ConnectPP---0.7.2.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SWV633-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n020.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 09:04:06 AM UTC 2026

% Result   : Unsatisfiable 228.24s 233.74s
% Output   : Proof 228.36s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
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_power__mono__even_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x,T_a),c_HOL_Oabs__class_Oabs(V_y,T_a),T_a)
    | c_lessequals(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_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__mono__even_0) ).

cnf(cls_nat__mult__dvd__cancel__disj_1,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(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),tc_nat),
    file('theBenchmark.p',cls_nat__mult__dvd__cancel__disj_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_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_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_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_lessI_0,axiom,
    c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat),
    file('theBenchmark.p',cls_lessI_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__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__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__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__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__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_abs__eq__mult_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_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Opordered__ring__abs(T_a) ),
    file('theBenchmark.p',cls_abs__eq__mult_0) ).

cnf(cls_abs__eq__mult_1,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_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Opordered__ring__abs(T_a) ),
    file('theBenchmark.p',cls_abs__eq__mult_1) ).

cnf(cls_abs__eq__mult_2,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_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Opordered__ring__abs(T_a) ),
    file('theBenchmark.p',cls_abs__eq__mult_2) ).

cnf(cls_abs__eq__mult_3,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_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Opordered__ring__abs(T_a) ),
    file('theBenchmark.p',cls_abs__eq__mult_3) ).

cnf(cls_div__mult1__eq_0,axiom,
    c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,tc_nat),V_c,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat),tc_nat),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat),tc_nat),V_c,tc_nat),tc_nat),
    file('theBenchmark.p',cls_div__mult1__eq_0) ).

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_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_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_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_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_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_gcd__lcm__complete__lattice__nat_Obot__least_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),V_x,tc_nat),
    file('theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Obot__least_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_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_nat__mult__div__cancel1_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
    | c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_nat__mult__div__cancel1_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_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__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_even__nat__equiv__def_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
    | c_Divides_Odiv__class_Omod(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('theBenchmark.p',cls_even__nat__equiv__def_1) ).

cnf(cls_even__nat__equiv__def_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
    | c_Divides_Odiv__class_Omod(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('theBenchmark.p',cls_even__nat__equiv__def_0) ).

cnf(cls_nat__mult__div__cancel__disj_0,axiom,
    c_Divides_Odiv__class_Odiv(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),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('theBenchmark.p',cls_nat__mult__div__cancel__disj_0) ).

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_abs__less__iff_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ 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_Oabs__class_Oabs(V_a,T_a),V_b,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__less__iff_2) ).

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_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_dvd_Oeq__iff_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(V_x,V_x,tc_nat),
    file('theBenchmark.p',cls_dvd_Oeq__iff_0) ).

cnf(cls_dvd__pos__nat_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_m,V_n,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ),
    file('theBenchmark.p',cls_dvd__pos__nat_0) ).

cnf(cls_dvd_Oless__trans_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat) ),
    file('theBenchmark.p',cls_dvd_Oless__trans_0) ).

cnf(cls_dvd_Oorder__trans_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat) ),
    file('theBenchmark.p',cls_dvd_Oorder__trans_0) ).

cnf(cls_abs__of__nonneg_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__of__nonneg_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_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_dvd_Oeq__iff_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
    | V_x = V_y ),
    file('theBenchmark.p',cls_dvd_Oeq__iff_2) ).

cnf(cls_dvd_Oantisym_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
    | V_x = V_y ),
    file('theBenchmark.p',cls_dvd_Oantisym_0) ).

cnf(cls_dvd_Oless__le_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
    | V_x = V_y
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat) ),
    file('theBenchmark.p',cls_dvd_Oless__le_0) ).

cnf(cls_dvd__antisym_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_n,V_m,tc_nat)
    | V_m = V_n ),
    file('theBenchmark.p',cls_dvd__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_dvd_Oantisym__conv_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
    | V_x = V_y ),
    file('theBenchmark.p',cls_dvd_Oantisym__conv_0) ).

cnf(cls_dvd_Ole__neq__trans_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,tc_nat)
    | V_a = V_b
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_a,tc_nat) ),
    file('theBenchmark.p',cls_dvd_Ole__neq__trans_0) ).

cnf(cls_dvd_Oneq__le__trans_0,axiom,
    ( V_a = V_b
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_a,tc_nat) ),
    file('theBenchmark.p',cls_dvd_Oneq__le__trans_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_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_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_estimate__by__abs_0,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)
    | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a)
    | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_estimate__by__abs_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_mod__if_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = V_m ),
    file('theBenchmark.p',cls_mod__if_0) ).

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_abs__le__zero__iff_0,axiom,
    ( ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__le__zero__iff_0) ).

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_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_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_abs__div__pos_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_x,T_a),V_y,T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_x,V_y,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_abs__div__pos_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_dvd__1__iff__1_1,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    file('theBenchmark.p',cls_dvd__1__iff__1_1) ).

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_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_abs__less__iff_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__less__iff_1) ).

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_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__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_even__nat__equiv__def2_1,axiom,
    c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),V_xa,tc_nat),tc_nat),
    file('theBenchmark.p',cls_even__nat__equiv__def2_1) ).

cnf(cls_diff__divide__distrib_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Ominus__class_Ominus(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_diff__divide__distrib_0) ).

cnf(cls_divide_Odiff_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Ominus__class_Ominus(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_Odiff_0) ).

cnf(cls_number__of__is__id_0,axiom,
    c_Int_Onumber__class_Onumber__of(V_k,tc_Int_Oint) = V_k,
    file('theBenchmark.p',cls_number__of__is__id_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_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_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_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_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_dvd__diff_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
    file('theBenchmark.p',cls_dvd__diff_0) ).

cnf(cls_eq__iff__diff__eq__0_0,axiom,
    ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

cnf(cls_right__minus__eq_1,axiom,
    ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_right__minus__eq_1) ).

cnf(cls_diff__0__right_0,axiom,
    ( c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_diff__0__right_0) ).

cnf(cls_diff__self_0,axiom,
    ( c_HOL_Ominus__class_Ominus(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_diff__self_0) ).

cnf(cls_class__ringb_Osubr0__iff_1,axiom,
    ( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).

cnf(cls_abs__of__neg_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__of__neg_0) ).

cnf(cls_abs__if_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a)
    | ~ class_Ring__and__Field_Oabs__if(T_a) ),
    file('theBenchmark.p',cls_abs__if_0) ).

cnf(cls_abs__if__lattice_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a)
    | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a)
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_abs__if__lattice_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_div__if_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('theBenchmark.p',cls_div__if_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_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_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_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_abs__le__D2_0,axiom,
    ( ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a)
    | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__le__D2_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_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_mod__mult2__eq_0,axiom,
    c_Divides_Odiv__class_Omod(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat),tc_nat),c_Divides_Odiv__class_Omod(V_a,V_b,tc_nat),tc_nat),
    file('theBenchmark.p',cls_mod__mult2__eq_0) ).

cnf(cls_DERIV__inverse__lemma_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a),V_h,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_h,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a),T_a)
    | ~ class_RealVector_Oreal__normed__field(T_a) ),
    file('theBenchmark.p',cls_DERIV__inverse__lemma_0) ).

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_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_mod__lemma_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_c,tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_r,V_b,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Omod(V_q,V_c,tc_nat),tc_nat),V_r,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_mod__lemma_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__le__zero__eq_4,axiom,
    ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_Power_Opower__class_Opower(V_x,V_n,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_4) ).

cnf(cls_power__less__zero__eq_2,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | 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)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__less__zero__eq_2) ).

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_abs__minus__one_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__minus__one_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_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_neg__one__even__power_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
    | c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),V_x,T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_neg__one__even__power_0) ).

cnf(cls_dvd__mult__cancel2_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),V_m,tc_nat)
    | V_n = c_HOL_Oone__class_Oone(tc_nat) ),
    file('theBenchmark.p',cls_dvd__mult__cancel2_0) ).

cnf(cls_dvd__mult__cancel1_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_m,tc_nat)
    | V_n = c_HOL_Oone__class_Oone(tc_nat) ),
    file('theBenchmark.p',cls_dvd__mult__cancel1_0) ).

cnf(cls_power__le__zero__eq_1,axiom,
    ( ~ c_lessequals(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | 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_1) ).

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_nat__dvd__1__iff__1_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | V_m = c_HOL_Oone__class_Oone(tc_nat) ),
    file('theBenchmark.p',cls_nat__dvd__1__iff__1_0) ).

cnf(cls_power__mono__odd_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | ~ c_lessequals(V_x,V_y,T_a)
    | c_lessequals(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_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__mono__odd_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_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_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_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_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_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_of__nat__add_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),T_a) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Osemiring__1(T_a) ),
    file('theBenchmark.p',cls_of__nat__add_0) ).

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_less__eqI_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_less__eqI_1) ).

cnf(cls_less__eqI_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_less__eqI_0) ).

cnf(cls_le__eqI_1,axiom,
    ( ~ c_lessequals(V_y_H,V_x_H,T_a)
    | c_lessequals(V_y,V_x,T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_le__eqI_1) ).

cnf(cls_le__eqI_0,axiom,
    ( ~ c_lessequals(V_y,V_x,T_a)
    | c_lessequals(V_y_H,V_x_H,T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_le__eqI_0) ).

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_inf__period_I4_J_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_x,c_HOL_Otimes__class_Otimes(V_k,V_D,T_a),T_a),V_t,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__ring(T_a)
    | ~ class_Ring__and__Field_Odvd(T_a) ),
    file('theBenchmark.p',cls_inf__period_I4_J_0) ).

cnf(cls_inf__period_I4_J_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_x,c_HOL_Otimes__class_Otimes(V_k,V_D,T_a),T_a),V_t,T_a),T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__ring(T_a)
    | ~ class_Ring__and__Field_Odvd(T_a) ),
    file('theBenchmark.p',cls_inf__period_I4_J_1) ).

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_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_power__less__zero__eq__number__of_0,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_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__less__zero__eq__number__of_0) ).

cnf(cls_abs__triangle__ineq2_0,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__triangle__ineq2_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_zero__less__power__eq_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | ~ 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_1) ).

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_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_of__nat__eq__iff_0,axiom,
    ( V_m = V_n
    | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)
    | ~ class_Nat_Osemiring__char__0(T_a) ),
    file('theBenchmark.p',cls_of__nat__eq__iff_0) ).

cnf(cls_int__int__eq_0,axiom,
    ( V_m = V_n
    | c_Nat_Osemiring__1__class_Oof__nat(V_m,tc_Int_Oint) != c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Int_Oint) ),
    file('theBenchmark.p',cls_int__int__eq_0) ).

cnf(cls_Nat__Transfer_Otransfer__int__nat__relations_I1_J_0,axiom,
    ( V_x = V_y
    | c_Nat_Osemiring__1__class_Oof__nat(V_x,tc_Int_Oint) != c_Nat_Osemiring__1__class_Oof__nat(V_y,tc_Int_Oint) ),
    file('theBenchmark.p',cls_Nat__Transfer_Otransfer__int__nat__relations_I1_J_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_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_zero__le__power__eq__number__of_2,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | c_lessequals(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)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__le__power__eq__number__of_2) ).

cnf(cls_zero__le__power__eq__number__of_0,axiom,
    ( ~ c_lessequals(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_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__le__power__eq__number__of_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_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_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_le__add__iff2_1,axiom,
    ( ~ c_lessequals(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
    | ~ class_Ring__and__Field_Opordered__ring(T_a) ),
    file('theBenchmark.p',cls_le__add__iff2_1) ).

cnf(cls_le__add__iff2_0,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
    | c_lessequals(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)
    | ~ class_Ring__and__Field_Opordered__ring(T_a) ),
    file('theBenchmark.p',cls_le__add__iff2_0) ).

cnf(cls_le__add__iff1_1,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
    | ~ class_Ring__and__Field_Opordered__ring(T_a) ),
    file('theBenchmark.p',cls_le__add__iff1_1) ).

cnf(cls_le__add__iff1_0,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)
    | ~ class_Ring__and__Field_Opordered__ring(T_a) ),
    file('theBenchmark.p',cls_le__add__iff1_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_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_abs__minus__le__zero_0,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__minus__le__zero_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_even__nat__div__two__times__two_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
    | c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_Divides_Odiv__class_Odiv(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat),tc_nat) = V_x ),
    file('theBenchmark.p',cls_even__nat__div__two__times__two_0) ).

cnf(cls_power__less__zero__eq_0,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_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__less__zero__eq_0) ).

cnf(cls_eq__add__iff2_1,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(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)
    | ~ class_Ring__and__Field_Oring(T_a) ),
    file('theBenchmark.p',cls_eq__add__iff2_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_abs__le__mult_0,axiom,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a)
    | ~ class_Ring__and__Field_Olordered__ring(T_a) ),
    file('theBenchmark.p',cls_abs__le__mult_0) ).

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_abs__le__D1_0,axiom,
    ( ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__le__D1_0) ).

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_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_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_zero__less__power__eq_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__less__power__eq_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_Suc__eq__plus1__left_0,axiom,
    c_Suc(V_n) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat),
    file('theBenchmark.p',cls_Suc__eq__plus1__left_0) ).

cnf(cls_Suc__eq__plus1_0,axiom,
    c_Suc(V_n) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    file('theBenchmark.p',cls_Suc__eq__plus1_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_abs__number__of_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_x,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(V_x,T_a),T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__number__of_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_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_dvd__mult__cancel1_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_m,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ),
    file('theBenchmark.p',cls_dvd__mult__cancel1_1) ).

cnf(cls_dvd__mult__cancel2_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),V_m,tc_nat),V_m,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ),
    file('theBenchmark.p',cls_dvd__mult__cancel2_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_abs__triangle__ineq3_0,axiom,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__triangle__ineq3_0) ).

cnf(cls_abs__mult__less_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_b,T_a),V_d,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(V_c,V_d,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__mult__less_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_diff__add__cancel_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_diff__add__cancel_0) ).

cnf(cls_mod__Suc_1,axiom,
    ( c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) = V_n
    | c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) ),
    file('theBenchmark.p',cls_mod__Suc_1) ).

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_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_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_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_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_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_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_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_power__less__zero__eq__number__of_2,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | 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)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__less__zero__eq__number__of_2) ).

cnf(cls_abs__eq__0_1,axiom,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__eq__0_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_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_abs__minus__commute_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__minus__commute_0) ).

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_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_odd__1__nat_0,axiom,
    ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    file('theBenchmark.p',cls_odd__1__nat_0) ).

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_div__1_0,axiom,
    c_Divides_Odiv__class_Odiv(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = V_m,
    file('theBenchmark.p',cls_div__1_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_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_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_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_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_abs__one_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__one_0) ).

cnf(cls_split__div__lemma_2,axiom,
    ( c_HOL_Oord__class_Oless(V_m,c_HOL_Otimes__class_Otimes(V_n,c_Suc(c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)),tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ),
    file('theBenchmark.p',cls_split__div__lemma_2) ).

cnf(cls_zero__less__power__eq_5,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | ~ 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),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__less__power__eq_5) ).

cnf(cls_diff__frac__eq_0,axiom,
    ( V_y = c_HOL_Ozero__class_Ozero(T_a)
    | V_z = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(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_diff__frac__eq_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_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__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_root1_0,axiom,
    c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
    file('theBenchmark.p',cls_root1_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_nat__mult__div__cancel__disj_1,axiom,
    ( V_k = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_nat__mult__div__cancel__disj_1) ).

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_div__add1__eq_0,axiom,
    c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,V_b,tc_nat),V_c,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_a,V_c,tc_nat),c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat),tc_nat),c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,tc_nat),c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat),tc_nat),V_c,tc_nat),tc_nat),
    file('theBenchmark.p',cls_div__add1__eq_0) ).

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_even__sum__nat_3,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_even__sum__nat_3) ).

cnf(cls_even__sum__nat_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_even__sum__nat_2) ).

cnf(cls_even__sum__nat_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ),
    file('theBenchmark.p',cls_even__sum__nat_1) ).

cnf(cls_even__sum__nat_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat) ),
    file('theBenchmark.p',cls_even__sum__nat_0) ).

cnf(cls_even__add_3,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_even__add_3) ).

cnf(cls_even__add_2,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_even__add_2) ).

cnf(cls_even__add_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat) ),
    file('theBenchmark.p',cls_even__add_1) ).

cnf(cls_even__add_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ),
    file('theBenchmark.p',cls_even__add_0) ).

cnf(cls_odd__add_3,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_odd__add_3) ).

cnf(cls_odd__add_2,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_odd__add_2) ).

cnf(cls_odd__add_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat) ),
    file('theBenchmark.p',cls_odd__add_1) ).

cnf(cls_odd__add_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ),
    file('theBenchmark.p',cls_odd__add_0) ).

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_odd__nat__plus__one__div__two_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
    | c_Divides_Odiv__class_Odiv(c_Suc(V_x),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_Suc(c_Divides_Odiv__class_Odiv(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)) ),
    file('theBenchmark.p',cls_odd__nat__plus__one__div__two_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__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_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_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_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_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_odd__nat__equiv__def_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
    | c_Divides_Odiv__class_Omod(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('theBenchmark.p',cls_odd__nat__equiv__def_1) ).

cnf(cls_odd__nat__equiv__def_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
    | c_Divides_Odiv__class_Omod(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('theBenchmark.p',cls_odd__nat__equiv__def_0) ).

cnf(cls_group__add__class_Odiff__0_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a)
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_group__add__class_Odiff__0_0) ).

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_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_Deriv_Oinverse__diff__inverse_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_Deriv_Oinverse__diff__inverse_0) ).

cnf(cls_diff__def_0,axiom,
    ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a)
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_diff__def_0) ).

cnf(cls_class__ring_Osub__add_0,axiom,
    ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_class__ring_Osub__add_0) ).

cnf(cls_diff__minus_0,axiom,
    ( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_diff__minus_0) ).

cnf(cls_ab__diff__minus_0,axiom,
    ( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_ab__diff__minus_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_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_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_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_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_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_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_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_abs__of__nat_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) = c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__of__nat_0) ).

cnf(cls_mod__diff__eq_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
    | ~ class_Divides_Oring__div(T_a) ),
    file('theBenchmark.p',cls_mod__diff__eq_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_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_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_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_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_dvd__1__left_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_k,tc_nat),
    file('theBenchmark.p',cls_dvd__1__left_0) ).

cnf(cls_abs__triangle__ineq_0,axiom,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__triangle__ineq_0) ).

cnf(cls_odd__nat__equiv__def2_1,axiom,
    ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),V_xa,tc_nat)),tc_nat),
    file('theBenchmark.p',cls_odd__nat__equiv__def2_1) ).

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_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_eq__eqI_0,axiom,
    ( V_x_H = V_y_H
    | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_eq__eqI_0) ).

cnf(cls_eq__eqI_1,axiom,
    ( V_xa = V_y
    | c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_eq__eqI_1) ).

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_power__le__zero__eq_5,axiom,
    ( c_lessequals(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__le__zero__eq_5) ).

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_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__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_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_mult_Oprod__diff__prod_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),T_a)
    | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    file('theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).

cnf(cls_zero__le__power__eq_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__le__power__eq_1) ).

cnf(cls_zero__le__power__iff_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | 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_2) ).

cnf(cls_zero__le__even__power_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a)
    | ~ class_OrderedGroup_Omonoid__mult(T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_zero__le__even__power_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_arith__simps_I31_J_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_arith__simps_I31_J_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_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_eq__iff__diff__eq__0_1,axiom,
    ( V_a = V_b
    | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).

cnf(cls_right__minus__eq_0,axiom,
    ( V_a = V_b
    | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_right__minus__eq_0) ).

cnf(cls_class__ringb_Osubr0__iff_0,axiom,
    ( V_x = V_y
    | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_class__ringb_Osubr0__iff_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_Deriv_Oadd__diff__add_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ominus__class_Ominus(V_c,V_d,T_a),T_a)
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_Deriv_Oadd__diff__add_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_power__le__zero__eq__number__of_4,axiom,
    ( c_Int_Onumber__class_Onumber__of(V_w,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat)
    | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | 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)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__le__zero__eq__number__of_4) ).

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_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_power__even__abs_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_x,T_a),V_n,T_a) = c_Power_Opower__class_Opower(V_x,V_n,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__even__abs_0) ).

cnf(cls_odd__pos_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ),
    file('theBenchmark.p',cls_odd__pos_0) ).

cnf(cls_power__le__zero__eq__number__of_2,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)
    | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__le__zero__eq__number__of_2) ).

cnf(cls_nat__dvd__1__iff__1_1,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    file('theBenchmark.p',cls_nat__dvd__1__iff__1_1) ).

cnf(cls_nonzero__number__of__Min_0,axiom,
    ( ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_nonzero__number__of__Min_0) ).

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_mod__Suc_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) != V_n ),
    file('theBenchmark.p',cls_mod__Suc_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_abs__diff__less__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_r,T_a),V_x,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__diff__less__iff_0) ).

cnf(cls_abs__inverse_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(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_abs__inverse_0) ).

cnf(cls_abs__divide_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(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_abs__divide_0) ).

cnf(cls_abs__of__pos_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__of__pos_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_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_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_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_abs__leI_0,axiom,
    ( ~ c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
    | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__leI_0) ).

cnf(cls_abs__le__iff_2,axiom,
    ( ~ c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
    | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__le__iff_2) ).

cnf(cls_root0_0,axiom,
    c_FFT__Mirabelle_Oroot(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
    file('theBenchmark.p',cls_root0_0) ).

cnf(cls_abs__minus__cancel_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_a,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__minus__cancel_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_minus__one__even__power_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
    | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),V_x,T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
    file('theBenchmark.p',cls_minus__one__even__power_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_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_abs__le__zero__iff_1,axiom,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__le__zero__iff_1) ).

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_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__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__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_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_of__nat__0_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Osemiring__1(T_a) ),
    file('theBenchmark.p',cls_of__nat__0_0) ).

cnf(cls_zero__less__power__eq_4,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | V_x = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__less__power__eq_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_of__nat__Suc_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_Suc(V_m),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),T_a)
    | ~ class_Ring__and__Field_Osemiring__1(T_a) ),
    file('theBenchmark.p',cls_of__nat__Suc_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_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_of__nat__1_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Osemiring__1(T_a) ),
    file('theBenchmark.p',cls_of__nat__1_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_dvd_Oless__trans_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat) ),
    file('theBenchmark.p',cls_dvd_Oless__trans_1) ).

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_mod__less__divisor_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
    | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_n,tc_nat) ),
    file('theBenchmark.p',cls_mod__less__divisor_0) ).

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_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_nonzero__abs__inverse_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_nonzero__abs__inverse_0) ).

cnf(cls_nonzero__abs__divide_0,axiom,
    ( V_b = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_nonzero__abs__divide_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_mod__diff__left__eq_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a)
    | ~ class_Divides_Oring__div(T_a) ),
    file('theBenchmark.p',cls_mod__diff__left__eq_0) ).

cnf(cls_mod__diff__right__eq_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
    | ~ class_Divides_Oring__div(T_a) ),
    file('theBenchmark.p',cls_mod__diff__right__eq_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_zero__le__power__eq__number__of_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat)
    | c_lessequals(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)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__le__power__eq__number__of_1) ).

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_odd__nat__div__two__times__two__plus__one_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
    | c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_Divides_Odiv__class_Odiv(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat),tc_nat)) = V_x ),
    file('theBenchmark.p',cls_odd__nat__div__two__times__two__plus__one_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_nat__number__of__Min_0,axiom,
    c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('theBenchmark.p',cls_nat__number__of__Min_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_zero__le__power__abs_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_a,T_a),V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__le__power__abs_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_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_div__Suc_0,axiom,
    c_Divides_Odiv__class_Odiv(c_Suc(V_a),V_c,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_a,V_c,tc_nat),c_Divides_Odiv__class_Odiv(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_c,tc_nat),tc_nat),c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,tc_nat),c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_c,tc_nat),tc_nat),V_c,tc_nat),tc_nat),
    file('theBenchmark.p',cls_div__Suc_0) ).

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_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_1,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_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat)
    | 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_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_DERIV__mult__lemma_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_c,V_d,T_a),T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_b,V_d,T_a),V_h,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_a,V_c,T_a),V_h,T_a),V_d,T_a),T_a)
    | ~ class_RealVector_Oreal__field(T_a) ),
    file('theBenchmark.p',cls_DERIV__mult__lemma_0) ).

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_abs__diff__triangle__ineq_0,axiom,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_c,T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_b,V_d,T_a),T_a),T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__diff__triangle__ineq_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_div__mult__self__is__m_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_n,tc_nat) = V_m ),
    file('theBenchmark.p',cls_div__mult__self__is__m_0) ).

cnf(cls_div__mult__self1__is__m_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),V_n,tc_nat) = V_m ),
    file('theBenchmark.p',cls_div__mult__self1__is__m_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_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_div__less_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('theBenchmark.p',cls_div__less_0) ).

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_of__nat__less__0__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_of__nat__less__0__iff_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_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_even__Suc_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(V_x),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ),
    file('theBenchmark.p',cls_even__Suc_0) ).

cnf(cls_even__Suc_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_Suc(V_x),tc_nat) ),
    file('theBenchmark.p',cls_even__Suc_1) ).

cnf(cls_dvd__1__iff__1_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
    | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('theBenchmark.p',cls_dvd__1__iff__1_0) ).

cnf(cls_abs__power__minus__one_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),V_n,T_a),T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__power__minus__one_0) ).

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_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_abs__of__nonpos_0,axiom,
    ( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__of__nonpos_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_diff__minus__eq__add_0,axiom,
    ( c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_diff__minus__eq__add_0) ).

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_mod__mult__self3_0,axiom,
    c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),V_m,tc_nat),V_n,tc_nat) = c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),
    file('theBenchmark.p',cls_mod__mult__self3_0) ).

cnf(cls_power__le__zero__eq__number__of_5,axiom,
    ( c_lessequals(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),T_a)
    | c_Int_Onumber__class_Onumber__of(V_w,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__le__zero__eq__number__of_5) ).

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_nat__mult__dvd__cancel__disj_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
    | V_k = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_nat__mult__dvd__cancel__disj_0) ).

cnf(cls_zero__le__imp__of__nat_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_zero__le__imp__of__nat_0) ).

cnf(cls_of__nat__0__le__iff_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_of__nat__0__le__iff_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_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_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_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_add__diff__cancel_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a
    | ~ class_OrderedGroup_Ogroup__add(T_a) ),
    file('theBenchmark.p',cls_add__diff__cancel_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_abs__diff__less__iff_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_r,T_a),V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_a,V_r,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__diff__less__iff_2) ).

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_minus__diff__eq_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a)
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_minus__diff__eq_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_dvd_Ole__less__trans_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat) ),
    file('theBenchmark.p',cls_dvd_Ole__less__trans_1) ).

cnf(cls_dvd_Oless__le__trans_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat) ),
    file('theBenchmark.p',cls_dvd_Oless__le__trans_1) ).

cnf(cls_lemma__not__even__div2_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Suc(c_Divides_Odiv__class_Odiv(V_n,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)) ),
    file('theBenchmark.p',cls_lemma__not__even__div2_0) ).

cnf(cls_Suc__n__div__2__gt__zero_0,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_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_Suc__n__div__2__gt__zero_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_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_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_eq__add__iff1_1,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Oring(T_a) ),
    file('theBenchmark.p',cls_eq__add__iff1_1) ).

cnf(cls_neg__power__if_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_n,T_a) = c_Power_Opower__class_Opower(V_x,V_n,T_a)
    | ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
    file('theBenchmark.p',cls_neg__power__if_0) ).

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_abs__idempotent_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_a,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__idempotent_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_eq__add__iff1_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) = V_d
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)
    | ~ class_Ring__and__Field_Oring(T_a) ),
    file('theBenchmark.p',cls_eq__add__iff1_0) ).

cnf(cls_eq__add__iff2_0,axiom,
    ( V_c = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)
    | ~ class_Ring__and__Field_Oring(T_a) ),
    file('theBenchmark.p',cls_eq__add__iff2_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_zero__less__abs__iff_1,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_zero__less__abs__iff_1) ).

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_number__of__Min_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_number__of__Min_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_Suc__times__mod__eq_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),V_k,tc_nat)
    | c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)),V_k,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
    file('theBenchmark.p',cls_Suc__times__mod__eq_0) ).

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_complex__i__not__one_0,axiom,
    c_Complex_Oii != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
    file('theBenchmark.p',cls_complex__i__not__one_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_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_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_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_eq__number__of__Pls__Min_0,axiom,
    c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint),
    file('theBenchmark.p',cls_eq__number__of__Pls__Min_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_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_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_abs__ge__minus__self_0,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__ge__minus__self_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_One__nat__def_0,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    file('theBenchmark.p',cls_One__nat__def_0) ).

cnf(cls_abs__ge__self_0,axiom,
    ( c_lessequals(V_a,c_HOL_Oabs__class_Oabs(V_a,T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__ge__self_0) ).

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_less__add__iff1_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)
    | ~ class_Ring__and__Field_Opordered__ring(T_a) ),
    file('theBenchmark.p',cls_less__add__iff1_0) ).

cnf(cls_less__add__iff1_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
    | ~ class_Ring__and__Field_Opordered__ring(T_a) ),
    file('theBenchmark.p',cls_less__add__iff1_1) ).

cnf(cls_less__add__iff2_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
    | c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)
    | ~ class_Ring__and__Field_Opordered__ring(T_a) ),
    file('theBenchmark.p',cls_less__add__iff2_0) ).

cnf(cls_less__add__iff2_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
    | ~ class_Ring__and__Field_Opordered__ring(T_a) ),
    file('theBenchmark.p',cls_less__add__iff2_1) ).

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_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_even__zero__nat_0,axiom,
    c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('theBenchmark.p',cls_even__zero__nat_0) ).

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_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_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_abs__less__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__less__iff_0) ).

cnf(cls_mod__mult__self4_0,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),V_m,tc_nat)),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat),
    file('theBenchmark.p',cls_mod__mult__self4_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_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_mult__eq__self__implies__10_0,axiom,
    ( V_n = c_HOL_Oone__class_Oone(tc_nat)
    | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
    | V_m != c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_mult__eq__self__implies__10_0) ).

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_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_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__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_abs__mult__self_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__mult__self_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_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_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_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_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_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_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_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_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_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_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__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__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_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_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_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_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_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__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__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_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_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_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_abs__mult_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__mult_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_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_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_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_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_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_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_mult__right_Odiff_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),T_a) = c_HOL_Ominus__class_Ominus(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_Odiff_0) ).

cnf(cls_mult_Odiff__right_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ominus__class_Ominus(V_b,V_b_H,T_a),T_a) = c_HOL_Ominus__class_Ominus(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_Odiff__right_0) ).

cnf(cls_mult_Odiff__left_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(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_Odiff__left_0) ).

cnf(cls_mult__left_Odiff_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Ominus__class_Ominus(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_Odiff_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_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_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_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_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_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_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__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_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_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_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_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_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_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__minus1_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),V_z,T_a) = c_HOL_Ouminus__class_Ouminus(V_z,T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_mult__minus1_0) ).

cnf(cls_mult__minus1__right_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(V_z,T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_mult__minus1__right_0) ).

cnf(cls_number__of__Bit1_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(V_w),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(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__ring(T_a) ),
    file('theBenchmark.p',cls_number__of__Bit1_0) ).

cnf(cls_divide__Numeral0_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__Numeral0_0) ).

cnf(cls_number__of__Bit0_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(c_Int_OBit0(V_w),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(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__ring(T_a) ),
    file('theBenchmark.p',cls_number__of__Bit0_0) ).

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_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_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_neg__one__odd__power_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
    | c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),V_x,T_a) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_neg__one__odd__power_0) ).

cnf(cls_half_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),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a),T_a),T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_half_0) ).

cnf(cls_Bit1__Min_0,axiom,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    file('theBenchmark.p',cls_Bit1__Min_0) ).

cnf(cls_rel__simps_I47_J_0,axiom,
    ( V_k = c_Int_OMin
    | c_Int_OBit1(V_k) != c_Int_OMin ),
    file('theBenchmark.p',cls_rel__simps_I47_J_0) ).

cnf(cls_rel__simps_I43_J_0,axiom,
    ( c_Int_OMin = V_l
    | c_Int_OMin != c_Int_OBit1(V_l) ),
    file('theBenchmark.p',cls_rel__simps_I43_J_0) ).

cnf(cls_rel__simps_I43_J_1,axiom,
    c_Int_OMin = c_Int_OBit1(c_Int_OMin),
    file('theBenchmark.p',cls_rel__simps_I43_J_1) ).

cnf(cls_rel__simps_I37_J_0,axiom,
    c_Int_OPls != c_Int_OMin,
    file('theBenchmark.p',cls_rel__simps_I37_J_0) ).

cnf(cls_rel__simps_I40_J_0,axiom,
    c_Int_OMin != c_Int_OPls,
    file('theBenchmark.p',cls_rel__simps_I40_J_0) ).

cnf(cls_rel__simps_I42_J_0,axiom,
    c_Int_OMin != c_Int_OBit0(V_l),
    file('theBenchmark.p',cls_rel__simps_I42_J_0) ).

cnf(cls_rel__simps_I45_J_0,axiom,
    c_Int_OBit0(V_k) != c_Int_OMin,
    file('theBenchmark.p',cls_rel__simps_I45_J_0) ).

cnf(cls_mod2__gr__0_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Omod(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat)
    | c_Divides_Odiv__class_Omod(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
    file('theBenchmark.p',cls_mod2__gr__0_0) ).

cnf(cls_gcd__lcm__complete__lattice__nat_Otop__greatest_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Otop__greatest_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_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_abs__power__minus_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_n,T_a),T_a) = c_HOL_Oabs__class_Oabs(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_abs__power__minus_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_mod__1_0,axiom,
    c_Divides_Odiv__class_Omod(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('theBenchmark.p',cls_mod__1_0) ).

cnf(cls_iszero__def_0,axiom,
    ( ~ c_Int_Oiszero(V_z,T_a)
    | V_z = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Osemiring__1(T_a) ),
    file('theBenchmark.p',cls_iszero__def_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_abs__mult__pos_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_y,T_a),V_x,T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_y,V_x,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__mult__pos_0) ).

cnf(cls_dvd__reduce_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_dvd__reduce_1) ).

cnf(cls_dvd__reduce_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat) ),
    file('theBenchmark.p',cls_dvd__reduce_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_abs__dvd__iff_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__dvd__iff_0) ).

cnf(cls_abs__dvd__iff_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__dvd__iff_1) ).

cnf(cls_dvd__abs__iff_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_dvd__abs__iff_0) ).

cnf(cls_dvd__abs__iff_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_dvd__abs__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_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_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__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_abs__number__of_1,axiom,
    ( c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_x,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(V_x,T_a),T_a) = c_Int_Onumber__class_Onumber__of(V_x,T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__number__of_1) ).

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_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_divide__minus1_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(V_x,T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__minus1_0) ).

cnf(cls_mod__diff__cong_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a_H,V_b_H,T_a),V_c,T_a)
    | 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_Oring__div(T_a) ),
    file('theBenchmark.p',cls_mod__diff__cong_0) ).

cnf(cls_nat__dvd__not__less_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_n,V_m,tc_nat) ),
    file('theBenchmark.p',cls_nat__dvd__not__less_0) ).

cnf(cls_le__iff__diff__le__0_0,axiom,
    ( ~ c_lessequals(V_a,V_b,T_a)
    | c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_le__iff__diff__le__0_0) ).

cnf(cls_le__iff__diff__le__0_1,axiom,
    ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_le__iff__diff__le__0_1) ).

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_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_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_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_less__iff__diff__less__0_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_less__iff__diff__less__0_0) ).

cnf(cls_less__iff__diff__less__0_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_less__iff__diff__less__0_1) ).

cnf(cls_abs__not__less__zero_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__not__less__zero_0) ).

cnf(cls_of__nat__less__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
    | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_of__nat__less__iff_0) ).

cnf(cls_of__nat__less__iff_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_of__nat__less__iff_1) ).

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__le__zero__eq_2,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)
    | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__le__zero__eq_2) ).

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_dvd__mult__cancel_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(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_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_dvd__mult__cancel_0) ).

cnf(cls_nat__mult__dvd__cancel1_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(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_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_nat__mult__dvd__cancel1_0) ).

cnf(cls_nat__mult__dvd__cancel1_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(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__dvd__cancel1_1) ).

cnf(cls_zero__less__power__eq__number__of_0,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)
    | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__less__power__eq__number__of_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_div__less__dividend_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
    | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat),V_m,tc_nat) ),
    file('theBenchmark.p',cls_div__less__dividend_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_nat__mod__eq__iff_1,axiom,
    ( c_Divides_Odiv__class_Omod(V_x,V_n,tc_nat) = c_Divides_Odiv__class_Omod(V_y,V_n,tc_nat)
    | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_n,V_xa,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(V_y,c_HOL_Otimes__class_Otimes(V_n,V_xb,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_nat__mod__eq__iff_1) ).

cnf(cls_of__nat__0__less__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_of__nat__0__less__iff_0) ).

cnf(cls_of__nat__0__less__iff_1,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(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_of__nat__0__less__iff_1) ).

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_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_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_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_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_zero__less__power__eq__number__of_5,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat)
    | ~ 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),c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__less__power__eq__number__of_5) ).

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_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_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_abs__triangle__ineq4_0,axiom,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__triangle__ineq4_0) ).

cnf(cls_neg__power__if_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_n,T_a) = c_HOL_Ouminus__class_Ouminus(c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
    file('theBenchmark.p',cls_neg__power__if_1) ).

cnf(cls_minus__one__odd__power_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
    | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),V_x,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
    file('theBenchmark.p',cls_minus__one__odd__power_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_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_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_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_mod2__gr__0_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Omod(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat)
    | c_Divides_Odiv__class_Omod(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    file('theBenchmark.p',cls_mod2__gr__0_1) ).

cnf(cls_div__2__gt__zero_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Divides_Odiv__class_Odiv(V_n,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_div__2__gt__zero_0) ).

cnf(cls_lemma__even__div2_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(V_n,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_lemma__even__div2_0) ).

cnf(cls_Suc__mod__eq__add3__mod__number__of_0,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(c_Suc(c_Suc(V_m))),c_Int_Onumber__class_Onumber__of(V_v,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_m,tc_nat),c_Int_Onumber__class_Onumber__of(V_v,tc_nat),tc_nat),
    file('theBenchmark.p',cls_Suc__mod__eq__add3__mod__number__of_0) ).

cnf(cls_Suc__div__eq__add3__div__number__of_0,axiom,
    c_Divides_Odiv__class_Odiv(c_Suc(c_Suc(c_Suc(V_m))),c_Int_Onumber__class_Onumber__of(V_v,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_m,tc_nat),c_Int_Onumber__class_Onumber__of(V_v,tc_nat),tc_nat),
    file('theBenchmark.p',cls_Suc__div__eq__add3__div__number__of_0) ).

cnf(cls_mod__Suc__eq__mod__add3_0,axiom,
    c_Divides_Odiv__class_Omod(V_m,c_Suc(c_Suc(c_Suc(V_n))),tc_nat) = c_Divides_Odiv__class_Omod(V_m,c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),tc_nat),
    file('theBenchmark.p',cls_mod__Suc__eq__mod__add3_0) ).

cnf(cls_Suc__mod__eq__add3__mod_0,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(c_Suc(c_Suc(V_m))),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_m,tc_nat),V_n,tc_nat),
    file('theBenchmark.p',cls_Suc__mod__eq__add3__mod_0) ).

cnf(cls_div__Suc__eq__div__add3_0,axiom,
    c_Divides_Odiv__class_Odiv(V_m,c_Suc(c_Suc(c_Suc(V_n))),tc_nat) = c_Divides_Odiv__class_Odiv(V_m,c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),tc_nat),
    file('theBenchmark.p',cls_div__Suc__eq__div__add3_0) ).

cnf(cls_Suc__div__eq__add3__div_0,axiom,
    c_Divides_Odiv__class_Odiv(c_Suc(c_Suc(c_Suc(V_m))),V_n,tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_m,tc_nat),V_n,tc_nat),
    file('theBenchmark.p',cls_Suc__div__eq__add3__div_0) ).

cnf(cls_power__one__right_0,axiom,
    ( c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a
    | ~ class_OrderedGroup_Omonoid__mult(T_a) ),
    file('theBenchmark.p',cls_power__one__right_0) ).

cnf(cls_class__semiring_Osemiring__rules_I33_J_0,axiom,
    ( c_Power_Opower__class_Opower(V_x,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_x
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_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_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_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_power__abs_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_a,T_a),V_n,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__abs_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_power__even__abs__number__of_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat)
    | c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_x,T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a) = c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power__even__abs__number__of_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__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__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__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_nat__1__eq__mult__iff_0,axiom,
    ( V_m = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_nat__1__eq__mult__iff_0) ).

cnf(cls_nat__1__eq__mult__iff_1,axiom,
    ( V_n = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) ),
    file('theBenchmark.p',cls_nat__1__eq__mult__iff_1) ).

cnf(cls_even__product__nat_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat) ),
    file('theBenchmark.p',cls_even__product__nat_0) ).

cnf(cls_div__mult2__eq_0,axiom,
    c_Divides_Odiv__class_Odiv(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat),
    file('theBenchmark.p',cls_div__mult2__eq_0) ).

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_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_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_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_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_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_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_even__product__nat_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_even__product__nat_1) ).

cnf(cls_even__product__nat_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_even__product__nat_2) ).

cnf(cls_nat__mult__dvd__cancel__disj_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(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__dvd__cancel__disj_2) ).

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_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_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_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_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__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_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_nat__1__eq__mult__iff_2,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    file('theBenchmark.p',cls_nat__1__eq__mult__iff_2) ).

cnf(cls_nat__mult__1_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) = V_n,
    file('theBenchmark.p',cls_nat__mult__1_0) ).

cnf(cls_nat__mult__1__right_0,axiom,
    c_HOL_Otimes__class_Otimes(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = V_n,
    file('theBenchmark.p',cls_nat__mult__1__right_0) ).

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_nat__mult__eq__1__iff_0,axiom,
    ( V_m = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    file('theBenchmark.p',cls_nat__mult__eq__1__iff_0) ).

cnf(cls_nat__mult__eq__1__iff_1,axiom,
    ( V_n = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    file('theBenchmark.p',cls_nat__mult__eq__1__iff_1) ).

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_nat__mult__eq__1__iff_2,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
    file('theBenchmark.p',cls_nat__mult__eq__1__iff_2) ).

cnf(cls_mod__mult__distrib_0,axiom,
    c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_k,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat),
    file('theBenchmark.p',cls_mod__mult__distrib_0) ).

cnf(cls_mod__mult__distrib2_0,axiom,
    c_HOL_Otimes__class_Otimes(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat),
    file('theBenchmark.p',cls_mod__mult__distrib2_0) ).

cnf(cls_half__gt__zero_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_r,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_r,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a),T_a),T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_half__gt__zero_0) ).

cnf(cls_half__gt__zero__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_r,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a),T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_r,T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_half__gt__zero__iff_0) ).

cnf(cls_less__2__cases_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_n,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat)
    | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('theBenchmark.p',cls_less__2__cases_0) ).

cnf(cls_mod__exhaust__less__4_0,axiom,
    ( c_Divides_Odiv__class_Omod(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Divides_Odiv__class_Omod(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
    | c_Divides_Odiv__class_Omod(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)
    | c_Divides_Odiv__class_Omod(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) ),
    file('theBenchmark.p',cls_mod__exhaust__less__4_0) ).

cnf(cls_double__number__of__Bit0_0,axiom,
    ( 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),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(V_w),T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_double__number__of__Bit0_0) ).

cnf(cls_numeral__1__eq__Suc__0_0,axiom,
    c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    file('theBenchmark.p',cls_numeral__1__eq__Suc__0_0) ).

cnf(cls_numeral__3__eq__3_0,axiom,
    c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Suc(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
    file('theBenchmark.p',cls_numeral__3__eq__3_0) ).

cnf(cls_Suc3__eq__add__3_0,axiom,
    c_Suc(c_Suc(c_Suc(V_n))) = c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),
    file('theBenchmark.p',cls_Suc3__eq__add__3_0) ).

cnf(cls_transfer__int__nat__numerals_I4_J_0,axiom,
    c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_Int_Oint),
    file('theBenchmark.p',cls_transfer__int__nat__numerals_I4_J_0) ).

cnf(cls_power2__less__imp__less_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power2__less__imp__less_0) ).

cnf(cls_sum__power2__le__zero__iff_1,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),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__idom(T_a) ),
    file('theBenchmark.p',cls_sum__power2__le__zero__iff_1) ).

cnf(cls_sum__power2__le__zero__iff_0,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),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__idom(T_a) ),
    file('theBenchmark.p',cls_sum__power2__le__zero__iff_0) ).

cnf(cls_sum__power2__le__zero__iff_2,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_sum__power2__le__zero__iff_2) ).

cnf(cls_sum__power2__gt__zero__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_sum__power2__gt__zero__iff_0) ).

cnf(cls_sum__power2__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_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_sum__power2__gt__zero__iff_2) ).

cnf(cls_sum__power2__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_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_sum__power2__gt__zero__iff_1) ).

cnf(cls_sum__power2__ge__zero_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_sum__power2__ge__zero_0) ).

cnf(cls_not__sum__power2__lt__zero_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_not__sum__power2__lt__zero_0) ).

cnf(cls_root__cancel_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
    | c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ),
    file('theBenchmark.p',cls_root__cancel_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_left__diff__distrib__number__of_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a) = c_HOL_Ominus__class_Ominus(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_Oring(T_a) ),
    file('theBenchmark.p',cls_left__diff__distrib__number__of_0) ).

cnf(cls_right__diff__distrib__number__of_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_HOL_Ominus__class_Ominus(V_b,V_c,T_a),T_a) = c_HOL_Ominus__class_Ominus(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_Oring(T_a) ),
    file('theBenchmark.p',cls_right__diff__distrib__number__of_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_iszero__number__of__Bit1_0,axiom,
    ( ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(V_w),T_a),T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Int_Oring__char__0(T_a) ),
    file('theBenchmark.p',cls_iszero__number__of__Bit1_0) ).

cnf(cls_comp__arith_I112_J_0,axiom,
    ( c_HOL_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_comp__arith_I112_J_0) ).

cnf(cls_number__of__Pls_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_number__of__Pls_0) ).

cnf(cls_iszero__number__of__Pls_0,axiom,
    ( c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a),T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_iszero__number__of__Pls_0) ).

cnf(cls_add__numeral__0_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a),V_a,T_a) = V_a
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_add__numeral__0_0) ).

cnf(cls_add__numeral__0__right_0,axiom,
    ( c_HOL_Oplus__class_Oplus(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a),T_a) = V_a
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_add__numeral__0__right_0) ).

cnf(cls_iszero__number__of__Bit0_0,axiom,
    ( ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(V_w),T_a),T_a)
    | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Int_Oring__char__0(T_a) ),
    file('theBenchmark.p',cls_iszero__number__of__Bit0_0) ).

cnf(cls_iszero__number__of__Bit0_1,axiom,
    ( ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(V_w),T_a),T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Int_Oring__char__0(T_a) ),
    file('theBenchmark.p',cls_iszero__number__of__Bit0_1) ).

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_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_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_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_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_one__add__one__is__two_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_one__add__one__is__two_0) ).

cnf(cls_of__nat__mult_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Osemiring__1(T_a) ),
    file('theBenchmark.p',cls_of__nat__mult_0) ).

cnf(cls_numeral__2__eq__2_0,axiom,
    c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    file('theBenchmark.p',cls_numeral__2__eq__2_0) ).

cnf(cls_div2__Suc__Suc_0,axiom,
    c_Divides_Odiv__class_Odiv(c_Suc(c_Suc(V_m)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Suc(c_Divides_Odiv__class_Odiv(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)),
    file('theBenchmark.p',cls_div2__Suc__Suc_0) ).

cnf(cls_iszero__0_0,axiom,
    ( c_Int_Oiszero(c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Osemiring__1(T_a) ),
    file('theBenchmark.p',cls_iszero__0_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_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_even__nat__plus__one__div__two_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
    | c_Divides_Odiv__class_Odiv(c_Suc(V_x),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_Divides_Odiv__class_Odiv(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
    file('theBenchmark.p',cls_even__nat__plus__one__div__two_0) ).

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_abs__if__lattice_1,axiom,
    ( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a
    | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a)
    | ~ class_Orderings_Olinorder(T_a) ),
    file('theBenchmark.p',cls_abs__if__lattice_1) ).

cnf(cls_abs__if_1,axiom,
    ( c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a
    | ~ class_Ring__and__Field_Oabs__if(T_a) ),
    file('theBenchmark.p',cls_abs__if_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_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_Lim_Ominus__diff__minus_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a)
    | ~ class_OrderedGroup_Oab__group__add(T_a) ),
    file('theBenchmark.p',cls_Lim_Ominus__diff__minus_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_abs__add__abs_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__add__abs_0) ).

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_mod__Suc__eq__Suc__mod_0,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)),V_n,tc_nat),
    file('theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).

cnf(cls_abs__eq__0_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__eq__0_0) ).

cnf(cls_zero__less__abs__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_zero__less__abs__iff_0) ).

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_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_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_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_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_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_mod__eq__0__iff_1,axiom,
    c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_d,V_x,tc_nat),V_d,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('theBenchmark.p',cls_mod__eq__0__iff_1) ).

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_division__ring__inverse__diff_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(V_b,V_a,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__diff_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_minus1__divide_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),V_x,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_x,T_a),T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_minus1__divide_0) ).

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_abs__diff__less__iff_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a)
    | c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_a,V_r,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__diff__less__iff_1) ).

cnf(cls_zero__less__power__eq__number__of_4,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat)
    | V_x = c_HOL_Ozero__class_Ozero(T_a)
    | 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)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__less__power__eq__number__of_4) ).

cnf(cls_not__iszero__1_0,axiom,
    ( ~ c_Int_Oiszero(c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ class_Ring__and__Field_Osemiring__1(T_a) ),
    file('theBenchmark.p',cls_not__iszero__1_0) ).

cnf(cls_zero__less__power__eq__number__of_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat)
    | ~ 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_1) ).

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_zero__le__power__iff_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__le__power__iff_0) ).

cnf(cls_zero__le__odd__power_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__le__odd__power_1) ).

cnf(cls_zero__le__odd__power_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__le__odd__power_0) ).

cnf(cls_zero__le__power__eq_2,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__le__power__eq_2) ).

cnf(cls_zero__le__power__eq_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a)
    | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__le__power__eq_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_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_abs__ge__zero_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
    file('theBenchmark.p',cls_abs__ge__zero_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_dvd__if__abs__eq_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(V_l,V_k,T_a)
    | c_HOL_Oabs__class_Oabs(V_l,T_a) != c_HOL_Oabs__class_Oabs(V_k,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_dvd__if__abs__eq_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_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_dvd_Oless__le__trans_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat) ),
    file('theBenchmark.p',cls_dvd_Oless__le__trans_0) ).

cnf(cls_dvd_Ole__less__trans_0,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat) ),
    file('theBenchmark.p',cls_dvd_Ole__less__trans_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_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_add__self__div__2_0,axiom,
    c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_m,V_m,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = V_m,
    file('theBenchmark.p',cls_add__self__div__2_0) ).

cnf(cls_nat__even__iff__2__dvd_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_x,tc_nat) ),
    file('theBenchmark.p',cls_nat__even__iff__2__dvd_0) ).

cnf(cls_nat__even__iff__2__dvd_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_x,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat) ),
    file('theBenchmark.p',cls_nat__even__iff__2__dvd_1) ).

cnf(cls_nat__1__add__1_0,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
    file('theBenchmark.p',cls_nat__1__add__1_0) ).

cnf(cls_add__2__eq__Suc_0,axiom,
    c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat) = c_Suc(c_Suc(V_n)),
    file('theBenchmark.p',cls_add__2__eq__Suc_0) ).

cnf(cls_add__2__eq__Suc_H_0,axiom,
    c_HOL_Oplus__class_Oplus(V_n,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Suc(c_Suc(V_n)),
    file('theBenchmark.p',cls_add__2__eq__Suc_H_0) ).

cnf(cls_transfer__int__nat__numerals_I3_J_0,axiom,
    c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_Int_Oint),
    file('theBenchmark.p',cls_transfer__int__nat__numerals_I3_J_0) ).

cnf(cls_pos2_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
    file('theBenchmark.p',cls_pos2_0) ).

cnf(cls_mod2__Suc__Suc_0,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(c_Suc(V_m)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
    file('theBenchmark.p',cls_mod2__Suc__Suc_0) ).

cnf(cls_comp__arith_I115_J_0,axiom,
    c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
    file('theBenchmark.p',cls_comp__arith_I115_J_0) ).

cnf(cls_even__even__mod__4__iff_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(V_n,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat) ),
    file('theBenchmark.p',cls_even__even__mod__4__iff_1) ).

cnf(cls_even__even__mod__4__iff_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(V_n,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat) ),
    file('theBenchmark.p',cls_even__even__mod__4__iff_0) ).

cnf(cls_comp__arith_I113_J_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),
    file('theBenchmark.p',cls_comp__arith_I113_J_0) ).

cnf(cls_nat__number__of__Pls_0,axiom,
    c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('theBenchmark.p',cls_nat__number__of__Pls_0) ).

cnf(cls_power__minus1__odd_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat)),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
    file('theBenchmark.p',cls_power__minus1__odd_0) ).

cnf(cls_odd__power__less__zero_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,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_odd__power__less__zero_0) ).

cnf(cls_odd__0__le__power__imp__0__le_0,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat)),T_a),T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_odd__0__le__power__imp__0__le_0) ).

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_sum__power2__eq__zero__iff_2,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_sum__power2__eq__zero__iff_2) ).

cnf(cls_power2__less__0_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),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_power2__less__0_0) ).

cnf(cls_zero__less__power2_0,axiom,
    ( ~ 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(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__less__power2_0) ).

cnf(cls_power2__le__imp__le_0,axiom,
    ( ~ c_lessequals(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | c_lessequals(V_x,V_y,T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power2__le__imp__le_0) ).

cnf(cls_sum__power2__eq__zero__iff_1,axiom,
    ( V_y = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_sum__power2__eq__zero__iff_1) ).

cnf(cls_sum__power2__eq__zero__iff_0,axiom,
    ( V_x = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_sum__power2__eq__zero__iff_0) ).

cnf(cls_zero__le__power2_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__le__power2_0) ).

cnf(cls_power2__eq__imp__eq_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)
    | V_x = V_y
    | c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) != c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_power2__eq__imp__eq_0) ).

cnf(cls_zero__less__power2_1,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__less__power2_1) ).

cnf(cls_odd__Suc__mult__two__ex_1,axiom,
    ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_x,tc_nat)),tc_nat),
    file('theBenchmark.p',cls_odd__Suc__mult__two__ex_1) ).

cnf(cls_even__mult__two__ex_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)
    | V_n = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1(V_n),tc_nat) ),
    file('theBenchmark.p',cls_even__mult__two__ex_0) ).

cnf(cls_root__unity_0,axiom,
    c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
    file('theBenchmark.p',cls_root__unity_0) ).

cnf(cls_inverse__numeral__1_0,axiom,
    ( c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a),T_a) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_inverse__numeral__1_0) ).

cnf(cls_divide__Numeral1_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a),T_a) = V_x
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__Numeral1_0) ).

cnf(cls_divide__numeral__1_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a),T_a) = V_a
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__numeral__1_0) ).

cnf(cls_numeral__1__eq__1_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_numeral__1__eq__1_0) ).

cnf(cls_comp__arith_I110_J_0,axiom,
    ( c_HOL_Oone__class_Oone(T_a) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_comp__arith_I110_J_0) ).

cnf(cls_not__iszero__Numeral1_0,axiom,
    ( ~ c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a),T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_not__iszero__Numeral1_0) ).

cnf(cls_nat__numeral__1__eq__1_0,axiom,
    c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
    file('theBenchmark.p',cls_nat__numeral__1__eq__1_0) ).

cnf(cls_Numeral1__eq1__nat_0,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),
    file('theBenchmark.p',cls_Numeral1__eq1__nat_0) ).

cnf(cls_power__minus1__even_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
    file('theBenchmark.p',cls_power__minus1__even_0) ).

cnf(cls_zero__le__even__power_H_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__le__even__power_H_0) ).

cnf(cls_even__power__le__0__imp__0_0,axiom,
    ( ~ c_lessequals(c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_k,tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_even__power__le__0__imp__0_0) ).

cnf(cls_power2__diff_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a),V_x,T_a),V_y,T_a),T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_power2__diff_0) ).

cnf(cls_power__m1__odd_0,axiom,
    ( c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat)),T_a) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_power__m1__odd_0) ).

cnf(cls_power__m1__even_0,axiom,
    ( c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_power__m1__even_0) ).

cnf(cls_mult__2_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a),V_z,T_a) = c_HOL_Oplus__class_Oplus(V_z,V_z,T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_mult__2_0) ).

cnf(cls_mult__2__right_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a),T_a) = c_HOL_Oplus__class_Oplus(V_z,V_z,T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_mult__2__right_0) ).

cnf(cls_zero__eq__power2_1,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__eq__power2_1) ).

cnf(cls_zero__power2_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Osemiring__1(T_a) ),
    file('theBenchmark.p',cls_zero__power2_0) ).

cnf(cls_zero__eq__power2_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_zero__eq__power2_0) ).

cnf(cls_power2__abs_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_a,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_power2__abs_0) ).

cnf(cls_one__power2_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ class_Ring__and__Field_Osemiring__1(T_a) ),
    file('theBenchmark.p',cls_one__power2_0) ).

cnf(cls_power2__minus_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a)
    | ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
    file('theBenchmark.p',cls_power2__minus_0) ).

cnf(cls_abs__power2_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a) = c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__power2_0) ).

cnf(cls_even__mult__two__ex_1,axiom,
    c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_x,tc_nat),tc_nat),
    file('theBenchmark.p',cls_even__mult__two__ex_1) ).

cnf(cls_nat__mult__2__right_0,axiom,
    c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat),
    file('theBenchmark.p',cls_nat__mult__2__right_0) ).

cnf(cls_nat__mult__2_0,axiom,
    c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat),
    file('theBenchmark.p',cls_nat__mult__2_0) ).

cnf(cls_root4_0,axiom,
    c_FFT__Mirabelle_Oroot(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)) = c_Complex_Oii,
    file('theBenchmark.p',cls_root4_0) ).

cnf(cls_comm__ring__1__class_Opower__minus__even_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),T_a)
    | ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
    file('theBenchmark.p',cls_comm__ring__1__class_Opower__minus__even_0) ).

cnf(cls_power2__sum_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a),V_x,T_a),V_y,T_a),T_a)
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_power2__sum_0) ).

cnf(cls_class__semiring_Osemiring__rules_I37_J_0,axiom,
    ( c_Power_Opower__class_Opower(V_x,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat)),T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I37_J_0) ).

cnf(cls_power__odd__eq_0,axiom,
    ( c_Power_Opower__class_Opower(V_a,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat)),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a)
    | ~ class_OrderedGroup_Omonoid__mult(T_a) ),
    file('theBenchmark.p',cls_power__odd__eq_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_class__semiring_Osemiring__rules_I29_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I29_J_0) ).

cnf(cls_Bit0__Pls_0,axiom,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    file('theBenchmark.p',cls_Bit0__Pls_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_rel__simps_I39_J_0,axiom,
    c_Int_OPls != c_Int_OBit1(V_l),
    file('theBenchmark.p',cls_rel__simps_I39_J_0) ).

cnf(cls_power2__eq__square__number__of_0,axiom,
    ( c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ class_OrderedGroup_Omonoid__mult(T_a) ),
    file('theBenchmark.p',cls_power2__eq__square__number__of_0) ).

cnf(cls_rel__simps_I46_J_0,axiom,
    c_Int_OBit1(V_k) != c_Int_OPls,
    file('theBenchmark.p',cls_rel__simps_I46_J_0) ).

cnf(cls_rel__simps_I44_J_0,axiom,
    ( V_k = c_Int_OPls
    | c_Int_OBit0(V_k) != c_Int_OPls ),
    file('theBenchmark.p',cls_rel__simps_I44_J_0) ).

cnf(cls_rel__simps_I48_J_0,axiom,
    ( V_k = V_l
    | c_Int_OBit0(V_k) != c_Int_OBit0(V_l) ),
    file('theBenchmark.p',cls_rel__simps_I48_J_0) ).

cnf(cls_power__even__eq_0,axiom,
    ( c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),T_a) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a)
    | ~ class_OrderedGroup_Omonoid__mult(T_a) ),
    file('theBenchmark.p',cls_power__even__eq_0) ).

cnf(cls_rel__simps_I50_J_0,axiom,
    c_Int_OBit1(V_k) != c_Int_OBit0(V_l),
    file('theBenchmark.p',cls_rel__simps_I50_J_0) ).

cnf(cls_rel__simps_I38_J_1,axiom,
    c_Int_OPls = c_Int_OBit0(c_Int_OPls),
    file('theBenchmark.p',cls_rel__simps_I38_J_1) ).

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_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_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_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_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_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_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_power2__eq__square_0,axiom,
    ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a)
    | ~ class_OrderedGroup_Omonoid__mult(T_a) ),
    file('theBenchmark.p',cls_power2__eq__square_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_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__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_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_mult__numeral__1_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a),V_a,T_a) = V_a
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_mult__numeral__1_0) ).

cnf(cls_mult__numeral__1__right_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a),T_a) = V_a
    | ~ class_Int_Onumber__ring(T_a) ),
    file('theBenchmark.p',cls_mult__numeral__1__right_0) ).

cnf(cls_rel__simps_I38_J_0,axiom,
    ( c_Int_OPls = V_l
    | c_Int_OPls != c_Int_OBit0(V_l) ),
    file('theBenchmark.p',cls_rel__simps_I38_J_0) ).

cnf(cls_rel__simps_I51_J_0,axiom,
    ( V_k = V_l
    | c_Int_OBit1(V_k) != c_Int_OBit1(V_l) ),
    file('theBenchmark.p',cls_rel__simps_I51_J_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_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_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_power3__eq__cube_0,axiom,
    ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),V_a,T_a)
    | ~ class_OrderedGroup_Omonoid__mult(T_a) ),
    file('theBenchmark.p',cls_power3__eq__cube_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_class__semiring_Osemiring__rules_I36_J_0,axiom,
    ( c_Power_Opower__class_Opower(V_x,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_n,T_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_class__semiring_Osemiring__rules_I36_J_0) ).

cnf(cls_rel__simps_I49_J_0,axiom,
    c_Int_OBit0(V_k) != c_Int_OBit1(V_l),
    file('theBenchmark.p',cls_rel__simps_I49_J_0) ).

cnf(cls_conjecture_0,negated_conjecture,
    c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
    file('theBenchmark.p',cls_conjecture_0) ).

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__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__1,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    file('theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

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__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    file('theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).

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_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__ab__group__add__abs,axiom,
    class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs) ).

cnf(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs,axiom,
    class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs) ).

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_Opordered__ring__abs,axiom,
    class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs) ).

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__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_Olordered__ring,axiom,
    class_Ring__and__Field_Olordered__ring(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Olordered__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__1,axiom,
    class_Ring__and__Field_Osemiring__1(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__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__Ring__and__Field_Oabs__if,axiom,
    class_Ring__and__Field_Oabs__if(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oabs__if) ).

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__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    file('theBenchmark.p',clsarity_Int__Oint__Nat_Osemiring__char__0) ).

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_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__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__1,axiom,
    class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__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__RealVector_Oreal__field,axiom,
    class_RealVector_Oreal__field(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).

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__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_Complex_Ocomplex),
    file('theBenchmark.p',clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) ).

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(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(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_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_5,axiom,
    ( c_HOL_Oabs__class_Oabs(Eq_x_0,Eq_x_1) = c_HOL_Oabs__class_Oabs(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_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_8,axiom,
    ( c_Suc(Eq_x_0) = c_Suc(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_9,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_10,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_11,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_12,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_13,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_14,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_15,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_16,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_17,axiom,
    ( c_HOL_Ominus__class_Ominus(Eq_x_0,Eq_x_1,Eq_x_2) = c_HOL_Ominus__class_Ominus(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,
    ( c_Nat_Osemiring__1__class_Oof__nat(Eq_x_0,Eq_x_1) = c_Nat_Osemiring__1__class_Oof__nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_19,axiom,
    ( c_FFT__Mirabelle_Oroot(Eq_x_0) = c_FFT__Mirabelle_Oroot(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_20,axiom,
    ( c_Int_OBit1(Eq_x_0) = c_Int_OBit1(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_21,axiom,
    ( c_Int_OBit0(Eq_x_0) = c_Int_OBit0(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_22,axiom,
    ( c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1(Eq_x_0) = c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_23,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_24,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_25,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_26,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_27,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(Eq_y_0,Eq_y_1)
    | ~ c_Parity_Oeven__odd__class_Oeven(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_28,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_29,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_30,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_31,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_32,axiom,
    ( class_Ring__and__Field_Opordered__ring__abs(Eq_y_0)
    | ~ class_Ring__and__Field_Opordered__ring__abs(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_33,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_34,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_35,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_36,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_37,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_38,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_39,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_40,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_41,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_42,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_43,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_44,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_45,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_46,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add__abs(Eq_y_0)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_47,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_48,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_49,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_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_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_52,axiom,
    ( class_OrderedGroup_Olordered__ab__group__add__abs(Eq_y_0)
    | ~ class_OrderedGroup_Olordered__ab__group__add__abs(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_53,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_54,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_55,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_56,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_57,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_58,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_59,axiom,
    ( class_Ring__and__Field_Oabs__if(Eq_y_0)
    | ~ class_Ring__and__Field_Oabs__if(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_60,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_61,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_62,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_63,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_64,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_65,axiom,
    ( class_Ring__and__Field_Osemiring__1(Eq_y_0)
    | ~ class_Ring__and__Field_Osemiring__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_66,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_67,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_68,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_69,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_70,axiom,
    ( class_Nat_Osemiring__char__0(Eq_y_0)
    | ~ class_Nat_Osemiring__char__0(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_71,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_72,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_73,axiom,
    ( class_Ring__and__Field_Olordered__ring(Eq_y_0)
    | ~ class_Ring__and__Field_Olordered__ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_74,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_75,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_76,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_77,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_78,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_79,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_80,axiom,
    ( c_Int_Oiszero(Eq_y_0,Eq_y_1)
    | ~ c_Int_Oiszero(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_81,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_82,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_83,axiom,
    ( class_RealVector_Oreal__field(Eq_y_0)
    | ~ class_RealVector_Oreal__field(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_84,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_85,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_86,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_87,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_88,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_89,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_90,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_91,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_92,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_93,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_94,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_95,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(sat_proved,plain,
    $false,
    inference(cadical,[status(thm)],[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWV633-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03  This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04  % Command  : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.59  % Computer : n020.cluster.edu
% 0.11/5.59  % Model    : x86_64 x86_64
% 0.11/5.59  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.59  % Memory   : 8046.5625MB
% 0.11/5.59  % OS       : Linux 6.8.0-71-generic
% 0.11/5.59  % CPULimit : 300
% 0.11/5.59  % WCLimit  : 300
% 0.11/5.59  % DateTime : Sun Sep 20 04:25:54 UTC 2026
% 0.11/5.59  % CPUTime  : 
% 228.24/233.74  % SZS status Unsatisfiable for theBenchmark
% 228.24/233.74  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------