ConnectPP---0.7.2.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : ALG339-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 08:12:40 AM UTC 2026

% Result   : Unsatisfiable 73.30s 74.15s
% Output   : Proof 73.39s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
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_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_divide__self__if_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__self__if_0) ).

cnf(cls_neg__equal__zero_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != V_a
    | ~ class_OrderedGroup_Oordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_neg__equal__zero_0) ).

cnf(cls_inverse__zero_0,axiom,
    ( c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
    file('theBenchmark.p',cls_inverse__zero_0) ).

cnf(cls_inverse__nonzero__iff__nonzero_1,axiom,
    ( c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).

cnf(cls_nonzero__inverse__eq__imp__eq_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | V_a = V_b
    | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a)
    | ~ class_Ring__and__Field_Odivision__ring(T_a) ),
    file('theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).

cnf(cls_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_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_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_double__eq__0__iff_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
    file('theBenchmark.p',cls_double__eq__0__iff_0) ).

cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).

cnf(cls_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_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_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_scaleR_Ozero__right_0,axiom,
    ( c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_scaleR_Ozero__right_0) ).

cnf(cls_scaleR__eq__0__iff_2,axiom,
    ( c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_RealVector_Oreal__vector(T_a) ),
    file('theBenchmark.p',cls_scaleR__eq__0__iff_2) ).

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_sgn__0__0_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_sgn__0__0_0) ).

cnf(cls_sgn__zero__iff_0,axiom,
    ( V_x = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Osgn__class_Osgn(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_sgn__zero__iff_0) ).

cnf(cls_exp__not__eq__zero_0,axiom,
    ( c_Transcendental_Oexp(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_RealVector_Oreal__normed__field(T_a)
    | ~ class_SEQ_Obanach(T_a) ),
    file('theBenchmark.p',cls_exp__not__eq__zero_0) ).

cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
    ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
    | ~ class_OrderedGroup_Omonoid__add(T_a) ),
    file('theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

cnf(cls_add__0__left_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a
    | ~ class_OrderedGroup_Omonoid__add(T_a) ),
    file('theBenchmark.p',cls_add__0__left_0) ).

cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
    ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
    file('theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
    ( V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).

cnf(cls_class__semiring_Oadd__0_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = V_x
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

cnf(cls_comm__monoid__add_Omult__1_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
    file('theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

cnf(cls_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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__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__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_sgn__zero_0,axiom,
    ( c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_sgn__zero_0) ).

cnf(cls_sgn0_0,axiom,
    ( c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Osgn__if(T_a) ),
    file('theBenchmark.p',cls_sgn0_0) ).

cnf(cls_sgn__0__0_1,axiom,
    ( c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_sgn__0__0_1) ).

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_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_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_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_scaleR__cancel__right_1,axiom,
    ( c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_RealVector_Oreal__vector(T_a) ),
    file('theBenchmark.p',cls_scaleR__cancel__right_1) ).

cnf(cls_scaleR__cancel__right_0,axiom,
    ( V_a = V_b
    | V_x = c_HOL_Ozero__class_Ozero(T_a)
    | c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a) != c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a)
    | ~ class_RealVector_Oreal__vector(T_a) ),
    file('theBenchmark.p',cls_scaleR__cancel__right_0) ).

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

cnf(cls_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_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_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_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_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_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_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_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_exp__add_0,axiom,
    ( c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(V_x,T_a),c_Transcendental_Oexp(V_y,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__field(T_a)
    | ~ class_SEQ_Obanach(T_a) ),
    file('theBenchmark.p',cls_exp__add_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_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_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_scaleR_Oadd__right_0,axiom,
    ( c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Oplus__class_Oplus(V_b,V_b_H,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),c_RealVector_OscaleR__class_OscaleR(V_a,V_b_H,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_scaleR_Oadd__right_0) ).

cnf(cls_scaleR__right_Oadd_0,axiom,
    ( c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a),T_a)
    | ~ class_RealVector_Oreal__vector(T_a) ),
    file('theBenchmark.p',cls_scaleR__right_Oadd_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__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_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_real__sqrt__mult_0,axiom,
    c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal),
    file('theBenchmark.p',cls_real__sqrt__mult_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_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_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_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_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_real__vector_Oscale__scale_0,axiom,
    ( c_RealVector_OscaleR__class_OscaleR(V_a,c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Otimes__class_Otimes(V_a,V_b,tc_RealDef_Oreal),V_x,T_a)
    | ~ class_RealVector_Oreal__vector(T_a) ),
    file('theBenchmark.p',cls_real__vector_Oscale__scale_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_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_scaleR__conv__of__real_0,axiom,
    ( c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(V_r,T_a),V_x,T_a)
    | ~ class_RealVector_Oreal__algebra__1(T_a) ),
    file('theBenchmark.p',cls_scaleR__conv__of__real_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_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_I23_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_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_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_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_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_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_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_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_real__mult__commute_0,axiom,
    c_HOL_Otimes__class_Otimes(V_z,V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,V_z,tc_RealDef_Oreal),
    file('theBenchmark.p',cls_real__mult__commute_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_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_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_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_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_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_of__real__eq__iff_0,axiom,
    ( V_x = V_y
    | c_RealVector_Oof__real(V_x,T_a) != c_RealVector_Oof__real(V_y,T_a)
    | ~ class_RealVector_Oreal__algebra__1(T_a) ),
    file('theBenchmark.p',cls_of__real__eq__iff_0) ).

cnf(cls_scaleR_Ominus__right_0,axiom,
    ( c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_scaleR_Ominus__right_0) ).

cnf(cls_scaleR__minus__right_0,axiom,
    ( c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a)
    | ~ class_RealVector_Oreal__vector(T_a) ),
    file('theBenchmark.p',cls_scaleR__minus__right_0) ).

cnf(cls_abs__norm__cancel_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(V_a,T_a),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(V_a,T_a)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_abs__norm__cancel_0) ).

cnf(cls_mult__sgn__abs_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_x,T_a),c_HOL_Oabs__class_Oabs(V_x,T_a),T_a) = V_x
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_mult__sgn__abs_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_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_real__of__nat__inject_0,axiom,
    ( V_n = V_m
    | c_RealDef_Oreal(V_n,tc_nat) != c_RealDef_Oreal(V_m,tc_nat) ),
    file('theBenchmark.p',cls_real__of__nat__inject_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_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_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_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_exp__of__real_0,axiom,
    ( c_Transcendental_Oexp(c_RealVector_Oof__real(V_x,T_a),T_a) = c_RealVector_Oof__real(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),T_a)
    | ~ class_RealVector_Oreal__normed__field(T_a)
    | ~ class_SEQ_Obanach(T_a) ),
    file('theBenchmark.p',cls_exp__of__real_0) ).

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_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__imp_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a
    | V_c = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_divide__eq__imp_0) ).

cnf(cls_eq__divide__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_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_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_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_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__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_sgn__minus_0,axiom,
    ( c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(V_x,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_sgn__minus_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_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_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_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_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_real__sqrt__eq__iff_0,axiom,
    ( V_x = V_y
    | c_NthRoot_Osqrt(V_x) != c_NthRoot_Osqrt(V_y) ),
    file('theBenchmark.p',cls_real__sqrt__eq__iff_0) ).

cnf(cls_exp__inj__iff_0,axiom,
    ( V_x = V_y
    | c_Transcendental_Oexp(V_x,tc_RealDef_Oreal) != c_Transcendental_Oexp(V_y,tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_exp__inj__iff_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_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_abs__real__of__nat__cancel_0,axiom,
    c_HOL_Oabs__class_Oabs(c_RealDef_Oreal(V_x,tc_nat),tc_RealDef_Oreal) = c_RealDef_Oreal(V_x,tc_nat),
    file('theBenchmark.p',cls_abs__real__of__nat__cancel_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_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_of__real__mult_0,axiom,
    ( c_RealVector_Oof__real(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),T_a) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(V_x,T_a),c_RealVector_Oof__real(V_y,T_a),T_a)
    | ~ class_RealVector_Oreal__algebra__1(T_a) ),
    file('theBenchmark.p',cls_of__real__mult_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_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_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_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_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__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__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__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__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__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_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_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_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_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_norm__sgn_0,axiom,
    ( c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_norm__sgn_0) ).

cnf(cls_scaleR__cancel__left_0,axiom,
    ( V_x = V_y
    | V_a = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a) != c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a)
    | ~ class_RealVector_Oreal__vector(T_a) ),
    file('theBenchmark.p',cls_scaleR__cancel__left_0) ).

cnf(cls_scaleR__cancel__left_1,axiom,
    ( c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,T_a) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,T_a)
    | ~ class_RealVector_Oreal__vector(T_a) ),
    file('theBenchmark.p',cls_scaleR__cancel__left_1) ).

cnf(cls_real__mult__right__cancel_0,axiom,
    ( V_a = V_b
    | V_c = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(V_a,V_c,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_b,V_c,tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_real__mult__right__cancel_0) ).

cnf(cls_real__mult__left__cancel_0,axiom,
    ( V_a = V_b
    | V_c = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_HOL_Otimes__class_Otimes(V_c,V_a,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_c,V_b,tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_real__mult__left__cancel_0) ).

cnf(cls_real__sqrt__eq__0__iff_0,axiom,
    ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_real__sqrt__eq__0__iff_0) ).

cnf(cls_pi__neq__zero_0,axiom,
    c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
    file('theBenchmark.p',cls_pi__neq__zero_0) ).

cnf(cls_real__sqrt__zero_0,axiom,
    c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
    file('theBenchmark.p',cls_real__sqrt__zero_0) ).

cnf(cls_real__root__zero_0,axiom,
    c_NthRoot_Oroot(V_n,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
    file('theBenchmark.p',cls_real__root__zero_0) ).

cnf(cls_dist__self_0,axiom,
    ( c_RealVector_Odist__class_Odist(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ class_RealVector_Ometric__space(T_a) ),
    file('theBenchmark.p',cls_dist__self_0) ).

cnf(cls_dist__eq__0__iff_0,axiom,
    ( V_x = V_y
    | c_RealVector_Odist__class_Odist(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ class_RealVector_Ometric__space(T_a) ),
    file('theBenchmark.p',cls_dist__eq__0__iff_0) ).

cnf(cls_exp__ln_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | c_Transcendental_Oexp(c_Transcendental_Oln(V_x),tc_RealDef_Oreal) = V_x ),
    file('theBenchmark.p',cls_exp__ln_0) ).

cnf(cls_exp__ln__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | c_Transcendental_Oexp(c_Transcendental_Oln(V_x),tc_RealDef_Oreal) != V_x ),
    file('theBenchmark.p',cls_exp__ln__iff_0) ).

cnf(cls_exp__less__cancel_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_Transcendental_Oexp(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_exp__less__cancel_0) ).

cnf(cls_exp__less__mono_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_Transcendental_Oexp(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_exp__less__mono_0) ).

cnf(cls_real__sqrt__less__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_real__sqrt__less__iff_0) ).

cnf(cls_real__sqrt__less__iff_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_real__sqrt__less__iff_1) ).

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_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_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_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_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_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__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__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_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_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__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__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_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_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_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__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_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_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_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_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_zero__less__power_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_zero__less__power_0) ).

cnf(cls_zero__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_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_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_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_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_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_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_divide__strict__right__mono__neg_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__field(T_a) ),
    file('theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).

cnf(cls_divide__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_Rational_Oordered__idom__class_Osgn__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_Osgn__class_Osgn(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_Rational_Oordered__idom__class_Osgn__less_1) ).

cnf(cls_Rational_Oordered__idom__class_Osgn__less_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(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_Rational_Oordered__idom__class_Osgn__less_0) ).

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_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_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_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_mult__less__cancel__right__disj_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
    file('theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).

cnf(cls_mult__less__cancel__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_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_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_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_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_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_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__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_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_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_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_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_pos__add__strict_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a)
    | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
    file('theBenchmark.p',cls_pos__add__strict_0) ).

cnf(cls_mult__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_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__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_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_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_Rational_Oordered__idom__class_Osgn__greater_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_Osgn__class_Osgn(V_a,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__greater_1) ).

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_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_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_norm__mult__less_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),V_r,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_y,T_a),V_s,tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(V_r,V_s,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    file('theBenchmark.p',cls_norm__mult__less_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_class__semiring_Osemiring__rules_I16_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,V_rx,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ry,T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

cnf(cls_real__mult__assoc_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_z1,V_z2,tc_RealDef_Oreal),V_z3,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_z1,c_HOL_Otimes__class_Otimes(V_z2,V_z3,tc_RealDef_Oreal),tc_RealDef_Oreal),
    file('theBenchmark.p',cls_real__mult__assoc_0) ).

cnf(cls_class__semiring_Omul__a_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Omul__a_0) ).

cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).

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

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

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

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

cnf(cls_class__semiring_Omul__d_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Omul__d_0) ).

cnf(cls_comm__semiring__class_Odistrib_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring(T_a) ),
    file('theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).

cnf(cls_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_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_mult_Ominus__left_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    file('theBenchmark.p',cls_mult_Ominus__left_0) ).

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

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

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

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

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

cnf(cls_sgn__sgn_0,axiom,
    ( c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) = c_HOL_Osgn__class_Osgn(V_a,T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_sgn__sgn_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_abs__sgn_0,axiom,
    ( c_HOL_Oabs__class_Oabs(V_k,T_a) = c_HOL_Otimes__class_Otimes(V_k,c_HOL_Osgn__class_Osgn(V_k,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_abs__sgn_0) ).

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

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

cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
    file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

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

cnf(cls_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_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_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_inverse__mult__distrib_0,axiom,
    ( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_Ring__and__Field_Ofield(T_a) ),
    file('theBenchmark.p',cls_inverse__mult__distrib_0) ).

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

cnf(cls_ln__unique_0,axiom,
    c_Transcendental_Oln(c_Transcendental_Oexp(V_y,tc_RealDef_Oreal)) = V_y,
    file('theBenchmark.p',cls_ln__unique_0) ).

cnf(cls_exp__ln__eq_0,axiom,
    c_Transcendental_Oln(c_Transcendental_Oexp(V_u,tc_RealDef_Oreal)) = V_u,
    file('theBenchmark.p',cls_exp__ln__eq_0) ).

cnf(cls_ln__exp_0,axiom,
    c_Transcendental_Oln(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal)) = V_x,
    file('theBenchmark.p',cls_ln__exp_0) ).

cnf(cls_dist__commute_0,axiom,
    ( c_RealVector_Odist__class_Odist(V_x,V_y,T_a) = c_RealVector_Odist__class_Odist(V_y,V_x,T_a)
    | ~ class_RealVector_Ometric__space(T_a) ),
    file('theBenchmark.p',cls_dist__commute_0) ).

cnf(cls_mult_OscaleR__left_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(V_r,V_a,T_a),V_b,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,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_OscaleR__left_0) ).

cnf(cls_mult__left_OscaleR_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),V_y,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,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_OscaleR_0) ).

cnf(cls_mult_OscaleR__right_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_a,c_RealVector_OscaleR__class_OscaleR(V_r,V_b,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,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_OscaleR__right_0) ).

cnf(cls_mult__right_OscaleR_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_xa,c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,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_OscaleR_0) ).

cnf(cls_mult__scaleR__left_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),V_y,T_a) = c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)
    | ~ class_RealVector_Oreal__algebra(T_a) ),
    file('theBenchmark.p',cls_mult__scaleR__left_0) ).

cnf(cls_mult__scaleR__right_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_x,c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)
    | ~ class_RealVector_Oreal__algebra(T_a) ),
    file('theBenchmark.p',cls_mult__scaleR__right_0) ).

cnf(cls_norm__scaleR_0,axiom,
    ( c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_norm__scaleR_0) ).

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_mult__exp__exp_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(V_x,T_a),c_Transcendental_Oexp(V_y,T_a),T_a) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__field(T_a)
    | ~ class_SEQ_Obanach(T_a) ),
    file('theBenchmark.p',cls_mult__exp__exp_0) ).

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_divide_OscaleR_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),V_y,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,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_OscaleR_0) ).

cnf(cls_norm__of__real_0,axiom,
    ( c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(V_r,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__algebra__1(T_a) ),
    file('theBenchmark.p',cls_norm__of__real_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_norm__minus__cancel_0,axiom,
    ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_norm__minus__cancel_0) ).

cnf(cls_scaleR_OscaleR__right_0,axiom,
    ( c_RealVector_OscaleR__class_OscaleR(V_a,c_RealVector_OscaleR__class_OscaleR(V_r,V_b,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_scaleR_OscaleR__right_0) ).

cnf(cls_scaleR__left__commute_0,axiom,
    ( c_RealVector_OscaleR__class_OscaleR(V_a,c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_b,c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a)
    | ~ class_RealVector_Oreal__vector(T_a) ),
    file('theBenchmark.p',cls_scaleR__left__commute_0) ).

cnf(cls_scaleR__right_OscaleR_0,axiom,
    ( c_RealVector_OscaleR__class_OscaleR(V_ra,c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_RealVector_OscaleR__class_OscaleR(V_ra,V_x,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_scaleR__right_OscaleR_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_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_norm__mult_0,axiom,
    ( c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_RealVector_Onorm__class_Onorm(V_y,T_a),tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__div__algebra(T_a) ),
    file('theBenchmark.p',cls_norm__mult_0) ).

cnf(cls_power__commutes_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_a,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ class_OrderedGroup_Omonoid__mult(T_a) ),
    file('theBenchmark.p',cls_power__commutes_0) ).

cnf(cls_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_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_class__ringb_Onoteq__reduce_0,axiom,
    ( V_a = V_b
    | V_c = V_d
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_d,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | ~ class_Ring__and__Field_Oidom(T_a) ),
    file('theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).

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

cnf(cls_abs__exp__cancel_0,axiom,
    c_HOL_Oabs__class_Oabs(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),
    file('theBenchmark.p',cls_abs__exp__cancel_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_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_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_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_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_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_minus__mult__commute_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Oring(T_a) ),
    file('theBenchmark.p',cls_minus__mult__commute_0) ).

cnf(cls_divide__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_real__sqrt__abs2_0,axiom,
    c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal)) = c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),
    file('theBenchmark.p',cls_real__sqrt__abs2_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_exp__minus_0,axiom,
    ( c_Transcendental_Oexp(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Oexp(V_x,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__field(T_a)
    | ~ class_SEQ_Obanach(T_a) ),
    file('theBenchmark.p',cls_exp__minus_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_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_sgn__mult_0,axiom,
    ( c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_x,T_a),c_HOL_Osgn__class_Osgn(V_y,T_a),T_a)
    | ~ class_RealVector_Oreal__normed__div__algebra(T_a) ),
    file('theBenchmark.p',cls_sgn__mult_0) ).

cnf(cls_sgn__times_0,axiom,
    ( c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Osgn__class_Osgn(V_b,T_a),T_a)
    | ~ class_Ring__and__Field_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_sgn__times_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_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_Rational_Oordered__idom__class_Osgn__greater_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Osgn__class_Osgn(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_Oordered__idom(T_a) ),
    file('theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__greater_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_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_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_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_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_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_norm__zero_0,axiom,
    ( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_norm__zero_0) ).

cnf(cls_scaleR__eq__0__iff_0,axiom,
    ( V_a = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | V_x = c_HOL_Ozero__class_Ozero(T_a)
    | c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_RealVector_Oreal__vector(T_a) ),
    file('theBenchmark.p',cls_scaleR__eq__0__iff_0) ).

cnf(cls_of__real__eq__0__iff_0,axiom,
    ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_RealVector_Oreal__algebra__1(T_a) ),
    file('theBenchmark.p',cls_of__real__eq__0__iff_0) ).

cnf(cls_of__real__0_0,axiom,
    ( c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_RealVector_Oreal__algebra__1(T_a) ),
    file('theBenchmark.p',cls_of__real__0_0) ).

cnf(cls_of__real_Ozero_0,axiom,
    ( c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_RealVector_Oreal__algebra__1(T_a)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_of__real_Ozero_0) ).

cnf(cls_norm__eq__zero_0,axiom,
    ( V_x = c_HOL_Ozero__class_Ozero(T_a)
    | c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_norm__eq__zero_0) ).

cnf(cls_scaleR_Ozero__left_0,axiom,
    ( c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_scaleR_Ozero__left_0) ).

cnf(cls_scaleR__eq__0__iff_1,axiom,
    ( c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ class_RealVector_Oreal__vector(T_a) ),
    file('theBenchmark.p',cls_scaleR__eq__0__iff_1) ).

cnf(cls_real__less__all__real2_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(V_y,c_RealDef_Oreal__of__preal(V_x),tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_real__less__all__real2_0) ).

cnf(cls_pi__gt__zero_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
    file('theBenchmark.p',cls_pi__gt__zero_0) ).

cnf(cls_not__real__square__gt__zero_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_not__real__square__gt__zero_0) ).

cnf(cls_real__abs__def_1,axiom,
    ( c_HOL_Oord__class_Oless(V_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r ),
    file('theBenchmark.p',cls_real__abs__def_1) ).

cnf(cls_mult__right_Opos__bounded_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(V_x,T_a),tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    file('theBenchmark.p',cls_mult__right_Opos__bounded_0) ).

cnf(cls_Re_Opos__bounded_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__XRe__Xpos__bounded__1__1,tc_RealDef_Oreal),
    file('theBenchmark.p',cls_Re_Opos__bounded_0) ).

cnf(cls_mult__left_Opos__bounded_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(V_y,T_a),tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    file('theBenchmark.p',cls_mult__left_Opos__bounded_0) ).

cnf(cls_not__real__square__gt__zero_1,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
    file('theBenchmark.p',cls_not__real__square__gt__zero_1) ).

cnf(cls_divide_Opos__bounded_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xdivide__Xpos__bounded__1__1(V_y,T_a),tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__field(T_a) ),
    file('theBenchmark.p',cls_divide_Opos__bounded_0) ).

cnf(cls_real__of__preal__zero__less_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(V_m),tc_RealDef_Oreal),
    file('theBenchmark.p',cls_real__of__preal__zero__less_0) ).

cnf(cls_real__gt__zero__preal__Ex_1,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(V_xa),tc_RealDef_Oreal),
    file('theBenchmark.p',cls_real__gt__zero__preal__Ex_1) ).

cnf(cls_scaleR__right_Opos__bounded_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1(V_vskULt,V_r,T_a),tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_scaleR__right_Opos__bounded_0) ).

cnf(cls_lemma__tan__total_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1(V_y),tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_lemma__tan__total_0) ).

cnf(cls_real__lbound__gt__zero_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d1,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2,tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(V_d1,V_d2),tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_real__lbound__gt__zero_0) ).

cnf(cls_realpow__pos__nth2_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_a,tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osko__NthRoot__Xrealpow__pos__nth2__1__1(V_a,V_n),tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_realpow__pos__nth2_0) ).

cnf(cls_lemma__interval_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,V_x,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,V_b,tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Deriv_Osko__Deriv__Xlemma__interval__1__1(V_a,V_b,V_x),tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_lemma__interval_0) ).

cnf(cls_real__sqrt__gt__zero_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x),tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_real__sqrt__gt__zero_0) ).

cnf(cls_real__sqrt__gt__0__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_real__sqrt__gt__0__iff_0) ).

cnf(cls_real__sqrt__gt__0__iff_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_real__sqrt__gt__0__iff_1) ).

cnf(cls_ln__less__cancel__iff_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y),tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_ln__less__cancel__iff_1) ).

cnf(cls_ln__less__cancel__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y),tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_ln__less__cancel__iff_0) ).

cnf(cls_ln__inj__iff_0,axiom,
    ( V_x = V_y
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | c_Transcendental_Oln(V_x) != c_Transcendental_Oln(V_y) ),
    file('theBenchmark.p',cls_ln__inj__iff_0) ).

cnf(cls_ln__less__self_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_Transcendental_Oln(V_x),V_x,tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_ln__less__self_0) ).

cnf(cls_root__def_2,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_NthRoot_Oroot(V_n,V_x) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_root__def_2) ).

cnf(cls_scaleR_Opos__bounded_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__Xpos__bounded__1__1(V_vskULo,T_a),tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_scaleR_Opos__bounded_0) ).

cnf(cls_lemma__interval__lt_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,V_x,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,V_b,tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Deriv_Osko__Deriv__Xlemma__interval__lt__1__1(V_a,V_b,V_x),tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_lemma__interval__lt_0) ).

cnf(cls_zero__less__dist__iff_1,axiom,
    ( V_x = V_y
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(V_x,V_y,T_a),tc_RealDef_Oreal)
    | ~ class_RealVector_Ometric__space(T_a) ),
    file('theBenchmark.p',cls_zero__less__dist__iff_1) ).

cnf(cls_of__real_Opos__bounded_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xof__real__Xpos__bounded__1__1(V_vskULr,T_a),tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__algebra__1(T_a)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_of__real_Opos__bounded_0) ).

cnf(cls_dist__not__less__zero_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ class_RealVector_Ometric__space(T_a) ),
    file('theBenchmark.p',cls_dist__not__less__zero_0) ).

cnf(cls_Im_Opos__bounded_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__XIm__Xpos__bounded__1__1,tc_RealDef_Oreal),
    file('theBenchmark.p',cls_Im_Opos__bounded_0) ).

cnf(cls_real__sqrt__not__eq__zero_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_real__sqrt__not__eq__zero_0) ).

cnf(cls_not__exp__less__zero_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
    file('theBenchmark.p',cls_not__exp__less__zero_0) ).

cnf(cls_real__mult__order_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_real__mult__order_0) ).

cnf(cls_real__lbound__gt__zero_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d1,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2,tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(V_d1,V_d2),V_d2,tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_real__lbound__gt__zero_2) ).

cnf(cls_real__lbound__gt__zero_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d1,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2,tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(V_d1,V_d2),V_d1,tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_real__lbound__gt__zero_1) ).

cnf(cls_zero__less__dist__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(V_x,V_x,T_a),tc_RealDef_Oreal)
    | ~ class_RealVector_Ometric__space(T_a) ),
    file('theBenchmark.p',cls_zero__less__dist__iff_0) ).

cnf(cls_not__real__of__nat__less__zero_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(V_n,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
    file('theBenchmark.p',cls_not__real__of__nat__less__zero_0) ).

cnf(cls_norm__not__less__zero_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_norm__not__less__zero_0) ).

cnf(cls_real__sqrt__lt__0__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_real__sqrt__lt__0__iff_0) ).

cnf(cls_real__sqrt__lt__0__iff_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_real__sqrt__lt__0__iff_1) ).

cnf(cls_pi__not__less__zero_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
    file('theBenchmark.p',cls_pi__not__less__zero_0) ).

cnf(cls_cnj_Opos__bounded_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__Xcnj__Xpos__bounded__1__1,tc_RealDef_Oreal),
    file('theBenchmark.p',cls_cnj_Opos__bounded_0) ).

cnf(cls_mult_Opos__bounded_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(V_vskULn,T_a),tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    file('theBenchmark.p',cls_mult_Opos__bounded_0) ).

cnf(cls_real__mult__less__mono2_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_z,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_real__mult__less__mono2_0) ).

cnf(cls_real__mult__less__iff1_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_real__mult__less__iff1_1) ).

cnf(cls_real__mult__less__iff1_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_real__mult__less__iff1_0) ).

cnf(cls_exp__gt__zero_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal),
    file('theBenchmark.p',cls_exp__gt__zero_0) ).

cnf(cls_scaleR__left_Opos__bounded_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__left__Xpos__bounded__1__1(V_x,T_a),tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_scaleR__left_Opos__bounded_0) ).

cnf(cls_zero__less__norm__iff_1,axiom,
    ( V_x = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_zero__less__norm__iff_1) ).

cnf(cls_zero__less__norm__iff_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a),tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    file('theBenchmark.p',cls_zero__less__norm__iff_0) ).

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_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_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_order__less__asym_H_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | ~ class_Orderings_Opreorder(T_a) ),
    file('theBenchmark.p',cls_order__less__asym_H_0) ).

cnf(cls_order__less__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_real__less__def_1,axiom,
    ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal),
    file('theBenchmark.p',cls_real__less__def_1) ).

cnf(cls_order__less__le_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
    | ~ class_Orderings_Oorder(T_a) ),
    file('theBenchmark.p',cls_order__less__le_1) ).

cnf(cls_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_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_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_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_conjecture_0,negated_conjecture,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_d1,tc_RealDef_Oreal),
    file('theBenchmark.p',cls_conjecture_0) ).

cnf(cls_conjecture_1,negated_conjecture,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_d2,tc_RealDef_Oreal),
    file('theBenchmark.p',cls_conjecture_1) ).

cnf(cls_conjecture_2,negated_conjecture,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,v_d1,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,v_d2,tc_RealDef_Oreal) ),
    file('theBenchmark.p',cls_conjecture_2) ).

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_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__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_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_Omult__zero,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    file('theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

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

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_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
    class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,axiom,
    class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs,axiom,
    class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors,axiom,
    class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict,axiom,
    class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) ).

cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
    class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,axiom,
    class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add,axiom,
    class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).

cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
    class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero,axiom,
    class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).

cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).

cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
    class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field,axiom,
    class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring,axiom,
    class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) ).

cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
    class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,axiom,
    class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).

cnf(clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1,axiom,
    class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,axiom,
    class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero,axiom,
    class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult,axiom,
    class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring,axiom,
    class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).

cnf(clsarity_RealDef__Oreal__RealVector_Oreal__algebra,axiom,
    class_RealVector_Oreal__algebra(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra) ).

cnf(clsarity_RealDef__Oreal__RealVector_Ometric__space,axiom,
    class_RealVector_Ometric__space(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Ometric__space) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add,axiom,
    class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).

cnf(clsarity_RealDef__Oreal__RealVector_Oreal__vector,axiom,
    class_RealVector_Oreal__vector(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__vector) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom,
    class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if,axiom,
    class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if,axiom,
    class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ofield,axiom,
    class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring,axiom,
    class_Ring__and__Field_Oring(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oidom,axiom,
    class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).

cnf(clsarity_RealDef__Oreal__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Nat_Osemiring__char__0) ).

cnf(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).

cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).

cnf(clsarity_RealDef__Oreal__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).

cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).

cnf(clsarity_RealDef__Oreal__Power_Opower,axiom,
    class_Power_Opower(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__Power_Opower) ).

cnf(clsarity_RealDef__Oreal__SEQ_Obanach,axiom,
    class_SEQ_Obanach(tc_RealDef_Oreal),
    file('theBenchmark.p',clsarity_RealDef__Oreal__SEQ_Obanach) ).

cnf(equality_1,axiom,
    Eq_x_0 = Eq_x_0,
    theory(equality,[reflexivity]) ).

cnf(equality_2,axiom,
    ( Eq_x_1 = Eq_x_0
    | Eq_x_0 != Eq_x_1 ),
    theory(equality,[symmetry]) ).

cnf(equality_3,axiom,
    ( Eq_x_0 = Eq_x_2
    | Eq_x_1 != Eq_x_2
    | Eq_x_0 != Eq_x_1 ),
    theory(equality,[transitivity]) ).

cnf(equality_4,axiom,
    ( c_HOL_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_5,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_6,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_7,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_8,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_9,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_10,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_11,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_12,axiom,
    ( c_RealVector_OscaleR__class_OscaleR(Eq_x_0,Eq_x_1,Eq_x_2) = c_RealVector_OscaleR__class_OscaleR(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_13,axiom,
    ( c_HOL_Osgn__class_Osgn(Eq_x_0,Eq_x_1) = c_HOL_Osgn__class_Osgn(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_14,axiom,
    ( c_Transcendental_Oexp(Eq_x_0,Eq_x_1) = c_Transcendental_Oexp(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_15,axiom,
    ( c_NthRoot_Osqrt(Eq_x_0) = c_NthRoot_Osqrt(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_16,axiom,
    ( c_RealVector_Oof__real(Eq_x_0,Eq_x_1) = c_RealVector_Oof__real(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_RealVector_Onorm__class_Onorm(Eq_x_0,Eq_x_1) = c_RealVector_Onorm__class_Onorm(Eq_y_0,Eq_y_1)
    | 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_RealDef_Oreal(Eq_x_0,Eq_x_1) = c_RealDef_Oreal(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_20,axiom,
    ( c_NthRoot_Oroot(Eq_x_0,Eq_x_1) = c_NthRoot_Oroot(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_21,axiom,
    ( c_RealVector_Odist__class_Odist(Eq_x_0,Eq_x_1,Eq_x_2) = c_RealVector_Odist__class_Odist(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

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

cnf(equality_23,axiom,
    ( c_RealDef_Oreal__of__preal(Eq_x_0) = c_RealDef_Oreal__of__preal(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_24,axiom,
    ( c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(Eq_x_0,Eq_x_1) = c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_25,axiom,
    ( c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(Eq_x_0,Eq_x_1) = c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_26,axiom,
    ( c_RealVector_Osko__RealVector__Xdivide__Xpos__bounded__1__1(Eq_x_0,Eq_x_1) = c_RealVector_Osko__RealVector__Xdivide__Xpos__bounded__1__1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_27,axiom,
    ( c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1(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_28,axiom,
    ( c_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1(Eq_x_0) = c_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_29,axiom,
    ( c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(Eq_x_0,Eq_x_1) = c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_30,axiom,
    ( c_NthRoot_Osko__NthRoot__Xrealpow__pos__nth2__1__1(Eq_x_0,Eq_x_1) = c_NthRoot_Osko__NthRoot__Xrealpow__pos__nth2__1__1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_31,axiom,
    ( c_Deriv_Osko__Deriv__Xlemma__interval__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_Deriv_Osko__Deriv__Xlemma__interval__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_32,axiom,
    ( c_RealVector_Osko__RealVector__XscaleR__Xpos__bounded__1__1(Eq_x_0,Eq_x_1) = c_RealVector_Osko__RealVector__XscaleR__Xpos__bounded__1__1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_33,axiom,
    ( c_Deriv_Osko__Deriv__Xlemma__interval__lt__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_Deriv_Osko__Deriv__Xlemma__interval__lt__1__1(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_34,axiom,
    ( c_RealVector_Osko__RealVector__Xof__real__Xpos__bounded__1__1(Eq_x_0,Eq_x_1) = c_RealVector_Osko__RealVector__Xof__real__Xpos__bounded__1__1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_35,axiom,
    ( c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(Eq_x_0,Eq_x_1) = c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_36,axiom,
    ( c_RealVector_Osko__RealVector__XscaleR__left__Xpos__bounded__1__1(Eq_x_0,Eq_x_1) = c_RealVector_Osko__RealVector__XscaleR__left__Xpos__bounded__1__1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_37,axiom,
    ( class_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_38,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_39,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_40,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_41,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_42,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_43,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_44,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_45,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_46,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_47,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_48,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_49,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_50,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_51,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_52,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_53,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_54,axiom,
    ( class_RealVector_Oreal__normed__vector(Eq_y_0)
    | ~ class_RealVector_Oreal__normed__vector(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_55,axiom,
    ( class_RealVector_Oreal__vector(Eq_y_0)
    | ~ class_RealVector_Oreal__vector(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_56,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_57,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_58,axiom,
    ( class_SEQ_Obanach(Eq_y_0)
    | ~ class_SEQ_Obanach(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_59,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_60,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_61,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_62,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_63,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_64,axiom,
    ( class_Ring__and__Field_Osgn__if(Eq_y_0)
    | ~ class_Ring__and__Field_Osgn__if(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_65,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_66,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_67,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_68,axiom,
    ( class_RealVector_Oreal__algebra__1(Eq_y_0)
    | ~ class_RealVector_Oreal__algebra__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_69,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_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_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_72,axiom,
    ( class_OrderedGroup_Oab__semigroup__idem__mult(Eq_y_0)
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_73,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_74,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_75,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_76,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_77,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_78,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_79,axiom,
    ( class_RealVector_Ometric__space(Eq_y_0)
    | ~ class_RealVector_Ometric__space(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_80,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_81,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_82,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_83,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_84,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_85,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_86,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(Eq_y_0)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_87,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(Eq_y_0)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_88,axiom,
    ( class_RealVector_Oreal__algebra(Eq_y_0)
    | ~ class_RealVector_Oreal__algebra(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_89,axiom,
    ( class_RealVector_Oreal__normed__algebra__1(Eq_y_0)
    | ~ class_RealVector_Oreal__normed__algebra__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_90,axiom,
    ( class_RealVector_Oreal__normed__div__algebra(Eq_y_0)
    | ~ class_RealVector_Oreal__normed__div__algebra(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_91,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_92,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_93,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_94,axiom,
    ( class_Orderings_Opreorder(Eq_y_0)
    | ~ class_Orderings_Opreorder(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
% 0.00/0.05  % Problem  : ALG339-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06  This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.07  % Command  : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/1.07  % Computer : n026.cluster.edu
% 0.21/1.07  % Model    : x86_64 x86_64
% 0.21/1.07  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/1.07  % Memory   : 8046.5625MB
% 0.21/1.07  % OS       : Linux 6.8.0-71-generic
% 0.21/1.07  % CPULimit : 300
% 0.21/1.07  % WCLimit  : 300
% 0.21/1.07  % DateTime : Sun Sep 20 10:55:08 UTC 2026
% 0.21/1.08  % CPUTime  : 
% 73.30/74.15  % SZS status Unsatisfiable for theBenchmark
% 73.30/74.15  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------