TSTP Solution File: ALG421-1 by Leo-III---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ALG421-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 18:15:31 EDT 2024
% Result : Unsatisfiable 13.63s 3.80s
% Output : Refutation 14.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 937
% Syntax : Number of formulae : 1784 ( 271 unt; 91 typ; 0 def)
% Number of atoms : 4327 (1308 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 22008 (2414 ~;2634 |; 0 &;16960 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 116 ( 116 >; 0 *; 0 +; 0 <<)
% Number of symbols : 93 ( 91 usr; 9 con; 0-3 aty)
% Number of variables : 4246 ( 0 ^4246 !; 0 ?;4246 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: $i > $i > $i > $i ).
thf(v_s_____type,type,
v_s____: $i ).
thf(v_x_type,type,
v_x: $i ).
thf(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
thf(v_u_____type,type,
v_u____: $i ).
thf(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(v_r_____type,type,
v_r____: $i ).
thf(c_Polynomial_Odegree_type,type,
c_Polynomial_Odegree: $i > $i > $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_type,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add__abs_type,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
thf(c_HOL_Oabs__class_Oabs_type,type,
c_HOL_Oabs__class_Oabs: $i > $i > $i ).
thf(class_OrderedGroup_Ogroup__add_type,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(c_HOL_Ouminus__class_Ouminus_type,type,
c_HOL_Ouminus__class_Ouminus: $i > $i > $i ).
thf(class_HOL_Ozero_type,type,
class_HOL_Ozero: $i > $o ).
thf(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: $i > $i > $i > $i ).
thf(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(class_OrderedGroup_Omonoid__add_type,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(class_Ring__and__Field_Oordered__field_type,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
thf(class_Ring__and__Field_Odivision__by__zero_type,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
thf(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Ocomm__ring__1_type,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
thf(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_type,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Divides_Osemiring__div_type,type,
class_Divides_Osemiring__div: $i > $o ).
thf(c_Ring__and__Field_Odvd__class_Odvd_type,type,
c_Ring__and__Field_Odvd__class_Odvd: $i > $i > $i > $o ).
thf(c_Divides_Odiv__class_Omod_type,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__semidom_type,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(class_Ring__and__Field_Oring__1__no__zero__divisors_type,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Oidom_type,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(class_Ring__and__Field_Omult__zero_type,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__0_type,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
thf(class_Int_Onumber__ring_type,type,
class_Int_Onumber__ring: $i > $o ).
thf(c_HOL_Oinverse__class_Oinverse_type,type,
c_HOL_Oinverse__class_Oinverse: $i > $i > $i ).
thf(class_Ring__and__Field_Oring__1_type,type,
class_Ring__and__Field_Oring__1: $i > $o ).
thf(c_Complex_Ocnj_type,type,
c_Complex_Ocnj: $i > $i ).
thf(class_Divides_Oring__div_type,type,
class_Divides_Oring__div: $i > $o ).
thf(c_Polynomial_Osmult_type,type,
c_Polynomial_Osmult: $i > $i > $i > $i ).
thf(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
thf(class_Ring__and__Field_Oordered__ring__strict_type,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add_type,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(class_Ring__and__Field_Ocomm__ring_type,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
thf(c_Polynomial_Opcompose_type,type,
c_Polynomial_Opcompose: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Osemiring__0_type,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(class_OrderedGroup_Ocancel__semigroup__add_type,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Odivision__ring_type,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_OrderedGroup_Ocancel__comm__monoid__add_type,type,
class_OrderedGroup_Ocancel__comm__monoid__add: $i > $o ).
thf(c_Polynomial_Omonom_type,type,
c_Polynomial_Omonom: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Ocomm__semiring_type,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(class_RealVector_Oreal__normed__field_type,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__mult_type,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_Lattices_Oboolean__algebra_type,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add__abs_type,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring__strict_type,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(class_Ring__and__Field_Ono__zero__divisors_type,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Ozero__neq__one_type,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(class_Ring__and__Field_Odvd_type,type,
class_Ring__and__Field_Odvd: $i > $o ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_type,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(v_na_____type,type,
v_na____: $i ).
thf(class_Ring__and__Field_Osemiring_type,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(class_OrderedGroup_Oordered__ab__group__add_type,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
thf(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly_type,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oabs__if_type,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
thf(class_Ring__and__Field_Opordered__ring_type,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
thf(c_Fun_Oid_type,type,
c_Fun_Oid: $i > $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__add_type,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_Ring__and__Field_Oring_type,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(class_Ring__and__Field_Oring__no__zero__divisors_type,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_type,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(t_a_type,type,
t_a: $i ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_type,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(class_RealVector_Oreal__field_type,type,
class_RealVector_Oreal__field: $i > $o ).
thf(201,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).
thf(1322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(667,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_Omonom @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__monom_0) ).
thf(2452,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_Omonom @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
thf(1411,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(78,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).
thf(1024,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(405,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_3) ).
thf(1823,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(331,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(1633,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(590,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
thf(2263,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(369,axiom,
! [B: $i,A: $i] :
( ( c_Fun_Oid @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__apply_0) ).
thf(1729,plain,
! [B: $i,A: $i] :
( ( c_Fun_Oid @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(652,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) )
| ( C = E )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
thf(2412,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) )
| ( C = E )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).
thf(1031,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(618,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
thf(2331,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(403,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ D @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DERIV__inverse__lemma_0) ).
thf(1818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ D @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
thf(1549,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_1) ).
thf(1554,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(549,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( B = C )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).
thf(2163,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( B = C )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(23,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_OpCons @ B @ C @ A )
!= ( c_Polynomial_OpCons @ D @ E @ A ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__eq__iff_0) ).
thf(892,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_OpCons @ B @ C @ A )
!= ( c_Polynomial_OpCons @ D @ E @ A ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(429,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Odvd @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) ).
thf(1879,plain,
! [A: $i] :
( ( class_Ring__and__Field_Odvd @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(207,axiom,
! [A: $i] :
( ( class_Int_Onumber__ring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
thf(1337,plain,
! [A: $i] :
( ( class_Int_Onumber__ring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(364,axiom,
! [A: $i] :
( ( class_OrderedGroup_Opordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) ).
thf(1718,plain,
! [A: $i] :
( ( class_OrderedGroup_Opordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(138,axiom,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(1168,plain,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(602,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(2295,plain,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(622,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
thf(2341,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(620,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
thf(2336,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(525,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
thf(2109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(300,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
thf(1559,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_5) ).
thf(1105,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
thf(1315,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(684,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(2499,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(703,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mult__distrib_0) ).
thf(2544,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(941,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(977,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
!= ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(1158,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
!= ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
thf(1005,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(792,axiom,
class_Ring__and__Field_Oring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
thf(2776,plain,
class_Ring__and__Field_Oring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(325,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(1618,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_7) ).
thf(994,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
thf(1401,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(245,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(1422,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
!= C )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
thf(1073,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
!= C )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(597,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
thf(2282,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(638,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__less_0) ).
thf(2380,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(861,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(270,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__num_0) ).
thf(1486,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(631,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).
thf(2363,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(419,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__eq__0__iff_1) ).
thf(1855,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(512,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).
thf(2077,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(238,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).
thf(1406,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(523,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).
thf(2104,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(732,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).
thf(2622,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(1068,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).
thf(1544,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(754,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
thf(2676,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(818,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(2837,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(179,axiom,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(1269,plain,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(467,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_1) ).
thf(1971,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(394,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(1793,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(345,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_OpCons @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_0) ).
thf(1671,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_OpCons @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(321,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
thf(1608,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(758,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__inverse_0) ).
thf(2686,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(196,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_8) ).
thf(1310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(557,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
thf(2184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(768,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
thf(2712,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(675,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__right_0) ).
thf(2476,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ C @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(1640,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ C @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_OpCons @ B @ C @ A ) @ ( tc_Polynomial_Opoly @ A ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_Polynomial_Opoly @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__pCons_0) ).
thf(945,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_OpCons @ B @ C @ A ) @ ( tc_Polynomial_Opoly @ A ) )
= ( c_Polynomial_OpCons @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_Polynomial_Opoly @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(215,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_1) ).
thf(1354,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(1458,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
thf(1497,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(562,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
thf(2195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_1) ).
thf(1164,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(478,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
thf(1999,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(181,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
thf(1275,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(539,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
thf(2141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(382,axiom,
! [A: $i] :
( ( class_OrderedGroup_Ocancel__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).
thf(1761,plain,
! [A: $i] :
( ( class_OrderedGroup_Ocancel__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(209,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).
thf(1342,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).
thf(913,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(1063,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(460,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
thf(1954,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(821,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).
thf(2844,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_0) ).
thf(1222,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(630,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Polynomial_Odegree @ ( c_Power_Opower__class_Opower @ ( c_Polynomial_OpCons @ B @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) @ A ) @ C @ ( tc_Polynomial_Opoly @ A ) ) @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_degree__linear__power_0) ).
thf(2360,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Polynomial_Odegree @ ( c_Power_Opower__class_Opower @ ( c_Polynomial_OpCons @ B @ ( c_Polynomial_OpCons @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) @ A ) @ C @ ( tc_Polynomial_Opoly @ A ) ) @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(150,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
thf(1196,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(772,axiom,
! [A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Odegree @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_degree__0_0) ).
thf(2723,plain,
! [A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Odegree @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(499,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(2046,plain,
class_OrderedGroup_Omonoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(443,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_2) ).
thf(1914,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(575,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_0) ).
thf(2227,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(488,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(2020,plain,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_2) ).
thf(1613,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(838,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
thf(2886,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(649,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
thf(2405,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(120,axiom,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(1127,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(787,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ B @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).
thf(2763,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(483,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(2010,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(451,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
thf(1935,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(337,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) )
| ( ( c_HOL_Oplus__class_Oplus @ B @ D @ A )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(1650,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) )
| ( ( c_HOL_Oplus__class_Oplus @ B @ D @ A )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(335,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_3) ).
thf(1645,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(446,axiom,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(1921,plain,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(439,axiom,
! [A: $i] :
( ( class_Orderings_Olinorder @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Olinorder) ).
thf(1904,plain,
! [A: $i] :
( ( class_Orderings_Olinorder @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(177,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(1265,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(358,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
thf(1703,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(744,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) @ A )
= ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__power__minus_0) ).
thf(2654,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) @ A )
= ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(186,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Ozero__neq__one @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
thf(1287,plain,
! [A: $i] :
( ( class_Ring__and__Field_Ozero__neq__one @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(360,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oidom @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oidom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
thf(1709,plain,
! [A: $i] :
( ( class_Ring__and__Field_Oidom @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oidom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(248,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).
thf(1430,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(473,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
thf(1985,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(762,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
thf(2698,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(621,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).
thf(2339,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(592,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(2269,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(426,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus_0) ).
thf(1871,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(533,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(2126,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(725,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).
thf(2603,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(617,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
thf(2328,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(664,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
thf(2444,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(571,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
thf(2217,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(594,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_Polynomial_Odegree @ ( c_Polynomial_Osmult @ B @ C @ A ) @ A )
= ( c_Polynomial_Odegree @ C @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_degree__smult__eq_1) ).
thf(2274,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_Polynomial_Odegree @ ( c_Polynomial_Osmult @ B @ C @ A ) @ A )
= ( c_Polynomial_Odegree @ C @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
thf(917,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(309,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__dvd__iff_1) ).
thf(1577,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
thf(1455,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(409,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
thf(1832,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(844,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_HOL_Otimes__class_Otimes @ E @ F @ A ) @ A ) @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ F @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__period_I4_J_1) ).
thf(2897,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_HOL_Otimes__class_Otimes @ E @ F @ A ) @ A ) @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ F @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(780,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_0) ).
thf(2745,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(713,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ F @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ F @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ F @ A ) @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DERIV__mult__lemma_0) ).
thf(2571,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ F @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ F @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ F @ A ) @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(628,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_0) ).
thf(2356,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(902,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(853,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(226,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).
thf(1379,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
thf(1013,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(374,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).
thf(1741,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(737,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A )
= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
thf(2635,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A )
= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less__neg_0) ).
thf(1568,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(692,axiom,
( v_s____
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sne_0) ).
thf(2520,plain,
( v_s____
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(547,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
thf(2158,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(490,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oring__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oidom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
thf(2024,plain,
! [A: $i] :
( ( class_Ring__and__Field_Oring__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oidom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(387,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus_0) ).
thf(1773,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(273,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Oone__class_Oone @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(1494,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Oone__class_Oone @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(219,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_1) ).
thf(1362,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(642,axiom,
class_Int_Onumber__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
thf(2388,plain,
class_Int_Onumber__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
thf(1100,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(164,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).
thf(1232,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(551,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) @ E @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(2169,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(282,axiom,
! [A: $i] :
( A
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(1514,plain,
! [A: $i] :
( A
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(169,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
thf(1247,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(706,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(2552,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(635,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
thf(2373,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(307,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__mult_0) ).
thf(1572,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(555,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__root_1) ).
thf(2178,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(271,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
thf(1489,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(457,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= B )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).
thf(1946,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= B )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(362,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_positive__imp__inverse__positive_0) ).
thf(1714,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).
thf(1373,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(243,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(1418,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(206,axiom,
! [B: $i,A: $i] :
( ( A
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(1334,plain,
! [B: $i,A: $i] :
( ( A
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(420,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ B @ A )
= ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
thf(1858,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ B @ A )
= ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(470,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_4) ).
thf(1978,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_4) ).
thf(1383,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(707,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Odegree @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ B @ C @ A ) @ A )
= ( c_Polynomial_Odegree @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_degree__offset__poly_0) ).
thf(2555,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Odegree @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ B @ C @ A ) @ A )
= ( c_Polynomial_Odegree @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(793,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
thf(2777,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(144,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
thf(1183,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(28,axiom,
! [A: $i] :
( ( class_OrderedGroup_Omonoid__mult @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).
thf(905,plain,
! [A: $i] :
( ( class_OrderedGroup_Omonoid__mult @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(192,axiom,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ B @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(1302,plain,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ B @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(342,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(1664,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(800,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
thf(2794,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(442,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(1911,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(795,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(2782,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(1040,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(842,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
thf(2893,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(836,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).
thf(2880,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(124,axiom,
! [A: $i] :
( ( class_OrderedGroup_Ocomm__monoid__mult @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).
thf(1136,plain,
! [A: $i] :
( ( class_OrderedGroup_Ocomm__monoid__mult @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(1151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_1) ).
thf(937,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(347,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).
thf(1677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(701,axiom,
! [A: $i] :
( ( ( c_Complex_Ocnj @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__zero__iff_0) ).
thf(2540,plain,
! [A: $i] :
( ( ( c_Complex_Ocnj @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(494,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(2034,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(225,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(1377,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(816,axiom,
class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
thf(2833,plain,
class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(678,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
thf(2483,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(9,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(866,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(117,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(1119,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
thf(1394,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(537,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_1) ).
thf(2137,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(249,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
thf(1433,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(152,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(1201,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(805,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
thf(2804,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Osmult @ B @ C @ A )
!= ( c_Polynomial_OpCons @ D @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synthetic__div__unique__lemma_0) ).
thf(1600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Osmult @ B @ C @ A )
!= ( c_Polynomial_OpCons @ D @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gt__half__sum_0) ).
thf(1697,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(770,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) )
| ( B = D )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).
thf(2718,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) )
| ( B = D )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(688,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
thf(2508,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ( ( c_Complex_Ocnj @ A )
!= ( c_Complex_Ocnj @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cancel__iff_0) ).
thf(981,plain,
! [B: $i,A: $i] :
( ( ( c_Complex_Ocnj @ A )
!= ( c_Complex_Ocnj @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(414,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
thf(1843,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(504,axiom,
! [A: $i] :
( ( class_OrderedGroup_Opordered__ab__group__add__abs @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs) ).
thf(2058,plain,
! [A: $i] :
( ( class_OrderedGroup_Opordered__ab__group__add__abs @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(436,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
thf(1896,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(877,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(560,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).
thf(2190,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(697,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
thf(2530,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(693,axiom,
class_Ring__and__Field_Ocomm__ring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
thf(2523,plain,
class_Ring__and__Field_Ocomm__ring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(395,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
thf(1796,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(210,axiom,
class_Ring__and__Field_Ocomm__semiring__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__0) ).
thf(1345,plain,
class_Ring__and__Field_Ocomm__semiring__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).
thf(988,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(644,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).
thf(2392,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(545,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__abs_0) ).
thf(2154,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(285,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(1521,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(469,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_3) ).
thf(1975,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(302,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(1564,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(422,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_0) ).
thf(1863,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(484,axiom,
class_Divides_Osemiring__div @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
thf(2011,plain,
class_Divides_Osemiring__div @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(154,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ F @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
thf(1206,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ F @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(920,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(674,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).
thf(2473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(714,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_1) ).
thf(2574,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(37,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__zero_0) ).
thf(925,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).
thf(1306,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(529,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__minus_0) ).
thf(2118,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(500,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__imp__positive_0) ).
thf(2047,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(777,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
thf(2737,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(603,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Otimes__class_Otimes @ B @ C @ ( tc_Polynomial_Opoly @ A ) ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Opoly @ B @ D @ A ) @ ( c_Polynomial_Opoly @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__mult_0) ).
thf(2296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Otimes__class_Otimes @ B @ C @ ( tc_Polynomial_Opoly @ A ) ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Opoly @ B @ D @ A ) @ ( c_Polynomial_Opoly @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(739,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
thf(2641,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(372,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Omonom @ B @ C @ A )
!= ( c_Polynomial_Omonom @ D @ C @ A ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monom__eq__iff_0) ).
thf(1736,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Omonom @ B @ C @ A )
!= ( c_Polynomial_Omonom @ D @ C @ A ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(506,axiom,
! [A: $i] :
( ( class_OrderedGroup_Ocancel__semigroup__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).
thf(2061,plain,
! [A: $i] :
( ( class_OrderedGroup_Ocancel__semigroup__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
thf(1470,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(519,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).
thf(2093,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(424,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(1868,plain,
class_OrderedGroup_Omonoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(639,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_Polynomial_Odegree @ ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_degree__smult__eq_0) ).
thf(2382,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_Polynomial_Odegree @ ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__divide_0) ).
thf(1047,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(92,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
thf(1057,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(135,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(1163,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(658,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
thf(2428,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(709,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(2560,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(584,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
thf(2249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(1042,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(284,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(1519,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(595,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_1) ).
thf(2277,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(172,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(1255,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(276,axiom,
class_Ring__and__Field_Osemiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(1502,plain,
class_Ring__and__Field_Osemiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(343,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(1666,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(222,axiom,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__lt__two__imp__zero__or__one_0) ).
thf(1370,plain,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(493,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).
thf(2032,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(535,axiom,
( ( c_Power_Opower__class_Opower @ v_r____ @ ( c_Polynomial_Odegree @ v_s____ @ tc_Complex_Ocomplex ) @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
= ( c_HOL_Otimes__class_Otimes @ v_s____ @ v_u____ @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_u_0) ).
thf(2132,plain,
( ( c_Power_Opower__class_Opower @ v_r____ @ ( c_Polynomial_Odegree @ v_s____ @ tc_Complex_Ocomplex ) @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
= ( c_HOL_Otimes__class_Otimes @ v_s____ @ v_u____ @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(696,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
thf(2528,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(431,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__ring @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
thf(1883,plain,
! [A: $i] :
( ( class_Ring__and__Field_Oring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__ring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(230,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).
thf(1387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(30,axiom,
class_HOL_Ozero @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Ozero) ).
thf(910,plain,
class_HOL_Ozero @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(306,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_0) ).
thf(1570,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_0) ).
thf(1174,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).
thf(1217,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(541,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
thf(2147,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).
thf(1238,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(486,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
thf(2015,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(411,axiom,
! [A: $i] :
( ( class_OrderedGroup_Oab__semigroup__mult @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
thf(1837,plain,
! [A: $i] :
( ( class_OrderedGroup_Oab__semigroup__mult @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(660,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel1_0) ).
thf(2433,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(459,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(1951,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(433,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__0__left_0) ).
thf(1888,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(351,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__minus_0) ).
thf(1687,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(327,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__less_0) ).
thf(1624,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(564,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).
thf(2200,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
thf(889,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(339,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__neg_0) ).
thf(1656,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(232,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(1392,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(188,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(1291,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(974,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(671,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc2_0) ).
thf(2464,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(453,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(1938,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(1,negated_conjecture,
( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Opoly @ v_s____ @ v_x @ tc_Complex_Ocomplex ) @ ( c_Polynomial_Opoly @ v_u____ @ v_x @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex )
!= ( c_Power_Opower__class_Opower @ ( c_Polynomial_Opoly @ v_r____ @ v_x @ tc_Complex_Ocomplex ) @ ( c_Polynomial_Odegree @ v_s____ @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(847,plain,
( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Opoly @ v_s____ @ v_x @ tc_Complex_Ocomplex ) @ ( c_Polynomial_Opoly @ v_u____ @ v_x @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex )
!= ( c_Power_Opower__class_Opower @ ( c_Polynomial_Opoly @ v_r____ @ v_x @ tc_Complex_Ocomplex ) @ ( c_Polynomial_Odegree @ v_s____ @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(734,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
thf(2628,plain,
class_Ring__and__Field_Ocomm__semiring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(751,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
thf(2670,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(466,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(1968,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(711,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
thf(2565,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(392,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
thf(1787,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(556,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inverse_0) ).
thf(2181,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(100,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Osemiring__0 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__0) ).
thf(1079,plain,
! [A: $i] :
( ( class_Ring__and__Field_Osemiring__0 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_5) ).
thf(1027,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(149,axiom,
class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
thf(1195,plain,
class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(568,axiom,
class_Ring__and__Field_Oring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).
thf(2211,plain,
class_Ring__and__Field_Oring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(623,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
thf(2344,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(610,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
thf(2313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(681,axiom,
( ( c_Complex_Ocnj @ ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Ozero_0) ).
thf(2492,plain,
( ( c_Complex_Ocnj @ ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(315,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__imp__negative_0) ).
thf(1592,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(472,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_2) ).
thf(1983,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(290,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__iff_0) ).
thf(1534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(398,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
thf(1804,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(843,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
thf(2895,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(820,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
thf(2841,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(224,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__half__sum_0) ).
thf(1375,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(773,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).
thf(2726,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(869,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(380,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_0) ).
thf(1755,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(738,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(2638,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(234,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_0) ).
thf(1397,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(218,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Ocomm__semiring__0 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
thf(1360,plain,
! [A: $i] :
( ( class_Ring__and__Field_Ocomm__semiring__0 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(582,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
thf(2245,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(1350,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
thf(1089,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(293,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
| ( ( c_Polynomial_Osmult @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_Polynomial_Opoly @ A ) ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ B @ C @ A ) @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__minus__right_0) ).
thf(1541,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
| ( ( c_Polynomial_Osmult @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_Polynomial_Opoly @ A ) ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ B @ C @ A ) @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(14,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(874,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(546,axiom,
class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
thf(2157,plain,
class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(1143,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(528,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(2115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(417,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).
thf(1851,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(386,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(1772,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(174,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(1259,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(48,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_9) ).
thf(948,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(803,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
thf(2801,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_1) ).
thf(1111,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(767,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
thf(2709,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(760,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_Polynomial_Odegree @ ( c_HOL_Otimes__class_Otimes @ B @ C @ ( tc_Polynomial_Opoly @ A ) ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Odegree @ B @ A ) @ ( c_Polynomial_Odegree @ C @ A ) @ tc_nat ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_degree__mult__eq_0) ).
thf(2692,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_Polynomial_Odegree @ ( c_HOL_Otimes__class_Otimes @ B @ C @ ( tc_Polynomial_Opoly @ A ) ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_Polynomial_Odegree @ B @ A ) @ ( c_Polynomial_Odegree @ C @ A ) @ tc_nat ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(313,axiom,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Omonom @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_Polynomial_OpCons @ B @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monom__0_0) ).
thf(1587,plain,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Omonom @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_Polynomial_OpCons @ B @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(1138,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(700,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
thf(2537,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(304,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(1567,plain,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(802,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(2798,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(834,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
thf(2877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ D @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
thf(933,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(814,axiom,
class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
thf(2830,plain,
class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(373,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(1739,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(830,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ B @ ( tc_Polynomial_Opoly @ A ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__poly__0__left_0) ).
thf(2868,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ B @ ( tc_Polynomial_Opoly @ A ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(502,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
thf(2053,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(312,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_2) ).
thf(1584,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(452,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(1937,plain,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__divide_0) ).
thf(1214,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).
thf(1016,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(970,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).
thf(1155,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(244,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__self_0) ).
thf(1419,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
= ( c_HOL_Oabs__class_Oabs @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
thf(884,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
= ( c_HOL_Oabs__class_Oabs @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(204,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
thf(1329,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(464,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(1964,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(455,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oabs__if @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= B )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_1) ).
thf(1942,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oabs__if @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= B )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(340,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__dvd_0) ).
thf(1659,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(1424,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(609,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(2312,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(668,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(2455,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(400,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(1810,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(552,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(2172,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(496,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_0) ).
thf(2038,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(254,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(1446,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(190,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(1297,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(256,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oordered__semiring__strict @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) ).
thf(1451,plain,
! [A: $i] :
( ( class_Ring__and__Field_Oordered__semiring__strict @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(292,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_5) ).
thf(1539,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).
thf(1131,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(683,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
thf(2497,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(396,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
thf(1799,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(427,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less__neg_0) ).
thf(1874,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(828,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Opoly @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ B @ C @ A ) @ D @ A )
= ( c_Polynomial_Opoly @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__offset__poly_0) ).
thf(2862,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Opoly @ ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ B @ C @ A ) @ D @ A )
= ( c_Polynomial_Opoly @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(788,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
thf(2766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(365,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).
thf(1720,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(593,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).
thf(2272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(538,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).
thf(2140,plain,
class_Ring__and__Field_Osemiring__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(287,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(1525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
thf(1825,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(598,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
thf(2285,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(388,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ( ( c_Suc @ A )
= B )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(1776,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ( ( c_Suc @ A )
= B )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(176,axiom,
! [A: $i] :
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(1263,plain,
! [A: $i] :
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(532,axiom,
class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
thf(2125,plain,
class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(108,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add) ).
thf(1099,plain,
class_OrderedGroup_Ocancel__comm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(62,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_0) ).
thf(985,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(846,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
thf(2900,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(641,axiom,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(2387,plain,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(297,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oordered__idom @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
thf(1552,plain,
! [A: $i] :
( ( class_Ring__and__Field_Oordered__idom @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(824,axiom,
( ( c_Power_Opower__class_Opower @ v_r____ @ ( c_Polynomial_Odegree @ v_s____ @ tc_Complex_Ocomplex ) @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
= ( c_HOL_Otimes__class_Otimes @ v_s____ @ v_u____ @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(2851,plain,
( ( c_Power_Opower__class_Opower @ v_r____ @ ( c_Polynomial_Odegree @ v_s____ @ tc_Complex_Ocomplex ) @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
= ( c_HOL_Otimes__class_Otimes @ v_s____ @ v_u____ @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
thf(1192,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(450,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__minus__eq_0) ).
thf(1932,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(717,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
thf(2581,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ B @ C @ A ) @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__minus__left_0) ).
thf(1060,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Osmult @ B @ C @ A ) @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(89,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(1050,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(31,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_9) ).
thf(911,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(686,axiom,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_2) ).
thf(2505,plain,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
thf(1002,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(808,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
thf(2813,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(199,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oordered__semidom @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) ).
thf(1318,plain,
! [A: $i] :
( ( class_Ring__and__Field_Oordered__semidom @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(565,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).
thf(2203,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(103,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(1086,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(389,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
thf(1779,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(354,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_2) ).
thf(1695,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(837,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__0_0) ).
thf(2883,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(415,axiom,
! [A: $i] :
( ( class_OrderedGroup_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Oab__group__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
thf(1846,plain,
! [A: $i] :
( ( class_OrderedGroup_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Oab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(83,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_4) ).
thf(1035,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(146,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__ring @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
thf(1187,plain,
! [A: $i] :
( ( class_Ring__and__Field_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__ring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(650,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ E @ A ) @ F @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ F @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
thf(2408,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ E @ A ) @ F @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ F @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(573,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
thf(2221,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(741,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
thf(2645,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(730,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
thf(2617,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__imp__dvd_0) ).
thf(953,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(477,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(1996,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(656,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
thf(2423,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(167,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__0_0) ).
thf(1241,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(704,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
!= ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
thf(2546,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
!= ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(786,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
thf(2761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(781,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Omonom @ B @ C @ A ) @ ( c_Polynomial_Omonom @ D @ E @ A ) @ ( tc_Polynomial_Opoly @ A ) )
= ( c_Polynomial_Omonom @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ E @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__monom_0) ).
thf(2748,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Omonom @ B @ C @ A ) @ ( c_Polynomial_Omonom @ D @ E @ A ) @ ( tc_Polynomial_Opoly @ A ) )
= ( c_Polynomial_Omonom @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ E @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
thf(1170,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(262,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(1466,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__abs__iff_1) ).
thf(1071,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(648,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__divide_0) ).
thf(2402,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(440,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
thf(1906,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(479,axiom,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(2001,plain,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(554,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
thf(2176,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(128,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(1146,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(462,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).
thf(1959,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(719,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) )
| ( C = E )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
thf(2585,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) )
| ( C = E )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).
thf(1219,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
thf(1483,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(856,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(330,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(1631,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(530,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
thf(2121,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(578,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
thf(2235,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(540,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).
thf(2144,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(774,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
thf(2729,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(336,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(1648,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).
thf(1727,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(280,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less_0) ).
thf(1510,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(586,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
thf(2253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(542,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).
thf(2149,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(316,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(1595,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(776,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
thf(2734,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(694,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
thf(2524,plain,
class_OrderedGroup_Oab__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(636,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
thf(2376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(131,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
thf(1154,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(827,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__inverse_0) ).
thf(2859,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(680,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).
thf(2489,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(379,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
thf(1752,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(449,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
thf(1929,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(52,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Omult__zero @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
thf(958,plain,
! [A: $i] :
( ( class_Ring__and__Field_Omult__zero @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(357,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Opordered__ring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) ).
thf(1701,plain,
! [A: $i] :
( ( class_Ring__and__Field_Opordered__ring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(1615,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(391,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ F @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).
thf(1784,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ F @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(798,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
thf(2789,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(119,axiom,
! [A: $i] :
( ( class_HOL_Ozero @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_HOL_Ozero @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Ozero) ).
thf(1125,plain,
! [A: $i] :
( ( class_HOL_Ozero @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_HOL_Ozero @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(695,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).
thf(2525,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(745,axiom,
class_Ring__and__Field_Ocomm__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
thf(2657,plain,
class_Ring__and__Field_Ocomm__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(753,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__1_0) ).
thf(2674,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(690,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Polynomial_Opoly @ ( c_Power_Opower__class_Opower @ B @ C @ ( tc_Polynomial_Opoly @ A ) ) @ D @ A )
= ( c_Power_Opower__class_Opower @ ( c_Polynomial_Opoly @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__power_0) ).
thf(2514,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Polynomial_Opoly @ ( c_Power_Opower__class_Opower @ B @ C @ ( tc_Polynomial_Opoly @ A ) ) @ D @ A )
= ( c_Power_Opower__class_Opower @ ( c_Polynomial_Opoly @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(712,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).
thf(2568,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(761,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
thf(2695,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
!= ( c_HOL_Oabs__class_Oabs @ C @ A ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__if__abs__eq_0) ).
thf(1226,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
!= ( c_HOL_Oabs__class_Oabs @ C @ A ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(813,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(2827,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(536,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
thf(2134,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(548,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
thf(2161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(277,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).
thf(1503,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(344,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oabs__if @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if) ).
thf(1669,plain,
! [A: $i] :
( ( class_Ring__and__Field_Oabs__if @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(42,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(936,plain,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(572,axiom,
class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
thf(2220,plain,
class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(492,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(2029,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(601,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
thf(2293,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(1312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(423,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).
thf(1865,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(112,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(1107,plain,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(205,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(1332,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(766,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(2706,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(550,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
thf(2166,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(657,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_Power_Opower__class_Opower @ B @ D @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
thf(2425,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_Power_Opower__class_Opower @ B @ D @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(161,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oidom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
thf(1224,plain,
! [A: $i] :
( ( class_Ring__and__Field_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oidom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(840,axiom,
class_RealVector_Oreal__field @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
thf(2891,plain,
class_RealVector_Oreal__field @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(607,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
thf(2308,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(663,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__1__right_0) ).
thf(2442,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(785,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_1) ).
thf(2759,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(503,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).
thf(2055,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
thf(1092,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(629,axiom,
! [B: $i,A: $i] :
( ( c_Complex_Ocnj @ ( c_Power_Opower__class_Opower @ A @ B @ tc_Complex_Ocomplex ) )
= ( c_Power_Opower__class_Opower @ ( c_Complex_Ocnj @ A ) @ B @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__power_0) ).
thf(2358,plain,
! [B: $i,A: $i] :
( ( c_Complex_Ocnj @ ( c_Power_Opower__class_Opower @ A @ B @ tc_Complex_Ocomplex ) )
= ( c_Power_Opower__class_Opower @ ( c_Complex_Ocnj @ A ) @ B @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(216,axiom,
! [A: $i] :
( ( class_Orderings_Opreorder @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Opreorder) ).
thf(1356,plain,
! [A: $i] :
( ( class_Orderings_Opreorder @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(513,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
thf(2079,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
thf(1282,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(543,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
thf(2151,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__div__pos_0) ).
thf(1574,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(366,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_3) ).
thf(1722,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(819,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
thf(2839,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(880,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(826,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
thf(2856,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(118,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero_0) ).
thf(1122,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(563,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(2197,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Omonom @ B @ C @ A ) @ ( tc_Polynomial_Opoly @ A ) )
= ( c_Polynomial_Omonom @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__monom_0) ).
thf(1209,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Omonom @ B @ C @ A ) @ ( tc_Polynomial_Opoly @ A ) )
= ( c_Polynomial_Omonom @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(771,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
thf(2721,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ D @ B @ A ) @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_0) ).
thf(900,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ D @ B @ A ) @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(755,axiom,
class_Ring__and__Field_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
thf(2679,plain,
class_Ring__and__Field_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(418,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_6) ).
thf(1853,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(239,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
thf(1408,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(515,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
thf(2084,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(570,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(2214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(653,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).
thf(2415,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(435,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).
thf(1894,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(791,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel1_1) ).
thf(2774,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(286,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(1524,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(64,axiom,
! [A: $i] :
( ( class_Divides_Oring__div @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ofield @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Oring__div) ).
thf(990,plain,
! [A: $i] :
( ( class_Divides_Oring__div @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ofield @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_Polynomial_Osmult @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__eq__0__iff_0) ).
thf(996,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_Polynomial_Osmult @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(583,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Polynomial_Osmult @ C @ D @ A ) @ ( tc_Polynomial_Opoly @ A ) )
= ( c_Polynomial_Osmult @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ ( tc_Polynomial_Opoly @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__smult__right_0) ).
thf(2246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Polynomial_Osmult @ C @ D @ A ) @ ( tc_Polynomial_Opoly @ A ) )
= ( c_Polynomial_Osmult @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ ( tc_Polynomial_Opoly @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(272,axiom,
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(1492,plain,
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(319,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(1603,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(604,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(2299,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(637,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).
thf(2378,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(352,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__minus__cong_0) ).
thf(1690,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ouminus__class_Ouminus @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(831,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__commutes_0) ).
thf(2871,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(251,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_OpCons @ B @ C @ A )
!= ( c_Polynomial_OpCons @ D @ E @ A ) )
| ( C = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__eq__iff_1) ).
thf(1439,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_OpCons @ B @ C @ A )
!= ( c_Polynomial_OpCons @ D @ E @ A ) )
| ( C = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(812,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__unique_0) ).
thf(2824,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(736,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).
thf(2632,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(779,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).
thf(2742,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(526,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ E @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
thf(2111,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ E @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(476,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__abs__divide_0) ).
thf(1993,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(794,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
thf(2780,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(784,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).
thf(2757,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(832,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
thf(2874,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(33,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Ocomm__ring__1 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
thf(915,plain,
! [A: $i] :
( ( class_Ring__and__Field_Ocomm__ring__1 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(260,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(1460,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(670,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
thf(2461,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(716,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__right_0) ).
thf(2578,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(208,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Osmult @ B @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__0__right_0) ).
thf(1339,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Osmult @ B @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(726,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__add_0) ).
thf(2605,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(858,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).
thf(1557,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(534,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
thf(2129,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(733,axiom,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Odegree @ ( c_Polynomial_OpCons @ B @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_degree__pCons__0_0) ).
thf(2625,plain,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Odegree @ ( c_Polynomial_OpCons @ B @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(589,axiom,
( ( c_Fun_Oid @ v_x @ t_a )
= v_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__def_0) ).
thf(2261,plain,
( ( c_Fun_Oid @ v_x @ t_a )
= v_x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(404,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
thf(1821,plain,
! [A: $i] :
( ( class_Ring__and__Field_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(370,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ B @ D @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__cancel_0) ).
thf(1731,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ B @ D @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(651,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
thf(2410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(202,axiom,
class_Ring__and__Field_Odvd @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
thf(1325,plain,
class_Ring__and__Field_Odvd @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(796,axiom,
class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
thf(2785,plain,
class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
thf(1029,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(24,axiom,
! [A: $i] :
( ( class_Orderings_Oorder @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Oorder) ).
thf(895,plain,
! [A: $i] :
( ( class_Orderings_Oorder @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(46,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oidom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(943,plain,
! [A: $i] :
( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oidom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono_0) ).
thf(1022,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(748,axiom,
class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
thf(2664,plain,
class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(142,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).
thf(1177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).
thf(1381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(654,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(2418,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(448,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
thf(1926,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(356,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).
thf(1699,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(569,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1_0) ).
thf(2212,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(288,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(1528,plain,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(516,axiom,
! [A: $i] :
( ( class_Power_Opower @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Power_Opower) ).
thf(2086,plain,
! [A: $i] :
( ( class_Power_Opower @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(334,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Osemiring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).
thf(1643,plain,
! [A: $i] :
( ( class_Ring__and__Field_Osemiring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(19,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(883,plain,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(633,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) )
| ( B = D )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).
thf(2369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) )
| ( B = D )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
thf(1113,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(267,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__one_0) ).
thf(1477,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Omonom @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monom__eq__0_0) ).
thf(1102,plain,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Omonom @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(468,axiom,
! [A: $i] :
( ( class_OrderedGroup_Omonoid__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).
thf(1973,plain,
! [A: $i] :
( ( class_OrderedGroup_Omonoid__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(509,axiom,
! [A: $i] :
( ( class_OrderedGroup_Oordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).
thf(2069,plain,
! [A: $i] :
( ( class_OrderedGroup_Oordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(301,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_5) ).
thf(1562,plain,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(151,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
thf(1198,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(413,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_negative__imp__inverse__negative_0) ).
thf(1841,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(662,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).
thf(2439,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
thf(1474,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(625,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono2_0) ).
thf(2350,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(1044,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(677,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
thf(2481,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(581,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
thf(2244,plain,
class_OrderedGroup_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(1000,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(699,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
thf(2535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(522,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(2101,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(220,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__abs__inverse_0) ).
thf(1364,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(170,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__abs__iff_0) ).
thf(1250,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(328,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_offset__poly__0_0) ).
thf(1626,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(729,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__over_0) ).
thf(2614,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(193,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).
thf(1304,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(749,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Osmult @ B @ ( c_Polynomial_Omonom @ C @ D @ A ) @ A )
= ( c_Polynomial_Omonom @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__monom_0) ).
thf(2665,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Osmult @ B @ ( c_Polynomial_Omonom @ C @ D @ A ) @ A )
= ( c_Polynomial_Omonom @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(263,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_0) ).
thf(1467,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(612,axiom,
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_2) ).
thf(2318,plain,
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(350,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_1) ).
thf(1684,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(182,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
thf(1277,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).
thf(1134,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(666,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
thf(2449,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(475,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
thf(1990,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(939,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(265,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
thf(1472,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(723,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__fieldgb_Odivide__inverse_0) ).
thf(2597,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(845,axiom,
class_OrderedGroup_Omonoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
thf(2899,plain,
class_OrderedGroup_Omonoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(56,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oring__1 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1) ).
thf(968,plain,
! [A: $i] :
( ( class_Ring__and__Field_Oring__1 @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(481,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ D @ A ) )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__num__frac_0) ).
thf(2005,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ D @ A ) )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(241,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(1413,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(1076,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(381,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__minus__eq_0) ).
thf(1758,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_5) ).
thf(1166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(1081,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(735,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
thf(2629,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(619,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1_0) ).
thf(2333,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(587,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_1) ).
thf(2256,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(377,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(1748,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(769,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).
thf(2715,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(283,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__divide_0) ).
thf(1516,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(463,axiom,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(1961,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(646,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ E @ A ) @ F @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ E @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ F @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
thf(2397,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ E @ A ) @ F @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ E @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ F @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(872,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(747,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult_0) ).
thf(2661,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(485,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).
thf(2012,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(720,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ E @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
thf(2588,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ E @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(553,axiom,
class_Ring__and__Field_Odvd @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).
thf(2175,plain,
class_Ring__and__Field_Odvd @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(811,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(2821,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(178,axiom,
! [A: $i] :
( ( class_OrderedGroup_Opordered__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) ).
thf(1267,plain,
! [A: $i] :
( ( class_OrderedGroup_Opordered__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(289,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= B )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
thf(1531,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= B )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(839,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_Opcompose @ B @ C @ A ) @ D @ A )
= ( c_Polynomial_Opoly @ B @ ( c_Polynomial_Opoly @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__pcompose_0) ).
thf(2888,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_Opcompose @ B @ C @ A ) @ D @ A )
= ( c_Polynomial_Opoly @ B @ ( c_Polynomial_Opoly @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(505,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(2060,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(375,axiom,
! [A: $i] :
( ( class_OrderedGroup_Oab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).
thf(1743,plain,
! [A: $i] :
( ( class_OrderedGroup_Oab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(561,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).
thf(2192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(887,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(775,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
thf(2732,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(171,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__1__left_0) ).
thf(1252,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Polynomial_Osmult @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(815,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).
thf(2831,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(759,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Osmult @ B @ ( c_Polynomial_Osmult @ C @ D @ A ) @ A )
= ( c_Polynomial_Osmult @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__smult_0) ).
thf(2689,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Osmult @ B @ ( c_Polynomial_Osmult @ C @ D @ A ) @ A )
= ( c_Polynomial_Osmult @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(425,axiom,
! [B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(1869,plain,
! [B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_OpCons @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_1) ).
thf(1235,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_OpCons @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(471,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
thf(1980,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(438,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Omonom @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monom__eq__0__iff_0) ).
thf(1901,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Omonom @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(615,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
thf(2322,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(348,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
thf(1679,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(498,axiom,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(2044,plain,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(185,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(1285,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(361,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).
thf(1711,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(90,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(1053,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(393,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(1790,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(474,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(1987,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(363,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(1716,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(574,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Omonom @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ C @ ( tc_Polynomial_Opoly @ A ) ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Polynomial_Opoly @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__replicate__append_0) ).
thf(2224,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Omonom @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ C @ ( tc_Polynomial_Opoly @ A ) ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Polynomial_Opoly @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(401,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_offset__poly__eq__0__iff_0) ).
thf(1813,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(191,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__iff_1) ).
thf(1300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(332,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(1637,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(763,axiom,
class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
thf(2700,plain,
class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(145,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
thf(1186,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(408,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).
thf(1830,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(383,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(1763,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(764,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ E @ A )
= ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).
thf(2701,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ E @ A )
= ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(679,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
thf(2486,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(121,axiom,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(1130,plain,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(310,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__inverse_0) ).
thf(1579,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(627,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
thf(2354,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(907,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(384,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(1766,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(397,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
thf(1802,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(702,axiom,
c_HOL_Oord__class_Oless @ ( c_Polynomial_Odegree @ v_s____ @ tc_Complex_Ocomplex ) @ v_na____ @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dsn_0) ).
thf(2543,plain,
c_HOL_Oord__class_Oless @ ( c_Polynomial_Odegree @ v_s____ @ tc_Complex_Ocomplex ) @ v_na____ @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(864,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(72,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(1008,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(841,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
thf(2892,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(823,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
thf(2848,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(591,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).
thf(2266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(1404,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(217,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
thf(1358,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(437,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
thf(1898,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
thf(1257,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(708,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power_1) ).
thf(2558,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(527,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
thf(2113,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
thf(1141,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Omonom @ B @ ( c_Suc @ C ) @ A )
= ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Polynomial_Omonom @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monom__Suc_0) ).
thf(1536,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Omonom @ B @ ( c_Suc @ C ) @ A )
= ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Polynomial_Omonom @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(214,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(1353,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(596,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).
thf(2279,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(613,axiom,
class_HOL_Ozero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
thf(2320,plain,
class_HOL_Ozero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(278,axiom,
! [A: $i] :
( ( class_OrderedGroup_Ocomm__monoid__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).
thf(1506,plain,
! [A: $i] :
( ( class_OrderedGroup_Ocomm__monoid__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(378,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ D @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(1749,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ D @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(247,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
thf(1427,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
thf(1094,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(689,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Suc @ B ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
thf(2511,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Suc @ B ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(430,axiom,
! [A: $i] :
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(1881,plain,
! [A: $i] :
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Ocancel__comm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(806,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_division__ring__inverse__add_0) ).
thf(2807,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).
thf(1272,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(412,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).
thf(1839,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(669,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(2458,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(676,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).
thf(2479,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(517,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
thf(2088,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(465,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).
thf(1966,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod_0) ).
thf(931,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(458,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(1949,plain,
! [A: $i] :
( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(410,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(1834,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(608,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
thf(2310,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(624,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse_0) ).
thf(2347,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
thf(1108,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(829,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
thf(2865,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(833,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
thf(2875,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(454,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(1940,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(445,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(1918,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(626,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
thf(2352,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_0) ).
thf(1084,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(810,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).
thf(2818,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__unique_0) ).
thf(1180,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(728,axiom,
! [B: $i,A: $i] :
( ( A
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__self__implies__10_0) ).
thf(2611,plain,
! [B: $i,A: $i] :
( ( A
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(616,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
thf(2325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(390,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__def_0) ).
thf(1781,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(567,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvdI_0) ).
thf(2209,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).
thf(1448,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(559,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
thf(2187,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(147,axiom,
! [A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__0__0_0) ).
thf(1189,plain,
! [A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_OpCons @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_Polynomial_Osmult @ B @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__eq__0__iff_2) ).
thf(1010,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_Polynomial_Osmult @ B @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(231,axiom,
! [A: $i] :
( ( class_Divides_Osemiring__div @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ofield @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Osemiring__div) ).
thf(1390,plain,
! [A: $i] :
( ( class_Divides_Osemiring__div @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ofield @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(606,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Odegree @ ( c_Polynomial_OpCons @ B @ C @ A ) @ A )
= ( c_Suc @ ( c_Polynomial_Odegree @ C @ A ) ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_degree__pCons__eq_0) ).
thf(2305,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Odegree @ ( c_Polynomial_OpCons @ B @ C @ A ) @ A )
= ( c_Suc @ ( c_Polynomial_Odegree @ C @ A ) ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(1289,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(257,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_2) ).
thf(1453,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(740,axiom,
! [B: $i,A: $i] :
( ( c_Complex_Ocnj @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_Complex_Ocomplex ) )
= ( c_HOL_Otimes__class_Otimes @ ( c_Complex_Ocnj @ A ) @ ( c_Complex_Ocnj @ B ) @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__mult_0) ).
thf(2643,plain,
! [B: $i,A: $i] :
( ( c_Complex_Ocnj @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_Complex_Ocomplex ) )
= ( c_HOL_Otimes__class_Otimes @ ( c_Complex_Ocnj @ A ) @ ( c_Complex_Ocnj @ B ) @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(510,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Oabs__class_Oabs @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
thf(2071,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Oabs__class_Oabs @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(746,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Osmult @ B @ ( c_Polynomial_OpCons @ C @ D @ A ) @ A )
= ( c_Polynomial_OpCons @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_Polynomial_Osmult @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__pCons_0) ).
thf(2658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Osmult @ B @ ( c_Polynomial_OpCons @ C @ D @ A ) @ A )
= ( c_Polynomial_OpCons @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_Polynomial_Osmult @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(371,axiom,
! [A: $i] :
( ( c_Complex_Ocnj @ ( c_Complex_Ocnj @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cnj_0) ).
thf(1734,plain,
! [A: $i] :
( ( c_Complex_Ocnj @ ( c_Complex_Ocnj @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(799,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono1_0) ).
thf(2792,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(399,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(1807,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(203,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(1326,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__fieldgb_Oinverse__divide_0) ).
thf(963,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(643,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(2389,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(521,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).
thf(2098,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(346,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_2) ).
thf(1674,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(329,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less_0) ).
thf(1629,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(376,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oabs__if @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_0) ).
thf(1745,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oabs__if @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(491,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(2026,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(727,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(2608,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
thf(1244,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(544,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ D @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) @ D @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).
thf(2152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ D @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(645,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) @ tc_nat ) )
| ( C = D )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).
thf(2394,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) @ tc_nat ) )
| ( C = D )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(721,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
thf(2591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(314,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
thf(1590,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(229,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(1385,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(722,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).
thf(2594,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(825,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_OpCons @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Polynomial_Opoly @ C @ D @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__pCons_0) ).
thf(2853,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_OpCons @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Polynomial_Opoly @ C @ D @ A ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(600,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
thf(2290,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(585,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ F @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ C @ F @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__period_I4_J_0) ).
thf(2251,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ F @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ C @ F @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(698,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult_0) ).
thf(2532,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(279,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_4) ).
thf(1508,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(665,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
thf(2447,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(421,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power_0) ).
thf(1861,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(514,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_3) ).
thf(2081,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(797,axiom,
( ( c_Polynomial_Odegree @ v_s____ @ tc_Complex_Ocomplex )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ds0_0) ).
thf(2786,plain,
( ( c_Polynomial_Odegree @ v_s____ @ tc_Complex_Ocomplex )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(801,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).
thf(2796,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(742,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc_0) ).
thf(2648,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(189,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).
thf(1294,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
thf(929,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(195,axiom,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
thf(1308,plain,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).
thf(1706,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(341,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).
thf(1661,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(520,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(2095,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(611,axiom,
! [A: $i] :
( ( ( c_Polynomial_Opoly @ v_s____ @ A @ tc_Complex_Ocomplex )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ( ( c_Polynomial_Opoly @ v_r____ @ A @ tc_Complex_Ocomplex )
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_impth_0) ).
thf(2315,plain,
! [A: $i] :
( ( ( c_Polynomial_Opoly @ v_s____ @ A @ tc_Complex_Ocomplex )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ( ( c_Polynomial_Opoly @ v_r____ @ A @ tc_Complex_Ocomplex )
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(647,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ F @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).
thf(2399,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ F @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(497,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
thf(2041,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(715,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc_0) ).
thf(2576,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(508,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__add_0) ).
thf(2066,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(756,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Odegree @ ( c_Polynomial_Omonom @ B @ C @ A ) @ A )
= C )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_degree__monom__eq_0) ).
thf(2680,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ozero @ A )
| ( ( c_Polynomial_Odegree @ ( c_Polynomial_Omonom @ B @ C @ A ) @ A )
= C )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(156,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
thf(1212,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(576,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_Polynomial_Opoly @ A ) ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Opoly @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__minus_0) ).
thf(2230,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
| ( ( c_Polynomial_Opoly @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_Polynomial_Opoly @ A ) ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_Polynomial_Opoly @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(495,axiom,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(2036,plain,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(778,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_0) ).
thf(2739,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(682,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ( D = E )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
thf(2494,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ( D = E )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(253,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Ocomm__semiring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).
thf(1444,plain,
! [A: $i] :
( ( class_Ring__and__Field_Ocomm__semiring @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(252,axiom,
! [A: $i] :
( ( c_Suc @ A )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
thf(1442,plain,
! [A: $i] :
( ( c_Suc @ A )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_6) ).
thf(1161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(655,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).
thf(2421,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(1348,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(281,axiom,
! [A: $i] :
( ( c_Suc @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
thf(1512,plain,
! [A: $i] :
( ( c_Suc @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(461,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(1957,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(640,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).
thf(2385,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(295,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
thf(1546,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(428,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__1_0) ).
thf(1876,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(129,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
thf(1148,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(501,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
thf(2050,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(867,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(480,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_8) ).
thf(2003,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).
thf(1116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(441,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_1) ).
thf(1908,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(531,axiom,
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).
thf(2123,plain,
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(588,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Polynomial_Odegree @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_Polynomial_Opoly @ A ) ) @ A )
= ( c_Polynomial_Odegree @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_degree__minus_0) ).
thf(2258,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Polynomial_Odegree @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_Polynomial_Opoly @ A ) ) @ A )
= ( c_Polynomial_Odegree @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(68,axiom,
class_Power_Opower @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(999,plain,
class_Power_Opower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(599,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
thf(2287,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(605,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ B @ A ) @ C @ A ) @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ E @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
thf(2302,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ B @ A ) @ C @ A ) @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(691,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
thf(2517,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(757,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Otimes__class_Otimes @ B @ E @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
thf(2683,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Otimes__class_Otimes @ B @ E @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(367,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).
thf(1725,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(1280,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__1_0) ).
thf(950,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).
thf(1097,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
thf(1229,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(577,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
thf(2233,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(809,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).
thf(2815,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(482,axiom,
! [A: $i] :
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(2008,plain,
! [A: $i] :
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(789,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I27_J_0) ).
thf(2768,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(268,axiom,
( v_na____
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n0_0) ).
thf(1480,plain,
( v_na____
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(250,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(1436,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(782,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).
thf(2751,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(402,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).
thf(1816,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(558,axiom,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
thf(2186,plain,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(353,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_7) ).
thf(1693,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(765,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).
thf(2704,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(91,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
thf(1056,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(632,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_1) ).
thf(2366,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
thf(1033,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(518,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(2091,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(434,axiom,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(1891,plain,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).
thf(960,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(750,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).
thf(2668,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
thf(955,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(743,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(2651,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(140,axiom,
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_4) ).
thf(1172,plain,
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(25,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ ( tc_Polynomial_Opoly @ A ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__poly__code_I1_J_0) ).
thf(897,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ ( tc_Polynomial_Opoly @ A ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(731,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_division__ring__inverse__diff_0) ).
thf(2619,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Opcompose @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pcompose__0_0) ).
thf(1065,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Opcompose @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(489,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
thf(2021,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(211,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(1346,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(507,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
thf(2063,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(322,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
thf(1610,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(705,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(2549,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(38,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(928,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(807,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ ( tc_Polynomial_Opoly @ A ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__poly__0__right_0) ).
thf(2810,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ ( tc_Polynomial_Opoly @ A ) )
= ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(659,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(2430,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(724,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
thf(2600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(672,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) )
| ( D
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
thf(2467,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) )
| ( D
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(718,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
thf(2583,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(65,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(992,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(687,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
thf(2507,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(850,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(317,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
thf(1597,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(432,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add_0) ).
thf(1885,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(12,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(871,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(634,axiom,
class_Ring__and__Field_Osemiring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
thf(2372,plain,
class_Ring__and__Field_Osemiring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(685,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(2502,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(580,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
thf(2241,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(1827,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(175,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_4) ).
thf(1261,plain,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(804,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
thf(2803,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(6,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(860,plain,
class_Orderings_Opreorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(822,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).
thf(2847,plain,
class_OrderedGroup_Ocancel__comm__monoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(311,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__dvd__iff_0) ).
thf(1582,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
thf(1019,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
thf(1500,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(447,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self_0) ).
thf(1923,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(235,axiom,
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_5) ).
thf(1399,plain,
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(326,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ ( c_Polynomial_OpCons @ B @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) @ C @ A )
= ( c_Polynomial_OpCons @ B @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_offset__poly__single_0) ).
thf(1621,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly @ ( c_Polynomial_OpCons @ B @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) @ C @ A )
= ( c_Polynomial_OpCons @ B @ ( c_HOL_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(320,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
thf(1606,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(783,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_Osmult @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Polynomial_Opoly @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__smult_0) ).
thf(2754,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_Polynomial_Opoly @ ( c_Polynomial_Osmult @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Polynomial_Opoly @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
thf(1320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(710,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
thf(2563,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(456,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(1945,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(487,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__add_0) ).
thf(2018,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(661,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).
thf(2436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(416,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(1848,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(242,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__diff_0) ).
thf(1416,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(817,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).
thf(2834,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(153,axiom,
! [A: $i] :
( ( class_OrderedGroup_Ogroup__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Oab__group__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
thf(1204,plain,
! [A: $i] :
( ( class_OrderedGroup_Ogroup__add @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_OrderedGroup_Oab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(524,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).
thf(2106,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(673,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Osmult @ B @ C @ A ) @ D @ ( tc_Polynomial_Opoly @ A ) )
= ( c_Polynomial_Osmult @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ ( tc_Polynomial_Opoly @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__smult__left_0) ).
thf(2470,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Polynomial_Osmult @ B @ C @ A ) @ D @ ( tc_Polynomial_Opoly @ A ) )
= ( c_Polynomial_Osmult @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ ( tc_Polynomial_Opoly @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(18,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(882,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(752,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ F @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
thf(2672,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ F @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(835,axiom,
class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
thf(2879,plain,
class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(614,axiom,
class_Power_Opower @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
thf(2321,plain,
class_Power_Opower @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(338,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(1653,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(221,axiom,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(1367,plain,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).
thf(923,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(566,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
thf(2206,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(349,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(1681,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(511,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= B )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).
thf(2074,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
| ( ( c_HOL_Oabs__class_Oabs @ B @ A )
= B )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oinverse__diff__inverse_0) ).
thf(1463,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(303,axiom,
! [A: $i] :
( ( class_Ring__and__Field_Oordered__ring__strict @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
thf(1565,plain,
! [A: $i] :
( ( class_Ring__and__Field_Oordered__ring__strict @ ( tc_Polynomial_Opoly @ A ) )
| ~ ( class_Ring__and__Field_Oordered__idom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(579,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
thf(2238,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
thf(1037,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(385,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
thf(1769,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(444,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(1917,plain,
class_Ring__and__Field_Omult__zero @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__power_0) ).
thf(972,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(790,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(2771,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(3430,plain,
$false,
inference(cvc4,[status(thm)],[1322,2452,1411,1024,1823,1633,2263,1729,2412,1031,2331,1818,1549,1554,2163,892,1879,1337,1718,1168,2295,2341,2336,2109,1559,1105,1315,2499,2544,941,977,1158,1005,2776,1618,994,1401,1422,1073,2282,2380,861,1486,2363,1855,2077,1406,2104,2622,1068,1544,2676,2837,1269,1971,1793,1671,1608,2686,1310,2184,2712,2476,1640,945,1354,1458,1497,2195,1164,1999,1275,2141,1761,1342,913,1063,1954,2844,1222,2360,1196,2723,2046,1914,2227,2020,1613,2886,2405,1127,2763,2010,1935,1650,1645,1921,1904,1265,1703,2654,1287,1709,1430,1985,2698,2339,2269,1871,2126,2603,2328,2444,2217,2274,917,1577,1455,1832,2897,2745,2571,2356,902,853,1379,1013,1741,2635,1568,2520,2158,2024,1773,1494,1362,2388,1100,1232,2169,1514,1247,2552,2373,1572,2178,1489,1946,1714,1373,1418,1334,1858,1978,1383,2555,966,2777,1183,905,1302,1664,2794,1911,2782,1040,2893,2880,1136,1151,937,1677,2540,2034,1377,2833,2483,866,1119,1394,2137,1433,1201,2804,1600,1697,2718,2508,981,1843,2058,1896,877,2190,2530,2523,1796,1345,988,2392,2154,1521,1975,1564,1863,2011,1206,920,2473,2574,925,1306,2118,2047,2737,2296,2641,1736,2061,1470,2093,1868,2382,1047,1057,1163,2428,2560,2249,1042,1519,2277,1255,1502,1666,1370,2032,2132,2528,1883,1387,910,1570,1174,1217,2147,1238,2015,1837,2433,1951,1888,1687,1624,2200,889,1656,1392,1291,974,2464,1938,847,2628,2670,1968,2565,1787,2181,1079,1027,1195,2211,2344,2313,2492,1592,1983,1534,1804,2895,2841,1375,2726,869,1755,2638,1397,1360,2245,1350,1089,1541,874,2157,1143,2115,1851,1772,1259,948,2801,1111,2709,2692,1587,1138,2537,1567,2798,2877,933,2830,1739,2868,2053,1584,1937,1214,1016,970,1155,1419,884,1329,1964,1942,1659,1424,2312,2455,1810,2172,2038,1446,1297,1451,1539,1131,2497,1799,1874,2862,2766,1720,2272,2140,1525,1825,2285,1776,1263,2125,1099,985,2900,2387,1552,2851,1192,1932,2581,1060,1050,911,2505,1002,2813,1318,2203,1086,1779,1695,2883,1846,1035,1187,2408,2221,2645,2617,953,1996,2423,1241,2546,2761,2748,1170,1466,1071,2402,1906,2001,2176,1146,1959,2585,1219,1483,856,1631,2121,2235,2144,2729,1648,1727,1510,2253,2149,1595,2734,2524,2376,1154,2859,2489,1752,1929,875,958,1701,1615,1784,2789,1125,2525,2657,2674,2514,2568,2695,1226,2827,2134,2161,1503,1669,936,2220,2029,2293,1312,1865,1107,1332,2706,2166,2425,1224,2891,2308,2442,2759,2055,1092,2358,1356,2079,1282,2151,1574,1722,2839,880,2856,1122,2197,1209,2721,900,2679,1853,1408,2084,2214,2415,1894,2774,1524,990,996,2246,1492,1603,2299,2378,1690,2871,1439,2824,2632,2742,2111,1993,2780,2757,2874,915,1460,2461,2578,1339,2605,858,1557,2129,2625,2261,1821,1731,2410,1325,2785,1029,895,943,1022,2664,1177,1381,2418,1926,1699,2212,1528,2086,1643,883,2369,1113,1477,1102,1973,2069,1562,1198,1841,2439,1474,2350,1044,2481,2244,1000,2535,2101,1364,1250,1626,2614,1304,2665,1467,2318,1684,1277,1134,2449,1990,939,1472,2597,2899,968,2005,1413,1076,1758,1166,1081,2629,2333,2256,1748,2715,1516,1961,2397,872,2661,2012,2588,2175,2821,1267,1531,2888,2060,1743,2192,887,2732,1252,2831,2689,1869,1235,1980,1901,2322,1679,2044,1285,1711,1053,1790,1987,1716,2224,1813,1300,1637,2700,1186,1830,1763,2701,2486,1130,1579,2354,907,1766,1802,2543,864,1008,2892,2848,2266,1404,1358,1898,1257,2558,2113,1141,1536,1353,2279,2320,1506,1749,1427,1094,2511,1881,2807,1272,1839,2458,2479,2088,1966,931,1949,1834,2310,2347,1108,2865,2875,1940,1918,2352,1084,2818,1180,2611,2325,1781,2209,1448,2187,1189,1010,1390,2305,1289,1453,2643,2071,2658,1734,2792,1807,1326,963,2389,2098,1674,1629,1745,2026,2608,1244,2152,2394,2591,1590,1385,2594,2853,2290,2251,2532,1508,2447,1861,2081,2786,2796,2648,1294,929,1308,1706,1661,2095,2315,2399,2041,2576,2066,2680,1212,2230,2036,2739,2494,1444,1442,1161,2421,1348,1512,1957,2385,1546,1876,1148,2050,867,2003,1116,1908,2123,2258,999,2287,2302,2517,2683,1725,1280,950,1097,1229,2233,2815,2008,2768,1480,1436,2751,1816,2186,1693,2704,1056,2366,1033,2091,1891,960,2668,955,2651,1172,897,2619,1065,2021,1346,2063,1610,2549,928,2810,2430,2600,2467,2583,992,2507,850,1597,1885,871,2372,2502,2241,1827,1261,2803,860,2847,1582,1019,1500,1923,1399,1621,1606,2754,1320,2563,1945,2018,2436,1848,1416,2834,1204,2106,2470,882,2672,2879,2321,1653,1367,923,2206,1681,2074,1463,1565,2238,1037,1769,1917,972,2771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG421-1 : TPTP v8.2.0. Released v4.1.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n021.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sat May 18 22:58:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.99/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.76/1.09 % [INFO] Parsing done (220ms).
% 1.76/1.10 % [INFO] Running in sequential loop mode.
% 2.28/1.29 % [INFO] eprover registered as external prover.
% 2.28/1.29 % [INFO] cvc4 registered as external prover.
% 2.28/1.30 % [INFO] Scanning for conjecture ...
% 2.69/1.41 % [INFO] Found a conjecture (or negated_conjecture) and 845 axioms. Running axiom selection ...
% 3.24/1.54 % [INFO] Axiom selection finished. Selected 845 axioms (removed 0 axioms).
% 3.86/1.71 % [INFO] Problem is propositional (TPTP CNF).
% 3.86/1.72 % [INFO] Type checking passed.
% 3.86/1.73 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 13.63/3.79 % External prover 'cvc4' found a proof!
% 13.63/3.79 % [INFO] Killing All external provers ...
% 13.63/3.79 % Time passed: 3263ms (effective reasoning time: 2694ms)
% 13.63/3.80 % Axioms used in derivation (845): cls_mult__eq__1__iff_1, cls_offset__poly__eq__0__iff_0, cls_less__iff__diff__less__0_0, cls_degree__mult__eq_0, cls_add__0__left_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oidom, cls_add__cancel__end_1, cls_power__0_0, cls_natgb_Oadd__r0__iff_1, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_mult__cancel2_0, cls_less__divide__eq_3, cls_not__one__less__zero_0, cls_poly__power_0, cls_mult__less__cancel__left__disj_5, cls_add__Suc__shift_0, cls_xt1_I9_J_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict, cls_pCons__0__0_0, cls_divide__eq__eq_3, cls_eq__add__iff2_1, cls_add__is__1_1, cls_mult__zero__right_0, cls_zero__less__one_0, cls_abs__div__pos_0, cls_abs__if__lattice_0, cls_class__ringb_Oadd__r0__iff_1, cls_u_0, cls_nat__mult__eq__1__iff_1, cls_Suc__inject_0, cls_dvd__mult2_0, cls_DERIV__mult__lemma_0, cls_divide__less__0__iff_0, cls_comm__semiring__class_Odistrib_0, cls_Suc__mono_0, cls_nat__0__less__mult__iff_1, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, cls_mod__mult__mult1_0, cls_smult__smult_0, cls_degree__pCons__eq_0, cls_divide__pos__pos_0, cls_smult__monom_0, cls_sne_0, cls_add__less__cancel__left_1, cls_mult__right_Ozero_0, cls_dvd__mult__right_0, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_zero__less__divide__iff_5, cls_left__add__mult__distrib_0, cls_inverse__zero__imp__zero_0, cls_mult__less__cancel__right__disj_0, cls_divide__self_0, cls_Suc__n__not__n_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ofield, cls_left__minus_0, cls_nat__1__eq__mult__iff_0, cls_square__eq__iff_1, cls_class__semiring_Osemiring__rules_I9_J_0, cls_minus__zero_0, cls_mult__less__cancel__left__disj_1, cls_mult__is__0_2, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult, cls_mult_Odiff__left_0, clsarity_Polynomial__Opoly__Orderings_Olinorder, cls_sum__squares__eq__zero__iff_0, cls_negative__imp__inverse__negative_0, cls_pcompose__0_0, cls_one__is__add_4, cls_nat__add__left__cancel__less_1, cls_power__eq__0__iff_1, cls_Lim_Ominus__diff__minus_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oring, cls_nat__lt__two__imp__zero__or__one_0, cls_degree__smult__eq_1, cls_inverse__eq__iff__eq_0, clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult, cls_less__antisym_0, cls_CHAINED_0, cls_less__add__Suc2_0, cls_nonzero__inverse__eq__divide_0, cls_not__sum__squares__lt__zero_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_diff__add__cancel_0, cls_pos__add__strict_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_less__half__sum_0, cls_degree__pCons__0_0, cls_mod__by__0_0, cls_add__is__1_2, cls_power__inject__exp_0, cls_mod__mod__cancel_0, cls_linorder__neqE_0, clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add, cls_divide__1_0, cls_add__strict__right__mono_0, cls_less__imp__inverse__less__neg_0, cls_add__is__0_0, cls_class__semiring_Osemiring__rules_I10_J_0, cls_add__imp__eq_0, cls_abs__mult__less_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors, cls_compl__eq__compl__iff_0, cls_inverse__less__1__iff_2, cls_inverse__1_0, cls_mod__add__eq_0, cls_termination__basic__simps_I1_J_0, cls_divide__less__eq_4, cls_minus__add__distrib_0, cls_zero__less__divide__iff_0, cls_dvd__diff_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_abs__dvd__iff_1, cls_Suc__lessI_0, cls_mod__add__left__eq_0, cls_less__Suc__eq_2, cls_not__less__eq_1, clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add, cls_nat__add__left__cancel__less_0, cls_minus__diff__eq_0, cls_one__is__add_1, cls_poly__mult_0, cls_power__less__zero__eq_1, cls_minus__divide__right_0, cls_inverse__negative__iff__negative_1, clsarity_nat__Orderings_Olinorder, cls_class__ringb_Onoteq__reduce_0, cls_minus__minus_0, cls_power__one_0, clsarity_nat__HOL_Ozero, cls_Suc__mult__cancel1_0, cls_left__inverse_0, cls_comm__monoid__add_Omult__assoc_0, cls_order__less__trans_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_add__cancel__21_1, cls_nat__mult__1_0, cls_minus__dvd__iff_1, cls_divide__eq__eq_0, cls_mod__mult__self1__is__0_0, cls_class__ring_Osub__add_0, cls_mod__mult__right__eq_0, cls_comm__monoid__add_Omult__1__right_0, cls_power__gt1_0, clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add, cls_abs__of__pos_0, cls_divide__less__eq_5, cls_neg__less__iff__less_1, cls_mod__diff__eq_0, clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict, cls_add__left__cancel_0, cls_less__minus__iff_0, cls_minus__monom_0, cls_power__less__imp__less__exp_0, cls_natgb_Oadd__mul__solve_0, cls_smult__minus__right_0, cls_poly__monom_0, cls_minus__pCons_0, cls_gr0I_0, cls_less__divide__eq_4, cls_inverse__divide_0, cls_eq__add__iff1_0, cls_mult__Suc__right_0, cls_complex__cnj__cancel__iff_0, cls_divide__strict__left__mono_0, cls_mult__less__cancel1_0, cls_minus__unique_0, cls_mult__less__cancel__left__disj_4, cls_class__ringb_Oadd__mul__solve_1, cls_mult__less__cancel2_1, cls_mod__add__self2_0, clsarity_Polynomial__Opoly__Ring__and__Field_Odvd, cls_add__gr__0_0, cls_mult__less__cancel__right__disj_3, cls_mult__eq__0__iff_0, cls_add__is__0_1, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_abs__less__iff_2, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_monom__eq__iff_0, cls_smult__pCons_0, cls_eq__divide__eq_4, clsarity_nat__Divides_Osemiring__div, cls_divide__eq__eq_4, clsarity_nat__OrderedGroup_Omonoid__mult, cls_double__add__less__zero__iff__single__less__zero_0, cls_add__less__mono_0, cls_divide__neg__neg_0, cls_n__less__n__mult__m_0, clsarity_nat__Ring__and__Field_Osemiring__0, cls_mult__smult__right_0, cls_abs__power__minus_0, cls_nat__mult__eq__cancel1_0, cls_ab__left__minus_0, cls_mod__by__1_0, clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult, cls_zero__less__double__add__iff__zero__less__single__add_0, cls_class__semiring_Omul__0_0, cls_right__inverse__eq_0, cls_field__power__not__zero_0, cls_neg__equal__iff__equal_0, cls_frac__eq__eq_0, clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add, cls_gr__implies__not0_0, cls_order__less__asym_0, cls_class__semiring_Osemiring__rules_I7_J_0, cls_abs__add__abs_0, cls_less__add__iff2_0, clsarity_nat__Ring__and__Field_Ocomm__semiring, cls_mult_Ozero__left_0, cls_smult__eq__0__iff_1, cls_less__iff__diff__less__0_1, cls_mod__minus__eq_0, clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__0, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_power__0__left_0, cls_double__eq__0__iff_1, cls_mult_Ozero__right_0, cls_complex__cnj__mult_0, cls_mult__strict__right__mono_0, cls_class__semiring_Omul__c_0, cls_Suc__mult__less__cancel1_0, cls_mult__pos__neg_0, cls_nat__0__less__mult__iff_0, cls_inverse__eq__1__iff_1, clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero, cls_order__less__asym_H_0, cls_poly__pcompose_0, clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult, cls_inverse__minus__eq_0, cls_divide__strict__left__mono__neg_0, cls_right__minus__eq_0, cls_mult__eq__1__iff_0, cls_mult__dvd__mono_0, cls_mult_Oadd__left_0, clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero, cls_add__cancel__end_0, cls_class__fieldgb_Oinverse__divide_0, cls_minus__less__iff_1, cls_dvd__mult__cancel__right_2, cls_monom__Suc_0, cls_minus__add__cancel_0, cls_power__Suc2_0, cls_inverse__nonzero__iff__nonzero_0, cls_less__divide__eq_7, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom, cls_smult__eq__0__iff_2, cls_power__one__over_0, cls_class__semiring_Osemiring__rules_I12_J_0, cls_nonzero__abs__inverse_0, cls_add__Suc_0, cls_id__apply_0, cls_abs__diff__less__iff_1, cls_mult__right_Oadd_0, cls_linorder__neqE__nat_0, cls_not__add__less2_0, clsarity_Polynomial__Opoly__HOL_Ozero, cls_xt1_I10_J_0, cls_mod__add__cong_0, cls_mult__is__0_1, cls_add__less__cancel__right_1, cls_mult__less__cancel2_2, cls_mod__mult__self1_0, cls_not__less__iff__gr__or__eq_0, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_degree__0_0, cls_no__zero__divisors_0, cls_mult__frac__num_0, cls_one__is__add_5, cls_power__gt1__lemma_0, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_divide__neg__pos_0, cls_mult__monom_0, cls_nat__add__left__commute_0, cls_add__divide__distrib_0, cls_degree__smult__eq_0, cls_abs__minus__commute_0, cls_cnj_Ozero_0, cls_divide__less__eq_0, cls_class__semiring_Osemiring__rules_I6_J_0, cls_class__semiring_Osemiring__rules_I2_J_0, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_mult__1__right_0, cls_add__strict__left__mono_0, cls_dvd__imp__mod__0_0, cls_less__divide__eq_2, cls_combine__common__factor_0, cls_zero__less__divide__iff_1, clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult, cls_mult__frac__frac_0, clsarity_nat__OrderedGroup_Ocomm__monoid__mult, cls_power__0__Suc_0, cls_power__strict__increasing_0, cls_add__less__mono1_0, cls_mod__minus__cong_0, cls_mult__neg__pos_0, cls_pCons__eq__0__iff_1, cls_mult__left_Odiff_0, cls_less__add__iff1_0, cls_abs__eq__0_0, cls_Suc__neq__Zero_0, cls_nat__mult__1__right_0, cls_power__eq__0__iff_2, cls_diff__minus_0, cls_monom__0_0, cls_class__ringb_Onoteq__reduce_1, cls_less__add__Suc1_0, cls_dvd__mod__iff_1, cls_power__mult_0, cls_inf__period_I4_J_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add, cls_mult__pos__neg2_0, cls_pCons__eq__iff_0, cls_add__is__1_0, cls_class__semiring_Osemiring__rules_I15_J_0, cls_mult__less__cancel__left__disj_0, cls_dvd__trans_0, cls_class__semiring_Oadd__a_0, cls_minus__mult__commute_0, cls_mod__mult__left__eq_0, cls_one__is__add_0, cls_zero__less__abs__iff_0, cls_class__semiring_Osemiring__rules_I19_J_0, cls_abs__diff__less__iff_2, cls_add__right__cancel_0, cls_mult_Odiff__right_0, cls_mult__less__cancel1_1, cls_smult__0__left_0, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring, cls_class__semiring_Osemiring__rules_I17_J_0, cls_class__semiring_Oadd__0_0, cls_comm__monoid__add_Omult__commute_0, cls_class__semiring_Osemiring__rules_I16_J_0, cls_mult__left__idem_0, clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add, cls_diff__def_0, cls_eq__divide__eq_0, cls_dvd__minus__iff_1, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1, cls_less__add__iff2_1, clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add, cls_divide__self__if_1, cls_zero__less__mult__pos_0, clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add, cls_class__semiring_Osemiring__rules_I1_J_0, clsarity_nat__Ring__and__Field_Ozero__neq__one, cls_eq__divide__eq_3, cls_inverse__negative__imp__negative_0, cls_divide_Ozero_0, cls_divide__self__if_0, clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add, clsarity_Polynomial__Opoly__Divides_Osemiring__div, cls_power__less__power__Suc_0, cls_poly__pCons_0, cls_dvd__abs__iff_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add, cls_abs__idempotent_0, cls_nat__add__assoc_0, cls_zero__less__two_0, clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors, cls_mult_Ominus__right_0, cls_less__add__one_0, cls_add__strict__mono_0, cls_neg__0__less__iff__less_0, cls_neg__less__0__iff__less_0, cls_nonzero__minus__divide__right_0, cls_power__strict__decreasing_0, cls_natgb_Onoteq__reduce_1, cls_One__nat__def_0, cls_smult__1__left_0, cls_dvd__triv__right_0, cls_class__ringb_Oadd__mul__solve_0, cls_degree__linear__power_0, cls_sum__squares__eq__zero__iff_1, cls_lessI_0, cls_less__iff__Suc__add_1, cls_not__add__less1_0, cls_neg__equal__0__iff__equal_0, cls_divide__less__0__iff_3, cls_divide__less__eq_8, cls_mult__less__cancel__right__disj_2, cls_zero__less__power_0, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if, cls_power__divide_0, cls_mult__strict__left__mono_0, cls_sum__squares__gt__zero__iff_2, cls_zero__less__power__eq_3, cls_add__cancel__21_0, cls_nonzero__inverse__minus__eq_0, clsarity_nat__OrderedGroup_Ocancel__semigroup__add, cls_eq__add__iff1_1, cls_less__Suc__eq__0__disj_3, cls_dvd__add_0, cls_divide__less__eq_1, cls_nat__1__eq__mult__iff_2, cls_less__add__eq__less_0, cls_ab__diff__minus_0, cls_class__semiring_Omul__d_0, cls_monom__eq__0__iff_0, cls_neg__equal__zero_1, cls_natgb_Oadd__scale__eq__noteq_0, cls_power__abs_0, cls_abs__minus__cancel_0, clsarity_Polynomial__Opoly__Power_Opower, cls_Deriv_Oinverse__diff__inverse_0, clsarity_Polynomial__Opoly__Divides_Oring__div, cls_no__zero__divirors__neq0_0, cls_mult__Suc_0, cls_less__divide__eq_8, cls_diff__self_0, cls_dvd__if__abs__eq_0, cls_mod__diff__cong_0, cls_zero__neq__one_0, cls_group__add__class_Odiff__0_0, cls_poly__0_0, cls_less__divide__eq_5, cls_class__semiring_Osemiring__rules_I5_J_0, clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one, cls_mod__mult__cong_0, cls_add__frac__eq_0, cls_inverse__nonzero__iff__nonzero_1, cls_dvd__mult__cancel__left_2, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict, cls_mult__right_Ominus_0, cls_power__Suc_0, cls_inverse__add_0, cls_natgb_Oadd__cancel_0, cls_zero__less__divide__iff_3, cls_mult__poly__0__left_0, cls_add__num__frac_0, cls_mult__smult__left_0, cls_dvd__refl_0, cls_abs__if_1, cls_inverse__eq__1__iff_0, clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring, cls_dvd__mult__cancel__right_1, cls_neq0__conv_1, cls_less__1__mult_0, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring, cls_minus__less__iff_0, cls_mult__less__cancel__right__disj_5, cls_mod__mult__self2_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one, cls_not__less__less__Suc__eq_0, cls_mult__is__0_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add, cls_add__diff__cancel_0, cls_Suc__mult__less__cancel1_1, clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add, cls_less__imp__inverse__less_0, cls_one__is__add_2, cls_add__less__cancel__right_0, cls_divide__zero_0, cls_add__Suc__right_0, clsarity_nat__Orderings_Opreorder, cls_class__semiring_Omul__a_0, cls_not__less__iff__gr__or__eq_1, cls_neg__0__equal__iff__equal_1, cls_power__inverse_0, cls_inverse__positive__iff__positive_0, cls_equation__minus__iff_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add, cls_zero__less__double__add__iff__zero__less__single__add_1, cls_nat__add__right__cancel_0, cls_class__semiring_Omul__1_0, clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero, clsarity_nat__Ring__and__Field_Odvd, clsarity_Complex__Ocomplex__Ring__and__Field_Oidom, cls_class__semiring_Osemiring__rules_I28_J_0, cls_right__inverse_0, cls_less__minus__iff_1, cls_inf__period_I4_J_1, clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring, cls_dvd__mod_0, cls_inverse__positive__iff__positive_1, cls_class__ringb_Oadd__scale__eq__noteq_0, cls_class__semiring_Osemiring__rules_I23_J_0, cls_less__divide__eq_1, cls_inverse__unique_0, clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1, cls_gr0__conv__Suc_1, cls_class__ringb_Oadd__cancel_0, cls_zero__less__divide__iff_2, cls_right__minus__eq_1, cls_impth_0, cls_less__not__refl_0, cls_not__square__less__zero_0, cls_linorder__antisym__conv3_0, clsarity_nat__OrderedGroup_Oab__semigroup__mult, cls_less__add__iff1_1, cls_mult__imp__less__div__pos_0, cls_diff__minus__eq__add_0, cls_mult__cancel1_1, cls_nonzero__abs__divide_0, cls_divide__zero__left_0, cls_linorder__neqE__ordered__idom_0, cls_class__semiring_Opwr__pwr_0, cls_mod__diff__right__eq_0, cls_add__mult__distrib_0, cls_dvd__triv__left_0, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1, cls_divide__pos__neg_0, cls_one__less__inverse__iff_2, cls_mod__add__self1_0, clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring, cls_abs__dvd__iff_0, cls_abs__less__iff_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oring, cls_mod__0_0, cls_class__semiring_Osemiring__rules_I3_J_0, cls_mult__eq__0__iff_2, cls_nat__1__eq__mult__iff_1, cls_id__def_0, cls_natgb_Onoteq__reduce_0, cls_class__ring_Oneg__mul_0, cls_mult__less__mono1_0, cls_mod__mod__trivial_0, cls_mult__strict__left__mono__comm_0, cls_class__ringb_Oadd__r0__iff_0, cls_linorder__neq__iff_1, cls_nat_Oinject_0, cls_add__lessD1_0, cls_less__SucE_0, cls_sum__squares__gt__zero__iff_1, cls_eq__divide__eq_2, clsarity_nat__Ring__and__Field_Osemiring, cls_eq__neg__iff__add__eq__0_1, cls_abs__mult__self_0, cls_mult__less__cancel__left__neg_1, cls_dvd__minus__iff_0, cls_divide_Odiff_0, cls_division__ring__inverse__add_0, cls_even__less__0__iff_1, cls_abs__not__less__zero_0, cls_smult__minus__left_0, cls_dvd__power_1, cls_one__dvd_0, cls_not__less__less__Suc__eq_1, cls_linorder__less__linear_0, cls_mult__less__mono2_0, cls_inverse__negative__iff__negative_0, clsarity_Complex__Ocomplex__Ring__and__Field_Odvd, cls_eq__eqI_0, cls_Suc__lessD_0, cls_divide__strict__right__mono__neg_0, cls_divide__less__eq_2, cls_dvd__mod__iff_0, cls_power__strict__increasing__iff_1, cls_minus__divide__divide_0, cls_divide__less__0__1__iff_0, cls_class__semiring_Opwr__Suc_0, clsarity_nat__Power_Opower, cls_nonzero__inverse__inverse__eq_0, cls_power__mult__distrib_0, cls_mult_Ominus__left_0, cls_Nat_Oadd__0__right_0, cls_eq__divide__imp_0, cls_class__semiring_Osemiring__rules_I11_J_0, cls_nat__mult__eq__1__iff_2, cls_nat_Osimps_I2_J_0, cls_Zero__neq__Suc_0, clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add, cls_poly__minus_0, cls_nat__neq__iff_0, cls_mult__less__cancel__left__pos_1, cls_monom__eq__0_0, cls_neg__0__less__iff__less_1, cls_mult__poly__0__right_0, cls_add__is__1_5, cls_minus__mult__left_0, cls_abs__divide_0, cls_add__neg__neg_0, cls_trans__less__add2_0, cls_minus__divide__left_0, cls_natgb_Oadd__r0__iff_0, cls_nonzero__inverse__eq__imp__eq_0, cls_add__is__1_4, cls_minus__poly__code_I1_J_0, cls_nat__mult__less__cancel1_1, cls_power__add_0, cls_divide__eq__imp_0, cls_zero__less__abs__iff_1, cls_divide__less__eq_7, cls_complex__cnj__zero__iff_0, cls_power__commutes_0, cls_class__semiring_Osemiring__rules_I33_J_0, cls_abs__if__lattice_1, cls_dvd__mult__cancel__left_1, cls_order__root_1, cls_mult__imp__div__pos__less_0, cls_double__eq__0__iff_0, cls_one__neq__zero_0, cls_divide__less__0__iff_5, cls_class__semiring_Osemiring__rules_I18_J_0, cls_mult__less__cancel2_0, cls_less__Suc0_0, cls_neg__less__0__iff__less_1, cls_add__minus__cancel_0, cls_divide__less__0__iff_2, cls_diff__0__right_0, cls_inverse__inverse__eq_0, cls_double__compl_0, cls_pCons__eq__0__iff_0, cls_mult__less__cancel__left__disj_3, cls_mult__left_Ominus_0, cls_pCons__eq__iff_1, cls_mult__1_0, cls_mult_Oadd__right_0, cls_dvd__abs__iff_1, cls_zmod__simps_I2_J_0, cls_dvd__mult__left_0, cls_mult__less__cancel1_2, cls_mod__mult__self2__is__0_0, cls_add__mult__distrib2_0, cls_mod__add__right__eq_0, clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add, cls_zero__less__power__eq_2, cls_comm__monoid__add_Omult__left__commute_0, cls_add__frac__num_0, cls_abs__mult_0, cls_neg__equal__zero_0, cls_sum__squares__eq__zero__iff_2, cls_diff__divide__distrib_0, cls_positive__imp__inverse__positive_0, cls_minus__mult__right_0, cls_zero__less__mult__pos2_0, cls_n__less__m__mult__n_0, cls_mod__mult__mult2_0, cls_mod__mult__eq_0, cls_mult__1__left_0, cls_one__less__inverse__iff_0, clsarity_Polynomial__Opoly__Orderings_Oorder, cls_comm__monoid__add_Omult__1_0, cls_frac__eq__eq_1, cls_mod__diff__left__eq_0, clsarity_Polynomial__Opoly__Int_Onumber__ring, cls_nat__mult__eq__1__iff_0, cls_poly__smult_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0, cls_degree__monom__eq_0, cls_mult__less__cancel__right__disj_4, cls_power__one__right_0, cls_degree__offset__poly_0, cls_double__add__less__zero__iff__single__less__zero_1, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors, cls_eq__add__iff2_0, cls_one__less__mult_0, cls_not__less__eq_0, cls_trans__less__add1_0, cls_class__semiring_Osemiring__rules_I35_J_0, cls_nat_Osimps_I3_J_0, cls_dsn_0, cls_less__trans__Suc_0, cls_zero__less__divide__1__iff_1, cls_abs__if_0, cls_mult__zero__left_0, cls_plus__nat_Oadd__0_0, cls_dvd__mult__cancel__right_0, clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult, cls_gt__half__sum_0, clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add, cls_n0_0, cls_one__less__inverse__iff_1, cls_add__is__0_2, cls_less__divide__eq_6, cls_nonzero__power__divide_0, cls_one__less__power_0, cls_power__Suc__less__one_0, cls_complex__cnj__cnj_0, cls_neg__0__equal__iff__equal_0, clsarity_Polynomial__Opoly__Orderings_Opreorder, cls_class__fieldgb_Odivide__inverse_0, cls_add__is__1_3, cls_divide__less__0__iff_1, cls_order__less__irrefl_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field, cls_class__semiring_Osemiring__rules_I27_J_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_diff__frac__eq_0, cls_power__eq__0__iff_0, cls_eq__eqI_1, cls_dvd__0__right_0, cls_class__semiring_Oadd__c_0, cls_mult__pos__pos_0, cls_less__eqI_0, cls_nat__add__left__cancel_0, cls_mult__strict__right__mono__neg_0, clsarity_nat__Ring__and__Field_Ono__zero__divisors, clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add, cls_less__minus__self__iff_1, cls_inverse__zero_0, cls_add__eq__self__zero_0, cls_inverse__less__imp__less__neg_0, cls_zero__less__divide__iff_4, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0, cls_synthetic__div__unique__lemma_0, cls_Suc__eq__plus1_0, cls_sum__squares__gt__zero__iff_0, cls_dvd__power_0, cls_equation__minus__iff_1, cls_class__semiring_Osemiring__rules_I8_J_0, cls_less__SucI_0, cls_divide__less__eq_9, cls_add__pos__pos_0, cls_inverse__eq__divide_0, cls_n__not__Suc__n_0, cls_divide_Oadd_0, cls_less__minus__self__iff_0, cls_poly__replicate__append_0, cls_DERIV__inverse__lemma_0, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring, cls_complex__cnj__power_0, cls_mult_Oprod__diff__prod_0, cls_zmod__simps_I1_J_0, clsarity_Complex__Ocomplex__Power_Opower, cls_nat__0__less__mult__iff_2, cls_not__less0_0, cls_nat__mult__assoc_0, cls_dvdI_0, cls_class__semiring_Opwr__mul_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_eq__iff__diff__eq__0_1, cls_class__ringb_Osubr0__iff_1, cls_divide__strict__right__mono_0, cls_abs__one_0, cls_nonzero__minus__divide__divide_0, cls_mult__divide__mult__cancel__right_0, cls_offset__poly__0_0, cls_mult__less__cancel__left__disj_2, cls_minus__add_0, cls_divide__inverse_0, cls_field__inverse_0, cls_abs__eq__0_1, cls_nat__mult__commute_0, cls_mult__less__cancel__right__disj_1, cls_add__less__cancel__left_0, cls_zmod__simps_I4_J_0, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs, cls_abs__inverse_0, cls_right__minus_0, cls_one__is__add_3, cls_minus__dvd__iff_0, cls_divide__less__eq_6, cls_class__semiring_Osemiring__rules_I25_J_0, cls_mult__eq__self__implies__10_0, cls_inverse__mult__distrib_0, cls_Suc__less__eq_0, cls_smult__eq__0__iff_0, cls_mult__eq__0__iff_1, cls_add__gr__0_2, cls_divide__less__eq_3, cls_less__divide__eq_0, cls_inverse__less__imp__less_0, cls_minus__equation__iff_1, clsarity_Complex__Ocomplex__RealVector_Oreal__field, cls_mult__cancel1_0, cls_eq__neg__iff__add__eq__0_0, cls_power__minus_0, cls_class__semiring_Opwr__0_0, cls_dvd__mod__imp__dvd_0, cls_nonzero__inverse__mult__distrib_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, cls_nonzero__power__inverse_0, cls_inverse__positive__imp__positive_0, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add, cls_add__gr__0_1, cls_dvd__mult_0, clsarity_nat__Ring__and__Field_Ocomm__semiring__0, cls_division__ring__inverse__diff_0, cls_power__strict__increasing__iff_0, cls_ds0_0, cls_smult__0__right_0, cls_termination__basic__simps_I2_J_0, cls_class__ringb_Osubr0__iff_0, cls_class__semiring_Omul__pwr_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add, cls_monoid__add__class_Oadd__0__right_0, cls_mult__idem_0, cls_less__Suc0_1, cls_divide__eq__eq_1, cls_minus__mult__minus_0, clsarity_nat__Ring__and__Field_Omult__zero, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_Suc__eq__plus1__left_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict, cls_eq__iff__diff__eq__0_0, cls_order__less__le_1, cls_nat__mult__less__cancel1_0, cls_divide_Ominus_0, cls_nat__less__le_1, cls_mult__divide__mult__cancel__left_0, cls_mult__left_Ozero_0, cls_natgb_Oadd__mul__solve_1, cls_divide__less__0__1__iff_1, cls_power__Suc__less_0, cls_less__divide__eq_9, cls_square__eq__iff_0, cls_zero__less__divide__1__iff_0, clsarity_nat__Orderings_Oorder, cls_nat__mult__eq__cancel__disj_0, cls_mult__neg__neg_0, cls_zero__less__Suc_0, cls_mult__less__cancel__left__neg_0, cls_class__semiring_Osemiring__rules_I4_J_0, clsarity_Complex__Ocomplex__Int_Onumber__ring, clsarity_nat__Ring__and__Field_Oordered__semiring__strict, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring, cls_mod__self_0, cls_less__eqI_1, cls_neg__less__iff__less_0, cls_power__0__left_1, cls_mult__right_Odiff_0, cls_divide__less__0__iff_4, cls_degree__minus_0, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0, cls_dvd__mult__cancel__left_0, cls_dvd__power__same_0, cls_even__less__0__iff_0, cls_offset__poly__single_0, cls_mult__left_Oadd_0, cls_class__semiring_Osemiring__rules_I13_J_0, cls_mult__cancel2_1, cls_mult__strict__left__mono__neg_0, cls_dvd__eq__mod__eq__0_1, cls_mult__eq__1__iff_2, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors, cls_abs__of__neg_0, clsarity_Complex__Ocomplex__HOL_Ozero, cls_abs__less__iff_1, cls_mult__less__cancel__left__pos_0, cls_nat__add__commute_0, cls_Deriv_Oadd__diff__add_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors, cls_class__semiring_Osemiring__rules_I22_J_0, cls_poly__offset__poly_0, cls_right__inverse__eq_1, cls_abs__diff__less__iff_0, cls_dvd__0__left_0
% 13.63/3.80 % No. of inferences in proof: 1693
% 13.63/3.80 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3263 ms resp. 2694 ms w/o parsing
% 14.50/4.00 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.50/4.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------