%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL784-1 : TPTP v9.3.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n014.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 11:23:50 AM UTC 2026 % Result : Unsatisfiable 0.27s 0.95s % Output : Proof 0.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL784-1 : TPTP v9.3.1. Released v4.1.0. % 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.11/0.36 % Computer : n014.cluster.edu % 0.11/0.36 % Model : x86_64 x86_64 % 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.36 % Memory : 8046.5625MB % 0.11/0.36 % OS : Linux 6.8.0-71-generic % 0.11/0.36 % CPULimit : 300 % 0.11/0.36 % WCLimit : 300 % 0.11/0.36 % DateTime : Fri Sep 4 23:14:28 UTC 2026 % 0.11/0.36 % CPUTime : % 0.19/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.19/0.54 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.27/0.95 % SZS status Unsatisfiable % 0.27/0.95 % SZS output start Proof % 0.27/0.98 ( % 0.27/0.98 (declare-sort $$unsorted 0) % 0.27/0.98 (declare-const tptp.c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2 (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_fequal (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1 (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.v_T_H____ $$unsorted) % 0.27/0.98 (declare-const tptp.v_ia______ $$unsorted) % 0.27/0.98 (declare-const tptp.v_rs____ $$unsorted) % 0.27/0.98 (declare-const tptp.v_n____ $$unsorted) % 0.27/0.98 (declare-const tptp.v_e____ $$unsorted) % 0.27/0.98 (declare-const tptp.v_u____ $$unsorted) % 0.27/0.98 (declare-const tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le (-> $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.class_Ring__and__Field_Oordered__semidom (-> $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.class_OrderedGroup_Osemigroup__add (-> $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.c_Type_Osko__Type__Xvar__app__types__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_OrderedGroup_Osemigroup__add (-> $$unsorted $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.c_OrderedGroup_Omonoid__add (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.class_OrderedGroup_Omonoid__add (-> $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.tc_fun (-> $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_Type_Otypings (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.c_HOL_Oplus__class_Oplus (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_Lambda_OdB_OdB__rec (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.class_Orderings_Olinorder (-> $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.c_Type_Osko__Type__Xlist__app__typeE__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.v_sko__InductTermi__XIT__Xcases__1 (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_List_Olist_ONil (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.class_OrderedGroup_Opordered__comm__monoid__add (-> $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.class_Orderings_Oorder (-> $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.c_List_Ofoldr (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.v_ea______ $$unsorted) % 0.27/0.98 (declare-const tptp.c_Type_Osko__Type__Xlist__app__typeD__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.tc_Type_Otype $$unsorted) % 0.27/0.98 (declare-const tptp.c_ListApplication_Osko__ListApplication__Xlem__1__2 (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_Lambda_Olift $$unsorted) % 0.27/0.98 (declare-const tptp.c_ListApplication_Osko__ListApplication__Xlem__1__3 (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_Lambda_Osubst $$unsorted) % 0.27/0.98 (declare-const tptp.c_Lambda_OdB_OAbs (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_HOL_Ozero__class_Ozero (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_Type_Oshift (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_Type_Otyping (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.hBOOL (-> $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.tc_bool $$unsorted) % 0.27/0.98 (declare-const tptp.c_Type_Osko__Type__Xvar__app__typesE__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.class_Ring__and__Field_Ocomm__semiring__1 (-> $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.v_sko__InductTermi__XIT__Xcases__5 (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_Type_Otype_OFun $$unsorted) % 0.27/0.98 (declare-const tptp.hAPP (-> $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.class_Int_Onumber__ring (-> $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.class_Ring__and__Field_Oidom (-> $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.c_HOL_Oord__class_Oless (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.c_List_Ofoldl (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_ListApplication_Osko__ListApplication__Xlem__1__1 (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.tc_Lambda_OdB $$unsorted) % 0.27/0.98 (declare-const tptp.class_Ring__and__Field_Oordered__idom (-> $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.class_OrderedGroup_Ocancel__semigroup__add (-> $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.class_OrderedGroup_Olordered__ab__group__add (-> $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.c_List_Omap (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_Lambda_OdB_OVar (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_InductTermi_OIT $$unsorted) % 0.27/0.98 (declare-const tptp.class_OrderedGroup_Ocancel__ab__semigroup__add (-> $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.c_List_Oappend (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.class_OrderedGroup_Ocomm__monoid__add (-> $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.c_Lambda_OdB_OApp $$unsorted) % 0.27/0.98 (declare-const tptp.c_ListApplication_Osko__ListApplication__Xlem__1__4 (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.t_a $$unsorted) % 0.27/0.98 (declare-const tptp.c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_ListOrder_Ostep1 (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.c_Transitive__Closure_Ortranclp (-> $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.v_T_Ha______ $$unsorted) % 0.27/0.98 (declare-const tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add (-> $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.c_Lambda_Obeta $$unsorted) % 0.27/0.98 (declare-const tptp.c_List_Olistsp (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.v_i____ $$unsorted) % 0.27/0.98 (declare-const tptp.v_T____ $$unsorted) % 0.27/0.98 (declare-const tptp.v_sko__InductTermi__XIT__Xcases__2 (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.v_sko__InductTermi__XIT__Xcases__3 (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.v_ua______ $$unsorted) % 0.27/0.98 (declare-const tptp.v_sko__InductTermi__XIT__Xcases__6 (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.tc_nat $$unsorted) % 0.27/0.98 (declare-const tptp.c_COMBC (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.v_sko__InductTermi__XIT__Xcases__4 (-> $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_Lambda_Oliftn (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_Lambda_OdB_OdB__case (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.class_OrderedGroup_Oab__group__add (-> $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.c_List_Olist_OCons (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.c_Lambda_Osubstn (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.27/0.98 (declare-const tptp.class_Orderings_Opreorder (-> $$unsorted Bool)) % 0.27/0.98 (declare-const tptp.class_OrderedGroup_Oab__semigroup__add (-> $$unsorted Bool)) % 0.27/0.98 (define @t1 () (@var "T_a" $$unsorted)) % 0.27/0.98 (define @t2 () (tptp.c_HOL_Ozero__class_Ozero @t1)) % 0.27/0.98 (define @t3 () (@var "V_a" $$unsorted)) % 0.27/0.98 (define @t4 () (= @t3 @t2)) % 0.27/0.98 (define @t5 () (@var "V_x" $$unsorted)) % 0.27/0.98 (define @t6 () (tptp.c_HOL_Oplus__class_Oplus @t1)) % 0.27/0.98 (define @t7 () (tptp.hAPP @t6 @t5)) % 0.27/0.98 (define @t8 () (not (tptp.class_Int_Onumber__ring @t1))) % 0.27/0.98 (define @t9 () (not (tptp.class_Ring__and__Field_Oidom @t1))) % 0.27/0.98 (define @t10 () (@var "V_P" $$unsorted)) % 0.27/0.98 (define @t11 () (not (tptp.hBOOL (tptp.hAPP @t10 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar (tptp.c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @t10)) (tptp.c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @t10) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))))) % 0.27/0.98 (define @t12 () (tptp.c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @t10)) % 0.27/0.98 (define @t13 () (@var "V_t" $$unsorted)) % 0.27/0.98 (define @t14 () (tptp.hBOOL (tptp.hAPP @t10 @t13))) % 0.27/0.98 (define @t15 () (@list @t10 @t13)) % 0.27/0.98 (define @t16 () (not (tptp.hBOOL (tptp.hAPP @t10 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar (tptp.c_ListApplication_Osko__ListApplication__Xlem__1__1 @t10)) (tptp.c_ListApplication_Osko__ListApplication__Xlem__1__2 @t10) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))))) % 0.27/0.98 (define @t17 () (tptp.c_ListApplication_Osko__ListApplication__Xlem__1__3 @t10)) % 0.27/0.98 (define @t18 () (@var "V_T" $$unsorted)) % 0.27/0.98 (define @t19 () (@var "V_ts" $$unsorted)) % 0.27/0.98 (define @t20 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t13 @t19 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.27/0.98 (define @t21 () (@var "V_e" $$unsorted)) % 0.27/0.98 (define @t22 () (tptp.c_Type_Otyping @t21 @t20 @t18)) % 0.27/0.98 (define @t23 () (not @t22)) % 0.27/0.98 (define @t24 () (tptp.c_Type_Osko__Type__Xlist__app__typeD__1__1 @t18 @t21 @t13 @t19)) % 0.27/0.98 (define @t25 () (@list @t21 @t13 @t18 @t19)) % 0.27/0.98 (define @t26 () (tptp.c_Type_Osko__Type__Xlist__app__typeE__1__1 @t18 @t21 @t13 @t19)) % 0.27/0.98 (define @t27 () (@list @t21 @t19 @t18 @t13)) % 0.27/0.98 (define @t28 () (tptp.c_List_Olist_ONil @t1)) % 0.27/0.98 (define @t29 () (@var "V_xs" $$unsorted)) % 0.27/0.98 (define @t30 () (tptp.c_List_Oappend @t29 (tptp.c_List_Olist_OCons @t5 @t28 @t1) @t1)) % 0.27/0.98 (define @t31 () (@var "V_y" $$unsorted)) % 0.27/0.98 (define @t32 () (@var "V_ys" $$unsorted)) % 0.27/0.98 (define @t33 () (tptp.c_List_Oappend @t32 (tptp.c_List_Olist_OCons @t31 @t28 @t1) @t1)) % 0.27/0.98 (define @t34 () (@var "V_r" $$unsorted)) % 0.27/0.98 (define @t35 () (not (tptp.c_ListOrder_Ostep1 @t34 @t33 @t30 @t1))) % 0.27/0.98 (define @t36 () (= @t31 @t5)) % 0.27/0.98 (define @t37 () (tptp.hAPP @t34 @t31)) % 0.27/0.98 (define @t38 () (tptp.hBOOL (tptp.hAPP @t37 @t5))) % 0.27/0.98 (define @t39 () (@var "T_b" $$unsorted)) % 0.27/0.98 (define @t40 () (@var "V_f" $$unsorted)) % 0.27/0.98 (define @t41 () (tptp.c_List_Oappend @t29 @t32 @t39)) % 0.27/0.98 (define @t42 () (tptp.hAPP @t6 @t31)) % 0.27/0.98 (define @t43 () (tptp.hAPP @t7 @t31)) % 0.27/0.98 (define @t44 () (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 @t1))) % 0.27/0.98 (define @t45 () (@list @t1 @t5 @t31)) % 0.27/0.98 (define @t46 () (@var "V_b" $$unsorted)) % 0.27/0.98 (define @t47 () (tptp.hAPP @t6 @t46)) % 0.27/0.98 (define @t48 () (tptp.hAPP @t47 @t3)) % 0.27/0.98 (define @t49 () (tptp.hAPP @t6 @t3)) % 0.27/0.98 (define @t50 () (tptp.hAPP @t49 @t46)) % 0.27/0.98 (define @t51 () (not (tptp.class_OrderedGroup_Ocomm__monoid__add @t1))) % 0.27/0.98 (define @t52 () (@list @t1 @t3 @t46)) % 0.27/0.98 (define @t53 () (@var "V_c" $$unsorted)) % 0.27/0.98 (define @t54 () (tptp.hAPP @t6 @t53)) % 0.27/0.98 (define @t55 () (tptp.hAPP @t54 @t3)) % 0.27/0.98 (define @t56 () (tptp.hAPP @t49 @t53)) % 0.27/0.98 (define @t57 () (@var "V_s" $$unsorted)) % 0.27/0.98 (define @t58 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t34) @t57)))) % 0.27/0.98 (define @t59 () (@var "V_i" $$unsorted)) % 0.27/0.98 (define @t60 () (tptp.hAPP tptp.c_Lambda_Osubst @t13)) % 0.27/0.98 (define @t61 () (tptp.hAPP @t60 @t57)) % 0.27/0.98 (define @t62 () (tptp.c_Transitive__Closure_Ortranclp tptp.c_Lambda_Obeta tptp.tc_Lambda_OdB)) % 0.27/0.98 (define @t63 () (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t62 (tptp.hAPP (tptp.hAPP @t60 @t34) @t59)) (tptp.hAPP @t61 @t59)))) % 0.27/0.98 (define @t64 () (@list @t13 @t34 @t59 @t57)) % 0.27/0.98 (define @t65 () (tptp.c_List_Oappend @t28 @t32 @t1)) % 0.27/0.98 (define @t66 () (tptp.c_List_Oappend @t29 @t28 @t1)) % 0.27/0.98 (define @t67 () (@list @t29 @t1)) % 0.27/0.98 (define @t68 () (@list @t5 @t1)) % 0.27/0.98 (define @t69 () (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t3)))) % 0.27/0.98 (define @t70 () (tptp.v_sko__InductTermi__XIT__Xcases__1 @t3)) % 0.27/0.98 (define @t71 () (tptp.c_List_Olistsp tptp.c_InductTermi_OIT @t70 tptp.tc_Lambda_OdB)) % 0.27/0.98 (define @t72 () (tptp.v_sko__InductTermi__XIT__Xcases__3 @t3)) % 0.27/0.98 (define @t73 () (= @t3 (tptp.c_Lambda_OdB_OAbs @t72))) % 0.27/0.98 (define @t74 () (tptp.v_sko__InductTermi__XIT__Xcases__5 @t3)) % 0.27/0.98 (define @t75 () (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t74))) % 0.27/0.98 (define @t76 () (@list @t3)) % 0.27/0.98 (define @t77 () (tptp.c_Transitive__Closure_Ortranclp @t34 @t1)) % 0.27/0.98 (define @t78 () (tptp.hAPP @t77 @t5)) % 0.27/0.98 (define @t79 () (tptp.hBOOL (tptp.hAPP @t78 @t31))) % 0.27/0.98 (define @t80 () (@var "V_z" $$unsorted)) % 0.27/0.98 (define @t81 () (tptp.hAPP @t77 @t3)) % 0.27/0.98 (define @t82 () (@var "V_zs" $$unsorted)) % 0.27/0.98 (define @t83 () (= @t32 @t82)) % 0.27/0.98 (define @t84 () (tptp.c_List_Oappend @t29 @t32 @t1)) % 0.27/0.98 (define @t85 () (@list @t29 @t32 @t1 @t82)) % 0.27/0.98 (define @t86 () (@var "V_A" $$unsorted)) % 0.27/0.98 (define @t87 () (@var "V_xa" $$unsorted)) % 0.27/0.98 (define @t88 () (tptp.c_List_Olist_OCons @t5 @t29 @t1)) % 0.27/0.98 (define @t89 () (not (tptp.c_ListOrder_Ostep1 @t34 (tptp.c_List_Olist_OCons @t31 @t32 @t1) @t88 @t1))) % 0.27/0.98 (define @t90 () (= @t29 @t32)) % 0.27/0.98 (define @t91 () (= @t5 @t31)) % 0.27/0.98 (define @t92 () (@var "V_dB" $$unsorted)) % 0.27/0.98 (define @t93 () (@var "V_f3" $$unsorted)) % 0.27/0.98 (define @t94 () (tptp.hAPP @t93 @t92)) % 0.27/0.98 (define @t95 () (tptp.c_Lambda_OdB_OAbs @t92)) % 0.27/0.98 (define @t96 () (@var "V_f2" $$unsorted)) % 0.27/0.98 (define @t97 () (@var "V_f1" $$unsorted)) % 0.27/0.98 (define @t98 () (@list @t97 @t96 @t93 @t92 @t1)) % 0.27/0.98 (define @t99 () (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t72))) % 0.27/0.98 (define @t100 () (tptp.v_sko__InductTermi__XIT__Xcases__6 @t3)) % 0.27/0.98 (define @t101 () (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) % 0.27/0.98 (define @t102 () (tptp.v_sko__InductTermi__XIT__Xcases__4 @t3)) % 0.27/0.98 (define @t103 () (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst @t102) @t74) @t101) @t100 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) % 0.27/0.98 (define @t104 () (tptp.c_List_Olistsp @t86 @t84 @t1)) % 0.27/0.98 (define @t105 () (not @t104)) % 0.27/0.98 (define @t106 () (tptp.c_List_Olistsp @t86 @t32 @t1)) % 0.27/0.98 (define @t107 () (tptp.c_List_Olistsp @t86 @t29 @t1)) % 0.27/0.98 (define @t108 () (@var "V_s_H" $$unsorted)) % 0.27/0.98 (define @t109 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t62 @t57) @t108)))) % 0.27/0.98 (define @t110 () (tptp.c_Lambda_OdB_OAbs @t57)) % 0.27/0.98 (define @t111 () (@var "V_us" $$unsorted)) % 0.27/0.98 (define @t112 () (@var "V_vs" $$unsorted)) % 0.27/0.98 (define @t113 () (tptp.c_List_Oappend @t29 @t5 @t1)) % 0.27/0.98 (define @t114 () (tptp.c_ListOrder_Ostep1 @t34 @t32 @t29 @t1)) % 0.27/0.98 (define @t115 () (not @t114)) % 0.27/0.98 (define @t116 () (@var "V_n" $$unsorted)) % 0.27/0.98 (define @t117 () (tptp.hAPP @t6 @t2)) % 0.27/0.98 (define @t118 () (not (tptp.class_OrderedGroup_Olordered__ab__group__add @t1))) % 0.27/0.98 (define @t119 () (@list @t1)) % 0.27/0.98 (define @t120 () (@var "V_Ts" $$unsorted)) % 0.27/0.98 (define @t121 () (not (tptp.c_Type_Otypings @t21 @t19 @t120))) % 0.27/0.98 (define @t122 () (tptp.c_HOL_Oord__class_Oless @t5 @t31 @t1)) % 0.27/0.98 (define @t123 () (not @t122)) % 0.27/0.98 (define @t124 () (not (tptp.class_Orderings_Opreorder @t1))) % 0.27/0.98 (define @t125 () (tptp.c_HOL_Oord__class_Oless @t31 @t5 @t1)) % 0.27/0.98 (define @t126 () (not @t125)) % 0.27/0.98 (define @t127 () (not (tptp.class_Orderings_Oorder @t1))) % 0.27/0.98 (define @t128 () (tptp.hAPP @t7 (tptp.hAPP @t42 @t80))) % 0.27/0.98 (define @t129 () (@list @t1 @t5 @t31 @t80)) % 0.27/0.98 (define @t130 () (tptp.hAPP @t7 @t80)) % 0.27/0.98 (define @t131 () (not (tptp.class_OrderedGroup_Oab__group__add @t1))) % 0.27/0.98 (define @t132 () (tptp.hAPP @t47 @t53)) % 0.27/0.98 (define @t133 () (tptp.hAPP @t49 @t132)) % 0.27/0.98 (define @t134 () (tptp.hAPP @t6 @t50)) % 0.27/0.98 (define @t135 () (tptp.hAPP @t134 @t53)) % 0.27/0.98 (define @t136 () (= @t135 @t133)) % 0.27/0.98 (define @t137 () (@list @t1 @t3 @t46 @t53)) % 0.27/0.98 (define @t138 () (not (tptp.class_OrderedGroup_Oab__semigroup__add @t1))) % 0.27/0.98 (define @t139 () (@var "V_d" $$unsorted)) % 0.27/0.98 (define @t140 () (tptp.hAPP @t6 @t56)) % 0.27/0.98 (define @t141 () (tptp.hAPP @t54 @t139)) % 0.27/0.98 (define @t142 () (tptp.hAPP @t49 @t141)) % 0.27/0.98 (define @t143 () (@list @t1 @t3 @t53 @t139)) % 0.27/0.98 (define @t144 () (@var "V_m" $$unsorted)) % 0.27/0.98 (define @t145 () (@list @t144)) % 0.27/0.98 (define @t146 () (@list @t116)) % 0.27/0.98 (define @t147 () (@var "V_u" $$unsorted)) % 0.27/0.98 (define @t148 () (@var "V_Q" $$unsorted)) % 0.27/0.98 (define @t149 () (@var "V_R" $$unsorted)) % 0.27/0.98 (define @t150 () (@var "T_c" $$unsorted)) % 0.27/0.98 (define @t151 () (tptp.c_List_Olist_ONil @t39)) % 0.27/0.98 (define @t152 () (tptp.c_List_Omap @t40 @t151 @t39 @t1)) % 0.27/0.98 (define @t153 () (= @t3 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar (tptp.v_sko__InductTermi__XIT__Xcases__2 @t3)) @t70 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) % 0.27/0.98 (define @t154 () (tptp.c_List_Omap (tptp.c_COMBC (tptp.c_COMBC tptp.c_Lambda_Osubst @t147 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB (tptp.tc_fun tptp.tc_nat tptp.tc_Lambda_OdB)) @t59 tptp.tc_Lambda_OdB tptp.tc_nat tptp.tc_Lambda_OdB) @t19 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.27/0.98 (define @t155 () (tptp.c_HOL_Oord__class_Oless @t3 @t2 @t1)) % 0.27/0.98 (define @t156 () (not @t155)) % 0.27/0.98 (define @t157 () (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add @t1))) % 0.27/0.98 (define @t158 () (tptp.c_List_Olist_OCons @t5 (tptp.c_List_Oappend @t87 @t82 @t1) @t1)) % 0.27/0.98 (define @t159 () (tptp.c_List_Olist_OCons @t5 @t87 @t1)) % 0.27/0.98 (define @t160 () (tptp.c_List_Oappend @t159 @t82 @t1)) % 0.27/0.98 (define @t161 () (@var "V_t_H" $$unsorted)) % 0.27/0.98 (define @t162 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t62 @t13) @t161)))) % 0.27/0.98 (define @t163 () (tptp.hAPP tptp.c_Lambda_OdB_OApp @t57)) % 0.27/0.98 (define @t164 () (tptp.hAPP @t163 @t13)) % 0.27/0.98 (define @t165 () (tptp.hAPP @t62 @t164)) % 0.27/0.98 (define @t166 () (tptp.hAPP tptp.c_Lambda_OdB_OApp @t108)) % 0.27/0.98 (define @t167 () (tptp.c_List_Ofoldr @t6 @t29 @t2 @t1 @t1)) % 0.27/0.98 (define @t168 () (tptp.c_List_Ofoldl @t6 @t3 @t29 @t1 @t1)) % 0.27/0.98 (define @t169 () (not (tptp.class_OrderedGroup_Omonoid__add @t1))) % 0.27/0.98 (define @t170 () (tptp.hAPP @t40 @t5)) % 0.27/0.98 (define @t171 () (@var "V_xb" $$unsorted)) % 0.27/0.98 (define @t172 () (tptp.c_List_Omap @t40 @t29 @t39 @t1)) % 0.27/0.98 (define @t173 () (tptp.c_List_Olist_OCons @t5 @t29 @t39)) % 0.27/0.98 (define @t174 () (= @t3 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs @t102)) @t74) @t100 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) % 0.27/0.98 (define @t175 () (= @t46 @t53)) % 0.27/0.98 (define @t176 () (not (= @t50 @t56))) % 0.27/0.98 (define @t177 () (not (tptp.class_OrderedGroup_Ocancel__semigroup__add @t1))) % 0.27/0.98 (define @t178 () (@list @t1 @t46 @t3 @t53)) % 0.27/0.98 (define @t179 () (@var "V_xs1" $$unsorted)) % 0.27/0.98 (define @t180 () (@var "V_list_H" $$unsorted)) % 0.27/0.98 (define @t181 () (@var "V_a_H" $$unsorted)) % 0.27/0.98 (define @t182 () (tptp.c_List_Olist_OCons @t181 @t180 @t1)) % 0.27/0.98 (define @t183 () (tptp.hAPP @t47 @t139)) % 0.27/0.98 (define @t184 () (@var "V_k" $$unsorted)) % 0.27/0.98 (define @t185 () (not (tptp.c_HOL_Oord__class_Oless @t59 @t184 tptp.tc_nat))) % 0.27/0.98 (define @t186 () (tptp.c_Lambda_OdB_OVar @t59)) % 0.27/0.98 (define @t187 () (not (tptp.c_Type_Otyping @t21 @t13 @t18))) % 0.27/0.98 (define @t188 () (tptp.c_Type_Otyping @t21 @t161 @t18)) % 0.27/0.98 (define @t189 () (@list @t21 @t161 @t18 @t13)) % 0.27/0.98 (define @t190 () (tptp.c_List_Omap (tptp.c_COMBC tptp.c_Lambda_Olift @t59 tptp.tc_Lambda_OdB tptp.tc_nat tptp.tc_Lambda_OdB) @t19 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.27/0.98 (define @t191 () (@var "V_U" $$unsorted)) % 0.27/0.98 (define @t192 () (tptp.c_Type_Oshift @t21 @t59 @t191 tptp.tc_Type_Otype)) % 0.27/0.98 (define @t193 () (tptp.hAPP tptp.c_Lambda_Olift @t57)) % 0.27/0.98 (define @t194 () (tptp.hAPP @t193 @t59)) % 0.27/0.98 (define @t195 () (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift @t34) @t59)) % 0.27/0.98 (define @t196 () (@list @t34 @t59 @t57)) % 0.27/0.98 (define @t197 () (tptp.c_Lambda_OdB_OVar @t5)) % 0.27/0.98 (define @t198 () (tptp.c_HOL_Oord__class_Oless @t5 @t5 tptp.tc_nat)) % 0.27/0.98 (define @t199 () (@list @t5 @t57)) % 0.27/0.98 (define @t200 () (tptp.c_List_Oappend @t28 @t88 @t1)) % 0.27/0.98 (define @t201 () (tptp.hAPP (tptp.hAPP @t60 @t147) @t59)) % 0.27/0.98 (define @t202 () (@var "V_e_H" $$unsorted)) % 0.27/0.98 (define @t203 () (= @t32 @t29)) % 0.27/0.98 (define @t204 () (tptp.c_List_Oappend @t28 @t28 @t1)) % 0.27/0.98 (define @t205 () (@list @t1 @t5)) % 0.27/0.98 (define @t206 () (= (tptp.hAPP @t117 @t3) @t3)) % 0.27/0.98 (define @t207 () (@list @t1 @t3)) % 0.27/0.98 (define @t208 () (= (tptp.hAPP @t49 @t2) @t3)) % 0.27/0.98 (define @t209 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t57) @t13)))) % 0.27/0.98 (define @t210 () (tptp.c_Lambda_OdB_OAbs @t13)) % 0.27/0.98 (define @t211 () (@list @t57 @t13)) % 0.27/0.98 (define @t212 () (@var "V_plus" $$unsorted)) % 0.27/0.98 (define @t213 () (@var "V_zero" $$unsorted)) % 0.27/0.98 (define @t214 () (not (tptp.c_OrderedGroup_Omonoid__add @t213 @t212 @t1))) % 0.27/0.98 (define @t215 () (tptp.hAPP @t212 @t3)) % 0.27/0.98 (define @t216 () (tptp.hAPP @t49 @t3)) % 0.27/0.98 (define @t217 () (tptp.c_HOL_Oord__class_Oless @t2 @t216 @t1)) % 0.27/0.98 (define @t218 () (tptp.c_HOL_Oord__class_Oless @t2 @t3 @t1)) % 0.27/0.98 (define @t219 () (not @t218)) % 0.27/0.98 (define @t220 () (= @t29 @t151)) % 0.27/0.98 (define @t221 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t62 @t34) @t57)))) % 0.27/0.98 (define @t222 () (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst @t57) @t13)) % 0.27/0.98 (define @t223 () (tptp.hAPP @t222 @t59)) % 0.27/0.98 (define @t224 () (tptp.hAPP tptp.c_Lambda_Osubst @t34)) % 0.27/0.98 (define @t225 () (tptp.hAPP (tptp.hAPP @t224 @t13) @t59)) % 0.27/0.98 (define @t226 () (@list @t34 @t13 @t59 @t57)) % 0.27/0.98 (define @t227 () (tptp.c_HOL_Oord__class_Oless @t216 @t2 @t1)) % 0.27/0.98 (define @t228 () (not @t227)) % 0.27/0.98 (define @t229 () (not (tptp.class_Ring__and__Field_Oordered__idom @t1))) % 0.27/0.98 (define @t230 () (@var "V_env" $$unsorted)) % 0.27/0.98 (define @t231 () (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun @t18) @t191)) % 0.27/0.98 (define @t232 () (tptp.c_HOL_Oord__class_Oless @t184 @t59 tptp.tc_nat)) % 0.27/0.98 (define @t233 () (= @t59 @t184)) % 0.27/0.98 (define @t234 () (@list @t59 @t57 @t184)) % 0.27/0.98 (define @t235 () (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t13)))) % 0.27/0.98 (define @t236 () (@var "V_Ta" $$unsorted)) % 0.27/0.98 (define @t237 () (@var "V_T1" $$unsorted)) % 0.27/0.98 (define @t238 () (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t147)))) % 0.27/0.98 (define @t239 () (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t201))) % 0.27/0.98 (define @t240 () (@var "V_T2" $$unsorted)) % 0.27/0.98 (define @t241 () (not (= tptp.v_T____ (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun @t237) @t240)))) % 0.27/0.98 (define @t242 () (@list @t237 @t240 @t13 @t147 @t59 @t21 @t236)) % 0.27/0.98 (define @t243 () (= @t29 @t28)) % 0.27/0.98 (define @t244 () (not (= @t28 @t84))) % 0.27/0.98 (define @t245 () (@list @t1 @t29 @t32)) % 0.27/0.98 (define @t246 () (= @t32 @t28)) % 0.27/0.98 (define @t247 () (@var "V_dB_H" $$unsorted)) % 0.27/0.98 (define @t248 () (tptp.c_Lambda_OdB_OAbs @t247)) % 0.27/0.98 (define @t249 () (not (= @t84 @t28))) % 0.27/0.98 (define @t250 () (@list @t29 @t32 @t1)) % 0.27/0.98 (define @t251 () (not (tptp.c_HOL_Oord__class_Oless @t5 @t5 @t1))) % 0.27/0.98 (define @t252 () (not (tptp.class_Orderings_Olinorder @t1))) % 0.27/0.98 (define @t253 () (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp @t110) @t13)) % 0.27/0.98 (define @t254 () (@list @t34 @t32 @t29 @t1 @t31 @t5)) % 0.27/0.98 (define @t255 () (not (tptp.c_OrderedGroup_Osemigroup__add @t212 @t1))) % 0.27/0.98 (define @t256 () (@list @t1 @t31 @t5)) % 0.27/0.98 (define @t257 () (= @t144 @t116)) % 0.27/0.98 (define @t258 () (tptp.c_HOL_Oord__class_Oless @t144 @t116 tptp.tc_nat)) % 0.27/0.98 (define @t259 () (tptp.c_HOL_Oord__class_Oless @t116 @t144 tptp.tc_nat)) % 0.27/0.98 (define @t260 () (tptp.c_HOL_Oord__class_Oless @t3 @t46 @t1)) % 0.27/0.98 (define @t261 () (not @t260)) % 0.27/0.98 (define @t262 () (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add @t1))) % 0.27/0.98 (define @t263 () (tptp.hAPP tptp.c_Lambda_Olift @t13)) % 0.27/0.98 (define @t264 () (tptp.hAPP @t263 @t59)) % 0.27/0.98 (define @t265 () (not (tptp.class_OrderedGroup_Osemigroup__add @t1))) % 0.27/0.98 (define @t266 () (@var "V_j" $$unsorted)) % 0.27/0.98 (define @t267 () (not (tptp.c_HOL_Oord__class_Oless @t266 @t59 tptp.tc_nat))) % 0.27/0.98 (define @t268 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t186 @t19 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.27/0.98 (define @t269 () (not (tptp.c_Type_Otyping @t21 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t268 @t111 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) @t18))) % 0.27/0.98 (define @t270 () (not (tptp.c_Type_Otyping @t21 @t268 @t191))) % 0.27/0.98 (define @t271 () (tptp.c_Type_Osko__Type__Xvar__app__types__1__1 @t18 @t191 @t21 @t111)) % 0.27/0.98 (define @t272 () (@var "V_type2_H" $$unsorted)) % 0.27/0.98 (define @t273 () (@var "V_type2" $$unsorted)) % 0.27/0.98 (define @t274 () (@var "V_type1_H" $$unsorted)) % 0.27/0.98 (define @t275 () (@var "V_type1" $$unsorted)) % 0.27/0.98 (define @t276 () (not (= (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun @t275) @t273) (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun @t274) @t272)))) % 0.27/0.98 (define @t277 () (@list @t275 @t273 @t274 @t272)) % 0.27/0.98 (define @t278 () (tptp.c_HOL_Oord__class_Oless @t56 @t132 @t1)) % 0.27/0.98 (define @t279 () (@list @t1 @t3 @t53 @t46)) % 0.27/0.98 (define @t280 () (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @t1))) % 0.27/0.98 (define @t281 () (tptp.c_HOL_Oord__class_Oless @t55 (tptp.hAPP @t54 @t46) @t1)) % 0.27/0.98 (define @t282 () (@list @t1 @t53 @t3 @t46)) % 0.27/0.98 (define @t283 () (@var "V_list" $$unsorted)) % 0.27/0.98 (define @t284 () (not (= (tptp.c_List_Olist_OCons @t3 @t283 @t1) @t182))) % 0.27/0.98 (define @t285 () (@list @t3 @t283 @t1 @t181 @t180)) % 0.27/0.98 (define @t286 () (not (= @t30 @t33))) % 0.27/0.98 (define @t287 () (@list @t29 @t5 @t1 @t32 @t31)) % 0.27/0.98 (define @t288 () (not (tptp.c_HOL_Oord__class_Oless @t46 @t3 @t1))) % 0.27/0.98 (define @t289 () (tptp.hBOOL (tptp.hAPP @t81 @t53))) % 0.27/0.98 (define @t290 () (@list @t34 @t1 @t3 @t53 @t46)) % 0.27/0.98 (define @t291 () (tptp.hAPP @t212 @t5)) % 0.27/0.98 (define @t292 () (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB)) % 0.27/0.98 (define @t293 () (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp @t34) @t57)) % 0.27/0.98 (define @t294 () (tptp.hAPP tptp.c_Lambda_OdB_OApp @t13)) % 0.27/0.98 (define @t295 () (tptp.hAPP @t294 @t147)) % 0.27/0.98 (define @t296 () (@list @t13 @t147 @t57 @t184)) % 0.27/0.98 (define @t297 () (@var "V_nat" $$unsorted)) % 0.27/0.98 (define @t298 () (tptp.c_Lambda_OdB_OVar @t297)) % 0.27/0.98 (define @t299 () (@var "V_dB2" $$unsorted)) % 0.27/0.98 (define @t300 () (@var "V_dB1" $$unsorted)) % 0.27/0.98 (define @t301 () (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp @t300) @t299)) % 0.27/0.98 (define @t302 () (not (tptp.c_Type_Otyping @t21 @t268 @t18))) % 0.27/0.98 (define @t303 () (tptp.c_Type_Osko__Type__Xvar__app__typesE__1__1 @t18 @t21 @t59 @t19)) % 0.27/0.98 (define @t304 () (@var "V_nat_H" $$unsorted)) % 0.27/0.98 (define @t305 () (@var "V_xd" $$unsorted)) % 0.27/0.98 (define @t306 () (tptp.hAPP @t97 @t297)) % 0.27/0.98 (define @t307 () (@var "V_ss" $$unsorted)) % 0.27/0.98 (define @t308 () (tptp.c_Lambda_OdB_OVar @t116)) % 0.27/0.98 (define @t309 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t308 @t307 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.27/0.98 (define @t310 () (@var "V_rs" $$unsorted)) % 0.27/0.98 (define @t311 () (tptp.c_Lambda_OdB_OVar @t144)) % 0.27/0.98 (define @t312 () (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t311 @t310 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) @t309))) % 0.27/0.98 (define @t313 () (@list @t144 @t310 @t116 @t307)) % 0.27/0.98 (define @t314 () (= @t310 @t307)) % 0.27/0.98 (define @t315 () (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OVar @t184)) @t147) @t184)) % 0.27/0.98 (define @t316 () (forall (@list @t184 @t147) (= @t315 @t147))) % 0.27/0.98 (define @t317 () (@var "V_xc" $$unsorted)) % 0.27/0.98 (define @t318 () (tptp.hAPP (tptp.hAPP @t96 @t300) @t299)) % 0.27/0.98 (define @t319 () (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t34)))) % 0.27/0.98 (define @t320 () (tptp.c_Lambda_OdB_OVar @t266)) % 0.27/0.98 (define @t321 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t57 @t307 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.27/0.98 (define @t322 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t34 @t307 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.27/0.98 (define @t323 () (@list @t34 @t307 @t57)) % 0.27/0.98 (define @t324 () (tptp.c_Lambda_OdB_OAbs @t34)) % 0.27/0.98 (define @t325 () (not (= @t321 @t324))) % 0.27/0.98 (define @t326 () (@list @t57 @t307 @t34)) % 0.27/0.98 (define @t327 () (= @t34 @t57)) % 0.27/0.98 (define @t328 () (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t324 @t310 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t110 @t307 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) % 0.27/0.98 (define @t329 () (@list @t34 @t310 @t57 @t307)) % 0.27/0.98 (define @t330 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t308 @t310 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.27/0.98 (define @t331 () (@var "V_dB1_H" $$unsorted)) % 0.27/0.98 (define @t332 () (@var "V_dB2_H" $$unsorted)) % 0.27/0.98 (define @t333 () (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp @t331) @t332)) % 0.27/0.98 (define @t334 () (not (= @t301 @t333))) % 0.27/0.98 (define @t335 () (@list @t300 @t299 @t331 @t332)) % 0.27/0.98 (define @t336 () (not (= @t311 @t321))) % 0.27/0.98 (define @t337 () (@list @t144 @t57 @t307)) % 0.27/0.98 (define @t338 () (= @t307 @t292)) % 0.27/0.98 (define @t339 () (not (= @t324 @t321))) % 0.27/0.98 (define @t340 () (@list @t34 @t57 @t307)) % 0.27/0.98 (define @t341 () (@list @t97 @t96 @t93 @t297 @t1)) % 0.27/0.98 (define @t342 () (@list @t13 @t59)) % 0.27/0.98 (define @t343 () (tptp.c_List_Ofoldl @t40 @t3 @t151 @t1 @t39)) % 0.27/0.98 (define @t344 () (forall (@list @t40 @t3 @t39 @t1) (= @t343 @t3))) % 0.27/0.98 (define @t345 () (tptp.hAPP @t263 @t184)) % 0.27/0.98 (define @t346 () (tptp.c_Lambda_OdB_OVar tptp.v_n____)) % 0.27/0.98 (define @t347 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t346 tptp.v_rs____ tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.27/0.98 (define @t348 () (@var "V_v" $$unsorted)) % 0.27/0.98 (define @t349 () (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t330) @t348)))) % 0.27/0.98 (define @t350 () (tptp.c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @t116 @t310 @t348)) % 0.27/0.98 (define @t351 () (@list @t97 @t96 @t93 @t300 @t299 @t1)) % 0.27/0.98 (define @t352 () (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t324 @t292 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) % 0.27/0.98 (define @t353 () (@list @t34)) % 0.27/0.98 (define @t354 () (tptp.hAPP tptp.c_Lambda_OdB_OApp @t147)) % 0.27/0.98 (define @t355 () (tptp.hAPP tptp.c_Lambda_Osubst @t347)) % 0.27/0.98 (define @t356 () (tptp.hAPP @t355 tptp.v_u____)) % 0.27/0.98 (define @t357 () (tptp.hAPP @t356 tptp.v_i____)) % 0.27/0.98 (define @t358 () (tptp.hAPP tptp.c_InductTermi_OIT @t357)) % 0.27/0.98 (define @t359 () (tptp.hBOOL @t358)) % 0.27/0.98 (define @t360 () (@var "T_1" $$unsorted)) % 0.27/0.98 (define @t361 () (@var "T_2" $$unsorted)) % 0.27/0.98 (define @t362 () (tptp.tc_fun @t361 @t360)) % 0.27/0.98 (define @t363 () (@list @t361 @t360)) % 0.27/0.98 (define @t364 () (@var "V_Y" $$unsorted)) % 0.27/0.98 (define @t365 () (@var "V_X" $$unsorted)) % 0.27/0.98 (assume @p1 (forall (@list @t1 @t5 @t3) (or @t9 @t8 (not (= @t5 (tptp.hAPP @t7 @t3))) @t4))) % 0.27/0.98 (assume @p2 (forall @t15 (or @t14 (not (tptp.hBOOL (tptp.hAPP @t10 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs @t12) (tptp.c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @t10) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) @t11))) % 0.27/0.98 (assume @p3 (forall @t15 (or (not (tptp.hBOOL (tptp.hAPP @t10 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs @t17) (tptp.c_ListApplication_Osko__ListApplication__Xlem__1__4 @t10) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) @t16 @t14))) % 0.27/0.98 (assume @p4 (forall @t25 (or (tptp.c_Type_Otyping @t21 @t13 (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun @t24 @t18 tptp.tc_Type_Otype tptp.tc_Type_Otype)) @t23))) % 0.27/0.98 (assume @p5 (forall @t25 (or (tptp.c_Type_Otyping @t21 @t13 (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun @t26 @t18 tptp.tc_Type_Otype tptp.tc_Type_Otype)) @t23))) % 0.27/0.98 (assume @p6 (forall @t27 (or (tptp.c_Type_Otypings @t21 @t19 @t26) @t23))) % 0.27/0.98 (assume @p7 (forall @t27 (or (tptp.c_Type_Otypings @t21 @t19 @t24) @t23))) % 0.27/0.98 (assume @p8 (forall (@list @t34 @t31 @t5 @t32 @t1 @t29) (or @t38 @t36 @t35))) % 0.27/0.98 (assume @p9 (forall (@list @t40 @t29 @t32 @t39 @t3 @t1) (= (tptp.c_List_Ofoldr @t40 @t41 @t3 @t39 @t1) (tptp.c_List_Ofoldr @t40 @t29 (tptp.c_List_Ofoldr @t40 @t32 @t3 @t39 @t1) @t39 @t1)))) % 0.27/0.98 (assume @p10 (forall @t45 (or @t44 (= @t43 (tptp.hAPP @t42 @t5))))) % 0.27/0.98 (assume @p11 (forall @t52 (or @t51 (= @t50 @t48)))) % 0.27/0.98 (assume @p12 (forall (@list @t1 @t3 @t53) (or @t44 (= @t56 @t55)))) % 0.27/0.98 (assume @p13 (forall @t64 (or @t63 @t58))) % 0.27/0.98 (assume @p14 (forall (@list @t32 @t1) (= @t32 @t65))) % 0.27/0.98 (assume @p15 (forall (@list @t1 @t32) (= @t65 @t32))) % 0.27/0.98 (assume @p16 (forall @t67 (= @t29 @t66))) % 0.27/0.98 (assume @p17 (forall @t68 (= @t5 (tptp.c_List_Oappend @t28 @t5 @t1)))) % 0.27/0.98 (assume @p18 (forall @t67 (= @t66 @t29))) % 0.27/0.98 (assume @p19 (forall @t76 (or @t75 @t73 @t71 @t69))) % 0.27/0.98 (assume @p20 (forall (@list @t34 @t1 @t5 @t80 @t31) (or (tptp.hBOOL (tptp.hAPP @t78 @t80)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t77 @t31) @t80))) (not @t79)))) % 0.27/0.98 (assume @p21 (forall (@list @t34 @t1 @t5) (tptp.hBOOL (tptp.hAPP @t78 @t5)))) % 0.27/0.98 (assume @p22 (forall (@list @t34 @t1 @t3) (tptp.hBOOL (tptp.hAPP @t81 @t3)))) % 0.27/0.98 (assume @p23 (tptp.c_Type_Otyping tptp.v_ea______ tptp.v_ua______ tptp.v_T____)) % 0.27/0.98 (assume @p24 (forall @t85 (or (not (= @t84 (tptp.c_List_Oappend @t29 @t82 @t1))) @t83))) % 0.27/0.98 (assume @p25 (forall (@list @t32 @t29 @t1 @t82) (or (not (= (tptp.c_List_Oappend @t32 @t29 @t1) (tptp.c_List_Oappend @t82 @t29 @t1))) @t83))) % 0.27/0.98 (assume @p26 (forall (@list @t86 @t1) (tptp.c_List_Olistsp @t86 @t28 @t1))) % 0.27/0.98 (assume @p27 (forall (@list @t34 @t31 @t87 @t5 @t1) (or (not (tptp.hBOOL (tptp.hAPP @t37 @t87))) (tptp.c_ListOrder_Ostep1 @t34 (tptp.c_List_Olist_OCons @t31 @t5 @t1) (tptp.c_List_Olist_OCons @t87 @t5 @t1) @t1)))) % 0.27/0.98 (assume @p28 (forall (@list @t5 @t31 @t29 @t32 @t34 @t1) (or @t91 @t90 @t89))) % 0.27/0.98 (assume @p29 (forall @t98 (= (tptp.c_Lambda_OdB_OdB__case @t97 @t96 @t93 @t95 @t1) @t94))) % 0.27/0.98 (assume @p30 (forall @t76 (or @t103 @t99 @t71 @t69))) % 0.27/0.98 (assume @p31 (forall (@list @t86 @t32 @t1 @t29) (or @t106 @t105))) % 0.27/0.98 (assume @p32 (forall (@list @t86 @t29 @t1 @t32) (or @t107 @t105))) % 0.27/0.98 (assume @p33 (forall (@list @t57 @t108) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t62 @t110) (tptp.c_Lambda_OdB_OAbs @t108))) @t109))) % 0.27/0.98 (assume @p34 (forall (@list @t34 @t5 @t112 @t1 @t111) (or (tptp.c_ListOrder_Ostep1 @t34 (tptp.c_List_Oappend @t5 @t112 @t1) (tptp.c_List_Oappend @t5 @t111 @t1) @t1) (not (tptp.c_ListOrder_Ostep1 @t34 @t112 @t111 @t1))))) % 0.27/0.98 (assume @p35 (forall (@list @t34 @t32 @t29 @t1 @t5) (or @t115 (tptp.c_ListOrder_Ostep1 @t34 (tptp.c_List_Oappend @t32 @t5 @t1) @t113 @t1)))) % 0.27/0.98 (assume @p36 (forall (@list @t13 @t57 @t116) (= (tptp.c_Lambda_Osubstn @t13 @t57 @t116) (tptp.hAPP (tptp.hAPP @t60 (tptp.c_Lambda_Oliftn @t116 @t57 @t101)) @t116)))) % 0.27/0.98 (assume @p37 (forall @t119 (or @t118 (= (tptp.hAPP @t117 @t2) @t2)))) % 0.27/0.98 (assume @p38 (forall (@list @t21 @t13 @t19 @t18 @t120) (or @t22 @t121 (not (tptp.c_Type_Otyping @t21 @t13 (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun @t120 @t18 tptp.tc_Type_Otype tptp.tc_Type_Otype)))))) % 0.27/0.98 (assume @p39 (forall (@list @t1 @t5 @t80 @t31) (or @t124 (tptp.c_HOL_Oord__class_Oless @t5 @t80 @t1) (not (tptp.c_HOL_Oord__class_Oless @t31 @t80 @t1)) @t123))) % 0.27/0.98 (assume @p40 (forall (@list @t1 @t80 @t5 @t31) (or @t127 (tptp.c_HOL_Oord__class_Oless @t80 @t5 @t1) (not (tptp.c_HOL_Oord__class_Oless @t80 @t31 @t1)) @t126))) % 0.27/0.98 (assume @p41 (forall @t129 (or @t44 (= @t128 (tptp.hAPP (tptp.hAPP @t6 @t43) @t80))))) % 0.27/0.98 (assume @p42 (forall @t129 (or @t131 (= @t128 (tptp.hAPP @t42 @t130))))) % 0.27/0.98 (assume @p43 (forall @t137 (or @t51 @t136))) % 0.27/0.98 (assume @p44 (forall @t137 (or @t51 (= @t133 (tptp.hAPP @t47 @t56))))) % 0.27/0.98 (assume @p45 (forall @t137 (or @t138 @t136))) % 0.27/0.98 (assume @p46 (forall @t143 (or @t44 (= @t142 (tptp.hAPP @t140 @t139))))) % 0.27/0.98 (assume @p47 (forall @t137 (or @t44 (= @t135 (tptp.hAPP @t140 @t46))))) % 0.27/0.98 (assume @p48 (forall @t143 (or @t44 (= @t142 (tptp.hAPP @t54 (tptp.hAPP @t49 @t139)))))) % 0.27/0.98 (assume @p49 (forall @t137 (or @t44 @t136))) % 0.27/0.98 (assume @p50 (forall @t145 (not (tptp.c_HOL_Oord__class_Oless @t144 @t101 tptp.tc_nat)))) % 0.27/0.98 (assume @p51 (forall @t146 (not (tptp.c_HOL_Oord__class_Oless @t116 @t101 tptp.tc_nat)))) % 0.27/0.98 (assume @p52 (forall (@list @t1 @t5 @t31 @t80 @t147) (or @t131 (not (= @t128 (tptp.hAPP @t42 @t147))) (= @t130 @t147)))) % 0.27/0.98 (assume @p53 (forall (@list @t10 @t148 @t39 @t150 @t1 @t149) (= (tptp.hAPP (tptp.c_COMBC @t10 @t148 @t39 @t150 @t1) @t149) (tptp.hAPP (tptp.hAPP @t10 @t149) @t148)))) % 0.27/0.98 (assume @p54 (forall (@list @t40 @t39 @t3 @t1) (= (tptp.c_List_Ofoldr @t40 @t151 @t3 @t39 @t1) @t3))) % 0.27/0.98 (assume @p55 (forall (@list @t40 @t39 @t1) (= @t152 @t28))) % 0.27/0.98 (assume @p56 (forall (@list @t34 @t31 @t5 @t32 @t29 @t1) (or @t38 @t114 @t35))) % 0.27/0.98 (assume @p57 (forall @t76 (or @t103 @t73 @t153 @t69))) % 0.27/0.98 (assume @p58 (forall (@list @t21 @t147 @t59 @t19 @t120 @t18) (or (tptp.c_Type_Otypings @t21 @t154 @t120) (not (tptp.c_Type_Otypings (tptp.c_Type_Oshift @t21 @t59 @t18 tptp.tc_Type_Otype) @t19 @t120)) (not (tptp.c_Type_Otyping @t21 @t147 @t18))))) % 0.27/0.98 (assume @p59 (forall @t52 (or @t157 (tptp.c_HOL_Oord__class_Oless @t50 @t2 @t1) (not (tptp.c_HOL_Oord__class_Oless @t46 @t2 @t1)) @t156))) % 0.27/0.98 (assume @p60 (forall (@list @t5 @t87 @t1 @t82) (= @t160 @t158))) % 0.27/0.98 (assume @p61 (forall (@list @t5 @t29 @t1 @t32) (= (tptp.c_List_Oappend @t88 @t32 @t1) (tptp.c_List_Olist_OCons @t5 @t84 @t1)))) % 0.27/0.98 (assume @p62 (forall (@list @t57 @t13 @t161) (or (tptp.hBOOL (tptp.hAPP @t165 (tptp.hAPP @t163 @t161))) @t162))) % 0.27/0.98 (assume @p63 (forall (@list @t57 @t13 @t108) (or (tptp.hBOOL (tptp.hAPP @t165 (tptp.hAPP @t166 @t13))) @t109))) % 0.27/0.98 (assume @p64 (forall (@list @t1 @t3 @t29) (or @t169 (= @t168 (tptp.hAPP @t49 @t167))))) % 0.27/0.98 (assume @p65 (forall (@list @t40 @t5 @t87 @t39 @t1) (= (tptp.c_List_Omap @t40 (tptp.c_List_Olist_OCons @t5 @t87 @t39) @t39 @t1) (tptp.c_List_Olist_OCons @t170 (tptp.c_List_Omap @t40 @t87 @t39 @t1) @t1)))) % 0.27/0.98 (assume @p66 (forall (@list @t40 @t87 @t171 @t39 @t1) (= (tptp.c_List_Olist_OCons (tptp.hAPP @t40 @t87) (tptp.c_List_Omap @t40 @t171 @t39 @t1) @t1) (tptp.c_List_Omap @t40 (tptp.c_List_Olist_OCons @t87 @t171 @t39) @t39 @t1)))) % 0.27/0.98 (assume @p67 (forall (@list @t40 @t5 @t29 @t39 @t1) (= (tptp.c_List_Omap @t40 @t173 @t39 @t1) (tptp.c_List_Olist_OCons @t170 @t172 @t1)))) % 0.27/0.98 (assume @p68 (forall @t76 (or @t174 @t73 @t71 @t69))) % 0.27/0.98 (assume @p69 (forall @t129 (or @t9 @t8 (not (= @t43 @t130)) (= @t31 @t80)))) % 0.27/0.98 (assume @p70 (forall @t137 (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add @t1)) @t176 @t175))) % 0.27/0.98 (assume @p71 (forall @t137 (or @t177 @t176 @t175))) % 0.27/0.98 (assume @p72 (forall @t178 (or @t177 (not (= @t48 @t55)) @t175))) % 0.27/0.98 (assume @p73 (forall (@list @t5 @t87 @t82 @t1) (= @t158 @t160))) % 0.27/0.98 (assume @p74 (forall (@list @t5 @t179 @t82 @t1) (= (tptp.c_List_Olist_OCons @t5 (tptp.c_List_Oappend @t179 @t82 @t1) @t1) (tptp.c_List_Oappend (tptp.c_List_Olist_OCons @t5 @t179 @t1) @t82 @t1)))) % 0.27/0.98 (assume @p75 (forall (@list @t5 @t87 @t1) (not (= @t159 @t28)))) % 0.27/0.98 (assume @p76 (forall (@list @t181 @t180 @t1) (not (= @t182 @t28)))) % 0.27/0.98 (assume @p77 (forall (@list @t5 @t31 @t34 @t32 @t1 @t29) (or @t91 @t38 @t89))) % 0.27/0.98 (assume @p78 (forall (@list @t1 @t3 @t46 @t53 @t139) (or @t44 (= (tptp.hAPP @t134 @t141) (tptp.hAPP @t140 @t183))))) % 0.27/0.98 (assume @p79 (forall (@list @t57 @t13 @t108 @t161) (or (tptp.hBOOL (tptp.hAPP @t165 (tptp.hAPP @t166 @t161))) @t162 @t109))) % 0.27/0.98 (assume @p80 (forall (@list @t116 @t59 @t184) (or (= (tptp.c_Lambda_Oliftn @t116 @t186 @t184) @t186) @t185))) % 0.27/0.98 (assume @p81 (forall @t189 (or @t188 @t187 @t162))) % 0.27/0.98 (assume @p82 (forall (@list @t21 @t59 @t191 @t19 @t120) (or (tptp.c_Type_Otypings @t192 @t190 @t120) @t121))) % 0.27/0.98 (assume @p83 (forall (@list @t59 @t184) (or (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift @t186) @t184) @t186) @t185))) % 0.27/0.98 (assume @p84 (forall @t196 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t195) @t194)) @t58))) % 0.27/0.98 (assume @p85 (forall (@list @t5 @t13 @t1) (not (= (tptp.c_List_Olist_OCons @t5 @t13 @t1) @t13)))) % 0.27/0.98 (assume @p86 (forall (@list @t29 @t5 @t1) (not (= @t29 @t88)))) % 0.27/0.98 (assume @p87 (forall @t76 (or @t174 @t99 @t153 @t69))) % 0.27/0.98 (assume @p88 (forall @t199 (or @t198 (= (tptp.c_Lambda_Osubstn @t197 @t57 @t5) (tptp.c_Lambda_Oliftn @t5 @t57 @t101))))) % 0.27/0.98 (assume @p89 (forall (@list @t5 @t29 @t1) (= @t88 @t200))) % 0.27/0.98 (assume @p90 (forall (@list @t202 @t147 @t191 @t59 @t13 @t18) (or (not (tptp.c_Type_Otyping @t202 @t147 @t191)) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift @t202 @t59 @t191 tptp.tc_Type_Otype) @t13 @t18)) (tptp.c_Type_Otyping @t202 @t201 @t18)))) % 0.27/0.98 (assume @p91 (forall (@list @t1 @t40 @t39) (= @t28 @t152))) % 0.27/0.98 (assume @p92 (forall (@list @t32 @t29 @t34 @t1 @t31 @t5) (or @t203 @t114 @t35))) % 0.27/0.98 (assume @p93 (forall @t119 (= @t28 @t204))) % 0.27/0.98 (assume @p94 (forall (@list @t34 @t1) (= (tptp.c_Transitive__Closure_Ortranclp @t77 @t1) @t77))) % 0.27/0.98 (assume @p95 (forall @t205 (or @t44 (= (tptp.hAPP @t117 @t5) @t5)))) % 0.27/0.98 (assume @p96 (forall @t207 (or @t51 @t206))) % 0.27/0.98 (assume @p97 (forall @t205 (or @t9 @t8 (= @t5 (tptp.hAPP @t7 @t2))))) % 0.27/0.98 (assume @p98 (forall @t207 (or @t51 @t208))) % 0.27/0.98 (assume @p99 (forall @t207 (or @t169 @t206))) % 0.27/0.98 (assume @p100 (forall @t207 (or @t169 @t208))) % 0.27/0.98 (assume @p101 (forall @t207 (or @t44 @t208))) % 0.27/0.98 (assume @p102 (forall @t207 (or @t44 @t206))) % 0.27/0.98 (assume @p103 (forall @t211 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t110) @t210)) @t209))) % 0.27/0.98 (assume @p104 (forall (@list @t212 @t3 @t213 @t1) (or (= (tptp.hAPP @t215 @t213) @t3) @t214))) % 0.27/0.98 (assume @p105 (forall (@list @t212 @t213 @t3 @t1) (or (= (tptp.hAPP (tptp.hAPP @t212 @t213) @t3) @t3) @t214))) % 0.27/0.98 (assume @p106 (forall @t207 (or @t118 @t218 (not @t217)))) % 0.27/0.98 (assume @p107 (forall @t207 (or @t118 @t217 @t219))) % 0.27/0.98 (assume @p108 (forall (@list @t1 @t40 @t29 @t39) (or (not (= @t28 @t172)) @t220))) % 0.27/0.98 (assume @p109 (forall @t226 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t62 @t225) @t223)) @t221))) % 0.27/0.98 (assume @p110 (forall @t64 (or @t63 @t221))) % 0.27/0.98 (assume @p111 (forall @t207 (or @t118 (not (= @t216 @t2)) @t4))) % 0.27/0.98 (assume @p112 (forall (@list @t1 @t29 @t3) (or @t138 (= (tptp.c_List_Ofoldr @t6 @t29 @t3 @t1 @t1) @t168)))) % 0.27/0.98 (assume @p113 (forall (@list @t34 @t1 @t5 @t31) (or @t79 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t34 @t5) @t31)))))) % 0.27/0.98 (assume @p114 (forall (@list @t34 @t1 @t29) (not (tptp.c_ListOrder_Ostep1 @t34 @t28 @t29 @t1)))) % 0.27/0.98 (assume @p115 (forall (@list @t34 @t29 @t1) (not (tptp.c_ListOrder_Ostep1 @t34 @t29 @t28 @t1)))) % 0.27/0.98 (assume @p116 (forall @t207 (or @t118 @t227 @t156))) % 0.27/0.98 (assume @p117 (forall @t207 (or @t118 @t155 @t228))) % 0.27/0.98 (assume @p118 (forall @t207 (or @t229 @t155 @t228))) % 0.27/0.98 (assume @p119 (forall @t207 (or @t229 @t227 @t156))) % 0.27/0.98 (assume @p120 (forall (@list @t1 @t5 @t82) (or @t169 (= (tptp.hAPP @t7 (tptp.c_List_Ofoldl @t6 @t2 @t82 @t1 @t1)) (tptp.c_List_Ofoldl @t6 @t5 @t82 @t1 @t1))))) % 0.27/0.98 (assume @p121 (forall (@list @t230 @t13 @t18 @t191) (or (tptp.c_Type_Otyping @t230 @t210 @t231) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift @t230 @t101 @t18 tptp.tc_Type_Otype) @t13 @t191))))) % 0.27/0.98 (assume @p122 (forall (@list @t21 @t5 @t18 @t1) (= (tptp.hAPP (tptp.c_Type_Oshift @t21 @t5 @t18 @t1) @t5) @t18))) % 0.27/0.98 (assume @p123 (forall @t234 (or (= (tptp.c_Lambda_Osubstn @t186 @t57 @t184) @t186) @t233 @t232))) % 0.27/0.98 (assume @p124 (forall @t242 (or @t241 @t239 (not (tptp.c_Type_Otyping @t21 @t147 @t237)) @t238 (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift @t21 @t59 @t237 tptp.tc_Type_Otype) @t13 @t236)) @t235))) % 0.27/0.98 (assume @p125 (forall @t242 (or @t241 @t239 (not (tptp.c_Type_Otyping @t21 @t147 @t240)) @t238 (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift @t21 @t59 @t240 tptp.tc_Type_Otype) @t13 @t236)) @t235))) % 0.27/0.98 (assume @p126 (forall @t245 (or @t244 @t243))) % 0.27/0.98 (assume @p127 (forall @t245 (or @t244 @t246))) % 0.27/0.98 (assume @p128 (forall (@list @t92 @t247) (or (not (= @t95 @t248)) (= @t92 @t247)))) % 0.27/0.98 (assume @p129 (forall @t250 (or @t249 @t243))) % 0.27/0.98 (assume @p130 (forall @t250 (or @t249 @t246))) % 0.27/0.98 (assume @p131 (forall @t76 (or @t75 @t99 @t71 @t69))) % 0.27/0.98 (assume @p132 (forall (@list @t5) (not @t198))) % 0.27/0.98 (assume @p133 (forall @t146 (not (tptp.c_HOL_Oord__class_Oless @t116 @t116 tptp.tc_nat)))) % 0.27/0.98 (assume @p134 (forall @t205 (or @t127 @t251))) % 0.27/0.98 (assume @p135 (forall @t205 (or @t252 @t251))) % 0.27/0.98 (assume @p136 (forall @t205 (or @t124 @t251))) % 0.27/0.98 (assume @p137 (forall @t211 (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t253) (tptp.hAPP @t222 @t101))))) % 0.27/0.98 (assume @p138 (forall @t196 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t62 @t195) @t194)) @t221))) % 0.27/0.98 (assume @p139 (forall @t52 (or @t157 (tptp.c_HOL_Oord__class_Oless @t2 @t50 @t1) (not (tptp.c_HOL_Oord__class_Oless @t2 @t46 @t1)) @t219))) % 0.27/0.98 (assume @p140 (forall @t254 (or @t114 @t90 @t89))) % 0.27/0.98 (assume @p141 (forall (@list @t212 @t3 @t46 @t53 @t1) (or (= (tptp.hAPP (tptp.hAPP @t212 (tptp.hAPP @t215 @t46)) @t53) (tptp.hAPP @t215 (tptp.hAPP (tptp.hAPP @t212 @t46) @t53))) @t255))) % 0.27/0.98 (assume @p142 (forall (@list @t40 @t29 @t32 @t39 @t1) (= (tptp.c_List_Omap @t40 @t41 @t39 @t1) (tptp.c_List_Oappend @t172 (tptp.c_List_Omap @t40 @t32 @t39 @t1) @t1)))) % 0.27/0.98 (assume @p143 (forall @t76 (or @t103 @t73 @t71 @t69))) % 0.27/0.98 (assume @p144 (forall @t256 (or @t229 @t125 @t122 @t91))) % 0.27/0.98 (assume @p145 (forall @t45 (or @t252 @t91 @t125 @t122))) % 0.27/0.98 (assume @p146 (forall (@list @t116 @t144) (or @t259 @t258 @t257))) % 0.27/0.98 (assume @p147 (forall (@list @t10 @t116 @t144) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t10 @t116) @t144)) @t259 @t257 @t258))) % 0.27/0.98 (assume @p148 (forall (@list @t31 @t5) (or (tptp.c_HOL_Oord__class_Oless @t31 @t5 tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless @t5 @t31 tptp.tc_nat) @t91))) % 0.27/0.98 (assume @p149 (forall @t256 (or @t252 @t125 @t122 @t91))) % 0.27/0.98 (assume @p150 (forall @t256 (or @t252 @t125 @t91 @t122))) % 0.27/0.98 (assume @p151 (forall @t45 (or @t252 @t91 @t122 @t125))) % 0.27/0.98 (assume @p152 (forall (@list @t1 @t3 @t53 @t46 @t139) (or @t262 (tptp.c_HOL_Oord__class_Oless @t56 @t183 @t1) (not (tptp.c_HOL_Oord__class_Oless @t53 @t139 @t1)) @t261))) % 0.27/0.98 (assume @p153 (forall (@list @t1 @t181 @t180) (not (= @t28 @t182)))) % 0.27/0.98 (assume @p154 (forall (@list @t230 @t57 @t13 @t191 @t18) (or (tptp.c_Type_Otyping @t230 @t164 @t191) (not (tptp.c_Type_Otyping @t230 @t13 @t18)) (not (tptp.c_Type_Otyping @t230 @t57 @t231))))) % 0.27/0.98 (assume @p155 (forall (@list @t1 @t29) (or @t169 (= (tptp.c_List_Ofoldl @t6 @t2 @t29 @t1 @t1) @t167)))) % 0.27/0.98 (assume @p156 (forall @t76 (or @t174 @t73 @t153 @t69))) % 0.27/0.98 (assume @p157 (forall (@list @t32 @t29 @t31 @t5 @t34 @t1) (or @t203 @t36 @t35))) % 0.27/0.98 (assume @p158 (forall (@list @t13 @t19 @t59) (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift @t20) @t59) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t264 @t190 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) % 0.27/0.98 (assume @p159 (forall @t146 (or (tptp.c_HOL_Oord__class_Oless @t101 @t116 tptp.tc_nat) (= @t116 @t101)))) % 0.27/0.98 (assume @p160 (forall (@list @t86 @t29 @t32 @t1) (or @t104 (not @t106) (not @t107)))) % 0.27/0.98 (assume @p161 (forall @t98 (= (tptp.c_Lambda_OdB_OdB__rec @t97 @t96 @t93 @t95 @t1) (tptp.hAPP @t94 (tptp.c_Lambda_OdB_OdB__rec @t97 @t96 @t93 @t92 @t1))))) % 0.27/0.98 (assume @p162 (forall (@list @t13 @t184) (= (tptp.c_Lambda_Oliftn @t101 @t13 @t184) @t13))) % 0.27/0.98 (assume @p163 (not (tptp.c_HOL_Oord__class_Oless @t101 @t101 tptp.tc_nat))) % 0.27/0.98 (assume @p164 (forall @t119 (or @t265 (tptp.c_OrderedGroup_Osemigroup__add @t6 @t1)))) % 0.27/0.98 (assume @p165 (forall (@list @t21 @t59 @t18 @t1 @t266) (or (= (tptp.hAPP (tptp.c_Type_Oshift @t21 @t59 @t18 @t1) @t266) (tptp.hAPP @t21 @t266)) @t267))) % 0.27/0.98 (assume @p166 (forall (@list @t191 @t18 @t21 @t111 @t59 @t19 @t120) (or (= @t191 (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun @t271 @t18 tptp.tc_Type_Otype tptp.tc_Type_Otype)) @t270 @t121 @t269))) % 0.27/0.98 (assume @p167 (forall (@list @t13 @t57) (= (tptp.c_Lambda_Osubstn @t13 @t57 @t101) (tptp.hAPP @t61 @t101)))) % 0.27/0.98 (assume @p168 (forall @t178 (or (not (tptp.class_Ring__and__Field_Oordered__semidom @t1)) (tptp.c_HOL_Oord__class_Oless @t46 @t56 @t1) (not (tptp.c_HOL_Oord__class_Oless @t46 @t53 @t1)) @t219))) % 0.27/0.98 (assume @p169 (forall (@list @t40 @t5 @t29 @t39 @t3 @t1) (= (tptp.c_List_Ofoldr @t40 @t173 @t3 @t39 @t1) (tptp.hAPP @t170 (tptp.c_List_Ofoldr @t40 @t29 @t3 @t39 @t1))))) % 0.27/0.98 (assume @p170 (forall (@list @t10 @t97 @t96 @t93 @t92) (or (not (tptp.hBOOL (tptp.hAPP @t10 (tptp.c_Lambda_OdB_OdB__case @t97 @t96 @t93 @t95 tptp.t_a)))) (tptp.hBOOL (tptp.hAPP @t10 @t94))))) % 0.27/0.98 (assume @p171 (forall (@list @t10 @t97 @t96 @t93 @t87) (or (not (tptp.hBOOL (tptp.hAPP @t10 (tptp.c_Lambda_OdB_OdB__case @t97 @t96 @t93 (tptp.c_Lambda_OdB_OAbs @t87) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP @t10 (tptp.hAPP @t93 @t87)))))) % 0.27/0.98 (assume @p172 (forall @t250 (or (not (= @t84 @t29)) @t246))) % 0.27/0.98 (assume @p173 (forall @t250 (or (not (= @t29 @t84)) @t246))) % 0.27/0.98 (assume @p174 (forall @t250 (or (not (= @t84 @t32)) @t243))) % 0.27/0.98 (assume @p175 (forall (@list @t32 @t29 @t1) (or (not (= @t32 @t84)) @t243))) % 0.27/0.98 (assume @p176 (forall @t277 (or @t276 (= @t273 @t272)))) % 0.27/0.98 (assume @p177 (forall @t277 (or @t276 (= @t275 @t274)))) % 0.27/0.98 (assume @p178 (forall (@list @t1 @t5 @t29) (= @t200 @t88))) % 0.27/0.98 (assume @p179 (forall @t279 (or @t262 @t278 @t261))) % 0.27/0.98 (assume @p180 (forall @t279 (or @t280 @t278 @t261))) % 0.27/0.98 (assume @p181 (forall @t137 (or @t280 @t260 (not @t278)))) % 0.27/0.98 (assume @p182 (forall @t282 (or @t262 @t281 @t261))) % 0.27/0.98 (assume @p183 (forall @t282 (or @t280 @t281 @t261))) % 0.27/0.98 (assume @p184 (forall @t137 (or @t280 @t260 (not @t281)))) % 0.27/0.98 (assume @p185 (forall @t76 (or @t174 @t99 @t71 @t69))) % 0.27/0.98 (assume @p186 (forall @t285 (or @t284 (= @t3 @t181)))) % 0.27/0.98 (assume @p187 (forall @t285 (or @t284 (= @t283 @t180)))) % 0.27/0.98 (assume @p188 (forall @t189 (or @t188 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t13) @t161))) @t187))) % 0.27/0.98 (assume @p189 (forall @t254 (or @t114 @t38 @t89))) % 0.27/0.98 (assume @p190 (forall (@list @t34 @t5 @t32 @t1 @t29) (or (tptp.c_ListOrder_Ostep1 @t34 (tptp.c_List_Olist_OCons @t5 @t32 @t1) @t88 @t1) @t115))) % 0.27/0.98 (assume @p191 (forall (@list @t40 @t29 @t39 @t1) (or (not (= @t172 @t28)) @t220))) % 0.27/0.98 (assume @p192 (forall @t287 (or @t286 @t90))) % 0.27/0.98 (assume @p193 (forall @t287 (or @t286 @t91))) % 0.27/0.98 (assume @p194 (tptp.c_Type_Otyping tptp.v_e____ tptp.v_u____ tptp.v_T____)) % 0.27/0.98 (assume @p195 (forall @t119 (= @t204 @t28))) % 0.27/0.98 (assume @p196 (forall (@list @t19) (or (tptp.c_List_Olistsp tptp.c_InductTermi_OIT (tptp.c_List_Omap (tptp.c_COMBC tptp.c_Lambda_Olift @t101 tptp.tc_Lambda_OdB tptp.tc_nat tptp.tc_Lambda_OdB) @t19 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB) (not (tptp.c_List_Olistsp tptp.c_InductTermi_OIT @t19 tptp.tc_Lambda_OdB))))) % 0.27/0.98 (assume @p197 (forall @t85 (= (tptp.c_List_Oappend @t84 @t82 @t1) (tptp.c_List_Oappend @t29 (tptp.c_List_Oappend @t32 @t82 @t1) @t1)))) % 0.27/0.98 (assume @p198 (forall (@list @t29 @t179 @t111 @t1) (= (tptp.c_List_Oappend @t29 (tptp.c_List_Oappend @t179 @t111 @t1) @t1) (tptp.c_List_Oappend (tptp.c_List_Oappend @t29 @t179 @t1) @t111 @t1)))) % 0.27/0.98 (assume @p199 (forall (@list @t82 @t5 @t1 @t32) (= (tptp.c_List_Oappend (tptp.c_List_Oappend @t82 @t5 @t1) @t32 @t1) (tptp.c_List_Oappend @t82 (tptp.c_List_Oappend @t5 @t32 @t1) @t1)))) % 0.27/0.98 (assume @p200 (forall (@list @t29 @t5 @t19 @t1) (= (tptp.c_List_Oappend @t29 (tptp.c_List_Oappend @t5 @t19 @t1) @t1) (tptp.c_List_Oappend @t113 @t19 @t1)))) % 0.27/0.98 (assume @p201 (forall (@list @t21 @t59 @t191 @t13 @t18) (or (tptp.c_Type_Otyping @t192 @t264 @t18) @t187))) % 0.27/0.98 (assume @p202 (forall @t52 (or @t127 @t261 @t288))) % 0.27/0.98 (assume @p203 (forall @t290 (or @t289 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t77 @t46) @t53))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t34 @t3) @t46)))))) % 0.27/0.98 (assume @p204 (forall @t290 (or @t289 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t34 @t46) @t53))) (not (tptp.hBOOL (tptp.hAPP @t81 @t46)))))) % 0.27/0.98 (assume @p205 (forall @t45 (or @t252 @t123 @t126))) % 0.27/0.98 (assume @p206 (forall @t256 (or @t124 @t126 @t123))) % 0.27/0.98 (assume @p207 (forall (@list @t1 @t46 @t3) (or @t124 @t288 @t261))) % 0.27/0.98 (assume @p208 (forall @t15 (or (tptp.hBOOL (tptp.hAPP @t10 @t17)) @t16 @t14))) % 0.27/0.98 (assume @p209 (forall (@list @t212 @t5 @t31 @t82 @t1) (or (= (tptp.c_List_Ofoldl @t212 (tptp.hAPP @t291 @t31) @t82 @t1 @t1) (tptp.hAPP @t291 (tptp.c_List_Ofoldl @t212 @t31 @t82 @t1 @t1))) @t255))) % 0.27/0.98 (assume @p210 (forall (@list @t34 @t57) (= @t293 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t293 @t292 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) % 0.27/0.98 (assume @p211 (forall @t296 (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst @t295) @t57) @t184) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.hAPP @t61 @t184)) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst @t147) @t57) @t184))))) % 0.27/0.98 (assume @p212 (forall (@list @t247 @t297) (not (= @t248 @t298)))) % 0.27/0.98 (assume @p213 (forall (@list @t300 @t299 @t247) (not (= @t301 @t248)))) % 0.27/0.98 (assume @p214 (forall (@list @t21 @t19 @t18 @t59) (or (tptp.c_Type_Otypings @t21 @t19 @t303) @t302))) % 0.27/0.98 (assume @p215 (forall (@list @t297 @t304) (or (not (= @t298 (tptp.c_Lambda_OdB_OVar @t304))) (= @t297 @t304)))) % 0.27/0.98 (assume @p216 (forall (@list @t10 @t97 @t96 @t93 @t305) (or (not (tptp.hBOOL (tptp.hAPP @t10 (tptp.c_Lambda_OdB_OdB__case @t97 @t96 @t93 (tptp.c_Lambda_OdB_OVar @t305) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP @t10 (tptp.hAPP @t97 @t305)))))) % 0.27/0.98 (assume @p217 (forall (@list @t10 @t97 @t96 @t93 @t297) (or (not (tptp.hBOOL (tptp.hAPP @t10 (tptp.c_Lambda_OdB_OdB__case @t97 @t96 @t93 @t298 tptp.t_a)))) (tptp.hBOOL (tptp.hAPP @t10 @t306))))) % 0.27/0.98 (assume @p218 (forall (@list @t247 @t300 @t299) (not (= @t248 @t301)))) % 0.27/0.98 (assume @p219 (forall @t313 (or @t312 @t257))) % 0.27/0.98 (assume @p220 (forall @t313 (or @t312 @t314))) % 0.27/0.98 (assume @p221 @t316) % 0.27/0.98 (assume @p222 (forall (@list @t10 @t97 @t96 @t93 @t171 @t317) (or (not (tptp.hBOOL (tptp.hAPP @t10 (tptp.c_Lambda_OdB_OdB__case @t97 @t96 @t93 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp @t171) @t317) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP @t10 (tptp.hAPP (tptp.hAPP @t96 @t171) @t317)))))) % 0.27/0.98 (assume @p223 (forall (@list @t10 @t97 @t96 @t93 @t300 @t299) (or (not (tptp.hBOOL (tptp.hAPP @t10 (tptp.c_Lambda_OdB_OdB__case @t97 @t96 @t93 @t301 tptp.t_a)))) (tptp.hBOOL (tptp.hAPP @t10 @t318))))) % 0.27/0.98 (assume @p224 (forall (@list @t34 @t59 @t266) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP @t224 @t186) @t266))) @t319))) % 0.27/0.98 (assume @p225 (forall (@list @t266 @t147 @t59) (or (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst @t320) @t147) @t59) @t320) @t267))) % 0.27/0.98 (assume @p226 (forall @t323 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP @t62 @t322) @t321)) @t221))) % 0.27/0.98 (assume @p227 (forall (@list @t34 @t57 @t13) (or (not (= @t293 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t13 @t292 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= @t293 @t13)))) % 0.27/0.98 (assume @p228 (forall (@list @t59 @t13) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t186) @t13))))) % 0.27/0.98 (assume @p229 (forall @t326 (or @t325 (= @t57 @t324)))) % 0.27/0.98 (assume @p230 (forall @t329 (or @t328 @t327))) % 0.27/0.98 (assume @p231 (forall @t329 (or @t328 @t314))) % 0.27/0.98 (assume @p232 (forall (@list @t116 @t310) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t330)) (not (tptp.c_List_Olistsp tptp.c_InductTermi_OIT @t310 tptp.tc_Lambda_OdB))))) % 0.27/0.98 (assume @p233 (forall @t335 (or @t334 (= @t300 @t331)))) % 0.27/0.98 (assume @p234 (forall @t335 (or @t334 (= @t299 @t332)))) % 0.27/0.98 (assume @p235 (forall (@list @t18 @t191 @t21 @t59 @t19) (or (= @t18 @t191) @t270 @t302))) % 0.27/0.98 (assume @p236 (forall (@list @t34 @t310 @t307) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t34 @t310 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) @t322)) (not (tptp.c_ListOrder_Ostep1 tptp.c_Lambda_Obeta @t310 @t307 tptp.tc_Lambda_OdB))))) % 0.27/0.98 (assume @p237 (forall @t15 (or @t14 (tptp.hBOOL (tptp.hAPP @t10 @t12)) @t11))) % 0.27/0.98 (assume @p238 (forall @t323 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t322) @t321)) @t58))) % 0.27/0.98 (assume @p239 (forall @t337 (or @t336 (= @t311 @t57)))) % 0.27/0.98 (assume @p240 (forall @t340 (or @t339 @t338))) % 0.27/0.98 (assume @p241 (forall @t341 (= (tptp.c_Lambda_OdB_OdB__rec @t97 @t96 @t93 @t298 @t1) @t306))) % 0.27/0.98 (assume @p242 (forall (@list @t297 @t331 @t332) (not (= @t298 @t333)))) % 0.27/0.98 (assume @p243 (forall (@list @t116 @t19 @t34 @t307) (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t308 @t19 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t324 @t307 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))))) % 0.27/0.98 (assume @p244 (forall @t342 (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t264)) @t235))) % 0.27/0.98 (assume @p245 @t344) % 0.27/0.98 (assume @p246 (forall @t340 (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 @t324) @t57) @t307 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t57))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP @t224 @t57) @t101) @t307 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))))))) % 0.27/0.98 (assume @p247 (forall @t76 (or @t103 @t99 @t153 @t69))) % 0.27/0.98 (assume @p248 (= tptp.v_n____ tptp.v_i____)) % 0.27/0.98 (assume @p249 (forall (@list @t297 @t247) (not (= @t298 @t248)))) % 0.27/0.98 (assume @p250 (forall @t146 (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t308)))) % 0.27/0.98 (assume @p251 (forall (@list @t21 @t59 @t18) (or (= (tptp.hAPP @t21 @t59) @t18) (not (tptp.c_Type_Otyping @t21 @t186 @t18))))) % 0.27/0.98 (assume @p252 (forall (@list @t1 @t5 @t31 @t82) (or @t265 (= (tptp.c_List_Ofoldl @t6 @t43 @t82 @t1 @t1) (tptp.hAPP @t7 (tptp.c_List_Ofoldl @t6 @t31 @t82 @t1 @t1)))))) % 0.27/0.98 (assume @p253 (forall @t76 (or @t75 @t73 @t153 @t69))) % 0.27/0.98 (assume @p254 (forall (@list @t57 @t13 @t184) (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift @t164) @t184) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.hAPP @t193 @t184)) @t345)))) % 0.27/0.98 (assume @p255 (forall (@list @t13 @t19 @t147 @t59) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst @t20) @t147) @t59) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t201 @t154 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) % 0.27/0.98 (assume @p256 (tptp.c_Type_Otyping (tptp.c_Type_Oshift tptp.v_ea______ tptp.v_ia______ tptp.v_T____ tptp.tc_Type_Otype) @t347 tptp.v_T_Ha______)) % 0.27/0.98 (assume @p257 (forall @t226 (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta @t225) @t223)) @t58))) % 0.27/0.98 (assume @p258 (forall @t234 (or (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst @t186) @t57) @t184) @t186) @t233 @t232))) % 0.27/0.98 (assume @p259 (forall (@list @t21 @t59 @t18 @t19) (or (tptp.c_Type_Otyping @t21 @t186 (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun @t303 @t18 tptp.tc_Type_Otype tptp.tc_Type_Otype)) @t302))) % 0.27/0.98 (assume @p260 (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT tptp.v_ua______))) % 0.27/0.98 (assume @p261 (tptp.c_Type_Otyping (tptp.c_Type_Oshift tptp.v_e____ tptp.v_i____ tptp.v_T____ tptp.tc_Type_Otype) @t347 tptp.v_T_H____)) % 0.27/0.98 (assume @p262 (forall (@list @t348 @t116 @t310) (or (= @t348 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t308 @t350 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) @t349))) % 0.27/0.98 (assume @p263 (forall @t351 (= (tptp.c_Lambda_OdB_OdB__case @t97 @t96 @t93 @t301 @t1) @t318))) % 0.27/0.98 (assume @p264 (forall (@list @t212 @t5 @t213 @t82 @t1) (or (= (tptp.hAPP @t291 (tptp.c_List_Ofoldl @t212 @t213 @t82 @t1 @t1)) (tptp.c_List_Ofoldl @t212 @t5 @t82 @t1 @t1)) @t214))) % 0.27/0.98 (assume @p265 (forall @t76 (or @t75 @t99 @t153 @t69))) % 0.27/0.98 (assume @p266 (forall @t145 (= @t311 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t311 @t292 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) % 0.27/0.98 (assume @p267 (forall @t341 (= (tptp.c_Lambda_OdB_OdB__case @t97 @t96 @t93 @t298 @t1) @t306))) % 0.27/0.98 (assume @p268 (forall @t199 (or @t198 (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst @t197) @t57) @t5) @t57)))) % 0.27/0.98 (assume @p269 (forall (@list @t40 @t3 @t5 @t29 @t39 @t1) (= (tptp.c_List_Ofoldl @t40 @t3 @t173 @t1 @t39) (tptp.c_List_Ofoldl @t40 (tptp.hAPP (tptp.hAPP @t40 @t3) @t5) @t29 @t1 @t39)))) % 0.27/0.98 (assume @p270 (forall @t353 (= @t324 @t352))) % 0.27/0.98 (assume @p271 (forall (@list @t34 @t57 @t13 @t19) (or (not (= @t293 @t20)) (= @t34 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t13 (tptp.c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @t34 @t57 @t13 @t19) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (= @t19 @t292)))) % 0.27/0.98 (assume @p272 (forall (@list @t230 @t5) (tptp.c_Type_Otyping @t230 @t197 (tptp.hAPP @t230 @t5)))) % 0.27/0.98 (assume @p273 (forall @t340 (or @t339 (= @t324 @t57)))) % 0.27/0.98 (assume @p274 (= tptp.v_rs____ @t292)) % 0.27/0.98 (assume @p275 (forall @t351 (= (tptp.c_Lambda_OdB_OdB__rec @t97 @t96 @t93 @t301 @t1) (tptp.hAPP (tptp.hAPP @t318 (tptp.c_Lambda_OdB_OdB__rec @t97 @t96 @t93 @t300 @t1)) (tptp.c_Lambda_OdB_OdB__rec @t97 @t96 @t93 @t299 @t1))))) % 0.27/0.98 (assume @p276 (forall (@list @t13) (= @t13 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2 @t13) (tptp.c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1 @t13) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) % 0.27/0.98 (assume @p277 (forall @t326 (or @t325 @t338))) % 0.27/0.98 (assume @p278 (forall (@list @t34 @t19 @t57) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t34 @t19 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp @t57 @t19 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) @t327))) % 0.27/0.98 (assume @p279 (forall (@list @t21 @t111 @t18 @t191 @t59 @t19 @t120) (or (tptp.c_Type_Otypings @t21 @t111 @t271) @t270 @t121 @t269))) % 0.27/0.98 (assume @p280 (forall @t353 (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT @t324)) @t319))) % 0.27/0.98 (assume @p281 (forall (@list @t147 @t57 @t13) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.hAPP @t354 @t57)) (tptp.hAPP @t354 @t13))) @t209))) % 0.27/0.98 (assume @p282 (forall (@list @t57 @t147 @t13) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.hAPP @t163 @t147)) @t295)) @t209))) % 0.27/0.98 (assume @p283 (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT tptp.v_u____))) % 0.27/0.98 (assume @p284 (forall (@list @t116 @t57 @t13 @t184) (= (tptp.c_Lambda_Oliftn @t116 @t164 @t184) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Oliftn @t116 @t57 @t184)) (tptp.c_Lambda_Oliftn @t116 @t13 @t184))))) % 0.27/0.98 (assume @p285 (forall (@list @t13 @t184 @t57) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst @t345) @t57) @t184) @t13))) % 0.27/0.98 (assume @p286 (forall @t353 (= @t352 @t324))) % 0.27/0.98 (assume @p287 (forall @t337 (or @t336 @t338))) % 0.27/0.98 (assume @p288 (forall @t342 (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP @t294 @t186))) @t235))) % 0.27/0.98 (assume @p289 (forall (@list @t310 @t116 @t348) (or (tptp.c_ListOrder_Ostep1 tptp.c_Lambda_Obeta @t310 @t350 tptp.tc_Lambda_OdB) @t349))) % 0.27/0.98 (assume @p290 (forall (@list @t57 @t13 @t116 @t307) (not (= @t253 @t309)))) % 0.27/0.98 (assume @p291 (forall @t296 (= (tptp.c_Lambda_Osubstn @t295 @t57 @t184) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Osubstn @t13 @t57 @t184)) (tptp.c_Lambda_Osubstn @t147 @t57 @t184))))) % 0.27/0.98 (assume @p292 (forall (@list @t40 @t3 @t29 @t32 @t39 @t1) (= (tptp.c_List_Ofoldl @t40 @t3 @t41 @t1 @t39) (tptp.c_List_Ofoldl @t40 (tptp.c_List_Ofoldl @t40 @t3 @t29 @t1 @t39) @t32 @t1 @t39)))) % 0.27/0.98 (assume @p293 (forall (@list @t331 @t332 @t297) (not (= @t333 @t298)))) % 0.27/0.98 (assume @p294 (not @t359)) % 0.27/0.98 (assume @p295 (forall @t363 (or (tptp.class_Orderings_Opreorder @t362) (not (tptp.class_Orderings_Opreorder @t360))))) % 0.27/0.98 (assume @p296 (forall @t363 (or (tptp.class_Orderings_Oorder @t362) (not (tptp.class_Orderings_Oorder @t360))))) % 0.27/0.98 (assume @p297 (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_nat)) % 0.27/0.98 (assume @p298 (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_nat)) % 0.27/0.98 (assume @p299 (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_nat)) % 0.27/0.98 (assume @p300 (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_nat)) % 0.27/0.98 (assume @p301 (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_nat)) % 0.27/0.98 (assume @p302 (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat)) % 0.27/0.98 (assume @p303 (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_nat)) % 0.27/0.98 (assume @p304 (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_nat)) % 0.27/0.98 (assume @p305 (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat)) % 0.27/0.98 (assume @p306 (tptp.class_OrderedGroup_Osemigroup__add tptp.tc_nat)) % 0.27/0.98 (assume @p307 (tptp.class_OrderedGroup_Omonoid__add tptp.tc_nat)) % 0.27/0.98 (assume @p308 (tptp.class_Orderings_Opreorder tptp.tc_nat)) % 0.27/0.98 (assume @p309 (tptp.class_Orderings_Olinorder tptp.tc_nat)) % 0.27/0.98 (assume @p310 (tptp.class_Orderings_Oorder tptp.tc_nat)) % 0.27/0.98 (assume @p311 (tptp.class_Orderings_Opreorder tptp.tc_bool)) % 0.27/0.98 (assume @p312 (tptp.class_Orderings_Oorder tptp.tc_bool)) % 0.27/0.98 (assume @p313 (forall @t68 (tptp.c_fequal @t5 @t5 @t1))) % 0.27/0.98 (assume @p314 (forall (@list @t365 @t364 @t1) (or (= @t365 @t364) (not (tptp.c_fequal @t365 @t364 @t1))))) % 0.27/0.98 (step @p315 :rule evaluate :args ((= false true))) % 0.27/0.98 (step @p316 :rule true_intro :premises (@p283)) % 0.27/0.98 (step @p317 :rule eq-symm :args (@t315 @t147)) % 0.27/0.98 (step @p318 :rule cong :premises (@p317) :args (@t316)) % 0.27/0.98 (step @p319 :rule eq_resolve :premises (@p221 @p318)) % 0.27/0.98 (step @p320 :rule instantiate :premises (@p319) :args ((@list tptp.v_n____ tptp.v_u____))) % 0.27/0.98 (step @p321 :rule symm :premises (@p320)) % 0.27/0.98 (step @p322 :rule symm :premises (@p248)) % 0.27/0.98 (step @p323 :rule refl :args (tptp.v_u____)) % 0.27/0.98 (step @p324 :rule eq-symm :args (@t343 @t3)) % 0.27/0.98 (step @p325 :rule cong :premises (@p324) :args (@t344)) % 0.27/0.98 (step @p326 :rule eq_resolve :premises (@p245 @p325)) % 0.27/0.98 (step @p327 :rule instantiate :premises (@p326) :args ((@list tptp.c_Lambda_OdB_OApp @t346 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) % 0.27/0.98 (step @p328 :rule symm :premises (@p327)) % 0.27/0.98 (step @p329 :rule refl :args (tptp.tc_Lambda_OdB)) % 0.27/0.98 (step @p330 :rule refl :args (@t346)) % 0.27/0.98 (step @p331 :rule refl :args (tptp.c_Lambda_OdB_OApp)) % 0.27/0.98 (step @p332 :rule cong :premises (@p331 @p330 @p274 @p329 @p329) :args (@t347)) % 0.27/0.98 (step @p333 :rule trans :premises (@p332 @p328)) % 0.27/0.98 (step @p334 :rule refl :args (tptp.c_Lambda_Osubst)) % 0.27/0.98 (step @p335 :rule cong :premises (@p334 @p333) :args (@t355)) % 0.27/0.98 (step @p336 :rule cong :premises (@p335 @p323) :args (@t356)) % 0.27/0.98 (step @p337 :rule cong :premises (@p336 @p322) :args (@t357)) % 0.27/0.98 (step @p338 :rule trans :premises (@p337 @p321)) % 0.27/0.98 (step @p339 :rule refl :args (tptp.c_InductTermi_OIT)) % 0.27/0.98 (step @p340 :rule cong :premises (@p339 @p338) :args (@t358)) % 0.27/0.98 (step @p341 :rule cong :premises (@p340) :args (@t359)) % 0.27/0.98 (step @p342 :rule false_intro :premises (@p294)) % 0.27/0.98 (step @p343 :rule symm :premises (@p342)) % 0.27/0.98 (step @p344 :rule trans :premises (@p343 @p341 @p316)) % 0.27/0.98 (step @p345 false :rule eq_resolve :premises (@p344 @p315)) % 0.27/0.98 ) % 0.27/0.98 % SZS output end Proof % 0.27/0.99 % cvc5 exiting %------------------------------------------------------------------------------