%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LCL822-1 : TPTP v9.3.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n006.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 0.43s 0.57s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL822-1 : TPTP v9.3.1. Released v4.1.0. % 0.00/0.03 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.08/0.36 % Computer : n006.cluster.edu % 0.08/0.36 % Model : x86_64 x86_64 % 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.36 % Memory : 8046.5625MB % 0.08/0.36 % OS : Linux 6.8.0-71-generic % 0.08/0.36 % CPULimit : 300 % 0.08/0.36 % WCLimit : 300 % 0.08/0.36 % DateTime : Sat Sep 5 20:33:01 UTC 2026 % 0.08/0.36 % CPUTime : % 0.26/0.47 start to proof:theBenchmark % 0.26/0.54 %------------------------------------------- % 0.26/0.54 % File :CSE---1.7 % 0.26/0.54 % Problem :theBenchmark % 0.26/0.54 % Transform :cnf % 0.26/0.54 % Format :tptp:raw % 0.26/0.54 % Command :java -jar mcs_scs.jar %d %s % 0.26/0.54 % 0.26/0.54 % Result :Theorem 0.018730s % 0.26/0.54 % Output :CNFRefutation 0.018730s % 0.26/0.55 %------------------------------------------- % 0.26/0.55 %------------------------------------------------------------------------------ % 0.26/0.55 % File : LCL822-1 : TPTP v9.3.1. Released v4.1.0. % 0.26/0.55 % Domain : Logic Calculi % 0.26/0.55 % Problem : Strong normalization of typed lambda calculus 196_31 % 0.26/0.55 % Version : Especial. % 0.26/0.55 % English : % 0.26/0.55 % 0.26/0.55 % Refs : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java % 0.26/0.55 % : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe % 0.26/0.55 % : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 0.26/0.55 % Source : [Nip10] % 0.26/0.55 % Names : StrongNorm-196_31 [Nip10] % 0.26/0.55 % 0.26/0.55 % Status : Unsatisfiable % 0.26/0.55 % Rating : 0.17 v9.3.0, 0.09 v9.1.0, 0.10 v8.1.0, 0.05 v7.5.0, 0.11 v7.4.0, 0.12 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.00 v6.0.0, 0.10 v5.5.0, 0.20 v5.4.0, 0.15 v5.3.0, 0.17 v5.2.0, 0.19 v5.1.0, 0.24 v5.0.0, 0.14 v4.1.0 % 0.26/0.55 % Syntax : Number of clauses : 231 ( 82 unt; 12 nHn; 134 RR) % 0.26/0.55 % Number of literals : 441 ( 139 equ; 215 neg) % 0.26/0.55 % Maximal clause size : 6 ( 1 avg) % 0.26/0.55 % Maximal term depth : 6 ( 2 avg) % 0.26/0.55 % Number of predicates : 16 ( 15 usr; 0 prp; 1-4 aty) % 0.26/0.55 % Number of functors : 51 ( 51 usr; 20 con; 0-6 aty) % 0.26/0.55 % Number of variables : 676 ( 127 sgn) % 0.26/0.55 % SPC : CNF_UNS_RFO_SEQ_NHN % 0.26/0.55 % 0.26/0.55 % Comments : % 0.26/0.55 %------------------------------------------------------------------------------ % 0.26/0.55 cnf(cls_rtranclp__idemp_0,axiom, % 0.26/0.55 c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a) = c_Transitive__Closure_Ortranclp(V_r,T_a) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_rtranclp__converseI_0,axiom, % 0.26/0.55 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y)) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_x)) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_rtranclp__converseD_0,axiom, % 0.26/0.55 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_x)) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y)) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_foldr_Osimps_I1_J_0,axiom, % 0.26/0.55 c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a) = V_a ). % 0.26/0.55 % 0.26/0.55 cnf(cls_conversepD_0,axiom, % 0.26/0.55 ( hBOOL(hAPP(hAPP(V_r,V_b),V_a)) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a),V_b)) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_conversep__iff_1,axiom, % 0.26/0.55 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a),V_b)) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(V_r,V_b),V_a)) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_conversep_Ocases_0,axiom, % 0.26/0.55 ( hBOOL(hAPP(hAPP(V_r,V_a2),V_a1)) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a1),V_a2)) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_conversep_Ointros_0,axiom, % 0.26/0.55 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_b),V_a)) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b)) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_append__step1I_0,axiom, % 0.26/0.55 ( ~ c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a) % 0.26/0.55 | c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,V_x,T_a),c_List_Oappend(V_xs,V_x,T_a),T_a) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_append__step1I_1,axiom, % 0.26/0.55 ( c_ListOrder_Ostep1(V_r,c_List_Oappend(V_x,V_vs,T_a),c_List_Oappend(V_x,V_us,T_a),T_a) % 0.26/0.55 | ~ c_ListOrder_Ostep1(V_r,V_vs,V_us,T_a) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_rtranclp_Ortrancl__refl_0,axiom, % 0.26/0.55 hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_Nitpick_Ortranclp__def_1,axiom, % 0.26/0.55 hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_accp__downwards_0,axiom, % 0.26/0.55 ( c_Wellfounded_Oaccp(V_r,V_b,T_a) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a)) % 0.26/0.55 | ~ c_Wellfounded_Oaccp(V_r,V_a,T_a) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_accp__downwards__aux_0,axiom, % 0.26/0.55 ( c_Wellfounded_Oaccp(V_r,V_b,T_a) % 0.26/0.55 | ~ c_Wellfounded_Oaccp(V_r,V_a,T_a) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a)) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_rtranclp__trans_0,axiom, % 0.26/0.55 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_z)) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_z)) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y)) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_IT__implies__termi_0,axiom, % 0.26/0.55 ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) % 0.26/0.55 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_termi__implies__IT_0,axiom, % 0.26/0.55 ( hBOOL(hAPP(c_InductTermi_OIT,V_r)) % 0.26/0.55 | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_r,tc_Lambda_OdB) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_foldr__append_0,axiom, % 0.26/0.55 c_List_Ofoldr(V_f,c_List_Oappend(V_xs,V_ys,T_b),V_a,T_b,T_a) = c_List_Ofoldr(V_f,V_xs,c_List_Ofoldr(V_f,V_ys,V_a,T_b,T_a),T_b,T_a) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_of__nat__eq__iff_0,axiom, % 0.26/0.55 ( ~ class_Nat_Osemiring__char__0(T_a) % 0.26/0.55 | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) % 0.26/0.55 | V_m = V_n ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_r__into__rtranclp_0,axiom, % 0.26/0.55 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y)) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(V_r,V_x),V_y)) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_not__Nil__step1_0,axiom, % 0.26/0.55 ~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_not__step1__Nil_0,axiom, % 0.26/0.55 ~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_conversep__eq_0,axiom, % 0.26/0.55 c_Predicate_Oconversep(c_fequal(T_a),T_a,T_a) = c_fequal(T_a) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_conversep__conversep_0,axiom, % 0.26/0.55 c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a) = V_r ). % 0.26/0.55 % 0.26/0.55 cnf(cls_converse__rtranclp__into__rtranclp_0,axiom, % 0.26/0.55 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c)) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_c)) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b)) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_rtranclp_Ortrancl__into__rtrancl_0,axiom, % 0.26/0.55 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c)) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(V_r,V_b),V_c)) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_b)) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_accp_Ocases_0,axiom, % 0.26/0.55 ( c_Wellfounded_Oaccp(V_r,V_y,T_a) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(V_r,V_y),V_a)) % 0.26/0.55 | ~ c_Wellfounded_Oaccp(V_r,V_a,T_a) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_accp__downward_0,axiom, % 0.26/0.55 ( c_Wellfounded_Oaccp(V_r,V_a,T_a) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b)) % 0.26/0.55 | ~ c_Wellfounded_Oaccp(V_r,V_b,T_a) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_of__nat__less__0__iff_0,axiom, % 0.26/0.55 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.26/0.55 | ~ 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) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_of__nat__0_0,axiom, % 0.26/0.55 ( ~ class_Ring__and__Field_Osemiring__1(T_a) % 0.26/0.55 | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_of__nat__less__iff_1,axiom, % 0.26/0.55 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.26/0.55 | 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) % 0.26/0.55 | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_of__nat__less__iff_0,axiom, % 0.26/0.55 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.26/0.55 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.26/0.55 | ~ 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) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_length__0__conv_1,axiom, % 0.26/0.55 c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_length__0__conv_0,axiom, % 0.26/0.55 ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) % 0.26/0.55 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_rtrancl__beta__App_0,axiom, % 0.26/0.55 ( 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))) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_rtrancl__beta__AppL_0,axiom, % 0.26/0.55 ( 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))) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_rtrancl__beta__AppR_0,axiom, % 0.26/0.55 ( 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))) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_rtrancl__beta__Abs_0,axiom, % 0.26/0.55 ( 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))) % 0.26/0.55 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)) ) ). % 0.26/0.55 % 0.26/0.55 cnf(cls_App__eq__foldl__conv_0,axiom, % 0.26/0.56 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) % 0.26/0.56 | hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = V_t ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_App__eq__foldl__conv_4,axiom, % 0.26/0.56 hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_subst__preserves__beta2_0,axiom, % 0.26/0.56 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(V_t,V_r,V_i)),c_Lambda_Osubst(V_t,V_s,V_i))) % 0.26/0.56 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_subst__preserves__beta_H_0,axiom, % 0.26/0.56 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(V_r,V_t,V_i)),c_Lambda_Osubst(V_s,V_t,V_i))) % 0.26/0.56 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_subst__preserves__beta2_H_0,axiom, % 0.26/0.56 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(V_t,V_r,V_i)),c_Lambda_Osubst(V_t,V_s,V_i))) % 0.26/0.56 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_head__Var__reduction_0,axiom, % 0.26/0.56 ( 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) % 0.26/0.56 | ~ 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)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_typing__elims_I2_J_1,axiom, % 0.26/0.56 ( hBOOL(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))) % 0.26/0.56 | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_T)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_subject__reduction_H_0,axiom, % 0.26/0.56 ( hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_t_H),V_T)) % 0.26/0.56 | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_t),V_T)) % 0.26/0.56 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_list__app__typeD_0,axiom, % 0.26/0.56 ( hBOOL(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))) % 0.26/0.56 | ~ hBOOL(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)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_list__app__typeE_0,axiom, % 0.26/0.56 ( hBOOL(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))) % 0.26/0.56 | ~ hBOOL(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)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_lift__preserves__beta_H_0,axiom, % 0.26/0.56 ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(V_r,V_i)),c_Lambda_Olift(V_s,V_i))) % 0.26/0.56 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_appR_0,axiom, % 0.26/0.56 ( 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))) % 0.26/0.56 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_appL_0,axiom, % 0.26/0.56 ( 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))) % 0.26/0.56 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_uIT_0,axiom, % 0.26/0.56 hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_subst__lift_0,axiom, % 0.26/0.56 c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ). % 0.26/0.56 % 0.26/0.56 cnf(cls_lift_Osimps_I1_J_0,axiom, % 0.26/0.56 ( c_Lambda_Olift(c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(V_i) % 0.26/0.56 | ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_lift__preserves__beta_0,axiom, % 0.26/0.56 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(V_r,V_i)),c_Lambda_Olift(V_s,V_i))) % 0.26/0.56 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_app__Var__IT_0,axiom, % 0.26/0.56 ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),c_Lambda_OdB_OVar(V_i)))) % 0.26/0.56 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_Nil__is__append__conv_2,axiom, % 0.26/0.56 c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_inf1E_1,axiom, % 0.26/0.56 ( hBOOL(hAPP(V_B,V_x)) % 0.26/0.56 | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_inf1E_0,axiom, % 0.26/0.56 ( hBOOL(hAPP(V_A,V_x)) % 0.26/0.56 | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_Abs__App__neq__Var__apps_0,axiom, % 0.26/0.56 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) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_abs_0,axiom, % 0.26/0.56 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_s)),c_Lambda_OdB_OAbs(V_t))) % 0.26/0.56 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_foldl__append_0,axiom, % 0.26/0.56 c_List_Ofoldl(V_f,V_a,c_List_Oappend(V_xs,V_ys,T_b),T_a,T_b) = c_List_Ofoldl(V_f,c_List_Ofoldl(V_f,V_a,V_xs,T_a,T_b),V_ys,T_a,T_b) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_dB_Osimps_I5_J_0,axiom, % 0.26/0.56 hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_list__app__typeI_0,axiom, % 0.26/0.56 ( hBOOL(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)) % 0.26/0.56 | ~ c_Type_Otypings(V_e,V_ts,V_Ts) % 0.26/0.56 | ~ hBOOL(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))) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_var__app__typesE_1,axiom, % 0.26/0.56 ( c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T,V_e,V_i,V_ts)) % 0.26/0.56 | ~ hBOOL(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)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_var__app__types_1,axiom, % 0.26/0.56 ( c_Type_Otypings(V_e,V_us,c_Type_Osko__Type__Xvar__app__types__1__1(V_T,V_U,V_e,V_us)) % 0.26/0.56 | ~ hBOOL(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)) % 0.26/0.56 | ~ c_Type_Otypings(V_e,V_ts,V_Ts) % 0.26/0.56 | ~ hBOOL(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)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_list__app__typeD_1,axiom, % 0.26/0.56 ( c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts)) % 0.26/0.56 | ~ hBOOL(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)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_list__app__typeE_1,axiom, % 0.26/0.56 ( c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeE__1__1(V_T,V_e,V_t,V_ts)) % 0.26/0.56 | ~ hBOOL(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)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_head__Var__reduction_1,axiom, % 0.26/0.56 ( 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) % 0.26/0.56 | ~ 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)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_of__nat__0__less__iff_0,axiom, % 0.26/0.56 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.26/0.56 | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.26/0.56 | ~ 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) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_of__nat__0__less__iff_1,axiom, % 0.26/0.56 ( ~ class_Ring__and__Field_Oordered__semidom(T_a) % 0.26/0.56 | 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) % 0.26/0.56 | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_var__app__types_0,axiom, % 0.26/0.56 ( 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) % 0.26/0.56 | ~ hBOOL(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)) % 0.26/0.56 | ~ c_Type_Otypings(V_e,V_ts,V_Ts) % 0.26/0.56 | ~ hBOOL(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)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_typing__elims_I2_J_0,axiom, % 0.26/0.56 ( hBOOL(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))) % 0.26/0.56 | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_T)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_Var__eq__apps__conv_2,axiom, % 0.26/0.56 c_Lambda_OdB_OVar(V_m) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_Var__eq__apps__conv_1,axiom, % 0.26/0.56 ( c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.26/0.56 | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_Abs__eq__apps__conv_1,axiom, % 0.26/0.56 ( c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.26/0.56 | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_Abs__eq__apps__conv_2,axiom, % 0.26/0.56 c_Lambda_OdB_OAbs(V_r) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_apps__eq__Abs__conv_1,axiom, % 0.26/0.56 ( c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r) % 0.26/0.56 | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_apps__eq__Abs__conv_2,axiom, % 0.26/0.56 c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(V_r) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_apps__preserves__beta2_0,axiom, % 0.26/0.56 ( 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))) % 0.26/0.56 | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_apps__preserves__betas_0,axiom, % 0.26/0.56 ( 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))) % 0.26/0.56 | ~ c_ListOrder_Ostep1(c_Lambda_Obeta,V_rs,V_ss,tc_Lambda_OdB) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_double__induction__lemma_0,axiom, % 0.26/0.56 ( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(V_r,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) % 0.26/0.56 | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_s,tc_Lambda_OdB) % 0.26/0.56 | c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r)),V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_length__greater__0__conv_1,axiom, % 0.26/0.56 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) % 0.26/0.56 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_length__greater__0__conv_0,axiom, % 0.26/0.56 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)),tc_nat) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_var__app__typesE_0,axiom, % 0.26/0.56 ( hBOOL(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))) % 0.26/0.56 | ~ hBOOL(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)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_Lambda_0,axiom, % 0.26/0.56 ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r))) % 0.26/0.56 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_r)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_apps__eq__tail__conv_0,axiom, % 0.26/0.56 ( 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) % 0.26/0.56 | V_r = V_s ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_Abs__eq__apps__conv_0,axiom, % 0.26/0.56 ( c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.26/0.56 | c_Lambda_OdB_OAbs(V_r) = V_s ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_inf__sup__aci_I1_J_0,axiom, % 0.26/0.56 ( ~ class_Lattices_Olattice(T_a) % 0.26/0.56 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_inf__commute_0,axiom, % 0.26/0.56 ( ~ class_Lattices_Olower__semilattice(T_a) % 0.26/0.56 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_Int__commute_0,axiom, % 0.26/0.56 c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_subst__Var_1,axiom, % 0.26/0.56 ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) % 0.26/0.56 | c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x) = V_s ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_not__less0_0,axiom, % 0.26/0.56 ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_gr__implies__not0_0,axiom, % 0.26/0.56 ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_xt1_I10_J_0,axiom, % 0.26/0.56 ( ~ class_Orderings_Oorder(T_a) % 0.26/0.56 | c_HOL_Oord__class_Oless(V_z,V_x,T_a) % 0.26/0.56 | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) % 0.26/0.56 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_order__less__trans_0,axiom, % 0.26/0.56 ( ~ class_Orderings_Opreorder(T_a) % 0.26/0.56 | c_HOL_Oord__class_Oless(V_x,V_z,T_a) % 0.26/0.56 | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) % 0.26/0.56 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_Var_I3_J_0,axiom, % 0.26/0.56 hBOOL(hAPP(c_InductTermi_OIT,v_ua______)) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_subst__Var_2,axiom, % 0.26/0.56 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_i),V_s,V_k) = c_Lambda_OdB_OVar(V_i) % 0.26/0.56 | V_i = V_k % 0.26/0.56 | c_HOL_Oord__class_Oless(V_k,V_i,tc_nat) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_subst__preserves__beta_0,axiom, % 0.26/0.56 ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(V_r,V_t,V_i)),c_Lambda_Osubst(V_s,V_t,V_i))) % 0.26/0.56 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_append__same__eq_0,axiom, % 0.26/0.56 ( c_List_Oappend(V_ys,V_xs,T_a) != c_List_Oappend(V_zs,V_xs,T_a) % 0.26/0.56 | V_ys = V_zs ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_same__append__eq_0,axiom, % 0.26/0.56 ( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Oappend(V_xs,V_zs,T_a) % 0.26/0.56 | V_ys = V_zs ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_append__Nil2_0,axiom, % 0.26/0.56 c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs ). % 0.26/0.56 % 0.26/0.56 cnf(cls_eq__Nil__appendI_0,axiom, % 0.26/0.56 V_x = c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_self__append__conv_1,axiom, % 0.26/0.56 V_xs = c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_append__Nil_0,axiom, % 0.26/0.56 c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys ). % 0.26/0.56 % 0.26/0.56 cnf(cls_self__append__conv2_1,axiom, % 0.26/0.56 V_ys = c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_lift_Osimps_I2_J_0,axiom, % 0.26/0.56 c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(V_s,V_k)),c_Lambda_Olift(V_t,V_k)) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_Var__IT_0,axiom, % 0.26/0.56 hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_dB_Osimps_I6_J_0,axiom, % 0.26/0.56 c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_Beta_0,axiom, % 0.26/0.56 ( 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))) % 0.26/0.56 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_s)) % 0.26/0.56 | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(V_r,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_foldl__Nil_0,axiom, % 0.26/0.56 c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a ). % 0.26/0.56 % 0.26/0.56 cnf(cls_lift__IT_0,axiom, % 0.26/0.56 ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(V_t,V_i))) % 0.26/0.56 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_Var__apps__neq__Abs__apps_0,axiom, % 0.26/0.56 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) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_inf__sup__aci_I2_J_0,axiom, % 0.26/0.56 ( ~ class_Lattices_Olattice(T_a) % 0.26/0.56 | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_inf__sup__aci_I3_J_0,axiom, % 0.26/0.56 ( ~ class_Lattices_Olattice(T_a) % 0.26/0.56 | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_inf__left__commute_0,axiom, % 0.26/0.56 ( ~ class_Lattices_Olower__semilattice(T_a) % 0.26/0.56 | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_inf__assoc_0,axiom, % 0.26/0.56 ( ~ class_Lattices_Olower__semilattice(T_a) % 0.26/0.56 | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_Int__assoc_0,axiom, % 0.26/0.56 c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_Int__left__commute_0,axiom, % 0.26/0.56 c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_Nil__is__append__conv_0,axiom, % 0.26/0.56 ( c_List_Olist_ONil(T_a) != c_List_Oappend(V_xs,V_ys,T_a) % 0.26/0.56 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_Nil__is__append__conv_1,axiom, % 0.26/0.56 ( c_List_Olist_ONil(T_a) != c_List_Oappend(V_xs,V_ys,T_a) % 0.26/0.56 | V_ys = c_List_Olist_ONil(T_a) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_dB_Osimps_I3_J_0,axiom, % 0.26/0.56 ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H) % 0.26/0.56 | V_dB = V_dB_H ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_append__is__Nil__conv_0,axiom, % 0.26/0.56 ( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Olist_ONil(T_a) % 0.26/0.56 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.26/0.56 % 0.26/0.56 cnf(cls_append__is__Nil__conv_1,axiom, % 0.26/0.56 ( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Olist_ONil(T_a) % 0.26/0.56 | V_ys = c_List_Olist_ONil(T_a) ) ). % 0.43/0.56 % 0.43/0.56 cnf(cls_dB_Osimps_I4_J_0,axiom, % 0.43/0.56 c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) ). % 0.43/0.56 % 0.43/0.56 cnf(cls_Var__eq__apps__conv_0,axiom, % 0.43/0.56 ( c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) % 0.43/0.56 | c_Lambda_OdB_OVar(V_m) = V_s ) ). % 0.43/0.56 % 0.43/0.56 cnf(cls_apps__preserves__beta_0,axiom, % 0.43/0.56 ( 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))) % 0.43/0.56 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)) ) ). % 0.43/0.56 % 0.43/0.56 cnf(cls_nat__less__le_1,axiom, % 0.43/0.56 ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ). % 0.43/0.56 % 0.43/0.56 cnf(cls_less__not__refl_0,axiom, % 0.43/0.56 ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ). % 0.43/0.56 % 0.43/0.56 cnf(cls_order__less__le_1,axiom, % 0.43/0.56 ( ~ class_Orderings_Oorder(T_a) % 0.43/0.56 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.43/0.56 % 0.43/0.56 cnf(cls_linorder__neq__iff_1,axiom, % 0.43/0.56 ( ~ class_Orderings_Olinorder(T_a) % 0.43/0.56 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.43/0.56 % 0.43/0.56 cnf(cls_order__less__irrefl_0,axiom, % 0.43/0.56 ( ~ class_Orderings_Opreorder(T_a) % 0.43/0.56 | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ). % 0.43/0.56 % 0.43/0.56 cnf(cls_beta_0,axiom, % 0.43/0.56 hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),c_Lambda_Osubst(V_s,V_t,c_HOL_Ozero__class_Ozero(tc_nat)))) ). % 0.43/0.56 % 0.43/0.56 cnf(cls_linorder__neqE__ordered__idom_0,axiom, % 0.43/0.56 ( ~ class_Ring__and__Field_Oordered__idom(T_a) % 0.43/0.56 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.43/0.56 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.43/0.56 | V_x = V_y ) ). % 0.43/0.56 % 0.43/0.56 cnf(cls_not__less__iff__gr__or__eq_0,axiom, % 0.43/0.56 ( ~ class_Orderings_Olinorder(T_a) % 0.43/0.56 | V_x = V_y % 0.43/0.57 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.43/0.57 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_nat__neq__iff_0,axiom, % 0.43/0.57 ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 0.43/0.57 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) % 0.43/0.57 | V_m = V_n ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_nat__less__cases_0,axiom, % 0.43/0.57 ( hBOOL(hAPP(hAPP(V_P,V_n),V_m)) % 0.43/0.57 | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) % 0.43/0.57 | V_m = V_n % 0.43/0.57 | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_var__app__type__eq_0,axiom, % 0.43/0.57 ( V_T = V_U % 0.43/0.57 | ~ hBOOL(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)) % 0.43/0.57 | ~ hBOOL(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)) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_linorder__neqE__nat_0,axiom, % 0.43/0.57 ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat) % 0.43/0.57 | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) % 0.43/0.57 | V_x = V_y ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_linorder__neqE_0,axiom, % 0.43/0.57 ( ~ class_Orderings_Olinorder(T_a) % 0.43/0.57 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.43/0.57 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.43/0.57 | V_x = V_y ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_linorder__less__linear_0,axiom, % 0.43/0.57 ( ~ class_Orderings_Olinorder(T_a) % 0.43/0.57 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.43/0.57 | V_x = V_y % 0.43/0.57 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_linorder__antisym__conv3_0,axiom, % 0.43/0.57 ( ~ class_Orderings_Olinorder(T_a) % 0.43/0.57 | V_x = V_y % 0.43/0.57 | c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.43/0.57 | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_dB_Osimps_I2_J_1,axiom, % 0.43/0.57 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) % 0.43/0.57 | V_dB2 = V_dB2_H ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_dB_Osimps_I2_J_0,axiom, % 0.43/0.57 ( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) % 0.43/0.57 | V_dB1 = V_dB1_H ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_IT_OVar_0,axiom, % 0.43/0.57 ( 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))) % 0.43/0.57 | ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_less__infI2_0,axiom, % 0.43/0.57 ( ~ class_Lattices_Olower__semilattice(T_a) % 0.43/0.57 | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a) % 0.43/0.57 | ~ c_HOL_Oord__class_Oless(V_b,V_x,T_a) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_less__infI1_0,axiom, % 0.43/0.57 ( ~ class_Lattices_Olower__semilattice(T_a) % 0.43/0.57 | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a) % 0.43/0.57 | ~ c_HOL_Oord__class_Oless(V_a,V_x,T_a) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_Abs__apps__eq__Abs__apps__conv_1,axiom, % 0.43/0.57 ( 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) % 0.43/0.57 | V_rs = V_ss ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_Abs__apps__eq__Abs__apps__conv_0,axiom, % 0.43/0.57 ( 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) % 0.43/0.57 | V_r = V_s ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_apps__eq__Abs__conv_0,axiom, % 0.43/0.57 ( c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r) % 0.43/0.57 | V_s = c_Lambda_OdB_OAbs(V_r) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_App_0,axiom, % 0.43/0.57 ( hBOOL(hAPP(hAPP(c_Type_Otyping(V_env),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_U)) % 0.43/0.57 | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_env),V_t),V_T)) % 0.43/0.57 | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_env),V_s),hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U))) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_beta__cases_I1_J_0,axiom, % 0.43/0.57 ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_gr0I_0,axiom, % 0.43/0.57 ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) % 0.43/0.57 | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_neq0__conv_1,axiom, % 0.43/0.57 ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_inf__sup__aci_I4_J_0,axiom, % 0.43/0.57 ( ~ class_Lattices_Olattice(T_a) % 0.43/0.57 | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_inf__left__idem_0,axiom, % 0.43/0.57 ( ~ class_Lattices_Olower__semilattice(T_a) % 0.43/0.57 | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_Int__left__absorb_0,axiom, % 0.43/0.57 c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_subst__lt_0,axiom, % 0.43/0.57 ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_j),V_u,V_i) = c_Lambda_OdB_OVar(V_j) % 0.43/0.57 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_subst__Var__IT_0,axiom, % 0.43/0.57 ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j))) % 0.43/0.57 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_r)) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_append__self__conv_0,axiom, % 0.43/0.57 ( c_List_Oappend(V_xs,V_ys,T_a) != V_xs % 0.43/0.57 | V_ys = c_List_Olist_ONil(T_a) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_self__append__conv_0,axiom, % 0.43/0.57 ( V_xs != c_List_Oappend(V_xs,V_ys,T_a) % 0.43/0.57 | V_ys = c_List_Olist_ONil(T_a) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_append__self__conv2_0,axiom, % 0.43/0.57 ( c_List_Oappend(V_xs,V_ys,T_a) != V_ys % 0.43/0.57 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_self__append__conv2_0,axiom, % 0.43/0.57 ( V_ys != c_List_Oappend(V_xs,V_ys,T_a) % 0.43/0.57 | V_xs = c_List_Olist_ONil(T_a) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_type_Osimps_I2_J_1,axiom, % 0.43/0.57 ( hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H) % 0.43/0.57 | V_type2 = V_type2_H ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_type_Osimps_I2_J_0,axiom, % 0.43/0.57 ( hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H) % 0.43/0.57 | V_type1 = V_type1_H ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_inf__idem_0,axiom, % 0.43/0.57 ( ~ class_Lattices_Olower__semilattice(T_a) % 0.43/0.57 | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_x,T_a) = V_x ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_Int__absorb_0,axiom, % 0.43/0.57 c_Lattices_Olower__semilattice__class_Oinf(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A ). % 0.43/0.57 % 0.43/0.57 cnf(cls_subst__eq_0,axiom, % 0.43/0.57 c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u ). % 0.43/0.57 % 0.43/0.57 cnf(cls_Var__apps__eq__Var__apps__conv_1,axiom, % 0.43/0.57 ( 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) % 0.43/0.57 | V_rs = V_ss ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_Var__apps__eq__Var__apps__conv_0,axiom, % 0.43/0.57 ( 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) % 0.43/0.57 | V_m = V_n ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_dB_Osimps_I9_J_0,axiom, % 0.43/0.57 c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_dB_Osimps_I1_J_0,axiom, % 0.43/0.57 ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H) % 0.43/0.57 | V_nat = V_nat_H ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_dB_Osimps_I8_J_0,axiom, % 0.43/0.57 hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_dB_Osimps_I7_J_0,axiom, % 0.43/0.57 c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_subst__App_0,axiom, % 0.43/0.57 c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(V_t,V_s,V_k)),c_Lambda_Osubst(V_u,V_s,V_k)) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_inf1I_0,axiom, % 0.43/0.57 ( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)) % 0.43/0.57 | ~ hBOOL(hAPP(V_B,V_x)) % 0.43/0.57 | ~ hBOOL(hAPP(V_A,V_x)) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_append__is__Nil__conv_2,axiom, % 0.43/0.57 c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_append__assoc_0,axiom, % 0.43/0.57 c_List_Oappend(c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a) = c_List_Oappend(V_xs,c_List_Oappend(V_ys,V_zs,T_a),T_a) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_append__eq__appendI_0,axiom, % 0.43/0.57 c_List_Oappend(V_xs,c_List_Oappend(V_xs1,V_us,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_xs1,T_a),V_us,T_a) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_append__eq__append__conv2_4,axiom, % 0.43/0.57 c_List_Oappend(c_List_Oappend(V_zs,V_x,T_a),V_ys,T_a) = c_List_Oappend(V_zs,c_List_Oappend(V_x,V_ys,T_a),T_a) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_append__eq__append__conv2_5,axiom, % 0.43/0.57 c_List_Oappend(V_xs,c_List_Oappend(V_x,V_ts,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_x,T_a),V_ts,T_a) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_xt1_I9_J_0,axiom, % 0.43/0.57 ( ~ class_Orderings_Oorder(T_a) % 0.43/0.57 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) % 0.43/0.57 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_not__less__iff__gr__or__eq_1,axiom, % 0.43/0.57 ( ~ class_Orderings_Olinorder(T_a) % 0.43/0.57 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) % 0.43/0.57 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_order__less__asym_0,axiom, % 0.43/0.57 ( ~ class_Orderings_Opreorder(T_a) % 0.43/0.57 | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) % 0.43/0.57 | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_order__less__asym_H_0,axiom, % 0.43/0.57 ( ~ class_Orderings_Opreorder(T_a) % 0.43/0.57 | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) % 0.43/0.57 | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_lift__type_0,axiom, % 0.43/0.57 ( hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype)),c_Lambda_Olift(V_t,V_i)),V_T)) % 0.43/0.57 | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_t),V_T)) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_uT_0,axiom, % 0.43/0.57 hBOOL(hAPP(hAPP(c_Type_Otyping(v_e____),v_u____),v_T____)) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_subject__reduction_0,axiom, % 0.43/0.57 ( hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_t_H),V_T)) % 0.43/0.57 | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H)) % 0.43/0.57 | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_t),V_T)) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_lists__typings_0,axiom, % 0.43/0.57 ( c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(V_e),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),V_ts,tc_Lambda_OdB) % 0.43/0.57 | ~ c_Type_Otypings(V_e,V_ts,V_Ts) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_image__image_0,axiom, % 0.43/0.57 c_Set_Oimage(V_f,c_Set_Oimage(V_g,V_A,T_c,T_b),T_b,T_a) = c_Set_Oimage(c_COMBB(V_f,V_g,T_b,T_a,T_c),V_A,T_c,T_a) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_shift__gt_0,axiom, % 0.43/0.57 ( hAPP(c_Type_Oshift(V_e,V_i,V_T,T_a),V_j) = hAPP(V_e,V_j) % 0.43/0.57 | ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_append__in__listsp__conv_2,axiom, % 0.43/0.57 ( c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a) % 0.43/0.57 | ~ c_List_Olistsp(V_A,V_ys,T_a) % 0.43/0.57 | ~ c_List_Olistsp(V_A,V_xs,T_a) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_in__listsp__conv__set_2,axiom, % 0.43/0.57 ( c_List_Olistsp(V_A,V_xs,T_a) % 0.43/0.57 | ~ hBOOL(hAPP(V_A,c_List_Osko__List__Xin__listsp__conv__set__1__1(V_A,V_xs,T_a))) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_listsp__infI_0,axiom, % 0.43/0.57 ( c_List_Olistsp(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_l,T_a) % 0.43/0.57 | ~ c_List_Olistsp(V_B,V_l,T_a) % 0.43/0.57 | ~ c_List_Olistsp(V_A,V_l,T_a) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_MI2_0,axiom, % 0.43/0.57 ( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2) % 0.43/0.57 | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(V_t,V_u,V_i))) % 0.43/0.57 | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_u),V_T2)) % 0.43/0.57 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u)) % 0.43/0.57 | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_T2,tc_Type_Otype)),V_t),V_Ta)) % 0.43/0.57 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_MI1_0,axiom, % 0.43/0.57 ( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2) % 0.43/0.57 | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(V_t,V_u,V_i))) % 0.43/0.57 | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),V_u),V_T1)) % 0.43/0.57 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u)) % 0.43/0.57 | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_T1,tc_Type_Otype)),V_t),V_Ta)) % 0.43/0.57 | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_shift__eq_0,axiom, % 0.43/0.57 hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ). % 0.43/0.57 % 0.43/0.57 cnf(cls_Abs_0,axiom, % 0.43/0.57 ( hBOOL(hAPP(hAPP(c_Type_Otyping(V_env),c_Lambda_OdB_OAbs(V_t)),hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U))) % 0.43/0.57 | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(V_env,c_HOL_Ozero__class_Ozero(tc_nat),V_T,tc_Type_Otype)),V_t),V_U)) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_typing__elims_I1_J_0,axiom, % 0.43/0.57 ( hAPP(V_e,V_i) = V_T % 0.43/0.57 | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e),c_Lambda_OdB_OVar(V_i)),V_T)) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_Var_I2_J_0,axiom, % 0.43/0.57 hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_Ha______)) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_False_0,axiom, % 0.43/0.57 v_n____ != v_i____ ). % 0.43/0.57 % 0.43/0.57 cnf(cls_Var_I4_J_0,axiom, % 0.43/0.57 hBOOL(hAPP(hAPP(c_Type_Otyping(v_ea______),v_ua______),v_T____)) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_listsp_ONil_0,axiom, % 0.43/0.57 c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_append__in__listsp__conv_1,axiom, % 0.43/0.57 ( c_List_Olistsp(V_A,V_ys,T_a) % 0.43/0.57 | ~ c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_append__in__listsp__conv_0,axiom, % 0.43/0.57 ( c_List_Olistsp(V_A,V_xs,T_a) % 0.43/0.57 | ~ c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_nT_0,axiom, % 0.43/0.57 hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_COMBB__def_0,axiom, % 0.43/0.57 hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R) = hAPP(V_P,hAPP(V_Q,V_R)) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_typing_OVar_0,axiom, % 0.43/0.57 hBOOL(hAPP(hAPP(c_Type_Otyping(V_env),c_Lambda_OdB_OVar(V_x)),hAPP(V_env,V_x))) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_subst__lemma_0,axiom, % 0.43/0.57 ( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(V_e_H),V_u),V_U)) % 0.43/0.57 | ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype)),V_t),V_T)) % 0.43/0.57 | hBOOL(hAPP(hAPP(c_Type_Otyping(V_e_H),c_Lambda_Osubst(V_t,V_u,V_i)),V_T)) ) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_CHAINED_0,axiom, % 0.43/0.57 c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,v_Ts____) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_conjecture_0,negated_conjecture, % 0.43/0.57 ~ c_List_Olistsp(c_COMBB(c_Ex(tc_Type_Otype),c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),v_rs____,tc_Lambda_OdB) ). % 0.43/0.57 % 0.43/0.57 cnf(clsarity_fun__Lattices_Olower__semilattice,axiom, % 0.43/0.57 ( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1)) % 0.43/0.57 | ~ class_Lattices_Olattice(T_1) ) ). % 0.43/0.57 % 0.43/0.57 cnf(clsarity_fun__Orderings_Opreorder,axiom, % 0.43/0.57 ( class_Orderings_Opreorder(tc_fun(T_2,T_1)) % 0.43/0.57 | ~ class_Orderings_Opreorder(T_1) ) ). % 0.43/0.57 % 0.43/0.57 cnf(clsarity_fun__Lattices_Olattice,axiom, % 0.43/0.57 ( class_Lattices_Olattice(tc_fun(T_2,T_1)) % 0.43/0.57 | ~ class_Lattices_Olattice(T_1) ) ). % 0.43/0.57 % 0.43/0.57 cnf(clsarity_fun__Orderings_Oorder,axiom, % 0.43/0.57 ( class_Orderings_Oorder(tc_fun(T_2,T_1)) % 0.43/0.57 | ~ class_Orderings_Oorder(T_1) ) ). % 0.43/0.57 % 0.43/0.57 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom, % 0.43/0.57 class_Ring__and__Field_Oordered__semidom(tc_nat) ). % 0.43/0.57 % 0.43/0.57 cnf(clsarity_nat__Lattices_Olower__semilattice,axiom, % 0.43/0.57 class_Lattices_Olower__semilattice(tc_nat) ). % 0.43/0.57 % 0.43/0.57 cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom, % 0.43/0.57 class_Ring__and__Field_Osemiring__1(tc_nat) ). % 0.43/0.57 % 0.43/0.57 cnf(clsarity_nat__Nat_Osemiring__char__0,axiom, % 0.43/0.57 class_Nat_Osemiring__char__0(tc_nat) ). % 0.43/0.57 % 0.43/0.57 cnf(clsarity_nat__Orderings_Opreorder,axiom, % 0.43/0.57 class_Orderings_Opreorder(tc_nat) ). % 0.43/0.57 % 0.43/0.57 cnf(clsarity_nat__Orderings_Olinorder,axiom, % 0.43/0.57 class_Orderings_Olinorder(tc_nat) ). % 0.43/0.57 % 0.43/0.57 cnf(clsarity_nat__Lattices_Olattice,axiom, % 0.43/0.57 class_Lattices_Olattice(tc_nat) ). % 0.43/0.57 % 0.43/0.57 cnf(clsarity_nat__Orderings_Oorder,axiom, % 0.43/0.57 class_Orderings_Oorder(tc_nat) ). % 0.43/0.57 % 0.43/0.57 cnf(clsarity_bool__Lattices_Olower__semilattice,axiom, % 0.43/0.57 class_Lattices_Olower__semilattice(tc_bool) ). % 0.43/0.57 % 0.43/0.57 cnf(clsarity_bool__Orderings_Opreorder,axiom, % 0.43/0.57 class_Orderings_Opreorder(tc_bool) ). % 0.43/0.57 % 0.43/0.57 cnf(clsarity_bool__Lattices_Olattice,axiom, % 0.43/0.57 class_Lattices_Olattice(tc_bool) ). % 0.43/0.57 % 0.43/0.57 cnf(clsarity_bool__Orderings_Oorder,axiom, % 0.43/0.57 class_Orderings_Oorder(tc_bool) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_ATP__Linkup_OCOMBC__def_0,axiom, % 0.43/0.57 c_COMBC(V_P,V_Q,V_R,T_b,T_c,T_a) = hAPP(hAPP(V_P,V_R),V_Q) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_ATP__Linkup_OCOMBB__def_0,axiom, % 0.43/0.57 hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R) = hAPP(V_P,hAPP(V_Q,V_R)) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom, % 0.43/0.57 hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)) ). % 0.43/0.57 % 0.43/0.57 cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom, % 0.43/0.57 ( V_X = V_Y % 0.43/0.57 | ~ hBOOL(hAPP(hAPP(c_fequal(T_a),V_X),V_Y)) ) ). % 0.43/0.57 % 0.43/0.57 %------------------------------------------------------------------------------ % 0.43/0.57 %------------------------------------------- % 0.43/0.57 % Proof found % 0.43/0.57 % SZS status Theorem for theBenchmark % 0.43/0.57 % SZS output start Proof % 0.43/0.57 %ClaNum:340(EqnAxiom:110) % 0.43/0.57 %VarNum:1212(SingletonVarNum:583) % 0.43/0.57 %MaxLitNum:6 % 0.43/0.57 %MaxfuncDepth:5 % 0.43/0.57 %SharedTerms:67 % 0.43/0.57 %goalClause: 191 % 0.43/0.57 %singleGoalClaCount:1 % 0.43/0.57 [111]P1(a1) % 0.43/0.57 [112]P9(a1) % 0.43/0.57 [113]P14(a1) % 0.43/0.57 [114]P2(a1) % 0.43/0.57 [115]P2(a2) % 0.43/0.57 [116]P8(a1) % 0.43/0.57 [117]P8(a2) % 0.43/0.57 [118]P10(a1) % 0.43/0.57 [119]P10(a2) % 0.43/0.57 [120]P12(a1) % 0.43/0.57 [121]P12(a2) % 0.43/0.57 [122]P11(a1) % 0.43/0.57 [173]~E(a48,a46) % 0.43/0.57 [123]P15(f7(a3,a39)) % 0.43/0.57 [124]P15(f7(a3,a50)) % 0.43/0.57 [158]P6(f28(a40,a46,a41,a37),a47,a44) % 0.43/0.57 [191]~P3(f5(f6(a37),f27(f28(a40,a46,a41,a37)),f38(a37,a2),a2,a36),a47,a36) % 0.43/0.57 [140]P15(f7(f7(f27(a40),a39),a41)) % 0.43/0.57 [141]P15(f7(f7(f27(a45),a50),a41)) % 0.43/0.57 [171]P15(f7(f7(f27(f28(a40,a46,a41,a37)),f18(a10,f9(a48),a47,a36,a36)),a42)) % 0.43/0.57 [172]P15(f7(f7(f27(f28(a45,a49,a41,a37)),f18(a10,f9(a48),a47,a36,a36)),a43)) % 0.43/0.57 [181]~P4(x1811,x1811,a1) % 0.43/0.57 [183]~P4(x1831,f4(a1),a1) % 0.43/0.57 [125]E(f20(f8(x1251),f35(x1251)),f4(a1)) % 0.43/0.57 [126]P15(f7(a3,f9(x1261))) % 0.43/0.57 [135]E(f24(f26(x1351),x1351,x1351),f26(x1351)) % 0.43/0.57 [186]~P4(f4(a1),f20(f8(x1861),f35(x1861)),a1) % 0.43/0.57 [128]P3(x1281,f8(x1282),x1282) % 0.43/0.57 [175]~E(f9(x1751),f12(x1752)) % 0.43/0.57 [127]E(f23(f23(x1271,x1272),x1272),f23(x1271,x1272)) % 0.43/0.57 [132]E(f13(x1321,f8(x1322),x1322),x1321) % 0.43/0.57 [133]E(f13(f8(x1331),x1332,x1331),x1332) % 0.43/0.57 [134]E(f14(f9(x1341),x1342,x1341),x1342) % 0.43/0.57 [138]E(f16(x1381,x1381,f38(x1382,a2)),x1381) % 0.43/0.57 [145]P15(f7(f7(f27(x1451),f9(x1452)),f7(x1451,x1452))) % 0.43/0.57 [142]P15(f7(f7(f26(x1421),x1422),x1422)) % 0.43/0.57 [159]P15(f7(f7(a11,f7(f7(a10,f12(x1591)),x1592)),f14(x1591,x1592,f4(a1)))) % 0.43/0.57 [185]~P15(f7(f7(a11,f9(x1851)),x1852)) % 0.43/0.57 [187]~P5(x1871,x1872,f8(x1873),x1873) % 0.43/0.57 [188]~P5(x1881,f8(x1882),x1883,x1882) % 0.43/0.57 [139]E(f14(f15(x1391,x1392),x1393,x1392),x1391) % 0.43/0.57 [143]E(f16(x1431,x1432,f38(x1433,a2)),f16(x1432,x1431,f38(x1433,a2))) % 0.43/0.57 [144]E(f24(f24(x1441,x1442,x1443),x1443,x1442),x1441) % 0.43/0.57 [149]E(f16(x1491,f16(x1491,x1492,f38(x1493,a2)),f38(x1493,a2)),f16(x1491,x1492,f38(x1493,a2))) % 0.43/0.57 [176]~E(f12(x1761),f7(f7(a10,x1762),x1763)) % 0.43/0.57 [177]~E(f9(x1771),f7(f7(a10,x1772),x1773)) % 0.43/0.57 [178]~E(f7(f7(a10,x1781),x1782),f12(x1783)) % 0.43/0.57 [179]~E(f7(f7(a10,x1791),x1792),f9(x1793)) % 0.43/0.57 [147]P15(f7(f7(f23(x1471,x1472),x1473),x1473)) % 0.43/0.57 [148]E(f7(f7(a10,f15(x1481,x1482)),f15(x1483,x1482)),f15(f7(f7(a10,x1481),x1483),x1482)) % 0.43/0.57 [153]E(f13(f13(x1531,x1532,x1533),x1534,x1533),f13(x1531,f13(x1532,x1534,x1533),x1533)) % 0.43/0.57 [154]E(f16(x1541,f16(x1542,x1543,f38(x1544,a2)),f38(x1544,a2)),f16(x1542,f16(x1541,x1543,f38(x1544,a2)),f38(x1544,a2))) % 0.43/0.57 [155]E(f16(f16(x1551,x1552,f38(x1553,a2)),x1554,f38(x1553,a2)),f16(x1551,f16(x1552,x1554,f38(x1553,a2)),f38(x1553,a2))) % 0.43/0.57 [157]E(f7(f28(x1571,x1572,x1573,x1574),x1572),x1573) % 0.43/0.57 [160]E(f18(x1601,x1602,f8(x1603),x1604,x1603),x1602) % 0.43/0.57 [161]E(f19(x1611,f8(x1612),x1613,x1612,x1614),x1613) % 0.43/0.57 [190]~E(f18(a10,f9(x1901),x1902,a36,a36),f18(a10,f12(x1903),x1904,a36,a36)) % 0.43/0.57 [156]E(f7(f7(a10,f14(x1561,x1562,x1563)),f14(x1564,x1562,x1563)),f14(f7(f7(a10,x1561),x1564),x1562,x1563)) % 0.43/0.57 [189]~E(f7(f7(a10,f12(x1891)),x1892),f18(a10,f9(x1893),x1894,a36,a36)) % 0.43/0.57 [167]E(f7(f5(x1671,x1672,x1673,x1674,x1675),x1676),f7(x1671,f7(x1672,x1676))) % 0.43/0.57 [168]E(f25(x1681,f25(x1682,x1683,x1684,x1685),x1685,x1686),f25(f5(x1681,x1682,x1685,x1686,x1684),x1683,x1684,x1686)) % 0.43/0.57 [169]E(f18(x1691,f18(x1691,x1692,x1693,x1694,x1695),x1696,x1694,x1695),f18(x1691,x1692,f13(x1693,x1696,x1695),x1694,x1695)) % 0.43/0.57 [170]E(f19(x1701,x1702,f19(x1701,x1703,x1704,x1705,x1706),x1705,x1706),f19(x1701,f13(x1702,x1703,x1705),x1704,x1705,x1706)) % 0.43/0.57 [201]E(x2011,f4(a1))+P4(f4(a1),x2011,a1) % 0.43/0.57 [244]P7(f24(a11,a36,a36),x2441,a36)+~P15(f7(a3,x2441)) % 0.43/0.57 [257]~P7(f24(a11,a36,a36),x2571,a36)+P15(f7(a3,x2571)) % 0.43/0.57 [194]~P14(x1941)+E(f21(f4(a1),x1941),f4(x1941)) % 0.43/0.57 [203]~P15(f7(a3,x2031))+P15(f7(a3,f12(x2031))) % 0.43/0.57 [208]~P4(x2082,x2082,x2081)+~P10(x2081) % 0.43/0.57 [209]~P4(x2092,x2092,x2091)+~P12(x2091) % 0.43/0.57 [210]~P4(x2102,x2102,x2101)+~P11(x2101) % 0.43/0.57 [192]E(x1921,x1922)+~E(f12(x1921),f12(x1922)) % 0.43/0.57 [193]E(x1931,x1932)+~E(f9(x1931),f9(x1932)) % 0.43/0.57 [195]~P2(x1952)+P2(f38(x1951,x1952)) % 0.43/0.57 [196]~P2(x1962)+P8(f38(x1961,x1962)) % 0.43/0.57 [197]~P10(x1972)+P10(f38(x1971,x1972)) % 0.43/0.57 [198]~P12(x1982)+P12(f38(x1981,x1982)) % 0.43/0.57 [202]~P8(x2022)+E(f16(x2021,x2021,x2022),x2021) % 0.43/0.57 [233]~P9(x2331)+~P4(f21(x2332,x2331),f4(x2331),x2331) % 0.43/0.57 [199]E(x1991,f8(x1992))+~E(f20(x1991,f35(x1992)),f4(a1)) % 0.43/0.57 [215]E(x2151,f8(x2152))+P4(f4(a1),f20(x2151,f35(x2152)),a1) % 0.43/0.57 [216]~P4(x2161,x2162,a1)+E(f15(f9(x2161),x2162),f9(x2161)) % 0.43/0.57 [232]~P15(f7(a3,x2321))+P15(f7(a3,f15(x2321,x2322))) % 0.43/0.57 [251]~P15(f7(f7(a11,x2511),x2512))+P15(f7(f7(a11,f12(x2511)),f12(x2512))) % 0.43/0.57 [254]~P15(f7(a3,x2541))+P15(f7(a3,f7(f7(a10,x2541),f9(x2542)))) % 0.43/0.57 [276]P15(f7(f7(f23(a11,a36),f12(x2761)),f12(x2762)))+~P15(f7(f7(f23(a11,a36),x2761),x2762)) % 0.43/0.57 [319]~P3(a3,x3192,a36)+P15(f7(a3,f18(a10,f9(x3191),x3192,a36,a36))) % 0.43/0.57 [206]~E(f13(x2063,x2061,x2062),x2063)+E(x2061,f8(x2062)) % 0.43/0.57 [207]~E(f13(x2071,x2073,x2072),x2073)+E(x2071,f8(x2072)) % 0.43/0.57 [213]~E(f13(x2133,x2131,x2132),f8(x2132))+E(x2131,f8(x2132)) % 0.43/0.57 [214]~E(f13(x2141,x2143,x2142),f8(x2142))+E(x2141,f8(x2142)) % 0.43/0.57 [220]~P2(x2203)+E(f16(x2201,x2202,x2203),f16(x2202,x2201,x2203)) % 0.43/0.57 [221]~P8(x2213)+E(f16(x2211,x2212,x2213),f16(x2212,x2211,x2213)) % 0.43/0.57 [304]~E(f12(x3042),f18(a10,x3043,x3041,a36,a36))+E(x3041,f8(a36)) % 0.43/0.57 [305]~E(f9(x3052),f18(a10,x3053,x3051,a36,a36))+E(x3051,f8(a36)) % 0.43/0.57 [306]~E(f18(a10,x3062,x3061,a36,a36),f12(x3063))+E(x3061,f8(a36)) % 0.43/0.57 [307]E(x3071,f12(x3072))+~E(f18(a10,x3071,x3073,a36,a36),f12(x3072)) % 0.43/0.57 [308]E(f12(x3081),x3082)+~E(f12(x3081),f18(a10,x3082,x3083,a36,a36)) % 0.43/0.57 [309]E(f9(x3091),x3092)+~E(f9(x3091),f18(a10,x3092,x3093,a36,a36)) % 0.43/0.57 [312]E(x3121,x3122)+~E(f18(a10,x3121,x3123,a36,a36),f18(a10,x3122,x3123,a36,a36)) % 0.43/0.57 [234]~P4(x2341,x2343,a1)+E(f14(f9(x2341),x2342,x2343),f9(x2341)) % 0.43/0.57 [248]~P2(x2483)+E(f16(x2481,f16(x2481,x2482,x2483),x2483),f16(x2481,x2482,x2483)) % 0.43/0.57 [249]~P8(x2493)+E(f16(x2491,f16(x2491,x2492,x2493),x2493),f16(x2491,x2492,x2493)) % 0.43/0.57 [269]~P15(f7(f7(a11,x2691),x2693))+P15(f7(f7(a11,f15(x2691,x2692)),f15(x2693,x2692))) % 0.43/0.57 [275]P3(x2751,x2752,x2753)+~P15(f7(x2751,f22(x2751,x2752,x2753))) % 0.43/0.57 [310]E(f7(f7(a10,x3101),x3102),x3103)+~E(f7(f7(a10,x3101),x3102),f18(a10,x3103,f8(a36),a36,a36)) % 0.43/0.57 [311]~P6(x3111,x3112,x3113)+P3(f5(f6(a37),f27(x3111),f38(a37,a2),a2,a36),x3112,a36) % 0.43/0.57 [326]~P15(f7(f7(a11,x3261),x3263))+P15(f7(f7(a11,f18(a10,x3261,x3262,a36,a36)),f18(a10,x3263,x3262,a36,a36))) % 0.43/0.57 [328]~P5(a11,x3282,x3283,a36)+P15(f7(f7(a11,f18(a10,x3281,x3282,a36,a36)),f18(a10,x3281,x3283,a36,a36))) % 0.43/0.57 [235]E(x2351,x2352)+~P15(f7(f7(f26(x2353),x2351),x2352)) % 0.43/0.57 [247]E(f7(x2471,x2472),x2473)+~P15(f7(f7(f27(x2471),f9(x2472)),x2473)) % 0.43/0.57 [260]~P15(f7(a3,x2601))+P15(f7(a3,f14(x2601,f9(x2602),x2603))) % 0.43/0.57 [280]P15(f7(f7(f23(a11,a36),f15(x2801,x2802)),f15(x2803,x2802)))+~P15(f7(f7(f23(a11,a36),x2801),x2803)) % 0.43/0.57 [284]~P15(f7(f7(a11,x2841),x2843))+P15(f7(f7(a11,f7(f7(a10,x2841),x2842)),f7(f7(a10,x2843),x2842))) % 0.43/0.57 [285]~P15(f7(f7(a11,x2852),x2853))+P15(f7(f7(a11,f7(f7(a10,x2851),x2852)),f7(f7(a10,x2851),x2853))) % 0.43/0.57 [290]~P15(f7(f7(f23(a11,a36),x2901),x2903))+P15(f7(f7(f23(a11,a36),f7(f7(a10,x2901),x2902)),f7(f7(a10,x2903),x2902))) % 0.43/0.57 [291]~P15(f7(f7(f23(a11,a36),x2912),x2913))+P15(f7(f7(f23(a11,a36),f7(f7(a10,x2911),x2912)),f7(f7(a10,x2911),x2913))) % 0.43/0.57 [327]P15(f7(f7(f23(a11,a36),f18(a10,x3271,x3272,a36,a36)),f18(a10,x3273,x3272,a36,a36)))+~P15(f7(f7(f23(a11,a36),x3271),x3273)) % 0.43/0.57 [329]P5(a11,x3291,f17(x3292,x3291,x3293),a36)+~P15(f7(f7(a11,f18(a10,f9(x3292),x3291,a36,a36)),x3293)) % 0.43/0.57 [333]E(f18(a10,f9(x3331),f17(x3331,x3332,x3333),a36,a36),x3333)+~P15(f7(f7(a11,f18(a10,f9(x3331),x3332,a36,a36)),x3333)) % 0.43/0.57 [236]E(x2361,x2362)+~E(f13(x2363,x2361,x2364),f13(x2363,x2362,x2364)) % 0.43/0.57 [237]E(x2371,x2372)+~E(f13(x2371,x2373,x2374),f13(x2372,x2373,x2374)) % 0.43/0.57 [261]P3(x2611,x2612,x2613)+~P3(x2611,f13(x2614,x2612,x2613),x2613) % 0.43/0.57 [262]P3(x2621,x2622,x2623)+~P3(x2621,f13(x2622,x2624,x2623),x2623) % 0.43/0.57 [222]E(x2221,x2222)+~E(f7(f7(a10,x2223),x2221),f7(f7(a10,x2224),x2222)) % 0.43/0.57 [223]E(x2231,x2232)+~E(f7(f7(a29,x2233),x2231),f7(f7(a29,x2234),x2232)) % 0.43/0.57 [224]E(x2241,x2242)+~E(f7(f7(a10,x2241),x2243),f7(f7(a10,x2242),x2244)) % 0.43/0.57 [225]E(x2251,x2252)+~E(f7(f7(a29,x2251),x2253),f7(f7(a29,x2252),x2254)) % 0.43/0.57 [264]~P2(x2644)+E(f16(x2641,f16(x2642,x2643,x2644),x2644),f16(x2642,f16(x2641,x2643,x2644),x2644)) % 0.43/0.57 [265]~P8(x2654)+E(f16(x2651,f16(x2652,x2653,x2654),x2654),f16(x2652,f16(x2651,x2653,x2654),x2654)) % 0.43/0.57 [266]~P2(x2663)+E(f16(f16(x2661,x2662,x2663),x2664,x2663),f16(x2661,f16(x2662,x2664,x2663),x2663)) % 0.43/0.57 [267]~P8(x2673)+E(f16(f16(x2671,x2672,x2673),x2674,x2673),f16(x2671,f16(x2672,x2674,x2673),x2673)) % 0.43/0.57 [289]~P15(f7(f7(a11,x2891),x2894))+P15(f7(f7(a11,f14(x2891,x2892,x2893)),f14(x2894,x2892,x2893))) % 0.43/0.57 [296]P15(f7(f7(f23(a11,a36),f14(x2961,x2962,x2963)),f14(x2961,x2964,x2963)))+~P15(f7(f7(a11,x2962),x2964)) % 0.43/0.57 [313]E(x3131,x3132)+~E(f18(a10,f12(x3133),x3131,a36,a36),f18(a10,f12(x3134),x3132,a36,a36)) % 0.43/0.57 [314]E(x3141,x3142)+~E(f18(a10,f9(x3143),x3141,a36,a36),f18(a10,f9(x3144),x3142,a36,a36)) % 0.43/0.57 [315]E(x3151,x3152)+~E(f18(a10,f12(x3151),x3153,a36,a36),f18(a10,f12(x3152),x3154,a36,a36)) % 0.43/0.57 [316]E(x3161,x3162)+~E(f18(a10,f9(x3161),x3163,a36,a36),f18(a10,f9(x3162),x3164,a36,a36)) % 0.43/0.57 [263]~P15(f7(f7(x2631,x2633),x2634))+P15(f7(f7(f23(x2631,x2632),x2633),x2634)) % 0.43/0.57 [278]P15(f7(x2781,x2782))+~P15(f7(f16(x2783,x2781,f38(x2784,a2)),x2782)) % 0.43/0.57 [279]P15(f7(x2791,x2792))+~P15(f7(f16(x2791,x2793,f38(x2794,a2)),x2792)) % 0.43/0.57 [298]P15(f7(f7(f23(a11,a36),f14(x2981,x2982,x2983)),f14(x2984,x2982,x2983)))+~P15(f7(f7(f23(a11,a36),x2981),x2984)) % 0.43/0.57 [299]P15(f7(f7(f23(a11,a36),f14(x2991,x2992,x2993)),f14(x2991,x2994,x2993)))+~P15(f7(f7(f23(a11,a36),x2992),x2994)) % 0.43/0.57 [330]P6(x3301,x3302,f31(x3303,x3301,x3304,x3302))+~P15(f7(f7(f27(x3301),f18(a10,x3304,x3302,a36,a36)),x3303)) % 0.43/0.57 [331]P6(x3311,x3312,f32(x3313,x3311,x3314,x3312))+~P15(f7(f7(f27(x3311),f18(a10,x3314,x3312,a36,a36)),x3313)) % 0.43/0.57 [335]~P15(f7(f7(f27(x3351),f18(a10,x3352,x3354,a36,a36)),x3353))+P15(f7(f7(f27(x3351),x3352),f19(a29,f31(x3353,x3351,x3352,x3354),x3353,a37,a37))) % 0.43/0.58 [336]~P15(f7(f7(f27(x3361),f18(a10,x3362,x3364,a36,a36)),x3363))+P15(f7(f7(f27(x3361),x3362),f19(a29,f32(x3363,x3361,x3362,x3364),x3363,a37,a37))) % 0.43/0.58 [301]~P15(f7(f7(f23(x3011,x3012),x3014),x3013))+P15(f7(f7(f23(f24(x3011,x3012,x3012),x3012),x3013),x3014)) % 0.43/0.58 [302]P15(f7(f7(f27(x3021),x3022),f30(x3023,x3021,x3024,x3022)))+~P15(f7(f7(f27(x3021),f7(f7(a10,x3024),x3022)),x3023)) % 0.43/0.58 [303]P15(f7(f7(f23(x3031,x3032),x3033),x3034))+~P15(f7(f7(f23(f24(x3031,x3032,x3032),x3032),x3034),x3033)) % 0.43/0.58 [318]~P15(f7(f7(f27(x3181),f7(f7(a10,x3182),x3184)),x3183))+P15(f7(f7(f27(x3181),x3182),f7(f7(a29,f30(x3183,x3181,x3182,x3184)),x3183))) % 0.43/0.58 [332]P6(x3321,x3322,f33(x3323,x3321,x3324,x3322))+~P15(f7(f7(f27(x3321),f18(a10,f9(x3324),x3322,a36,a36)),x3323)) % 0.43/0.58 [337]P15(f7(f7(f27(x3371),f9(x3372)),f19(a29,f33(x3373,x3371,x3372,x3374),x3373,a37,a37)))+~P15(f7(f7(f27(x3371),f18(a10,f9(x3372),x3374,a36,a36)),x3373)) % 0.43/0.58 [320]P15(f7(f7(f27(x3201),f12(x3202)),f7(f7(a29,x3203),x3204)))+~P15(f7(f7(f27(f28(x3201,f4(a1),x3203,a37)),x3202),x3204)) % 0.43/0.58 [292]~P5(x2921,x2922,x2925,x2924)+P5(x2921,f13(x2922,x2923,x2924),f13(x2925,x2923,x2924),x2924) % 0.43/0.58 [293]~P5(x2931,x2933,x2935,x2934)+P5(x2931,f13(x2932,x2933,x2934),f13(x2932,x2935,x2934),x2934) % 0.43/0.58 [281]~P4(x2815,x2812,a1)+E(f7(f28(x2811,x2812,x2813,x2814),x2815),f7(x2811,x2815)) % 0.43/0.58 [287]~P15(f7(f7(x2871,x2875),x2874))+P15(f7(f7(f24(x2871,x2872,x2873),x2874),x2875)) % 0.43/0.58 [295]P15(f7(f7(x2951,x2952),x2953))+~P15(f7(f7(f24(x2951,x2954,x2955),x2953),x2952)) % 0.43/0.58 [317]~P15(f7(f7(f27(x3171),x3174),x3175))+P15(f7(f7(f27(f28(x3171,x3172,x3173,a37)),f15(x3174,x3172)),x3175)) % 0.43/0.58 [218]E(x2181,x2182)+P4(x2182,x2181,a1)+P4(x2181,x2182,a1) % 0.43/0.58 [242]~P9(x2421)+P4(f4(x2421),f21(x2422,x2421),x2421)+~P4(f4(a1),x2422,a1) % 0.43/0.58 [246]~P9(x2462)+~P4(f4(x2462),f21(x2461,x2462),x2462)+P4(f4(a1),x2461,a1) % 0.43/0.58 [238]~P4(x2383,x2382,x2381)+~P10(x2381)+~P4(x2382,x2383,x2381) % 0.43/0.58 [240]~P4(x2403,x2402,x2401)+~P12(x2401)+~P4(x2402,x2403,x2401) % 0.43/0.58 [241]~P4(x2413,x2412,x2411)+~P11(x2411)+~P4(x2412,x2413,x2411) % 0.43/0.58 [200]~P1(x2003)+E(x2001,x2002)+~E(f21(x2001,x2003),f21(x2002,x2003)) % 0.43/0.58 [245]~P9(x2452)+~P4(x2451,x2453,a1)+P4(f21(x2451,x2452),f21(x2453,x2452),x2452) % 0.43/0.58 [250]~P9(x2503)+~P4(f21(x2501,x2503),f21(x2502,x2503),x2503)+P4(x2501,x2502,a1) % 0.43/0.58 [231]E(x2311,x2312)+P4(x2312,x2311,a1)+E(f14(f9(x2311),x2313,x2312),f9(x2311)) % 0.43/0.58 [324]~P7(f24(a11,a36,a36),x3242,a36)+~P7(f24(a11,a36,a36),f18(a10,f14(x3241,x3242,f4(a1)),x3243,a36,a36),a36)+P7(f24(a11,a36,a36),f18(a10,f7(f7(a10,f12(x3241)),x3242),x3243,a36,a36),a36) % 0.43/0.58 [325]~P15(f7(a3,x3252))+~P15(f7(a3,f18(a10,f14(x3251,x3252,f4(a1)),x3253,a36,a36)))+P15(f7(a3,f18(a10,f7(f7(a10,f12(x3251)),x3252),x3253,a36,a36))) % 0.43/0.58 [255]~P8(x2553)+~P4(x2552,x2554,x2553)+P4(f16(x2551,x2552,x2553),x2554,x2553) % 0.43/0.58 [256]~P8(x2563)+~P4(x2561,x2564,x2563)+P4(f16(x2561,x2562,x2563),x2564,x2563) % 0.43/0.58 [268]~P3(x2681,x2683,x2684)+~P3(x2681,x2682,x2684)+P3(x2681,f13(x2682,x2683,x2684),x2684) % 0.43/0.58 [259]P7(x2591,x2592,x2593)+~P7(x2591,x2594,x2593)+~P15(f7(f7(x2591,x2592),x2594)) % 0.43/0.58 [270]~P3(x2702,x2704,x2703)+~P3(x2701,x2704,x2703)+P3(f16(x2701,x2702,f38(x2703,a2)),x2704,x2703) % 0.43/0.58 [271]~P15(f7(f7(a11,x2714),x2712))+~P15(f7(f7(f27(x2711),x2714),x2713))+P15(f7(f7(f27(x2711),x2712),x2713)) % 0.43/0.58 [272]~P15(f7(x2722,x2724))+~P15(f7(x2721,x2724))+P15(f7(f16(x2721,x2722,f38(x2723,a2)),x2724)) % 0.43/0.58 [274]P7(x2741,x2742,x2743)+~P7(x2741,x2744,x2743)+~P15(f7(f7(f23(x2741,x2743),x2742),x2744)) % 0.43/0.58 [277]P15(f7(f7(f27(x2771),x2772),x2773))+~P15(f7(f7(f27(x2771),x2774),x2773))+~P15(f7(f7(f23(a11,a36),x2774),x2772)) % 0.43/0.58 [300]~P15(f7(f7(f23(a11,a36),x3001),x3003))+~P15(f7(f7(f23(a11,a36),x3002),x3004))+P15(f7(f7(f23(a11,a36),f7(f7(a10,x3001),x3002)),f7(f7(a10,x3003),x3004))) % 0.43/0.58 [282]~P15(f7(f7(x2821,x2825),x2824))+~P15(f7(f7(f23(x2821,x2822),x2823),x2825))+P15(f7(f7(f23(x2821,x2822),x2823),x2824)) % 0.43/0.58 [283]~P15(f7(f7(x2831,x2833),x2835))+~P15(f7(f7(f23(x2831,x2832),x2835),x2834))+P15(f7(f7(f23(x2831,x2832),x2833),x2834)) % 0.43/0.58 [288]~P15(f7(f7(f23(x2881,x2882),x2883),x2885))+P15(f7(f7(f23(x2881,x2882),x2883),x2884))+~P15(f7(f7(f23(x2881,x2882),x2885),x2884)) % 0.43/0.58 [334]~P6(x3341,x3343,x3345)+~P15(f7(f7(f27(x3341),x3342),f19(a29,x3345,x3344,a37,a37)))+P15(f7(f7(f27(x3341),f18(a10,x3342,x3343,a36,a36)),x3344)) % 0.43/0.58 [297]~P15(f7(f7(f27(x2971),x2973),x2975))+~P15(f7(f7(f27(x2971),x2972),f7(f7(a29,x2975),x2974)))+P15(f7(f7(f27(x2971),f7(f7(a10,x2972),x2973)),x2974)) % 0.43/0.58 [338]E(x3381,x3382)+~P15(f7(f7(f27(x3383),f18(a10,f9(x3384),x3385,a36,a36)),x3381))+~P15(f7(f7(f27(x3383),f18(a10,f9(x3384),x3385,a36,a36)),x3382)) % 0.43/0.58 [323]P15(f7(f7(f27(x3231),f14(x3232,x3233,x3234)),x3235))+~P15(f7(f7(f27(x3231),x3233),x3236))+~P15(f7(f7(f27(f28(x3231,x3234,x3236,a37)),x3232),x3235)) % 0.43/0.58 [229]P4(x2291,x2292,x2293)+~P11(x2293)+E(x2291,x2292)+P4(x2292,x2291,x2293) % 0.43/0.58 [230]P4(x2301,x2302,x2303)+~P13(x2303)+E(x2301,x2302)+P4(x2302,x2301,x2303) % 0.43/0.58 [252]~P10(x2523)+~P4(x2521,x2524,x2523)+P4(x2521,x2522,x2523)+~P4(x2524,x2522,x2523) % 0.43/0.58 [253]~P12(x2533)+~P4(x2531,x2534,x2533)+P4(x2531,x2532,x2533)+~P4(x2534,x2532,x2533) % 0.43/0.58 [339]~P6(x3391,x3395,x3396)+P6(x3391,x3392,f34(x3393,x3394,x3391,x3392))+~P15(f7(f7(f27(x3391),f18(a10,f9(x3397),x3395,a36,a36)),x3394))+~P15(f7(f7(f27(x3391),f18(a10,f18(a10,f9(x3397),x3395,a36,a36),x3392,a36,a36)),x3393)) % 0.43/0.58 [340]~P6(x3403,x3405,x3406)+E(f19(a29,f34(x3401,x3402,x3403,x3404),x3401,a37,a37),x3402)+~P15(f7(f7(f27(x3403),f18(a10,f9(x3407),x3405,a36,a36)),x3402))+~P15(f7(f7(f27(x3403),f18(a10,f18(a10,f9(x3407),x3405,a36,a36),x3404,a36,a36)),x3401)) % 0.43/0.58 [321]~P15(f7(a3,x3212))+~P15(f7(a3,x3211))+~E(f7(f7(a29,x3214),x3215),a41)+P15(f7(a3,f14(x3211,x3212,x3213)))+~P15(f7(f7(f27(x3216),x3212),x3215))+~P15(f7(f7(f27(f28(x3216,x3213,x3215,a37)),x3211),x3217)) % 0.43/0.58 [322]~P15(f7(a3,x3222))+~P15(f7(a3,x3221))+~E(f7(f7(a29,x3224),x3225),a41)+P15(f7(a3,f14(x3221,x3222,x3223)))+~P15(f7(f7(f27(x3226),x3222),x3224))+~P15(f7(f7(f27(f28(x3226,x3223,x3224,a37)),x3221),x3227)) % 0.43/0.58 %EqnAxiom % 0.43/0.58 [1]E(x11,x11) % 0.43/0.58 [2]E(x22,x21)+~E(x21,x22) % 0.43/0.58 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.43/0.58 [4]~E(x41,x42)+E(f7(x41,x43),f7(x42,x43)) % 0.43/0.58 [5]~E(x51,x52)+E(f7(x53,x51),f7(x53,x52)) % 0.43/0.58 [6]~E(x61,x62)+E(f18(x61,x63,x64,x65,x66),f18(x62,x63,x64,x65,x66)) % 0.43/0.58 [7]~E(x71,x72)+E(f18(x73,x71,x74,x75,x76),f18(x73,x72,x74,x75,x76)) % 0.43/0.58 [8]~E(x81,x82)+E(f18(x83,x84,x81,x85,x86),f18(x83,x84,x82,x85,x86)) % 0.43/0.58 [9]~E(x91,x92)+E(f18(x93,x94,x95,x91,x96),f18(x93,x94,x95,x92,x96)) % 0.43/0.58 [10]~E(x101,x102)+E(f18(x103,x104,x105,x106,x101),f18(x103,x104,x105,x106,x102)) % 0.43/0.58 [11]~E(x111,x112)+E(f8(x111),f8(x112)) % 0.43/0.58 [12]~E(x121,x122)+E(f35(x121),f35(x122)) % 0.43/0.58 [13]~E(x131,x132)+E(f20(x131,x133),f20(x132,x133)) % 0.43/0.58 [14]~E(x141,x142)+E(f20(x143,x141),f20(x143,x142)) % 0.43/0.58 [15]~E(x151,x152)+E(f4(x151),f4(x152)) % 0.43/0.58 [16]~E(x161,x162)+E(f9(x161),f9(x162)) % 0.43/0.58 [17]~E(x171,x172)+E(f23(x171,x173),f23(x172,x173)) % 0.43/0.58 [18]~E(x181,x182)+E(f23(x183,x181),f23(x183,x182)) % 0.43/0.58 [19]~E(x191,x192)+E(f27(x191),f27(x192)) % 0.43/0.58 [20]~E(x201,x202)+E(f12(x201),f12(x202)) % 0.43/0.58 [21]~E(x211,x212)+E(f24(x211,x213,x214),f24(x212,x213,x214)) % 0.43/0.58 [22]~E(x221,x222)+E(f24(x223,x221,x224),f24(x223,x222,x224)) % 0.43/0.58 [23]~E(x231,x232)+E(f24(x233,x234,x231),f24(x233,x234,x232)) % 0.43/0.58 [24]~E(x241,x242)+E(f13(x241,x243,x244),f13(x242,x243,x244)) % 0.43/0.58 [25]~E(x251,x252)+E(f13(x253,x251,x254),f13(x253,x252,x254)) % 0.43/0.58 [26]~E(x261,x262)+E(f13(x263,x264,x261),f13(x263,x264,x262)) % 0.43/0.58 [27]~E(x271,x272)+E(f28(x271,x273,x274,x275),f28(x272,x273,x274,x275)) % 0.43/0.58 [28]~E(x281,x282)+E(f28(x283,x281,x284,x285),f28(x283,x282,x284,x285)) % 0.43/0.58 [29]~E(x291,x292)+E(f28(x293,x294,x291,x295),f28(x293,x294,x292,x295)) % 0.43/0.58 [30]~E(x301,x302)+E(f28(x303,x304,x305,x301),f28(x303,x304,x305,x302)) % 0.43/0.58 [31]~E(x311,x312)+E(f38(x311,x313),f38(x312,x313)) % 0.43/0.58 [32]~E(x321,x322)+E(f38(x323,x321),f38(x323,x322)) % 0.43/0.58 [33]~E(x331,x332)+E(f21(x331,x333),f21(x332,x333)) % 0.43/0.58 [34]~E(x341,x342)+E(f21(x343,x341),f21(x343,x342)) % 0.43/0.58 [35]~E(x351,x352)+E(f14(x351,x353,x354),f14(x352,x353,x354)) % 0.43/0.58 [36]~E(x361,x362)+E(f14(x363,x361,x364),f14(x363,x362,x364)) % 0.43/0.58 [37]~E(x371,x372)+E(f14(x373,x374,x371),f14(x373,x374,x372)) % 0.43/0.58 [38]~E(x381,x382)+E(f6(x381),f6(x382)) % 0.43/0.58 [39]~E(x391,x392)+E(f19(x391,x393,x394,x395,x396),f19(x392,x393,x394,x395,x396)) % 0.43/0.58 [40]~E(x401,x402)+E(f19(x403,x401,x404,x405,x406),f19(x403,x402,x404,x405,x406)) % 0.43/0.58 [41]~E(x411,x412)+E(f19(x413,x414,x411,x415,x416),f19(x413,x414,x412,x415,x416)) % 0.43/0.58 [42]~E(x421,x422)+E(f19(x423,x424,x425,x421,x426),f19(x423,x424,x425,x422,x426)) % 0.43/0.58 [43]~E(x431,x432)+E(f19(x433,x434,x435,x436,x431),f19(x433,x434,x435,x436,x432)) % 0.43/0.58 [44]~E(x441,x442)+E(f31(x441,x443,x444,x445),f31(x442,x443,x444,x445)) % 0.43/0.58 [45]~E(x451,x452)+E(f31(x453,x451,x454,x455),f31(x453,x452,x454,x455)) % 0.43/0.58 [46]~E(x461,x462)+E(f31(x463,x464,x461,x465),f31(x463,x464,x462,x465)) % 0.43/0.58 [47]~E(x471,x472)+E(f31(x473,x474,x475,x471),f31(x473,x474,x475,x472)) % 0.43/0.58 [48]~E(x481,x482)+E(f16(x481,x483,x484),f16(x482,x483,x484)) % 0.43/0.58 [49]~E(x491,x492)+E(f16(x493,x491,x494),f16(x493,x492,x494)) % 0.43/0.58 [50]~E(x501,x502)+E(f16(x503,x504,x501),f16(x503,x504,x502)) % 0.43/0.58 [51]~E(x511,x512)+E(f5(x511,x513,x514,x515,x516),f5(x512,x513,x514,x515,x516)) % 0.43/0.58 [52]~E(x521,x522)+E(f5(x523,x521,x524,x525,x526),f5(x523,x522,x524,x525,x526)) % 0.43/0.58 [53]~E(x531,x532)+E(f5(x533,x534,x531,x535,x536),f5(x533,x534,x532,x535,x536)) % 0.43/0.58 [54]~E(x541,x542)+E(f5(x543,x544,x545,x541,x546),f5(x543,x544,x545,x542,x546)) % 0.43/0.58 [55]~E(x551,x552)+E(f5(x553,x554,x555,x556,x551),f5(x553,x554,x555,x556,x552)) % 0.43/0.58 [56]~E(x561,x562)+E(f33(x561,x563,x564,x565),f33(x562,x563,x564,x565)) % 0.43/0.58 [57]~E(x571,x572)+E(f33(x573,x571,x574,x575),f33(x573,x572,x574,x575)) % 0.43/0.58 [58]~E(x581,x582)+E(f33(x583,x584,x581,x585),f33(x583,x584,x582,x585)) % 0.43/0.58 [59]~E(x591,x592)+E(f33(x593,x594,x595,x591),f33(x593,x594,x595,x592)) % 0.43/0.58 [60]~E(x601,x602)+E(f15(x601,x603),f15(x602,x603)) % 0.43/0.58 [61]~E(x611,x612)+E(f15(x613,x611),f15(x613,x612)) % 0.43/0.58 [62]~E(x621,x622)+E(f30(x621,x623,x624,x625),f30(x622,x623,x624,x625)) % 0.43/0.58 [63]~E(x631,x632)+E(f30(x633,x631,x634,x635),f30(x633,x632,x634,x635)) % 0.43/0.58 [64]~E(x641,x642)+E(f30(x643,x644,x641,x645),f30(x643,x644,x642,x645)) % 0.43/0.58 [65]~E(x651,x652)+E(f30(x653,x654,x655,x651),f30(x653,x654,x655,x652)) % 0.43/0.58 [66]~E(x661,x662)+E(f26(x661),f26(x662)) % 0.43/0.58 [67]~E(x671,x672)+E(f17(x671,x673,x674),f17(x672,x673,x674)) % 0.43/0.58 [68]~E(x681,x682)+E(f17(x683,x681,x684),f17(x683,x682,x684)) % 0.43/0.58 [69]~E(x691,x692)+E(f17(x693,x694,x691),f17(x693,x694,x692)) % 0.43/0.58 [70]~E(x701,x702)+E(f34(x701,x703,x704,x705),f34(x702,x703,x704,x705)) % 0.43/0.58 [71]~E(x711,x712)+E(f34(x713,x711,x714,x715),f34(x713,x712,x714,x715)) % 0.43/0.58 [72]~E(x721,x722)+E(f34(x723,x724,x721,x725),f34(x723,x724,x722,x725)) % 0.43/0.58 [73]~E(x731,x732)+E(f34(x733,x734,x735,x731),f34(x733,x734,x735,x732)) % 0.43/0.58 [74]~E(x741,x742)+E(f22(x741,x743,x744),f22(x742,x743,x744)) % 0.43/0.58 [75]~E(x751,x752)+E(f22(x753,x751,x754),f22(x753,x752,x754)) % 0.43/0.58 [76]~E(x761,x762)+E(f22(x763,x764,x761),f22(x763,x764,x762)) % 0.43/0.58 [77]~E(x771,x772)+E(f32(x771,x773,x774,x775),f32(x772,x773,x774,x775)) % 0.43/0.58 [78]~E(x781,x782)+E(f32(x783,x781,x784,x785),f32(x783,x782,x784,x785)) % 0.43/0.58 [79]~E(x791,x792)+E(f32(x793,x794,x791,x795),f32(x793,x794,x792,x795)) % 0.43/0.58 [80]~E(x801,x802)+E(f32(x803,x804,x805,x801),f32(x803,x804,x805,x802)) % 0.43/0.58 [81]~E(x811,x812)+E(f25(x811,x813,x814,x815),f25(x812,x813,x814,x815)) % 0.43/0.58 [82]~E(x821,x822)+E(f25(x823,x821,x824,x825),f25(x823,x822,x824,x825)) % 0.43/0.58 [83]~E(x831,x832)+E(f25(x833,x834,x831,x835),f25(x833,x834,x832,x835)) % 0.43/0.58 [84]~E(x841,x842)+E(f25(x843,x844,x845,x841),f25(x843,x844,x845,x842)) % 0.43/0.58 [85]~P1(x851)+P1(x852)+~E(x851,x852) % 0.43/0.58 [86]~P9(x861)+P9(x862)+~E(x861,x862) % 0.43/0.58 [87]~P14(x871)+P14(x872)+~E(x871,x872) % 0.43/0.58 [88]~P2(x881)+P2(x882)+~E(x881,x882) % 0.43/0.58 [89]~P15(x891)+P15(x892)+~E(x891,x892) % 0.43/0.58 [90]~P8(x901)+P8(x902)+~E(x901,x902) % 0.43/0.58 [91]P7(x912,x913,x914)+~E(x911,x912)+~P7(x911,x913,x914) % 0.43/0.58 [92]P7(x923,x922,x924)+~E(x921,x922)+~P7(x923,x921,x924) % 0.43/0.58 [93]P7(x933,x934,x932)+~E(x931,x932)+~P7(x933,x934,x931) % 0.43/0.58 [94]~P10(x941)+P10(x942)+~E(x941,x942) % 0.43/0.58 [95]P3(x952,x953,x954)+~E(x951,x952)+~P3(x951,x953,x954) % 0.43/0.58 [96]P3(x963,x962,x964)+~E(x961,x962)+~P3(x963,x961,x964) % 0.43/0.58 [97]P3(x973,x974,x972)+~E(x971,x972)+~P3(x973,x974,x971) % 0.43/0.58 [98]~P12(x981)+P12(x982)+~E(x981,x982) % 0.43/0.58 [99]P6(x992,x993,x994)+~E(x991,x992)+~P6(x991,x993,x994) % 0.43/0.58 [100]P6(x1003,x1002,x1004)+~E(x1001,x1002)+~P6(x1003,x1001,x1004) % 0.43/0.58 [101]P6(x1013,x1014,x1012)+~E(x1011,x1012)+~P6(x1013,x1014,x1011) % 0.43/0.58 [102]~P11(x1021)+P11(x1022)+~E(x1021,x1022) % 0.43/0.58 [103]P4(x1032,x1033,x1034)+~E(x1031,x1032)+~P4(x1031,x1033,x1034) % 0.43/0.58 [104]P4(x1043,x1042,x1044)+~E(x1041,x1042)+~P4(x1043,x1041,x1044) % 0.43/0.58 [105]P4(x1053,x1054,x1052)+~E(x1051,x1052)+~P4(x1053,x1054,x1051) % 0.43/0.58 [106]~P13(x1061)+P13(x1062)+~E(x1061,x1062) % 0.43/0.58 [107]P5(x1072,x1073,x1074,x1075)+~E(x1071,x1072)+~P5(x1071,x1073,x1074,x1075) % 0.43/0.58 [108]P5(x1083,x1082,x1084,x1085)+~E(x1081,x1082)+~P5(x1083,x1081,x1084,x1085) % 0.43/0.58 [109]P5(x1093,x1094,x1092,x1095)+~E(x1091,x1092)+~P5(x1093,x1094,x1091,x1095) % 0.43/0.58 [110]P5(x1103,x1104,x1105,x1102)+~E(x1101,x1102)+~P5(x1103,x1104,x1105,x1101) % 0.43/0.58 % 0.43/0.58 %------------------------------------------- % 0.43/0.58 cnf(355,plain, % 0.43/0.58 ($false), % 0.43/0.58 inference(scs_inference,[],[158,191,311]), % 0.43/0.58 ['proof']). % 0.43/0.58 % SZS output end Proof % 0.43/0.58 % Total time :0.018730s %------------------------------------------------------------------------------