%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL806-1 : TPTP v9.3.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n019.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 11:23:54 AM UTC 2026 % Result : Unsatisfiable 0.76s 1.04s % Output : Proof 0.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL806-1 : TPTP v9.3.1. Released v4.1.0. % 0.00/0.05 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.10/0.37 % Computer : n019.cluster.edu % 0.10/0.37 % Model : x86_64 x86_64 % 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.37 % Memory : 8046.5625MB % 0.10/0.37 % OS : Linux 6.8.0-71-generic % 0.10/0.37 % CPULimit : 300 % 0.10/0.37 % WCLimit : 300 % 0.10/0.37 % DateTime : Fri Sep 4 12:46:08 UTC 2026 % 0.10/0.37 % CPUTime : % 0.32/0.56 %----Proving TF0_NAR, FOF, or CNF % 0.32/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.76/1.04 % SZS status Unsatisfiable % 0.76/1.04 % SZS output start Proof % 0.76/1.07 ( % 0.76/1.07 (declare-sort $$unsorted 0) % 0.76/1.07 (declare-const tptp.v_xb $$unsorted) % 0.76/1.07 (declare-const tptp.v_xc $$unsorted) % 0.76/1.07 (declare-const tptp.c_COMBB (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.v_sko__local__XCons__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.v_b____ $$unsorted) % 0.76/1.07 (declare-const tptp.c_Fun_Ofcomp (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.class_Orderings_Oorder (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.tc_fun (-> $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_List_Omap (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.v_a____ $$unsorted) % 0.76/1.07 (declare-const tptp.v_u____ $$unsorted) % 0.76/1.07 (declare-const tptp.c_Type_Osko__Type__Xtyping__elims__2__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.v_x $$unsorted) % 0.76/1.07 (declare-const tptp.class_OrderedGroup_Ocancel__semigroup__add (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.class_OrderedGroup_Ocancel__ab__semigroup__add (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.c_COMBS (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.v_T_H____ $$unsorted) % 0.76/1.07 (declare-const tptp.c_COMBK (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.class_Orderings_Opreorder (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.class_OrderedGroup_Ocomm__monoid__add (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.v_bs____ $$unsorted) % 0.76/1.07 (declare-const tptp.class_Ring__and__Field_Ocomm__semiring__1 (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.class_OrderedGroup_Oab__semigroup__add (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.v_i____ $$unsorted) % 0.76/1.07 (declare-const tptp.class_Ring__and__Field_Oordered__idom (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.v_sko__local__XCons__Xhyps__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.class_OrderedGroup_Opordered__comm__monoid__add (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.class_OrderedGroup_Olordered__ab__group__add (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.tc_Type_Otype $$unsorted) % 0.76/1.07 (declare-const tptp.hAPP (-> $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_Type_Oshift (-> $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_Nat_Osize__class_Osize (-> $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_Type_Osko__Type__Xabs__typeE__1__1 (-> $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.v_ea______ $$unsorted) % 0.76/1.07 (declare-const tptp.c_InductTermi_OIT $$unsorted) % 0.76/1.07 (declare-const tptp.v_rs____ $$unsorted) % 0.76/1.07 (declare-const tptp.class_Ring__and__Field_Oidom (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.c_Ex (-> $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_Type_Osko__Type__Xlist__app__typeD__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_Suc (-> $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.v_sko__CHAINED__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_Type_Otype_OFun $$unsorted) % 0.76/1.07 (declare-const tptp.v_as____ $$unsorted) % 0.76/1.07 (declare-const tptp.v_e____ $$unsorted) % 0.76/1.07 (declare-const tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.v_ua______ $$unsorted) % 0.76/1.07 (declare-const tptp.c_Nat_Osemiring__1__class_Oof__nat__aux (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_implies $$unsorted) % 0.76/1.07 (declare-const tptp.tc_Lambda_OdB $$unsorted) % 0.76/1.07 (declare-const tptp.t_a $$unsorted) % 0.76/1.07 (declare-const tptp.class_Ring__and__Field_Osemiring__1 (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.tc_bool $$unsorted) % 0.76/1.07 (declare-const tptp.v_Ts____ $$unsorted) % 0.76/1.07 (declare-const tptp.c_Type_Osko__Type__Xtyping__elims__3__2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_and $$unsorted) % 0.76/1.07 (declare-const tptp.c_Lambda_Obeta $$unsorted) % 0.76/1.07 (declare-const tptp.c_List_Ofoldl (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.v_xa $$unsorted) % 0.76/1.07 (declare-const tptp.c_Transitive__Closure_Ortranclp (-> $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.class_Int_Onumber__ring (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.c_Lambda_Osubst $$unsorted) % 0.76/1.07 (declare-const tptp.c_Type_Otype_Otype__size (-> $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_HOL_Ozero__class_Ozero (-> $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_All (-> $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.class_Nat_Osemiring__char__0 (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.c_HOL_Oone__class_Oone (-> $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_Lambda_OdB_OAbs (-> $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_Lambda_OdB_OApp $$unsorted) % 0.76/1.07 (declare-const tptp.c_Fun_Oid (-> $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_Lambda_Oliftn (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.class_OrderedGroup_Osemigroup__add (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.hBOOL (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.c_Lambda_Osubstn (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.class_Orderings_Olinorder (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.class_OrderedGroup_Ogroup__add (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.c_Nat_Osemiring__1__class_Oof__nat (-> $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_HOL_Ominus__class_Ominus (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.class_OrderedGroup_Oab__group__add (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.c_Type_Osko__Type__Xlist__app__typeE__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_fequal (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.c_Type_Otyping $$unsorted) % 0.76/1.07 (declare-const tptp.c_Lambda_OdB_OVar (-> $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_Type_Osko__Type__Xabs__typeE__1__2 (-> $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.v_ia______ $$unsorted) % 0.76/1.07 (declare-const tptp.c_List_Olistsp (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.tc_nat $$unsorted) % 0.76/1.07 (declare-const tptp.c_Type_Osko__Type__Xvar__app__types__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_HOL_Oplus__class_Oplus (-> $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.v_T_Ha______ $$unsorted) % 0.76/1.07 (declare-const tptp.c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_Type_Otypings (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.c_COMBC (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_Lambda_Olift $$unsorted) % 0.76/1.07 (declare-const tptp.c_List_Ofoldr (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.c_HOL_Oord__class_Oless (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.class_OrderedGroup_Omonoid__add (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.v_n____ $$unsorted) % 0.76/1.07 (declare-const tptp.v_T____ $$unsorted) % 0.76/1.07 (declare-const tptp.c_Nat_Ocompow (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.class_Ring__and__Field_Ozero__neq__one (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.c_ListOrder_Ostep1 (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.c_Fun_Ocomp (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.class_Ring__and__Field_Oordered__semidom (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.c_Type_Osko__Type__Xvar__app__typesE__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (declare-const tptp.v_T_H_H____ $$unsorted) % 0.76/1.07 (declare-const tptp.class_OrderedGroup_Opordered__ab__group__add (-> $$unsorted Bool)) % 0.76/1.07 (declare-const tptp.c_Type_Osko__Type__Xtyping__elims__3__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.76/1.07 (define @t1 () (@var "V_ss" $$unsorted)) % 0.76/1.07 (define @t2 () (@var "V_rs" $$unsorted)) % 0.76/1.07 (define @t3 () (@var "V_r" $$unsorted)) % 0.76/1.07 (define @t4 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t3 @t1 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.76/1.07 (define @t5 () (@var "V_n" $$unsorted)) % 0.76/1.07 (define @t6 () (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) % 0.76/1.07 (define @t7 () (tptp.c_HOL_Oord__class_Oless @t6 @t5 tptp.tc_nat)) % 0.76/1.07 (define @t8 () (not @t7)) % 0.76/1.07 (define @t9 () (@var "V_m" $$unsorted)) % 0.76/1.07 (define @t10 () (tptp.c_HOL_Oord__class_Oless @t6 @t9 tptp.tc_nat)) % 0.76/1.07 (define @t11 () (not @t10)) % 0.76/1.07 (define @t12 () (tptp.c_HOL_Ominus__class_Ominus @t9 @t5 tptp.tc_nat)) % 0.76/1.07 (define @t13 () (@list @t9 @t5)) % 0.76/1.07 (define @t14 () (tptp.c_HOL_Oord__class_Oless @t9 @t5 tptp.tc_nat)) % 0.76/1.07 (define @t15 () (not @t14)) % 0.76/1.07 (define @t16 () (tptp.c_HOL_Ominus__class_Ominus @t5 @t9 tptp.tc_nat)) % 0.76/1.07 (define @t17 () (tptp.c_HOL_Oord__class_Oless @t6 @t16 tptp.tc_nat)) % 0.76/1.07 (define @t18 () (@list @t5 @t9)) % 0.76/1.07 (define @t19 () (@var "V_b" $$unsorted)) % 0.76/1.07 (define @t20 () (@var "V_a" $$unsorted)) % 0.76/1.07 (define @t21 () (@var "V_P" $$unsorted)) % 0.76/1.07 (define @t22 () (@var "T_a" $$unsorted)) % 0.76/1.07 (define @t23 () (tptp.c_HOL_Oord__class_Oless @t20 @t19 @t22)) % 0.76/1.07 (define @t24 () (not @t23)) % 0.76/1.07 (define @t25 () (tptp.c_HOL_Ozero__class_Ozero @t22)) % 0.76/1.07 (define @t26 () (tptp.c_HOL_Ominus__class_Ominus @t20 @t19 @t22)) % 0.76/1.07 (define @t27 () (tptp.c_HOL_Oord__class_Oless @t26 @t25 @t22)) % 0.76/1.07 (define @t28 () (not (tptp.class_OrderedGroup_Opordered__ab__group__add @t22))) % 0.76/1.07 (define @t29 () (@list @t22 @t20 @t19)) % 0.76/1.07 (define @t30 () (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat)) % 0.76/1.07 (define @t31 () (tptp.hAPP @t30 @t5)) % 0.76/1.07 (define @t32 () (@var "V_y_H" $$unsorted)) % 0.76/1.07 (define @t33 () (@var "V_x_H" $$unsorted)) % 0.76/1.07 (define @t34 () (tptp.c_HOL_Oord__class_Oless @t33 @t32 @t22)) % 0.76/1.07 (define @t35 () (@var "V_y" $$unsorted)) % 0.76/1.07 (define @t36 () (@var "V_x" $$unsorted)) % 0.76/1.07 (define @t37 () (tptp.c_HOL_Oord__class_Oless @t36 @t35 @t22)) % 0.76/1.07 (define @t38 () (tptp.c_HOL_Ominus__class_Ominus @t33 @t32 @t22)) % 0.76/1.07 (define @t39 () (tptp.c_HOL_Ominus__class_Ominus @t36 @t35 @t22)) % 0.76/1.07 (define @t40 () (not (= @t39 @t38))) % 0.76/1.07 (define @t41 () (@list @t22 @t36 @t35 @t33 @t32)) % 0.76/1.07 (define @t42 () (not @t37)) % 0.76/1.07 (define @t43 () (@var "V_j" $$unsorted)) % 0.76/1.07 (define @t44 () (@var "V_k" $$unsorted)) % 0.76/1.07 (define @t45 () (@var "V_i" $$unsorted)) % 0.76/1.07 (define @t46 () (tptp.hAPP @t30 @t45)) % 0.76/1.07 (define @t47 () (tptp.hAPP @t46 @t44)) % 0.76/1.07 (define @t48 () (tptp.c_HOL_Oord__class_Oless @t47 @t43 tptp.tc_nat)) % 0.76/1.07 (define @t49 () (tptp.c_HOL_Oord__class_Oless @t45 (tptp.c_HOL_Ominus__class_Ominus @t43 @t44 tptp.tc_nat) tptp.tc_nat)) % 0.76/1.07 (define @t50 () (@list @t45 @t43 @t44)) % 0.76/1.07 (define @t51 () (@list @t45 @t44 @t43)) % 0.76/1.07 (define @t52 () (@var "V_inc" $$unsorted)) % 0.76/1.07 (define @t53 () (not (tptp.class_Ring__and__Field_Osemiring__1 @t22))) % 0.76/1.07 (define @t54 () (= @t9 @t5)) % 0.76/1.07 (define @t55 () (not (tptp.c_HOL_Oord__class_Oless @t43 @t44 tptp.tc_nat))) % 0.76/1.07 (define @t56 () (tptp.c_Suc @t5)) % 0.76/1.07 (define @t57 () (tptp.c_Suc @t9)) % 0.76/1.07 (define @t58 () (@list @t9)) % 0.76/1.07 (define @t59 () (tptp.c_HOL_Ominus__class_Ominus @t36 @t36 @t22)) % 0.76/1.07 (define @t60 () (= @t59 @t25)) % 0.76/1.07 (define @t61 () (not (tptp.class_Int_Onumber__ring @t22))) % 0.76/1.07 (define @t62 () (not (tptp.class_Ring__and__Field_Oidom @t22))) % 0.76/1.07 (define @t63 () (@list @t22 @t36)) % 0.76/1.07 (define @t64 () (not (tptp.class_OrderedGroup_Ogroup__add @t22))) % 0.76/1.07 (define @t65 () (@list @t22 @t20)) % 0.76/1.07 (define @t66 () (not (tptp.class_OrderedGroup_Oab__group__add @t22))) % 0.76/1.07 (define @t67 () (@var "V_l" $$unsorted)) % 0.76/1.07 (define @t68 () (tptp.c_HOL_Oone__class_Oone tptp.tc_nat)) % 0.76/1.07 (define @t69 () (@list @t5)) % 0.76/1.07 (define @t70 () (tptp.c_HOL_Oplus__class_Oplus @t22)) % 0.76/1.07 (define @t71 () (tptp.hAPP @t30 @t19)) % 0.76/1.07 (define @t72 () (@var "V_d" $$unsorted)) % 0.76/1.07 (define @t73 () (tptp.hAPP @t31 @t9)) % 0.76/1.07 (define @t74 () (tptp.hAPP @t30 @t43)) % 0.76/1.07 (define @t75 () (tptp.hAPP @t74 @t44)) % 0.76/1.07 (define @t76 () (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus @t45 @t43 tptp.tc_nat) @t44 tptp.tc_nat)) % 0.76/1.07 (define @t77 () (@var "V_xa" $$unsorted)) % 0.76/1.07 (define @t78 () (tptp.hAPP @t31 @t44)) % 0.76/1.07 (define @t79 () (tptp.hAPP @t30 @t9)) % 0.76/1.07 (define @t80 () (tptp.hAPP @t79 @t44)) % 0.76/1.07 (define @t81 () (@list @t9 @t44 @t5)) % 0.76/1.07 (define @t82 () (tptp.hAPP @t30 @t44)) % 0.76/1.07 (define @t83 () (tptp.hAPP @t82 @t5)) % 0.76/1.07 (define @t84 () (tptp.hAPP @t82 @t9)) % 0.76/1.07 (define @t85 () (@list @t44 @t9 @t5)) % 0.76/1.07 (define @t86 () (= @t36 @t35)) % 0.76/1.07 (define @t87 () (@list @t22 @t36 @t35)) % 0.76/1.07 (define @t88 () (= @t20 @t19)) % 0.76/1.07 (define @t89 () (not (= @t26 @t25))) % 0.76/1.07 (define @t90 () (tptp.c_Suc @t44)) % 0.76/1.07 (define @t91 () (@list @t9 @t5 @t44)) % 0.76/1.07 (define @t92 () (tptp.c_HOL_Ominus__class_Ominus @t9 @t68 tptp.tc_nat)) % 0.76/1.07 (define @t93 () (@var "V_v" $$unsorted)) % 0.76/1.07 (define @t94 () (tptp.c_Lambda_OdB_OVar @t5)) % 0.76/1.07 (define @t95 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t94 @t2 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.76/1.07 (define @t96 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t95) @t93)))) % 0.76/1.07 (define @t97 () (tptp.c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @t5 @t2 @t93)) % 0.76/1.07 (define @t98 () (tptp.hAPP @t79 @t5)) % 0.76/1.07 (define @t99 () (tptp.hAPP @t70 @t20)) % 0.76/1.07 (define @t100 () (tptp.hAPP @t99 @t19)) % 0.76/1.07 (define @t101 () (tptp.c_Suc @t45)) % 0.76/1.07 (define @t102 () (tptp.c_Suc @t6)) % 0.76/1.07 (define @t103 () (not (tptp.c_HOL_Oord__class_Oless @t45 @t43 tptp.tc_nat))) % 0.76/1.07 (define @t104 () (tptp.c_HOL_Ominus__class_Ominus @t43 @t68 tptp.tc_nat)) % 0.76/1.07 (define @t105 () (@var "V_e" $$unsorted)) % 0.76/1.07 (define @t106 () (@var "V_T" $$unsorted)) % 0.76/1.07 (define @t107 () (tptp.c_Type_Oshift @t22)) % 0.76/1.07 (define @t108 () (tptp.hAPP @t107 @t105)) % 0.76/1.07 (define @t109 () (tptp.hAPP @t108 @t45)) % 0.76/1.07 (define @t110 () (tptp.hAPP (tptp.hAPP @t109 @t106) @t43)) % 0.76/1.07 (define @t111 () (@list @t22 @t105 @t45 @t106 @t43)) % 0.76/1.07 (define @t112 () (tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus @t5 @t68 tptp.tc_nat))) % 0.76/1.07 (define @t113 () (= @t9 @t6)) % 0.76/1.07 (define @t114 () (@var "V_type2" $$unsorted)) % 0.76/1.07 (define @t115 () (@var "V_type1" $$unsorted)) % 0.76/1.07 (define @t116 () (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun @t115) @t114)) % 0.76/1.07 (define @t117 () (@list @t115 @t114)) % 0.76/1.07 (define @t118 () (@var "V_u" $$unsorted)) % 0.76/1.07 (define @t119 () (tptp.c_Lambda_OdB_OVar @t43)) % 0.76/1.07 (define @t120 () (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst @t119) @t118) @t45)) % 0.76/1.07 (define @t121 () (@list @t43 @t118 @t45)) % 0.76/1.07 (define @t122 () (tptp.c_HOL_Oord__class_Oless @t44 @t45 tptp.tc_nat)) % 0.76/1.07 (define @t123 () (not @t122)) % 0.76/1.07 (define @t124 () (tptp.c_Lambda_OdB_OVar (tptp.c_HOL_Ominus__class_Ominus @t45 @t68 tptp.tc_nat))) % 0.76/1.07 (define @t125 () (@var "V_s" $$unsorted)) % 0.76/1.07 (define @t126 () (tptp.c_Lambda_OdB_OVar @t45)) % 0.76/1.07 (define @t127 () (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst @t126) @t125) @t44)) % 0.76/1.07 (define @t128 () (@list @t45 @t125 @t44)) % 0.76/1.07 (define @t129 () (@var "V_ts" $$unsorted)) % 0.76/1.07 (define @t130 () (@var "V_t" $$unsorted)) % 0.76/1.07 (define @t131 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t130 @t129 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.76/1.07 (define @t132 () (tptp.hAPP tptp.c_Type_Otyping @t105)) % 0.76/1.07 (define @t133 () (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t132 @t131) @t106))) % 0.76/1.07 (define @t134 () (not @t133)) % 0.76/1.07 (define @t135 () (tptp.c_Type_Osko__Type__Xlist__app__typeE__1__1 @t106 @t105 @t130 @t129)) % 0.76/1.07 (define @t136 () (@list @t105 @t129 @t106 @t130)) % 0.76/1.07 (define @t137 () (tptp.c_Type_Osko__Type__Xlist__app__typeD__1__1 @t106 @t105 @t130 @t129)) % 0.76/1.07 (define @t138 () (tptp.c_Lambda_Osubstn @t126 @t125 @t44)) % 0.76/1.07 (define @t139 () (tptp.c_HOL_Oone__class_Oone @t22)) % 0.76/1.07 (define @t140 () (tptp.c_Nat_Osemiring__1__class_Oof__nat @t5 @t22)) % 0.76/1.07 (define @t141 () (@list @t22 @t5)) % 0.76/1.07 (define @t142 () (tptp.hAPP @t132 @t130)) % 0.76/1.07 (define @t143 () (@list @t105 @t130 @t106 @t129)) % 0.76/1.07 (define @t144 () (tptp.c_Lambda_OdB_OVar tptp.v_n____)) % 0.76/1.07 (define @t145 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t144 tptp.v_rs____ tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.76/1.07 (define @t146 () (tptp.c_Type_Oshift tptp.tc_Type_Otype)) % 0.76/1.07 (define @t147 () (@var "V_f" $$unsorted)) % 0.76/1.07 (define @t148 () (tptp.c_Nat_Ocompow @t5 @t147 @t22 @t22)) % 0.76/1.07 (define @t149 () (tptp.c_Transitive__Closure_Ortranclp @t3 @t22)) % 0.76/1.07 (define @t150 () (tptp.hAPP @t149 @t36)) % 0.76/1.07 (define @t151 () (tptp.hBOOL (tptp.hAPP @t150 @t35))) % 0.76/1.07 (define @t152 () (= @t9 @t102)) % 0.76/1.07 (define @t153 () (= @t5 @t102)) % 0.76/1.07 (define @t154 () (not (= @t102 @t98))) % 0.76/1.07 (define @t155 () (= @t5 @t6)) % 0.76/1.07 (define @t156 () (@var "V_zs" $$unsorted)) % 0.76/1.07 (define @t157 () (tptp.hAPP @t70 @t36)) % 0.76/1.07 (define @t158 () (not (tptp.class_OrderedGroup_Omonoid__add @t22))) % 0.76/1.07 (define @t159 () (not (tptp.class_Ring__and__Field_Ozero__neq__one @t22))) % 0.76/1.07 (define @t160 () (@list @t22)) % 0.76/1.07 (define @t161 () (tptp.c_HOL_Oord__class_Oless @t9 @t56 tptp.tc_nat)) % 0.76/1.07 (define @t162 () (tptp.c_HOL_Oord__class_Oless @t5 @t9 tptp.tc_nat)) % 0.76/1.07 (define @t163 () (tptp.c_HOL_Oord__class_Oless @t5 @t57 tptp.tc_nat)) % 0.76/1.07 (define @t164 () (not @t163)) % 0.76/1.07 (define @t165 () (tptp.hAPP (tptp.hAPP @t30 @t102) @t6)) % 0.76/1.07 (define @t166 () (tptp.c_HOL_Oord__class_Oless @t45 @t44 tptp.tc_nat)) % 0.76/1.07 (define @t167 () (tptp.c_Lambda_Oliftn @t5 @t126 @t44)) % 0.76/1.07 (define @t168 () (@list @t5 @t45 @t44)) % 0.76/1.07 (define @t169 () (tptp.hAPP @t82 @t68)) % 0.76/1.07 (define @t170 () (tptp.c_Lambda_OdB_OAbs @t125)) % 0.76/1.07 (define @t171 () (@var "V_c" $$unsorted)) % 0.76/1.07 (define @t172 () (tptp.hAPP @t70 @t19)) % 0.76/1.07 (define @t173 () (tptp.hAPP @t172 @t72)) % 0.76/1.07 (define @t174 () (tptp.hAPP @t99 @t171)) % 0.76/1.07 (define @t175 () (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add @t22))) % 0.76/1.07 (define @t176 () (not (tptp.c_HOL_Oord__class_Oless @t44 @t67 tptp.tc_nat))) % 0.76/1.07 (define @t177 () (@var "V_nat_H" $$unsorted)) % 0.76/1.07 (define @t178 () (tptp.c_Suc @t177)) % 0.76/1.07 (define @t179 () (@list @t177)) % 0.76/1.07 (define @t180 () (tptp.c_Suc @t36)) % 0.76/1.07 (define @t181 () (tptp.c_HOL_Oord__class_Oless @t36 @t180 tptp.tc_nat)) % 0.76/1.07 (define @t182 () (@list @t36)) % 0.76/1.07 (define @t183 () (@var "V_xs" $$unsorted)) % 0.76/1.07 (define @t184 () (tptp.c_List_Ofoldr @t70 @t183 @t25 @t22 @t22)) % 0.76/1.07 (define @t185 () (not (tptp.class_Ring__and__Field_Oordered__semidom @t22))) % 0.76/1.07 (define @t186 () (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB)) % 0.76/1.07 (define @t187 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t186 @t3) @t125)))) % 0.76/1.07 (define @t188 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t125 @t1 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.76/1.07 (define @t189 () (@list @t3 @t1 @t125)) % 0.76/1.07 (define @t190 () (tptp.hAPP @t46 @t43)) % 0.76/1.07 (define @t191 () (tptp.hAPP @t172 @t171)) % 0.76/1.07 (define @t192 () (tptp.c_HOL_Oord__class_Oless @t174 @t191 @t22)) % 0.76/1.07 (define @t193 () (@list @t22 @t20 @t171 @t19)) % 0.76/1.07 (define @t194 () (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @t22))) % 0.76/1.07 (define @t195 () (@list @t22 @t20 @t19 @t171)) % 0.76/1.07 (define @t196 () (tptp.hAPP @t70 @t171)) % 0.76/1.07 (define @t197 () (tptp.hAPP @t196 @t20)) % 0.76/1.07 (define @t198 () (tptp.c_HOL_Oord__class_Oless @t197 (tptp.hAPP @t196 @t19) @t22)) % 0.76/1.07 (define @t199 () (@list @t22 @t171 @t20 @t19)) % 0.76/1.07 (define @t200 () (tptp.c_HOL_Oord__class_Oless @t84 @t83 tptp.tc_nat)) % 0.76/1.07 (define @t201 () (tptp.hAPP @t30 @t6)) % 0.76/1.07 (define @t202 () (tptp.hAPP @t201 @t102)) % 0.76/1.07 (define @t203 () (tptp.c_HOL_Oord__class_Oless @t57 @t5 tptp.tc_nat)) % 0.76/1.07 (define @t204 () (tptp.c_Nat_Osemiring__1__class_Oof__nat @t9 @t22)) % 0.76/1.07 (define @t205 () (@list @t22 @t9 @t5)) % 0.76/1.07 (define @t206 () (not (= @t98 @t102))) % 0.76/1.07 (define @t207 () (tptp.hAPP tptp.c_Lambda_Olift @t125)) % 0.76/1.07 (define @t208 () (tptp.hAPP @t149 @t20)) % 0.76/1.07 (define @t209 () (tptp.hBOOL (tptp.hAPP @t208 @t171))) % 0.76/1.07 (define @t210 () (@list @t3 @t22 @t20 @t171 @t19)) % 0.76/1.07 (define @t211 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t126 @t129 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.76/1.07 (define @t212 () (tptp.hAPP @t132 @t211)) % 0.76/1.07 (define @t213 () (not (tptp.hBOOL (tptp.hAPP @t212 @t106)))) % 0.76/1.07 (define @t214 () (tptp.c_Type_Osko__Type__Xvar__app__typesE__1__1 @t106 @t105 @t45 @t129)) % 0.76/1.07 (define @t215 () (tptp.hAPP @t132 @t126)) % 0.76/1.07 (define @t216 () (tptp.c_Lambda_OdB_OVar @t36)) % 0.76/1.07 (define @t217 () (tptp.c_HOL_Oord__class_Oless @t36 @t36 tptp.tc_nat)) % 0.76/1.07 (define @t218 () (@list @t36 @t125)) % 0.76/1.07 (define @t219 () (tptp.hAPP @t46 @t68)) % 0.76/1.07 (define @t220 () (tptp.hAPP @t207 @t45)) % 0.76/1.07 (define @t221 () (tptp.hAPP tptp.c_Lambda_Olift @t130)) % 0.76/1.07 (define @t222 () (tptp.hAPP tptp.c_Lambda_Osubst @t130)) % 0.76/1.07 (define @t223 () (tptp.hAPP @t222 @t125)) % 0.76/1.07 (define @t224 () (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift (tptp.hAPP @t223 @t43)) @t45)) % 0.76/1.07 (define @t225 () (@list @t130 @t125 @t43 @t45)) % 0.76/1.07 (define @t226 () (tptp.hAPP @t74 @t68)) % 0.76/1.07 (define @t227 () (not (tptp.c_HOL_Oord__class_Oless @t45 @t226 tptp.tc_nat))) % 0.76/1.07 (define @t228 () (tptp.hAPP @t221 @t45)) % 0.76/1.07 (define @t229 () (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift @t126) @t44)) % 0.76/1.07 (define @t230 () (@list @t45 @t44)) % 0.76/1.07 (define @t231 () (tptp.c_Lambda_OdB_OAbs @t130)) % 0.76/1.07 (define @t232 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t132 @t231) @t106)))) % 0.76/1.07 (define @t233 () (tptp.c_Type_Osko__Type__Xtyping__elims__3__2 @t106 @t105 @t130)) % 0.76/1.07 (define @t234 () (tptp.c_Type_Osko__Type__Xtyping__elims__3__1 @t106 @t105 @t130)) % 0.76/1.07 (define @t235 () (@var "V_us" $$unsorted)) % 0.76/1.07 (define @t236 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t132 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t211 @t235 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) @t106)))) % 0.76/1.07 (define @t237 () (@var "V_Ts" $$unsorted)) % 0.76/1.07 (define @t238 () (not (tptp.c_Type_Otypings @t105 @t129 @t237))) % 0.76/1.07 (define @t239 () (@var "V_U" $$unsorted)) % 0.76/1.07 (define @t240 () (not (tptp.hBOOL (tptp.hAPP @t212 @t239)))) % 0.76/1.07 (define @t241 () (tptp.c_Type_Osko__Type__Xvar__app__types__1__1 @t106 @t239 @t105 @t235)) % 0.76/1.07 (define @t242 () (tptp.c_HOL_Oord__class_Oless @t25 @t20 @t22)) % 0.76/1.07 (define @t243 () (not @t242)) % 0.76/1.07 (define @t244 () (tptp.hAPP @t99 @t20)) % 0.76/1.07 (define @t245 () (tptp.c_HOL_Oord__class_Oless @t25 @t244 @t22)) % 0.76/1.07 (define @t246 () (not (tptp.class_OrderedGroup_Olordered__ab__group__add @t22))) % 0.76/1.07 (define @t247 () (@list @t22 @t9)) % 0.76/1.07 (define @t248 () (tptp.c_HOL_Oord__class_Oless @t20 @t25 @t22)) % 0.76/1.07 (define @t249 () (not @t248)) % 0.76/1.07 (define @t250 () (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add @t22))) % 0.76/1.07 (define @t251 () (tptp.c_HOL_Oord__class_Oless @t244 @t25 @t22)) % 0.76/1.07 (define @t252 () (not @t251)) % 0.76/1.07 (define @t253 () (not (tptp.class_Ring__and__Field_Oordered__idom @t22))) % 0.76/1.07 (define @t254 () (@list @t22 @t19 @t20 @t171)) % 0.76/1.07 (define @t255 () (tptp.c_HOL_Oord__class_Oless @t204 @t140 @t22)) % 0.76/1.07 (define @t256 () (tptp.c_HOL_Oord__class_Oless @t6 @t98 tptp.tc_nat)) % 0.76/1.07 (define @t257 () (@var "V_s_H" $$unsorted)) % 0.76/1.07 (define @t258 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t186 @t125) @t257)))) % 0.76/1.07 (define @t259 () (@var "V_t_H" $$unsorted)) % 0.76/1.07 (define @t260 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t186 @t130) @t259)))) % 0.76/1.07 (define @t261 () (tptp.hAPP tptp.c_Lambda_OdB_OApp @t257)) % 0.76/1.07 (define @t262 () (tptp.hAPP tptp.c_Lambda_OdB_OApp @t125)) % 0.76/1.07 (define @t263 () (tptp.hAPP @t262 @t130)) % 0.76/1.07 (define @t264 () (tptp.hAPP @t186 @t263)) % 0.76/1.07 (define @t265 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t3) @t125)))) % 0.76/1.07 (define @t266 () (tptp.c_Lambda_OdB_OAbs @t3)) % 0.76/1.07 (define @t267 () (@list @t3 @t125 @t1)) % 0.76/1.07 (define @t268 () (= @t2 @t1)) % 0.76/1.07 (define @t269 () (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t266 @t2 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t170 @t1 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) % 0.76/1.07 (define @t270 () (@list @t3 @t2 @t125 @t1)) % 0.76/1.07 (define @t271 () (= @t3 @t125)) % 0.76/1.07 (define @t272 () (tptp.c_List_Ofoldl @t70 @t20 @t183 @t22 @t22)) % 0.76/1.07 (define @t273 () (not (tptp.class_OrderedGroup_Oab__semigroup__add @t22))) % 0.76/1.07 (define @t274 () (@var "V_nat" $$unsorted)) % 0.76/1.07 (define @t275 () (= @t274 @t177)) % 0.76/1.07 (define @t276 () (@list @t274 @t177)) % 0.76/1.07 (define @t277 () (= @t20 @t25)) % 0.76/1.07 (define @t278 () (not (= @t98 @t6))) % 0.76/1.07 (define @t279 () (tptp.c_Lambda_Oliftn @t5 @t130 @t44)) % 0.76/1.07 (define @t280 () (tptp.hAPP @t30 @t36)) % 0.76/1.07 (define @t281 () (tptp.hAPP @t157 @t35)) % 0.76/1.07 (define @t282 () (tptp.hAPP @t70 @t35)) % 0.76/1.07 (define @t283 () (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 @t22))) % 0.76/1.07 (define @t284 () (tptp.hAPP @t172 @t20)) % 0.76/1.07 (define @t285 () (not (tptp.class_OrderedGroup_Ocomm__monoid__add @t22))) % 0.76/1.07 (define @t286 () (@list @t130 @t125 @t44)) % 0.76/1.07 (define @t287 () (@var "V_z" $$unsorted)) % 0.76/1.07 (define @t288 () (tptp.hAPP @t30 @t35)) % 0.76/1.07 (define @t289 () (tptp.hAPP @t288 @t287)) % 0.76/1.07 (define @t290 () (tptp.c_HOL_Oord__class_Oless @t36 @t289 tptp.tc_nat)) % 0.76/1.07 (define @t291 () (@list @t36 @t35 @t287)) % 0.76/1.07 (define @t292 () (tptp.c_HOL_Oord__class_Oless @t36 @t35 tptp.tc_nat)) % 0.76/1.07 (define @t293 () (@list @t45 @t9)) % 0.76/1.07 (define @t294 () (tptp.c_Suc @t98)) % 0.76/1.07 (define @t295 () (tptp.hAPP (tptp.hAPP @t30 @t57) @t5)) % 0.76/1.07 (define @t296 () (tptp.hAPP @t79 @t56)) % 0.76/1.07 (define @t297 () (tptp.hAPP @t70 @t25)) % 0.76/1.07 (define @t298 () (tptp.hAPP @t157 (tptp.hAPP @t282 @t287))) % 0.76/1.07 (define @t299 () (@list @t22 @t36 @t35 @t287)) % 0.76/1.07 (define @t300 () (tptp.hAPP @t157 @t287)) % 0.76/1.07 (define @t301 () (tptp.hAPP @t280 @t287)) % 0.76/1.07 (define @t302 () (tptp.hAPP @t99 @t191)) % 0.76/1.07 (define @t303 () (tptp.hAPP @t70 @t100)) % 0.76/1.07 (define @t304 () (tptp.hAPP @t303 @t171)) % 0.76/1.07 (define @t305 () (= @t304 @t302)) % 0.76/1.07 (define @t306 () (tptp.hAPP @t70 @t174)) % 0.76/1.07 (define @t307 () (tptp.hAPP @t196 @t72)) % 0.76/1.07 (define @t308 () (tptp.hAPP @t99 @t307)) % 0.76/1.07 (define @t309 () (@list @t22 @t20 @t171 @t72)) % 0.76/1.07 (define @t310 () (@var "V_Q" $$unsorted)) % 0.76/1.07 (define @t311 () (@var "T_b" $$unsorted)) % 0.76/1.07 (define @t312 () (tptp.hAPP @t147 @t36)) % 0.76/1.07 (define @t313 () (tptp.hAPP @t70 @t139)) % 0.76/1.07 (define @t314 () (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun tptp.v_Ts____ tptp.v_T_H____ tptp.tc_Type_Otype tptp.tc_Type_Otype)) % 0.76/1.07 (define @t315 () (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun tptp.v_T_H_H____) @t314)) % 0.76/1.07 (define @t316 () (= @t35 @t287)) % 0.76/1.07 (define @t317 () (= @t19 @t171)) % 0.76/1.07 (define @t318 () (not (= @t100 @t174))) % 0.76/1.07 (define @t319 () (not (tptp.class_OrderedGroup_Ocancel__semigroup__add @t22))) % 0.76/1.07 (define @t320 () (tptp.hAPP (tptp.hAPP @t222 @t118) @t45)) % 0.76/1.07 (define @t321 () (tptp.hAPP tptp.c_Lambda_Osubst @t118)) % 0.76/1.07 (define @t322 () (tptp.hAPP @t221 @t44)) % 0.76/1.07 (define @t323 () (= (tptp.hAPP @t297 @t20) @t20)) % 0.76/1.07 (define @t324 () (= (tptp.hAPP @t99 @t25) @t20)) % 0.76/1.07 (define @t325 () (tptp.hAPP tptp.c_Lambda_OdB_OApp @t130)) % 0.76/1.07 (define @t326 () (tptp.hAPP @t325 @t118)) % 0.76/1.07 (define @t327 () (@list @t130 @t118 @t125 @t44)) % 0.76/1.07 (define @t328 () (tptp.c_HOL_Oord__class_Oless @t57 @t56 tptp.tc_nat)) % 0.76/1.07 (define @t329 () (not @t166)) % 0.76/1.07 (define @t330 () (= @t45 @t44)) % 0.76/1.07 (define @t331 () (@var "T_c" $$unsorted)) % 0.76/1.07 (define @t332 () (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t186 (tptp.hAPP (tptp.hAPP @t222 @t3) @t45)) (tptp.hAPP @t223 @t45)))) % 0.76/1.07 (define @t333 () (@list @t130 @t3 @t45 @t125)) % 0.76/1.07 (define @t334 () (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst @t125) @t130)) % 0.76/1.07 (define @t335 () (tptp.hAPP @t334 @t45)) % 0.76/1.07 (define @t336 () (tptp.hAPP tptp.c_Lambda_Osubst @t3)) % 0.76/1.07 (define @t337 () (tptp.hAPP (tptp.hAPP @t336 @t130) @t45)) % 0.76/1.07 (define @t338 () (@list @t3 @t130 @t45 @t125)) % 0.76/1.07 (define @t339 () (tptp.c_Lambda_OdB_OVar @t9)) % 0.76/1.07 (define @t340 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t94 @t1 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.76/1.07 (define @t341 () (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t339 @t2 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) @t340))) % 0.76/1.07 (define @t342 () (@list @t9 @t2 @t5 @t1)) % 0.76/1.07 (define @t343 () (tptp.hAPP (tptp.hAPP (tptp.hAPP @t146 tptp.v_e____) tptp.v_i____) tptp.v_T____)) % 0.76/1.07 (define @t344 () (tptp.hAPP tptp.c_Type_Otyping @t343)) % 0.76/1.07 (define @t345 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t132 @t326) @t106)))) % 0.76/1.07 (define @t346 () (tptp.c_Type_Osko__Type__Xtyping__elims__2__1 @t106 @t105 @t130 @t118)) % 0.76/1.07 (define @t347 () (tptp.hAPP @t132 @t118)) % 0.76/1.07 (define @t348 () (tptp.c_Fun_Oid @t22)) % 0.76/1.07 (define @t349 () (not (tptp.hBOOL (tptp.hAPP @t142 @t106)))) % 0.76/1.07 (define @t350 () (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t132 @t259) @t106))) % 0.76/1.07 (define @t351 () (@list @t105 @t259 @t106 @t130)) % 0.76/1.07 (define @t352 () (tptp.hAPP @t146 @t105)) % 0.76/1.07 (define @t353 () (tptp.hAPP @t352 @t6)) % 0.76/1.07 (define @t354 () (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift @t3) @t45)) % 0.76/1.07 (define @t355 () (@list @t3 @t45 @t125)) % 0.76/1.07 (define @t356 () (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping tptp.v_e____) tptp.v_u____)) % 0.76/1.07 (define @t357 () (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp @t170) @t130)) % 0.76/1.07 (define @t358 () (tptp.c_HOL_Oord__class_Oless @t25 @t140 @t22)) % 0.76/1.07 (define @t359 () (tptp.c_COMBC tptp.tc_Lambda_OdB tptp.tc_nat tptp.tc_Lambda_OdB)) % 0.76/1.07 (define @t360 () (tptp.hAPP @t359 tptp.c_Lambda_Olift)) % 0.76/1.07 (define @t361 () (tptp.c_List_Omap (tptp.hAPP @t360 @t45) @t129 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.76/1.07 (define @t362 () (tptp.tc_fun tptp.tc_nat tptp.tc_Lambda_OdB)) % 0.76/1.07 (define @t363 () (tptp.hAPP (tptp.c_COMBC tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB @t362) tptp.c_Lambda_Osubst)) % 0.76/1.07 (define @t364 () (tptp.hAPP @t360 @t6)) % 0.76/1.07 (define @t365 () (tptp.c_List_Omap (tptp.hAPP (tptp.hAPP @t359 (tptp.hAPP @t363 @t118)) @t45) @t129 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.76/1.07 (define @t366 () (tptp.c_Lambda_OdB_OVar @t274)) % 0.76/1.07 (define @t367 () (@var "V_dB2_H" $$unsorted)) % 0.76/1.07 (define @t368 () (@var "V_dB1_H" $$unsorted)) % 0.76/1.07 (define @t369 () (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp @t368) @t367)) % 0.76/1.07 (define @t370 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t125) @t130)))) % 0.76/1.07 (define @t371 () (@list @t125 @t130)) % 0.76/1.07 (define @t372 () (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t130)))) % 0.76/1.07 (define @t373 () (@list @t130 @t45)) % 0.76/1.07 (define @t374 () (tptp.hAPP @t352 @t45)) % 0.76/1.07 (define @t375 () (tptp.hAPP @t374 @t239)) % 0.76/1.07 (define @t376 () (tptp.hAPP tptp.c_Lambda_OdB_OApp @t118)) % 0.76/1.07 (define @t377 () (tptp.hAPP @t20 (tptp.hAPP @t19 @t93))) % 0.76/1.07 (define @t378 () (tptp.c_Fun_Oid @t311)) % 0.76/1.07 (define @t379 () (tptp.c_Fun_Ocomp @t20 @t19 @t331 @t311 @t22)) % 0.76/1.07 (define @t380 () (@var "V_g" $$unsorted)) % 0.76/1.07 (define @t381 () (tptp.c_Fun_Ocomp @t147 @t380 @t311 @t22 @t331)) % 0.76/1.07 (define @t382 () (@var "V_R" $$unsorted)) % 0.76/1.07 (define @t383 () (tptp.c_HOL_Oord__class_Oless @t35 @t36 @t22)) % 0.76/1.07 (define @t384 () (not @t383)) % 0.76/1.07 (define @t385 () (not (tptp.class_Orderings_Oorder @t22))) % 0.76/1.07 (define @t386 () (not (tptp.class_Orderings_Opreorder @t22))) % 0.76/1.07 (define @t387 () (tptp.hAPP @t147 (tptp.hAPP @t380 @t36))) % 0.76/1.07 (define @t388 () (tptp.hAPP @t381 @t36)) % 0.76/1.07 (define @t389 () (@var "V_dB_H" $$unsorted)) % 0.76/1.07 (define @t390 () (tptp.c_Lambda_OdB_OAbs @t389)) % 0.76/1.07 (define @t391 () (@var "V_dB" $$unsorted)) % 0.76/1.07 (define @t392 () (not (tptp.c_HOL_Oord__class_Oless @t36 @t36 @t22))) % 0.76/1.07 (define @t393 () (not (tptp.class_Orderings_Olinorder @t22))) % 0.76/1.07 (define @t394 () (@list @t22 @t35 @t36)) % 0.76/1.07 (define @t395 () (@var "V_dB2" $$unsorted)) % 0.76/1.07 (define @t396 () (@var "V_dB1" $$unsorted)) % 0.76/1.07 (define @t397 () (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp @t396) @t395)) % 0.76/1.07 (define @t398 () (not (= @t397 @t369))) % 0.76/1.07 (define @t399 () (@list @t396 @t395 @t368 @t367)) % 0.76/1.07 (define @t400 () (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun @t106) @t239)) % 0.76/1.07 (define @t401 () (@var "V_env" $$unsorted)) % 0.76/1.07 (define @t402 () (tptp.hAPP tptp.c_Type_Otyping @t401)) % 0.76/1.07 (define @t403 () (@var "T_d" $$unsorted)) % 0.76/1.07 (define @t404 () (@var "V_h" $$unsorted)) % 0.76/1.07 (define @t405 () (not (tptp.c_HOL_Oord__class_Oless @t43 @t45 tptp.tc_nat))) % 0.76/1.07 (define @t406 () (@var "V_type2_H" $$unsorted)) % 0.76/1.07 (define @t407 () (@var "V_type1_H" $$unsorted)) % 0.76/1.07 (define @t408 () (not (= @t116 (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun @t407) @t406)))) % 0.76/1.07 (define @t409 () (@list @t115 @t114 @t407 @t406)) % 0.76/1.07 (define @t410 () (@var "T_e" $$unsorted)) % 0.76/1.07 (define @t411 () (@var "V_g_H" $$unsorted)) % 0.76/1.07 (define @t412 () (@var "V_f_H" $$unsorted)) % 0.76/1.07 (define @t413 () (not (tptp.c_HOL_Oord__class_Oless @t19 @t20 @t22))) % 0.76/1.07 (define @t414 () (@var "V_T_H" $$unsorted)) % 0.76/1.07 (define @t415 () (@var "V_ia" $$unsorted)) % 0.76/1.07 (define @t416 () (@var "V_ea" $$unsorted)) % 0.76/1.07 (define @t417 () (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t118)))) % 0.76/1.07 (define @t418 () (tptp.hAPP tptp.c_Lambda_Osubst tptp.v_b____)) % 0.76/1.07 (define @t419 () (forall (@list @t118 @t415 @t416 @t414) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP @t418 @t118) @t415))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping @t416) @t118) tptp.v_T____))) @t417 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping (tptp.hAPP (tptp.hAPP (tptp.hAPP @t146 @t416) @t415) tptp.v_T____)) tptp.v_b____) @t414)))))) % 0.76/1.07 (define @t420 () (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t3)))) % 0.76/1.07 (define @t421 () (@list @t147 @t380 @t331 @t311)) % 0.76/1.07 (define @t422 () (@var "V_Ta" $$unsorted)) % 0.76/1.07 (define @t423 () (@var "V_T2" $$unsorted)) % 0.76/1.07 (define @t424 () (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t320))) % 0.76/1.07 (define @t425 () (@var "V_T1" $$unsorted)) % 0.76/1.07 (define @t426 () (not (= tptp.v_T____ (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun @t425) @t423)))) % 0.76/1.07 (define @t427 () (@list @t425 @t423 @t130 @t118 @t45 @t105 @t422)) % 0.76/1.07 (define @t428 () (tptp.hAPP @t344 tptp.v_b____)) % 0.76/1.07 (define @t429 () (@var "V_e_H" $$unsorted)) % 0.76/1.07 (define @t430 () (tptp.hAPP tptp.c_Type_Otyping @t429)) % 0.76/1.07 (define @t431 () (tptp.tc_fun tptp.tc_Type_Otype tptp.tc_bool)) % 0.76/1.07 (define @t432 () (tptp.tc_fun tptp.tc_nat tptp.tc_bool)) % 0.76/1.07 (define @t433 () (tptp.tc_fun tptp.tc_Lambda_OdB @t432)) % 0.76/1.07 (define @t434 () (tptp.tc_fun tptp.tc_nat tptp.tc_Type_Otype)) % 0.76/1.07 (define @t435 () (tptp.tc_fun tptp.tc_Lambda_OdB tptp.tc_bool)) % 0.76/1.07 (define @t436 () (tptp.tc_fun tptp.tc_Type_Otype @t435)) % 0.76/1.07 (define @t437 () (tptp.tc_fun tptp.tc_Lambda_OdB @t431)) % 0.76/1.07 (define @t438 () (tptp.tc_fun tptp.tc_bool tptp.tc_bool)) % 0.76/1.07 (define @t439 () (tptp.c_COMBB tptp.tc_bool @t438 tptp.tc_Lambda_OdB)) % 0.76/1.07 (define @t440 () (tptp.hAPP @t439 tptp.c_implies)) % 0.76/1.07 (define @t441 () (tptp.tc_fun tptp.tc_Lambda_OdB @t438)) % 0.76/1.07 (define @t442 () (tptp.tc_fun @t432 @t432)) % 0.76/1.07 (define @t443 () (tptp.hAPP (tptp.c_COMBB @t438 @t442 tptp.tc_Lambda_OdB) (tptp.c_COMBB tptp.tc_bool tptp.tc_bool tptp.tc_nat))) % 0.76/1.07 (define @t444 () (tptp.tc_fun tptp.tc_Lambda_OdB @t442)) % 0.76/1.07 (define @t445 () (tptp.c_COMBS tptp.tc_Lambda_OdB @t432 @t432)) % 0.76/1.07 (define @t446 () (tptp.tc_fun @t433 @t433)) % 0.76/1.07 (define @t447 () (tptp.tc_fun @t434 @t433)) % 0.76/1.08 (define @t448 () (tptp.tc_fun tptp.tc_nat @t434)) % 0.76/1.08 (define @t449 () (tptp.tc_fun tptp.tc_nat @t437)) % 0.76/1.08 (define @t450 () (tptp.tc_fun tptp.tc_nat @t431)) % 0.76/1.08 (define @t451 () (tptp.tc_fun tptp.tc_Type_Otype @t432)) % 0.76/1.08 (define @t452 () (tptp.tc_fun @t434 @t451)) % 0.76/1.08 (define @t453 () (tptp.tc_fun tptp.tc_nat @t438)) % 0.76/1.08 (define @t454 () (tptp.tc_fun tptp.tc_Type_Otype @t453)) % 0.76/1.08 (define @t455 () (tptp.tc_fun @t434 @t454)) % 0.76/1.08 (define @t456 () (tptp.tc_fun tptp.tc_Type_Otype @t442)) % 0.76/1.08 (define @t457 () (tptp.tc_fun @t434 @t456)) % 0.76/1.08 (define @t458 () (tptp.tc_fun tptp.tc_Type_Otype @t446)) % 0.76/1.08 (define @t459 () (tptp.tc_fun @t434 @t458)) % 0.76/1.08 (define @t460 () (tptp.tc_fun tptp.tc_Type_Otype @t433)) % 0.76/1.08 (define @t461 () (tptp.tc_fun @t433 @t460)) % 0.76/1.08 (define @t462 () (tptp.tc_fun @t434 @t461)) % 0.76/1.08 (define @t463 () (tptp.tc_fun @t434 @t460)) % 0.76/1.08 (define @t464 () (tptp.tc_fun @t434 @t436)) % 0.76/1.08 (define @t465 () (tptp.tc_fun @t434 @t431)) % 0.76/1.08 (define @t466 () (tptp.tc_fun @t434 tptp.tc_bool)) % 0.76/1.08 (define @t467 () (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping (tptp.hAPP (tptp.hAPP (tptp.hAPP @t146 tptp.v_x) tptp.v_xc) tptp.v_T____)) tptp.v_b____) tptp.v_xa))) % 0.76/1.08 (define @t468 () (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT tptp.v_xb))) % 0.76/1.08 (define @t469 () (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping tptp.v_x) tptp.v_xb) tptp.v_T____))) % 0.76/1.08 (define @t470 () (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP @t418 tptp.v_xb) tptp.v_xc)))) % 0.76/1.08 (define @t471 () (@var "T_1" $$unsorted)) % 0.76/1.08 (define @t472 () (@var "T_2" $$unsorted)) % 0.76/1.08 (define @t473 () (tptp.tc_fun @t472 @t471)) % 0.76/1.08 (define @t474 () (@list @t472 @t471)) % 0.76/1.08 (define @t475 () (@var "V_Y" $$unsorted)) % 0.76/1.08 (define @t476 () (@var "V_X" $$unsorted)) % 0.76/1.08 (define @t477 () (not @t467)) % 0.76/1.08 (define @t478 () (not @t468)) % 0.76/1.08 (define @t479 () (not @t469)) % 0.76/1.08 (define @t480 () (or @t470 @t479 @t478 @t477)) % 0.76/1.08 (define @t481 () (not @t480)) % 0.76/1.08 (assume @p1 (forall (@list @t3 @t2 @t1) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t3 @t2 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) @t4)) (not (tptp.c_ListOrder_Ostep1 tptp.c_Lambda_Obeta @t2 @t1 tptp.tc_Lambda_OdB))))) % 0.76/1.08 (assume @p2 (forall @t13 (or (tptp.c_HOL_Oord__class_Oless @t12 @t9 tptp.tc_nat) @t11 @t8))) % 0.76/1.08 (assume @p3 (forall @t18 (or @t17 @t15))) % 0.76/1.08 (assume @p4 (forall @t13 (or @t14 (not @t17)))) % 0.76/1.08 (assume @p5 (forall (@list @t21 @t20 @t19) (or (tptp.hBOOL (tptp.hAPP @t21 @t6)) (not (tptp.c_HOL_Oord__class_Oless @t20 @t19 tptp.tc_nat)) (not (tptp.hBOOL (tptp.hAPP @t21 (tptp.c_HOL_Ominus__class_Ominus @t20 @t19 tptp.tc_nat))))))) % 0.76/1.08 (assume @p6 (forall @t29 (or @t28 @t27 @t24))) % 0.76/1.08 (assume @p7 (forall @t29 (or @t28 @t23 (not @t27)))) % 0.76/1.08 (assume @p8 (forall @t18 (or (= (tptp.hAPP @t31 @t12) @t9) @t14))) % 0.76/1.08 (assume @p9 (forall @t41 (or @t28 @t40 @t37 (not @t34)))) % 0.76/1.08 (assume @p10 (forall @t41 (or @t28 @t40 @t34 @t42))) % 0.76/1.08 (assume @p11 (forall @t50 (or @t49 (not @t48)))) % 0.76/1.08 (assume @p12 (forall @t51 (or @t48 (not @t49)))) % 0.76/1.08 (assume @p13 (forall (@list @t22 @t52 @t45) (or @t53 (= (tptp.c_Nat_Osemiring__1__class_Oof__nat__aux @t52 @t6 @t45 @t22) @t45)))) % 0.76/1.08 (assume @p14 (forall @t18 (or (not (= @t16 @t6)) (not (= @t12 @t6)) @t54))) % 0.76/1.08 (assume @p15 (forall (@list @t43 @t5 @t44) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus @t43 @t5 tptp.tc_nat) @t44 tptp.tc_nat) @t55))) % 0.76/1.08 (assume @p16 (forall @t13 (= (tptp.c_HOL_Ominus__class_Ominus @t57 @t56 tptp.tc_nat) @t12))) % 0.76/1.08 (assume @p17 (forall @t58 (= (tptp.c_HOL_Ominus__class_Ominus @t9 @t6 tptp.tc_nat) @t9))) % 0.76/1.08 (assume @p18 (forall @t58 (= (tptp.c_HOL_Ominus__class_Ominus @t9 @t9 tptp.tc_nat) @t6))) % 0.76/1.08 (assume @p19 (forall @t63 (or @t62 @t61 @t60))) % 0.76/1.08 (assume @p20 (forall @t65 (or @t64 (= (tptp.c_HOL_Ominus__class_Ominus @t20 @t20 @t22) @t25)))) % 0.76/1.08 (assume @p21 (forall @t65 (or @t64 (= (tptp.c_HOL_Ominus__class_Ominus @t20 @t25 @t22) @t20)))) % 0.76/1.08 (assume @p22 (forall @t63 (or @t64 @t60))) % 0.76/1.08 (assume @p23 (forall @t63 (or @t66 @t60))) % 0.76/1.08 (assume @p24 (forall (@list @t67 @t5 @t9) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus @t67 @t5 tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus @t67 @t9 tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless @t9 @t67 tptp.tc_nat)) @t15))) % 0.76/1.08 (assume @p25 (forall @t69 (= (tptp.c_HOL_Ominus__class_Ominus @t56 @t68 tptp.tc_nat) @t5))) % 0.76/1.08 (assume @p26 (forall @t29 (or @t64 (= (tptp.hAPP (tptp.hAPP @t70 @t26) @t19) @t20)))) % 0.76/1.08 (assume @p27 (forall (@list @t21 @t19 @t36) (or (not (tptp.hBOOL (tptp.hAPP @t21 (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP @t71 @t36) @t19 tptp.tc_nat)))) (tptp.hBOOL (tptp.hAPP @t21 @t36))))) % 0.76/1.08 (assume @p28 (forall (@list @t21 @t19 @t72) (or (not (tptp.hBOOL (tptp.hAPP @t21 (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP @t71 @t72) @t19 tptp.tc_nat)))) (tptp.hBOOL (tptp.hAPP @t21 @t72))))) % 0.76/1.08 (assume @p29 (forall @t13 (tptp.c_HOL_Oord__class_Oless @t12 @t57 tptp.tc_nat))) % 0.76/1.08 (assume @p30 (forall (@list @t22 @t52 @t5 @t45) (or @t53 (= (tptp.c_Nat_Osemiring__1__class_Oof__nat__aux @t52 @t56 @t45 @t22) (tptp.c_Nat_Osemiring__1__class_Oof__nat__aux @t52 @t5 (tptp.hAPP @t52 @t45) @t22))))) % 0.76/1.08 (assume @p31 (forall @t18 (= (tptp.c_HOL_Ominus__class_Ominus @t5 @t73 tptp.tc_nat) @t6))) % 0.76/1.08 (assume @p32 (forall @t50 (= @t76 (tptp.c_HOL_Ominus__class_Ominus @t45 @t75 tptp.tc_nat)))) % 0.76/1.08 (assume @p33 (forall (@list @t22 @t77 @t35 @t36) (or @t66 (not (= (tptp.c_HOL_Ominus__class_Ominus @t77 @t35 @t22) @t59)) (= @t77 @t35)))) % 0.76/1.08 (assume @p34 (forall (@list @t22 @t36 @t33 @t32) (or @t66 (not (= @t59 @t38)) (= @t33 @t32)))) % 0.76/1.08 (assume @p35 (forall @t69 (= (tptp.c_HOL_Ominus__class_Ominus @t6 @t5 tptp.tc_nat) @t6))) % 0.76/1.08 (assume @p36 (forall @t81 (= (tptp.c_HOL_Ominus__class_Ominus @t80 @t78 tptp.tc_nat) @t12))) % 0.76/1.08 (assume @p37 (forall @t85 (= (tptp.c_HOL_Ominus__class_Ominus @t84 @t83 tptp.tc_nat) @t12))) % 0.76/1.08 (assume @p38 (forall @t87 (or @t62 @t61 (not (= @t39 @t25)) @t86))) % 0.76/1.08 (assume @p39 (forall @t29 (or @t64 @t89 @t88))) % 0.76/1.08 (assume @p40 (forall @t29 (or @t66 @t89 @t88))) % 0.76/1.08 (assume @p41 (forall @t50 (= @t76 (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus @t45 @t44 tptp.tc_nat) @t43 tptp.tc_nat)))) % 0.76/1.08 (assume @p42 (forall @t91 (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus @t57 @t5 tptp.tc_nat) @t90 tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus @t12 @t44 tptp.tc_nat)))) % 0.76/1.08 (assume @p43 (forall @t13 (= (tptp.c_HOL_Ominus__class_Ominus @t9 @t56 tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus @t92 @t5 tptp.tc_nat)))) % 0.76/1.08 (assume @p44 (forall (@list @t2 @t5 @t93) (or (tptp.c_ListOrder_Ostep1 tptp.c_Lambda_Obeta @t2 @t97 tptp.tc_Lambda_OdB) @t96))) % 0.76/1.08 (assume @p45 (forall @t13 (= (tptp.c_HOL_Ominus__class_Ominus @t98 @t5 tptp.tc_nat) @t9))) % 0.76/1.08 (assume @p46 (forall @t18 (= (tptp.c_HOL_Ominus__class_Ominus @t73 @t5 tptp.tc_nat) @t9))) % 0.76/1.08 (assume @p47 (forall @t29 (or @t64 (= (tptp.c_HOL_Ominus__class_Ominus @t100 @t19 @t22) @t20)))) % 0.76/1.08 (assume @p48 (forall (@list @t5 @t45) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus @t5 @t101 tptp.tc_nat) @t5 tptp.tc_nat) @t8))) % 0.76/1.08 (assume @p49 (forall @t69 (or (= (tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus @t5 @t102 tptp.tc_nat)) @t5) @t8))) % 0.76/1.08 (assume @p50 (forall @t111 (or (= @t110 (tptp.hAPP @t105 @t104)) @t103))) % 0.76/1.08 (assume @p51 (forall @t69 (or (= @t112 @t5) @t8))) % 0.76/1.08 (assume @p52 (forall @t69 (or (= @t5 @t112) @t8))) % 0.76/1.08 (assume @p53 (forall @t13 (or (= @t98 (tptp.c_Suc (tptp.hAPP (tptp.hAPP @t30 @t92) @t5))) @t113))) % 0.76/1.08 (assume @p54 (forall @t117 (= (tptp.c_Type_Otype_Otype__size @t116) (tptp.hAPP (tptp.hAPP @t30 (tptp.hAPP (tptp.hAPP @t30 (tptp.c_Type_Otype_Otype__size @t115)) (tptp.c_Type_Otype_Otype__size @t114))) @t102)))) % 0.76/1.08 (assume @p55 (forall @t117 (= (tptp.c_Nat_Osize__class_Osize @t116 tptp.tc_Type_Otype) (tptp.hAPP (tptp.hAPP @t30 (tptp.hAPP (tptp.hAPP @t30 (tptp.c_Nat_Osize__class_Osize @t115 tptp.tc_Type_Otype)) (tptp.c_Nat_Osize__class_Osize @t114 tptp.tc_Type_Otype))) @t102)))) % 0.76/1.08 (assume @p56 (forall (@list @t93 @t5 @t2) (or (= @t93 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t94 @t97 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) @t96))) % 0.76/1.08 (assume @p57 (forall @t121 (or (= @t120 (tptp.c_Lambda_OdB_OVar @t104)) @t103))) % 0.76/1.08 (assume @p58 (forall @t128 (or (= @t127 @t124) @t123))) % 0.76/1.08 (assume @p59 (forall @t136 (or (tptp.c_Type_Otypings @t105 @t129 @t135) @t134))) % 0.76/1.08 (assume @p60 (forall @t136 (or (tptp.c_Type_Otypings @t105 @t129 @t137) @t134))) % 0.76/1.08 (assume @p61 (forall @t128 (or (= @t138 @t124) @t123))) % 0.76/1.08 (assume @p62 (forall @t141 (or @t53 (= @t140 (tptp.c_Nat_Osemiring__1__class_Oof__nat__aux (tptp.hAPP (tptp.hAPP (tptp.c_COMBC @t22 @t22 @t22) @t70) @t139) @t5 @t25 @t22))))) % 0.76/1.08 (assume @p63 (forall @t143 (or (tptp.hBOOL (tptp.hAPP @t142 (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun @t137 @t106 tptp.tc_Type_Otype tptp.tc_Type_Otype))) @t134))) % 0.76/1.08 (assume @p64 (forall @t143 (or (tptp.hBOOL (tptp.hAPP @t142 (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun @t135 @t106 tptp.tc_Type_Otype tptp.tc_Type_Otype))) @t134))) % 0.76/1.08 (assume @p65 (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping (tptp.hAPP (tptp.hAPP (tptp.hAPP @t146 tptp.v_ea______) tptp.v_ia______) tptp.v_T____)) @t145) tptp.v_T_Ha______))) % 0.76/1.08 (assume @p66 (forall (@list @t5 @t147 @t22) (= (tptp.c_Nat_Ocompow @t56 @t147 @t22 @t22) (tptp.c_Fun_Ocomp @t147 @t148 @t22 @t22 @t22)))) % 0.76/1.08 (assume @p67 (forall (@list @t3 @t22 @t36 @t35) (or @t151 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t3 @t36) @t35)))))) % 0.76/1.08 (assume @p68 (forall @t13 (or @t154 @t153 @t152))) % 0.76/1.08 (assume @p69 (forall @t13 (or @t154 @t113 @t155))) % 0.76/1.08 (assume @p70 (forall (@list @t22 @t36 @t156) (or @t158 (= (tptp.hAPP @t157 (tptp.c_List_Ofoldl @t70 @t25 @t156 @t22 @t22)) (tptp.c_List_Ofoldl @t70 @t36 @t156 @t22 @t22))))) % 0.76/1.08 (assume @p71 (forall @t160 (or @t159 (not (= @t139 @t25))))) % 0.76/1.08 (assume @p72 (forall @t13 (or @t54 @t14 (not @t161)))) % 0.76/1.08 (assume @p73 (forall @t13 (or @t54 @t164 @t162))) % 0.76/1.08 (assume @p74 (forall @t18 (or (= @t5 @t9) @t164 @t162))) % 0.76/1.08 (assume @p75 (= @t102 @t165)) % 0.76/1.08 (assume @p76 (forall @t168 (or (= @t167 (tptp.c_Lambda_OdB_OVar (tptp.hAPP @t46 @t5))) @t166))) % 0.76/1.08 (assume @p77 (forall (@list @t5 @t125 @t44) (= (tptp.c_Lambda_Oliftn @t5 @t170 @t44) (tptp.c_Lambda_OdB_OAbs (tptp.c_Lambda_Oliftn @t5 @t125 @t169))))) % 0.76/1.08 (assume @p78 (forall (@list @t22 @t20 @t171 @t19 @t72) (or @t175 (tptp.c_HOL_Oord__class_Oless @t174 @t173 @t22) (not (tptp.c_HOL_Oord__class_Oless @t171 @t72 @t22)) @t24))) % 0.76/1.08 (assume @p79 (forall (@list @t45 @t44 @t43 @t67) (or (tptp.c_HOL_Oord__class_Oless @t47 (tptp.hAPP @t74 @t67) tptp.tc_nat) @t176 @t103))) % 0.76/1.08 (assume @p80 (forall @t179 (not (= @t178 @t6)))) % 0.76/1.08 (assume @p81 (forall @t58 (not (= @t57 @t6)))) % 0.76/1.08 (assume @p82 (forall @t69 (tptp.c_HOL_Oord__class_Oless @t5 @t56 tptp.tc_nat))) % 0.76/1.08 (assume @p83 (forall @t182 @t181)) % 0.76/1.08 (assume @p84 (forall @t51 (or (tptp.c_HOL_Oord__class_Oless @t101 @t44 tptp.tc_nat) @t55 @t103))) % 0.76/1.08 (assume @p85 (forall (@list @t22 @t183) (or @t158 (= (tptp.c_List_Ofoldl @t70 @t25 @t183 @t22 @t22) @t184)))) % 0.76/1.08 (assume @p86 (forall @t65 (or @t185 (tptp.c_HOL_Oord__class_Oless @t20 (tptp.hAPP @t99 @t139) @t22)))) % 0.76/1.08 (assume @p87 (forall @t189 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t186 @t4) @t188)) @t187))) % 0.76/1.08 (assume @p88 (forall (@list @t130 @t44) (= (tptp.c_Lambda_Oliftn @t6 @t130 @t44) @t130))) % 0.76/1.08 (assume @p89 (forall (@list @t45 @t43) (not (tptp.c_HOL_Oord__class_Oless @t190 @t45 tptp.tc_nat)))) % 0.76/1.08 (assume @p90 (forall (@list @t43 @t45) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP @t74 @t45) @t45 tptp.tc_nat)))) % 0.76/1.08 (assume @p91 (forall @t69 (not (= @t56 @t5)))) % 0.76/1.08 (assume @p92 (forall @t69 (not (= @t5 @t56)))) % 0.76/1.08 (assume @p93 (forall @t193 (or @t175 @t192 @t24))) % 0.76/1.08 (assume @p94 (forall @t193 (or @t194 @t192 @t24))) % 0.76/1.08 (assume @p95 (forall @t195 (or @t194 @t23 (not @t192)))) % 0.76/1.08 (assume @p96 (forall @t199 (or @t175 @t198 @t24))) % 0.76/1.08 (assume @p97 (forall @t199 (or @t194 @t198 @t24))) % 0.76/1.08 (assume @p98 (forall @t195 (or @t194 @t23 (not @t198)))) % 0.76/1.08 (assume @p99 (forall @t51 (or (tptp.c_HOL_Oord__class_Oless @t47 @t75 tptp.tc_nat) @t103))) % 0.76/1.08 (assume @p100 (forall @t91 (or @t14 (not @t200)))) % 0.76/1.08 (assume @p101 (forall @t85 (or @t200 @t15))) % 0.76/1.08 (assume @p102 (= @t202 @t102)) % 0.76/1.08 (assume @p103 (forall @t13 (or @t14 (not @t203)))) % 0.76/1.08 (assume @p104 (forall @t13 (or @t161 @t15))) % 0.76/1.08 (assume @p105 (forall @t205 (or @t53 (= (tptp.c_Nat_Osemiring__1__class_Oof__nat @t98 @t22) (tptp.hAPP (tptp.hAPP @t70 @t204) @t140))))) % 0.76/1.08 (assume @p106 (forall @t13 (or @t206 @t153 @t152))) % 0.76/1.08 (assume @p107 (forall @t13 (or @t206 @t113 @t155))) % 0.76/1.08 (assume @p108 (forall (@list @t125 @t44) (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift @t170) @t44) (tptp.c_Lambda_OdB_OAbs (tptp.hAPP @t207 @t169))))) % 0.76/1.08 (assume @p109 (forall @t210 (or @t209 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t149 @t19) @t171))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t3 @t20) @t19)))))) % 0.76/1.08 (assume @p110 (forall @t210 (or @t209 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t3 @t19) @t171))) (not (tptp.hBOOL (tptp.hAPP @t208 @t19)))))) % 0.76/1.08 (assume @p111 (forall (@list @t105 @t45 @t106 @t129) (or (tptp.hBOOL (tptp.hAPP @t215 (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun @t214 @t106 tptp.tc_Type_Otype tptp.tc_Type_Otype))) @t213))) % 0.76/1.08 (assume @p112 (forall @t218 (or @t217 (= (tptp.c_Lambda_Osubstn @t216 @t125 @t36) (tptp.c_Lambda_Oliftn @t36 @t125 @t6))))) % 0.76/1.08 (assume @p113 (forall (@list @t5 @t2) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t95)) (not (tptp.c_List_Olistsp tptp.c_InductTermi_OIT @t2 tptp.tc_Lambda_OdB))))) % 0.76/1.08 (assume @p114 (forall @t225 (or (= @t224 (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.hAPP @t221 @t219)) @t220) @t43)) (not (tptp.c_HOL_Oord__class_Oless @t43 @t219 tptp.tc_nat))))) % 0.76/1.08 (assume @p115 (forall @t225 (or (= @t224 (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst @t228) @t220) @t226)) @t227))) % 0.76/1.08 (assume @p116 (forall @t230 (or (= @t229 (tptp.c_Lambda_OdB_OVar @t219)) @t166))) % 0.76/1.08 (assume @p117 (forall (@list @t106 @t105 @t130) (or (= @t106 (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun @t234) @t233)) @t232))) % 0.76/1.08 (assume @p118 (forall (@list @t239 @t106 @t105 @t235 @t45 @t129 @t237) (or (= @t239 (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun @t241 @t106 tptp.tc_Type_Otype tptp.tc_Type_Otype)) @t240 @t238 @t236))) % 0.76/1.08 (assume @p119 (forall @t65 (or @t246 @t245 @t243))) % 0.76/1.08 (assume @p120 (forall @t65 (or @t246 @t242 (not @t245)))) % 0.76/1.08 (assume @p121 (forall @t247 (or @t185 (not (tptp.c_HOL_Oord__class_Oless @t204 @t25 @t22))))) % 0.76/1.08 (assume @p122 (forall @t29 (or @t250 (tptp.c_HOL_Oord__class_Oless @t100 @t25 @t22) (not (tptp.c_HOL_Oord__class_Oless @t19 @t25 @t22)) @t249))) % 0.76/1.08 (assume @p123 (forall @t65 (or @t246 @t251 @t249))) % 0.76/1.08 (assume @p124 (forall @t65 (or @t246 @t248 @t252))) % 0.76/1.08 (assume @p125 (forall @t65 (or @t253 @t248 @t252))) % 0.76/1.08 (assume @p126 (forall @t65 (or @t253 @t251 @t249))) % 0.76/1.08 (assume @p127 (forall @t160 (or @t185 (not (tptp.c_HOL_Oord__class_Oless @t139 @t25 @t22))))) % 0.76/1.08 (assume @p128 (forall @t29 (or @t250 (tptp.c_HOL_Oord__class_Oless @t25 @t100 @t22) (not (tptp.c_HOL_Oord__class_Oless @t25 @t19 @t22)) @t243))) % 0.76/1.08 (assume @p129 (forall @t160 (or @t185 (tptp.c_HOL_Oord__class_Oless @t25 @t139 @t22)))) % 0.76/1.08 (assume @p130 (forall @t254 (or @t185 (tptp.c_HOL_Oord__class_Oless @t19 @t174 @t22) (not (tptp.c_HOL_Oord__class_Oless @t19 @t171 @t22)) @t243))) % 0.76/1.08 (assume @p131 (forall @t160 (or @t53 (= (tptp.c_Nat_Osemiring__1__class_Oof__nat @t6 @t22) @t25)))) % 0.76/1.08 (assume @p132 (forall @t205 (or @t185 @t255 @t15))) % 0.76/1.08 (assume @p133 (forall @t205 (or @t185 @t14 (not @t255)))) % 0.76/1.08 (assume @p134 (forall @t13 (or @t256 @t11))) % 0.76/1.08 (assume @p135 (forall @t13 (or @t256 @t8))) % 0.76/1.08 (assume @p136 (forall @t182 (tptp.c_HOL_Oord__class_Oless @t6 @t180 tptp.tc_nat))) % 0.76/1.08 (assume @p137 (forall @t69 (tptp.c_HOL_Oord__class_Oless @t6 @t56 tptp.tc_nat))) % 0.76/1.08 (assume @p138 (forall @t18 (or @t7 @t10 (not @t256)))) % 0.76/1.08 (assume @p139 (forall @t69 (or @t155 (not (tptp.c_HOL_Oord__class_Oless @t5 @t102 tptp.tc_nat))))) % 0.76/1.08 (assume @p140 (tptp.c_HOL_Oord__class_Oless @t6 @t102 tptp.tc_nat)) % 0.76/1.08 (assume @p141 (forall (@list @t125 @t130 @t257 @t259) (or (tptp.hBOOL (tptp.hAPP @t264 (tptp.hAPP @t261 @t259))) @t260 @t258))) % 0.76/1.08 (assume @p142 (forall (@list @t125 @t130 @t257) (or (tptp.hBOOL (tptp.hAPP @t264 (tptp.hAPP @t261 @t130))) @t258))) % 0.76/1.08 (assume @p143 (forall (@list @t125 @t130 @t259) (or (tptp.hBOOL (tptp.hAPP @t264 (tptp.hAPP @t262 @t259))) @t260))) % 0.76/1.08 (assume @p144 (forall @t189 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t4) @t188)) @t265))) % 0.76/1.08 (assume @p145 (forall @t267 (or (not (= @t266 @t188)) (= @t266 @t125)))) % 0.76/1.08 (assume @p146 (forall @t270 (or @t269 @t268))) % 0.76/1.08 (assume @p147 (forall @t270 (or @t269 @t271))) % 0.76/1.08 (assume @p148 (forall (@list @t125 @t1 @t3) (or (not (= @t188 @t266)) (= @t125 @t266)))) % 0.76/1.08 (assume @p149 (forall (@list @t130 @t125) (= (tptp.c_Lambda_Osubstn @t130 @t125 @t6) (tptp.hAPP @t223 @t6)))) % 0.76/1.08 (assume @p150 (forall (@list @t125 @t257) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t186 @t170) (tptp.c_Lambda_OdB_OAbs @t257))) @t258))) % 0.76/1.08 (assume @p151 (= tptp.v_n____ tptp.v_i____)) % 0.76/1.08 (assume @p152 (= @t68 @t102)) % 0.76/1.08 (assume @p153 (forall (@list @t22 @t183 @t20) (or @t273 (= (tptp.c_List_Ofoldr @t70 @t183 @t20 @t22 @t22) @t272)))) % 0.76/1.08 (assume @p154 (forall @t276 (or (not (= (tptp.c_Suc @t274) @t178)) @t275))) % 0.76/1.08 (assume @p155 (forall (@list @t36 @t35) (or (not (= @t180 (tptp.c_Suc @t35))) @t86))) % 0.76/1.08 (assume @p156 (forall @t65 (or @t246 (not (= @t244 @t25)) @t277))) % 0.76/1.08 (assume @p157 (forall @t13 (or @t278 @t155))) % 0.76/1.08 (assume @p158 (forall @t13 (or @t278 @t113))) % 0.76/1.08 (assume @p159 (forall (@list @t5 @t130 @t44) (= (tptp.c_Lambda_Oliftn @t56 @t130 @t44) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift @t279) @t44)))) % 0.76/1.08 (assume @p160 (forall (@list @t36 @t20) (or (not (= @t36 (tptp.hAPP @t280 @t20))) (= @t20 @t6)))) % 0.76/1.08 (assume @p161 (forall @t13 (or (not (= @t98 @t9)) @t155))) % 0.76/1.08 (assume @p162 (forall (@list @t22 @t36 @t20) (or @t62 @t61 (not (= @t36 (tptp.hAPP @t157 @t20))) @t277))) % 0.76/1.08 (assume @p163 (forall @t205 (or (not (tptp.class_Nat_Osemiring__char__0 @t22)) (not (= @t204 @t140)) @t54))) % 0.76/1.08 (assume @p164 (forall (@list @t22 @t36 @t35 @t156) (or (not (tptp.class_OrderedGroup_Osemigroup__add @t22)) (= (tptp.c_List_Ofoldl @t70 @t281 @t156 @t22 @t22) (tptp.hAPP @t157 (tptp.c_List_Ofoldl @t70 @t35 @t156 @t22 @t22)))))) % 0.76/1.08 (assume @p165 (forall @t87 (or @t283 (= @t281 (tptp.hAPP @t282 @t36))))) % 0.76/1.08 (assume @p166 (forall (@list @t9 @t67 @t44 @t5) (or (not (= (tptp.hAPP @t79 @t67) @t83)) @t176 @t14))) % 0.76/1.08 (assume @p167 (forall @t13 (= @t98 @t73))) % 0.76/1.08 (assume @p168 (forall @t29 (or @t285 (= @t100 @t284)))) % 0.76/1.08 (assume @p169 (forall (@list @t22 @t20 @t171) (or @t283 (= @t174 @t197)))) % 0.76/1.08 (assume @p170 (forall @t286 (= (tptp.c_Lambda_Osubstn @t231 @t125 @t44) (tptp.c_Lambda_OdB_OAbs (tptp.c_Lambda_Osubstn @t130 @t125 @t169))))) % 0.76/1.08 (assume @p171 (forall (@list @t45 @t9 @t43) (or (tptp.c_HOL_Oord__class_Oless @t45 (tptp.hAPP @t79 @t43) tptp.tc_nat) @t103))) % 0.76/1.08 (assume @p172 (forall (@list @t45 @t43 @t9) (or (tptp.c_HOL_Oord__class_Oless @t45 (tptp.hAPP @t74 @t9) tptp.tc_nat) @t103))) % 0.76/1.08 (assume @p173 (forall @t51 (or @t166 (not (tptp.c_HOL_Oord__class_Oless @t190 @t44 tptp.tc_nat))))) % 0.76/1.08 (assume @p174 (forall @t291 (or @t290 (not (tptp.c_HOL_Oord__class_Oless @t36 @t287 tptp.tc_nat))))) % 0.76/1.08 (assume @p175 (forall @t291 (or @t290 (not @t292)))) % 0.76/1.08 (assume @p176 (forall (@list @t9 @t36) (tptp.c_HOL_Oord__class_Oless @t9 (tptp.c_Suc (tptp.hAPP @t79 @t36)) tptp.tc_nat))) % 0.76/1.08 (assume @p177 (forall @t293 (tptp.c_HOL_Oord__class_Oless @t45 (tptp.c_Suc (tptp.hAPP @t79 @t45)) tptp.tc_nat))) % 0.76/1.08 (assume @p178 (forall @t293 (tptp.c_HOL_Oord__class_Oless @t45 (tptp.c_Suc (tptp.hAPP @t46 @t9)) tptp.tc_nat))) % 0.76/1.08 (assume @p179 (forall @t58 (not (= @t6 @t57)))) % 0.76/1.08 (assume @p180 (forall @t179 (not (= @t6 @t178)))) % 0.76/1.08 (assume @p181 (forall @t13 (= @t295 @t294))) % 0.76/1.08 (assume @p182 (forall @t13 (= @t296 @t294))) % 0.76/1.08 (assume @p183 (forall (@list @t3 @t22 @t36 @t287 @t35) (or (tptp.hBOOL (tptp.hAPP @t150 @t287)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t149 @t35) @t287))) (not @t151)))) % 0.76/1.08 (assume @p184 (forall (@list @t3 @t22 @t36) (tptp.hBOOL (tptp.hAPP @t150 @t36)))) % 0.76/1.08 (assume @p185 (forall (@list @t3 @t22 @t20) (tptp.hBOOL (tptp.hAPP @t208 @t20)))) % 0.76/1.08 (assume @p186 (forall (@list @t9 @t5 @t147 @t22) (= (tptp.c_Nat_Ocompow @t98 @t147 @t22 @t22) (tptp.c_Fun_Ocomp (tptp.c_Nat_Ocompow @t9 @t147 @t22 @t22) @t148 @t22 @t22 @t22)))) % 0.76/1.08 (assume @p187 (= @t165 @t102)) % 0.76/1.08 (assume @p188 (forall @t69 (= @t56 (tptp.hAPP (tptp.hAPP @t30 @t68) @t5)))) % 0.76/1.08 (assume @p189 (forall @t69 (= @t56 (tptp.hAPP @t31 @t68)))) % 0.76/1.08 (assume @p190 (forall (@list @t130 @t125 @t5) (= (tptp.c_Lambda_Osubstn @t130 @t125 @t5) (tptp.hAPP (tptp.hAPP @t222 (tptp.c_Lambda_Oliftn @t5 @t125 @t6)) @t5)))) % 0.76/1.08 (assume @p191 (forall @t160 (or @t246 (= (tptp.hAPP @t297 @t25) @t25)))) % 0.76/1.08 (assume @p192 (= (tptp.hAPP @t201 @t6) @t6)) % 0.76/1.08 (assume @p193 (forall @t299 (or @t283 (= @t298 (tptp.hAPP (tptp.hAPP @t70 @t281) @t287))))) % 0.76/1.08 (assume @p194 (forall @t299 (or @t66 (= @t298 (tptp.hAPP @t282 @t300))))) % 0.76/1.08 (assume @p195 (forall @t291 (= (tptp.hAPP @t280 @t289) (tptp.hAPP @t288 @t301)))) % 0.76/1.08 (assume @p196 (forall @t91 (= (tptp.hAPP (tptp.hAPP @t30 @t98) @t44) (tptp.hAPP @t79 @t78)))) % 0.76/1.08 (assume @p197 (forall @t195 (or @t285 @t305))) % 0.76/1.08 (assume @p198 (forall @t195 (or @t285 (= @t302 (tptp.hAPP @t172 @t174))))) % 0.76/1.08 (assume @p199 (forall @t195 (or @t273 @t305))) % 0.76/1.08 (assume @p200 (forall @t309 (or @t283 (= @t308 (tptp.hAPP @t306 @t72))))) % 0.76/1.08 (assume @p201 (forall @t195 (or @t283 (= @t304 (tptp.hAPP @t306 @t19))))) % 0.76/1.08 (assume @p202 (forall @t309 (or @t283 (= @t308 (tptp.hAPP @t196 (tptp.hAPP @t99 @t72)))))) % 0.76/1.08 (assume @p203 (forall @t195 (or @t283 @t305))) % 0.76/1.08 (assume @p204 (forall (@list @t22 @t36 @t35 @t287 @t118) (or @t66 (not (= @t298 (tptp.hAPP @t282 @t118))) (= @t300 @t118)))) % 0.76/1.08 (assume @p205 (forall (@list @t21 @t22 @t311 @t310) (= (tptp.hAPP (tptp.c_COMBK @t21 @t22 @t311) @t310) @t21))) % 0.76/1.08 (assume @p206 (= @t102 @t202)) % 0.76/1.08 (assume @p207 (forall @t160 (or @t53 (= (tptp.c_Nat_Osemiring__1__class_Oof__nat @t68 @t22) @t139)))) % 0.76/1.08 (assume @p208 (forall @t160 (or @t159 (not (= @t25 @t139))))) % 0.76/1.08 (assume @p209 (forall (@list @t147 @t5 @t22 @t36) (= (tptp.hAPP @t147 (tptp.hAPP @t148 @t36)) (tptp.hAPP @t148 @t312)))) % 0.76/1.08 (assume @p210 (forall @t13 (or @t154 @t153 @t155))) % 0.76/1.08 (assume @p211 (forall @t13 (or @t154 @t113 @t152))) % 0.76/1.08 (assume @p212 (forall @t247 (or @t53 (= (tptp.c_Nat_Osemiring__1__class_Oof__nat @t57 @t22) (tptp.hAPP @t313 @t204))))) % 0.76/1.08 (assume @p213 (forall @t13 (= @t295 @t296))) % 0.76/1.08 (assume @p214 (= tptp.v_T____ @t315)) % 0.76/1.08 (assume @p215 (forall (@list @t22 @t20 @t183) (or @t158 (= @t272 (tptp.hAPP @t99 @t184))))) % 0.76/1.08 (assume @p216 (forall @t13 (or @t203 (= @t57 @t5) @t15))) % 0.76/1.08 (assume @p217 (forall @t291 (or (not (= (tptp.hAPP @t280 @t35) @t301)) @t316))) % 0.76/1.08 (assume @p218 (forall @t81 (or (not (= @t80 @t78)) @t54))) % 0.76/1.08 (assume @p219 (forall @t85 (or (not (= @t84 @t83)) @t54))) % 0.76/1.08 (assume @p220 (forall @t299 (or @t62 @t61 (not (= @t281 @t300)) @t316))) % 0.76/1.08 (assume @p221 (forall @t195 (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add @t22)) @t318 @t317))) % 0.76/1.08 (assume @p222 (forall @t195 (or @t319 @t318 @t317))) % 0.76/1.08 (assume @p223 (forall @t254 (or @t319 (not (= @t284 @t197)) @t317))) % 0.76/1.08 (assume @p224 (forall (@list @t130 @t93 @t45 @t43 @t118) (or (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.hAPP (tptp.hAPP @t222 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift @t93) @t45)) (tptp.c_Suc @t43))) (tptp.hAPP (tptp.hAPP @t321 @t93) @t43)) @t45) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst @t320) @t93) @t43)) @t227))) % 0.76/1.08 (assume @p225 (forall (@list @t3 @t129 @t125) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t3 @t129 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t125 @t129 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) @t271))) % 0.76/1.08 (assume @p226 (forall @t13 (or @t206 @t153 @t155))) % 0.76/1.08 (assume @p227 (forall @t13 (or @t206 @t113 @t152))) % 0.76/1.08 (assume @p228 (forall (@list @t22 @t20 @t19 @t171 @t72) (or @t283 (= (tptp.hAPP @t303 @t307) (tptp.hAPP @t306 @t173))))) % 0.76/1.08 (assume @p229 (forall (@list @t5 @t125 @t130 @t44) (= (tptp.c_Lambda_Oliftn @t5 @t263 @t44) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Oliftn @t5 @t125 @t44)) @t279)))) % 0.76/1.08 (assume @p230 (forall @t182 (or @t217 @t181))) % 0.76/1.08 (assume @p231 (forall @t13 (or @t15 @t164))) % 0.76/1.08 (assume @p232 (forall @t18 (or @t163 @t14))) % 0.76/1.08 (assume @p233 (forall (@list @t130 @t45 @t44) (or (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift @t228) @t90) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift @t322) @t45)) (not (tptp.c_HOL_Oord__class_Oless @t45 @t169 tptp.tc_nat))))) % 0.76/1.08 (assume @p234 (forall @t160 (or @t185 (tptp.c_HOL_Oord__class_Oless @t25 (tptp.hAPP @t313 @t139) @t22)))) % 0.76/1.08 (assume @p235 (forall (@list @t3 @t22) (= (tptp.c_Transitive__Closure_Ortranclp @t149 @t22) @t149))) % 0.76/1.08 (assume @p236 (forall @t63 (or @t283 (= (tptp.hAPP @t297 @t36) @t36)))) % 0.76/1.08 (assume @p237 (forall @t65 (or @t285 @t323))) % 0.76/1.08 (assume @p238 (forall @t182 (= @t36 (tptp.hAPP @t280 @t6)))) % 0.76/1.08 (assume @p239 (forall @t69 (= (tptp.hAPP @t201 @t5) @t5))) % 0.76/1.08 (assume @p240 (forall @t58 (= (tptp.hAPP @t79 @t6) @t9))) % 0.76/1.08 (assume @p241 (forall @t63 (or @t62 @t61 (= @t36 (tptp.hAPP @t157 @t25))))) % 0.76/1.08 (assume @p242 (forall @t65 (or @t285 @t324))) % 0.76/1.08 (assume @p243 (forall @t65 (or @t158 @t323))) % 0.76/1.08 (assume @p244 (forall @t65 (or @t158 @t324))) % 0.76/1.08 (assume @p245 (forall @t65 (or @t283 @t324))) % 0.76/1.08 (assume @p246 (forall @t65 (or @t283 @t323))) % 0.76/1.08 (assume @p247 (forall @t327 (= (tptp.c_Lambda_Osubstn @t326 @t125 @t44) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Osubstn @t130 @t125 @t44)) (tptp.c_Lambda_Osubstn @t118 @t125 @t44))))) % 0.76/1.08 (assume @p248 (forall (@list @t36 @t5) (or (tptp.c_HOL_Oord__class_Oless @t180 @t56 tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless @t36 @t5 tptp.tc_nat))))) % 0.76/1.08 (assume @p249 (forall @t13 (or @t14 (not @t328)))) % 0.76/1.08 (assume @p250 (forall @t13 (or @t328 @t15))) % 0.76/1.08 (assume @p251 (forall @t168 (or (= @t167 @t126) @t329))) % 0.76/1.08 (assume @p252 (forall @t128 (or (= @t138 @t126) @t330 @t122))) % 0.76/1.08 (assume @p253 (forall (@list @t171 @t311 @t331 @t147) (= (tptp.hAPP (tptp.c_Fun_Ocomp (tptp.c_COMBK @t171 @t311 @t331) @t147 @t331 @t311 tptp.t_a) tptp.v_x) @t171))) % 0.76/1.08 (assume @p254 (forall @t333 (or @t332 @t265))) % 0.76/1.08 (assume @p255 (forall @t338 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t186 @t337) @t335)) @t187))) % 0.76/1.08 (assume @p256 (forall @t333 (or @t332 @t187))) % 0.76/1.08 (assume @p257 (forall (@list @t9 @t125 @t1) (or (not (= @t339 @t188)) (= @t339 @t125)))) % 0.76/1.08 (assume @p258 (forall @t342 (or @t341 @t268))) % 0.76/1.08 (assume @p259 (forall @t342 (or @t341 @t54))) % 0.76/1.08 (assume @p260 (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t344 @t145) tptp.v_T_H____))) % 0.76/1.08 (assume @p261 (forall (@list @t105 @t118 @t106 @t130) (or (tptp.hBOOL (tptp.hAPP @t347 @t346)) @t345))) % 0.76/1.08 (assume @p262 (forall (@list @t147 @t22) (= (tptp.c_Nat_Ocompow @t6 @t147 @t22 @t22) @t348))) % 0.76/1.08 (assume @p263 (forall @t286 (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst @t231) @t125) @t44) (tptp.c_Lambda_OdB_OAbs (tptp.hAPP (tptp.hAPP @t222 (tptp.hAPP @t207 @t6)) @t169))))) % 0.76/1.08 (assume @p264 (forall @t351 (or @t350 @t349 @t260))) % 0.76/1.08 (assume @p265 (forall (@list @t22 @t105 @t45 @t239 @t106) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP @t107 (tptp.hAPP @t109 @t239)) @t6) @t106) (tptp.hAPP (tptp.hAPP (tptp.hAPP @t107 (tptp.hAPP (tptp.hAPP @t108 @t6) @t106)) @t101) @t239)))) % 0.76/1.08 (assume @p266 (forall (@list @t105 @t106 @t130) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping (tptp.hAPP @t353 @t234)) @t130) @t233)) @t232))) % 0.76/1.08 (assume @p267 (forall (@list @t105 @t130 @t106) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping (tptp.hAPP @t353 (tptp.c_Type_Osko__Type__Xabs__typeE__1__1 @t105 @t130))) @t130) (tptp.c_Type_Osko__Type__Xabs__typeE__1__2 @t105 @t130))) @t232))) % 0.76/1.08 (assume @p268 (forall (@list @t105 @t235 @t106 @t239 @t45 @t129 @t237) (or (tptp.c_Type_Otypings @t105 @t235 @t241) @t240 @t238 @t236))) % 0.76/1.08 (assume @p269 (forall (@list @t105 @t129 @t106 @t45) (or (tptp.c_Type_Otypings @t105 @t129 @t214) @t213))) % 0.76/1.08 (assume @p270 (forall @t355 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t186 @t354) @t220)) @t187))) % 0.76/1.08 (assume @p271 (forall (@list @t105 @t130 @t129 @t106 @t237) (or @t133 @t238 (not (tptp.hBOOL (tptp.hAPP @t142 (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun @t237 @t106 tptp.tc_Type_Otype tptp.tc_Type_Otype))))))) % 0.76/1.08 (assume @p272 (tptp.hBOOL (tptp.hAPP @t356 @t315))) % 0.76/1.08 (assume @p273 (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t344 @t144) @t315))) % 0.76/1.08 (assume @p274 (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t344 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp @t144) tptp.v_a____)) @t314))) % 0.76/1.08 (assume @p275 (forall (@list @t125 @t130 @t5 @t1) (not (= @t357 @t340)))) % 0.76/1.08 (assume @p276 (forall (@list @t5 @t129 @t3 @t1) (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t94 @t129 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t266 @t1 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))))) % 0.76/1.08 (assume @p277 (tptp.c_Type_Otypings @t343 tptp.v_as____ tptp.v_Ts____)) % 0.76/1.08 (assume @p278 (forall (@list @t106 @t239 @t105 @t45 @t129) (or (= @t106 @t239) @t240 @t213))) % 0.76/1.08 (assume @p279 (forall (@list @t105 @t130 @t106 @t118) (or (tptp.hBOOL (tptp.hAPP @t142 (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun @t346) @t106))) @t345))) % 0.76/1.08 (assume @p280 (forall @t141 (or @t185 @t358 @t8))) % 0.76/1.08 (assume @p281 (forall @t141 (or @t185 @t7 (not @t358)))) % 0.76/1.08 (assume @p282 (forall (@list @t130 @t129 @t45) (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift @t131) @t45) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t228 @t361 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) % 0.76/1.08 (assume @p283 (forall @t267 (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp @t266) @t125) @t1 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t125))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP @t336 @t125) @t6) @t1 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))))))) % 0.76/1.08 (assume @p284 (tptp.c_List_Olistsp tptp.c_InductTermi_OIT (tptp.c_List_Omap @t364 (tptp.c_List_Omap (tptp.hAPP (tptp.hAPP @t359 (tptp.hAPP @t363 tptp.v_u____)) tptp.v_i____) tptp.v_bs____ tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB)) % 0.76/1.08 (assume @p285 (forall (@list @t129) (or (tptp.c_List_Olistsp tptp.c_InductTermi_OIT (tptp.c_List_Omap @t364 @t129 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB) (not (tptp.c_List_Olistsp tptp.c_InductTermi_OIT @t129 tptp.tc_Lambda_OdB))))) % 0.76/1.08 (assume @p286 (forall (@list @t130 @t129 @t118 @t45) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst @t131) @t118) @t45) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t320 @t365 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) % 0.76/1.08 (assume @p287 (forall (@list @t368 @t367 @t274) (not (= @t369 @t366)))) % 0.76/1.08 (assume @p288 (forall @t63 (= (tptp.hAPP @t348 @t36) @t36))) % 0.76/1.08 (assume @p289 (forall @t371 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t170) @t231)) @t370))) % 0.76/1.08 (assume @p290 (forall @t373 (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP @t325 @t126))) @t372))) % 0.76/1.08 (assume @p291 (forall @t355 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t354) @t220)) @t265))) % 0.76/1.08 (assume @p292 (forall @t230 (or (= @t229 @t126) @t329))) % 0.76/1.08 (assume @p293 (forall (@list @t105 @t45 @t239 @t129 @t237) (or (tptp.c_Type_Otypings @t375 @t361 @t237) @t238))) % 0.76/1.08 (assume @p294 (forall (@list @t125 @t118 @t130) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.hAPP @t262 @t118)) @t326)) @t370))) % 0.76/1.08 (assume @p295 (forall (@list @t118 @t125 @t130) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.hAPP @t376 @t125)) (tptp.hAPP @t376 @t130))) @t370))) % 0.76/1.08 (assume @p296 (forall (@list @t20 @t19 @t331 @t311 @t22 @t171 @t93) (or (not (= @t379 (tptp.c_Fun_Ocomp @t378 @t171 @t311 @t311 @t22))) (= @t377 (tptp.hAPP @t171 @t93))))) % 0.76/1.08 (assume @p297 (forall (@list @t147 @t380 @t183 @t331 @t311 @t22) (= (tptp.c_List_Omap @t147 (tptp.c_List_Omap @t380 @t183 @t331 @t311) @t311 @t22) (tptp.c_List_Omap @t381 @t183 @t331 @t22)))) % 0.76/1.08 (assume @p298 (forall @t218 (or @t217 (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst @t216) @t125) @t36) @t125)))) % 0.76/1.08 (assume @p299 (forall (@list @t311 @t331 @t22 @t21 @t310 @t382) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBC @t311 @t331 @t22) @t21) @t310) @t382) (tptp.hAPP (tptp.hAPP @t21 @t382) @t310)))) % 0.76/1.08 (assume @p300 (forall @t69 (not (tptp.c_HOL_Oord__class_Oless @t5 @t6 tptp.tc_nat)))) % 0.76/1.08 (assume @p301 (forall @t58 (not (tptp.c_HOL_Oord__class_Oless @t9 @t6 tptp.tc_nat)))) % 0.76/1.08 (assume @p302 (forall (@list @t22 @t287 @t36 @t35) (or @t385 (tptp.c_HOL_Oord__class_Oless @t287 @t36 @t22) (not (tptp.c_HOL_Oord__class_Oless @t287 @t35 @t22)) @t384))) % 0.76/1.08 (assume @p303 (forall (@list @t22 @t36 @t287 @t35) (or @t386 (tptp.c_HOL_Oord__class_Oless @t36 @t287 @t22) (not (tptp.c_HOL_Oord__class_Oless @t35 @t287 @t22)) @t42))) % 0.76/1.08 (assume @p304 (forall (@list @t311 @t380 @t22) (= (tptp.c_Fun_Ocomp @t378 @t380 @t311 @t311 @t22) @t380))) % 0.76/1.08 (assume @p305 (forall (@list @t147 @t22 @t311) (= (tptp.c_Fun_Ocomp @t147 @t348 @t22 @t311 @t22) @t147))) % 0.76/1.08 (assume @p306 (forall @t128 (or (= @t127 @t126) @t330 @t122))) % 0.76/1.08 (assume @p307 (forall (@list @t125 @t130 @t44) (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift @t263) @t44) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.hAPP @t207 @t44)) @t322)))) % 0.76/1.08 (assume @p308 (forall (@list @t147 @t380 @t311 @t22 @t331 @t36) (= @t388 @t387))) % 0.76/1.08 (assume @p309 (forall (@list @t20 @t19 @t93 @t331 @t311 @t22) (= @t377 (tptp.hAPP @t379 @t93)))) % 0.76/1.08 (assume @p310 (forall (@list @t274 @t389) (not (= @t366 @t390)))) % 0.76/1.08 (assume @p311 (forall (@list @t391 @t389) (or (not (= (tptp.c_Lambda_OdB_OAbs @t391) @t390)) (= @t391 @t389)))) % 0.76/1.08 (assume @p312 (forall (@list @t274 @t368 @t367) (not (= @t366 @t369)))) % 0.76/1.08 (assume @p313 (forall @t182 (not @t217))) % 0.76/1.08 (assume @p314 (forall @t69 (not (tptp.c_HOL_Oord__class_Oless @t5 @t5 tptp.tc_nat)))) % 0.76/1.08 (assume @p315 (forall @t63 (or @t385 @t392))) % 0.76/1.08 (assume @p316 (forall @t63 (or @t393 @t392))) % 0.76/1.08 (assume @p317 (forall @t63 (or @t386 @t392))) % 0.76/1.08 (assume @p318 (forall @t371 (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t357) (tptp.hAPP @t334 @t6))))) % 0.76/1.08 (assume @p319 (forall @t394 (or @t253 @t383 @t37 @t86))) % 0.76/1.08 (assume @p320 (forall @t87 (or @t393 @t86 @t383 @t37))) % 0.76/1.08 (assume @p321 (forall @t18 (or @t162 @t14 @t54))) % 0.76/1.08 (assume @p322 (forall (@list @t21 @t5 @t9) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t21 @t5) @t9)) @t162 @t54 @t14))) % 0.76/1.08 (assume @p323 (forall (@list @t35 @t36) (or (tptp.c_HOL_Oord__class_Oless @t35 @t36 tptp.tc_nat) @t292 @t86))) % 0.76/1.08 (assume @p324 (forall @t394 (or @t393 @t383 @t37 @t86))) % 0.76/1.08 (assume @p325 (forall @t394 (or @t393 @t383 @t86 @t37))) % 0.76/1.08 (assume @p326 (forall @t87 (or @t393 @t86 @t37 @t383))) % 0.76/1.08 (assume @p327 (forall @t399 (or @t398 (= @t395 @t367)))) % 0.76/1.08 (assume @p328 (forall @t399 (or @t398 (= @t396 @t368)))) % 0.76/1.08 (assume @p329 (forall (@list @t401 @t125 @t130 @t239 @t106) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t402 @t263) @t239)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t402 @t130) @t106))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t402 @t125) @t400)))))) % 0.76/1.08 (assume @p330 (forall (@list @t45 @t130) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t126) @t130))))) % 0.76/1.08 (assume @p331 (forall (@list @t147 @t380 @t311 @t331 @t22 @t36) (= (tptp.hAPP (tptp.c_Fun_Ofcomp @t147 @t380 @t311 @t331 @t22) @t36) (tptp.hAPP @t380 @t312)))) % 0.76/1.08 (assume @p332 (forall @t69 (or @t7 @t155))) % 0.76/1.08 (assume @p333 (forall (@list @t147 @t380 @t404 @t403 @t331 @t22 @t311) (= (tptp.c_Fun_Ocomp @t147 (tptp.c_Fun_Ocomp @t380 @t404 @t403 @t331 @t22) @t331 @t311 @t22) (tptp.c_Fun_Ocomp (tptp.c_Fun_Ocomp @t147 @t380 @t331 @t311 @t403) @t404 @t403 @t311 @t22)))) % 0.76/1.08 (assume @p334 (not (tptp.c_HOL_Oord__class_Oless @t6 @t6 tptp.tc_nat))) % 0.76/1.08 (assume @p335 (forall @t121 (or (= @t120 @t119) @t405))) % 0.76/1.08 (assume @p336 (forall (@list @t147 @t311 @t22) (= (tptp.c_Fun_Ofcomp @t147 @t378 @t22 @t311 @t311) @t147))) % 0.76/1.08 (assume @p337 (forall (@list @t22 @t380 @t311) (= (tptp.c_Fun_Ofcomp @t348 @t380 @t22 @t22 @t311) @t380))) % 0.76/1.08 (assume @p338 (forall @t409 (or @t408 (= @t114 @t406)))) % 0.76/1.08 (assume @p339 (forall @t409 (or @t408 (= @t115 @t407)))) % 0.76/1.08 (assume @p340 (forall (@list @t389 @t396 @t395) (not (= @t390 @t397)))) % 0.76/1.08 (assume @p341 (forall @t276 (or (not (= @t366 (tptp.c_Lambda_OdB_OVar @t177))) @t275))) % 0.76/1.08 (assume @p342 (forall (@list @t396 @t395 @t389) (not (= @t397 @t390)))) % 0.76/1.08 (assume @p343 (forall (@list @t389 @t274) (not (= @t390 @t366)))) % 0.76/1.08 (assume @p344 (forall (@list @t20 @t19 @t331 @t311 @t22 @t171 @t72 @t403 @t93) (or (not (= @t379 (tptp.c_Fun_Ocomp @t171 @t72 @t403 @t311 @t22))) (= @t377 (tptp.hAPP @t171 (tptp.hAPP @t72 @t93)))))) % 0.76/1.08 (assume @p345 (forall (@list @t147 @t380 @t36 @t412 @t411 @t33 @t311 @t22 @t331 @t403 @t410) (or (not (= @t387 (tptp.hAPP @t412 (tptp.hAPP @t411 @t33)))) (= @t388 (tptp.hAPP (tptp.c_Fun_Ocomp @t412 @t411 @t403 @t22 @t410) @t33))))) % 0.76/1.08 (assume @p346 (forall (@list @t147 @t380 @t22 @t403 @t331 @t404 @t311) (= (tptp.c_Fun_Ofcomp (tptp.c_Fun_Ofcomp @t147 @t380 @t22 @t403 @t331) @t404 @t22 @t331 @t311) (tptp.c_Fun_Ofcomp @t147 (tptp.c_Fun_Ofcomp @t380 @t404 @t403 @t331 @t311) @t22 @t403 @t311)))) % 0.76/1.08 (assume @p347 (forall @t29 (or @t385 @t24 @t413))) % 0.76/1.08 (assume @p348 (forall @t87 (or @t393 @t42 @t384))) % 0.76/1.08 (assume @p349 (forall @t394 (or @t386 @t384 @t42))) % 0.76/1.08 (assume @p350 (forall (@list @t22 @t19 @t20) (or @t386 @t413 @t24))) % 0.76/1.08 (assume @p351 (forall (@list @t105 @t45 @t239 @t130 @t106) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping @t375) @t228) @t106)) @t349))) % 0.76/1.08 (assume @p352 (tptp.hBOOL (tptp.hAPP @t356 tptp.v_T____))) % 0.76/1.08 (assume @p353 @t419) % 0.76/1.08 (assume @p354 (forall @t327 (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst @t326) @t125) @t44) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.hAPP @t223 @t44)) (tptp.hAPP (tptp.hAPP @t321 @t125) @t44))))) % 0.76/1.08 (assume @p355 (forall @t351 (or @t350 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t130) @t259))) @t349))) % 0.76/1.08 (assume @p356 (forall (@list @t44 @t118) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OVar @t44)) @t118) @t44) @t118))) % 0.76/1.08 (assume @p357 (forall (@list @t3 @t45 @t43) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP @t336 @t126) @t43))) @t420))) % 0.76/1.08 (assume @p358 (forall @t421 (= (tptp.hAPP (tptp.c_Fun_Ocomp @t147 @t380 @t331 @t311 tptp.t_a) tptp.v_x) (tptp.hAPP @t147 (tptp.hAPP @t380 tptp.v_x))))) % 0.76/1.08 (assume @p359 (forall @t111 (or (= @t110 (tptp.hAPP @t105 @t43)) @t405))) % 0.76/1.08 (assume @p360 (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t344 tptp.v_a____) tptp.v_T_H_H____))) % 0.76/1.08 (assume @p361 (= (tptp.hAPP (tptp.c_Fun_Oid tptp.t_a) tptp.v_x) tptp.v_x)) % 0.76/1.08 (assume @p362 (forall @t373 (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t228)) @t372))) % 0.76/1.08 (assume @p363 (forall @t427 (or @t426 @t424 (not (tptp.hBOOL (tptp.hAPP @t347 @t423))) @t417 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping (tptp.hAPP @t374 @t423)) @t130) @t422))) @t372))) % 0.76/1.08 (assume @p364 (forall @t427 (or @t426 @t424 (not (tptp.hBOOL (tptp.hAPP @t347 @t425))) @t417 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping (tptp.hAPP @t374 @t425)) @t130) @t422))) @t372))) % 0.76/1.08 (assume @p365 (forall (@list @t22 @t105 @t36 @t106) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP @t108 @t36) @t106) @t36) @t106))) % 0.76/1.08 (assume @p366 (forall (@list @t401 @t130 @t106 @t239) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t402 @t231) @t400)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping (tptp.hAPP (tptp.hAPP (tptp.hAPP @t146 @t401) @t6) @t106)) @t130) @t239)))))) % 0.76/1.08 (assume @p367 (forall @t69 (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t94)))) % 0.76/1.08 (assume @p368 (forall (@list @t105 @t45 @t106) (or (= (tptp.hAPP @t105 @t45) @t106) (not (tptp.hBOOL (tptp.hAPP @t215 @t106)))))) % 0.76/1.08 (assume @p369 (tptp.hBOOL (tptp.hAPP @t428 (tptp.v_sko__local__XCons__Xhyps__1__1 tptp.v_T____ tptp.v_b____ tptp.v_e____ tptp.v_i____)))) % 0.76/1.08 (assume @p370 (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping tptp.v_ea______) tptp.v_ua______) tptp.v_T____))) % 0.76/1.08 (assume @p371 (forall @t338 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t337) @t335)) @t265))) % 0.76/1.08 (assume @p372 (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT tptp.v_ua______))) % 0.76/1.08 (assume @p373 (tptp.hBOOL (tptp.hAPP @t428 (tptp.v_sko__local__XCons__1__1 tptp.v_T____ tptp.v_b____ tptp.v_e____ tptp.v_i____)))) % 0.76/1.08 (assume @p374 (forall (@list @t105 @t118 @t45 @t129 @t237 @t106) (or (tptp.c_Type_Otypings @t105 @t365 @t237) (not (tptp.c_Type_Otypings (tptp.hAPP @t374 @t106) @t129 @t237)) (not (tptp.hBOOL (tptp.hAPP @t347 @t106)))))) % 0.76/1.08 (assume @p375 (forall (@list @t401 @t36) (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t402 @t216) (tptp.hAPP @t401 @t36))))) % 0.76/1.08 (assume @p376 (forall (@list @t3) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t266)) @t420))) % 0.76/1.08 (assume @p377 (forall @t421 (= (tptp.hAPP (tptp.c_Fun_Ofcomp @t147 @t380 tptp.t_a @t331 @t311) tptp.v_x) (tptp.hAPP @t380 (tptp.hAPP @t147 tptp.v_x))))) % 0.76/1.08 (assume @p378 (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT tptp.v_u____))) % 0.76/1.08 (assume @p379 (forall (@list @t130 @t44 @t125) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst @t322) @t125) @t44) @t130))) % 0.76/1.08 (assume @p380 (forall (@list @t429 @t118 @t239 @t45 @t130 @t106) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t430 @t118) @t239))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Type_Otyping (tptp.hAPP (tptp.hAPP (tptp.hAPP @t146 @t429) @t45) @t239)) @t130) @t106))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t430 @t320) @t106))))) % 0.76/1.08 (assume @p381 (tptp.c_List_Olistsp (tptp.hAPP (tptp.hAPP (tptp.c_COMBS tptp.tc_Lambda_OdB tptp.tc_bool tptp.tc_bool) (tptp.hAPP (tptp.hAPP @t439 tptp.c_and) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB @t466 tptp.tc_bool tptp.tc_Lambda_OdB) (tptp.c_All @t434)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB @t465 @t466 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB @t431 tptp.tc_bool @t434) (tptp.c_All tptp.tc_Type_Otype))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB @t464 @t465 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB @t436 @t431 @t434) (tptp.hAPP (tptp.c_COMBB @t435 tptp.tc_bool tptp.tc_Type_Otype) (tptp.c_All tptp.tc_Lambda_OdB)))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB @t463 @t464 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB @t460 @t436 @t434) (tptp.hAPP (tptp.c_COMBB @t433 @t435 tptp.tc_Type_Otype) (tptp.hAPP (tptp.c_COMBB @t432 tptp.tc_bool tptp.tc_Lambda_OdB) (tptp.c_All tptp.tc_nat))))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBS tptp.tc_Lambda_OdB @t447 @t463) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB @t462 (tptp.tc_fun @t447 @t463) tptp.tc_Lambda_OdB) (tptp.c_COMBS @t434 @t433 @t460)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB @t459 @t462 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB @t458 @t461 @t434) (tptp.c_COMBC tptp.tc_Type_Otype @t433 @t433))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB @t457 @t459 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB @t456 @t458 @t434) (tptp.hAPP (tptp.c_COMBB @t442 @t446 tptp.tc_Type_Otype) (tptp.c_COMBB @t432 @t432 tptp.tc_Lambda_OdB)))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB @t455 @t457 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB @t454 @t456 @t434) (tptp.hAPP (tptp.c_COMBB @t453 @t442 tptp.tc_Type_Otype) (tptp.c_COMBS tptp.tc_nat tptp.tc_bool tptp.tc_bool)))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB @t452 @t455 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB @t451 @t454 @t434) (tptp.hAPP (tptp.c_COMBB @t432 @t453 tptp.tc_Type_Otype) (tptp.hAPP (tptp.c_COMBB tptp.tc_bool @t438 tptp.tc_nat) tptp.c_implies)))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun @t434 @t450) @t452 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB @t450 @t451 @t434) (tptp.c_COMBC tptp.tc_nat tptp.tc_Type_Otype tptp.tc_bool))) (tptp.hAPP (tptp.c_COMBC @t434 tptp.tc_Lambda_OdB @t450) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB @t449 (tptp.tc_fun tptp.tc_Lambda_OdB @t450) @t434) (tptp.c_COMBC tptp.tc_nat tptp.tc_Lambda_OdB @t431)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB @t448 @t449 @t434) (tptp.hAPP (tptp.c_COMBB @t434 @t437 tptp.tc_nat) tptp.c_Type_Otyping)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC @t434 tptp.tc_Type_Otype @t448) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_nat (tptp.tc_fun tptp.tc_Type_Otype @t434)) (tptp.tc_fun tptp.tc_Type_Otype @t448) @t434) (tptp.c_COMBC tptp.tc_nat tptp.tc_Type_Otype @t434)) @t146)) tptp.v_T____))))))))))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB @t447 @t447 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB @t433 @t433 @t434) (tptp.hAPP @t445 (tptp.hAPP @t443 (tptp.hAPP @t440 tptp.c_InductTermi_OIT))))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB @t433 @t447 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBC @t434 @t433 @t433) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB @t444 @t446 @t434) @t445) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB @t441 @t444 @t434) @t443) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB @t435 @t441 @t434) @t440) (tptp.hAPP (tptp.hAPP (tptp.c_COMBC @t434 tptp.tc_Type_Otype @t435) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB @t437 @t436 @t434) (tptp.c_COMBC tptp.tc_Lambda_OdB tptp.tc_Type_Otype tptp.tc_bool)) tptp.c_Type_Otyping)) tptp.v_T____)))))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Lambda_OdB @t362) @t433 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB @t362 @t432 tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.c_COMBB tptp.tc_Lambda_OdB tptp.tc_bool tptp.tc_nat) tptp.c_InductTermi_OIT))) tptp.c_Lambda_Osubst)))))))))) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB @t431 tptp.tc_bool tptp.tc_Lambda_OdB) (tptp.c_Ex tptp.tc_Type_Otype)) @t344)) tptp.v_bs____ tptp.tc_Lambda_OdB)) % 0.76/1.08 (assume @p382 (tptp.hBOOL (tptp.hAPP @t428 (tptp.v_sko__CHAINED__1 tptp.v_T____ tptp.v_b____ tptp.v_e____ tptp.v_i____)))) % 0.76/1.08 (assume @p383 @t467) % 0.76/1.08 (assume @p384 @t468) % 0.76/1.08 (assume @p385 @t469) % 0.76/1.08 (assume @p386 (not @t470)) % 0.76/1.08 (assume @p387 (forall @t474 (or (tptp.class_Orderings_Opreorder @t473) (not (tptp.class_Orderings_Opreorder @t471))))) % 0.76/1.08 (assume @p388 (forall @t474 (or (tptp.class_Orderings_Oorder @t473) (not (tptp.class_Orderings_Oorder @t471))))) % 0.76/1.08 (assume @p389 (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_nat)) % 0.76/1.08 (assume @p390 (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_nat)) % 0.76/1.08 (assume @p391 (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_nat)) % 0.76/1.08 (assume @p392 (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_nat)) % 0.76/1.08 (assume @p393 (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_nat)) % 0.76/1.08 (assume @p394 (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat)) % 0.76/1.08 (assume @p395 (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_nat)) % 0.76/1.08 (assume @p396 (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_nat)) % 0.76/1.08 (assume @p397 (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat)) % 0.76/1.08 (assume @p398 (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_nat)) % 0.76/1.08 (assume @p399 (tptp.class_OrderedGroup_Osemigroup__add tptp.tc_nat)) % 0.76/1.08 (assume @p400 (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_nat)) % 0.76/1.08 (assume @p401 (tptp.class_OrderedGroup_Omonoid__add tptp.tc_nat)) % 0.76/1.08 (assume @p402 (tptp.class_Nat_Osemiring__char__0 tptp.tc_nat)) % 0.76/1.08 (assume @p403 (tptp.class_Orderings_Opreorder tptp.tc_nat)) % 0.76/1.08 (assume @p404 (tptp.class_Orderings_Olinorder tptp.tc_nat)) % 0.76/1.08 (assume @p405 (tptp.class_Orderings_Oorder tptp.tc_nat)) % 0.76/1.08 (assume @p406 (tptp.class_Orderings_Opreorder tptp.tc_bool)) % 0.76/1.08 (assume @p407 (tptp.class_Orderings_Oorder tptp.tc_bool)) % 0.76/1.08 (assume @p408 (forall (@list @t36 @t22) (tptp.c_fequal @t36 @t36 @t22))) % 0.76/1.08 (assume @p409 (forall (@list @t476 @t475 @t22) (or (= @t476 @t475) (not (tptp.c_fequal @t476 @t475 @t22))))) % 0.76/1.08 (step @p410 :rule cnf_or_pos :args (@t480)) % 0.76/1.08 (step @p411 :rule reordering :premises (@p410) :args ((or @t470 @t477 @t478 @t479 @t481))) % 0.76/1.08 (step @p412 :rule chain_m_resolution :premises (@p411 @p386 @p383 @p384 @p385) :args (@t481 (@list true false false false) (@list @t470 @t467 @t468 @t469))) % 0.76/1.08 (assume-push @p419 @t419) % 0.76/1.08 (step @p414 :rule instantiate :premises (@p353) :args ((@list tptp.v_xb tptp.v_xc tptp.v_x tptp.v_xa))) % 0.76/1.08 (step-pop @p420 :rule scope :premises (@p414)) % 0.76/1.08 (step @p415 :rule process_scope :premises (@p420) :args (@t480)) % 0.76/1.08 (step @p417 :rule implies_elim :premises (@p415)) % 0.76/1.08 (step @p418 false :rule chain_m_resolution :premises (@p417 @p412 @p353) :args (false (@list true false) (@list @t480 @t419))) % 0.76/1.08 ) % 0.76/1.08 % SZS output end Proof % 0.76/1.08 % cvc5 exiting %------------------------------------------------------------------------------