]~E(x51,x52)+E(f21(x51),f21(x52)) % 0.59/0.72 [6]~E(x61,x62)+E(f4(x61),f4(x62)) % 0.59/0.72 [7]~E(x71,x72)+E(f5(x71),f5(x72)) % 0.59/0.72 [8]~E(x81,x82)+E(f23(x81,x83),f23(x82,x83)) % 0.59/0.72 [9]~E(x91,x92)+E(f23(x93,x91),f23(x93,x92)) % 0.59/0.72 [10]~E(x101,x102)+E(f31(x101,x103,x104,x105,x106),f31(x102,x103,x104,x105,x106)) % 0.59/0.72 [11]~E(x111,x112)+E(f31(x113,x111,x114,x115,x116),f31(x113,x112,x114,x115,x116)) % 0.59/0.72 [12]~E(x121,x122)+E(f31(x123,x124,x121,x125,x126),f31(x123,x124,x122,x125,x126)) % 0.59/0.72 [13]~E(x131,x132)+E(f31(x133,x134,x135,x131,x136),f31(x133,x134,x135,x132,x136)) % 0.59/0.72 [14]~E(x141,x142)+E(f31(x143,x144,x145,x146,x141),f31(x143,x144,x145,x146,x142)) % 0.59/0.72 [15]~E(x151,x152)+E(f14(x151),f14(x152)) % 0.59/0.72 [16]~E(x161,x162)+E(f54(x161,x163),f54(x162,x163)) % 0.59/0.72 [17]~E(x171,x172)+E(f54(x173,x171),f54(x173,x172)) % 0.59/0.72 [18]~E(x181,x182)+E(f24(x181,x183),f24(x182,x183)) % 0.59/0.72 [19]~E(x191,x192)+E(f24(x193,x191),f24(x193,x192)) % 0.59/0.72 [20]~E(x201,x202)+E(f16(x201),f16(x202)) % 0.59/0.72 [21]~E(x211,x212)+E(f7(x211,x213,x214),f7(x212,x213,x214)) % 0.59/0.72 [22]~E(x221,x222)+E(f7(x223,x221,x224),f7(x223,x222,x224)) % 0.59/0.72 [23]~E(x231,x232)+E(f7(x233,x234,x231),f7(x233,x234,x232)) % 0.59/0.72 [24]~E(x241,x242)+E(f8(x241,x243,x244),f8(x242,x243,x244)) % 0.59/0.72 [25]~E(x251,x252)+E(f8(x253,x251,x254),f8(x253,x252,x254)) % 0.59/0.72 [26]~E(x261,x262)+E(f8(x263,x264,x261),f8(x263,x264,x262)) % 0.59/0.72 [27]~E(x271,x272)+E(f12(x271),f12(x272)) % 0.59/0.72 [28]~E(x281,x282)+E(f38(x281),f38(x282)) % 0.59/0.72 [29]~E(x291,x292)+E(f10(x291,x293,x294,x295,x296),f10(x292,x293,x294,x295,x296)) % 0.59/0.72 [30]~E(x301,x302)+E(f10(x303,x301,x304,x305,x306),f10(x303,x302,x304,x305,x306)) % 0.59/0.72 [31]~E(x311,x312)+E(f10(x313,x314,x311,x315,x316),f10(x313,x314,x312,x315,x316)) % 0.59/0.72 [32]~E(x321,x322)+E(f10(x323,x324,x325,x321,x326),f10(x323,x324,x325,x322,x326)) % 0.59/0.72 [33]~E(x331,x332)+E(f10(x333,x334,x335,x336,x331),f10(x333,x334,x335,x336,x332)) % 0.59/0.72 [34]~E(x341,x342)+E(f9(x341),f9(x342)) % 0.59/0.72 [35]~E(x351,x352)+E(f18(x351),f18(x352)) % 0.59/0.72 [36]~E(x361,x362)+E(f33(x361,x363,x364,x365,x366),f33(x362,x363,x364,x365,x366)) % 0.59/0.72 [37]~E(x371,x372)+E(f33(x373,x371,x374,x375,x376),f33(x373,x372,x374,x375,x376)) % 0.59/0.72 [38]~E(x381,x382)+E(f33(x383,x384,x381,x385,x386),f33(x383,x384,x382,x385,x386)) % 0.59/0.72 [39]~E(x391,x392)+E(f33(x393,x394,x395,x391,x396),f33(x393,x394,x395,x392,x396)) % 0.59/0.72 [40]~E(x401,x402)+E(f33(x403,x404,x405,x406,x401),f33(x403,x404,x405,x406,x402)) % 0.59/0.72 [41]~E(x411,x412)+E(f15(x411,x413,x414),f15(x412,x413,x414)) % 0.59/0.72 [42]~E(x421,x422)+E(f15(x423,x421,x424),f15(x423,x422,x424)) % 0.59/0.72 [43]~E(x431,x432)+E(f15(x433,x434,x431),f15(x433,x434,x432)) % 0.59/0.72 [44]~E(x441,x442)+E(f13(x441,x443,x444,x445,x446),f13(x442,x443,x444,x445,x446)) % 0.59/0.72 [45]~E(x451,x452)+E(f13(x453,x451,x454,x455,x456),f13(x453,x452,x454,x455,x456)) % 0.59/0.72 [46]~E(x461,x462)+E(f13(x463,x464,x461,x465,x466),f13(x463,x464,x462,x465,x466)) % 0.59/0.72 [47]~E(x471,x472)+E(f13(x473,x474,x475,x471,x476),f13(x473,x474,x475,x472,x476)) % 0.59/0.72 [48]~E(x481,x482)+E(f13(x483,x484,x485,x486,x481),f13(x483,x484,x485,x486,x482)) % 0.59/0.72 [49]~E(x491,x492)+E(f41(x491,x493,x494),f41(x492,x493,x494)) % 0.59/0.72 [50]~E(x501,x502)+E(f41(x503,x501,x504),f41(x503,x502,x504)) % 0.59/0.72 [51]~E(x511,x512)+E(f41(x513,x514,x511),f41(x513,x514,x512)) % 0.59/0.72 [52]~E(x521,x522)+E(f32(x521,x523,x524),f32(x522,x523,x524)) % 0.59/0.72 [53]~E(x531,x532)+E(f32(x533,x531,x534),f32(x533,x532,x534)) % 0.59/0.72 [54]~E(x541,x542)+E(f32(x543,x544,x541),f32(x543,x544,x542)) % 0.59/0.72 [55]~E(x551,x552)+E(f36(x551,x553),f36(x552,x553)) % 0.59/0.72 [56]~E(x561,x562)+E(f36(x563,x561),f36(x563,x562)) % 0.59/0.72 [57]~E(x571,x572)+E(f25(x571,x573,x574),f25(x572,x573,x574)) % 0.59/0.72 [58]~E(x581,x582)+E(f25(x583,x581,x584),f25(x583,x582,x584)) % 0.59/0.72 [59]~E(x591,x592)+E(f25(x593,x594,x591),f25(x593,x594,x592)) % 0.59/0.72 [60]~E(x601,x602)+E(f11(x601,x603,x604),f11(x602,x603,x604)) % 0.59/0.72 [61]~E(x611,x612)+E(f11(x613,x611,x614),f11(x613,x612,x614)) % 0.59/0.72 [62]~E(x621,x622)+E(f11(x623,x624,x621),f11(x623,x624,x622)) % 0.59/0.72 [63]~E(x631,x632)+E(f30(x631,x633,x634,x635),f30(x632,x633,x634,x635)) % 0.59/0.72 [64]~E(x641,x642)+E(f30(x643,x641,x644,x645),f30(x643,x642,x644,x645)) % 0.59/0.72 [65]~E(x651,x652)+E(f30(x653,x654,x651,x655),f30(x653,x654,x652,x655)) % 0.59/0.72 [66]~E(x661,x662)+E(f30(x663,x664,x665,x661),f30(x663,x664,x665,x662)) % 0.59/0.72 [67]~E(x671,x672)+E(f34(x671,x673),f34(x672,x673)) % 0.59/0.72 [68]~E(x681,x682)+E(f34(x683,x681),f34(x683,x682)) % 0.59/0.72 [69]~E(x691,x692)+E(f29(x691,x693,x694,x695),f29(x692,x693,x694,x695)) % 0.59/0.72 [70]~E(x701,x702)+E(f29(x703,x701,x704,x705),f29(x703,x702,x704,x705)) % 0.59/0.72 [71]~E(x711,x712)+E(f29(x713,x714,x711,x715),f29(x713,x714,x712,x715)) % 0.59/0.72 [72]~E(x721,x722)+E(f29(x723,x724,x725,x721),f29(x723,x724,x725,x722)) % 0.59/0.72 [73]~E(x731,x732)+E(f35(x731,x733,x734,x735),f35(x732,x733,x734,x735)) % 0.59/0.72 [74]~E(x741,x742)+E(f35(x743,x741,x744,x745),f35(x743,x742,x744,x745)) % 0.59/0.72 [75]~E(x751,x752)+E(f35(x753,x754,x751,x755),f35(x753,x754,x752,x755)) % 0.59/0.72 [76]~E(x761,x762)+E(f35(x763,x764,x765,x761),f35(x763,x764,x765,x762)) % 0.59/0.72 [77]~E(x771,x772)+E(f70(x771,x773,x774,x775),f70(x772,x773,x774,x775)) % 0.59/0.72 [78]~E(x781,x782)+E(f70(x783,x781,x784,x785),f70(x783,x782,x784,x785)) % 0.59/0.72 [79]~E(x791,x792)+E(f70(x793,x794,x791,x795),f70(x793,x794,x792,x795)) % 0.59/0.72 [80]~E(x801,x802)+E(f70(x803,x804,x805,x801),f70(x803,x804,x805,x802)) % 0.59/0.72 [81]~E(x811,x812)+E(f47(x811,x813,x814),f47(x812,x813,x814)) % 0.59/0.72 [82]~E(x821,x822)+E(f47(x823,x821,x824),f47(x823,x822,x824)) % 0.59/0.72 [83]~E(x831,x832)+E(f47(x833,x834,x831),f47(x833,x834,x832)) % 0.59/0.72 [84]~E(x841,x842)+E(f6(x841,x843,x844),f6(x842,x843,x844)) % 0.59/0.72 [85]~E(x851,x852)+E(f6(x853,x851,x854),f6(x853,x852,x854)) % 0.59/0.72 [86]~E(x861,x862)+E(f6(x863,x864,x861),f6(x863,x864,x862)) % 0.59/0.72 [87]~E(x871,x872)+E(f49(x871,x873,x874,x875),f49(x872,x873,x874,x875)) % 0.59/0.72 [88]~E(x881,x882)+E(f49(x883,x881,x884,x885),f49(x883,x882,x884,x885)) % 0.59/0.72 [89]~E(x891,x892)+E(f49(x893,x894,x891,x895),f49(x893,x894,x892,x895)) % 0.59/0.72 [90]~E(x901,x902)+E(f49(x903,x904,x905,x901),f49(x903,x904,x905,x902)) % 0.59/0.72 [91]~E(x911,x912)+E(f45(x911,x913,x914,x915),f45(x912,x913,x914,x915)) % 0.59/0.72 [92]~E(x921,x922)+E(f45(x923,x921,x924,x925),f45(x923,x922,x924,x925)) % 0.59/0.72 [93]~E(x931,x932)+E(f45(x933,x934,x931,x935),f45(x933,x934,x932,x935)) % 0.59/0.72 [94]~E(x941,x942)+E(f45(x943,x944,x945,x941),f45(x943,x944,x945,x942)) % 0.59/0.72 [95]~E(x951,x952)+E(f46(x951,x953,x954,x955),f46(x952,x953,x954,x955)) % 0.59/0.72 [96]~E(x961,x962)+E(f46(x963,x961,x964,x965),f46(x963,x962,x964,x965)) % 0.59/0.72 [97]~E(x971,x972)+E(f46(x973,x974,x971,x975),f46(x973,x974,x972,x975)) % 0.59/0.72 [98]~E(x981,x982)+E(f46(x983,x984,x985,x981),f46(x983,x984,x985,x982)) % 0.59/0.72 [99]~E(x991,x992)+E(f28(x991,x993),f28(x992,x993)) % 0.59/0.72 [100]~E(x1001,x1002)+E(f28(x1003,x1001),f28(x1003,x1002)) % 0.59/0.72 [101]~E(x1011,x1012)+E(f66(x1011,x1013,x1014,x1015),f66(x1012,x1013,x1014,x1015)) % 0.59/0.72 [102]~E(x1021,x1022)+E(f66(x1023,x1021,x1024,x1025),f66(x1023,x1022,x1024,x1025)) % 0.59/0.72 [103]~E(x1031,x1032)+E(f66(x1033,x1034,x1031,x1035),f66(x1033,x1034,x1032,x1035)) % 0.59/0.72 [104]~E(x1041,x1042)+E(f66(x1043,x1044,x1045,x1041),f66(x1043,x1044,x1045,x1042)) % 0.59/0.72 [105]~E(x1051,x1052)+E(f39(x1051),f39(x1052)) % 0.59/0.72 [106]~E(x1061,x1062)+E(f44(x1061,x1063),f44(x1062,x1063)) % 0.59/0.72 [107]~E(x1071,x1072)+E(f44(x1073,x1071),f44(x1073,x1072)) % 0.59/0.72 [108]~E(x1081,x1082)+E(f48(x1081,x1083,x1084,x1085),f48(x1082,x1083,x1084,x1085)) % 0.59/0.72 [109]~E(x1091,x1092)+E(f48(x1093,x1091,x1094,x1095),f48(x1093,x1092,x1094,x1095)) % 0.59/0.72 [110]~E(x1101,x1102)+E(f48(x1103,x1104,x1101,x1105),f48(x1103,x1104,x1102,x1105)) % 0.59/0.72 [111]~E(x1111,x1112)+E(f48(x1113,x1114,x1115,x1111),f48(x1113,x1114,x1115,x1112)) % 0.59/0.72 [112]~E(x1121,x1122)+E(f43(x1121,x1123),f43(x1122,x1123)) % 0.59/0.72 [113]~E(x1131,x1132)+E(f43(x1133,x1131),f43(x1133,x1132)) % 0.59/0.72 [114]~E(x1141,x1142)+E(f65(x1141,x1143,x1144,x1145),f65(x1142,x1143,x1144,x1145)) % 0.59/0.72 [115]~E(x1151,x1152)+E(f65(x1153,x1151,x1154,x1155),f65(x1153,x1152,x1154,x1155)) % 0.59/0.72 [116]~E(x1161,x1162)+E(f65(x1163,x1164,x1161,x1165),f65(x1163,x1164,x1162,x1165)) % 0.59/0.72 [117]~E(x1171,x1172)+E(f65(x1173,x1174,x1175,x1171),f65(x1173,x1174,x1175,x1172)) % 0.59/0.72 [118]~E(x1181,x1182)+E(f42(x1181,x1183,x1184,x1185),f42(x1182,x1183,x1184,x1185)) % 0.59/0.72 [119]~E(x1191,x1192)+E(f42(x1193,x1191,x1194,x1195),f42(x1193,x1192,x1194,x1195)) % 0.59/0.72 [120]~E(x1201,x1202)+E(f42(x1203,x1204,x1201,x1205),f42(x1203,x1204,x1202,x1205)) % 0.59/0.72 [121]~E(x1211,x1212)+E(f42(x1213,x1214,x1215,x1211),f42(x1213,x1214,x1215,x1212)) % 0.59/0.72 [122]~P1(x1221)+P1(x1222)+~E(x1221,x1222) % 0.59/0.72 [123]~P2(x1231)+P2(x1232)+~E(x1231,x1232) % 0.59/0.72 [124]~P29(x1241)+P29(x1242)+~E(x1241,x1242) % 0.59/0.72 [125]~P17(x1251)+P17(x1252)+~E(x1251,x1252) % 0.59/0.72 [126]~P20(x1261)+P20(x1262)+~E(x1261,x1262) % 0.59/0.72 [127]~P18(x1271)+P18(x1272)+~E(x1271,x1272) % 0.59/0.72 [128]~P21(x1281)+P21(x1282)+~E(x1281,x1282) % 0.59/0.72 [129]~P3(x1291)+P3(x1292)+~E(x1291,x1292) % 0.59/0.72 [130]~P4(x1301)+P4(x1302)+~E(x1301,x1302) % 0.59/0.72 [131]~P22(x1311)+P22(x1312)+~E(x1311,x1312) % 0.59/0.72 [132]~P23(x1321)+P23(x1322)+~E(x1321,x1322) % 0.59/0.72 [133]~P12(x1331)+P12(x1332)+~E(x1331,x1332) % 0.59/0.72 [134]~P13(x1341)+P13(x1342)+~E(x1341,x1342) % 0.59/0.72 [135]~P14(x1351)+P14(x1352)+~E(x1351,x1352) % 0.59/0.72 [136]~P24(x1361)+P24(x1362)+~E(x1361,x1362) % 0.59/0.72 [137]~P30(x1371)+P30(x1372)+~E(x1371,x1372) % 0.59/0.72 [138]~P26(x1381)+P26(x1382)+~E(x1381,x1382) % 0.59/0.72 [139]P6(x1392,x1393,x1394)+~E(x1391,x1392)+~P6(x1391,x1393,x1394) % 0.59/0.72 [140]P6(x1403,x1402,x1404)+~E(x1401,x1402)+~P6(x1403,x1401,x1404) % 0.59/0.72 [141]P6(x1413,x1414,x1412)+~E(x1411,x1412)+~P6(x1413,x1414,x1411) % 0.59/0.72 [142]~P25(x1421)+P25(x1422)+~E(x1421,x1422) % 0.59/0.72 [143]~P19(x1431)+P19(x1432)+~E(x1431,x1432) % 0.59/0.72 [144]P9(x1442,x1443,x1444)+~E(x1441,x1442)+~P9(x1441,x1443,x1444) % 0.59/0.72 [145]P9(x1453,x1452,x1454)+~E(x1451,x1452)+~P9(x1453,x1451,x1454) % 0.59/0.72 [146]P9(x1463,x1464,x1462)+~E(x1461,x1462)+~P9(x1463,x1464,x1461) % 0.59/0.72 [147]~P10(x1471)+P10(x1472)+~E(x1471,x1472) % 0.59/0.72 [148]P7(x1482,x1483,x1484)+~E(x1481,x1482)+~P7(x1481,x1483,x1484) % 0.59/0.72 [149]P7(x1493,x1492,x1494)+~E(x1491,x1492)+~P7(x1493,x1491,x1494) % 0.59/0.72 [150]P7(x1503,x1504,x1502)+~E(x1501,x1502)+~P7(x1503,x1504,x1501) % 0.59/0.72 [151]P5(x1512,x1513,x1514)+~E(x1511,x1512)+~P5(x1511,x1513,x1514) % 0.59/0.72 [152]P5(x1523,x1522,x1524)+~E(x1521,x1522)+~P5(x1523,x1521,x1524) % 0.59/0.72 [153]P5(x1533,x1534,x1532)+~E(x1531,x1532)+~P5(x1533,x1534,x1531) % 0.59/0.72 [154]~P16(x1541)+P16(x1542)+~E(x1541,x1542) % 0.59/0.72 [155]~P28(x1551)+P28(x1552)+~E(x1551,x1552) % 0.59/0.72 [156]~P27(x1561)+P27(x1562)+~E(x1561,x1562) % 0.59/0.72 [157]~P11(x1571)+P11(x1572)+~E(x1571,x1572) % 0.59/0.72 [158]~P15(x1581)+P15(x1582)+~E(x1581,x1582) % 0.59/0.72 [159]P8(x1592,x1593,x1594,x1595)+~E(x1591,x1592)+~P8(x1591,x1593,x1594,x1595) % 0.59/0.72 [160]P8(x1603,x1602,x1604,x1605)+~E(x1601,x1602)+~P8(x1603,x1601,x1604,x1605) % 0.59/0.72 [161]P8(x1613,x1614,x1612,x1615)+~E(x1611,x1612)+~P8(x1613,x1614,x1611,x1615) % 0.59/0.72 [162]P8(x1623,x1624,x1625,x1622)+~E(x1621,x1622)+~P8(x1623,x1624,x1625,x1621) % 0.59/0.72 % 0.59/0.72 %------------------------------------------- % 0.59/0.72 cnf(608,plain, % 0.59/0.72 ($false), % 0.59/0.72 inference(scs_inference,[],[188,211,310,264,538]), % 0.59/0.72 ['proof']). % 0.59/0.72 % SZS output end Proof % 0.59/0.72 % Total time :0.048763s %------------------------------------------------------------------------------