ConnectPP---0.7.2.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : ALG429-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 08:12:49 AM UTC 2026

% Result   : Unsatisfiable 150.25s 150.51s
% Output   : Proof 150.30s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_divide__le__eq__number__of_3,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of_3) ).

cnf(cls_divide__le__eq__number__of_2,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,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_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of_2) ).

cnf(cls_one__less__inverse__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_one__less__inverse__iff_0) ).

cnf(cls_div__mult__div__if__dvd_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_w,T_a)
    | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),c_Divides_Odiv__class_Odiv(V_w,V_z,T_a),T_a) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_x,V_w,T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__mult__div__if__dvd_0) ).

cnf(cls_divide__eq__eq__number__of1_3,axiom,
    ( c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) = V_a
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__eq__eq__number__of1_3) ).

cnf(cls_eq__divide__eq__number__of1_3,axiom,
    ( c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_eq__divide__eq__number__of1_3) ).

cnf(cls_neg__le__0__iff__le_0,axiom,
    ( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_neg__le__0__iff__le_0) ).

cnf(cls_neg__le__0__iff__le_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_neg__le__0__iff__le_1) ).

cnf(cls_power__0_0,axiom,
    ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Power_Opower(T_a) ),
    file('theBenchmark.p',cls_power__0_0) ).

cnf(cls_class__semiring_Opwr__0_0,axiom,
    ( c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Opwr__0_0) ).

cnf(cls_divide__le__eq__number__of1_2,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of1_2) ).

cnf(cls_divide__le__eq__number__of1_3,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_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_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of1_3) ).

cnf(cls_le__divide__eq__number__of1_2,axiom,
    ( ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of1_2) ).

cnf(cls_le__divide__eq__number__of1_3,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of1_3) ).

cnf(cls_div__mult__mult1__if_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__mult__mult1__if_0) ).

cnf(cls_mod__add__self1_0,axiom,
    ( 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)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__add__self1_0) ).

cnf(cls_mod__add__self2_0,axiom,
    ( 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)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__add__self2_0) ).

cnf(cls_mult__le__0__iff_0,axiom,
    ( ~ 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_a,T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__le__0__iff_0) ).

cnf(cls_mult__le__0__iff_1,axiom,
    ( ~ 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_a,T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__le__0__iff_1) ).

cnf(cls_mult__le__0__iff_2,axiom,
    ( ~ 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(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__le__0__iff_2) ).

cnf(cls_mult__le__0__iff_3,axiom,
    ( ~ 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_b,T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__le__0__iff_3) ).

cnf(cls_mult__neg__pos_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_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(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__neg__pos_0) ).

cnf(cls_mult__pos__neg_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_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_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__pos__neg_0) ).

cnf(cls_mult__pos__neg2_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_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_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__pos__neg2_0) ).

cnf(cls_add__minus__cancel_0,axiom,
    ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a),T_a) = V_b
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_add__minus__cancel_0) ).

cnf(cls_pCons__eq__iff_1,axiom,
    ( V_p = V_q
    | c_Polynomial_OpCons(V_a,V_p,T_a) != c_Polynomial_OpCons(V_b,V_q,T_a)
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_pCons__eq__iff_1) ).

cnf(cls_pCons__eq__iff_0,axiom,
    ( V_a = V_b
    | c_Polynomial_OpCons(V_a,V_p,T_a) != c_Polynomial_OpCons(V_b,V_q,T_a)
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_pCons__eq__iff_0) ).

cnf(cls_pos__add__strict_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a)
    | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_pos__add__strict_0) ).

cnf(cls_mult__cancel2_1,axiom,
    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),
    file('theBenchmark.p',cls_mult__cancel2_1) ).

cnf(cls_mult__cancel1_1,axiom,
    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),
    file('theBenchmark.p',cls_mult__cancel1_1) ).

cnf(cls_inverse__negative__imp__negative_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__negative__imp__negative_0) ).

cnf(cls_power__less__power__Suc_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__less__power__Suc_0) ).

cnf(cls_inverse__divide_0,axiom,
    ( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_b,V_a,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_inverse__divide_0) ).

cnf(cls_mult__mono1_0,axiom,
    ( ~ c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(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)
    | ~ class_Ring__and__Field_Omult__mono1(T_a) ),
    file('theBenchmark.p',cls_mult__mono1_0) ).

cnf(cls_mult__left__mono_0,axiom,
    ( ~ c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(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)
    | ~ class_Ring__and__Field_Omult__mono(T_a) ),
    file('theBenchmark.p',cls_mult__left__mono_0) ).

cnf(cls_mult__right__mono_0,axiom,
    ( ~ c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(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)
    | ~ class_Ring__and__Field_Omult__mono(T_a) ),
    file('theBenchmark.p',cls_mult__right__mono_0) ).

cnf(cls_mult__left__mono__neg_0,axiom,
    ( ~ c_lessequals(V_b,V_a,T_a)
    | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_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)
    | ~ class_Ring__and__Field_Opordered__ring(T_a) ),
    file('theBenchmark.p',cls_mult__left__mono__neg_0) ).

cnf(cls_mult__right__mono__neg_0,axiom,
    ( ~ c_lessequals(V_b,V_a,T_a)
    | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),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)
    | ~ class_Ring__and__Field_Opordered__ring(T_a) ),
    file('theBenchmark.p',cls_mult__right__mono__neg_0) ).

cnf(cls_natgb_Oadd__scale__eq__noteq_0,axiom,
    ( V_r = c_HOL_Ozero__class_Ozero(tc_nat)
    | V_c = V_d
    | 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) ),
    file('theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).

cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom,
    ( V_r = c_HOL_Ozero__class_Ozero(T_a)
    | V_c = V_d
    | 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)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).

cnf(cls_sum__squares__eq__zero__iff_0,axiom,
    ( V_x = 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) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).

cnf(cls_sum__squares__eq__zero__iff_1,axiom,
    ( V_y = 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) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).

cnf(cls_n__not__Suc__n_0,axiom,
    V_n != c_Suc(V_n),
    file('theBenchmark.p',cls_n__not__Suc__n_0) ).

cnf(cls_Suc__n__not__n_0,axiom,
    c_Suc(V_n) != V_n,
    file('theBenchmark.p',cls_Suc__n__not__n_0) ).

cnf(cls_inverse__unique_0,axiom,
    ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b
    | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_inverse__unique_0) ).

cnf(cls_power__0__left__number__of_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a)
    | c_Int_Onumber__class_Onumber__of(V_w,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_Power_Opower(T_a)
    | ~ class_Ring__and__Field_Osemiring__0(T_a) ),
    file('theBenchmark.p',cls_power__0__left__number__of_0) ).

cnf(cls_divide__less__eq_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),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(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq_0) ).

cnf(cls_divide__less__eq_6,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,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(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq_6) ).

cnf(cls_less__divide__eq_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(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(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq_0) ).

cnf(cls_less__divide__eq_6,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,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,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq_6) ).

cnf(cls_mult__imp__div__pos__less_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_mult__imp__div__pos__less_0) ).

cnf(cls_mult__imp__less__div__pos_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a)
    | c_HOL_Oord__class_Oless(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_mult__imp__less__div__pos_0) ).

cnf(cls_smult__pCons_0,axiom,
    ( c_Polynomial_Osmult(V_a,c_Polynomial_OpCons(V_b,V_p,T_a),T_a) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_Polynomial_Osmult(V_a,V_p,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_smult__pCons_0) ).

cnf(cls_zero__less__divide__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_zero__less__divide__iff_0) ).

cnf(cls_divide__le__eq__number__of_9,axiom,
    ( ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of_9) ).

cnf(cls_mult__left__idem_0,axiom,
    ( 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)
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) ),
    file('theBenchmark.p',cls_mult__left__idem_0) ).

cnf(cls_less__add__one_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_less__add__one_0) ).

cnf(cls_le__eq__neg_1,axiom,
    ( ~ 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_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_le__eq__neg_1) ).

cnf(cls_le__eq__neg_0,axiom,
    ( ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_le__eq__neg_0) ).

cnf(cls_mult__less__cancel1_1,axiom,
    ( ~ 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) ),
    file('theBenchmark.p',cls_mult__less__cancel1_1) ).

cnf(cls_mult__less__cancel2_1,axiom,
    ( ~ 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) ),
    file('theBenchmark.p',cls_mult__less__cancel2_1) ).

cnf(cls_minus__mult__right_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Oring(T_a) ),
    file('theBenchmark.p',cls_minus__mult__right_0) ).

cnf(cls_minus__mult__left_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
    | ~ class_Ring__and__Field_Oring(T_a) ),
    file('theBenchmark.p',cls_minus__mult__left_0) ).

cnf(cls_mult__frac__frac_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_z,V_w,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_y,V_w,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_mult__frac__frac_0) ).

cnf(cls_add__le__cancel__right_1,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
    file('theBenchmark.p',cls_add__le__cancel__right_1) ).

cnf(cls_add__le__cancel__right_0,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
    file('theBenchmark.p',cls_add__le__cancel__right_0) ).

cnf(cls_add__le__cancel__left_1,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
    file('theBenchmark.p',cls_add__le__cancel__left_1) ).

cnf(cls_add__le__cancel__left_0,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
    file('theBenchmark.p',cls_add__le__cancel__left_0) ).

cnf(cls_add__right__mono_0,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) ),
    file('theBenchmark.p',cls_add__right__mono_0) ).

cnf(cls_add__left__mono_0,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) ),
    file('theBenchmark.p',cls_add__left__mono_0) ).

cnf(cls_add__le__mono1_0,axiom,
    ( ~ c_lessequals(V_i,V_j,tc_nat)
    | 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) ),
    file('theBenchmark.p',cls_add__le__mono1_0) ).

cnf(cls_nat__add__left__cancel__le_0,axiom,
    ( ~ 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) ),
    file('theBenchmark.p',cls_nat__add__left__cancel__le_0) ).

cnf(cls_nat__add__left__cancel__le_1,axiom,
    ( ~ 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) ),
    file('theBenchmark.p',cls_nat__add__left__cancel__le_1) ).

cnf(cls_lessI_0,axiom,
    c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat),
    file('theBenchmark.p',cls_lessI_0) ).

cnf(cls_less__Suc__eq_2,axiom,
    c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat),
    file('theBenchmark.p',cls_less__Suc__eq_2) ).

cnf(cls_less__trans__Suc_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
    | c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat) ),
    file('theBenchmark.p',cls_less__trans__Suc_0) ).

cnf(cls_linorder__neqE__ordered__idom_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

cnf(cls_not__less__iff__gr__or__eq_0,axiom,
    ( c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | V_x = V_y
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

cnf(cls_linorder__antisym__conv3_0,axiom,
    ( 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
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_linorder__antisym__conv3_0) ).

cnf(cls_linorder__less__linear_0,axiom,
    ( c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | V_x = V_y
    | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_linorder__less__linear_0) ).

cnf(cls_pdivmod__rel__unique_1,axiom,
    ( ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q1,V_r1,T_a)
    | ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q2,V_r2,T_a)
    | V_r1 = V_r2
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_pdivmod__rel__unique_1) ).

cnf(cls_pdivmod__rel__unique_0,axiom,
    ( ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q1,V_r1,T_a)
    | ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q2,V_r2,T_a)
    | V_q1 = V_q2
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_pdivmod__rel__unique_0) ).

cnf(cls_order__antisym__conv_0,axiom,
    ( ~ c_lessequals(V_y,V_x,T_a)
    | ~ c_lessequals(V_x,V_y,T_a)
    | V_x = V_y
    | ~ class_Orderings_Oorder(T_a) ),
    file('theBenchmark.p',cls_order__antisym__conv_0) ).

cnf(cls_le__antisym_0,axiom,
    ( ~ c_lessequals(V_m,V_n,tc_nat)
    | ~ c_lessequals(V_n,V_m,tc_nat)
    | V_m = V_n ),
    file('theBenchmark.p',cls_le__antisym_0) ).

cnf(cls_nat__neq__iff_0,axiom,
    ( V_m = V_n
    | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ),
    file('theBenchmark.p',cls_nat__neq__iff_0) ).

cnf(cls_linorder__neqE__nat_0,axiom,
    ( V_x = V_y
    | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
    | c_HOL_Oord__class_Oless(V_y,V_x,tc_nat) ),
    file('theBenchmark.p',cls_linorder__neqE__nat_0) ).

cnf(cls_order__eq__iff_2,axiom,
    ( ~ c_lessequals(V_x,V_y,T_a)
    | ~ c_lessequals(V_y,V_x,T_a)
    | V_x = V_y
    | ~ class_Orderings_Oorder(T_a) ),
    file('theBenchmark.p',cls_order__eq__iff_2) ).

cnf(cls_linorder__neqE_0,axiom,
    ( 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)
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_linorder__neqE_0) ).

cnf(cls_order__antisym_0,axiom,
    ( ~ c_lessequals(V_x,V_y,T_a)
    | ~ c_lessequals(V_y,V_x,T_a)
    | V_x = V_y
    | ~ class_Orderings_Oorder(T_a) ),
    file('theBenchmark.p',cls_order__antisym_0) ).

cnf(cls_power__gt1__lemma_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__gt1__lemma_0) ).

cnf(cls_compl__eq__compl__iff_0,axiom,
    ( V_x = V_y
    | c_HOL_Ouminus__class_Ouminus(V_x,T_a) != c_HOL_Ouminus__class_Ouminus(V_y,T_a)
    | ~ class_Lattices_Oboolean__algebra(T_a) ),
    file('theBenchmark.p',cls_compl__eq__compl__iff_0) ).

cnf(cls_neg__equal__iff__equal_0,axiom,
    ( V_a = V_b
    | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(V_b,T_a)
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_neg__equal__iff__equal_0) ).

cnf(cls_div__smult__right_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_Divides_Odiv__class_Odiv(V_x,c_Polynomial_Osmult(V_a,V_y,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)),T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_div__smult__right_0) ).

cnf(cls_le__0__eq_0,axiom,
    ( ~ c_lessequals(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('theBenchmark.p',cls_le__0__eq_0) ).

cnf(cls_eq__divide__imp_0,axiom,
    ( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a)
    | V_c = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_eq__divide__imp_0) ).

cnf(cls_divide__eq__imp_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a
    | V_c = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__eq__imp_0) ).

cnf(cls_eq__divide__eq_3,axiom,
    ( V_c = c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_eq__divide__eq_3) ).

cnf(cls_divide__eq__eq_3,axiom,
    ( V_c = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__eq__eq_3) ).

cnf(cls_divide__le__0__1__iff_1,axiom,
    ( ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__0__1__iff_1) ).

cnf(cls_divide__le__0__1__iff_0,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_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)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__0__1__iff_0) ).

cnf(cls_divide__eq__eq__number__of_1,axiom,
    ( c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) != c_Int_Onumber__class_Onumber__of(V_w,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__eq__eq__number__of_1) ).

cnf(cls_divide__eq__eq__number__of_2,axiom,
    ( c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_Int_Onumber__class_Onumber__of(V_w,T_a)
    | c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__eq__eq__number__of_2) ).

cnf(cls_inverse__less__1__iff_1,axiom,
    ( ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__less__1__iff_1) ).

cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).

cnf(cls_sum__squares__le__zero__iff_2,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).

cnf(cls_div__mult__self2__is__id_0,axiom,
    ( V_b = c_HOL_Ozero__class_Ozero(T_a)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = V_a
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__mult__self2__is__id_0) ).

cnf(cls_div__mult__self1__is__id_0,axiom,
    ( V_b = c_HOL_Ozero__class_Ozero(T_a)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = V_a
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__mult__self1__is__id_0) ).

cnf(cls_add__nonpos__neg_0,axiom,
    ( ~ c_lessequals(V_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_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
    file('theBenchmark.p',cls_add__nonpos__neg_0) ).

cnf(cls_add__neg__nonpos_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
    file('theBenchmark.p',cls_add__neg__nonpos_0) ).

cnf(cls_neg__less__iff__less_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_neg__less__iff__less_1) ).

cnf(cls_neg__less__iff__less_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_neg__less__iff__less_0) ).

cnf(cls_le__divide__eq_8,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq_8) ).

cnf(cls_divide__le__eq_8,axiom,
    ( ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq_8) ).

cnf(cls_not__sum__squares__lt__zero_0,axiom,
    ( ~ 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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).

cnf(cls_eq__divide__eq__number__of1_4,axiom,
    ( c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_eq__divide__eq__number__of1_4) ).

cnf(cls_mult__Suc__right_0,axiom,
    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),
    file('theBenchmark.p',cls_mult__Suc__right_0) ).

cnf(cls_mult__Suc_0,axiom,
    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),
    file('theBenchmark.p',cls_mult__Suc_0) ).

cnf(cls_zero__less__mult__pos2_0,axiom,
    ( ~ 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)
    | ~ 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),V_b,T_a)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
    file('theBenchmark.p',cls_zero__less__mult__pos2_0) ).

cnf(cls_zero__less__mult__pos_0,axiom,
    ( ~ 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_a,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
    file('theBenchmark.p',cls_zero__less__mult__pos_0) ).

cnf(cls_mult__pos__pos_0,axiom,
    ( ~ 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),V_b,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)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__pos__pos_0) ).

cnf(cls_mult__neg__neg_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_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),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__neg__neg_0) ).

cnf(cls_nat__0__less__mult__iff_2,axiom,
    ( ~ 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)
    | 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) ),
    file('theBenchmark.p',cls_nat__0__less__mult__iff_2) ).

cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).

cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).

cnf(cls_even__less__0__iff_0,axiom,
    ( ~ 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)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_even__less__0__iff_0) ).

cnf(cls_even__less__0__iff_1,axiom,
    ( ~ 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)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_even__less__0__iff_1) ).

cnf(cls_mult__is__0_0,axiom,
    ( V_m = c_HOL_Ozero__class_Ozero(tc_nat)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('theBenchmark.p',cls_mult__is__0_0) ).

cnf(cls_add__nonneg__eq__0__iff_1,axiom,
    ( V_y = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
    file('theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).

cnf(cls_add__nonneg__eq__0__iff_0,axiom,
    ( V_x = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
    file('theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).

cnf(cls_add__is__0_0,axiom,
    ( V_m = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('theBenchmark.p',cls_add__is__0_0) ).

cnf(cls_add__is__0_1,axiom,
    ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('theBenchmark.p',cls_add__is__0_1) ).

cnf(cls_eq__divide__eq__number__of_1,axiom,
    ( c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_eq__divide__eq__number__of_1) ).

cnf(cls_eq__divide__eq__number__of_2,axiom,
    ( c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_eq__divide__eq__number__of_2) ).

cnf(cls_pdivmod__rel__smult__left_0,axiom,
    ( ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q,V_r,T_a)
    | c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(V_a,V_x,T_a),V_y,c_Polynomial_Osmult(V_a,V_q,T_a),c_Polynomial_Osmult(V_a,V_r,T_a),T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_pdivmod__rel__smult__left_0) ).

cnf(cls_eq__divide__eq__number__of1_2,axiom,
    ( c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_eq__divide__eq__number__of1_2) ).

cnf(cls_class__semiring_Omul__pwr_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_nat),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).

cnf(cls_square__eq__iff_0,axiom,
    ( V_a = V_b
    | V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a)
    | c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) != c_HOL_Otimes__class_Otimes(V_b,V_b,T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_square__eq__iff_0) ).

cnf(cls_mult__less__imp__less__right_0,axiom,
    ( ~ 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_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__imp__less__right_0) ).

cnf(cls_mult__less__imp__less__left_0,axiom,
    ( ~ 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_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__imp__less__left_0) ).

cnf(cls_mult__right__less__imp__less_0,axiom,
    ( ~ 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_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ class_Ring__and__Field_Oordered__semiring(T_a) ),
    file('theBenchmark.p',cls_mult__right__less__imp__less_0) ).

cnf(cls_mult__left__less__imp__less_0,axiom,
    ( ~ 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_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ class_Ring__and__Field_Oordered__semiring(T_a) ),
    file('theBenchmark.p',cls_mult__left__less__imp__less_0) ).

cnf(cls_mult__imp__le__div__pos_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a)
    | c_lessequals(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_mult__imp__le__div__pos_0) ).

cnf(cls_mult__imp__div__pos__le_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | ~ c_lessequals(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_mult__imp__div__pos__le_0) ).

cnf(cls_le__divide__eq_6,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq_6) ).

cnf(cls_le__divide__eq_0,axiom,
    ( ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(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_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq_0) ).

cnf(cls_divide__le__eq_6,axiom,
    ( ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq_6) ).

cnf(cls_divide__le__eq_0,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq_0) ).

cnf(cls_natgb_Oadd__r0__iff_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(tc_nat)
    | V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) ),
    file('theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).

cnf(cls_add__eq__self__zero_0,axiom,
    ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != V_m ),
    file('theBenchmark.p',cls_add__eq__self__zero_0) ).

cnf(cls_synthetic__div__pCons_0,axiom,
    ( c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(V_a,V_p,T_a),V_c,T_a) = c_Polynomial_OpCons(c_Polynomial_Opoly(V_p,V_c,T_a),c_Polynomial_Osynthetic__div(V_p,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_synthetic__div__pCons_0) ).

cnf(cls_le__divide__eq__number__of_8,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of_8) ).

cnf(cls_minus__pCons_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(V_a,V_p,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_p,tc_Polynomial_Opoly(T_a)),T_a)
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_minus__pCons_0) ).

cnf(cls_zero__less__divide__iff_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_zero__less__divide__iff_1) ).

cnf(cls_zero__less__divide__iff_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(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(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_zero__less__divide__iff_2) ).

cnf(cls_zero__less__divide__iff_3,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(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(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_zero__less__divide__iff_3) ).

cnf(cls_divide__nonneg__neg_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__nonneg__neg_0) ).

cnf(cls_divide__nonpos__pos_0,axiom,
    ( ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__nonpos__pos_0) ).

cnf(cls_mult__idem_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = V_x
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) ),
    file('theBenchmark.p',cls_mult__idem_0) ).

cnf(cls_mult__strict__mono_H_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,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_d,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__strict__mono_H_0) ).

cnf(cls_monom__0_0,axiom,
    ( c_Polynomial_Omonom(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a)
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_monom__0_0) ).

cnf(cls_mult__le__cancel2_2,axiom,
    ( ~ c_lessequals(V_m,V_n,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) ),
    file('theBenchmark.p',cls_mult__le__cancel2_2) ).

cnf(cls_mult__le__cancel1_2,axiom,
    ( ~ 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) ),
    file('theBenchmark.p',cls_mult__le__cancel1_2) ).

cnf(cls_mult__le__mono2_0,axiom,
    ( ~ c_lessequals(V_i,V_j,tc_nat)
    | 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) ),
    file('theBenchmark.p',cls_mult__le__mono2_0) ).

cnf(cls_mult__le__mono1_0,axiom,
    ( ~ c_lessequals(V_i,V_j,tc_nat)
    | 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) ),
    file('theBenchmark.p',cls_mult__le__mono1_0) ).

cnf(cls_less__SucI_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ),
    file('theBenchmark.p',cls_less__SucI_0) ).

cnf(cls_Suc__lessD_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat)
    | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_Suc__lessD_0) ).

cnf(cls_inverse__eq__iff__eq_0,axiom,
    ( V_a = V_b
    | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_inverse__eq__iff__eq_0) ).

cnf(cls_less__divide__eq__number__of_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(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(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of_0) ).

cnf(cls_less__divide__eq__number__of_6,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of_6) ).

cnf(cls_Suc__mult__cancel1_0,axiom,
    ( V_m = V_n
    | 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) ),
    file('theBenchmark.p',cls_Suc__mult__cancel1_0) ).

cnf(cls_le__divide__eq__number__of_6,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of_6) ).

cnf(cls_le__divide__eq__number__of_0,axiom,
    ( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(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_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of_0) ).

cnf(cls_le__divide__eq__number__of_7,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
    | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of_7) ).

cnf(cls_le__divide__eq__number__of_5,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
    | ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of_5) ).

cnf(cls_zero__less__power__eq__number__of_3,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),T_a)
    | c_Int_Onumber__class_Onumber__of(V_w,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__less__power__eq__number__of_3) ).

cnf(cls_zmod__simps_I2_J_0,axiom,
    ( 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)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_zmod__simps_I2_J_0) ).

cnf(cls_zmod__simps_I1_J_0,axiom,
    ( 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)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_zmod__simps_I1_J_0) ).

cnf(cls_add__is__1_2,axiom,
    ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
    | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('theBenchmark.p',cls_add__is__1_2) ).

cnf(cls_add__is__1_1,axiom,
    ( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('theBenchmark.p',cls_add__is__1_1) ).

cnf(cls_mod__div__decomp_0,axiom,
    ( V_a = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__div__decomp_0) ).

cnf(cls_mod__div__equality_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) = V_a
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__div__equality_0) ).

cnf(cls_mod__div__equality2_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) = V_a
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__div__equality2_0) ).

cnf(cls_order__less__le_2,axiom,
    ( ~ c_lessequals(V_x,V_y,T_a)
    | V_x = V_y
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ class_Orderings_Oorder(T_a) ),
    file('theBenchmark.p',cls_order__less__le_2) ).

cnf(cls_order__le__less_0,axiom,
    ( ~ c_lessequals(V_x,V_y,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | V_x = V_y
    | ~ class_Orderings_Oorder(T_a) ),
    file('theBenchmark.p',cls_order__le__less_0) ).

cnf(cls_le__neq__implies__less_0,axiom,
    ( ~ c_lessequals(V_m,V_n,tc_nat)
    | V_m = V_n
    | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_le__neq__implies__less_0) ).

cnf(cls_le__eq__less__or__eq_0,axiom,
    ( ~ c_lessequals(V_m,V_n,tc_nat)
    | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | V_m = V_n ),
    file('theBenchmark.p',cls_le__eq__less__or__eq_0) ).

cnf(cls_nat__less__le_2,axiom,
    ( ~ c_lessequals(V_m,V_n,tc_nat)
    | V_m = V_n
    | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_nat__less__le_2) ).

cnf(cls_order__le__neq__trans_0,axiom,
    ( ~ c_lessequals(V_a,V_b,T_a)
    | V_a = V_b
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ class_Orderings_Oorder(T_a) ),
    file('theBenchmark.p',cls_order__le__neq__trans_0) ).

cnf(cls_order__neq__le__trans_0,axiom,
    ( V_a = V_b
    | ~ c_lessequals(V_a,V_b,T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ class_Orderings_Oorder(T_a) ),
    file('theBenchmark.p',cls_order__neq__le__trans_0) ).

cnf(cls_linorder__antisym__conv1_0,axiom,
    ( c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ c_lessequals(V_x,V_y,T_a)
    | V_x = V_y
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_linorder__antisym__conv1_0) ).

cnf(cls_linorder__antisym__conv2_0,axiom,
    ( ~ c_lessequals(V_x,V_y,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | V_x = V_y
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_linorder__antisym__conv2_0) ).

cnf(cls_xt1_I12_J_0,axiom,
    ( V_a = V_b
    | ~ c_lessequals(V_b,V_a,T_a)
    | c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | ~ class_Orderings_Oorder(T_a) ),
    file('theBenchmark.p',cls_xt1_I12_J_0) ).

cnf(cls_xt1_I11_J_0,axiom,
    ( ~ c_lessequals(V_b,V_a,T_a)
    | V_a = V_b
    | c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | ~ class_Orderings_Oorder(T_a) ),
    file('theBenchmark.p',cls_xt1_I11_J_0) ).

cnf(cls_divide__right__mono_0,axiom,
    ( ~ c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__right__mono_0) ).

cnf(cls_divide__right__mono__neg_0,axiom,
    ( ~ c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__right__mono__neg_0) ).

cnf(cls_inverse__minus__eq_0,axiom,
    ( c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_inverse__minus__eq_0) ).

cnf(cls_split__mult__pos__le_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_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)
    | ~ class_Ring__and__Field_Opordered__ring(T_a) ),
    file('theBenchmark.p',cls_split__mult__pos__le_0) ).

cnf(cls_split__mult__pos__le_1,axiom,
    ( ~ 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_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Opordered__ring(T_a) ),
    file('theBenchmark.p',cls_split__mult__pos__le_1) ).

cnf(cls_mult__nonpos__nonpos_0,axiom,
    ( ~ 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_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Opordered__ring(T_a) ),
    file('theBenchmark.p',cls_mult__nonpos__nonpos_0) ).

cnf(cls_zero__le__square_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_zero__le__square_0) ).

cnf(cls_zero__le__mult__iff_4,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_zero__le__mult__iff_4) ).

cnf(cls_zero__le__mult__iff_5,axiom,
    ( ~ 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_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_zero__le__mult__iff_5) ).

cnf(cls_mult__nonneg__nonneg_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_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)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
    file('theBenchmark.p',cls_mult__nonneg__nonneg_0) ).

cnf(cls_right__inverse__eq_0,axiom,
    ( V_a = V_b
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_right__inverse__eq_0) ).

cnf(cls_class__ring_Oneg__mul_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(V_x,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),V_x,T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_class__ring_Oneg__mul_0) ).

cnf(cls_dvd__div__neg_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a)
    | c_Divides_Odiv__class_Odiv(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),T_a)
    | ~ class_Divides_Oring__div(T_a) ),
    file('theBenchmark.p',cls_dvd__div__neg_0) ).

cnf(cls_dvd__neg__div_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a)
    | c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),T_a)
    | ~ class_Divides_Oring__div(T_a) ),
    file('theBenchmark.p',cls_dvd__neg__div_0) ).

cnf(cls_divide__le__eq__number__of1_7,axiom,
    ( ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_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_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of1_7) ).

cnf(cls_le__divide__eq__number__of1_7,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of1_7) ).

cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom,
    ( 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)
    | ~ class_OrderedGroup_Oab__semigroup__mult(T_a) ),
    file('theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

cnf(cls_nat__mult__assoc_0,axiom,
    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),
    file('theBenchmark.p',cls_nat__mult__assoc_0) ).

cnf(cls_class__semiring_Omul__a_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Omul__a_0) ).

cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).

cnf(cls_mult__right_Oadd_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),c_HOL_Otimes__class_Otimes(V_xa,V_y,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    file('theBenchmark.p',cls_mult__right_Oadd_0) ).

cnf(cls_mult_Oadd__right_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oplus__class_Oplus(V_b,V_b_H,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b_H,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    file('theBenchmark.p',cls_mult_Oadd__right_0) ).

cnf(cls_mult__left_Oadd_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_ya,T_a),c_HOL_Otimes__class_Otimes(V_y,V_ya,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    file('theBenchmark.p',cls_mult__left_Oadd_0) ).

cnf(cls_mult_Oadd__left_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    file('theBenchmark.p',cls_mult_Oadd__left_0) ).

cnf(cls_add__mult__distrib2_0,axiom,
    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),
    file('theBenchmark.p',cls_add__mult__distrib2_0) ).

cnf(cls_add__mult__distrib_0,axiom,
    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),
    file('theBenchmark.p',cls_add__mult__distrib_0) ).

cnf(cls_class__semiring_Omul__d_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Omul__d_0) ).

cnf(cls_comm__semiring__class_Odistrib_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring(T_a) ),
    file('theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).

cnf(cls_coeff__minus_0,axiom,
    ( c_Polynomial_Ocoeff(c_HOL_Ouminus__class_Ouminus(V_p,tc_Polynomial_Opoly(T_a)),V_n,T_a) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Ocoeff(V_p,V_n,T_a),T_a)
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_coeff__minus_0) ).

cnf(cls_frac__less_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a)
    | ~ c_lessequals(V_w,V_z,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_z,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_w,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_frac__less_0) ).

cnf(cls_add__gr__0_2,axiom,
    ( ~ 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_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_add__gr__0_2) ).

cnf(cls_add__gr__0_1,axiom,
    ( ~ 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) ),
    file('theBenchmark.p',cls_add__gr__0_1) ).

cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

cnf(cls_minus__divide__right_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_minus__divide__right_0) ).

cnf(cls_minus__divide__left_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_minus__divide__left_0) ).

cnf(cls_power__le__imp__le__exp_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
    | ~ c_lessequals(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | c_lessequals(V_m,V_n,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__le__imp__le__exp_0) ).

cnf(cls_power__increasing__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a)
    | ~ c_lessequals(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a)
    | c_lessequals(V_x,V_y,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__increasing__iff_0) ).

cnf(cls_power__increasing__iff_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a)
    | ~ c_lessequals(V_x,V_y,tc_nat)
    | c_lessequals(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__increasing__iff_1) ).

cnf(cls_divide__le__eq__number__of_6,axiom,
    ( ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of_6) ).

cnf(cls_divide__le__eq__number__of_0,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of_0) ).

cnf(cls_one__le__inverse__iff_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ c_lessequals(V_x,c_HOL_Oone__class_Oone(T_a),T_a)
    | c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_one__le__inverse__iff_2) ).

cnf(cls_zero__le__mult__iff_0,axiom,
    ( ~ 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_a,T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_zero__le__mult__iff_0) ).

cnf(cls_zero__le__mult__iff_1,axiom,
    ( ~ 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_a,T_a)
    | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_zero__le__mult__iff_1) ).

cnf(cls_zero__le__mult__iff_2,axiom,
    ( ~ 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(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_zero__le__mult__iff_2) ).

cnf(cls_zero__le__mult__iff_3,axiom,
    ( ~ 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(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_zero__le__mult__iff_3) ).

cnf(cls_synthetic__div__unique__lemma_0,axiom,
    ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Osmult(V_c,V_p,T_a) != c_Polynomial_OpCons(V_a,V_p,T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_synthetic__div__unique__lemma_0) ).

cnf(cls_sum__squares__gt__zero__iff_0,axiom,
    ( ~ 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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).

cnf(cls_eq__divide__eq__number__of_0,axiom,
    ( V_c = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a) = V_b
    | c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_eq__divide__eq__number__of_0) ).

cnf(cls_nonzero__inverse__eq__divide_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_nonzero__inverse__eq__divide_0) ).

cnf(cls_mod__smult__left_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_Polynomial_Osmult(V_a,V_x,T_a),V_y,tc_Polynomial_Opoly(T_a)) = c_Polynomial_Osmult(V_a,c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)),T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_mod__smult__left_0) ).

cnf(cls_div__add__self1_0,axiom,
    ( V_b = c_HOL_Ozero__class_Ozero(T_a)
    | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_b,V_a,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__add__self1_0) ).

cnf(cls_div__add__self2_0,axiom,
    ( V_b = c_HOL_Ozero__class_Ozero(T_a)
    | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__add__self2_0) ).

cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).

cnf(cls_zero__less__two_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_zero__less__two_0) ).

cnf(cls_mult__eq__1__iff_0,axiom,
    ( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('theBenchmark.p',cls_mult__eq__1__iff_0) ).

cnf(cls_mult__eq__1__iff_1,axiom,
    ( V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('theBenchmark.p',cls_mult__eq__1__iff_1) ).

cnf(cls_inverse__le__1__iff_1,axiom,
    ( ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__le__1__iff_1) ).

cnf(cls_sum__squares__ge__zero_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_sum__squares__ge__zero_0) ).

cnf(cls_pdivmod__rel__smult__right_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q,V_r,T_a)
    | c_Polynomial_Opdivmod__rel(V_x,c_Polynomial_Osmult(V_a,V_y,T_a),c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_q,T_a),V_r,T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_pdivmod__rel__smult__right_0) ).

cnf(cls_zero__le__divide__1__iff_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_zero__le__divide__1__iff_1) ).

cnf(cls_zero__le__divide__1__iff_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_zero__le__divide__1__iff_0) ).

cnf(cls_divide__le__0__iff_5,axiom,
    ( ~ 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_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__0__iff_5) ).

cnf(cls_divide__le__0__iff_4,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__0__iff_4) ).

cnf(cls_termination__basic__simps_I1_J_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
    | c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).

cnf(cls_termination__basic__simps_I2_J_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,V_z,tc_nat)
    | c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).

cnf(cls_add__lessD1_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat)
    | c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ),
    file('theBenchmark.p',cls_add__lessD1_0) ).

cnf(cls_trans__less__add1_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
    | c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_trans__less__add1_0) ).

cnf(cls_trans__less__add2_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
    | c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_trans__less__add2_0) ).

cnf(cls_Suc__leI_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | c_lessequals(c_Suc(V_m),V_n,tc_nat) ),
    file('theBenchmark.p',cls_Suc__leI_0) ).

cnf(cls_Suc__le__eq_0,axiom,
    ( ~ c_lessequals(c_Suc(V_m),V_n,tc_nat)
    | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_Suc__le__eq_0) ).

cnf(cls_less__eq__Suc__le_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
    | c_lessequals(c_Suc(V_n),V_m,tc_nat) ),
    file('theBenchmark.p',cls_less__eq__Suc__le_0) ).

cnf(cls_less__eq__Suc__le_1,axiom,
    ( ~ c_lessequals(c_Suc(V_n),V_m,tc_nat)
    | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ),
    file('theBenchmark.p',cls_less__eq__Suc__le_1) ).

cnf(cls_add__increasing2_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(V_b,V_a,T_a)
    | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
    file('theBenchmark.p',cls_add__increasing2_0) ).

cnf(cls_add__increasing_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(V_b,V_c,T_a)
    | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
    file('theBenchmark.p',cls_add__increasing_0) ).

cnf(cls_less__add__Suc1_0,axiom,
    c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_i,V_m,tc_nat)),tc_nat),
    file('theBenchmark.p',cls_less__add__Suc1_0) ).

cnf(cls_less__add__Suc2_0,axiom,
    c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_i,tc_nat)),tc_nat),
    file('theBenchmark.p',cls_less__add__Suc2_0) ).

cnf(cls_less__iff__Suc__add_1,axiom,
    c_HOL_Oord__class_Oless(V_m,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat)),tc_nat),
    file('theBenchmark.p',cls_less__iff__Suc__add_1) ).

cnf(cls_nat_Osimps_I2_J_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H),
    file('theBenchmark.p',cls_nat_Osimps_I2_J_0) ).

cnf(cls_Zero__neq__Suc_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m),
    file('theBenchmark.p',cls_Zero__neq__Suc_0) ).

cnf(cls_div__add_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,T_a)
    | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_x,V_z,T_a),c_Divides_Odiv__class_Odiv(V_y,V_z,T_a),T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__add_0) ).

cnf(cls_neg__le__iff__le_0,axiom,
    ( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_neg__le__iff__le_0) ).

cnf(cls_le__imp__neg__le_0,axiom,
    ( ~ c_lessequals(V_a,V_b,T_a)
    | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_le__imp__neg__le_0) ).

cnf(cls_poly__offset__poly_0,axiom,
    ( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),V_x,T_a) = c_Polynomial_Opoly(V_p,c_HOL_Oplus__class_Oplus(V_h,V_x,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_poly__offset__poly_0) ).

cnf(cls_order_1,axiom,
    ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),c_Suc(c_Polynomial_Oorder(V_a,V_p,T_a)),tc_Polynomial_Opoly(T_a)),V_p,tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_order_1) ).

cnf(cls_mult__strict__mono_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,V_d,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_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_d,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__strict__mono_0) ).

cnf(cls_inverse__eq__divide_0,axiom,
    ( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_inverse__eq__divide_0) ).

cnf(cls_class__fieldgb_Oinverse__divide_0,axiom,
    ( c_HOL_Oinverse__class_Oinverse(V_x,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_x,T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_class__fieldgb_Oinverse__divide_0) ).

cnf(cls_zmod__simps_I4_J_0,axiom,
    ( 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)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_zmod__simps_I4_J_0) ).

cnf(cls_divide__less__eq__number__of_4,axiom,
    ( 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(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,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_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of_4) ).

cnf(cls_divide__less__eq__number__of_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,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_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of_1) ).

cnf(cls_div__smult__left_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(V_a,V_x,T_a),V_y,tc_Polynomial_Opoly(T_a)) = c_Polynomial_Osmult(V_a,c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)),T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_div__smult__left_0) ).

cnf(cls_less__divide__eq__number__of1_9,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of1_9) ).

cnf(cls_divide__less__eq__number__of1_9,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),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_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of1_9) ).

cnf(cls_divide__less__eq__number__of_8,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,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_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of_8) ).

cnf(cls_divide__left__mono__neg_0,axiom,
    ( ~ c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_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)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__left__mono__neg_0) ).

cnf(cls_divide__left__mono_0,axiom,
    ( ~ c_lessequals(V_b,V_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),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__left__mono_0) ).

cnf(cls_mult__1__right_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a
    | ~ class_OrderedGroup_Omonoid__mult(T_a) ),
    file('theBenchmark.p',cls_mult__1__right_0) ).

cnf(cls_mult__1__left_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a
    | ~ class_OrderedGroup_Omonoid__mult(T_a) ),
    file('theBenchmark.p',cls_mult__1__left_0) ).

cnf(cls_mult__1_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a
    | ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) ),
    file('theBenchmark.p',cls_mult__1_0) ).

cnf(cls_class__semiring_Omul__1_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_x,T_a) = V_x
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Omul__1_0) ).

cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I11_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).

cnf(cls_poly__replicate__append_0,axiom,
    ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(c_HOL_Oone__class_Oone(T_a),V_n,T_a),V_p,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Polynomial_Opoly(V_p,V_x,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
    file('theBenchmark.p',cls_poly__replicate__append_0) ).

cnf(cls_pdivmod__rel_0,axiom,
    ( c_Polynomial_Opdivmod__rel(V_x,V_y,c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)),c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)),T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_pdivmod__rel_0) ).

cnf(cls_frac__less2_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ c_lessequals(V_x,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a)
    | ~ c_HOL_Oord__class_Oless(V_w,V_z,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_z,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_w,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_frac__less2_0) ).

cnf(cls_add__is__1_4,axiom,
    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)),
    file('theBenchmark.p',cls_add__is__1_4) ).

cnf(cls_power__one__over_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_power__one__over_0) ).

cnf(cls_nonzero__minus__divide__right_0,axiom,
    ( V_b = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_nonzero__minus__divide__right_0) ).

cnf(cls_neg__less__0__iff__less_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_neg__less__0__iff__less_1) ).

cnf(cls_neg__less__0__iff__less_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),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)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_neg__less__0__iff__less_0) ).

cnf(cls_class__ringb_Oadd__mul__solve_1,axiom,
    ( 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)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).

cnf(cls_class__ringb_Onoteq__reduce_1,axiom,
    ( 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)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).

cnf(cls_natgb_Oadd__mul__solve_1,axiom,
    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),
    file('theBenchmark.p',cls_natgb_Oadd__mul__solve_1) ).

cnf(cls_natgb_Onoteq__reduce_1,axiom,
    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),
    file('theBenchmark.p',cls_natgb_Onoteq__reduce_1) ).

cnf(cls_less__Suc0_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('theBenchmark.p',cls_less__Suc0_0) ).

cnf(cls_power__le__zero__eq__number__of_0,axiom,
    ( ~ c_lessequals(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_Int_Onumber__class_Onumber__of(V_w,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__le__zero__eq__number__of_0) ).

cnf(cls_poly__gcd__left__commute_0,axiom,
    ( c_Polynomial_Opoly__gcd(V_x,c_Polynomial_Opoly__gcd(V_y,V_z,T_a),T_a) = c_Polynomial_Opoly__gcd(V_y,c_Polynomial_Opoly__gcd(V_x,V_z,T_a),T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__left__commute_0) ).

cnf(cls_poly__gcd__assoc_0,axiom,
    ( c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(V_x,V_y,T_a),V_z,T_a) = c_Polynomial_Opoly__gcd(V_x,c_Polynomial_Opoly__gcd(V_y,V_z,T_a),T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__assoc_0) ).

cnf(cls_degree__monom__le_0,axiom,
    ( c_lessequals(c_Polynomial_Odegree(c_Polynomial_Omonom(V_a,V_n,T_a),T_a),V_n,tc_nat)
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_degree__monom__le_0) ).

cnf(cls_less__divide__eq__number__of1_7,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,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)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of1_7) ).

cnf(cls_divide__less__eq__number__of1_7,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),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)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of1_7) ).

cnf(cls_inverse__inverse__eq_0,axiom,
    ( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_inverse__inverse__eq_0) ).

cnf(cls_mult__le__cancel1_1,axiom,
    ( 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) ),
    file('theBenchmark.p',cls_mult__le__cancel1_1) ).

cnf(cls_mult__le__cancel2_1,axiom,
    ( 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) ),
    file('theBenchmark.p',cls_mult__le__cancel2_1) ).

cnf(cls_less__divide__eq__number__of1_8,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of1_8) ).

cnf(cls_divide__less__eq__number__of1_8,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of1_8) ).

cnf(cls_class__semiring_Opwr__Suc_0,axiom,
    ( c_Power_Opower__class_Opower(V_x,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).

cnf(cls_power__Suc2_0,axiom,
    ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_a,T_a)
    | ~ class_OrderedGroup_Omonoid__mult(T_a) ),
    file('theBenchmark.p',cls_power__Suc2_0) ).

cnf(cls_power__Suc_0,axiom,
    ( c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ class_Power_Opower(T_a) ),
    file('theBenchmark.p',cls_power__Suc_0) ).

cnf(cls_class__semiring_Osemiring__rules_I35_J_0,axiom,
    ( c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a) = c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).

cnf(cls_poly__gcd__minus__right_0,axiom,
    ( c_Polynomial_Opoly__gcd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Opoly__gcd(V_x,V_y,T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__minus__right_0) ).

cnf(cls_poly__gcd__minus__left_0,axiom,
    ( c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(V_x,tc_Polynomial_Opoly(T_a)),V_y,T_a) = c_Polynomial_Opoly__gcd(V_x,V_y,T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__minus__left_0) ).

cnf(cls_add__nonneg__eq__0__iff_2,axiom,
    ( 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)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
    file('theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).

cnf(cls_class__semiring_Omul__c_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Omul__c_0) ).

cnf(cls_add__is__0_2,axiom,
    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),
    file('theBenchmark.p',cls_add__is__0_2) ).

cnf(cls_nat__mult__commute_0,axiom,
    c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) = c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),
    file('theBenchmark.p',cls_nat__mult__commute_0) ).

cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

cnf(cls_mod__add__eq_0,axiom,
    ( 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)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__add__eq_0) ).

cnf(cls_divide__le__eq__number__of_1,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,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_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of_1) ).

cnf(cls_divide__le__eq__number__of_4,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of_4) ).

cnf(cls_xt1_I10_J_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
    | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
    | ~ class_Orderings_Oorder(T_a) ),
    file('theBenchmark.p',cls_xt1_I10_J_0) ).

cnf(cls_order__less__trans_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
    | ~ class_Orderings_Opreorder(T_a) ),
    file('theBenchmark.p',cls_order__less__trans_0) ).

cnf(cls_coeff__smult_0,axiom,
    ( c_Polynomial_Ocoeff(c_Polynomial_Osmult(V_a,V_p,T_a),V_n,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Ocoeff(V_p,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_coeff__smult_0) ).

cnf(cls_coeff__monom_1,axiom,
    ( V_m = V_n
    | c_Polynomial_Ocoeff(c_Polynomial_Omonom(V_a,V_m,T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_coeff__monom_1) ).

cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
    ( 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)
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
    file('theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
    ( 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)
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
    file('theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

cnf(cls_class__semiring_Oadd__a_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

cnf(cls_nat__add__assoc_0,axiom,
    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),
    file('theBenchmark.p',cls_nat__add__assoc_0) ).

cnf(cls_nat__add__left__commute_0,axiom,
    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),
    file('theBenchmark.p',cls_nat__add__left__commute_0) ).

cnf(cls_add__cancel__21_1,axiom,
    ( 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)
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_add__cancel__21_1) ).

cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
    ( 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)
    | ~ class_OrderedGroup_Oab__semigroup__add(T_a) ),
    file('theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

cnf(cls_mult_Ominus__left_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    file('theBenchmark.p',cls_mult_Ominus__left_0) ).

cnf(cls_mult__left_Ominus_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    file('theBenchmark.p',cls_mult__left_Ominus_0) ).

cnf(cls_mult_Ominus__right_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    file('theBenchmark.p',cls_mult_Ominus__right_0) ).

cnf(cls_mult__right_Ominus_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    file('theBenchmark.p',cls_mult__right_Ominus_0) ).

cnf(cls_square__eq__iff_1,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_b,V_b,T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_square__eq__iff_1) ).

cnf(cls_minus__mult__minus_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)
    | ~ class_Ring__and__Field_Oring(T_a) ),
    file('theBenchmark.p',cls_minus__mult__minus_0) ).

cnf(cls_field__inverse_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_field__inverse_0) ).

cnf(cls_left__inverse_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_left__inverse_0) ).

cnf(cls_right__inverse_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_right__inverse_0) ).

cnf(cls_mult__le__mono_0,axiom,
    ( ~ c_lessequals(V_i,V_j,tc_nat)
    | ~ c_lessequals(V_k,V_l,tc_nat)
    | 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) ),
    file('theBenchmark.p',cls_mult__le__mono_0) ).

cnf(cls_le__cube_0,axiom,
    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),
    file('theBenchmark.p',cls_le__cube_0) ).

cnf(cls_mult__mono_0,axiom,
    ( ~ c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(V_c,V_d,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_c,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)
    | ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
    file('theBenchmark.p',cls_mult__mono_0) ).

cnf(cls_mult__mono_H_0,axiom,
    ( ~ c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(V_c,V_d,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(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_d,T_a),T_a)
    | ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
    file('theBenchmark.p',cls_mult__mono_H_0) ).

cnf(cls_div__mult__mult1_0,axiom,
    ( V_c = c_HOL_Ozero__class_Ozero(T_a)
    | c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(V_a,V_b,T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__mult__mult1_0) ).

cnf(cls_div__mult__mult2_0,axiom,
    ( V_c = c_HOL_Ozero__class_Ozero(T_a)
    | c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(V_a,V_b,T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__mult__mult2_0) ).

cnf(cls_eq__divide__eq__number__of_4,axiom,
    ( c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_c,T_a)
    | c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_eq__divide__eq__number__of_4) ).

cnf(cls_divide__less__eq_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),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(V_c,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)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq_2) ).

cnf(cls_divide__less__eq_3,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,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_a,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq_3) ).

cnf(cls_divide__less__eq_8,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,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_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq_8) ).

cnf(cls_divide__less__eq_9,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,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_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq_9) ).

cnf(cls_less__divide__eq_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(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_c,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)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq_2) ).

cnf(cls_less__divide__eq_3,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,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,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq_3) ).

cnf(cls_less__divide__eq_8,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,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_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq_8) ).

cnf(cls_less__divide__eq_9,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq_9) ).

cnf(cls_not__less__less__Suc__eq_1,axiom,
    ( c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat)
    | c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ),
    file('theBenchmark.p',cls_not__less__less__Suc__eq_1) ).

cnf(cls_not__less__eq_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_not__less__eq_1) ).

cnf(cls_not__less__eq_0,axiom,
    ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ),
    file('theBenchmark.p',cls_not__less__eq_0) ).

cnf(cls_smult__monom_0,axiom,
    ( c_Polynomial_Osmult(V_a,c_Polynomial_Omonom(V_b,V_n,T_a),T_a) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_n,T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_smult__monom_0) ).

cnf(cls_le__SucE_0,axiom,
    ( ~ c_lessequals(V_m,c_Suc(V_n),tc_nat)
    | c_lessequals(V_m,V_n,tc_nat)
    | V_m = c_Suc(V_n) ),
    file('theBenchmark.p',cls_le__SucE_0) ).

cnf(cls_power__Suc__less_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__Suc__less_0) ).

cnf(cls_mult__less__cancel__left__disj_0,axiom,
    ( ~ 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_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).

cnf(cls_mult__less__cancel__left__disj_3,axiom,
    ( ~ 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(V_b,V_a,T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).

cnf(cls_mult__less__cancel__right__disj_0,axiom,
    ( ~ 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_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).

cnf(cls_mult__less__cancel__right__disj_3,axiom,
    ( ~ 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(V_b,V_a,T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).

cnf(cls_mod__minus__eq_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_b,T_a)
    | ~ class_Divides_Oring__div(T_a) ),
    file('theBenchmark.p',cls_mod__minus__eq_0) ).

cnf(cls_divide__neg__neg_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__neg__neg_0) ).

cnf(cls_divide__pos__pos_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__pos__pos_0) ).

cnf(cls_zero__less__divide__iff_4,axiom,
    ( ~ 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),V_b,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_zero__less__divide__iff_4) ).

cnf(cls_zero__less__divide__iff_5,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_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),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_zero__less__divide__iff_5) ).

cnf(cls_smult__1__left_0,axiom,
    ( c_Polynomial_Osmult(c_HOL_Oone__class_Oone(T_a),V_p,T_a) = V_p
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_smult__1__left_0) ).

cnf(cls_one__less__inverse__iff_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a)
    | c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_one__less__inverse__iff_1) ).

cnf(cls_inverse__add_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_inverse__add_0) ).

cnf(cls_division__ring__inverse__add_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_division__ring__inverse__add_0) ).

cnf(cls_poly__gcd__monic_2,axiom,
    ( V_y = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(V_x,V_y,T_a),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(V_x,V_y,T_a),T_a),T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__monic_2) ).

cnf(cls_poly__gcd__monic_1,axiom,
    ( V_x = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(V_x,V_y,T_a),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(V_x,V_y,T_a),T_a),T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__monic_1) ).

cnf(cls_gt__half__sum_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_a,V_b,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),V_b,T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_gt__half__sum_0) ).

cnf(cls_less__half__sum_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_a,V_b,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),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__half__sum_0) ).

cnf(cls_offset__poly__single_0,axiom,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),V_h,T_a) = c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_offset__poly__single_0) ).

cnf(cls_add__frac__num_0,axiom,
    ( V_y = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a),V_y,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_add__frac__num_0) ).

cnf(cls_add__num__frac_0,axiom,
    ( V_y = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oplus__class_Oplus(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a),V_y,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_add__num__frac_0) ).

cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

cnf(cls_nonzero__minus__divide__divide_0,axiom,
    ( V_b = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).

cnf(cls_divide__strict__right__mono_0,axiom,
    ( ~ 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)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__strict__right__mono_0) ).

cnf(cls_divide__strict__right__mono__neg_0,axiom,
    ( ~ 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)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).

cnf(cls_divide__nonneg__pos_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__nonneg__pos_0) ).

cnf(cls_divide__nonpos__neg_0,axiom,
    ( ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__nonpos__neg_0) ).

cnf(cls_mult__left__le__one__le_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_y,V_x,T_a),V_x,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_mult__left__le__one__le_0) ).

cnf(cls_mult__right__le__one__le_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_x,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_mult__right__le__one__le_0) ).

cnf(cls_divide__1_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__1_0) ).

cnf(cls_poly__gcd__code_0,axiom,
    ( c_Polynomial_Opoly__gcd(V_x,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Ocoeff(V_x,c_Polynomial_Odegree(V_x,T_a),T_a),T_a),V_x,T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__code_0) ).

cnf(cls_nat__add__right__cancel_0,axiom,
    ( V_m = V_n
    | c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat) != c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat) ),
    file('theBenchmark.p',cls_nat__add__right__cancel_0) ).

cnf(cls_nat__add__left__cancel_0,axiom,
    ( V_m = V_n
    | c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ),
    file('theBenchmark.p',cls_nat__add__left__cancel_0) ).

cnf(cls_natgb_Oadd__cancel_0,axiom,
    ( V_y = V_z
    | c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat) != c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat) ),
    file('theBenchmark.p',cls_natgb_Oadd__cancel_0) ).

cnf(cls_class__ringb_Oadd__cancel_0,axiom,
    ( V_y = V_z
    | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Oplus__class_Oplus(V_x,V_z,T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).

cnf(cls_add__imp__eq_0,axiom,
    ( V_b = V_c
    | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a) ),
    file('theBenchmark.p',cls_add__imp__eq_0) ).

cnf(cls_add__left__cancel_0,axiom,
    ( V_b = V_c
    | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) ),
    file('theBenchmark.p',cls_add__left__cancel_0) ).

cnf(cls_add__right__cancel_0,axiom,
    ( V_b = V_c
    | c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) != c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) ),
    file('theBenchmark.p',cls_add__right__cancel_0) ).

cnf(cls_not__square__less__zero_0,axiom,
    ( ~ 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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_not__square__less__zero_0) ).

cnf(cls_mult__le__0__iff_4,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__le__0__iff_4) ).

cnf(cls_mult__le__0__iff_5,axiom,
    ( ~ 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_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__le__0__iff_5) ).

cnf(cls_split__mult__neg__le_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_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)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
    file('theBenchmark.p',cls_split__mult__neg__le_0) ).

cnf(cls_split__mult__neg__le_1,axiom,
    ( ~ 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_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
    file('theBenchmark.p',cls_split__mult__neg__le_1) ).

cnf(cls_mult__nonneg__nonpos_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_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)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
    file('theBenchmark.p',cls_mult__nonneg__nonpos_0) ).

cnf(cls_mult__nonpos__nonneg_0,axiom,
    ( ~ 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_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
    file('theBenchmark.p',cls_mult__nonpos__nonneg_0) ).

cnf(cls_mult__nonneg__nonpos2_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
    file('theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).

cnf(cls_inverse__mult__distrib_0,axiom,
    ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_inverse__mult__distrib_0) ).

cnf(cls_nonzero__inverse__mult__distrib_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).

cnf(cls_add__nonneg__pos_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_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),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
    file('theBenchmark.p',cls_add__nonneg__pos_0) ).

cnf(cls_add__pos__nonneg_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_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),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
    file('theBenchmark.p',cls_add__pos__nonneg_0) ).

cnf(cls_mult__monom_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(V_a,V_m,T_a),c_Polynomial_Omonom(V_b,V_n,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_mult__monom_0) ).

cnf(cls_divide__eq__eq__number__of_4,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_c,T_a) = c_Int_Onumber__class_Onumber__of(V_w,T_a)
    | c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__eq__eq__number__of_4) ).

cnf(cls_divide__less__eq__number__of_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,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_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of_0) ).

cnf(cls_divide__less__eq__number__of_6,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),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(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of_6) ).

cnf(cls_divide__le__eq__number__of1_8,axiom,
    ( ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of1_8) ).

cnf(cls_le__divide__eq__number__of1_8,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of1_8) ).

cnf(cls_divide__le__eq_5,axiom,
    ( 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),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq_5) ).

cnf(cls_divide__le__eq_7,axiom,
    ( ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | c_HOL_Oord__class_Oless(V_c,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_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq_7) ).

cnf(cls_le__divide__eq_5,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq_5) ).

cnf(cls_le__divide__eq_7,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq_7) ).

cnf(cls_one__less__mult_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,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)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_one__less__mult_0) ).

cnf(cls_add__Suc__shift_0,axiom,
    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),
    file('theBenchmark.p',cls_add__Suc__shift_0) ).

cnf(cls_one__is__add_3,axiom,
    ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
    | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_one__is__add_3) ).

cnf(cls_one__is__add_0,axiom,
    ( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_one__is__add_0) ).

cnf(cls_minus__monom_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_Polynomial_Omonom(V_a,V_n,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_n,T_a)
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_minus__monom_0) ).

cnf(cls_power__increasing_0,axiom,
    ( ~ c_lessequals(V_n,V_N,tc_nat)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
    | c_lessequals(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_a,V_N,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__increasing_0) ).

cnf(cls_one__is__add_5,axiom,
    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),
    file('theBenchmark.p',cls_one__is__add_5) ).

cnf(cls_neg__0__le__iff__le_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_neg__0__le__iff__le_0) ).

cnf(cls_neg__0__le__iff__le_1,axiom,
    ( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_neg__0__le__iff__le_1) ).

cnf(cls_divide__less__eq__number__of1_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of1_1) ).

cnf(cls_divide__less__eq__number__of1_4,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of1_4) ).

cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).

cnf(cls_add__gr__0_0,axiom,
    ( ~ 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)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ),
    file('theBenchmark.p',cls_add__gr__0_0) ).

cnf(cls_power__add_0,axiom,
    ( c_Power_Opower__class_Opower(V_a,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ class_OrderedGroup_Omonoid__mult(T_a) ),
    file('theBenchmark.p',cls_power__add_0) ).

cnf(cls_termination__basic__simps_I3_J_0,axiom,
    ( ~ c_lessequals(V_x,V_y,tc_nat)
    | c_lessequals(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).

cnf(cls_termination__basic__simps_I4_J_0,axiom,
    ( ~ c_lessequals(V_x,V_z,tc_nat)
    | c_lessequals(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).

cnf(cls_add__leE_0,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),V_n,tc_nat)
    | c_lessequals(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_add__leE_0) ).

cnf(cls_add__leE_1,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),V_n,tc_nat)
    | c_lessequals(V_k,V_n,tc_nat) ),
    file('theBenchmark.p',cls_add__leE_1) ).

cnf(cls_trans__le__add1_0,axiom,
    ( ~ c_lessequals(V_i,V_j,tc_nat)
    | c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_trans__le__add1_0) ).

cnf(cls_trans__le__add2_0,axiom,
    ( ~ c_lessequals(V_i,V_j,tc_nat)
    | c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_trans__le__add2_0) ).

cnf(cls_poly__div__minus__right_0,axiom,
    ( c_Divides_Odiv__class_Odiv(V_x,c_HOL_Ouminus__class_Ouminus(V_y,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__div__minus__right_0) ).

cnf(cls_poly__div__minus__left_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(V_x,tc_Polynomial_Opoly(T_a)),V_y,tc_Polynomial_Opoly(T_a)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__div__minus__left_0) ).

cnf(cls_less__le__not__le_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ c_lessequals(V_y,V_x,T_a)
    | ~ class_Orderings_Opreorder(T_a) ),
    file('theBenchmark.p',cls_less__le__not__le_1) ).

cnf(cls_not__leE_0,axiom,
    ( c_lessequals(V_y,V_x,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_not__leE_0) ).

cnf(cls_linorder__antisym__conv2_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
    | ~ c_lessequals(V_x,V_x,T_a)
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_linorder__antisym__conv2_1) ).

cnf(cls_linorder__antisym__conv1_1,axiom,
    ( c_lessequals(V_x,V_x,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_x,T_a)
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_linorder__antisym__conv1_1) ).

cnf(cls_linorder__not__less_1,axiom,
    ( ~ c_lessequals(V_y,V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_linorder__not__less_1) ).

cnf(cls_linorder__not__less_0,axiom,
    ( c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | c_lessequals(V_y,V_x,T_a)
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_linorder__not__less_0) ).

cnf(cls_linorder__not__le_0,axiom,
    ( c_lessequals(V_x,V_y,T_a)
    | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_linorder__not__le_0) ).

cnf(cls_linorder__not__le_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | ~ c_lessequals(V_x,V_y,T_a)
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_linorder__not__le_1) ).

cnf(cls_right__inverse__eq_1,axiom,
    ( c_HOL_Oinverse__class_Odivide(V_x,V_x,T_a) = c_HOL_Oone__class_Oone(T_a)
    | V_x = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_right__inverse__eq_1) ).

cnf(cls_divide__self_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__self_0) ).

cnf(cls_divide__self__if_1,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__self__if_1) ).

cnf(cls_mod__add__right__eq_0,axiom,
    ( 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)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__add__right__eq_0) ).

cnf(cls_mod__add__left__eq_0,axiom,
    ( 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)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__add__left__eq_0) ).

cnf(cls_zero__le__divide__iff_3,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),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)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_zero__le__divide__iff_3) ).

cnf(cls_zero__le__divide__iff_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,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)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_zero__le__divide__iff_2) ).

cnf(cls_zero__le__divide__iff_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_zero__le__divide__iff_1) ).

cnf(cls_zero__le__divide__iff_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_zero__le__divide__iff_0) ).

cnf(cls_add__strict__increasing2_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a)
    | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
    file('theBenchmark.p',cls_add__strict__increasing2_0) ).

cnf(cls_right__distrib__number__of_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_v,T_a),V_b,T_a),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_v,T_a),V_c,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Osemiring(T_a) ),
    file('theBenchmark.p',cls_right__distrib__number__of_0) ).

cnf(cls_nat__mult__eq__cancel1_0,axiom,
    ( V_m = V_n
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
    | c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) ),
    file('theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).

cnf(cls_mult__less__cancel1_0,axiom,
    ( ~ 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) ),
    file('theBenchmark.p',cls_mult__less__cancel1_0) ).

cnf(cls_mult__less__cancel2_0,axiom,
    ( ~ 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(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ),
    file('theBenchmark.p',cls_mult__less__cancel2_0) ).

cnf(cls_inverse__le__1__iff_0,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a)
    | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Oone__class_Oone(T_a),V_x,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__le__1__iff_0) ).

cnf(cls_mod__poly__eq_0,axiom,
    ( ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q,V_r,T_a)
    | c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)) = V_r
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_mod__poly__eq_0) ).

cnf(cls_mult__right__le__imp__le_0,axiom,
    ( ~ 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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__right__le__imp__le_0) ).

cnf(cls_mult__left__le__imp__le_0,axiom,
    ( ~ 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)
    | c_lessequals(V_a,V_b,T_a)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__left__le__imp__le_0) ).

cnf(cls_mult__le__cancel__left__pos_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).

cnf(cls_mult__le__cancel__left__pos_0,axiom,
    ( ~ 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)
    | c_lessequals(V_a,V_b,T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).

cnf(cls_mult__le__cancel__left__neg_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).

cnf(cls_mult__le__cancel__left__neg_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_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_lessequals(V_b,V_a,T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).

cnf(cls_nat__mult__le__cancel1_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
    | ~ 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) ),
    file('theBenchmark.p',cls_nat__mult__le__cancel1_1) ).

cnf(cls_nat__mult__le__cancel1_0,axiom,
    ( ~ 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)
    | c_lessequals(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_nat__mult__le__cancel1_0) ).

cnf(cls_mult__le__cancel1_0,axiom,
    ( ~ 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)
    | c_lessequals(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_mult__le__cancel1_0) ).

cnf(cls_mult__le__cancel2_0,axiom,
    ( ~ 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)
    | c_lessequals(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_mult__le__cancel2_0) ).

cnf(cls_nat__lt__two__imp__zero__or__one_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)
    | V_x = c_HOL_Ozero__class_Ozero(tc_nat)
    | V_x = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('theBenchmark.p',cls_nat__lt__two__imp__zero__or__one_0) ).

cnf(cls_eq__number__of_0,axiom,
    ( V_x = V_y
    | c_Int_Onumber__class_Onumber__of(V_x,T_a) != c_Int_Onumber__class_Onumber__of(V_y,T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Int_Oring__char__0(T_a) ),
    file('theBenchmark.p',cls_eq__number__of_0) ).

cnf(cls_minus__divide__divide_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_minus__divide__divide_0) ).

cnf(cls_divide_Ominus_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__field(T_a) ),
    file('theBenchmark.p',cls_divide_Ominus_0) ).

cnf(cls_poly__minus_0,axiom,
    ( c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(V_p,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(V_p,V_x,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__ring(T_a) ),
    file('theBenchmark.p',cls_poly__minus_0) ).

cnf(cls_gr0__conv__Suc_1,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat),
    file('theBenchmark.p',cls_gr0__conv__Suc_1) ).

cnf(cls_zero__less__Suc_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat),
    file('theBenchmark.p',cls_zero__less__Suc_0) ).

cnf(cls_one__le__inverse__iff_0,axiom,
    ( ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_one__le__inverse__iff_0) ).

cnf(cls_one__less__power_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_one__less__power_0) ).

cnf(cls_combine__common__factor_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Osemiring(T_a) ),
    file('theBenchmark.p',cls_combine__common__factor_0) ).

cnf(cls_left__add__mult__distrib_0,axiom,
    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),
    file('theBenchmark.p',cls_left__add__mult__distrib_0) ).

cnf(cls_eq__neg__iff__add__eq__0_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).

cnf(cls_ab__left__minus_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_ab__left__minus_0) ).

cnf(cls_right__minus_0,axiom,
    ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_right__minus_0) ).

cnf(cls_left__minus_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_left__minus_0) ).

cnf(cls_nat__0__less__mult__iff_0,axiom,
    ( ~ 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_m,tc_nat) ),
    file('theBenchmark.p',cls_nat__0__less__mult__iff_0) ).

cnf(cls_nat__0__less__mult__iff_1,axiom,
    ( ~ 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) ),
    file('theBenchmark.p',cls_nat__0__less__mult__iff_1) ).

cnf(cls_add__neg__neg_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_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_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
    file('theBenchmark.p',cls_add__neg__neg_0) ).

cnf(cls_power__strict__mono_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__strict__mono_0) ).

cnf(cls_sum__squares__le__zero__iff_1,axiom,
    ( ~ 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)
    | V_y = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).

cnf(cls_sum__squares__le__zero__iff_0,axiom,
    ( ~ 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)
    | V_x = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).

cnf(cls_inverse__nonpositive__iff__nonpositive_1,axiom,
    ( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_1) ).

cnf(cls_inverse__nonpositive__iff__nonpositive_0,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(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)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_0) ).

cnf(cls_le0_0,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),
    file('theBenchmark.p',cls_le0_0) ).

cnf(cls_dvd__div__mult_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
    | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_c,T_a) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),V_a,T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_dvd__div__mult_0) ).

cnf(cls_Suc__mult__less__cancel1_0,axiom,
    ( ~ 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) ),
    file('theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).

cnf(cls_Suc__mult__less__cancel1_1,axiom,
    ( ~ 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) ),
    file('theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).

cnf(cls_Suc__lessI_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | c_Suc(V_m) = V_n
    | c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) ),
    file('theBenchmark.p',cls_Suc__lessI_0) ).

cnf(cls_not__less__eq__eq_0,axiom,
    ( c_lessequals(V_m,V_n,tc_nat)
    | c_lessequals(c_Suc(V_n),V_m,tc_nat) ),
    file('theBenchmark.p',cls_not__less__eq__eq_0) ).

cnf(cls_not__less__eq__eq_1,axiom,
    ( ~ c_lessequals(c_Suc(V_n),V_m,tc_nat)
    | ~ c_lessequals(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_not__less__eq__eq_1) ).

cnf(cls_inverse__eq__1__iff_0,axiom,
    ( V_x = c_HOL_Oone__class_Oone(T_a)
    | c_HOL_Oinverse__class_Oinverse(V_x,T_a) != c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_inverse__eq__1__iff_0) ).

cnf(cls_inverse__less__1__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a)
    | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_x,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__less__1__iff_0) ).

cnf(cls_coeff__mult__degree__sum_0,axiom,
    ( c_Polynomial_Ocoeff(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Ocoeff(V_p,c_Polynomial_Odegree(V_p,T_a),T_a),c_Polynomial_Ocoeff(V_q,c_Polynomial_Odegree(V_q,T_a),T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_coeff__mult__degree__sum_0) ).

cnf(cls_less__divide__eq__number__of1_6,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of1_6) ).

cnf(cls_less__divide__eq__number__of1_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of1_0) ).

cnf(cls_divide__less__eq__number__of1_6,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of1_6) ).

cnf(cls_divide__less__eq__number__of1_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of1_0) ).

cnf(cls_positive__imp__inverse__positive_0,axiom,
    ( ~ 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_Oinverse__class_Oinverse(V_a,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_positive__imp__inverse__positive_0) ).

cnf(cls_inverse__positive__iff__positive_1,axiom,
    ( ~ 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_Oinverse__class_Oinverse(V_a,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__positive__iff__positive_1) ).

cnf(cls_inverse__positive__iff__positive_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__positive__iff__positive_0) ).

cnf(cls_mod__mult__right__eq_0,axiom,
    ( 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)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__mult__right__eq_0) ).

cnf(cls_mod__mult__left__eq_0,axiom,
    ( 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)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__mult__left__eq_0) ).

cnf(cls_add__is__1_0,axiom,
    ( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('theBenchmark.p',cls_add__is__1_0) ).

cnf(cls_add__is__1_3,axiom,
    ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
    | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('theBenchmark.p',cls_add__is__1_3) ).

cnf(cls_Suc__mult__le__cancel1_0,axiom,
    ( ~ 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) ),
    file('theBenchmark.p',cls_Suc__mult__le__cancel1_0) ).

cnf(cls_Suc__mult__le__cancel1_1,axiom,
    ( ~ 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) ),
    file('theBenchmark.p',cls_Suc__mult__le__cancel1_1) ).

cnf(cls_sum__squares__gt__zero__iff_2,axiom,
    ( V_y = c_HOL_Ozero__class_Ozero(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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).

cnf(cls_sum__squares__gt__zero__iff_1,axiom,
    ( V_x = c_HOL_Ozero__class_Ozero(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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).

cnf(cls_poly__smult_0,axiom,
    ( c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_poly__smult_0) ).

cnf(cls_divide__less__0__iff_3,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(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_b,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__0__iff_3) ).

cnf(cls_divide__less__0__iff_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(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)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__0__iff_2) ).

cnf(cls_divide__less__0__iff_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(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_a,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__0__iff_1) ).

cnf(cls_divide__less__0__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(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_a,T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__0__iff_0) ).

cnf(cls_power__eq__imp__eq__base_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_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(tc_nat),V_n,tc_nat)
    | V_a = V_b
    | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_Power_Opower__class_Opower(V_b,V_n,T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__eq__imp__eq__base_0) ).

cnf(cls_add__cancel__end_0,axiom,
    ( V_x = c_HOL_Ouminus__class_Ouminus(V_z,T_a)
    | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != V_y
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_add__cancel__end_0) ).

cnf(cls_less__divide__eq__number__of1_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of1_1) ).

cnf(cls_less__divide__eq__number__of1_4,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of1_4) ).

cnf(cls_coeff__monom_0,axiom,
    ( c_Polynomial_Ocoeff(c_Polynomial_Omonom(V_a,V_x,T_a),V_x,T_a) = V_a
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_coeff__monom_0) ).

cnf(cls_inverse__positive__imp__positive_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__positive__imp__positive_0) ).

cnf(cls_divide__less__eq__number__of1_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),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)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of1_2) ).

cnf(cls_divide__less__eq__number__of1_3,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),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)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of1_3) ).

cnf(cls_less__divide__eq__number__of1_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,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)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of1_2) ).

cnf(cls_less__divide__eq__number__of1_3,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,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)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of1_3) ).

cnf(cls_add__cancel__21_0,axiom,
    ( c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) = V_u
    | 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)
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_add__cancel__21_0) ).

cnf(cls_one__le__mult__iff_1,axiom,
    ( ~ 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) ),
    file('theBenchmark.p',cls_one__le__mult__iff_1) ).

cnf(cls_one__le__mult__iff_0,axiom,
    ( ~ 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_m,tc_nat) ),
    file('theBenchmark.p',cls_one__le__mult__iff_0) ).

cnf(cls_gr__implies__not0_0,axiom,
    ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('theBenchmark.p',cls_gr__implies__not0_0) ).

cnf(cls_not__less0_0,axiom,
    ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('theBenchmark.p',cls_not__less0_0) ).

cnf(cls_psize__def_0,axiom,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_psize__def_0) ).

cnf(cls_power__Suc__less__one_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__Suc__less__one_0) ).

cnf(cls_inverse__less__imp__less_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__less__imp__less_0) ).

cnf(cls_less__imp__inverse__less_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_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_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__imp__inverse__less_0) ).

cnf(cls_inverse__less__imp__less__neg_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(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_b,V_a,T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__less__imp__less__neg_0) ).

cnf(cls_less__imp__inverse__less__neg_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,V_b,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_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__imp__inverse__less__neg_0) ).

cnf(cls_mod__smult__right_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_Divides_Odiv__class_Omod(V_x,c_Polynomial_Osmult(V_a,V_y,T_a),tc_Polynomial_Opoly(T_a)) = c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_mod__smult__right_0) ).

cnf(cls_add__nonneg__nonneg_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_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_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
    file('theBenchmark.p',cls_add__nonneg__nonneg_0) ).

cnf(cls_less__Suc__eq__le_1,axiom,
    ( ~ c_lessequals(V_m,V_n,tc_nat)
    | c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ),
    file('theBenchmark.p',cls_less__Suc__eq__le_1) ).

cnf(cls_less__Suc__eq__le_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)
    | c_lessequals(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_less__Suc__eq__le_0) ).

cnf(cls_le__less__Suc__eq_1,axiom,
    ( c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat)
    | ~ c_lessequals(V_x,V_x,tc_nat) ),
    file('theBenchmark.p',cls_le__less__Suc__eq_1) ).

cnf(cls_degree__pCons__le_0,axiom,
    ( c_lessequals(c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a),c_Suc(c_Polynomial_Odegree(V_p,T_a)),tc_nat)
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_degree__pCons__le_0) ).

cnf(cls_add__le__mono_0,axiom,
    ( ~ c_lessequals(V_i,V_j,tc_nat)
    | ~ c_lessequals(V_k,V_l,tc_nat)
    | 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) ),
    file('theBenchmark.p',cls_add__le__mono_0) ).

cnf(cls_add__mono_0,axiom,
    ( ~ c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(V_c,V_d,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)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) ),
    file('theBenchmark.p',cls_add__mono_0) ).

cnf(cls_inverse__nonnegative__iff__nonnegative_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_0) ).

cnf(cls_inverse__nonnegative__iff__nonnegative_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_1) ).

cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).

cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).

cnf(cls_divide__less__0__1__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_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)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__0__1__iff_0) ).

cnf(cls_divide__less__0__1__iff_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__0__1__iff_1) ).

cnf(cls_mod__mod__trivial_0,axiom,
    ( 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)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__mod__trivial_0) ).

cnf(cls_div__self_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_Divides_Odiv__class_Odiv(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__self_0) ).

cnf(cls_add__strict__increasing_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(V_b,V_c,T_a)
    | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
    file('theBenchmark.p',cls_add__strict__increasing_0) ).

cnf(cls_smult__minus__left_0,axiom,
    ( c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_p,T_a) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(V_a,V_p,T_a),tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ocomm__ring(T_a) ),
    file('theBenchmark.p',cls_smult__minus__left_0) ).

cnf(cls_smult__minus__right_0,axiom,
    ( c_Polynomial_Osmult(V_a,c_HOL_Ouminus__class_Ouminus(V_p,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(V_a,V_p,T_a),tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ocomm__ring(T_a) ),
    file('theBenchmark.p',cls_smult__minus__right_0) ).

cnf(cls_le__minus__self__iff_0,axiom,
    ( ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_le__minus__self__iff_0) ).

cnf(cls_le__minus__self__iff_1,axiom,
    ( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_le__minus__self__iff_1) ).

cnf(cls_minus__le__self__iff_0,axiom,
    ( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_minus__le__self__iff_0) ).

cnf(cls_minus__le__self__iff_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_minus__le__self__iff_1) ).

cnf(cls_less__eq__neg__nonpos_0,axiom,
    ( ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_OrderedGroup_Oordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_less__eq__neg__nonpos_0) ).

cnf(cls_less__eq__neg__nonpos_1,axiom,
    ( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ class_OrderedGroup_Oordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_less__eq__neg__nonpos_1) ).

cnf(cls_neg__less__eq__nonneg_0,axiom,
    ( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ class_OrderedGroup_Oordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_neg__less__eq__nonneg_0) ).

cnf(cls_neg__less__eq__nonneg_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a)
    | ~ class_OrderedGroup_Oordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_neg__less__eq__nonneg_1) ).

cnf(cls_divide__le__eq__number__of_8,axiom,
    ( ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of_8) ).

cnf(cls_one__le__power_0,axiom,
    ( ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
    | c_lessequals(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_one__le__power_0) ).

cnf(cls_coeff__pCons__Suc_0,axiom,
    ( c_Polynomial_Ocoeff(c_Polynomial_OpCons(V_a,V_p,T_a),c_Suc(V_n),T_a) = c_Polynomial_Ocoeff(V_p,V_n,T_a)
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_coeff__pCons__Suc_0) ).

cnf(cls_add__Suc_0,axiom,
    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)),
    file('theBenchmark.p',cls_add__Suc_0) ).

cnf(cls_add__Suc__right_0,axiom,
    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)),
    file('theBenchmark.p',cls_add__Suc__right_0) ).

cnf(cls_div__mod__equality_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__mod__equality_0) ).

cnf(cls_div__mod__equality2_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__mod__equality2_0) ).

cnf(cls_poly__mult_0,axiom,
    ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_poly__mult_0) ).

cnf(cls_divide__le__eq__number__of1_1,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of1_1) ).

cnf(cls_divide__le__eq__number__of1_4,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of1_4) ).

cnf(cls_le__divide__eq__number__of1_1,axiom,
    ( ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of1_1) ).

cnf(cls_le__divide__eq__number__of1_4,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of1_4) ).

cnf(cls_power__strict__decreasing_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_N,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__strict__decreasing_0) ).

cnf(cls_complex__cnj__cnj_0,axiom,
    c_Complex_Ocnj(c_Complex_Ocnj(V_z)) = V_z,
    file('theBenchmark.p',cls_complex__cnj__cnj_0) ).

cnf(cls_psize__eq__0__iff_0,axiom,
    ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_psize__eq__0__iff_0) ).

cnf(cls_power__decreasing_0,axiom,
    ( ~ c_lessequals(V_n,V_N,tc_nat)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(V_a,c_HOL_Oone__class_Oone(T_a),T_a)
    | c_lessequals(c_Power_Opower__class_Opower(V_a,V_N,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__decreasing_0) ).

cnf(cls_divide__less__eq__number__of_5,axiom,
    ( 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(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of_5) ).

cnf(cls_divide__less__eq__number__of_7,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),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(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of_7) ).

cnf(cls_divide__less__eq__number__of1_5,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),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_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of1_5) ).

cnf(cls_less__divide__eq__number__of1_5,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of1_5) ).

cnf(cls_divide__less__eq__number__of_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,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_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of_2) ).

cnf(cls_divide__less__eq__number__of_3,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,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),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of_3) ).

cnf(cls_divide__less__eq__number__of_9,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq__number__of_9) ).

cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

cnf(cls_less__add__eq__less_0,axiom,
    ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
    | c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ),
    file('theBenchmark.p',cls_less__add__eq__less_0) ).

cnf(cls_nat__add__commute_0,axiom,
    c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),
    file('theBenchmark.p',cls_nat__add__commute_0) ).

cnf(cls_class__semiring_Oadd__c_0,axiom,
    ( c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_y,V_x,T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
    ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a)
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
    file('theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

cnf(cls_divide__le__0__iff_0,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(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_a,T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__0__iff_0) ).

cnf(cls_divide__le__0__iff_1,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(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_a,T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__0__iff_1) ).

cnf(cls_divide__le__0__iff_2,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(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)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__0__iff_2) ).

cnf(cls_divide__le__0__iff_3,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(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_b,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__0__iff_3) ).

cnf(cls_power__minus_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_n,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),V_n,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oring__1(T_a) ),
    file('theBenchmark.p',cls_power__minus_0) ).

cnf(cls_inverse__le__imp__le_0,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_lessequals(V_b,V_a,T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__le__imp__le_0) ).

cnf(cls_le__imp__inverse__le_0,axiom,
    ( ~ c_lessequals(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__imp__inverse__le_0) ).

cnf(cls_inverse__le__imp__le__neg_0,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_b,V_a,T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__le__imp__le__neg_0) ).

cnf(cls_le__imp__inverse__le__neg_0,axiom,
    ( ~ c_lessequals(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__imp__inverse__le__neg_0) ).

cnf(cls_mod__div__trivial_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__div__trivial_0) ).

cnf(cls_mod__minus__cong_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a_H,T_a),V_b,T_a)
    | c_Divides_Odiv__class_Omod(V_a,V_b,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_b,T_a)
    | ~ class_Divides_Oring__div(T_a) ),
    file('theBenchmark.p',cls_mod__minus__cong_0) ).

cnf(cls_mod__mult__eq_0,axiom,
    ( 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)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__mult__eq_0) ).

cnf(cls_mult__cancel2_0,axiom,
    ( V_m = V_n
    | V_k = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat) != c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat) ),
    file('theBenchmark.p',cls_mult__cancel2_0) ).

cnf(cls_mult__cancel1_0,axiom,
    ( V_m = V_n
    | V_k = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) ),
    file('theBenchmark.p',cls_mult__cancel1_0) ).

cnf(cls_nat__mult__eq__cancel__disj_0,axiom,
    ( V_k = c_HOL_Ozero__class_Ozero(tc_nat)
    | V_m = V_n
    | c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) ),
    file('theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).

cnf(cls_div__mult__self1_0,axiom,
    ( V_b = c_HOL_Ozero__class_Ozero(T_a)
    | c_Divides_Odiv__class_Odiv(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_HOL_Oplus__class_Oplus(V_c,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__mult__self1_0) ).

cnf(cls_div__mult__self2_0,axiom,
    ( V_b = c_HOL_Ozero__class_Ozero(T_a)
    | c_Divides_Odiv__class_Odiv(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_HOL_Oplus__class_Oplus(V_c,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__mult__self2_0) ).

cnf(cls_divide__less__eq_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),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(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq_1) ).

cnf(cls_divide__less__eq_4,axiom,
    ( 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),V_b,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_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq_4) ).

cnf(cls_divide__less__eq_5,axiom,
    ( 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),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_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq_5) ).

cnf(cls_divide__less__eq_7,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,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(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__eq_7) ).

cnf(cls_less__divide__eq_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(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_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq_1) ).

cnf(cls_less__divide__eq_4,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,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_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq_4) ).

cnf(cls_less__divide__eq_5,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq_5) ).

cnf(cls_less__divide__eq_7,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,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,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq_7) ).

cnf(cls_eq__divide__eq__number__of_3,axiom,
    ( V_c = c_HOL_Ozero__class_Ozero(T_a)
    | c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_c,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_eq__divide__eq__number__of_3) ).

cnf(cls_mult__divide__mult__cancel__right_0,axiom,
    ( V_c = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(V_a,V_b,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).

cnf(cls_mult__divide__mult__cancel__left_0,axiom,
    ( V_c = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(V_a,V_b,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).

cnf(cls_le__Suc__eq_2,axiom,
    c_lessequals(c_Suc(V_n),c_Suc(V_n),tc_nat),
    file('theBenchmark.p',cls_le__Suc__eq_2) ).

cnf(cls_le__divide__eq__number__of1_6,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of1_6) ).

cnf(cls_le__divide__eq__number__of1_0,axiom,
    ( ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of1_0) ).

cnf(cls_divide__le__eq__number__of1_6,axiom,
    ( ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of1_6) ).

cnf(cls_divide__le__eq__number__of1_0,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of1_0) ).

cnf(cls_le__square_0,axiom,
    c_lessequals(V_m,c_HOL_Otimes__class_Otimes(V_m,V_m,tc_nat),tc_nat),
    file('theBenchmark.p',cls_le__square_0) ).

cnf(cls_mult__frac__num_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),V_y,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_mult__frac__num_0) ).

cnf(cls_mult__smult__right_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_Osmult(V_a,c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_mult__smult__right_0) ).

cnf(cls_mult__smult__left_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a)) = c_Polynomial_Osmult(V_a,c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_mult__smult__left_0) ).

cnf(cls_dvd__mult__div__cancel_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
    | c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),T_a) = V_b
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_dvd__mult__div__cancel_0) ).

cnf(cls_dvd__div__mult__self_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
    | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_a,T_a) = V_b
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_dvd__div__mult__self_0) ).

cnf(cls_mult__strict__left__mono__comm_0,axiom,
    ( ~ 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)
    | 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)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).

cnf(cls_mult__less__cancel__right__disj_5,axiom,
    ( ~ 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)
    | 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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).

cnf(cls_mult__less__cancel__right__disj_4,axiom,
    ( ~ 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)
    | 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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).

cnf(cls_mult__strict__right__mono_0,axiom,
    ( ~ 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)
    | 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)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__strict__right__mono_0) ).

cnf(cls_mult__strict__right__mono__neg_0,axiom,
    ( ~ 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)
    | 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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).

cnf(cls_mult__less__cancel__left__disj_5,axiom,
    ( ~ 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)
    | 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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).

cnf(cls_mult__less__cancel__left__disj_4,axiom,
    ( ~ 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)
    | 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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).

cnf(cls_mult__strict__left__mono_0,axiom,
    ( ~ 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)
    | 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)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__strict__left__mono_0) ).

cnf(cls_mult__strict__left__mono__neg_0,axiom,
    ( ~ 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)
    | 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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).

cnf(cls_mult__less__cancel__left__pos_1,axiom,
    ( ~ 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)
    | 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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).

cnf(cls_mult__less__cancel__left__pos_0,axiom,
    ( ~ 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)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).

cnf(cls_mult__less__cancel__left__neg_1,axiom,
    ( ~ 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)
    | 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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).

cnf(cls_mult__less__cancel__left__neg_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_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_b,V_a,T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).

cnf(cls_nat__mult__less__cancel1_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
    | ~ 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) ),
    file('theBenchmark.p',cls_nat__mult__less__cancel1_1) ).

cnf(cls_nat__mult__less__cancel1_0,axiom,
    ( ~ 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)
    | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_nat__mult__less__cancel1_0) ).

cnf(cls_mult__less__mono1_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
    | ~ 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_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_k,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_mult__less__mono1_0) ).

cnf(cls_mult__less__mono2_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
    | ~ 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_i,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_j,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_mult__less__mono2_0) ).

cnf(cls_mult__less__cancel1_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
    | ~ 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) ),
    file('theBenchmark.p',cls_mult__less__cancel1_2) ).

cnf(cls_mult__less__cancel2_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
    | ~ 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) ),
    file('theBenchmark.p',cls_mult__less__cancel2_2) ).

cnf(cls_mod__mult__self2_0,axiom,
    ( 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)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__mult__self2_0) ).

cnf(cls_mod__mult__self1_0,axiom,
    ( 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)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__mult__self1_0) ).

cnf(cls_smult__smult_0,axiom,
    ( c_Polynomial_Osmult(V_a,c_Polynomial_Osmult(V_b,V_p,T_a),T_a) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_p,T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_smult__smult_0) ).

cnf(cls_natgb_Oadd__r0__iff_1,axiom,
    V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).

cnf(cls_Nat_Oadd__0__right_0,axiom,
    c_HOL_Oplus__class_Oplus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m,
    file('theBenchmark.p',cls_Nat_Oadd__0__right_0) ).

cnf(cls_plus__nat_Oadd__0_0,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n,
    file('theBenchmark.p',cls_plus__nat_Oadd__0_0) ).

cnf(cls_le__divide__eq_9,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq_9) ).

cnf(cls_le__divide__eq_3,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq_3) ).

cnf(cls_le__divide__eq_2,axiom,
    ( ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(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_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq_2) ).

cnf(cls_divide__le__eq_9,axiom,
    ( ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq_9) ).

cnf(cls_divide__le__eq_3,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | c_HOL_Oord__class_Oless(V_c,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_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq_3) ).

cnf(cls_divide__le__eq_2,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),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(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq_2) ).

cnf(cls_id__apply_0,axiom,
    c_Fun_Oid(V_x,T_a) = V_x,
    file('theBenchmark.p',cls_id__apply_0) ).

cnf(cls_add__divide__distrib_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_add__divide__distrib_0) ).

cnf(cls_divide_Oadd_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_ya,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_ya,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__field(T_a) ),
    file('theBenchmark.p',cls_divide_Oadd_0) ).

cnf(cls_less__1__mult_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_m,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),c_HOL_Otimes__class_Otimes(V_m,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_less__1__mult_0) ).

cnf(cls_minus__equation__iff_1,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_minus__equation__iff_1) ).

cnf(cls_equation__minus__iff_1,axiom,
    ( V_a = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_equation__minus__iff_1) ).

cnf(cls_equation__minus__iff_0,axiom,
    ( V_b = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_equation__minus__iff_0) ).

cnf(cls_double__compl_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = V_x
    | ~ class_Lattices_Oboolean__algebra(T_a) ),
    file('theBenchmark.p',cls_double__compl_0) ).

cnf(cls_minus__minus_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_minus__minus_0) ).

cnf(cls_div__by__1_0,axiom,
    ( c_Divides_Odiv__class_Odiv(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__by__1_0) ).

cnf(cls_add__less__le__mono_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_lessequals(V_c,V_d,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)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) ),
    file('theBenchmark.p',cls_add__less__le__mono_0) ).

cnf(cls_add__le__less__mono_0,axiom,
    ( ~ c_lessequals(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,V_d,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)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) ),
    file('theBenchmark.p',cls_add__le__less__mono_0) ).

cnf(cls_Suc__mono_0,axiom,
    ( ~ 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) ),
    file('theBenchmark.p',cls_Suc__mono_0) ).

cnf(cls_Suc__less__eq_0,axiom,
    ( ~ 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) ),
    file('theBenchmark.p',cls_Suc__less__eq_0) ).

cnf(cls_less__Suc__eq__0__disj_3,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,V_n,tc_nat)
    | c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat) ),
    file('theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).

cnf(cls_minus__less__iff_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_minus__less__iff_1) ).

cnf(cls_minus__less__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_minus__less__iff_0) ).

cnf(cls_less__minus__iff_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_less__minus__iff_1) ).

cnf(cls_less__minus__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_less__minus__iff_0) ).

cnf(cls_minus__le__iff_1,axiom,
    ( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a)
    | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_minus__le__iff_1) ).

cnf(cls_minus__le__iff_0,axiom,
    ( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
    | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_minus__le__iff_0) ).

cnf(cls_le__minus__iff_1,axiom,
    ( ~ c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_le__minus__iff_1) ).

cnf(cls_le__minus__iff_0,axiom,
    ( ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_le__minus__iff_0) ).

cnf(cls_poly__gcd__unique_11,axiom,
    ( c_Polynomial_Opoly__gcd(V_x,V_y,T_a) = V_d
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_x,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_y,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(V_d,V_x,V_y,T_a),V_d,tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Ocoeff(V_d,c_Polynomial_Odegree(V_d,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | c_Polynomial_Ocoeff(V_d,c_Polynomial_Odegree(V_d,T_a),T_a) != c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__unique_11) ).

cnf(cls_poly__gcd__unique_3,axiom,
    ( c_Polynomial_Opoly__gcd(V_x,V_y,T_a) = V_d
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_x,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_y,tc_Polynomial_Opoly(T_a))
    | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(V_d,V_x,V_y,T_a),V_x,tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Ocoeff(V_d,c_Polynomial_Odegree(V_d,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | c_Polynomial_Ocoeff(V_d,c_Polynomial_Odegree(V_d,T_a),T_a) != c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__unique_3) ).

cnf(cls_poly__gcd__unique_7,axiom,
    ( c_Polynomial_Opoly__gcd(V_x,V_y,T_a) = V_d
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_x,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_y,tc_Polynomial_Opoly(T_a))
    | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(V_d,V_x,V_y,T_a),V_y,tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Ocoeff(V_d,c_Polynomial_Odegree(V_d,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | c_Polynomial_Ocoeff(V_d,c_Polynomial_Odegree(V_d,T_a),T_a) != c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__unique_7) ).

cnf(cls_poly__gcd__unique_0,axiom,
    ( c_Polynomial_Opoly__gcd(V_x,V_y,T_a) = V_d
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_x,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_y,tc_Polynomial_Opoly(T_a))
    | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(V_d,V_x,V_y,T_a),V_x,tc_Polynomial_Opoly(T_a))
    | V_x = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Ocoeff(V_d,c_Polynomial_Odegree(V_d,T_a),T_a) != c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__unique_0) ).

cnf(cls_poly__gcd__unique_1,axiom,
    ( c_Polynomial_Opoly__gcd(V_x,V_y,T_a) = V_d
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_x,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_y,tc_Polynomial_Opoly(T_a))
    | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(V_d,V_x,V_y,T_a),V_x,tc_Polynomial_Opoly(T_a))
    | V_y = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Ocoeff(V_d,c_Polynomial_Odegree(V_d,T_a),T_a) != c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__unique_1) ).

cnf(cls_poly__gcd__unique_4,axiom,
    ( c_Polynomial_Opoly__gcd(V_x,V_y,T_a) = V_d
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_x,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_y,tc_Polynomial_Opoly(T_a))
    | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(V_d,V_x,V_y,T_a),V_y,tc_Polynomial_Opoly(T_a))
    | V_x = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Ocoeff(V_d,c_Polynomial_Odegree(V_d,T_a),T_a) != c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__unique_4) ).

cnf(cls_poly__gcd__unique_5,axiom,
    ( c_Polynomial_Opoly__gcd(V_x,V_y,T_a) = V_d
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_x,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_y,tc_Polynomial_Opoly(T_a))
    | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(V_d,V_x,V_y,T_a),V_y,tc_Polynomial_Opoly(T_a))
    | V_y = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Ocoeff(V_d,c_Polynomial_Odegree(V_d,T_a),T_a) != c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__unique_5) ).

cnf(cls_poly__gcd__unique_8,axiom,
    ( c_Polynomial_Opoly__gcd(V_x,V_y,T_a) = V_d
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_x,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_y,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(V_d,V_x,V_y,T_a),V_d,tc_Polynomial_Opoly(T_a))
    | V_x = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Ocoeff(V_d,c_Polynomial_Odegree(V_d,T_a),T_a) != c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__unique_8) ).

cnf(cls_poly__gcd__unique_9,axiom,
    ( c_Polynomial_Opoly__gcd(V_x,V_y,T_a) = V_d
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_x,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_y,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(V_d,V_x,V_y,T_a),V_d,tc_Polynomial_Opoly(T_a))
    | V_y = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Ocoeff(V_d,c_Polynomial_Odegree(V_d,T_a),T_a) != c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__unique_9) ).

cnf(cls_coeff__linear__power_0,axiom,
    ( c_Polynomial_Ocoeff(c_Power_Opower__class_Opower(c_Polynomial_OpCons(V_a,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_n,tc_Polynomial_Opoly(T_a)),V_n,T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_coeff__linear__power_0) ).

cnf(cls_order_0,axiom,
    ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),c_Polynomial_Oorder(V_a,V_p,T_a),tc_Polynomial_Opoly(T_a)),V_p,tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_order_0) ).

cnf(cls_order__1_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),c_Polynomial_Oorder(V_a,V_p,T_a),tc_Polynomial_Opoly(T_a)),V_p,tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_order__1_0) ).

cnf(cls_eq__divide__eq_2,axiom,
    ( c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_eq__divide__eq_2) ).

cnf(cls_neg__equal__zero_1,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Oordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_neg__equal__zero_1) ).

cnf(cls_minus__zero_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_minus__zero_0) ).

cnf(cls_inverse__zero__imp__zero_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_inverse__zero__imp__zero_0) ).

cnf(cls_inverse__nonzero__iff__nonzero_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_inverse__nonzero__iff__nonzero_0) ).

cnf(cls_neg__0__equal__iff__equal_1,axiom,
    ( c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).

cnf(cls_mult__eq__0__iff_2,axiom,
    ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) ),
    file('theBenchmark.p',cls_mult__eq__0__iff_2) ).

cnf(cls_mult__eq__0__iff_1,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) ),
    file('theBenchmark.p',cls_mult__eq__0__iff_1) ).

cnf(cls_mult__zero__right_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Omult__zero(T_a) ),
    file('theBenchmark.p',cls_mult__zero__right_0) ).

cnf(cls_mult__zero__left_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Omult__zero(T_a) ),
    file('theBenchmark.p',cls_mult__zero__left_0) ).

cnf(cls_class__semiring_Omul__0_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Omul__0_0) ).

cnf(cls_mult__right_Ozero_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    file('theBenchmark.p',cls_mult__right_Ozero_0) ).

cnf(cls_mult_Ozero__right_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    file('theBenchmark.p',cls_mult_Ozero__right_0) ).

cnf(cls_mult_Ozero__left_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    file('theBenchmark.p',cls_mult_Ozero__left_0) ).

cnf(cls_mult__left_Ozero_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    file('theBenchmark.p',cls_mult__left_Ozero_0) ).

cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).

cnf(cls_mod__self_0,axiom,
    ( c_Divides_Odiv__class_Omod(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__self_0) ).

cnf(cls_mod__by__0_0,axiom,
    ( c_Divides_Odiv__class_Omod(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__by__0_0) ).

cnf(cls_zero__neq__one_0,axiom,
    ( c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
    file('theBenchmark.p',cls_zero__neq__one_0) ).

cnf(cls_nonzero__inverse__inverse__eq_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).

cnf(cls_inverse__le__1__iff_2,axiom,
    ( ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_x,T_a)
    | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__le__1__iff_2) ).

cnf(cls_class__semiring_Osemiring__rules_I4_J_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).

cnf(cls_div__poly__eq_0,axiom,
    ( ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q,V_r,T_a)
    | c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)) = V_q
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_div__poly__eq_0) ).

cnf(cls_nat_Oinject_0,axiom,
    ( V_nat = V_nat_H
    | c_Suc(V_nat) != c_Suc(V_nat_H) ),
    file('theBenchmark.p',cls_nat_Oinject_0) ).

cnf(cls_Suc__inject_0,axiom,
    ( V_x = V_y
    | c_Suc(V_x) != c_Suc(V_y) ),
    file('theBenchmark.p',cls_Suc__inject_0) ).

cnf(cls_less__divide__eq__number__of_5,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of_5) ).

cnf(cls_less__divide__eq__number__of_7,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
    | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of_7) ).

cnf(cls_less__divide__eq__number__of_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(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_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of_2) ).

cnf(cls_less__divide__eq__number__of_3,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of_3) ).

cnf(cls_less__divide__eq__number__of_9,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of_9) ).

cnf(cls_divide__eq__eq__number__of1_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__eq__eq__number__of1_0) ).

cnf(cls_eq__divide__eq__number__of1_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) = V_b
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_eq__divide__eq__number__of1_0) ).

cnf(cls_eq__divide__eq_4,axiom,
    ( c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a),V_c,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_eq__divide__eq_4) ).

cnf(cls_mod__add__cong_0,axiom,
    ( 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)
    | 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(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__add__cong_0) ).

cnf(cls_less__Suc0_1,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    file('theBenchmark.p',cls_less__Suc0_1) ).

cnf(cls_one__is__add_2,axiom,
    ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
    | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_one__is__add_2) ).

cnf(cls_one__is__add_1,axiom,
    ( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_one__is__add_1) ).

cnf(cls_minus__unique_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b
    | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_minus__unique_0) ).

cnf(cls_eq__neg__iff__add__eq__0_1,axiom,
    ( V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a)
    | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).

cnf(cls_not__one__less__zero_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_not__one__less__zero_0) ).

cnf(cls_natgb_Onoteq__reduce_0,axiom,
    ( V_a = V_b
    | V_c = V_d
    | 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) ),
    file('theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).

cnf(cls_natgb_Oadd__mul__solve_0,axiom,
    ( V_w = V_x
    | V_y = V_z
    | 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) ),
    file('theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).

cnf(cls_class__ringb_Onoteq__reduce_0,axiom,
    ( V_a = V_b
    | V_c = V_d
    | 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)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).

cnf(cls_class__ringb_Oadd__mul__solve_0,axiom,
    ( V_w = V_x
    | V_y = V_z
    | 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)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).

cnf(cls_nonzero__inverse__minus__eq_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).

cnf(cls_less__divide__eq__number__of_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(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_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of_1) ).

cnf(cls_less__divide__eq__number__of_4,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),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(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of_4) ).

cnf(cls_not__less__less__Suc__eq_0,axiom,
    ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
    | V_n = V_m ),
    file('theBenchmark.p',cls_not__less__less__Suc__eq_0) ).

cnf(cls_less__antisym_0,axiom,
    ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
    | V_m = V_n ),
    file('theBenchmark.p',cls_less__antisym_0) ).

cnf(cls_less__SucE_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)
    | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | V_m = V_n ),
    file('theBenchmark.p',cls_less__SucE_0) ).

cnf(cls_mod__mult__cong_0,axiom,
    ( 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)
    | 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(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__mult__cong_0) ).

cnf(cls_divide__eq__eq__number__of_3,axiom,
    ( V_c = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_c,T_a) = c_Int_Onumber__class_Onumber__of(V_w,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__eq__eq__number__of_3) ).

cnf(cls_less__divide__eq__number__of_8,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),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(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_less__divide__eq__number__of_8) ).

cnf(cls_le__divide__eq__number__of_4,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of_4) ).

cnf(cls_le__divide__eq__number__of_1,axiom,
    ( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(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_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of_1) ).

cnf(cls_add__frac__eq_0,axiom,
    ( V_y = c_HOL_Ozero__class_Ozero(T_a)
    | V_z = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_add__frac__eq_0) ).

cnf(cls_mult__eq__1__iff_2,axiom,
    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)),
    file('theBenchmark.p',cls_mult__eq__1__iff_2) ).

cnf(cls_zero__less__power__eq__number__of_2,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),T_a)
    | c_Int_Onumber__class_Onumber__of(V_w,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__less__power__eq__number__of_2) ).

cnf(cls_divide__eq__eq_0,axiom,
    ( V_c = c_HOL_Ozero__class_Ozero(T_a)
    | V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__eq__eq_0) ).

cnf(cls_eq__divide__eq_0,axiom,
    ( V_c = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_eq__divide__eq_0) ).

cnf(cls_zero__le__one_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_zero__le__one_0) ).

cnf(cls_mult__is__0_2,axiom,
    c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('theBenchmark.p',cls_mult__is__0_2) ).

cnf(cls_mult__is__0_1,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('theBenchmark.p',cls_mult__is__0_1) ).

cnf(cls_degree__mult__le_0,axiom,
    ( c_lessequals(c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a),c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_degree__mult__le_0) ).

cnf(cls_class__semiring_Osemiring__rules_I2_J_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).

cnf(cls_left__distrib__number__of_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a),c_HOL_Otimes__class_Otimes(V_b,c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Osemiring(T_a) ),
    file('theBenchmark.p',cls_left__distrib__number__of_0) ).

cnf(cls_mod__by__1_0,axiom,
    ( c_Divides_Odiv__class_Omod(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__by__1_0) ).

cnf(cls_one__le__inverse__iff_1,axiom,
    ( ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a)
    | c_lessequals(V_x,c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_one__le__inverse__iff_1) ).

cnf(cls_one__is__add_4,axiom,
    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),
    file('theBenchmark.p',cls_one__is__add_4) ).

cnf(cls_linorder__neq__iff_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_linorder__neq__iff_1) ).

cnf(cls_order__less__le_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
    | ~ class_Orderings_Oorder(T_a) ),
    file('theBenchmark.p',cls_order__less__le_1) ).

cnf(cls_less__not__refl_0,axiom,
    ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
    file('theBenchmark.p',cls_less__not__refl_0) ).

cnf(cls_nat__less__le_1,axiom,
    ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
    file('theBenchmark.p',cls_nat__less__le_1) ).

cnf(cls_order__less__irrefl_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
    | ~ class_Orderings_Opreorder(T_a) ),
    file('theBenchmark.p',cls_order__less__irrefl_0) ).

cnf(cls_less__le__not__le_2,axiom,
    ( ~ c_lessequals(V_x,V_y,T_a)
    | c_lessequals(V_y,V_x,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ class_Orderings_Opreorder(T_a) ),
    file('theBenchmark.p',cls_less__le__not__le_2) ).

cnf(cls_add__pos__pos_0,axiom,
    ( ~ 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),V_b,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)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
    file('theBenchmark.p',cls_add__pos__pos_0) ).

cnf(cls_le__Suc__ex__iff_1,axiom,
    c_lessequals(V_k,c_HOL_Oplus__class_Oplus(V_k,V_x,tc_nat),tc_nat),
    file('theBenchmark.p',cls_le__Suc__ex__iff_1) ).

cnf(cls_le__iff__add_1,axiom,
    c_lessequals(V_m,c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat),tc_nat),
    file('theBenchmark.p',cls_le__iff__add_1) ).

cnf(cls_le__add2_0,axiom,
    c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat),
    file('theBenchmark.p',cls_le__add2_0) ).

cnf(cls_le__add1_0,axiom,
    c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat),
    file('theBenchmark.p',cls_le__add1_0) ).

cnf(cls_not__one__le__zero_0,axiom,
    ( ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_not__one__le__zero_0) ).

cnf(cls_inverse__negative__iff__negative_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(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)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__negative__iff__negative_0) ).

cnf(cls_inverse__negative__iff__negative_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__negative__iff__negative_1) ).

cnf(cls_negative__imp__inverse__negative_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_negative__imp__inverse__negative_0) ).

cnf(cls_add__less__mono_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
    | 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) ),
    file('theBenchmark.p',cls_add__less__mono_0) ).

cnf(cls_add__strict__mono_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,V_d,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)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) ),
    file('theBenchmark.p',cls_add__strict__mono_0) ).

cnf(cls_order__le__less_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | c_lessequals(V_x,V_y,T_a)
    | ~ class_Orderings_Oorder(T_a) ),
    file('theBenchmark.p',cls_order__le__less_1) ).

cnf(cls_nat__less__le_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | c_lessequals(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_nat__less__le_0) ).

cnf(cls_order__less__imp__le_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | c_lessequals(V_x,V_y,T_a)
    | ~ class_Orderings_Opreorder(T_a) ),
    file('theBenchmark.p',cls_order__less__imp__le_0) ).

cnf(cls_termination__basic__simps_I5_J_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
    | c_lessequals(V_x,V_y,tc_nat) ),
    file('theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).

cnf(cls_add__cancel__end_1,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_z,T_a),c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = V_y
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_add__cancel__end_1) ).

cnf(cls_minus__add__cancel_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) = V_b
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_minus__add__cancel_0) ).

cnf(cls_inverse__eq__1__iff_1,axiom,
    ( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_inverse__eq__1__iff_1) ).

cnf(cls_one__less__inverse__iff_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_one__less__inverse__iff_2) ).

cnf(cls_inverse__1_0,axiom,
    ( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_inverse__1_0) ).

cnf(cls_zero__le__divide__iff_4,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_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_Oinverse__class_Odivide(V_a,V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_zero__le__divide__iff_4) ).

cnf(cls_zero__le__divide__iff_5,axiom,
    ( ~ 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_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_zero__le__divide__iff_5) ).

cnf(cls_poly__mod__minus__right_0,axiom,
    ( c_Divides_Odiv__class_Omod(V_x,c_HOL_Ouminus__class_Ouminus(V_y,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__mod__minus__right_0) ).

cnf(cls_Suc__neq__Zero_0,axiom,
    c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat),
    file('theBenchmark.p',cls_Suc__neq__Zero_0) ).

cnf(cls_nat_Osimps_I3_J_0,axiom,
    c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat),
    file('theBenchmark.p',cls_nat_Osimps_I3_J_0) ).

cnf(cls_frac__le_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ c_lessequals(V_x,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a)
    | ~ c_lessequals(V_w,V_z,T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_z,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_w,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_frac__le_0) ).

cnf(cls_power__gt1_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__gt1_0) ).

cnf(cls_coeff__pCons__0_0,axiom,
    ( c_Polynomial_Ocoeff(c_Polynomial_OpCons(V_a,V_p,T_a),c_HOL_Ozero__class_Ozero(tc_nat),T_a) = V_a
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_coeff__pCons__0_0) ).

cnf(cls_divide__eq__eq__number__of1_4,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__eq__eq__number__of1_4) ).

cnf(cls_zero__less__one_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_zero__less__one_0) ).

cnf(cls_divide__strict__left__mono_0,axiom,
    ( ~ 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_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_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__strict__left__mono_0) ).

cnf(cls_divide__strict__left__mono__neg_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,V_b,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),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).

cnf(cls_mult__le__less__imp__less_0,axiom,
    ( ~ c_lessequals(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,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_d,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__le__less__imp__less_0) ).

cnf(cls_mult__less__le__imp__less_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_lessequals(V_c,V_d,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),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_d,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__le__imp__less_0) ).

cnf(cls_power__inject__exp_0,axiom,
    ( V_m = V_n
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
    | c_Power_Opower__class_Opower(V_a,V_m,T_a) != c_Power_Opower__class_Opower(V_a,V_n,T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__inject__exp_0) ).

cnf(cls_le__number__of__eq__not__less_0,axiom,
    ( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_le__number__of__eq__not__less_0) ).

cnf(cls_le__number__of__eq__not__less_1,axiom,
    ( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a)
    | c_lessequals(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_le__number__of__eq__not__less_1) ).

cnf(cls_complex__cnj__cancel__iff_0,axiom,
    ( V_x = V_y
    | c_Complex_Ocnj(V_x) != c_Complex_Ocnj(V_y) ),
    file('theBenchmark.p',cls_complex__cnj__cancel__iff_0) ).

cnf(cls_gr0I_0,axiom,
    ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ),
    file('theBenchmark.p',cls_gr0I_0) ).

cnf(cls_poly__gcd__commute_0,axiom,
    ( c_Polynomial_Opoly__gcd(V_x,V_y,T_a) = c_Polynomial_Opoly__gcd(V_y,V_x,T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__commute_0) ).

cnf(cls_divide__eq__eq__number__of1_1,axiom,
    ( c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__eq__eq__number__of1_1) ).

cnf(cls_class__semiring_Osemiring__rules_I27_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I27_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I28_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_q,T_a),V_x,T_a) = c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).

cnf(cls_minus__mult__commute_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Oring(T_a) ),
    file('theBenchmark.p',cls_minus__mult__commute_0) ).

cnf(cls_divide__self__if_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__self__if_0) ).

cnf(cls_neg__equal__zero_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != V_a
    | ~ class_OrderedGroup_Oordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_neg__equal__zero_0) ).

cnf(cls_inverse__zero_0,axiom,
    ( c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
    file('theBenchmark.p',cls_inverse__zero_0) ).

cnf(cls_inverse__nonzero__iff__nonzero_1,axiom,
    ( c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).

cnf(cls_nonzero__inverse__eq__imp__eq_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | V_a = V_b
    | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a)
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).

cnf(cls_neg__equal__0__iff__equal_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).

cnf(cls_one__neq__zero_0,axiom,
    ( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
    file('theBenchmark.p',cls_one__neq__zero_0) ).

cnf(cls_mult__eq__0__iff_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) ),
    file('theBenchmark.p',cls_mult__eq__0__iff_0) ).

cnf(cls_no__zero__divisors_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) ),
    file('theBenchmark.p',cls_no__zero__divisors_0) ).

cnf(cls_no__zero__divirors__neq0_0,axiom,
    ( V_b = c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Ono__zero__divisors(T_a) ),
    file('theBenchmark.p',cls_no__zero__divirors__neq0_0) ).

cnf(cls_div__by__0_0,axiom,
    ( c_Divides_Odiv__class_Odiv(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__by__0_0) ).

cnf(cls_div__0_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__0_0) ).

cnf(cls_double__eq__0__iff_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_double__eq__0__iff_0) ).

cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).

cnf(cls_mod__0_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__0_0) ).

cnf(cls_double__eq__0__iff_1,axiom,
    ( 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)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_double__eq__0__iff_1) ).

cnf(cls_neg__0__equal__iff__equal_0,axiom,
    ( c_HOL_Ozero__class_Ozero(T_a) = V_a
    | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Ouminus__class_Ouminus(V_a,T_a)
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).

cnf(cls_divide__zero__left_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__zero__left_0) ).

cnf(cls_divide__eq__eq_1,axiom,
    ( c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__eq__eq_1) ).

cnf(cls_divide__zero_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__zero_0) ).

cnf(cls_divide_Ozero_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_RealVector_Oreal__normed__field(T_a) ),
    file('theBenchmark.p',cls_divide_Ozero_0) ).

cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
    ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
    | ~ class_OrderedGroup_Omonoid__add(T_a) ),
    file('theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

cnf(cls_add__0__left_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a
    | ~ class_OrderedGroup_Omonoid__add(T_a) ),
    file('theBenchmark.p',cls_add__0__left_0) ).

cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
    ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
    file('theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
    ( V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).

cnf(cls_class__semiring_Oadd__0_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = V_x
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

cnf(cls_comm__monoid__add_Omult__1_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
    file('theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

cnf(cls_dvd__eq__mod__eq__0__number__of_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(V_x,T_a),c_Int_Onumber__class_Onumber__of(V_y,T_a),T_a)
    | c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(V_y,T_a),c_Int_Onumber__class_Onumber__of(V_x,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Divides_Osemiring__div(T_a)
    | ~ class_Int_Onumber(T_a) ),
    file('theBenchmark.p',cls_dvd__eq__mod__eq__0__number__of_1) ).

cnf(cls_dvd__eq__mod__eq__0__number__of_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(V_x,T_a),c_Int_Onumber__class_Onumber__of(V_y,T_a),T_a)
    | c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(V_y,T_a),c_Int_Onumber__class_Onumber__of(V_x,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Divides_Osemiring__div(T_a)
    | ~ class_Int_Onumber(T_a) ),
    file('theBenchmark.p',cls_dvd__eq__mod__eq__0__number__of_0) ).

cnf(cls_power__le__imp__le__base_0,axiom,
    ( ~ c_lessequals(c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),c_Power_Opower__class_Opower(V_b,c_Suc(V_n),T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__le__imp__le__base_0) ).

cnf(cls_power__le__zero__eq_0,axiom,
    ( ~ c_lessequals(c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__le__zero__eq_0) ).

cnf(cls_power__eq__0__iff__number__of_2,axiom,
    ( c_Int_Onumber__class_Onumber__of(V_w,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Power_Opower(T_a)
    | ~ class_Ring__and__Field_Omult__zero(T_a)
    | ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
    | ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
    file('theBenchmark.p',cls_power__eq__0__iff__number__of_2) ).

cnf(cls_power__0__left__number__of_1,axiom,
    ( c_Int_Onumber__class_Onumber__of(V_w,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Power_Opower(T_a)
    | ~ class_Ring__and__Field_Osemiring__0(T_a) ),
    file('theBenchmark.p',cls_power__0__left__number__of_1) ).

cnf(cls_power__0__left_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Power_Opower(T_a)
    | ~ class_Ring__and__Field_Osemiring__0(T_a) ),
    file('theBenchmark.p',cls_power__0__left_0) ).

cnf(cls_power__le__zero__eq__number__of_3,axiom,
    ( ~ c_lessequals(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | V_x = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__le__zero__eq__number__of_3) ).

cnf(cls_power__inject__base_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | V_a = V_b
    | c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) != c_Power_Opower__class_Opower(V_b,c_Suc(V_n),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__inject__base_0) ).

cnf(cls_zero__less__power__eq_3,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__less__power__eq_3) ).

cnf(cls_power__eq__0__iff__number__of_1,axiom,
    ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | c_Int_Onumber__class_Onumber__of(V_w,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_Power_Opower(T_a)
    | ~ class_Ring__and__Field_Omult__zero(T_a)
    | ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
    | ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
    file('theBenchmark.p',cls_power__eq__0__iff__number__of_1) ).

cnf(cls_power__less__imp__less__base_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__less__imp__less__base_0) ).

cnf(cls_zero__less__power__eq_2,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a),T_a)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__less__power__eq_2) ).

cnf(cls_power__less__zero__eq__number__of_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__less__zero__eq__number__of_1) ).

cnf(cls_mult__dvd__mono_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_d,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_mult__dvd__mono_0) ).

cnf(cls_mod__mod__cancel_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_b,T_a)
    | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(V_a,V_c,T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__mod__cancel_0) ).

cnf(cls_dvd__mult__cancel__right_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_dvd__mult__cancel__right_2) ).

cnf(cls_dvd__mult__cancel__left_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_dvd__mult__cancel__left_2) ).

cnf(cls_minus__dvd__iff_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a)
    | ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
    file('theBenchmark.p',cls_minus__dvd__iff_1) ).

cnf(cls_minus__dvd__iff_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a)
    | ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
    file('theBenchmark.p',cls_minus__dvd__iff_0) ).

cnf(cls_dvd__minus__iff_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
    file('theBenchmark.p',cls_dvd__minus__iff_1) ).

cnf(cls_dvd__minus__iff_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a)
    | ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
    file('theBenchmark.p',cls_dvd__minus__iff_0) ).

cnf(cls_div__dvd__div_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__dvd__div_1) ).

cnf(cls_div__dvd__div_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__dvd__div_0) ).

cnf(cls_dvd__add_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_dvd__add_0) ).

cnf(cls_dvd__mult__right_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_dvd__mult__right_0) ).

cnf(cls_dvd__mult__left_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_dvd__mult__left_0) ).

cnf(cls_dvd__mult2_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_dvd__mult2_0) ).

cnf(cls_dvd__mult_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_dvd__mult_0) ).

cnf(cls_one__dvd_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_one__dvd_0) ).

cnf(cls_dvd__mod__imp__dvd_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_dvd__mod__imp__dvd_0) ).

cnf(cls_dvd__mod__iff_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_dvd__mod__iff_1) ).

cnf(cls_dvd__mod__iff_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_dvd__mod__iff_0) ).

cnf(cls_dvd__mod_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_dvd__mod_0) ).

cnf(cls_dvd__triv__right_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_dvd__triv__right_0) ).

cnf(cls_dvd__triv__left_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_dvd__triv__left_0) ).

cnf(cls_dvdI_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(V_b,c_HOL_Otimes__class_Otimes(V_b,V_k,T_a),T_a)
    | ~ class_Ring__and__Field_Odvd(T_a) ),
    file('theBenchmark.p',cls_dvdI_0) ).

cnf(cls_dvd__power_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_dvd__power_0) ).

cnf(cls_power__mult_0,axiom,
    ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a)
    | ~ class_OrderedGroup_Omonoid__mult(T_a) ),
    file('theBenchmark.p',cls_power__mult_0) ).

cnf(cls_power__commutes_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_a,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ class_OrderedGroup_Omonoid__mult(T_a) ),
    file('theBenchmark.p',cls_power__commutes_0) ).

cnf(cls_power__one_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_OrderedGroup_Omonoid__mult(T_a) ),
    file('theBenchmark.p',cls_power__one_0) ).

cnf(cls_power__inverse_0,axiom,
    ( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_power__inverse_0) ).

cnf(cls_power__mult__distrib_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_n,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) ),
    file('theBenchmark.p',cls_power__mult__distrib_0) ).

cnf(cls_class__semiring_Opwr__mul_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_q,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_q,T_a),c_Power_Opower__class_Opower(V_y,V_q,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).

cnf(cls_power__divide_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_power__divide_0) ).

cnf(cls_class__semiring_Opwr__pwr_0,axiom,
    ( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_x,V_p,T_a),V_q,T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Otimes__class_Otimes(V_p,V_q,tc_nat),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).

cnf(cls_le__degree_0,axiom,
    ( c_Polynomial_Ocoeff(V_p,V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | c_lessequals(V_n,c_Polynomial_Odegree(V_p,T_a),tc_nat)
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_le__degree_0) ).

cnf(cls_coeff__eq__0_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),V_n,tc_nat)
    | c_Polynomial_Ocoeff(V_p,V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_coeff__eq__0_0) ).

cnf(cls_degree__smult__eq_0,axiom,
    ( c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(T_a),V_p,T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_degree__smult__eq_0) ).

cnf(cls_eq__zero__or__degree__less_0,axiom,
    ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),V_n,tc_nat)
    | ~ c_lessequals(c_Polynomial_Odegree(V_p,T_a),V_n,tc_nat)
    | c_Polynomial_Ocoeff(V_p,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_eq__zero__or__degree__less_0) ).

cnf(cls_order__root_2,axiom,
    ( c_Polynomial_Oorder(V_a,V_p,T_a) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Polynomial_Opoly(V_p,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_order__root_2) ).

cnf(cls_smult__0__right_0,axiom,
    ( c_Polynomial_Osmult(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_smult__0__right_0) ).

cnf(cls_smult__eq__0__iff_2,axiom,
    ( c_Polynomial_Osmult(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_smult__eq__0__iff_2) ).

cnf(cls_minus__poly__code_I1_J_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_minus__poly__code_I1_J_0) ).

cnf(cls_synthetic__div__0_0,axiom,
    ( c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_synthetic__div__0_0) ).

cnf(cls_mult__poly__0__right_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_mult__poly__0__right_0) ).

cnf(cls_mult__poly__0__left_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,tc_Polynomial_Opoly(T_a)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_mult__poly__0__left_0) ).

cnf(cls_pCons__eq__0__iff_1,axiom,
    ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_pCons__eq__0__iff_1) ).

cnf(cls_pdivmod__rel__by__0_0,axiom,
    ( c_Polynomial_Opdivmod__rel(V_x,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x,T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_pdivmod__rel__by__0_0) ).

cnf(cls_offset__poly__eq__0__iff_0,axiom,
    ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_offset__poly__eq__0__iff_0) ).

cnf(cls_pdivmod__rel__0_0,axiom,
    ( c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_pdivmod__rel__0_0) ).

cnf(cls_poly__gcd__zero__iff_1,axiom,
    ( V_y = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Opoly__gcd(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__zero__iff_1) ).

cnf(cls_poly__gcd__zero__iff_0,axiom,
    ( V_x = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Opoly__gcd(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__zero__iff_0) ).

cnf(cls_pdivmod__rel__by__0__iff_0,axiom,
    ( ~ c_Polynomial_Opdivmod__rel(V_x,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,V_r,T_a)
    | V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_pdivmod__rel__by__0__iff_0) ).

cnf(cls_pdivmod__rel__0__iff_1,axiom,
    ( ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,V_q,V_r,T_a)
    | V_r = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_pdivmod__rel__0__iff_1) ).

cnf(cls_pdivmod__rel__0__iff_0,axiom,
    ( ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,V_q,V_r,T_a)
    | V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_pdivmod__rel__0__iff_0) ).

cnf(cls_pdivmod__rel__def_1,axiom,
    ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ c_Polynomial_Opdivmod__rel(V_x,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,V_r,T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_pdivmod__rel__def_1) ).

cnf(cls_pdivmod__rel__by__0__iff_1,axiom,
    ( ~ c_Polynomial_Opdivmod__rel(V_x,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,V_r,T_a)
    | V_r = V_x
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_pdivmod__rel__by__0__iff_1) ).

cnf(cls_poly__gcd__0__0_0,axiom,
    ( c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__0__0_0) ).

cnf(cls_offset__poly__0_0,axiom,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_h,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_offset__poly__0_0) ).

cnf(cls_pcompose__0_0,axiom,
    ( c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_pcompose__0_0) ).

cnf(cls_neq0__conv_1,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('theBenchmark.p',cls_neq0__conv_1) ).

cnf(cls_divide__eq__eq__number__of_0,axiom,
    ( V_c = c_HOL_Ozero__class_Ozero(T_a)
    | V_b = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a)
    | c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a) != c_Int_Onumber__class_Onumber__of(V_w,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__eq__eq__number__of_0) ).

cnf(cls_le__SucI_0,axiom,
    ( ~ c_lessequals(V_m,V_n,tc_nat)
    | c_lessequals(V_m,c_Suc(V_n),tc_nat) ),
    file('theBenchmark.p',cls_le__SucI_0) ).

cnf(cls_Suc__leD_0,axiom,
    ( ~ c_lessequals(c_Suc(V_m),V_n,tc_nat)
    | c_lessequals(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_Suc__leD_0) ).

cnf(cls_n__less__n__mult__m_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,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(V_n,c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_n__less__n__mult__m_0) ).

cnf(cls_n__less__m__mult__n_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,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(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_n__less__m__mult__n_0) ).

cnf(cls_divide__inverse_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__inverse_0) ).

cnf(cls_class__fieldgb_Odivide__inverse_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_class__fieldgb_Odivide__inverse_0) ).

cnf(cls_poly__gcd__code_1,axiom,
    ( V_y = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Opoly__gcd(V_x,V_y,T_a) = c_Polynomial_Opoly__gcd(V_y,c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)),T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__code_1) ).

cnf(cls_Suc__n__not__le__n_0,axiom,
    ~ c_lessequals(c_Suc(V_n),V_n,tc_nat),
    file('theBenchmark.p',cls_Suc__n__not__le__n_0) ).

cnf(cls_zero__less__divide__1__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_zero__less__divide__1__iff_0) ).

cnf(cls_zero__less__divide__1__iff_1,axiom,
    ( ~ 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),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_zero__less__divide__1__iff_1) ).

cnf(cls_inverse__eq__divide__number__of_0,axiom,
    ( c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_inverse__eq__divide__number__of_0) ).

cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).

cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).

cnf(cls_power__less__imp__less__exp_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__less__imp__less__exp_0) ).

cnf(cls_power__strict__increasing_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_a,V_N,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__strict__increasing_0) ).

cnf(cls_power__strict__increasing__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__strict__increasing__iff_0) ).

cnf(cls_power__strict__increasing__iff_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__strict__increasing__iff_1) ).

cnf(cls_degree__pcompose__le_0,axiom,
    ( c_lessequals(c_Polynomial_Odegree(c_Polynomial_Opcompose(V_p,V_q,T_a),T_a),c_HOL_Otimes__class_Otimes(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_degree__pcompose__le_0) ).

cnf(cls_le__divide__eq__number__of_9,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
    | ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of_9) ).

cnf(cls_le__divide__eq__number__of_3,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of_3) ).

cnf(cls_le__divide__eq__number__of_2,axiom,
    ( ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(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_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of_2) ).

cnf(cls_not__add__less2_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_i,tc_nat),
    file('theBenchmark.p',cls_not__add__less2_0) ).

cnf(cls_not__add__less1_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_i,tc_nat),
    file('theBenchmark.p',cls_not__add__less1_0) ).

cnf(cls_poly__div__mult__right_0,axiom,
    ( c_Divides_Odiv__class_Odiv(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)),V_z,tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__div__mult__right_0) ).

cnf(cls_le__0__eq_1,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('theBenchmark.p',cls_le__0__eq_1) ).

cnf(cls_divide__le__eq_1,axiom,
    ( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),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(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq_1) ).

cnf(cls_divide__le__eq_4,axiom,
    ( 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),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq_4) ).

cnf(cls_le__divide__eq_1,axiom,
    ( ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(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_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq_1) ).

cnf(cls_le__divide__eq_4,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq_4) ).

cnf(cls_divide__le__eq__number__of1_5,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of1_5) ).

cnf(cls_le__divide__eq__number__of1_5,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of1_5) ).

cnf(cls_divide__neg__pos_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__neg__pos_0) ).

cnf(cls_divide__pos__neg_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__pos__neg_0) ).

cnf(cls_divide__less__0__iff_4,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_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_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__0__iff_4) ).

cnf(cls_divide__less__0__iff_5,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_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(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__less__0__iff_5) ).

cnf(cls_add__less__mono1_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
    | 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) ),
    file('theBenchmark.p',cls_add__less__mono1_0) ).

cnf(cls_nat__add__left__cancel__less_0,axiom,
    ( ~ 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) ),
    file('theBenchmark.p',cls_nat__add__left__cancel__less_0) ).

cnf(cls_nat__add__left__cancel__less_1,axiom,
    ( ~ 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) ),
    file('theBenchmark.p',cls_nat__add__left__cancel__less_1) ).

cnf(cls_add__less__cancel__left_0,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
    file('theBenchmark.p',cls_add__less__cancel__left_0) ).

cnf(cls_add__less__cancel__left_1,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
    file('theBenchmark.p',cls_add__less__cancel__left_1) ).

cnf(cls_add__strict__left__mono_0,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) ),
    file('theBenchmark.p',cls_add__strict__left__mono_0) ).

cnf(cls_add__less__cancel__right_0,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
    file('theBenchmark.p',cls_add__less__cancel__right_0) ).

cnf(cls_add__less__cancel__right_1,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
    file('theBenchmark.p',cls_add__less__cancel__right_1) ).

cnf(cls_add__strict__right__mono_0,axiom,
    ( ~ 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)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) ),
    file('theBenchmark.p',cls_add__strict__right__mono_0) ).

cnf(cls_one__le__mult__iff_2,axiom,
    ( ~ 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)),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) ),
    file('theBenchmark.p',cls_one__le__mult__iff_2) ).

cnf(cls_order__eq__refl_0,axiom,
    ( c_lessequals(V_x,V_x,T_a)
    | ~ class_Orderings_Opreorder(T_a) ),
    file('theBenchmark.p',cls_order__eq__refl_0) ).

cnf(cls_order__eq__iff_0,axiom,
    ( c_lessequals(V_x,V_x,T_a)
    | ~ class_Orderings_Oorder(T_a) ),
    file('theBenchmark.p',cls_order__eq__iff_0) ).

cnf(cls_eq__imp__le_0,axiom,
    c_lessequals(V_x,V_x,tc_nat),
    file('theBenchmark.p',cls_eq__imp__le_0) ).

cnf(cls_le__trans_0,axiom,
    ( ~ c_lessequals(V_i,V_j,tc_nat)
    | ~ c_lessequals(V_j,V_k,tc_nat)
    | c_lessequals(V_i,V_k,tc_nat) ),
    file('theBenchmark.p',cls_le__trans_0) ).

cnf(cls_le__refl_0,axiom,
    c_lessequals(V_n,V_n,tc_nat),
    file('theBenchmark.p',cls_le__refl_0) ).

cnf(cls_order__le__less__trans_0,axiom,
    ( ~ c_lessequals(V_x,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
    | ~ class_Orderings_Opreorder(T_a) ),
    file('theBenchmark.p',cls_order__le__less__trans_0) ).

cnf(cls_order__less__le__trans_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ c_lessequals(V_y,V_z,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
    | ~ class_Orderings_Opreorder(T_a) ),
    file('theBenchmark.p',cls_order__less__le__trans_0) ).

cnf(cls_le__add__right__mono_0,axiom,
    ( ~ c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
    | ~ c_lessequals(V_c,V_d,T_a)
    | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_le__add__right__mono_0) ).

cnf(cls_order__trans_0,axiom,
    ( ~ c_lessequals(V_x,V_y,T_a)
    | ~ c_lessequals(V_y,V_z,T_a)
    | c_lessequals(V_x,V_z,T_a)
    | ~ class_Orderings_Opreorder(T_a) ),
    file('theBenchmark.p',cls_order__trans_0) ).

cnf(cls_add__nonpos__nonpos_0,axiom,
    ( ~ 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_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
    file('theBenchmark.p',cls_add__nonpos__nonpos_0) ).

cnf(cls_xt1_I8_J_0,axiom,
    ( ~ c_lessequals(V_y,V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
    | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
    | ~ class_Orderings_Oorder(T_a) ),
    file('theBenchmark.p',cls_xt1_I8_J_0) ).

cnf(cls_xt1_I7_J_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | ~ c_lessequals(V_z,V_y,T_a)
    | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
    | ~ class_Orderings_Oorder(T_a) ),
    file('theBenchmark.p',cls_xt1_I7_J_0) ).

cnf(cls_xt1_I6_J_0,axiom,
    ( ~ c_lessequals(V_y,V_x,T_a)
    | ~ c_lessequals(V_z,V_y,T_a)
    | c_lessequals(V_z,V_x,T_a)
    | ~ class_Orderings_Oorder(T_a) ),
    file('theBenchmark.p',cls_xt1_I6_J_0) ).

cnf(cls_inverse__less__1__iff_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_x,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_inverse__less__1__iff_2) ).

cnf(cls_mod__poly__less_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_x,T_a),c_Polynomial_Odegree(V_y,T_a),tc_nat)
    | c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)) = V_x
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_mod__poly__less_0) ).

cnf(cls_add__is__1_5,axiom,
    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)),
    file('theBenchmark.p',cls_add__is__1_5) ).

cnf(cls_divide__le__eq__number__of_7,axiom,
    ( ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
    | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of_7) ).

cnf(cls_divide__le__eq__number__of_5,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of_5) ).

cnf(cls_poly__pCons_0,axiom,
    ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_poly__pCons_0) ).

cnf(cls_mod__mult__self1__is__0_0,axiom,
    ( 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)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__mult__self1__is__0_0) ).

cnf(cls_mod__mult__self2__is__0_0,axiom,
    ( 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)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__mult__self2__is__0_0) ).

cnf(cls_divide__le__eq__number__of1_9,axiom,
    ( ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__le__eq__number__of1_9) ).

cnf(cls_le__divide__eq__number__of1_9,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_le__divide__eq__number__of1_9) ).

cnf(cls_le__less__Suc__eq_0,axiom,
    ( ~ c_lessequals(V_m,V_n,tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
    | V_n = V_m ),
    file('theBenchmark.p',cls_le__less__Suc__eq_0) ).

cnf(cls_semiring__div__class_Omod__div__equality_H_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),T_a) = V_a
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_semiring__div__class_Omod__div__equality_H_0) ).

cnf(cls_sum__squares__eq__zero__iff_2,axiom,
    ( 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)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).

cnf(cls_mult__less__cancel__left__disj_1,axiom,
    ( ~ 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_b,V_a,T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).

cnf(cls_mult__less__cancel__left__disj_2,axiom,
    ( ~ 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(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).

cnf(cls_mult__less__cancel__right__disj_1,axiom,
    ( ~ 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_b,V_a,T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).

cnf(cls_mult__less__cancel__right__disj_2,axiom,
    ( ~ 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(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).

cnf(cls_monom__Suc_0,axiom,
    ( c_Polynomial_Omonom(V_a,c_Suc(V_n),T_a) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_Polynomial_Omonom(V_a,V_n,T_a),T_a)
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_monom__Suc_0) ).

cnf(cls_neg__0__less__iff__less_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_neg__0__less__iff__less_0) ).

cnf(cls_neg__0__less__iff__less_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_neg__0__less__iff__less_1) ).

cnf(cls_frac__eq__eq_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) = c_HOL_Otimes__class_Otimes(V_w,V_y,T_a)
    | V_y = c_HOL_Ozero__class_Ozero(T_a)
    | V_z = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) != c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_frac__eq__eq_0) ).

cnf(cls_frac__eq__eq_1,axiom,
    ( c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a)
    | V_y = c_HOL_Ozero__class_Ozero(T_a)
    | V_z = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) != c_HOL_Otimes__class_Otimes(V_w,V_y,T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_frac__eq__eq_1) ).

cnf(cls_poly__mod__minus__left_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_x,tc_Polynomial_Opoly(T_a)),V_y,tc_Polynomial_Opoly(T_a)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__mod__minus__left_0) ).

cnf(cls_mod__mult__mult1_0,axiom,
    ( 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)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__mult__mult1_0) ).

cnf(cls_mod__mult__mult2_0,axiom,
    ( 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)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_mod__mult__mult2_0) ).

cnf(cls_less__minus__self__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_less__minus__self__iff_0) ).

cnf(cls_less__minus__self__iff_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_less__minus__self__iff_1) ).

cnf(cls_Suc__le__mono_1,axiom,
    ( ~ c_lessequals(V_n,V_m,tc_nat)
    | c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ),
    file('theBenchmark.p',cls_Suc__le__mono_1) ).

cnf(cls_Suc__le__mono_0,axiom,
    ( ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat)
    | c_lessequals(V_n,V_m,tc_nat) ),
    file('theBenchmark.p',cls_Suc__le__mono_0) ).

cnf(cls_divide__eq__eq_4,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a),V_c,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__eq__eq_4) ).

cnf(cls_monom__eq__iff_0,axiom,
    ( V_a = V_b
    | c_Polynomial_Omonom(V_a,V_n,T_a) != c_Polynomial_Omonom(V_b,V_n,T_a)
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_monom__eq__iff_0) ).

cnf(cls_minus__add_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_minus__add_0) ).

cnf(cls_minus__add__distrib_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_minus__add__distrib_0) ).

cnf(cls_degree__smult__le_0,axiom,
    ( c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(V_a,V_p,T_a),T_a),c_Polynomial_Odegree(V_p,T_a),tc_nat)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_degree__smult__le_0) ).

cnf(cls_order__less__asym_H_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | ~ class_Orderings_Opreorder(T_a) ),
    file('theBenchmark.p',cls_order__less__asym_H_0) ).

cnf(cls_order__less__asym_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | ~ class_Orderings_Opreorder(T_a) ),
    file('theBenchmark.p',cls_order__less__asym_0) ).

cnf(cls_linorder__linear_0,axiom,
    ( c_lessequals(V_x,V_y,T_a)
    | c_lessequals(V_y,V_x,T_a)
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_linorder__linear_0) ).

cnf(cls_nat__le__linear_0,axiom,
    ( c_lessequals(V_m,V_n,tc_nat)
    | c_lessequals(V_n,V_m,tc_nat) ),
    file('theBenchmark.p',cls_nat__le__linear_0) ).

cnf(cls_not__less__iff__gr__or__eq_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

cnf(cls_xt1_I9_J_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ class_Orderings_Oorder(T_a) ),
    file('theBenchmark.p',cls_xt1_I9_J_0) ).

cnf(cls_synthetic__div__eq__0__iff_1,axiom,
    ( c_Polynomial_Osynthetic__div(V_p,V_c,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Odegree(V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_synthetic__div__eq__0__iff_1) ).

cnf(cls_synthetic__div__eq__0__iff_0,axiom,
    ( c_Polynomial_Odegree(V_p,T_a) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Polynomial_Osynthetic__div(V_p,V_c,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_synthetic__div__eq__0__iff_0) ).

cnf(cls_pdivmod__rel__def_2,axiom,
    ( ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q,V_r,T_a)
    | V_y = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | V_r = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_r,T_a),c_Polynomial_Odegree(V_y,T_a),tc_nat)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_pdivmod__rel__def_2) ).

cnf(cls_degree__mult__eq_0,axiom,
    ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_degree__mult__eq_0) ).

cnf(cls_degree__pCons__0_0,axiom,
    ( c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_degree__pCons__0_0) ).

cnf(cls_div__poly__less_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_x,T_a),c_Polynomial_Odegree(V_y,T_a),tc_nat)
    | c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_div__poly__less_0) ).

cnf(cls_psize__def_1,axiom,
    ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(V_p,T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a))
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_psize__def_1) ).

cnf(cls_order__degree_0,axiom,
    ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_lessequals(c_Polynomial_Oorder(V_a,V_p,T_a),c_Polynomial_Odegree(V_p,T_a),tc_nat)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_order__degree_0) ).

cnf(cls_degree__pCons__eq_0,axiom,
    ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a))
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_degree__pCons__eq_0) ).

cnf(cls_degree__mod__less_0,axiom,
    ( V_y = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)),T_a),c_Polynomial_Odegree(V_y,T_a),tc_nat)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_degree__mod__less_0) ).

cnf(cls_poly__monom_0,axiom,
    ( c_Polynomial_Opoly(c_Polynomial_Omonom(V_a,V_n,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_poly__monom_0) ).

cnf(cls_degree__minus_0,axiom,
    ( c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(V_p,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_p,T_a)
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_degree__minus_0) ).

cnf(cls_degree__offset__poly_0,axiom,
    ( c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a) = c_Polynomial_Odegree(V_p,T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_degree__offset__poly_0) ).

cnf(cls_id__def_0,axiom,
    c_Fun_Oid(v_x,t_a) = v_x,
    file('theBenchmark.p',cls_id__def_0) ).

cnf(cls_poly__gcd__greatest_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_x,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_y,tc_Polynomial_Opoly(T_a))
    | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Polynomial_Opoly__gcd(V_x,V_y,T_a),tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__greatest_0) ).

cnf(cls_dvd__poly__gcd__iff_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_x,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_y,tc_Polynomial_Opoly(T_a))
    | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Polynomial_Opoly__gcd(V_x,V_y,T_a),tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_dvd__poly__gcd__iff_2) ).

cnf(cls_poly__gcd__dvd1_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(V_x,V_y,T_a),V_x,tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__dvd1_0) ).

cnf(cls_poly__gcd__dvd2_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(V_x,V_y,T_a),V_y,tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__dvd2_0) ).

cnf(cls_dvd__poly__gcd__iff_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Polynomial_Opoly__gcd(V_x,V_y,T_a),tc_Polynomial_Opoly(T_a))
    | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_y,tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_dvd__poly__gcd__iff_1) ).

cnf(cls_dvd__poly__gcd__iff_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Polynomial_Opoly__gcd(V_x,V_y,T_a),tc_Polynomial_Opoly(T_a))
    | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_x,tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_dvd__poly__gcd__iff_0) ).

cnf(cls_smult__dvd__cancel_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a))
    | c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_smult__dvd__cancel_0) ).

cnf(cls_dvd__smult_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
    | c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_dvd__smult_0) ).

cnf(cls_poly__pcompose_0,axiom,
    ( c_Polynomial_Opoly(c_Polynomial_Opcompose(V_p,V_q,T_a),V_x,T_a) = c_Polynomial_Opoly(V_p,c_Polynomial_Opoly(V_q,V_x,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_poly__pcompose_0) ).

cnf(cls_degree__power__le_0,axiom,
    ( c_lessequals(c_Polynomial_Odegree(c_Power_Opower__class_Opower(V_p,V_n,tc_Polynomial_Opoly(T_a)),T_a),c_HOL_Otimes__class_Otimes(c_Polynomial_Odegree(V_p,T_a),V_n,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_degree__power__le_0) ).

cnf(cls_complex__i__not__zero_0,axiom,
    c_Complex_Oii != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    file('theBenchmark.p',cls_complex__i__not__zero_0) ).

cnf(cls_complex__cnj__zero__iff_0,axiom,
    ( V_z = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | c_Complex_Ocnj(V_z) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    file('theBenchmark.p',cls_complex__cnj__zero__iff_0) ).

cnf(cls_cnj_Ozero_0,axiom,
    c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    file('theBenchmark.p',cls_cnj_Ozero_0) ).

cnf(cls_fundamental__theorem__of__algebra__alt_0,axiom,
    ( c_Polynomial_Opoly(V_p,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(V_p),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(V_p) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    file('theBenchmark.p',cls_fundamental__theorem__of__algebra__alt_0) ).

cnf(cls_poly__gcd__unique_10,axiom,
    ( c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = V_d
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(V_d,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),V_d,tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Ocoeff(V_d,c_Polynomial_Odegree(V_d,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__unique_10) ).

cnf(cls_poly__gcd__unique_2,axiom,
    ( c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = V_d
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))
    | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(V_d,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Ocoeff(V_d,c_Polynomial_Odegree(V_d,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__unique_2) ).

cnf(cls_poly__eq__0__iff__dvd_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(V_c,T_a),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_p,tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Opoly(V_p,V_c,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_poly__eq__0__iff__dvd_1) ).

cnf(cls_poly__eq__0__iff__dvd_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(V_c,T_a),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_p,tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Opoly(V_p,V_c,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_poly__eq__0__iff__dvd_0) ).

cnf(cls_dvd__iff__poly__eq__0_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(V_c,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_p,tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Opoly(V_p,c_HOL_Ouminus__class_Ouminus(V_c,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_dvd__iff__poly__eq__0_1) ).

cnf(cls_dvd__iff__poly__eq__0_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(V_c,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_p,tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Opoly(V_p,c_HOL_Ouminus__class_Ouminus(V_c,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_dvd__iff__poly__eq__0_0) ).

cnf(cls_fundamental__theorem__of__algebra__alt_1,axiom,
    ( V_p = c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(V_p),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
    | c_Polynomial_Opoly(V_p,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(V_p),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    file('theBenchmark.p',cls_fundamental__theorem__of__algebra__alt_1) ).

cnf(cls_poly__gcd__monic_0,axiom,
    ( c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_poly__gcd__monic_0) ).

cnf(cls_order__root_0,axiom,
    ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_order__root_0) ).

cnf(cls_degree__linear__power_0,axiom,
    ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(V_a,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_n,tc_Polynomial_Opoly(T_a)),T_a) = V_n
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_degree__linear__power_0) ).

cnf(cls_dvd__eq__mod__eq__0_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
    | c_Divides_Odiv__class_Omod(V_b,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).

cnf(cls_dvd__imp__mod__0_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
    | c_Divides_Odiv__class_Omod(V_b,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_dvd__imp__mod__0_0) ).

cnf(cls_dvd__mult__cancel__right_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a),T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_dvd__mult__cancel__right_1) ).

cnf(cls_dvd__mult__cancel__left_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_dvd__mult__cancel__left_1) ).

cnf(cls_dvd__mult__cancel__right_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
    | V_c = c_HOL_Ozero__class_Ozero(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_dvd__mult__cancel__right_0) ).

cnf(cls_dvd__mult__cancel__left_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
    | V_c = c_HOL_Ozero__class_Ozero(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_dvd__mult__cancel__left_0) ).

cnf(cls_nonzero__power__divide_0,axiom,
    ( V_b = c_HOL_Ozero__class_Ozero(T_a)
    | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_nonzero__power__divide_0) ).

cnf(cls_nonzero__power__inverse_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a)
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_nonzero__power__inverse_0) ).

cnf(cls_zero__less__power_0,axiom,
    ( ~ 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_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_zero__less__power_0) ).

cnf(cls_zero__le__power_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_zero__le__power_0) ).

cnf(cls_zero__le__power__iff_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__le__power__iff_1) ).

cnf(cls_power__0__left_1,axiom,
    ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Power_Opower(T_a)
    | ~ class_Ring__and__Field_Osemiring__0(T_a) ),
    file('theBenchmark.p',cls_power__0__left_1) ).

cnf(cls_power__eq__0__iff_2,axiom,
    ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Power_Opower(T_a)
    | ~ class_Ring__and__Field_Omult__zero(T_a)
    | ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
    | ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
    file('theBenchmark.p',cls_power__eq__0__iff_2) ).

cnf(cls_power__0__Suc_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Suc(V_n),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Power_Opower(T_a)
    | ~ class_Ring__and__Field_Osemiring__0(T_a) ),
    file('theBenchmark.p',cls_power__0__Suc_0) ).

cnf(cls_power__eq__0__iff_1,axiom,
    ( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Power_Opower(T_a)
    | ~ class_Ring__and__Field_Omult__zero(T_a)
    | ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
    | ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
    file('theBenchmark.p',cls_power__eq__0__iff_1) ).

cnf(cls_power__mono_0,axiom,
    ( ~ c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_lessequals(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power__mono_0) ).

cnf(cls_power__less__zero__eq_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__less__zero__eq_1) ).

cnf(cls_power__le__zero__eq_3,axiom,
    ( ~ c_lessequals(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | V_x = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__le__zero__eq_3) ).

cnf(cls_power__eq__0__iff__number__of_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Power_Opower(T_a)
    | ~ class_Ring__and__Field_Omult__zero(T_a)
    | ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
    | ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
    file('theBenchmark.p',cls_power__eq__0__iff__number__of_0) ).

cnf(cls_power__le__dvd_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_b,T_a)
    | ~ c_lessequals(V_m,V_n,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_b,T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_power__le__dvd_0) ).

cnf(cls_dvd__power__le_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a)
    | ~ c_lessequals(V_n,V_m,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_m,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_dvd__power__le_0) ).

cnf(cls_div__power_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a)
    | c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),V_n,T_a) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a)
    | ~ class_Divides_Osemiring__div(T_a) ),
    file('theBenchmark.p',cls_div__power_0) ).

cnf(cls_le__imp__power__dvd_0,axiom,
    ( ~ c_lessequals(V_m,V_n,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_le__imp__power__dvd_0) ).

cnf(cls_dvd__power_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_dvd__power_1) ).

cnf(cls_smult__0__left_0,axiom,
    ( c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(T_a),V_p,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_smult__0__left_0) ).

cnf(cls_smult__eq__0__iff_1,axiom,
    ( c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(T_a),V_p,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_smult__eq__0__iff_1) ).

cnf(cls_pCons__eq__0__iff_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_pCons__eq__0__iff_0) ).

cnf(cls_smult__eq__0__iff_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Osmult(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_smult__eq__0__iff_0) ).

cnf(cls_pCons__0__0_0,axiom,
    ( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_pCons__0__0_0) ).

cnf(cls_monom__eq__0__iff_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_Polynomial_Omonom(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_monom__eq__0__iff_0) ).

cnf(cls_monom__eq__0_0,axiom,
    ( c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_monom__eq__0_0) ).

cnf(cls_coeff__0_0,axiom,
    ( c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_coeff__0_0) ).

cnf(cls_degree__monom__eq_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_Polynomial_Odegree(c_Polynomial_Omonom(V_a,V_n,T_a),T_a) = V_n
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_degree__monom__eq_0) ).

cnf(cls_degree__smult__eq_1,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_Polynomial_Odegree(c_Polynomial_Osmult(V_a,V_p,T_a),T_a) = c_Polynomial_Odegree(V_p,T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_degree__smult__eq_1) ).

cnf(cls_dvd__smult__cancel_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))
    | V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_dvd__smult__cancel_0) ).

cnf(cls_smult__dvd_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
    | V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_smult__dvd_0) ).

cnf(cls_dvd__smult__iff_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))
    | c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_dvd__smult__iff_0) ).

cnf(cls_dvd__smult__iff_1,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
    | c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_dvd__smult__iff_1) ).

cnf(cls_smult__dvd__iff_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a))
    | V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_smult__dvd__iff_1) ).

cnf(cls_smult__dvd__iff_2,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
    | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_smult__dvd__iff_2) ).

cnf(cls_poly__decompose__lemma_0,axiom,
    ( V_z = c_HOL_Ozero__class_Ozero(t_a)
    | c_Polynomial_Opoly(V_p,V_z,t_a) = c_HOL_Ozero__class_Ozero(t_a)
    | v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(V_p) != c_HOL_Ozero__class_Ozero(t_a)
    | ~ class_Ring__and__Field_Oidom(t_a) ),
    file('theBenchmark.p',cls_poly__decompose__lemma_0) ).

cnf(cls_degree__0_0,axiom,
    ( c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_degree__0_0) ).

cnf(cls_smult__dvd__iff_4,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))
    | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(V_a,V_p,T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_smult__dvd__iff_4) ).

cnf(cls_poly__dvd__antisym_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_q,V_p,tc_Polynomial_Opoly(T_a))
    | V_p = V_q
    | c_Polynomial_Ocoeff(V_p,c_Polynomial_Odegree(V_p,T_a),T_a) != c_Polynomial_Ocoeff(V_q,c_Polynomial_Odegree(V_q,T_a),T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_poly__dvd__antisym_0) ).

cnf(cls_leading__coeff__0__iff_1,axiom,
    ( c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_leading__coeff__0__iff_1) ).

cnf(cls_leading__coeff__0__iff_0,axiom,
    ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Ocoeff(V_p,c_Polynomial_Odegree(V_p,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_HOL_Ozero(T_a) ),
    file('theBenchmark.p',cls_leading__coeff__0__iff_0) ).

cnf(cls_smult__dvd__iff_0,axiom,
    ( V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(T_a),V_p,T_a),V_q,tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_smult__dvd__iff_0) ).

cnf(cls_smult__dvd__iff_3,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(T_a),V_p,T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_smult__dvd__iff_3) ).

cnf(cls_dvd__imp__degree__le_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
    | V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_dvd__imp__degree__le_0) ).

cnf(cls_nullstellensatz__lemma_1,axiom,
    ( c_Polynomial_Odegree(V_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Power_Opower__class_Opower(V_q,c_Polynomial_Odegree(V_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | c_Polynomial_Opoly(V_q,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(V_p,V_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    file('theBenchmark.p',cls_nullstellensatz__lemma_1) ).

cnf(cls_nullstellensatz__lemma_0,axiom,
    ( c_Polynomial_Odegree(V_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Power_Opower__class_Opower(V_q,c_Polynomial_Odegree(V_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | c_Polynomial_Opoly(V_p,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(V_p,V_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    file('theBenchmark.p',cls_nullstellensatz__lemma_0) ).

cnf(cls_dvd__0__right_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_dvd__0__right_0) ).

cnf(cls_dvd__0__left_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_dvd__0__left_0) ).

cnf(cls_poly__0_0,axiom,
    ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
    file('theBenchmark.p',cls_poly__0_0) ).

cnf(cls_order__root_1,axiom,
    ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_order__root_1) ).

cnf(cls_field__power__not__zero_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oring__1__no__zero__divisors(T_a) ),
    file('theBenchmark.p',cls_field__power__not__zero_0) ).

cnf(cls_power__eq__0__iff_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Power_Opower(T_a)
    | ~ class_Ring__and__Field_Omult__zero(T_a)
    | ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
    | ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
    file('theBenchmark.p',cls_power__eq__0__iff_0) ).

cnf(cls_dvd__trans_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_dvd__trans_0) ).

cnf(cls_dvd__refl_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(V_a,V_a,T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_dvd__refl_0) ).

cnf(cls_pe_0,axiom,
    v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    file('theBenchmark.p',cls_pe_0) ).

cnf(cls_poly__power_0,axiom,
    ( c_Polynomial_Opoly(c_Power_Opower__class_Opower(V_p,V_n,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(V_p,V_x,T_a),V_n,T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_poly__power_0) ).

cnf(cls_dvd__power__same_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_dvd__power__same_0) ).

cnf(cls_CHAINED_5,axiom,
    ( c_Polynomial_Opoly(v_q,V_xa,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
    | v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | c_Polynomial_Opoly(v_p,V_xa,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    file('theBenchmark.p',cls_CHAINED_5) ).

cnf(cls_CHAINED_4,axiom,
    ( c_Polynomial_Opoly(v_q,V_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | c_Polynomial_Opoly(v_p,V_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    file('theBenchmark.p',cls_CHAINED_4) ).

cnf(cls_CHAINED_3,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    file('theBenchmark.p',cls_CHAINED_3) ).

cnf(cls_CHAINED_2,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    file('theBenchmark.p',cls_CHAINED_2) ).

cnf(cls_CHAINED_1,axiom,
    ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    file('theBenchmark.p',cls_CHAINED_1) ).

cnf(cls_CHAINED_0,axiom,
    ( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    file('theBenchmark.p',cls_CHAINED_0) ).

cnf(cls_CHAINED_5_01,axiom,
    ( c_Polynomial_Opoly(v_q,V_xa,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
    | v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | c_Polynomial_Opoly(v_p,V_xa,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    file('theBenchmark.p',cls_CHAINED_5_01) ).

cnf(cls_CHAINED_4_02,axiom,
    ( c_Polynomial_Opoly(v_q,V_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | c_Polynomial_Opoly(v_p,V_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    file('theBenchmark.p',cls_CHAINED_4_02) ).

cnf(cls_CHAINED_3_03,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    file('theBenchmark.p',cls_CHAINED_3_03) ).

cnf(cls_CHAINED_2_04,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Polynomial_Opoly(v_q,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    file('theBenchmark.p',cls_CHAINED_2_04) ).

cnf(cls_CHAINED_1_05,axiom,
    ( c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('theBenchmark.p',cls_CHAINED_1_05) ).

cnf(cls_CHAINED_0_06,axiom,
    ( c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_p,v_q),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('theBenchmark.p',cls_CHAINED_0_06) ).

cnf(cls_conjecture_0,negated_conjecture,
    ( c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    file('theBenchmark.p',cls_conjecture_0) ).

cnf(cls_conjecture_1,negated_conjecture,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    file('theBenchmark.p',cls_conjecture_1) ).

cnf(cls_conjecture_2,negated_conjecture,
    ( c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    file('theBenchmark.p',cls_conjecture_2) ).

cnf(cls_conjecture_3,negated_conjecture,
    ( c_Polynomial_Opoly(v_q,v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    file('theBenchmark.p',cls_conjecture_3) ).

cnf(cls_conjecture_4,negated_conjecture,
    ( c_Polynomial_Opoly(v_q,V_xa,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | c_Polynomial_Opoly(v_p,V_xa,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    file('theBenchmark.p',cls_conjecture_4) ).

cnf(cls_conjecture_5,negated_conjecture,
    ( c_Polynomial_Opoly(v_q,V_xb,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Power_Opower__class_Opower(v_q,c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | v_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | c_Polynomial_Opoly(v_p,V_xb,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    file('theBenchmark.p',cls_conjecture_5) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add,axiom,
    ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(T_1)
    | class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add,axiom,
    class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).

cnf(clsarity_Int__Oint__OrderedGroup_Ocancel__comm__monoid__add,axiom,
    class_OrderedGroup_Ocancel__comm__monoid__add(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__comm__monoid__add) ).

cnf(clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add,axiom,
    class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
    file('theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add) ).

cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    file('theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    file('theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    file('theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).

cnf(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    file('theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).

cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    file('theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).

cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    file('theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    file('theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    file('theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

cnf(clsarity_nat__Ring__and__Field_Opordered__semiring,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    file('theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).

cnf(clsarity_nat__Ring__and__Field_Oordered__semiring,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_nat),
    file('theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).

cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    file('theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).

cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    file('theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    file('theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__0,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
    file('theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__0) ).

cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    file('theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    file('theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).

cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    file('theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    file('theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat),
    file('theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).

cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    file('theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).

cnf(clsarity_nat__Ring__and__Field_Omult__mono1,axiom,
    class_Ring__and__Field_Omult__mono1(tc_nat),
    file('theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).

cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    file('theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

cnf(clsarity_nat__Ring__and__Field_Omult__mono,axiom,
    class_Ring__and__Field_Omult__mono(tc_nat),
    file('theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).

cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    file('theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).

cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    file('theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    file('theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

cnf(clsarity_nat__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_nat),
    file('theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).

cnf(clsarity_nat__Ring__and__Field_Odvd,axiom,
    class_Ring__and__Field_Odvd(tc_nat),
    file('theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).

cnf(clsarity_nat__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

cnf(clsarity_nat__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

cnf(clsarity_nat__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_nat),
    file('theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

cnf(clsarity_nat__Power_Opower,axiom,
    class_Power_Opower(tc_nat),
    file('theBenchmark.p',clsarity_nat__Power_Opower) ).

cnf(clsarity_nat__Int_Onumber,axiom,
    class_Int_Onumber(tc_nat),
    file('theBenchmark.p',clsarity_nat__Int_Onumber) ).

cnf(clsarity_nat__HOL_Ozero,axiom,
    class_HOL_Ozero(tc_nat),
    file('theBenchmark.p',clsarity_nat__HOL_Ozero) ).

cnf(clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
    class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) ).

cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).

cnf(clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors,axiom,
    class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) ).

cnf(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict,axiom,
    class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) ).

cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).

cnf(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add,axiom,
    class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).

cnf(clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add,axiom,
    class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add) ).

cnf(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__0,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__0) ).

cnf(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) ).

cnf(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) ).

cnf(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__ring,axiom,
    class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) ).

cnf(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__idom,axiom,
    class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1,axiom,
    class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Osemiring__0,axiom,
    class_Ring__and__Field_Osemiring__0(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Omult__mono1,axiom,
    class_Ring__and__Field_Omult__mono1(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono1) ).

cnf(clsarity_Int__Oint__OrderedGroup_Oab__group__add,axiom,
    class_OrderedGroup_Oab__group__add(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Omult__zero,axiom,
    class_Ring__and__Field_Omult__zero(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Omult__mono,axiom,
    class_Ring__and__Field_Omult__mono(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__ring,axiom,
    class_Ring__and__Field_Ocomm__ring(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring) ).

cnf(clsarity_Int__Oint__OrderedGroup_Omonoid__mult,axiom,
    class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Osemiring,axiom,
    class_Ring__and__Field_Osemiring(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring) ).

cnf(clsarity_Int__Oint__OrderedGroup_Omonoid__add,axiom,
    class_OrderedGroup_Omonoid__add(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).

cnf(clsarity_Int__Oint__OrderedGroup_Ogroup__add,axiom,
    class_OrderedGroup_Ogroup__add(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Oring__1,axiom,
    class_Ring__and__Field_Oring__1(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1) ).

cnf(clsarity_Int__Oint__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Divides_Osemiring__div) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Oring,axiom,
    class_Ring__and__Field_Oring(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Oidom,axiom,
    class_Ring__and__Field_Oidom(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Odvd,axiom,
    class_Ring__and__Field_Odvd(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Odvd) ).

cnf(clsarity_Int__Oint__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).

cnf(clsarity_Int__Oint__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).

cnf(clsarity_Int__Oint__Divides_Oring__div,axiom,
    class_Divides_Oring__div(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Divides_Oring__div) ).

cnf(clsarity_Int__Oint__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).

cnf(clsarity_Int__Oint__Int_Oring__char__0,axiom,
    class_Int_Oring__char__0(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).

cnf(clsarity_Int__Oint__Int_Onumber__ring,axiom,
    class_Int_Onumber__ring(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).

cnf(clsarity_Int__Oint__Power_Opower,axiom,
    class_Power_Opower(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).

cnf(clsarity_Int__Oint__Int_Onumber,axiom,
    class_Int_Onumber(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).

cnf(clsarity_Int__Oint__HOL_Ozero,axiom,
    class_HOL_Ozero(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__HOL_Ozero) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
    class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,axiom,
    class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom,
    class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).

cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring,axiom,
    class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).

cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
    class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,axiom,
    class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0,axiom,
    class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,axiom,
    class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,axiom,
    class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring,axiom,
    class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
    class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring,axiom,
    class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add,axiom,
    class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
    class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1,axiom,
    class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
    class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring,axiom,
    class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
    class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odvd,axiom,
    class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).

cnf(clsarity_Complex__Ocomplex__Int_Oring__char__0,axiom,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).

cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).

cnf(clsarity_Complex__Ocomplex__Power_Opower,axiom,
    class_Power_Opower(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).

cnf(clsarity_Complex__Ocomplex__Int_Onumber,axiom,
    class_Int_Onumber(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber) ).

cnf(clsarity_Complex__Ocomplex__HOL_Ozero,axiom,
    class_HOL_Ozero(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_1)
    | class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_1)
    | class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
    ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(T_1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add,axiom,
    ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(T_1)
    | class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_1)
    | class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_1)
    | class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_1)
    | class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_1)
    | class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_1)
    | class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_1)
    | class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_1)
    | class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_1)
    | class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_1)
    | class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(T_1)
    | class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_1)
    | class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__0) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_1)
    | class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_1)
    | class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(T_1)
    | class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_1)
    | class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_1)
    | class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_1)
    | class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_1)
    | class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(T_1)
    | class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1) ).

cnf(clsarity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_1)
    | class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Osemiring__div) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(T_1)
    | class_Ring__and__Field_Oring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oidom,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_1)
    | class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Odvd,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_1)
    | class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) ).

cnf(clsarity_Polynomial__Opoly__Orderings_Opreorder,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Opreorder) ).

cnf(clsarity_Polynomial__Opoly__Orderings_Olinorder,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Olinorder) ).

cnf(clsarity_Polynomial__Opoly__Divides_Oring__div,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_1)
    | class_Divides_Oring__div(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Oring__div) ).

cnf(clsarity_Polynomial__Opoly__Orderings_Oorder,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Oorder) ).

cnf(clsarity_Polynomial__Opoly__Int_Oring__char__0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_1)
    | class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Int_Oring__char__0) ).

cnf(clsarity_Polynomial__Opoly__Int_Onumber__ring,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(T_1)
    | class_Int_Onumber__ring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).

cnf(clsarity_Polynomial__Opoly__Power_Opower,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_1)
    | class_Power_Opower(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Power_Opower) ).

cnf(clsarity_Polynomial__Opoly__Int_Onumber,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(T_1)
    | class_Int_Onumber(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber) ).

cnf(clsarity_Polynomial__Opoly__HOL_Ozero,axiom,
    ( ~ class_HOL_Ozero(T_1)
    | class_HOL_Ozero(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Ozero) ).

cnf(cls_add__nonneg__eq__0__iff_2_simplified,plain,
    ( 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)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
    inference(simplify_clause,[status(thm)],[cls_add__nonneg__eq__0__iff_2]) ).

cnf(cls_poly__gcd__unique_10_simplified,plain,
    ( c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = V_d
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(V_d,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),V_d,tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Ocoeff(V_d,c_Polynomial_Odegree(V_d,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    inference(simplify_clause,[status(thm)],[cls_poly__gcd__unique_10]) ).

cnf(cls_poly__gcd__unique_2_simplified,plain,
    ( c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = V_d
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))
    | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(V_d,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Ocoeff(V_d,c_Polynomial_Odegree(V_d,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    inference(simplify_clause,[status(thm)],[cls_poly__gcd__unique_2]) ).

cnf(equality_1,axiom,
    Eq_x_0 = Eq_x_0,
    theory(equality,[reflexivity]) ).

cnf(equality_2,axiom,
    ( Eq_x_1 = Eq_x_0
    | Eq_x_0 != Eq_x_1 ),
    theory(equality,[symmetry]) ).

cnf(equality_3,axiom,
    ( Eq_x_0 = Eq_x_2
    | Eq_x_1 != Eq_x_2
    | Eq_x_0 != Eq_x_1 ),
    theory(equality,[transitivity]) ).

cnf(equality_4,axiom,
    ( c_HOL_Oinverse__class_Odivide(Eq_x_0,Eq_x_1,Eq_x_2) = c_HOL_Oinverse__class_Odivide(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_5,axiom,
    ( c_Int_Onumber__class_Onumber__of(Eq_x_0,Eq_x_1) = c_Int_Onumber__class_Onumber__of(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_6,axiom,
    ( c_HOL_Ozero__class_Ozero(Eq_x_0) = c_HOL_Ozero__class_Ozero(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_7,axiom,
    ( c_HOL_Oone__class_Oone(Eq_x_0) = c_HOL_Oone__class_Oone(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_8,axiom,
    ( c_HOL_Oinverse__class_Oinverse(Eq_x_0,Eq_x_1) = c_HOL_Oinverse__class_Oinverse(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_9,axiom,
    ( c_Divides_Odiv__class_Odiv(Eq_x_0,Eq_x_1,Eq_x_2) = c_Divides_Odiv__class_Odiv(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_10,axiom,
    ( c_HOL_Otimes__class_Otimes(Eq_x_0,Eq_x_1,Eq_x_2) = c_HOL_Otimes__class_Otimes(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_11,axiom,
    ( c_HOL_Ouminus__class_Ouminus(Eq_x_0,Eq_x_1) = c_HOL_Ouminus__class_Ouminus(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_12,axiom,
    ( c_Power_Opower__class_Opower(Eq_x_0,Eq_x_1,Eq_x_2) = c_Power_Opower__class_Opower(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_13,axiom,
    ( c_HOL_Oplus__class_Oplus(Eq_x_0,Eq_x_1,Eq_x_2) = c_HOL_Oplus__class_Oplus(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_14,axiom,
    ( c_Divides_Odiv__class_Omod(Eq_x_0,Eq_x_1,Eq_x_2) = c_Divides_Odiv__class_Omod(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_15,axiom,
    ( c_Polynomial_OpCons(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_OpCons(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_16,axiom,
    ( c_Suc(Eq_x_0) = c_Suc(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_17,axiom,
    ( c_Polynomial_Osmult(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Osmult(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_18,axiom,
    ( tc_Polynomial_Opoly(Eq_x_0) = tc_Polynomial_Opoly(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_19,axiom,
    ( c_Polynomial_Osynthetic__div(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Osynthetic__div(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_20,axiom,
    ( c_Polynomial_Opoly(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Opoly(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_21,axiom,
    ( c_Polynomial_Omonom(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Omonom(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_22,axiom,
    ( c_Polynomial_Ocoeff(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Ocoeff(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_23,axiom,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(Eq_x_0,Eq_x_1,Eq_x_2) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_24,axiom,
    ( c_Polynomial_Oorder(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Oorder(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_25,axiom,
    ( c_Polynomial_Opoly__gcd(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Opoly__gcd(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_26,axiom,
    ( c_Polynomial_Odegree(Eq_x_0,Eq_x_1) = c_Polynomial_Odegree(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_27,axiom,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(Eq_x_0,Eq_x_1) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_28,axiom,
    ( c_Complex_Ocnj(Eq_x_0) = c_Complex_Ocnj(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_29,axiom,
    ( c_Fun_Oid(Eq_x_0,Eq_x_1) = c_Fun_Oid(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_30,axiom,
    ( c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Polynomial_Osko__Polynomial__Xpoly__gcd__unique__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_31,axiom,
    ( c_Polynomial_Opcompose(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Opcompose(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_32,axiom,
    ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(Eq_x_0) = v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_33,axiom,
    ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(Eq_x_0) = v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_34,axiom,
    ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(Eq_x_0) = v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_35,axiom,
    ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(Eq_x_0,Eq_x_1) = v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xnullstellensatz__lemma__1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_36,axiom,
    ( v_sko__CHAINED__1(Eq_x_0,Eq_x_1) = v_sko__CHAINED__1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_37,axiom,
    ( class_Ring__and__Field_Oordered__field(Eq_y_0)
    | ~ class_Ring__and__Field_Oordered__field(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_38,axiom,
    ( class_Ring__and__Field_Odivision__by__zero(Eq_y_0)
    | ~ class_Ring__and__Field_Odivision__by__zero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_39,axiom,
    ( class_Int_Onumber(Eq_y_0)
    | ~ class_Int_Onumber(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_40,axiom,
    ( c_lessequals(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_lessequals(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_41,axiom,
    ( c_HOL_Oord__class_Oless(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_HOL_Oord__class_Oless(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_42,axiom,
    ( class_Divides_Osemiring__div(Eq_y_0)
    | ~ class_Divides_Osemiring__div(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_43,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_44,axiom,
    ( class_Ring__and__Field_Ofield(Eq_y_0)
    | ~ class_Ring__and__Field_Ofield(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_45,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(Eq_y_0)
    | ~ class_OrderedGroup_Opordered__ab__group__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_46,axiom,
    ( class_Power_Opower(Eq_y_0)
    | ~ class_Power_Opower(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_47,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(Eq_y_0)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_48,axiom,
    ( class_Ring__and__Field_Oordered__ring__strict(Eq_y_0)
    | ~ class_Ring__and__Field_Oordered__ring__strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_49,axiom,
    ( class_Ring__and__Field_Oordered__semiring__strict(Eq_y_0)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_50,axiom,
    ( class_OrderedGroup_Ogroup__add(Eq_y_0)
    | ~ class_OrderedGroup_Ogroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_51,axiom,
    ( class_HOL_Ozero(Eq_y_0)
    | ~ class_HOL_Ozero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_52,axiom,
    ( class_Ring__and__Field_Oordered__semidom(Eq_y_0)
    | ~ class_Ring__and__Field_Oordered__semidom(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_53,axiom,
    ( class_Ring__and__Field_Omult__mono1(Eq_y_0)
    | ~ class_Ring__and__Field_Omult__mono1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_54,axiom,
    ( class_Ring__and__Field_Omult__mono(Eq_y_0)
    | ~ class_Ring__and__Field_Omult__mono(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_55,axiom,
    ( class_Ring__and__Field_Opordered__ring(Eq_y_0)
    | ~ class_Ring__and__Field_Opordered__ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_56,axiom,
    ( class_Ring__and__Field_Oidom(Eq_y_0)
    | ~ class_Ring__and__Field_Oidom(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_57,axiom,
    ( class_Int_Onumber__ring(Eq_y_0)
    | ~ class_Int_Onumber__ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_58,axiom,
    ( class_Ring__and__Field_Odivision__ring(Eq_y_0)
    | ~ class_Ring__and__Field_Odivision__ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_59,axiom,
    ( class_Ring__and__Field_Osemiring__0(Eq_y_0)
    | ~ class_Ring__and__Field_Osemiring__0(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_60,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(Eq_y_0)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_61,axiom,
    ( class_OrderedGroup_Oab__semigroup__idem__mult(Eq_y_0)
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_62,axiom,
    ( class_OrderedGroup_Olordered__ab__group__add(Eq_y_0)
    | ~ class_OrderedGroup_Olordered__ab__group__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_63,axiom,
    ( class_Ring__and__Field_Oring(Eq_y_0)
    | ~ class_Ring__and__Field_Oring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_64,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(Eq_y_0)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_65,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(Eq_y_0)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_66,axiom,
    ( class_Ring__and__Field_Oordered__idom(Eq_y_0)
    | ~ class_Ring__and__Field_Oordered__idom(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_67,axiom,
    ( class_Orderings_Olinorder(Eq_y_0)
    | ~ class_Orderings_Olinorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_68,axiom,
    ( c_Polynomial_Opdivmod__rel(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ c_Polynomial_Opdivmod__rel(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_69,axiom,
    ( class_Orderings_Oorder(Eq_y_0)
    | ~ class_Orderings_Oorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_70,axiom,
    ( class_Lattices_Oboolean__algebra(Eq_y_0)
    | ~ class_Lattices_Oboolean__algebra(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_71,axiom,
    ( class_OrderedGroup_Opordered__comm__monoid__add(Eq_y_0)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_72,axiom,
    ( class_Ring__and__Field_Oordered__semiring(Eq_y_0)
    | ~ class_Ring__and__Field_Oordered__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_73,axiom,
    ( class_OrderedGroup_Oab__group__add(Eq_y_0)
    | ~ class_OrderedGroup_Oab__group__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_74,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(Eq_y_0)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_75,axiom,
    ( class_Divides_Oring__div(Eq_y_0)
    | ~ class_Divides_Oring__div(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_76,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(Eq_y_0)
    | ~ class_OrderedGroup_Oab__semigroup__mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_77,axiom,
    ( class_RealVector_Oreal__normed__algebra(Eq_y_0)
    | ~ class_RealVector_Oreal__normed__algebra(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_78,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(Eq_y_0)
    | ~ class_Ring__and__Field_Ocomm__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_79,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(Eq_y_0)
    | ~ class_OrderedGroup_Ocomm__monoid__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_80,axiom,
    ( class_OrderedGroup_Omonoid__mult(Eq_y_0)
    | ~ class_OrderedGroup_Omonoid__mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_81,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(Eq_y_0)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_82,axiom,
    ( class_Ring__and__Field_Ocomm__ring__1(Eq_y_0)
    | ~ class_Ring__and__Field_Ocomm__ring__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_83,axiom,
    ( class_Orderings_Opreorder(Eq_y_0)
    | ~ class_Orderings_Opreorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_84,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(Eq_y_0)
    | ~ class_OrderedGroup_Oab__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_85,axiom,
    ( class_Ring__and__Field_Opordered__semiring(Eq_y_0)
    | ~ class_Ring__and__Field_Opordered__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_86,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(Eq_y_0)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_87,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(Eq_y_0)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_88,axiom,
    ( class_Ring__and__Field_Osemiring(Eq_y_0)
    | ~ class_Ring__and__Field_Osemiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_89,axiom,
    ( class_Int_Oring__char__0(Eq_y_0)
    | ~ class_Int_Oring__char__0(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_90,axiom,
    ( class_RealVector_Oreal__normed__field(Eq_y_0)
    | ~ class_RealVector_Oreal__normed__field(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_91,axiom,
    ( class_Ring__and__Field_Ocomm__ring(Eq_y_0)
    | ~ class_Ring__and__Field_Ocomm__ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_92,axiom,
    ( class_OrderedGroup_Oordered__ab__group__add(Eq_y_0)
    | ~ class_OrderedGroup_Oordered__ab__group__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_93,axiom,
    ( class_Ring__and__Field_Oring__1(Eq_y_0)
    | ~ class_Ring__and__Field_Oring__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_94,axiom,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(Eq_y_0)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_95,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(Eq_y_0)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_96,axiom,
    ( class_Ring__and__Field_Oring__no__zero__divisors(Eq_y_0)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_97,axiom,
    ( class_Ring__and__Field_Omult__zero(Eq_y_0)
    | ~ class_Ring__and__Field_Omult__zero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_98,axiom,
    ( class_Ring__and__Field_Ozero__neq__one(Eq_y_0)
    | ~ class_Ring__and__Field_Ozero__neq__one(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_99,axiom,
    ( class_Ring__and__Field_Ono__zero__divisors(Eq_y_0)
    | ~ class_Ring__and__Field_Ono__zero__divisors(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_100,axiom,
    ( class_OrderedGroup_Omonoid__add(Eq_y_0)
    | ~ class_OrderedGroup_Omonoid__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_101,axiom,
    ( class_Ring__and__Field_Odvd(Eq_y_0)
    | ~ class_Ring__and__Field_Odvd(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_102,axiom,
    ( class_Ring__and__Field_Oring__1__no__zero__divisors(Eq_y_0)
    | ~ class_Ring__and__Field_Oring__1__no__zero__divisors(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_103,axiom,
    ( class_OrderedGroup_Ocancel__comm__monoid__add(Eq_y_0)
    | ~ class_OrderedGroup_Ocancel__comm__monoid__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(sat_proved,plain,
    $false,
    inference(cadical,[status(thm)],[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : ALG429-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03  This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.03  % Command  : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.33  % Computer : n007.cluster.edu
% 0.07/0.33  % Model    : x86_64 x86_64
% 0.07/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33  % Memory   : 8046.5625MB
% 0.07/0.33  % OS       : Linux 6.8.0-71-generic
% 0.07/0.34  % CPULimit : 300
% 0.07/0.34  % WCLimit  : 300
% 0.07/0.34  % DateTime : Sun Sep 20 11:23:05 UTC 2026
% 0.07/0.34  % CPUTime  : 
% 150.25/150.51  % SZS status Unsatisfiable for theBenchmark
% 150.25/150.51  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------