TSTP Solution File: LCL755-1 by ConnectPP---0.3.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : LCL755-1 : 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 : n006.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 : Mon Mar 25 14:21:10 EDT 2024
% Result : Unsatisfiable 12.19s 12.35s
% Output : Proof 12.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL755-1 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.12 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Mar 20 18:36:44 EDT 2024
% 0.13/0.34 % CPUTime :
% 12.19/12.35 % SZS status Unsatisfiable for theBenchmark
% 12.19/12.35 % SZS output start Proof for theBenchmark
% 12.19/12.35
% 12.19/12.35 % Problem matrix:
% 12.19/12.35 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 12.19/12.35 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 12.19/12.35 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 12.19/12.35 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( c_Orderings_Oord__class_Omax(__eqx_0, __eqx_1, __eqx_2) = c_Orderings_Oord__class_Omax(__eqy_0, __eqy_1, __eqy_2)) )).
% 12.19/12.35 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( c_Orderings_Oord__class_Omin(__eqx_0, __eqx_1, __eqx_2) = c_Orderings_Oord__class_Omin(__eqy_0, __eqy_1, __eqy_2)) )).
% 12.19/12.35 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( c_HOL_Oplus__class_Oplus(__eqx_0, __eqx_1, __eqx_2) = c_HOL_Oplus__class_Oplus(__eqy_0, __eqy_1, __eqy_2)) )).
% 12.19/12.35 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( c_HOL_Ozero__class_Ozero(__eqx_0) = c_HOL_Ozero__class_Ozero(__eqy_0)) )).
% 12.19/12.35 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( c_Suc(__eqx_0) = c_Suc(__eqy_0)) )).
% 12.19/12.35 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( c_HOL_Oone__class_Oone(__eqx_0) = c_HOL_Oone__class_Oone(__eqy_0)) )).
% 12.19/12.35 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( c_HOL_Ominus__class_Ominus(__eqx_0, __eqx_1, __eqx_2) = c_HOL_Ominus__class_Ominus(__eqy_0, __eqy_1, __eqy_2)) )).
% 12.19/12.35 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( c_HOL_Otimes__class_Otimes(__eqx_0, __eqx_1, __eqx_2) = c_HOL_Otimes__class_Otimes(__eqy_0, __eqy_1, __eqy_2)) )).
% 12.19/12.35 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( c_Divides_Odiv__class_Omod(__eqx_0, __eqx_1, __eqx_2) = c_Divides_Odiv__class_Omod(__eqy_0, __eqy_1, __eqy_2)) )).
% 12.19/12.35 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( c_Lambda_OdB_OApp(__eqx_0, __eqx_1) = c_Lambda_OdB_OApp(__eqy_0, __eqy_1)) )).
% 12.19/12.35 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( c_Lambda_Olift(__eqx_0, __eqx_1) = c_Lambda_Olift(__eqy_0, __eqy_1)) )).
% 12.19/12.35 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( c_Lambda_OdB_OVar(__eqx_0) = c_Lambda_OdB_OVar(__eqy_0)) )).
% 12.19/12.35 cnf(matrix-15, 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)) )).
% 12.19/12.35 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( c_Lambda_OdB_OAbs(__eqx_0) = c_Lambda_OdB_OAbs(__eqy_0)) )).
% 12.19/12.35 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ~class_Orderings_Olinorder(__eqx_0) | class_Orderings_Olinorder(__eqy_0) )).
% 12.19/12.35 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~c_lessequals(__eqx_0, __eqx_1, __eqx_2) | c_lessequals(__eqy_0, __eqy_1, __eqy_2) )).
% 12.19/12.35 cnf(matrix-19, 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) )).
% 12.19/12.35 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Ocomm__monoid__add(__eqx_0) | class_OrderedGroup_Ocomm__monoid__add(__eqy_0) )).
% 12.19/12.35 cnf(matrix-21, 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) )).
% 12.19/12.35 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Opordered__ring(__eqx_0) | class_Ring__and__Field_Opordered__ring(__eqy_0) )).
% 12.19/12.35 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Oordered__ring__strict(__eqx_0) | class_Ring__and__Field_Oordered__ring__strict(__eqy_0) )).
% 12.19/12.35 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ~class_Divides_Osemiring__div(__eqx_0) | class_Divides_Osemiring__div(__eqy_0) )).
% 12.19/12.35 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Ocomm__semiring__1(__eqx_0) | class_Ring__and__Field_Ocomm__semiring__1(__eqy_0) )).
% 12.19/12.35 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Oidom(__eqx_0) | class_Ring__and__Field_Oidom(__eqy_0) )).
% 12.19/12.35 cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ~class_Int_Onumber__ring(__eqx_0) | class_Int_Onumber__ring(__eqy_0) )).
% 12.19/12.35 cnf(matrix-28, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Oordered__semiring__strict(__eqx_0) | class_Ring__and__Field_Oordered__semiring__strict(__eqy_0) )).
% 12.19/12.35 cnf(matrix-29, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Oordered__semiring(__eqx_0) | class_Ring__and__Field_Oordered__semiring(__eqy_0) )).
% 12.19/12.35 cnf(matrix-30, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Oab__group__add(__eqx_0) | class_OrderedGroup_Oab__group__add(__eqy_0) )).
% 12.19/12.35 cnf(matrix-31, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Ogroup__add(__eqx_0) | class_OrderedGroup_Ogroup__add(__eqy_0) )).
% 12.19/12.35 cnf(matrix-32, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Oring(__eqx_0) | class_Ring__and__Field_Oring(__eqy_0) )).
% 12.19/12.35 cnf(matrix-33, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Opordered__ab__group__add(__eqx_0) | class_OrderedGroup_Opordered__ab__group__add(__eqy_0) )).
% 12.19/12.35 cnf(matrix-34, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Ocomm__monoid__mult(__eqx_0) | class_OrderedGroup_Ocomm__monoid__mult(__eqy_0) )).
% 12.19/12.35 cnf(matrix-35, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Omonoid__mult(__eqx_0) | class_OrderedGroup_Omonoid__mult(__eqy_0) )).
% 12.19/12.35 cnf(matrix-36, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Olordered__ab__group__add(__eqx_0) | class_OrderedGroup_Olordered__ab__group__add(__eqy_0) )).
% 12.19/12.35 cnf(matrix-37, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Opordered__ab__semigroup__add(__eqx_0) | class_OrderedGroup_Opordered__ab__semigroup__add(__eqy_0) )).
% 12.19/12.35 cnf(matrix-38, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Opordered__comm__monoid__add(__eqx_0) | class_OrderedGroup_Opordered__comm__monoid__add(__eqy_0) )).
% 12.19/12.35 cnf(matrix-39, plain, ( ( __eqx_0 != __eqy_0) | ~class_Orderings_Opreorder(__eqx_0) | class_Orderings_Opreorder(__eqy_0) )).
% 12.19/12.35 cnf(matrix-40, plain, ( ( __eqx_0 != __eqy_0) | ~class_Orderings_Oorder(__eqx_0) | class_Orderings_Oorder(__eqy_0) )).
% 12.19/12.35 cnf(matrix-41, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Oab__semigroup__add(__eqx_0) | class_OrderedGroup_Oab__semigroup__add(__eqy_0) )).
% 12.19/12.35 cnf(matrix-42, plain, ( ( __eqx_0 != __eqy_0) | ~class_Divides_Oring__div(__eqx_0) | class_Divides_Oring__div(__eqy_0) )).
% 12.19/12.35 cnf(matrix-43, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Oring__no__zero__divisors(__eqx_0) | class_Ring__and__Field_Oring__no__zero__divisors(__eqy_0) )).
% 12.19/12.35 cnf(matrix-44, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Ono__zero__divisors(__eqx_0) | class_Ring__and__Field_Ono__zero__divisors(__eqy_0) )).
% 12.19/12.35 cnf(matrix-45, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Oordered__idom(__eqx_0) | class_Ring__and__Field_Oordered__idom(__eqy_0) )).
% 12.19/12.35 cnf(matrix-46, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Oordered__semidom(__eqx_0) | class_Ring__and__Field_Oordered__semidom(__eqy_0) )).
% 12.19/12.35 cnf(matrix-47, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Ozero__neq__one(__eqx_0) | class_Ring__and__Field_Ozero__neq__one(__eqy_0) )).
% 12.19/12.35 cnf(matrix-48, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Omult__zero(__eqx_0) | class_Ring__and__Field_Omult__zero(__eqy_0) )).
% 12.19/12.35 cnf(matrix-49, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Osemiring(__eqx_0) | class_Ring__and__Field_Osemiring(__eqy_0) )).
% 12.19/12.35 cnf(matrix-50, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Opordered__cancel__semiring(__eqx_0) | class_Ring__and__Field_Opordered__cancel__semiring(__eqy_0) )).
% 12.19/12.35 cnf(matrix-51, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~c_Lambda_Obeta(__eqx_0, __eqx_1) | c_Lambda_Obeta(__eqy_0, __eqy_1) )).
% 12.19/12.35 cnf(matrix-52, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Opordered__cancel__ab__semigroup__add(__eqx_0) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(__eqy_0) )).
% 12.19/12.35 cnf(matrix-53, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Oab__semigroup__idem__mult(__eqx_0) | class_OrderedGroup_Oab__semigroup__idem__mult(__eqy_0) )).
% 12.19/12.35 cnf(matrix-54, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Omult__mono(__eqx_0) | class_Ring__and__Field_Omult__mono(__eqy_0) )).
% 12.19/12.35 cnf(matrix-55, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Omult__mono1(__eqx_0) | class_Ring__and__Field_Omult__mono1(__eqy_0) )).
% 12.19/12.35 cnf(matrix-56, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Ocancel__ab__semigroup__add(__eqx_0) | class_OrderedGroup_Ocancel__ab__semigroup__add(__eqy_0) )).
% 12.19/12.35 cnf(matrix-57, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Ocancel__semigroup__add(__eqx_0) | class_OrderedGroup_Ocancel__semigroup__add(__eqy_0) )).
% 12.19/12.35 cnf(matrix-58, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Oordered__comm__semiring__strict(__eqx_0) | class_Ring__and__Field_Oordered__comm__semiring__strict(__eqy_0) )).
% 12.19/12.35 cnf(matrix-59, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Opordered__semiring(__eqx_0) | class_Ring__and__Field_Opordered__semiring(__eqy_0) )).
% 12.19/12.35 cnf(matrix-60, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Omonoid__add(__eqx_0) | class_OrderedGroup_Omonoid__add(__eqy_0) )).
% 12.19/12.35 cnf(matrix-61, plain, ( ( __eqx_0 != __eqy_0) | ~class_OrderedGroup_Oab__semigroup__mult(__eqx_0) | class_OrderedGroup_Oab__semigroup__mult(__eqy_0) )).
% 12.19/12.35 cnf(matrix-62, plain, ( ( __eqx_0 != __eqy_0) | ~class_Ring__and__Field_Ocomm__semiring(__eqx_0) | class_Ring__and__Field_Ocomm__semiring(__eqy_0) )).
% 12.19/12.35 cnf(matrix-63, plain, ( ( __eqx_0 != __eqy_0) | ~c_InductTermi_OIT(__eqx_0) | c_InductTermi_OIT(__eqy_0) )).
% 12.19/12.35 cnf(matrix-64, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(c_Orderings_Oord__class_Omax(V_x, V_y, T_a), V_z, T_a) | ~c_lessequals(V_y, V_z, T_a) | ~c_lessequals(V_x, V_z, T_a) )).
% 12.19/12.35 cnf(matrix-65, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(c_Orderings_Oord__class_Omax(V_y, V_z, T_a), V_x, T_a) | ~c_lessequals(V_z, V_x, T_a) | ~c_lessequals(V_y, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-66, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(c_Orderings_Oord__class_Omax(V_a, V_b, T_a), V_x, T_a) | ~c_lessequals(V_b, V_x, T_a) | ~c_lessequals(V_a, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-67, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_x, c_Orderings_Oord__class_Omax(V_x, V_y, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-68, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_y, c_Orderings_Oord__class_Omax(V_x, V_y, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-69, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_y, V_z, T_a), V_x, T_a) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_y, V_x, T_a), c_Orderings_Oord__class_Omin(V_z, V_x, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-70, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omin(V_x, c_Orderings_Oord__class_Omax(V_y, V_z, T_a), T_a) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_x, V_y, T_a), c_Orderings_Oord__class_Omin(V_x, V_z, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-71, plain, ( ~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) | ~class_OrderedGroup_Ocomm__monoid__add(T_a) | c_lessequals(V_b, c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), T_a) | ~c_lessequals(V_b, V_c, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) )).
% 12.19/12.35 cnf(matrix-72, plain, ( ~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) | ~class_OrderedGroup_Ocomm__monoid__add(T_a) | c_lessequals(V_b, c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), T_a) | ~c_lessequals(V_b, V_a, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) )).
% 12.19/12.35 cnf(matrix-73, plain, ( c_lessequals(c_Suc(V_m), V_n, tc_nat) | ~c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-74, plain, ( c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ~c_lessequals(c_Suc(V_m), V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-75, plain, ( c_lessequals(c_Suc(V_n), V_m, tc_nat) | ~c_HOL_Oord__class_Oless(V_n, V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-76, plain, ( c_HOL_Oord__class_Oless(V_n, V_m, tc_nat) | ~c_lessequals(c_Suc(V_n), V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-77, plain, ( c_HOL_Oord__class_Oless(V_x, c_HOL_Oplus__class_Oplus(V_y, V_z, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(V_x, V_y, tc_nat) )).
% 12.19/12.35 cnf(matrix-78, plain, ( c_HOL_Oord__class_Oless(V_x, c_HOL_Oplus__class_Oplus(V_y, V_z, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(V_x, V_z, tc_nat) )).
% 12.19/12.35 cnf(matrix-79, plain, ( c_HOL_Oord__class_Oless(V_i, V_k, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i, V_j, tc_nat), V_k, tc_nat) )).
% 12.19/12.35 cnf(matrix-80, plain, ( c_HOL_Oord__class_Oless(V_i, c_HOL_Oplus__class_Oplus(V_j, V_m, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-81, plain, ( c_HOL_Oord__class_Oless(V_i, c_HOL_Oplus__class_Oplus(V_m, V_j, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-82, plain, ( ( c_HOL_Ominus__class_Ominus(c_Suc(V_n), c_HOL_Oone__class_Oone(tc_nat), tc_nat) = V_n) )).
% 12.19/12.35 cnf(matrix-83, plain, ( ~class_Ring__and__Field_Opordered__ring(T_a) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_e, T_a), V_c, T_a), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b, V_e, T_a), V_d, T_a), T_a) | ~c_lessequals(V_c, c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b, V_a, T_a), V_e, T_a), V_d, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-84, plain, ( ~class_Ring__and__Field_Opordered__ring(T_a) | c_lessequals(V_c, c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b, V_a, T_a), V_e, T_a), V_d, T_a), T_a) | ~c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_e, T_a), V_c, T_a), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b, V_e, T_a), V_d, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-85, plain, ( ~class_Ring__and__Field_Opordered__ring(T_a) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_e, T_a), V_c, T_a), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b, V_e, T_a), V_d, T_a), T_a) | ~c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a, V_b, T_a), V_e, T_a), V_c, T_a), V_d, T_a) )).
% 12.19/12.35 cnf(matrix-86, plain, ( ~class_Ring__and__Field_Opordered__ring(T_a) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a, V_b, T_a), V_e, T_a), V_c, T_a), V_d, T_a) | ~c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_e, T_a), V_c, T_a), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b, V_e, T_a), V_d, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-87, plain, ( ( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(V_k, V_m, tc_nat)), V_k, tc_nat) = c_HOL_Oone__class_Oone(tc_nat)) | ~c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat), V_k, tc_nat) )).
% 12.19/12.35 cnf(matrix-88, plain, ( ( c_HOL_Ominus__class_Ominus(c_Suc(V_m), V_n, tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m, V_n, tc_nat))) | ~c_lessequals(V_n, V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-89, plain, ( ( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat), c_HOL_Oone__class_Oone(tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-90, plain, ( ( c_Lambda_Olift(c_Lambda_OdB_OApp(V_s, V_t), V_k) = c_Lambda_OdB_OApp(c_Lambda_Olift(V_s, V_k), c_Lambda_Olift(V_t, V_k))) )).
% 12.19/12.35 cnf(matrix-91, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x, V_x, T_a), c_HOL_Otimes__class_Otimes(V_y, V_y, T_a), T_a), T_a) )).
% 12.19/12.35 cnf(matrix-92, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) = V_a) )).
% 12.19/12.35 cnf(matrix-93, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(V_a, V_a, T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-94, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Oplus__class_Oplus(V_a, V_c, T_a) = c_HOL_Oplus__class_Oplus(V_c, V_a, T_a)) )).
% 12.19/12.35 cnf(matrix-95, plain, ( ~class_OrderedGroup_Ocomm__monoid__add(T_a) | ( c_HOL_Oplus__class_Oplus(V_a, V_b, T_a) = c_HOL_Oplus__class_Oplus(V_b, V_a, T_a)) )).
% 12.19/12.35 cnf(matrix-96, plain, ( ( c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat) = c_HOL_Oplus__class_Oplus(V_n, V_m, tc_nat)) )).
% 12.19/12.35 cnf(matrix-97, plain, ( ( c_HOL_Oplus__class_Oplus(V_m, V_l, tc_nat) != c_HOL_Oplus__class_Oplus(V_k, V_n, tc_nat)) | ~c_HOL_Oord__class_Oless(V_k, V_l, tc_nat) | c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-98, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Oplus__class_Oplus(V_x, V_y, T_a) = c_HOL_Oplus__class_Oplus(V_y, V_x, T_a)) )).
% 12.19/12.35 cnf(matrix-99, plain, ( ( c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) | ( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) )).
% 12.19/12.35 cnf(matrix-100, plain, ( ( c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) | ( V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) )).
% 12.19/12.35 cnf(matrix-101, plain, ( c_lessequals(c_Divides_Odiv__class_Omod(V_m, V_n, tc_nat), V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-102, plain, ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_l, V_n, tc_nat), c_HOL_Ominus__class_Ominus(V_l, V_m, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(V_m, V_l, tc_nat) | ~c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-103, plain, ( ~class_Ring__and__Field_Oidom(T_a) | ~class_Int_Onumber__ring(T_a) | ( V_x != c_HOL_Oplus__class_Oplus(V_x, V_a, T_a)) | ( V_a = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-104, plain, ( ( c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat) != V_m) | ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-105, plain, ( ( V_x != c_HOL_Oplus__class_Oplus(V_x, V_a, tc_nat)) | ( V_a = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-106, plain, ( ~class_Ring__and__Field_Oordered__semiring__strict(T_a) | c_HOL_Oord__class_Oless(V_a, V_b, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-107, plain, ( ~class_Ring__and__Field_Oordered__semiring__strict(T_a) | c_HOL_Oord__class_Oless(V_a, V_b, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-108, plain, ( ~class_Ring__and__Field_Oordered__semiring(T_a) | c_HOL_Oord__class_Oless(V_a, V_b, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-109, plain, ( ~class_Ring__and__Field_Oordered__semiring(T_a) | c_HOL_Oord__class_Oless(V_a, V_b, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-110, plain, ( ~class_OrderedGroup_Oab__group__add(T_a) | ( c_HOL_Ominus__class_Ominus(V_x, V_x, T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-111, plain, ( ~class_OrderedGroup_Ogroup__add(T_a) | ( c_HOL_Ominus__class_Ominus(V_x, V_x, T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-112, plain, ( ~class_OrderedGroup_Ogroup__add(T_a) | ( c_HOL_Ominus__class_Ominus(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) = V_a) )).
% 12.19/12.35 cnf(matrix-113, plain, ( ~class_OrderedGroup_Ogroup__add(T_a) | ( c_HOL_Ominus__class_Ominus(V_a, V_a, T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-114, plain, ( ~class_Ring__and__Field_Oidom(T_a) | ~class_Int_Onumber__ring(T_a) | ( c_HOL_Ominus__class_Ominus(V_x, V_x, T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-115, plain, ( ( c_HOL_Ominus__class_Ominus(V_m, V_m, tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-116, plain, ( ( c_HOL_Ominus__class_Ominus(V_m, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) = V_m) )).
% 12.19/12.35 cnf(matrix-117, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), V_c, T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a, V_c, T_a), c_Divides_Odiv__class_Omod(V_b, V_c, T_a), T_a), V_c, T_a)) )).
% 12.19/12.35 cnf(matrix-118, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_z, V_y, T_a) | c_lessequals(V_z, V_x, T_a) | ~c_lessequals(V_z, c_Orderings_Oord__class_Omax(V_x, V_y, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-119, plain, ( ~c_lessequals(V_j, V_i, tc_nat) | ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i, V_u, tc_nat), V_m, tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j, V_u, tc_nat), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i, V_j, tc_nat), V_u, tc_nat), V_m, tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-120, plain, ( ( c_HOL_Otimes__class_Otimes(V_k, V_m, tc_nat) != c_HOL_Otimes__class_Otimes(V_k, V_n, tc_nat)) | ( V_m = V_n) | ( V_k = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-121, plain, ( ( c_HOL_Otimes__class_Otimes(V_k, V_m, tc_nat) != c_HOL_Otimes__class_Otimes(V_k, V_n, tc_nat)) | ( V_k = c_HOL_Ozero__class_Ozero(tc_nat)) | ( V_m = V_n) )).
% 12.19/12.35 cnf(matrix-122, plain, ( ( c_HOL_Otimes__class_Otimes(V_m, V_k, tc_nat) != c_HOL_Otimes__class_Otimes(V_n, V_k, tc_nat)) | ( V_k = c_HOL_Ozero__class_Ozero(tc_nat)) | ( V_m = V_n) )).
% 12.19/12.35 cnf(matrix-123, plain, ( c_lessequals(V_i, c_HOL_Ominus__class_Ominus(V_j, V_k, tc_nat), tc_nat) | ~c_lessequals(c_HOL_Oplus__class_Oplus(V_i, V_k, tc_nat), V_j, tc_nat) | ~c_lessequals(V_k, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-124, plain, ( c_lessequals(c_HOL_Oplus__class_Oplus(V_i, V_k, tc_nat), V_j, tc_nat) | ~c_lessequals(V_i, c_HOL_Ominus__class_Ominus(V_j, V_k, tc_nat), tc_nat) | ~c_lessequals(V_k, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-125, plain, ( c_HOL_Oord__class_Oless(V_m, c_Suc(c_HOL_Oplus__class_Oplus(V_m, V_x, tc_nat)), tc_nat) )).
% 12.19/12.35 cnf(matrix-126, plain, ( c_HOL_Oord__class_Oless(V_i, c_Suc(c_HOL_Oplus__class_Oplus(V_m, V_i, tc_nat)), tc_nat) )).
% 12.19/12.35 cnf(matrix-127, plain, ( c_HOL_Oord__class_Oless(V_i, c_Suc(c_HOL_Oplus__class_Oplus(V_i, V_m, tc_nat)), tc_nat) )).
% 12.19/12.35 cnf(matrix-128, plain, ( ~class_Ring__and__Field_Oring(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_e, T_a), V_c, T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b, V_e, T_a), V_d, T_a)) | ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a, V_b, T_a), V_e, T_a), V_c, T_a) = V_d) )).
% 12.19/12.35 cnf(matrix-129, plain, ( ~class_Ring__and__Field_Oring(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_e, T_a), V_c, T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b, V_e, T_a), V_d, T_a)) | ( V_c = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b, V_a, T_a), V_e, T_a), V_d, T_a)) )).
% 12.19/12.35 cnf(matrix-130, plain, ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i, V_u, tc_nat), V_m, tc_nat), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j, V_u, tc_nat), V_n, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(V_m, c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j, V_i, tc_nat), V_u, tc_nat), V_n, tc_nat), tc_nat) | ~c_lessequals(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-131, plain, ( c_HOL_Oord__class_Oless(V_m, c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j, V_i, tc_nat), V_u, tc_nat), V_n, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i, V_u, tc_nat), V_m, tc_nat), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j, V_u, tc_nat), V_n, tc_nat), tc_nat) | ~c_lessequals(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-132, plain, ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i, V_u, tc_nat), V_m, tc_nat), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j, V_u, tc_nat), V_n, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i, V_j, tc_nat), V_u, tc_nat), V_m, tc_nat), V_n, tc_nat) | ~c_lessequals(V_j, V_i, tc_nat) )).
% 12.19/12.35 cnf(matrix-133, plain, ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i, V_j, tc_nat), V_u, tc_nat), V_m, tc_nat), V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i, V_u, tc_nat), V_m, tc_nat), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j, V_u, tc_nat), V_n, tc_nat), tc_nat) | ~c_lessequals(V_j, V_i, tc_nat) )).
% 12.19/12.35 cnf(matrix-134, plain, ( ~class_Ring__and__Field_Oring(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_e, T_a), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b, V_a, T_a), V_e, T_a), V_d, T_a), T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b, V_e, T_a), V_d, T_a)) )).
% 12.19/12.35 cnf(matrix-135, plain, ( ~class_Ring__and__Field_Oordered__semiring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_d, T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_b, T_a) | ~c_HOL_Oord__class_Oless(V_c, V_d, T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-136, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a, V_c, T_a), V_b, T_a), V_c, T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), V_c, T_a)) )).
% 12.19/12.35 cnf(matrix-137, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(c_Orderings_Oord__class_Omin(V_x, V_y, T_a), V_x, T_a) )).
% 12.19/12.35 cnf(matrix-138, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(c_Orderings_Oord__class_Omin(V_x, V_y, T_a), V_y, T_a) )).
% 12.19/12.35 cnf(matrix-139, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_x, c_Orderings_Oord__class_Omin(V_a, V_b, T_a), T_a) | ~c_lessequals(V_x, V_b, T_a) | ~c_lessequals(V_x, V_a, T_a) )).
% 12.19/12.35 cnf(matrix-140, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_x, c_Orderings_Oord__class_Omin(V_y, V_z, T_a), T_a) | ~c_lessequals(V_x, V_z, T_a) | ~c_lessequals(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-141, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_x, c_Orderings_Oord__class_Omin(V_y, V_z, T_a), T_a) | ~c_lessequals(V_x, V_z, T_a) | ~c_lessequals(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-142, plain, ( ~class_Ring__and__Field_Oring(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_e, T_a), V_c, T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b, V_e, T_a), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a, V_b, T_a), V_e, T_a), V_c, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-143, plain, ( ( c_HOL_Ominus__class_Ominus(V_m, V_n, tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)) | ~c_lessequals(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-144, plain, ( ( c_HOL_Ominus__class_Ominus(V_m, V_n, tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)) | c_lessequals(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-145, plain, ( ~class_OrderedGroup_Opordered__ab__group__add(T_a) | ( c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(V_x, V_y, T_a), V_z, T_a) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(V_x, V_z, T_a), c_HOL_Ominus__class_Ominus(V_y, V_z, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-146, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x, V_y, T_a), V_z, T_a) | ~c_HOL_Oord__class_Oless(V_y, V_z, T_a) | ~c_HOL_Oord__class_Oless(V_x, V_z, T_a) )).
% 12.19/12.35 cnf(matrix-147, plain, ( ( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(V_j, V_k, tc_nat)), V_m, tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(V_j), c_HOL_Oplus__class_Oplus(V_k, V_m, tc_nat), tc_nat)) | ~c_lessequals(V_k, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-148, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a), V_x, T_a) = V_x) )).
% 12.19/12.35 cnf(matrix-149, plain, ( ( c_HOL_Otimes__class_Otimes(V_n, c_HOL_Oone__class_Oone(tc_nat), tc_nat) = V_n) )).
% 12.19/12.35 cnf(matrix-150, plain, ( ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat), V_n, tc_nat) = V_n) )).
% 12.19/12.35 cnf(matrix-151, plain, ( ~class_OrderedGroup_Ocomm__monoid__mult(T_a) | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a), V_a, T_a) = V_a) )).
% 12.19/12.35 cnf(matrix-152, plain, ( ~class_OrderedGroup_Omonoid__mult(T_a) | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a), V_a, T_a) = V_a) )).
% 12.19/12.35 cnf(matrix-153, plain, ( ~class_OrderedGroup_Omonoid__mult(T_a) | ( c_HOL_Otimes__class_Otimes(V_a, c_HOL_Oone__class_Oone(T_a), T_a) = V_a) )).
% 12.19/12.35 cnf(matrix-154, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Otimes__class_Otimes(V_a, c_HOL_Oone__class_Oone(T_a), T_a) = V_a) )).
% 12.19/12.35 cnf(matrix-155, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a), V_a, T_a) = V_a) )).
% 12.19/12.35 cnf(matrix-156, plain, ( ~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) | ~class_OrderedGroup_Ocomm__monoid__add(T_a) | c_HOL_Oord__class_Oless(V_b, c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), T_a) | ~c_lessequals(V_b, V_c, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) )).
% 12.19/12.35 cnf(matrix-157, plain, ( c_HOL_Oord__class_Oless(V_m, c_HOL_Oplus__class_Oplus(V_n, V_k, tc_nat), tc_nat) | ~c_lessequals(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_k, tc_nat) )).
% 12.19/12.35 cnf(matrix-158, plain, ( ( c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) )).
% 12.19/12.35 cnf(matrix-159, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a, V_b, T_a), V_b, T_a) = c_Divides_Odiv__class_Omod(V_a, V_b, T_a)) )).
% 12.19/12.35 cnf(matrix-160, plain, ( ( c_Suc(V_n) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat), V_n, tc_nat)) )).
% 12.19/12.35 cnf(matrix-161, plain, ( ( c_Suc(V_n) = c_HOL_Oplus__class_Oplus(V_n, c_HOL_Oone__class_Oone(tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-162, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-163, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(V_z, c_Orderings_Oord__class_Omin(V_x, V_y, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_z, V_y, T_a) | ~c_HOL_Oord__class_Oless(V_z, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-164, plain, ( ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x, V_y, tc_nat), c_HOL_Otimes__class_Otimes(V_x, V_z, tc_nat), tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x, V_z, tc_nat), c_HOL_Otimes__class_Otimes(V_x, V_y, tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-165, plain, ( ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x, V_c, tc_nat), c_HOL_Otimes__class_Otimes(V_x, V_d, tc_nat), tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x, V_d, tc_nat), c_HOL_Otimes__class_Otimes(V_x, V_c, tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-166, plain, ( ~class_Ring__and__Field_Oidom(T_a) | ~class_Int_Onumber__ring(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x, V_c, T_a), c_HOL_Otimes__class_Otimes(V_x, V_d, T_a), T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x, V_d, T_a), c_HOL_Otimes__class_Otimes(V_x, V_c, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-167, plain, ( ~class_Ring__and__Field_Oidom(T_a) | ~class_Int_Onumber__ring(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x, V_y, T_a), c_HOL_Otimes__class_Otimes(V_x, V_z, T_a), T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x, V_z, T_a), c_HOL_Otimes__class_Otimes(V_x, V_y, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-168, plain, ( ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)) | ~c_HOL_Oord__class_Oless(V_n, c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), tc_nat) )).
% 12.19/12.35 cnf(matrix-169, plain, ( ~class_OrderedGroup_Olordered__ab__group__add(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Oplus__class_Oplus(V_a, V_a, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-170, plain, ( ~class_OrderedGroup_Olordered__ab__group__add(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Oplus__class_Oplus(V_a, V_a, T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) )).
% 12.19/12.35 cnf(matrix-171, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omin(V_x, c_Orderings_Oord__class_Omin(V_x, V_y, T_a), T_a) = c_Orderings_Oord__class_Omin(V_x, V_y, T_a)) )).
% 12.19/12.35 cnf(matrix-172, plain, ( ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i, V_u, tc_nat), V_m, tc_nat), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j, V_u, tc_nat), V_n, tc_nat), tc_nat) = c_HOL_Ominus__class_Ominus(V_m, c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j, V_i, tc_nat), V_u, tc_nat), V_n, tc_nat), tc_nat)) | ~c_lessequals(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-173, plain, ( ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i, V_u, tc_nat), V_m, tc_nat), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j, V_u, tc_nat), V_n, tc_nat), tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i, V_j, tc_nat), V_u, tc_nat), V_m, tc_nat), V_n, tc_nat)) | ~c_lessequals(V_j, V_i, tc_nat) )).
% 12.19/12.35 cnf(matrix-174, plain, ( ~class_OrderedGroup_Ogroup__add(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a, V_b, T_a), V_b, T_a) = V_a) )).
% 12.19/12.35 cnf(matrix-175, plain, ( c_lessequals(c_HOL_Otimes__class_Otimes(V_m, V_k, tc_nat), c_HOL_Otimes__class_Otimes(V_n, V_k, tc_nat), tc_nat) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_k, tc_nat) )).
% 12.19/12.35 cnf(matrix-176, plain, ( c_lessequals(c_HOL_Otimes__class_Otimes(V_k, V_m, tc_nat), c_HOL_Otimes__class_Otimes(V_k, V_n, tc_nat), tc_nat) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_k, tc_nat) )).
% 12.19/12.35 cnf(matrix-177, plain, ( c_lessequals(c_HOL_Oplus__class_Oplus(V_i, V_k, tc_nat), c_HOL_Oplus__class_Oplus(V_j, V_l, tc_nat), tc_nat) | ~c_lessequals(V_k, V_l, tc_nat) | ~c_lessequals(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-178, plain, ( ~class_OrderedGroup_Opordered__ab__semigroup__add(T_a) | c_lessequals(c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), c_HOL_Oplus__class_Oplus(V_b, V_d, T_a), T_a) | ~c_lessequals(V_c, V_d, T_a) | ~c_lessequals(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-179, plain, ( c_HOL_Oord__class_Oless(V_m, c_Suc(V_n), tc_nat) | ~c_lessequals(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-180, plain, ( c_lessequals(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(V_m, c_Suc(V_n), tc_nat) )).
% 12.19/12.35 cnf(matrix-181, plain, ( ~c_lessequals(V_x, V_x, tc_nat) | c_HOL_Oord__class_Oless(V_x, c_Suc(V_x), tc_nat) )).
% 12.19/12.35 cnf(matrix-182, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Otimes__class_Otimes(V_x, V_y, T_a) = c_HOL_Otimes__class_Otimes(V_y, V_x, T_a)) )).
% 12.19/12.35 cnf(matrix-183, plain, ( ( c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat) = c_HOL_Otimes__class_Otimes(V_n, V_m, tc_nat)) )).
% 12.19/12.35 cnf(matrix-184, plain, ( ~class_OrderedGroup_Olordered__ab__group__add(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-185, plain, ( ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-186, plain, ( ~class_OrderedGroup_Opordered__comm__monoid__add(T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-187, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Otimes__class_Otimes(V_a, V_b, T_a) = c_HOL_Otimes__class_Otimes(V_b, V_a, T_a)) )).
% 12.19/12.35 cnf(matrix-188, plain, ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m, V_n, tc_nat), c_Suc(V_m), tc_nat) )).
% 12.19/12.35 cnf(matrix-189, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), V_c, T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a, V_c, T_a), c_Divides_Odiv__class_Omod(V_b, V_c, T_a), T_a), V_c, T_a)) )).
% 12.19/12.35 cnf(matrix-190, plain, ( ~class_OrderedGroup_Opordered__comm__monoid__add(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_b, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) )).
% 12.19/12.35 cnf(matrix-191, plain, ( ( c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat) = c_HOL_Oplus__class_Oplus(V_n, c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_m, c_HOL_Oone__class_Oone(tc_nat), tc_nat), V_n, tc_nat), tc_nat)) | ( V_m = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-192, 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) )).
% 12.19/12.35 cnf(matrix-193, 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) )).
% 12.19/12.35 cnf(matrix-194, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omax(V_x, V_y, T_a) = V_y) | ~c_lessequals(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-195, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omax(V_x, V_y, T_a) != V_y) | c_lessequals(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-196, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omax(V_x, V_y, T_a) = V_x) | ~c_lessequals(V_y, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-197, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Oplus__class_Oplus(V_x, c_HOL_Oplus__class_Oplus(V_y, V_z, T_a), T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_x, V_y, T_a), V_z, T_a)) )).
% 12.19/12.35 cnf(matrix-198, plain, ( ~class_OrderedGroup_Oab__group__add(T_a) | ( c_HOL_Oplus__class_Oplus(V_x, c_HOL_Oplus__class_Oplus(V_y, V_z, T_a), T_a) = c_HOL_Oplus__class_Oplus(V_y, c_HOL_Oplus__class_Oplus(V_x, V_z, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-199, plain, ( ( c_HOL_Oplus__class_Oplus(V_x, c_HOL_Oplus__class_Oplus(V_y, V_z, tc_nat), tc_nat) = c_HOL_Oplus__class_Oplus(V_y, c_HOL_Oplus__class_Oplus(V_x, V_z, tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-200, plain, ( ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat), V_k, tc_nat) = c_HOL_Oplus__class_Oplus(V_m, c_HOL_Oplus__class_Oplus(V_n, V_k, tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-201, plain, ( ~class_OrderedGroup_Ocomm__monoid__add(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), V_c, T_a) = c_HOL_Oplus__class_Oplus(V_a, c_HOL_Oplus__class_Oplus(V_b, V_c, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-202, plain, ( ~class_OrderedGroup_Ocomm__monoid__add(T_a) | ( c_HOL_Oplus__class_Oplus(V_a, c_HOL_Oplus__class_Oplus(V_b, V_c, T_a), T_a) = c_HOL_Oplus__class_Oplus(V_b, c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-203, plain, ( ~class_OrderedGroup_Oab__semigroup__add(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), V_c, T_a) = c_HOL_Oplus__class_Oplus(V_a, c_HOL_Oplus__class_Oplus(V_b, V_c, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-204, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Oplus__class_Oplus(V_a, c_HOL_Oplus__class_Oplus(V_c, V_d, T_a), T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), V_d, T_a)) )).
% 12.19/12.35 cnf(matrix-205, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), V_c, T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), V_b, T_a)) )).
% 12.19/12.35 cnf(matrix-206, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Oplus__class_Oplus(V_a, c_HOL_Oplus__class_Oplus(V_c, V_d, T_a), T_a) = c_HOL_Oplus__class_Oplus(V_c, c_HOL_Oplus__class_Oplus(V_a, V_d, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-207, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), V_c, T_a) = c_HOL_Oplus__class_Oplus(V_a, c_HOL_Oplus__class_Oplus(V_b, V_c, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-208, plain, ( 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(tc_nat), V_m, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-209, plain, ( ~c_HOL_Oord__class_Oless(V_m, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-210, plain, ( ~c_HOL_Oord__class_Oless(V_n, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-211, plain, ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), V_n, tc_nat) | ~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-212, plain, ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), V_m, tc_nat) | ~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-213, plain, ( ~class_OrderedGroup_Oab__group__add(T_a) | ( c_HOL_Oplus__class_Oplus(V_x, c_HOL_Oplus__class_Oplus(V_y, V_z, T_a), T_a) != c_HOL_Oplus__class_Oplus(V_y, V_u, T_a)) | ( c_HOL_Oplus__class_Oplus(V_x, V_z, T_a) = V_u) )).
% 12.19/12.35 cnf(matrix-214, plain, ( c_lessequals(V_i, c_HOL_Oplus__class_Oplus(V_m, V_j, tc_nat), tc_nat) | ~c_lessequals(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-215, plain, ( c_lessequals(V_i, c_HOL_Oplus__class_Oplus(V_j, V_m, tc_nat), tc_nat) | ~c_lessequals(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-216, plain, ( c_lessequals(V_k, V_n, tc_nat) | ~c_lessequals(c_HOL_Oplus__class_Oplus(V_m, V_k, tc_nat), V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-217, plain, ( c_lessequals(V_m, V_n, tc_nat) | ~c_lessequals(c_HOL_Oplus__class_Oplus(V_m, V_k, tc_nat), V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-218, plain, ( c_lessequals(V_x, c_HOL_Oplus__class_Oplus(V_y, V_z, tc_nat), tc_nat) | ~c_lessequals(V_x, V_z, tc_nat) )).
% 12.19/12.35 cnf(matrix-219, plain, ( c_lessequals(V_x, c_HOL_Oplus__class_Oplus(V_y, V_z, tc_nat), tc_nat) | ~c_lessequals(V_x, V_y, tc_nat) )).
% 12.19/12.35 cnf(matrix-220, plain, ( ~class_Divides_Oring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a, V_b, T_a), V_c, T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a, V_c, T_a), V_b, T_a), V_c, T_a)) )).
% 12.19/12.35 cnf(matrix-221, plain, ( ~class_Divides_Oring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a, V_b, T_a), V_c, T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a, c_Divides_Odiv__class_Omod(V_b, V_c, T_a), T_a), V_c, T_a)) )).
% 12.19/12.35 cnf(matrix-222, plain, ( ( c_Lambda_Olift(c_Lambda_OdB_OVar(V_i), V_k) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(V_i, c_HOL_Oone__class_Oone(tc_nat), tc_nat))) | c_HOL_Oord__class_Oless(V_i, V_k, tc_nat) )).
% 12.19/12.35 cnf(matrix-223, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_x, V_z, T_a) | ~c_lessequals(V_x, c_Orderings_Oord__class_Omin(V_y, V_z, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-224, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_x, V_y, T_a) | ~c_lessequals(V_x, c_Orderings_Oord__class_Omin(V_y, V_z, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-225, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(c_Orderings_Oord__class_Omin(V_x, V_y, T_a), V_z, T_a) | ~c_lessequals(V_y, V_z, T_a) )).
% 12.19/12.35 cnf(matrix-226, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(c_Orderings_Oord__class_Omin(V_x, V_y, T_a), V_z, T_a) | ~c_lessequals(V_x, V_z, T_a) )).
% 12.19/12.35 cnf(matrix-227, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(c_Orderings_Oord__class_Omin(V_a, V_b, T_a), V_x, T_a) | ~c_lessequals(V_b, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-228, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(c_Orderings_Oord__class_Omin(V_a, V_b, T_a), V_x, T_a) | ~c_lessequals(V_a, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-229, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_x, V_b, T_a) | ~c_lessequals(V_x, c_Orderings_Oord__class_Omin(V_a, V_b, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-230, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_x, V_a, T_a) | ~c_lessequals(V_x, c_Orderings_Oord__class_Omin(V_a, V_b, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-231, plain, ( ( c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-232, plain, ( ( c_Orderings_Oord__class_Omin(V_n, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-233, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Oplus__class_Oplus(V_m, V_m, T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a), c_HOL_Oone__class_Oone(T_a), T_a), V_m, T_a)) )).
% 12.19/12.35 cnf(matrix-234, plain, ( ~class_OrderedGroup_Opordered__comm__monoid__add(T_a) | ( c_HOL_Oplus__class_Oplus(V_x, V_y, T_a) != c_HOL_Ozero__class_Ozero(T_a)) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_y, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_x, T_a) | ( V_y = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-235, plain, ( ~class_OrderedGroup_Opordered__comm__monoid__add(T_a) | ( c_HOL_Oplus__class_Oplus(V_x, V_y, T_a) != c_HOL_Ozero__class_Ozero(T_a)) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_y, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_x, T_a) | ( V_x = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-236, plain, ( ( c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)) | ( V_m = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-237, plain, ( ( c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)) | ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-238, plain, ( ~class_OrderedGroup_Olordered__ab__group__add(T_a) | ( c_HOL_Oplus__class_Oplus(V_a, V_a, T_a) != c_HOL_Ozero__class_Ozero(T_a)) | ( V_a = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-239, plain, ( ( c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) )).
% 12.19/12.35 cnf(matrix-240, plain, ( ~class_Ring__and__Field_Opordered__ring(T_a) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_e, T_a), V_c, T_a), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b, V_e, T_a), V_d, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_c, c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b, V_a, T_a), V_e, T_a), V_d, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-241, plain, ( ~class_Ring__and__Field_Opordered__ring(T_a) | c_HOL_Oord__class_Oless(V_c, c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b, V_a, T_a), V_e, T_a), V_d, T_a), T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_e, T_a), V_c, T_a), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b, V_e, T_a), V_d, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-242, plain, ( ~class_Ring__and__Field_Opordered__ring(T_a) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_e, T_a), V_c, T_a), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b, V_e, T_a), V_d, T_a), T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a, V_b, T_a), V_e, T_a), V_c, T_a), V_d, T_a) )).
% 12.19/12.35 cnf(matrix-243, plain, ( ~class_Ring__and__Field_Opordered__ring(T_a) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a, V_b, T_a), V_e, T_a), V_c, T_a), V_d, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_e, T_a), V_c, T_a), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b, V_e, T_a), V_d, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-244, plain, ( ( c_Divides_Odiv__class_Omod(V_m, V_n, tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_m, V_n, tc_nat), V_n, tc_nat)) | ~c_lessequals(V_n, V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-245, plain, ( ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i, V_u, tc_nat), V_m, tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j, V_u, tc_nat), V_n, tc_nat)) | ~c_lessequals(V_j, V_i, tc_nat) | ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i, V_j, tc_nat), V_u, tc_nat), V_m, tc_nat) = V_n) )).
% 12.19/12.35 cnf(matrix-246, plain, ( ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i, V_u, tc_nat), V_m, tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j, V_u, tc_nat), V_n, tc_nat)) | ~c_lessequals(V_i, V_j, tc_nat) | ( V_m = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j, V_i, tc_nat), V_u, tc_nat), V_n, tc_nat)) )).
% 12.19/12.35 cnf(matrix-247, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_y, V_z, T_a) | c_lessequals(V_x, V_z, T_a) | ~c_lessequals(c_Orderings_Oord__class_Omin(V_x, V_y, T_a), V_z, T_a) )).
% 12.19/12.35 cnf(matrix-248, plain, ( ~c_lessequals(V_i, V_j, tc_nat) | ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i, V_u, tc_nat), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j, V_i, tc_nat), V_u, tc_nat), V_n, tc_nat), tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j, V_u, tc_nat), V_n, tc_nat)) )).
% 12.19/12.35 cnf(matrix-249, plain, ( ~class_Ring__and__Field_Oring__no__zero__divisors(T_a) | ( c_HOL_Otimes__class_Otimes(V_a, V_b, T_a) != c_HOL_Ozero__class_Ozero(T_a)) | ( V_b = c_HOL_Ozero__class_Ozero(T_a)) | ( V_a = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-250, plain, ( ~class_Ring__and__Field_Ono__zero__divisors(T_a) | ( c_HOL_Otimes__class_Otimes(V_a, V_b, T_a) != c_HOL_Ozero__class_Ozero(T_a)) | ( V_b = c_HOL_Ozero__class_Ozero(T_a)) | ( V_a = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-251, plain, ( ~class_Ring__and__Field_Ono__zero__divisors(T_a) | ( c_HOL_Otimes__class_Otimes(V_a, V_b, T_a) != c_HOL_Ozero__class_Ozero(T_a)) | ( V_a = c_HOL_Ozero__class_Ozero(T_a)) | ( V_b = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-252, plain, ( ( c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)) | ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)) | ( V_m = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-253, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(V_b, V_c, T_a) != c_Divides_Odiv__class_Omod(V_b_H, V_c, T_a)) | ( c_Divides_Odiv__class_Omod(V_a, V_c, T_a) != c_Divides_Odiv__class_Omod(V_a_H, V_c, T_a)) | ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), V_c, T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a_H, V_b_H, T_a), V_c, T_a)) )).
% 12.19/12.35 cnf(matrix-254, plain, ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), tc_nat) )).
% 12.19/12.35 cnf(matrix-255, plain, ( ~class_OrderedGroup_Olordered__ab__group__add(T_a) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a, V_a, T_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) )).
% 12.19/12.35 cnf(matrix-256, 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(c_HOL_Oplus__class_Oplus(V_a, V_a, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-257, 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(c_HOL_Oplus__class_Oplus(V_a, V_a, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-258, plain, ( ~class_Ring__and__Field_Oordered__idom(T_a) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a, V_a, T_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) )).
% 12.19/12.35 cnf(matrix-259, plain, ( ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat)) | ( V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) | ( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) )).
% 12.19/12.35 cnf(matrix-260, plain, ( ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat)) | ( V_m = c_HOL_Ozero__class_Ozero(tc_nat)) | ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-261, plain, ( ~class_Ring__and__Field_Oordered__semiring__strict(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) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Otimes__class_Otimes(V_b, V_a, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-262, plain, ( ~class_Ring__and__Field_Oordered__semiring__strict(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) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-263, plain, ( ~class_Ring__and__Field_Oordered__semiring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), 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) )).
% 12.19/12.35 cnf(matrix-264, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Otimes__class_Otimes(V_a, V_b, 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) )).
% 12.19/12.35 cnf(matrix-265, plain, ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat), tc_nat) | ~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(tc_nat), V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-266, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_y, V_z, T_a) | ~c_lessequals(c_Orderings_Oord__class_Omax(V_x, V_y, T_a), V_z, T_a) )).
% 12.19/12.35 cnf(matrix-267, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_x, V_z, T_a) | ~c_lessequals(c_Orderings_Oord__class_Omax(V_x, V_y, T_a), V_z, T_a) )).
% 12.19/12.35 cnf(matrix-268, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_z, c_Orderings_Oord__class_Omax(V_x, V_y, T_a), T_a) | ~c_lessequals(V_z, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-269, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_z, c_Orderings_Oord__class_Omax(V_x, V_y, T_a), T_a) | ~c_lessequals(V_z, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-270, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_x, c_Orderings_Oord__class_Omax(V_a, V_b, T_a), T_a) | ~c_lessequals(V_x, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-271, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_x, c_Orderings_Oord__class_Omax(V_a, V_b, T_a), T_a) | ~c_lessequals(V_x, V_a, T_a) )).
% 12.19/12.35 cnf(matrix-272, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_b, V_x, T_a) | ~c_lessequals(c_Orderings_Oord__class_Omax(V_a, V_b, T_a), V_x, T_a) )).
% 12.19/12.35 cnf(matrix-273, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_a, V_x, T_a) | ~c_lessequals(c_Orderings_Oord__class_Omax(V_a, V_b, T_a), V_x, T_a) )).
% 12.19/12.35 cnf(matrix-274, plain, ( c_lessequals(V_j, c_HOL_Oplus__class_Oplus(V_i, V_k, tc_nat), tc_nat) | ~c_lessequals(c_HOL_Ominus__class_Ominus(V_j, V_k, tc_nat), V_i, tc_nat) )).
% 12.19/12.35 cnf(matrix-275, plain, ( c_lessequals(c_HOL_Ominus__class_Ominus(V_j, V_k, tc_nat), V_i, tc_nat) | ~c_lessequals(V_j, c_HOL_Oplus__class_Oplus(V_i, V_k, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-276, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(V_z, V_y, T_a) | c_HOL_Oord__class_Oless(V_z, V_x, T_a) | ~c_HOL_Oord__class_Oless(V_z, c_Orderings_Oord__class_Omax(V_x, V_y, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-277, plain, ( ( c_HOL_Otimes__class_Otimes(V_m, c_Suc(V_n), tc_nat) = c_HOL_Oplus__class_Oplus(V_m, c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-278, plain, ( ( c_HOL_Otimes__class_Otimes(c_Suc(V_m), V_n, tc_nat) = c_HOL_Oplus__class_Oplus(V_n, c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-279, plain, ( ~class_Ring__and__Field_Oordered__semidom(T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-280, plain, ( ~class_Ring__and__Field_Ozero__neq__one(T_a) | ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-281, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x, V_x, T_a), c_HOL_Otimes__class_Otimes(V_y, V_y, T_a), T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-282, plain, ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i, V_j, tc_nat), V_u, tc_nat), V_m, tc_nat), V_n, tc_nat) | ~c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i, V_u, tc_nat), V_m, tc_nat), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j, V_u, tc_nat), V_n, tc_nat), tc_nat) | ~c_lessequals(V_j, V_i, tc_nat) )).
% 12.19/12.35 cnf(matrix-283, plain, ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i, V_u, tc_nat), V_m, tc_nat), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j, V_u, tc_nat), V_n, tc_nat), tc_nat) | ~c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i, V_j, tc_nat), V_u, tc_nat), V_m, tc_nat), V_n, tc_nat) | ~c_lessequals(V_j, V_i, tc_nat) )).
% 12.19/12.35 cnf(matrix-284, plain, ( c_lessequals(V_m, c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j, V_i, tc_nat), V_u, tc_nat), V_n, tc_nat), tc_nat) | ~c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i, V_u, tc_nat), V_m, tc_nat), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j, V_u, tc_nat), V_n, tc_nat), tc_nat) | ~c_lessequals(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-285, plain, ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i, V_u, tc_nat), V_m, tc_nat), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j, V_u, tc_nat), V_n, tc_nat), tc_nat) | ~c_lessequals(V_m, c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j, V_i, tc_nat), V_u, tc_nat), V_n, tc_nat), tc_nat) | ~c_lessequals(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-286, plain, ( ( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k, V_n, tc_nat), V_m, tc_nat)), V_n, tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(V_m), V_n, tc_nat)) )).
% 12.19/12.35 cnf(matrix-287, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(V_y, V_z, T_a) | c_HOL_Oord__class_Oless(V_x, V_z, T_a) | ~c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x, V_y, T_a), V_z, T_a) )).
% 12.19/12.35 cnf(matrix-288, plain, ( ~class_Ring__and__Field_Oidom(T_a) | ~class_Int_Onumber__ring(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w, V_y, T_a), c_HOL_Otimes__class_Otimes(V_x, V_z, T_a), T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w, V_z, T_a), c_HOL_Otimes__class_Otimes(V_x, V_y, T_a), T_a)) | ( V_y = V_z) | ( V_w = V_x) )).
% 12.19/12.35 cnf(matrix-289, plain, ( ~class_Ring__and__Field_Oidom(T_a) | ~class_Int_Onumber__ring(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_d, T_a), T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_d, T_a), c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a)) | ( V_c = V_d) | ( V_a = V_b) )).
% 12.19/12.35 cnf(matrix-290, plain, ( ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_c, tc_nat), c_HOL_Otimes__class_Otimes(V_b, V_d, tc_nat), tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_d, tc_nat), c_HOL_Otimes__class_Otimes(V_b, V_c, tc_nat), tc_nat)) | ( V_c = V_d) | ( V_a = V_b) )).
% 12.19/12.35 cnf(matrix-291, plain, ( ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w, V_y, tc_nat), c_HOL_Otimes__class_Otimes(V_x, V_z, tc_nat), tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w, V_z, tc_nat), c_HOL_Otimes__class_Otimes(V_x, V_y, tc_nat), tc_nat)) | ( V_y = V_z) | ( V_w = V_x) )).
% 12.19/12.35 cnf(matrix-292, plain, ( ~class_OrderedGroup_Opordered__comm__monoid__add(T_a) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), 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_lessequals(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-293, plain, ( ~class_OrderedGroup_Opordered__comm__monoid__add(T_a) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(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) )).
% 12.19/12.35 cnf(matrix-294, plain, ( ( V_m != c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat)) | ( V_m = c_HOL_Ozero__class_Ozero(tc_nat)) | ( V_n = c_HOL_Oone__class_Oone(tc_nat)) )).
% 12.19/12.35 cnf(matrix-295, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Ozero__class_Ozero(T_a), T_a), c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Ozero__class_Ozero(T_a), T_a), T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-296, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(V_b, V_c, T_a) != c_Divides_Odiv__class_Omod(V_b_H, V_c, T_a)) | ( c_Divides_Odiv__class_Omod(V_a, V_c, T_a) != c_Divides_Odiv__class_Omod(V_a_H, V_c, T_a)) | ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), V_c, T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a_H, V_b_H, T_a), V_c, T_a)) )).
% 12.19/12.35 cnf(matrix-297, plain, ( ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i, V_j, tc_nat), V_k, tc_nat) = c_HOL_Oplus__class_Oplus(V_i, c_HOL_Ominus__class_Ominus(V_j, V_k, tc_nat), tc_nat)) | ~c_lessequals(V_k, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-298, plain, ( ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_j, V_i, tc_nat), V_k, tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j, V_k, tc_nat), V_i, tc_nat)) | ~c_lessequals(V_k, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-299, plain, ( ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) )).
% 12.19/12.35 cnf(matrix-300, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx, V_ly, T_a), c_HOL_Otimes__class_Otimes(V_rx, V_ry, T_a), T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx, V_rx, T_a), c_HOL_Otimes__class_Otimes(V_ly, V_ry, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-301, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx, V_ly, T_a), c_HOL_Otimes__class_Otimes(V_rx, V_ry, T_a), T_a) = c_HOL_Otimes__class_Otimes(V_lx, c_HOL_Otimes__class_Otimes(V_ly, c_HOL_Otimes__class_Otimes(V_rx, V_ry, T_a), T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-302, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx, V_ly, T_a), c_HOL_Otimes__class_Otimes(V_rx, V_ry, T_a), T_a) = c_HOL_Otimes__class_Otimes(V_rx, c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx, V_ly, T_a), V_ry, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-303, plain, ( ~class_Ring__and__Field_Oordered__semidom(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Oone__class_Oone(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-304, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-305, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Otimes__class_Otimes(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-306, plain, ( ~class_Ring__and__Field_Oring__no__zero__divisors(T_a) | ( c_HOL_Otimes__class_Otimes(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-307, plain, ( ~class_Ring__and__Field_Oring__no__zero__divisors(T_a) | ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a), V_b, T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-308, plain, ( ~class_Ring__and__Field_Omult__zero(T_a) | ( c_HOL_Otimes__class_Otimes(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-309, plain, ( ~class_Ring__and__Field_Omult__zero(T_a) | ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-310, plain, ( ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-311, plain, ( ( c_HOL_Otimes__class_Otimes(V_m, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-312, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a), V_x, T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-313, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_m, T_a), V_m, T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a, c_HOL_Oone__class_Oone(T_a), T_a), V_m, T_a)) )).
% 12.19/12.35 cnf(matrix-314, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Oplus__class_Oplus(V_m, c_HOL_Otimes__class_Otimes(V_a, V_m, T_a), T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a, c_HOL_Oone__class_Oone(T_a), T_a), V_m, T_a)) )).
% 12.19/12.35 cnf(matrix-315, plain, ( ( c_HOL_Ominus__class_Ominus(V_i, c_HOL_Ominus__class_Ominus(V_j, V_k, tc_nat), tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i, V_k, tc_nat), V_j, tc_nat)) | ~c_lessequals(V_k, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-316, plain, ( ( c_Divides_Odiv__class_Omod(V_m, c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-317, plain, ( ( c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_m, c_HOL_Oone__class_Oone(tc_nat), tc_nat), V_n, tc_nat))) | ( V_m = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-318, plain, ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j, V_n, tc_nat), V_k, tc_nat) | ~c_HOL_Oord__class_Oless(V_j, V_k, tc_nat) )).
% 12.19/12.35 cnf(matrix-319, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(V_a, c_HOL_Oone__class_Oone(T_a), T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-320, plain, ( ( c_Divides_Odiv__class_Omod(V_m, V_n, tc_nat) = V_m) | ~c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-321, plain, ( ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), c_HOL_Ozero__class_Ozero(tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-322, plain, ( ~class_Orderings_Opreorder(T_a) | c_HOL_Oord__class_Oless(V_x, V_y, T_a) | c_lessequals(V_y, V_x, T_a) | ~c_lessequals(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-323, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omin(V_x, V_y, T_a) = V_x) | ~c_lessequals(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-324, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omin(V_x, V_y, T_a) != V_x) | c_lessequals(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-325, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omin(V_x, V_y, T_a) = V_y) | ~c_lessequals(V_y, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-326, plain, ( ~class_OrderedGroup_Opordered__ab__group__add(T_a) | ( c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(V_x, V_y, T_a), V_z, T_a) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(V_x, V_z, T_a), c_HOL_Ominus__class_Ominus(V_y, V_z, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-327, plain, ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(V_m, V_n, tc_nat), V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-328, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(V_x, V_y, T_a) | c_lessequals(V_y, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-329, plain, ( ~class_Orderings_Olinorder(T_a) | ~c_lessequals(V_x, V_x, T_a) | ~c_HOL_Oord__class_Oless(V_x, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-330, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(V_x, V_x, T_a) | c_lessequals(V_x, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-331, plain, ( ~class_Orderings_Olinorder(T_a) | ~c_HOL_Oord__class_Oless(V_x, V_y, T_a) | ~c_lessequals(V_y, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-332, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_y, V_x, T_a) | c_HOL_Oord__class_Oless(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-333, plain, ( ~class_Orderings_Olinorder(T_a) | ~c_lessequals(V_x, V_y, T_a) | ~c_HOL_Oord__class_Oless(V_y, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-334, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(V_y, V_x, T_a) | c_lessequals(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-335, plain, ( ~class_Orderings_Opreorder(T_a) | ~c_lessequals(V_y, V_x, T_a) | ~c_HOL_Oord__class_Oless(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-336, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), V_c, T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a, V_c, T_a), V_b, T_a), V_c, T_a)) )).
% 12.19/12.35 cnf(matrix-337, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), V_c, T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a, c_Divides_Odiv__class_Omod(V_b, V_c, T_a), T_a), V_c, T_a)) )).
% 12.19/12.35 cnf(matrix-338, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(V_x, V_y, T_a), V_z, T_a) = c_Orderings_Oord__class_Omin(V_x, c_Orderings_Oord__class_Omin(V_y, V_z, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-339, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omin(V_x, c_Orderings_Oord__class_Omin(V_y, V_z, T_a), T_a) = c_Orderings_Oord__class_Omin(V_y, c_Orderings_Oord__class_Omin(V_x, V_z, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-340, plain, ( ( c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat) != c_HOL_Oone__class_Oone(tc_nat)) | ( V_n = c_HOL_Oone__class_Oone(tc_nat)) )).
% 12.19/12.35 cnf(matrix-341, plain, ( ( c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat) != c_HOL_Oone__class_Oone(tc_nat)) | ( V_m = c_HOL_Oone__class_Oone(tc_nat)) )).
% 12.19/12.35 cnf(matrix-342, plain, ( ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), tc_nat)) )).
% 12.19/12.35 cnf(matrix-343, plain, ( ~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) | ~class_OrderedGroup_Ocomm__monoid__add(T_a) | c_HOL_Oord__class_Oless(V_b, c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_b, V_c, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) )).
% 12.19/12.35 cnf(matrix-344, plain, ( c_lessequals(c_HOL_Ominus__class_Ominus(V_l, V_n, tc_nat), c_HOL_Ominus__class_Ominus(V_l, V_m, tc_nat), tc_nat) | ~c_lessequals(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-345, plain, ( c_lessequals(c_HOL_Ominus__class_Ominus(V_m, V_l, tc_nat), c_HOL_Ominus__class_Ominus(V_n, V_l, tc_nat), tc_nat) | ~c_lessequals(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-346, plain, ( c_lessequals(c_HOL_Ominus__class_Ominus(V_m, V_k, tc_nat), c_HOL_Ominus__class_Ominus(V_n, V_k, tc_nat), tc_nat) | ~c_lessequals(V_m, V_n, tc_nat) | ~c_lessequals(V_k, V_n, tc_nat) | ~c_lessequals(V_k, V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-347, plain, ( c_lessequals(V_m, V_n, tc_nat) | ~c_lessequals(c_HOL_Ominus__class_Ominus(V_m, V_k, tc_nat), c_HOL_Ominus__class_Ominus(V_n, V_k, tc_nat), tc_nat) | ~c_lessequals(V_k, V_n, tc_nat) | ~c_lessequals(V_k, V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-348, plain, ( ( c_HOL_Ominus__class_Ominus(V_n, c_HOL_Oplus__class_Oplus(V_n, V_m, tc_nat), tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-349, plain, ( ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i, V_j, tc_nat), V_k, tc_nat) = c_HOL_Ominus__class_Ominus(V_i, c_HOL_Oplus__class_Oplus(V_j, V_k, tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-350, plain, ( ~class_OrderedGroup_Oab__group__add(T_a) | ( c_HOL_Ominus__class_Ominus(V_xa, V_y, T_a) != c_HOL_Ominus__class_Ominus(V_x, V_x, T_a)) | ( V_xa = V_y) )).
% 12.19/12.35 cnf(matrix-351, plain, ( ~class_OrderedGroup_Oab__group__add(T_a) | ( c_HOL_Ominus__class_Ominus(V_x, V_x, T_a) != c_HOL_Ominus__class_Ominus(V_x_H, V_y_H, T_a)) | ( V_x_H = V_y_H) )).
% 12.19/12.35 cnf(matrix-352, plain, ( ( c_HOL_Ominus__class_Ominus(V_m, V_k, tc_nat) != c_HOL_Ominus__class_Ominus(V_n, V_k, tc_nat)) | ~c_lessequals(V_k, V_n, tc_nat) | ~c_lessequals(V_k, V_m, tc_nat) | ( V_m = V_n) )).
% 12.19/12.35 cnf(matrix-353, plain, ( ~class_Ring__and__Field_Ozero__neq__one(T_a) | ( c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a)) )).
% 12.19/12.35 cnf(matrix-354, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omin(V_x, c_Orderings_Oord__class_Omax(V_x, V_y, T_a), T_a) = V_x) )).
% 12.19/12.35 cnf(matrix-355, plain, ( ( c_HOL_Otimes__class_Otimes(V_k, V_m, tc_nat) != c_HOL_Otimes__class_Otimes(V_k, V_n, tc_nat)) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_k, tc_nat) | ( V_m = V_n) )).
% 12.19/12.35 cnf(matrix-356, plain, ( ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat)) | ( V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) | ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-357, plain, ( ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat)) | ( V_m = c_HOL_Ozero__class_Ozero(tc_nat)) | ( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) )).
% 12.19/12.35 cnf(matrix-358, plain, ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_k, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m, V_k, tc_nat), c_HOL_Otimes__class_Otimes(V_n, V_k, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-359, plain, ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_k, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k, V_m, tc_nat), c_HOL_Otimes__class_Otimes(V_k, V_n, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-360, plain, ( c_lessequals(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_k, tc_nat) | ~c_lessequals(c_HOL_Otimes__class_Otimes(V_m, V_k, tc_nat), c_HOL_Otimes__class_Otimes(V_n, V_k, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-361, plain, ( c_lessequals(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_k, tc_nat) | ~c_lessequals(c_HOL_Otimes__class_Otimes(V_k, V_m, tc_nat), c_HOL_Otimes__class_Otimes(V_k, V_n, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-362, plain, ( c_lessequals(V_m, V_n, tc_nat) | ~c_lessequals(c_HOL_Otimes__class_Otimes(V_k, V_m, tc_nat), c_HOL_Otimes__class_Otimes(V_k, V_n, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_k, tc_nat) )).
% 12.19/12.35 cnf(matrix-363, plain, ( c_lessequals(c_HOL_Otimes__class_Otimes(V_k, V_m, tc_nat), c_HOL_Otimes__class_Otimes(V_k, V_n, tc_nat), tc_nat) | ~c_lessequals(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_k, tc_nat) )).
% 12.19/12.35 cnf(matrix-364, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(V_b, V_a, T_a) | ~c_lessequals(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_c, c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-365, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) | ~c_lessequals(V_b, V_a, T_a) | ~c_HOL_Oord__class_Oless(V_c, c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-366, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(V_a, V_b, T_a) | ~c_lessequals(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) )).
% 12.19/12.35 cnf(matrix-367, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) | ~c_lessequals(V_a, V_b, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) )).
% 12.19/12.35 cnf(matrix-368, plain, ( ~class_Ring__and__Field_Oordered__semiring__strict(T_a) | c_lessequals(V_a, V_b, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_lessequals(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-369, plain, ( ~class_Ring__and__Field_Oordered__semiring__strict(T_a) | c_lessequals(V_a, V_b, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_lessequals(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-370, plain, ( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), V_m, tc_nat) | ~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-371, plain, ( ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-372, plain, ( ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m, V_k, tc_nat), c_HOL_Oplus__class_Oplus(V_n, V_k, tc_nat), tc_nat) = c_HOL_Ominus__class_Ominus(V_m, V_n, tc_nat)) )).
% 12.19/12.35 cnf(matrix-373, plain, ( ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k, V_m, tc_nat), c_HOL_Oplus__class_Oplus(V_k, V_n, tc_nat), tc_nat) = c_HOL_Ominus__class_Ominus(V_m, V_n, tc_nat)) )).
% 12.19/12.35 cnf(matrix-374, plain, ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(V_n), tc_nat) )).
% 12.19/12.35 cnf(matrix-375, plain, ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(V_x), tc_nat) )).
% 12.19/12.35 cnf(matrix-376, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(V_x, c_Orderings_Oord__class_Omax(V_a, V_b, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_x, V_a, T_a) )).
% 12.19/12.35 cnf(matrix-377, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(V_x, c_Orderings_Oord__class_Omax(V_a, V_b, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_x, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-378, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(V_z, c_Orderings_Oord__class_Omax(V_x, V_y, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_z, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-379, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(V_z, c_Orderings_Oord__class_Omax(V_x, V_y, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_z, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-380, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(V_x, V_z, T_a) | ~c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x, V_y, T_a), V_z, T_a) )).
% 12.19/12.35 cnf(matrix-381, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(V_y, V_z, T_a) | ~c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x, V_y, T_a), V_z, T_a) )).
% 12.19/12.35 cnf(matrix-382, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omin(V_x, V_y, T_a) = c_Orderings_Oord__class_Omin(V_y, V_x, T_a)) )).
% 12.19/12.35 cnf(matrix-383, plain, ( ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i, V_u, tc_nat), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j, V_u, tc_nat), V_k, tc_nat), tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_i, V_j, tc_nat), V_u, tc_nat), V_k, tc_nat)) )).
% 12.19/12.35 cnf(matrix-384, plain, ( ~class_Ring__and__Field_Osemiring(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_e, T_a), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b, V_e, T_a), V_c, T_a), T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), V_e, T_a), V_c, T_a)) )).
% 12.19/12.35 cnf(matrix-385, plain, ( ( c_Lambda_Olift(c_Lambda_Osubst(V_t, V_s, V_j), V_i) = c_Lambda_Osubst(c_Lambda_Olift(V_t, V_i), c_Lambda_Olift(V_s, V_i), c_HOL_Oplus__class_Oplus(V_j, c_HOL_Oone__class_Oone(tc_nat), tc_nat))) | ~c_HOL_Oord__class_Oless(V_i, c_HOL_Oplus__class_Oplus(V_j, c_HOL_Oone__class_Oone(tc_nat), tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-386, plain, ( c_lessequals(c_HOL_Ominus__class_Ominus(V_m, V_n, tc_nat), V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-387, plain, ( 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(tc_nat), c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-388, plain, ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_m, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-389, plain, ( ~class_OrderedGroup_Opordered__comm__monoid__add(T_a) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), 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) )).
% 12.19/12.35 cnf(matrix-390, plain, ( ~class_Ring__and__Field_Oidom(T_a) | ~class_Int_Onumber__ring(T_a) | ( c_HOL_Ominus__class_Ominus(V_x, V_y, T_a) != c_HOL_Ozero__class_Ozero(T_a)) | ( V_x = V_y) )).
% 12.19/12.35 cnf(matrix-391, plain, ( ~class_OrderedGroup_Ogroup__add(T_a) | ( c_HOL_Ominus__class_Ominus(V_a, V_b, T_a) != c_HOL_Ozero__class_Ozero(T_a)) | ( V_a = V_b) )).
% 12.19/12.35 cnf(matrix-392, plain, ( ~class_OrderedGroup_Oab__group__add(T_a) | ( c_HOL_Ominus__class_Ominus(V_a, V_b, T_a) != c_HOL_Ozero__class_Ozero(T_a)) | ( V_a = V_b) )).
% 12.19/12.35 cnf(matrix-393, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | ( V_x = c_HOL_Ozero__class_Ozero(T_a)) | ~c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x, V_x, T_a), c_HOL_Otimes__class_Otimes(V_y, V_y, T_a), T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-394, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | ( V_y = c_HOL_Ozero__class_Ozero(T_a)) | ~c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x, V_x, T_a), c_HOL_Otimes__class_Otimes(V_y, V_y, T_a), T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-395, plain, ( ( c_HOL_Otimes__class_Otimes(V_k, c_HOL_Ominus__class_Ominus(V_m, V_n, tc_nat), tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_k, V_m, tc_nat), c_HOL_Otimes__class_Otimes(V_k, V_n, tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-396, plain, ( ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_m, V_n, tc_nat), V_k, tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_m, V_k, tc_nat), c_HOL_Otimes__class_Otimes(V_n, V_k, tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-397, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a, V_b, T_a), V_x, T_a) | ~c_HOL_Oord__class_Oless(V_a, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-398, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a, V_b, T_a), V_x, T_a) | ~c_HOL_Oord__class_Oless(V_b, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-399, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(V_z, V_x, T_a) | ~c_HOL_Oord__class_Oless(V_z, c_Orderings_Oord__class_Omin(V_x, V_y, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-400, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(V_z, V_y, T_a) | ~c_HOL_Oord__class_Oless(V_z, c_Orderings_Oord__class_Omin(V_x, V_y, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-401, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x, V_y, T_a), V_z, T_a) | ~c_HOL_Oord__class_Oless(V_x, V_z, T_a) )).
% 12.19/12.35 cnf(matrix-402, plain, ( ~class_Orderings_Olinorder(T_a) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x, V_y, T_a), V_z, T_a) | ~c_HOL_Oord__class_Oless(V_y, V_z, T_a) )).
% 12.19/12.35 cnf(matrix-403, plain, ( ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m, V_k, tc_nat), c_HOL_Ominus__class_Ominus(V_n, V_k, tc_nat), tc_nat) = c_HOL_Ominus__class_Ominus(V_m, V_n, tc_nat)) | ~c_lessequals(V_k, V_n, tc_nat) | ~c_lessequals(V_k, V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-404, plain, ( ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i, V_j, tc_nat), V_k, tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i, V_k, tc_nat), V_j, tc_nat)) )).
% 12.19/12.35 cnf(matrix-405, plain, ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-406, plain, ( ~class_OrderedGroup_Opordered__comm__monoid__add(T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_b, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) )).
% 12.19/12.35 cnf(matrix-407, plain, ( ~class_OrderedGroup_Opordered__comm__monoid__add(T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), T_a) | ~c_lessequals(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) )).
% 12.19/12.35 cnf(matrix-408, plain, ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a, V_c, tc_nat), c_HOL_Ominus__class_Ominus(V_b, V_c, tc_nat), tc_nat) | ~c_lessequals(V_c, V_a, tc_nat) | ~c_HOL_Oord__class_Oless(V_a, V_b, tc_nat) )).
% 12.19/12.35 cnf(matrix-409, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(V_b, c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) )).
% 12.19/12.35 cnf(matrix-410, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_b, T_a) | ~c_lessequals(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-411, plain, ( ~class_Ring__and__Field_Opordered__cancel__semiring(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(V_b, c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) )).
% 12.19/12.35 cnf(matrix-412, plain, ( ~class_Ring__and__Field_Opordered__cancel__semiring(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_b, T_a) | ~c_lessequals(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-413, plain, ( ~class_Ring__and__Field_Opordered__cancel__semiring(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(V_b, c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) )).
% 12.19/12.35 cnf(matrix-414, plain, ( ~class_Ring__and__Field_Opordered__cancel__semiring(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_b, T_a) | ~c_lessequals(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-415, plain, ( ~class_Ring__and__Field_Opordered__cancel__semiring(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_b, V_a, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(V_b, c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) )).
% 12.19/12.35 cnf(matrix-416, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a, V_a, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-417, plain, ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k), V_m, tc_nat), c_HOL_Otimes__class_Otimes(c_Suc(V_k), V_n, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-418, plain, ( c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k), V_m, tc_nat), c_HOL_Otimes__class_Otimes(c_Suc(V_k), V_n, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-419, plain, ( ( c_HOL_Oplus__class_Oplus(V_x, V_y, tc_nat) != c_HOL_Oplus__class_Oplus(V_x, V_z, tc_nat)) | ( V_y = V_z) )).
% 12.19/12.35 cnf(matrix-420, plain, ( ( c_HOL_Oplus__class_Oplus(V_m, V_k, tc_nat) != c_HOL_Oplus__class_Oplus(V_n, V_k, tc_nat)) | ( V_m = V_n) )).
% 12.19/12.35 cnf(matrix-421, plain, ( ( c_HOL_Oplus__class_Oplus(V_k, V_m, tc_nat) != c_HOL_Oplus__class_Oplus(V_k, V_n, tc_nat)) | ( V_m = V_n) )).
% 12.19/12.35 cnf(matrix-422, plain, ( ~class_Ring__and__Field_Oidom(T_a) | ~class_Int_Onumber__ring(T_a) | ( c_HOL_Oplus__class_Oplus(V_x, V_y, T_a) != c_HOL_Oplus__class_Oplus(V_x, V_z, T_a)) | ( V_y = V_z) )).
% 12.19/12.35 cnf(matrix-423, plain, ( ~c_HOL_Oord__class_Oless(V_x, V_x, tc_nat) )).
% 12.19/12.35 cnf(matrix-424, plain, ( ~c_HOL_Oord__class_Oless(V_n, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-425, plain, ( ~class_Orderings_Oorder(T_a) | ~c_HOL_Oord__class_Oless(V_x, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-426, plain, ( ~class_Orderings_Olinorder(T_a) | ~c_HOL_Oord__class_Oless(V_x, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-427, plain, ( ~class_Orderings_Opreorder(T_a) | ~c_HOL_Oord__class_Oless(V_x, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-428, plain, ( ~c_lessequals(V_i, c_HOL_Oplus__class_Oplus(V_k, V_i, tc_nat), tc_nat) | ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k, V_i, tc_nat), V_i, tc_nat) = V_k) )).
% 12.19/12.35 cnf(matrix-429, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omin(V_x, V_x, T_a) = V_x) )).
% 12.19/12.35 cnf(matrix-430, plain, ( ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)) | ~c_lessequals(V_n, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-431, plain, ( c_Lambda_Obeta(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))) )).
% 12.19/12.35 cnf(matrix-432, plain, ( ~class_OrderedGroup_Opordered__comm__monoid__add(T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), 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) )).
% 12.19/12.35 cnf(matrix-433, plain, ( c_lessequals(V_n, c_HOL_Oplus__class_Oplus(V_n, V_m, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-434, plain, ( c_lessequals(V_n, c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-435, plain, ( c_lessequals(V_m, c_HOL_Oplus__class_Oplus(V_m, V_x, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-436, plain, ( ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_n, V_m, tc_nat), V_m, tc_nat) = c_Orderings_Oord__class_Omax(V_n, V_m, tc_nat)) )).
% 12.19/12.35 cnf(matrix-437, plain, ( ~class_Ring__and__Field_Oordered__semidom(T_a) | ~c_lessequals(c_HOL_Oone__class_Oone(T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-438, 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) )).
% 12.19/12.35 cnf(matrix-439, 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) )).
% 12.19/12.35 cnf(matrix-440, plain, ( ( V_m = V_n) | ~c_lessequals(V_n, V_m, tc_nat) | ~c_lessequals(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-441, 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) )).
% 12.19/12.35 cnf(matrix-442, plain, ( ( c_HOL_Ominus__class_Ominus(V_n, V_m, tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)) | ( c_HOL_Ominus__class_Ominus(V_m, V_n, tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)) | ( V_m = V_n) )).
% 12.19/12.35 cnf(matrix-443, 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) )).
% 12.19/12.35 cnf(matrix-444, plain, ( ~class_Orderings_Oorder(T_a) | ( V_x = V_y) | ~c_lessequals(V_y, V_x, T_a) | ~c_lessequals(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-445, 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) )).
% 12.19/12.35 cnf(matrix-446, plain, ( ~class_Orderings_Oorder(T_a) | ( V_x = V_y) | ~c_lessequals(V_y, V_x, T_a) | ~c_lessequals(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-447, plain, ( ~class_Orderings_Oorder(T_a) | ( V_x = V_y) | ~c_lessequals(V_x, V_y, T_a) | ~c_lessequals(V_y, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-448, 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) )).
% 12.19/12.35 cnf(matrix-449, 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) )).
% 12.19/12.35 cnf(matrix-450, plain, ( ~class_Divides_Oring__div(T_a) | ( c_Divides_Odiv__class_Omod(V_b, V_c, T_a) != c_Divides_Odiv__class_Omod(V_b_H, V_c, T_a)) | ( c_Divides_Odiv__class_Omod(V_a, V_c, T_a) != c_Divides_Odiv__class_Omod(V_a_H, V_c, T_a)) | ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a, V_b, T_a), V_c, T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a_H, V_b_H, T_a), V_c, T_a)) )).
% 12.19/12.35 cnf(matrix-451, plain, ( ~class_OrderedGroup_Opordered__ab__group__add(T_a) | c_lessequals(V_a, V_b, T_a) | ~c_lessequals(c_HOL_Ominus__class_Ominus(V_a, V_b, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-452, plain, ( ~class_OrderedGroup_Opordered__ab__group__add(T_a) | c_lessequals(c_HOL_Ominus__class_Ominus(V_a, V_b, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-453, plain, ( ( c_Suc(c_HOL_Ominus__class_Ominus(V_n, c_HOL_Oone__class_Oone(tc_nat), tc_nat)) = V_n) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-454, plain, ( ( V_n = c_Suc(c_HOL_Ominus__class_Ominus(V_n, c_HOL_Oone__class_Oone(tc_nat), tc_nat))) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-455, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omax(V_x, V_x, T_a) = V_x) )).
% 12.19/12.35 cnf(matrix-456, plain, ( ( c_Lambda_OdB_OApp(V_dB1, V_dB2) != c_Lambda_OdB_OApp(V_dB1_H, V_dB2_H)) | ( V_dB2 = V_dB2_H) )).
% 12.19/12.35 cnf(matrix-457, plain, ( ( c_Lambda_OdB_OApp(V_dB1, V_dB2) != c_Lambda_OdB_OApp(V_dB1_H, V_dB2_H)) | ( V_dB1 = V_dB1_H) )).
% 12.19/12.35 cnf(matrix-458, plain, ( ~class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), c_HOL_Oplus__class_Oplus(V_b, V_d, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_c, V_d, T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-459, plain, ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i, V_k, tc_nat), c_HOL_Oplus__class_Oplus(V_j, V_l, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(V_k, V_l, tc_nat) | ~c_HOL_Oord__class_Oless(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-460, plain, ( c_lessequals(V_x, V_y, tc_nat) | ~c_HOL_Oord__class_Oless(V_x, V_y, tc_nat) )).
% 12.19/12.35 cnf(matrix-461, plain, ( c_lessequals(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-462, plain, ( ~class_Orderings_Oorder(T_a) | c_lessequals(V_x, V_y, T_a) | ~c_HOL_Oord__class_Oless(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-463, plain, ( ~class_Orderings_Opreorder(T_a) | c_lessequals(V_x, V_y, T_a) | ~c_HOL_Oord__class_Oless(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-464, plain, ( ( c_HOL_Ominus__class_Ominus(V_m, c_Suc(c_HOL_Ominus__class_Ominus(V_j, V_k, tc_nat)), tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m, V_k, tc_nat), c_Suc(V_j), tc_nat)) | ~c_lessequals(V_k, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-465, plain, ( ~class_OrderedGroup_Opordered__ab__group__add(T_a) | c_HOL_Oord__class_Oless(V_a, V_b, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a, V_b, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-466, plain, ( ~class_OrderedGroup_Opordered__ab__group__add(T_a) | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a, V_b, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-467, plain, ( ~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) | c_lessequals(c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), c_HOL_Oplus__class_Oplus(V_b, V_c, T_a), T_a) | ~c_lessequals(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-468, plain, ( ~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) | c_lessequals(V_a, V_b, T_a) | ~c_lessequals(c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), c_HOL_Oplus__class_Oplus(V_b, V_c, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-469, plain, ( ~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) | c_lessequals(c_HOL_Oplus__class_Oplus(V_c, V_a, T_a), c_HOL_Oplus__class_Oplus(V_c, V_b, T_a), T_a) | ~c_lessequals(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-470, plain, ( ~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) | c_lessequals(V_a, V_b, T_a) | ~c_lessequals(c_HOL_Oplus__class_Oplus(V_c, V_a, T_a), c_HOL_Oplus__class_Oplus(V_c, V_b, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-471, plain, ( ~class_OrderedGroup_Opordered__ab__semigroup__add(T_a) | c_lessequals(c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), c_HOL_Oplus__class_Oplus(V_b, V_c, T_a), T_a) | ~c_lessequals(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-472, plain, ( ~class_OrderedGroup_Opordered__ab__semigroup__add(T_a) | c_lessequals(c_HOL_Oplus__class_Oplus(V_c, V_a, T_a), c_HOL_Oplus__class_Oplus(V_c, V_b, T_a), T_a) | ~c_lessequals(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-473, plain, ( c_lessequals(c_HOL_Oplus__class_Oplus(V_i, V_k, tc_nat), c_HOL_Oplus__class_Oplus(V_j, V_k, tc_nat), tc_nat) | ~c_lessequals(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-474, plain, ( c_lessequals(V_m, V_n, tc_nat) | ~c_lessequals(c_HOL_Oplus__class_Oplus(V_k, V_m, tc_nat), c_HOL_Oplus__class_Oplus(V_k, V_n, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-475, plain, ( c_lessequals(c_HOL_Oplus__class_Oplus(V_k, V_m, tc_nat), c_HOL_Oplus__class_Oplus(V_k, V_n, tc_nat), tc_nat) | ~c_lessequals(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-476, plain, ( ~class_Ring__and__Field_Oordered__semidom(T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Oone__class_Oone(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-477, plain, ( ~c_lessequals(V_i, V_j, tc_nat) | ( V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j, V_i, tc_nat), V_i, tc_nat)) )).
% 12.19/12.35 cnf(matrix-478, plain, ( ( c_HOL_Oplus__class_Oplus(V_n, c_HOL_Ominus__class_Ominus(V_m, V_n, tc_nat), tc_nat) = V_m) | ~c_lessequals(V_n, V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-479, plain, ( ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_m, V_n, tc_nat), V_n, tc_nat) = V_m) | ~c_lessequals(V_n, V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-480, plain, ( c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k, V_m, tc_nat), c_HOL_Otimes__class_Otimes(V_k, V_n, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-481, plain, ( c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m, V_k, tc_nat), c_HOL_Otimes__class_Otimes(V_n, V_k, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-482, plain, ( ~class_Ring__and__Field_Oordered__semidom(T_a) | c_HOL_Oord__class_Oless(V_a, c_HOL_Oplus__class_Oplus(V_a, c_HOL_Oone__class_Oone(T_a), T_a), T_a) )).
% 12.19/12.35 cnf(matrix-483, plain, ( ( c_HOL_Oplus__class_Oplus(V_i, c_HOL_Ominus__class_Ominus(V_j, V_k, tc_nat), tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i, V_j, tc_nat), V_k, tc_nat)) | ~c_lessequals(V_k, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-484, plain, ( ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j, V_k, tc_nat), V_i, tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_j, V_i, tc_nat), V_k, tc_nat)) | ~c_lessequals(V_k, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-485, plain, ( ~class_OrderedGroup_Oab__semigroup__idem__mult(T_a) | ( c_HOL_Otimes__class_Otimes(V_x, c_HOL_Otimes__class_Otimes(V_x, V_y, T_a), T_a) = c_HOL_Otimes__class_Otimes(V_x, V_y, T_a)) )).
% 12.19/12.35 cnf(matrix-486, plain, ( ( c_HOL_Oplus__class_Oplus(V_x, c_HOL_Otimes__class_Otimes(V_n, V_xa, tc_nat), tc_nat) != c_HOL_Oplus__class_Oplus(V_y, c_HOL_Otimes__class_Otimes(V_n, V_xb, tc_nat), tc_nat)) | ( c_Divides_Odiv__class_Omod(V_x, V_n, tc_nat) = c_Divides_Odiv__class_Omod(V_y, V_n, tc_nat)) )).
% 12.19/12.35 cnf(matrix-487, plain, ( ~class_Ring__and__Field_Oordered__semiring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_d, T_a), T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) | ~c_lessequals(V_c, V_d, T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-488, plain, ( ~class_Ring__and__Field_Oordered__semiring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_d, T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) | ~c_HOL_Oord__class_Oless(V_c, V_d, T_a) | ~c_lessequals(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-489, 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)) )).
% 12.19/12.35 cnf(matrix-490, plain, ( ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-491, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), V_b, T_a) = c_Divides_Odiv__class_Omod(V_a, V_b, T_a)) )).
% 12.19/12.35 cnf(matrix-492, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_b, V_a, T_a), V_b, T_a) = c_Divides_Odiv__class_Omod(V_a, V_b, T_a)) )).
% 12.19/12.35 cnf(matrix-493, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_b, T_a) | c_lessequals(V_b, c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-494, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) | c_lessequals(V_b, c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-495, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_b, T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) | ~c_lessequals(c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-496, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) | ~c_lessequals(c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-497, plain, ( ~class_Ring__and__Field_Oordered__semiring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_b, V_a, T_a), 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(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) )).
% 12.19/12.35 cnf(matrix-498, plain, ( ~class_Ring__and__Field_Oordered__semiring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), 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(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) )).
% 12.19/12.35 cnf(matrix-499, plain, ( ~class_Ring__and__Field_Oordered__semiring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_b, T_a) | ~c_HOL_Oord__class_Oless(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-500, plain, ( c_HOL_Oord__class_Oless(V_n, c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), V_m, tc_nat) | ~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-501, plain, ( c_HOL_Oord__class_Oless(V_n, c_HOL_Otimes__class_Otimes(V_n, V_m, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), V_m, tc_nat) | ~c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-502, plain, ( c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m, V_k, tc_nat), c_HOL_Ominus__class_Ominus(V_n, V_k, tc_nat), tc_nat) | ~c_lessequals(V_k, V_n, tc_nat) | ~c_lessequals(V_k, V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-503, plain, ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m, V_k, tc_nat), c_HOL_Ominus__class_Ominus(V_n, V_k, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ~c_lessequals(V_k, V_n, tc_nat) | ~c_lessequals(V_k, V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-504, plain, ( ~class_Ring__and__Field_Oordered__semidom(T_a) | c_HOL_Oord__class_Oless(V_b, c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), 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) )).
% 12.19/12.35 cnf(matrix-505, plain, ( ~class_OrderedGroup_Olordered__ab__group__add(T_a) | c_lessequals(c_HOL_Oplus__class_Oplus(V_a, V_a, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-506, plain, ( ~class_OrderedGroup_Olordered__ab__group__add(T_a) | c_lessequals(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(c_HOL_Oplus__class_Oplus(V_a, V_a, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-507, plain, ( ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat), V_m, tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat)) )).
% 12.19/12.35 cnf(matrix-508, plain, ( ( c_HOL_Otimes__class_Otimes(V_m, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) = c_HOL_Otimes__class_Otimes(V_n, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-509, plain, ( ~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i, V_j, tc_nat), V_i, tc_nat) )).
% 12.19/12.35 cnf(matrix-510, plain, ( ~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j, V_i, tc_nat), V_i, tc_nat) )).
% 12.19/12.35 cnf(matrix-511, plain, ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b, c_Divides_Odiv__class_Omod(V_q, V_c, tc_nat), tc_nat), V_r, tc_nat), c_HOL_Otimes__class_Otimes(V_b, V_c, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(V_r, V_b, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_c, tc_nat) )).
% 12.19/12.35 cnf(matrix-512, plain, ( ~class_Ring__and__Field_Opordered__ring(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a) | ~c_lessequals(V_c, c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(V_b, V_a, T_a) )).
% 12.19/12.35 cnf(matrix-513, plain, ( ~class_Ring__and__Field_Opordered__ring(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) | ~c_lessequals(V_c, c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(V_b, V_a, T_a) )).
% 12.19/12.35 cnf(matrix-514, plain, ( ~class_Ring__and__Field_Omult__mono(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_lessequals(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-515, plain, ( ~class_Ring__and__Field_Omult__mono(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_lessequals(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-516, plain, ( ~class_Ring__and__Field_Omult__mono1(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_lessequals(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-517, plain, ( ( c_Divides_Odiv__class_Omod(V_m, V_n, tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_m, V_n, tc_nat), V_n, tc_nat)) | c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-518, plain, ( ~class_Ring__and__Field_Oidom(T_a) | ~class_Int_Onumber__ring(T_a) | ( c_HOL_Oplus__class_Oplus(V_x, c_HOL_Otimes__class_Otimes(V_r, V_c, T_a), T_a) != c_HOL_Oplus__class_Oplus(V_x, c_HOL_Otimes__class_Otimes(V_r, V_d, T_a), T_a)) | ( V_c = V_d) | ( V_r = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-519, plain, ( ( c_HOL_Oplus__class_Oplus(V_x, c_HOL_Otimes__class_Otimes(V_r, V_c, tc_nat), tc_nat) != c_HOL_Oplus__class_Oplus(V_x, c_HOL_Otimes__class_Otimes(V_r, V_d, tc_nat), tc_nat)) | ( V_c = V_d) | ( V_r = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-520, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x, V_x, T_a), c_HOL_Otimes__class_Otimes(V_y, V_y, T_a), T_a) != c_HOL_Ozero__class_Ozero(T_a)) | ( V_y = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-521, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x, V_x, T_a), c_HOL_Otimes__class_Otimes(V_y, V_y, T_a), T_a) != c_HOL_Ozero__class_Ozero(T_a)) | ( V_x = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-522, plain, ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-523, plain, ( ~class_OrderedGroup_Ocancel__ab__semigroup__add(T_a) | ( c_HOL_Oplus__class_Oplus(V_a, V_b, T_a) != c_HOL_Oplus__class_Oplus(V_a, V_c, T_a)) | ( V_b = V_c) )).
% 12.19/12.35 cnf(matrix-524, plain, ( ~class_OrderedGroup_Ocancel__semigroup__add(T_a) | ( c_HOL_Oplus__class_Oplus(V_a, V_b, T_a) != c_HOL_Oplus__class_Oplus(V_a, V_c, T_a)) | ( V_b = V_c) )).
% 12.19/12.35 cnf(matrix-525, plain, ( ~class_OrderedGroup_Ocancel__semigroup__add(T_a) | ( c_HOL_Oplus__class_Oplus(V_b, V_a, T_a) != c_HOL_Oplus__class_Oplus(V_c, V_a, T_a)) | ( V_b = V_c) )).
% 12.19/12.35 cnf(matrix-526, plain, ( ( c_Lambda_Osubst(c_Lambda_OdB_OAbs(V_t), V_s, V_k) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(V_t, c_Lambda_Olift(V_s, c_HOL_Ozero__class_Ozero(tc_nat)), c_HOL_Oplus__class_Oplus(V_k, c_HOL_Oone__class_Oone(tc_nat), tc_nat)))) )).
% 12.19/12.35 cnf(matrix-527, plain, ( c_lessequals(c_Divides_Odiv__class_Omod(V_m, V_n, tc_nat), V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-528, plain, ( ~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) | ( c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(V_x, V_y, T_a), V_z, T_a) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(V_x, V_z, T_a), c_HOL_Oplus__class_Oplus(V_y, V_z, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-529, plain, ( c_lessequals(V_m, c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n, V_m, tc_nat), V_k, tc_nat), tc_nat) | ~c_lessequals(V_k, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-530, plain, ( ~class_Ring__and__Field_Oordered__idom(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_x, V_y, T_a), V_x, T_a) | ~c_lessequals(V_y, c_HOL_Oone__class_Oone(T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_y, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_x, T_a) )).
% 12.19/12.35 cnf(matrix-531, plain, ( ~class_Ring__and__Field_Oordered__idom(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_y, V_x, T_a), V_x, T_a) | ~c_lessequals(V_y, c_HOL_Oone__class_Oone(T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_y, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_x, T_a) )).
% 12.19/12.35 cnf(matrix-532, plain, ( ~class_Divides_Oring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a, V_b, T_a), V_c, T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a, V_c, T_a), c_Divides_Odiv__class_Omod(V_b, V_c, T_a), T_a), V_c, T_a)) )).
% 12.19/12.35 cnf(matrix-533, plain, ( ( c_Suc(c_Divides_Odiv__class_Omod(V_m, V_n, tc_nat)) != V_n) | ( c_Divides_Odiv__class_Omod(c_Suc(V_m), V_n, tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-534, plain, ( ( c_Lambda_Osubst(c_Lambda_Osubst(V_t, c_Lambda_Olift(V_v, V_i), c_Suc(V_j)), c_Lambda_Osubst(V_u, V_v, V_j), V_i) = c_Lambda_Osubst(c_Lambda_Osubst(V_t, V_u, V_i), V_v, V_j)) | ~c_HOL_Oord__class_Oless(V_i, c_HOL_Oplus__class_Oplus(V_j, c_HOL_Oone__class_Oone(tc_nat), tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-535, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), V_c, T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a, V_c, T_a), V_b, T_a), V_c, T_a)) )).
% 12.19/12.35 cnf(matrix-536, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), V_c, T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a, c_Divides_Odiv__class_Omod(V_b, V_c, T_a), T_a), V_c, T_a)) )).
% 12.19/12.35 cnf(matrix-537, plain, ( ( c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) | ( V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) | ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-538, plain, ( ( c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) | ( V_m = c_HOL_Ozero__class_Ozero(tc_nat)) | ( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) )).
% 12.19/12.35 cnf(matrix-539, plain, ( ( c_HOL_Ominus__class_Ominus(V_m, c_Suc(V_n), tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m, c_HOL_Oone__class_Oone(tc_nat), tc_nat), V_n, tc_nat)) )).
% 12.19/12.35 cnf(matrix-540, plain, ( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(V_k), V_m, tc_nat), c_HOL_Otimes__class_Otimes(c_Suc(V_k), V_n, tc_nat), tc_nat) | ~c_lessequals(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-541, plain, ( c_lessequals(V_m, V_n, tc_nat) | ~c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(V_k), V_m, tc_nat), c_HOL_Otimes__class_Otimes(c_Suc(V_k), V_n, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-542, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x, V_x, T_a), c_HOL_Otimes__class_Otimes(V_y, V_y, T_a), T_a), T_a) | ( V_x = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-543, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x, V_x, T_a), c_HOL_Otimes__class_Otimes(V_y, V_y, T_a), T_a), T_a) | ( V_y = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-544, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), c_HOL_Oplus__class_Oplus(V_c, V_d, T_a), T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), c_HOL_Oplus__class_Oplus(V_b, V_d, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-545, plain, ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_u, V_s), c_Lambda_OdB_OApp(V_u, V_t)) | ~c_Lambda_Obeta(V_s, V_t) )).
% 12.19/12.35 cnf(matrix-546, plain, ( c_Lambda_Obeta(c_Lambda_OdB_OApp(V_s, V_u), c_Lambda_OdB_OApp(V_t, V_u)) | ~c_Lambda_Obeta(V_s, V_t) )).
% 12.19/12.35 cnf(matrix-547, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omax(V_x, V_y, T_a) = c_Orderings_Oord__class_Omax(V_y, V_x, T_a)) )).
% 12.19/12.35 cnf(matrix-548, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_x, V_y, T_a), c_Orderings_Oord__class_Omin(V_x, V_z, T_a), T_a), c_Orderings_Oord__class_Omin(V_x, c_Orderings_Oord__class_Omax(V_y, V_z, T_a), T_a), T_a) )).
% 12.19/12.35 cnf(matrix-549, plain, ( ( c_Orderings_Oord__class_Omax(V_n, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) = V_n) )).
% 12.19/12.35 cnf(matrix-550, plain, ( ( c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) = V_n) )).
% 12.19/12.35 cnf(matrix-551, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omax(V_x, c_Orderings_Oord__class_Omin(V_x, V_y, T_a), T_a) = V_x) )).
% 12.19/12.35 cnf(matrix-552, plain, ( c_lessequals(V_m, c_HOL_Otimes__class_Otimes(V_m, V_m, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-553, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(V_c, c_HOL_Ozero__class_Ozero(T_a), T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-554, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(V_b, V_a, T_a) | c_HOL_Oord__class_Oless(V_a, V_b, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-555, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(V_c, c_HOL_Ozero__class_Ozero(T_a), T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-556, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(V_b, V_a, T_a) | c_HOL_Oord__class_Oless(V_a, V_b, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-557, plain, ( ( c_HOL_Ominus__class_Ominus(V_n, c_HOL_Ominus__class_Ominus(V_n, V_i, tc_nat), tc_nat) = V_i) | ~c_lessequals(V_i, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-558, plain, ( ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat), c_HOL_Oone__class_Oone(tc_nat), tc_nat) = c_HOL_Oone__class_Oone(tc_nat)) )).
% 12.19/12.35 cnf(matrix-559, 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) )).
% 12.19/12.35 cnf(matrix-560, plain, ( c_Lambda_Obeta(c_Lambda_Olift(V_r, V_i), c_Lambda_Olift(V_s, V_i)) | ~c_Lambda_Obeta(V_r, V_s) )).
% 12.19/12.35 cnf(matrix-561, plain, ( ( c_Lambda_Olift(c_Lambda_Osubst(V_t, V_s, V_j), V_i) = c_Lambda_Osubst(c_Lambda_Olift(V_t, c_HOL_Oplus__class_Oplus(V_i, c_HOL_Oone__class_Oone(tc_nat), tc_nat)), c_Lambda_Olift(V_s, V_i), V_j)) | ~c_HOL_Oord__class_Oless(V_j, c_HOL_Oplus__class_Oplus(V_i, c_HOL_Oone__class_Oone(tc_nat), tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-562, plain, ( ( c_Lambda_Olift(c_Lambda_Olift(V_t, V_i), c_Suc(V_k)) = c_Lambda_Olift(c_Lambda_Olift(V_t, V_k), V_i)) | ~c_HOL_Oord__class_Oless(V_i, c_HOL_Oplus__class_Oplus(V_k, c_HOL_Oone__class_Oone(tc_nat), tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-563, plain, ( ( c_HOL_Otimes__class_Otimes(V_k, c_Divides_Odiv__class_Omod(V_m, V_n, tc_nat), tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_k, V_m, tc_nat), c_HOL_Otimes__class_Otimes(V_k, V_n, tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-564, plain, ( ( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_m, V_n, tc_nat), V_k, tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_m, V_k, tc_nat), c_HOL_Otimes__class_Otimes(V_n, V_k, tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-565, plain, ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m, V_k, tc_nat), c_HOL_Otimes__class_Otimes(V_n, V_k, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_k, tc_nat) )).
% 12.19/12.35 cnf(matrix-566, plain, ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k, V_m, tc_nat), c_HOL_Otimes__class_Otimes(V_k, V_n, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_k, tc_nat) )).
% 12.19/12.35 cnf(matrix-567, plain, ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k, V_i, tc_nat), c_HOL_Otimes__class_Otimes(V_k, V_j, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_k, tc_nat) | ~c_HOL_Oord__class_Oless(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-568, plain, ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_i, V_k, tc_nat), c_HOL_Otimes__class_Otimes(V_j, V_k, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_k, tc_nat) | ~c_HOL_Oord__class_Oless(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-569, plain, ( c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k, V_m, tc_nat), c_HOL_Otimes__class_Otimes(V_k, V_n, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_k, tc_nat) )).
% 12.19/12.35 cnf(matrix-570, plain, ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k, V_m, tc_nat), c_HOL_Otimes__class_Otimes(V_k, V_n, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_k, tc_nat) )).
% 12.19/12.35 cnf(matrix-571, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(V_b, V_a, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_c, c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-572, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_b, V_a, T_a) | ~c_HOL_Oord__class_Oless(V_c, c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-573, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(V_a, V_b, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) )).
% 12.19/12.35 cnf(matrix-574, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) )).
% 12.19/12.35 cnf(matrix-575, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_c, c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_HOL_Oord__class_Oless(V_b, V_a, T_a) )).
% 12.19/12.35 cnf(matrix-576, plain, ( ~class_Ring__and__Field_Oordered__semiring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-577, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) )).
% 12.19/12.35 cnf(matrix-578, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_b, V_a, T_a) | ~c_HOL_Oord__class_Oless(V_c, c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-579, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_c, c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_HOL_Oord__class_Oless(V_b, V_a, T_a) )).
% 12.19/12.35 cnf(matrix-580, plain, ( ~class_Ring__and__Field_Oordered__semiring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-581, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) )).
% 12.19/12.35 cnf(matrix-582, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_b, V_a, T_a) | ~c_HOL_Oord__class_Oless(V_c, c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-583, plain, ( ~class_Ring__and__Field_Oordered__comm__semiring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-584, plain, ( ~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) | ( c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(V_x, V_y, T_a), V_z, T_a) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(V_x, V_z, T_a), c_HOL_Oplus__class_Oplus(V_y, V_z, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-585, plain, ( c_lessequals(c_HOL_Otimes__class_Otimes(V_i, V_k, tc_nat), c_HOL_Otimes__class_Otimes(V_j, V_l, tc_nat), tc_nat) | ~c_lessequals(V_k, V_l, tc_nat) | ~c_lessequals(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-586, plain, ( c_lessequals(V_m, c_HOL_Otimes__class_Otimes(V_m, c_HOL_Otimes__class_Otimes(V_m, V_m, tc_nat), tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-587, plain, ( ~class_Ring__and__Field_Opordered__semiring(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_d, T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_b, T_a) | ~c_lessequals(V_c, V_d, T_a) | ~c_lessequals(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-588, plain, ( ~class_Ring__and__Field_Opordered__semiring(T_a) | c_lessequals(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_d, T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) | ~c_lessequals(V_c, V_d, T_a) | ~c_lessequals(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-589, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(V_x, V_y, T_a), V_z, T_a) = c_Orderings_Oord__class_Omax(V_x, c_Orderings_Oord__class_Omax(V_y, V_z, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-590, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omax(V_x, c_Orderings_Oord__class_Omax(V_y, V_z, T_a), T_a) = c_Orderings_Oord__class_Omax(V_y, c_Orderings_Oord__class_Omax(V_x, V_z, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-591, plain, ( ~class_Ring__and__Field_Oordered__semidom(T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a), c_HOL_Oone__class_Oone(T_a), T_a), T_a) )).
% 12.19/12.35 cnf(matrix-592, plain, ( ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k, V_n, tc_nat), V_m, tc_nat), V_n, tc_nat) = c_Divides_Odiv__class_Omod(V_m, V_n, tc_nat)) )).
% 12.19/12.35 cnf(matrix-593, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a, c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a), V_b, T_a) = c_Divides_Odiv__class_Omod(V_a, V_b, T_a)) )).
% 12.19/12.35 cnf(matrix-594, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a, c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a), V_b, T_a) = c_Divides_Odiv__class_Omod(V_a, V_b, T_a)) )).
% 12.19/12.35 cnf(matrix-595, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_m, T_a), c_HOL_Otimes__class_Otimes(V_b, V_m, T_a), T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), V_m, T_a)) )).
% 12.19/12.35 cnf(matrix-596, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a), V_x, T_a) = V_x) )).
% 12.19/12.35 cnf(matrix-597, plain, ( ~class_OrderedGroup_Ocomm__monoid__add(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) = V_a) )).
% 12.19/12.35 cnf(matrix-598, plain, ( ( V_x = c_HOL_Oplus__class_Oplus(V_x, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-599, plain, ( ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) = V_n) )).
% 12.19/12.35 cnf(matrix-600, plain, ( ( c_HOL_Oplus__class_Oplus(V_m, c_HOL_Ozero__class_Ozero(tc_nat), tc_nat) = V_m) )).
% 12.19/12.35 cnf(matrix-601, plain, ( ~class_Ring__and__Field_Oidom(T_a) | ~class_Int_Onumber__ring(T_a) | ( V_x = c_HOL_Oplus__class_Oplus(V_x, c_HOL_Ozero__class_Ozero(T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-602, plain, ( ~class_OrderedGroup_Ocomm__monoid__add(T_a) | ( c_HOL_Oplus__class_Oplus(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) = V_a) )).
% 12.19/12.35 cnf(matrix-603, plain, ( ~class_OrderedGroup_Omonoid__add(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) = V_a) )).
% 12.19/12.35 cnf(matrix-604, plain, ( ~class_OrderedGroup_Omonoid__add(T_a) | ( c_HOL_Oplus__class_Oplus(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) = V_a) )).
% 12.19/12.35 cnf(matrix-605, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Oplus__class_Oplus(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) = V_a) )).
% 12.19/12.35 cnf(matrix-606, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) = V_a) )).
% 12.19/12.35 cnf(matrix-607, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Ozero__class_Ozero(T_a), T_a), c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Ozero__class_Ozero(T_a), T_a), T_a), T_a) )).
% 12.19/12.35 cnf(matrix-608, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omax(V_x, c_Orderings_Oord__class_Omax(V_x, V_y, T_a), T_a) = c_Orderings_Oord__class_Omax(V_x, V_y, T_a)) )).
% 12.19/12.35 cnf(matrix-609, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-610, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(V_b, c_HOL_Ozero__class_Ozero(T_a), T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-611, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_b, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-612, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(V_b, c_HOL_Ozero__class_Ozero(T_a), T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_b, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-613, plain, ( ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat), V_n, tc_nat) = V_m) )).
% 12.19/12.35 cnf(matrix-614, plain, ( ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n, V_m, tc_nat), V_n, tc_nat) = V_m) )).
% 12.19/12.35 cnf(matrix-615, plain, ( ~class_OrderedGroup_Ogroup__add(T_a) | ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), V_b, T_a) = V_a) )).
% 12.19/12.35 cnf(matrix-616, plain, ( ~class_Ring__and__Field_Oordered__semidom(T_a) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a), c_HOL_Otimes__class_Otimes(V_m, V_n, T_a), T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a), V_n, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a), V_m, T_a) )).
% 12.19/12.35 cnf(matrix-617, plain, ( ~class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), c_HOL_Oplus__class_Oplus(V_b, V_d, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_c, V_d, T_a) | ~c_lessequals(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-618, plain, ( ~class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), c_HOL_Oplus__class_Oplus(V_b, V_d, T_a), T_a) | ~c_lessequals(V_c, V_d, T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-619, plain, ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-620, plain, ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-621, 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), c_HOL_Oplus__class_Oplus(V_a, V_a, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-622, plain, ( ~class_OrderedGroup_Olordered__ab__group__add(T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Oplus__class_Oplus(V_a, V_a, T_a), T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) )).
% 12.19/12.35 cnf(matrix-623, plain, ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i, V_k, tc_nat), V_j, tc_nat) | ~c_HOL_Oord__class_Oless(V_i, c_HOL_Ominus__class_Ominus(V_j, V_k, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-624, plain, ( c_HOL_Oord__class_Oless(V_i, c_HOL_Ominus__class_Ominus(V_j, V_k, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i, V_k, tc_nat), V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-625, plain, ( ~class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), c_HOL_Oplus__class_Oplus(V_b, V_c, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-626, plain, ( ~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), c_HOL_Oplus__class_Oplus(V_b, V_c, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-627, 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(c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), c_HOL_Oplus__class_Oplus(V_b, V_c, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-628, plain, ( ~class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c, V_a, T_a), c_HOL_Oplus__class_Oplus(V_c, V_b, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-629, plain, ( ~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c, V_a, T_a), c_HOL_Oplus__class_Oplus(V_c, V_b, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-630, 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(c_HOL_Oplus__class_Oplus(V_c, V_a, T_a), c_HOL_Oplus__class_Oplus(V_c, V_b, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-631, plain, ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i, V_k, tc_nat), c_HOL_Oplus__class_Oplus(V_j, V_k, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-632, plain, ( c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_k, V_m, tc_nat), c_HOL_Oplus__class_Oplus(V_k, V_n, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-633, plain, ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_k, V_m, tc_nat), c_HOL_Oplus__class_Oplus(V_k, V_n, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-634, plain, ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat), tc_nat) | ~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), V_n, tc_nat) | ~c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-635, plain, ( ~class_Orderings_Oorder(T_a) | c_lessequals(V_z, V_x, T_a) | ~c_lessequals(V_z, V_y, T_a) | ~c_lessequals(V_y, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-636, plain, ( ~class_Orderings_Oorder(T_a) | c_HOL_Oord__class_Oless(V_z, V_x, T_a) | ~c_lessequals(V_z, V_y, T_a) | ~c_HOL_Oord__class_Oless(V_y, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-637, 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_lessequals(V_y, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-638, plain, ( ~class_OrderedGroup_Opordered__comm__monoid__add(T_a) | c_lessequals(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(V_b, c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-639, plain, ( ~class_Orderings_Opreorder(T_a) | c_lessequals(V_x, V_z, T_a) | ~c_lessequals(V_y, V_z, T_a) | ~c_lessequals(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-640, plain, ( c_lessequals(V_n, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-641, plain, ( c_lessequals(V_i, V_k, tc_nat) | ~c_lessequals(V_j, V_k, tc_nat) | ~c_lessequals(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-642, plain, ( c_lessequals(V_x, V_x, tc_nat) )).
% 12.19/12.35 cnf(matrix-643, plain, ( ~class_Orderings_Oorder(T_a) | c_lessequals(V_x, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-644, plain, ( ~class_Orderings_Opreorder(T_a) | c_lessequals(V_x, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-645, 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_lessequals(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-646, plain, ( ~class_Orderings_Opreorder(T_a) | c_HOL_Oord__class_Oless(V_x, V_z, T_a) | ~c_lessequals(V_y, V_z, T_a) | ~c_HOL_Oord__class_Oless(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-647, plain, ( ~class_OrderedGroup_Opordered__ab__group__add(T_a) | c_lessequals(V_a, c_HOL_Oplus__class_Oplus(V_b, V_d, T_a), T_a) | ~c_lessequals(V_c, V_d, T_a) | ~c_lessequals(V_a, c_HOL_Oplus__class_Oplus(V_b, V_c, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-648, plain, ( ( c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(V_m, V_i, tc_nat), c_HOL_Ominus__class_Ominus(V_n, V_i, tc_nat), tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(V_m, V_n, tc_nat), V_i, tc_nat)) )).
% 12.19/12.35 cnf(matrix-649, plain, ( ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat), c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) )).
% 12.19/12.35 cnf(matrix-650, plain, ( ~class_OrderedGroup_Oab__semigroup__idem__mult(T_a) | ( c_HOL_Otimes__class_Otimes(V_x, V_x, T_a) = V_x) )).
% 12.19/12.35 cnf(matrix-651, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), V_b, T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-652, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_b, V_a, T_a), V_b, T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-653, plain, ( ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_d, V_x, tc_nat), V_d, tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-654, plain, ( ~class_Ring__and__Field_Oordered__semiring__strict(T_a) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_d, T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) | ~c_HOL_Oord__class_Oless(V_c, V_d, T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-655, plain, ( ( V_n = V_m) | ~c_HOL_Oord__class_Oless(V_n, c_Suc(V_m), tc_nat) | ~c_lessequals(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-656, plain, ( c_lessequals(c_HOL_Otimes__class_Otimes(V_i, V_k, tc_nat), c_HOL_Otimes__class_Otimes(V_j, V_k, tc_nat), tc_nat) | ~c_lessequals(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-657, plain, ( c_lessequals(c_HOL_Otimes__class_Otimes(V_k, V_i, tc_nat), c_HOL_Otimes__class_Otimes(V_k, V_j, tc_nat), tc_nat) | ~c_lessequals(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-658, plain, ( c_lessequals(c_HOL_Otimes__class_Otimes(V_k, V_m, tc_nat), c_HOL_Otimes__class_Otimes(V_k, V_n, tc_nat), tc_nat) | ~c_lessequals(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-659, plain, ( c_lessequals(c_HOL_Otimes__class_Otimes(V_m, V_k, tc_nat), c_HOL_Otimes__class_Otimes(V_n, V_k, tc_nat), tc_nat) | ~c_lessequals(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-660, plain, ( c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Ominus__class_Ominus(V_n, V_m, tc_nat), tc_nat) )).
% 12.19/12.35 cnf(matrix-661, plain, ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), c_HOL_Ominus__class_Ominus(V_n, V_m, tc_nat), tc_nat) | ~c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-662, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Ozero__class_Ozero(T_a), T_a), c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Ozero__class_Ozero(T_a), T_a), T_a) = c_HOL_Ozero__class_Ozero(T_a)) )).
% 12.19/12.35 cnf(matrix-663, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(V_c, c_HOL_Ozero__class_Ozero(T_a), T_a) | c_HOL_Oord__class_Oless(V_a, V_b, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-664, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(V_b, V_a, T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-665, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(V_c, c_HOL_Ozero__class_Ozero(T_a), T_a) | c_HOL_Oord__class_Oless(V_a, V_b, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-666, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_HOL_Oord__class_Oless(V_b, V_a, T_a) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-667, plain, ( ( c_Suc(c_HOL_Ominus__class_Ominus(V_n, c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)), tc_nat)) = V_n) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-668, plain, ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m, V_n, tc_nat), V_m, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_m, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-669, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(c_Orderings_Oord__class_Omax(V_x, c_Orderings_Oord__class_Omin(V_y, V_z, T_a), T_a), c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_x, V_y, T_a), c_Orderings_Oord__class_Omax(V_x, V_z, T_a), T_a), T_a) )).
% 12.19/12.35 cnf(matrix-670, plain, ( ~class_OrderedGroup_Opordered__ab__group__add(T_a) | ( c_HOL_Ominus__class_Ominus(V_x, V_y, T_a) != c_HOL_Ominus__class_Ominus(V_x_H, V_y_H, T_a)) | c_lessequals(V_y_H, V_x_H, T_a) | ~c_lessequals(V_y, V_x, T_a) )).
% 12.19/12.35 cnf(matrix-671, plain, ( ~class_OrderedGroup_Opordered__ab__group__add(T_a) | ( c_HOL_Ominus__class_Ominus(V_x, V_y, T_a) != c_HOL_Ominus__class_Ominus(V_x_H, V_y_H, T_a)) | c_lessequals(V_y, V_x, T_a) | ~c_lessequals(V_y_H, V_x_H, T_a) )).
% 12.19/12.35 cnf(matrix-672, plain, ( ~class_OrderedGroup_Opordered__ab__group__add(T_a) | ( c_HOL_Ominus__class_Ominus(V_x, V_y, T_a) != c_HOL_Ominus__class_Ominus(V_x_H, V_y_H, T_a)) | c_HOL_Oord__class_Oless(V_x_H, V_y_H, T_a) | ~c_HOL_Oord__class_Oless(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-673, plain, ( ~class_OrderedGroup_Opordered__ab__group__add(T_a) | ( c_HOL_Ominus__class_Ominus(V_x, V_y, T_a) != c_HOL_Ominus__class_Ominus(V_x_H, V_y_H, T_a)) | c_HOL_Oord__class_Oless(V_x, V_y, T_a) | ~c_HOL_Oord__class_Oless(V_x_H, V_y_H, T_a) )).
% 12.19/12.35 cnf(matrix-674, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a, V_c, T_a), V_b, T_a), V_c, T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), V_c, T_a)) )).
% 12.19/12.35 cnf(matrix-675, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a, c_Divides_Odiv__class_Omod(V_b, V_c, T_a), T_a), V_c, T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), V_c, T_a)) )).
% 12.19/12.35 cnf(matrix-676, plain, ( ( c_HOL_Oplus__class_Oplus(V_n, c_HOL_Ominus__class_Ominus(V_m, V_n, tc_nat), tc_nat) = V_m) | c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-677, plain, ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_n, c_Suc(V_i), tc_nat), V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat), V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-678, plain, ( ( c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) | ( V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) | ( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) )).
% 12.19/12.35 cnf(matrix-679, plain, ( ( c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) | ( V_m = c_HOL_Ozero__class_Ozero(tc_nat)) | ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-680, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_y, V_z, T_a), V_x, T_a) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_y, V_x, T_a), c_Orderings_Oord__class_Omax(V_z, V_x, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-681, plain, ( ~class_Orderings_Olinorder(T_a) | ( c_Orderings_Oord__class_Omax(V_x, c_Orderings_Oord__class_Omin(V_y, V_z, T_a), T_a) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_x, V_y, T_a), c_Orderings_Oord__class_Omax(V_x, V_z, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-682, plain, ( ~class_Orderings_Oorder(T_a) | c_HOL_Oord__class_Oless(V_b, V_a, T_a) | ( V_a = V_b) | ~c_lessequals(V_b, V_a, T_a) )).
% 12.19/12.35 cnf(matrix-683, plain, ( ~class_Orderings_Oorder(T_a) | c_HOL_Oord__class_Oless(V_b, V_a, T_a) | ~c_lessequals(V_b, V_a, T_a) | ( V_a = V_b) )).
% 12.19/12.35 cnf(matrix-684, plain, ( c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ( V_m = V_n) | ~c_lessequals(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-685, plain, ( ( V_m = V_n) | c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ~c_lessequals(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-686, plain, ( c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ( V_m = V_n) | ~c_lessequals(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-687, plain, ( ~class_Orderings_Oorder(T_a) | ( V_x = V_y) | c_HOL_Oord__class_Oless(V_x, V_y, T_a) | ~c_lessequals(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-688, plain, ( ~class_Orderings_Oorder(T_a) | c_HOL_Oord__class_Oless(V_x, V_y, T_a) | ( V_x = V_y) | ~c_lessequals(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-689, plain, ( ~class_Orderings_Oorder(T_a) | c_HOL_Oord__class_Oless(V_a, V_b, T_a) | ( V_a = V_b) | ~c_lessequals(V_a, V_b, T_a) )).
% 12.19/12.35 cnf(matrix-690, plain, ( ~class_Orderings_Oorder(T_a) | c_HOL_Oord__class_Oless(V_a, V_b, T_a) | ~c_lessequals(V_a, V_b, T_a) | ( V_a = V_b) )).
% 12.19/12.35 cnf(matrix-691, plain, ( ~class_Orderings_Olinorder(T_a) | ( V_x = V_y) | ~c_lessequals(V_x, V_y, T_a) | c_HOL_Oord__class_Oless(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-692, plain, ( ~class_Orderings_Olinorder(T_a) | ( V_x = V_y) | c_HOL_Oord__class_Oless(V_x, V_y, T_a) | ~c_lessequals(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-693, plain, ( ~class_Ring__and__Field_Opordered__cancel__semiring(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_b, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) )).
% 12.19/12.35 cnf(matrix-694, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), T_a) | ~c_lessequals(V_b, c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-695, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_b, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) )).
% 12.19/12.35 cnf(matrix-696, plain, ( ~class_Ring__and__Field_Oordered__ring__strict(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Otimes__class_Otimes(V_a, V_a, T_a), T_a) )).
% 12.19/12.35 cnf(matrix-697, plain, ( ~class_Ring__and__Field_Opordered__ring(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), T_a) | ~c_lessequals(V_b, c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-698, plain, ( ~class_Ring__and__Field_Opordered__ring(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), T_a) | ~c_lessequals(V_b, c_HOL_Ozero__class_Ozero(T_a), T_a) | ~c_lessequals(V_a, c_HOL_Ozero__class_Ozero(T_a), T_a) )).
% 12.19/12.35 cnf(matrix-699, plain, ( ~class_Ring__and__Field_Opordered__ring(T_a) | c_lessequals(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_b, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a) )).
% 12.19/12.35 cnf(matrix-700, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a, V_b, T_a), V_c, T_a)) )).
% 12.19/12.35 cnf(matrix-701, plain, ( ~class_Divides_Osemiring__div(T_a) | ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_c, V_a, T_a), c_HOL_Otimes__class_Otimes(V_c, V_b, T_a), T_a) = c_HOL_Otimes__class_Otimes(V_c, c_Divides_Odiv__class_Omod(V_a, V_b, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-702, plain, ( ( c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s), V_k) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s, c_HOL_Oplus__class_Oplus(V_k, c_HOL_Oone__class_Oone(tc_nat), tc_nat)))) )).
% 12.19/12.35 cnf(matrix-703, plain, ( ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat)) | ( V_m = c_HOL_Oone__class_Oone(tc_nat)) )).
% 12.19/12.35 cnf(matrix-704, plain, ( ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat)) | ( V_n = c_HOL_Oone__class_Oone(tc_nat)) )).
% 12.19/12.35 cnf(matrix-705, plain, ( ~class_OrderedGroup_Oab__semigroup__mult(T_a) | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a, V_b, T_a), V_c, T_a) = c_HOL_Otimes__class_Otimes(V_a, c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-706, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx, V_ly, T_a), V_rx, T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx, V_rx, T_a), V_ly, T_a)) )).
% 12.19/12.35 cnf(matrix-707, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx, V_ly, T_a), V_rx, T_a) = c_HOL_Otimes__class_Otimes(V_lx, c_HOL_Otimes__class_Otimes(V_ly, V_rx, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-708, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Otimes__class_Otimes(V_lx, c_HOL_Otimes__class_Otimes(V_rx, V_ry, T_a), T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx, V_rx, T_a), V_ry, T_a)) )).
% 12.19/12.35 cnf(matrix-709, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Otimes__class_Otimes(V_lx, c_HOL_Otimes__class_Otimes(V_rx, V_ry, T_a), T_a) = c_HOL_Otimes__class_Otimes(V_rx, c_HOL_Otimes__class_Otimes(V_lx, V_ry, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-710, plain, ( ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat), V_k, tc_nat) = c_HOL_Otimes__class_Otimes(V_m, c_HOL_Otimes__class_Otimes(V_n, V_k, tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-711, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Otimes__class_Otimes(V_x, c_HOL_Otimes__class_Otimes(V_y, V_z, T_a), T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x, V_y, T_a), V_z, T_a)) )).
% 12.19/12.35 cnf(matrix-712, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), V_c, T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-713, plain, ( ~class_Ring__and__Field_Ocomm__semiring(T_a) | ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), V_c, T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-714, plain, ( ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat), V_k, tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_m, V_k, tc_nat), c_HOL_Otimes__class_Otimes(V_n, V_k, tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-715, plain, ( ( c_HOL_Otimes__class_Otimes(V_k, c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat), tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k, V_m, tc_nat), c_HOL_Otimes__class_Otimes(V_k, V_n, tc_nat), tc_nat)) )).
% 12.19/12.35 cnf(matrix-716, plain, ( ~class_Ring__and__Field_Ocomm__semiring__1(T_a) | ( c_HOL_Otimes__class_Otimes(V_x, c_HOL_Oplus__class_Oplus(V_y, V_z, T_a), T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x, V_y, T_a), c_HOL_Otimes__class_Otimes(V_x, V_z, T_a), T_a)) )).
% 12.19/12.35 cnf(matrix-717, 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) )).
% 12.19/12.35 cnf(matrix-718, 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) )).
% 12.19/12.35 cnf(matrix-719, plain, ( c_lessequals(V_n, V_m, tc_nat) | c_lessequals(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-720, plain, ( ~class_Orderings_Olinorder(T_a) | c_lessequals(V_y, V_x, T_a) | c_lessequals(V_x, V_y, T_a) )).
% 12.19/12.35 cnf(matrix-721, 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) )).
% 12.19/12.35 cnf(matrix-722, 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) )).
% 12.19/12.35 cnf(matrix-723, plain, ( c_lessequals(c_Suc(V_n), c_Suc(V_m), tc_nat) | ~c_lessequals(V_n, V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-724, plain, ( c_lessequals(V_n, V_m, tc_nat) | ~c_lessequals(c_Suc(V_n), c_Suc(V_m), tc_nat) )).
% 12.19/12.35 cnf(matrix-725, plain, ( ( c_HOL_Otimes__class_Otimes(c_Suc(V_k), V_m, tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(V_k), V_n, tc_nat)) | ( V_m = V_n) )).
% 12.19/12.35 cnf(matrix-726, plain, ( ( c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t, V_u), V_s, V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t, V_s, V_k), c_Lambda_Osubst(V_u, V_s, V_k))) )).
% 12.19/12.35 cnf(matrix-727, plain, ( c_HOL_Oord__class_Oless(V_m, c_Suc(V_n), tc_nat) | ~c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-728, plain, ( c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_Suc(V_m), V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-729, plain, ( ( c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat)) )).
% 12.19/12.35 cnf(matrix-730, plain, ( ( c_Lambda_OdB_OApp(V_dB1, V_dB2) != c_Lambda_OdB_OAbs(V_dB_H)) )).
% 12.19/12.35 cnf(matrix-731, plain, ( ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H)) | ( V_nat = V_nat_H) )).
% 12.19/12.35 cnf(matrix-732, plain, ( ( c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OApp(V_dB1, V_dB2)) )).
% 12.19/12.35 cnf(matrix-733, plain, ( ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k), V_u, V_k) = V_u) )).
% 12.19/12.35 cnf(matrix-734, plain, ( ( c_Divides_Odiv__class_Omod(c_Suc(V_m), V_n, tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(V_m, V_n, tc_nat)), V_n, tc_nat)) )).
% 12.19/12.35 cnf(matrix-735, plain, ( ( V_n != c_Suc(V_n)) )).
% 12.19/12.35 cnf(matrix-736, plain, ( ( c_Suc(V_n) != V_n) )).
% 12.19/12.35 cnf(matrix-737, 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) )).
% 12.19/12.35 cnf(matrix-738, plain, ( ~c_lessequals(c_Suc(V_n), V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-739, plain, ( c_lessequals(V_m, c_Suc(V_n), tc_nat) | ~c_lessequals(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-740, plain, ( c_lessequals(V_m, V_n, tc_nat) | ~c_lessequals(c_Suc(V_m), V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-741, plain, ( ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_i), V_s, V_k) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(V_i, c_HOL_Oone__class_Oone(tc_nat), tc_nat))) | ~c_HOL_Oord__class_Oless(V_k, V_i, tc_nat) )).
% 12.19/12.35 cnf(matrix-742, plain, ( ( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_j), V_u, V_i) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(V_j, c_HOL_Oone__class_Oone(tc_nat), tc_nat))) | ~c_HOL_Oord__class_Oless(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-743, plain, ( c_HOL_Oord__class_Oless(c_Suc(V_i), V_k, tc_nat) | ~c_HOL_Oord__class_Oless(V_j, V_k, tc_nat) | ~c_HOL_Oord__class_Oless(V_i, V_j, tc_nat) )).
% 12.19/12.35 cnf(matrix-744, plain, ( c_HOL_Oord__class_Oless(V_x, c_Suc(V_x), tc_nat) )).
% 12.19/12.35 cnf(matrix-745, plain, ( c_HOL_Oord__class_Oless(V_n, c_Suc(V_n), tc_nat) )).
% 12.19/12.35 cnf(matrix-746, plain, ( ~c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i), V_t) )).
% 12.19/12.35 cnf(matrix-747, plain, ( ( c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-748, plain, ( ( c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat)) )).
% 12.19/12.35 cnf(matrix-749, plain, ( ( V_n = V_m) | ~c_HOL_Oord__class_Oless(V_n, c_Suc(V_m), tc_nat) | c_HOL_Oord__class_Oless(V_n, V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-750, plain, ( ( V_m = V_n) | ~c_HOL_Oord__class_Oless(V_n, c_Suc(V_m), tc_nat) | c_HOL_Oord__class_Oless(V_n, V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-751, plain, ( ( V_m = V_n) | c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(V_m, c_Suc(V_n), tc_nat) )).
% 12.19/12.35 cnf(matrix-752, plain, ( ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OApp(V_dB1_H, V_dB2_H)) )).
% 12.19/12.35 cnf(matrix-753, plain, ( ( c_HOL_Ominus__class_Ominus(c_Suc(V_m), c_Suc(V_n), tc_nat) = c_HOL_Ominus__class_Ominus(V_m, V_n, tc_nat)) )).
% 12.19/12.35 cnf(matrix-754, plain, ( ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H)) | ( V_dB = V_dB_H) )).
% 12.19/12.35 cnf(matrix-755, plain, ( c_InductTermi_OIT(c_Lambda_Olift(V_t, V_i)) | ~c_InductTermi_OIT(V_t) )).
% 12.19/12.35 cnf(matrix-756, plain, ( ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H)) )).
% 12.19/12.35 cnf(matrix-757, plain, ( ( c_Suc(V_nat) != c_Suc(V_nat_H)) | ( V_nat = V_nat_H) )).
% 12.19/12.35 cnf(matrix-758, plain, ( ( c_Suc(V_x) != c_Suc(V_y)) | ( V_x = V_y) )).
% 12.19/12.35 cnf(matrix-759, plain, ( ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m)) )).
% 12.19/12.35 cnf(matrix-760, plain, ( ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H)) )).
% 12.19/12.35 cnf(matrix-761, plain, ( ( c_HOL_Oplus__class_Oplus(c_Suc(V_m), V_n, tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat))) )).
% 12.19/12.35 cnf(matrix-762, plain, ( ( c_HOL_Oplus__class_Oplus(V_m, c_Suc(V_n), tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m, V_n, tc_nat))) )).
% 12.19/12.35 cnf(matrix-763, plain, ( c_Lambda_Obeta(c_Lambda_Osubst(V_r, V_t, V_i), c_Lambda_Osubst(V_s, V_t, V_i)) | ~c_Lambda_Obeta(V_r, V_s) )).
% 12.19/12.35 cnf(matrix-764, plain, ( ( c_Orderings_Oord__class_Omax(c_Suc(V_m), c_Suc(V_n), tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(V_m, V_n, tc_nat))) )).
% 12.19/12.35 cnf(matrix-765, 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) )).
% 12.19/12.35 cnf(matrix-766, plain, ( ( c_Divides_Odiv__class_Omod(c_Suc(V_m), V_n, tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(V_m, V_n, tc_nat))) | ( c_Suc(c_Divides_Odiv__class_Omod(V_m, V_n, tc_nat)) = V_n) )).
% 12.19/12.35 cnf(matrix-767, 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) )).
% 12.19/12.35 cnf(matrix-768, plain, ( ( c_HOL_Oplus__class_Oplus(c_Suc(V_m), V_n, tc_nat) = c_HOL_Oplus__class_Oplus(V_m, c_Suc(V_n), tc_nat)) )).
% 12.19/12.35 cnf(matrix-769, plain, ( c_HOL_Oord__class_Oless(c_Suc(V_m), V_n, tc_nat) | ( c_Suc(V_m) = V_n) | ~c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-770, plain, ( ~c_lessequals(V_m, V_n, tc_nat) | ~c_lessequals(c_Suc(V_n), V_m, tc_nat) )).
% 12.19/12.35 cnf(matrix-771, plain, ( c_lessequals(c_Suc(V_n), V_m, tc_nat) | c_lessequals(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-772, plain, ( ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(V_m), V_n, tc_nat), c_Suc(V_k), tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m, V_n, tc_nat), V_k, tc_nat)) )).
% 12.19/12.35 cnf(matrix-773, plain, ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r)) | ~c_InductTermi_OIT(V_r) )).
% 12.19/12.35 cnf(matrix-774, plain, ( c_lessequals(c_Suc(V_n), c_Suc(V_n), tc_nat) )).
% 12.19/12.35 cnf(matrix-775, plain, ( ( c_Lambda_Osubst(c_Lambda_Olift(V_t, V_k), V_s, V_k) = V_t) )).
% 12.19/12.35 cnf(matrix-776, plain, ( ( c_Orderings_Oord__class_Omin(c_Suc(V_m), c_Suc(V_n), tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(V_m, V_n, tc_nat))) )).
% 12.19/12.35 cnf(matrix-777, plain, ( ( V_m = c_Suc(V_n)) | c_lessequals(V_m, V_n, tc_nat) | ~c_lessequals(V_m, c_Suc(V_n), tc_nat) )).
% 12.19/12.35 cnf(matrix-778, plain, ( c_HOL_Oord__class_Oless(V_x, V_x, tc_nat) | c_HOL_Oord__class_Oless(V_x, c_Suc(V_x), tc_nat) )).
% 12.19/12.35 cnf(matrix-779, plain, ( ~c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(V_n, c_Suc(V_m), tc_nat) )).
% 12.19/12.35 cnf(matrix-780, plain, ( c_HOL_Oord__class_Oless(V_n, c_Suc(V_m), tc_nat) | c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-781, plain, ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s), c_Lambda_OdB_OAbs(V_t)) | ~c_Lambda_Obeta(V_s, V_t) )).
% 12.19/12.35 cnf(matrix-782, plain, ( ( c_Lambda_OdB_OApp(V_dB1_H, V_dB2_H) != c_Lambda_OdB_OVar(V_nat)) )).
% 12.19/12.35 cnf(matrix-783, plain, ( c_HOL_Oord__class_Oless(c_Suc(V_x), c_Suc(V_n), tc_nat) | ~c_HOL_Oord__class_Oless(V_x, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-784, plain, ( c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) | ~c_HOL_Oord__class_Oless(c_Suc(V_m), c_Suc(V_n), tc_nat) )).
% 12.19/12.35 cnf(matrix-785, plain, ( c_HOL_Oord__class_Oless(c_Suc(V_m), c_Suc(V_n), tc_nat) | ~c_HOL_Oord__class_Oless(V_m, V_n, tc_nat) )).
% 12.19/12.35 cnf(matrix-786, plain, ( c_InductTermi_OIT(v_ra) )).
% 12.19/12.35 cnf(matrix-787, plain, ( c_InductTermi_OIT(c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(V_i), V_j)) )).
% 12.19/12.35 cnf(matrix-788, plain, ( ~c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja)))) )).
% 12.19/12.35 cnf(matrix-789, plain, ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) )).
% 12.19/12.35 cnf(matrix-790, plain, ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) )).
% 12.19/12.35 cnf(matrix-791, plain, ( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) )).
% 12.19/12.35 cnf(matrix-792, plain, ( class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) )).
% 12.19/12.35 cnf(matrix-793, plain, ( class_Ring__and__Field_Oordered__semiring__strict(tc_nat) )).
% 12.19/12.35 cnf(matrix-794, plain, ( class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) )).
% 12.19/12.35 cnf(matrix-795, plain, ( class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) )).
% 12.19/12.35 cnf(matrix-796, plain, ( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) )).
% 12.19/12.35 cnf(matrix-797, plain, ( class_OrderedGroup_Ocancel__semigroup__add(tc_nat) )).
% 12.19/12.35 cnf(matrix-798, plain, ( class_Ring__and__Field_Opordered__semiring(tc_nat) )).
% 12.19/12.35 cnf(matrix-799, plain, ( class_Ring__and__Field_Oordered__semiring(tc_nat) )).
% 12.19/12.35 cnf(matrix-800, plain, ( class_Ring__and__Field_Ono__zero__divisors(tc_nat) )).
% 12.19/12.35 cnf(matrix-801, plain, ( class_Ring__and__Field_Oordered__semidom(tc_nat) )).
% 12.19/12.35 cnf(matrix-802, plain, ( class_Ring__and__Field_Ocomm__semiring__1(tc_nat) )).
% 12.19/12.35 cnf(matrix-803, plain, ( class_OrderedGroup_Oab__semigroup__mult(tc_nat) )).
% 12.19/12.35 cnf(matrix-804, plain, ( class_OrderedGroup_Ocomm__monoid__mult(tc_nat) )).
% 12.19/12.35 cnf(matrix-805, plain, ( class_OrderedGroup_Oab__semigroup__add(tc_nat) )).
% 12.19/12.35 cnf(matrix-806, plain, ( class_Ring__and__Field_Ocomm__semiring(tc_nat) )).
% 12.19/12.35 cnf(matrix-807, plain, ( class_OrderedGroup_Ocomm__monoid__add(tc_nat) )).
% 12.19/12.35 cnf(matrix-808, plain, ( class_Ring__and__Field_Ozero__neq__one(tc_nat) )).
% 12.19/12.35 cnf(matrix-809, plain, ( class_Ring__and__Field_Omult__mono1(tc_nat) )).
% 12.19/12.35 cnf(matrix-810, plain, ( class_Ring__and__Field_Omult__zero(tc_nat) )).
% 12.19/12.35 cnf(matrix-811, plain, ( class_Ring__and__Field_Omult__mono(tc_nat) )).
% 12.19/12.35 cnf(matrix-812, plain, ( class_OrderedGroup_Omonoid__mult(tc_nat) )).
% 12.19/12.35 cnf(matrix-813, plain, ( class_Ring__and__Field_Osemiring(tc_nat) )).
% 12.19/12.35 cnf(matrix-814, plain, ( class_OrderedGroup_Omonoid__add(tc_nat) )).
% 12.19/12.35 cnf(matrix-815, plain, ( class_Divides_Osemiring__div(tc_nat) )).
% 12.19/12.35 cnf(matrix-816, plain, ( class_Orderings_Opreorder(tc_nat) )).
% 12.19/12.35 cnf(matrix-817, plain, ( class_Orderings_Olinorder(tc_nat) )).
% 12.19/12.35 cnf(matrix-818, plain, ( class_Orderings_Oorder(tc_nat) )).
% 12.19/12.35
% 12.19/12.35 % Proof stack:
% 12.19/12.35 cnf(proof-stack, plain,
% 12.19/12.35 proof_stack(
% 12.19/12.35 start(787),
% 12.19/12.35 left_branch(0, 773, 1, 2),
% 12.19/12.35 left_branch(0, 788, 0, 3),
% 12.19/12.35 right_branch(3),
% 12.19/12.35 right_branch(2)
% 12.19/12.35 )).
% 12.19/12.35 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------