%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ALG436-1 : 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 : n015.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 08:12:50 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.45s
% Output : Proof 0.11s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_neg__equal__iff__equal_0,axiom,
( V_a = V_b
| c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(V_b,T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_neg__equal__iff__equal_0) ).
cnf(cls_eq__divide__imp_0,axiom,
( V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_eq__divide__imp_0) ).
cnf(cls_divide__eq__imp_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a
| V_c = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_divide__eq__imp_0) ).
cnf(cls_eq__divide__eq_3,axiom,
( V_c = c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_eq__divide__eq_3) ).
cnf(cls_divide__eq__eq_3,axiom,
( V_c = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_divide__eq__eq_3) ).
cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_ry,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
cnf(cls_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_div__mult__self2__is__id_0,axiom,
( V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = V_a
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__mult__self2__is__id_0) ).
cnf(cls_div__mult__self1__is__id_0,axiom,
( V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = V_a
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__mult__self1__is__id_0) ).
cnf(cls_one__neq__zero_0,axiom,
( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('theBenchmark.p',cls_one__neq__zero_0) ).
cnf(cls_mult__eq__0__iff_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) ),
file('theBenchmark.p',cls_mult__eq__0__iff_0) ).
cnf(cls_no__zero__divisors_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) ),
file('theBenchmark.p',cls_no__zero__divisors_0) ).
cnf(cls_no__zero__divirors__neq0_0,axiom,
( V_b = c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) ),
file('theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
cnf(cls_diff__divide__distrib_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_diff__divide__distrib_0) ).
cnf(cls_divide_Odiff_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(V_x,V_ya,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_ya,T_a),T_a)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
file('theBenchmark.p',cls_divide_Odiff_0) ).
cnf(cls_div__by__0_0,axiom,
( c_Divides_Odiv__class_Odiv(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__by__0_0) ).
cnf(cls_div__0_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__0_0) ).
cnf(cls_double__eq__0__iff_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_double__eq__0__iff_0) ).
cnf(cls_eq__iff__diff__eq__0_0,axiom,
( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
cnf(cls_right__minus__eq_1,axiom,
( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_right__minus__eq_1) ).
cnf(cls_diff__0__right_0,axiom,
( c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_diff__0__right_0) ).
cnf(cls_diff__self_0,axiom,
( c_HOL_Ominus__class_Ominus(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_diff__self_0) ).
cnf(cls_class__ringb_Osubr0__iff_1,axiom,
( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
cnf(cls_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_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_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_dvd__mult__cancel__left_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
cnf(cls_dvd__mult__cancel__right_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a),T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
cnf(cls_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_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_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_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_div__mult__div__if__dvd_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_w,T_a)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),c_Divides_Odiv__class_Odiv(V_w,V_z,T_a),T_a) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_x,V_w,T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__mult__div__if__dvd_0) ).
cnf(cls_div__mult__mult1__if_0,axiom,
( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__mult__mult1__if_0) ).
cnf(cls_mod__add__self1_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_b,V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__add__self1_0) ).
cnf(cls_mod__add__self2_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__add__self2_0) ).
cnf(cls_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_DERIV__inverse__lemma_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a),V_h,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_h,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a),T_a)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
file('theBenchmark.p',cls_DERIV__inverse__lemma_0) ).
cnf(cls_inverse__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_inverse__unique_0,axiom,
( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b
| c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Odivision__ring(T_a) ),
file('theBenchmark.p',cls_inverse__unique_0) ).
cnf(cls_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_nonzero__inverse__eq__imp__eq_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| V_a = V_b
| c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a)
| ~ class_Ring__and__Field_Odivision__ring(T_a) ),
file('theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
cnf(cls_inverse__nonzero__iff__nonzero_1,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Odivision__ring(T_a) ),
file('theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).
cnf(cls_inverse__zero_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) ),
file('theBenchmark.p',cls_inverse__zero_0) ).
cnf(cls_class__semiring_Opwr__mul_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_q,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_q,T_a),c_Power_Opower__class_Opower(V_y,V_q,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
cnf(cls_power__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_zmod__simps_I2_J_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_zmod__simps_I2_J_0) ).
cnf(cls_zmod__simps_I1_J_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_zmod__simps_I1_J_0) ).
cnf(cls_inf__period_I4_J_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_x,c_HOL_Otimes__class_Otimes(V_k,V_D,T_a),T_a),V_t,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__ring(T_a)
| ~ class_Ring__and__Field_Odvd(T_a) ),
file('theBenchmark.p',cls_inf__period_I4_J_0) ).
cnf(cls_inf__period_I4_J_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_x,c_HOL_Otimes__class_Otimes(V_k,V_D,T_a),T_a),V_t,T_a),T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__ring(T_a)
| ~ class_Ring__and__Field_Odvd(T_a) ),
file('theBenchmark.p',cls_inf__period_I4_J_1) ).
cnf(cls_mod__div__decomp_0,axiom,
( V_a = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__div__decomp_0) ).
cnf(cls_mod__div__equality_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) = V_a
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__div__equality_0) ).
cnf(cls_mod__div__equality2_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) = V_a
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__div__equality2_0) ).
cnf(cls_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_right__inverse__eq_0,axiom,
( V_a = V_b
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_right__inverse__eq_0) ).
cnf(cls_class__ring_Oneg__mul_0,axiom,
( c_HOL_Ouminus__class_Ouminus(V_x,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),V_x,T_a)
| ~ class_Int_Onumber__ring(T_a) ),
file('theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
cnf(cls_dvd__div__neg_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a)
| c_Divides_Odiv__class_Odiv(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),T_a)
| ~ class_Divides_Oring__div(T_a) ),
file('theBenchmark.p',cls_dvd__div__neg_0) ).
cnf(cls_dvd__neg__div_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),T_a)
| ~ class_Divides_Oring__div(T_a) ),
file('theBenchmark.p',cls_dvd__neg__div_0) ).
cnf(cls_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_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_smult__dvd__iff_2,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a))
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_smult__dvd__iff_2) ).
cnf(cls_smult__dvd__iff_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a))
| V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_smult__dvd__iff_1) ).
cnf(cls_dvd__smult__iff_1,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_dvd__smult__iff_1) ).
cnf(cls_dvd__smult__iff_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))
| c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_dvd__smult__iff_0) ).
cnf(cls_smult__dvd_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a))
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_smult__dvd_0) ).
cnf(cls_dvd__smult__cancel_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))
| V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_dvd__smult__cancel_0) ).
cnf(cls_abs__minus__commute_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
file('theBenchmark.p',cls_abs__minus__commute_0) ).
cnf(cls_minus__divide__right_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_minus__divide__right_0) ).
cnf(cls_minus__divide__left_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_minus__divide__left_0) ).
cnf(cls_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_nonzero__inverse__eq__divide_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_nonzero__inverse__eq__divide_0) ).
cnf(cls_div__add__self1_0,axiom,
( V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_b,V_a,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),c_HOL_Oone__class_Oone(T_a),T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__add__self1_0) ).
cnf(cls_div__add__self2_0,axiom,
( V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),c_HOL_Oone__class_Oone(T_a),T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__add__self2_0) ).
cnf(cls_abs__one_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('theBenchmark.p',cls_abs__one_0) ).
cnf(cls_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_diff__frac__eq_0,axiom,
( V_y = c_HOL_Ozero__class_Ozero(T_a)
| V_z = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_diff__frac__eq_0) ).
cnf(cls_mult_Ominus__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
file('theBenchmark.p',cls_mult_Ominus__left_0) ).
cnf(cls_mult__left_Ominus_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
file('theBenchmark.p',cls_mult__left_Ominus_0) ).
cnf(cls_mult_Ominus__right_0,axiom,
( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
file('theBenchmark.p',cls_mult_Ominus__right_0) ).
cnf(cls_mult__right_Ominus_0,axiom,
( c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
file('theBenchmark.p',cls_mult__right_Ominus_0) ).
cnf(cls_square__eq__iff_1,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_b,V_b,T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_square__eq__iff_1) ).
cnf(cls_minus__mult__minus_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oring(T_a) ),
file('theBenchmark.p',cls_minus__mult__minus_0) ).
cnf(cls_field__inverse_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_field__inverse_0) ).
cnf(cls_left__inverse_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Odivision__ring(T_a) ),
file('theBenchmark.p',cls_left__inverse_0) ).
cnf(cls_right__inverse_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Odivision__ring(T_a) ),
file('theBenchmark.p',cls_right__inverse_0) ).
cnf(cls_div__mult__mult1_0,axiom,
( V_c = c_HOL_Ozero__class_Ozero(T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__mult__mult1_0) ).
cnf(cls_div__mult__mult2_0,axiom,
( V_c = c_HOL_Ozero__class_Ozero(T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__mult__mult2_0) ).
cnf(cls_mod__minus__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_b,T_a)
| ~ class_Divides_Oring__div(T_a) ),
file('theBenchmark.p',cls_mod__minus__eq_0) ).
cnf(cls_smult__1__left_0,axiom,
( c_Polynomial_Osmult(c_HOL_Oone__class_Oone(T_a),V_p,T_a) = V_p
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_smult__1__left_0) ).
cnf(cls_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_group__add__class_Odiff__0_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
cnf(cls_add__frac__num_0,axiom,
( V_y = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a),V_y,T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_add__frac__num_0) ).
cnf(cls_add__num__frac_0,axiom,
( V_y = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oplus__class_Oplus(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a),V_y,T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_add__num__frac_0) ).
cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
cnf(cls_Deriv_Oinverse__diff__inverse_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a),T_a)
| ~ class_Ring__and__Field_Odivision__ring(T_a) ),
file('theBenchmark.p',cls_Deriv_Oinverse__diff__inverse_0) ).
cnf(cls_diff__rat__def_0,axiom,
c_HOL_Ominus__class_Ominus(V_q,V_r,tc_Rational_Orat) = c_HOL_Oplus__class_Oplus(V_q,c_HOL_Ouminus__class_Ouminus(V_r,tc_Rational_Orat),tc_Rational_Orat),
file('theBenchmark.p',cls_diff__rat__def_0) ).
cnf(cls_diff__def_0,axiom,
( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_diff__def_0) ).
cnf(cls_class__ring_Osub__add_0,axiom,
( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a)
| ~ class_Int_Onumber__ring(T_a) ),
file('theBenchmark.p',cls_class__ring_Osub__add_0) ).
cnf(cls_diff__minus_0,axiom,
( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_diff__minus_0) ).
cnf(cls_ab__diff__minus_0,axiom,
( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_ab__diff__minus_0) ).
cnf(cls_nonzero__minus__divide__divide_0,axiom,
( V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
cnf(cls_mod__diff__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
| ~ class_Divides_Oring__div(T_a) ),
file('theBenchmark.p',cls_mod__diff__eq_0) ).
cnf(cls_divide__1_0,axiom,
( c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_divide__1_0) ).
cnf(cls_divide__self__if_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_divide__self__if_0) ).
cnf(cls_dvd__power_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__power_1) ).
cnf(cls_eq__add__iff2_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)
| ~ class_Ring__and__Field_Oring(T_a) ),
file('theBenchmark.p',cls_eq__add__iff2_1) ).
cnf(cls_div__add_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_x,V_z,T_a),c_Divides_Odiv__class_Odiv(V_y,V_z,T_a),T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__add_0) ).
cnf(cls_inverse__eq__divide_0,axiom,
( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_inverse__eq__divide_0) ).
cnf(cls_class__fieldgb_Oinverse__divide_0,axiom,
( c_HOL_Oinverse__class_Oinverse(V_x,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_x,T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_class__fieldgb_Oinverse__divide_0) ).
cnf(cls_zmod__simps_I4_J_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_zmod__simps_I4_J_0) ).
cnf(cls_mult__1__right_0,axiom,
( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
file('theBenchmark.p',cls_mult__1__right_0) ).
cnf(cls_mult__1__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
file('theBenchmark.p',cls_mult__1__left_0) ).
cnf(cls_mult__1_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a
| ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) ),
file('theBenchmark.p',cls_mult__1_0) ).
cnf(cls_class__semiring_Omul__1_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_x,T_a) = V_x
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Omul__1_0) ).
cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom,
( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I11_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
cnf(cls_power__one__over_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_power__one__over_0) ).
cnf(cls_nonzero__minus__divide__right_0,axiom,
( V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
cnf(cls_mod__0_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__0_0) ).
cnf(cls_class__ringb_Oadd__mul__solve_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
cnf(cls_class__ringb_Onoteq__reduce_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
cnf(cls_poly__gcd__left__commute_0,axiom,
( c_Polynomial_Opoly__gcd(V_x,c_Polynomial_Opoly__gcd(V_y,V_z,T_a),T_a) = c_Polynomial_Opoly__gcd(V_y,c_Polynomial_Opoly__gcd(V_x,V_z,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_poly__gcd__left__commute_0) ).
cnf(cls_poly__gcd__assoc_0,axiom,
( c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(V_x,V_y,T_a),V_z,T_a) = c_Polynomial_Opoly__gcd(V_x,c_Polynomial_Opoly__gcd(V_y,V_z,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_poly__gcd__assoc_0) ).
cnf(cls_diff__add__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_diff__add__cancel_0) ).
cnf(cls_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_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_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_class__semiring_Osemiring__rules_I7_J_0,axiom,
( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
cnf(cls_mod__add__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__add__eq_0) ).
cnf(cls_abs__eq__0_1,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
file('theBenchmark.p',cls_abs__eq__0_1) ).
cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
cnf(cls_class__semiring_Oadd__a_0,axiom,
( c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
cnf(cls_add__cancel__21_1,axiom,
( c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_add__cancel__21_1) ).
cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Oab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_d,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
cnf(cls_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_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_right__inverse__eq_1,axiom,
( c_HOL_Oinverse__class_Odivide(V_x,V_x,T_a) = c_HOL_Oone__class_Oone(T_a)
| V_x = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_right__inverse__eq_1) ).
cnf(cls_divide__self_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_divide__self_0) ).
cnf(cls_divide__self__if_1,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_divide__self__if_1) ).
cnf(cls_mod__add__right__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__add__right__eq_0) ).
cnf(cls_mod__add__left__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__add__left__eq_0) ).
cnf(cls_eq__eqI_0,axiom,
( V_x_H = V_y_H
| c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_eq__eqI_0) ).
cnf(cls_eq__eqI_1,axiom,
( V_xa = V_y
| c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_eq__eqI_1) ).
cnf(cls_minus__divide__divide_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_minus__divide__divide_0) ).
cnf(cls_divide_Ominus_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
file('theBenchmark.p',cls_divide_Ominus_0) ).
cnf(cls_mult_Oprod__diff__prod_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),T_a)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
file('theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
cnf(cls_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_eq__neg__iff__add__eq__0_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
cnf(cls_ab__left__minus_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_ab__left__minus_0) ).
cnf(cls_right__minus_0,axiom,
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_right__minus_0) ).
cnf(cls_left__minus_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_left__minus_0) ).
cnf(cls_eq__iff__diff__eq__0_1,axiom,
( V_a = V_b
| c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
cnf(cls_right__minus__eq_0,axiom,
( V_a = V_b
| c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_right__minus__eq_0) ).
cnf(cls_class__ringb_Osubr0__iff_0,axiom,
( V_x = V_y
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
cnf(cls_mult__right_Odiff_0,axiom,
( c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),c_HOL_Otimes__class_Otimes(V_xa,V_y,T_a),T_a)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
file('theBenchmark.p',cls_mult__right_Odiff_0) ).
cnf(cls_mult_Odiff__right_0,axiom,
( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ominus__class_Ominus(V_b,V_b_H,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b_H,T_a),T_a)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
file('theBenchmark.p',cls_mult_Odiff__right_0) ).
cnf(cls_mult_Odiff__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
file('theBenchmark.p',cls_mult_Odiff__left_0) ).
cnf(cls_mult__left_Odiff_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_ya,T_a),c_HOL_Otimes__class_Otimes(V_y,V_ya,T_a),T_a)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
file('theBenchmark.p',cls_mult__left_Odiff_0) ).
cnf(cls_Deriv_Oadd__diff__add_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ominus__class_Ominus(V_c,V_d,T_a),T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
cnf(cls_divide__zero__left_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_divide__zero__left_0) ).
cnf(cls_divide__eq__eq_1,axiom,
( c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_divide__eq__eq_1) ).
cnf(cls_divide__zero_0,axiom,
( c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_divide__zero_0) ).
cnf(cls_divide_Ozero_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
file('theBenchmark.p',cls_divide_Ozero_0) ).
cnf(cls_dvd__div__mult_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_c,T_a) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),V_a,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_dvd__div__mult_0) ).
cnf(cls_inverse__eq__1__iff_0,axiom,
( V_x = c_HOL_Oone__class_Oone(T_a)
| c_HOL_Oinverse__class_Oinverse(V_x,T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_inverse__eq__1__iff_0) ).
cnf(cls_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_abs__inverse_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a) ),
file('theBenchmark.p',cls_abs__inverse_0) ).
cnf(cls_abs__divide_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Oordered__field(T_a) ),
file('theBenchmark.p',cls_abs__divide_0) ).
cnf(cls_mod__mult__right__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__right__eq_0) ).
cnf(cls_mod__mult__left__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__left__eq_0) ).
cnf(cls_add__cancel__end_0,axiom,
( V_x = c_HOL_Ouminus__class_Ouminus(V_z,T_a)
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != V_y
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_add__cancel__end_0) ).
cnf(cls_mult__divide__mult__cancel__right_0,axiom,
( V_c = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
cnf(cls_mult__divide__mult__cancel__left_0,axiom,
( V_c = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).
cnf(cls_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_dvd__mult__div__cancel_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),T_a) = V_b
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_dvd__mult__div__cancel_0) ).
cnf(cls_dvd__div__mult__self_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_a,T_a) = V_b
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_dvd__div__mult__self_0) ).
cnf(cls_diff__minus__eq__add_0,axiom,
( c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_diff__minus__eq__add_0) ).
cnf(cls_mod__mult__self2_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__self2_0) ).
cnf(cls_mod__mult__self1_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__self1_0) ).
cnf(cls_smult__smult_0,axiom,
( c_Polynomial_Osmult(V_a,c_Polynomial_Osmult(V_b,V_p,T_a),T_a) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_p,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_a) ),
file('theBenchmark.p',cls_smult__smult_0) ).
cnf(cls_dvd__mult__cancel__right_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_dvd__mult__cancel__right_0) ).
cnf(cls_dvd__mult__cancel__left_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
cnf(cls_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_add__diff__cancel_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_add__diff__cancel_0) ).
cnf(cls_add__divide__distrib_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_add__divide__distrib_0) ).
cnf(cls_divide_Oadd_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_ya,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_ya,T_a),T_a)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
file('theBenchmark.p',cls_divide_Oadd_0) ).
cnf(cls_minus__equation__iff_1,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_minus__equation__iff_1) ).
cnf(cls_equation__minus__iff_1,axiom,
( V_a = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_equation__minus__iff_1) ).
cnf(cls_equation__minus__iff_0,axiom,
( V_b = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_equation__minus__iff_0) ).
cnf(cls_double__compl_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = V_x
| ~ class_Lattices_Oboolean__algebra(T_a) ),
file('theBenchmark.p',cls_double__compl_0) ).
cnf(cls_minus__minus_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_minus__minus_0) ).
cnf(cls_div__by__1_0,axiom,
( c_Divides_Odiv__class_Odiv(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__by__1_0) ).
cnf(cls_minus__diff__eq_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_minus__diff__eq_0) ).
cnf(cls_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_dvd__imp__mod__0_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Divides_Odiv__class_Omod(V_b,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_dvd__imp__mod__0_0) ).
cnf(cls_dvd__eq__mod__eq__0_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Divides_Odiv__class_Omod(V_b,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).
cnf(cls_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_zero__neq__one_0,axiom,
( c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('theBenchmark.p',cls_zero__neq__one_0) ).
cnf(cls_nonzero__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_power__one_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
file('theBenchmark.p',cls_power__one_0) ).
cnf(cls_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_mod__diff__left__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a)
| ~ class_Divides_Oring__div(T_a) ),
file('theBenchmark.p',cls_mod__diff__left__eq_0) ).
cnf(cls_mod__diff__right__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
| ~ class_Divides_Oring__div(T_a) ),
file('theBenchmark.p',cls_mod__diff__right__eq_0) ).
cnf(cls_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_DERIV__mult__lemma_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_c,V_d,T_a),T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_b,V_d,T_a),V_h,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_a,V_c,T_a),V_h,T_a),V_d,T_a),T_a)
| ~ class_RealVector_Oreal__field(T_a) ),
file('theBenchmark.p',cls_DERIV__mult__lemma_0) ).
cnf(cls_mod__mod__trivial_0,axiom,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mod__trivial_0) ).
cnf(cls_div__self_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_Divides_Odiv__class_Odiv(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__self_0) ).
cnf(cls_eq__add__iff1_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),T_a)
| ~ class_Ring__and__Field_Oring(T_a) ),
file('theBenchmark.p',cls_eq__add__iff1_1) ).
cnf(cls_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_eq__add__iff1_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) = V_d
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)
| ~ class_Ring__and__Field_Oring(T_a) ),
file('theBenchmark.p',cls_eq__add__iff1_0) ).
cnf(cls_eq__add__iff2_0,axiom,
( V_c = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)
| ~ class_Ring__and__Field_Oring(T_a) ),
file('theBenchmark.p',cls_eq__add__iff2_0) ).
cnf(cls_div__mod__equality_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__mod__equality_0) ).
cnf(cls_div__mod__equality2_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__mod__equality2_0) ).
cnf(cls_mod__by__0_0,axiom,
( c_Divides_Odiv__class_Omod(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__by__0_0) ).
cnf(cls_mod__self_0,axiom,
( c_Divides_Odiv__class_Omod(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__self_0) ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
cnf(cls_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_power__minus_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_n,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),V_n,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oring__1(T_a) ),
file('theBenchmark.p',cls_power__minus_0) ).
cnf(cls_mod__div__trivial_0,axiom,
( c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__div__trivial_0) ).
cnf(cls_mod__minus__cong_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a_H,T_a),V_b,T_a)
| c_Divides_Odiv__class_Omod(V_a,V_b,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_b,T_a)
| ~ class_Divides_Oring__div(T_a) ),
file('theBenchmark.p',cls_mod__minus__cong_0) ).
cnf(cls_mod__mult__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__eq_0) ).
cnf(cls_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_div__mult__self1_0,axiom,
( V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(V_c,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__mult__self1_0) ).
cnf(cls_div__mult__self2_0,axiom,
( V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(V_c,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__mult__self2_0) ).
cnf(cls_class__semiring_Osemiring__rules_I4_J_0,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_m,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
cnf(cls_eq__divide__eq_4,axiom,
( c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a),V_c,T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_eq__divide__eq_4) ).
cnf(cls_mod__add__cong_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a_H,V_b_H,T_a),V_c,T_a)
| c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
| c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__add__cong_0) ).
cnf(cls_minus__unique_0,axiom,
( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b
| c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_minus__unique_0) ).
cnf(cls_eq__neg__iff__add__eq__0_1,axiom,
( V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
cnf(cls_div__power_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a)
| c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),V_n,T_a) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__power_0) ).
cnf(cls_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__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_mod__mult__cong_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a_H,V_b_H,T_a),V_c,T_a)
| c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
| c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__cong_0) ).
cnf(cls_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_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_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_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_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_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__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_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_abs__power__minus_0,axiom,
( c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_n,T_a),T_a) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('theBenchmark.p',cls_abs__power__minus_0) ).
cnf(cls_class__semiring_Osemiring__rules_I2_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),V_m,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom,
( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
cnf(cls_mod__by__1_0,axiom,
( c_Divides_Odiv__class_Omod(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__by__1_0) ).
cnf(cls_mod__diff__cong_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a_H,V_b_H,T_a),V_c,T_a)
| c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
| c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
| ~ class_Divides_Oring__div(T_a) ),
file('theBenchmark.p',cls_mod__diff__cong_0) ).
cnf(cls_add__cancel__end_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_z,T_a),c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = V_y
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_add__cancel__end_1) ).
cnf(cls_minus__add__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) = V_b
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_minus__add__cancel_0) ).
cnf(cls_inverse__eq__1__iff_1,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_inverse__eq__1__iff_1) ).
cnf(cls_inverse__1_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Odivision__ring(T_a) ),
file('theBenchmark.p',cls_inverse__1_0) ).
cnf(cls_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_poly__gcd__commute_0,axiom,
( c_Polynomial_Opoly__gcd(V_x,V_y,T_a) = c_Polynomial_Opoly__gcd(V_y,V_x,T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_poly__gcd__commute_0) ).
cnf(cls_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_minus__zero_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_minus__zero_0) ).
cnf(cls_neg__equal__zero_1,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Oordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_neg__equal__zero_1) ).
cnf(cls_divide__rat__def_0,axiom,
c_HOL_Oinverse__class_Odivide(V_q,V_r,tc_Rational_Orat) = c_HOL_Otimes__class_Otimes(V_q,c_HOL_Oinverse__class_Oinverse(V_r,tc_Rational_Orat),tc_Rational_Orat),
file('theBenchmark.p',cls_divide__rat__def_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_Lim_Ominus__diff__minus_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
cnf(cls_nonzero__power__divide_0,axiom,
( V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_nonzero__power__divide_0) ).
cnf(cls_abs__add__abs_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a) ),
file('theBenchmark.p',cls_abs__add__abs_0) ).
cnf(cls_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_mod__mult__self1__is__0_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
cnf(cls_mod__mult__self2__is__0_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
cnf(cls_division__ring__inverse__diff_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a)
| ~ class_Ring__and__Field_Odivision__ring(T_a) ),
file('theBenchmark.p',cls_division__ring__inverse__diff_0) ).
cnf(cls_semiring__div__class_Omod__div__equality_H_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),T_a) = V_a
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_semiring__div__class_Omod__div__equality_H_0) ).
cnf(cls_sum__squares__eq__zero__iff_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
cnf(cls_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_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_mod__mult__mult1_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_c,c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__mult1_0) ).
cnf(cls_mod__mult__mult2_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__mult2_0) ).
cnf(cls_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_dvd__if__abs__eq_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(V_l,V_k,T_a)
| c_HOL_Oabs__class_Oabs(V_l,T_a) != c_HOL_Oabs__class_Oabs(V_k,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('theBenchmark.p',cls_dvd__if__abs__eq_0) ).
cnf(cls_mult__dvd__mono_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_d,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_mult__dvd__mono_0) ).
cnf(cls_mod__mod__cancel_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_b,T_a)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(V_a,V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mod__cancel_0) ).
cnf(cls_poly__gcd__greatest_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_x,tc_Polynomial_Opoly(T_a))
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_y,tc_Polynomial_Opoly(T_a))
| c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Polynomial_Opoly__gcd(V_x,V_y,T_a),tc_Polynomial_Opoly(T_a))
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_poly__gcd__greatest_0) ).
cnf(cls_dvd__poly__gcd__iff_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_x,tc_Polynomial_Opoly(T_a))
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_y,tc_Polynomial_Opoly(T_a))
| c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Polynomial_Opoly__gcd(V_x,V_y,T_a),tc_Polynomial_Opoly(T_a))
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_dvd__poly__gcd__iff_2) ).
cnf(cls_poly__gcd__dvd1_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(V_x,V_y,T_a),V_x,tc_Polynomial_Opoly(T_a))
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_poly__gcd__dvd1_0) ).
cnf(cls_poly__gcd__dvd2_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(V_x,V_y,T_a),V_y,tc_Polynomial_Opoly(T_a))
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_poly__gcd__dvd2_0) ).
cnf(cls_dvd__abs__iff_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('theBenchmark.p',cls_dvd__abs__iff_1) ).
cnf(cls_dvd__abs__iff_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('theBenchmark.p',cls_dvd__abs__iff_0) ).
cnf(cls_abs__dvd__iff_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('theBenchmark.p',cls_abs__dvd__iff_1) ).
cnf(cls_abs__dvd__iff_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('theBenchmark.p',cls_abs__dvd__iff_0) ).
cnf(cls_dvd__0__right_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__0__right_0) ).
cnf(cls_pp_H_0,axiom,
c_Ring__and__Field_Odvd__class_Odvd(v_p,v_p_H,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('theBenchmark.p',cls_pp_H_0) ).
cnf(cls_dvd__poly__gcd__iff_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Polynomial_Opoly__gcd(V_x,V_y,T_a),tc_Polynomial_Opoly(T_a))
| c_Ring__and__Field_Odvd__class_Odvd(V_k,V_y,tc_Polynomial_Opoly(T_a))
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_dvd__poly__gcd__iff_1) ).
cnf(cls_dvd__poly__gcd__iff_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Polynomial_Opoly__gcd(V_x,V_y,T_a),tc_Polynomial_Opoly(T_a))
| c_Ring__and__Field_Odvd__class_Odvd(V_k,V_x,tc_Polynomial_Opoly(T_a))
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('theBenchmark.p',cls_dvd__poly__gcd__iff_0) ).
cnf(cls_dvd__mult__cancel__right_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
cnf(cls_dvd__mult__cancel__left_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
cnf(cls_dvd__0__left_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__0__left_0) ).
cnf(cls_minus__dvd__iff_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('theBenchmark.p',cls_minus__dvd__iff_1) ).
cnf(cls_minus__dvd__iff_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('theBenchmark.p',cls_minus__dvd__iff_0) ).
cnf(cls_dvd__minus__iff_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('theBenchmark.p',cls_dvd__minus__iff_1) ).
cnf(cls_dvd__minus__iff_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('theBenchmark.p',cls_dvd__minus__iff_0) ).
cnf(cls_div__dvd__div_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__dvd__div_1) ).
cnf(cls_div__dvd__div_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_div__dvd__div_0) ).
cnf(cls_dvd__add_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__add_0) ).
cnf(cls_dvd__mult__right_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__mult__right_0) ).
cnf(cls_dvd__mult__left_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__mult__left_0) ).
cnf(cls_dvd__mult2_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__mult2_0) ).
cnf(cls_dvd__mult_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__mult_0) ).
cnf(cls_one__dvd_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_one__dvd_0) ).
cnf(cls_dvd__trans_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__trans_0) ).
cnf(cls_dvd__refl_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(V_a,V_a,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__refl_0) ).
cnf(cls_dvd__diff_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('theBenchmark.p',cls_dvd__diff_0) ).
cnf(cls_dvd__mod__imp__dvd_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_dvd__mod__imp__dvd_0) ).
cnf(cls_dvd__mod__iff_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_dvd__mod__iff_1) ).
cnf(cls_dvd__mod__iff_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_dvd__mod__iff_0) ).
cnf(cls_dvd__mod_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_dvd__mod_0) ).
cnf(cls_dvd__triv__right_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__triv__right_0) ).
cnf(cls_dvd__triv__left_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__triv__left_0) ).
cnf(cls_dvdI_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(V_b,c_HOL_Otimes__class_Otimes(V_b,V_k,T_a),T_a)
| ~ class_Ring__and__Field_Odvd(T_a) ),
file('theBenchmark.p',cls_dvdI_0) ).
cnf(cls_poly__divides__pad__const__rule_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('theBenchmark.p',cls_poly__divides__pad__const__rule_0) ).
cnf(cls_smult__dvd__cancel_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a))
| c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_smult__dvd__cancel_0) ).
cnf(cls_dvd__smult_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__smult_0) ).
cnf(cls_diff__rat__def__raw_0,axiom,
c_HOL_Ominus__class_Ominus(v_q,v_r,tc_Rational_Orat) = c_HOL_Oplus__class_Oplus(v_q,c_HOL_Ouminus__class_Ouminus(v_r,tc_Rational_Orat),tc_Rational_Orat),
file('theBenchmark.p',cls_diff__rat__def__raw_0) ).
cnf(cls_divide__rat__def__raw_0,axiom,
c_HOL_Oinverse__class_Odivide(v_q,v_r,tc_Rational_Orat) = c_HOL_Otimes__class_Otimes(v_q,c_HOL_Oinverse__class_Oinverse(v_r,tc_Rational_Orat),tc_Rational_Orat),
file('theBenchmark.p',cls_divide__rat__def__raw_0) ).
cnf(cls_dvd__power__same_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__power__same_0) ).
cnf(cls_CHAINED_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_r,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_CHAINED_0_01,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,v_r,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_conjecture_0,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_r,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,v_r,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add,axiom,
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(T_1)
| class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).
cnf(clsarity_Rational__Orat__OrderedGroup_Ocancel__comm__monoid__add,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__OrderedGroup_Ocancel__comm__monoid__add) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Oring__1__no__zero__divisors) ).
cnf(clsarity_Rational__Orat__OrderedGroup_Opordered__ab__group__add__abs,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__OrderedGroup_Opordered__ab__group__add__abs) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Oring__no__zero__divisors) ).
cnf(clsarity_Rational__Orat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Oordered__ring__strict,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Oordered__ring__strict) ).
cnf(clsarity_Rational__Orat__OrderedGroup_Oordered__ab__group__add,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__OrderedGroup_Oordered__ab__group__add) ).
cnf(clsarity_Rational__Orat__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Ono__zero__divisors) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Odivision__by__zero) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Ocomm__semiring__0) ).
cnf(clsarity_Rational__Orat__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__OrderedGroup_Oab__semigroup__mult) ).
cnf(clsarity_Rational__Orat__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__OrderedGroup_Ocomm__monoid__mult) ).
cnf(clsarity_Rational__Orat__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Oordered__field,axiom,
class_Ring__and__Field_Oordered__field(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Oordered__field) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Odivision__ring,axiom,
class_Ring__and__Field_Odivision__ring(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Odivision__ring) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Ocomm__semiring) ).
cnf(clsarity_Rational__Orat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Ozero__neq__one) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Oordered__idom,axiom,
class_Ring__and__Field_Oordered__idom(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Oordered__idom) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Ocomm__ring__1,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Ocomm__ring__1) ).
cnf(clsarity_Rational__Orat__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__OrderedGroup_Oab__group__add) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Omult__zero) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Ocomm__ring,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Ocomm__ring) ).
cnf(clsarity_Rational__Orat__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__OrderedGroup_Omonoid__mult) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Osemiring) ).
cnf(clsarity_Rational__Orat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__OrderedGroup_Omonoid__add) ).
cnf(clsarity_Rational__Orat__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__OrderedGroup_Ogroup__add) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Oring__1,axiom,
class_Ring__and__Field_Oring__1(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Oring__1) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Ofield) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Oring,axiom,
class_Ring__and__Field_Oring(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Oring) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Oidom) ).
cnf(clsarity_Rational__Orat__Ring__and__Field_Odvd,axiom,
class_Ring__and__Field_Odvd(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Ring__and__Field_Odvd) ).
cnf(clsarity_Rational__Orat__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Int_Onumber__ring) ).
cnf(clsarity_Rational__Orat__Power_Opower,axiom,
class_Power_Opower(tc_Rational_Orat),
file('theBenchmark.p',clsarity_Rational__Orat__Power_Opower) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__field,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odvd,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).
cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
cnf(clsarity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
( ~ class_Ring__and__Field_Oidom(T_1)
| class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_1)
| class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors,axiom,
( ~ class_Ring__and__Field_Oidom(T_1)
| class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(T_1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_1)
| class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_1)
| class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add,axiom,
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(T_1)
| class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors,axiom,
( ~ class_Ring__and__Field_Oidom(T_1)
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_1)
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_1)
| class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_1)
| class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_1)
| class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_1)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_1)
| class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_1)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_1)
| class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_1)
| class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_1)
| class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_1)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_1)
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(T_1)
| class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_1)
| class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_1)
| class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_1)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_1)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_1)
| class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1) ).
cnf(clsarity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
( ~ class_Ring__and__Field_Ofield(T_1)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Osemiring__div) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(T_1)
| class_Ring__and__Field_Oring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oidom,axiom,
( ~ class_Ring__and__Field_Oidom(T_1)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Odvd,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_1)
| class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) ).
cnf(clsarity_Polynomial__Opoly__Divides_Oring__div,axiom,
( ~ class_Ring__and__Field_Ofield(T_1)
| class_Divides_Oring__div(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Oring__div) ).
cnf(clsarity_Polynomial__Opoly__Int_Onumber__ring,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_1)
| class_Int_Onumber__ring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
cnf(clsarity_Polynomial__Opoly__Power_Opower,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_1)
| class_Power_Opower(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',clsarity_Polynomial__Opoly__Power_Opower) ).
cnf(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_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_5,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_6,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_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_Divides_Odiv__class_Odiv(Eq_x_0,Eq_x_1,Eq_x_2) = c_Divides_Odiv__class_Odiv(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( c_HOL_Oone__class_Oone(Eq_x_0) = c_HOL_Oone__class_Oone(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( c_HOL_Ominus__class_Ominus(Eq_x_0,Eq_x_1,Eq_x_2) = c_HOL_Ominus__class_Ominus(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,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_12,axiom,
( c_Power_Opower__class_Opower(Eq_x_0,Eq_x_1,Eq_x_2) = c_Power_Opower__class_Opower(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( c_HOL_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_14,axiom,
( c_Divides_Odiv__class_Omod(Eq_x_0,Eq_x_1,Eq_x_2) = c_Divides_Odiv__class_Omod(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( c_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_16,axiom,
( c_Polynomial_Osmult(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Osmult(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( tc_Polynomial_Opoly(Eq_x_0) = tc_Polynomial_Opoly(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( c_Polynomial_Opoly__gcd(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Opoly__gcd(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,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_20,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_21,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_22,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_23,axiom,
( class_Divides_Osemiring__div(Eq_y_0)
| ~ class_Divides_Osemiring__div(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,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_25,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_26,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_27,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_28,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_29,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_30,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_31,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_32,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_33,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,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_35,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_36,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_37,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_38,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_39,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_40,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_41,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_42,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_43,axiom,
( class_Ring__and__Field_Odvd(Eq_y_0)
| ~ class_Ring__and__Field_Odvd(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,axiom,
( class_Ring__and__Field_Ocomm__ring(Eq_y_0)
| ~ class_Ring__and__Field_Ocomm__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_45,axiom,
( class_Divides_Oring__div(Eq_y_0)
| ~ class_Divides_Oring__div(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_46,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_47,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_48,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_49,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_50,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_51,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_52,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_53,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_54,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_55,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_56,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(Eq_y_0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_57,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_58,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_59,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_60,axiom,
( class_RealVector_Oreal__field(Eq_y_0)
| ~ class_RealVector_Oreal__field(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_61,axiom,
( class_Ring__and__Field_Oring__1(Eq_y_0)
| ~ class_Ring__and__Field_Oring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_62,axiom,
( class_Ring__and__Field_Ocomm__ring__1(Eq_y_0)
| ~ class_Ring__and__Field_Ocomm__ring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_63,axiom,
( class_OrderedGroup_Ocancel__comm__monoid__add(Eq_y_0)
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG436-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 11:27:21 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------