TSTP Solution File: LCL817-1 by ConnectPP---0.2.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ConnectPP---0.2.2
% Problem : LCL817-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Mar 6 09:10:30 EST 2024
% Result : Unsatisfiable 8.21s 8.42s
% Output : Proof 8.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL817-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Mar 3 15:27:49 EST 2024
% 0.12/0.34 % CPUTime :
% 8.21/8.42 % SZS status Unsatisfiable for theBenchmark
% 8.21/8.42 % SZS output start Proof for theBenchmark
% 8.21/8.42
% 8.21/8.42 % Problem matrix:
% 8.21/8.42 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 8.21/8.42 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 8.21/8.42 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 8.21/8.42 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( c_List_Oappend(__eqx_0, __eqx_1, __eqx_2) = c_List_Oappend(__eqy_0, __eqy_1, __eqy_2)) )).
% 8.21/8.42 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( c_List_Olist_ONil(__eqx_0) = c_List_Olist_ONil(__eqy_0)) )).
% 8.21/8.42 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( c_List_Olist_OCons(__eqx_0, __eqx_1, __eqx_2) = c_List_Olist_OCons(__eqy_0, __eqy_1, __eqy_2)) )).
% 8.21/8.42 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( hAPP(__eqx_0, __eqx_1) = hAPP(__eqy_0, __eqy_1)) )).
% 8.21/8.42 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( __eqx_4 != __eqy_4) | ( c_List_Ofoldr(__eqx_0, __eqx_1, __eqx_2, __eqx_3, __eqx_4) = c_List_Ofoldr(__eqy_0, __eqy_1, __eqy_2, __eqy_3, __eqy_4)) )).
% 8.21/8.42 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( c_Type_Osko__Type__Xtypes__snocE__1__2(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = c_Type_Osko__Type__Xtypes__snocE__1__2(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 8.21/8.42 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( __eqx_4 != __eqy_4) | ( c_List_Ofoldl(__eqx_0, __eqx_1, __eqx_2, __eqx_3, __eqx_4) = c_List_Ofoldl(__eqy_0, __eqy_1, __eqy_2, __eqy_3, __eqy_4)) )).
% 8.21/8.42 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( c_HOL_Ozero__class_Ozero(__eqx_0) = c_HOL_Ozero__class_Ozero(__eqy_0)) )).
% 8.21/8.42 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( c_HOL_Oplus__class_Oplus(__eqx_0) = c_HOL_Oplus__class_Oplus(__eqy_0)) )).
% 8.21/8.42 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( c_Nat_Osemiring__1__class_Oof__nat(__eqx_0, __eqx_1) = c_Nat_Osemiring__1__class_Oof__nat(__eqy_0, __eqy_1)) )).
% 8.21/8.42 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( c_Predicate_Oconversep(__eqx_0, __eqx_1, __eqx_2) = c_Predicate_Oconversep(__eqy_0, __eqy_1, __eqy_2)) )).
% 8.21/8.42 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( c_Transitive__Closure_Ortranclp(__eqx_0, __eqx_1) = c_Transitive__Closure_Ortranclp(__eqy_0, __eqy_1)) )).
% 8.21/8.42 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( c_fequal(__eqx_0) = c_fequal(__eqy_0)) )).
% 8.21/8.42 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( c_Lambda_OdB_OAbs(__eqx_0) = c_Lambda_OdB_OAbs(__eqy_0)) )).
% 8.21/8.42 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( c_Lambda_OdB_OVar(__eqx_0) = c_Lambda_OdB_OVar(__eqy_0)) )).
% 8.21/8.42 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( c_Type_Osko__Type__Xvar__app__typesE__1__1(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = c_Type_Osko__Type__Xvar__app__typesE__1__1(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 8.21/8.42 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( c_Type_Osko__Type__Xlist__app__typeD__1__1(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = c_Type_Osko__Type__Xlist__app__typeD__1__1(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 8.21/8.42 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( c_Type_Oshift(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = c_Type_Oshift(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 8.21/8.42 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( c_Lambda_Osubst(__eqx_0, __eqx_1, __eqx_2) = c_Lambda_Osubst(__eqy_0, __eqy_1, __eqy_2)) )).
% 8.21/8.42 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( c_Type_Osko__Type__Xlist__app__typeE__1__1(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = c_Type_Osko__Type__Xlist__app__typeE__1__1(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 8.21/8.42 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( c_Type_Osko__Type__Xvar__app__types__1__1(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = c_Type_Osko__Type__Xvar__app__types__1__1(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 8.21/8.42 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(__eqx_0, __eqx_1, __eqx_2) = c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(__eqy_0, __eqy_1, __eqy_2)) )).
% 8.21/8.42 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( c_Type_Osko__Type__Xtyping__elims__2__1(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = c_Type_Osko__Type__Xtyping__elims__2__1(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 8.21/8.42 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( c_Lambda_Olift(__eqx_0, __eqx_1) = c_Lambda_Olift(__eqy_0, __eqy_1)) )).
% 8.21/8.42 cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( tc_fun(__eqx_0, __eqx_1) = tc_fun(__eqy_0, __eqy_1)) )).
% 8.21/8.42 cnf(matrix-28, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~c_List_Olistsp(__eqx_0, __eqx_1, __eqx_2) | c_List_Olistsp(__eqy_0, __eqy_1, __eqy_2) )).
% 8.21/8.42 cnf(matrix-29, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ~c_ListOrder_Ostep1(__eqx_0, __eqx_1, __eqx_2, __eqx_3) | c_ListOrder_Ostep1(__eqy_0, __eqy_1, __eqy_2, __eqy_3) )).
% 8.21/8.42 cnf(matrix-30, plain, ( ( __eqx_0 != __eqy_0) | ~hBOOL(__eqx_0) | hBOOL(__eqy_0) )).
% 8.21/8.42 cnf(matrix-31, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~c_Type_Otyping(__eqx_0, __eqx_1, __eqx_2) | c_Type_Otyping(__eqy_0, __eqy_1, __eqy_2) )).
% 8.21/8.42 cnf(matrix-32, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~c_Type_Otypings(__eqx_0, __eqx_1, __eqx_2) | c_Type_Otypings(__eqy_0, __eqy_1, __eqy_2) )).
% 8.21/8.42 cnf(matrix-33, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Olordered__ab__group__add(__eqx_0) | class_OrderedGroup_Olordered__ab__group__add(__eqy_0) )).
% 8.21/8.42 cnf(matrix-34, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~c_HOL_Oord__class_Oless(__eqx_0, __eqx_1, __eqx_2) | c_HOL_Oord__class_Oless(__eqy_0, __eqy_1, __eqy_2) )).
% 8.21/8.42 cnf(matrix-35, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Ocomm__semiring__1(__eqx_0) | class_Ring__and__Field_Ocomm__semiring__1(__eqy_0) )).
% 8.21/8.42 cnf(matrix-36, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Omonoid__add(__eqx_0) | class_OrderedGroup_Omonoid__add(__eqy_0) )).
% 8.21/8.42 cnf(matrix-37, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Ocomm__monoid__add(__eqx_0) | class_OrderedGroup_Ocomm__monoid__add(__eqy_0) )).
% 8.21/8.42 cnf(matrix-38, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Oidom(__eqx_0) | class_Ring__and__Field_Oidom(__eqy_0) )).
% 8.21/8.42 cnf(matrix-39, plain, ( ( __eqx_0 != __eqy_0) | ~class_Int_Onumber__ring(__eqx_0) | class_Int_Onumber__ring(__eqy_0) )).
% 8.21/8.42 cnf(matrix-40, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Oordered__semidom(__eqx_0) | class_Ring__and__Field_Oordered__semidom(__eqy_0) )).
% 8.21/8.42 cnf(matrix-41, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Ocancel__semigroup__add(__eqx_0) | class_OrderedGroup_Ocancel__semigroup__add(__eqy_0) )).
% 8.21/8.42 cnf(matrix-42, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Ocancel__ab__semigroup__add(__eqx_0) | class_OrderedGroup_Ocancel__ab__semigroup__add(__eqy_0) )).
% 8.21/8.42 cnf(matrix-43, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Opordered__comm__monoid__add(__eqx_0) | class_OrderedGroup_Opordered__comm__monoid__add(__eqy_0) )).
% 8.21/8.42 cnf(matrix-44, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Osemiring__1(__eqx_0) | class_Ring__and__Field_Osemiring__1(__eqy_0) )).
% 8.21/8.42 cnf(matrix-45, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Oab__group__add(__eqx_0) | class_OrderedGroup_Oab__group__add(__eqy_0) )).
% 8.21/8.42 cnf(matrix-46, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Oab__semigroup__add(__eqx_0) | class_OrderedGroup_Oab__semigroup__add(__eqy_0) )).
% 8.21/8.42 cnf(matrix-47, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~c_Wellfounded_Oaccp(__eqx_0, __eqx_1, __eqx_2) | c_Wellfounded_Oaccp(__eqy_0, __eqy_1, __eqy_2) )).
% 8.21/8.42 cnf(matrix-48, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Osemigroup__add(__eqx_0) | class_OrderedGroup_Osemigroup__add(__eqy_0) )).
% 8.21/8.42 cnf(matrix-49, plain, ( ( __eqx_0 != __eqy_0) | ~class_Nat_Osemiring__char__0(__eqx_0) | class_Nat_Osemiring__char__0(__eqy_0) )).
% 8.21/8.42 cnf(matrix-50, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Oordered__idom(__eqx_0) | class_Ring__and__Field_Oordered__idom(__eqy_0) )).
% 8.21/8.42 cnf(matrix-51, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Opordered__cancel__ab__semigroup__add(__eqx_0) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(__eqy_0) )).
% 8.21/8.42 cnf(matrix-52, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(__eqx_0) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(__eqy_0) )).
% 8.21/8.42 cnf(matrix-53, plain, ( ( __eqx_0 != __eqy_0) | ~class_Orderings_Opreorder(__eqx_0) | class_Orderings_Opreorder(__eqy_0) )).
% 8.21/8.42 cnf(matrix-54, plain, ( ( __eqx_0 != __eqy_0) | ~class_Orderings_Olinorder(__eqx_0) | class_Orderings_Olinorder(__eqy_0) )).
% 8.21/8.42 cnf(matrix-55, plain, ( ( __eqx_0 != __eqy_0) | ~class_Orderings_Oorder(__eqx_0) | class_Orderings_Oorder(__eqy_0) )).
% 8.21/8.42 cnf(matrix-56, plain, ( ( c_List_Oappend(V_xs, c_List_Oappend(V_x, V_ts, T_a), T_a) = c_List_Oappend(c_List_Oappend(V_xs, V_x, T_a), V_ts, T_a)) )).
% 8.21/8.42 cnf(matrix-57, plain, ( ( c_List_Oappend(c_List_Oappend(V_zs, V_x, T_a), V_ys, T_a) = c_List_Oappend(V_zs, c_List_Oappend(V_x, V_ys, T_a), T_a)) )).
% 8.21/8.42 cnf(matrix-58, plain, ( ( c_List_Oappend(V_xs, c_List_Oappend(V_xs1, V_us, T_a), T_a) = c_List_Oappend(c_List_Oappend(V_xs, V_xs1, T_a), V_us, T_a)) )).
% 8.21/8.42 cnf(matrix-59, plain, ( ( c_List_Oappend(c_List_Oappend(V_xs, V_ys, T_a), V_zs, T_a) = c_List_Oappend(V_xs, c_List_Oappend(V_ys, V_zs, T_a), T_a)) )).
% 8.21/8.42 cnf(matrix-60, plain, ( ( c_List_Oappend(c_List_Olist_ONil(T_a), c_List_Olist_ONil(T_a), T_a) = c_List_Olist_ONil(T_a)) )).
% 8.21/8.42 cnf(matrix-61, plain, ( ( c_List_Oappend(V_xs, c_List_Olist_OCons(V_x, c_List_Olist_ONil(T_a), T_a), T_a) != c_List_Oappend(V_ys, c_List_Olist_OCons(V_y, c_List_Olist_ONil(T_a), T_a), T_a)) | ( V_x = V_y) )).
% 8.21/8.42 cnf(matrix-62, plain, ( ( c_List_Oappend(V_xs, c_List_Olist_OCons(V_x, c_List_Olist_ONil(T_a), T_a), T_a) != c_List_Oappend(V_ys, c_List_Olist_OCons(V_y, c_List_Olist_ONil(T_a), T_a), T_a)) | ( V_xs = V_ys) )).
% 8.21/8.42 cnf(matrix-63, plain, ( ( c_List_Oappend(c_List_Olist_ONil(T_a), c_List_Olist_OCons(V_x, V_xs, T_a), T_a) = c_List_Olist_OCons(V_x, V_xs, T_a)) )).
% 8.21/8.42 cnf(matrix-64, plain, ( ( V_ys != c_List_Oappend(V_xs, V_ys, T_a)) | ( V_xs = c_List_Olist_ONil(T_a)) )).
% 8.21/8.42 cnf(matrix-65, plain, ( ( c_List_Oappend(V_xs, V_ys, T_a) != V_ys) | ( V_xs = c_List_Olist_ONil(T_a)) )).
% 8.21/8.42 cnf(matrix-66, plain, ( ( V_xs != c_List_Oappend(V_xs, V_ys, T_a)) | ( V_ys = c_List_Olist_ONil(T_a)) )).
% 8.21/8.42 cnf(matrix-67, plain, ( ( c_List_Oappend(V_xs, V_ys, T_a) != V_xs) | ( V_ys = c_List_Olist_ONil(T_a)) )).
% 8.21/8.42 cnf(matrix-68, plain, ( c_List_Olistsp(V_A, c_List_Oappend(V_xs, V_ys, T_a), T_a) | ~c_List_Olistsp(V_A, V_ys, T_a) | ~c_List_Olistsp(V_A, V_xs, T_a) )).
% 8.21/8.42 cnf(matrix-69, plain, ( ( V_ys = V_xs) | ( V_y = V_x) | ~c_ListOrder_Ostep1(V_r, c_List_Oappend(V_ys, c_List_Olist_OCons(V_y, c_List_Olist_ONil(T_a), T_a), T_a), c_List_Oappend(V_xs, c_List_Olist_OCons(V_x, c_List_Olist_ONil(T_a), T_a), T_a), T_a) )).
% 8.21/8.42 cnf(matrix-70, plain, ( ( c_List_Oappend(V_xs, V_ys, T_a) != c_List_Olist_ONil(T_a)) | ( V_ys = c_List_Olist_ONil(T_a)) )).
% 8.21/8.42 cnf(matrix-71, plain, ( ( c_List_Oappend(V_xs, V_ys, T_a) != c_List_Olist_ONil(T_a)) | ( V_xs = c_List_Olist_ONil(T_a)) )).
% 8.21/8.42 cnf(matrix-72, plain, ( ( c_List_Olist_ONil(T_a) != c_List_Oappend(V_xs, V_ys, T_a)) | ( V_ys = c_List_Olist_ONil(T_a)) )).
% 8.21/8.42 cnf(matrix-73, plain, ( ( c_List_Olist_ONil(T_a) != c_List_Oappend(V_xs, V_ys, T_a)) | ( V_xs = c_List_Olist_ONil(T_a)) )).
% 8.21/8.42 cnf(matrix-74, plain, ( hBOOL(hAPP(hAPP(V_r, V_y), V_x)) | ( V_y = V_x) | ~c_ListOrder_Ostep1(V_r, c_List_Oappend(V_ys, c_List_Olist_OCons(V_y, c_List_Olist_ONil(T_a), T_a), T_a), c_List_Oappend(V_xs, c_List_Olist_OCons(V_x, c_List_Olist_ONil(T_a), T_a), T_a), T_a) )).
% 8.21/8.42 cnf(matrix-75, plain, ( ( c_List_Ofoldr(V_f, c_List_Oappend(V_xs, V_ys, T_b), V_a, T_b, T_a) = c_List_Ofoldr(V_f, V_xs, c_List_Ofoldr(V_f, V_ys, V_a, T_b, T_a), T_b, T_a)) )).
% 8.21/8.42 cnf(matrix-76, plain, ( ( V_ys = c_List_Oappend(c_List_Olist_ONil(T_a), V_ys, T_a)) )).
% 8.21/8.42 cnf(matrix-77, plain, ( ( c_List_Oappend(c_List_Olist_ONil(T_a), V_ys, T_a) = V_ys) )).
% 8.21/8.42 cnf(matrix-78, plain, ( ( V_xs = c_List_Oappend(V_xs, c_List_Olist_ONil(T_a), T_a)) )).
% 8.21/8.42 cnf(matrix-79, plain, ( ( V_x = c_List_Oappend(c_List_Olist_ONil(T_a), V_x, T_a)) )).
% 8.21/8.42 cnf(matrix-80, plain, ( ( c_List_Oappend(V_xs, c_List_Olist_ONil(T_a), T_a) = V_xs) )).
% 8.21/8.42 cnf(matrix-81, plain, ( ( c_List_Oappend(V_xs, V_ys, T_a) != c_List_Oappend(V_xs, V_zs, T_a)) | ( V_ys = V_zs) )).
% 8.21/8.42 cnf(matrix-82, plain, ( ( c_List_Oappend(V_ys, V_xs, T_a) != c_List_Oappend(V_zs, V_xs, T_a)) | ( V_ys = V_zs) )).
% 8.21/8.42 cnf(matrix-83, plain, ( c_List_Olistsp(V_A, V_ys, T_a) | ~c_List_Olistsp(V_A, c_List_Oappend(V_xs, V_ys, T_a), T_a) )).
% 8.21/8.42 cnf(matrix-84, plain, ( c_List_Olistsp(V_A, V_xs, T_a) | ~c_List_Olistsp(V_A, c_List_Oappend(V_xs, V_ys, T_a), T_a) )).
% 8.21/8.42 cnf(matrix-85, plain, ( c_ListOrder_Ostep1(V_r, c_List_Oappend(V_x, V_vs, T_a), c_List_Oappend(V_x, V_us, T_a), T_a) | ~c_ListOrder_Ostep1(V_r, V_vs, V_us, T_a) )).
% 8.21/8.42 cnf(matrix-86, plain, ( ~c_ListOrder_Ostep1(V_r, V_ys, V_xs, T_a) | c_ListOrder_Ostep1(V_r, c_List_Oappend(V_ys, V_x, T_a), c_List_Oappend(V_xs, V_x, T_a), T_a) )).
% 8.21/8.42 cnf(matrix-87, plain, ( hBOOL(hAPP(hAPP(V_r, V_y), V_x)) | c_ListOrder_Ostep1(V_r, V_ys, V_xs, T_a) | ~c_ListOrder_Ostep1(V_r, c_List_Oappend(V_ys, c_List_Olist_OCons(V_y, c_List_Olist_ONil(T_a), T_a), T_a), c_List_Oappend(V_xs, c_List_Olist_OCons(V_x, c_List_Olist_ONil(T_a), T_a), T_a), T_a) )).
% 8.21/8.42 cnf(matrix-88, plain, ( c_Type_Otyping(V_e, V_t, c_Type_Osko__Type__Xtypes__snocE__1__2(V_Ts, V_e, V_t, V_ts)) | ~c_Type_Otypings(V_e, c_List_Oappend(V_ts, c_List_Olist_OCons(V_t, c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB), V_Ts) )).
% 8.21/8.42 cnf(matrix-89, plain, ( ( c_List_Oappend(c_List_Olist_OCons(V_x, V_xa, T_a), V_zs, T_a) = c_List_Olist_OCons(V_x, c_List_Oappend(V_xa, V_zs, T_a), T_a)) )).
% 8.21/8.42 cnf(matrix-90, plain, ( ( c_List_Oappend(c_List_Olist_OCons(V_x, V_xs, T_a), V_ys, T_a) = c_List_Olist_OCons(V_x, c_List_Oappend(V_xs, V_ys, T_a), T_a)) )).
% 8.21/8.42 cnf(matrix-91, plain, ( ( c_List_Olist_OCons(V_x, c_List_Oappend(V_xa, V_zs, T_a), T_a) = c_List_Oappend(c_List_Olist_OCons(V_x, V_xa, T_a), V_zs, T_a)) )).
% 8.21/8.42 cnf(matrix-92, plain, ( ( c_List_Olist_OCons(V_x, c_List_Oappend(V_xs1, V_zs, T_a), T_a) = c_List_Oappend(c_List_Olist_OCons(V_x, V_xs1, T_a), V_zs, T_a)) )).
% 8.21/8.42 cnf(matrix-93, plain, ( ( c_List_Olist_OCons(V_x, V_xs, T_a) = c_List_Oappend(c_List_Olist_ONil(T_a), c_List_Olist_OCons(V_x, V_xs, T_a), T_a)) )).
% 8.21/8.42 cnf(matrix-94, plain, ( ( V_ys = V_xs) | c_ListOrder_Ostep1(V_r, V_ys, V_xs, T_a) | ~c_ListOrder_Ostep1(V_r, c_List_Oappend(V_ys, c_List_Olist_OCons(V_y, c_List_Olist_ONil(T_a), T_a), T_a), c_List_Oappend(V_xs, c_List_Olist_OCons(V_x, c_List_Olist_ONil(T_a), T_a), T_a), T_a) )).
% 8.21/8.42 cnf(matrix-95, plain, ( ( c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a), c_List_Olist_ONil(T_a), T_a)) )).
% 8.21/8.42 cnf(matrix-96, plain, ( ( c_List_Ofoldl(V_f, V_a, c_List_Oappend(V_xs, V_ys, T_b), T_a, T_b) = c_List_Ofoldl(V_f, c_List_Ofoldl(V_f, V_a, V_xs, T_a, T_b), V_ys, T_a, T_b)) )).
% 8.21/8.42 cnf(matrix-97, plain, ( ~class_OrderedGroup_Olordered__ab__group__add(T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_a), T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) )).
% 8.21/8.42 cnf(matrix-98, plain, ( ~class_OrderedGroup_Olordered__ab__group__add(T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_a), T_a) )).
% 8.21/8.42 cnf(matrix-99, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), c_HOL_Ozero__class_Ozero(T_a)), V_a) = V_a) )).
% 8.21/8.42 cnf(matrix-100, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), c_HOL_Ozero__class_Ozero(T_a)) = V_a) )).
% 8.21/8.42 cnf(matrix-101, plain, ( ~class_OrderedGroup_Omonoid__add(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), c_HOL_Ozero__class_Ozero(T_a)) = V_a) )).
% 8.21/8.42 cnf(matrix-102, plain, ( ~class_OrderedGroup_Omonoid__add(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), c_HOL_Ozero__class_Ozero(T_a)), V_a) = V_a) )).
% 8.21/8.42 cnf(matrix-103, plain, ( ~class_OrderedGroup_Ocomm__monoid__add(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), c_HOL_Ozero__class_Ozero(T_a)) = V_a) )).
% 8.21/8.42 cnf(matrix-104, plain, ( ~class_Ring__and__Field_Oidom(T_a) | ~class_Int_Onumber__ring(T_a) | ( V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_x), c_HOL_Ozero__class_Ozero(T_a))) )).
% 8.21/8.42 cnf(matrix-105, plain, ( ~class_OrderedGroup_Ocomm__monoid__add(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), c_HOL_Ozero__class_Ozero(T_a)), V_a) = V_a) )).
% 8.21/8.42 cnf(matrix-106, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), c_HOL_Ozero__class_Ozero(T_a)), V_x) = V_x) )).
% 8.21/8.42 cnf(matrix-107, plain, ( ( V_xs != c_List_Olist_OCons(V_x, V_xs, T_a)) )).
% 8.21/8.42 cnf(matrix-108, plain, ( ( c_List_Olist_OCons(V_x, V_t, T_a) != V_t) )).
% 8.21/8.42 cnf(matrix-109, plain, ( ~class_Ring__and__Field_Oordered__semidom(T_a) | ~c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 8.21/8.42 cnf(matrix-110, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_b)), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_c), V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_c)), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_b), V_d))) )).
% 8.21/8.42 cnf(matrix-111, plain, ( ( V_x = V_y) | hBOOL(hAPP(hAPP(V_r, V_y), V_x)) | ~c_ListOrder_Ostep1(V_r, c_List_Olist_OCons(V_y, V_ys, T_a), c_List_Olist_OCons(V_x, V_xs, T_a), T_a) )).
% 8.21/8.42 cnf(matrix-112, plain, ( ( c_List_Olist_OCons(V_a_H, V_list_H, T_a) != c_List_Olist_ONil(T_a)) )).
% 8.21/8.42 cnf(matrix-113, plain, ( ( c_List_Olist_OCons(V_x, V_xa, T_a) != c_List_Olist_ONil(T_a)) )).
% 8.21/8.42 cnf(matrix-114, plain, ( ~class_OrderedGroup_Ocancel__semigroup__add(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_b), V_a) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_c), V_a)) | ( V_b = V_c) )).
% 8.21/8.42 cnf(matrix-115, plain, ( ~class_OrderedGroup_Ocancel__semigroup__add(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_b) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_c)) | ( V_b = V_c) )).
% 8.21/8.42 cnf(matrix-116, plain, ( ~class_OrderedGroup_Ocancel__ab__semigroup__add(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_b) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_c)) | ( V_b = V_c) )).
% 8.21/8.42 cnf(matrix-117, plain, ( ~class_Ring__and__Field_Oidom(T_a) | ~class_Int_Onumber__ring(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_x), V_y) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_x), V_z)) | ( V_y = V_z) )).
% 8.21/8.42 cnf(matrix-118, plain, ( ~class_OrderedGroup_Opordered__comm__monoid__add(T_a) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_b), c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_HOL_Oord__class_Oless(V_b, c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_HOL_Oord__class_Oless(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 8.21/8.42 cnf(matrix-119, plain, ( ~class_Ring__and__Field_Osemiring__1(T_a) | ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat), T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 8.21/8.42 cnf(matrix-120, plain, ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r, T_a, T_a), T_a), V_x), V_y)) | ~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r, T_a), V_y), V_x)) )).
% 8.21/8.42 cnf(matrix-121, plain, ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r, T_a), V_y), V_x)) | ~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r, T_a, T_a), T_a), V_x), V_y)) )).
% 8.21/8.42 cnf(matrix-122, plain, ( ( c_List_Ofoldl(V_f, V_a, c_List_Olist_OCons(V_x, V_xs, T_b), T_a, T_b) = c_List_Ofoldl(V_f, hAPP(hAPP(V_f, V_a), V_x), V_xs, T_a, T_b)) )).
% 8.21/8.42 cnf(matrix-123, plain, ( ( c_List_Ofoldr(V_f, c_List_Olist_ONil(T_b), V_a, T_b, T_a) = V_a) )).
% 8.21/8.42 cnf(matrix-124, plain, ( ~class_OrderedGroup_Oab__group__add(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_x), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_y), V_z)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_y), V_u)) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_x), V_z) = V_u) )).
% 8.21/8.42 cnf(matrix-125, plain, ( hBOOL(hAPP(hAPP(V_r, V_b), V_a)) | ~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r, T_a, T_b), V_a), V_b)) )).
% 8.21/8.42 cnf(matrix-126, plain, ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r, T_a, T_b), V_a), V_b)) | ~hBOOL(hAPP(hAPP(V_r, V_b), V_a)) )).
% 8.21/8.42 cnf(matrix-127, plain, ( hBOOL(hAPP(hAPP(V_r, V_a2), V_a1)) | ~hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r, T_a, T_b), V_a1), V_a2)) )).
% 8.21/8.42 cnf(matrix-128, plain, ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r, T_a, T_b), V_b), V_a)) | ~hBOOL(hAPP(hAPP(V_r, V_a), V_b)) )).
% 8.21/8.42 cnf(matrix-129, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_b)), V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_b), V_c))) )).
% 8.21/8.42 cnf(matrix-130, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_c), V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_c), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_d))) )).
% 8.21/8.42 cnf(matrix-131, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_b)), V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_c)), V_b)) )).
% 8.21/8.42 cnf(matrix-132, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_c), V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_c)), V_d)) )).
% 8.21/8.42 cnf(matrix-133, plain, ( ~class_OrderedGroup_Oab__semigroup__add(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_b)), V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_b), V_c))) )).
% 8.21/8.42 cnf(matrix-134, plain, ( ~class_OrderedGroup_Ocomm__monoid__add(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_b), V_c)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_b), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_c))) )).
% 8.21/8.42 cnf(matrix-135, plain, ( ~class_OrderedGroup_Ocomm__monoid__add(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_b)), V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_b), V_c))) )).
% 8.21/8.42 cnf(matrix-136, plain, ( ~class_OrderedGroup_Oab__group__add(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_x), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_y), V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_y), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_x), V_z))) )).
% 8.21/8.42 cnf(matrix-137, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_x), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_y), V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_x), V_y)), V_z)) )).
% 8.21/8.42 cnf(matrix-138, plain, ( ~class_OrderedGroup_Olordered__ab__group__add(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), c_HOL_Ozero__class_Ozero(T_a)), c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 8.21/8.42 cnf(matrix-139, plain, ( hBOOL(hAPP(c_InductTermi_OIT, v_ua______)) )).
% 8.21/8.42 cnf(matrix-140, plain, ( ( V_x = V_y) | ( V_xs = V_ys) | ~c_ListOrder_Ostep1(V_r, c_List_Olist_OCons(V_y, V_ys, T_a), c_List_Olist_OCons(V_x, V_xs, T_a), T_a) )).
% 8.21/8.42 cnf(matrix-141, plain, ( ~hBOOL(hAPP(hAPP(V_r, V_y), V_xa)) | c_ListOrder_Ostep1(V_r, c_List_Olist_OCons(V_y, V_x, T_a), c_List_Olist_OCons(V_xa, V_x, T_a), T_a) )).
% 8.21/8.42 cnf(matrix-142, plain, ( c_List_Olistsp(V_A, c_List_Olist_ONil(T_a), T_a) )).
% 8.21/8.42 cnf(matrix-143, plain, ( c_Wellfounded_Oaccp(V_r, V_b, T_a) | ~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r, T_a), V_b), V_a)) | ~c_Wellfounded_Oaccp(V_r, V_a, T_a) )).
% 8.21/8.42 cnf(matrix-144, plain, ( c_Wellfounded_Oaccp(V_r, V_b, T_a) | ~c_Wellfounded_Oaccp(V_r, V_a, T_a) | ~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r, T_a), V_b), V_a)) )).
% 8.21/8.42 cnf(matrix-145, plain, ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta, tc_Lambda_OdB, tc_Lambda_OdB), V_t, tc_Lambda_OdB) | ~hBOOL(hAPP(c_InductTermi_OIT, V_t)) )).
% 8.21/8.42 cnf(matrix-146, plain, ( hBOOL(hAPP(c_InductTermi_OIT, V_r)) | ~c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta, tc_Lambda_OdB, tc_Lambda_OdB), V_r, tc_Lambda_OdB) )).
% 8.21/8.42 cnf(matrix-147, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_c), V_a)) )).
% 8.21/8.42 cnf(matrix-148, plain, ( ~class_OrderedGroup_Ocomm__monoid__add(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_b) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_b), V_a)) )).
% 8.21/8.42 cnf(matrix-149, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_x), V_y) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_y), V_x)) )).
% 8.21/8.42 cnf(matrix-150, plain, ( ~class_OrderedGroup_Osemigroup__add(T_a) | ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_x), V_y), V_zs, T_a, T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_x), c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a), V_y, V_zs, T_a, T_a))) )).
% 8.21/8.42 cnf(matrix-151, plain, ( ~class_Nat_Osemiring__char__0(T_a) | ( c_Nat_Osemiring__1__class_Oof__nat(V_m, T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n, T_a)) | ( V_m = V_n) )).
% 8.21/8.42 cnf(matrix-152, plain, ( ~class_Ring__and__Field_Oidom(T_a) | ~class_Int_Onumber__ring(T_a) | ( V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_x), V_a)) | ( V_a = c_HOL_Ozero__class_Ozero(T_a)) )).
% 8.21/8.42 cnf(matrix-153, plain, ( ~class_OrderedGroup_Olordered__ab__group__add(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_a) != c_HOL_Ozero__class_Ozero(T_a)) | ( V_a = c_HOL_Ozero__class_Ozero(T_a)) )).
% 8.21/8.42 cnf(matrix-154, plain, ( ~class_OrderedGroup_Oab__semigroup__add(T_a) | ( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a), V_xs, V_a, T_a, T_a) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a), V_a, V_xs, T_a, T_a)) )).
% 8.21/8.42 cnf(matrix-155, plain, ( ~c_ListOrder_Ostep1(V_r, c_List_Olist_ONil(T_a), V_xs, T_a) )).
% 8.21/8.42 cnf(matrix-156, plain, ( ~c_ListOrder_Ostep1(V_r, V_xs, c_List_Olist_ONil(T_a), T_a) )).
% 8.21/8.42 cnf(matrix-157, plain, ( ~class_OrderedGroup_Olordered__ab__group__add(T_a) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_a), c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_HOL_Oord__class_Oless(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 8.21/8.42 cnf(matrix-158, plain, ( ~class_OrderedGroup_Olordered__ab__group__add(T_a) | c_HOL_Oord__class_Oless(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_a), c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 8.21/8.42 cnf(matrix-159, plain, ( ~class_Ring__and__Field_Oordered__idom(T_a) | c_HOL_Oord__class_Oless(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_a), c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 8.21/8.42 cnf(matrix-160, plain, ( ~class_Ring__and__Field_Oordered__idom(T_a) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_a), c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_HOL_Oord__class_Oless(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 8.21/8.42 cnf(matrix-161, plain, ( ~class_OrderedGroup_Omonoid__add(T_a) | ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_x), c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a), c_HOL_Ozero__class_Ozero(T_a), V_zs, T_a, T_a)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a), V_x, V_zs, T_a, T_a)) )).
% 8.21/8.42 cnf(matrix-162, plain, ( ( c_List_Ofoldl(V_f, V_a, c_List_Olist_ONil(T_b), T_a, T_b) = V_a) )).
% 8.21/8.42 cnf(matrix-163, plain, ( ( V_r != c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, V_r), V_s), V_xa, tc_Lambda_OdB, tc_Lambda_OdB)) | ( hAPP(hAPP(c_Lambda_OdB_OApp, V_r), V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, V_r), V_s), c_List_Oappend(V_xa, c_List_Olist_OCons(V_s, c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)) )).
% 8.21/8.42 cnf(matrix-164, plain, ( ( c_Predicate_Oconversep(c_fequal(T_a), T_a, T_a) = c_fequal(T_a)) )).
% 8.21/8.42 cnf(matrix-165, plain, ( ~class_OrderedGroup_Opordered__comm__monoid__add(T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_b), T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_b, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) )).
% 8.21/8.42 cnf(matrix-166, plain, ( c_ListOrder_Ostep1(V_r, V_ys, V_xs, T_a) | ( V_xs = V_ys) | ~c_ListOrder_Ostep1(V_r, c_List_Olist_OCons(V_y, V_ys, T_a), c_List_Olist_OCons(V_x, V_xs, T_a), T_a) )).
% 8.21/8.42 cnf(matrix-167, plain, ( ~class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_c), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_b), V_d), T_a) | ~c_HOL_Oord__class_Oless(V_c, V_d, T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 8.21/8.42 cnf(matrix-168, plain, ( ( c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H, V_list_H, T_a)) )).
% 8.21/8.42 cnf(matrix-169, plain, ( ~class_Ring__and__Field_Oordered__semidom(T_a) | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m, T_a), c_Nat_Osemiring__1__class_Oof__nat(V_n, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) )).
% 8.21/8.42 cnf(matrix-170, plain, ( ~class_Ring__and__Field_Oordered__semidom(T_a) | c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m, T_a), c_Nat_Osemiring__1__class_Oof__nat(V_n, T_a), T_a) )).
% 8.21/8.42 cnf(matrix-171, plain, ( ( hAPP(hAPP(c_Lambda_OdB_OApp, V_r), V_s) != c_List_Ofoldl(c_Lambda_OdB_OApp, V_t, c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)) | ( hAPP(hAPP(c_Lambda_OdB_OApp, V_r), V_s) = V_t) )).
% 8.21/8.42 cnf(matrix-172, plain, ( ~class_Ring__and__Field_Oordered__semidom(T_a) | c_HOL_Oord__class_Oless(V_b, hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_c), T_a) | ~c_HOL_Oord__class_Oless(V_b, V_c, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) )).
% 8.21/8.42 cnf(matrix-173, plain, ( ( c_List_Ofoldr(V_f, c_List_Olist_OCons(V_x, V_xs, T_b), V_a, T_b, T_a) = hAPP(hAPP(V_f, V_x), c_List_Ofoldr(V_f, V_xs, V_a, T_b, T_a))) )).
% 8.21/8.42 cnf(matrix-174, plain, ( ( c_Predicate_Oconversep(c_Predicate_Oconversep(V_r, T_a, T_b), T_b, T_a) = V_r) )).
% 8.21/8.42 cnf(matrix-175, plain, ( ~class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_c), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_b), V_c), T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 8.21/8.42 cnf(matrix-176, plain, ( ~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_c), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_b), V_c), T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 8.21/8.42 cnf(matrix-177, plain, ( ~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) | c_HOL_Oord__class_Oless(V_a, V_b, T_a) | ~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), V_c), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_b), V_c), T_a) )).
% 8.21/8.42 cnf(matrix-178, plain, ( ~class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_c), V_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_c), V_b), T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 8.21/8.42 cnf(matrix-179, plain, ( ~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_c), V_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_c), V_b), T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 8.21/8.42 cnf(matrix-180, plain, ( ~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) | c_HOL_Oord__class_Oless(V_a, V_b, T_a) | ~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_c), V_a), hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_c), V_b), T_a) )).
% 8.21/8.42 cnf(matrix-181, plain, ( ( c_List_Olist_OCons(V_a, V_list, T_a) != c_List_Olist_OCons(V_a_H, V_list_H, T_a)) | ( V_a = V_a_H) )).
% 8.21/8.42 cnf(matrix-182, plain, ( ( c_List_Olist_OCons(V_a, V_list, T_a) != c_List_Olist_OCons(V_a_H, V_list_H, T_a)) | ( V_list = V_list_H) )).
% 8.21/8.42 cnf(matrix-183, plain, ( c_ListOrder_Ostep1(V_r, V_ys, V_xs, T_a) | hBOOL(hAPP(hAPP(V_r, V_y), V_x)) | ~c_ListOrder_Ostep1(V_r, c_List_Olist_OCons(V_y, V_ys, T_a), c_List_Olist_OCons(V_x, V_xs, T_a), T_a) )).
% 8.21/8.42 cnf(matrix-184, plain, ( c_ListOrder_Ostep1(V_r, c_List_Olist_OCons(V_x, V_ys, T_a), c_List_Olist_OCons(V_x, V_xs, T_a), T_a) | ~c_ListOrder_Ostep1(V_r, V_ys, V_xs, T_a) )).
% 8.21/8.42 cnf(matrix-185, plain, ( ( hAPP(hAPP(c_Lambda_OdB_OApp, c_List_Ofoldl(c_Lambda_OdB_OApp, V_t, V_ts, tc_Lambda_OdB, tc_Lambda_OdB)), V_u) = c_List_Ofoldl(c_Lambda_OdB_OApp, V_t, c_List_Oappend(V_ts, c_List_Olist_OCons(V_u, c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)) )).
% 8.21/8.42 cnf(matrix-186, plain, ( ( hAPP(hAPP(c_Lambda_OdB_OApp, V_r), V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, V_r), V_s), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)) )).
% 8.21/8.42 cnf(matrix-187, plain, ( ( c_List_Oappend(V_x, c_List_Olist_OCons(V_s, c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB) = c_List_Olist_ONil(tc_Lambda_OdB)) | ( hAPP(hAPP(c_Lambda_OdB_OApp, c_List_Ofoldl(c_Lambda_OdB_OApp, V_t, V_x, tc_Lambda_OdB, tc_Lambda_OdB)), V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp, V_t, c_List_Oappend(V_x, c_List_Olist_OCons(V_s, c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)) )).
% 8.21/8.42 cnf(matrix-188, plain, ( c_Wellfounded_Oaccp(V_r, V_y, T_a) | ~hBOOL(hAPP(hAPP(V_r, V_y), V_a)) | ~c_Wellfounded_Oaccp(V_r, V_a, T_a) )).
% 8.21/8.42 cnf(matrix-189, plain, ( c_Wellfounded_Oaccp(V_r, V_a, T_a) | ~hBOOL(hAPP(hAPP(V_r, V_a), V_b)) | ~c_Wellfounded_Oaccp(V_r, V_b, T_a) )).
% 8.21/8.42 cnf(matrix-190, plain, ( ~class_Orderings_Opreorder(T_a) | ~c_HOL_Oord__class_Oless(V_b, V_a, T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 8.21/8.42 cnf(matrix-191, plain, ( ~class_Orderings_Opreorder(T_a) | ~c_HOL_Oord__class_Oless(V_y, V_x, T_a) | ~c_HOL_Oord__class_Oless(V_x, V_y, T_a) )).
% 8.21/8.42 cnf(matrix-192, plain, ( ~class_Orderings_Olinorder(T_a) | ~c_HOL_Oord__class_Oless(V_x, V_y, T_a) | ~c_HOL_Oord__class_Oless(V_y, V_x, T_a) )).
% 8.21/8.42 cnf(matrix-193, plain, ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r, T_a), V_a), V_c)) | ~hBOOL(hAPP(hAPP(V_r, V_b), V_c)) | ~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r, T_a), V_a), V_b)) )).
% 8.21/8.42 cnf(matrix-194, plain, ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r, T_a), V_a), V_c)) | ~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r, T_a), V_b), V_c)) | ~hBOOL(hAPP(hAPP(V_r, V_a), V_b)) )).
% 8.21/8.42 cnf(matrix-195, plain, ( ~class_Orderings_Oorder(T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) | ~c_HOL_Oord__class_Oless(V_b, V_a, T_a) )).
% 8.21/8.42 cnf(matrix-196, plain, ( ( c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat)) )).
% 8.21/8.42 cnf(matrix-197, plain, ( ( hAPP(hAPP(c_Lambda_OdB_OApp, V_dB1), V_dB2) != c_Lambda_OdB_OAbs(V_dB_H)) )).
% 8.21/8.42 cnf(matrix-198, plain, ( c_Type_Otypings(V_e, V_ts, c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T, V_e, V_i, V_ts)) | ~c_Type_Otyping(V_e, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_i), V_ts, tc_Lambda_OdB, tc_Lambda_OdB), V_T) )).
% 8.21/8.42 cnf(matrix-199, plain, ( ( c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp, V_dB1), V_dB2)) )).
% 8.21/8.42 cnf(matrix-200, plain, ( c_Type_Otypings(V_e, V_ts, c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T, V_e, V_t, V_ts)) | ~c_Type_Otyping(V_e, c_List_Ofoldl(c_Lambda_OdB_OApp, V_t, V_ts, tc_Lambda_OdB, tc_Lambda_OdB), V_T) )).
% 8.21/8.42 cnf(matrix-201, plain, ( ( hAPP(c_Type_Oshift(V_e, V_i, V_T, T_a), V_j) = hAPP(V_e, V_j)) | ~c_HOL_Oord__class_Oless(V_j, V_i, tc_nat) )).
% 8.21/8.42 cnf(matrix-202, plain, ( ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) )).
% 8.21/8.42 cnf(matrix-203, plain, ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) | ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 8.21/8.42 cnf(matrix-204, plain, ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, V_r, V_ss, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, V_s, V_ss, tc_Lambda_OdB, tc_Lambda_OdB))) | ~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), V_r), V_s)) )).
% 8.21/8.42 cnf(matrix-205, plain, ( ~class_Ring__and__Field_Oordered__semidom(T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), c_Nat_Osemiring__1__class_Oof__nat(V_n, T_a), T_a) )).
% 8.21/8.42 cnf(matrix-206, plain, ( ~class_Ring__and__Field_Oordered__semidom(T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), c_Nat_Osemiring__1__class_Oof__nat(V_n, T_a), T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) )).
% 8.21/8.42 cnf(matrix-207, plain, ( ~class_OrderedGroup_Omonoid__add(T_a) | ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a), c_HOL_Ozero__class_Ozero(T_a), V_xs, T_a, T_a) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a), V_xs, c_HOL_Ozero__class_Ozero(T_a), T_a, T_a)) )).
% 8.21/8.42 cnf(matrix-208, plain, ( ( c_List_Ofoldl(c_Lambda_OdB_OApp, V_s, V_ss, tc_Lambda_OdB, tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r)) | ( V_s = c_Lambda_OdB_OAbs(V_r)) )).
% 8.21/8.42 cnf(matrix-209, plain, ( ( c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(V_r), V_rs, tc_Lambda_OdB, tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(V_s), V_ss, tc_Lambda_OdB, tc_Lambda_OdB)) | ( V_r = V_s) )).
% 8.21/8.42 cnf(matrix-210, plain, ( ( c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(V_r), V_rs, tc_Lambda_OdB, tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(V_s), V_ss, tc_Lambda_OdB, tc_Lambda_OdB)) | ( V_rs = V_ss) )).
% 8.21/8.42 cnf(matrix-211, plain, ( ~class_Orderings_Olinorder(T_a) | ( V_x = V_y) | c_HOL_Oord__class_Oless(V_x, V_y, T_a) | c_HOL_Oord__class_Oless(V_y, V_x, T_a) )).
% 8.21/8.42 cnf(matrix-212, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(V_y, V_x, T_a) | ( V_x = V_y) | c_HOL_Oord__class_Oless(V_x, V_y, T_a) )).
% 8.21/8.42 cnf(matrix-213, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(V_y, V_x, T_a) | c_HOL_Oord__class_Oless(V_x, V_y, T_a) | ( V_x = V_y) )).
% 8.21/8.42 cnf(matrix-214, plain, ( c_HOL_Oord__class_Oless(V_y, V_x, tc_nat) | c_HOL_Oord__class_Oless(V_x, V_y, tc_nat) | ( V_x = V_y) )).
% 8.21/8.42 cnf(matrix-215, plain, ( hBOOL(hAPP(hAPP(V_P, V_n), V_m)) | c_HOL_Oord__class_Oless(V_n, V_m, tc_nat) | ( V_m = V_n) | c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) )).
% 8.21/8.42 cnf(matrix-216, plain, ( c_HOL_Oord__class_Oless(V_n, V_m, tc_nat) | c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ( V_m = V_n) )).
% 8.21/8.42 cnf(matrix-217, plain, ( ~class_Orderings_Olinorder(T_a) | ( V_x = V_y) | c_HOL_Oord__class_Oless(V_y, V_x, T_a) | c_HOL_Oord__class_Oless(V_x, V_y, T_a) )).
% 8.21/8.42 cnf(matrix-218, plain, ( ~class_Ring__and__Field_Oordered__idom(T_a) | c_HOL_Oord__class_Oless(V_y, V_x, T_a) | c_HOL_Oord__class_Oless(V_x, V_y, T_a) | ( V_x = V_y) )).
% 8.21/8.42 cnf(matrix-219, plain, ( hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, V_r, V_rs, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, V_r, V_ss, tc_Lambda_OdB, tc_Lambda_OdB))) | ~c_ListOrder_Ostep1(c_Lambda_Obeta, V_rs, V_ss, tc_Lambda_OdB) )).
% 8.21/8.42 cnf(matrix-220, plain, ( ~class_Orderings_Opreorder(T_a) | ~c_HOL_Oord__class_Oless(V_x, V_x, T_a) )).
% 8.21/8.42 cnf(matrix-221, plain, ( ~class_Orderings_Olinorder(T_a) | ~c_HOL_Oord__class_Oless(V_x, V_x, T_a) )).
% 8.21/8.42 cnf(matrix-222, plain, ( ~class_Orderings_Oorder(T_a) | ~c_HOL_Oord__class_Oless(V_x, V_x, T_a) )).
% 8.21/8.42 cnf(matrix-223, plain, ( ~c_HOL_Oord__class_Oless(V_n, V_n, tc_nat) )).
% 8.21/8.42 cnf(matrix-224, plain, ( ~c_HOL_Oord__class_Oless(V_x, V_x, tc_nat) )).
% 8.21/8.42 cnf(matrix-225, plain, ( ( c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp, V_s, V_ss, tc_Lambda_OdB, tc_Lambda_OdB)) | ( V_ss = c_List_Olist_ONil(tc_Lambda_OdB)) )).
% 8.21/8.42 cnf(matrix-226, plain, ( ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H)) | ( V_dB = V_dB_H) )).
% 8.21/8.42 cnf(matrix-227, plain, ( ( c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_n), V_ts, tc_Lambda_OdB, tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(V_r), V_ss, tc_Lambda_OdB, tc_Lambda_OdB)) )).
% 8.21/8.42 cnf(matrix-228, plain, ( hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(V_r)), V_s), V_ss, tc_Lambda_OdB, tc_Lambda_OdB))) | ~hBOOL(hAPP(c_InductTermi_OIT, V_s)) | ~hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_Osubst(V_r, V_s, c_HOL_Ozero__class_Ozero(tc_nat)), V_ss, tc_Lambda_OdB, tc_Lambda_OdB))) )).
% 8.21/8.42 cnf(matrix-229, plain, ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r, T_a), V_x), V_y)) | ~hBOOL(hAPP(hAPP(V_r, V_x), V_y)) )).
% 8.21/8.42 cnf(matrix-230, plain, ( ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H)) )).
% 8.21/8.42 cnf(matrix-231, plain, ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r, T_a), V_x), V_z)) | ~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r, T_a), V_y), V_z)) | ~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r, T_a), V_x), V_y)) )).
% 8.21/8.42 cnf(matrix-232, plain, ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r, T_a), V_x), V_x)) )).
% 8.21/8.42 cnf(matrix-233, plain, ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r, T_a), V_a), V_a)) )).
% 8.21/8.42 cnf(matrix-234, plain, ( c_Type_Otyping(v_ea______, v_ua______, v_T____) )).
% 8.21/8.42 cnf(matrix-235, plain, ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), c_Lambda_OdB_OAbs(V_s)), c_Lambda_OdB_OAbs(V_s_H))) | ~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), V_s), V_s_H)) )).
% 8.21/8.42 cnf(matrix-236, plain, ( ~c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta, tc_Lambda_OdB, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_Osubst(V_r, V_s, c_HOL_Ozero__class_Ozero(tc_nat)), V_ss, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB) | ~c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta, tc_Lambda_OdB, tc_Lambda_OdB), V_s, tc_Lambda_OdB) | c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta, tc_Lambda_OdB, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(V_r)), V_s), V_ss, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB) )).
% 8.21/8.42 cnf(matrix-237, plain, ( ~class_Orderings_Opreorder(T_a) | c_HOL_Oord__class_Oless(V_x, V_z, T_a) | ~c_HOL_Oord__class_Oless(V_y, V_z, T_a) | ~c_HOL_Oord__class_Oless(V_x, V_y, T_a) )).
% 8.21/8.42 cnf(matrix-238, plain, ( ~class_Orderings_Oorder(T_a) | c_HOL_Oord__class_Oless(V_z, V_x, T_a) | ~c_HOL_Oord__class_Oless(V_z, V_y, T_a) | ~c_HOL_Oord__class_Oless(V_y, V_x, T_a) )).
% 8.21/8.42 cnf(matrix-239, plain, ( ( c_Lambda_OdB_OVar(V_m) = c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_m), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)) )).
% 8.21/8.42 cnf(matrix-240, plain, ( ~c_HOL_Oord__class_Oless(V_m, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) )).
% 8.21/8.42 cnf(matrix-241, plain, ( ~c_HOL_Oord__class_Oless(V_n, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) )).
% 8.21/8.42 cnf(matrix-242, plain, ( c_Type_Otypings(V_e, V_ts, c_Type_Osko__Type__Xlist__app__typeE__1__1(V_T, V_e, V_t, V_ts)) | ~c_Type_Otyping(V_e, c_List_Ofoldl(c_Lambda_OdB_OApp, V_t, V_ts, tc_Lambda_OdB, tc_Lambda_OdB), V_T) )).
% 8.21/8.42 cnf(matrix-243, plain, ( ( c_Lambda_OdB_OAbs(V_r) = c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(V_r), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB)) )).
% 8.21/8.42 cnf(matrix-244, plain, ( ( c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp, V_s, V_ss, tc_Lambda_OdB, tc_Lambda_OdB)) | ( c_Lambda_OdB_OAbs(V_r) = V_s) )).
% 8.21/8.42 cnf(matrix-245, plain, ( ~class_OrderedGroup_Omonoid__add(T_a) | ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a), V_a, V_xs, T_a, T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a), V_a), c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a), V_xs, c_HOL_Ozero__class_Ozero(T_a), T_a, T_a))) )).
% 8.21/8.42 cnf(matrix-246, plain, ( ( c_List_Ofoldl(c_Lambda_OdB_OApp, V_s, V_ss, tc_Lambda_OdB, tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r)) | ( V_ss = c_List_Olist_ONil(tc_Lambda_OdB)) )).
% 8.21/8.42 cnf(matrix-247, plain, ( ( c_List_Ofoldl(c_Lambda_OdB_OApp, V_r, V_ts, tc_Lambda_OdB, tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp, V_s, V_ts, tc_Lambda_OdB, tc_Lambda_OdB)) | ( V_r = V_s) )).
% 8.21/8.42 cnf(matrix-248, plain, ( c_Type_Otypings(V_e, V_us, c_Type_Osko__Type__Xvar__app__types__1__1(V_T, V_U, V_e, V_us)) | ~c_Type_Otyping(V_e, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_i), V_ts, tc_Lambda_OdB, tc_Lambda_OdB), V_U) | ~c_Type_Otypings(V_e, V_ts, V_Ts) | ~c_Type_Otyping(V_e, c_List_Ofoldl(c_Lambda_OdB_OApp, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_i), V_ts, tc_Lambda_OdB, tc_Lambda_OdB), V_us, tc_Lambda_OdB, tc_Lambda_OdB), V_T) )).
% 8.21/8.42 cnf(matrix-249, plain, ( hBOOL(hAPP(c_InductTermi_OIT, c_Lambda_OdB_OAbs(V_r))) | ~hBOOL(hAPP(c_InductTermi_OIT, V_r)) )).
% 8.21/8.42 cnf(matrix-250, plain, ( ( v_rs____ = c_List_Olist_OCons(v_a____, v_as____, tc_Lambda_OdB)) )).
% 8.21/8.42 cnf(matrix-251, plain, ( ( c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(V_r), c_List_Olist_ONil(tc_Lambda_OdB), tc_Lambda_OdB, tc_Lambda_OdB) = c_Lambda_OdB_OAbs(V_r)) )).
% 8.21/8.42 cnf(matrix-252, plain, ( ( c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp, V_s, V_ss, tc_Lambda_OdB, tc_Lambda_OdB)) | ( V_ss = c_List_Olist_ONil(tc_Lambda_OdB)) )).
% 8.21/8.42 cnf(matrix-253, plain, ( c_ListOrder_Ostep1(c_Lambda_Obeta, V_rs, c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(V_n, V_rs, V_v), tc_Lambda_OdB) | ~hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_n), V_rs, tc_Lambda_OdB, tc_Lambda_OdB)), V_v)) )).
% 8.21/8.42 cnf(matrix-254, plain, ( ( hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(V_s)), V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_n), V_ss, tc_Lambda_OdB, tc_Lambda_OdB)) )).
% 8.21/8.42 cnf(matrix-255, plain, ( ( c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r, T_a), T_a) = c_Transitive__Closure_Ortranclp(V_r, T_a)) )).
% 8.21/8.42 cnf(matrix-256, plain, ( hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_Lambda_OdB_OAbs(V_s)), c_Lambda_OdB_OAbs(V_t))) | ~hBOOL(hAPP(hAPP(c_Lambda_Obeta, V_s), V_t)) )).
% 8.21/8.42 cnf(matrix-257, plain, ( ( hAPP(hAPP(c_Lambda_OdB_OApp, V_dB1_H), V_dB2_H) != c_Lambda_OdB_OVar(V_nat)) )).
% 8.21/8.42 cnf(matrix-258, plain, ( c_Type_Otyping(V_e, V_t, hAPP(hAPP(c_Type_Otype_OFun, c_Type_Osko__Type__Xtyping__elims__2__1(V_T, V_e, V_t, V_u)), V_T)) | ~c_Type_Otyping(V_e, hAPP(hAPP(c_Lambda_OdB_OApp, V_t), V_u), V_T) )).
% 8.21/8.42 cnf(matrix-259, plain, ( hBOOL(hAPP(c_InductTermi_OIT, hAPP(hAPP(c_Lambda_OdB_OApp, V_t), c_Lambda_OdB_OVar(V_i)))) | ~hBOOL(hAPP(c_InductTermi_OIT, V_t)) )).
% 8.21/8.42 cnf(matrix-260, plain, ( c_Type_Otyping(V_e, V_t, c_List_Ofoldr(c_Type_Otype_OFun, c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T, V_e, V_t, V_ts), V_T, tc_Type_Otype, tc_Type_Otype)) | ~c_Type_Otyping(V_e, c_List_Ofoldl(c_Lambda_OdB_OApp, V_t, V_ts, tc_Lambda_OdB, tc_Lambda_OdB), V_T) )).
% 8.21/8.42 cnf(matrix-261, plain, ( hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_Lambda_Olift(V_r, V_i)), c_Lambda_Olift(V_s, V_i))) | ~hBOOL(hAPP(hAPP(c_Lambda_Obeta, V_r), V_s)) )).
% 8.21/8.42 cnf(matrix-262, plain, ( ( c_Lambda_Olift(c_Lambda_OdB_OVar(V_i), V_k) = c_Lambda_OdB_OVar(V_i)) | ~c_HOL_Oord__class_Oless(V_i, V_k, tc_nat) )).
% 8.21/8.42 cnf(matrix-263, plain, ( c_Type_Otyping(V_e, V_t_H, V_T) | ~c_Type_Otyping(V_e, V_t, V_T) | ~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), V_t), V_t_H)) )).
% 8.21/8.42 cnf(matrix-264, plain, ( hBOOL(hAPP(hAPP(c_Lambda_Obeta, hAPP(hAPP(c_Lambda_OdB_OApp, V_s), V_u)), hAPP(hAPP(c_Lambda_OdB_OApp, V_t), V_u))) | ~hBOOL(hAPP(hAPP(c_Lambda_Obeta, V_s), V_t)) )).
% 8.21/8.42 cnf(matrix-265, plain, ( hBOOL(hAPP(hAPP(c_Lambda_Obeta, hAPP(hAPP(c_Lambda_OdB_OApp, V_u), V_s)), hAPP(hAPP(c_Lambda_OdB_OApp, V_u), V_t))) | ~hBOOL(hAPP(hAPP(c_Lambda_Obeta, V_s), V_t)) )).
% 8.21/8.42 cnf(matrix-266, plain, ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), hAPP(hAPP(c_Lambda_OdB_OApp, V_s), V_t)), hAPP(hAPP(c_Lambda_OdB_OApp, V_s_H), V_t_H))) | ~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), V_t), V_t_H)) | ~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), V_s), V_s_H)) )).
% 8.21/8.42 cnf(matrix-267, plain, ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), hAPP(hAPP(c_Lambda_OdB_OApp, V_s), V_t)), hAPP(hAPP(c_Lambda_OdB_OApp, V_s_H), V_t))) | ~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), V_s), V_s_H)) )).
% 8.21/8.42 cnf(matrix-268, plain, ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), hAPP(hAPP(c_Lambda_OdB_OApp, V_s), V_t)), hAPP(hAPP(c_Lambda_OdB_OApp, V_s), V_t_H))) | ~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), V_t), V_t_H)) )).
% 8.21/8.42 cnf(matrix-269, plain, ( ( v_T____ = hAPP(hAPP(c_Type_Otype_OFun, v_T_H_H____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype))) )).
% 8.21/8.42 cnf(matrix-270, plain, ( c_HOL_Oord__class_Oless(V_x, V_x, tc_nat) | ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x), V_s, V_x) = V_s) )).
% 8.21/8.42 cnf(matrix-271, plain, ( c_Type_Otyping(V_e, V_u, c_Type_Osko__Type__Xtyping__elims__2__1(V_T, V_e, V_t, V_u)) | ~c_Type_Otyping(V_e, hAPP(hAPP(c_Lambda_OdB_OApp, V_t), V_u), V_T) )).
% 8.21/8.42 cnf(matrix-272, plain, ( ( V_v = c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_n), c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(V_n, V_rs, V_v), tc_Lambda_OdB, tc_Lambda_OdB)) | ~hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_n), V_rs, tc_Lambda_OdB, tc_Lambda_OdB)), V_v)) )).
% 8.21/8.42 cnf(matrix-273, plain, ( c_Type_Otyping(V_e, c_List_Ofoldl(c_Lambda_OdB_OApp, V_t, V_ts, tc_Lambda_OdB, tc_Lambda_OdB), V_T) | ~c_Type_Otypings(V_e, V_ts, V_Ts) | ~c_Type_Otyping(V_e, V_t, c_List_Ofoldr(c_Type_Otype_OFun, V_Ts, V_T, tc_Type_Otype, tc_Type_Otype)) )).
% 8.21/8.42 cnf(matrix-274, plain, ( c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____), v_rs____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____) )).
% 8.21/8.42 cnf(matrix-275, plain, ( c_Type_Otyping(V_e, c_Lambda_OdB_OVar(V_i), c_List_Ofoldr(c_Type_Otype_OFun, c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T, V_e, V_i, V_ts), V_T, tc_Type_Otype, tc_Type_Otype)) | ~c_Type_Otyping(V_e, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_i), V_ts, tc_Lambda_OdB, tc_Lambda_OdB), V_T) )).
% 8.21/8.42 cnf(matrix-276, plain, ( ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_i), V_s, V_k) = c_Lambda_OdB_OVar(V_i)) | ( V_i = V_k) | c_HOL_Oord__class_Oless(V_k, V_i, tc_nat) )).
% 8.21/8.42 cnf(matrix-277, plain, ( c_Type_Otyping(V_e, V_t, c_List_Ofoldr(c_Type_Otype_OFun, c_Type_Osko__Type__Xlist__app__typeE__1__1(V_T, V_e, V_t, V_ts), V_T, tc_Type_Otype, tc_Type_Otype)) | ~c_Type_Otyping(V_e, c_List_Ofoldl(c_Lambda_OdB_OApp, V_t, V_ts, tc_Lambda_OdB, tc_Lambda_OdB), V_T) )).
% 8.21/8.42 cnf(matrix-278, plain, ( c_Type_Otypings(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_as____, v_Ts____) )).
% 8.21/8.42 cnf(matrix-279, plain, ( c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____)), v_a____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype)) )).
% 8.21/8.42 cnf(matrix-280, plain, ( c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_Lambda_OdB_OVar(v_n____), hAPP(hAPP(c_Type_Otype_OFun, v_T_H_H____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype))) )).
% 8.21/8.42 cnf(matrix-281, plain, ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), c_Lambda_Osubst(V_t, V_r, V_i)), c_Lambda_Osubst(V_t, V_s, V_i))) | ~hBOOL(hAPP(hAPP(c_Lambda_Obeta, V_r), V_s)) )).
% 8.21/8.42 cnf(matrix-282, plain, ( c_Type_Otyping(c_Type_Oshift(v_ea______, v_ia______, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(v_n____), v_rs____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_Ha______) )).
% 8.21/8.42 cnf(matrix-283, plain, ( ( c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp, V_s), V_t), V_k) = hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_Olift(V_s, V_k)), c_Lambda_Olift(V_t, V_k))) )).
% 8.21/8.42 cnf(matrix-284, plain, ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), c_Lambda_Osubst(V_r, V_t, V_i)), c_Lambda_Osubst(V_s, V_t, V_i))) | ~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), V_r), V_s)) )).
% 8.21/8.42 cnf(matrix-285, plain, ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), c_Lambda_Osubst(V_t, V_r, V_i)), c_Lambda_Osubst(V_t, V_s, V_i))) | ~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), V_r), V_s)) )).
% 8.21/8.42 cnf(matrix-286, plain, ( hBOOL(hAPP(c_InductTermi_OIT, c_Lambda_OdB_OVar(V_n))) )).
% 8.21/8.42 cnf(matrix-287, plain, ( c_Type_Otyping(V_env, c_Lambda_OdB_OAbs(V_t), hAPP(hAPP(c_Type_Otype_OFun, V_T), V_U)) | ~c_Type_Otyping(c_Type_Oshift(V_env, c_HOL_Ozero__class_Ozero(tc_nat), V_T, tc_Type_Otype), V_t, V_U) )).
% 8.21/8.42 cnf(matrix-288, plain, ( ( hAPP(c_Type_Oshift(V_e, V_x, V_T, T_a), V_x) = V_T) )).
% 8.21/8.42 cnf(matrix-289, plain, ( ( v_T____ != hAPP(hAPP(c_Type_Otype_OFun, V_T1), V_T2)) | hBOOL(hAPP(c_InductTermi_OIT, c_Lambda_Osubst(V_t, V_u, V_i))) | ~c_Type_Otyping(V_e, V_u, V_T1) | ~hBOOL(hAPP(c_InductTermi_OIT, V_u)) | ~c_Type_Otyping(c_Type_Oshift(V_e, V_i, V_T1, tc_Type_Otype), V_t, V_Ta) | ~hBOOL(hAPP(c_InductTermi_OIT, V_t)) )).
% 8.21/8.42 cnf(matrix-290, plain, ( ( v_T____ != hAPP(hAPP(c_Type_Otype_OFun, V_T1), V_T2)) | hBOOL(hAPP(c_InductTermi_OIT, c_Lambda_Osubst(V_t, V_u, V_i))) | ~c_Type_Otyping(V_e, V_u, V_T2) | ~hBOOL(hAPP(c_InductTermi_OIT, V_u)) | ~c_Type_Otyping(c_Type_Oshift(V_e, V_i, V_T2, tc_Type_Otype), V_t, V_Ta) | ~hBOOL(hAPP(c_InductTermi_OIT, V_t)) )).
% 8.21/8.42 cnf(matrix-291, plain, ( hBOOL(hAPP(c_InductTermi_OIT, c_Lambda_Olift(V_t, V_i))) | ~hBOOL(hAPP(c_InductTermi_OIT, V_t)) )).
% 8.21/8.42 cnf(matrix-292, plain, ( ( c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp, V_dB1_H), V_dB2_H)) )).
% 8.21/8.42 cnf(matrix-293, plain, ( ( c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp, V_s, V_ss, tc_Lambda_OdB, tc_Lambda_OdB)) | ( c_Lambda_OdB_OVar(V_m) = V_s) )).
% 8.21/8.42 cnf(matrix-294, plain, ( hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, V_r, V_ss, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, V_s, V_ss, tc_Lambda_OdB, tc_Lambda_OdB))) | ~hBOOL(hAPP(hAPP(c_Lambda_Obeta, V_r), V_s)) )).
% 8.21/8.42 cnf(matrix-295, plain, ( hBOOL(hAPP(hAPP(c_Lambda_Obeta, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(V_s)), V_t)), c_Lambda_Osubst(V_s, V_t, c_HOL_Ozero__class_Ozero(tc_nat)))) )).
% 8.21/8.42 cnf(matrix-296, plain, ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), c_Lambda_Olift(V_r, V_i)), c_Lambda_Olift(V_s, V_i))) | ~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), V_r), V_s)) )).
% 8.21/8.42 cnf(matrix-297, plain, ( ( V_T = V_U) | ~c_Type_Otyping(V_e, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_i), V_ts, tc_Lambda_OdB, tc_Lambda_OdB), V_U) | ~c_Type_Otyping(V_e, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_i), V_ts, tc_Lambda_OdB, tc_Lambda_OdB), V_T) )).
% 8.21/8.42 cnf(matrix-298, plain, ( ( hAPP(hAPP(c_Lambda_OdB_OApp, V_dB1), V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp, V_dB1_H), V_dB2_H)) | ( V_dB2 = V_dB2_H) )).
% 8.21/8.42 cnf(matrix-299, plain, ( ( hAPP(hAPP(c_Lambda_OdB_OApp, V_dB1), V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp, V_dB1_H), V_dB2_H)) | ( V_dB1 = V_dB1_H) )).
% 8.21/8.42 cnf(matrix-300, plain, ( hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_n), V_rs, tc_Lambda_OdB, tc_Lambda_OdB))) | ~c_List_Olistsp(c_InductTermi_OIT, V_rs, tc_Lambda_OdB) )).
% 8.21/8.42 cnf(matrix-301, plain, ( c_Type_Otyping(V_env, hAPP(hAPP(c_Lambda_OdB_OApp, V_s), V_t), V_U) | ~c_Type_Otyping(V_env, V_t, V_T) | ~c_Type_Otyping(V_env, V_s, hAPP(hAPP(c_Type_Otype_OFun, V_T), V_U)) )).
% 8.21/8.42 cnf(matrix-302, plain, ( ~hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_Lambda_OdB_OVar(V_i)), V_t)) )).
% 8.21/8.42 cnf(matrix-303, plain, ( ( V_U = c_List_Ofoldr(c_Type_Otype_OFun, c_Type_Osko__Type__Xvar__app__types__1__1(V_T, V_U, V_e, V_us), V_T, tc_Type_Otype, tc_Type_Otype)) | ~c_Type_Otyping(V_e, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_i), V_ts, tc_Lambda_OdB, tc_Lambda_OdB), V_U) | ~c_Type_Otypings(V_e, V_ts, V_Ts) | ~c_Type_Otyping(V_e, c_List_Ofoldl(c_Lambda_OdB_OApp, c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_i), V_ts, tc_Lambda_OdB, tc_Lambda_OdB), V_us, tc_Lambda_OdB, tc_Lambda_OdB), V_T) )).
% 8.21/8.42 cnf(matrix-304, plain, ( ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_j), V_u, V_i) = c_Lambda_OdB_OVar(V_j)) | ~c_HOL_Oord__class_Oless(V_j, V_i, tc_nat) )).
% 8.21/8.42 cnf(matrix-305, plain, ( hBOOL(hAPP(c_InductTermi_OIT, c_Lambda_Osubst(V_r, c_Lambda_OdB_OVar(V_i), V_j))) | ~hBOOL(hAPP(c_InductTermi_OIT, V_r)) )).
% 8.21/8.42 cnf(matrix-306, plain, ( ( hAPP(hAPP(c_Type_Otype_OFun, V_type1), V_type2) != hAPP(hAPP(c_Type_Otype_OFun, V_type1_H), V_type2_H)) | ( V_type2 = V_type2_H) )).
% 8.21/8.42 cnf(matrix-307, plain, ( ( hAPP(hAPP(c_Type_Otype_OFun, V_type1), V_type2) != hAPP(hAPP(c_Type_Otype_OFun, V_type1_H), V_type2_H)) | ( V_type1 = V_type1_H) )).
% 8.21/8.42 cnf(matrix-308, plain, ( ( c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_m), V_rs, tc_Lambda_OdB, tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_n), V_ss, tc_Lambda_OdB, tc_Lambda_OdB)) | ( V_rs = V_ss) )).
% 8.21/8.42 cnf(matrix-309, plain, ( ( c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_m), V_rs, tc_Lambda_OdB, tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp, c_Lambda_OdB_OVar(V_n), V_ss, tc_Lambda_OdB, tc_Lambda_OdB)) | ( V_m = V_n) )).
% 8.21/8.42 cnf(matrix-310, plain, ( ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H)) | ( V_nat = V_nat_H) )).
% 8.21/8.42 cnf(matrix-311, plain, ( c_Type_Otyping(c_Type_Oshift(V_e, V_i, V_U, tc_Type_Otype), c_Lambda_Olift(V_t, V_i), V_T) | ~c_Type_Otyping(V_e, V_t, V_T) )).
% 8.21/8.42 cnf(matrix-312, plain, ( c_Type_Otyping(v_e____, v_u____, v_T____) )).
% 8.21/8.42 cnf(matrix-313, plain, ( ( c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp, V_t), V_u), V_s, V_k) = hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_Osubst(V_t, V_s, V_k)), c_Lambda_Osubst(V_u, V_s, V_k))) )).
% 8.21/8.42 cnf(matrix-314, plain, ( c_Type_Otyping(V_e, V_t_H, V_T) | ~hBOOL(hAPP(hAPP(c_Lambda_Obeta, V_t), V_t_H)) | ~c_Type_Otyping(V_e, V_t, V_T) )).
% 8.21/8.42 cnf(matrix-315, plain, ( ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k), V_u, V_k) = V_u) )).
% 8.21/8.42 cnf(matrix-316, plain, ( c_Type_Otyping(v_e____, v_u____, hAPP(hAPP(c_Type_Otype_OFun, v_T_H_H____), c_List_Ofoldr(c_Type_Otype_OFun, v_Ts____, v_T_H____, tc_Type_Otype, tc_Type_Otype))) )).
% 8.21/8.42 cnf(matrix-317, plain, ( c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_a____, v_T_H_H____) )).
% 8.21/8.42 cnf(matrix-318, plain, ( ( v_n____ = v_i____) )).
% 8.21/8.42 cnf(matrix-319, plain, ( ( hAPP(V_e, V_i) = V_T) | ~c_Type_Otyping(V_e, c_Lambda_OdB_OVar(V_i), V_T) )).
% 8.21/8.42 cnf(matrix-320, plain, ( hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_Lambda_Osubst(V_r, V_t, V_i)), c_Lambda_Osubst(V_s, V_t, V_i))) | ~hBOOL(hAPP(hAPP(c_Lambda_Obeta, V_r), V_s)) )).
% 8.21/8.42 cnf(matrix-321, plain, ( c_Type_Otyping(V_env, c_Lambda_OdB_OVar(V_x), hAPP(V_env, V_x)) )).
% 8.21/8.42 cnf(matrix-322, plain, ( hBOOL(hAPP(c_InductTermi_OIT, v_u____)) )).
% 8.21/8.42 cnf(matrix-323, plain, ( ( c_Lambda_Osubst(c_Lambda_Olift(V_t, V_k), V_s, V_k) = V_t) )).
% 8.21/8.42 cnf(matrix-324, plain, ( ~c_Type_Otyping(V_e_H, V_u, V_U) | ~c_Type_Otyping(c_Type_Oshift(V_e_H, V_i, V_U, tc_Type_Otype), V_t, V_T) | c_Type_Otyping(V_e_H, c_Lambda_Osubst(V_t, V_u, V_i), V_T) )).
% 8.21/8.42 cnf(matrix-325, plain, ( c_Type_Otyping(v_e____, v_u____, v_T____) )).
% 8.21/8.42 cnf(matrix-326, plain, ( c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), v_a____, v_T_H_H____) )).
% 8.21/8.42 cnf(matrix-327, plain, ( ~c_Type_Otyping(v_e____, c_Lambda_Osubst(v_a____, v_u____, v_i____), v_T_H_H____) )).
% 8.21/8.42 cnf(matrix-328, plain, ( class_Orderings_Opreorder(tc_fun(T_2, T_1)) | ~class_Orderings_Opreorder(T_1) )).
% 8.21/8.42 cnf(matrix-329, plain, ( class_Orderings_Oorder(tc_fun(T_2, T_1)) | ~class_Orderings_Oorder(T_1) )).
% 8.21/8.42 cnf(matrix-330, plain, ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) )).
% 8.21/8.42 cnf(matrix-331, plain, ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) )).
% 8.21/8.42 cnf(matrix-332, plain, ( class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) )).
% 8.21/8.42 cnf(matrix-333, plain, ( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) )).
% 8.21/8.42 cnf(matrix-334, plain, ( class_OrderedGroup_Ocancel__semigroup__add(tc_nat) )).
% 8.21/8.42 cnf(matrix-335, plain, ( class_Ring__and__Field_Oordered__semidom(tc_nat) )).
% 8.21/8.42 cnf(matrix-336, plain, ( class_Ring__and__Field_Ocomm__semiring__1(tc_nat) )).
% 8.21/8.42 cnf(matrix-337, plain, ( class_OrderedGroup_Oab__semigroup__add(tc_nat) )).
% 8.21/8.42 cnf(matrix-338, plain, ( class_OrderedGroup_Ocomm__monoid__add(tc_nat) )).
% 8.21/8.42 cnf(matrix-339, plain, ( class_OrderedGroup_Osemigroup__add(tc_nat) )).
% 8.21/8.42 cnf(matrix-340, plain, ( class_Ring__and__Field_Osemiring__1(tc_nat) )).
% 8.21/8.42 cnf(matrix-341, plain, ( class_OrderedGroup_Omonoid__add(tc_nat) )).
% 8.21/8.42 cnf(matrix-342, plain, ( class_Nat_Osemiring__char__0(tc_nat) )).
% 8.21/8.42 cnf(matrix-343, plain, ( class_Orderings_Opreorder(tc_nat) )).
% 8.21/8.42 cnf(matrix-344, plain, ( class_Orderings_Olinorder(tc_nat) )).
% 8.21/8.42 cnf(matrix-345, plain, ( class_Orderings_Oorder(tc_nat) )).
% 8.21/8.42 cnf(matrix-346, plain, ( class_Orderings_Opreorder(tc_bool) )).
% 8.21/8.42 cnf(matrix-347, plain, ( class_Orderings_Oorder(tc_bool) )).
% 8.21/8.42 cnf(matrix-348, plain, ( hBOOL(hAPP(hAPP(c_fequal(T_a), V_x), V_x)) )).
% 8.21/8.42 cnf(matrix-349, plain, ( ( V_X = V_Y) | ~hBOOL(hAPP(hAPP(c_fequal(T_a), V_X), V_Y)) )).
% 8.21/8.42
% 8.21/8.42 % Proof stack:
% 8.21/8.42 cnf(proof-stack, plain,
% 8.21/8.42 proof_stack(
% 8.21/8.42 start(327),
% 8.21/8.42 left_branch(0, 324, 2, 2),
% 8.21/8.42 left_branch(0, 325, 0, 3),
% 8.21/8.42 right_branch(3),
% 8.21/8.42 left_branch(0, 326, 0, 4),
% 8.21/8.42 right_branch(4),
% 8.21/8.42 right_branch(2)
% 8.21/8.42 )).
% 8.21/8.42 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------